{"cot_id": "57674f7f80969bce6ec9ae3bcc82681989b58b3f8015585c893572e1486a4b92", "datapoint": {"question": "Calculate the following: (9*z**3 - 48*z)*(39*z**3 - 52*z**2 - 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "351*z**6 - 468*z**5 - 1872*z**4 + 2442*z**3 + 288*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 0, "polynomial_expr": "(9*z**3 - 48*z)*(39*z**3 - 52*z**2 - 6)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9*z**3 - 48*z)*(39*z**3 - 52*z**2 - 6)\nExpanding the part (9*z**3 - 48*z) using the distributive property, and we got: (-48*z)*(39*z**3 - 52*z**2 - 6) + (9*z**3)*(39*z**3 - 52*z**2 - 6)\n#Step 2:\nCurrent expression: (-48*z)*(39*z**3 - 52*z**2 - 6) + (9*z**3)*(39*z**3 - 52*z**2 - 6)\nSimplifying the partial expression: (-48*z)*(39*z**3 - 52*z**2 - 6)\nExpanding the part (39*z**3 - 52*z**2 - 6) using the distributive property, and we got: (-48*z)*(-52*z**2) + (-48*z)*(39*z**3) - (-1)*288*z\nReplacing (-48*z)*(39*z**3 - 52*z**2 - 6) with (-48*z)*(-52*z**2) + (-48*z)*(39*z**3) - (-1)*288*z in the overall expression.\n#Step 3:\nCurrent expression: (-48*z)*(-52*z**2) + (-48*z)*(39*z**3) - 6*(-48)*z + (9*z**3)*(39*z**3 - 52*z**2 - 6)\nSimplifying the partial expression: (9*z**3)*(39*z**3 - 52*z**2 - 6)\nExpanding the part (39*z**3 - 52*z**2 - 6) using the distributive property, and we got: -54*z**3 + (-52*z**2)*(9*z**3) + (9*z**3)*(39*z**3)\nReplacing (9*z**3)*(39*z**3 - 52*z**2 - 6) with -54*z**3 + (-52*z**2)*(9*z**3) + (9*z**3)*(39*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-48*z)*(-52*z**2) + (-48*z)*(39*z**3) - 6*9*z**3 - 6*(-48)*z + (-52*z**2)*(9*z**3) + (9*z**3)*(39*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-52*z**2)*(-48*z) = 2496*z**3\n (-52*z**2)*(9*z**3) = -468*z**5\n (39*z**3)*(-48*z) = -1872*z**4\n (39*z**3)*(9*z**3) = 351*z**6\n -6*-48*z = 288*z\n -6*9*z**3 = -54*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 351*z**6 - 468*z**5 - 1872*z**4 - 54*z**3 + 2496*z**3 + 288*z\nCombining like terms, got 351*z**6 - 468*z**5 - 1872*z**4 + 2442*z**3 + 288*z\n#Step 6:\nCurrent expression: 351*z**6 - 468*z**5 - 1872*z**4 + 2442*z**3 + 288*z\nNo more calculations needed.\n351*z**6 - 468*z**5 - 1872*z**4 + 2442*z**3 + 288*z", "generated_answer": "351*z**6 - 468*z**5 - 1872*z**4 + 2442*z**3 + 288*z", "step_length": 6} {"cot_id": "71a6879a6d09a61bbf54af09462d0b5d4765dad2d4f6815bc41a4341998e14d2", "datapoint": {"question": "Calculate the following: (37*x**2 + 8*x + 49)*(-82*x**3 + 4*x - 25)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-3034*x**5 - 656*x**4 - 3870*x**3 - 893*x**2 - 4*x - 1225", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1, "polynomial_expr": "(37*x**2 + 8*x + 49)*(-82*x**3 + 4*x - 25)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (37*x**2 + 8*x + 49)*(-82*x**3 + 4*x - 25)\nExpanding the part (-82*x**3 + 4*x - 25) using the distributive property, and we got: (4*x)*(37*x**2 + 8*x + 49) + (-82*x**3)*(37*x**2 + 8*x + 49) - 25*(37*x**2 + 8*x + 49)\n#Step 2:\nCurrent expression: (4*x)*(37*x**2 + 8*x + 49) + (-82*x**3)*(37*x**2 + 8*x + 49) - 25*(37*x**2 + 8*x + 49)\nSimplifying the partial expression: -25*(37*x**2 + 8*x + 49)\nExpanding the part (37*x**2 + 8*x + 49) using the distributive property, and we got: (8*x)*(-25) + (37*x**2)*(-25) + 49*(-25)\nReplacing -25*(37*x**2 + 8*x + 49) with (8*x)*(-25) + (37*x**2)*(-25) + 49*(-25) in the overall expression.\n#Step 3:\nCurrent expression: (4*x)*(37*x**2 + 8*x + 49) + (8*x)*(-25) + (37*x**2)*(-25) + (-82*x**3)*(37*x**2 + 8*x + 49) - 1225\nSimplifying the partial expression: (-82*x**3)*(37*x**2 + 8*x + 49)\nExpanding the part (37*x**2 + 8*x + 49) using the distributive property, and we got: 49*(-82*x**3) + (8*x)*(-82*x**3) + (37*x**2)*(-82*x**3)\nReplacing (-82*x**3)*(37*x**2 + 8*x + 49) with 49*(-82*x**3) + (8*x)*(-82*x**3) + (37*x**2)*(-82*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 49*(-82)*x**3 + (4*x)*(37*x**2 + 8*x + 49) + (8*x)*(-82*x**3) + (8*x)*(-25) + (37*x**2)*(-82*x**3) + (37*x**2)*(-25) - 1225\nSimplifying the partial expression: (4*x)*(37*x**2 + 8*x + 49)\nExpanding the part (37*x**2 + 8*x + 49) using the distributive property, and we got: 49*(4*x) + (4*x)*(8*x) + (4*x)*(37*x**2)\nReplacing (4*x)*(37*x**2 + 8*x + 49) with 49*(4*x) + (4*x)*(8*x) + (4*x)*(37*x**2) in the overall expression.\n#Step 5:\nCurrent expression: 49*(-82)*x**3 + 49*4*x + (4*x)*(8*x) + (4*x)*(37*x**2) + (8*x)*(-82*x**3) + (8*x)*(-25) + (37*x**2)*(-82*x**3) + (37*x**2)*(-25) - 1225\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (8*x)*-25 = -200*x\n (8*x)*(-82*x**3) = -656*x**4\n (8*x)*(4*x) = 32*x**2\n (37*x**2)*-25 = -925*x**2\n (37*x**2)*(-82*x**3) = -3034*x**5\n (37*x**2)*(4*x) = 148*x**3\n 49*-82*x**3 = -4018*x**3\n 49*4*x = 196*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -3034*x**5 - 656*x**4 - 4018*x**3 + 148*x**3 - 925*x**2 + 32*x**2 - 200*x + 196*x - 1225\nCombining like terms, got -3034*x**5 - 656*x**4 - 3870*x**3 - 893*x**2 - 4*x - 1225\n#Step 7:\nCurrent expression: -3034*x**5 - 656*x**4 - 3870*x**3 - 893*x**2 - 4*x - 1225\nNo more calculations needed.\n-3034*x**5 - 656*x**4 - 3870*x**3 - 893*x**2 - 4*x - 1225", "generated_answer": "-3034*x**5 - 656*x**4 - 3870*x**3 - 893*x**2 - 4*x - 1225", "step_length": 7} {"cot_id": "e99b16b0386b3067ce257b588cd2321b4580ea9c6507c1cf377cabfa14332bcc", "datapoint": {"question": "Calculate the following: (25*y**2 + 11*y)*(15*y**3 - 25)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "375*y**5 + 165*y**4 - 625*y**2 - 275*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2, "polynomial_expr": "(25*y**2 + 11*y)*(15*y**3 - 25)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (25*y**2 + 11*y)*(15*y**3 - 25)\nExpanding the part (15*y**3 - 25) using the distributive property, and we got: (15*y**3)*(25*y**2 + 11*y) - 25*(25*y**2 + 11*y)\n#Step 2:\nCurrent expression: (15*y**3)*(25*y**2 + 11*y) - 25*(25*y**2 + 11*y)\nSimplifying the partial expression: -25*(25*y**2 + 11*y)\nExpanding the part (25*y**2 + 11*y) using the distributive property, and we got: (11*y)*(-25) + (25*y**2)*(-25)\nReplacing -25*(25*y**2 + 11*y) with (11*y)*(-25) + (25*y**2)*(-25) in the overall expression.\n#Step 3:\nCurrent expression: (11*y)*(-25) + (25*y**2)*(-25) + (15*y**3)*(25*y**2 + 11*y)\nSimplifying the partial expression: (15*y**3)*(25*y**2 + 11*y)\nExpanding the part (25*y**2 + 11*y) using the distributive property, and we got: (11*y)*(15*y**3) + (25*y**2)*(15*y**3)\nReplacing (15*y**3)*(25*y**2 + 11*y) with (11*y)*(15*y**3) + (25*y**2)*(15*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (11*y)*(15*y**3) + (11*y)*(-25) + (25*y**2)*(15*y**3) + (25*y**2)*(-25)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (11*y)*-25 = -275*y\n (11*y)*(15*y**3) = 165*y**4\n (25*y**2)*-25 = -625*y**2\n (25*y**2)*(15*y**3) = 375*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 375*y**5 + 165*y**4 - 625*y**2 - 275*y\nNo more calculations needed.\n375*y**5 + 165*y**4 - 625*y**2 - 275*y", "generated_answer": "375*y**5 + 165*y**4 - 625*y**2 - 275*y", "step_length": 5} {"cot_id": "a752472df12e1785f1cad5bfd8dc88776d7314d15b6310821bdab42c13998cad", "datapoint": {"question": "Calculate the following: (-19*y**3 + 8*y)*(48*y**3 - 53)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-912*y**6 + 384*y**4 + 1007*y**3 - 424*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 3, "polynomial_expr": "(-19*y**3 + 8*y)*(48*y**3 - 53)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-19*y**3 + 8*y)*(48*y**3 - 53)\nExpanding the part (48*y**3 - 53) using the distributive property, and we got: (48*y**3)*(-19*y**3 + 8*y) - 53*(-19*y**3 + 8*y)\n#Step 2:\nCurrent expression: (48*y**3)*(-19*y**3 + 8*y) - 53*(-19*y**3 + 8*y)\nSimplifying the partial expression: -53*(-19*y**3 + 8*y)\nExpanding the part (-19*y**3 + 8*y) using the distributive property, and we got: (8*y)*(-53) - 19*y**3*(-53)\nReplacing -53*(-19*y**3 + 8*y) with (8*y)*(-53) - 19*y**3*(-53) in the overall expression.\n#Step 3:\nCurrent expression: (8*y)*(-53) - 19*y**3*(-53) + (48*y**3)*(-19*y**3 + 8*y)\nSimplifying the partial expression: (48*y**3)*(-19*y**3 + 8*y)\nExpanding the part (-19*y**3 + 8*y) using the distributive property, and we got: (8*y)*(48*y**3) + (-19*y**3)*(48*y**3)\nReplacing (48*y**3)*(-19*y**3 + 8*y) with (8*y)*(48*y**3) + (-19*y**3)*(48*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (8*y)*(48*y**3) + (8*y)*(-53) + (-19*y**3)*(48*y**3) - 19*y**3*(-53)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*y**3)*-53 = 1007*y**3\n (-19*y**3)*(48*y**3) = -912*y**6\n (8*y)*-53 = -424*y\n (8*y)*(48*y**3) = 384*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -912*y**6 + 384*y**4 + 1007*y**3 - 424*y\nNo more calculations needed.\n-912*y**6 + 384*y**4 + 1007*y**3 - 424*y", "generated_answer": "-912*y**6 + 384*y**4 + 1007*y**3 - 424*y", "step_length": 5} {"cot_id": "85bdf3f7bfa0c07fde90b87b4c7d44187860dcbf473df74ef4fe56235dbc6a98", "datapoint": {"question": "Calculate the following: (38 - 10*x)*(9*x**2 - 5*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-90*x**3 + 392*x**2 - 190*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 4, "polynomial_expr": "(38 - 10*x)*(9*x**2 - 5*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (38 - 10*x)*(9*x**2 - 5*x)\nExpanding the part (38 - 10*x) using the distributive property, and we got: (-10*x)*(9*x**2 - 5*x) + 38*(9*x**2 - 5*x)\n#Step 2:\nCurrent expression: (-10*x)*(9*x**2 - 5*x) + 38*(9*x**2 - 5*x)\nSimplifying the partial expression: 38*(9*x**2 - 5*x)\nExpanding the part (9*x**2 - 5*x) using the distributive property, and we got: -5*x*38 + (9*x**2)*38\nReplacing 38*(9*x**2 - 5*x) with -5*x*38 + (9*x**2)*38 in the overall expression.\n#Step 3:\nCurrent expression: (-10*x)*(9*x**2 - 5*x) - 5*x*38 + (9*x**2)*38\nSimplifying the partial expression: (-10*x)*(9*x**2 - 5*x)\nExpanding the part (9*x**2 - 5*x) using the distributive property, and we got: (-10*x)*(-5*x) + (-10*x)*(9*x**2)\nReplacing (-10*x)*(9*x**2 - 5*x) with (-10*x)*(-5*x) + (-10*x)*(9*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-10*x)*(-5*x) + (-10*x)*(9*x**2) - 5*x*38 + (9*x**2)*38\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-5*x)*38 = -190*x\n (-5*x)*(-10*x) = 50*x**2\n (9*x**2)*38 = 342*x**2\n (9*x**2)*(-10*x) = -90*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -90*x**3 + 50*x**2 + 342*x**2 - 190*x\nCombining like terms, got -90*x**3 + 392*x**2 - 190*x\n#Step 6:\nCurrent expression: -90*x**3 + 392*x**2 - 190*x\nNo more calculations needed.\n-90*x**3 + 392*x**2 - 190*x", "generated_answer": "-90*x**3 + 392*x**2 - 190*x", "step_length": 6} {"cot_id": "f27b44065455b31c5f5c91e25f63aa7406854929a8aa46659e85e5b6c73d1f84", "datapoint": {"question": "Calculate the following: 22*y**2*(31*y**3 + y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "682*y**5 + 22*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 5, "polynomial_expr": "22*y**2*(31*y**3 + y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 22*y**2*(31*y**3 + y)\nExpanding the part (31*y**3 + y) using the distributive property, and we got: y*(22*y**2) + (22*y**2)*(31*y**3)\n#Step 2:\nCurrent expression: y*(22*y**2) + (22*y**2)*(31*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n y*(22*y**2) = 22*y**3\n (31*y**3)*(22*y**2) = 682*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 682*y**5 + 22*y**3\nNo more calculations needed.\n682*y**5 + 22*y**3", "generated_answer": "682*y**5 + 22*y**3", "step_length": 3} {"cot_id": "4af1336d56c15470ebab7b274ce4c57e7e08bdbe45103b9ac94f14bf37359b9c", "datapoint": {"question": "Simplify this expression: (26 - 43*z**3)*(36*z + 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1548*z**4 - 1419*z**3 + 936*z + 858", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 6, "polynomial_expr": "(26 - 43*z**3)*(36*z + 33)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (26 - 43*z**3)*(36*z + 33)\nExpanding the part (26 - 43*z**3) using the distributive property, and we got: (-43*z**3)*(36*z + 33) + 26*(36*z + 33)\n#Step 2:\nCurrent expression: (-43*z**3)*(36*z + 33) + 26*(36*z + 33)\nSimplifying the partial expression: 26*(36*z + 33)\nExpanding the part (36*z + 33) using the distributive property, and we got: (36*z)*26 + 33*26\nReplacing 26*(36*z + 33) with (36*z)*26 + 33*26 in the overall expression.\n#Step 3:\nCurrent expression: (36*z)*26 + (-43*z**3)*(36*z + 33) + 858\nSimplifying the partial expression: (-43*z**3)*(36*z + 33)\nExpanding the part (36*z + 33) using the distributive property, and we got: 33*(-43*z**3) + (36*z)*(-43*z**3)\nReplacing (-43*z**3)*(36*z + 33) with 33*(-43*z**3) + (36*z)*(-43*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 33*(-43)*z**3 + (36*z)*(-43*z**3) + (36*z)*26 + 858\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (36*z)*26 = 936*z\n (36*z)*(-43*z**3) = -1548*z**4\n 33*-43*z**3 = -1419*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1548*z**4 - 1419*z**3 + 936*z + 858\nNo more calculations needed.\n-1548*z**4 - 1419*z**3 + 936*z + 858", "generated_answer": "-1548*z**4 - 1419*z**3 + 936*z + 858", "step_length": 5} {"cot_id": "c04309399ddd9bca3689df43e59e51da5ce230fe6898573d75e15f66766aef93", "datapoint": {"question": "Calculate the following: (-41*x**2 + 33*x)*(39*x**2 - 35*x + 3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1599*x**4 + 2722*x**3 - 1278*x**2 + 99*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 7, "polynomial_expr": "(-41*x**2 + 33*x)*(39*x**2 - 35*x + 3)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-41*x**2 + 33*x)*(39*x**2 - 35*x + 3)\nExpanding the part (-41*x**2 + 33*x) using the distributive property, and we got: (33*x)*(39*x**2 - 35*x + 3) + (-41*x**2)*(39*x**2 - 35*x + 3)\n#Step 2:\nCurrent expression: (33*x)*(39*x**2 - 35*x + 3) + (-41*x**2)*(39*x**2 - 35*x + 3)\nSimplifying the partial expression: (-41*x**2)*(39*x**2 - 35*x + 3)\nExpanding the part (39*x**2 - 35*x + 3) using the distributive property, and we got: (-35*x)*(-41*x**2) + 3*(-41*x**2) + (-41*x**2)*(39*x**2)\nReplacing (-41*x**2)*(39*x**2 - 35*x + 3) with (-35*x)*(-41*x**2) + 3*(-41*x**2) + (-41*x**2)*(39*x**2) in the overall expression.\n#Step 3:\nCurrent expression: (-35*x)*(-41*x**2) + 3*(-41)*x**2 + (33*x)*(39*x**2 - 35*x + 3) + (-41*x**2)*(39*x**2)\nSimplifying the partial expression: (33*x)*(39*x**2 - 35*x + 3)\nExpanding the part (39*x**2 - 35*x + 3) using the distributive property, and we got: (-35*x)*(33*x) + 3*(33*x) + (33*x)*(39*x**2)\nReplacing (33*x)*(39*x**2 - 35*x + 3) with (-35*x)*(33*x) + 3*(33*x) + (33*x)*(39*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-35*x)*(33*x) + (-35*x)*(-41*x**2) + 3*(-41)*x**2 + 3*33*x + (33*x)*(39*x**2) + (-41*x**2)*(39*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*x)*(-41*x**2) = 1435*x**3\n (-35*x)*(33*x) = -1155*x**2\n (39*x**2)*(-41*x**2) = -1599*x**4\n (39*x**2)*(33*x) = 1287*x**3\n 3*-41*x**2 = -123*x**2\n 3*33*x = 99*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1599*x**4 + 1287*x**3 + 1435*x**3 - 1155*x**2 - 123*x**2 + 99*x\nCombining like terms, got -1599*x**4 + 2722*x**3 - 1278*x**2 + 99*x\n#Step 6:\nCurrent expression: -1599*x**4 + 2722*x**3 - 1278*x**2 + 99*x\nNo more calculations needed.\n-1599*x**4 + 2722*x**3 - 1278*x**2 + 99*x", "generated_answer": "-1599*x**4 + 2722*x**3 - 1278*x**2 + 99*x", "step_length": 6} {"cot_id": "4b6cd17fc72d8222d4008fd5d2b9a66338ffe8e0081e834f226fd3924ac1bf24", "datapoint": {"question": "Simplify this expression: -13*y*(62 - 50*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "650*y**2 - 806*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 8, "polynomial_expr": "-13*y*(62 - 50*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -13*y*(62 - 50*y)\nExpanding the part (62 - 50*y) using the distributive property, and we got: (-50*y)*(-13*y) + 62*(-13*y)\n#Step 2:\nCurrent expression: (-50*y)*(-13*y) + 62*(-13*y)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 62*(-13*y) = -806*y\n (-50*y)*(-13*y) = 650*y**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 650*y**2 - 806*y\nNo more calculations needed.\n650*y**2 - 806*y", "generated_answer": "650*y**2 - 806*y", "step_length": 3} {"cot_id": "3013ca75a38f1cc5f92465c7956b671110fa0d9842439b5a42b9c874286f38bf", "datapoint": {"question": "Simplify this expression: (26*x**3 + 15*x**2)*(24*x**3 + 32*x**2 + 26*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "624*x**6 + 1192*x**5 + 1156*x**4 + 390*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 9, "polynomial_expr": "(26*x**3 + 15*x**2)*(24*x**3 + 32*x**2 + 26*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (26*x**3 + 15*x**2)*(24*x**3 + 32*x**2 + 26*x)\nExpanding the part (26*x**3 + 15*x**2) using the distributive property, and we got: (15*x**2)*(24*x**3 + 32*x**2 + 26*x) + (26*x**3)*(24*x**3 + 32*x**2 + 26*x)\n#Step 2:\nCurrent expression: (15*x**2)*(24*x**3 + 32*x**2 + 26*x) + (26*x**3)*(24*x**3 + 32*x**2 + 26*x)\nSimplifying the partial expression: (15*x**2)*(24*x**3 + 32*x**2 + 26*x)\nExpanding the part (24*x**3 + 32*x**2 + 26*x) using the distributive property, and we got: (26*x)*(15*x**2) + (15*x**2)*(32*x**2) + (15*x**2)*(24*x**3)\nReplacing (15*x**2)*(24*x**3 + 32*x**2 + 26*x) with (26*x)*(15*x**2) + (15*x**2)*(32*x**2) + (15*x**2)*(24*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (26*x)*(15*x**2) + (15*x**2)*(32*x**2) + (15*x**2)*(24*x**3) + (26*x**3)*(24*x**3 + 32*x**2 + 26*x)\nSimplifying the partial expression: (26*x**3)*(24*x**3 + 32*x**2 + 26*x)\nExpanding the part (24*x**3 + 32*x**2 + 26*x) using the distributive property, and we got: (26*x)*(26*x**3) + (32*x**2)*(26*x**3) + (24*x**3)*(26*x**3)\nReplacing (26*x**3)*(24*x**3 + 32*x**2 + 26*x) with (26*x)*(26*x**3) + (32*x**2)*(26*x**3) + (24*x**3)*(26*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (26*x)*(15*x**2) + (26*x)*(26*x**3) + (15*x**2)*(32*x**2) + (15*x**2)*(24*x**3) + (32*x**2)*(26*x**3) + (24*x**3)*(26*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (24*x**3)*(15*x**2) = 360*x**5\n (24*x**3)*(26*x**3) = 624*x**6\n (26*x)*(15*x**2) = 390*x**3\n (26*x)*(26*x**3) = 676*x**4\n (32*x**2)*(15*x**2) = 480*x**4\n (32*x**2)*(26*x**3) = 832*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 624*x**6 + 360*x**5 + 832*x**5 + 480*x**4 + 676*x**4 + 390*x**3\nCombining like terms, got 624*x**6 + 1192*x**5 + 1156*x**4 + 390*x**3\n#Step 6:\nCurrent expression: 624*x**6 + 1192*x**5 + 1156*x**4 + 390*x**3\nNo more calculations needed.\n624*x**6 + 1192*x**5 + 1156*x**4 + 390*x**3", "generated_answer": "624*x**6 + 1192*x**5 + 1156*x**4 + 390*x**3", "step_length": 6} {"cot_id": "fb52045fbcdd0048ecabe92cb88ac8babaec18bccb6a5283229012ea49a2e83c", "datapoint": {"question": "Simplify this expression: (9*y**2 + 36)*(-41*y**3 - 25*y**2 - 5)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-369*y**5 - 225*y**4 - 1476*y**3 - 945*y**2 - 180", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 10, "polynomial_expr": "(9*y**2 + 36)*(-41*y**3 - 25*y**2 - 5)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9*y**2 + 36)*(-41*y**3 - 25*y**2 - 5)\nExpanding the part (9*y**2 + 36) using the distributive property, and we got: (9*y**2)*(-41*y**3 - 25*y**2 - 5) + 36*(-41*y**3 - 25*y**2 - 5)\n#Step 2:\nCurrent expression: (9*y**2)*(-41*y**3 - 25*y**2 - 5) + 36*(-41*y**3 - 25*y**2 - 5)\nSimplifying the partial expression: 36*(-41*y**3 - 25*y**2 - 5)\nExpanding the part (-41*y**3 - 25*y**2 - 5) using the distributive property, and we got: -25*y**2*36 - 41*y**3*36 - 5*36\nReplacing 36*(-41*y**3 - 25*y**2 - 5) with -25*y**2*36 - 41*y**3*36 - 5*36 in the overall expression.\n#Step 3:\nCurrent expression: -25*y**2*36 + (9*y**2)*(-41*y**3 - 25*y**2 - 5) - 41*y**3*36 - 180\nSimplifying the partial expression: (9*y**2)*(-41*y**3 - 25*y**2 - 5)\nExpanding the part (-41*y**3 - 25*y**2 - 5) using the distributive property, and we got: -45*y**2 + (-25*y**2)*(9*y**2) + (9*y**2)*(-41*y**3)\nReplacing (9*y**2)*(-41*y**3 - 25*y**2 - 5) with -45*y**2 + (-25*y**2)*(9*y**2) + (9*y**2)*(-41*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -5*9*y**2 + (-25*y**2)*(9*y**2) - 25*y**2*36 + (9*y**2)*(-41*y**3) - 41*y**3*36 - 180\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*y**3)*36 = -1476*y**3\n (-41*y**3)*(9*y**2) = -369*y**5\n (-25*y**2)*36 = -900*y**2\n (-25*y**2)*(9*y**2) = -225*y**4\n -5*9*y**2 = -45*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -369*y**5 - 225*y**4 - 1476*y**3 - 900*y**2 - 45*y**2 - 180\nCombining like terms, got -369*y**5 - 225*y**4 - 1476*y**3 - 945*y**2 - 180\n#Step 6:\nCurrent expression: -369*y**5 - 225*y**4 - 1476*y**3 - 945*y**2 - 180\nNo more calculations needed.\n-369*y**5 - 225*y**4 - 1476*y**3 - 945*y**2 - 180", "generated_answer": "-369*y**5 - 225*y**4 - 1476*y**3 - 945*y**2 - 180", "step_length": 6} {"cot_id": "a7d2d4c1e4d8b658c695b9ba3534e79c3255f5d608ad65d6b53a195dc42aa125", "datapoint": {"question": "Calculate the following: (-17*z**3 + 11*z)*(47*z**3 + 33*z**2 + 34*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-799*z**6 - 561*z**5 - 61*z**4 + 363*z**3 + 374*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 11, "polynomial_expr": "(-17*z**3 + 11*z)*(47*z**3 + 33*z**2 + 34*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-17*z**3 + 11*z)*(47*z**3 + 33*z**2 + 34*z)\nExpanding the part (-17*z**3 + 11*z) using the distributive property, and we got: (11*z)*(47*z**3 + 33*z**2 + 34*z) + (-17*z**3)*(47*z**3 + 33*z**2 + 34*z)\n#Step 2:\nCurrent expression: (11*z)*(47*z**3 + 33*z**2 + 34*z) + (-17*z**3)*(47*z**3 + 33*z**2 + 34*z)\nSimplifying the partial expression: (-17*z**3)*(47*z**3 + 33*z**2 + 34*z)\nExpanding the part (47*z**3 + 33*z**2 + 34*z) using the distributive property, and we got: (34*z)*(-17*z**3) + (33*z**2)*(-17*z**3) + (-17*z**3)*(47*z**3)\nReplacing (-17*z**3)*(47*z**3 + 33*z**2 + 34*z) with (34*z)*(-17*z**3) + (33*z**2)*(-17*z**3) + (-17*z**3)*(47*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (11*z)*(47*z**3 + 33*z**2 + 34*z) + (34*z)*(-17*z**3) + (33*z**2)*(-17*z**3) + (-17*z**3)*(47*z**3)\nSimplifying the partial expression: (11*z)*(47*z**3 + 33*z**2 + 34*z)\nExpanding the part (47*z**3 + 33*z**2 + 34*z) using the distributive property, and we got: (11*z)*(34*z) + (11*z)*(33*z**2) + (11*z)*(47*z**3)\nReplacing (11*z)*(47*z**3 + 33*z**2 + 34*z) with (11*z)*(34*z) + (11*z)*(33*z**2) + (11*z)*(47*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (11*z)*(34*z) + (11*z)*(33*z**2) + (11*z)*(47*z**3) + (34*z)*(-17*z**3) + (33*z**2)*(-17*z**3) + (-17*z**3)*(47*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (33*z**2)*(-17*z**3) = -561*z**5\n (33*z**2)*(11*z) = 363*z**3\n (34*z)*(-17*z**3) = -578*z**4\n (34*z)*(11*z) = 374*z**2\n (47*z**3)*(-17*z**3) = -799*z**6\n (47*z**3)*(11*z) = 517*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -799*z**6 - 561*z**5 - 578*z**4 + 517*z**4 + 363*z**3 + 374*z**2\nCombining like terms, got -799*z**6 - 561*z**5 - 61*z**4 + 363*z**3 + 374*z**2\n#Step 6:\nCurrent expression: -799*z**6 - 561*z**5 - 61*z**4 + 363*z**3 + 374*z**2\nNo more calculations needed.\n-799*z**6 - 561*z**5 - 61*z**4 + 363*z**3 + 374*z**2", "generated_answer": "-799*z**6 - 561*z**5 - 61*z**4 + 363*z**3 + 374*z**2", "step_length": 6} {"cot_id": "8b00715d2441580c040c4fa31f61c92a550b6e7457b7fbee8cf9c50618fee1fb", "datapoint": {"question": "Calculate the following: (10*x**3 - 14)*(76*x**2 + 29*x - 18)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "760*x**5 + 290*x**4 - 180*x**3 - 1064*x**2 - 406*x + 252", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 12, "polynomial_expr": "(10*x**3 - 14)*(76*x**2 + 29*x - 18)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (10*x**3 - 14)*(76*x**2 + 29*x - 18)\nExpanding the part (10*x**3 - 14) using the distributive property, and we got: (10*x**3)*(76*x**2 + 29*x - 18) - 14*(76*x**2 + 29*x - 18)\n#Step 2:\nCurrent expression: (10*x**3)*(76*x**2 + 29*x - 18) - 14*(76*x**2 + 29*x - 18)\nSimplifying the partial expression: -14*(76*x**2 + 29*x - 18)\nExpanding the part (76*x**2 + 29*x - 18) using the distributive property, and we got: (29*x)*(-14) + (76*x**2)*(-14) - 18*(-14)\nReplacing -14*(76*x**2 + 29*x - 18) with (29*x)*(-14) + (76*x**2)*(-14) - 18*(-14) in the overall expression.\n#Step 3:\nCurrent expression: (29*x)*(-14) + (76*x**2)*(-14) + (10*x**3)*(76*x**2 + 29*x - 18) + 252\nSimplifying the partial expression: (10*x**3)*(76*x**2 + 29*x - 18)\nExpanding the part (76*x**2 + 29*x - 18) using the distributive property, and we got: -180*x**3 + (29*x)*(10*x**3) + (76*x**2)*(10*x**3)\nReplacing (10*x**3)*(76*x**2 + 29*x - 18) with -180*x**3 + (29*x)*(10*x**3) + (76*x**2)*(10*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -18*10*x**3 + (29*x)*(10*x**3) + (29*x)*(-14) + (76*x**2)*(10*x**3) + (76*x**2)*(-14) + 252\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (29*x)*-14 = -406*x\n (29*x)*(10*x**3) = 290*x**4\n (76*x**2)*-14 = -1064*x**2\n (76*x**2)*(10*x**3) = 760*x**5\n -18*10*x**3 = -180*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 760*x**5 + 290*x**4 - 180*x**3 - 1064*x**2 - 406*x + 252\nNo more calculations needed.\n760*x**5 + 290*x**4 - 180*x**3 - 1064*x**2 - 406*x + 252", "generated_answer": "760*x**5 + 290*x**4 - 180*x**3 - 1064*x**2 - 406*x + 252", "step_length": 5} {"cot_id": "b3dddcba3d8f3ead77e62ef68be0f5fc0caf06abc6e1977438ec8a6796ff436d", "datapoint": {"question": "Simplify this expression: (48*x**2 - 48)*(22*x**3 + 28*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1056*x**5 + 288*x**3 - 1344*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 13, "polynomial_expr": "(48*x**2 - 48)*(22*x**3 + 28*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (48*x**2 - 48)*(22*x**3 + 28*x)\nExpanding the part (48*x**2 - 48) using the distributive property, and we got: (48*x**2)*(22*x**3 + 28*x) - 48*(22*x**3 + 28*x)\n#Step 2:\nCurrent expression: (48*x**2)*(22*x**3 + 28*x) - 48*(22*x**3 + 28*x)\nSimplifying the partial expression: -48*(22*x**3 + 28*x)\nExpanding the part (22*x**3 + 28*x) using the distributive property, and we got: (28*x)*(-48) + (22*x**3)*(-48)\nReplacing -48*(22*x**3 + 28*x) with (28*x)*(-48) + (22*x**3)*(-48) in the overall expression.\n#Step 3:\nCurrent expression: (28*x)*(-48) + (48*x**2)*(22*x**3 + 28*x) + (22*x**3)*(-48)\nSimplifying the partial expression: (48*x**2)*(22*x**3 + 28*x)\nExpanding the part (22*x**3 + 28*x) using the distributive property, and we got: (28*x)*(48*x**2) + (48*x**2)*(22*x**3)\nReplacing (48*x**2)*(22*x**3 + 28*x) with (28*x)*(48*x**2) + (48*x**2)*(22*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (28*x)*(48*x**2) + (28*x)*(-48) + (48*x**2)*(22*x**3) + (22*x**3)*(-48)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (22*x**3)*-48 = -1056*x**3\n (22*x**3)*(48*x**2) = 1056*x**5\n (28*x)*-48 = -1344*x\n (28*x)*(48*x**2) = 1344*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1056*x**5 - 1056*x**3 + 1344*x**3 - 1344*x\nCombining like terms, got 1056*x**5 + 288*x**3 - 1344*x\n#Step 6:\nCurrent expression: 1056*x**5 + 288*x**3 - 1344*x\nNo more calculations needed.\n1056*x**5 + 288*x**3 - 1344*x", "generated_answer": "1056*x**5 + 288*x**3 - 1344*x", "step_length": 6} {"cot_id": "029bd8aab6c8b659a4ab37f8ce91754845192849dd0d71ec656a9398b5bf808a", "datapoint": {"question": "Simplify this expression: 4480*z**3 - 4704*z + 3024\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "4480*z**3 - 4704*z + 3024", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 14, "polynomial_expr": "4480*z**3 - 4704*z + 3024", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 4480*z**3 - 4704*z + 3024\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 4480*z**3 - 4704*z + 3024\nNo more calculations needed.\n4480*z**3 - 4704*z + 3024", "generated_answer": "4480*z**3 - 4704*z + 3024", "step_length": 2} {"cot_id": "b57f201ec52eed45397d8ddf2074bde7ec30fd55e3e311e3d42b747009c07ca5", "datapoint": {"question": "Simplify this expression: (42 - 8*x**3)*(-49*x**3 - 39*x + 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "392*x**6 + 312*x**4 - 2442*x**3 - 1638*x + 2016", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 15, "polynomial_expr": "(42 - 8*x**3)*(-49*x**3 - 39*x + 48)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (42 - 8*x**3)*(-49*x**3 - 39*x + 48)\nExpanding the part (42 - 8*x**3) using the distributive property, and we got: (-8*x**3)*(-49*x**3 - 39*x + 48) + 42*(-49*x**3 - 39*x + 48)\n#Step 2:\nCurrent expression: (-8*x**3)*(-49*x**3 - 39*x + 48) + 42*(-49*x**3 - 39*x + 48)\nSimplifying the partial expression: 42*(-49*x**3 - 39*x + 48)\nExpanding the part (-49*x**3 - 39*x + 48) using the distributive property, and we got: -39*x*42 - 49*x**3*42 + 48*42\nReplacing 42*(-49*x**3 - 39*x + 48) with -39*x*42 - 49*x**3*42 + 48*42 in the overall expression.\n#Step 3:\nCurrent expression: -39*x*42 - 49*x**3*42 + (-8*x**3)*(-49*x**3 - 39*x + 48) + 2016\nSimplifying the partial expression: (-8*x**3)*(-49*x**3 - 39*x + 48)\nExpanding the part (-49*x**3 - 39*x + 48) using the distributive property, and we got: (-39*x)*(-8*x**3) + 48*(-8*x**3) + (-49*x**3)*(-8*x**3)\nReplacing (-8*x**3)*(-49*x**3 - 39*x + 48) with (-39*x)*(-8*x**3) + 48*(-8*x**3) + (-49*x**3)*(-8*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-39*x)*(-8*x**3) - 39*x*42 + 48*(-8)*x**3 + (-49*x**3)*(-8*x**3) - 49*x**3*42 + 2016\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*x**3)*42 = -2058*x**3\n (-49*x**3)*(-8*x**3) = 392*x**6\n (-39*x)*42 = -1638*x\n (-39*x)*(-8*x**3) = 312*x**4\n 48*-8*x**3 = -384*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 392*x**6 + 312*x**4 - 2058*x**3 - 384*x**3 - 1638*x + 2016\nCombining like terms, got 392*x**6 + 312*x**4 - 2442*x**3 - 1638*x + 2016\n#Step 6:\nCurrent expression: 392*x**6 + 312*x**4 - 2442*x**3 - 1638*x + 2016\nNo more calculations needed.\n392*x**6 + 312*x**4 - 2442*x**3 - 1638*x + 2016", "generated_answer": "392*x**6 + 312*x**4 - 2442*x**3 - 1638*x + 2016", "step_length": 6} {"cot_id": "74fca68def14eb61ef79a87438366c4df1fefc22e972eb5e9bf1e38a7f833592", "datapoint": {"question": "Calculate the following: (-29*z**2 - 48)*(-7*z**3 + 17*z**2 + 27*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "203*z**5 - 493*z**4 - 447*z**3 - 816*z**2 - 1296*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 16, "polynomial_expr": "(-29*z**2 - 48)*(-7*z**3 + 17*z**2 + 27*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-29*z**2 - 48)*(-7*z**3 + 17*z**2 + 27*z)\nExpanding the part (-29*z**2 - 48) using the distributive property, and we got: (-29*z**2)*(-7*z**3 + 17*z**2 + 27*z) - 48*(-7*z**3 + 17*z**2 + 27*z)\n#Step 2:\nCurrent expression: (-29*z**2)*(-7*z**3 + 17*z**2 + 27*z) - 48*(-7*z**3 + 17*z**2 + 27*z)\nSimplifying the partial expression: -48*(-7*z**3 + 17*z**2 + 27*z)\nExpanding the part (-7*z**3 + 17*z**2 + 27*z) using the distributive property, and we got: (27*z)*(-48) + (17*z**2)*(-48) - 7*z**3*(-48)\nReplacing -48*(-7*z**3 + 17*z**2 + 27*z) with (27*z)*(-48) + (17*z**2)*(-48) - 7*z**3*(-48) in the overall expression.\n#Step 3:\nCurrent expression: (27*z)*(-48) + (-29*z**2)*(-7*z**3 + 17*z**2 + 27*z) + (17*z**2)*(-48) - 7*z**3*(-48)\nSimplifying the partial expression: (-29*z**2)*(-7*z**3 + 17*z**2 + 27*z)\nExpanding the part (-7*z**3 + 17*z**2 + 27*z) using the distributive property, and we got: (27*z)*(-29*z**2) + (-29*z**2)*(17*z**2) + (-29*z**2)*(-7*z**3)\nReplacing (-29*z**2)*(-7*z**3 + 17*z**2 + 27*z) with (27*z)*(-29*z**2) + (-29*z**2)*(17*z**2) + (-29*z**2)*(-7*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (27*z)*(-29*z**2) + (27*z)*(-48) + (-29*z**2)*(17*z**2) + (-29*z**2)*(-7*z**3) + (17*z**2)*(-48) - 7*z**3*(-48)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-7*z**3)*-48 = 336*z**3\n (-7*z**3)*(-29*z**2) = 203*z**5\n (17*z**2)*-48 = -816*z**2\n (17*z**2)*(-29*z**2) = -493*z**4\n (27*z)*-48 = -1296*z\n (27*z)*(-29*z**2) = -783*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 203*z**5 - 493*z**4 - 783*z**3 + 336*z**3 - 816*z**2 - 1296*z\nCombining like terms, got 203*z**5 - 493*z**4 - 447*z**3 - 816*z**2 - 1296*z\n#Step 6:\nCurrent expression: 203*z**5 - 493*z**4 - 447*z**3 - 816*z**2 - 1296*z\nNo more calculations needed.\n203*z**5 - 493*z**4 - 447*z**3 - 816*z**2 - 1296*z", "generated_answer": "203*z**5 - 493*z**4 - 447*z**3 - 816*z**2 - 1296*z", "step_length": 6} {"cot_id": "8c605379db2c827d4f1379f51eab5dc909b7c8b66506e49b1dcbe59226ff3061", "datapoint": {"question": "Simplify this expression: (38*x**2 + 10*x)*(-x**3 + 35*x**2 - 10*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-38*x**5 + 1320*x**4 - 30*x**3 - 100*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 17, "polynomial_expr": "(38*x**2 + 10*x)*(-x**3 + 35*x**2 - 10*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (38*x**2 + 10*x)*(-x**3 + 35*x**2 - 10*x)\nExpanding the part (38*x**2 + 10*x) using the distributive property, and we got: (10*x)*(-x**3 + 35*x**2 - 10*x) + (38*x**2)*(-x**3 + 35*x**2 - 10*x)\n#Step 2:\nCurrent expression: (10*x)*(-x**3 + 35*x**2 - 10*x) + (38*x**2)*(-x**3 + 35*x**2 - 10*x)\nSimplifying the partial expression: (10*x)*(-x**3 + 35*x**2 - 10*x)\nExpanding the part (-x**3 + 35*x**2 - 10*x) using the distributive property, and we got: (-10*x)*(10*x) + (10*x)*(35*x**2) + (10*x)*(-x**3)\nReplacing (10*x)*(-x**3 + 35*x**2 - 10*x) with (-10*x)*(10*x) + (10*x)*(35*x**2) + (10*x)*(-x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-10*x)*(10*x) + (10*x)*(35*x**2) + (10*x)*(-x**3) + (38*x**2)*(-x**3 + 35*x**2 - 10*x)\nSimplifying the partial expression: (38*x**2)*(-x**3 + 35*x**2 - 10*x)\nExpanding the part (-x**3 + 35*x**2 - 10*x) using the distributive property, and we got: (-10*x)*(38*x**2) + (35*x**2)*(38*x**2) + (38*x**2)*(-x**3)\nReplacing (38*x**2)*(-x**3 + 35*x**2 - 10*x) with (-10*x)*(38*x**2) + (35*x**2)*(38*x**2) + (38*x**2)*(-x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-10*x)*(10*x) + (-10*x)*(38*x**2) + (10*x)*(35*x**2) + (10*x)*(-x**3) + (35*x**2)*(38*x**2) + (38*x**2)*(-x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-x**3)*(10*x) = -10*x**4\n (-x**3)*(38*x**2) = -38*x**5\n (-10*x)*(10*x) = -100*x**2\n (-10*x)*(38*x**2) = -380*x**3\n (35*x**2)*(10*x) = 350*x**3\n (35*x**2)*(38*x**2) = 1330*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -38*x**5 - 10*x**4 + 1330*x**4 - 380*x**3 + 350*x**3 - 100*x**2\nCombining like terms, got -38*x**5 + 1320*x**4 - 30*x**3 - 100*x**2\n#Step 6:\nCurrent expression: -38*x**5 + 1320*x**4 - 30*x**3 - 100*x**2\nNo more calculations needed.\n-38*x**5 + 1320*x**4 - 30*x**3 - 100*x**2", "generated_answer": "-38*x**5 + 1320*x**4 - 30*x**3 - 100*x**2", "step_length": 6} {"cot_id": "bbddb911cedbe8b5d61e88cd133ab888ba1aa9e317ee560bab6c5d4722cb9f57", "datapoint": {"question": "Simplify this expression: (-41*y**3 - 47)*(3*y**3 + 31*y**2 - 10*y - 12)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-123*y**6 - 1271*y**5 + 410*y**4 + 351*y**3 - 1457*y**2 + 470*y + 564", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 18, "polynomial_expr": "(-41*y**3 - 47)*(3*y**3 + 31*y**2 - 10*y - 12)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-41*y**3 - 47)*(3*y**3 + 31*y**2 - 10*y - 12)\nExpanding the part (-41*y**3 - 47) using the distributive property, and we got: (-41*y**3)*(3*y**3 + 31*y**2 - 10*y - 12) - 47*(3*y**3 + 31*y**2 - 10*y - 12)\n#Step 2:\nCurrent expression: (-41*y**3)*(3*y**3 + 31*y**2 - 10*y - 12) - 47*(3*y**3 + 31*y**2 - 10*y - 12)\nSimplifying the partial expression: -47*(3*y**3 + 31*y**2 - 10*y - 12)\nExpanding the part (3*y**3 + 31*y**2 - 10*y - 12) using the distributive property, and we got: -10*y*(-47) + (31*y**2)*(-47) + (3*y**3)*(-47) - 12*(-47)\nReplacing -47*(3*y**3 + 31*y**2 - 10*y - 12) with -10*y*(-47) + (31*y**2)*(-47) + (3*y**3)*(-47) - 12*(-47) in the overall expression.\n#Step 3:\nCurrent expression: -10*y*(-47) + (31*y**2)*(-47) + (-41*y**3)*(3*y**3 + 31*y**2 - 10*y - 12) + (3*y**3)*(-47) + 564\nSimplifying the partial expression: (-41*y**3)*(3*y**3 + 31*y**2 - 10*y - 12)\nExpanding the part (3*y**3 + 31*y**2 - 10*y - 12) using the distributive property, and we got: (-10*y)*(-41*y**3) - (-1)*492*y**3 + (31*y**2)*(-41*y**3) + (-41*y**3)*(3*y**3)\nReplacing (-41*y**3)*(3*y**3 + 31*y**2 - 10*y - 12) with (-10*y)*(-41*y**3) - (-1)*492*y**3 + (31*y**2)*(-41*y**3) + (-41*y**3)*(3*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-10*y)*(-41*y**3) - 10*y*(-47) - 12*(-41)*y**3 + (31*y**2)*(-41*y**3) + (31*y**2)*(-47) + (-41*y**3)*(3*y**3) + (3*y**3)*(-47) + 564\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*y)*-47 = 470*y\n (-10*y)*(-41*y**3) = 410*y**4\n (3*y**3)*-47 = -141*y**3\n (3*y**3)*(-41*y**3) = -123*y**6\n (31*y**2)*-47 = -1457*y**2\n (31*y**2)*(-41*y**3) = -1271*y**5\n -12*-41*y**3 = 492*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -123*y**6 - 1271*y**5 + 410*y**4 - 141*y**3 + 492*y**3 - 1457*y**2 + 470*y + 564\nCombining like terms, got -123*y**6 - 1271*y**5 + 410*y**4 + 351*y**3 - 1457*y**2 + 470*y + 564\n#Step 6:\nCurrent expression: -123*y**6 - 1271*y**5 + 410*y**4 + 351*y**3 - 1457*y**2 + 470*y + 564\nNo more calculations needed.\n-123*y**6 - 1271*y**5 + 410*y**4 + 351*y**3 - 1457*y**2 + 470*y + 564", "generated_answer": "-123*y**6 - 1271*y**5 + 410*y**4 + 351*y**3 - 1457*y**2 + 470*y + 564", "step_length": 6} {"cot_id": "538427b80b09032fe2856891ff2f34f6499fe774f1d715cfb2c1c8f389af2a3e", "datapoint": {"question": "Simplify this expression: 11*y**3*(-68*y**3 - 14*y - 22)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-748*y**6 - 154*y**4 - 242*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 19, "polynomial_expr": "11*y**3*(-68*y**3 - 14*y - 22)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 11*y**3*(-68*y**3 - 14*y - 22)\nExpanding the part (-68*y**3 - 14*y - 22) using the distributive property, and we got: (-14*y)*(11*y**3) - 242*y**3 + (-68*y**3)*(11*y**3)\n#Step 2:\nCurrent expression: (-14*y)*(11*y**3) - 242*y**3 + (-68*y**3)*(11*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -22*(11*y**3) = -242*y**3\n (-68*y**3)*(11*y**3) = -748*y**6\n (-14*y)*(11*y**3) = -154*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -748*y**6 - 154*y**4 - 242*y**3\nNo more calculations needed.\n-748*y**6 - 154*y**4 - 242*y**3", "generated_answer": "-748*y**6 - 154*y**4 - 242*y**3", "step_length": 3} {"cot_id": "e27fd2ecfbf3e1df2a254e04b6fa61121a15761905a862f0b085998c08e669f0", "datapoint": {"question": "Simplify this expression: (-16*z**2 - 43*z)*(11*z**3 + 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-176*z**5 - 473*z**4 - 656*z**2 - 1763*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 20, "polynomial_expr": "(-16*z**2 - 43*z)*(11*z**3 + 41)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-16*z**2 - 43*z)*(11*z**3 + 41)\nExpanding the part (11*z**3 + 41) using the distributive property, and we got: (11*z**3)*(-16*z**2 - 43*z) + 41*(-16*z**2 - 43*z)\n#Step 2:\nCurrent expression: (11*z**3)*(-16*z**2 - 43*z) + 41*(-16*z**2 - 43*z)\nSimplifying the partial expression: 41*(-16*z**2 - 43*z)\nExpanding the part (-16*z**2 - 43*z) using the distributive property, and we got: -43*z*41 - 16*z**2*41\nReplacing 41*(-16*z**2 - 43*z) with -43*z*41 - 16*z**2*41 in the overall expression.\n#Step 3:\nCurrent expression: -43*z*41 - 16*z**2*41 + (11*z**3)*(-16*z**2 - 43*z)\nSimplifying the partial expression: (11*z**3)*(-16*z**2 - 43*z)\nExpanding the part (-16*z**2 - 43*z) using the distributive property, and we got: (-43*z)*(11*z**3) + (-16*z**2)*(11*z**3)\nReplacing (11*z**3)*(-16*z**2 - 43*z) with (-43*z)*(11*z**3) + (-16*z**2)*(11*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-43*z)*(11*z**3) - 43*z*41 + (-16*z**2)*(11*z**3) - 16*z**2*41\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-43*z)*41 = -1763*z\n (-43*z)*(11*z**3) = -473*z**4\n (-16*z**2)*41 = -656*z**2\n (-16*z**2)*(11*z**3) = -176*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -176*z**5 - 473*z**4 - 656*z**2 - 1763*z\nNo more calculations needed.\n-176*z**5 - 473*z**4 - 656*z**2 - 1763*z", "generated_answer": "-176*z**5 - 473*z**4 - 656*z**2 - 1763*z", "step_length": 5} {"cot_id": "74c618442b4c4a8c1211b29bcd1d6b67e27197506468875ecb9b2c18d1d75123", "datapoint": {"question": "Calculate the following: (-25*y**3 + 17*y**2 - 13*y)*(19*y**3 - 9*y - 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-475*y**6 + 323*y**5 - 22*y**4 + 822*y**3 - 546*y**2 + 507*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 21, "polynomial_expr": "(-25*y**3 + 17*y**2 - 13*y)*(19*y**3 - 9*y - 39)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-25*y**3 + 17*y**2 - 13*y)*(19*y**3 - 9*y - 39)\nExpanding the part (19*y**3 - 9*y - 39) using the distributive property, and we got: (-9*y)*(-25*y**3 + 17*y**2 - 13*y) + (19*y**3)*(-25*y**3 + 17*y**2 - 13*y) - 39*(-25*y**3 + 17*y**2 - 13*y)\n#Step 2:\nCurrent expression: (-9*y)*(-25*y**3 + 17*y**2 - 13*y) + (19*y**3)*(-25*y**3 + 17*y**2 - 13*y) - 39*(-25*y**3 + 17*y**2 - 13*y)\nSimplifying the partial expression: -39*(-25*y**3 + 17*y**2 - 13*y)\nExpanding the part (-25*y**3 + 17*y**2 - 13*y) using the distributive property, and we got: -13*y*(-39) + (17*y**2)*(-39) - 25*y**3*(-39)\nReplacing -39*(-25*y**3 + 17*y**2 - 13*y) with -13*y*(-39) + (17*y**2)*(-39) - 25*y**3*(-39) in the overall expression.\n#Step 3:\nCurrent expression: -13*y*(-39) + (-9*y)*(-25*y**3 + 17*y**2 - 13*y) + (17*y**2)*(-39) - 25*y**3*(-39) + (19*y**3)*(-25*y**3 + 17*y**2 - 13*y)\nSimplifying the partial expression: (-9*y)*(-25*y**3 + 17*y**2 - 13*y)\nExpanding the part (-25*y**3 + 17*y**2 - 13*y) using the distributive property, and we got: (-13*y)*(-9*y) + (-9*y)*(17*y**2) + (-9*y)*(-25*y**3)\nReplacing (-9*y)*(-25*y**3 + 17*y**2 - 13*y) with (-13*y)*(-9*y) + (-9*y)*(17*y**2) + (-9*y)*(-25*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-13*y)*(-9*y) - 13*y*(-39) + (-9*y)*(17*y**2) + (-9*y)*(-25*y**3) + (17*y**2)*(-39) - 25*y**3*(-39) + (19*y**3)*(-25*y**3 + 17*y**2 - 13*y)\nSimplifying the partial expression: (19*y**3)*(-25*y**3 + 17*y**2 - 13*y)\nExpanding the part (-25*y**3 + 17*y**2 - 13*y) using the distributive property, and we got: (-13*y)*(19*y**3) + (17*y**2)*(19*y**3) + (-25*y**3)*(19*y**3)\nReplacing (19*y**3)*(-25*y**3 + 17*y**2 - 13*y) with (-13*y)*(19*y**3) + (17*y**2)*(19*y**3) + (-25*y**3)*(19*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-13*y)*(-9*y) + (-13*y)*(19*y**3) - 13*y*(-39) + (-9*y)*(17*y**2) + (-9*y)*(-25*y**3) + (17*y**2)*(19*y**3) + (17*y**2)*(-39) + (-25*y**3)*(19*y**3) - 25*y**3*(-39)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*y**3)*-39 = 975*y**3\n (-25*y**3)*(-9*y) = 225*y**4\n (-25*y**3)*(19*y**3) = -475*y**6\n (-13*y)*-39 = 507*y\n (-13*y)*(-9*y) = 117*y**2\n (-13*y)*(19*y**3) = -247*y**4\n (17*y**2)*-39 = -663*y**2\n (17*y**2)*(-9*y) = -153*y**3\n (17*y**2)*(19*y**3) = 323*y**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -475*y**6 + 323*y**5 - 247*y**4 + 225*y**4 - 153*y**3 + 975*y**3 - 663*y**2 + 117*y**2 + 507*y\nCombining like terms, got -475*y**6 + 323*y**5 - 22*y**4 + 822*y**3 - 546*y**2 + 507*y\n#Step 7:\nCurrent expression: -475*y**6 + 323*y**5 - 22*y**4 + 822*y**3 - 546*y**2 + 507*y\nNo more calculations needed.\n-475*y**6 + 323*y**5 - 22*y**4 + 822*y**3 - 546*y**2 + 507*y", "generated_answer": "-475*y**6 + 323*y**5 - 22*y**4 + 822*y**3 - 546*y**2 + 507*y", "step_length": 7} {"cot_id": "3c27618f4853fd1f7329fb0580d5f2952e88aef87ff5aab898d596917c4ffff7", "datapoint": {"question": "Simplify this expression: (-44*y**3 + 40*y**2 - 32)*(-y**3 + 6*y**2 + 29)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "44*y**6 - 304*y**5 + 240*y**4 - 1244*y**3 + 968*y**2 - 928", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 22, "polynomial_expr": "(-44*y**3 + 40*y**2 - 32)*(-y**3 + 6*y**2 + 29)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-44*y**3 + 40*y**2 - 32)*(-y**3 + 6*y**2 + 29)\nExpanding the part (-44*y**3 + 40*y**2 - 32) using the distributive property, and we got: (40*y**2)*(-y**3 + 6*y**2 + 29) + (-44*y**3)*(-y**3 + 6*y**2 + 29) - 32*(-y**3 + 6*y**2 + 29)\n#Step 2:\nCurrent expression: (40*y**2)*(-y**3 + 6*y**2 + 29) + (-44*y**3)*(-y**3 + 6*y**2 + 29) - 32*(-y**3 + 6*y**2 + 29)\nSimplifying the partial expression: -32*(-y**3 + 6*y**2 + 29)\nExpanding the part (-y**3 + 6*y**2 + 29) using the distributive property, and we got: (6*y**2)*(-32) - y**3*(-32) + 29*(-32)\nReplacing -32*(-y**3 + 6*y**2 + 29) with (6*y**2)*(-32) - y**3*(-32) + 29*(-32) in the overall expression.\n#Step 3:\nCurrent expression: (6*y**2)*(-32) + (40*y**2)*(-y**3 + 6*y**2 + 29) + (-44*y**3)*(-y**3 + 6*y**2 + 29) - y**3*(-32) - 928\nSimplifying the partial expression: (-44*y**3)*(-y**3 + 6*y**2 + 29)\nExpanding the part (-y**3 + 6*y**2 + 29) using the distributive property, and we got: 29*(-44*y**3) + (6*y**2)*(-44*y**3) + (-44*y**3)*(-y**3)\nReplacing (-44*y**3)*(-y**3 + 6*y**2 + 29) with 29*(-44*y**3) + (6*y**2)*(-44*y**3) + (-44*y**3)*(-y**3) in the overall expression.\n#Step 4:\nCurrent expression: 29*(-44)*y**3 + (6*y**2)*(-44*y**3) + (6*y**2)*(-32) + (40*y**2)*(-y**3 + 6*y**2 + 29) + (-44*y**3)*(-y**3) - y**3*(-32) - 928\nSimplifying the partial expression: (40*y**2)*(-y**3 + 6*y**2 + 29)\nExpanding the part (-y**3 + 6*y**2 + 29) using the distributive property, and we got: 29*(40*y**2) + (6*y**2)*(40*y**2) + (40*y**2)*(-y**3)\nReplacing (40*y**2)*(-y**3 + 6*y**2 + 29) with 29*(40*y**2) + (6*y**2)*(40*y**2) + (40*y**2)*(-y**3) in the overall expression.\n#Step 5:\nCurrent expression: 29*(-44)*y**3 + 29*40*y**2 + (6*y**2)*(40*y**2) + (6*y**2)*(-44*y**3) + (6*y**2)*(-32) + (40*y**2)*(-y**3) + (-44*y**3)*(-y**3) - y**3*(-32) - 928\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-y**3)*-32 = 32*y**3\n (-y**3)*(-44*y**3) = 44*y**6\n (-y**3)*(40*y**2) = -40*y**5\n (6*y**2)*-32 = -192*y**2\n (6*y**2)*(-44*y**3) = -264*y**5\n (6*y**2)*(40*y**2) = 240*y**4\n 29*-44*y**3 = -1276*y**3\n 29*40*y**2 = 1160*y**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 44*y**6 - 264*y**5 - 40*y**5 + 240*y**4 - 1276*y**3 + 32*y**3 - 192*y**2 + 1160*y**2 - 928\nCombining like terms, got 44*y**6 - 304*y**5 + 240*y**4 - 1244*y**3 + 968*y**2 - 928\n#Step 7:\nCurrent expression: 44*y**6 - 304*y**5 + 240*y**4 - 1244*y**3 + 968*y**2 - 928\nNo more calculations needed.\n44*y**6 - 304*y**5 + 240*y**4 - 1244*y**3 + 968*y**2 - 928", "generated_answer": "44*y**6 - 304*y**5 + 240*y**4 - 1244*y**3 + 968*y**2 - 928", "step_length": 7} {"cot_id": "41e12f21b0d14a7e2fc6e5ea07dcf75cec70cda43eb58080d0886eec7f6fccf9", "datapoint": {"question": "Simplify this expression: 6*y**2*(56*y**2 - 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "336*y**4 - 198*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 23, "polynomial_expr": "6*y**2*(56*y**2 - 33)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 6*y**2*(56*y**2 - 33)\nExpanding the part (56*y**2 - 33) using the distributive property, and we got: -198*y**2 + (6*y**2)*(56*y**2)\n#Step 2:\nCurrent expression: -198*y**2 + (6*y**2)*(56*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -33*(6*y**2) = -198*y**2\n (56*y**2)*(6*y**2) = 336*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 336*y**4 - 198*y**2\nNo more calculations needed.\n336*y**4 - 198*y**2", "generated_answer": "336*y**4 - 198*y**2", "step_length": 3} {"cot_id": "92f5aa397cf136e3a1f32990a6b1f0bd616542f8ea85a139f74077a2cf1c9a71", "datapoint": {"question": "Calculate the following: (46*x - 47)*(-16*x**3 + 36*x - 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-736*x**4 + 752*x**3 + 1656*x**2 - 3164*x + 1504", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 24, "polynomial_expr": "(46*x - 47)*(-16*x**3 + 36*x - 32)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (46*x - 47)*(-16*x**3 + 36*x - 32)\nExpanding the part (46*x - 47) using the distributive property, and we got: (46*x)*(-16*x**3 + 36*x - 32) - 47*(-16*x**3 + 36*x - 32)\n#Step 2:\nCurrent expression: (46*x)*(-16*x**3 + 36*x - 32) - 47*(-16*x**3 + 36*x - 32)\nSimplifying the partial expression: -47*(-16*x**3 + 36*x - 32)\nExpanding the part (-16*x**3 + 36*x - 32) using the distributive property, and we got: (36*x)*(-47) - 16*x**3*(-47) - 32*(-47)\nReplacing -47*(-16*x**3 + 36*x - 32) with (36*x)*(-47) - 16*x**3*(-47) - 32*(-47) in the overall expression.\n#Step 3:\nCurrent expression: (36*x)*(-47) + (46*x)*(-16*x**3 + 36*x - 32) - 16*x**3*(-47) + 1504\nSimplifying the partial expression: (46*x)*(-16*x**3 + 36*x - 32)\nExpanding the part (-16*x**3 + 36*x - 32) using the distributive property, and we got: -1472*x + (36*x)*(46*x) + (46*x)*(-16*x**3)\nReplacing (46*x)*(-16*x**3 + 36*x - 32) with -1472*x + (36*x)*(46*x) + (46*x)*(-16*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -32*46*x + (36*x)*(46*x) + (36*x)*(-47) + (46*x)*(-16*x**3) - 16*x**3*(-47) + 1504\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-16*x**3)*-47 = 752*x**3\n (-16*x**3)*(46*x) = -736*x**4\n (36*x)*-47 = -1692*x\n (36*x)*(46*x) = 1656*x**2\n -32*46*x = -1472*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -736*x**4 + 752*x**3 + 1656*x**2 - 1692*x - 1472*x + 1504\nCombining like terms, got -736*x**4 + 752*x**3 + 1656*x**2 - 3164*x + 1504\n#Step 6:\nCurrent expression: -736*x**4 + 752*x**3 + 1656*x**2 - 3164*x + 1504\nNo more calculations needed.\n-736*x**4 + 752*x**3 + 1656*x**2 - 3164*x + 1504", "generated_answer": "-736*x**4 + 752*x**3 + 1656*x**2 - 3164*x + 1504", "step_length": 6} {"cot_id": "d0df849248673414acde390792ce255d9898e8b4ef3b072f4662864d8e4dc9bf", "datapoint": {"question": "Simplify this expression: (18 - 69*x**3)*(-7*x**3 - 12*x**2 - 26*x - 29)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "483*x**6 + 828*x**5 + 1794*x**4 + 1875*x**3 - 216*x**2 - 468*x - 522", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 25, "polynomial_expr": "(18 - 69*x**3)*(-7*x**3 - 12*x**2 - 26*x - 29)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (18 - 69*x**3)*(-7*x**3 - 12*x**2 - 26*x - 29)\nExpanding the part (18 - 69*x**3) using the distributive property, and we got: (-69*x**3)*(-7*x**3 - 12*x**2 - 26*x - 29) + 18*(-7*x**3 - 12*x**2 - 26*x - 29)\n#Step 2:\nCurrent expression: (-69*x**3)*(-7*x**3 - 12*x**2 - 26*x - 29) + 18*(-7*x**3 - 12*x**2 - 26*x - 29)\nSimplifying the partial expression: 18*(-7*x**3 - 12*x**2 - 26*x - 29)\nExpanding the part (-7*x**3 - 12*x**2 - 26*x - 29) using the distributive property, and we got: -26*x*18 - 12*x**2*18 - 7*x**3*18 - 29*18\nReplacing 18*(-7*x**3 - 12*x**2 - 26*x - 29) with -26*x*18 - 12*x**2*18 - 7*x**3*18 - 29*18 in the overall expression.\n#Step 3:\nCurrent expression: -26*x*18 - 12*x**2*18 + (-69*x**3)*(-7*x**3 - 12*x**2 - 26*x - 29) - 7*x**3*18 - 522\nSimplifying the partial expression: (-69*x**3)*(-7*x**3 - 12*x**2 - 26*x - 29)\nExpanding the part (-7*x**3 - 12*x**2 - 26*x - 29) using the distributive property, and we got: (-26*x)*(-69*x**3) - (-1)*2001*x**3 + (-12*x**2)*(-69*x**3) + (-69*x**3)*(-7*x**3)\nReplacing (-69*x**3)*(-7*x**3 - 12*x**2 - 26*x - 29) with (-26*x)*(-69*x**3) - (-1)*2001*x**3 + (-12*x**2)*(-69*x**3) + (-69*x**3)*(-7*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-26*x)*(-69*x**3) - 26*x*18 - 29*(-69)*x**3 + (-12*x**2)*(-69*x**3) - 12*x**2*18 + (-69*x**3)*(-7*x**3) - 7*x**3*18 - 522\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-26*x)*18 = -468*x\n (-26*x)*(-69*x**3) = 1794*x**4\n (-12*x**2)*18 = -216*x**2\n (-12*x**2)*(-69*x**3) = 828*x**5\n (-7*x**3)*18 = -126*x**3\n (-7*x**3)*(-69*x**3) = 483*x**6\n -29*-69*x**3 = 2001*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 483*x**6 + 828*x**5 + 1794*x**4 - 126*x**3 + 2001*x**3 - 216*x**2 - 468*x - 522\nCombining like terms, got 483*x**6 + 828*x**5 + 1794*x**4 + 1875*x**3 - 216*x**2 - 468*x - 522\n#Step 6:\nCurrent expression: 483*x**6 + 828*x**5 + 1794*x**4 + 1875*x**3 - 216*x**2 - 468*x - 522\nNo more calculations needed.\n483*x**6 + 828*x**5 + 1794*x**4 + 1875*x**3 - 216*x**2 - 468*x - 522", "generated_answer": "483*x**6 + 828*x**5 + 1794*x**4 + 1875*x**3 - 216*x**2 - 468*x - 522", "step_length": 6} {"cot_id": "b0d530ed008d6f1936de70dfb875feca97d61b9c7a8edaf5e30d79753b7ad196", "datapoint": {"question": "Simplify this expression: (-72*z**3 - 47*z**2 - 39)*(48*z**3 - 16*z**2 - 83*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-3456*z**6 - 1104*z**5 + 6728*z**4 + 2029*z**3 + 624*z**2 + 3237*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 26, "polynomial_expr": "(-72*z**3 - 47*z**2 - 39)*(48*z**3 - 16*z**2 - 83*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-72*z**3 - 47*z**2 - 39)*(48*z**3 - 16*z**2 - 83*z)\nExpanding the part (-72*z**3 - 47*z**2 - 39) using the distributive property, and we got: (-47*z**2)*(48*z**3 - 16*z**2 - 83*z) + (-72*z**3)*(48*z**3 - 16*z**2 - 83*z) - 39*(48*z**3 - 16*z**2 - 83*z)\n#Step 2:\nCurrent expression: (-47*z**2)*(48*z**3 - 16*z**2 - 83*z) + (-72*z**3)*(48*z**3 - 16*z**2 - 83*z) - 39*(48*z**3 - 16*z**2 - 83*z)\nSimplifying the partial expression: -39*(48*z**3 - 16*z**2 - 83*z)\nExpanding the part (48*z**3 - 16*z**2 - 83*z) using the distributive property, and we got: -83*z*(-39) - 16*z**2*(-39) + (48*z**3)*(-39)\nReplacing -39*(48*z**3 - 16*z**2 - 83*z) with -83*z*(-39) - 16*z**2*(-39) + (48*z**3)*(-39) in the overall expression.\n#Step 3:\nCurrent expression: -83*z*(-39) + (-47*z**2)*(48*z**3 - 16*z**2 - 83*z) - 16*z**2*(-39) + (-72*z**3)*(48*z**3 - 16*z**2 - 83*z) + (48*z**3)*(-39)\nSimplifying the partial expression: (-72*z**3)*(48*z**3 - 16*z**2 - 83*z)\nExpanding the part (48*z**3 - 16*z**2 - 83*z) using the distributive property, and we got: (-83*z)*(-72*z**3) + (-16*z**2)*(-72*z**3) + (-72*z**3)*(48*z**3)\nReplacing (-72*z**3)*(48*z**3 - 16*z**2 - 83*z) with (-83*z)*(-72*z**3) + (-16*z**2)*(-72*z**3) + (-72*z**3)*(48*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-83*z)*(-72*z**3) - 83*z*(-39) + (-47*z**2)*(48*z**3 - 16*z**2 - 83*z) + (-16*z**2)*(-72*z**3) - 16*z**2*(-39) + (-72*z**3)*(48*z**3) + (48*z**3)*(-39)\nSimplifying the partial expression: (-47*z**2)*(48*z**3 - 16*z**2 - 83*z)\nExpanding the part (48*z**3 - 16*z**2 - 83*z) using the distributive property, and we got: (-83*z)*(-47*z**2) + (-47*z**2)*(-16*z**2) + (-47*z**2)*(48*z**3)\nReplacing (-47*z**2)*(48*z**3 - 16*z**2 - 83*z) with (-83*z)*(-47*z**2) + (-47*z**2)*(-16*z**2) + (-47*z**2)*(48*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-83*z)*(-47*z**2) + (-83*z)*(-72*z**3) - 83*z*(-39) + (-47*z**2)*(-16*z**2) + (-47*z**2)*(48*z**3) + (-16*z**2)*(-72*z**3) - 16*z**2*(-39) + (-72*z**3)*(48*z**3) + (48*z**3)*(-39)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-83*z)*-39 = 3237*z\n (-83*z)*(-72*z**3) = 5976*z**4\n (-83*z)*(-47*z**2) = 3901*z**3\n (-16*z**2)*-39 = 624*z**2\n (-16*z**2)*(-72*z**3) = 1152*z**5\n (-16*z**2)*(-47*z**2) = 752*z**4\n (48*z**3)*-39 = -1872*z**3\n (48*z**3)*(-72*z**3) = -3456*z**6\n (48*z**3)*(-47*z**2) = -2256*z**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -3456*z**6 - 2256*z**5 + 1152*z**5 + 752*z**4 + 5976*z**4 - 1872*z**3 + 3901*z**3 + 624*z**2 + 3237*z\nCombining like terms, got -3456*z**6 - 1104*z**5 + 6728*z**4 + 2029*z**3 + 624*z**2 + 3237*z\n#Step 7:\nCurrent expression: -3456*z**6 - 1104*z**5 + 6728*z**4 + 2029*z**3 + 624*z**2 + 3237*z\nNo more calculations needed.\n-3456*z**6 - 1104*z**5 + 6728*z**4 + 2029*z**3 + 624*z**2 + 3237*z", "generated_answer": "-3456*z**6 - 1104*z**5 + 6728*z**4 + 2029*z**3 + 624*z**2 + 3237*z", "step_length": 7} {"cot_id": "9329d377c19c8434a6355948e91aabc90b8b45aec1c898020da539d2f70f12d7", "datapoint": {"question": "Simplify this expression: (-26*z**3 + 16*z**2)*(11*z**3 - 21*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-286*z**6 + 722*z**5 - 336*z**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 27, "polynomial_expr": "(-26*z**3 + 16*z**2)*(11*z**3 - 21*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-26*z**3 + 16*z**2)*(11*z**3 - 21*z**2)\nExpanding the part (-26*z**3 + 16*z**2) using the distributive property, and we got: (16*z**2)*(11*z**3 - 21*z**2) + (-26*z**3)*(11*z**3 - 21*z**2)\n#Step 2:\nCurrent expression: (16*z**2)*(11*z**3 - 21*z**2) + (-26*z**3)*(11*z**3 - 21*z**2)\nSimplifying the partial expression: (-26*z**3)*(11*z**3 - 21*z**2)\nExpanding the part (11*z**3 - 21*z**2) using the distributive property, and we got: (-21*z**2)*(-26*z**3) + (-26*z**3)*(11*z**3)\nReplacing (-26*z**3)*(11*z**3 - 21*z**2) with (-21*z**2)*(-26*z**3) + (-26*z**3)*(11*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-21*z**2)*(-26*z**3) + (16*z**2)*(11*z**3 - 21*z**2) + (-26*z**3)*(11*z**3)\nSimplifying the partial expression: (16*z**2)*(11*z**3 - 21*z**2)\nExpanding the part (11*z**3 - 21*z**2) using the distributive property, and we got: (-21*z**2)*(16*z**2) + (16*z**2)*(11*z**3)\nReplacing (16*z**2)*(11*z**3 - 21*z**2) with (-21*z**2)*(16*z**2) + (16*z**2)*(11*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-21*z**2)*(16*z**2) + (-21*z**2)*(-26*z**3) + (16*z**2)*(11*z**3) + (-26*z**3)*(11*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-21*z**2)*(-26*z**3) = 546*z**5\n (-21*z**2)*(16*z**2) = -336*z**4\n (11*z**3)*(-26*z**3) = -286*z**6\n (11*z**3)*(16*z**2) = 176*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -286*z**6 + 176*z**5 + 546*z**5 - 336*z**4\nCombining like terms, got -286*z**6 + 722*z**5 - 336*z**4\n#Step 6:\nCurrent expression: -286*z**6 + 722*z**5 - 336*z**4\nNo more calculations needed.\n-286*z**6 + 722*z**5 - 336*z**4", "generated_answer": "-286*z**6 + 722*z**5 - 336*z**4", "step_length": 6} {"cot_id": "7fe997af6f79672a566a13f11ffee11621a105b3ecdc4bbfb840ad1ea5cb5ea5", "datapoint": {"question": "Calculate the following: (51 - 57*x**3)*(25*x**3 + 5*x**2 - 6*x - 19)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1425*x**6 - 285*x**5 + 342*x**4 + 2358*x**3 + 255*x**2 - 306*x - 969", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 28, "polynomial_expr": "(51 - 57*x**3)*(25*x**3 + 5*x**2 - 6*x - 19)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (51 - 57*x**3)*(25*x**3 + 5*x**2 - 6*x - 19)\nExpanding the part (51 - 57*x**3) using the distributive property, and we got: (-57*x**3)*(25*x**3 + 5*x**2 - 6*x - 19) + 51*(25*x**3 + 5*x**2 - 6*x - 19)\n#Step 2:\nCurrent expression: (-57*x**3)*(25*x**3 + 5*x**2 - 6*x - 19) + 51*(25*x**3 + 5*x**2 - 6*x - 19)\nSimplifying the partial expression: 51*(25*x**3 + 5*x**2 - 6*x - 19)\nExpanding the part (25*x**3 + 5*x**2 - 6*x - 19) using the distributive property, and we got: -6*x*51 + (5*x**2)*51 + (25*x**3)*51 - 19*51\nReplacing 51*(25*x**3 + 5*x**2 - 6*x - 19) with -6*x*51 + (5*x**2)*51 + (25*x**3)*51 - 19*51 in the overall expression.\n#Step 3:\nCurrent expression: -6*x*51 + (5*x**2)*51 + (-57*x**3)*(25*x**3 + 5*x**2 - 6*x - 19) + (25*x**3)*51 - 969\nSimplifying the partial expression: (-57*x**3)*(25*x**3 + 5*x**2 - 6*x - 19)\nExpanding the part (25*x**3 + 5*x**2 - 6*x - 19) using the distributive property, and we got: (-6*x)*(-57*x**3) - (-1)*1083*x**3 + (5*x**2)*(-57*x**3) + (-57*x**3)*(25*x**3)\nReplacing (-57*x**3)*(25*x**3 + 5*x**2 - 6*x - 19) with (-6*x)*(-57*x**3) - (-1)*1083*x**3 + (5*x**2)*(-57*x**3) + (-57*x**3)*(25*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-6*x)*(-57*x**3) - 6*x*51 - 19*(-57)*x**3 + (5*x**2)*(-57*x**3) + (5*x**2)*51 + (-57*x**3)*(25*x**3) + (25*x**3)*51 - 969\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-6*x)*51 = -306*x\n (-6*x)*(-57*x**3) = 342*x**4\n (5*x**2)*51 = 255*x**2\n (5*x**2)*(-57*x**3) = -285*x**5\n (25*x**3)*51 = 1275*x**3\n (25*x**3)*(-57*x**3) = -1425*x**6\n -19*-57*x**3 = 1083*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1425*x**6 - 285*x**5 + 342*x**4 + 1083*x**3 + 1275*x**3 + 255*x**2 - 306*x - 969\nCombining like terms, got -1425*x**6 - 285*x**5 + 342*x**4 + 2358*x**3 + 255*x**2 - 306*x - 969\n#Step 6:\nCurrent expression: -1425*x**6 - 285*x**5 + 342*x**4 + 2358*x**3 + 255*x**2 - 306*x - 969\nNo more calculations needed.\n-1425*x**6 - 285*x**5 + 342*x**4 + 2358*x**3 + 255*x**2 - 306*x - 969", "generated_answer": "-1425*x**6 - 285*x**5 + 342*x**4 + 2358*x**3 + 255*x**2 - 306*x - 969", "step_length": 6} {"cot_id": "fa8aab3a5c633b2af9d9c090c93f1bfb7cb1b9f1e1866e38d9e5d46897101af2", "datapoint": {"question": "Calculate the following: (46*y**3 - 10)*(-39*y**3 + 24*y**2 + 15)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1794*y**6 + 1104*y**5 + 1080*y**3 - 240*y**2 - 150", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 29, "polynomial_expr": "(46*y**3 - 10)*(-39*y**3 + 24*y**2 + 15)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (46*y**3 - 10)*(-39*y**3 + 24*y**2 + 15)\nExpanding the part (46*y**3 - 10) using the distributive property, and we got: (46*y**3)*(-39*y**3 + 24*y**2 + 15) - 10*(-39*y**3 + 24*y**2 + 15)\n#Step 2:\nCurrent expression: (46*y**3)*(-39*y**3 + 24*y**2 + 15) - 10*(-39*y**3 + 24*y**2 + 15)\nSimplifying the partial expression: -10*(-39*y**3 + 24*y**2 + 15)\nExpanding the part (-39*y**3 + 24*y**2 + 15) using the distributive property, and we got: (24*y**2)*(-10) - 39*y**3*(-10) + 15*(-10)\nReplacing -10*(-39*y**3 + 24*y**2 + 15) with (24*y**2)*(-10) - 39*y**3*(-10) + 15*(-10) in the overall expression.\n#Step 3:\nCurrent expression: (24*y**2)*(-10) - 39*y**3*(-10) + (46*y**3)*(-39*y**3 + 24*y**2 + 15) - 150\nSimplifying the partial expression: (46*y**3)*(-39*y**3 + 24*y**2 + 15)\nExpanding the part (-39*y**3 + 24*y**2 + 15) using the distributive property, and we got: 15*(46*y**3) + (24*y**2)*(46*y**3) + (-39*y**3)*(46*y**3)\nReplacing (46*y**3)*(-39*y**3 + 24*y**2 + 15) with 15*(46*y**3) + (24*y**2)*(46*y**3) + (-39*y**3)*(46*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 15*46*y**3 + (24*y**2)*(46*y**3) + (24*y**2)*(-10) + (-39*y**3)*(46*y**3) - 39*y**3*(-10) - 150\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*y**3)*-10 = 390*y**3\n (-39*y**3)*(46*y**3) = -1794*y**6\n (24*y**2)*-10 = -240*y**2\n (24*y**2)*(46*y**3) = 1104*y**5\n 15*46*y**3 = 690*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1794*y**6 + 1104*y**5 + 390*y**3 + 690*y**3 - 240*y**2 - 150\nCombining like terms, got -1794*y**6 + 1104*y**5 + 1080*y**3 - 240*y**2 - 150\n#Step 6:\nCurrent expression: -1794*y**6 + 1104*y**5 + 1080*y**3 - 240*y**2 - 150\nNo more calculations needed.\n-1794*y**6 + 1104*y**5 + 1080*y**3 - 240*y**2 - 150", "generated_answer": "-1794*y**6 + 1104*y**5 + 1080*y**3 - 240*y**2 - 150", "step_length": 6} {"cot_id": "efcaae803e2bb1b859360188b2cba0f99575860e8c3f2497a43118afd958aa9a", "datapoint": {"question": "Calculate the following: (46 - 90*x**2)*(15*x**3 + 41*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1350*x**5 - 3000*x**3 + 1886*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 30, "polynomial_expr": "(46 - 90*x**2)*(15*x**3 + 41*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (46 - 90*x**2)*(15*x**3 + 41*x)\nExpanding the part (46 - 90*x**2) using the distributive property, and we got: (-90*x**2)*(15*x**3 + 41*x) + 46*(15*x**3 + 41*x)\n#Step 2:\nCurrent expression: (-90*x**2)*(15*x**3 + 41*x) + 46*(15*x**3 + 41*x)\nSimplifying the partial expression: 46*(15*x**3 + 41*x)\nExpanding the part (15*x**3 + 41*x) using the distributive property, and we got: (41*x)*46 + (15*x**3)*46\nReplacing 46*(15*x**3 + 41*x) with (41*x)*46 + (15*x**3)*46 in the overall expression.\n#Step 3:\nCurrent expression: (41*x)*46 + (-90*x**2)*(15*x**3 + 41*x) + (15*x**3)*46\nSimplifying the partial expression: (-90*x**2)*(15*x**3 + 41*x)\nExpanding the part (15*x**3 + 41*x) using the distributive property, and we got: (41*x)*(-90*x**2) + (-90*x**2)*(15*x**3)\nReplacing (-90*x**2)*(15*x**3 + 41*x) with (41*x)*(-90*x**2) + (-90*x**2)*(15*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (41*x)*(-90*x**2) + (41*x)*46 + (-90*x**2)*(15*x**3) + (15*x**3)*46\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (15*x**3)*46 = 690*x**3\n (15*x**3)*(-90*x**2) = -1350*x**5\n (41*x)*46 = 1886*x\n (41*x)*(-90*x**2) = -3690*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1350*x**5 - 3690*x**3 + 690*x**3 + 1886*x\nCombining like terms, got -1350*x**5 - 3000*x**3 + 1886*x\n#Step 6:\nCurrent expression: -1350*x**5 - 3000*x**3 + 1886*x\nNo more calculations needed.\n-1350*x**5 - 3000*x**3 + 1886*x", "generated_answer": "-1350*x**5 - 3000*x**3 + 1886*x", "step_length": 6} {"cot_id": "e444d86b2fb67fadf672b778eab56e7c5ccc6d443c6ddb0a8f283ef431801084", "datapoint": {"question": "Simplify this expression: (-32*y**2 + 27*y)*(-38*y**3 - 2*y - 65)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1216*y**5 - 1026*y**4 + 64*y**3 + 2026*y**2 - 1755*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 31, "polynomial_expr": "(-32*y**2 + 27*y)*(-38*y**3 - 2*y - 65)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-32*y**2 + 27*y)*(-38*y**3 - 2*y - 65)\nExpanding the part (-32*y**2 + 27*y) using the distributive property, and we got: (27*y)*(-38*y**3 - 2*y - 65) + (-32*y**2)*(-38*y**3 - 2*y - 65)\n#Step 2:\nCurrent expression: (27*y)*(-38*y**3 - 2*y - 65) + (-32*y**2)*(-38*y**3 - 2*y - 65)\nSimplifying the partial expression: (-32*y**2)*(-38*y**3 - 2*y - 65)\nExpanding the part (-38*y**3 - 2*y - 65) using the distributive property, and we got: (-2*y)*(-32*y**2) - (-1)*2080*y**2 + (-32*y**2)*(-38*y**3)\nReplacing (-32*y**2)*(-38*y**3 - 2*y - 65) with (-2*y)*(-32*y**2) - (-1)*2080*y**2 + (-32*y**2)*(-38*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-2*y)*(-32*y**2) - 65*(-32)*y**2 + (27*y)*(-38*y**3 - 2*y - 65) + (-32*y**2)*(-38*y**3)\nSimplifying the partial expression: (27*y)*(-38*y**3 - 2*y - 65)\nExpanding the part (-38*y**3 - 2*y - 65) using the distributive property, and we got: (-2*y)*(27*y) - 1755*y + (27*y)*(-38*y**3)\nReplacing (27*y)*(-38*y**3 - 2*y - 65) with (-2*y)*(27*y) - 1755*y + (27*y)*(-38*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-2*y)*(27*y) + (-2*y)*(-32*y**2) - 65*(-32)*y**2 - 65*27*y + (27*y)*(-38*y**3) + (-32*y**2)*(-38*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*y**3)*(-32*y**2) = 1216*y**5\n (-38*y**3)*(27*y) = -1026*y**4\n (-2*y)*(-32*y**2) = 64*y**3\n (-2*y)*(27*y) = -54*y**2\n -65*-32*y**2 = 2080*y**2\n -65*27*y = -1755*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1216*y**5 - 1026*y**4 + 64*y**3 - 54*y**2 + 2080*y**2 - 1755*y\nCombining like terms, got 1216*y**5 - 1026*y**4 + 64*y**3 + 2026*y**2 - 1755*y\n#Step 6:\nCurrent expression: 1216*y**5 - 1026*y**4 + 64*y**3 + 2026*y**2 - 1755*y\nNo more calculations needed.\n1216*y**5 - 1026*y**4 + 64*y**3 + 2026*y**2 - 1755*y", "generated_answer": "1216*y**5 - 1026*y**4 + 64*y**3 + 2026*y**2 - 1755*y", "step_length": 6} {"cot_id": "554792ef274b0d5b1c3631317ba713496f15da0cfd654f97626b7f4e276b26eb", "datapoint": {"question": "Calculate the following: -52*z*(18*z**3 - 15*z**2 + 3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-936*z**4 + 780*z**3 - 156*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 32, "polynomial_expr": "-52*z*(18*z**3 - 15*z**2 + 3)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -52*z*(18*z**3 - 15*z**2 + 3)\nExpanding the part (18*z**3 - 15*z**2 + 3) using the distributive property, and we got: (-52*z)*(-15*z**2) + (-52*z)*(18*z**3) + 3*(-52*z)\n#Step 2:\nCurrent expression: (-52*z)*(-15*z**2) + (-52*z)*(18*z**3) + 3*(-52*z)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 3*(-52*z) = -156*z\n (-15*z**2)*(-52*z) = 780*z**3\n (18*z**3)*(-52*z) = -936*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -936*z**4 + 780*z**3 - 156*z\nNo more calculations needed.\n-936*z**4 + 780*z**3 - 156*z", "generated_answer": "-936*z**4 + 780*z**3 - 156*z", "step_length": 3} {"cot_id": "930fc466a154355c39450d0253858ba16615a7ba694fc9ca64f837fdb23ada1a", "datapoint": {"question": "Calculate the following: (3*y**2 + y)*(18*y**2 + 11*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "54*y**4 + 51*y**3 + 11*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 33, "polynomial_expr": "(3*y**2 + y)*(18*y**2 + 11*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (3*y**2 + y)*(18*y**2 + 11*y)\nExpanding the part (3*y**2 + y) using the distributive property, and we got: y*(18*y**2 + 11*y) + (3*y**2)*(18*y**2 + 11*y)\n#Step 2:\nCurrent expression: y*(18*y**2 + 11*y) + (3*y**2)*(18*y**2 + 11*y)\nSimplifying the partial expression: y*(18*y**2 + 11*y)\nExpanding the part (18*y**2 + 11*y) using the distributive property, and we got: y*(11*y) + y*(18*y**2)\nReplacing y*(18*y**2 + 11*y) with y*(11*y) + y*(18*y**2) in the overall expression.\n#Step 3:\nCurrent expression: y*(11*y) + y*(18*y**2) + (3*y**2)*(18*y**2 + 11*y)\nSimplifying the partial expression: (3*y**2)*(18*y**2 + 11*y)\nExpanding the part (18*y**2 + 11*y) using the distributive property, and we got: (11*y)*(3*y**2) + (3*y**2)*(18*y**2)\nReplacing (3*y**2)*(18*y**2 + 11*y) with (11*y)*(3*y**2) + (3*y**2)*(18*y**2) in the overall expression.\n#Step 4:\nCurrent expression: y*(11*y) + y*(18*y**2) + (11*y)*(3*y**2) + (3*y**2)*(18*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (11*y)*y = 11*y**2\n (11*y)*(3*y**2) = 33*y**3\n (18*y**2)*y = 18*y**3\n (18*y**2)*(3*y**2) = 54*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 54*y**4 + 18*y**3 + 33*y**3 + 11*y**2\nCombining like terms, got 54*y**4 + 51*y**3 + 11*y**2\n#Step 6:\nCurrent expression: 54*y**4 + 51*y**3 + 11*y**2\nNo more calculations needed.\n54*y**4 + 51*y**3 + 11*y**2", "generated_answer": "54*y**4 + 51*y**3 + 11*y**2", "step_length": 6} {"cot_id": "cd479d90a14306f56bfaa3c1804e82fbf376fda35e5c84ff30abf164d1589422", "datapoint": {"question": "Calculate the following: (-29*y**2 - 29*y)*(-35*y**3 + 27*y**2 - 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1015*y**5 + 232*y**4 - 783*y**3 + 580*y**2 + 580*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 34, "polynomial_expr": "(-29*y**2 - 29*y)*(-35*y**3 + 27*y**2 - 20)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-29*y**2 - 29*y)*(-35*y**3 + 27*y**2 - 20)\nExpanding the part (-29*y**2 - 29*y) using the distributive property, and we got: (-29*y)*(-35*y**3 + 27*y**2 - 20) + (-29*y**2)*(-35*y**3 + 27*y**2 - 20)\n#Step 2:\nCurrent expression: (-29*y)*(-35*y**3 + 27*y**2 - 20) + (-29*y**2)*(-35*y**3 + 27*y**2 - 20)\nSimplifying the partial expression: (-29*y)*(-35*y**3 + 27*y**2 - 20)\nExpanding the part (-35*y**3 + 27*y**2 - 20) using the distributive property, and we got: (-29*y)*(27*y**2) + (-29*y)*(-35*y**3) - (-1)*580*y\nReplacing (-29*y)*(-35*y**3 + 27*y**2 - 20) with (-29*y)*(27*y**2) + (-29*y)*(-35*y**3) - (-1)*580*y in the overall expression.\n#Step 3:\nCurrent expression: (-29*y)*(27*y**2) + (-29*y)*(-35*y**3) - 20*(-29)*y + (-29*y**2)*(-35*y**3 + 27*y**2 - 20)\nSimplifying the partial expression: (-29*y**2)*(-35*y**3 + 27*y**2 - 20)\nExpanding the part (-35*y**3 + 27*y**2 - 20) using the distributive property, and we got: -(-1)*580*y**2 + (-29*y**2)*(27*y**2) + (-29*y**2)*(-35*y**3)\nReplacing (-29*y**2)*(-35*y**3 + 27*y**2 - 20) with -(-1)*580*y**2 + (-29*y**2)*(27*y**2) + (-29*y**2)*(-35*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-29*y)*(27*y**2) + (-29*y)*(-35*y**3) - 20*(-29)*y**2 - 20*(-29)*y + (-29*y**2)*(27*y**2) + (-29*y**2)*(-35*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*y**3)*(-29*y) = 1015*y**4\n (-35*y**3)*(-29*y**2) = 1015*y**5\n (27*y**2)*(-29*y) = -783*y**3\n (27*y**2)*(-29*y**2) = -783*y**4\n -20*-29*y = 580*y\n -20*-29*y**2 = 580*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1015*y**5 - 783*y**4 + 1015*y**4 - 783*y**3 + 580*y**2 + 580*y\nCombining like terms, got 1015*y**5 + 232*y**4 - 783*y**3 + 580*y**2 + 580*y\n#Step 6:\nCurrent expression: 1015*y**5 + 232*y**4 - 783*y**3 + 580*y**2 + 580*y\nNo more calculations needed.\n1015*y**5 + 232*y**4 - 783*y**3 + 580*y**2 + 580*y", "generated_answer": "1015*y**5 + 232*y**4 - 783*y**3 + 580*y**2 + 580*y", "step_length": 6} {"cot_id": "584b8cfbc12c00b1600bccc07ee6cf497346422f95d077505dd274d89a962268", "datapoint": {"question": "Calculate the following: (16 - 8*y)*(41*y**3 - 15*y**2 - 40)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-328*y**4 + 776*y**3 - 240*y**2 + 320*y - 640", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 35, "polynomial_expr": "(16 - 8*y)*(41*y**3 - 15*y**2 - 40)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (16 - 8*y)*(41*y**3 - 15*y**2 - 40)\nExpanding the part (16 - 8*y) using the distributive property, and we got: (-8*y)*(41*y**3 - 15*y**2 - 40) + 16*(41*y**3 - 15*y**2 - 40)\n#Step 2:\nCurrent expression: (-8*y)*(41*y**3 - 15*y**2 - 40) + 16*(41*y**3 - 15*y**2 - 40)\nSimplifying the partial expression: 16*(41*y**3 - 15*y**2 - 40)\nExpanding the part (41*y**3 - 15*y**2 - 40) using the distributive property, and we got: -15*y**2*16 + (41*y**3)*16 - 40*16\nReplacing 16*(41*y**3 - 15*y**2 - 40) with -15*y**2*16 + (41*y**3)*16 - 40*16 in the overall expression.\n#Step 3:\nCurrent expression: (-8*y)*(41*y**3 - 15*y**2 - 40) - 15*y**2*16 + (41*y**3)*16 - 640\nSimplifying the partial expression: (-8*y)*(41*y**3 - 15*y**2 - 40)\nExpanding the part (41*y**3 - 15*y**2 - 40) using the distributive property, and we got: (-8*y)*(-15*y**2) + (-8*y)*(41*y**3) - (-1)*320*y\nReplacing (-8*y)*(41*y**3 - 15*y**2 - 40) with (-8*y)*(-15*y**2) + (-8*y)*(41*y**3) - (-1)*320*y in the overall expression.\n#Step 4:\nCurrent expression: (-8*y)*(-15*y**2) + (-8*y)*(41*y**3) - 40*(-8)*y - 15*y**2*16 + (41*y**3)*16 - 640\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-15*y**2)*16 = -240*y**2\n (-15*y**2)*(-8*y) = 120*y**3\n (41*y**3)*16 = 656*y**3\n (41*y**3)*(-8*y) = -328*y**4\n -40*-8*y = 320*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -328*y**4 + 120*y**3 + 656*y**3 - 240*y**2 + 320*y - 640\nCombining like terms, got -328*y**4 + 776*y**3 - 240*y**2 + 320*y - 640\n#Step 6:\nCurrent expression: -328*y**4 + 776*y**3 - 240*y**2 + 320*y - 640\nNo more calculations needed.\n-328*y**4 + 776*y**3 - 240*y**2 + 320*y - 640", "generated_answer": "-328*y**4 + 776*y**3 - 240*y**2 + 320*y - 640", "step_length": 6} {"cot_id": "8e89f4ed74b2c3acf47235154caabbda429c23be67b929d09d45c63bfafb48ae", "datapoint": {"question": "Simplify this expression: (43*x**2 + 29)*(22*x**3 + 25*x - 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "946*x**5 + 1713*x**3 - 688*x**2 + 725*x - 464", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 36, "polynomial_expr": "(43*x**2 + 29)*(22*x**3 + 25*x - 16)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (43*x**2 + 29)*(22*x**3 + 25*x - 16)\nExpanding the part (43*x**2 + 29) using the distributive property, and we got: (43*x**2)*(22*x**3 + 25*x - 16) + 29*(22*x**3 + 25*x - 16)\n#Step 2:\nCurrent expression: (43*x**2)*(22*x**3 + 25*x - 16) + 29*(22*x**3 + 25*x - 16)\nSimplifying the partial expression: 29*(22*x**3 + 25*x - 16)\nExpanding the part (22*x**3 + 25*x - 16) using the distributive property, and we got: (25*x)*29 + (22*x**3)*29 - 16*29\nReplacing 29*(22*x**3 + 25*x - 16) with (25*x)*29 + (22*x**3)*29 - 16*29 in the overall expression.\n#Step 3:\nCurrent expression: (25*x)*29 + (43*x**2)*(22*x**3 + 25*x - 16) + (22*x**3)*29 - 464\nSimplifying the partial expression: (43*x**2)*(22*x**3 + 25*x - 16)\nExpanding the part (22*x**3 + 25*x - 16) using the distributive property, and we got: -688*x**2 + (25*x)*(43*x**2) + (43*x**2)*(22*x**3)\nReplacing (43*x**2)*(22*x**3 + 25*x - 16) with -688*x**2 + (25*x)*(43*x**2) + (43*x**2)*(22*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -16*43*x**2 + (25*x)*(43*x**2) + (25*x)*29 + (43*x**2)*(22*x**3) + (22*x**3)*29 - 464\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (22*x**3)*29 = 638*x**3\n (22*x**3)*(43*x**2) = 946*x**5\n (25*x)*29 = 725*x\n (25*x)*(43*x**2) = 1075*x**3\n -16*43*x**2 = -688*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 946*x**5 + 638*x**3 + 1075*x**3 - 688*x**2 + 725*x - 464\nCombining like terms, got 946*x**5 + 1713*x**3 - 688*x**2 + 725*x - 464\n#Step 6:\nCurrent expression: 946*x**5 + 1713*x**3 - 688*x**2 + 725*x - 464\nNo more calculations needed.\n946*x**5 + 1713*x**3 - 688*x**2 + 725*x - 464", "generated_answer": "946*x**5 + 1713*x**3 - 688*x**2 + 725*x - 464", "step_length": 6} {"cot_id": "16df464616d4d948a8d003914d9b62ef51eee4747b49177aa9d53d8d05de6fba", "datapoint": {"question": "Calculate the following: (-56*x**3 - x**2)*(-47*x**3 - 23*x - 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2632*x**6 + 47*x**5 + 1288*x**4 + 2207*x**3 + 39*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 37, "polynomial_expr": "(-56*x**3 - x**2)*(-47*x**3 - 23*x - 39)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-56*x**3 - x**2)*(-47*x**3 - 23*x - 39)\nExpanding the part (-56*x**3 - x**2) using the distributive property, and we got: (-x**2)*(-47*x**3 - 23*x - 39) + (-56*x**3)*(-47*x**3 - 23*x - 39)\n#Step 2:\nCurrent expression: (-x**2)*(-47*x**3 - 23*x - 39) + (-56*x**3)*(-47*x**3 - 23*x - 39)\nSimplifying the partial expression: (-x**2)*(-47*x**3 - 23*x - 39)\nExpanding the part (-47*x**3 - 23*x - 39) using the distributive property, and we got: (-23*x)*(-x**2) - (-1)*39*x**2 + (-x**2)*(-47*x**3)\nReplacing (-x**2)*(-47*x**3 - 23*x - 39) with (-23*x)*(-x**2) - (-1)*39*x**2 + (-x**2)*(-47*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-23*x)*(-x**2) - 39*(-1)*x**2 + (-x**2)*(-47*x**3) + (-56*x**3)*(-47*x**3 - 23*x - 39)\nSimplifying the partial expression: (-56*x**3)*(-47*x**3 - 23*x - 39)\nExpanding the part (-47*x**3 - 23*x - 39) using the distributive property, and we got: (-23*x)*(-56*x**3) - (-1)*2184*x**3 + (-56*x**3)*(-47*x**3)\nReplacing (-56*x**3)*(-47*x**3 - 23*x - 39) with (-23*x)*(-56*x**3) - (-1)*2184*x**3 + (-56*x**3)*(-47*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-23*x)*(-x**2) + (-23*x)*(-56*x**3) - 39*(-56)*x**3 - 39*(-1)*x**2 + (-x**2)*(-47*x**3) + (-56*x**3)*(-47*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*x**3)*(-x**2) = 47*x**5\n (-47*x**3)*(-56*x**3) = 2632*x**6\n (-23*x)*(-x**2) = 23*x**3\n (-23*x)*(-56*x**3) = 1288*x**4\n -39*-1*x**2 = 39*x**2\n -39*-56*x**3 = 2184*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2632*x**6 + 47*x**5 + 1288*x**4 + 23*x**3 + 2184*x**3 + 39*x**2\nCombining like terms, got 2632*x**6 + 47*x**5 + 1288*x**4 + 2207*x**3 + 39*x**2\n#Step 6:\nCurrent expression: 2632*x**6 + 47*x**5 + 1288*x**4 + 2207*x**3 + 39*x**2\nNo more calculations needed.\n2632*x**6 + 47*x**5 + 1288*x**4 + 2207*x**3 + 39*x**2", "generated_answer": "2632*x**6 + 47*x**5 + 1288*x**4 + 2207*x**3 + 39*x**2", "step_length": 6} {"cot_id": "6efb692d811415c60d2388e7b397a85b0fb6ae1ee8c2b47eb177e75368cd757e", "datapoint": {"question": "Simplify this expression: (40 - 34*y**3)*(-40*y**3 - 45*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1360*y**6 + 1530*y**5 - 1600*y**3 - 1800*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 38, "polynomial_expr": "(40 - 34*y**3)*(-40*y**3 - 45*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (40 - 34*y**3)*(-40*y**3 - 45*y**2)\nExpanding the part (40 - 34*y**3) using the distributive property, and we got: (-34*y**3)*(-40*y**3 - 45*y**2) + 40*(-40*y**3 - 45*y**2)\n#Step 2:\nCurrent expression: (-34*y**3)*(-40*y**3 - 45*y**2) + 40*(-40*y**3 - 45*y**2)\nSimplifying the partial expression: 40*(-40*y**3 - 45*y**2)\nExpanding the part (-40*y**3 - 45*y**2) using the distributive property, and we got: -45*y**2*40 - 40*y**3*40\nReplacing 40*(-40*y**3 - 45*y**2) with -45*y**2*40 - 40*y**3*40 in the overall expression.\n#Step 3:\nCurrent expression: -45*y**2*40 - 40*y**3*40 + (-34*y**3)*(-40*y**3 - 45*y**2)\nSimplifying the partial expression: (-34*y**3)*(-40*y**3 - 45*y**2)\nExpanding the part (-40*y**3 - 45*y**2) using the distributive property, and we got: (-45*y**2)*(-34*y**3) + (-40*y**3)*(-34*y**3)\nReplacing (-34*y**3)*(-40*y**3 - 45*y**2) with (-45*y**2)*(-34*y**3) + (-40*y**3)*(-34*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-45*y**2)*(-34*y**3) - 45*y**2*40 + (-40*y**3)*(-34*y**3) - 40*y**3*40\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*y**2)*40 = -1800*y**2\n (-45*y**2)*(-34*y**3) = 1530*y**5\n (-40*y**3)*40 = -1600*y**3\n (-40*y**3)*(-34*y**3) = 1360*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1360*y**6 + 1530*y**5 - 1600*y**3 - 1800*y**2\nNo more calculations needed.\n1360*y**6 + 1530*y**5 - 1600*y**3 - 1800*y**2", "generated_answer": "1360*y**6 + 1530*y**5 - 1600*y**3 - 1800*y**2", "step_length": 5} {"cot_id": "bb063cb83ba751e16aeaf7f5415e9249c16601b19c6189c46227fbe53b932694", "datapoint": {"question": "Simplify this expression: (44 - 33*z)*(44*z**3 - 36*z**2 - 2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1452*z**4 + 3124*z**3 - 1584*z**2 + 66*z - 88", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 39, "polynomial_expr": "(44 - 33*z)*(44*z**3 - 36*z**2 - 2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (44 - 33*z)*(44*z**3 - 36*z**2 - 2)\nExpanding the part (44 - 33*z) using the distributive property, and we got: (-33*z)*(44*z**3 - 36*z**2 - 2) + 44*(44*z**3 - 36*z**2 - 2)\n#Step 2:\nCurrent expression: (-33*z)*(44*z**3 - 36*z**2 - 2) + 44*(44*z**3 - 36*z**2 - 2)\nSimplifying the partial expression: 44*(44*z**3 - 36*z**2 - 2)\nExpanding the part (44*z**3 - 36*z**2 - 2) using the distributive property, and we got: -36*z**2*44 + (44*z**3)*44 - 2*44\nReplacing 44*(44*z**3 - 36*z**2 - 2) with -36*z**2*44 + (44*z**3)*44 - 2*44 in the overall expression.\n#Step 3:\nCurrent expression: (-33*z)*(44*z**3 - 36*z**2 - 2) - 36*z**2*44 + (44*z**3)*44 - 88\nSimplifying the partial expression: (-33*z)*(44*z**3 - 36*z**2 - 2)\nExpanding the part (44*z**3 - 36*z**2 - 2) using the distributive property, and we got: (-33*z)*(-36*z**2) + (-33*z)*(44*z**3) - (-1)*66*z\nReplacing (-33*z)*(44*z**3 - 36*z**2 - 2) with (-33*z)*(-36*z**2) + (-33*z)*(44*z**3) - (-1)*66*z in the overall expression.\n#Step 4:\nCurrent expression: (-33*z)*(-36*z**2) + (-33*z)*(44*z**3) - 2*(-33)*z - 36*z**2*44 + (44*z**3)*44 - 88\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*z**2)*44 = -1584*z**2\n (-36*z**2)*(-33*z) = 1188*z**3\n (44*z**3)*44 = 1936*z**3\n (44*z**3)*(-33*z) = -1452*z**4\n -2*-33*z = 66*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1452*z**4 + 1188*z**3 + 1936*z**3 - 1584*z**2 + 66*z - 88\nCombining like terms, got -1452*z**4 + 3124*z**3 - 1584*z**2 + 66*z - 88\n#Step 6:\nCurrent expression: -1452*z**4 + 3124*z**3 - 1584*z**2 + 66*z - 88\nNo more calculations needed.\n-1452*z**4 + 3124*z**3 - 1584*z**2 + 66*z - 88", "generated_answer": "-1452*z**4 + 3124*z**3 - 1584*z**2 + 66*z - 88", "step_length": 6} {"cot_id": "798dac8dcbd3554db855100453cffb174148d76e7659f110b8fbf7ddc9535dfb", "datapoint": {"question": "Simplify this expression: (-8*x**3 + 21*x**2)*(-3*x**3 - 44*x**2 + 12)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "24*x**6 + 289*x**5 - 924*x**4 - 96*x**3 + 252*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 40, "polynomial_expr": "(-8*x**3 + 21*x**2)*(-3*x**3 - 44*x**2 + 12)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-8*x**3 + 21*x**2)*(-3*x**3 - 44*x**2 + 12)\nExpanding the part (-8*x**3 + 21*x**2) using the distributive property, and we got: (21*x**2)*(-3*x**3 - 44*x**2 + 12) + (-8*x**3)*(-3*x**3 - 44*x**2 + 12)\n#Step 2:\nCurrent expression: (21*x**2)*(-3*x**3 - 44*x**2 + 12) + (-8*x**3)*(-3*x**3 - 44*x**2 + 12)\nSimplifying the partial expression: (-8*x**3)*(-3*x**3 - 44*x**2 + 12)\nExpanding the part (-3*x**3 - 44*x**2 + 12) using the distributive property, and we got: 12*(-8*x**3) + (-44*x**2)*(-8*x**3) + (-8*x**3)*(-3*x**3)\nReplacing (-8*x**3)*(-3*x**3 - 44*x**2 + 12) with 12*(-8*x**3) + (-44*x**2)*(-8*x**3) + (-8*x**3)*(-3*x**3) in the overall expression.\n#Step 3:\nCurrent expression: 12*(-8)*x**3 + (-44*x**2)*(-8*x**3) + (21*x**2)*(-3*x**3 - 44*x**2 + 12) + (-8*x**3)*(-3*x**3)\nSimplifying the partial expression: (21*x**2)*(-3*x**3 - 44*x**2 + 12)\nExpanding the part (-3*x**3 - 44*x**2 + 12) using the distributive property, and we got: 12*(21*x**2) + (-44*x**2)*(21*x**2) + (21*x**2)*(-3*x**3)\nReplacing (21*x**2)*(-3*x**3 - 44*x**2 + 12) with 12*(21*x**2) + (-44*x**2)*(21*x**2) + (21*x**2)*(-3*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 12*(-8)*x**3 + 12*21*x**2 + (-44*x**2)*(21*x**2) + (-44*x**2)*(-8*x**3) + (21*x**2)*(-3*x**3) + (-8*x**3)*(-3*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-44*x**2)*(-8*x**3) = 352*x**5\n (-44*x**2)*(21*x**2) = -924*x**4\n (-3*x**3)*(-8*x**3) = 24*x**6\n (-3*x**3)*(21*x**2) = -63*x**5\n 12*-8*x**3 = -96*x**3\n 12*21*x**2 = 252*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 24*x**6 - 63*x**5 + 352*x**5 - 924*x**4 - 96*x**3 + 252*x**2\nCombining like terms, got 24*x**6 + 289*x**5 - 924*x**4 - 96*x**3 + 252*x**2\n#Step 6:\nCurrent expression: 24*x**6 + 289*x**5 - 924*x**4 - 96*x**3 + 252*x**2\nNo more calculations needed.\n24*x**6 + 289*x**5 - 924*x**4 - 96*x**3 + 252*x**2", "generated_answer": "24*x**6 + 289*x**5 - 924*x**4 - 96*x**3 + 252*x**2", "step_length": 6} {"cot_id": "df152de1236daa25d52949172e5daf24866eeadc42edf0d226efde099a34128e", "datapoint": {"question": "Simplify this expression: (-9*y**2 - 42)*(-6*y**3 + 13*y**2 + 23*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "54*y**5 - 117*y**4 + 45*y**3 - 546*y**2 - 966*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 41, "polynomial_expr": "(-9*y**2 - 42)*(-6*y**3 + 13*y**2 + 23*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-9*y**2 - 42)*(-6*y**3 + 13*y**2 + 23*y)\nExpanding the part (-9*y**2 - 42) using the distributive property, and we got: (-9*y**2)*(-6*y**3 + 13*y**2 + 23*y) - 42*(-6*y**3 + 13*y**2 + 23*y)\n#Step 2:\nCurrent expression: (-9*y**2)*(-6*y**3 + 13*y**2 + 23*y) - 42*(-6*y**3 + 13*y**2 + 23*y)\nSimplifying the partial expression: -42*(-6*y**3 + 13*y**2 + 23*y)\nExpanding the part (-6*y**3 + 13*y**2 + 23*y) using the distributive property, and we got: (23*y)*(-42) + (13*y**2)*(-42) - 6*y**3*(-42)\nReplacing -42*(-6*y**3 + 13*y**2 + 23*y) with (23*y)*(-42) + (13*y**2)*(-42) - 6*y**3*(-42) in the overall expression.\n#Step 3:\nCurrent expression: (23*y)*(-42) + (-9*y**2)*(-6*y**3 + 13*y**2 + 23*y) + (13*y**2)*(-42) - 6*y**3*(-42)\nSimplifying the partial expression: (-9*y**2)*(-6*y**3 + 13*y**2 + 23*y)\nExpanding the part (-6*y**3 + 13*y**2 + 23*y) using the distributive property, and we got: (23*y)*(-9*y**2) + (-9*y**2)*(13*y**2) + (-9*y**2)*(-6*y**3)\nReplacing (-9*y**2)*(-6*y**3 + 13*y**2 + 23*y) with (23*y)*(-9*y**2) + (-9*y**2)*(13*y**2) + (-9*y**2)*(-6*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (23*y)*(-9*y**2) + (23*y)*(-42) + (-9*y**2)*(13*y**2) + (-9*y**2)*(-6*y**3) + (13*y**2)*(-42) - 6*y**3*(-42)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-6*y**3)*-42 = 252*y**3\n (-6*y**3)*(-9*y**2) = 54*y**5\n (13*y**2)*-42 = -546*y**2\n (13*y**2)*(-9*y**2) = -117*y**4\n (23*y)*-42 = -966*y\n (23*y)*(-9*y**2) = -207*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 54*y**5 - 117*y**4 - 207*y**3 + 252*y**3 - 546*y**2 - 966*y\nCombining like terms, got 54*y**5 - 117*y**4 + 45*y**3 - 546*y**2 - 966*y\n#Step 6:\nCurrent expression: 54*y**5 - 117*y**4 + 45*y**3 - 546*y**2 - 966*y\nNo more calculations needed.\n54*y**5 - 117*y**4 + 45*y**3 - 546*y**2 - 966*y", "generated_answer": "54*y**5 - 117*y**4 + 45*y**3 - 546*y**2 - 966*y", "step_length": 6} {"cot_id": "86ff66646421c47f2f2e0808d1c88dfb8e2d5c2dc6f53b3bfe766d2641c660dc", "datapoint": {"question": "Simplify this expression: 93*z*(32*z**3 + 43*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2976*z**4 + 3999*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 42, "polynomial_expr": "93*z*(32*z**3 + 43*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 93*z*(32*z**3 + 43*z)\nExpanding the part (32*z**3 + 43*z) using the distributive property, and we got: (43*z)*(93*z) + (93*z)*(32*z**3)\n#Step 2:\nCurrent expression: (43*z)*(93*z) + (93*z)*(32*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (32*z**3)*(93*z) = 2976*z**4\n (43*z)*(93*z) = 3999*z**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 2976*z**4 + 3999*z**2\nNo more calculations needed.\n2976*z**4 + 3999*z**2", "generated_answer": "2976*z**4 + 3999*z**2", "step_length": 3} {"cot_id": "dcfefd9973999a36f8df30b364599b9ede2e594a7ccbe77fa5a06297f6e38311", "datapoint": {"question": "Calculate the following: (54*x**3 + 8*x)*(44*x**3 + 50*x**2 - 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2376*x**6 + 2700*x**5 + 352*x**4 - 302*x**3 - 104*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 43, "polynomial_expr": "(54*x**3 + 8*x)*(44*x**3 + 50*x**2 - 13)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (54*x**3 + 8*x)*(44*x**3 + 50*x**2 - 13)\nExpanding the part (54*x**3 + 8*x) using the distributive property, and we got: (8*x)*(44*x**3 + 50*x**2 - 13) + (54*x**3)*(44*x**3 + 50*x**2 - 13)\n#Step 2:\nCurrent expression: (8*x)*(44*x**3 + 50*x**2 - 13) + (54*x**3)*(44*x**3 + 50*x**2 - 13)\nSimplifying the partial expression: (8*x)*(44*x**3 + 50*x**2 - 13)\nExpanding the part (44*x**3 + 50*x**2 - 13) using the distributive property, and we got: -104*x + (8*x)*(50*x**2) + (8*x)*(44*x**3)\nReplacing (8*x)*(44*x**3 + 50*x**2 - 13) with -104*x + (8*x)*(50*x**2) + (8*x)*(44*x**3) in the overall expression.\n#Step 3:\nCurrent expression: -13*8*x + (8*x)*(50*x**2) + (8*x)*(44*x**3) + (54*x**3)*(44*x**3 + 50*x**2 - 13)\nSimplifying the partial expression: (54*x**3)*(44*x**3 + 50*x**2 - 13)\nExpanding the part (44*x**3 + 50*x**2 - 13) using the distributive property, and we got: -702*x**3 + (50*x**2)*(54*x**3) + (44*x**3)*(54*x**3)\nReplacing (54*x**3)*(44*x**3 + 50*x**2 - 13) with -702*x**3 + (50*x**2)*(54*x**3) + (44*x**3)*(54*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -13*54*x**3 - 13*8*x + (8*x)*(50*x**2) + (8*x)*(44*x**3) + (50*x**2)*(54*x**3) + (44*x**3)*(54*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (44*x**3)*(8*x) = 352*x**4\n (44*x**3)*(54*x**3) = 2376*x**6\n (50*x**2)*(8*x) = 400*x**3\n (50*x**2)*(54*x**3) = 2700*x**5\n -13*8*x = -104*x\n -13*54*x**3 = -702*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2376*x**6 + 2700*x**5 + 352*x**4 - 702*x**3 + 400*x**3 - 104*x\nCombining like terms, got 2376*x**6 + 2700*x**5 + 352*x**4 - 302*x**3 - 104*x\n#Step 6:\nCurrent expression: 2376*x**6 + 2700*x**5 + 352*x**4 - 302*x**3 - 104*x\nNo more calculations needed.\n2376*x**6 + 2700*x**5 + 352*x**4 - 302*x**3 - 104*x", "generated_answer": "2376*x**6 + 2700*x**5 + 352*x**4 - 302*x**3 - 104*x", "step_length": 6} {"cot_id": "b7a92c9848fa9e41f4656946a9b66c61bdee4d73c379e3724221a79ef938533c", "datapoint": {"question": "Simplify this expression: (30*x - 53)*(48*x**2 + 59*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1440*x**3 - 774*x**2 - 3127*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 44, "polynomial_expr": "(30*x - 53)*(48*x**2 + 59*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (30*x - 53)*(48*x**2 + 59*x)\nExpanding the part (30*x - 53) using the distributive property, and we got: (30*x)*(48*x**2 + 59*x) - 53*(48*x**2 + 59*x)\n#Step 2:\nCurrent expression: (30*x)*(48*x**2 + 59*x) - 53*(48*x**2 + 59*x)\nSimplifying the partial expression: -53*(48*x**2 + 59*x)\nExpanding the part (48*x**2 + 59*x) using the distributive property, and we got: (59*x)*(-53) + (48*x**2)*(-53)\nReplacing -53*(48*x**2 + 59*x) with (59*x)*(-53) + (48*x**2)*(-53) in the overall expression.\n#Step 3:\nCurrent expression: (30*x)*(48*x**2 + 59*x) + (59*x)*(-53) + (48*x**2)*(-53)\nSimplifying the partial expression: (30*x)*(48*x**2 + 59*x)\nExpanding the part (48*x**2 + 59*x) using the distributive property, and we got: (30*x)*(59*x) + (30*x)*(48*x**2)\nReplacing (30*x)*(48*x**2 + 59*x) with (30*x)*(59*x) + (30*x)*(48*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (30*x)*(59*x) + (30*x)*(48*x**2) + (59*x)*(-53) + (48*x**2)*(-53)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (48*x**2)*-53 = -2544*x**2\n (48*x**2)*(30*x) = 1440*x**3\n (59*x)*-53 = -3127*x\n (59*x)*(30*x) = 1770*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1440*x**3 - 2544*x**2 + 1770*x**2 - 3127*x\nCombining like terms, got 1440*x**3 - 774*x**2 - 3127*x\n#Step 6:\nCurrent expression: 1440*x**3 - 774*x**2 - 3127*x\nNo more calculations needed.\n1440*x**3 - 774*x**2 - 3127*x", "generated_answer": "1440*x**3 - 774*x**2 - 3127*x", "step_length": 6} {"cot_id": "777945e500aa360edb82130fd043cad41988eeb3c5486c5f6b617fa5d5c5f184", "datapoint": {"question": "Calculate the following: (-32*x**2 - 5*x)*(41*x**2 + 25*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1312*x**4 - 1005*x**3 - 125*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 45, "polynomial_expr": "(-32*x**2 - 5*x)*(41*x**2 + 25*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-32*x**2 - 5*x)*(41*x**2 + 25*x)\nExpanding the part (-32*x**2 - 5*x) using the distributive property, and we got: (-5*x)*(41*x**2 + 25*x) + (-32*x**2)*(41*x**2 + 25*x)\n#Step 2:\nCurrent expression: (-5*x)*(41*x**2 + 25*x) + (-32*x**2)*(41*x**2 + 25*x)\nSimplifying the partial expression: (-32*x**2)*(41*x**2 + 25*x)\nExpanding the part (41*x**2 + 25*x) using the distributive property, and we got: (25*x)*(-32*x**2) + (-32*x**2)*(41*x**2)\nReplacing (-32*x**2)*(41*x**2 + 25*x) with (25*x)*(-32*x**2) + (-32*x**2)*(41*x**2) in the overall expression.\n#Step 3:\nCurrent expression: (-5*x)*(41*x**2 + 25*x) + (25*x)*(-32*x**2) + (-32*x**2)*(41*x**2)\nSimplifying the partial expression: (-5*x)*(41*x**2 + 25*x)\nExpanding the part (41*x**2 + 25*x) using the distributive property, and we got: (-5*x)*(25*x) + (-5*x)*(41*x**2)\nReplacing (-5*x)*(41*x**2 + 25*x) with (-5*x)*(25*x) + (-5*x)*(41*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-5*x)*(25*x) + (-5*x)*(41*x**2) + (25*x)*(-32*x**2) + (-32*x**2)*(41*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (25*x)*(-32*x**2) = -800*x**3\n (25*x)*(-5*x) = -125*x**2\n (41*x**2)*(-32*x**2) = -1312*x**4\n (41*x**2)*(-5*x) = -205*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1312*x**4 - 800*x**3 - 205*x**3 - 125*x**2\nCombining like terms, got -1312*x**4 - 1005*x**3 - 125*x**2\n#Step 6:\nCurrent expression: -1312*x**4 - 1005*x**3 - 125*x**2\nNo more calculations needed.\n-1312*x**4 - 1005*x**3 - 125*x**2", "generated_answer": "-1312*x**4 - 1005*x**3 - 125*x**2", "step_length": 6} {"cot_id": "df69d43c7cfeae55fed5aeea7806ce4d455e52399d189a59364455b147ab931e", "datapoint": {"question": "Calculate the following: (45 - 29*y**2)*(57*y**3 - 44*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1653*y**5 + 1276*y**4 + 2565*y**3 - 1980*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 46, "polynomial_expr": "(45 - 29*y**2)*(57*y**3 - 44*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (45 - 29*y**2)*(57*y**3 - 44*y**2)\nExpanding the part (45 - 29*y**2) using the distributive property, and we got: (-29*y**2)*(57*y**3 - 44*y**2) + 45*(57*y**3 - 44*y**2)\n#Step 2:\nCurrent expression: (-29*y**2)*(57*y**3 - 44*y**2) + 45*(57*y**3 - 44*y**2)\nSimplifying the partial expression: 45*(57*y**3 - 44*y**2)\nExpanding the part (57*y**3 - 44*y**2) using the distributive property, and we got: -44*y**2*45 + (57*y**3)*45\nReplacing 45*(57*y**3 - 44*y**2) with -44*y**2*45 + (57*y**3)*45 in the overall expression.\n#Step 3:\nCurrent expression: -44*y**2*45 + (-29*y**2)*(57*y**3 - 44*y**2) + (57*y**3)*45\nSimplifying the partial expression: (-29*y**2)*(57*y**3 - 44*y**2)\nExpanding the part (57*y**3 - 44*y**2) using the distributive property, and we got: (-44*y**2)*(-29*y**2) + (-29*y**2)*(57*y**3)\nReplacing (-29*y**2)*(57*y**3 - 44*y**2) with (-44*y**2)*(-29*y**2) + (-29*y**2)*(57*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-44*y**2)*(-29*y**2) - 44*y**2*45 + (-29*y**2)*(57*y**3) + (57*y**3)*45\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-44*y**2)*45 = -1980*y**2\n (-44*y**2)*(-29*y**2) = 1276*y**4\n (57*y**3)*45 = 2565*y**3\n (57*y**3)*(-29*y**2) = -1653*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1653*y**5 + 1276*y**4 + 2565*y**3 - 1980*y**2\nNo more calculations needed.\n-1653*y**5 + 1276*y**4 + 2565*y**3 - 1980*y**2", "generated_answer": "-1653*y**5 + 1276*y**4 + 2565*y**3 - 1980*y**2", "step_length": 5} {"cot_id": "81f5d4cd340ab9eb7e1e01f6309fa01622c427a7da5c1253218fd70d085b9ce7", "datapoint": {"question": "Simplify this expression: (27*x**2 - 23*x)*(11*x**3 - 45*x**2 + 15)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "297*x**5 - 1468*x**4 + 1035*x**3 + 405*x**2 - 345*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 47, "polynomial_expr": "(27*x**2 - 23*x)*(11*x**3 - 45*x**2 + 15)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*x**2 - 23*x)*(11*x**3 - 45*x**2 + 15)\nExpanding the part (27*x**2 - 23*x) using the distributive property, and we got: (-23*x)*(11*x**3 - 45*x**2 + 15) + (27*x**2)*(11*x**3 - 45*x**2 + 15)\n#Step 2:\nCurrent expression: (-23*x)*(11*x**3 - 45*x**2 + 15) + (27*x**2)*(11*x**3 - 45*x**2 + 15)\nSimplifying the partial expression: (-23*x)*(11*x**3 - 45*x**2 + 15)\nExpanding the part (11*x**3 - 45*x**2 + 15) using the distributive property, and we got: (-23*x)*(-45*x**2) + (-23*x)*(11*x**3) + 15*(-23*x)\nReplacing (-23*x)*(11*x**3 - 45*x**2 + 15) with (-23*x)*(-45*x**2) + (-23*x)*(11*x**3) + 15*(-23*x) in the overall expression.\n#Step 3:\nCurrent expression: (-23*x)*(-45*x**2) + (-23*x)*(11*x**3) + 15*(-23)*x + (27*x**2)*(11*x**3 - 45*x**2 + 15)\nSimplifying the partial expression: (27*x**2)*(11*x**3 - 45*x**2 + 15)\nExpanding the part (11*x**3 - 45*x**2 + 15) using the distributive property, and we got: 15*(27*x**2) + (-45*x**2)*(27*x**2) + (27*x**2)*(11*x**3)\nReplacing (27*x**2)*(11*x**3 - 45*x**2 + 15) with 15*(27*x**2) + (-45*x**2)*(27*x**2) + (27*x**2)*(11*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-23*x)*(-45*x**2) + (-23*x)*(11*x**3) + 15*27*x**2 + 15*(-23)*x + (-45*x**2)*(27*x**2) + (27*x**2)*(11*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*x**2)*(-23*x) = 1035*x**3\n (-45*x**2)*(27*x**2) = -1215*x**4\n (11*x**3)*(-23*x) = -253*x**4\n (11*x**3)*(27*x**2) = 297*x**5\n 15*-23*x = -345*x\n 15*27*x**2 = 405*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 297*x**5 - 1215*x**4 - 253*x**4 + 1035*x**3 + 405*x**2 - 345*x\nCombining like terms, got 297*x**5 - 1468*x**4 + 1035*x**3 + 405*x**2 - 345*x\n#Step 6:\nCurrent expression: 297*x**5 - 1468*x**4 + 1035*x**3 + 405*x**2 - 345*x\nNo more calculations needed.\n297*x**5 - 1468*x**4 + 1035*x**3 + 405*x**2 - 345*x", "generated_answer": "297*x**5 - 1468*x**4 + 1035*x**3 + 405*x**2 - 345*x", "step_length": 6} {"cot_id": "f5cc25ae3c2c8e5e6e655175a744378966f45be9c9e1b6620ff364e9f027109e", "datapoint": {"question": "Simplify this expression: (2 - 44*x**3)*(23*x**3 + 23*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1012*x**6 - 1012*x**5 + 46*x**3 + 46*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 48, "polynomial_expr": "(2 - 44*x**3)*(23*x**3 + 23*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2 - 44*x**3)*(23*x**3 + 23*x**2)\nExpanding the part (2 - 44*x**3) using the distributive property, and we got: (-44*x**3)*(23*x**3 + 23*x**2) + 2*(23*x**3 + 23*x**2)\n#Step 2:\nCurrent expression: (-44*x**3)*(23*x**3 + 23*x**2) + 2*(23*x**3 + 23*x**2)\nSimplifying the partial expression: 2*(23*x**3 + 23*x**2)\nExpanding the part (23*x**3 + 23*x**2) using the distributive property, and we got: (23*x**2)*2 + (23*x**3)*2\nReplacing 2*(23*x**3 + 23*x**2) with (23*x**2)*2 + (23*x**3)*2 in the overall expression.\n#Step 3:\nCurrent expression: (23*x**2)*2 + (-44*x**3)*(23*x**3 + 23*x**2) + (23*x**3)*2\nSimplifying the partial expression: (-44*x**3)*(23*x**3 + 23*x**2)\nExpanding the part (23*x**3 + 23*x**2) using the distributive property, and we got: (23*x**2)*(-44*x**3) + (-44*x**3)*(23*x**3)\nReplacing (-44*x**3)*(23*x**3 + 23*x**2) with (23*x**2)*(-44*x**3) + (-44*x**3)*(23*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (23*x**2)*(-44*x**3) + (23*x**2)*2 + (-44*x**3)*(23*x**3) + (23*x**3)*2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (23*x**2)*2 = 46*x**2\n (23*x**2)*(-44*x**3) = -1012*x**5\n (23*x**3)*2 = 46*x**3\n (23*x**3)*(-44*x**3) = -1012*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1012*x**6 - 1012*x**5 + 46*x**3 + 46*x**2\nNo more calculations needed.\n-1012*x**6 - 1012*x**5 + 46*x**3 + 46*x**2", "generated_answer": "-1012*x**6 - 1012*x**5 + 46*x**3 + 46*x**2", "step_length": 5} {"cot_id": "ce94ec5a7675f99ffa859c1c0bd12b4249d48a69b66dd877f4cc2b9723a2a14a", "datapoint": {"question": "Calculate the following: (-54*x**3 - 61)*(6*x**3 + 25*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-324*x**6 - 1350*x**4 - 366*x**3 - 1525*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 49, "polynomial_expr": "(-54*x**3 - 61)*(6*x**3 + 25*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-54*x**3 - 61)*(6*x**3 + 25*x)\nExpanding the part (-54*x**3 - 61) using the distributive property, and we got: (-54*x**3)*(6*x**3 + 25*x) - 61*(6*x**3 + 25*x)\n#Step 2:\nCurrent expression: (-54*x**3)*(6*x**3 + 25*x) - 61*(6*x**3 + 25*x)\nSimplifying the partial expression: -61*(6*x**3 + 25*x)\nExpanding the part (6*x**3 + 25*x) using the distributive property, and we got: (25*x)*(-61) + (6*x**3)*(-61)\nReplacing -61*(6*x**3 + 25*x) with (25*x)*(-61) + (6*x**3)*(-61) in the overall expression.\n#Step 3:\nCurrent expression: (25*x)*(-61) + (-54*x**3)*(6*x**3 + 25*x) + (6*x**3)*(-61)\nSimplifying the partial expression: (-54*x**3)*(6*x**3 + 25*x)\nExpanding the part (6*x**3 + 25*x) using the distributive property, and we got: (25*x)*(-54*x**3) + (-54*x**3)*(6*x**3)\nReplacing (-54*x**3)*(6*x**3 + 25*x) with (25*x)*(-54*x**3) + (-54*x**3)*(6*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (25*x)*(-54*x**3) + (25*x)*(-61) + (-54*x**3)*(6*x**3) + (6*x**3)*(-61)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (6*x**3)*-61 = -366*x**3\n (6*x**3)*(-54*x**3) = -324*x**6\n (25*x)*-61 = -1525*x\n (25*x)*(-54*x**3) = -1350*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -324*x**6 - 1350*x**4 - 366*x**3 - 1525*x\nNo more calculations needed.\n-324*x**6 - 1350*x**4 - 366*x**3 - 1525*x", "generated_answer": "-324*x**6 - 1350*x**4 - 366*x**3 - 1525*x", "step_length": 5} {"cot_id": "460950dbddc4028442cd960674a270fd9293b5ab02259585700d9fa3fc050df4", "datapoint": {"question": "Simplify this expression: 3430*y**3 - 350*y + 2310\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "3430*y**3 - 350*y + 2310", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 50, "polynomial_expr": "3430*y**3 - 350*y + 2310", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 3430*y**3 - 350*y + 2310\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 3430*y**3 - 350*y + 2310\nNo more calculations needed.\n3430*y**3 - 350*y + 2310", "generated_answer": "3430*y**3 - 350*y + 2310", "step_length": 2} {"cot_id": "879c2bcf86cb1a26c5df9414c30b7f5a6dd36adb34b6f929a60d8f6a273e4701", "datapoint": {"question": "Calculate the following: (26*y**3 - 6*y)*(45*y**3 + 24*y**2 + 42)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1170*y**6 + 624*y**5 - 270*y**4 + 948*y**3 - 252*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 51, "polynomial_expr": "(26*y**3 - 6*y)*(45*y**3 + 24*y**2 + 42)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (26*y**3 - 6*y)*(45*y**3 + 24*y**2 + 42)\nExpanding the part (26*y**3 - 6*y) using the distributive property, and we got: (-6*y)*(45*y**3 + 24*y**2 + 42) + (26*y**3)*(45*y**3 + 24*y**2 + 42)\n#Step 2:\nCurrent expression: (-6*y)*(45*y**3 + 24*y**2 + 42) + (26*y**3)*(45*y**3 + 24*y**2 + 42)\nSimplifying the partial expression: (-6*y)*(45*y**3 + 24*y**2 + 42)\nExpanding the part (45*y**3 + 24*y**2 + 42) using the distributive property, and we got: (-6*y)*(24*y**2) + (-6*y)*(45*y**3) + 42*(-6*y)\nReplacing (-6*y)*(45*y**3 + 24*y**2 + 42) with (-6*y)*(24*y**2) + (-6*y)*(45*y**3) + 42*(-6*y) in the overall expression.\n#Step 3:\nCurrent expression: (-6*y)*(24*y**2) + (-6*y)*(45*y**3) + 42*(-6)*y + (26*y**3)*(45*y**3 + 24*y**2 + 42)\nSimplifying the partial expression: (26*y**3)*(45*y**3 + 24*y**2 + 42)\nExpanding the part (45*y**3 + 24*y**2 + 42) using the distributive property, and we got: 42*(26*y**3) + (24*y**2)*(26*y**3) + (26*y**3)*(45*y**3)\nReplacing (26*y**3)*(45*y**3 + 24*y**2 + 42) with 42*(26*y**3) + (24*y**2)*(26*y**3) + (26*y**3)*(45*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-6*y)*(24*y**2) + (-6*y)*(45*y**3) + 42*26*y**3 + 42*(-6)*y + (24*y**2)*(26*y**3) + (26*y**3)*(45*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (24*y**2)*(-6*y) = -144*y**3\n (24*y**2)*(26*y**3) = 624*y**5\n (45*y**3)*(-6*y) = -270*y**4\n (45*y**3)*(26*y**3) = 1170*y**6\n 42*-6*y = -252*y\n 42*26*y**3 = 1092*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1170*y**6 + 624*y**5 - 270*y**4 - 144*y**3 + 1092*y**3 - 252*y\nCombining like terms, got 1170*y**6 + 624*y**5 - 270*y**4 + 948*y**3 - 252*y\n#Step 6:\nCurrent expression: 1170*y**6 + 624*y**5 - 270*y**4 + 948*y**3 - 252*y\nNo more calculations needed.\n1170*y**6 + 624*y**5 - 270*y**4 + 948*y**3 - 252*y", "generated_answer": "1170*y**6 + 624*y**5 - 270*y**4 + 948*y**3 - 252*y", "step_length": 6} {"cot_id": "b0b98952520c09d616882e9a6263d3a6029930640c9d6e2832e5b4a8270766bd", "datapoint": {"question": "Calculate the following: (-2*z**2 - 18*z)*(-2*z**2 + 56*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "4*z**4 - 76*z**3 - 1008*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 52, "polynomial_expr": "(-2*z**2 - 18*z)*(-2*z**2 + 56*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-2*z**2 - 18*z)*(-2*z**2 + 56*z)\nExpanding the part (-2*z**2 - 18*z) using the distributive property, and we got: (-18*z)*(-2*z**2 + 56*z) + (-2*z**2)*(-2*z**2 + 56*z)\n#Step 2:\nCurrent expression: (-18*z)*(-2*z**2 + 56*z) + (-2*z**2)*(-2*z**2 + 56*z)\nSimplifying the partial expression: (-18*z)*(-2*z**2 + 56*z)\nExpanding the part (-2*z**2 + 56*z) using the distributive property, and we got: (-18*z)*(56*z) + (-18*z)*(-2*z**2)\nReplacing (-18*z)*(-2*z**2 + 56*z) with (-18*z)*(56*z) + (-18*z)*(-2*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-18*z)*(56*z) + (-18*z)*(-2*z**2) + (-2*z**2)*(-2*z**2 + 56*z)\nSimplifying the partial expression: (-2*z**2)*(-2*z**2 + 56*z)\nExpanding the part (-2*z**2 + 56*z) using the distributive property, and we got: (56*z)*(-2*z**2) + (-2*z**2)*(-2*z**2)\nReplacing (-2*z**2)*(-2*z**2 + 56*z) with (56*z)*(-2*z**2) + (-2*z**2)*(-2*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-18*z)*(56*z) + (-18*z)*(-2*z**2) + (56*z)*(-2*z**2) + (-2*z**2)*(-2*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-2*z**2)*(-18*z) = 36*z**3\n (-2*z**2)*(-2*z**2) = 4*z**4\n (56*z)*(-18*z) = -1008*z**2\n (56*z)*(-2*z**2) = -112*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 4*z**4 - 112*z**3 + 36*z**3 - 1008*z**2\nCombining like terms, got 4*z**4 - 76*z**3 - 1008*z**2\n#Step 6:\nCurrent expression: 4*z**4 - 76*z**3 - 1008*z**2\nNo more calculations needed.\n4*z**4 - 76*z**3 - 1008*z**2", "generated_answer": "4*z**4 - 76*z**3 - 1008*z**2", "step_length": 6} {"cot_id": "38c79ac9bfe24d1589c9d96707e53adf14877ebba208d2a7106cf88879ba7076", "datapoint": {"question": "Simplify this expression: (52*z**3 + 2)*(12*z**2 - 32*z + 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "624*z**5 - 1664*z**4 + 2028*z**3 + 24*z**2 - 64*z + 78", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 53, "polynomial_expr": "(52*z**3 + 2)*(12*z**2 - 32*z + 39)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (52*z**3 + 2)*(12*z**2 - 32*z + 39)\nExpanding the part (52*z**3 + 2) using the distributive property, and we got: (52*z**3)*(12*z**2 - 32*z + 39) + 2*(12*z**2 - 32*z + 39)\n#Step 2:\nCurrent expression: (52*z**3)*(12*z**2 - 32*z + 39) + 2*(12*z**2 - 32*z + 39)\nSimplifying the partial expression: 2*(12*z**2 - 32*z + 39)\nExpanding the part (12*z**2 - 32*z + 39) using the distributive property, and we got: -32*z*2 + (12*z**2)*2 + 39*2\nReplacing 2*(12*z**2 - 32*z + 39) with -32*z*2 + (12*z**2)*2 + 39*2 in the overall expression.\n#Step 3:\nCurrent expression: -32*z*2 + (12*z**2)*2 + (52*z**3)*(12*z**2 - 32*z + 39) + 78\nSimplifying the partial expression: (52*z**3)*(12*z**2 - 32*z + 39)\nExpanding the part (12*z**2 - 32*z + 39) using the distributive property, and we got: (-32*z)*(52*z**3) + 39*(52*z**3) + (12*z**2)*(52*z**3)\nReplacing (52*z**3)*(12*z**2 - 32*z + 39) with (-32*z)*(52*z**3) + 39*(52*z**3) + (12*z**2)*(52*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-32*z)*(52*z**3) - 32*z*2 + 39*52*z**3 + (12*z**2)*(52*z**3) + (12*z**2)*2 + 78\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*z)*2 = -64*z\n (-32*z)*(52*z**3) = -1664*z**4\n (12*z**2)*2 = 24*z**2\n (12*z**2)*(52*z**3) = 624*z**5\n 39*52*z**3 = 2028*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 624*z**5 - 1664*z**4 + 2028*z**3 + 24*z**2 - 64*z + 78\nNo more calculations needed.\n624*z**5 - 1664*z**4 + 2028*z**3 + 24*z**2 - 64*z + 78", "generated_answer": "624*z**5 - 1664*z**4 + 2028*z**3 + 24*z**2 - 64*z + 78", "step_length": 5} {"cot_id": "e23f281ab99b7813603cbb41d36ccfae2d82040ad165bdb2aa9413c10be9140c", "datapoint": {"question": "Calculate the following: (-30*y**2 - 23*y)*(y**3 - 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-30*y**5 - 23*y**4 + 840*y**2 + 644*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 54, "polynomial_expr": "(-30*y**2 - 23*y)*(y**3 - 28)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-30*y**2 - 23*y)*(y**3 - 28)\nExpanding the part (y**3 - 28) using the distributive property, and we got: y**3*(-30*y**2 - 23*y) - 28*(-30*y**2 - 23*y)\n#Step 2:\nCurrent expression: y**3*(-30*y**2 - 23*y) - 28*(-30*y**2 - 23*y)\nSimplifying the partial expression: -28*(-30*y**2 - 23*y)\nExpanding the part (-30*y**2 - 23*y) using the distributive property, and we got: -23*y*(-28) - 30*y**2*(-28)\nReplacing -28*(-30*y**2 - 23*y) with -23*y*(-28) - 30*y**2*(-28) in the overall expression.\n#Step 3:\nCurrent expression: -23*y*(-28) + y**3*(-30*y**2 - 23*y) - 30*y**2*(-28)\nSimplifying the partial expression: y**3*(-30*y**2 - 23*y)\nExpanding the part (-30*y**2 - 23*y) using the distributive property, and we got: (-23*y)*y**3 + (-30*y**2)*y**3\nReplacing y**3*(-30*y**2 - 23*y) with (-23*y)*y**3 + (-30*y**2)*y**3 in the overall expression.\n#Step 4:\nCurrent expression: (-23*y)*y**3 - 23*y*(-28) + (-30*y**2)*y**3 - 30*y**2*(-28)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*y**2)*-28 = 840*y**2\n (-30*y**2)*y**3 = -30*y**5\n (-23*y)*-28 = 644*y\n (-23*y)*y**3 = -23*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -30*y**5 - 23*y**4 + 840*y**2 + 644*y\nNo more calculations needed.\n-30*y**5 - 23*y**4 + 840*y**2 + 644*y", "generated_answer": "-30*y**5 - 23*y**4 + 840*y**2 + 644*y", "step_length": 5} {"cot_id": "540e465690f7bb61c6de631846abd0fc35415f040f6393b312bd2b89e2ea539d", "datapoint": {"question": "Simplify this expression: (-18*x**2 + 7*x)*(29*x**3 + 12*x**2 - 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-522*x**5 - 13*x**4 + 84*x**3 + 252*x**2 - 98*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 55, "polynomial_expr": "(-18*x**2 + 7*x)*(29*x**3 + 12*x**2 - 14)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-18*x**2 + 7*x)*(29*x**3 + 12*x**2 - 14)\nExpanding the part (-18*x**2 + 7*x) using the distributive property, and we got: (7*x)*(29*x**3 + 12*x**2 - 14) + (-18*x**2)*(29*x**3 + 12*x**2 - 14)\n#Step 2:\nCurrent expression: (7*x)*(29*x**3 + 12*x**2 - 14) + (-18*x**2)*(29*x**3 + 12*x**2 - 14)\nSimplifying the partial expression: (-18*x**2)*(29*x**3 + 12*x**2 - 14)\nExpanding the part (29*x**3 + 12*x**2 - 14) using the distributive property, and we got: -(-1)*252*x**2 + (-18*x**2)*(12*x**2) + (-18*x**2)*(29*x**3)\nReplacing (-18*x**2)*(29*x**3 + 12*x**2 - 14) with -(-1)*252*x**2 + (-18*x**2)*(12*x**2) + (-18*x**2)*(29*x**3) in the overall expression.\n#Step 3:\nCurrent expression: -14*(-18)*x**2 + (7*x)*(29*x**3 + 12*x**2 - 14) + (-18*x**2)*(12*x**2) + (-18*x**2)*(29*x**3)\nSimplifying the partial expression: (7*x)*(29*x**3 + 12*x**2 - 14)\nExpanding the part (29*x**3 + 12*x**2 - 14) using the distributive property, and we got: -98*x + (7*x)*(12*x**2) + (7*x)*(29*x**3)\nReplacing (7*x)*(29*x**3 + 12*x**2 - 14) with -98*x + (7*x)*(12*x**2) + (7*x)*(29*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -14*(-18)*x**2 - 14*7*x + (7*x)*(12*x**2) + (7*x)*(29*x**3) + (-18*x**2)*(12*x**2) + (-18*x**2)*(29*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (12*x**2)*(-18*x**2) = -216*x**4\n (12*x**2)*(7*x) = 84*x**3\n (29*x**3)*(-18*x**2) = -522*x**5\n (29*x**3)*(7*x) = 203*x**4\n -14*-18*x**2 = 252*x**2\n -14*7*x = -98*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -522*x**5 - 216*x**4 + 203*x**4 + 84*x**3 + 252*x**2 - 98*x\nCombining like terms, got -522*x**5 - 13*x**4 + 84*x**3 + 252*x**2 - 98*x\n#Step 6:\nCurrent expression: -522*x**5 - 13*x**4 + 84*x**3 + 252*x**2 - 98*x\nNo more calculations needed.\n-522*x**5 - 13*x**4 + 84*x**3 + 252*x**2 - 98*x", "generated_answer": "-522*x**5 - 13*x**4 + 84*x**3 + 252*x**2 - 98*x", "step_length": 6} {"cot_id": "5c3d9176595fb6f7199fdeb6b24a3e295c98cc04bf5caac7bd44400131d63808", "datapoint": {"question": "Simplify this expression: (46*y**3 - 13*y**2)*(50*y**3 - 42*y**2 - 99*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2300*y**6 - 2582*y**5 - 4008*y**4 + 1287*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 56, "polynomial_expr": "(46*y**3 - 13*y**2)*(50*y**3 - 42*y**2 - 99*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (46*y**3 - 13*y**2)*(50*y**3 - 42*y**2 - 99*y)\nExpanding the part (46*y**3 - 13*y**2) using the distributive property, and we got: (-13*y**2)*(50*y**3 - 42*y**2 - 99*y) + (46*y**3)*(50*y**3 - 42*y**2 - 99*y)\n#Step 2:\nCurrent expression: (-13*y**2)*(50*y**3 - 42*y**2 - 99*y) + (46*y**3)*(50*y**3 - 42*y**2 - 99*y)\nSimplifying the partial expression: (-13*y**2)*(50*y**3 - 42*y**2 - 99*y)\nExpanding the part (50*y**3 - 42*y**2 - 99*y) using the distributive property, and we got: (-99*y)*(-13*y**2) + (-42*y**2)*(-13*y**2) + (-13*y**2)*(50*y**3)\nReplacing (-13*y**2)*(50*y**3 - 42*y**2 - 99*y) with (-99*y)*(-13*y**2) + (-42*y**2)*(-13*y**2) + (-13*y**2)*(50*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-99*y)*(-13*y**2) + (-42*y**2)*(-13*y**2) + (-13*y**2)*(50*y**3) + (46*y**3)*(50*y**3 - 42*y**2 - 99*y)\nSimplifying the partial expression: (46*y**3)*(50*y**3 - 42*y**2 - 99*y)\nExpanding the part (50*y**3 - 42*y**2 - 99*y) using the distributive property, and we got: (-99*y)*(46*y**3) + (-42*y**2)*(46*y**3) + (46*y**3)*(50*y**3)\nReplacing (46*y**3)*(50*y**3 - 42*y**2 - 99*y) with (-99*y)*(46*y**3) + (-42*y**2)*(46*y**3) + (46*y**3)*(50*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-99*y)*(-13*y**2) + (-99*y)*(46*y**3) + (-42*y**2)*(-13*y**2) + (-42*y**2)*(46*y**3) + (-13*y**2)*(50*y**3) + (46*y**3)*(50*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-99*y)*(-13*y**2) = 1287*y**3\n (-99*y)*(46*y**3) = -4554*y**4\n (-42*y**2)*(-13*y**2) = 546*y**4\n (-42*y**2)*(46*y**3) = -1932*y**5\n (50*y**3)*(-13*y**2) = -650*y**5\n (50*y**3)*(46*y**3) = 2300*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2300*y**6 - 1932*y**5 - 650*y**5 - 4554*y**4 + 546*y**4 + 1287*y**3\nCombining like terms, got 2300*y**6 - 2582*y**5 - 4008*y**4 + 1287*y**3\n#Step 6:\nCurrent expression: 2300*y**6 - 2582*y**5 - 4008*y**4 + 1287*y**3\nNo more calculations needed.\n2300*y**6 - 2582*y**5 - 4008*y**4 + 1287*y**3", "generated_answer": "2300*y**6 - 2582*y**5 - 4008*y**4 + 1287*y**3", "step_length": 6} {"cot_id": "0ce362a8986c47ccacd331ed9c91b2d67f8fa513b77f7afcdc5575aad5a94a05", "datapoint": {"question": "Calculate the following: (-9*y**3 - 39)*(34*y**3 + 8)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-306*y**6 - 1398*y**3 - 312", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 57, "polynomial_expr": "(-9*y**3 - 39)*(34*y**3 + 8)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-9*y**3 - 39)*(34*y**3 + 8)\nExpanding the part (-9*y**3 - 39) using the distributive property, and we got: (-9*y**3)*(34*y**3 + 8) - 39*(34*y**3 + 8)\n#Step 2:\nCurrent expression: (-9*y**3)*(34*y**3 + 8) - 39*(34*y**3 + 8)\nSimplifying the partial expression: -39*(34*y**3 + 8)\nExpanding the part (34*y**3 + 8) using the distributive property, and we got: (34*y**3)*(-39) + 8*(-39)\nReplacing -39*(34*y**3 + 8) with (34*y**3)*(-39) + 8*(-39) in the overall expression.\n#Step 3:\nCurrent expression: (-9*y**3)*(34*y**3 + 8) + (34*y**3)*(-39) - 312\nSimplifying the partial expression: (-9*y**3)*(34*y**3 + 8)\nExpanding the part (34*y**3 + 8) using the distributive property, and we got: 8*(-9*y**3) + (-9*y**3)*(34*y**3)\nReplacing (-9*y**3)*(34*y**3 + 8) with 8*(-9*y**3) + (-9*y**3)*(34*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 8*(-9)*y**3 + (-9*y**3)*(34*y**3) + (34*y**3)*(-39) - 312\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (34*y**3)*-39 = -1326*y**3\n (34*y**3)*(-9*y**3) = -306*y**6\n 8*-9*y**3 = -72*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -306*y**6 - 1326*y**3 - 72*y**3 - 312\nCombining like terms, got -306*y**6 - 1398*y**3 - 312\n#Step 6:\nCurrent expression: -306*y**6 - 1398*y**3 - 312\nNo more calculations needed.\n-306*y**6 - 1398*y**3 - 312", "generated_answer": "-306*y**6 - 1398*y**3 - 312", "step_length": 6} {"cot_id": "a29aa18b31f573f2370f8822133f20df99451e331d5edaea9cc05941451cf10d", "datapoint": {"question": "Simplify this expression: (17*x - 22)*(-47*x**2 - 8*x + 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-799*x**3 + 898*x**2 + 1026*x - 1100", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 58, "polynomial_expr": "(17*x - 22)*(-47*x**2 - 8*x + 50)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (17*x - 22)*(-47*x**2 - 8*x + 50)\nExpanding the part (17*x - 22) using the distributive property, and we got: (17*x)*(-47*x**2 - 8*x + 50) - 22*(-47*x**2 - 8*x + 50)\n#Step 2:\nCurrent expression: (17*x)*(-47*x**2 - 8*x + 50) - 22*(-47*x**2 - 8*x + 50)\nSimplifying the partial expression: -22*(-47*x**2 - 8*x + 50)\nExpanding the part (-47*x**2 - 8*x + 50) using the distributive property, and we got: -8*x*(-22) - 47*x**2*(-22) + 50*(-22)\nReplacing -22*(-47*x**2 - 8*x + 50) with -8*x*(-22) - 47*x**2*(-22) + 50*(-22) in the overall expression.\n#Step 3:\nCurrent expression: -8*x*(-22) + (17*x)*(-47*x**2 - 8*x + 50) - 47*x**2*(-22) - 1100\nSimplifying the partial expression: (17*x)*(-47*x**2 - 8*x + 50)\nExpanding the part (-47*x**2 - 8*x + 50) using the distributive property, and we got: (-8*x)*(17*x) + 50*(17*x) + (17*x)*(-47*x**2)\nReplacing (17*x)*(-47*x**2 - 8*x + 50) with (-8*x)*(17*x) + 50*(17*x) + (17*x)*(-47*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-8*x)*(17*x) - 8*x*(-22) + 50*17*x + (17*x)*(-47*x**2) - 47*x**2*(-22) - 1100\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*x**2)*-22 = 1034*x**2\n (-47*x**2)*(17*x) = -799*x**3\n (-8*x)*-22 = 176*x\n (-8*x)*(17*x) = -136*x**2\n 50*17*x = 850*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -799*x**3 - 136*x**2 + 1034*x**2 + 176*x + 850*x - 1100\nCombining like terms, got -799*x**3 + 898*x**2 + 1026*x - 1100\n#Step 6:\nCurrent expression: -799*x**3 + 898*x**2 + 1026*x - 1100\nNo more calculations needed.\n-799*x**3 + 898*x**2 + 1026*x - 1100", "generated_answer": "-799*x**3 + 898*x**2 + 1026*x - 1100", "step_length": 6} {"cot_id": "30bf364e11f2cf522281cd4868c75d4a1d615b6b433dac2c78ed9ee8f5a5a846", "datapoint": {"question": "Calculate the following: (-29*z - 17)*(-4*z**2 + 14*z + 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "116*z**3 - 338*z**2 - 1195*z - 561", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 59, "polynomial_expr": "(-29*z - 17)*(-4*z**2 + 14*z + 33)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-29*z - 17)*(-4*z**2 + 14*z + 33)\nExpanding the part (-29*z - 17) using the distributive property, and we got: (-29*z)*(-4*z**2 + 14*z + 33) - 17*(-4*z**2 + 14*z + 33)\n#Step 2:\nCurrent expression: (-29*z)*(-4*z**2 + 14*z + 33) - 17*(-4*z**2 + 14*z + 33)\nSimplifying the partial expression: -17*(-4*z**2 + 14*z + 33)\nExpanding the part (-4*z**2 + 14*z + 33) using the distributive property, and we got: (14*z)*(-17) - 4*z**2*(-17) + 33*(-17)\nReplacing -17*(-4*z**2 + 14*z + 33) with (14*z)*(-17) - 4*z**2*(-17) + 33*(-17) in the overall expression.\n#Step 3:\nCurrent expression: (-29*z)*(-4*z**2 + 14*z + 33) + (14*z)*(-17) - 4*z**2*(-17) - 561\nSimplifying the partial expression: (-29*z)*(-4*z**2 + 14*z + 33)\nExpanding the part (-4*z**2 + 14*z + 33) using the distributive property, and we got: (-29*z)*(14*z) + (-29*z)*(-4*z**2) + 33*(-29*z)\nReplacing (-29*z)*(-4*z**2 + 14*z + 33) with (-29*z)*(14*z) + (-29*z)*(-4*z**2) + 33*(-29*z) in the overall expression.\n#Step 4:\nCurrent expression: (-29*z)*(14*z) + (-29*z)*(-4*z**2) + 33*(-29)*z + (14*z)*(-17) - 4*z**2*(-17) - 561\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-4*z**2)*-17 = 68*z**2\n (-4*z**2)*(-29*z) = 116*z**3\n (14*z)*-17 = -238*z\n (14*z)*(-29*z) = -406*z**2\n 33*-29*z = -957*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 116*z**3 - 406*z**2 + 68*z**2 - 957*z - 238*z - 561\nCombining like terms, got 116*z**3 - 338*z**2 - 1195*z - 561\n#Step 6:\nCurrent expression: 116*z**3 - 338*z**2 - 1195*z - 561\nNo more calculations needed.\n116*z**3 - 338*z**2 - 1195*z - 561", "generated_answer": "116*z**3 - 338*z**2 - 1195*z - 561", "step_length": 6} {"cot_id": "0edf59d4149bc049c386957cd8e07e87055ae9334d5c902b88db274768098e45", "datapoint": {"question": "Simplify this expression: (47 - 25*x**3)*(40*x**3 - 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1000*x**6 + 2780*x**3 - 1692", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 60, "polynomial_expr": "(47 - 25*x**3)*(40*x**3 - 36)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (47 - 25*x**3)*(40*x**3 - 36)\nExpanding the part (40*x**3 - 36) using the distributive property, and we got: (40*x**3)*(47 - 25*x**3) - 36*(47 - 25*x**3)\n#Step 2:\nCurrent expression: (40*x**3)*(47 - 25*x**3) - 36*(47 - 25*x**3)\nSimplifying the partial expression: -36*(47 - 25*x**3)\nExpanding the part (47 - 25*x**3) using the distributive property, and we got: -25*x**3*(-36) + 47*(-36)\nReplacing -36*(47 - 25*x**3) with -25*x**3*(-36) + 47*(-36) in the overall expression.\n#Step 3:\nCurrent expression: -25*x**3*(-36) + (40*x**3)*(47 - 25*x**3) - 1692\nSimplifying the partial expression: (40*x**3)*(47 - 25*x**3)\nExpanding the part (47 - 25*x**3) using the distributive property, and we got: 47*(40*x**3) + (-25*x**3)*(40*x**3)\nReplacing (40*x**3)*(47 - 25*x**3) with 47*(40*x**3) + (-25*x**3)*(40*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 47*40*x**3 + (-25*x**3)*(40*x**3) - 25*x**3*(-36) - 1692\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*x**3)*-36 = 900*x**3\n (-25*x**3)*(40*x**3) = -1000*x**6\n 47*40*x**3 = 1880*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1000*x**6 + 900*x**3 + 1880*x**3 - 1692\nCombining like terms, got -1000*x**6 + 2780*x**3 - 1692\n#Step 6:\nCurrent expression: -1000*x**6 + 2780*x**3 - 1692\nNo more calculations needed.\n-1000*x**6 + 2780*x**3 - 1692", "generated_answer": "-1000*x**6 + 2780*x**3 - 1692", "step_length": 6} {"cot_id": "6f04d7494c8b9dba071cb0651a4f790e20c23d33c60d412583f0762ab49607fe", "datapoint": {"question": "Calculate the following: (7 - 38*z**3)*(39*z**3 - 8*z**2 + 30*z + 45)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1482*z**6 + 304*z**5 - 1140*z**4 - 1437*z**3 - 56*z**2 + 210*z + 315", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 61, "polynomial_expr": "(7 - 38*z**3)*(39*z**3 - 8*z**2 + 30*z + 45)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7 - 38*z**3)*(39*z**3 - 8*z**2 + 30*z + 45)\nExpanding the part (7 - 38*z**3) using the distributive property, and we got: (-38*z**3)*(39*z**3 - 8*z**2 + 30*z + 45) + 7*(39*z**3 - 8*z**2 + 30*z + 45)\n#Step 2:\nCurrent expression: (-38*z**3)*(39*z**3 - 8*z**2 + 30*z + 45) + 7*(39*z**3 - 8*z**2 + 30*z + 45)\nSimplifying the partial expression: 7*(39*z**3 - 8*z**2 + 30*z + 45)\nExpanding the part (39*z**3 - 8*z**2 + 30*z + 45) using the distributive property, and we got: (30*z)*7 - 8*z**2*7 + (39*z**3)*7 + 45*7\nReplacing 7*(39*z**3 - 8*z**2 + 30*z + 45) with (30*z)*7 - 8*z**2*7 + (39*z**3)*7 + 45*7 in the overall expression.\n#Step 3:\nCurrent expression: (30*z)*7 - 8*z**2*7 + (-38*z**3)*(39*z**3 - 8*z**2 + 30*z + 45) + (39*z**3)*7 + 315\nSimplifying the partial expression: (-38*z**3)*(39*z**3 - 8*z**2 + 30*z + 45)\nExpanding the part (39*z**3 - 8*z**2 + 30*z + 45) using the distributive property, and we got: 45*(-38*z**3) + (30*z)*(-38*z**3) + (-8*z**2)*(-38*z**3) + (-38*z**3)*(39*z**3)\nReplacing (-38*z**3)*(39*z**3 - 8*z**2 + 30*z + 45) with 45*(-38*z**3) + (30*z)*(-38*z**3) + (-8*z**2)*(-38*z**3) + (-38*z**3)*(39*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 45*(-38)*z**3 + (30*z)*(-38*z**3) + (30*z)*7 + (-8*z**2)*(-38*z**3) - 8*z**2*7 + (-38*z**3)*(39*z**3) + (39*z**3)*7 + 315\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-8*z**2)*7 = -56*z**2\n (-8*z**2)*(-38*z**3) = 304*z**5\n (30*z)*7 = 210*z\n (30*z)*(-38*z**3) = -1140*z**4\n (39*z**3)*7 = 273*z**3\n (39*z**3)*(-38*z**3) = -1482*z**6\n 45*-38*z**3 = -1710*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1482*z**6 + 304*z**5 - 1140*z**4 - 1710*z**3 + 273*z**3 - 56*z**2 + 210*z + 315\nCombining like terms, got -1482*z**6 + 304*z**5 - 1140*z**4 - 1437*z**3 - 56*z**2 + 210*z + 315\n#Step 6:\nCurrent expression: -1482*z**6 + 304*z**5 - 1140*z**4 - 1437*z**3 - 56*z**2 + 210*z + 315\nNo more calculations needed.\n-1482*z**6 + 304*z**5 - 1140*z**4 - 1437*z**3 - 56*z**2 + 210*z + 315", "generated_answer": "-1482*z**6 + 304*z**5 - 1140*z**4 - 1437*z**3 - 56*z**2 + 210*z + 315", "step_length": 6} {"cot_id": "ed0196e7514d2083c5f6ca0f507ce1aee0b100c62aa428357790e4171041caca", "datapoint": {"question": "Calculate the following: (-10*x - 51)*(-38*x**2 + 24*x + 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "380*x**3 + 1698*x**2 - 1434*x - 1071", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 62, "polynomial_expr": "(-10*x - 51)*(-38*x**2 + 24*x + 21)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-10*x - 51)*(-38*x**2 + 24*x + 21)\nExpanding the part (-10*x - 51) using the distributive property, and we got: (-10*x)*(-38*x**2 + 24*x + 21) - 51*(-38*x**2 + 24*x + 21)\n#Step 2:\nCurrent expression: (-10*x)*(-38*x**2 + 24*x + 21) - 51*(-38*x**2 + 24*x + 21)\nSimplifying the partial expression: -51*(-38*x**2 + 24*x + 21)\nExpanding the part (-38*x**2 + 24*x + 21) using the distributive property, and we got: (24*x)*(-51) - 38*x**2*(-51) + 21*(-51)\nReplacing -51*(-38*x**2 + 24*x + 21) with (24*x)*(-51) - 38*x**2*(-51) + 21*(-51) in the overall expression.\n#Step 3:\nCurrent expression: (-10*x)*(-38*x**2 + 24*x + 21) + (24*x)*(-51) - 38*x**2*(-51) - 1071\nSimplifying the partial expression: (-10*x)*(-38*x**2 + 24*x + 21)\nExpanding the part (-38*x**2 + 24*x + 21) using the distributive property, and we got: (-10*x)*(24*x) + (-10*x)*(-38*x**2) + 21*(-10*x)\nReplacing (-10*x)*(-38*x**2 + 24*x + 21) with (-10*x)*(24*x) + (-10*x)*(-38*x**2) + 21*(-10*x) in the overall expression.\n#Step 4:\nCurrent expression: (-10*x)*(24*x) + (-10*x)*(-38*x**2) + 21*(-10)*x + (24*x)*(-51) - 38*x**2*(-51) - 1071\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*x**2)*-51 = 1938*x**2\n (-38*x**2)*(-10*x) = 380*x**3\n (24*x)*-51 = -1224*x\n (24*x)*(-10*x) = -240*x**2\n 21*-10*x = -210*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 380*x**3 - 240*x**2 + 1938*x**2 - 1224*x - 210*x - 1071\nCombining like terms, got 380*x**3 + 1698*x**2 - 1434*x - 1071\n#Step 6:\nCurrent expression: 380*x**3 + 1698*x**2 - 1434*x - 1071\nNo more calculations needed.\n380*x**3 + 1698*x**2 - 1434*x - 1071", "generated_answer": "380*x**3 + 1698*x**2 - 1434*x - 1071", "step_length": 6} {"cot_id": "b4475701b58a5e5a71399babe18c7a092710d4816656d367c7905414ab771628", "datapoint": {"question": "Simplify this expression: (41*z**2 + 44)*(3*z**3 - 50*z + 23)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "123*z**5 - 1918*z**3 + 943*z**2 - 2200*z + 1012", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 63, "polynomial_expr": "(41*z**2 + 44)*(3*z**3 - 50*z + 23)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (41*z**2 + 44)*(3*z**3 - 50*z + 23)\nExpanding the part (41*z**2 + 44) using the distributive property, and we got: (41*z**2)*(3*z**3 - 50*z + 23) + 44*(3*z**3 - 50*z + 23)\n#Step 2:\nCurrent expression: (41*z**2)*(3*z**3 - 50*z + 23) + 44*(3*z**3 - 50*z + 23)\nSimplifying the partial expression: 44*(3*z**3 - 50*z + 23)\nExpanding the part (3*z**3 - 50*z + 23) using the distributive property, and we got: -50*z*44 + (3*z**3)*44 + 23*44\nReplacing 44*(3*z**3 - 50*z + 23) with -50*z*44 + (3*z**3)*44 + 23*44 in the overall expression.\n#Step 3:\nCurrent expression: -50*z*44 + (41*z**2)*(3*z**3 - 50*z + 23) + (3*z**3)*44 + 1012\nSimplifying the partial expression: (41*z**2)*(3*z**3 - 50*z + 23)\nExpanding the part (3*z**3 - 50*z + 23) using the distributive property, and we got: (-50*z)*(41*z**2) + 23*(41*z**2) + (41*z**2)*(3*z**3)\nReplacing (41*z**2)*(3*z**3 - 50*z + 23) with (-50*z)*(41*z**2) + 23*(41*z**2) + (41*z**2)*(3*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-50*z)*(41*z**2) - 50*z*44 + 23*41*z**2 + (41*z**2)*(3*z**3) + (3*z**3)*44 + 1012\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-50*z)*44 = -2200*z\n (-50*z)*(41*z**2) = -2050*z**3\n (3*z**3)*44 = 132*z**3\n (3*z**3)*(41*z**2) = 123*z**5\n 23*41*z**2 = 943*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 123*z**5 - 2050*z**3 + 132*z**3 + 943*z**2 - 2200*z + 1012\nCombining like terms, got 123*z**5 - 1918*z**3 + 943*z**2 - 2200*z + 1012\n#Step 6:\nCurrent expression: 123*z**5 - 1918*z**3 + 943*z**2 - 2200*z + 1012\nNo more calculations needed.\n123*z**5 - 1918*z**3 + 943*z**2 - 2200*z + 1012", "generated_answer": "123*z**5 - 1918*z**3 + 943*z**2 - 2200*z + 1012", "step_length": 6} {"cot_id": "998e0217468377918345cf6dedc6cd56e80a1e17de9e8a9f0d0d1da7c1a39d32", "datapoint": {"question": "Calculate the following: (-72*z**2 + 42*z)*(-17*z**3 - 36*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1224*z**5 + 1878*z**4 - 1512*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 64, "polynomial_expr": "(-72*z**2 + 42*z)*(-17*z**3 - 36*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-72*z**2 + 42*z)*(-17*z**3 - 36*z**2)\nExpanding the part (-72*z**2 + 42*z) using the distributive property, and we got: (42*z)*(-17*z**3 - 36*z**2) + (-72*z**2)*(-17*z**3 - 36*z**2)\n#Step 2:\nCurrent expression: (42*z)*(-17*z**3 - 36*z**2) + (-72*z**2)*(-17*z**3 - 36*z**2)\nSimplifying the partial expression: (-72*z**2)*(-17*z**3 - 36*z**2)\nExpanding the part (-17*z**3 - 36*z**2) using the distributive property, and we got: (-72*z**2)*(-36*z**2) + (-72*z**2)*(-17*z**3)\nReplacing (-72*z**2)*(-17*z**3 - 36*z**2) with (-72*z**2)*(-36*z**2) + (-72*z**2)*(-17*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (42*z)*(-17*z**3 - 36*z**2) + (-72*z**2)*(-36*z**2) + (-72*z**2)*(-17*z**3)\nSimplifying the partial expression: (42*z)*(-17*z**3 - 36*z**2)\nExpanding the part (-17*z**3 - 36*z**2) using the distributive property, and we got: (42*z)*(-36*z**2) + (42*z)*(-17*z**3)\nReplacing (42*z)*(-17*z**3 - 36*z**2) with (42*z)*(-36*z**2) + (42*z)*(-17*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (42*z)*(-36*z**2) + (42*z)*(-17*z**3) + (-72*z**2)*(-36*z**2) + (-72*z**2)*(-17*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*z**2)*(-72*z**2) = 2592*z**4\n (-36*z**2)*(42*z) = -1512*z**3\n (-17*z**3)*(-72*z**2) = 1224*z**5\n (-17*z**3)*(42*z) = -714*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1224*z**5 - 714*z**4 + 2592*z**4 - 1512*z**3\nCombining like terms, got 1224*z**5 + 1878*z**4 - 1512*z**3\n#Step 6:\nCurrent expression: 1224*z**5 + 1878*z**4 - 1512*z**3\nNo more calculations needed.\n1224*z**5 + 1878*z**4 - 1512*z**3", "generated_answer": "1224*z**5 + 1878*z**4 - 1512*z**3", "step_length": 6} {"cot_id": "f1863c32e9a729aefb98a8ee28b9924639744a1ba31696563fd66161bb23db9f", "datapoint": {"question": "Simplify this expression: -1519*x**2 - 341*x\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1519*x**2 - 341*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 65, "polynomial_expr": "-1519*x**2 - 341*x", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -1519*x**2 - 341*x\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -1519*x**2 - 341*x\nNo more calculations needed.\n-1519*x**2 - 341*x", "generated_answer": "-1519*x**2 - 341*x", "step_length": 2} {"cot_id": "3a86873b48fa4f662be62e9b088adc4caf3ca89dbeb5ecd66e1b3a67ef5acabf", "datapoint": {"question": "Calculate the following: (-44*x**2 + 13*x)*(7*x**2 + 45*x + 25)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-308*x**4 - 1889*x**3 - 515*x**2 + 325*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 66, "polynomial_expr": "(-44*x**2 + 13*x)*(7*x**2 + 45*x + 25)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-44*x**2 + 13*x)*(7*x**2 + 45*x + 25)\nExpanding the part (-44*x**2 + 13*x) using the distributive property, and we got: (13*x)*(7*x**2 + 45*x + 25) + (-44*x**2)*(7*x**2 + 45*x + 25)\n#Step 2:\nCurrent expression: (13*x)*(7*x**2 + 45*x + 25) + (-44*x**2)*(7*x**2 + 45*x + 25)\nSimplifying the partial expression: (-44*x**2)*(7*x**2 + 45*x + 25)\nExpanding the part (7*x**2 + 45*x + 25) using the distributive property, and we got: 25*(-44*x**2) + (45*x)*(-44*x**2) + (-44*x**2)*(7*x**2)\nReplacing (-44*x**2)*(7*x**2 + 45*x + 25) with 25*(-44*x**2) + (45*x)*(-44*x**2) + (-44*x**2)*(7*x**2) in the overall expression.\n#Step 3:\nCurrent expression: 25*(-44)*x**2 + (13*x)*(7*x**2 + 45*x + 25) + (45*x)*(-44*x**2) + (-44*x**2)*(7*x**2)\nSimplifying the partial expression: (13*x)*(7*x**2 + 45*x + 25)\nExpanding the part (7*x**2 + 45*x + 25) using the distributive property, and we got: 25*(13*x) + (13*x)*(45*x) + (13*x)*(7*x**2)\nReplacing (13*x)*(7*x**2 + 45*x + 25) with 25*(13*x) + (13*x)*(45*x) + (13*x)*(7*x**2) in the overall expression.\n#Step 4:\nCurrent expression: 25*(-44)*x**2 + 25*13*x + (13*x)*(45*x) + (13*x)*(7*x**2) + (45*x)*(-44*x**2) + (-44*x**2)*(7*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (7*x**2)*(-44*x**2) = -308*x**4\n (7*x**2)*(13*x) = 91*x**3\n (45*x)*(-44*x**2) = -1980*x**3\n (45*x)*(13*x) = 585*x**2\n 25*-44*x**2 = -1100*x**2\n 25*13*x = 325*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -308*x**4 - 1980*x**3 + 91*x**3 - 1100*x**2 + 585*x**2 + 325*x\nCombining like terms, got -308*x**4 - 1889*x**3 - 515*x**2 + 325*x\n#Step 6:\nCurrent expression: -308*x**4 - 1889*x**3 - 515*x**2 + 325*x\nNo more calculations needed.\n-308*x**4 - 1889*x**3 - 515*x**2 + 325*x", "generated_answer": "-308*x**4 - 1889*x**3 - 515*x**2 + 325*x", "step_length": 6} {"cot_id": "9485ff8b5785ad888f7e83c363b38885239c0e4d7cd8e8f5dd839a466347fe26", "datapoint": {"question": "Simplify this expression: (43 - 53*y)*(8*y**3 + 33*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-424*y**4 - 1405*y**3 + 1419*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 67, "polynomial_expr": "(43 - 53*y)*(8*y**3 + 33*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (43 - 53*y)*(8*y**3 + 33*y**2)\nExpanding the part (43 - 53*y) using the distributive property, and we got: (-53*y)*(8*y**3 + 33*y**2) + 43*(8*y**3 + 33*y**2)\n#Step 2:\nCurrent expression: (-53*y)*(8*y**3 + 33*y**2) + 43*(8*y**3 + 33*y**2)\nSimplifying the partial expression: 43*(8*y**3 + 33*y**2)\nExpanding the part (8*y**3 + 33*y**2) using the distributive property, and we got: (33*y**2)*43 + (8*y**3)*43\nReplacing 43*(8*y**3 + 33*y**2) with (33*y**2)*43 + (8*y**3)*43 in the overall expression.\n#Step 3:\nCurrent expression: (-53*y)*(8*y**3 + 33*y**2) + (33*y**2)*43 + (8*y**3)*43\nSimplifying the partial expression: (-53*y)*(8*y**3 + 33*y**2)\nExpanding the part (8*y**3 + 33*y**2) using the distributive property, and we got: (-53*y)*(33*y**2) + (-53*y)*(8*y**3)\nReplacing (-53*y)*(8*y**3 + 33*y**2) with (-53*y)*(33*y**2) + (-53*y)*(8*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-53*y)*(33*y**2) + (-53*y)*(8*y**3) + (33*y**2)*43 + (8*y**3)*43\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (8*y**3)*43 = 344*y**3\n (8*y**3)*(-53*y) = -424*y**4\n (33*y**2)*43 = 1419*y**2\n (33*y**2)*(-53*y) = -1749*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -424*y**4 - 1749*y**3 + 344*y**3 + 1419*y**2\nCombining like terms, got -424*y**4 - 1405*y**3 + 1419*y**2\n#Step 6:\nCurrent expression: -424*y**4 - 1405*y**3 + 1419*y**2\nNo more calculations needed.\n-424*y**4 - 1405*y**3 + 1419*y**2", "generated_answer": "-424*y**4 - 1405*y**3 + 1419*y**2", "step_length": 6} {"cot_id": "375351b8f1155447a8f8489062abe6bab927fb4c84c65f8c2aa9e27cf4406865", "datapoint": {"question": "Calculate the following: 8*y**3*(45*y**3 + 64*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "360*y**6 + 512*y**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 68, "polynomial_expr": "8*y**3*(45*y**3 + 64*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 8*y**3*(45*y**3 + 64*y)\nExpanding the part (45*y**3 + 64*y) using the distributive property, and we got: (64*y)*(8*y**3) + (8*y**3)*(45*y**3)\n#Step 2:\nCurrent expression: (64*y)*(8*y**3) + (8*y**3)*(45*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (45*y**3)*(8*y**3) = 360*y**6\n (64*y)*(8*y**3) = 512*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 360*y**6 + 512*y**4\nNo more calculations needed.\n360*y**6 + 512*y**4", "generated_answer": "360*y**6 + 512*y**4", "step_length": 3} {"cot_id": "00ff05b80ee02132bc0dd405795d0c5d68a84f1e2ba876d1663ce99f3d41346c", "datapoint": {"question": "Simplify this expression: (-13*x**3 - 25)*(27*x**3 - 47*x**2 + 25)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-351*x**6 + 611*x**5 - 1000*x**3 + 1175*x**2 - 625", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 69, "polynomial_expr": "(-13*x**3 - 25)*(27*x**3 - 47*x**2 + 25)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-13*x**3 - 25)*(27*x**3 - 47*x**2 + 25)\nExpanding the part (-13*x**3 - 25) using the distributive property, and we got: (-13*x**3)*(27*x**3 - 47*x**2 + 25) - 25*(27*x**3 - 47*x**2 + 25)\n#Step 2:\nCurrent expression: (-13*x**3)*(27*x**3 - 47*x**2 + 25) - 25*(27*x**3 - 47*x**2 + 25)\nSimplifying the partial expression: -25*(27*x**3 - 47*x**2 + 25)\nExpanding the part (27*x**3 - 47*x**2 + 25) using the distributive property, and we got: -47*x**2*(-25) + (27*x**3)*(-25) + 25*(-25)\nReplacing -25*(27*x**3 - 47*x**2 + 25) with -47*x**2*(-25) + (27*x**3)*(-25) + 25*(-25) in the overall expression.\n#Step 3:\nCurrent expression: -47*x**2*(-25) + (-13*x**3)*(27*x**3 - 47*x**2 + 25) + (27*x**3)*(-25) - 625\nSimplifying the partial expression: (-13*x**3)*(27*x**3 - 47*x**2 + 25)\nExpanding the part (27*x**3 - 47*x**2 + 25) using the distributive property, and we got: 25*(-13*x**3) + (-47*x**2)*(-13*x**3) + (-13*x**3)*(27*x**3)\nReplacing (-13*x**3)*(27*x**3 - 47*x**2 + 25) with 25*(-13*x**3) + (-47*x**2)*(-13*x**3) + (-13*x**3)*(27*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 25*(-13)*x**3 + (-47*x**2)*(-13*x**3) - 47*x**2*(-25) + (-13*x**3)*(27*x**3) + (27*x**3)*(-25) - 625\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*x**2)*-25 = 1175*x**2\n (-47*x**2)*(-13*x**3) = 611*x**5\n (27*x**3)*-25 = -675*x**3\n (27*x**3)*(-13*x**3) = -351*x**6\n 25*-13*x**3 = -325*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -351*x**6 + 611*x**5 - 675*x**3 - 325*x**3 + 1175*x**2 - 625\nCombining like terms, got -351*x**6 + 611*x**5 - 1000*x**3 + 1175*x**2 - 625\n#Step 6:\nCurrent expression: -351*x**6 + 611*x**5 - 1000*x**3 + 1175*x**2 - 625\nNo more calculations needed.\n-351*x**6 + 611*x**5 - 1000*x**3 + 1175*x**2 - 625", "generated_answer": "-351*x**6 + 611*x**5 - 1000*x**3 + 1175*x**2 - 625", "step_length": 6} {"cot_id": "6b7995801fc927d8d5801d2c53e5128a411320addc0ae5b9f4210c351b317d34", "datapoint": {"question": "Calculate the following: (57 - 34*y)*(-30*y**3 + 14*y**2 - 11*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1020*y**4 - 2186*y**3 + 1172*y**2 - 627*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 70, "polynomial_expr": "(57 - 34*y)*(-30*y**3 + 14*y**2 - 11*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (57 - 34*y)*(-30*y**3 + 14*y**2 - 11*y)\nExpanding the part (57 - 34*y) using the distributive property, and we got: (-34*y)*(-30*y**3 + 14*y**2 - 11*y) + 57*(-30*y**3 + 14*y**2 - 11*y)\n#Step 2:\nCurrent expression: (-34*y)*(-30*y**3 + 14*y**2 - 11*y) + 57*(-30*y**3 + 14*y**2 - 11*y)\nSimplifying the partial expression: 57*(-30*y**3 + 14*y**2 - 11*y)\nExpanding the part (-30*y**3 + 14*y**2 - 11*y) using the distributive property, and we got: -11*y*57 + (14*y**2)*57 - 30*y**3*57\nReplacing 57*(-30*y**3 + 14*y**2 - 11*y) with -11*y*57 + (14*y**2)*57 - 30*y**3*57 in the overall expression.\n#Step 3:\nCurrent expression: (-34*y)*(-30*y**3 + 14*y**2 - 11*y) - 11*y*57 + (14*y**2)*57 - 30*y**3*57\nSimplifying the partial expression: (-34*y)*(-30*y**3 + 14*y**2 - 11*y)\nExpanding the part (-30*y**3 + 14*y**2 - 11*y) using the distributive property, and we got: (-34*y)*(-11*y) + (-34*y)*(14*y**2) + (-34*y)*(-30*y**3)\nReplacing (-34*y)*(-30*y**3 + 14*y**2 - 11*y) with (-34*y)*(-11*y) + (-34*y)*(14*y**2) + (-34*y)*(-30*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-34*y)*(-11*y) + (-34*y)*(14*y**2) + (-34*y)*(-30*y**3) - 11*y*57 + (14*y**2)*57 - 30*y**3*57\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*y**3)*57 = -1710*y**3\n (-30*y**3)*(-34*y) = 1020*y**4\n (-11*y)*57 = -627*y\n (-11*y)*(-34*y) = 374*y**2\n (14*y**2)*57 = 798*y**2\n (14*y**2)*(-34*y) = -476*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1020*y**4 - 1710*y**3 - 476*y**3 + 374*y**2 + 798*y**2 - 627*y\nCombining like terms, got 1020*y**4 - 2186*y**3 + 1172*y**2 - 627*y\n#Step 6:\nCurrent expression: 1020*y**4 - 2186*y**3 + 1172*y**2 - 627*y\nNo more calculations needed.\n1020*y**4 - 2186*y**3 + 1172*y**2 - 627*y", "generated_answer": "1020*y**4 - 2186*y**3 + 1172*y**2 - 627*y", "step_length": 6} {"cot_id": "93933d129a68804f5778b8e6ece1216fd7583b488870422bcc8046f9887ce9d7", "datapoint": {"question": "Simplify this expression: (-31*x**2 - 2*x)*(-13*x**3 + 20*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "403*x**5 + 26*x**4 - 620*x**3 - 40*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 71, "polynomial_expr": "(-31*x**2 - 2*x)*(-13*x**3 + 20*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-31*x**2 - 2*x)*(-13*x**3 + 20*x)\nExpanding the part (-31*x**2 - 2*x) using the distributive property, and we got: (-2*x)*(-13*x**3 + 20*x) + (-31*x**2)*(-13*x**3 + 20*x)\n#Step 2:\nCurrent expression: (-2*x)*(-13*x**3 + 20*x) + (-31*x**2)*(-13*x**3 + 20*x)\nSimplifying the partial expression: (-31*x**2)*(-13*x**3 + 20*x)\nExpanding the part (-13*x**3 + 20*x) using the distributive property, and we got: (20*x)*(-31*x**2) + (-31*x**2)*(-13*x**3)\nReplacing (-31*x**2)*(-13*x**3 + 20*x) with (20*x)*(-31*x**2) + (-31*x**2)*(-13*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-2*x)*(-13*x**3 + 20*x) + (20*x)*(-31*x**2) + (-31*x**2)*(-13*x**3)\nSimplifying the partial expression: (-2*x)*(-13*x**3 + 20*x)\nExpanding the part (-13*x**3 + 20*x) using the distributive property, and we got: (-2*x)*(20*x) + (-2*x)*(-13*x**3)\nReplacing (-2*x)*(-13*x**3 + 20*x) with (-2*x)*(20*x) + (-2*x)*(-13*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-2*x)*(20*x) + (-2*x)*(-13*x**3) + (20*x)*(-31*x**2) + (-31*x**2)*(-13*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*x**3)*(-31*x**2) = 403*x**5\n (-13*x**3)*(-2*x) = 26*x**4\n (20*x)*(-31*x**2) = -620*x**3\n (20*x)*(-2*x) = -40*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 403*x**5 + 26*x**4 - 620*x**3 - 40*x**2\nNo more calculations needed.\n403*x**5 + 26*x**4 - 620*x**3 - 40*x**2", "generated_answer": "403*x**5 + 26*x**4 - 620*x**3 - 40*x**2", "step_length": 5} {"cot_id": "018ff07d0591693bb0d5872812055da9a89007b266e703338eca7c0b67cd3d72", "datapoint": {"question": "Simplify this expression: (34*x**2 + 47)*(28*x**3 + 63*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "952*x**5 + 2142*x**4 + 1316*x**3 + 2961*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 72, "polynomial_expr": "(34*x**2 + 47)*(28*x**3 + 63*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (34*x**2 + 47)*(28*x**3 + 63*x**2)\nExpanding the part (34*x**2 + 47) using the distributive property, and we got: (34*x**2)*(28*x**3 + 63*x**2) + 47*(28*x**3 + 63*x**2)\n#Step 2:\nCurrent expression: (34*x**2)*(28*x**3 + 63*x**2) + 47*(28*x**3 + 63*x**2)\nSimplifying the partial expression: 47*(28*x**3 + 63*x**2)\nExpanding the part (28*x**3 + 63*x**2) using the distributive property, and we got: (63*x**2)*47 + (28*x**3)*47\nReplacing 47*(28*x**3 + 63*x**2) with (63*x**2)*47 + (28*x**3)*47 in the overall expression.\n#Step 3:\nCurrent expression: (34*x**2)*(28*x**3 + 63*x**2) + (63*x**2)*47 + (28*x**3)*47\nSimplifying the partial expression: (34*x**2)*(28*x**3 + 63*x**2)\nExpanding the part (28*x**3 + 63*x**2) using the distributive property, and we got: (34*x**2)*(63*x**2) + (34*x**2)*(28*x**3)\nReplacing (34*x**2)*(28*x**3 + 63*x**2) with (34*x**2)*(63*x**2) + (34*x**2)*(28*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (34*x**2)*(63*x**2) + (34*x**2)*(28*x**3) + (63*x**2)*47 + (28*x**3)*47\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (28*x**3)*47 = 1316*x**3\n (28*x**3)*(34*x**2) = 952*x**5\n (63*x**2)*47 = 2961*x**2\n (63*x**2)*(34*x**2) = 2142*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 952*x**5 + 2142*x**4 + 1316*x**3 + 2961*x**2\nNo more calculations needed.\n952*x**5 + 2142*x**4 + 1316*x**3 + 2961*x**2", "generated_answer": "952*x**5 + 2142*x**4 + 1316*x**3 + 2961*x**2", "step_length": 5} {"cot_id": "d116211f58daeb7920da350878d460078bfa077a868a41028617f4cd38385478", "datapoint": {"question": "Simplify this expression: (-19*y - 65)*(-35*y**3 + 36*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "665*y**4 + 2275*y**3 - 684*y**2 - 2340*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 73, "polynomial_expr": "(-19*y - 65)*(-35*y**3 + 36*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-19*y - 65)*(-35*y**3 + 36*y)\nExpanding the part (-19*y - 65) using the distributive property, and we got: (-19*y)*(-35*y**3 + 36*y) - 65*(-35*y**3 + 36*y)\n#Step 2:\nCurrent expression: (-19*y)*(-35*y**3 + 36*y) - 65*(-35*y**3 + 36*y)\nSimplifying the partial expression: -65*(-35*y**3 + 36*y)\nExpanding the part (-35*y**3 + 36*y) using the distributive property, and we got: (36*y)*(-65) - 35*y**3*(-65)\nReplacing -65*(-35*y**3 + 36*y) with (36*y)*(-65) - 35*y**3*(-65) in the overall expression.\n#Step 3:\nCurrent expression: (-19*y)*(-35*y**3 + 36*y) + (36*y)*(-65) - 35*y**3*(-65)\nSimplifying the partial expression: (-19*y)*(-35*y**3 + 36*y)\nExpanding the part (-35*y**3 + 36*y) using the distributive property, and we got: (-19*y)*(36*y) + (-19*y)*(-35*y**3)\nReplacing (-19*y)*(-35*y**3 + 36*y) with (-19*y)*(36*y) + (-19*y)*(-35*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-19*y)*(36*y) + (-19*y)*(-35*y**3) + (36*y)*(-65) - 35*y**3*(-65)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*y**3)*-65 = 2275*y**3\n (-35*y**3)*(-19*y) = 665*y**4\n (36*y)*-65 = -2340*y\n (36*y)*(-19*y) = -684*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 665*y**4 + 2275*y**3 - 684*y**2 - 2340*y\nNo more calculations needed.\n665*y**4 + 2275*y**3 - 684*y**2 - 2340*y", "generated_answer": "665*y**4 + 2275*y**3 - 684*y**2 - 2340*y", "step_length": 5} {"cot_id": "1dc1400c84c9cd88390f892b9e0f7d97145574d41716c43d62974769c09cc7e7", "datapoint": {"question": "Simplify this expression: (49*z**3 + 31*z**2)*(-37*z**3 + 27*z**2 - 21*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1813*z**6 + 176*z**5 - 192*z**4 - 651*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 74, "polynomial_expr": "(49*z**3 + 31*z**2)*(-37*z**3 + 27*z**2 - 21*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (49*z**3 + 31*z**2)*(-37*z**3 + 27*z**2 - 21*z)\nExpanding the part (49*z**3 + 31*z**2) using the distributive property, and we got: (31*z**2)*(-37*z**3 + 27*z**2 - 21*z) + (49*z**3)*(-37*z**3 + 27*z**2 - 21*z)\n#Step 2:\nCurrent expression: (31*z**2)*(-37*z**3 + 27*z**2 - 21*z) + (49*z**3)*(-37*z**3 + 27*z**2 - 21*z)\nSimplifying the partial expression: (31*z**2)*(-37*z**3 + 27*z**2 - 21*z)\nExpanding the part (-37*z**3 + 27*z**2 - 21*z) using the distributive property, and we got: (-21*z)*(31*z**2) + (27*z**2)*(31*z**2) + (31*z**2)*(-37*z**3)\nReplacing (31*z**2)*(-37*z**3 + 27*z**2 - 21*z) with (-21*z)*(31*z**2) + (27*z**2)*(31*z**2) + (31*z**2)*(-37*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-21*z)*(31*z**2) + (27*z**2)*(31*z**2) + (31*z**2)*(-37*z**3) + (49*z**3)*(-37*z**3 + 27*z**2 - 21*z)\nSimplifying the partial expression: (49*z**3)*(-37*z**3 + 27*z**2 - 21*z)\nExpanding the part (-37*z**3 + 27*z**2 - 21*z) using the distributive property, and we got: (-21*z)*(49*z**3) + (27*z**2)*(49*z**3) + (-37*z**3)*(49*z**3)\nReplacing (49*z**3)*(-37*z**3 + 27*z**2 - 21*z) with (-21*z)*(49*z**3) + (27*z**2)*(49*z**3) + (-37*z**3)*(49*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-21*z)*(31*z**2) + (-21*z)*(49*z**3) + (27*z**2)*(31*z**2) + (27*z**2)*(49*z**3) + (31*z**2)*(-37*z**3) + (-37*z**3)*(49*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*z**3)*(31*z**2) = -1147*z**5\n (-37*z**3)*(49*z**3) = -1813*z**6\n (-21*z)*(31*z**2) = -651*z**3\n (-21*z)*(49*z**3) = -1029*z**4\n (27*z**2)*(31*z**2) = 837*z**4\n (27*z**2)*(49*z**3) = 1323*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1813*z**6 - 1147*z**5 + 1323*z**5 - 1029*z**4 + 837*z**4 - 651*z**3\nCombining like terms, got -1813*z**6 + 176*z**5 - 192*z**4 - 651*z**3\n#Step 6:\nCurrent expression: -1813*z**6 + 176*z**5 - 192*z**4 - 651*z**3\nNo more calculations needed.\n-1813*z**6 + 176*z**5 - 192*z**4 - 651*z**3", "generated_answer": "-1813*z**6 + 176*z**5 - 192*z**4 - 651*z**3", "step_length": 6} {"cot_id": "3e794ea45b97dc05c6be7ce8567c179c47a054afd0556dfe94dec2c4ae1cda8f", "datapoint": {"question": "Calculate the following: 50*x**3*(4*x**3 - 34*x**2 - 42*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "200*x**6 - 1700*x**5 - 2100*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 75, "polynomial_expr": "50*x**3*(4*x**3 - 34*x**2 - 42*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 50*x**3*(4*x**3 - 34*x**2 - 42*x)\nExpanding the part (4*x**3 - 34*x**2 - 42*x) using the distributive property, and we got: (-42*x)*(50*x**3) + (-34*x**2)*(50*x**3) + (4*x**3)*(50*x**3)\n#Step 2:\nCurrent expression: (-42*x)*(50*x**3) + (-34*x**2)*(50*x**3) + (4*x**3)*(50*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*x)*(50*x**3) = -2100*x**4\n (-34*x**2)*(50*x**3) = -1700*x**5\n (4*x**3)*(50*x**3) = 200*x**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 200*x**6 - 1700*x**5 - 2100*x**4\nNo more calculations needed.\n200*x**6 - 1700*x**5 - 2100*x**4", "generated_answer": "200*x**6 - 1700*x**5 - 2100*x**4", "step_length": 3} {"cot_id": "1f1f3115ab807ba7fc57252687d16c09b7e7a9bb9b00b4aa481e8f5efe48cabf", "datapoint": {"question": "Simplify this expression: (2*z**2 - 9*z)*(44*z**3 + 25*z + 59)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "88*z**5 - 396*z**4 + 50*z**3 - 107*z**2 - 531*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 76, "polynomial_expr": "(2*z**2 - 9*z)*(44*z**3 + 25*z + 59)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2*z**2 - 9*z)*(44*z**3 + 25*z + 59)\nExpanding the part (2*z**2 - 9*z) using the distributive property, and we got: (-9*z)*(44*z**3 + 25*z + 59) + (2*z**2)*(44*z**3 + 25*z + 59)\n#Step 2:\nCurrent expression: (-9*z)*(44*z**3 + 25*z + 59) + (2*z**2)*(44*z**3 + 25*z + 59)\nSimplifying the partial expression: (-9*z)*(44*z**3 + 25*z + 59)\nExpanding the part (44*z**3 + 25*z + 59) using the distributive property, and we got: (-9*z)*(25*z) + (-9*z)*(44*z**3) + 59*(-9*z)\nReplacing (-9*z)*(44*z**3 + 25*z + 59) with (-9*z)*(25*z) + (-9*z)*(44*z**3) + 59*(-9*z) in the overall expression.\n#Step 3:\nCurrent expression: (-9*z)*(25*z) + (-9*z)*(44*z**3) + 59*(-9)*z + (2*z**2)*(44*z**3 + 25*z + 59)\nSimplifying the partial expression: (2*z**2)*(44*z**3 + 25*z + 59)\nExpanding the part (44*z**3 + 25*z + 59) using the distributive property, and we got: 59*(2*z**2) + (25*z)*(2*z**2) + (2*z**2)*(44*z**3)\nReplacing (2*z**2)*(44*z**3 + 25*z + 59) with 59*(2*z**2) + (25*z)*(2*z**2) + (2*z**2)*(44*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-9*z)*(25*z) + (-9*z)*(44*z**3) + 59*2*z**2 + 59*(-9)*z + (25*z)*(2*z**2) + (2*z**2)*(44*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (25*z)*(-9*z) = -225*z**2\n (25*z)*(2*z**2) = 50*z**3\n (44*z**3)*(-9*z) = -396*z**4\n (44*z**3)*(2*z**2) = 88*z**5\n 59*-9*z = -531*z\n 59*2*z**2 = 118*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 88*z**5 - 396*z**4 + 50*z**3 - 225*z**2 + 118*z**2 - 531*z\nCombining like terms, got 88*z**5 - 396*z**4 + 50*z**3 - 107*z**2 - 531*z\n#Step 6:\nCurrent expression: 88*z**5 - 396*z**4 + 50*z**3 - 107*z**2 - 531*z\nNo more calculations needed.\n88*z**5 - 396*z**4 + 50*z**3 - 107*z**2 - 531*z", "generated_answer": "88*z**5 - 396*z**4 + 50*z**3 - 107*z**2 - 531*z", "step_length": 6} {"cot_id": "c0cc9c7b492f8c8b6aad2778fcc49ab8c46740cc6ba4c78d2c89824b63953b7c", "datapoint": {"question": "Simplify this expression: (28*y**3 + y**2 - 22)*(-38*y**3 - 35*y**2 - 17*y + 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1064*y**6 - 1018*y**5 - 511*y**4 + 1603*y**3 + 798*y**2 + 374*y - 616", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 77, "polynomial_expr": "(28*y**3 + y**2 - 22)*(-38*y**3 - 35*y**2 - 17*y + 28)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28*y**3 + y**2 - 22)*(-38*y**3 - 35*y**2 - 17*y + 28)\nExpanding the part (28*y**3 + y**2 - 22) using the distributive property, and we got: y**2*(-38*y**3 - 35*y**2 - 17*y + 28) + (28*y**3)*(-38*y**3 - 35*y**2 - 17*y + 28) - 22*(-38*y**3 - 35*y**2 - 17*y + 28)\n#Step 2:\nCurrent expression: y**2*(-38*y**3 - 35*y**2 - 17*y + 28) + (28*y**3)*(-38*y**3 - 35*y**2 - 17*y + 28) - 22*(-38*y**3 - 35*y**2 - 17*y + 28)\nSimplifying the partial expression: -22*(-38*y**3 - 35*y**2 - 17*y + 28)\nExpanding the part (-38*y**3 - 35*y**2 - 17*y + 28) using the distributive property, and we got: -17*y*(-22) - 35*y**2*(-22) - 38*y**3*(-22) + 28*(-22)\nReplacing -22*(-38*y**3 - 35*y**2 - 17*y + 28) with -17*y*(-22) - 35*y**2*(-22) - 38*y**3*(-22) + 28*(-22) in the overall expression.\n#Step 3:\nCurrent expression: -17*y*(-22) + y**2*(-38*y**3 - 35*y**2 - 17*y + 28) - 35*y**2*(-22) - 38*y**3*(-22) + (28*y**3)*(-38*y**3 - 35*y**2 - 17*y + 28) - 616\nSimplifying the partial expression: y**2*(-38*y**3 - 35*y**2 - 17*y + 28)\nExpanding the part (-38*y**3 - 35*y**2 - 17*y + 28) using the distributive property, and we got: (-17*y)*y**2 + (-35*y**2)*y**2 + y**2*(-38*y**3) + 28*y**2\nReplacing y**2*(-38*y**3 - 35*y**2 - 17*y + 28) with (-17*y)*y**2 + (-35*y**2)*y**2 + y**2*(-38*y**3) + 28*y**2 in the overall expression.\n#Step 4:\nCurrent expression: (-17*y)*y**2 - 17*y*(-22) + (-35*y**2)*y**2 + y**2*(-38*y**3) + 28*y**2 - 35*y**2*(-22) - 38*y**3*(-22) + (28*y**3)*(-38*y**3 - 35*y**2 - 17*y + 28) - 616\nSimplifying the partial expression: (28*y**3)*(-38*y**3 - 35*y**2 - 17*y + 28)\nExpanding the part (-38*y**3 - 35*y**2 - 17*y + 28) using the distributive property, and we got: (-17*y)*(28*y**3) + 28*(28*y**3) + (-35*y**2)*(28*y**3) + (-38*y**3)*(28*y**3)\nReplacing (28*y**3)*(-38*y**3 - 35*y**2 - 17*y + 28) with (-17*y)*(28*y**3) + 28*(28*y**3) + (-35*y**2)*(28*y**3) + (-38*y**3)*(28*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-17*y)*y**2 + (-17*y)*(28*y**3) - 17*y*(-22) + 28*28*y**3 + (-35*y**2)*y**2 + y**2*(-38*y**3) + 28*y**2 + (-35*y**2)*(28*y**3) - 35*y**2*(-22) + (-38*y**3)*(28*y**3) - 38*y**3*(-22) - 616\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*y**3)*-22 = 836*y**3\n (-38*y**3)*y**2 = -38*y**5\n (-38*y**3)*(28*y**3) = -1064*y**6\n (-35*y**2)*-22 = 770*y**2\n (-35*y**2)*y**2 = -35*y**4\n (-35*y**2)*(28*y**3) = -980*y**5\n (-17*y)*-22 = 374*y\n (-17*y)*y**2 = -17*y**3\n (-17*y)*(28*y**3) = -476*y**4\n 28*28*y**3 = 784*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1064*y**6 - 980*y**5 - 38*y**5 - 476*y**4 - 35*y**4 - 17*y**3 + 784*y**3 + 836*y**3 + 28*y**2 + 770*y**2 + 374*y - 616\nCombining like terms, got -1064*y**6 - 1018*y**5 - 511*y**4 + 1603*y**3 + 798*y**2 + 374*y - 616\n#Step 7:\nCurrent expression: -1064*y**6 - 1018*y**5 - 511*y**4 + 1603*y**3 + 798*y**2 + 374*y - 616\nNo more calculations needed.\n-1064*y**6 - 1018*y**5 - 511*y**4 + 1603*y**3 + 798*y**2 + 374*y - 616", "generated_answer": "-1064*y**6 - 1018*y**5 - 511*y**4 + 1603*y**3 + 798*y**2 + 374*y - 616", "step_length": 7} {"cot_id": "e5d173dcec5b15f948ddcf724028ddc4959193c943ad55558f06793a0c189bb2", "datapoint": {"question": "Simplify this expression: (14 - 41*z**2)*(-13*z**3 - 5*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "533*z**5 + 23*z**3 - 70*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 78, "polynomial_expr": "(14 - 41*z**2)*(-13*z**3 - 5*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14 - 41*z**2)*(-13*z**3 - 5*z)\nExpanding the part (14 - 41*z**2) using the distributive property, and we got: (-41*z**2)*(-13*z**3 - 5*z) + 14*(-13*z**3 - 5*z)\n#Step 2:\nCurrent expression: (-41*z**2)*(-13*z**3 - 5*z) + 14*(-13*z**3 - 5*z)\nSimplifying the partial expression: 14*(-13*z**3 - 5*z)\nExpanding the part (-13*z**3 - 5*z) using the distributive property, and we got: -5*z*14 - 13*z**3*14\nReplacing 14*(-13*z**3 - 5*z) with -5*z*14 - 13*z**3*14 in the overall expression.\n#Step 3:\nCurrent expression: -5*z*14 + (-41*z**2)*(-13*z**3 - 5*z) - 13*z**3*14\nSimplifying the partial expression: (-41*z**2)*(-13*z**3 - 5*z)\nExpanding the part (-13*z**3 - 5*z) using the distributive property, and we got: (-5*z)*(-41*z**2) + (-41*z**2)*(-13*z**3)\nReplacing (-41*z**2)*(-13*z**3 - 5*z) with (-5*z)*(-41*z**2) + (-41*z**2)*(-13*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-5*z)*(-41*z**2) - 5*z*14 + (-41*z**2)*(-13*z**3) - 13*z**3*14\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*z**3)*14 = -182*z**3\n (-13*z**3)*(-41*z**2) = 533*z**5\n (-5*z)*14 = -70*z\n (-5*z)*(-41*z**2) = 205*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 533*z**5 - 182*z**3 + 205*z**3 - 70*z\nCombining like terms, got 533*z**5 + 23*z**3 - 70*z\n#Step 6:\nCurrent expression: 533*z**5 + 23*z**3 - 70*z\nNo more calculations needed.\n533*z**5 + 23*z**3 - 70*z", "generated_answer": "533*z**5 + 23*z**3 - 70*z", "step_length": 6} {"cot_id": "19d5a4fdccead1a717d608276c6dc9bdea07bf4f7b748f50f4bdd139a73cc91b", "datapoint": {"question": "Simplify this expression: (28*x + 79)*(-28*x**2 - 28*x - 43)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-784*x**3 - 2996*x**2 - 3416*x - 3397", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 79, "polynomial_expr": "(28*x + 79)*(-28*x**2 - 28*x - 43)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28*x + 79)*(-28*x**2 - 28*x - 43)\nExpanding the part (28*x + 79) using the distributive property, and we got: (28*x)*(-28*x**2 - 28*x - 43) + 79*(-28*x**2 - 28*x - 43)\n#Step 2:\nCurrent expression: (28*x)*(-28*x**2 - 28*x - 43) + 79*(-28*x**2 - 28*x - 43)\nSimplifying the partial expression: 79*(-28*x**2 - 28*x - 43)\nExpanding the part (-28*x**2 - 28*x - 43) using the distributive property, and we got: -28*x*79 - 28*x**2*79 - 43*79\nReplacing 79*(-28*x**2 - 28*x - 43) with -28*x*79 - 28*x**2*79 - 43*79 in the overall expression.\n#Step 3:\nCurrent expression: -28*x*79 + (28*x)*(-28*x**2 - 28*x - 43) - 28*x**2*79 - 3397\nSimplifying the partial expression: (28*x)*(-28*x**2 - 28*x - 43)\nExpanding the part (-28*x**2 - 28*x - 43) using the distributive property, and we got: (-28*x)*(28*x) - 1204*x + (28*x)*(-28*x**2)\nReplacing (28*x)*(-28*x**2 - 28*x - 43) with (-28*x)*(28*x) - 1204*x + (28*x)*(-28*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-28*x)*(28*x) - 28*x*79 - 43*28*x + (28*x)*(-28*x**2) - 28*x**2*79 - 3397\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*x)*79 = -2212*x\n (-28*x)*(28*x) = -784*x**2\n (-28*x**2)*79 = -2212*x**2\n (-28*x**2)*(28*x) = -784*x**3\n -43*28*x = -1204*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -784*x**3 - 2212*x**2 - 784*x**2 - 2212*x - 1204*x - 3397\nCombining like terms, got -784*x**3 - 2996*x**2 - 3416*x - 3397\n#Step 6:\nCurrent expression: -784*x**3 - 2996*x**2 - 3416*x - 3397\nNo more calculations needed.\n-784*x**3 - 2996*x**2 - 3416*x - 3397", "generated_answer": "-784*x**3 - 2996*x**2 - 3416*x - 3397", "step_length": 6} {"cot_id": "d9627a00b039fcf3962be6be05cd080ca46ea3d5590cc5e386f4f40707975048", "datapoint": {"question": "Calculate the following: (47 - 10*z**2)*(20*z**3 - 63)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-200*z**5 + 940*z**3 + 630*z**2 - 2961", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 80, "polynomial_expr": "(47 - 10*z**2)*(20*z**3 - 63)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (47 - 10*z**2)*(20*z**3 - 63)\nExpanding the part (20*z**3 - 63) using the distributive property, and we got: (20*z**3)*(47 - 10*z**2) - 63*(47 - 10*z**2)\n#Step 2:\nCurrent expression: (20*z**3)*(47 - 10*z**2) - 63*(47 - 10*z**2)\nSimplifying the partial expression: -63*(47 - 10*z**2)\nExpanding the part (47 - 10*z**2) using the distributive property, and we got: -10*z**2*(-63) + 47*(-63)\nReplacing -63*(47 - 10*z**2) with -10*z**2*(-63) + 47*(-63) in the overall expression.\n#Step 3:\nCurrent expression: -10*z**2*(-63) + (20*z**3)*(47 - 10*z**2) - 2961\nSimplifying the partial expression: (20*z**3)*(47 - 10*z**2)\nExpanding the part (47 - 10*z**2) using the distributive property, and we got: 47*(20*z**3) + (-10*z**2)*(20*z**3)\nReplacing (20*z**3)*(47 - 10*z**2) with 47*(20*z**3) + (-10*z**2)*(20*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 47*20*z**3 + (-10*z**2)*(20*z**3) - 10*z**2*(-63) - 2961\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*z**2)*-63 = 630*z**2\n (-10*z**2)*(20*z**3) = -200*z**5\n 47*20*z**3 = 940*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -200*z**5 + 940*z**3 + 630*z**2 - 2961\nNo more calculations needed.\n-200*z**5 + 940*z**3 + 630*z**2 - 2961", "generated_answer": "-200*z**5 + 940*z**3 + 630*z**2 - 2961", "step_length": 5} {"cot_id": "f6709338d5c337c751614000942d3fe12b0a9adaa6cafc9a5bdd3ee8a09ea1d2", "datapoint": {"question": "Simplify this expression: -47*x**3*(22*x**2 - 11*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1034*x**5 + 517*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 81, "polynomial_expr": "-47*x**3*(22*x**2 - 11*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -47*x**3*(22*x**2 - 11*x)\nExpanding the part (22*x**2 - 11*x) using the distributive property, and we got: (-11*x)*(-47*x**3) + (22*x**2)*(-47*x**3)\n#Step 2:\nCurrent expression: (-11*x)*(-47*x**3) + (22*x**2)*(-47*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*x)*(-47*x**3) = 517*x**4\n (22*x**2)*(-47*x**3) = -1034*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1034*x**5 + 517*x**4\nNo more calculations needed.\n-1034*x**5 + 517*x**4", "generated_answer": "-1034*x**5 + 517*x**4", "step_length": 3} {"cot_id": "8363a43f7df236c27bd1f0b3b6eed36e868f2e0e768dbb153dfeeb429adadcf4", "datapoint": {"question": "Simplify this expression: (-24*y**3 - 4*y**2)*(-14*y**3 - 51*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "336*y**6 + 1280*y**5 + 204*y**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 82, "polynomial_expr": "(-24*y**3 - 4*y**2)*(-14*y**3 - 51*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-24*y**3 - 4*y**2)*(-14*y**3 - 51*y**2)\nExpanding the part (-14*y**3 - 51*y**2) using the distributive property, and we got: (-51*y**2)*(-24*y**3 - 4*y**2) + (-14*y**3)*(-24*y**3 - 4*y**2)\n#Step 2:\nCurrent expression: (-51*y**2)*(-24*y**3 - 4*y**2) + (-14*y**3)*(-24*y**3 - 4*y**2)\nSimplifying the partial expression: (-51*y**2)*(-24*y**3 - 4*y**2)\nExpanding the part (-24*y**3 - 4*y**2) using the distributive property, and we got: (-51*y**2)*(-4*y**2) + (-51*y**2)*(-24*y**3)\nReplacing (-51*y**2)*(-24*y**3 - 4*y**2) with (-51*y**2)*(-4*y**2) + (-51*y**2)*(-24*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-51*y**2)*(-4*y**2) + (-51*y**2)*(-24*y**3) + (-14*y**3)*(-24*y**3 - 4*y**2)\nSimplifying the partial expression: (-14*y**3)*(-24*y**3 - 4*y**2)\nExpanding the part (-24*y**3 - 4*y**2) using the distributive property, and we got: (-4*y**2)*(-14*y**3) + (-24*y**3)*(-14*y**3)\nReplacing (-14*y**3)*(-24*y**3 - 4*y**2) with (-4*y**2)*(-14*y**3) + (-24*y**3)*(-14*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-51*y**2)*(-4*y**2) + (-51*y**2)*(-24*y**3) + (-4*y**2)*(-14*y**3) + (-24*y**3)*(-14*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-24*y**3)*(-51*y**2) = 1224*y**5\n (-24*y**3)*(-14*y**3) = 336*y**6\n (-4*y**2)*(-51*y**2) = 204*y**4\n (-4*y**2)*(-14*y**3) = 56*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 336*y**6 + 56*y**5 + 1224*y**5 + 204*y**4\nCombining like terms, got 336*y**6 + 1280*y**5 + 204*y**4\n#Step 6:\nCurrent expression: 336*y**6 + 1280*y**5 + 204*y**4\nNo more calculations needed.\n336*y**6 + 1280*y**5 + 204*y**4", "generated_answer": "336*y**6 + 1280*y**5 + 204*y**4", "step_length": 6} {"cot_id": "0aec29432bc908af7851d430f70bb23cddb52fc80b3bbdaa6ba5bbd8bec5b0f4", "datapoint": {"question": "Simplify this expression: (12*x**3 + 41*x - 19)*(10*x**3 + 39*x**2 + x - 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "120*x**6 + 468*x**5 + 422*x**4 + 1169*x**3 - 700*x**2 - 839*x + 380", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 83, "polynomial_expr": "(12*x**3 + 41*x - 19)*(10*x**3 + 39*x**2 + x - 20)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (12*x**3 + 41*x - 19)*(10*x**3 + 39*x**2 + x - 20)\nExpanding the part (12*x**3 + 41*x - 19) using the distributive property, and we got: (41*x)*(10*x**3 + 39*x**2 + x - 20) + (12*x**3)*(10*x**3 + 39*x**2 + x - 20) - 19*(10*x**3 + 39*x**2 + x - 20)\n#Step 2:\nCurrent expression: (41*x)*(10*x**3 + 39*x**2 + x - 20) + (12*x**3)*(10*x**3 + 39*x**2 + x - 20) - 19*(10*x**3 + 39*x**2 + x - 20)\nSimplifying the partial expression: -19*(10*x**3 + 39*x**2 + x - 20)\nExpanding the part (10*x**3 + 39*x**2 + x - 20) using the distributive property, and we got: x*(-19) + (39*x**2)*(-19) + (10*x**3)*(-19) - 20*(-19)\nReplacing -19*(10*x**3 + 39*x**2 + x - 20) with x*(-19) + (39*x**2)*(-19) + (10*x**3)*(-19) - 20*(-19) in the overall expression.\n#Step 3:\nCurrent expression: x*(-19) + (41*x)*(10*x**3 + 39*x**2 + x - 20) + (39*x**2)*(-19) + (10*x**3)*(-19) + (12*x**3)*(10*x**3 + 39*x**2 + x - 20) + 380\nSimplifying the partial expression: (12*x**3)*(10*x**3 + 39*x**2 + x - 20)\nExpanding the part (10*x**3 + 39*x**2 + x - 20) using the distributive property, and we got: -240*x**3 + x*(12*x**3) + (39*x**2)*(12*x**3) + (10*x**3)*(12*x**3)\nReplacing (12*x**3)*(10*x**3 + 39*x**2 + x - 20) with -240*x**3 + x*(12*x**3) + (39*x**2)*(12*x**3) + (10*x**3)*(12*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -20*12*x**3 + x*(12*x**3) + x*(-19) + (41*x)*(10*x**3 + 39*x**2 + x - 20) + (39*x**2)*(12*x**3) + (39*x**2)*(-19) + (10*x**3)*(12*x**3) + (10*x**3)*(-19) + 380\nSimplifying the partial expression: (41*x)*(10*x**3 + 39*x**2 + x - 20)\nExpanding the part (10*x**3 + 39*x**2 + x - 20) using the distributive property, and we got: x*(41*x) - 820*x + (41*x)*(39*x**2) + (41*x)*(10*x**3)\nReplacing (41*x)*(10*x**3 + 39*x**2 + x - 20) with x*(41*x) - 820*x + (41*x)*(39*x**2) + (41*x)*(10*x**3) in the overall expression.\n#Step 5:\nCurrent expression: -20*12*x**3 + x*(41*x) + x*(12*x**3) - 20*41*x + x*(-19) + (41*x)*(39*x**2) + (41*x)*(10*x**3) + (39*x**2)*(12*x**3) + (39*x**2)*(-19) + (10*x**3)*(12*x**3) + (10*x**3)*(-19) + 380\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n x*-19 = -19*x\n x*(12*x**3) = 12*x**4\n x*(41*x) = 41*x**2\n (10*x**3)*-19 = -190*x**3\n (10*x**3)*(12*x**3) = 120*x**6\n (10*x**3)*(41*x) = 410*x**4\n (39*x**2)*-19 = -741*x**2\n (39*x**2)*(12*x**3) = 468*x**5\n (39*x**2)*(41*x) = 1599*x**3\n -20*12*x**3 = -240*x**3\n -20*41*x = -820*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 120*x**6 + 468*x**5 + 12*x**4 + 410*x**4 - 240*x**3 - 190*x**3 + 1599*x**3 - 741*x**2 + 41*x**2 - 820*x - 19*x + 380\nCombining like terms, got 120*x**6 + 468*x**5 + 422*x**4 + 1169*x**3 - 700*x**2 - 839*x + 380\n#Step 7:\nCurrent expression: 120*x**6 + 468*x**5 + 422*x**4 + 1169*x**3 - 700*x**2 - 839*x + 380\nNo more calculations needed.\n120*x**6 + 468*x**5 + 422*x**4 + 1169*x**3 - 700*x**2 - 839*x + 380", "generated_answer": "120*x**6 + 468*x**5 + 422*x**4 + 1169*x**3 - 700*x**2 - 839*x + 380", "step_length": 7} {"cot_id": "546337bd2579d05d1cab1ed828d4da7e8e039c88419e4b3a62189cdfc3ed24e0", "datapoint": {"question": "Simplify this expression: (15 - 68*z**2)*(9*z**2 - 19)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-612*z**4 + 1427*z**2 - 285", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 84, "polynomial_expr": "(15 - 68*z**2)*(9*z**2 - 19)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (15 - 68*z**2)*(9*z**2 - 19)\nExpanding the part (9*z**2 - 19) using the distributive property, and we got: (9*z**2)*(15 - 68*z**2) - 19*(15 - 68*z**2)\n#Step 2:\nCurrent expression: (9*z**2)*(15 - 68*z**2) - 19*(15 - 68*z**2)\nSimplifying the partial expression: -19*(15 - 68*z**2)\nExpanding the part (15 - 68*z**2) using the distributive property, and we got: -68*z**2*(-19) + 15*(-19)\nReplacing -19*(15 - 68*z**2) with -68*z**2*(-19) + 15*(-19) in the overall expression.\n#Step 3:\nCurrent expression: -68*z**2*(-19) + (9*z**2)*(15 - 68*z**2) - 285\nSimplifying the partial expression: (9*z**2)*(15 - 68*z**2)\nExpanding the part (15 - 68*z**2) using the distributive property, and we got: 15*(9*z**2) + (-68*z**2)*(9*z**2)\nReplacing (9*z**2)*(15 - 68*z**2) with 15*(9*z**2) + (-68*z**2)*(9*z**2) in the overall expression.\n#Step 4:\nCurrent expression: 15*9*z**2 + (-68*z**2)*(9*z**2) - 68*z**2*(-19) - 285\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-68*z**2)*-19 = 1292*z**2\n (-68*z**2)*(9*z**2) = -612*z**4\n 15*9*z**2 = 135*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -612*z**4 + 135*z**2 + 1292*z**2 - 285\nCombining like terms, got -612*z**4 + 1427*z**2 - 285\n#Step 6:\nCurrent expression: -612*z**4 + 1427*z**2 - 285\nNo more calculations needed.\n-612*z**4 + 1427*z**2 - 285", "generated_answer": "-612*z**4 + 1427*z**2 - 285", "step_length": 6} {"cot_id": "0cdd871061acd2648b7398d883734a45a9fb8205ef473fe6ec9eb22a02a155aa", "datapoint": {"question": "Calculate the following: (2*x**2 - 27)*(20*x**3 + 21*x**2 + 71*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "40*x**5 + 42*x**4 - 398*x**3 - 567*x**2 - 1917*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 85, "polynomial_expr": "(2*x**2 - 27)*(20*x**3 + 21*x**2 + 71*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2*x**2 - 27)*(20*x**3 + 21*x**2 + 71*x)\nExpanding the part (2*x**2 - 27) using the distributive property, and we got: (2*x**2)*(20*x**3 + 21*x**2 + 71*x) - 27*(20*x**3 + 21*x**2 + 71*x)\n#Step 2:\nCurrent expression: (2*x**2)*(20*x**3 + 21*x**2 + 71*x) - 27*(20*x**3 + 21*x**2 + 71*x)\nSimplifying the partial expression: -27*(20*x**3 + 21*x**2 + 71*x)\nExpanding the part (20*x**3 + 21*x**2 + 71*x) using the distributive property, and we got: (71*x)*(-27) + (21*x**2)*(-27) + (20*x**3)*(-27)\nReplacing -27*(20*x**3 + 21*x**2 + 71*x) with (71*x)*(-27) + (21*x**2)*(-27) + (20*x**3)*(-27) in the overall expression.\n#Step 3:\nCurrent expression: (71*x)*(-27) + (2*x**2)*(20*x**3 + 21*x**2 + 71*x) + (21*x**2)*(-27) + (20*x**3)*(-27)\nSimplifying the partial expression: (2*x**2)*(20*x**3 + 21*x**2 + 71*x)\nExpanding the part (20*x**3 + 21*x**2 + 71*x) using the distributive property, and we got: (71*x)*(2*x**2) + (2*x**2)*(21*x**2) + (2*x**2)*(20*x**3)\nReplacing (2*x**2)*(20*x**3 + 21*x**2 + 71*x) with (71*x)*(2*x**2) + (2*x**2)*(21*x**2) + (2*x**2)*(20*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (71*x)*(2*x**2) + (71*x)*(-27) + (2*x**2)*(21*x**2) + (2*x**2)*(20*x**3) + (21*x**2)*(-27) + (20*x**3)*(-27)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (20*x**3)*-27 = -540*x**3\n (20*x**3)*(2*x**2) = 40*x**5\n (21*x**2)*-27 = -567*x**2\n (21*x**2)*(2*x**2) = 42*x**4\n (71*x)*-27 = -1917*x\n (71*x)*(2*x**2) = 142*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 40*x**5 + 42*x**4 - 540*x**3 + 142*x**3 - 567*x**2 - 1917*x\nCombining like terms, got 40*x**5 + 42*x**4 - 398*x**3 - 567*x**2 - 1917*x\n#Step 6:\nCurrent expression: 40*x**5 + 42*x**4 - 398*x**3 - 567*x**2 - 1917*x\nNo more calculations needed.\n40*x**5 + 42*x**4 - 398*x**3 - 567*x**2 - 1917*x", "generated_answer": "40*x**5 + 42*x**4 - 398*x**3 - 567*x**2 - 1917*x", "step_length": 6} {"cot_id": "d8ae152351c8228c28a804cedfcffeb27053dbc7118e84da3a71ec375b11b84b", "datapoint": {"question": "Calculate the following: (-13*x**3 + 26*x**2)*(-7*x**2 - 8*x - 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "91*x**5 - 78*x**4 + 104*x**3 - 624*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 86, "polynomial_expr": "(-13*x**3 + 26*x**2)*(-7*x**2 - 8*x - 24)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-13*x**3 + 26*x**2)*(-7*x**2 - 8*x - 24)\nExpanding the part (-13*x**3 + 26*x**2) using the distributive property, and we got: (26*x**2)*(-7*x**2 - 8*x - 24) + (-13*x**3)*(-7*x**2 - 8*x - 24)\n#Step 2:\nCurrent expression: (26*x**2)*(-7*x**2 - 8*x - 24) + (-13*x**3)*(-7*x**2 - 8*x - 24)\nSimplifying the partial expression: (-13*x**3)*(-7*x**2 - 8*x - 24)\nExpanding the part (-7*x**2 - 8*x - 24) using the distributive property, and we got: (-8*x)*(-13*x**3) - (-1)*312*x**3 + (-7*x**2)*(-13*x**3)\nReplacing (-13*x**3)*(-7*x**2 - 8*x - 24) with (-8*x)*(-13*x**3) - (-1)*312*x**3 + (-7*x**2)*(-13*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-8*x)*(-13*x**3) - 24*(-13)*x**3 + (-7*x**2)*(-13*x**3) + (26*x**2)*(-7*x**2 - 8*x - 24)\nSimplifying the partial expression: (26*x**2)*(-7*x**2 - 8*x - 24)\nExpanding the part (-7*x**2 - 8*x - 24) using the distributive property, and we got: (-8*x)*(26*x**2) - 624*x**2 + (-7*x**2)*(26*x**2)\nReplacing (26*x**2)*(-7*x**2 - 8*x - 24) with (-8*x)*(26*x**2) - 624*x**2 + (-7*x**2)*(26*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-8*x)*(26*x**2) + (-8*x)*(-13*x**3) - 24*(-13)*x**3 - 24*26*x**2 + (-7*x**2)*(26*x**2) + (-7*x**2)*(-13*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-8*x)*(-13*x**3) = 104*x**4\n (-8*x)*(26*x**2) = -208*x**3\n (-7*x**2)*(-13*x**3) = 91*x**5\n (-7*x**2)*(26*x**2) = -182*x**4\n -24*-13*x**3 = 312*x**3\n -24*26*x**2 = -624*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 91*x**5 - 182*x**4 + 104*x**4 - 208*x**3 + 312*x**3 - 624*x**2\nCombining like terms, got 91*x**5 - 78*x**4 + 104*x**3 - 624*x**2\n#Step 6:\nCurrent expression: 91*x**5 - 78*x**4 + 104*x**3 - 624*x**2\nNo more calculations needed.\n91*x**5 - 78*x**4 + 104*x**3 - 624*x**2", "generated_answer": "91*x**5 - 78*x**4 + 104*x**3 - 624*x**2", "step_length": 6} {"cot_id": "e41d3304c794c8b42ce20e4cf57c247a802bba6f124c2f0db5c3cf1199d7805d", "datapoint": {"question": "Calculate the following: (9*z**2 + 58)*(45*z**2 - 22)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "405*z**4 + 2412*z**2 - 1276", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 87, "polynomial_expr": "(9*z**2 + 58)*(45*z**2 - 22)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9*z**2 + 58)*(45*z**2 - 22)\nExpanding the part (45*z**2 - 22) using the distributive property, and we got: (45*z**2)*(9*z**2 + 58) - 22*(9*z**2 + 58)\n#Step 2:\nCurrent expression: (45*z**2)*(9*z**2 + 58) - 22*(9*z**2 + 58)\nSimplifying the partial expression: -22*(9*z**2 + 58)\nExpanding the part (9*z**2 + 58) using the distributive property, and we got: (9*z**2)*(-22) + 58*(-22)\nReplacing -22*(9*z**2 + 58) with (9*z**2)*(-22) + 58*(-22) in the overall expression.\n#Step 3:\nCurrent expression: (9*z**2)*(-22) + (45*z**2)*(9*z**2 + 58) - 1276\nSimplifying the partial expression: (45*z**2)*(9*z**2 + 58)\nExpanding the part (9*z**2 + 58) using the distributive property, and we got: 58*(45*z**2) + (9*z**2)*(45*z**2)\nReplacing (45*z**2)*(9*z**2 + 58) with 58*(45*z**2) + (9*z**2)*(45*z**2) in the overall expression.\n#Step 4:\nCurrent expression: 58*45*z**2 + (9*z**2)*(45*z**2) + (9*z**2)*(-22) - 1276\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (9*z**2)*-22 = -198*z**2\n (9*z**2)*(45*z**2) = 405*z**4\n 58*45*z**2 = 2610*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 405*z**4 - 198*z**2 + 2610*z**2 - 1276\nCombining like terms, got 405*z**4 + 2412*z**2 - 1276\n#Step 6:\nCurrent expression: 405*z**4 + 2412*z**2 - 1276\nNo more calculations needed.\n405*z**4 + 2412*z**2 - 1276", "generated_answer": "405*z**4 + 2412*z**2 - 1276", "step_length": 6} {"cot_id": "97d5a3694ec37cf1ec3d61559adbd999bf7ad051fa4be98f22063c144fb3611c", "datapoint": {"question": "Calculate the following: (48*z**2 - 2*z + 22)*(34*z**3 - 2*z**2 - 49*z + 42)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1632*z**5 - 164*z**4 - 1600*z**3 + 2070*z**2 - 1162*z + 924", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 88, "polynomial_expr": "(48*z**2 - 2*z + 22)*(34*z**3 - 2*z**2 - 49*z + 42)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (48*z**2 - 2*z + 22)*(34*z**3 - 2*z**2 - 49*z + 42)\nExpanding the part (48*z**2 - 2*z + 22) using the distributive property, and we got: (-2*z)*(34*z**3 - 2*z**2 - 49*z + 42) + (48*z**2)*(34*z**3 - 2*z**2 - 49*z + 42) + 22*(34*z**3 - 2*z**2 - 49*z + 42)\n#Step 2:\nCurrent expression: (-2*z)*(34*z**3 - 2*z**2 - 49*z + 42) + (48*z**2)*(34*z**3 - 2*z**2 - 49*z + 42) + 22*(34*z**3 - 2*z**2 - 49*z + 42)\nSimplifying the partial expression: 22*(34*z**3 - 2*z**2 - 49*z + 42)\nExpanding the part (34*z**3 - 2*z**2 - 49*z + 42) using the distributive property, and we got: -49*z*22 - 2*z**2*22 + (34*z**3)*22 + 42*22\nReplacing 22*(34*z**3 - 2*z**2 - 49*z + 42) with -49*z*22 - 2*z**2*22 + (34*z**3)*22 + 42*22 in the overall expression.\n#Step 3:\nCurrent expression: -49*z*22 + (-2*z)*(34*z**3 - 2*z**2 - 49*z + 42) - 2*z**2*22 + (48*z**2)*(34*z**3 - 2*z**2 - 49*z + 42) + (34*z**3)*22 + 924\nSimplifying the partial expression: (-2*z)*(34*z**3 - 2*z**2 - 49*z + 42)\nExpanding the part (34*z**3 - 2*z**2 - 49*z + 42) using the distributive property, and we got: (-49*z)*(-2*z) + (-2*z)*(-2*z**2) + (-2*z)*(34*z**3) + 42*(-2*z)\nReplacing (-2*z)*(34*z**3 - 2*z**2 - 49*z + 42) with (-49*z)*(-2*z) + (-2*z)*(-2*z**2) + (-2*z)*(34*z**3) + 42*(-2*z) in the overall expression.\n#Step 4:\nCurrent expression: (-49*z)*(-2*z) - 49*z*22 + (-2*z)*(-2*z**2) + (-2*z)*(34*z**3) + 42*(-2)*z - 2*z**2*22 + (48*z**2)*(34*z**3 - 2*z**2 - 49*z + 42) + (34*z**3)*22 + 924\nSimplifying the partial expression: (48*z**2)*(34*z**3 - 2*z**2 - 49*z + 42)\nExpanding the part (34*z**3 - 2*z**2 - 49*z + 42) using the distributive property, and we got: (-49*z)*(48*z**2) + 42*(48*z**2) + (-2*z**2)*(48*z**2) + (48*z**2)*(34*z**3)\nReplacing (48*z**2)*(34*z**3 - 2*z**2 - 49*z + 42) with (-49*z)*(48*z**2) + 42*(48*z**2) + (-2*z**2)*(48*z**2) + (48*z**2)*(34*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-49*z)*(-2*z) + (-49*z)*(48*z**2) - 49*z*22 + (-2*z)*(-2*z**2) + (-2*z)*(34*z**3) + 42*48*z**2 + 42*(-2)*z + (-2*z**2)*(48*z**2) - 2*z**2*22 + (48*z**2)*(34*z**3) + (34*z**3)*22 + 924\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*z)*22 = -1078*z\n (-49*z)*(-2*z) = 98*z**2\n (-49*z)*(48*z**2) = -2352*z**3\n (-2*z**2)*22 = -44*z**2\n (-2*z**2)*(-2*z) = 4*z**3\n (-2*z**2)*(48*z**2) = -96*z**4\n (34*z**3)*22 = 748*z**3\n (34*z**3)*(-2*z) = -68*z**4\n (34*z**3)*(48*z**2) = 1632*z**5\n 42*-2*z = -84*z\n 42*48*z**2 = 2016*z**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1632*z**5 - 96*z**4 - 68*z**4 - 2352*z**3 + 4*z**3 + 748*z**3 - 44*z**2 + 98*z**2 + 2016*z**2 - 1078*z - 84*z + 924\nCombining like terms, got 1632*z**5 - 164*z**4 - 1600*z**3 + 2070*z**2 - 1162*z + 924\n#Step 7:\nCurrent expression: 1632*z**5 - 164*z**4 - 1600*z**3 + 2070*z**2 - 1162*z + 924\nNo more calculations needed.\n1632*z**5 - 164*z**4 - 1600*z**3 + 2070*z**2 - 1162*z + 924", "generated_answer": "1632*z**5 - 164*z**4 - 1600*z**3 + 2070*z**2 - 1162*z + 924", "step_length": 7} {"cot_id": "e86a9aaf57aa05925b26e5d18c7da4b1bbdc49e8da83abb8c79048163f9d2b32", "datapoint": {"question": "Calculate the following: (107 - 48*y**3)*(14*y**3 + 9*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-672*y**6 - 432*y**5 + 1498*y**3 + 963*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 89, "polynomial_expr": "(107 - 48*y**3)*(14*y**3 + 9*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (107 - 48*y**3)*(14*y**3 + 9*y**2)\nExpanding the part (107 - 48*y**3) using the distributive property, and we got: (-48*y**3)*(14*y**3 + 9*y**2) + 107*(14*y**3 + 9*y**2)\n#Step 2:\nCurrent expression: (-48*y**3)*(14*y**3 + 9*y**2) + 107*(14*y**3 + 9*y**2)\nSimplifying the partial expression: 107*(14*y**3 + 9*y**2)\nExpanding the part (14*y**3 + 9*y**2) using the distributive property, and we got: (9*y**2)*107 + (14*y**3)*107\nReplacing 107*(14*y**3 + 9*y**2) with (9*y**2)*107 + (14*y**3)*107 in the overall expression.\n#Step 3:\nCurrent expression: (9*y**2)*107 + (-48*y**3)*(14*y**3 + 9*y**2) + (14*y**3)*107\nSimplifying the partial expression: (-48*y**3)*(14*y**3 + 9*y**2)\nExpanding the part (14*y**3 + 9*y**2) using the distributive property, and we got: (9*y**2)*(-48*y**3) + (-48*y**3)*(14*y**3)\nReplacing (-48*y**3)*(14*y**3 + 9*y**2) with (9*y**2)*(-48*y**3) + (-48*y**3)*(14*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (9*y**2)*(-48*y**3) + (9*y**2)*107 + (-48*y**3)*(14*y**3) + (14*y**3)*107\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (9*y**2)*107 = 963*y**2\n (9*y**2)*(-48*y**3) = -432*y**5\n (14*y**3)*107 = 1498*y**3\n (14*y**3)*(-48*y**3) = -672*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -672*y**6 - 432*y**5 + 1498*y**3 + 963*y**2\nNo more calculations needed.\n-672*y**6 - 432*y**5 + 1498*y**3 + 963*y**2", "generated_answer": "-672*y**6 - 432*y**5 + 1498*y**3 + 963*y**2", "step_length": 5} {"cot_id": "c1cbd4be180950fcd953356993285c5f8cf67ff59b874dca81cb83ac3c23d786", "datapoint": {"question": "Calculate the following: (4 - 15*y**3)*(32*y**2 + 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-480*y**5 - 255*y**3 + 128*y**2 + 68", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 90, "polynomial_expr": "(4 - 15*y**3)*(32*y**2 + 17)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (4 - 15*y**3)*(32*y**2 + 17)\nExpanding the part (4 - 15*y**3) using the distributive property, and we got: (-15*y**3)*(32*y**2 + 17) + 4*(32*y**2 + 17)\n#Step 2:\nCurrent expression: (-15*y**3)*(32*y**2 + 17) + 4*(32*y**2 + 17)\nSimplifying the partial expression: 4*(32*y**2 + 17)\nExpanding the part (32*y**2 + 17) using the distributive property, and we got: (32*y**2)*4 + 17*4\nReplacing 4*(32*y**2 + 17) with (32*y**2)*4 + 17*4 in the overall expression.\n#Step 3:\nCurrent expression: (32*y**2)*4 + (-15*y**3)*(32*y**2 + 17) + 68\nSimplifying the partial expression: (-15*y**3)*(32*y**2 + 17)\nExpanding the part (32*y**2 + 17) using the distributive property, and we got: 17*(-15*y**3) + (32*y**2)*(-15*y**3)\nReplacing (-15*y**3)*(32*y**2 + 17) with 17*(-15*y**3) + (32*y**2)*(-15*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 17*(-15)*y**3 + (32*y**2)*(-15*y**3) + (32*y**2)*4 + 68\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (32*y**2)*4 = 128*y**2\n (32*y**2)*(-15*y**3) = -480*y**5\n 17*-15*y**3 = -255*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -480*y**5 - 255*y**3 + 128*y**2 + 68\nNo more calculations needed.\n-480*y**5 - 255*y**3 + 128*y**2 + 68", "generated_answer": "-480*y**5 - 255*y**3 + 128*y**2 + 68", "step_length": 5} {"cot_id": "0021969a67c46ac036211da3d85ad8b1768ea3071483ec2778abee9c3541a8f5", "datapoint": {"question": "Simplify this expression: (-11*y**3 + y**2)*(45*y**3 + 40*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-495*y**6 + 45*y**5 - 440*y**4 + 40*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 91, "polynomial_expr": "(-11*y**3 + y**2)*(45*y**3 + 40*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-11*y**3 + y**2)*(45*y**3 + 40*y)\nExpanding the part (-11*y**3 + y**2) using the distributive property, and we got: y**2*(45*y**3 + 40*y) + (-11*y**3)*(45*y**3 + 40*y)\n#Step 2:\nCurrent expression: y**2*(45*y**3 + 40*y) + (-11*y**3)*(45*y**3 + 40*y)\nSimplifying the partial expression: y**2*(45*y**3 + 40*y)\nExpanding the part (45*y**3 + 40*y) using the distributive property, and we got: (40*y)*y**2 + y**2*(45*y**3)\nReplacing y**2*(45*y**3 + 40*y) with (40*y)*y**2 + y**2*(45*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (40*y)*y**2 + y**2*(45*y**3) + (-11*y**3)*(45*y**3 + 40*y)\nSimplifying the partial expression: (-11*y**3)*(45*y**3 + 40*y)\nExpanding the part (45*y**3 + 40*y) using the distributive property, and we got: (40*y)*(-11*y**3) + (-11*y**3)*(45*y**3)\nReplacing (-11*y**3)*(45*y**3 + 40*y) with (40*y)*(-11*y**3) + (-11*y**3)*(45*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (40*y)*y**2 + y**2*(45*y**3) + (40*y)*(-11*y**3) + (-11*y**3)*(45*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (40*y)*y**2 = 40*y**3\n (40*y)*(-11*y**3) = -440*y**4\n (45*y**3)*y**2 = 45*y**5\n (45*y**3)*(-11*y**3) = -495*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -495*y**6 + 45*y**5 - 440*y**4 + 40*y**3\nNo more calculations needed.\n-495*y**6 + 45*y**5 - 440*y**4 + 40*y**3", "generated_answer": "-495*y**6 + 45*y**5 - 440*y**4 + 40*y**3", "step_length": 5} {"cot_id": "591875c90ba0029ae681b6aa265b8bfbb474c0e9c0aa3e68f9c70e458daf1764", "datapoint": {"question": "Calculate the following: -14*y*(-33*y**2 - 61)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "462*y**3 + 854*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 92, "polynomial_expr": "-14*y*(-33*y**2 - 61)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -14*y*(-33*y**2 - 61)\nExpanding the part (-33*y**2 - 61) using the distributive property, and we got: (-14*y)*(-33*y**2) - (-1)*854*y\n#Step 2:\nCurrent expression: (-14*y)*(-33*y**2) - (-1)*854*y\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -61*(-14*y) = 854*y\n (-33*y**2)*(-14*y) = 462*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 462*y**3 + 854*y\nNo more calculations needed.\n462*y**3 + 854*y", "generated_answer": "462*y**3 + 854*y", "step_length": 3} {"cot_id": "3dc919dbed32c3f903133af61b5aac6a868765149bb89cbba9674508635cad0c", "datapoint": {"question": "Simplify this expression: (-18*z**3 + 19*z)*(-46*z**3 - 59*z - 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "828*z**6 + 188*z**4 + 18*z**3 - 1121*z**2 - 19*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 93, "polynomial_expr": "(-18*z**3 + 19*z)*(-46*z**3 - 59*z - 1)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-18*z**3 + 19*z)*(-46*z**3 - 59*z - 1)\nExpanding the part (-18*z**3 + 19*z) using the distributive property, and we got: (19*z)*(-46*z**3 - 59*z - 1) + (-18*z**3)*(-46*z**3 - 59*z - 1)\n#Step 2:\nCurrent expression: (19*z)*(-46*z**3 - 59*z - 1) + (-18*z**3)*(-46*z**3 - 59*z - 1)\nSimplifying the partial expression: (-18*z**3)*(-46*z**3 - 59*z - 1)\nExpanding the part (-46*z**3 - 59*z - 1) using the distributive property, and we got: (-59*z)*(-18*z**3) - (-1)*18*z**3 + (-46*z**3)*(-18*z**3)\nReplacing (-18*z**3)*(-46*z**3 - 59*z - 1) with (-59*z)*(-18*z**3) - (-1)*18*z**3 + (-46*z**3)*(-18*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-59*z)*(-18*z**3) - 1*(-18)*z**3 + (19*z)*(-46*z**3 - 59*z - 1) + (-46*z**3)*(-18*z**3)\nSimplifying the partial expression: (19*z)*(-46*z**3 - 59*z - 1)\nExpanding the part (-46*z**3 - 59*z - 1) using the distributive property, and we got: (-59*z)*(19*z) - 19*z + (19*z)*(-46*z**3)\nReplacing (19*z)*(-46*z**3 - 59*z - 1) with (-59*z)*(19*z) - 19*z + (19*z)*(-46*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-59*z)*(19*z) + (-59*z)*(-18*z**3) - 1*(-18)*z**3 - 1*19*z + (19*z)*(-46*z**3) + (-46*z**3)*(-18*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-59*z)*(-18*z**3) = 1062*z**4\n (-59*z)*(19*z) = -1121*z**2\n (-46*z**3)*(-18*z**3) = 828*z**6\n (-46*z**3)*(19*z) = -874*z**4\n -1*-18*z**3 = 18*z**3\n -1*19*z = -19*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 828*z**6 - 874*z**4 + 1062*z**4 + 18*z**3 - 1121*z**2 - 19*z\nCombining like terms, got 828*z**6 + 188*z**4 + 18*z**3 - 1121*z**2 - 19*z\n#Step 6:\nCurrent expression: 828*z**6 + 188*z**4 + 18*z**3 - 1121*z**2 - 19*z\nNo more calculations needed.\n828*z**6 + 188*z**4 + 18*z**3 - 1121*z**2 - 19*z", "generated_answer": "828*z**6 + 188*z**4 + 18*z**3 - 1121*z**2 - 19*z", "step_length": 6} {"cot_id": "778dcda8daf27398d61ce254c5e1f7b656871e6e817f34abdfa0fce522d41fc8", "datapoint": {"question": "Simplify this expression: (-4*z**3 - 2*z**2)*(3*z**3 + 31*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-12*z**6 - 6*z**5 - 124*z**4 - 62*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 94, "polynomial_expr": "(-4*z**3 - 2*z**2)*(3*z**3 + 31*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-4*z**3 - 2*z**2)*(3*z**3 + 31*z)\nExpanding the part (-4*z**3 - 2*z**2) using the distributive property, and we got: (-2*z**2)*(3*z**3 + 31*z) + (-4*z**3)*(3*z**3 + 31*z)\n#Step 2:\nCurrent expression: (-2*z**2)*(3*z**3 + 31*z) + (-4*z**3)*(3*z**3 + 31*z)\nSimplifying the partial expression: (-4*z**3)*(3*z**3 + 31*z)\nExpanding the part (3*z**3 + 31*z) using the distributive property, and we got: (31*z)*(-4*z**3) + (-4*z**3)*(3*z**3)\nReplacing (-4*z**3)*(3*z**3 + 31*z) with (31*z)*(-4*z**3) + (-4*z**3)*(3*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (31*z)*(-4*z**3) + (-2*z**2)*(3*z**3 + 31*z) + (-4*z**3)*(3*z**3)\nSimplifying the partial expression: (-2*z**2)*(3*z**3 + 31*z)\nExpanding the part (3*z**3 + 31*z) using the distributive property, and we got: (31*z)*(-2*z**2) + (-2*z**2)*(3*z**3)\nReplacing (-2*z**2)*(3*z**3 + 31*z) with (31*z)*(-2*z**2) + (-2*z**2)*(3*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (31*z)*(-2*z**2) + (31*z)*(-4*z**3) + (-2*z**2)*(3*z**3) + (-4*z**3)*(3*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (3*z**3)*(-4*z**3) = -12*z**6\n (3*z**3)*(-2*z**2) = -6*z**5\n (31*z)*(-4*z**3) = -124*z**4\n (31*z)*(-2*z**2) = -62*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -12*z**6 - 6*z**5 - 124*z**4 - 62*z**3\nNo more calculations needed.\n-12*z**6 - 6*z**5 - 124*z**4 - 62*z**3", "generated_answer": "-12*z**6 - 6*z**5 - 124*z**4 - 62*z**3", "step_length": 5} {"cot_id": "1344e1a81f11ad1c2cf5e1e60fcae4cb73a7707c11e34e0b94eb003223ff9a34", "datapoint": {"question": "Simplify this expression: (5 - 34*x**2)*(33*x**2 + 23*x - 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1122*x**4 - 782*x**3 + 879*x**2 + 115*x - 105", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 95, "polynomial_expr": "(5 - 34*x**2)*(33*x**2 + 23*x - 21)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (5 - 34*x**2)*(33*x**2 + 23*x - 21)\nExpanding the part (5 - 34*x**2) using the distributive property, and we got: (-34*x**2)*(33*x**2 + 23*x - 21) + 5*(33*x**2 + 23*x - 21)\n#Step 2:\nCurrent expression: (-34*x**2)*(33*x**2 + 23*x - 21) + 5*(33*x**2 + 23*x - 21)\nSimplifying the partial expression: 5*(33*x**2 + 23*x - 21)\nExpanding the part (33*x**2 + 23*x - 21) using the distributive property, and we got: (23*x)*5 + (33*x**2)*5 - 21*5\nReplacing 5*(33*x**2 + 23*x - 21) with (23*x)*5 + (33*x**2)*5 - 21*5 in the overall expression.\n#Step 3:\nCurrent expression: (23*x)*5 + (-34*x**2)*(33*x**2 + 23*x - 21) + (33*x**2)*5 - 105\nSimplifying the partial expression: (-34*x**2)*(33*x**2 + 23*x - 21)\nExpanding the part (33*x**2 + 23*x - 21) using the distributive property, and we got: -(-1)*714*x**2 + (23*x)*(-34*x**2) + (-34*x**2)*(33*x**2)\nReplacing (-34*x**2)*(33*x**2 + 23*x - 21) with -(-1)*714*x**2 + (23*x)*(-34*x**2) + (-34*x**2)*(33*x**2) in the overall expression.\n#Step 4:\nCurrent expression: -21*(-34)*x**2 + (23*x)*(-34*x**2) + (23*x)*5 + (-34*x**2)*(33*x**2) + (33*x**2)*5 - 105\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (23*x)*5 = 115*x\n (23*x)*(-34*x**2) = -782*x**3\n (33*x**2)*5 = 165*x**2\n (33*x**2)*(-34*x**2) = -1122*x**4\n -21*-34*x**2 = 714*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1122*x**4 - 782*x**3 + 165*x**2 + 714*x**2 + 115*x - 105\nCombining like terms, got -1122*x**4 - 782*x**3 + 879*x**2 + 115*x - 105\n#Step 6:\nCurrent expression: -1122*x**4 - 782*x**3 + 879*x**2 + 115*x - 105\nNo more calculations needed.\n-1122*x**4 - 782*x**3 + 879*x**2 + 115*x - 105", "generated_answer": "-1122*x**4 - 782*x**3 + 879*x**2 + 115*x - 105", "step_length": 6} {"cot_id": "b8aa9dc5f64bf20b4c8128078c3f85da49e98cd641a799a8fddbdb5c4387aa1f", "datapoint": {"question": "Simplify this expression: (-45*x**2 - 47)*(45*x**3 - 35*x + 65)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2025*x**5 - 540*x**3 - 2925*x**2 + 1645*x - 3055", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 96, "polynomial_expr": "(-45*x**2 - 47)*(45*x**3 - 35*x + 65)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-45*x**2 - 47)*(45*x**3 - 35*x + 65)\nExpanding the part (-45*x**2 - 47) using the distributive property, and we got: (-45*x**2)*(45*x**3 - 35*x + 65) - 47*(45*x**3 - 35*x + 65)\n#Step 2:\nCurrent expression: (-45*x**2)*(45*x**3 - 35*x + 65) - 47*(45*x**3 - 35*x + 65)\nSimplifying the partial expression: -47*(45*x**3 - 35*x + 65)\nExpanding the part (45*x**3 - 35*x + 65) using the distributive property, and we got: -35*x*(-47) + (45*x**3)*(-47) + 65*(-47)\nReplacing -47*(45*x**3 - 35*x + 65) with -35*x*(-47) + (45*x**3)*(-47) + 65*(-47) in the overall expression.\n#Step 3:\nCurrent expression: -35*x*(-47) + (-45*x**2)*(45*x**3 - 35*x + 65) + (45*x**3)*(-47) - 3055\nSimplifying the partial expression: (-45*x**2)*(45*x**3 - 35*x + 65)\nExpanding the part (45*x**3 - 35*x + 65) using the distributive property, and we got: (-35*x)*(-45*x**2) + 65*(-45*x**2) + (-45*x**2)*(45*x**3)\nReplacing (-45*x**2)*(45*x**3 - 35*x + 65) with (-35*x)*(-45*x**2) + 65*(-45*x**2) + (-45*x**2)*(45*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-35*x)*(-45*x**2) - 35*x*(-47) + 65*(-45)*x**2 + (-45*x**2)*(45*x**3) + (45*x**3)*(-47) - 3055\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*x)*-47 = 1645*x\n (-35*x)*(-45*x**2) = 1575*x**3\n (45*x**3)*-47 = -2115*x**3\n (45*x**3)*(-45*x**2) = -2025*x**5\n 65*-45*x**2 = -2925*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2025*x**5 - 2115*x**3 + 1575*x**3 - 2925*x**2 + 1645*x - 3055\nCombining like terms, got -2025*x**5 - 540*x**3 - 2925*x**2 + 1645*x - 3055\n#Step 6:\nCurrent expression: -2025*x**5 - 540*x**3 - 2925*x**2 + 1645*x - 3055\nNo more calculations needed.\n-2025*x**5 - 540*x**3 - 2925*x**2 + 1645*x - 3055", "generated_answer": "-2025*x**5 - 540*x**3 - 2925*x**2 + 1645*x - 3055", "step_length": 6} {"cot_id": "aba0f8c78cba41a0d6b191f5a0d27f3c7909a2408fd624d018815f44c20b79ee", "datapoint": {"question": "Simplify this expression: (-14*x**2 - 31)*(-22*x**2 + 36*x + 67)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "308*x**4 - 504*x**3 - 256*x**2 - 1116*x - 2077", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 97, "polynomial_expr": "(-14*x**2 - 31)*(-22*x**2 + 36*x + 67)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-14*x**2 - 31)*(-22*x**2 + 36*x + 67)\nExpanding the part (-14*x**2 - 31) using the distributive property, and we got: (-14*x**2)*(-22*x**2 + 36*x + 67) - 31*(-22*x**2 + 36*x + 67)\n#Step 2:\nCurrent expression: (-14*x**2)*(-22*x**2 + 36*x + 67) - 31*(-22*x**2 + 36*x + 67)\nSimplifying the partial expression: -31*(-22*x**2 + 36*x + 67)\nExpanding the part (-22*x**2 + 36*x + 67) using the distributive property, and we got: (36*x)*(-31) - 22*x**2*(-31) + 67*(-31)\nReplacing -31*(-22*x**2 + 36*x + 67) with (36*x)*(-31) - 22*x**2*(-31) + 67*(-31) in the overall expression.\n#Step 3:\nCurrent expression: (36*x)*(-31) - 22*x**2*(-31) + (-14*x**2)*(-22*x**2 + 36*x + 67) - 2077\nSimplifying the partial expression: (-14*x**2)*(-22*x**2 + 36*x + 67)\nExpanding the part (-22*x**2 + 36*x + 67) using the distributive property, and we got: 67*(-14*x**2) + (36*x)*(-14*x**2) + (-22*x**2)*(-14*x**2)\nReplacing (-14*x**2)*(-22*x**2 + 36*x + 67) with 67*(-14*x**2) + (36*x)*(-14*x**2) + (-22*x**2)*(-14*x**2) in the overall expression.\n#Step 4:\nCurrent expression: 67*(-14)*x**2 + (36*x)*(-14*x**2) + (36*x)*(-31) + (-22*x**2)*(-14*x**2) - 22*x**2*(-31) - 2077\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*x**2)*-31 = 682*x**2\n (-22*x**2)*(-14*x**2) = 308*x**4\n (36*x)*-31 = -1116*x\n (36*x)*(-14*x**2) = -504*x**3\n 67*-14*x**2 = -938*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 308*x**4 - 504*x**3 - 938*x**2 + 682*x**2 - 1116*x - 2077\nCombining like terms, got 308*x**4 - 504*x**3 - 256*x**2 - 1116*x - 2077\n#Step 6:\nCurrent expression: 308*x**4 - 504*x**3 - 256*x**2 - 1116*x - 2077\nNo more calculations needed.\n308*x**4 - 504*x**3 - 256*x**2 - 1116*x - 2077", "generated_answer": "308*x**4 - 504*x**3 - 256*x**2 - 1116*x - 2077", "step_length": 6} {"cot_id": "841af3e60ac93598632bfe7d950d77383be8ebb47f9e784ad0efb72aa6456bd7", "datapoint": {"question": "Simplify this expression: (46*x**3 + 17*x)*(27*x**3 + 20*x + 15)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1242*x**6 + 1379*x**4 + 690*x**3 + 340*x**2 + 255*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 98, "polynomial_expr": "(46*x**3 + 17*x)*(27*x**3 + 20*x + 15)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (46*x**3 + 17*x)*(27*x**3 + 20*x + 15)\nExpanding the part (46*x**3 + 17*x) using the distributive property, and we got: (17*x)*(27*x**3 + 20*x + 15) + (46*x**3)*(27*x**3 + 20*x + 15)\n#Step 2:\nCurrent expression: (17*x)*(27*x**3 + 20*x + 15) + (46*x**3)*(27*x**3 + 20*x + 15)\nSimplifying the partial expression: (17*x)*(27*x**3 + 20*x + 15)\nExpanding the part (27*x**3 + 20*x + 15) using the distributive property, and we got: 15*(17*x) + (17*x)*(20*x) + (17*x)*(27*x**3)\nReplacing (17*x)*(27*x**3 + 20*x + 15) with 15*(17*x) + (17*x)*(20*x) + (17*x)*(27*x**3) in the overall expression.\n#Step 3:\nCurrent expression: 15*17*x + (17*x)*(20*x) + (17*x)*(27*x**3) + (46*x**3)*(27*x**3 + 20*x + 15)\nSimplifying the partial expression: (46*x**3)*(27*x**3 + 20*x + 15)\nExpanding the part (27*x**3 + 20*x + 15) using the distributive property, and we got: 15*(46*x**3) + (20*x)*(46*x**3) + (27*x**3)*(46*x**3)\nReplacing (46*x**3)*(27*x**3 + 20*x + 15) with 15*(46*x**3) + (20*x)*(46*x**3) + (27*x**3)*(46*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 15*46*x**3 + 15*17*x + (17*x)*(20*x) + (17*x)*(27*x**3) + (20*x)*(46*x**3) + (27*x**3)*(46*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (20*x)*(17*x) = 340*x**2\n (20*x)*(46*x**3) = 920*x**4\n (27*x**3)*(17*x) = 459*x**4\n (27*x**3)*(46*x**3) = 1242*x**6\n 15*17*x = 255*x\n 15*46*x**3 = 690*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1242*x**6 + 459*x**4 + 920*x**4 + 690*x**3 + 340*x**2 + 255*x\nCombining like terms, got 1242*x**6 + 1379*x**4 + 690*x**3 + 340*x**2 + 255*x\n#Step 6:\nCurrent expression: 1242*x**6 + 1379*x**4 + 690*x**3 + 340*x**2 + 255*x\nNo more calculations needed.\n1242*x**6 + 1379*x**4 + 690*x**3 + 340*x**2 + 255*x", "generated_answer": "1242*x**6 + 1379*x**4 + 690*x**3 + 340*x**2 + 255*x", "step_length": 6} {"cot_id": "58ba8e7c8696815c77e80d4c41dfb469fa147b6b3c2c657e53e102d37f9b6180", "datapoint": {"question": "Calculate the following: (23*z**2 - 35*z + 36)*(72*z**3 - 22*z**2 + 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1656*z**5 - 3026*z**4 + 3362*z**3 - 79*z**2 - 1085*z + 1116", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 99, "polynomial_expr": "(23*z**2 - 35*z + 36)*(72*z**3 - 22*z**2 + 31)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (23*z**2 - 35*z + 36)*(72*z**3 - 22*z**2 + 31)\nExpanding the part (72*z**3 - 22*z**2 + 31) using the distributive property, and we got: (-22*z**2)*(23*z**2 - 35*z + 36) + (72*z**3)*(23*z**2 - 35*z + 36) + 31*(23*z**2 - 35*z + 36)\n#Step 2:\nCurrent expression: (-22*z**2)*(23*z**2 - 35*z + 36) + (72*z**3)*(23*z**2 - 35*z + 36) + 31*(23*z**2 - 35*z + 36)\nSimplifying the partial expression: 31*(23*z**2 - 35*z + 36)\nExpanding the part (23*z**2 - 35*z + 36) using the distributive property, and we got: -35*z*31 + (23*z**2)*31 + 36*31\nReplacing 31*(23*z**2 - 35*z + 36) with -35*z*31 + (23*z**2)*31 + 36*31 in the overall expression.\n#Step 3:\nCurrent expression: -35*z*31 + (-22*z**2)*(23*z**2 - 35*z + 36) + (23*z**2)*31 + (72*z**3)*(23*z**2 - 35*z + 36) + 1116\nSimplifying the partial expression: (-22*z**2)*(23*z**2 - 35*z + 36)\nExpanding the part (23*z**2 - 35*z + 36) using the distributive property, and we got: (-35*z)*(-22*z**2) + 36*(-22*z**2) + (-22*z**2)*(23*z**2)\nReplacing (-22*z**2)*(23*z**2 - 35*z + 36) with (-35*z)*(-22*z**2) + 36*(-22*z**2) + (-22*z**2)*(23*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-35*z)*(-22*z**2) - 35*z*31 + 36*(-22)*z**2 + (-22*z**2)*(23*z**2) + (23*z**2)*31 + (72*z**3)*(23*z**2 - 35*z + 36) + 1116\nSimplifying the partial expression: (72*z**3)*(23*z**2 - 35*z + 36)\nExpanding the part (23*z**2 - 35*z + 36) using the distributive property, and we got: (-35*z)*(72*z**3) + 36*(72*z**3) + (23*z**2)*(72*z**3)\nReplacing (72*z**3)*(23*z**2 - 35*z + 36) with (-35*z)*(72*z**3) + 36*(72*z**3) + (23*z**2)*(72*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-35*z)*(-22*z**2) + (-35*z)*(72*z**3) - 35*z*31 + 36*72*z**3 + 36*(-22)*z**2 + (-22*z**2)*(23*z**2) + (23*z**2)*(72*z**3) + (23*z**2)*31 + 1116\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*z)*31 = -1085*z\n (-35*z)*(-22*z**2) = 770*z**3\n (-35*z)*(72*z**3) = -2520*z**4\n (23*z**2)*31 = 713*z**2\n (23*z**2)*(-22*z**2) = -506*z**4\n (23*z**2)*(72*z**3) = 1656*z**5\n 36*-22*z**2 = -792*z**2\n 36*72*z**3 = 2592*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1656*z**5 - 2520*z**4 - 506*z**4 + 770*z**3 + 2592*z**3 - 792*z**2 + 713*z**2 - 1085*z + 1116\nCombining like terms, got 1656*z**5 - 3026*z**4 + 3362*z**3 - 79*z**2 - 1085*z + 1116\n#Step 7:\nCurrent expression: 1656*z**5 - 3026*z**4 + 3362*z**3 - 79*z**2 - 1085*z + 1116\nNo more calculations needed.\n1656*z**5 - 3026*z**4 + 3362*z**3 - 79*z**2 - 1085*z + 1116", "generated_answer": "1656*z**5 - 3026*z**4 + 3362*z**3 - 79*z**2 - 1085*z + 1116", "step_length": 7} {"cot_id": "d2f5c4792660f5e685ea0deabc8f1f05aaf88c8ab912190683f332525dbd1c7c", "datapoint": {"question": "Simplify this expression: (37 - 35*z**3)*(-17*z**3 - 32*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "595*z**6 + 1120*z**4 - 629*z**3 - 1184*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 100, "polynomial_expr": "(37 - 35*z**3)*(-17*z**3 - 32*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (37 - 35*z**3)*(-17*z**3 - 32*z)\nExpanding the part (37 - 35*z**3) using the distributive property, and we got: (-35*z**3)*(-17*z**3 - 32*z) + 37*(-17*z**3 - 32*z)\n#Step 2:\nCurrent expression: (-35*z**3)*(-17*z**3 - 32*z) + 37*(-17*z**3 - 32*z)\nSimplifying the partial expression: 37*(-17*z**3 - 32*z)\nExpanding the part (-17*z**3 - 32*z) using the distributive property, and we got: -32*z*37 - 17*z**3*37\nReplacing 37*(-17*z**3 - 32*z) with -32*z*37 - 17*z**3*37 in the overall expression.\n#Step 3:\nCurrent expression: -32*z*37 + (-35*z**3)*(-17*z**3 - 32*z) - 17*z**3*37\nSimplifying the partial expression: (-35*z**3)*(-17*z**3 - 32*z)\nExpanding the part (-17*z**3 - 32*z) using the distributive property, and we got: (-32*z)*(-35*z**3) + (-35*z**3)*(-17*z**3)\nReplacing (-35*z**3)*(-17*z**3 - 32*z) with (-32*z)*(-35*z**3) + (-35*z**3)*(-17*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-32*z)*(-35*z**3) - 32*z*37 + (-35*z**3)*(-17*z**3) - 17*z**3*37\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*z)*37 = -1184*z\n (-32*z)*(-35*z**3) = 1120*z**4\n (-17*z**3)*37 = -629*z**3\n (-17*z**3)*(-35*z**3) = 595*z**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 595*z**6 + 1120*z**4 - 629*z**3 - 1184*z\nNo more calculations needed.\n595*z**6 + 1120*z**4 - 629*z**3 - 1184*z", "generated_answer": "595*z**6 + 1120*z**4 - 629*z**3 - 1184*z", "step_length": 5} {"cot_id": "cfb32752797935b65341c53076a71a11c2e5184f2f288429dec74cc060af60e8", "datapoint": {"question": "Calculate the following: (-47*x**3 - 15)*(32*x**3 + 8*x**2 - 19*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1504*x**6 - 376*x**5 + 893*x**4 - 480*x**3 - 120*x**2 + 285*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 101, "polynomial_expr": "(-47*x**3 - 15)*(32*x**3 + 8*x**2 - 19*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-47*x**3 - 15)*(32*x**3 + 8*x**2 - 19*x)\nExpanding the part (-47*x**3 - 15) using the distributive property, and we got: (-47*x**3)*(32*x**3 + 8*x**2 - 19*x) - 15*(32*x**3 + 8*x**2 - 19*x)\n#Step 2:\nCurrent expression: (-47*x**3)*(32*x**3 + 8*x**2 - 19*x) - 15*(32*x**3 + 8*x**2 - 19*x)\nSimplifying the partial expression: -15*(32*x**3 + 8*x**2 - 19*x)\nExpanding the part (32*x**3 + 8*x**2 - 19*x) using the distributive property, and we got: -19*x*(-15) + (8*x**2)*(-15) + (32*x**3)*(-15)\nReplacing -15*(32*x**3 + 8*x**2 - 19*x) with -19*x*(-15) + (8*x**2)*(-15) + (32*x**3)*(-15) in the overall expression.\n#Step 3:\nCurrent expression: -19*x*(-15) + (8*x**2)*(-15) + (-47*x**3)*(32*x**3 + 8*x**2 - 19*x) + (32*x**3)*(-15)\nSimplifying the partial expression: (-47*x**3)*(32*x**3 + 8*x**2 - 19*x)\nExpanding the part (32*x**3 + 8*x**2 - 19*x) using the distributive property, and we got: (-19*x)*(-47*x**3) + (8*x**2)*(-47*x**3) + (-47*x**3)*(32*x**3)\nReplacing (-47*x**3)*(32*x**3 + 8*x**2 - 19*x) with (-19*x)*(-47*x**3) + (8*x**2)*(-47*x**3) + (-47*x**3)*(32*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-19*x)*(-47*x**3) - 19*x*(-15) + (8*x**2)*(-47*x**3) + (8*x**2)*(-15) + (-47*x**3)*(32*x**3) + (32*x**3)*(-15)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*x)*-15 = 285*x\n (-19*x)*(-47*x**3) = 893*x**4\n (8*x**2)*-15 = -120*x**2\n (8*x**2)*(-47*x**3) = -376*x**5\n (32*x**3)*-15 = -480*x**3\n (32*x**3)*(-47*x**3) = -1504*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1504*x**6 - 376*x**5 + 893*x**4 - 480*x**3 - 120*x**2 + 285*x\nNo more calculations needed.\n-1504*x**6 - 376*x**5 + 893*x**4 - 480*x**3 - 120*x**2 + 285*x", "generated_answer": "-1504*x**6 - 376*x**5 + 893*x**4 - 480*x**3 - 120*x**2 + 285*x", "step_length": 5} {"cot_id": "20d899756d8289e327ded61746c75b046bf0f5495f389f18fea1ee6ba9124b84", "datapoint": {"question": "Calculate the following: (10*y**2 + 6)*(-27*y**3 - 16*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-270*y**5 - 322*y**3 - 96*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 102, "polynomial_expr": "(10*y**2 + 6)*(-27*y**3 - 16*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (10*y**2 + 6)*(-27*y**3 - 16*y)\nExpanding the part (10*y**2 + 6) using the distributive property, and we got: (10*y**2)*(-27*y**3 - 16*y) + 6*(-27*y**3 - 16*y)\n#Step 2:\nCurrent expression: (10*y**2)*(-27*y**3 - 16*y) + 6*(-27*y**3 - 16*y)\nSimplifying the partial expression: 6*(-27*y**3 - 16*y)\nExpanding the part (-27*y**3 - 16*y) using the distributive property, and we got: -16*y*6 - 27*y**3*6\nReplacing 6*(-27*y**3 - 16*y) with -16*y*6 - 27*y**3*6 in the overall expression.\n#Step 3:\nCurrent expression: -16*y*6 + (10*y**2)*(-27*y**3 - 16*y) - 27*y**3*6\nSimplifying the partial expression: (10*y**2)*(-27*y**3 - 16*y)\nExpanding the part (-27*y**3 - 16*y) using the distributive property, and we got: (-16*y)*(10*y**2) + (10*y**2)*(-27*y**3)\nReplacing (10*y**2)*(-27*y**3 - 16*y) with (-16*y)*(10*y**2) + (10*y**2)*(-27*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-16*y)*(10*y**2) - 16*y*6 + (10*y**2)*(-27*y**3) - 27*y**3*6\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*y**3)*6 = -162*y**3\n (-27*y**3)*(10*y**2) = -270*y**5\n (-16*y)*6 = -96*y\n (-16*y)*(10*y**2) = -160*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -270*y**5 - 162*y**3 - 160*y**3 - 96*y\nCombining like terms, got -270*y**5 - 322*y**3 - 96*y\n#Step 6:\nCurrent expression: -270*y**5 - 322*y**3 - 96*y\nNo more calculations needed.\n-270*y**5 - 322*y**3 - 96*y", "generated_answer": "-270*y**5 - 322*y**3 - 96*y", "step_length": 6} {"cot_id": "76fea3b123b9df391254a552fc81b5d474f5bd5bcec8410b27ad67ab52f8404b", "datapoint": {"question": "Calculate the following: y*(-18*y**3 + 42*y**2 + 2*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-18*y**4 + 42*y**3 + 2*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 103, "polynomial_expr": "y*(-18*y**3 + 42*y**2 + 2*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: y*(-18*y**3 + 42*y**2 + 2*y)\nExpanding the part (-18*y**3 + 42*y**2 + 2*y) using the distributive property, and we got: y*(2*y) + y*(42*y**2) + y*(-18*y**3)\n#Step 2:\nCurrent expression: y*(2*y) + y*(42*y**2) + y*(-18*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-18*y**3)*y = -18*y**4\n (2*y)*y = 2*y**2\n (42*y**2)*y = 42*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -18*y**4 + 42*y**3 + 2*y**2\nNo more calculations needed.\n-18*y**4 + 42*y**3 + 2*y**2", "generated_answer": "-18*y**4 + 42*y**3 + 2*y**2", "step_length": 3} {"cot_id": "38daa18d0c1c3751e08e5fa5171d1fd22cc899e4e4440e2880cd40a3e42c9ca2", "datapoint": {"question": "Simplify this expression: (27*x**2 - 41*x + 3)*(x**3 + 22*x + 54)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "27*x**5 - 41*x**4 + 597*x**3 + 556*x**2 - 2148*x + 162", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 104, "polynomial_expr": "(27*x**2 - 41*x + 3)*(x**3 + 22*x + 54)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*x**2 - 41*x + 3)*(x**3 + 22*x + 54)\nExpanding the part (27*x**2 - 41*x + 3) using the distributive property, and we got: (-41*x)*(x**3 + 22*x + 54) + (27*x**2)*(x**3 + 22*x + 54) + 3*(x**3 + 22*x + 54)\n#Step 2:\nCurrent expression: (-41*x)*(x**3 + 22*x + 54) + (27*x**2)*(x**3 + 22*x + 54) + 3*(x**3 + 22*x + 54)\nSimplifying the partial expression: 3*(x**3 + 22*x + 54)\nExpanding the part (x**3 + 22*x + 54) using the distributive property, and we got: x**3*3 + (22*x)*3 + 54*3\nReplacing 3*(x**3 + 22*x + 54) with x**3*3 + (22*x)*3 + 54*3 in the overall expression.\n#Step 3:\nCurrent expression: (-41*x)*(x**3 + 22*x + 54) + x**3*3 + (22*x)*3 + (27*x**2)*(x**3 + 22*x + 54) + 162\nSimplifying the partial expression: (-41*x)*(x**3 + 22*x + 54)\nExpanding the part (x**3 + 22*x + 54) using the distributive property, and we got: (-41*x)*x**3 + (-41*x)*(22*x) + 54*(-41*x)\nReplacing (-41*x)*(x**3 + 22*x + 54) with (-41*x)*x**3 + (-41*x)*(22*x) + 54*(-41*x) in the overall expression.\n#Step 4:\nCurrent expression: (-41*x)*x**3 + (-41*x)*(22*x) + x**3*3 + 54*(-41)*x + (22*x)*3 + (27*x**2)*(x**3 + 22*x + 54) + 162\nSimplifying the partial expression: (27*x**2)*(x**3 + 22*x + 54)\nExpanding the part (x**3 + 22*x + 54) using the distributive property, and we got: (27*x**2)*x**3 + 54*(27*x**2) + (22*x)*(27*x**2)\nReplacing (27*x**2)*(x**3 + 22*x + 54) with (27*x**2)*x**3 + 54*(27*x**2) + (22*x)*(27*x**2) in the overall expression.\n#Step 5:\nCurrent expression: (-41*x)*x**3 + (-41*x)*(22*x) + (27*x**2)*x**3 + x**3*3 + 54*27*x**2 + 54*(-41)*x + (22*x)*(27*x**2) + (22*x)*3 + 162\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n x**3*3 = 3*x**3\n x**3*(-41*x) = -41*x**4\n x**3*(27*x**2) = 27*x**5\n (22*x)*3 = 66*x\n (22*x)*(-41*x) = -902*x**2\n (22*x)*(27*x**2) = 594*x**3\n 54*-41*x = -2214*x\n 54*27*x**2 = 1458*x**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 27*x**5 - 41*x**4 + 3*x**3 + 594*x**3 - 902*x**2 + 1458*x**2 - 2214*x + 66*x + 162\nCombining like terms, got 27*x**5 - 41*x**4 + 597*x**3 + 556*x**2 - 2148*x + 162\n#Step 7:\nCurrent expression: 27*x**5 - 41*x**4 + 597*x**3 + 556*x**2 - 2148*x + 162\nNo more calculations needed.\n27*x**5 - 41*x**4 + 597*x**3 + 556*x**2 - 2148*x + 162", "generated_answer": "27*x**5 - 41*x**4 + 597*x**3 + 556*x**2 - 2148*x + 162", "step_length": 7} {"cot_id": "1e94e9712b0ab412d9c8fc3b699057696377bf4c90230c0a25eb4a502804cd11", "datapoint": {"question": "Simplify this expression: (47 - 27*z)*(-30*z**3 - 29*z**2 - 48*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "810*z**4 - 627*z**3 - 67*z**2 - 2256*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 105, "polynomial_expr": "(47 - 27*z)*(-30*z**3 - 29*z**2 - 48*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (47 - 27*z)*(-30*z**3 - 29*z**2 - 48*z)\nExpanding the part (47 - 27*z) using the distributive property, and we got: (-27*z)*(-30*z**3 - 29*z**2 - 48*z) + 47*(-30*z**3 - 29*z**2 - 48*z)\n#Step 2:\nCurrent expression: (-27*z)*(-30*z**3 - 29*z**2 - 48*z) + 47*(-30*z**3 - 29*z**2 - 48*z)\nSimplifying the partial expression: 47*(-30*z**3 - 29*z**2 - 48*z)\nExpanding the part (-30*z**3 - 29*z**2 - 48*z) using the distributive property, and we got: -48*z*47 - 29*z**2*47 - 30*z**3*47\nReplacing 47*(-30*z**3 - 29*z**2 - 48*z) with -48*z*47 - 29*z**2*47 - 30*z**3*47 in the overall expression.\n#Step 3:\nCurrent expression: -48*z*47 + (-27*z)*(-30*z**3 - 29*z**2 - 48*z) - 29*z**2*47 - 30*z**3*47\nSimplifying the partial expression: (-27*z)*(-30*z**3 - 29*z**2 - 48*z)\nExpanding the part (-30*z**3 - 29*z**2 - 48*z) using the distributive property, and we got: (-48*z)*(-27*z) + (-27*z)*(-29*z**2) + (-27*z)*(-30*z**3)\nReplacing (-27*z)*(-30*z**3 - 29*z**2 - 48*z) with (-48*z)*(-27*z) + (-27*z)*(-29*z**2) + (-27*z)*(-30*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-48*z)*(-27*z) - 48*z*47 + (-27*z)*(-29*z**2) + (-27*z)*(-30*z**3) - 29*z**2*47 - 30*z**3*47\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*z)*47 = -2256*z\n (-48*z)*(-27*z) = 1296*z**2\n (-30*z**3)*47 = -1410*z**3\n (-30*z**3)*(-27*z) = 810*z**4\n (-29*z**2)*47 = -1363*z**2\n (-29*z**2)*(-27*z) = 783*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 810*z**4 - 1410*z**3 + 783*z**3 - 1363*z**2 + 1296*z**2 - 2256*z\nCombining like terms, got 810*z**4 - 627*z**3 - 67*z**2 - 2256*z\n#Step 6:\nCurrent expression: 810*z**4 - 627*z**3 - 67*z**2 - 2256*z\nNo more calculations needed.\n810*z**4 - 627*z**3 - 67*z**2 - 2256*z", "generated_answer": "810*z**4 - 627*z**3 - 67*z**2 - 2256*z", "step_length": 6} {"cot_id": "1a017443f70be91af0c4693c8ad57c26d719ea7f01c777ee17ca933e3ccf2055", "datapoint": {"question": "Simplify this expression: (-21*y - 42)*(-40*y**3 - 43*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "840*y**4 + 1680*y**3 + 903*y**2 + 1806*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 106, "polynomial_expr": "(-21*y - 42)*(-40*y**3 - 43*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-21*y - 42)*(-40*y**3 - 43*y)\nExpanding the part (-21*y - 42) using the distributive property, and we got: (-21*y)*(-40*y**3 - 43*y) - 42*(-40*y**3 - 43*y)\n#Step 2:\nCurrent expression: (-21*y)*(-40*y**3 - 43*y) - 42*(-40*y**3 - 43*y)\nSimplifying the partial expression: -42*(-40*y**3 - 43*y)\nExpanding the part (-40*y**3 - 43*y) using the distributive property, and we got: -43*y*(-42) - 40*y**3*(-42)\nReplacing -42*(-40*y**3 - 43*y) with -43*y*(-42) - 40*y**3*(-42) in the overall expression.\n#Step 3:\nCurrent expression: -43*y*(-42) + (-21*y)*(-40*y**3 - 43*y) - 40*y**3*(-42)\nSimplifying the partial expression: (-21*y)*(-40*y**3 - 43*y)\nExpanding the part (-40*y**3 - 43*y) using the distributive property, and we got: (-43*y)*(-21*y) + (-21*y)*(-40*y**3)\nReplacing (-21*y)*(-40*y**3 - 43*y) with (-43*y)*(-21*y) + (-21*y)*(-40*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-43*y)*(-21*y) - 43*y*(-42) + (-21*y)*(-40*y**3) - 40*y**3*(-42)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-43*y)*-42 = 1806*y\n (-43*y)*(-21*y) = 903*y**2\n (-40*y**3)*-42 = 1680*y**3\n (-40*y**3)*(-21*y) = 840*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 840*y**4 + 1680*y**3 + 903*y**2 + 1806*y\nNo more calculations needed.\n840*y**4 + 1680*y**3 + 903*y**2 + 1806*y", "generated_answer": "840*y**4 + 1680*y**3 + 903*y**2 + 1806*y", "step_length": 5} {"cot_id": "13baa8d84b9cc7b81b9ecd04377813b3d9e917b335b7b0a254966f1fd3b3f0e2", "datapoint": {"question": "Calculate the following: (-26*x - 23)*(-13*x**3 - 25*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "338*x**4 + 299*x**3 + 650*x**2 + 575*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 107, "polynomial_expr": "(-26*x - 23)*(-13*x**3 - 25*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-26*x - 23)*(-13*x**3 - 25*x)\nExpanding the part (-26*x - 23) using the distributive property, and we got: (-26*x)*(-13*x**3 - 25*x) - 23*(-13*x**3 - 25*x)\n#Step 2:\nCurrent expression: (-26*x)*(-13*x**3 - 25*x) - 23*(-13*x**3 - 25*x)\nSimplifying the partial expression: -23*(-13*x**3 - 25*x)\nExpanding the part (-13*x**3 - 25*x) using the distributive property, and we got: -25*x*(-23) - 13*x**3*(-23)\nReplacing -23*(-13*x**3 - 25*x) with -25*x*(-23) - 13*x**3*(-23) in the overall expression.\n#Step 3:\nCurrent expression: (-26*x)*(-13*x**3 - 25*x) - 25*x*(-23) - 13*x**3*(-23)\nSimplifying the partial expression: (-26*x)*(-13*x**3 - 25*x)\nExpanding the part (-13*x**3 - 25*x) using the distributive property, and we got: (-26*x)*(-25*x) + (-26*x)*(-13*x**3)\nReplacing (-26*x)*(-13*x**3 - 25*x) with (-26*x)*(-25*x) + (-26*x)*(-13*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-26*x)*(-25*x) + (-26*x)*(-13*x**3) - 25*x*(-23) - 13*x**3*(-23)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*x)*-23 = 575*x\n (-25*x)*(-26*x) = 650*x**2\n (-13*x**3)*-23 = 299*x**3\n (-13*x**3)*(-26*x) = 338*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 338*x**4 + 299*x**3 + 650*x**2 + 575*x\nNo more calculations needed.\n338*x**4 + 299*x**3 + 650*x**2 + 575*x", "generated_answer": "338*x**4 + 299*x**3 + 650*x**2 + 575*x", "step_length": 5} {"cot_id": "c5f54b4360e24c0b45f795084409ab2ff20343132b6b3befa0ab3e9b14def1c2", "datapoint": {"question": "Simplify this expression: (15*y - 10)*(-29*y**2 - 25*y - 9)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-435*y**3 - 85*y**2 + 115*y + 90", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 108, "polynomial_expr": "(15*y - 10)*(-29*y**2 - 25*y - 9)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (15*y - 10)*(-29*y**2 - 25*y - 9)\nExpanding the part (15*y - 10) using the distributive property, and we got: (15*y)*(-29*y**2 - 25*y - 9) - 10*(-29*y**2 - 25*y - 9)\n#Step 2:\nCurrent expression: (15*y)*(-29*y**2 - 25*y - 9) - 10*(-29*y**2 - 25*y - 9)\nSimplifying the partial expression: -10*(-29*y**2 - 25*y - 9)\nExpanding the part (-29*y**2 - 25*y - 9) using the distributive property, and we got: -25*y*(-10) - 29*y**2*(-10) - 9*(-10)\nReplacing -10*(-29*y**2 - 25*y - 9) with -25*y*(-10) - 29*y**2*(-10) - 9*(-10) in the overall expression.\n#Step 3:\nCurrent expression: -25*y*(-10) + (15*y)*(-29*y**2 - 25*y - 9) - 29*y**2*(-10) + 90\nSimplifying the partial expression: (15*y)*(-29*y**2 - 25*y - 9)\nExpanding the part (-29*y**2 - 25*y - 9) using the distributive property, and we got: (-25*y)*(15*y) - 135*y + (15*y)*(-29*y**2)\nReplacing (15*y)*(-29*y**2 - 25*y - 9) with (-25*y)*(15*y) - 135*y + (15*y)*(-29*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-25*y)*(15*y) - 25*y*(-10) - 9*15*y + (15*y)*(-29*y**2) - 29*y**2*(-10) + 90\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*y**2)*-10 = 290*y**2\n (-29*y**2)*(15*y) = -435*y**3\n (-25*y)*-10 = 250*y\n (-25*y)*(15*y) = -375*y**2\n -9*15*y = -135*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -435*y**3 - 375*y**2 + 290*y**2 - 135*y + 250*y + 90\nCombining like terms, got -435*y**3 - 85*y**2 + 115*y + 90\n#Step 6:\nCurrent expression: -435*y**3 - 85*y**2 + 115*y + 90\nNo more calculations needed.\n-435*y**3 - 85*y**2 + 115*y + 90", "generated_answer": "-435*y**3 - 85*y**2 + 115*y + 90", "step_length": 6} {"cot_id": "b1416dbb5db68bd1a2edb4e7e33c56056e6e7fba3c764acc90943d9153bbf194", "datapoint": {"question": "Simplify this expression: (27 - 36*z**3)*(30*z**3 + 30*z**2 + 19*z - 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1080*z**6 - 1080*z**5 - 684*z**4 + 2286*z**3 + 810*z**2 + 513*z - 1107", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 109, "polynomial_expr": "(27 - 36*z**3)*(30*z**3 + 30*z**2 + 19*z - 41)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27 - 36*z**3)*(30*z**3 + 30*z**2 + 19*z - 41)\nExpanding the part (27 - 36*z**3) using the distributive property, and we got: (-36*z**3)*(30*z**3 + 30*z**2 + 19*z - 41) + 27*(30*z**3 + 30*z**2 + 19*z - 41)\n#Step 2:\nCurrent expression: (-36*z**3)*(30*z**3 + 30*z**2 + 19*z - 41) + 27*(30*z**3 + 30*z**2 + 19*z - 41)\nSimplifying the partial expression: 27*(30*z**3 + 30*z**2 + 19*z - 41)\nExpanding the part (30*z**3 + 30*z**2 + 19*z - 41) using the distributive property, and we got: (19*z)*27 + (30*z**2)*27 + (30*z**3)*27 - 41*27\nReplacing 27*(30*z**3 + 30*z**2 + 19*z - 41) with (19*z)*27 + (30*z**2)*27 + (30*z**3)*27 - 41*27 in the overall expression.\n#Step 3:\nCurrent expression: (19*z)*27 + (30*z**2)*27 + (-36*z**3)*(30*z**3 + 30*z**2 + 19*z - 41) + (30*z**3)*27 - 1107\nSimplifying the partial expression: (-36*z**3)*(30*z**3 + 30*z**2 + 19*z - 41)\nExpanding the part (30*z**3 + 30*z**2 + 19*z - 41) using the distributive property, and we got: -(-1)*1476*z**3 + (19*z)*(-36*z**3) + (30*z**2)*(-36*z**3) + (-36*z**3)*(30*z**3)\nReplacing (-36*z**3)*(30*z**3 + 30*z**2 + 19*z - 41) with -(-1)*1476*z**3 + (19*z)*(-36*z**3) + (30*z**2)*(-36*z**3) + (-36*z**3)*(30*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -41*(-36)*z**3 + (19*z)*(-36*z**3) + (19*z)*27 + (30*z**2)*(-36*z**3) + (30*z**2)*27 + (-36*z**3)*(30*z**3) + (30*z**3)*27 - 1107\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (19*z)*27 = 513*z\n (19*z)*(-36*z**3) = -684*z**4\n (30*z**2)*27 = 810*z**2\n (30*z**2)*(-36*z**3) = -1080*z**5\n (30*z**3)*27 = 810*z**3\n (30*z**3)*(-36*z**3) = -1080*z**6\n -41*-36*z**3 = 1476*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1080*z**6 - 1080*z**5 - 684*z**4 + 810*z**3 + 1476*z**3 + 810*z**2 + 513*z - 1107\nCombining like terms, got -1080*z**6 - 1080*z**5 - 684*z**4 + 2286*z**3 + 810*z**2 + 513*z - 1107\n#Step 6:\nCurrent expression: -1080*z**6 - 1080*z**5 - 684*z**4 + 2286*z**3 + 810*z**2 + 513*z - 1107\nNo more calculations needed.\n-1080*z**6 - 1080*z**5 - 684*z**4 + 2286*z**3 + 810*z**2 + 513*z - 1107", "generated_answer": "-1080*z**6 - 1080*z**5 - 684*z**4 + 2286*z**3 + 810*z**2 + 513*z - 1107", "step_length": 6} {"cot_id": "35cf21c4f1d6e10b32e56ed48efb119bd48bb405e9bef130bcb52104e2a7f098", "datapoint": {"question": "Calculate the following: (5*y**3 + 49*y**2)*(19*y**3 - 39*y + 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "95*y**6 + 931*y**5 - 195*y**4 - 1831*y**3 + 784*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 110, "polynomial_expr": "(5*y**3 + 49*y**2)*(19*y**3 - 39*y + 16)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (5*y**3 + 49*y**2)*(19*y**3 - 39*y + 16)\nExpanding the part (5*y**3 + 49*y**2) using the distributive property, and we got: (49*y**2)*(19*y**3 - 39*y + 16) + (5*y**3)*(19*y**3 - 39*y + 16)\n#Step 2:\nCurrent expression: (49*y**2)*(19*y**3 - 39*y + 16) + (5*y**3)*(19*y**3 - 39*y + 16)\nSimplifying the partial expression: (5*y**3)*(19*y**3 - 39*y + 16)\nExpanding the part (19*y**3 - 39*y + 16) using the distributive property, and we got: (-39*y)*(5*y**3) + 16*(5*y**3) + (5*y**3)*(19*y**3)\nReplacing (5*y**3)*(19*y**3 - 39*y + 16) with (-39*y)*(5*y**3) + 16*(5*y**3) + (5*y**3)*(19*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-39*y)*(5*y**3) + 16*5*y**3 + (49*y**2)*(19*y**3 - 39*y + 16) + (5*y**3)*(19*y**3)\nSimplifying the partial expression: (49*y**2)*(19*y**3 - 39*y + 16)\nExpanding the part (19*y**3 - 39*y + 16) using the distributive property, and we got: (-39*y)*(49*y**2) + 16*(49*y**2) + (49*y**2)*(19*y**3)\nReplacing (49*y**2)*(19*y**3 - 39*y + 16) with (-39*y)*(49*y**2) + 16*(49*y**2) + (49*y**2)*(19*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-39*y)*(49*y**2) + (-39*y)*(5*y**3) + 16*5*y**3 + 16*49*y**2 + (49*y**2)*(19*y**3) + (5*y**3)*(19*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*y)*(5*y**3) = -195*y**4\n (-39*y)*(49*y**2) = -1911*y**3\n (19*y**3)*(5*y**3) = 95*y**6\n (19*y**3)*(49*y**2) = 931*y**5\n 16*5*y**3 = 80*y**3\n 16*49*y**2 = 784*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 95*y**6 + 931*y**5 - 195*y**4 - 1911*y**3 + 80*y**3 + 784*y**2\nCombining like terms, got 95*y**6 + 931*y**5 - 195*y**4 - 1831*y**3 + 784*y**2\n#Step 6:\nCurrent expression: 95*y**6 + 931*y**5 - 195*y**4 - 1831*y**3 + 784*y**2\nNo more calculations needed.\n95*y**6 + 931*y**5 - 195*y**4 - 1831*y**3 + 784*y**2", "generated_answer": "95*y**6 + 931*y**5 - 195*y**4 - 1831*y**3 + 784*y**2", "step_length": 6} {"cot_id": "fc14e8814f844bf70d6fd967a74d519e677112b4bd8d9bd9572a9f52ff894d5e", "datapoint": {"question": "Simplify this expression: (33*y + 39)*(17*y**2 + 37*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "561*y**3 + 1884*y**2 + 1443*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 111, "polynomial_expr": "(33*y + 39)*(17*y**2 + 37*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (33*y + 39)*(17*y**2 + 37*y)\nExpanding the part (33*y + 39) using the distributive property, and we got: (33*y)*(17*y**2 + 37*y) + 39*(17*y**2 + 37*y)\n#Step 2:\nCurrent expression: (33*y)*(17*y**2 + 37*y) + 39*(17*y**2 + 37*y)\nSimplifying the partial expression: 39*(17*y**2 + 37*y)\nExpanding the part (17*y**2 + 37*y) using the distributive property, and we got: (37*y)*39 + (17*y**2)*39\nReplacing 39*(17*y**2 + 37*y) with (37*y)*39 + (17*y**2)*39 in the overall expression.\n#Step 3:\nCurrent expression: (33*y)*(17*y**2 + 37*y) + (37*y)*39 + (17*y**2)*39\nSimplifying the partial expression: (33*y)*(17*y**2 + 37*y)\nExpanding the part (17*y**2 + 37*y) using the distributive property, and we got: (33*y)*(37*y) + (33*y)*(17*y**2)\nReplacing (33*y)*(17*y**2 + 37*y) with (33*y)*(37*y) + (33*y)*(17*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (33*y)*(37*y) + (33*y)*(17*y**2) + (37*y)*39 + (17*y**2)*39\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (17*y**2)*39 = 663*y**2\n (17*y**2)*(33*y) = 561*y**3\n (37*y)*39 = 1443*y\n (37*y)*(33*y) = 1221*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 561*y**3 + 663*y**2 + 1221*y**2 + 1443*y\nCombining like terms, got 561*y**3 + 1884*y**2 + 1443*y\n#Step 6:\nCurrent expression: 561*y**3 + 1884*y**2 + 1443*y\nNo more calculations needed.\n561*y**3 + 1884*y**2 + 1443*y", "generated_answer": "561*y**3 + 1884*y**2 + 1443*y", "step_length": 6} {"cot_id": "7e5be07fac68a5d15d1f1293789f89b08427e4b2396436363e462e6a46cfa118", "datapoint": {"question": "Calculate the following: (48*x**3 + 4*x)*(14*x**3 + 29*x**2 + 28*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "672*x**6 + 1392*x**5 + 1400*x**4 + 116*x**3 + 112*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 112, "polynomial_expr": "(48*x**3 + 4*x)*(14*x**3 + 29*x**2 + 28*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (48*x**3 + 4*x)*(14*x**3 + 29*x**2 + 28*x)\nExpanding the part (48*x**3 + 4*x) using the distributive property, and we got: (4*x)*(14*x**3 + 29*x**2 + 28*x) + (48*x**3)*(14*x**3 + 29*x**2 + 28*x)\n#Step 2:\nCurrent expression: (4*x)*(14*x**3 + 29*x**2 + 28*x) + (48*x**3)*(14*x**3 + 29*x**2 + 28*x)\nSimplifying the partial expression: (4*x)*(14*x**3 + 29*x**2 + 28*x)\nExpanding the part (14*x**3 + 29*x**2 + 28*x) using the distributive property, and we got: (4*x)*(28*x) + (4*x)*(29*x**2) + (4*x)*(14*x**3)\nReplacing (4*x)*(14*x**3 + 29*x**2 + 28*x) with (4*x)*(28*x) + (4*x)*(29*x**2) + (4*x)*(14*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (4*x)*(28*x) + (4*x)*(29*x**2) + (4*x)*(14*x**3) + (48*x**3)*(14*x**3 + 29*x**2 + 28*x)\nSimplifying the partial expression: (48*x**3)*(14*x**3 + 29*x**2 + 28*x)\nExpanding the part (14*x**3 + 29*x**2 + 28*x) using the distributive property, and we got: (28*x)*(48*x**3) + (29*x**2)*(48*x**3) + (14*x**3)*(48*x**3)\nReplacing (48*x**3)*(14*x**3 + 29*x**2 + 28*x) with (28*x)*(48*x**3) + (29*x**2)*(48*x**3) + (14*x**3)*(48*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (4*x)*(28*x) + (4*x)*(29*x**2) + (4*x)*(14*x**3) + (28*x)*(48*x**3) + (29*x**2)*(48*x**3) + (14*x**3)*(48*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (14*x**3)*(4*x) = 56*x**4\n (14*x**3)*(48*x**3) = 672*x**6\n (28*x)*(4*x) = 112*x**2\n (28*x)*(48*x**3) = 1344*x**4\n (29*x**2)*(4*x) = 116*x**3\n (29*x**2)*(48*x**3) = 1392*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 672*x**6 + 1392*x**5 + 56*x**4 + 1344*x**4 + 116*x**3 + 112*x**2\nCombining like terms, got 672*x**6 + 1392*x**5 + 1400*x**4 + 116*x**3 + 112*x**2\n#Step 6:\nCurrent expression: 672*x**6 + 1392*x**5 + 1400*x**4 + 116*x**3 + 112*x**2\nNo more calculations needed.\n672*x**6 + 1392*x**5 + 1400*x**4 + 116*x**3 + 112*x**2", "generated_answer": "672*x**6 + 1392*x**5 + 1400*x**4 + 116*x**3 + 112*x**2", "step_length": 6} {"cot_id": "17753bd38cb1ef5d592f236abcffff5a76fab9d7c03347f5778c74321b9d2003", "datapoint": {"question": "Simplify this expression: 75*z**3*(8*z**3 + 50*z**2 + 27*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "600*z**6 + 3750*z**5 + 2025*z**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 113, "polynomial_expr": "75*z**3*(8*z**3 + 50*z**2 + 27*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 75*z**3*(8*z**3 + 50*z**2 + 27*z)\nExpanding the part (8*z**3 + 50*z**2 + 27*z) using the distributive property, and we got: (27*z)*(75*z**3) + (50*z**2)*(75*z**3) + (8*z**3)*(75*z**3)\n#Step 2:\nCurrent expression: (27*z)*(75*z**3) + (50*z**2)*(75*z**3) + (8*z**3)*(75*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (8*z**3)*(75*z**3) = 600*z**6\n (27*z)*(75*z**3) = 2025*z**4\n (50*z**2)*(75*z**3) = 3750*z**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 600*z**6 + 3750*z**5 + 2025*z**4\nNo more calculations needed.\n600*z**6 + 3750*z**5 + 2025*z**4", "generated_answer": "600*z**6 + 3750*z**5 + 2025*z**4", "step_length": 3} {"cot_id": "c4f0fe2fa87b52c0f3de0b688d4921e037cc4cdc50abf419a5d01930c8456927", "datapoint": {"question": "Calculate the following: 54*y**3*(-10*y**3 - 29*y**2 - 16*y + 11)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-540*y**6 - 1566*y**5 - 864*y**4 + 594*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 114, "polynomial_expr": "54*y**3*(-10*y**3 - 29*y**2 - 16*y + 11)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 54*y**3*(-10*y**3 - 29*y**2 - 16*y + 11)\nExpanding the part (-10*y**3 - 29*y**2 - 16*y + 11) using the distributive property, and we got: (-16*y)*(54*y**3) + 11*(54*y**3) + (-29*y**2)*(54*y**3) + (-10*y**3)*(54*y**3)\n#Step 2:\nCurrent expression: (-16*y)*(54*y**3) + 11*(54*y**3) + (-29*y**2)*(54*y**3) + (-10*y**3)*(54*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 11*(54*y**3) = 594*y**3\n (-29*y**2)*(54*y**3) = -1566*y**5\n (-16*y)*(54*y**3) = -864*y**4\n (-10*y**3)*(54*y**3) = -540*y**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -540*y**6 - 1566*y**5 - 864*y**4 + 594*y**3\nNo more calculations needed.\n-540*y**6 - 1566*y**5 - 864*y**4 + 594*y**3", "generated_answer": "-540*y**6 - 1566*y**5 - 864*y**4 + 594*y**3", "step_length": 3} {"cot_id": "c89ae93672f8ff41cc0a00016ce93d99682a2169b044a6cedbca847aa9b79158", "datapoint": {"question": "Calculate the following: (-11*z**3 - 23)*(-7*z**3 - 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "77*z**6 + 227*z**3 + 138", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 115, "polynomial_expr": "(-11*z**3 - 23)*(-7*z**3 - 6)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-11*z**3 - 23)*(-7*z**3 - 6)\nExpanding the part (-11*z**3 - 23) using the distributive property, and we got: (-11*z**3)*(-7*z**3 - 6) - 23*(-7*z**3 - 6)\n#Step 2:\nCurrent expression: (-11*z**3)*(-7*z**3 - 6) - 23*(-7*z**3 - 6)\nSimplifying the partial expression: -23*(-7*z**3 - 6)\nExpanding the part (-7*z**3 - 6) using the distributive property, and we got: -7*z**3*(-23) - 6*(-23)\nReplacing -23*(-7*z**3 - 6) with -7*z**3*(-23) - 6*(-23) in the overall expression.\n#Step 3:\nCurrent expression: (-11*z**3)*(-7*z**3 - 6) - 7*z**3*(-23) + 138\nSimplifying the partial expression: (-11*z**3)*(-7*z**3 - 6)\nExpanding the part (-7*z**3 - 6) using the distributive property, and we got: -(-1)*66*z**3 + (-11*z**3)*(-7*z**3)\nReplacing (-11*z**3)*(-7*z**3 - 6) with -(-1)*66*z**3 + (-11*z**3)*(-7*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -6*(-11)*z**3 + (-11*z**3)*(-7*z**3) - 7*z**3*(-23) + 138\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-7*z**3)*-23 = 161*z**3\n (-7*z**3)*(-11*z**3) = 77*z**6\n -6*-11*z**3 = 66*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 77*z**6 + 66*z**3 + 161*z**3 + 138\nCombining like terms, got 77*z**6 + 227*z**3 + 138\n#Step 6:\nCurrent expression: 77*z**6 + 227*z**3 + 138\nNo more calculations needed.\n77*z**6 + 227*z**3 + 138", "generated_answer": "77*z**6 + 227*z**3 + 138", "step_length": 6} {"cot_id": "a609ea54ed6cdef032613f4773bf63081f8f4ad2ff91b87553dfc63920da8162", "datapoint": {"question": "Calculate the following: 104*z**5\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "104*z**5", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 116, "polynomial_expr": "104*z**5", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 104*z**5\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 104*z**5\nNo more calculations needed.\n104*z**5", "generated_answer": "104*z**5", "step_length": 2} {"cot_id": "d3ba5b3eb528d745de85ecee84341641eaa8ff467675a51db52b56c06c18540c", "datapoint": {"question": "Simplify this expression: (31*y**2 - 21*y)*(-46*y**2 + 3*y + 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1426*y**4 + 1059*y**3 + 433*y**2 - 336*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 117, "polynomial_expr": "(31*y**2 - 21*y)*(-46*y**2 + 3*y + 16)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31*y**2 - 21*y)*(-46*y**2 + 3*y + 16)\nExpanding the part (31*y**2 - 21*y) using the distributive property, and we got: (-21*y)*(-46*y**2 + 3*y + 16) + (31*y**2)*(-46*y**2 + 3*y + 16)\n#Step 2:\nCurrent expression: (-21*y)*(-46*y**2 + 3*y + 16) + (31*y**2)*(-46*y**2 + 3*y + 16)\nSimplifying the partial expression: (-21*y)*(-46*y**2 + 3*y + 16)\nExpanding the part (-46*y**2 + 3*y + 16) using the distributive property, and we got: (-21*y)*(3*y) + (-21*y)*(-46*y**2) + 16*(-21*y)\nReplacing (-21*y)*(-46*y**2 + 3*y + 16) with (-21*y)*(3*y) + (-21*y)*(-46*y**2) + 16*(-21*y) in the overall expression.\n#Step 3:\nCurrent expression: (-21*y)*(3*y) + (-21*y)*(-46*y**2) + 16*(-21)*y + (31*y**2)*(-46*y**2 + 3*y + 16)\nSimplifying the partial expression: (31*y**2)*(-46*y**2 + 3*y + 16)\nExpanding the part (-46*y**2 + 3*y + 16) using the distributive property, and we got: 16*(31*y**2) + (3*y)*(31*y**2) + (-46*y**2)*(31*y**2)\nReplacing (31*y**2)*(-46*y**2 + 3*y + 16) with 16*(31*y**2) + (3*y)*(31*y**2) + (-46*y**2)*(31*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-21*y)*(3*y) + (-21*y)*(-46*y**2) + 16*31*y**2 + 16*(-21)*y + (3*y)*(31*y**2) + (-46*y**2)*(31*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*y**2)*(-21*y) = 966*y**3\n (-46*y**2)*(31*y**2) = -1426*y**4\n (3*y)*(-21*y) = -63*y**2\n (3*y)*(31*y**2) = 93*y**3\n 16*-21*y = -336*y\n 16*31*y**2 = 496*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1426*y**4 + 93*y**3 + 966*y**3 - 63*y**2 + 496*y**2 - 336*y\nCombining like terms, got -1426*y**4 + 1059*y**3 + 433*y**2 - 336*y\n#Step 6:\nCurrent expression: -1426*y**4 + 1059*y**3 + 433*y**2 - 336*y\nNo more calculations needed.\n-1426*y**4 + 1059*y**3 + 433*y**2 - 336*y", "generated_answer": "-1426*y**4 + 1059*y**3 + 433*y**2 - 336*y", "step_length": 6} {"cot_id": "0e364bd680895936af9ff755a97370141af6bd483395014773c018c83d82ba7f", "datapoint": {"question": "Calculate the following: (-4*x**3 - 41*x**2)*(20*x**3 + 12*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-80*x**6 - 868*x**5 - 492*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 118, "polynomial_expr": "(-4*x**3 - 41*x**2)*(20*x**3 + 12*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-4*x**3 - 41*x**2)*(20*x**3 + 12*x**2)\nExpanding the part (-4*x**3 - 41*x**2) using the distributive property, and we got: (-41*x**2)*(20*x**3 + 12*x**2) + (-4*x**3)*(20*x**3 + 12*x**2)\n#Step 2:\nCurrent expression: (-41*x**2)*(20*x**3 + 12*x**2) + (-4*x**3)*(20*x**3 + 12*x**2)\nSimplifying the partial expression: (-41*x**2)*(20*x**3 + 12*x**2)\nExpanding the part (20*x**3 + 12*x**2) using the distributive property, and we got: (-41*x**2)*(12*x**2) + (-41*x**2)*(20*x**3)\nReplacing (-41*x**2)*(20*x**3 + 12*x**2) with (-41*x**2)*(12*x**2) + (-41*x**2)*(20*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-41*x**2)*(12*x**2) + (-41*x**2)*(20*x**3) + (-4*x**3)*(20*x**3 + 12*x**2)\nSimplifying the partial expression: (-4*x**3)*(20*x**3 + 12*x**2)\nExpanding the part (20*x**3 + 12*x**2) using the distributive property, and we got: (12*x**2)*(-4*x**3) + (-4*x**3)*(20*x**3)\nReplacing (-4*x**3)*(20*x**3 + 12*x**2) with (12*x**2)*(-4*x**3) + (-4*x**3)*(20*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-41*x**2)*(12*x**2) + (-41*x**2)*(20*x**3) + (12*x**2)*(-4*x**3) + (-4*x**3)*(20*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (12*x**2)*(-41*x**2) = -492*x**4\n (12*x**2)*(-4*x**3) = -48*x**5\n (20*x**3)*(-41*x**2) = -820*x**5\n (20*x**3)*(-4*x**3) = -80*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -80*x**6 - 820*x**5 - 48*x**5 - 492*x**4\nCombining like terms, got -80*x**6 - 868*x**5 - 492*x**4\n#Step 6:\nCurrent expression: -80*x**6 - 868*x**5 - 492*x**4\nNo more calculations needed.\n-80*x**6 - 868*x**5 - 492*x**4", "generated_answer": "-80*x**6 - 868*x**5 - 492*x**4", "step_length": 6} {"cot_id": "e3890feb40328b7f6c44d14a4677a0dca44ec704cce8fc4788771813ebacfe13", "datapoint": {"question": "Calculate the following: (11 - 82*z**2)*(86*z**3 + 50*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-7052*z**5 - 3154*z**3 + 550*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 119, "polynomial_expr": "(11 - 82*z**2)*(86*z**3 + 50*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11 - 82*z**2)*(86*z**3 + 50*z)\nExpanding the part (11 - 82*z**2) using the distributive property, and we got: (-82*z**2)*(86*z**3 + 50*z) + 11*(86*z**3 + 50*z)\n#Step 2:\nCurrent expression: (-82*z**2)*(86*z**3 + 50*z) + 11*(86*z**3 + 50*z)\nSimplifying the partial expression: 11*(86*z**3 + 50*z)\nExpanding the part (86*z**3 + 50*z) using the distributive property, and we got: (50*z)*11 + (86*z**3)*11\nReplacing 11*(86*z**3 + 50*z) with (50*z)*11 + (86*z**3)*11 in the overall expression.\n#Step 3:\nCurrent expression: (50*z)*11 + (-82*z**2)*(86*z**3 + 50*z) + (86*z**3)*11\nSimplifying the partial expression: (-82*z**2)*(86*z**3 + 50*z)\nExpanding the part (86*z**3 + 50*z) using the distributive property, and we got: (50*z)*(-82*z**2) + (-82*z**2)*(86*z**3)\nReplacing (-82*z**2)*(86*z**3 + 50*z) with (50*z)*(-82*z**2) + (-82*z**2)*(86*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (50*z)*(-82*z**2) + (50*z)*11 + (-82*z**2)*(86*z**3) + (86*z**3)*11\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (50*z)*11 = 550*z\n (50*z)*(-82*z**2) = -4100*z**3\n (86*z**3)*11 = 946*z**3\n (86*z**3)*(-82*z**2) = -7052*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -7052*z**5 - 4100*z**3 + 946*z**3 + 550*z\nCombining like terms, got -7052*z**5 - 3154*z**3 + 550*z\n#Step 6:\nCurrent expression: -7052*z**5 - 3154*z**3 + 550*z\nNo more calculations needed.\n-7052*z**5 - 3154*z**3 + 550*z", "generated_answer": "-7052*z**5 - 3154*z**3 + 550*z", "step_length": 6} {"cot_id": "193452cfb714b478fbbe0a897e1bd9de58441c616dfa225f5226f4d0363a0015", "datapoint": {"question": "Simplify this expression: (27*x**3 - 42*x**2)*(-13*x**3 - 40*x**2 - 21*x - 2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-351*x**6 - 534*x**5 + 1113*x**4 + 828*x**3 + 84*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 120, "polynomial_expr": "(27*x**3 - 42*x**2)*(-13*x**3 - 40*x**2 - 21*x - 2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*x**3 - 42*x**2)*(-13*x**3 - 40*x**2 - 21*x - 2)\nExpanding the part (27*x**3 - 42*x**2) using the distributive property, and we got: (-42*x**2)*(-13*x**3 - 40*x**2 - 21*x - 2) + (27*x**3)*(-13*x**3 - 40*x**2 - 21*x - 2)\n#Step 2:\nCurrent expression: (-42*x**2)*(-13*x**3 - 40*x**2 - 21*x - 2) + (27*x**3)*(-13*x**3 - 40*x**2 - 21*x - 2)\nSimplifying the partial expression: (-42*x**2)*(-13*x**3 - 40*x**2 - 21*x - 2)\nExpanding the part (-13*x**3 - 40*x**2 - 21*x - 2) using the distributive property, and we got: (-21*x)*(-42*x**2) - (-1)*84*x**2 + (-42*x**2)*(-40*x**2) + (-42*x**2)*(-13*x**3)\nReplacing (-42*x**2)*(-13*x**3 - 40*x**2 - 21*x - 2) with (-21*x)*(-42*x**2) - (-1)*84*x**2 + (-42*x**2)*(-40*x**2) + (-42*x**2)*(-13*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-21*x)*(-42*x**2) - 2*(-42)*x**2 + (-42*x**2)*(-40*x**2) + (-42*x**2)*(-13*x**3) + (27*x**3)*(-13*x**3 - 40*x**2 - 21*x - 2)\nSimplifying the partial expression: (27*x**3)*(-13*x**3 - 40*x**2 - 21*x - 2)\nExpanding the part (-13*x**3 - 40*x**2 - 21*x - 2) using the distributive property, and we got: (-21*x)*(27*x**3) - 54*x**3 + (-40*x**2)*(27*x**3) + (-13*x**3)*(27*x**3)\nReplacing (27*x**3)*(-13*x**3 - 40*x**2 - 21*x - 2) with (-21*x)*(27*x**3) - 54*x**3 + (-40*x**2)*(27*x**3) + (-13*x**3)*(27*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-21*x)*(-42*x**2) + (-21*x)*(27*x**3) - 2*27*x**3 - 2*(-42)*x**2 + (-42*x**2)*(-40*x**2) + (-42*x**2)*(-13*x**3) + (-40*x**2)*(27*x**3) + (-13*x**3)*(27*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*x**2)*(-42*x**2) = 1680*x**4\n (-40*x**2)*(27*x**3) = -1080*x**5\n (-21*x)*(-42*x**2) = 882*x**3\n (-21*x)*(27*x**3) = -567*x**4\n (-13*x**3)*(-42*x**2) = 546*x**5\n (-13*x**3)*(27*x**3) = -351*x**6\n -2*-42*x**2 = 84*x**2\n -2*27*x**3 = -54*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -351*x**6 - 1080*x**5 + 546*x**5 - 567*x**4 + 1680*x**4 - 54*x**3 + 882*x**3 + 84*x**2\nCombining like terms, got -351*x**6 - 534*x**5 + 1113*x**4 + 828*x**3 + 84*x**2\n#Step 6:\nCurrent expression: -351*x**6 - 534*x**5 + 1113*x**4 + 828*x**3 + 84*x**2\nNo more calculations needed.\n-351*x**6 - 534*x**5 + 1113*x**4 + 828*x**3 + 84*x**2", "generated_answer": "-351*x**6 - 534*x**5 + 1113*x**4 + 828*x**3 + 84*x**2", "step_length": 6} {"cot_id": "391174e986af03fc59cf9bf1a9ff37d5ef8fec24cb3ee8b0037ce3fb648799cf", "datapoint": {"question": "Calculate the following: (-37*z**3 - 5*z)*(40*z**3 + 12*z**2 - 43)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1480*z**6 - 444*z**5 - 200*z**4 + 1531*z**3 + 215*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 121, "polynomial_expr": "(-37*z**3 - 5*z)*(40*z**3 + 12*z**2 - 43)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-37*z**3 - 5*z)*(40*z**3 + 12*z**2 - 43)\nExpanding the part (-37*z**3 - 5*z) using the distributive property, and we got: (-5*z)*(40*z**3 + 12*z**2 - 43) + (-37*z**3)*(40*z**3 + 12*z**2 - 43)\n#Step 2:\nCurrent expression: (-5*z)*(40*z**3 + 12*z**2 - 43) + (-37*z**3)*(40*z**3 + 12*z**2 - 43)\nSimplifying the partial expression: (-37*z**3)*(40*z**3 + 12*z**2 - 43)\nExpanding the part (40*z**3 + 12*z**2 - 43) using the distributive property, and we got: -(-1)*1591*z**3 + (12*z**2)*(-37*z**3) + (-37*z**3)*(40*z**3)\nReplacing (-37*z**3)*(40*z**3 + 12*z**2 - 43) with -(-1)*1591*z**3 + (12*z**2)*(-37*z**3) + (-37*z**3)*(40*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-5*z)*(40*z**3 + 12*z**2 - 43) - 43*(-37)*z**3 + (12*z**2)*(-37*z**3) + (-37*z**3)*(40*z**3)\nSimplifying the partial expression: (-5*z)*(40*z**3 + 12*z**2 - 43)\nExpanding the part (40*z**3 + 12*z**2 - 43) using the distributive property, and we got: (-5*z)*(12*z**2) + (-5*z)*(40*z**3) - (-1)*215*z\nReplacing (-5*z)*(40*z**3 + 12*z**2 - 43) with (-5*z)*(12*z**2) + (-5*z)*(40*z**3) - (-1)*215*z in the overall expression.\n#Step 4:\nCurrent expression: (-5*z)*(12*z**2) + (-5*z)*(40*z**3) - 43*(-37)*z**3 - 43*(-5)*z + (12*z**2)*(-37*z**3) + (-37*z**3)*(40*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (12*z**2)*(-37*z**3) = -444*z**5\n (12*z**2)*(-5*z) = -60*z**3\n (40*z**3)*(-37*z**3) = -1480*z**6\n (40*z**3)*(-5*z) = -200*z**4\n -43*-37*z**3 = 1591*z**3\n -43*-5*z = 215*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1480*z**6 - 444*z**5 - 200*z**4 - 60*z**3 + 1591*z**3 + 215*z\nCombining like terms, got -1480*z**6 - 444*z**5 - 200*z**4 + 1531*z**3 + 215*z\n#Step 6:\nCurrent expression: -1480*z**6 - 444*z**5 - 200*z**4 + 1531*z**3 + 215*z\nNo more calculations needed.\n-1480*z**6 - 444*z**5 - 200*z**4 + 1531*z**3 + 215*z", "generated_answer": "-1480*z**6 - 444*z**5 - 200*z**4 + 1531*z**3 + 215*z", "step_length": 6} {"cot_id": "2a2088858676209de3f338efa58b48b7c09c42039cd6254c782536ccaec8f5b5", "datapoint": {"question": "Calculate the following: 96*x*(30*x**3 - 8*x - 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2880*x**4 - 768*x**2 - 96*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 122, "polynomial_expr": "96*x*(30*x**3 - 8*x - 1)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 96*x*(30*x**3 - 8*x - 1)\nExpanding the part (30*x**3 - 8*x - 1) using the distributive property, and we got: (-8*x)*(96*x) - 96*x + (96*x)*(30*x**3)\n#Step 2:\nCurrent expression: (-8*x)*(96*x) - 96*x + (96*x)*(30*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -1*(96*x) = -96*x\n (-8*x)*(96*x) = -768*x**2\n (30*x**3)*(96*x) = 2880*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 2880*x**4 - 768*x**2 - 96*x\nNo more calculations needed.\n2880*x**4 - 768*x**2 - 96*x", "generated_answer": "2880*x**4 - 768*x**2 - 96*x", "step_length": 3} {"cot_id": "3b5bbd19d38ee91f40c7d646af76d45fa95e0cc022be508127f94d06e160edd0", "datapoint": {"question": "Simplify this expression: (34*x**3 + 27*x + 44)*(12*x**3 + 44*x**2 - 28*x - 4)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "408*x**6 + 1496*x**5 - 628*x**4 + 1580*x**3 + 1180*x**2 - 1340*x - 176", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 123, "polynomial_expr": "(34*x**3 + 27*x + 44)*(12*x**3 + 44*x**2 - 28*x - 4)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (34*x**3 + 27*x + 44)*(12*x**3 + 44*x**2 - 28*x - 4)\nExpanding the part (34*x**3 + 27*x + 44) using the distributive property, and we got: (27*x)*(12*x**3 + 44*x**2 - 28*x - 4) + (34*x**3)*(12*x**3 + 44*x**2 - 28*x - 4) + 44*(12*x**3 + 44*x**2 - 28*x - 4)\n#Step 2:\nCurrent expression: (27*x)*(12*x**3 + 44*x**2 - 28*x - 4) + (34*x**3)*(12*x**3 + 44*x**2 - 28*x - 4) + 44*(12*x**3 + 44*x**2 - 28*x - 4)\nSimplifying the partial expression: 44*(12*x**3 + 44*x**2 - 28*x - 4)\nExpanding the part (12*x**3 + 44*x**2 - 28*x - 4) using the distributive property, and we got: -28*x*44 + (44*x**2)*44 + (12*x**3)*44 - 4*44\nReplacing 44*(12*x**3 + 44*x**2 - 28*x - 4) with -28*x*44 + (44*x**2)*44 + (12*x**3)*44 - 4*44 in the overall expression.\n#Step 3:\nCurrent expression: -28*x*44 + (27*x)*(12*x**3 + 44*x**2 - 28*x - 4) + (44*x**2)*44 + (12*x**3)*44 + (34*x**3)*(12*x**3 + 44*x**2 - 28*x - 4) - 176\nSimplifying the partial expression: (27*x)*(12*x**3 + 44*x**2 - 28*x - 4)\nExpanding the part (12*x**3 + 44*x**2 - 28*x - 4) using the distributive property, and we got: (-28*x)*(27*x) - 108*x + (27*x)*(44*x**2) + (27*x)*(12*x**3)\nReplacing (27*x)*(12*x**3 + 44*x**2 - 28*x - 4) with (-28*x)*(27*x) - 108*x + (27*x)*(44*x**2) + (27*x)*(12*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-28*x)*(27*x) - 28*x*44 - 4*27*x + (27*x)*(44*x**2) + (27*x)*(12*x**3) + (44*x**2)*44 + (12*x**3)*44 + (34*x**3)*(12*x**3 + 44*x**2 - 28*x - 4) - 176\nSimplifying the partial expression: (34*x**3)*(12*x**3 + 44*x**2 - 28*x - 4)\nExpanding the part (12*x**3 + 44*x**2 - 28*x - 4) using the distributive property, and we got: (-28*x)*(34*x**3) - 136*x**3 + (44*x**2)*(34*x**3) + (12*x**3)*(34*x**3)\nReplacing (34*x**3)*(12*x**3 + 44*x**2 - 28*x - 4) with (-28*x)*(34*x**3) - 136*x**3 + (44*x**2)*(34*x**3) + (12*x**3)*(34*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-28*x)*(27*x) + (-28*x)*(34*x**3) - 28*x*44 - 4*34*x**3 - 4*27*x + (27*x)*(44*x**2) + (27*x)*(12*x**3) + (44*x**2)*(34*x**3) + (44*x**2)*44 + (12*x**3)*(34*x**3) + (12*x**3)*44 - 176\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*x)*44 = -1232*x\n (-28*x)*(27*x) = -756*x**2\n (-28*x)*(34*x**3) = -952*x**4\n (12*x**3)*44 = 528*x**3\n (12*x**3)*(27*x) = 324*x**4\n (12*x**3)*(34*x**3) = 408*x**6\n (44*x**2)*44 = 1936*x**2\n (44*x**2)*(27*x) = 1188*x**3\n (44*x**2)*(34*x**3) = 1496*x**5\n -4*27*x = -108*x\n -4*34*x**3 = -136*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 408*x**6 + 1496*x**5 - 952*x**4 + 324*x**4 - 136*x**3 + 528*x**3 + 1188*x**3 - 756*x**2 + 1936*x**2 - 1232*x - 108*x - 176\nCombining like terms, got 408*x**6 + 1496*x**5 - 628*x**4 + 1580*x**3 + 1180*x**2 - 1340*x - 176\n#Step 7:\nCurrent expression: 408*x**6 + 1496*x**5 - 628*x**4 + 1580*x**3 + 1180*x**2 - 1340*x - 176\nNo more calculations needed.\n408*x**6 + 1496*x**5 - 628*x**4 + 1580*x**3 + 1180*x**2 - 1340*x - 176", "generated_answer": "408*x**6 + 1496*x**5 - 628*x**4 + 1580*x**3 + 1180*x**2 - 1340*x - 176", "step_length": 7} {"cot_id": "f58fcadd6da4ff32a8793ad4dfd4f973e94d843fe4739f34dbf002e98db9aa97", "datapoint": {"question": "Simplify this expression: (13 - 31*x**2)*(11*x**2 - 25*x + 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-341*x**4 + 775*x**3 - 74*x**2 - 325*x + 91", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 124, "polynomial_expr": "(13 - 31*x**2)*(11*x**2 - 25*x + 7)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (13 - 31*x**2)*(11*x**2 - 25*x + 7)\nExpanding the part (13 - 31*x**2) using the distributive property, and we got: (-31*x**2)*(11*x**2 - 25*x + 7) + 13*(11*x**2 - 25*x + 7)\n#Step 2:\nCurrent expression: (-31*x**2)*(11*x**2 - 25*x + 7) + 13*(11*x**2 - 25*x + 7)\nSimplifying the partial expression: 13*(11*x**2 - 25*x + 7)\nExpanding the part (11*x**2 - 25*x + 7) using the distributive property, and we got: -25*x*13 + (11*x**2)*13 + 7*13\nReplacing 13*(11*x**2 - 25*x + 7) with -25*x*13 + (11*x**2)*13 + 7*13 in the overall expression.\n#Step 3:\nCurrent expression: -25*x*13 + (-31*x**2)*(11*x**2 - 25*x + 7) + (11*x**2)*13 + 91\nSimplifying the partial expression: (-31*x**2)*(11*x**2 - 25*x + 7)\nExpanding the part (11*x**2 - 25*x + 7) using the distributive property, and we got: (-25*x)*(-31*x**2) + 7*(-31*x**2) + (-31*x**2)*(11*x**2)\nReplacing (-31*x**2)*(11*x**2 - 25*x + 7) with (-25*x)*(-31*x**2) + 7*(-31*x**2) + (-31*x**2)*(11*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-25*x)*(-31*x**2) - 25*x*13 + 7*(-31)*x**2 + (-31*x**2)*(11*x**2) + (11*x**2)*13 + 91\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*x)*13 = -325*x\n (-25*x)*(-31*x**2) = 775*x**3\n (11*x**2)*13 = 143*x**2\n (11*x**2)*(-31*x**2) = -341*x**4\n 7*-31*x**2 = -217*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -341*x**4 + 775*x**3 - 217*x**2 + 143*x**2 - 325*x + 91\nCombining like terms, got -341*x**4 + 775*x**3 - 74*x**2 - 325*x + 91\n#Step 6:\nCurrent expression: -341*x**4 + 775*x**3 - 74*x**2 - 325*x + 91\nNo more calculations needed.\n-341*x**4 + 775*x**3 - 74*x**2 - 325*x + 91", "generated_answer": "-341*x**4 + 775*x**3 - 74*x**2 - 325*x + 91", "step_length": 6} {"cot_id": "a57f6e5aae268a46de7e775a69a6841d53cc198a40870046c01d7f3946e6fd31", "datapoint": {"question": "Calculate the following: (28*x**2 + 84*x)*(49*x**3 + 35*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1372*x**5 + 4116*x**4 + 980*x**3 + 2940*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 125, "polynomial_expr": "(28*x**2 + 84*x)*(49*x**3 + 35*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28*x**2 + 84*x)*(49*x**3 + 35*x)\nExpanding the part (28*x**2 + 84*x) using the distributive property, and we got: (84*x)*(49*x**3 + 35*x) + (28*x**2)*(49*x**3 + 35*x)\n#Step 2:\nCurrent expression: (84*x)*(49*x**3 + 35*x) + (28*x**2)*(49*x**3 + 35*x)\nSimplifying the partial expression: (28*x**2)*(49*x**3 + 35*x)\nExpanding the part (49*x**3 + 35*x) using the distributive property, and we got: (35*x)*(28*x**2) + (28*x**2)*(49*x**3)\nReplacing (28*x**2)*(49*x**3 + 35*x) with (35*x)*(28*x**2) + (28*x**2)*(49*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (35*x)*(28*x**2) + (84*x)*(49*x**3 + 35*x) + (28*x**2)*(49*x**3)\nSimplifying the partial expression: (84*x)*(49*x**3 + 35*x)\nExpanding the part (49*x**3 + 35*x) using the distributive property, and we got: (35*x)*(84*x) + (84*x)*(49*x**3)\nReplacing (84*x)*(49*x**3 + 35*x) with (35*x)*(84*x) + (84*x)*(49*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (35*x)*(84*x) + (35*x)*(28*x**2) + (84*x)*(49*x**3) + (28*x**2)*(49*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (35*x)*(28*x**2) = 980*x**3\n (35*x)*(84*x) = 2940*x**2\n (49*x**3)*(28*x**2) = 1372*x**5\n (49*x**3)*(84*x) = 4116*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1372*x**5 + 4116*x**4 + 980*x**3 + 2940*x**2\nNo more calculations needed.\n1372*x**5 + 4116*x**4 + 980*x**3 + 2940*x**2", "generated_answer": "1372*x**5 + 4116*x**4 + 980*x**3 + 2940*x**2", "step_length": 5} {"cot_id": "6c8c66d9fc77092c1458adfc3deff6372a29689cb75514c222105c0b13675490", "datapoint": {"question": "Calculate the following: (-27*z - 38)*(-29*z**2 - 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "783*z**3 + 1102*z**2 + 945*z + 1330", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 126, "polynomial_expr": "(-27*z - 38)*(-29*z**2 - 35)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-27*z - 38)*(-29*z**2 - 35)\nExpanding the part (-27*z - 38) using the distributive property, and we got: (-27*z)*(-29*z**2 - 35) - 38*(-29*z**2 - 35)\n#Step 2:\nCurrent expression: (-27*z)*(-29*z**2 - 35) - 38*(-29*z**2 - 35)\nSimplifying the partial expression: -38*(-29*z**2 - 35)\nExpanding the part (-29*z**2 - 35) using the distributive property, and we got: -29*z**2*(-38) - 35*(-38)\nReplacing -38*(-29*z**2 - 35) with -29*z**2*(-38) - 35*(-38) in the overall expression.\n#Step 3:\nCurrent expression: (-27*z)*(-29*z**2 - 35) - 29*z**2*(-38) + 1330\nSimplifying the partial expression: (-27*z)*(-29*z**2 - 35)\nExpanding the part (-29*z**2 - 35) using the distributive property, and we got: (-27*z)*(-29*z**2) - (-1)*945*z\nReplacing (-27*z)*(-29*z**2 - 35) with (-27*z)*(-29*z**2) - (-1)*945*z in the overall expression.\n#Step 4:\nCurrent expression: (-27*z)*(-29*z**2) - 35*(-27)*z - 29*z**2*(-38) + 1330\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*z**2)*-38 = 1102*z**2\n (-29*z**2)*(-27*z) = 783*z**3\n -35*-27*z = 945*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 783*z**3 + 1102*z**2 + 945*z + 1330\nNo more calculations needed.\n783*z**3 + 1102*z**2 + 945*z + 1330", "generated_answer": "783*z**3 + 1102*z**2 + 945*z + 1330", "step_length": 5} {"cot_id": "e3d1378f2e15bf0a47bd3f2e65b05cb3bca0e148bd0234aeccc55c7e45d25cb5", "datapoint": {"question": "Simplify this expression: -2914*y**3 - 558*y**2 + 1426*y\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2914*y**3 - 558*y**2 + 1426*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 127, "polynomial_expr": "-2914*y**3 - 558*y**2 + 1426*y", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -2914*y**3 - 558*y**2 + 1426*y\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -2914*y**3 - 558*y**2 + 1426*y\nNo more calculations needed.\n-2914*y**3 - 558*y**2 + 1426*y", "generated_answer": "-2914*y**3 - 558*y**2 + 1426*y", "step_length": 2} {"cot_id": "a1e1ea5242aa5b867825851d61d3405ae5c4013218631306d7862291b1942df3", "datapoint": {"question": "Calculate the following: (-37*y**2 - 30*y - 23)*(-38*y**3 + y**2 - 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1406*y**5 + 1103*y**4 + 844*y**3 + 199*y**2 + 180*y + 138", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 128, "polynomial_expr": "(-37*y**2 - 30*y - 23)*(-38*y**3 + y**2 - 6)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-37*y**2 - 30*y - 23)*(-38*y**3 + y**2 - 6)\nExpanding the part (-37*y**2 - 30*y - 23) using the distributive property, and we got: (-30*y)*(-38*y**3 + y**2 - 6) + (-37*y**2)*(-38*y**3 + y**2 - 6) - 23*(-38*y**3 + y**2 - 6)\n#Step 2:\nCurrent expression: (-30*y)*(-38*y**3 + y**2 - 6) + (-37*y**2)*(-38*y**3 + y**2 - 6) - 23*(-38*y**3 + y**2 - 6)\nSimplifying the partial expression: -23*(-38*y**3 + y**2 - 6)\nExpanding the part (-38*y**3 + y**2 - 6) using the distributive property, and we got: y**2*(-23) - 38*y**3*(-23) - 6*(-23)\nReplacing -23*(-38*y**3 + y**2 - 6) with y**2*(-23) - 38*y**3*(-23) - 6*(-23) in the overall expression.\n#Step 3:\nCurrent expression: (-30*y)*(-38*y**3 + y**2 - 6) + y**2*(-23) + (-37*y**2)*(-38*y**3 + y**2 - 6) - 38*y**3*(-23) + 138\nSimplifying the partial expression: (-37*y**2)*(-38*y**3 + y**2 - 6)\nExpanding the part (-38*y**3 + y**2 - 6) using the distributive property, and we got: (-37*y**2)*y**2 - (-1)*222*y**2 + (-37*y**2)*(-38*y**3)\nReplacing (-37*y**2)*(-38*y**3 + y**2 - 6) with (-37*y**2)*y**2 - (-1)*222*y**2 + (-37*y**2)*(-38*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-30*y)*(-38*y**3 + y**2 - 6) + (-37*y**2)*y**2 + y**2*(-23) - 6*(-37)*y**2 + (-37*y**2)*(-38*y**3) - 38*y**3*(-23) + 138\nSimplifying the partial expression: (-30*y)*(-38*y**3 + y**2 - 6)\nExpanding the part (-38*y**3 + y**2 - 6) using the distributive property, and we got: (-30*y)*y**2 + (-30*y)*(-38*y**3) - (-1)*180*y\nReplacing (-30*y)*(-38*y**3 + y**2 - 6) with (-30*y)*y**2 + (-30*y)*(-38*y**3) - (-1)*180*y in the overall expression.\n#Step 5:\nCurrent expression: (-30*y)*y**2 + (-30*y)*(-38*y**3) + (-37*y**2)*y**2 + y**2*(-23) - 6*(-37)*y**2 - 6*(-30)*y + (-37*y**2)*(-38*y**3) - 38*y**3*(-23) + 138\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n y**2*-23 = -23*y**2\n y**2*(-37*y**2) = -37*y**4\n y**2*(-30*y) = -30*y**3\n (-38*y**3)*-23 = 874*y**3\n (-38*y**3)*(-37*y**2) = 1406*y**5\n (-38*y**3)*(-30*y) = 1140*y**4\n -6*-37*y**2 = 222*y**2\n -6*-30*y = 180*y\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1406*y**5 - 37*y**4 + 1140*y**4 - 30*y**3 + 874*y**3 - 23*y**2 + 222*y**2 + 180*y + 138\nCombining like terms, got 1406*y**5 + 1103*y**4 + 844*y**3 + 199*y**2 + 180*y + 138\n#Step 7:\nCurrent expression: 1406*y**5 + 1103*y**4 + 844*y**3 + 199*y**2 + 180*y + 138\nNo more calculations needed.\n1406*y**5 + 1103*y**4 + 844*y**3 + 199*y**2 + 180*y + 138", "generated_answer": "1406*y**5 + 1103*y**4 + 844*y**3 + 199*y**2 + 180*y + 138", "step_length": 7} {"cot_id": "c7df9a9677ec0b99973f4672b5e4e7f750af14a0eb44afbf532f3bc8dba36150", "datapoint": {"question": "Simplify this expression: 260*z**2 - 273\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "260*z**2 - 273", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 129, "polynomial_expr": "260*z**2 - 273", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 260*z**2 - 273\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 260*z**2 - 273\nNo more calculations needed.\n260*z**2 - 273", "generated_answer": "260*z**2 - 273", "step_length": 2} {"cot_id": "3676a963184b05e0a578c801061f13ca30a6ae7290472e1fa5aced25fbded0de", "datapoint": {"question": "Simplify this expression: -17*y**3*(26*y**2 + 20*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-442*y**5 - 340*y**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 130, "polynomial_expr": "-17*y**3*(26*y**2 + 20*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -17*y**3*(26*y**2 + 20*y)\nExpanding the part (26*y**2 + 20*y) using the distributive property, and we got: (20*y)*(-17*y**3) + (26*y**2)*(-17*y**3)\n#Step 2:\nCurrent expression: (20*y)*(-17*y**3) + (26*y**2)*(-17*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (20*y)*(-17*y**3) = -340*y**4\n (26*y**2)*(-17*y**3) = -442*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -442*y**5 - 340*y**4\nNo more calculations needed.\n-442*y**5 - 340*y**4", "generated_answer": "-442*y**5 - 340*y**4", "step_length": 3} {"cot_id": "4619eed6145b9e4cda7f5adf80051a055268b826d9b94a263eeb29c97c9779d7", "datapoint": {"question": "Calculate the following: (26*y**2 + 51*y)*(-5*y**3 - 10*y + 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-130*y**5 - 255*y**4 - 260*y**3 + 556*y**2 + 2091*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 131, "polynomial_expr": "(26*y**2 + 51*y)*(-5*y**3 - 10*y + 41)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (26*y**2 + 51*y)*(-5*y**3 - 10*y + 41)\nExpanding the part (26*y**2 + 51*y) using the distributive property, and we got: (51*y)*(-5*y**3 - 10*y + 41) + (26*y**2)*(-5*y**3 - 10*y + 41)\n#Step 2:\nCurrent expression: (51*y)*(-5*y**3 - 10*y + 41) + (26*y**2)*(-5*y**3 - 10*y + 41)\nSimplifying the partial expression: (26*y**2)*(-5*y**3 - 10*y + 41)\nExpanding the part (-5*y**3 - 10*y + 41) using the distributive property, and we got: (-10*y)*(26*y**2) + 41*(26*y**2) + (26*y**2)*(-5*y**3)\nReplacing (26*y**2)*(-5*y**3 - 10*y + 41) with (-10*y)*(26*y**2) + 41*(26*y**2) + (26*y**2)*(-5*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-10*y)*(26*y**2) + 41*26*y**2 + (51*y)*(-5*y**3 - 10*y + 41) + (26*y**2)*(-5*y**3)\nSimplifying the partial expression: (51*y)*(-5*y**3 - 10*y + 41)\nExpanding the part (-5*y**3 - 10*y + 41) using the distributive property, and we got: (-10*y)*(51*y) + 41*(51*y) + (51*y)*(-5*y**3)\nReplacing (51*y)*(-5*y**3 - 10*y + 41) with (-10*y)*(51*y) + 41*(51*y) + (51*y)*(-5*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-10*y)*(51*y) + (-10*y)*(26*y**2) + 41*26*y**2 + 41*51*y + (51*y)*(-5*y**3) + (26*y**2)*(-5*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*y)*(26*y**2) = -260*y**3\n (-10*y)*(51*y) = -510*y**2\n (-5*y**3)*(26*y**2) = -130*y**5\n (-5*y**3)*(51*y) = -255*y**4\n 41*26*y**2 = 1066*y**2\n 41*51*y = 2091*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -130*y**5 - 255*y**4 - 260*y**3 - 510*y**2 + 1066*y**2 + 2091*y\nCombining like terms, got -130*y**5 - 255*y**4 - 260*y**3 + 556*y**2 + 2091*y\n#Step 6:\nCurrent expression: -130*y**5 - 255*y**4 - 260*y**3 + 556*y**2 + 2091*y\nNo more calculations needed.\n-130*y**5 - 255*y**4 - 260*y**3 + 556*y**2 + 2091*y", "generated_answer": "-130*y**5 - 255*y**4 - 260*y**3 + 556*y**2 + 2091*y", "step_length": 6} {"cot_id": "845045476c3fffdc6193bff88a132291a64d27900b0962c68c47a6d6f89d1cf9", "datapoint": {"question": "Simplify this expression: 73*x**2*(-32*x**2 + 16*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2336*x**4 + 1168*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 132, "polynomial_expr": "73*x**2*(-32*x**2 + 16*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 73*x**2*(-32*x**2 + 16*x)\nExpanding the part (-32*x**2 + 16*x) using the distributive property, and we got: (16*x)*(73*x**2) + (-32*x**2)*(73*x**2)\n#Step 2:\nCurrent expression: (16*x)*(73*x**2) + (-32*x**2)*(73*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*x**2)*(73*x**2) = -2336*x**4\n (16*x)*(73*x**2) = 1168*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -2336*x**4 + 1168*x**3\nNo more calculations needed.\n-2336*x**4 + 1168*x**3", "generated_answer": "-2336*x**4 + 1168*x**3", "step_length": 3} {"cot_id": "77862a58243b579e9b023c2b2c41e1ebf5de4d5295eac9e4c180cb3d121a0594", "datapoint": {"question": "Calculate the following: (47 - 39*y**3)*(-30*y**3 - 35*y + 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1170*y**6 + 1365*y**4 - 3282*y**3 - 1645*y + 2256", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 133, "polynomial_expr": "(47 - 39*y**3)*(-30*y**3 - 35*y + 48)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (47 - 39*y**3)*(-30*y**3 - 35*y + 48)\nExpanding the part (47 - 39*y**3) using the distributive property, and we got: (-39*y**3)*(-30*y**3 - 35*y + 48) + 47*(-30*y**3 - 35*y + 48)\n#Step 2:\nCurrent expression: (-39*y**3)*(-30*y**3 - 35*y + 48) + 47*(-30*y**3 - 35*y + 48)\nSimplifying the partial expression: 47*(-30*y**3 - 35*y + 48)\nExpanding the part (-30*y**3 - 35*y + 48) using the distributive property, and we got: -35*y*47 - 30*y**3*47 + 48*47\nReplacing 47*(-30*y**3 - 35*y + 48) with -35*y*47 - 30*y**3*47 + 48*47 in the overall expression.\n#Step 3:\nCurrent expression: -35*y*47 + (-39*y**3)*(-30*y**3 - 35*y + 48) - 30*y**3*47 + 2256\nSimplifying the partial expression: (-39*y**3)*(-30*y**3 - 35*y + 48)\nExpanding the part (-30*y**3 - 35*y + 48) using the distributive property, and we got: (-35*y)*(-39*y**3) + 48*(-39*y**3) + (-39*y**3)*(-30*y**3)\nReplacing (-39*y**3)*(-30*y**3 - 35*y + 48) with (-35*y)*(-39*y**3) + 48*(-39*y**3) + (-39*y**3)*(-30*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-35*y)*(-39*y**3) - 35*y*47 + 48*(-39)*y**3 + (-39*y**3)*(-30*y**3) - 30*y**3*47 + 2256\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*y)*47 = -1645*y\n (-35*y)*(-39*y**3) = 1365*y**4\n (-30*y**3)*47 = -1410*y**3\n (-30*y**3)*(-39*y**3) = 1170*y**6\n 48*-39*y**3 = -1872*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1170*y**6 + 1365*y**4 - 1872*y**3 - 1410*y**3 - 1645*y + 2256\nCombining like terms, got 1170*y**6 + 1365*y**4 - 3282*y**3 - 1645*y + 2256\n#Step 6:\nCurrent expression: 1170*y**6 + 1365*y**4 - 3282*y**3 - 1645*y + 2256\nNo more calculations needed.\n1170*y**6 + 1365*y**4 - 3282*y**3 - 1645*y + 2256", "generated_answer": "1170*y**6 + 1365*y**4 - 3282*y**3 - 1645*y + 2256", "step_length": 6} {"cot_id": "94abd6fe77815e123d2c911603ec1e30f4754a7379952cb59687821e3126efa8", "datapoint": {"question": "Calculate the following: (-4*x**2 - 31*x)*(25*x**2 + 50*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-100*x**4 - 975*x**3 - 1550*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 134, "polynomial_expr": "(-4*x**2 - 31*x)*(25*x**2 + 50*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-4*x**2 - 31*x)*(25*x**2 + 50*x)\nExpanding the part (-4*x**2 - 31*x) using the distributive property, and we got: (-31*x)*(25*x**2 + 50*x) + (-4*x**2)*(25*x**2 + 50*x)\n#Step 2:\nCurrent expression: (-31*x)*(25*x**2 + 50*x) + (-4*x**2)*(25*x**2 + 50*x)\nSimplifying the partial expression: (-31*x)*(25*x**2 + 50*x)\nExpanding the part (25*x**2 + 50*x) using the distributive property, and we got: (-31*x)*(50*x) + (-31*x)*(25*x**2)\nReplacing (-31*x)*(25*x**2 + 50*x) with (-31*x)*(50*x) + (-31*x)*(25*x**2) in the overall expression.\n#Step 3:\nCurrent expression: (-31*x)*(50*x) + (-31*x)*(25*x**2) + (-4*x**2)*(25*x**2 + 50*x)\nSimplifying the partial expression: (-4*x**2)*(25*x**2 + 50*x)\nExpanding the part (25*x**2 + 50*x) using the distributive property, and we got: (50*x)*(-4*x**2) + (-4*x**2)*(25*x**2)\nReplacing (-4*x**2)*(25*x**2 + 50*x) with (50*x)*(-4*x**2) + (-4*x**2)*(25*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-31*x)*(50*x) + (-31*x)*(25*x**2) + (50*x)*(-4*x**2) + (-4*x**2)*(25*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (25*x**2)*(-31*x) = -775*x**3\n (25*x**2)*(-4*x**2) = -100*x**4\n (50*x)*(-31*x) = -1550*x**2\n (50*x)*(-4*x**2) = -200*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -100*x**4 - 775*x**3 - 200*x**3 - 1550*x**2\nCombining like terms, got -100*x**4 - 975*x**3 - 1550*x**2\n#Step 6:\nCurrent expression: -100*x**4 - 975*x**3 - 1550*x**2\nNo more calculations needed.\n-100*x**4 - 975*x**3 - 1550*x**2", "generated_answer": "-100*x**4 - 975*x**3 - 1550*x**2", "step_length": 6} {"cot_id": "4441a29b68e314c8861ceb3d56fb96feebae30d83e96c89ecb10f9e820d5f6c5", "datapoint": {"question": "Calculate the following: (42*x**2 - 26*x + 38)*(24*x**3 + 36*x**2 - 6*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1008*x**5 + 888*x**4 - 276*x**3 + 1524*x**2 - 228*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 135, "polynomial_expr": "(42*x**2 - 26*x + 38)*(24*x**3 + 36*x**2 - 6*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (42*x**2 - 26*x + 38)*(24*x**3 + 36*x**2 - 6*x)\nExpanding the part (42*x**2 - 26*x + 38) using the distributive property, and we got: (-26*x)*(24*x**3 + 36*x**2 - 6*x) + (42*x**2)*(24*x**3 + 36*x**2 - 6*x) + 38*(24*x**3 + 36*x**2 - 6*x)\n#Step 2:\nCurrent expression: (-26*x)*(24*x**3 + 36*x**2 - 6*x) + (42*x**2)*(24*x**3 + 36*x**2 - 6*x) + 38*(24*x**3 + 36*x**2 - 6*x)\nSimplifying the partial expression: 38*(24*x**3 + 36*x**2 - 6*x)\nExpanding the part (24*x**3 + 36*x**2 - 6*x) using the distributive property, and we got: -6*x*38 + (36*x**2)*38 + (24*x**3)*38\nReplacing 38*(24*x**3 + 36*x**2 - 6*x) with -6*x*38 + (36*x**2)*38 + (24*x**3)*38 in the overall expression.\n#Step 3:\nCurrent expression: (-26*x)*(24*x**3 + 36*x**2 - 6*x) - 6*x*38 + (36*x**2)*38 + (42*x**2)*(24*x**3 + 36*x**2 - 6*x) + (24*x**3)*38\nSimplifying the partial expression: (-26*x)*(24*x**3 + 36*x**2 - 6*x)\nExpanding the part (24*x**3 + 36*x**2 - 6*x) using the distributive property, and we got: (-26*x)*(-6*x) + (-26*x)*(36*x**2) + (-26*x)*(24*x**3)\nReplacing (-26*x)*(24*x**3 + 36*x**2 - 6*x) with (-26*x)*(-6*x) + (-26*x)*(36*x**2) + (-26*x)*(24*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-26*x)*(-6*x) + (-26*x)*(36*x**2) + (-26*x)*(24*x**3) - 6*x*38 + (36*x**2)*38 + (42*x**2)*(24*x**3 + 36*x**2 - 6*x) + (24*x**3)*38\nSimplifying the partial expression: (42*x**2)*(24*x**3 + 36*x**2 - 6*x)\nExpanding the part (24*x**3 + 36*x**2 - 6*x) using the distributive property, and we got: (-6*x)*(42*x**2) + (36*x**2)*(42*x**2) + (42*x**2)*(24*x**3)\nReplacing (42*x**2)*(24*x**3 + 36*x**2 - 6*x) with (-6*x)*(42*x**2) + (36*x**2)*(42*x**2) + (42*x**2)*(24*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-26*x)*(-6*x) + (-26*x)*(36*x**2) + (-26*x)*(24*x**3) + (-6*x)*(42*x**2) - 6*x*38 + (36*x**2)*(42*x**2) + (36*x**2)*38 + (42*x**2)*(24*x**3) + (24*x**3)*38\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-6*x)*38 = -228*x\n (-6*x)*(-26*x) = 156*x**2\n (-6*x)*(42*x**2) = -252*x**3\n (24*x**3)*38 = 912*x**3\n (24*x**3)*(-26*x) = -624*x**4\n (24*x**3)*(42*x**2) = 1008*x**5\n (36*x**2)*38 = 1368*x**2\n (36*x**2)*(-26*x) = -936*x**3\n (36*x**2)*(42*x**2) = 1512*x**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1008*x**5 - 624*x**4 + 1512*x**4 - 936*x**3 - 252*x**3 + 912*x**3 + 156*x**2 + 1368*x**2 - 228*x\nCombining like terms, got 1008*x**5 + 888*x**4 - 276*x**3 + 1524*x**2 - 228*x\n#Step 7:\nCurrent expression: 1008*x**5 + 888*x**4 - 276*x**3 + 1524*x**2 - 228*x\nNo more calculations needed.\n1008*x**5 + 888*x**4 - 276*x**3 + 1524*x**2 - 228*x", "generated_answer": "1008*x**5 + 888*x**4 - 276*x**3 + 1524*x**2 - 228*x", "step_length": 7} {"cot_id": "15d89e425c416c016a7aebe4aeb2204a964bd4d9e69c92c5b12d89d9cc2c8fa6", "datapoint": {"question": "Simplify this expression: (7 - 34*x**3)*(-18*x**3 - 15*x**2 + 29)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "612*x**6 + 510*x**5 - 1112*x**3 - 105*x**2 + 203", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 136, "polynomial_expr": "(7 - 34*x**3)*(-18*x**3 - 15*x**2 + 29)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7 - 34*x**3)*(-18*x**3 - 15*x**2 + 29)\nExpanding the part (7 - 34*x**3) using the distributive property, and we got: (-34*x**3)*(-18*x**3 - 15*x**2 + 29) + 7*(-18*x**3 - 15*x**2 + 29)\n#Step 2:\nCurrent expression: (-34*x**3)*(-18*x**3 - 15*x**2 + 29) + 7*(-18*x**3 - 15*x**2 + 29)\nSimplifying the partial expression: 7*(-18*x**3 - 15*x**2 + 29)\nExpanding the part (-18*x**3 - 15*x**2 + 29) using the distributive property, and we got: -15*x**2*7 - 18*x**3*7 + 29*7\nReplacing 7*(-18*x**3 - 15*x**2 + 29) with -15*x**2*7 - 18*x**3*7 + 29*7 in the overall expression.\n#Step 3:\nCurrent expression: -15*x**2*7 + (-34*x**3)*(-18*x**3 - 15*x**2 + 29) - 18*x**3*7 + 203\nSimplifying the partial expression: (-34*x**3)*(-18*x**3 - 15*x**2 + 29)\nExpanding the part (-18*x**3 - 15*x**2 + 29) using the distributive property, and we got: 29*(-34*x**3) + (-15*x**2)*(-34*x**3) + (-34*x**3)*(-18*x**3)\nReplacing (-34*x**3)*(-18*x**3 - 15*x**2 + 29) with 29*(-34*x**3) + (-15*x**2)*(-34*x**3) + (-34*x**3)*(-18*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 29*(-34)*x**3 + (-15*x**2)*(-34*x**3) - 15*x**2*7 + (-34*x**3)*(-18*x**3) - 18*x**3*7 + 203\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-18*x**3)*7 = -126*x**3\n (-18*x**3)*(-34*x**3) = 612*x**6\n (-15*x**2)*7 = -105*x**2\n (-15*x**2)*(-34*x**3) = 510*x**5\n 29*-34*x**3 = -986*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 612*x**6 + 510*x**5 - 986*x**3 - 126*x**3 - 105*x**2 + 203\nCombining like terms, got 612*x**6 + 510*x**5 - 1112*x**3 - 105*x**2 + 203\n#Step 6:\nCurrent expression: 612*x**6 + 510*x**5 - 1112*x**3 - 105*x**2 + 203\nNo more calculations needed.\n612*x**6 + 510*x**5 - 1112*x**3 - 105*x**2 + 203", "generated_answer": "612*x**6 + 510*x**5 - 1112*x**3 - 105*x**2 + 203", "step_length": 6} {"cot_id": "36ee529ea4497983858801a4763c731989feee648c9aa7adf8382ddb06aa8525", "datapoint": {"question": "Simplify this expression: -8*x**2*(-27*x**2 - 13*x - 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "216*x**4 + 104*x**3 + 256*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 137, "polynomial_expr": "-8*x**2*(-27*x**2 - 13*x - 32)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -8*x**2*(-27*x**2 - 13*x - 32)\nExpanding the part (-27*x**2 - 13*x - 32) using the distributive property, and we got: (-13*x)*(-8*x**2) - (-1)*256*x**2 + (-27*x**2)*(-8*x**2)\n#Step 2:\nCurrent expression: (-13*x)*(-8*x**2) - (-1)*256*x**2 + (-27*x**2)*(-8*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -32*(-8*x**2) = 256*x**2\n (-27*x**2)*(-8*x**2) = 216*x**4\n (-13*x)*(-8*x**2) = 104*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 216*x**4 + 104*x**3 + 256*x**2\nNo more calculations needed.\n216*x**4 + 104*x**3 + 256*x**2", "generated_answer": "216*x**4 + 104*x**3 + 256*x**2", "step_length": 3} {"cot_id": "526088c8fec230a03c017d66cabed113a2b3eee2e025b31336eb6595b970b50e", "datapoint": {"question": "Simplify this expression: (12*x**3 - 42*x)*(-33*x**3 - x**2 - 42*x - 3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-396*x**6 - 12*x**5 + 882*x**4 + 6*x**3 + 1764*x**2 + 126*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 138, "polynomial_expr": "(12*x**3 - 42*x)*(-33*x**3 - x**2 - 42*x - 3)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (12*x**3 - 42*x)*(-33*x**3 - x**2 - 42*x - 3)\nExpanding the part (12*x**3 - 42*x) using the distributive property, and we got: (-42*x)*(-33*x**3 - x**2 - 42*x - 3) + (12*x**3)*(-33*x**3 - x**2 - 42*x - 3)\n#Step 2:\nCurrent expression: (-42*x)*(-33*x**3 - x**2 - 42*x - 3) + (12*x**3)*(-33*x**3 - x**2 - 42*x - 3)\nSimplifying the partial expression: (-42*x)*(-33*x**3 - x**2 - 42*x - 3)\nExpanding the part (-33*x**3 - x**2 - 42*x - 3) using the distributive property, and we got: (-42*x)*(-x**2) + (-42*x)*(-33*x**3) + (-42*x)*(-42*x) - (-1)*126*x\nReplacing (-42*x)*(-33*x**3 - x**2 - 42*x - 3) with (-42*x)*(-x**2) + (-42*x)*(-33*x**3) + (-42*x)*(-42*x) - (-1)*126*x in the overall expression.\n#Step 3:\nCurrent expression: (-42*x)*(-x**2) + (-42*x)*(-33*x**3) + (-42*x)*(-42*x) - 3*(-42)*x + (12*x**3)*(-33*x**3 - x**2 - 42*x - 3)\nSimplifying the partial expression: (12*x**3)*(-33*x**3 - x**2 - 42*x - 3)\nExpanding the part (-33*x**3 - x**2 - 42*x - 3) using the distributive property, and we got: (-42*x)*(12*x**3) - 36*x**3 + (-x**2)*(12*x**3) + (-33*x**3)*(12*x**3)\nReplacing (12*x**3)*(-33*x**3 - x**2 - 42*x - 3) with (-42*x)*(12*x**3) - 36*x**3 + (-x**2)*(12*x**3) + (-33*x**3)*(12*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-42*x)*(-x**2) + (-42*x)*(-33*x**3) + (-42*x)*(12*x**3) + (-42*x)*(-42*x) - 3*12*x**3 - 3*(-42)*x + (-x**2)*(12*x**3) + (-33*x**3)*(12*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-x**2)*(-42*x) = 42*x**3\n (-x**2)*(12*x**3) = -12*x**5\n (-42*x)*(-42*x) = 1764*x**2\n (-42*x)*(12*x**3) = -504*x**4\n (-33*x**3)*(-42*x) = 1386*x**4\n (-33*x**3)*(12*x**3) = -396*x**6\n -3*-42*x = 126*x\n -3*12*x**3 = -36*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -396*x**6 - 12*x**5 - 504*x**4 + 1386*x**4 - 36*x**3 + 42*x**3 + 1764*x**2 + 126*x\nCombining like terms, got -396*x**6 - 12*x**5 + 882*x**4 + 6*x**3 + 1764*x**2 + 126*x\n#Step 6:\nCurrent expression: -396*x**6 - 12*x**5 + 882*x**4 + 6*x**3 + 1764*x**2 + 126*x\nNo more calculations needed.\n-396*x**6 - 12*x**5 + 882*x**4 + 6*x**3 + 1764*x**2 + 126*x", "generated_answer": "-396*x**6 - 12*x**5 + 882*x**4 + 6*x**3 + 1764*x**2 + 126*x", "step_length": 6} {"cot_id": "57f8f5da9c75d199172a6c54bc269178ab068f7248a64ef46ddda66a954f2239", "datapoint": {"question": "Simplify this expression: 71*z*(-16*z**3 + 29*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1136*z**4 + 2059*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 139, "polynomial_expr": "71*z*(-16*z**3 + 29*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 71*z*(-16*z**3 + 29*z**2)\nExpanding the part (-16*z**3 + 29*z**2) using the distributive property, and we got: (71*z)*(29*z**2) + (71*z)*(-16*z**3)\n#Step 2:\nCurrent expression: (71*z)*(29*z**2) + (71*z)*(-16*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-16*z**3)*(71*z) = -1136*z**4\n (29*z**2)*(71*z) = 2059*z**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1136*z**4 + 2059*z**3\nNo more calculations needed.\n-1136*z**4 + 2059*z**3", "generated_answer": "-1136*z**4 + 2059*z**3", "step_length": 3} {"cot_id": "9789557e771372f98f1d9ed0746a1e4ec4f1b9c7cd910ac99d5034239a983d21", "datapoint": {"question": "Simplify this expression: (6*y**3 + 3*y**2)*(19*y**3 - 15*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "114*y**6 + 57*y**5 - 90*y**4 - 45*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 140, "polynomial_expr": "(6*y**3 + 3*y**2)*(19*y**3 - 15*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6*y**3 + 3*y**2)*(19*y**3 - 15*y)\nExpanding the part (19*y**3 - 15*y) using the distributive property, and we got: (-15*y)*(6*y**3 + 3*y**2) + (19*y**3)*(6*y**3 + 3*y**2)\n#Step 2:\nCurrent expression: (-15*y)*(6*y**3 + 3*y**2) + (19*y**3)*(6*y**3 + 3*y**2)\nSimplifying the partial expression: (-15*y)*(6*y**3 + 3*y**2)\nExpanding the part (6*y**3 + 3*y**2) using the distributive property, and we got: (-15*y)*(3*y**2) + (-15*y)*(6*y**3)\nReplacing (-15*y)*(6*y**3 + 3*y**2) with (-15*y)*(3*y**2) + (-15*y)*(6*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-15*y)*(3*y**2) + (-15*y)*(6*y**3) + (19*y**3)*(6*y**3 + 3*y**2)\nSimplifying the partial expression: (19*y**3)*(6*y**3 + 3*y**2)\nExpanding the part (6*y**3 + 3*y**2) using the distributive property, and we got: (3*y**2)*(19*y**3) + (6*y**3)*(19*y**3)\nReplacing (19*y**3)*(6*y**3 + 3*y**2) with (3*y**2)*(19*y**3) + (6*y**3)*(19*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-15*y)*(3*y**2) + (-15*y)*(6*y**3) + (3*y**2)*(19*y**3) + (6*y**3)*(19*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (3*y**2)*(-15*y) = -45*y**3\n (3*y**2)*(19*y**3) = 57*y**5\n (6*y**3)*(-15*y) = -90*y**4\n (6*y**3)*(19*y**3) = 114*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 114*y**6 + 57*y**5 - 90*y**4 - 45*y**3\nNo more calculations needed.\n114*y**6 + 57*y**5 - 90*y**4 - 45*y**3", "generated_answer": "114*y**6 + 57*y**5 - 90*y**4 - 45*y**3", "step_length": 5} {"cot_id": "6b15e2b1060ffdfecdd9061dc9f87b1f918fa1bd43799dfa208a47d179b167bc", "datapoint": {"question": "Simplify this expression: (-x**2 + 18*x)*(-27*x**3 - x + 45)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "27*x**5 - 486*x**4 + x**3 - 63*x**2 + 810*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 141, "polynomial_expr": "(-x**2 + 18*x)*(-27*x**3 - x + 45)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-x**2 + 18*x)*(-27*x**3 - x + 45)\nExpanding the part (-x**2 + 18*x) using the distributive property, and we got: (18*x)*(-27*x**3 - x + 45) + (-x**2)*(-27*x**3 - x + 45)\n#Step 2:\nCurrent expression: (18*x)*(-27*x**3 - x + 45) + (-x**2)*(-27*x**3 - x + 45)\nSimplifying the partial expression: (-x**2)*(-27*x**3 - x + 45)\nExpanding the part (-27*x**3 - x + 45) using the distributive property, and we got: (-x)*(-x**2) + 45*(-x**2) + (-x**2)*(-27*x**3)\nReplacing (-x**2)*(-27*x**3 - x + 45) with (-x)*(-x**2) + 45*(-x**2) + (-x**2)*(-27*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-x)*(-x**2) + 45*(-1)*x**2 + (18*x)*(-27*x**3 - x + 45) + (-x**2)*(-27*x**3)\nSimplifying the partial expression: (18*x)*(-27*x**3 - x + 45)\nExpanding the part (-27*x**3 - x + 45) using the distributive property, and we got: (-x)*(18*x) + 45*(18*x) + (18*x)*(-27*x**3)\nReplacing (18*x)*(-27*x**3 - x + 45) with (-x)*(18*x) + 45*(18*x) + (18*x)*(-27*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-x)*(18*x) + (-x)*(-x**2) + 45*(-1)*x**2 + 45*18*x + (18*x)*(-27*x**3) + (-x**2)*(-27*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-x)*(-x**2) = x**3\n (-x)*(18*x) = -18*x**2\n (-27*x**3)*(-x**2) = 27*x**5\n (-27*x**3)*(18*x) = -486*x**4\n 45*-1*x**2 = -45*x**2\n 45*18*x = 810*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 27*x**5 - 486*x**4 + x**3 - 45*x**2 - 18*x**2 + 810*x\nCombining like terms, got 27*x**5 - 486*x**4 + x**3 - 63*x**2 + 810*x\n#Step 6:\nCurrent expression: 27*x**5 - 486*x**4 + x**3 - 63*x**2 + 810*x\nNo more calculations needed.\n27*x**5 - 486*x**4 + x**3 - 63*x**2 + 810*x", "generated_answer": "27*x**5 - 486*x**4 + x**3 - 63*x**2 + 810*x", "step_length": 6} {"cot_id": "e32ab6adf94eb80873ad09711420f57c1a9660f0b9bfbc32cc9019fba5711ca4", "datapoint": {"question": "Simplify this expression: (47 - 45*y)*(-28*y**3 - 18*y + 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1260*y**4 - 1316*y**3 + 810*y**2 - 1791*y + 987", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 142, "polynomial_expr": "(47 - 45*y)*(-28*y**3 - 18*y + 21)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (47 - 45*y)*(-28*y**3 - 18*y + 21)\nExpanding the part (47 - 45*y) using the distributive property, and we got: (-45*y)*(-28*y**3 - 18*y + 21) + 47*(-28*y**3 - 18*y + 21)\n#Step 2:\nCurrent expression: (-45*y)*(-28*y**3 - 18*y + 21) + 47*(-28*y**3 - 18*y + 21)\nSimplifying the partial expression: 47*(-28*y**3 - 18*y + 21)\nExpanding the part (-28*y**3 - 18*y + 21) using the distributive property, and we got: -18*y*47 - 28*y**3*47 + 21*47\nReplacing 47*(-28*y**3 - 18*y + 21) with -18*y*47 - 28*y**3*47 + 21*47 in the overall expression.\n#Step 3:\nCurrent expression: (-45*y)*(-28*y**3 - 18*y + 21) - 18*y*47 - 28*y**3*47 + 987\nSimplifying the partial expression: (-45*y)*(-28*y**3 - 18*y + 21)\nExpanding the part (-28*y**3 - 18*y + 21) using the distributive property, and we got: (-45*y)*(-18*y) + (-45*y)*(-28*y**3) + 21*(-45*y)\nReplacing (-45*y)*(-28*y**3 - 18*y + 21) with (-45*y)*(-18*y) + (-45*y)*(-28*y**3) + 21*(-45*y) in the overall expression.\n#Step 4:\nCurrent expression: (-45*y)*(-18*y) + (-45*y)*(-28*y**3) - 18*y*47 + 21*(-45)*y - 28*y**3*47 + 987\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*y**3)*47 = -1316*y**3\n (-28*y**3)*(-45*y) = 1260*y**4\n (-18*y)*47 = -846*y\n (-18*y)*(-45*y) = 810*y**2\n 21*-45*y = -945*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1260*y**4 - 1316*y**3 + 810*y**2 - 945*y - 846*y + 987\nCombining like terms, got 1260*y**4 - 1316*y**3 + 810*y**2 - 1791*y + 987\n#Step 6:\nCurrent expression: 1260*y**4 - 1316*y**3 + 810*y**2 - 1791*y + 987\nNo more calculations needed.\n1260*y**4 - 1316*y**3 + 810*y**2 - 1791*y + 987", "generated_answer": "1260*y**4 - 1316*y**3 + 810*y**2 - 1791*y + 987", "step_length": 6} {"cot_id": "d02dcf1cc927b97eb464d9044121bfd6615e697023e2f1dee24652695c9c0492", "datapoint": {"question": "Calculate the following: (-20*x**3 - 26)*(17*x**3 + 25*x**2 + 52)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-340*x**6 - 500*x**5 - 1482*x**3 - 650*x**2 - 1352", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 143, "polynomial_expr": "(-20*x**3 - 26)*(17*x**3 + 25*x**2 + 52)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-20*x**3 - 26)*(17*x**3 + 25*x**2 + 52)\nExpanding the part (-20*x**3 - 26) using the distributive property, and we got: (-20*x**3)*(17*x**3 + 25*x**2 + 52) - 26*(17*x**3 + 25*x**2 + 52)\n#Step 2:\nCurrent expression: (-20*x**3)*(17*x**3 + 25*x**2 + 52) - 26*(17*x**3 + 25*x**2 + 52)\nSimplifying the partial expression: -26*(17*x**3 + 25*x**2 + 52)\nExpanding the part (17*x**3 + 25*x**2 + 52) using the distributive property, and we got: (25*x**2)*(-26) + (17*x**3)*(-26) + 52*(-26)\nReplacing -26*(17*x**3 + 25*x**2 + 52) with (25*x**2)*(-26) + (17*x**3)*(-26) + 52*(-26) in the overall expression.\n#Step 3:\nCurrent expression: (25*x**2)*(-26) + (-20*x**3)*(17*x**3 + 25*x**2 + 52) + (17*x**3)*(-26) - 1352\nSimplifying the partial expression: (-20*x**3)*(17*x**3 + 25*x**2 + 52)\nExpanding the part (17*x**3 + 25*x**2 + 52) using the distributive property, and we got: 52*(-20*x**3) + (25*x**2)*(-20*x**3) + (-20*x**3)*(17*x**3)\nReplacing (-20*x**3)*(17*x**3 + 25*x**2 + 52) with 52*(-20*x**3) + (25*x**2)*(-20*x**3) + (-20*x**3)*(17*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 52*(-20)*x**3 + (25*x**2)*(-20*x**3) + (25*x**2)*(-26) + (-20*x**3)*(17*x**3) + (17*x**3)*(-26) - 1352\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (17*x**3)*-26 = -442*x**3\n (17*x**3)*(-20*x**3) = -340*x**6\n (25*x**2)*-26 = -650*x**2\n (25*x**2)*(-20*x**3) = -500*x**5\n 52*-20*x**3 = -1040*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -340*x**6 - 500*x**5 - 1040*x**3 - 442*x**3 - 650*x**2 - 1352\nCombining like terms, got -340*x**6 - 500*x**5 - 1482*x**3 - 650*x**2 - 1352\n#Step 6:\nCurrent expression: -340*x**6 - 500*x**5 - 1482*x**3 - 650*x**2 - 1352\nNo more calculations needed.\n-340*x**6 - 500*x**5 - 1482*x**3 - 650*x**2 - 1352", "generated_answer": "-340*x**6 - 500*x**5 - 1482*x**3 - 650*x**2 - 1352", "step_length": 6} {"cot_id": "68230a4a3e7118dbfbe602c5b2fc0645ba85a12b7f9a97dfc6fac57d5de091b3", "datapoint": {"question": "Simplify this expression: (14*y**3 - 31*y**2)*(31*y**3 + 50*y**2 - 16*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "434*y**6 - 261*y**5 - 1774*y**4 + 496*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 144, "polynomial_expr": "(14*y**3 - 31*y**2)*(31*y**3 + 50*y**2 - 16*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14*y**3 - 31*y**2)*(31*y**3 + 50*y**2 - 16*y)\nExpanding the part (14*y**3 - 31*y**2) using the distributive property, and we got: (-31*y**2)*(31*y**3 + 50*y**2 - 16*y) + (14*y**3)*(31*y**3 + 50*y**2 - 16*y)\n#Step 2:\nCurrent expression: (-31*y**2)*(31*y**3 + 50*y**2 - 16*y) + (14*y**3)*(31*y**3 + 50*y**2 - 16*y)\nSimplifying the partial expression: (-31*y**2)*(31*y**3 + 50*y**2 - 16*y)\nExpanding the part (31*y**3 + 50*y**2 - 16*y) using the distributive property, and we got: (-16*y)*(-31*y**2) + (-31*y**2)*(50*y**2) + (-31*y**2)*(31*y**3)\nReplacing (-31*y**2)*(31*y**3 + 50*y**2 - 16*y) with (-16*y)*(-31*y**2) + (-31*y**2)*(50*y**2) + (-31*y**2)*(31*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-16*y)*(-31*y**2) + (-31*y**2)*(50*y**2) + (-31*y**2)*(31*y**3) + (14*y**3)*(31*y**3 + 50*y**2 - 16*y)\nSimplifying the partial expression: (14*y**3)*(31*y**3 + 50*y**2 - 16*y)\nExpanding the part (31*y**3 + 50*y**2 - 16*y) using the distributive property, and we got: (-16*y)*(14*y**3) + (50*y**2)*(14*y**3) + (14*y**3)*(31*y**3)\nReplacing (14*y**3)*(31*y**3 + 50*y**2 - 16*y) with (-16*y)*(14*y**3) + (50*y**2)*(14*y**3) + (14*y**3)*(31*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-16*y)*(-31*y**2) + (-16*y)*(14*y**3) + (-31*y**2)*(50*y**2) + (-31*y**2)*(31*y**3) + (50*y**2)*(14*y**3) + (14*y**3)*(31*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-16*y)*(-31*y**2) = 496*y**3\n (-16*y)*(14*y**3) = -224*y**4\n (31*y**3)*(-31*y**2) = -961*y**5\n (31*y**3)*(14*y**3) = 434*y**6\n (50*y**2)*(-31*y**2) = -1550*y**4\n (50*y**2)*(14*y**3) = 700*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 434*y**6 - 961*y**5 + 700*y**5 - 1550*y**4 - 224*y**4 + 496*y**3\nCombining like terms, got 434*y**6 - 261*y**5 - 1774*y**4 + 496*y**3\n#Step 6:\nCurrent expression: 434*y**6 - 261*y**5 - 1774*y**4 + 496*y**3\nNo more calculations needed.\n434*y**6 - 261*y**5 - 1774*y**4 + 496*y**3", "generated_answer": "434*y**6 - 261*y**5 - 1774*y**4 + 496*y**3", "step_length": 6} {"cot_id": "7bd680ecf6c30dec87de144f3074a05628f534cb19b2779cc380d0b00d6d2d87", "datapoint": {"question": "Calculate the following: -19*y*(10*y**3 + 35*y**2 - 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-190*y**4 - 665*y**3 + 684*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 145, "polynomial_expr": "-19*y*(10*y**3 + 35*y**2 - 36)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -19*y*(10*y**3 + 35*y**2 - 36)\nExpanding the part (10*y**3 + 35*y**2 - 36) using the distributive property, and we got: (-19*y)*(35*y**2) + (-19*y)*(10*y**3) - (-1)*684*y\n#Step 2:\nCurrent expression: (-19*y)*(35*y**2) + (-19*y)*(10*y**3) - (-1)*684*y\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -36*(-19*y) = 684*y\n (10*y**3)*(-19*y) = -190*y**4\n (35*y**2)*(-19*y) = -665*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -190*y**4 - 665*y**3 + 684*y\nNo more calculations needed.\n-190*y**4 - 665*y**3 + 684*y", "generated_answer": "-190*y**4 - 665*y**3 + 684*y", "step_length": 3} {"cot_id": "7dd5e1c7d19d5dc5044913c4d13bde28646ef464cb95c82c4ed83549731c1b13", "datapoint": {"question": "Simplify this expression: (7*z**3 - 46*z**2)*(-18*z**2 - 23*z - 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-126*z**5 + 667*z**4 + 1051*z**3 + 46*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 146, "polynomial_expr": "(7*z**3 - 46*z**2)*(-18*z**2 - 23*z - 1)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7*z**3 - 46*z**2)*(-18*z**2 - 23*z - 1)\nExpanding the part (7*z**3 - 46*z**2) using the distributive property, and we got: (-46*z**2)*(-18*z**2 - 23*z - 1) + (7*z**3)*(-18*z**2 - 23*z - 1)\n#Step 2:\nCurrent expression: (-46*z**2)*(-18*z**2 - 23*z - 1) + (7*z**3)*(-18*z**2 - 23*z - 1)\nSimplifying the partial expression: (-46*z**2)*(-18*z**2 - 23*z - 1)\nExpanding the part (-18*z**2 - 23*z - 1) using the distributive property, and we got: (-23*z)*(-46*z**2) - (-1)*46*z**2 + (-46*z**2)*(-18*z**2)\nReplacing (-46*z**2)*(-18*z**2 - 23*z - 1) with (-23*z)*(-46*z**2) - (-1)*46*z**2 + (-46*z**2)*(-18*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-23*z)*(-46*z**2) - 1*(-46)*z**2 + (-46*z**2)*(-18*z**2) + (7*z**3)*(-18*z**2 - 23*z - 1)\nSimplifying the partial expression: (7*z**3)*(-18*z**2 - 23*z - 1)\nExpanding the part (-18*z**2 - 23*z - 1) using the distributive property, and we got: (-23*z)*(7*z**3) - 7*z**3 + (-18*z**2)*(7*z**3)\nReplacing (7*z**3)*(-18*z**2 - 23*z - 1) with (-23*z)*(7*z**3) - 7*z**3 + (-18*z**2)*(7*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-23*z)*(-46*z**2) + (-23*z)*(7*z**3) - 1*7*z**3 - 1*(-46)*z**2 + (-46*z**2)*(-18*z**2) + (-18*z**2)*(7*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*z)*(-46*z**2) = 1058*z**3\n (-23*z)*(7*z**3) = -161*z**4\n (-18*z**2)*(-46*z**2) = 828*z**4\n (-18*z**2)*(7*z**3) = -126*z**5\n -1*-46*z**2 = 46*z**2\n -1*7*z**3 = -7*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -126*z**5 - 161*z**4 + 828*z**4 - 7*z**3 + 1058*z**3 + 46*z**2\nCombining like terms, got -126*z**5 + 667*z**4 + 1051*z**3 + 46*z**2\n#Step 6:\nCurrent expression: -126*z**5 + 667*z**4 + 1051*z**3 + 46*z**2\nNo more calculations needed.\n-126*z**5 + 667*z**4 + 1051*z**3 + 46*z**2", "generated_answer": "-126*z**5 + 667*z**4 + 1051*z**3 + 46*z**2", "step_length": 6} {"cot_id": "f836e76ef6547bdfce245a221e9a5137712b1b310a273a49b0a4f0340bcee1ea", "datapoint": {"question": "Simplify this expression: 85*y**3*(-40*y**3 - 3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-3400*y**6 - 255*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 147, "polynomial_expr": "85*y**3*(-40*y**3 - 3)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 85*y**3*(-40*y**3 - 3)\nExpanding the part (-40*y**3 - 3) using the distributive property, and we got: -255*y**3 + (-40*y**3)*(85*y**3)\n#Step 2:\nCurrent expression: -255*y**3 + (-40*y**3)*(85*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -3*(85*y**3) = -255*y**3\n (-40*y**3)*(85*y**3) = -3400*y**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -3400*y**6 - 255*y**3\nNo more calculations needed.\n-3400*y**6 - 255*y**3", "generated_answer": "-3400*y**6 - 255*y**3", "step_length": 3} {"cot_id": "72839cce601df122b15373df410138f37d51bc6c7b126b117f4448592a3378d2", "datapoint": {"question": "Calculate the following: (20*x - 24)*(-37*x**2 + 71*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-740*x**3 + 2308*x**2 - 1704*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 148, "polynomial_expr": "(20*x - 24)*(-37*x**2 + 71*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (20*x - 24)*(-37*x**2 + 71*x)\nExpanding the part (20*x - 24) using the distributive property, and we got: (20*x)*(-37*x**2 + 71*x) - 24*(-37*x**2 + 71*x)\n#Step 2:\nCurrent expression: (20*x)*(-37*x**2 + 71*x) - 24*(-37*x**2 + 71*x)\nSimplifying the partial expression: -24*(-37*x**2 + 71*x)\nExpanding the part (-37*x**2 + 71*x) using the distributive property, and we got: (71*x)*(-24) - 37*x**2*(-24)\nReplacing -24*(-37*x**2 + 71*x) with (71*x)*(-24) - 37*x**2*(-24) in the overall expression.\n#Step 3:\nCurrent expression: (20*x)*(-37*x**2 + 71*x) + (71*x)*(-24) - 37*x**2*(-24)\nSimplifying the partial expression: (20*x)*(-37*x**2 + 71*x)\nExpanding the part (-37*x**2 + 71*x) using the distributive property, and we got: (20*x)*(71*x) + (20*x)*(-37*x**2)\nReplacing (20*x)*(-37*x**2 + 71*x) with (20*x)*(71*x) + (20*x)*(-37*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (20*x)*(71*x) + (20*x)*(-37*x**2) + (71*x)*(-24) - 37*x**2*(-24)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*x**2)*-24 = 888*x**2\n (-37*x**2)*(20*x) = -740*x**3\n (71*x)*-24 = -1704*x\n (71*x)*(20*x) = 1420*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -740*x**3 + 888*x**2 + 1420*x**2 - 1704*x\nCombining like terms, got -740*x**3 + 2308*x**2 - 1704*x\n#Step 6:\nCurrent expression: -740*x**3 + 2308*x**2 - 1704*x\nNo more calculations needed.\n-740*x**3 + 2308*x**2 - 1704*x", "generated_answer": "-740*x**3 + 2308*x**2 - 1704*x", "step_length": 6} {"cot_id": "f80f8ce53d2484027a18b17500e39296eb34a725c9f0306fe9298befd7dbe74f", "datapoint": {"question": "Simplify this expression: (-8*z**3 - 73*z**2)*(-15*z**3 - 17*z + 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "120*z**6 + 1095*z**5 + 136*z**4 + 1193*z**3 - 438*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 149, "polynomial_expr": "(-8*z**3 - 73*z**2)*(-15*z**3 - 17*z + 6)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-8*z**3 - 73*z**2)*(-15*z**3 - 17*z + 6)\nExpanding the part (-8*z**3 - 73*z**2) using the distributive property, and we got: (-73*z**2)*(-15*z**3 - 17*z + 6) + (-8*z**3)*(-15*z**3 - 17*z + 6)\n#Step 2:\nCurrent expression: (-73*z**2)*(-15*z**3 - 17*z + 6) + (-8*z**3)*(-15*z**3 - 17*z + 6)\nSimplifying the partial expression: (-73*z**2)*(-15*z**3 - 17*z + 6)\nExpanding the part (-15*z**3 - 17*z + 6) using the distributive property, and we got: (-17*z)*(-73*z**2) + 6*(-73*z**2) + (-73*z**2)*(-15*z**3)\nReplacing (-73*z**2)*(-15*z**3 - 17*z + 6) with (-17*z)*(-73*z**2) + 6*(-73*z**2) + (-73*z**2)*(-15*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-17*z)*(-73*z**2) + 6*(-73)*z**2 + (-73*z**2)*(-15*z**3) + (-8*z**3)*(-15*z**3 - 17*z + 6)\nSimplifying the partial expression: (-8*z**3)*(-15*z**3 - 17*z + 6)\nExpanding the part (-15*z**3 - 17*z + 6) using the distributive property, and we got: (-17*z)*(-8*z**3) + 6*(-8*z**3) + (-15*z**3)*(-8*z**3)\nReplacing (-8*z**3)*(-15*z**3 - 17*z + 6) with (-17*z)*(-8*z**3) + 6*(-8*z**3) + (-15*z**3)*(-8*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-17*z)*(-73*z**2) + (-17*z)*(-8*z**3) + 6*(-8)*z**3 + 6*(-73)*z**2 + (-73*z**2)*(-15*z**3) + (-15*z**3)*(-8*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-17*z)*(-73*z**2) = 1241*z**3\n (-17*z)*(-8*z**3) = 136*z**4\n (-15*z**3)*(-73*z**2) = 1095*z**5\n (-15*z**3)*(-8*z**3) = 120*z**6\n 6*-73*z**2 = -438*z**2\n 6*-8*z**3 = -48*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 120*z**6 + 1095*z**5 + 136*z**4 - 48*z**3 + 1241*z**3 - 438*z**2\nCombining like terms, got 120*z**6 + 1095*z**5 + 136*z**4 + 1193*z**3 - 438*z**2\n#Step 6:\nCurrent expression: 120*z**6 + 1095*z**5 + 136*z**4 + 1193*z**3 - 438*z**2\nNo more calculations needed.\n120*z**6 + 1095*z**5 + 136*z**4 + 1193*z**3 - 438*z**2", "generated_answer": "120*z**6 + 1095*z**5 + 136*z**4 + 1193*z**3 - 438*z**2", "step_length": 6} {"cot_id": "612294c3bcf8d056c32d13d64c27611e625d3658409b1670a28f4dca944f377d", "datapoint": {"question": "Calculate the following: -1100*y**2 + 1500*y\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1100*y**2 + 1500*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 150, "polynomial_expr": "-1100*y**2 + 1500*y", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -1100*y**2 + 1500*y\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -1100*y**2 + 1500*y\nNo more calculations needed.\n-1100*y**2 + 1500*y", "generated_answer": "-1100*y**2 + 1500*y", "step_length": 2} {"cot_id": "f2909b9098b1755a07cc7410d428d3c87873b26f32becae3afed04d65a1ff562", "datapoint": {"question": "Simplify this expression: (68*z + 35)*(-15*z**3 + 20*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1020*z**4 - 525*z**3 + 1360*z**2 + 700*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 151, "polynomial_expr": "(68*z + 35)*(-15*z**3 + 20*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (68*z + 35)*(-15*z**3 + 20*z)\nExpanding the part (68*z + 35) using the distributive property, and we got: (68*z)*(-15*z**3 + 20*z) + 35*(-15*z**3 + 20*z)\n#Step 2:\nCurrent expression: (68*z)*(-15*z**3 + 20*z) + 35*(-15*z**3 + 20*z)\nSimplifying the partial expression: 35*(-15*z**3 + 20*z)\nExpanding the part (-15*z**3 + 20*z) using the distributive property, and we got: (20*z)*35 - 15*z**3*35\nReplacing 35*(-15*z**3 + 20*z) with (20*z)*35 - 15*z**3*35 in the overall expression.\n#Step 3:\nCurrent expression: (20*z)*35 + (68*z)*(-15*z**3 + 20*z) - 15*z**3*35\nSimplifying the partial expression: (68*z)*(-15*z**3 + 20*z)\nExpanding the part (-15*z**3 + 20*z) using the distributive property, and we got: (20*z)*(68*z) + (68*z)*(-15*z**3)\nReplacing (68*z)*(-15*z**3 + 20*z) with (20*z)*(68*z) + (68*z)*(-15*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (20*z)*(68*z) + (20*z)*35 + (68*z)*(-15*z**3) - 15*z**3*35\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-15*z**3)*35 = -525*z**3\n (-15*z**3)*(68*z) = -1020*z**4\n (20*z)*35 = 700*z\n (20*z)*(68*z) = 1360*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1020*z**4 - 525*z**3 + 1360*z**2 + 700*z\nNo more calculations needed.\n-1020*z**4 - 525*z**3 + 1360*z**2 + 700*z", "generated_answer": "-1020*z**4 - 525*z**3 + 1360*z**2 + 700*z", "step_length": 5} {"cot_id": "b592eecc5b6a34799fb338d9c350c48ac85bb4d93b0c7370074c2e5dea2c489a", "datapoint": {"question": "Simplify this expression: (-11*z**2 + 30*z + 83)*(46*z**2 - 10*z + 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-506*z**4 + 1490*z**3 + 3254*z**2 - 110*z + 1992", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 152, "polynomial_expr": "(-11*z**2 + 30*z + 83)*(46*z**2 - 10*z + 24)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-11*z**2 + 30*z + 83)*(46*z**2 - 10*z + 24)\nExpanding the part (46*z**2 - 10*z + 24) using the distributive property, and we got: (-10*z)*(-11*z**2 + 30*z + 83) + (46*z**2)*(-11*z**2 + 30*z + 83) + 24*(-11*z**2 + 30*z + 83)\n#Step 2:\nCurrent expression: (-10*z)*(-11*z**2 + 30*z + 83) + (46*z**2)*(-11*z**2 + 30*z + 83) + 24*(-11*z**2 + 30*z + 83)\nSimplifying the partial expression: 24*(-11*z**2 + 30*z + 83)\nExpanding the part (-11*z**2 + 30*z + 83) using the distributive property, and we got: (30*z)*24 - 11*z**2*24 + 83*24\nReplacing 24*(-11*z**2 + 30*z + 83) with (30*z)*24 - 11*z**2*24 + 83*24 in the overall expression.\n#Step 3:\nCurrent expression: (-10*z)*(-11*z**2 + 30*z + 83) + (30*z)*24 - 11*z**2*24 + (46*z**2)*(-11*z**2 + 30*z + 83) + 1992\nSimplifying the partial expression: (-10*z)*(-11*z**2 + 30*z + 83)\nExpanding the part (-11*z**2 + 30*z + 83) using the distributive property, and we got: (-10*z)*(30*z) + (-10*z)*(-11*z**2) + 83*(-10*z)\nReplacing (-10*z)*(-11*z**2 + 30*z + 83) with (-10*z)*(30*z) + (-10*z)*(-11*z**2) + 83*(-10*z) in the overall expression.\n#Step 4:\nCurrent expression: (-10*z)*(30*z) + (-10*z)*(-11*z**2) + 83*(-10)*z + (30*z)*24 - 11*z**2*24 + (46*z**2)*(-11*z**2 + 30*z + 83) + 1992\nSimplifying the partial expression: (46*z**2)*(-11*z**2 + 30*z + 83)\nExpanding the part (-11*z**2 + 30*z + 83) using the distributive property, and we got: 83*(46*z**2) + (30*z)*(46*z**2) + (-11*z**2)*(46*z**2)\nReplacing (46*z**2)*(-11*z**2 + 30*z + 83) with 83*(46*z**2) + (30*z)*(46*z**2) + (-11*z**2)*(46*z**2) in the overall expression.\n#Step 5:\nCurrent expression: (-10*z)*(30*z) + (-10*z)*(-11*z**2) + 83*46*z**2 + 83*(-10)*z + (30*z)*(46*z**2) + (30*z)*24 + (-11*z**2)*(46*z**2) - 11*z**2*24 + 1992\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*z**2)*24 = -264*z**2\n (-11*z**2)*(-10*z) = 110*z**3\n (-11*z**2)*(46*z**2) = -506*z**4\n (30*z)*24 = 720*z\n (30*z)*(-10*z) = -300*z**2\n (30*z)*(46*z**2) = 1380*z**3\n 83*-10*z = -830*z\n 83*46*z**2 = 3818*z**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -506*z**4 + 110*z**3 + 1380*z**3 - 300*z**2 - 264*z**2 + 3818*z**2 - 830*z + 720*z + 1992\nCombining like terms, got -506*z**4 + 1490*z**3 + 3254*z**2 - 110*z + 1992\n#Step 7:\nCurrent expression: -506*z**4 + 1490*z**3 + 3254*z**2 - 110*z + 1992\nNo more calculations needed.\n-506*z**4 + 1490*z**3 + 3254*z**2 - 110*z + 1992", "generated_answer": "-506*z**4 + 1490*z**3 + 3254*z**2 - 110*z + 1992", "step_length": 7} {"cot_id": "4fa0eb727df6511d18b7f943582064091ff792d9c4fad2ce13f7f36cec5e520d", "datapoint": {"question": "Simplify this expression: (42 - 14*z**2)*(33*z**2 + 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-462*z**4 + 1050*z**2 + 1008", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 153, "polynomial_expr": "(42 - 14*z**2)*(33*z**2 + 24)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (42 - 14*z**2)*(33*z**2 + 24)\nExpanding the part (33*z**2 + 24) using the distributive property, and we got: (33*z**2)*(42 - 14*z**2) + 24*(42 - 14*z**2)\n#Step 2:\nCurrent expression: (33*z**2)*(42 - 14*z**2) + 24*(42 - 14*z**2)\nSimplifying the partial expression: 24*(42 - 14*z**2)\nExpanding the part (42 - 14*z**2) using the distributive property, and we got: -14*z**2*24 + 42*24\nReplacing 24*(42 - 14*z**2) with -14*z**2*24 + 42*24 in the overall expression.\n#Step 3:\nCurrent expression: -14*z**2*24 + (33*z**2)*(42 - 14*z**2) + 1008\nSimplifying the partial expression: (33*z**2)*(42 - 14*z**2)\nExpanding the part (42 - 14*z**2) using the distributive property, and we got: 42*(33*z**2) + (-14*z**2)*(33*z**2)\nReplacing (33*z**2)*(42 - 14*z**2) with 42*(33*z**2) + (-14*z**2)*(33*z**2) in the overall expression.\n#Step 4:\nCurrent expression: 42*33*z**2 + (-14*z**2)*(33*z**2) - 14*z**2*24 + 1008\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-14*z**2)*24 = -336*z**2\n (-14*z**2)*(33*z**2) = -462*z**4\n 42*33*z**2 = 1386*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -462*z**4 - 336*z**2 + 1386*z**2 + 1008\nCombining like terms, got -462*z**4 + 1050*z**2 + 1008\n#Step 6:\nCurrent expression: -462*z**4 + 1050*z**2 + 1008\nNo more calculations needed.\n-462*z**4 + 1050*z**2 + 1008", "generated_answer": "-462*z**4 + 1050*z**2 + 1008", "step_length": 6} {"cot_id": "bec7260307ec980ea2b68ba5d2556dabfc4847cc6bf9a031c2a3c9fac913ea71", "datapoint": {"question": "Calculate the following: (5*z**2 + 65*z)*(21*z**3 + 50*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "105*z**5 + 1615*z**4 + 3250*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 154, "polynomial_expr": "(5*z**2 + 65*z)*(21*z**3 + 50*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (5*z**2 + 65*z)*(21*z**3 + 50*z**2)\nExpanding the part (5*z**2 + 65*z) using the distributive property, and we got: (65*z)*(21*z**3 + 50*z**2) + (5*z**2)*(21*z**3 + 50*z**2)\n#Step 2:\nCurrent expression: (65*z)*(21*z**3 + 50*z**2) + (5*z**2)*(21*z**3 + 50*z**2)\nSimplifying the partial expression: (5*z**2)*(21*z**3 + 50*z**2)\nExpanding the part (21*z**3 + 50*z**2) using the distributive property, and we got: (5*z**2)*(50*z**2) + (5*z**2)*(21*z**3)\nReplacing (5*z**2)*(21*z**3 + 50*z**2) with (5*z**2)*(50*z**2) + (5*z**2)*(21*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (65*z)*(21*z**3 + 50*z**2) + (5*z**2)*(50*z**2) + (5*z**2)*(21*z**3)\nSimplifying the partial expression: (65*z)*(21*z**3 + 50*z**2)\nExpanding the part (21*z**3 + 50*z**2) using the distributive property, and we got: (65*z)*(50*z**2) + (65*z)*(21*z**3)\nReplacing (65*z)*(21*z**3 + 50*z**2) with (65*z)*(50*z**2) + (65*z)*(21*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (65*z)*(50*z**2) + (65*z)*(21*z**3) + (5*z**2)*(50*z**2) + (5*z**2)*(21*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (21*z**3)*(5*z**2) = 105*z**5\n (21*z**3)*(65*z) = 1365*z**4\n (50*z**2)*(5*z**2) = 250*z**4\n (50*z**2)*(65*z) = 3250*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 105*z**5 + 250*z**4 + 1365*z**4 + 3250*z**3\nCombining like terms, got 105*z**5 + 1615*z**4 + 3250*z**3\n#Step 6:\nCurrent expression: 105*z**5 + 1615*z**4 + 3250*z**3\nNo more calculations needed.\n105*z**5 + 1615*z**4 + 3250*z**3", "generated_answer": "105*z**5 + 1615*z**4 + 3250*z**3", "step_length": 6} {"cot_id": "6ee7e611c560bf3269e26bb14ae3562a703987963a1b07031677f75b4174bf79", "datapoint": {"question": "Calculate the following: -27*z**3*(30*z**3 + 38*z**2 - 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-810*z**6 - 1026*z**5 + 1188*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 155, "polynomial_expr": "-27*z**3*(30*z**3 + 38*z**2 - 44)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -27*z**3*(30*z**3 + 38*z**2 - 44)\nExpanding the part (30*z**3 + 38*z**2 - 44) using the distributive property, and we got: -(-1)*1188*z**3 + (38*z**2)*(-27*z**3) + (-27*z**3)*(30*z**3)\n#Step 2:\nCurrent expression: -(-1)*1188*z**3 + (38*z**2)*(-27*z**3) + (-27*z**3)*(30*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -44*(-27*z**3) = 1188*z**3\n (30*z**3)*(-27*z**3) = -810*z**6\n (38*z**2)*(-27*z**3) = -1026*z**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -810*z**6 - 1026*z**5 + 1188*z**3\nNo more calculations needed.\n-810*z**6 - 1026*z**5 + 1188*z**3", "generated_answer": "-810*z**6 - 1026*z**5 + 1188*z**3", "step_length": 3} {"cot_id": "83e36a806197b92b3d7faf625d26fefcf71e6c854987823e5d8d961c596e4e60", "datapoint": {"question": "Simplify this expression: (-35*x**2 + 25*x)*(-43*x**3 - 34*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1505*x**5 + 115*x**4 - 850*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 156, "polynomial_expr": "(-35*x**2 + 25*x)*(-43*x**3 - 34*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-35*x**2 + 25*x)*(-43*x**3 - 34*x**2)\nExpanding the part (-43*x**3 - 34*x**2) using the distributive property, and we got: (-34*x**2)*(-35*x**2 + 25*x) + (-43*x**3)*(-35*x**2 + 25*x)\n#Step 2:\nCurrent expression: (-34*x**2)*(-35*x**2 + 25*x) + (-43*x**3)*(-35*x**2 + 25*x)\nSimplifying the partial expression: (-43*x**3)*(-35*x**2 + 25*x)\nExpanding the part (-35*x**2 + 25*x) using the distributive property, and we got: (25*x)*(-43*x**3) + (-35*x**2)*(-43*x**3)\nReplacing (-43*x**3)*(-35*x**2 + 25*x) with (25*x)*(-43*x**3) + (-35*x**2)*(-43*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (25*x)*(-43*x**3) + (-35*x**2)*(-43*x**3) + (-34*x**2)*(-35*x**2 + 25*x)\nSimplifying the partial expression: (-34*x**2)*(-35*x**2 + 25*x)\nExpanding the part (-35*x**2 + 25*x) using the distributive property, and we got: (25*x)*(-34*x**2) + (-35*x**2)*(-34*x**2)\nReplacing (-34*x**2)*(-35*x**2 + 25*x) with (25*x)*(-34*x**2) + (-35*x**2)*(-34*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (25*x)*(-34*x**2) + (25*x)*(-43*x**3) + (-35*x**2)*(-34*x**2) + (-35*x**2)*(-43*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*x**2)*(-43*x**3) = 1505*x**5\n (-35*x**2)*(-34*x**2) = 1190*x**4\n (25*x)*(-43*x**3) = -1075*x**4\n (25*x)*(-34*x**2) = -850*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1505*x**5 - 1075*x**4 + 1190*x**4 - 850*x**3\nCombining like terms, got 1505*x**5 + 115*x**4 - 850*x**3\n#Step 6:\nCurrent expression: 1505*x**5 + 115*x**4 - 850*x**3\nNo more calculations needed.\n1505*x**5 + 115*x**4 - 850*x**3", "generated_answer": "1505*x**5 + 115*x**4 - 850*x**3", "step_length": 6} {"cot_id": "03d3ff4bad420924e482a844502616288b2cdb356d5d47345f1e342203664da7", "datapoint": {"question": "Calculate the following: -38*y*(-17*y**2 + 45*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "646*y**3 - 1710*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 157, "polynomial_expr": "-38*y*(-17*y**2 + 45*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -38*y*(-17*y**2 + 45*y)\nExpanding the part (-17*y**2 + 45*y) using the distributive property, and we got: (-38*y)*(45*y) + (-38*y)*(-17*y**2)\n#Step 2:\nCurrent expression: (-38*y)*(45*y) + (-38*y)*(-17*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-17*y**2)*(-38*y) = 646*y**3\n (45*y)*(-38*y) = -1710*y**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 646*y**3 - 1710*y**2\nNo more calculations needed.\n646*y**3 - 1710*y**2", "generated_answer": "646*y**3 - 1710*y**2", "step_length": 3} {"cot_id": "92340eba3f78db0449a1a6a02ef3400cebf5197e5b19c2602f30810f061c2080", "datapoint": {"question": "Simplify this expression: (-45*x**3 - 13*x)*(-29*x**2 - 28*x + 46)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1305*x**5 + 1260*x**4 - 1693*x**3 + 364*x**2 - 598*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 158, "polynomial_expr": "(-45*x**3 - 13*x)*(-29*x**2 - 28*x + 46)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-45*x**3 - 13*x)*(-29*x**2 - 28*x + 46)\nExpanding the part (-45*x**3 - 13*x) using the distributive property, and we got: (-13*x)*(-29*x**2 - 28*x + 46) + (-45*x**3)*(-29*x**2 - 28*x + 46)\n#Step 2:\nCurrent expression: (-13*x)*(-29*x**2 - 28*x + 46) + (-45*x**3)*(-29*x**2 - 28*x + 46)\nSimplifying the partial expression: (-45*x**3)*(-29*x**2 - 28*x + 46)\nExpanding the part (-29*x**2 - 28*x + 46) using the distributive property, and we got: (-28*x)*(-45*x**3) + 46*(-45*x**3) + (-29*x**2)*(-45*x**3)\nReplacing (-45*x**3)*(-29*x**2 - 28*x + 46) with (-28*x)*(-45*x**3) + 46*(-45*x**3) + (-29*x**2)*(-45*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-28*x)*(-45*x**3) + (-13*x)*(-29*x**2 - 28*x + 46) + 46*(-45)*x**3 + (-29*x**2)*(-45*x**3)\nSimplifying the partial expression: (-13*x)*(-29*x**2 - 28*x + 46)\nExpanding the part (-29*x**2 - 28*x + 46) using the distributive property, and we got: (-28*x)*(-13*x) + (-13*x)*(-29*x**2) + 46*(-13*x)\nReplacing (-13*x)*(-29*x**2 - 28*x + 46) with (-28*x)*(-13*x) + (-13*x)*(-29*x**2) + 46*(-13*x) in the overall expression.\n#Step 4:\nCurrent expression: (-28*x)*(-13*x) + (-28*x)*(-45*x**3) + (-13*x)*(-29*x**2) + 46*(-45)*x**3 + 46*(-13)*x + (-29*x**2)*(-45*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*x**2)*(-45*x**3) = 1305*x**5\n (-29*x**2)*(-13*x) = 377*x**3\n (-28*x)*(-45*x**3) = 1260*x**4\n (-28*x)*(-13*x) = 364*x**2\n 46*-45*x**3 = -2070*x**3\n 46*-13*x = -598*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1305*x**5 + 1260*x**4 - 2070*x**3 + 377*x**3 + 364*x**2 - 598*x\nCombining like terms, got 1305*x**5 + 1260*x**4 - 1693*x**3 + 364*x**2 - 598*x\n#Step 6:\nCurrent expression: 1305*x**5 + 1260*x**4 - 1693*x**3 + 364*x**2 - 598*x\nNo more calculations needed.\n1305*x**5 + 1260*x**4 - 1693*x**3 + 364*x**2 - 598*x", "generated_answer": "1305*x**5 + 1260*x**4 - 1693*x**3 + 364*x**2 - 598*x", "step_length": 6} {"cot_id": "38e50784eb766a371fd8a02bd9e0886837279bce8ea2cb456a532b20f4b7278f", "datapoint": {"question": "Simplify this expression: (27*x**3 - x**2)*(-77*x**3 - 13*x + 15)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2079*x**6 + 77*x**5 - 351*x**4 + 418*x**3 - 15*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 159, "polynomial_expr": "(27*x**3 - x**2)*(-77*x**3 - 13*x + 15)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*x**3 - x**2)*(-77*x**3 - 13*x + 15)\nExpanding the part (27*x**3 - x**2) using the distributive property, and we got: (-x**2)*(-77*x**3 - 13*x + 15) + (27*x**3)*(-77*x**3 - 13*x + 15)\n#Step 2:\nCurrent expression: (-x**2)*(-77*x**3 - 13*x + 15) + (27*x**3)*(-77*x**3 - 13*x + 15)\nSimplifying the partial expression: (-x**2)*(-77*x**3 - 13*x + 15)\nExpanding the part (-77*x**3 - 13*x + 15) using the distributive property, and we got: (-13*x)*(-x**2) + 15*(-x**2) + (-x**2)*(-77*x**3)\nReplacing (-x**2)*(-77*x**3 - 13*x + 15) with (-13*x)*(-x**2) + 15*(-x**2) + (-x**2)*(-77*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-13*x)*(-x**2) + 15*(-1)*x**2 + (-x**2)*(-77*x**3) + (27*x**3)*(-77*x**3 - 13*x + 15)\nSimplifying the partial expression: (27*x**3)*(-77*x**3 - 13*x + 15)\nExpanding the part (-77*x**3 - 13*x + 15) using the distributive property, and we got: (-13*x)*(27*x**3) + 15*(27*x**3) + (-77*x**3)*(27*x**3)\nReplacing (27*x**3)*(-77*x**3 - 13*x + 15) with (-13*x)*(27*x**3) + 15*(27*x**3) + (-77*x**3)*(27*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-13*x)*(-x**2) + (-13*x)*(27*x**3) + 15*27*x**3 + 15*(-1)*x**2 + (-x**2)*(-77*x**3) + (-77*x**3)*(27*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-77*x**3)*(-x**2) = 77*x**5\n (-77*x**3)*(27*x**3) = -2079*x**6\n (-13*x)*(-x**2) = 13*x**3\n (-13*x)*(27*x**3) = -351*x**4\n 15*-1*x**2 = -15*x**2\n 15*27*x**3 = 405*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2079*x**6 + 77*x**5 - 351*x**4 + 13*x**3 + 405*x**3 - 15*x**2\nCombining like terms, got -2079*x**6 + 77*x**5 - 351*x**4 + 418*x**3 - 15*x**2\n#Step 6:\nCurrent expression: -2079*x**6 + 77*x**5 - 351*x**4 + 418*x**3 - 15*x**2\nNo more calculations needed.\n-2079*x**6 + 77*x**5 - 351*x**4 + 418*x**3 - 15*x**2", "generated_answer": "-2079*x**6 + 77*x**5 - 351*x**4 + 418*x**3 - 15*x**2", "step_length": 6} {"cot_id": "93716cab2aa9e9bc2d94f2e0f709aa181eb90ba10d4a21c5edf82a6b00a1b11f", "datapoint": {"question": "Calculate the following: (27 - 21*y**2)*(29*y**3 - 4*y**2 + 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-609*y**5 + 84*y**4 + 783*y**3 - 381*y**2 + 351", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 160, "polynomial_expr": "(27 - 21*y**2)*(29*y**3 - 4*y**2 + 13)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27 - 21*y**2)*(29*y**3 - 4*y**2 + 13)\nExpanding the part (27 - 21*y**2) using the distributive property, and we got: (-21*y**2)*(29*y**3 - 4*y**2 + 13) + 27*(29*y**3 - 4*y**2 + 13)\n#Step 2:\nCurrent expression: (-21*y**2)*(29*y**3 - 4*y**2 + 13) + 27*(29*y**3 - 4*y**2 + 13)\nSimplifying the partial expression: 27*(29*y**3 - 4*y**2 + 13)\nExpanding the part (29*y**3 - 4*y**2 + 13) using the distributive property, and we got: -4*y**2*27 + (29*y**3)*27 + 13*27\nReplacing 27*(29*y**3 - 4*y**2 + 13) with -4*y**2*27 + (29*y**3)*27 + 13*27 in the overall expression.\n#Step 3:\nCurrent expression: (-21*y**2)*(29*y**3 - 4*y**2 + 13) - 4*y**2*27 + (29*y**3)*27 + 351\nSimplifying the partial expression: (-21*y**2)*(29*y**3 - 4*y**2 + 13)\nExpanding the part (29*y**3 - 4*y**2 + 13) using the distributive property, and we got: 13*(-21*y**2) + (-21*y**2)*(-4*y**2) + (-21*y**2)*(29*y**3)\nReplacing (-21*y**2)*(29*y**3 - 4*y**2 + 13) with 13*(-21*y**2) + (-21*y**2)*(-4*y**2) + (-21*y**2)*(29*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 13*(-21)*y**2 + (-21*y**2)*(-4*y**2) + (-21*y**2)*(29*y**3) - 4*y**2*27 + (29*y**3)*27 + 351\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-4*y**2)*27 = -108*y**2\n (-4*y**2)*(-21*y**2) = 84*y**4\n (29*y**3)*27 = 783*y**3\n (29*y**3)*(-21*y**2) = -609*y**5\n 13*-21*y**2 = -273*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -609*y**5 + 84*y**4 + 783*y**3 - 273*y**2 - 108*y**2 + 351\nCombining like terms, got -609*y**5 + 84*y**4 + 783*y**3 - 381*y**2 + 351\n#Step 6:\nCurrent expression: -609*y**5 + 84*y**4 + 783*y**3 - 381*y**2 + 351\nNo more calculations needed.\n-609*y**5 + 84*y**4 + 783*y**3 - 381*y**2 + 351", "generated_answer": "-609*y**5 + 84*y**4 + 783*y**3 - 381*y**2 + 351", "step_length": 6} {"cot_id": "d3881c6c6717a3063fe62341f56d819cbe9d78d0beec46958e7b471d7f7a78ab", "datapoint": {"question": "Calculate the following: (48*x**2 + 33*x)*(39*x**2 + 47*x - 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1872*x**4 + 3543*x**3 - 321*x**2 - 1287*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 161, "polynomial_expr": "(48*x**2 + 33*x)*(39*x**2 + 47*x - 39)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (48*x**2 + 33*x)*(39*x**2 + 47*x - 39)\nExpanding the part (48*x**2 + 33*x) using the distributive property, and we got: (33*x)*(39*x**2 + 47*x - 39) + (48*x**2)*(39*x**2 + 47*x - 39)\n#Step 2:\nCurrent expression: (33*x)*(39*x**2 + 47*x - 39) + (48*x**2)*(39*x**2 + 47*x - 39)\nSimplifying the partial expression: (33*x)*(39*x**2 + 47*x - 39)\nExpanding the part (39*x**2 + 47*x - 39) using the distributive property, and we got: -1287*x + (33*x)*(47*x) + (33*x)*(39*x**2)\nReplacing (33*x)*(39*x**2 + 47*x - 39) with -1287*x + (33*x)*(47*x) + (33*x)*(39*x**2) in the overall expression.\n#Step 3:\nCurrent expression: -39*33*x + (33*x)*(47*x) + (33*x)*(39*x**2) + (48*x**2)*(39*x**2 + 47*x - 39)\nSimplifying the partial expression: (48*x**2)*(39*x**2 + 47*x - 39)\nExpanding the part (39*x**2 + 47*x - 39) using the distributive property, and we got: -1872*x**2 + (47*x)*(48*x**2) + (39*x**2)*(48*x**2)\nReplacing (48*x**2)*(39*x**2 + 47*x - 39) with -1872*x**2 + (47*x)*(48*x**2) + (39*x**2)*(48*x**2) in the overall expression.\n#Step 4:\nCurrent expression: -39*48*x**2 - 39*33*x + (33*x)*(47*x) + (33*x)*(39*x**2) + (47*x)*(48*x**2) + (39*x**2)*(48*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (39*x**2)*(33*x) = 1287*x**3\n (39*x**2)*(48*x**2) = 1872*x**4\n (47*x)*(33*x) = 1551*x**2\n (47*x)*(48*x**2) = 2256*x**3\n -39*33*x = -1287*x\n -39*48*x**2 = -1872*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1872*x**4 + 1287*x**3 + 2256*x**3 - 1872*x**2 + 1551*x**2 - 1287*x\nCombining like terms, got 1872*x**4 + 3543*x**3 - 321*x**2 - 1287*x\n#Step 6:\nCurrent expression: 1872*x**4 + 3543*x**3 - 321*x**2 - 1287*x\nNo more calculations needed.\n1872*x**4 + 3543*x**3 - 321*x**2 - 1287*x", "generated_answer": "1872*x**4 + 3543*x**3 - 321*x**2 - 1287*x", "step_length": 6} {"cot_id": "f15554b8b50946bcbf40fa3f5230df516c703717ae004697eb05a14b863608de", "datapoint": {"question": "Calculate the following: (-20*y**2 + 34*y - 26)*(22*y**3 - 5*y**2 + 11*y - 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-440*y**5 + 848*y**4 - 962*y**3 + 784*y**2 - 762*y + 364", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 162, "polynomial_expr": "(-20*y**2 + 34*y - 26)*(22*y**3 - 5*y**2 + 11*y - 14)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-20*y**2 + 34*y - 26)*(22*y**3 - 5*y**2 + 11*y - 14)\nExpanding the part (-20*y**2 + 34*y - 26) using the distributive property, and we got: (34*y)*(22*y**3 - 5*y**2 + 11*y - 14) + (-20*y**2)*(22*y**3 - 5*y**2 + 11*y - 14) - 26*(22*y**3 - 5*y**2 + 11*y - 14)\n#Step 2:\nCurrent expression: (34*y)*(22*y**3 - 5*y**2 + 11*y - 14) + (-20*y**2)*(22*y**3 - 5*y**2 + 11*y - 14) - 26*(22*y**3 - 5*y**2 + 11*y - 14)\nSimplifying the partial expression: -26*(22*y**3 - 5*y**2 + 11*y - 14)\nExpanding the part (22*y**3 - 5*y**2 + 11*y - 14) using the distributive property, and we got: (11*y)*(-26) - 5*y**2*(-26) + (22*y**3)*(-26) - 14*(-26)\nReplacing -26*(22*y**3 - 5*y**2 + 11*y - 14) with (11*y)*(-26) - 5*y**2*(-26) + (22*y**3)*(-26) - 14*(-26) in the overall expression.\n#Step 3:\nCurrent expression: (11*y)*(-26) + (34*y)*(22*y**3 - 5*y**2 + 11*y - 14) + (-20*y**2)*(22*y**3 - 5*y**2 + 11*y - 14) - 5*y**2*(-26) + (22*y**3)*(-26) + 364\nSimplifying the partial expression: (-20*y**2)*(22*y**3 - 5*y**2 + 11*y - 14)\nExpanding the part (22*y**3 - 5*y**2 + 11*y - 14) using the distributive property, and we got: -(-1)*280*y**2 + (11*y)*(-20*y**2) + (-20*y**2)*(-5*y**2) + (-20*y**2)*(22*y**3)\nReplacing (-20*y**2)*(22*y**3 - 5*y**2 + 11*y - 14) with -(-1)*280*y**2 + (11*y)*(-20*y**2) + (-20*y**2)*(-5*y**2) + (-20*y**2)*(22*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -14*(-20)*y**2 + (11*y)*(-20*y**2) + (11*y)*(-26) + (34*y)*(22*y**3 - 5*y**2 + 11*y - 14) + (-20*y**2)*(-5*y**2) + (-20*y**2)*(22*y**3) - 5*y**2*(-26) + (22*y**3)*(-26) + 364\nSimplifying the partial expression: (34*y)*(22*y**3 - 5*y**2 + 11*y - 14)\nExpanding the part (22*y**3 - 5*y**2 + 11*y - 14) using the distributive property, and we got: -476*y + (11*y)*(34*y) + (34*y)*(-5*y**2) + (34*y)*(22*y**3)\nReplacing (34*y)*(22*y**3 - 5*y**2 + 11*y - 14) with -476*y + (11*y)*(34*y) + (34*y)*(-5*y**2) + (34*y)*(22*y**3) in the overall expression.\n#Step 5:\nCurrent expression: -14*(-20)*y**2 - 14*34*y + (11*y)*(34*y) + (11*y)*(-20*y**2) + (11*y)*(-26) + (34*y)*(-5*y**2) + (34*y)*(22*y**3) + (-20*y**2)*(-5*y**2) + (-20*y**2)*(22*y**3) - 5*y**2*(-26) + (22*y**3)*(-26) + 364\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-5*y**2)*-26 = 130*y**2\n (-5*y**2)*(-20*y**2) = 100*y**4\n (-5*y**2)*(34*y) = -170*y**3\n (11*y)*-26 = -286*y\n (11*y)*(-20*y**2) = -220*y**3\n (11*y)*(34*y) = 374*y**2\n (22*y**3)*-26 = -572*y**3\n (22*y**3)*(-20*y**2) = -440*y**5\n (22*y**3)*(34*y) = 748*y**4\n -14*-20*y**2 = 280*y**2\n -14*34*y = -476*y\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -440*y**5 + 100*y**4 + 748*y**4 - 572*y**3 - 220*y**3 - 170*y**3 + 130*y**2 + 280*y**2 + 374*y**2 - 476*y - 286*y + 364\nCombining like terms, got -440*y**5 + 848*y**4 - 962*y**3 + 784*y**2 - 762*y + 364\n#Step 7:\nCurrent expression: -440*y**5 + 848*y**4 - 962*y**3 + 784*y**2 - 762*y + 364\nNo more calculations needed.\n-440*y**5 + 848*y**4 - 962*y**3 + 784*y**2 - 762*y + 364", "generated_answer": "-440*y**5 + 848*y**4 - 962*y**3 + 784*y**2 - 762*y + 364", "step_length": 7} {"cot_id": "4b9a4e1b84bd6d70dee1d29aabe07bcdf9203a928c9c6a9844b815bd40fa56dd", "datapoint": {"question": "Simplify this expression: (95*y + 44)*(-7*y**2 - 51)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-665*y**3 - 308*y**2 - 4845*y - 2244", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 163, "polynomial_expr": "(95*y + 44)*(-7*y**2 - 51)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (95*y + 44)*(-7*y**2 - 51)\nExpanding the part (-7*y**2 - 51) using the distributive property, and we got: (-7*y**2)*(95*y + 44) - 51*(95*y + 44)\n#Step 2:\nCurrent expression: (-7*y**2)*(95*y + 44) - 51*(95*y + 44)\nSimplifying the partial expression: -51*(95*y + 44)\nExpanding the part (95*y + 44) using the distributive property, and we got: (95*y)*(-51) + 44*(-51)\nReplacing -51*(95*y + 44) with (95*y)*(-51) + 44*(-51) in the overall expression.\n#Step 3:\nCurrent expression: (95*y)*(-51) + (-7*y**2)*(95*y + 44) - 2244\nSimplifying the partial expression: (-7*y**2)*(95*y + 44)\nExpanding the part (95*y + 44) using the distributive property, and we got: 44*(-7*y**2) + (95*y)*(-7*y**2)\nReplacing (-7*y**2)*(95*y + 44) with 44*(-7*y**2) + (95*y)*(-7*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 44*(-7)*y**2 + (95*y)*(-7*y**2) + (95*y)*(-51) - 2244\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (95*y)*-51 = -4845*y\n (95*y)*(-7*y**2) = -665*y**3\n 44*-7*y**2 = -308*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -665*y**3 - 308*y**2 - 4845*y - 2244\nNo more calculations needed.\n-665*y**3 - 308*y**2 - 4845*y - 2244", "generated_answer": "-665*y**3 - 308*y**2 - 4845*y - 2244", "step_length": 5} {"cot_id": "14ec4db1c04a65ce03c9db6722453b28dbe24bd38ffb1c86c220fcb84ed93f92", "datapoint": {"question": "Calculate the following: 2200*x**3 - 450\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2200*x**3 - 450", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 164, "polynomial_expr": "2200*x**3 - 450", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 2200*x**3 - 450\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 2200*x**3 - 450\nNo more calculations needed.\n2200*x**3 - 450", "generated_answer": "2200*x**3 - 450", "step_length": 2} {"cot_id": "00ddf3612636f214b9477d81af898c5f4e033149c6289b682a2443cb986a57c2", "datapoint": {"question": "Calculate the following: (5*z**3 + 14)*(10*z**3 - 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "50*z**6 + 55*z**3 - 238", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 165, "polynomial_expr": "(5*z**3 + 14)*(10*z**3 - 17)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (5*z**3 + 14)*(10*z**3 - 17)\nExpanding the part (10*z**3 - 17) using the distributive property, and we got: (10*z**3)*(5*z**3 + 14) - 17*(5*z**3 + 14)\n#Step 2:\nCurrent expression: (10*z**3)*(5*z**3 + 14) - 17*(5*z**3 + 14)\nSimplifying the partial expression: -17*(5*z**3 + 14)\nExpanding the part (5*z**3 + 14) using the distributive property, and we got: (5*z**3)*(-17) + 14*(-17)\nReplacing -17*(5*z**3 + 14) with (5*z**3)*(-17) + 14*(-17) in the overall expression.\n#Step 3:\nCurrent expression: (5*z**3)*(-17) + (10*z**3)*(5*z**3 + 14) - 238\nSimplifying the partial expression: (10*z**3)*(5*z**3 + 14)\nExpanding the part (5*z**3 + 14) using the distributive property, and we got: 14*(10*z**3) + (5*z**3)*(10*z**3)\nReplacing (10*z**3)*(5*z**3 + 14) with 14*(10*z**3) + (5*z**3)*(10*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 14*10*z**3 + (5*z**3)*(10*z**3) + (5*z**3)*(-17) - 238\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (5*z**3)*-17 = -85*z**3\n (5*z**3)*(10*z**3) = 50*z**6\n 14*10*z**3 = 140*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 50*z**6 - 85*z**3 + 140*z**3 - 238\nCombining like terms, got 50*z**6 + 55*z**3 - 238\n#Step 6:\nCurrent expression: 50*z**6 + 55*z**3 - 238\nNo more calculations needed.\n50*z**6 + 55*z**3 - 238", "generated_answer": "50*z**6 + 55*z**3 - 238", "step_length": 6} {"cot_id": "e032c65a8c1dc519207b407114463b7a72345383acfede700281dcff3499263d", "datapoint": {"question": "Simplify this expression: (32 - 68*y**2)*(-40*y**2 + 37*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2720*y**4 - 2516*y**3 - 1280*y**2 + 1184*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 166, "polynomial_expr": "(32 - 68*y**2)*(-40*y**2 + 37*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (32 - 68*y**2)*(-40*y**2 + 37*y)\nExpanding the part (32 - 68*y**2) using the distributive property, and we got: (-68*y**2)*(-40*y**2 + 37*y) + 32*(-40*y**2 + 37*y)\n#Step 2:\nCurrent expression: (-68*y**2)*(-40*y**2 + 37*y) + 32*(-40*y**2 + 37*y)\nSimplifying the partial expression: 32*(-40*y**2 + 37*y)\nExpanding the part (-40*y**2 + 37*y) using the distributive property, and we got: (37*y)*32 - 40*y**2*32\nReplacing 32*(-40*y**2 + 37*y) with (37*y)*32 - 40*y**2*32 in the overall expression.\n#Step 3:\nCurrent expression: (37*y)*32 + (-68*y**2)*(-40*y**2 + 37*y) - 40*y**2*32\nSimplifying the partial expression: (-68*y**2)*(-40*y**2 + 37*y)\nExpanding the part (-40*y**2 + 37*y) using the distributive property, and we got: (37*y)*(-68*y**2) + (-68*y**2)*(-40*y**2)\nReplacing (-68*y**2)*(-40*y**2 + 37*y) with (37*y)*(-68*y**2) + (-68*y**2)*(-40*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (37*y)*(-68*y**2) + (37*y)*32 + (-68*y**2)*(-40*y**2) - 40*y**2*32\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*y**2)*32 = -1280*y**2\n (-40*y**2)*(-68*y**2) = 2720*y**4\n (37*y)*32 = 1184*y\n (37*y)*(-68*y**2) = -2516*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2720*y**4 - 2516*y**3 - 1280*y**2 + 1184*y\nNo more calculations needed.\n2720*y**4 - 2516*y**3 - 1280*y**2 + 1184*y", "generated_answer": "2720*y**4 - 2516*y**3 - 1280*y**2 + 1184*y", "step_length": 5} {"cot_id": "d64f153170451618a951fdc9b61f400dd2d84bac4f084cafdb7e86b581ad6f40", "datapoint": {"question": "Simplify this expression: -925*z - 1100\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-925*z - 1100", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 167, "polynomial_expr": "-925*z - 1100", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -925*z - 1100\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -925*z - 1100\nNo more calculations needed.\n-925*z - 1100", "generated_answer": "-925*z - 1100", "step_length": 2} {"cot_id": "106b87af51b6f76a0818cf3af28d8b6ecae7dd6c98b29089000856febf4255e8", "datapoint": {"question": "Calculate the following: (-35*y**3 + 42*y**2)*(60*y**3 + 55*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2100*y**6 + 595*y**5 + 2310*y**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 168, "polynomial_expr": "(-35*y**3 + 42*y**2)*(60*y**3 + 55*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-35*y**3 + 42*y**2)*(60*y**3 + 55*y**2)\nExpanding the part (-35*y**3 + 42*y**2) using the distributive property, and we got: (42*y**2)*(60*y**3 + 55*y**2) + (-35*y**3)*(60*y**3 + 55*y**2)\n#Step 2:\nCurrent expression: (42*y**2)*(60*y**3 + 55*y**2) + (-35*y**3)*(60*y**3 + 55*y**2)\nSimplifying the partial expression: (-35*y**3)*(60*y**3 + 55*y**2)\nExpanding the part (60*y**3 + 55*y**2) using the distributive property, and we got: (55*y**2)*(-35*y**3) + (-35*y**3)*(60*y**3)\nReplacing (-35*y**3)*(60*y**3 + 55*y**2) with (55*y**2)*(-35*y**3) + (-35*y**3)*(60*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (42*y**2)*(60*y**3 + 55*y**2) + (55*y**2)*(-35*y**3) + (-35*y**3)*(60*y**3)\nSimplifying the partial expression: (42*y**2)*(60*y**3 + 55*y**2)\nExpanding the part (60*y**3 + 55*y**2) using the distributive property, and we got: (42*y**2)*(55*y**2) + (42*y**2)*(60*y**3)\nReplacing (42*y**2)*(60*y**3 + 55*y**2) with (42*y**2)*(55*y**2) + (42*y**2)*(60*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (42*y**2)*(55*y**2) + (42*y**2)*(60*y**3) + (55*y**2)*(-35*y**3) + (-35*y**3)*(60*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (55*y**2)*(-35*y**3) = -1925*y**5\n (55*y**2)*(42*y**2) = 2310*y**4\n (60*y**3)*(-35*y**3) = -2100*y**6\n (60*y**3)*(42*y**2) = 2520*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2100*y**6 - 1925*y**5 + 2520*y**5 + 2310*y**4\nCombining like terms, got -2100*y**6 + 595*y**5 + 2310*y**4\n#Step 6:\nCurrent expression: -2100*y**6 + 595*y**5 + 2310*y**4\nNo more calculations needed.\n-2100*y**6 + 595*y**5 + 2310*y**4", "generated_answer": "-2100*y**6 + 595*y**5 + 2310*y**4", "step_length": 6} {"cot_id": "0d40d17d38dd2d1ecc4207d7cc6e0d0d86a2c967cd96e2ba47b00385ebd57a13", "datapoint": {"question": "Simplify this expression: (11*z**2 + 46*z + 71)*(-16*z**3 + 41*z - 66)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-176*z**5 - 736*z**4 - 685*z**3 + 1160*z**2 - 125*z - 4686", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 169, "polynomial_expr": "(11*z**2 + 46*z + 71)*(-16*z**3 + 41*z - 66)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11*z**2 + 46*z + 71)*(-16*z**3 + 41*z - 66)\nExpanding the part (-16*z**3 + 41*z - 66) using the distributive property, and we got: (41*z)*(11*z**2 + 46*z + 71) + (-16*z**3)*(11*z**2 + 46*z + 71) - 66*(11*z**2 + 46*z + 71)\n#Step 2:\nCurrent expression: (41*z)*(11*z**2 + 46*z + 71) + (-16*z**3)*(11*z**2 + 46*z + 71) - 66*(11*z**2 + 46*z + 71)\nSimplifying the partial expression: -66*(11*z**2 + 46*z + 71)\nExpanding the part (11*z**2 + 46*z + 71) using the distributive property, and we got: (46*z)*(-66) + (11*z**2)*(-66) + 71*(-66)\nReplacing -66*(11*z**2 + 46*z + 71) with (46*z)*(-66) + (11*z**2)*(-66) + 71*(-66) in the overall expression.\n#Step 3:\nCurrent expression: (41*z)*(11*z**2 + 46*z + 71) + (46*z)*(-66) + (11*z**2)*(-66) + (-16*z**3)*(11*z**2 + 46*z + 71) - 4686\nSimplifying the partial expression: (-16*z**3)*(11*z**2 + 46*z + 71)\nExpanding the part (11*z**2 + 46*z + 71) using the distributive property, and we got: 71*(-16*z**3) + (46*z)*(-16*z**3) + (11*z**2)*(-16*z**3)\nReplacing (-16*z**3)*(11*z**2 + 46*z + 71) with 71*(-16*z**3) + (46*z)*(-16*z**3) + (11*z**2)*(-16*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 71*(-16)*z**3 + (41*z)*(11*z**2 + 46*z + 71) + (46*z)*(-16*z**3) + (46*z)*(-66) + (11*z**2)*(-16*z**3) + (11*z**2)*(-66) - 4686\nSimplifying the partial expression: (41*z)*(11*z**2 + 46*z + 71)\nExpanding the part (11*z**2 + 46*z + 71) using the distributive property, and we got: 71*(41*z) + (41*z)*(46*z) + (41*z)*(11*z**2)\nReplacing (41*z)*(11*z**2 + 46*z + 71) with 71*(41*z) + (41*z)*(46*z) + (41*z)*(11*z**2) in the overall expression.\n#Step 5:\nCurrent expression: 71*(-16)*z**3 + 71*41*z + (41*z)*(46*z) + (41*z)*(11*z**2) + (46*z)*(-16*z**3) + (46*z)*(-66) + (11*z**2)*(-16*z**3) + (11*z**2)*(-66) - 4686\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (11*z**2)*-66 = -726*z**2\n (11*z**2)*(-16*z**3) = -176*z**5\n (11*z**2)*(41*z) = 451*z**3\n (46*z)*-66 = -3036*z\n (46*z)*(-16*z**3) = -736*z**4\n (46*z)*(41*z) = 1886*z**2\n 71*-16*z**3 = -1136*z**3\n 71*41*z = 2911*z\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -176*z**5 - 736*z**4 - 1136*z**3 + 451*z**3 - 726*z**2 + 1886*z**2 - 3036*z + 2911*z - 4686\nCombining like terms, got -176*z**5 - 736*z**4 - 685*z**3 + 1160*z**2 - 125*z - 4686\n#Step 7:\nCurrent expression: -176*z**5 - 736*z**4 - 685*z**3 + 1160*z**2 - 125*z - 4686\nNo more calculations needed.\n-176*z**5 - 736*z**4 - 685*z**3 + 1160*z**2 - 125*z - 4686", "generated_answer": "-176*z**5 - 736*z**4 - 685*z**3 + 1160*z**2 - 125*z - 4686", "step_length": 7} {"cot_id": "e113da655438f6b7322aa18b12b5d2a91a7fb104c28bb85a9f11d561f1658a49", "datapoint": {"question": "Simplify this expression: -75*y**3*(-38*y**3 + 34*y + 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2850*y**6 - 2550*y**4 - 2100*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 170, "polynomial_expr": "-75*y**3*(-38*y**3 + 34*y + 28)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -75*y**3*(-38*y**3 + 34*y + 28)\nExpanding the part (-38*y**3 + 34*y + 28) using the distributive property, and we got: 28*(-75*y**3) + (34*y)*(-75*y**3) + (-75*y**3)*(-38*y**3)\n#Step 2:\nCurrent expression: 28*(-75*y**3) + (34*y)*(-75*y**3) + (-75*y**3)*(-38*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 28*(-75*y**3) = -2100*y**3\n (-38*y**3)*(-75*y**3) = 2850*y**6\n (34*y)*(-75*y**3) = -2550*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 2850*y**6 - 2550*y**4 - 2100*y**3\nNo more calculations needed.\n2850*y**6 - 2550*y**4 - 2100*y**3", "generated_answer": "2850*y**6 - 2550*y**4 - 2100*y**3", "step_length": 3} {"cot_id": "c0cd89c3310f46223f198c8e81309e543682e3234b41dbc400163fa58e2d74f4", "datapoint": {"question": "Simplify this expression: (-35*x**2 - 19*x)*(-36*x**3 + 13*x**2 + 34)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1260*x**5 + 229*x**4 - 247*x**3 - 1190*x**2 - 646*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 171, "polynomial_expr": "(-35*x**2 - 19*x)*(-36*x**3 + 13*x**2 + 34)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-35*x**2 - 19*x)*(-36*x**3 + 13*x**2 + 34)\nExpanding the part (-35*x**2 - 19*x) using the distributive property, and we got: (-19*x)*(-36*x**3 + 13*x**2 + 34) + (-35*x**2)*(-36*x**3 + 13*x**2 + 34)\n#Step 2:\nCurrent expression: (-19*x)*(-36*x**3 + 13*x**2 + 34) + (-35*x**2)*(-36*x**3 + 13*x**2 + 34)\nSimplifying the partial expression: (-35*x**2)*(-36*x**3 + 13*x**2 + 34)\nExpanding the part (-36*x**3 + 13*x**2 + 34) using the distributive property, and we got: 34*(-35*x**2) + (-35*x**2)*(13*x**2) + (-35*x**2)*(-36*x**3)\nReplacing (-35*x**2)*(-36*x**3 + 13*x**2 + 34) with 34*(-35*x**2) + (-35*x**2)*(13*x**2) + (-35*x**2)*(-36*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-19*x)*(-36*x**3 + 13*x**2 + 34) + 34*(-35)*x**2 + (-35*x**2)*(13*x**2) + (-35*x**2)*(-36*x**3)\nSimplifying the partial expression: (-19*x)*(-36*x**3 + 13*x**2 + 34)\nExpanding the part (-36*x**3 + 13*x**2 + 34) using the distributive property, and we got: (-19*x)*(13*x**2) + (-19*x)*(-36*x**3) + 34*(-19*x)\nReplacing (-19*x)*(-36*x**3 + 13*x**2 + 34) with (-19*x)*(13*x**2) + (-19*x)*(-36*x**3) + 34*(-19*x) in the overall expression.\n#Step 4:\nCurrent expression: (-19*x)*(13*x**2) + (-19*x)*(-36*x**3) + 34*(-35)*x**2 + 34*(-19)*x + (-35*x**2)*(13*x**2) + (-35*x**2)*(-36*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*x**3)*(-35*x**2) = 1260*x**5\n (-36*x**3)*(-19*x) = 684*x**4\n (13*x**2)*(-35*x**2) = -455*x**4\n (13*x**2)*(-19*x) = -247*x**3\n 34*-35*x**2 = -1190*x**2\n 34*-19*x = -646*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1260*x**5 - 455*x**4 + 684*x**4 - 247*x**3 - 1190*x**2 - 646*x\nCombining like terms, got 1260*x**5 + 229*x**4 - 247*x**3 - 1190*x**2 - 646*x\n#Step 6:\nCurrent expression: 1260*x**5 + 229*x**4 - 247*x**3 - 1190*x**2 - 646*x\nNo more calculations needed.\n1260*x**5 + 229*x**4 - 247*x**3 - 1190*x**2 - 646*x", "generated_answer": "1260*x**5 + 229*x**4 - 247*x**3 - 1190*x**2 - 646*x", "step_length": 6} {"cot_id": "720f1536f7ac592799aa0a9f783c4892271bb654fab5c00e179157927b51feee", "datapoint": {"question": "Calculate the following: (53*z**3 + 54*z)*(-27*z**3 + 20*z**2 + 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1431*z**6 + 1060*z**5 - 1458*z**4 + 3677*z**3 + 2646*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 172, "polynomial_expr": "(53*z**3 + 54*z)*(-27*z**3 + 20*z**2 + 49)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (53*z**3 + 54*z)*(-27*z**3 + 20*z**2 + 49)\nExpanding the part (53*z**3 + 54*z) using the distributive property, and we got: (54*z)*(-27*z**3 + 20*z**2 + 49) + (53*z**3)*(-27*z**3 + 20*z**2 + 49)\n#Step 2:\nCurrent expression: (54*z)*(-27*z**3 + 20*z**2 + 49) + (53*z**3)*(-27*z**3 + 20*z**2 + 49)\nSimplifying the partial expression: (53*z**3)*(-27*z**3 + 20*z**2 + 49)\nExpanding the part (-27*z**3 + 20*z**2 + 49) using the distributive property, and we got: 49*(53*z**3) + (20*z**2)*(53*z**3) + (-27*z**3)*(53*z**3)\nReplacing (53*z**3)*(-27*z**3 + 20*z**2 + 49) with 49*(53*z**3) + (20*z**2)*(53*z**3) + (-27*z**3)*(53*z**3) in the overall expression.\n#Step 3:\nCurrent expression: 49*53*z**3 + (54*z)*(-27*z**3 + 20*z**2 + 49) + (20*z**2)*(53*z**3) + (-27*z**3)*(53*z**3)\nSimplifying the partial expression: (54*z)*(-27*z**3 + 20*z**2 + 49)\nExpanding the part (-27*z**3 + 20*z**2 + 49) using the distributive property, and we got: 49*(54*z) + (54*z)*(20*z**2) + (54*z)*(-27*z**3)\nReplacing (54*z)*(-27*z**3 + 20*z**2 + 49) with 49*(54*z) + (54*z)*(20*z**2) + (54*z)*(-27*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 49*53*z**3 + 49*54*z + (54*z)*(20*z**2) + (54*z)*(-27*z**3) + (20*z**2)*(53*z**3) + (-27*z**3)*(53*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*z**3)*(53*z**3) = -1431*z**6\n (-27*z**3)*(54*z) = -1458*z**4\n (20*z**2)*(53*z**3) = 1060*z**5\n (20*z**2)*(54*z) = 1080*z**3\n 49*53*z**3 = 2597*z**3\n 49*54*z = 2646*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1431*z**6 + 1060*z**5 - 1458*z**4 + 1080*z**3 + 2597*z**3 + 2646*z\nCombining like terms, got -1431*z**6 + 1060*z**5 - 1458*z**4 + 3677*z**3 + 2646*z\n#Step 6:\nCurrent expression: -1431*z**6 + 1060*z**5 - 1458*z**4 + 3677*z**3 + 2646*z\nNo more calculations needed.\n-1431*z**6 + 1060*z**5 - 1458*z**4 + 3677*z**3 + 2646*z", "generated_answer": "-1431*z**6 + 1060*z**5 - 1458*z**4 + 3677*z**3 + 2646*z", "step_length": 6} {"cot_id": "e4fbaeb5c636b0c472cc63414f6658cde41323fe616e3f490b92323b3487a679", "datapoint": {"question": "Calculate the following: (-3*x**3 - 19)*(8*x**3 - 8)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-24*x**6 - 128*x**3 + 152", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 173, "polynomial_expr": "(-3*x**3 - 19)*(8*x**3 - 8)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-3*x**3 - 19)*(8*x**3 - 8)\nExpanding the part (-3*x**3 - 19) using the distributive property, and we got: (-3*x**3)*(8*x**3 - 8) - 19*(8*x**3 - 8)\n#Step 2:\nCurrent expression: (-3*x**3)*(8*x**3 - 8) - 19*(8*x**3 - 8)\nSimplifying the partial expression: -19*(8*x**3 - 8)\nExpanding the part (8*x**3 - 8) using the distributive property, and we got: (8*x**3)*(-19) - 8*(-19)\nReplacing -19*(8*x**3 - 8) with (8*x**3)*(-19) - 8*(-19) in the overall expression.\n#Step 3:\nCurrent expression: (-3*x**3)*(8*x**3 - 8) + (8*x**3)*(-19) + 152\nSimplifying the partial expression: (-3*x**3)*(8*x**3 - 8)\nExpanding the part (8*x**3 - 8) using the distributive property, and we got: -(-1)*24*x**3 + (-3*x**3)*(8*x**3)\nReplacing (-3*x**3)*(8*x**3 - 8) with -(-1)*24*x**3 + (-3*x**3)*(8*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -8*(-3)*x**3 + (-3*x**3)*(8*x**3) + (8*x**3)*(-19) + 152\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (8*x**3)*-19 = -152*x**3\n (8*x**3)*(-3*x**3) = -24*x**6\n -8*-3*x**3 = 24*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -24*x**6 - 152*x**3 + 24*x**3 + 152\nCombining like terms, got -24*x**6 - 128*x**3 + 152\n#Step 6:\nCurrent expression: -24*x**6 - 128*x**3 + 152\nNo more calculations needed.\n-24*x**6 - 128*x**3 + 152", "generated_answer": "-24*x**6 - 128*x**3 + 152", "step_length": 6} {"cot_id": "0782685d0a9485f340172ab959d861cd7bb211135b75aea42bd228f1960f1e7e", "datapoint": {"question": "Calculate the following: -23*x*(44*x**3 - 7*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1012*x**4 + 161*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 174, "polynomial_expr": "-23*x*(44*x**3 - 7*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -23*x*(44*x**3 - 7*x)\nExpanding the part (44*x**3 - 7*x) using the distributive property, and we got: (-23*x)*(-7*x) + (-23*x)*(44*x**3)\n#Step 2:\nCurrent expression: (-23*x)*(-7*x) + (-23*x)*(44*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-7*x)*(-23*x) = 161*x**2\n (44*x**3)*(-23*x) = -1012*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1012*x**4 + 161*x**2\nNo more calculations needed.\n-1012*x**4 + 161*x**2", "generated_answer": "-1012*x**4 + 161*x**2", "step_length": 3} {"cot_id": "3810f6a095412fc55cb1239d303bfc5d13f24965859419bdd60ab90da0b3d3ed", "datapoint": {"question": "Calculate the following: (10*y - 17)*(4*y**3 + 50*y**2 - 46)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "40*y**4 + 432*y**3 - 850*y**2 - 460*y + 782", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 175, "polynomial_expr": "(10*y - 17)*(4*y**3 + 50*y**2 - 46)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (10*y - 17)*(4*y**3 + 50*y**2 - 46)\nExpanding the part (10*y - 17) using the distributive property, and we got: (10*y)*(4*y**3 + 50*y**2 - 46) - 17*(4*y**3 + 50*y**2 - 46)\n#Step 2:\nCurrent expression: (10*y)*(4*y**3 + 50*y**2 - 46) - 17*(4*y**3 + 50*y**2 - 46)\nSimplifying the partial expression: -17*(4*y**3 + 50*y**2 - 46)\nExpanding the part (4*y**3 + 50*y**2 - 46) using the distributive property, and we got: (50*y**2)*(-17) + (4*y**3)*(-17) - 46*(-17)\nReplacing -17*(4*y**3 + 50*y**2 - 46) with (50*y**2)*(-17) + (4*y**3)*(-17) - 46*(-17) in the overall expression.\n#Step 3:\nCurrent expression: (10*y)*(4*y**3 + 50*y**2 - 46) + (50*y**2)*(-17) + (4*y**3)*(-17) + 782\nSimplifying the partial expression: (10*y)*(4*y**3 + 50*y**2 - 46)\nExpanding the part (4*y**3 + 50*y**2 - 46) using the distributive property, and we got: -460*y + (10*y)*(50*y**2) + (10*y)*(4*y**3)\nReplacing (10*y)*(4*y**3 + 50*y**2 - 46) with -460*y + (10*y)*(50*y**2) + (10*y)*(4*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -46*10*y + (10*y)*(50*y**2) + (10*y)*(4*y**3) + (50*y**2)*(-17) + (4*y**3)*(-17) + 782\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (4*y**3)*-17 = -68*y**3\n (4*y**3)*(10*y) = 40*y**4\n (50*y**2)*-17 = -850*y**2\n (50*y**2)*(10*y) = 500*y**3\n -46*10*y = -460*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 40*y**4 - 68*y**3 + 500*y**3 - 850*y**2 - 460*y + 782\nCombining like terms, got 40*y**4 + 432*y**3 - 850*y**2 - 460*y + 782\n#Step 6:\nCurrent expression: 40*y**4 + 432*y**3 - 850*y**2 - 460*y + 782\nNo more calculations needed.\n40*y**4 + 432*y**3 - 850*y**2 - 460*y + 782", "generated_answer": "40*y**4 + 432*y**3 - 850*y**2 - 460*y + 782", "step_length": 6} {"cot_id": "ebffe357a09b660b3f861199bf4f663665be315aea6a898a48d720e2cbeecf9f", "datapoint": {"question": "Calculate the following: -53*y*(19 - 38*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2014*y**3 - 1007*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 176, "polynomial_expr": "-53*y*(19 - 38*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -53*y*(19 - 38*y**2)\nExpanding the part (19 - 38*y**2) using the distributive property, and we got: (-53*y)*(-38*y**2) + 19*(-53*y)\n#Step 2:\nCurrent expression: (-53*y)*(-38*y**2) + 19*(-53*y)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 19*(-53*y) = -1007*y\n (-38*y**2)*(-53*y) = 2014*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 2014*y**3 - 1007*y\nNo more calculations needed.\n2014*y**3 - 1007*y", "generated_answer": "2014*y**3 - 1007*y", "step_length": 3} {"cot_id": "77e248ec6426f4d5ecb88303dbfdf61c038c7bd5066f833722618e4d79b5698f", "datapoint": {"question": "Simplify this expression: (-23*z**2 - 4*z)*(22*z**2 - 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-506*z**4 - 88*z**3 + 230*z**2 + 40*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 177, "polynomial_expr": "(-23*z**2 - 4*z)*(22*z**2 - 10)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-23*z**2 - 4*z)*(22*z**2 - 10)\nExpanding the part (22*z**2 - 10) using the distributive property, and we got: (22*z**2)*(-23*z**2 - 4*z) - 10*(-23*z**2 - 4*z)\n#Step 2:\nCurrent expression: (22*z**2)*(-23*z**2 - 4*z) - 10*(-23*z**2 - 4*z)\nSimplifying the partial expression: -10*(-23*z**2 - 4*z)\nExpanding the part (-23*z**2 - 4*z) using the distributive property, and we got: -4*z*(-10) - 23*z**2*(-10)\nReplacing -10*(-23*z**2 - 4*z) with -4*z*(-10) - 23*z**2*(-10) in the overall expression.\n#Step 3:\nCurrent expression: -4*z*(-10) - 23*z**2*(-10) + (22*z**2)*(-23*z**2 - 4*z)\nSimplifying the partial expression: (22*z**2)*(-23*z**2 - 4*z)\nExpanding the part (-23*z**2 - 4*z) using the distributive property, and we got: (-4*z)*(22*z**2) + (-23*z**2)*(22*z**2)\nReplacing (22*z**2)*(-23*z**2 - 4*z) with (-4*z)*(22*z**2) + (-23*z**2)*(22*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-4*z)*(22*z**2) - 4*z*(-10) + (-23*z**2)*(22*z**2) - 23*z**2*(-10)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*z**2)*-10 = 230*z**2\n (-23*z**2)*(22*z**2) = -506*z**4\n (-4*z)*-10 = 40*z\n (-4*z)*(22*z**2) = -88*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -506*z**4 - 88*z**3 + 230*z**2 + 40*z\nNo more calculations needed.\n-506*z**4 - 88*z**3 + 230*z**2 + 40*z", "generated_answer": "-506*z**4 - 88*z**3 + 230*z**2 + 40*z", "step_length": 5} {"cot_id": "1585195918cc8648e699ee3d159e9d584da5f7a935a8aee263c33b3e9c5ff04d", "datapoint": {"question": "Simplify this expression: (-53*z**2 - 46*z)*(-51*z**3 - 46*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2703*z**5 + 2346*z**4 + 2438*z**3 + 2116*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 178, "polynomial_expr": "(-53*z**2 - 46*z)*(-51*z**3 - 46*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-53*z**2 - 46*z)*(-51*z**3 - 46*z)\nExpanding the part (-53*z**2 - 46*z) using the distributive property, and we got: (-46*z)*(-51*z**3 - 46*z) + (-53*z**2)*(-51*z**3 - 46*z)\n#Step 2:\nCurrent expression: (-46*z)*(-51*z**3 - 46*z) + (-53*z**2)*(-51*z**3 - 46*z)\nSimplifying the partial expression: (-53*z**2)*(-51*z**3 - 46*z)\nExpanding the part (-51*z**3 - 46*z) using the distributive property, and we got: (-46*z)*(-53*z**2) + (-53*z**2)*(-51*z**3)\nReplacing (-53*z**2)*(-51*z**3 - 46*z) with (-46*z)*(-53*z**2) + (-53*z**2)*(-51*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-46*z)*(-53*z**2) + (-46*z)*(-51*z**3 - 46*z) + (-53*z**2)*(-51*z**3)\nSimplifying the partial expression: (-46*z)*(-51*z**3 - 46*z)\nExpanding the part (-51*z**3 - 46*z) using the distributive property, and we got: (-46*z)*(-51*z**3) + (-46*z)*(-46*z)\nReplacing (-46*z)*(-51*z**3 - 46*z) with (-46*z)*(-51*z**3) + (-46*z)*(-46*z) in the overall expression.\n#Step 4:\nCurrent expression: (-46*z)*(-53*z**2) + (-46*z)*(-51*z**3) + (-46*z)*(-46*z) + (-53*z**2)*(-51*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-51*z**3)*(-53*z**2) = 2703*z**5\n (-51*z**3)*(-46*z) = 2346*z**4\n (-46*z)*(-53*z**2) = 2438*z**3\n (-46*z)*(-46*z) = 2116*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2703*z**5 + 2346*z**4 + 2438*z**3 + 2116*z**2\nNo more calculations needed.\n2703*z**5 + 2346*z**4 + 2438*z**3 + 2116*z**2", "generated_answer": "2703*z**5 + 2346*z**4 + 2438*z**3 + 2116*z**2", "step_length": 5} {"cot_id": "98c29895f941e63a81a0aa6a9ba19a81845ed3e0d83e815187abd51d8ab9815e", "datapoint": {"question": "Simplify this expression: (32*x**2 + 50)*(36*x**3 - 57*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1152*x**5 - 24*x**3 - 2850*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 179, "polynomial_expr": "(32*x**2 + 50)*(36*x**3 - 57*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (32*x**2 + 50)*(36*x**3 - 57*x)\nExpanding the part (32*x**2 + 50) using the distributive property, and we got: (32*x**2)*(36*x**3 - 57*x) + 50*(36*x**3 - 57*x)\n#Step 2:\nCurrent expression: (32*x**2)*(36*x**3 - 57*x) + 50*(36*x**3 - 57*x)\nSimplifying the partial expression: 50*(36*x**3 - 57*x)\nExpanding the part (36*x**3 - 57*x) using the distributive property, and we got: -57*x*50 + (36*x**3)*50\nReplacing 50*(36*x**3 - 57*x) with -57*x*50 + (36*x**3)*50 in the overall expression.\n#Step 3:\nCurrent expression: -57*x*50 + (32*x**2)*(36*x**3 - 57*x) + (36*x**3)*50\nSimplifying the partial expression: (32*x**2)*(36*x**3 - 57*x)\nExpanding the part (36*x**3 - 57*x) using the distributive property, and we got: (-57*x)*(32*x**2) + (32*x**2)*(36*x**3)\nReplacing (32*x**2)*(36*x**3 - 57*x) with (-57*x)*(32*x**2) + (32*x**2)*(36*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-57*x)*(32*x**2) - 57*x*50 + (32*x**2)*(36*x**3) + (36*x**3)*50\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-57*x)*50 = -2850*x\n (-57*x)*(32*x**2) = -1824*x**3\n (36*x**3)*50 = 1800*x**3\n (36*x**3)*(32*x**2) = 1152*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1152*x**5 - 1824*x**3 + 1800*x**3 - 2850*x\nCombining like terms, got 1152*x**5 - 24*x**3 - 2850*x\n#Step 6:\nCurrent expression: 1152*x**5 - 24*x**3 - 2850*x\nNo more calculations needed.\n1152*x**5 - 24*x**3 - 2850*x", "generated_answer": "1152*x**5 - 24*x**3 - 2850*x", "step_length": 6} {"cot_id": "e3be4bf89f06bf4fe4e5a719474bbc57268e19262e9169bad8494875e1715a86", "datapoint": {"question": "Simplify this expression: (-14*x**3 - 20*x)*(-7*x**3 - 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "98*x**6 + 140*x**4 + 448*x**3 + 640*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 180, "polynomial_expr": "(-14*x**3 - 20*x)*(-7*x**3 - 32)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-14*x**3 - 20*x)*(-7*x**3 - 32)\nExpanding the part (-7*x**3 - 32) using the distributive property, and we got: (-7*x**3)*(-14*x**3 - 20*x) - 32*(-14*x**3 - 20*x)\n#Step 2:\nCurrent expression: (-7*x**3)*(-14*x**3 - 20*x) - 32*(-14*x**3 - 20*x)\nSimplifying the partial expression: -32*(-14*x**3 - 20*x)\nExpanding the part (-14*x**3 - 20*x) using the distributive property, and we got: -20*x*(-32) - 14*x**3*(-32)\nReplacing -32*(-14*x**3 - 20*x) with -20*x*(-32) - 14*x**3*(-32) in the overall expression.\n#Step 3:\nCurrent expression: -20*x*(-32) - 14*x**3*(-32) + (-7*x**3)*(-14*x**3 - 20*x)\nSimplifying the partial expression: (-7*x**3)*(-14*x**3 - 20*x)\nExpanding the part (-14*x**3 - 20*x) using the distributive property, and we got: (-20*x)*(-7*x**3) + (-14*x**3)*(-7*x**3)\nReplacing (-7*x**3)*(-14*x**3 - 20*x) with (-20*x)*(-7*x**3) + (-14*x**3)*(-7*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-20*x)*(-7*x**3) - 20*x*(-32) + (-14*x**3)*(-7*x**3) - 14*x**3*(-32)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*x)*-32 = 640*x\n (-20*x)*(-7*x**3) = 140*x**4\n (-14*x**3)*-32 = 448*x**3\n (-14*x**3)*(-7*x**3) = 98*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 98*x**6 + 140*x**4 + 448*x**3 + 640*x\nNo more calculations needed.\n98*x**6 + 140*x**4 + 448*x**3 + 640*x", "generated_answer": "98*x**6 + 140*x**4 + 448*x**3 + 640*x", "step_length": 5} {"cot_id": "e34593c90d6bd7904b64091203e5e2dcd912822384105ba2e97a8a887e9c3310", "datapoint": {"question": "Calculate the following: (76*y**3 + 13*y**2)*(14*y**3 - 23*y + 5)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1064*y**6 + 182*y**5 - 1748*y**4 + 81*y**3 + 65*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 181, "polynomial_expr": "(76*y**3 + 13*y**2)*(14*y**3 - 23*y + 5)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (76*y**3 + 13*y**2)*(14*y**3 - 23*y + 5)\nExpanding the part (76*y**3 + 13*y**2) using the distributive property, and we got: (13*y**2)*(14*y**3 - 23*y + 5) + (76*y**3)*(14*y**3 - 23*y + 5)\n#Step 2:\nCurrent expression: (13*y**2)*(14*y**3 - 23*y + 5) + (76*y**3)*(14*y**3 - 23*y + 5)\nSimplifying the partial expression: (13*y**2)*(14*y**3 - 23*y + 5)\nExpanding the part (14*y**3 - 23*y + 5) using the distributive property, and we got: (-23*y)*(13*y**2) + 5*(13*y**2) + (13*y**2)*(14*y**3)\nReplacing (13*y**2)*(14*y**3 - 23*y + 5) with (-23*y)*(13*y**2) + 5*(13*y**2) + (13*y**2)*(14*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-23*y)*(13*y**2) + 5*13*y**2 + (13*y**2)*(14*y**3) + (76*y**3)*(14*y**3 - 23*y + 5)\nSimplifying the partial expression: (76*y**3)*(14*y**3 - 23*y + 5)\nExpanding the part (14*y**3 - 23*y + 5) using the distributive property, and we got: (-23*y)*(76*y**3) + 5*(76*y**3) + (14*y**3)*(76*y**3)\nReplacing (76*y**3)*(14*y**3 - 23*y + 5) with (-23*y)*(76*y**3) + 5*(76*y**3) + (14*y**3)*(76*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-23*y)*(13*y**2) + (-23*y)*(76*y**3) + 5*76*y**3 + 5*13*y**2 + (13*y**2)*(14*y**3) + (14*y**3)*(76*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*y)*(13*y**2) = -299*y**3\n (-23*y)*(76*y**3) = -1748*y**4\n (14*y**3)*(13*y**2) = 182*y**5\n (14*y**3)*(76*y**3) = 1064*y**6\n 5*13*y**2 = 65*y**2\n 5*76*y**3 = 380*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1064*y**6 + 182*y**5 - 1748*y**4 - 299*y**3 + 380*y**3 + 65*y**2\nCombining like terms, got 1064*y**6 + 182*y**5 - 1748*y**4 + 81*y**3 + 65*y**2\n#Step 6:\nCurrent expression: 1064*y**6 + 182*y**5 - 1748*y**4 + 81*y**3 + 65*y**2\nNo more calculations needed.\n1064*y**6 + 182*y**5 - 1748*y**4 + 81*y**3 + 65*y**2", "generated_answer": "1064*y**6 + 182*y**5 - 1748*y**4 + 81*y**3 + 65*y**2", "step_length": 6} {"cot_id": "ddbec4628229eedc86af315c3133436a60a565e6221cfcdc9a376cc7baf0a47d", "datapoint": {"question": "Calculate the following: 22*x**3*(21*x**2 - 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "462*x**5 - 1056*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 182, "polynomial_expr": "22*x**3*(21*x**2 - 48)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 22*x**3*(21*x**2 - 48)\nExpanding the part (21*x**2 - 48) using the distributive property, and we got: -1056*x**3 + (21*x**2)*(22*x**3)\n#Step 2:\nCurrent expression: -1056*x**3 + (21*x**2)*(22*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -48*(22*x**3) = -1056*x**3\n (21*x**2)*(22*x**3) = 462*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 462*x**5 - 1056*x**3\nNo more calculations needed.\n462*x**5 - 1056*x**3", "generated_answer": "462*x**5 - 1056*x**3", "step_length": 3} {"cot_id": "ed0ea5a96c73b764a032d57b150ea03b701fecbebad55b869205ed8bedd8e6cd", "datapoint": {"question": "Simplify this expression: 24*z**3 + 56*z**2 - 28*z + 36\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "24*z**3 + 56*z**2 - 28*z + 36", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 183, "polynomial_expr": "24*z**3 + 56*z**2 - 28*z + 36", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 24*z**3 + 56*z**2 - 28*z + 36\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 24*z**3 + 56*z**2 - 28*z + 36\nNo more calculations needed.\n24*z**3 + 56*z**2 - 28*z + 36", "generated_answer": "24*z**3 + 56*z**2 - 28*z + 36", "step_length": 2} {"cot_id": "b3946576ee95a78ddbd8f812b1cdd20e7bfcce6deb5a93bcc291b5ba4a714ec7", "datapoint": {"question": "Simplify this expression: (-36*y**3 - 12*y)*(-36*y**3 + 22*y**2 + 70*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1296*y**6 - 792*y**5 - 2088*y**4 - 264*y**3 - 840*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 184, "polynomial_expr": "(-36*y**3 - 12*y)*(-36*y**3 + 22*y**2 + 70*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-36*y**3 - 12*y)*(-36*y**3 + 22*y**2 + 70*y)\nExpanding the part (-36*y**3 - 12*y) using the distributive property, and we got: (-12*y)*(-36*y**3 + 22*y**2 + 70*y) + (-36*y**3)*(-36*y**3 + 22*y**2 + 70*y)\n#Step 2:\nCurrent expression: (-12*y)*(-36*y**3 + 22*y**2 + 70*y) + (-36*y**3)*(-36*y**3 + 22*y**2 + 70*y)\nSimplifying the partial expression: (-36*y**3)*(-36*y**3 + 22*y**2 + 70*y)\nExpanding the part (-36*y**3 + 22*y**2 + 70*y) using the distributive property, and we got: (70*y)*(-36*y**3) + (22*y**2)*(-36*y**3) + (-36*y**3)*(-36*y**3)\nReplacing (-36*y**3)*(-36*y**3 + 22*y**2 + 70*y) with (70*y)*(-36*y**3) + (22*y**2)*(-36*y**3) + (-36*y**3)*(-36*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-12*y)*(-36*y**3 + 22*y**2 + 70*y) + (70*y)*(-36*y**3) + (22*y**2)*(-36*y**3) + (-36*y**3)*(-36*y**3)\nSimplifying the partial expression: (-12*y)*(-36*y**3 + 22*y**2 + 70*y)\nExpanding the part (-36*y**3 + 22*y**2 + 70*y) using the distributive property, and we got: (-12*y)*(70*y) + (-12*y)*(22*y**2) + (-12*y)*(-36*y**3)\nReplacing (-12*y)*(-36*y**3 + 22*y**2 + 70*y) with (-12*y)*(70*y) + (-12*y)*(22*y**2) + (-12*y)*(-36*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-12*y)*(70*y) + (-12*y)*(22*y**2) + (-12*y)*(-36*y**3) + (70*y)*(-36*y**3) + (22*y**2)*(-36*y**3) + (-36*y**3)*(-36*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*y**3)*(-36*y**3) = 1296*y**6\n (-36*y**3)*(-12*y) = 432*y**4\n (22*y**2)*(-36*y**3) = -792*y**5\n (22*y**2)*(-12*y) = -264*y**3\n (70*y)*(-36*y**3) = -2520*y**4\n (70*y)*(-12*y) = -840*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1296*y**6 - 792*y**5 - 2520*y**4 + 432*y**4 - 264*y**3 - 840*y**2\nCombining like terms, got 1296*y**6 - 792*y**5 - 2088*y**4 - 264*y**3 - 840*y**2\n#Step 6:\nCurrent expression: 1296*y**6 - 792*y**5 - 2088*y**4 - 264*y**3 - 840*y**2\nNo more calculations needed.\n1296*y**6 - 792*y**5 - 2088*y**4 - 264*y**3 - 840*y**2", "generated_answer": "1296*y**6 - 792*y**5 - 2088*y**4 - 264*y**3 - 840*y**2", "step_length": 6} {"cot_id": "d6ed7ec9d27266c5ac9be389d7926f49f0bdb949db624378640fc8fc1ff17906", "datapoint": {"question": "Calculate the following: (27*y**3 + 29)*(-46*y**3 + 16*y**2 - 12)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1242*y**6 + 432*y**5 - 1658*y**3 + 464*y**2 - 348", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 185, "polynomial_expr": "(27*y**3 + 29)*(-46*y**3 + 16*y**2 - 12)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*y**3 + 29)*(-46*y**3 + 16*y**2 - 12)\nExpanding the part (27*y**3 + 29) using the distributive property, and we got: (27*y**3)*(-46*y**3 + 16*y**2 - 12) + 29*(-46*y**3 + 16*y**2 - 12)\n#Step 2:\nCurrent expression: (27*y**3)*(-46*y**3 + 16*y**2 - 12) + 29*(-46*y**3 + 16*y**2 - 12)\nSimplifying the partial expression: 29*(-46*y**3 + 16*y**2 - 12)\nExpanding the part (-46*y**3 + 16*y**2 - 12) using the distributive property, and we got: (16*y**2)*29 - 46*y**3*29 - 12*29\nReplacing 29*(-46*y**3 + 16*y**2 - 12) with (16*y**2)*29 - 46*y**3*29 - 12*29 in the overall expression.\n#Step 3:\nCurrent expression: (16*y**2)*29 - 46*y**3*29 + (27*y**3)*(-46*y**3 + 16*y**2 - 12) - 348\nSimplifying the partial expression: (27*y**3)*(-46*y**3 + 16*y**2 - 12)\nExpanding the part (-46*y**3 + 16*y**2 - 12) using the distributive property, and we got: -324*y**3 + (16*y**2)*(27*y**3) + (-46*y**3)*(27*y**3)\nReplacing (27*y**3)*(-46*y**3 + 16*y**2 - 12) with -324*y**3 + (16*y**2)*(27*y**3) + (-46*y**3)*(27*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -12*27*y**3 + (16*y**2)*(27*y**3) + (16*y**2)*29 + (-46*y**3)*(27*y**3) - 46*y**3*29 - 348\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*y**3)*29 = -1334*y**3\n (-46*y**3)*(27*y**3) = -1242*y**6\n (16*y**2)*29 = 464*y**2\n (16*y**2)*(27*y**3) = 432*y**5\n -12*27*y**3 = -324*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1242*y**6 + 432*y**5 - 1334*y**3 - 324*y**3 + 464*y**2 - 348\nCombining like terms, got -1242*y**6 + 432*y**5 - 1658*y**3 + 464*y**2 - 348\n#Step 6:\nCurrent expression: -1242*y**6 + 432*y**5 - 1658*y**3 + 464*y**2 - 348\nNo more calculations needed.\n-1242*y**6 + 432*y**5 - 1658*y**3 + 464*y**2 - 348", "generated_answer": "-1242*y**6 + 432*y**5 - 1658*y**3 + 464*y**2 - 348", "step_length": 6} {"cot_id": "1e904e08e0f5cb1ed92b450c14e6dbe6b1148f8dd12426a766979181af714a98", "datapoint": {"question": "Simplify this expression: (37*z**3 - 10*z**2 + 27*z)*(10*z**3 + 39*z**2 + 9*z - 15)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "370*z**6 + 1343*z**5 + 213*z**4 + 408*z**3 + 393*z**2 - 405*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 186, "polynomial_expr": "(37*z**3 - 10*z**2 + 27*z)*(10*z**3 + 39*z**2 + 9*z - 15)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (37*z**3 - 10*z**2 + 27*z)*(10*z**3 + 39*z**2 + 9*z - 15)\nExpanding the part (37*z**3 - 10*z**2 + 27*z) using the distributive property, and we got: (27*z)*(10*z**3 + 39*z**2 + 9*z - 15) + (-10*z**2)*(10*z**3 + 39*z**2 + 9*z - 15) + (37*z**3)*(10*z**3 + 39*z**2 + 9*z - 15)\n#Step 2:\nCurrent expression: (27*z)*(10*z**3 + 39*z**2 + 9*z - 15) + (-10*z**2)*(10*z**3 + 39*z**2 + 9*z - 15) + (37*z**3)*(10*z**3 + 39*z**2 + 9*z - 15)\nSimplifying the partial expression: (-10*z**2)*(10*z**3 + 39*z**2 + 9*z - 15)\nExpanding the part (10*z**3 + 39*z**2 + 9*z - 15) using the distributive property, and we got: -(-1)*150*z**2 + (9*z)*(-10*z**2) + (-10*z**2)*(39*z**2) + (-10*z**2)*(10*z**3)\nReplacing (-10*z**2)*(10*z**3 + 39*z**2 + 9*z - 15) with -(-1)*150*z**2 + (9*z)*(-10*z**2) + (-10*z**2)*(39*z**2) + (-10*z**2)*(10*z**3) in the overall expression.\n#Step 3:\nCurrent expression: -15*(-10)*z**2 + (9*z)*(-10*z**2) + (27*z)*(10*z**3 + 39*z**2 + 9*z - 15) + (-10*z**2)*(39*z**2) + (-10*z**2)*(10*z**3) + (37*z**3)*(10*z**3 + 39*z**2 + 9*z - 15)\nSimplifying the partial expression: (27*z)*(10*z**3 + 39*z**2 + 9*z - 15)\nExpanding the part (10*z**3 + 39*z**2 + 9*z - 15) using the distributive property, and we got: -405*z + (9*z)*(27*z) + (27*z)*(39*z**2) + (27*z)*(10*z**3)\nReplacing (27*z)*(10*z**3 + 39*z**2 + 9*z - 15) with -405*z + (9*z)*(27*z) + (27*z)*(39*z**2) + (27*z)*(10*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -15*(-10)*z**2 - 15*27*z + (9*z)*(27*z) + (9*z)*(-10*z**2) + (27*z)*(39*z**2) + (27*z)*(10*z**3) + (-10*z**2)*(39*z**2) + (-10*z**2)*(10*z**3) + (37*z**3)*(10*z**3 + 39*z**2 + 9*z - 15)\nSimplifying the partial expression: (37*z**3)*(10*z**3 + 39*z**2 + 9*z - 15)\nExpanding the part (10*z**3 + 39*z**2 + 9*z - 15) using the distributive property, and we got: -555*z**3 + (9*z)*(37*z**3) + (39*z**2)*(37*z**3) + (10*z**3)*(37*z**3)\nReplacing (37*z**3)*(10*z**3 + 39*z**2 + 9*z - 15) with -555*z**3 + (9*z)*(37*z**3) + (39*z**2)*(37*z**3) + (10*z**3)*(37*z**3) in the overall expression.\n#Step 5:\nCurrent expression: -15*37*z**3 - 15*(-10)*z**2 - 15*27*z + (9*z)*(27*z) + (9*z)*(-10*z**2) + (9*z)*(37*z**3) + (27*z)*(39*z**2) + (27*z)*(10*z**3) + (-10*z**2)*(39*z**2) + (-10*z**2)*(10*z**3) + (39*z**2)*(37*z**3) + (10*z**3)*(37*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (9*z)*(-10*z**2) = -90*z**3\n (9*z)*(27*z) = 243*z**2\n (9*z)*(37*z**3) = 333*z**4\n (10*z**3)*(-10*z**2) = -100*z**5\n (10*z**3)*(27*z) = 270*z**4\n (10*z**3)*(37*z**3) = 370*z**6\n (39*z**2)*(-10*z**2) = -390*z**4\n (39*z**2)*(27*z) = 1053*z**3\n (39*z**2)*(37*z**3) = 1443*z**5\n -15*-10*z**2 = 150*z**2\n -15*27*z = -405*z\n -15*37*z**3 = -555*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 370*z**6 - 100*z**5 + 1443*z**5 - 390*z**4 + 270*z**4 + 333*z**4 - 555*z**3 - 90*z**3 + 1053*z**3 + 150*z**2 + 243*z**2 - 405*z\nCombining like terms, got 370*z**6 + 1343*z**5 + 213*z**4 + 408*z**3 + 393*z**2 - 405*z\n#Step 7:\nCurrent expression: 370*z**6 + 1343*z**5 + 213*z**4 + 408*z**3 + 393*z**2 - 405*z\nNo more calculations needed.\n370*z**6 + 1343*z**5 + 213*z**4 + 408*z**3 + 393*z**2 - 405*z", "generated_answer": "370*z**6 + 1343*z**5 + 213*z**4 + 408*z**3 + 393*z**2 - 405*z", "step_length": 7} {"cot_id": "974ab0d41d517fa3ac25902fa91a0daa994b63c2017439d7c2d1b40a5b34b15e", "datapoint": {"question": "Calculate the following: (35*z**2 + 41)*(-4*z**3 - 37*z - 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-140*z**5 - 1459*z**3 - 35*z**2 - 1517*z - 41", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 187, "polynomial_expr": "(35*z**2 + 41)*(-4*z**3 - 37*z - 1)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (35*z**2 + 41)*(-4*z**3 - 37*z - 1)\nExpanding the part (35*z**2 + 41) using the distributive property, and we got: (35*z**2)*(-4*z**3 - 37*z - 1) + 41*(-4*z**3 - 37*z - 1)\n#Step 2:\nCurrent expression: (35*z**2)*(-4*z**3 - 37*z - 1) + 41*(-4*z**3 - 37*z - 1)\nSimplifying the partial expression: 41*(-4*z**3 - 37*z - 1)\nExpanding the part (-4*z**3 - 37*z - 1) using the distributive property, and we got: -37*z*41 - 4*z**3*41 - 1*41\nReplacing 41*(-4*z**3 - 37*z - 1) with -37*z*41 - 4*z**3*41 - 1*41 in the overall expression.\n#Step 3:\nCurrent expression: -37*z*41 + (35*z**2)*(-4*z**3 - 37*z - 1) - 4*z**3*41 - 41\nSimplifying the partial expression: (35*z**2)*(-4*z**3 - 37*z - 1)\nExpanding the part (-4*z**3 - 37*z - 1) using the distributive property, and we got: (-37*z)*(35*z**2) - 35*z**2 + (35*z**2)*(-4*z**3)\nReplacing (35*z**2)*(-4*z**3 - 37*z - 1) with (-37*z)*(35*z**2) - 35*z**2 + (35*z**2)*(-4*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-37*z)*(35*z**2) - 37*z*41 - 1*35*z**2 + (35*z**2)*(-4*z**3) - 4*z**3*41 - 41\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*z)*41 = -1517*z\n (-37*z)*(35*z**2) = -1295*z**3\n (-4*z**3)*41 = -164*z**3\n (-4*z**3)*(35*z**2) = -140*z**5\n -1*35*z**2 = -35*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -140*z**5 - 1295*z**3 - 164*z**3 - 35*z**2 - 1517*z - 41\nCombining like terms, got -140*z**5 - 1459*z**3 - 35*z**2 - 1517*z - 41\n#Step 6:\nCurrent expression: -140*z**5 - 1459*z**3 - 35*z**2 - 1517*z - 41\nNo more calculations needed.\n-140*z**5 - 1459*z**3 - 35*z**2 - 1517*z - 41", "generated_answer": "-140*z**5 - 1459*z**3 - 35*z**2 - 1517*z - 41", "step_length": 6} {"cot_id": "2e028bfbdb7e252aae307615d3cc97f446f9f763f092f1762e4fe104316877a4", "datapoint": {"question": "Simplify this expression: (-3*z**3 + 31*z**2)*(-40*z**3 + 50*z - 46)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "120*z**6 - 1240*z**5 - 150*z**4 + 1688*z**3 - 1426*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 188, "polynomial_expr": "(-3*z**3 + 31*z**2)*(-40*z**3 + 50*z - 46)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-3*z**3 + 31*z**2)*(-40*z**3 + 50*z - 46)\nExpanding the part (-3*z**3 + 31*z**2) using the distributive property, and we got: (31*z**2)*(-40*z**3 + 50*z - 46) + (-3*z**3)*(-40*z**3 + 50*z - 46)\n#Step 2:\nCurrent expression: (31*z**2)*(-40*z**3 + 50*z - 46) + (-3*z**3)*(-40*z**3 + 50*z - 46)\nSimplifying the partial expression: (-3*z**3)*(-40*z**3 + 50*z - 46)\nExpanding the part (-40*z**3 + 50*z - 46) using the distributive property, and we got: -(-1)*138*z**3 + (50*z)*(-3*z**3) + (-40*z**3)*(-3*z**3)\nReplacing (-3*z**3)*(-40*z**3 + 50*z - 46) with -(-1)*138*z**3 + (50*z)*(-3*z**3) + (-40*z**3)*(-3*z**3) in the overall expression.\n#Step 3:\nCurrent expression: -46*(-3)*z**3 + (50*z)*(-3*z**3) + (31*z**2)*(-40*z**3 + 50*z - 46) + (-40*z**3)*(-3*z**3)\nSimplifying the partial expression: (31*z**2)*(-40*z**3 + 50*z - 46)\nExpanding the part (-40*z**3 + 50*z - 46) using the distributive property, and we got: -1426*z**2 + (50*z)*(31*z**2) + (31*z**2)*(-40*z**3)\nReplacing (31*z**2)*(-40*z**3 + 50*z - 46) with -1426*z**2 + (50*z)*(31*z**2) + (31*z**2)*(-40*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -46*(-3)*z**3 - 46*31*z**2 + (50*z)*(31*z**2) + (50*z)*(-3*z**3) + (31*z**2)*(-40*z**3) + (-40*z**3)*(-3*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*z**3)*(-3*z**3) = 120*z**6\n (-40*z**3)*(31*z**2) = -1240*z**5\n (50*z)*(-3*z**3) = -150*z**4\n (50*z)*(31*z**2) = 1550*z**3\n -46*-3*z**3 = 138*z**3\n -46*31*z**2 = -1426*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 120*z**6 - 1240*z**5 - 150*z**4 + 138*z**3 + 1550*z**3 - 1426*z**2\nCombining like terms, got 120*z**6 - 1240*z**5 - 150*z**4 + 1688*z**3 - 1426*z**2\n#Step 6:\nCurrent expression: 120*z**6 - 1240*z**5 - 150*z**4 + 1688*z**3 - 1426*z**2\nNo more calculations needed.\n120*z**6 - 1240*z**5 - 150*z**4 + 1688*z**3 - 1426*z**2", "generated_answer": "120*z**6 - 1240*z**5 - 150*z**4 + 1688*z**3 - 1426*z**2", "step_length": 6} {"cot_id": "3e1cb88ba91eec1d1316ed548fb3f3b0006d74071fde2eb954ccd3f7abba7f11", "datapoint": {"question": "Calculate the following: (13*x**2 - 37)*(46*x**2 + 27*x + 2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "598*x**4 + 351*x**3 - 1676*x**2 - 999*x - 74", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 189, "polynomial_expr": "(13*x**2 - 37)*(46*x**2 + 27*x + 2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (13*x**2 - 37)*(46*x**2 + 27*x + 2)\nExpanding the part (13*x**2 - 37) using the distributive property, and we got: (13*x**2)*(46*x**2 + 27*x + 2) - 37*(46*x**2 + 27*x + 2)\n#Step 2:\nCurrent expression: (13*x**2)*(46*x**2 + 27*x + 2) - 37*(46*x**2 + 27*x + 2)\nSimplifying the partial expression: -37*(46*x**2 + 27*x + 2)\nExpanding the part (46*x**2 + 27*x + 2) using the distributive property, and we got: (27*x)*(-37) + (46*x**2)*(-37) + 2*(-37)\nReplacing -37*(46*x**2 + 27*x + 2) with (27*x)*(-37) + (46*x**2)*(-37) + 2*(-37) in the overall expression.\n#Step 3:\nCurrent expression: (27*x)*(-37) + (13*x**2)*(46*x**2 + 27*x + 2) + (46*x**2)*(-37) - 74\nSimplifying the partial expression: (13*x**2)*(46*x**2 + 27*x + 2)\nExpanding the part (46*x**2 + 27*x + 2) using the distributive property, and we got: 2*(13*x**2) + (27*x)*(13*x**2) + (13*x**2)*(46*x**2)\nReplacing (13*x**2)*(46*x**2 + 27*x + 2) with 2*(13*x**2) + (27*x)*(13*x**2) + (13*x**2)*(46*x**2) in the overall expression.\n#Step 4:\nCurrent expression: 2*13*x**2 + (27*x)*(13*x**2) + (27*x)*(-37) + (13*x**2)*(46*x**2) + (46*x**2)*(-37) - 74\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (27*x)*-37 = -999*x\n (27*x)*(13*x**2) = 351*x**3\n (46*x**2)*-37 = -1702*x**2\n (46*x**2)*(13*x**2) = 598*x**4\n 2*13*x**2 = 26*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 598*x**4 + 351*x**3 - 1702*x**2 + 26*x**2 - 999*x - 74\nCombining like terms, got 598*x**4 + 351*x**3 - 1676*x**2 - 999*x - 74\n#Step 6:\nCurrent expression: 598*x**4 + 351*x**3 - 1676*x**2 - 999*x - 74\nNo more calculations needed.\n598*x**4 + 351*x**3 - 1676*x**2 - 999*x - 74", "generated_answer": "598*x**4 + 351*x**3 - 1676*x**2 - 999*x - 74", "step_length": 6} {"cot_id": "25ec7412ae41b7e5029fd908ac9d248931a68ba47b08d62c6fa7af487570cc22", "datapoint": {"question": "Calculate the following: (27 - 8*y)*(6*y**3 + 18*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-48*y**4 + 162*y**3 - 144*y**2 + 486*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 190, "polynomial_expr": "(27 - 8*y)*(6*y**3 + 18*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27 - 8*y)*(6*y**3 + 18*y)\nExpanding the part (27 - 8*y) using the distributive property, and we got: (-8*y)*(6*y**3 + 18*y) + 27*(6*y**3 + 18*y)\n#Step 2:\nCurrent expression: (-8*y)*(6*y**3 + 18*y) + 27*(6*y**3 + 18*y)\nSimplifying the partial expression: 27*(6*y**3 + 18*y)\nExpanding the part (6*y**3 + 18*y) using the distributive property, and we got: (18*y)*27 + (6*y**3)*27\nReplacing 27*(6*y**3 + 18*y) with (18*y)*27 + (6*y**3)*27 in the overall expression.\n#Step 3:\nCurrent expression: (-8*y)*(6*y**3 + 18*y) + (18*y)*27 + (6*y**3)*27\nSimplifying the partial expression: (-8*y)*(6*y**3 + 18*y)\nExpanding the part (6*y**3 + 18*y) using the distributive property, and we got: (-8*y)*(18*y) + (-8*y)*(6*y**3)\nReplacing (-8*y)*(6*y**3 + 18*y) with (-8*y)*(18*y) + (-8*y)*(6*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-8*y)*(18*y) + (-8*y)*(6*y**3) + (18*y)*27 + (6*y**3)*27\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (6*y**3)*27 = 162*y**3\n (6*y**3)*(-8*y) = -48*y**4\n (18*y)*27 = 486*y\n (18*y)*(-8*y) = -144*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -48*y**4 + 162*y**3 - 144*y**2 + 486*y\nNo more calculations needed.\n-48*y**4 + 162*y**3 - 144*y**2 + 486*y", "generated_answer": "-48*y**4 + 162*y**3 - 144*y**2 + 486*y", "step_length": 5} {"cot_id": "90b5a35e28b10038cde1e542ce9cea1d2ed68bc4cb6b4f65571b3f8b66e99305", "datapoint": {"question": "Calculate the following: (-8*z**2 - 6*z + 87)*(-51*z**3 + 15*z**2 + 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "408*z**5 + 186*z**4 - 4527*z**3 + 953*z**2 - 264*z + 3828", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 191, "polynomial_expr": "(-8*z**2 - 6*z + 87)*(-51*z**3 + 15*z**2 + 44)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-8*z**2 - 6*z + 87)*(-51*z**3 + 15*z**2 + 44)\nExpanding the part (-51*z**3 + 15*z**2 + 44) using the distributive property, and we got: (15*z**2)*(-8*z**2 - 6*z + 87) + (-51*z**3)*(-8*z**2 - 6*z + 87) + 44*(-8*z**2 - 6*z + 87)\n#Step 2:\nCurrent expression: (15*z**2)*(-8*z**2 - 6*z + 87) + (-51*z**3)*(-8*z**2 - 6*z + 87) + 44*(-8*z**2 - 6*z + 87)\nSimplifying the partial expression: 44*(-8*z**2 - 6*z + 87)\nExpanding the part (-8*z**2 - 6*z + 87) using the distributive property, and we got: -6*z*44 - 8*z**2*44 + 87*44\nReplacing 44*(-8*z**2 - 6*z + 87) with -6*z*44 - 8*z**2*44 + 87*44 in the overall expression.\n#Step 3:\nCurrent expression: -6*z*44 - 8*z**2*44 + (15*z**2)*(-8*z**2 - 6*z + 87) + (-51*z**3)*(-8*z**2 - 6*z + 87) + 3828\nSimplifying the partial expression: (-51*z**3)*(-8*z**2 - 6*z + 87)\nExpanding the part (-8*z**2 - 6*z + 87) using the distributive property, and we got: (-6*z)*(-51*z**3) + 87*(-51*z**3) + (-8*z**2)*(-51*z**3)\nReplacing (-51*z**3)*(-8*z**2 - 6*z + 87) with (-6*z)*(-51*z**3) + 87*(-51*z**3) + (-8*z**2)*(-51*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-6*z)*(-51*z**3) - 6*z*44 + 87*(-51)*z**3 + (-8*z**2)*(-51*z**3) - 8*z**2*44 + (15*z**2)*(-8*z**2 - 6*z + 87) + 3828\nSimplifying the partial expression: (15*z**2)*(-8*z**2 - 6*z + 87)\nExpanding the part (-8*z**2 - 6*z + 87) using the distributive property, and we got: (-6*z)*(15*z**2) + 87*(15*z**2) + (-8*z**2)*(15*z**2)\nReplacing (15*z**2)*(-8*z**2 - 6*z + 87) with (-6*z)*(15*z**2) + 87*(15*z**2) + (-8*z**2)*(15*z**2) in the overall expression.\n#Step 5:\nCurrent expression: (-6*z)*(15*z**2) + (-6*z)*(-51*z**3) - 6*z*44 + 87*(-51)*z**3 + 87*15*z**2 + (-8*z**2)*(15*z**2) + (-8*z**2)*(-51*z**3) - 8*z**2*44 + 3828\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-8*z**2)*44 = -352*z**2\n (-8*z**2)*(-51*z**3) = 408*z**5\n (-8*z**2)*(15*z**2) = -120*z**4\n (-6*z)*44 = -264*z\n (-6*z)*(-51*z**3) = 306*z**4\n (-6*z)*(15*z**2) = -90*z**3\n 87*-51*z**3 = -4437*z**3\n 87*15*z**2 = 1305*z**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 408*z**5 - 120*z**4 + 306*z**4 - 4437*z**3 - 90*z**3 - 352*z**2 + 1305*z**2 - 264*z + 3828\nCombining like terms, got 408*z**5 + 186*z**4 - 4527*z**3 + 953*z**2 - 264*z + 3828\n#Step 7:\nCurrent expression: 408*z**5 + 186*z**4 - 4527*z**3 + 953*z**2 - 264*z + 3828\nNo more calculations needed.\n408*z**5 + 186*z**4 - 4527*z**3 + 953*z**2 - 264*z + 3828", "generated_answer": "408*z**5 + 186*z**4 - 4527*z**3 + 953*z**2 - 264*z + 3828", "step_length": 7} {"cot_id": "ffece8e8a436609422df18907d02b81214cd3ab52978ec0518a535296270be67", "datapoint": {"question": "Calculate the following: (38*y**2 + 31)*(-39*y**3 + 24*y**2 - 5*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1482*y**5 + 912*y**4 - 1399*y**3 + 744*y**2 - 155*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 192, "polynomial_expr": "(38*y**2 + 31)*(-39*y**3 + 24*y**2 - 5*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (38*y**2 + 31)*(-39*y**3 + 24*y**2 - 5*y)\nExpanding the part (38*y**2 + 31) using the distributive property, and we got: (38*y**2)*(-39*y**3 + 24*y**2 - 5*y) + 31*(-39*y**3 + 24*y**2 - 5*y)\n#Step 2:\nCurrent expression: (38*y**2)*(-39*y**3 + 24*y**2 - 5*y) + 31*(-39*y**3 + 24*y**2 - 5*y)\nSimplifying the partial expression: 31*(-39*y**3 + 24*y**2 - 5*y)\nExpanding the part (-39*y**3 + 24*y**2 - 5*y) using the distributive property, and we got: -5*y*31 + (24*y**2)*31 - 39*y**3*31\nReplacing 31*(-39*y**3 + 24*y**2 - 5*y) with -5*y*31 + (24*y**2)*31 - 39*y**3*31 in the overall expression.\n#Step 3:\nCurrent expression: -5*y*31 + (24*y**2)*31 + (38*y**2)*(-39*y**3 + 24*y**2 - 5*y) - 39*y**3*31\nSimplifying the partial expression: (38*y**2)*(-39*y**3 + 24*y**2 - 5*y)\nExpanding the part (-39*y**3 + 24*y**2 - 5*y) using the distributive property, and we got: (-5*y)*(38*y**2) + (24*y**2)*(38*y**2) + (38*y**2)*(-39*y**3)\nReplacing (38*y**2)*(-39*y**3 + 24*y**2 - 5*y) with (-5*y)*(38*y**2) + (24*y**2)*(38*y**2) + (38*y**2)*(-39*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-5*y)*(38*y**2) - 5*y*31 + (24*y**2)*(38*y**2) + (24*y**2)*31 + (38*y**2)*(-39*y**3) - 39*y**3*31\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*y**3)*31 = -1209*y**3\n (-39*y**3)*(38*y**2) = -1482*y**5\n (-5*y)*31 = -155*y\n (-5*y)*(38*y**2) = -190*y**3\n (24*y**2)*31 = 744*y**2\n (24*y**2)*(38*y**2) = 912*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1482*y**5 + 912*y**4 - 1209*y**3 - 190*y**3 + 744*y**2 - 155*y\nCombining like terms, got -1482*y**5 + 912*y**4 - 1399*y**3 + 744*y**2 - 155*y\n#Step 6:\nCurrent expression: -1482*y**5 + 912*y**4 - 1399*y**3 + 744*y**2 - 155*y\nNo more calculations needed.\n-1482*y**5 + 912*y**4 - 1399*y**3 + 744*y**2 - 155*y", "generated_answer": "-1482*y**5 + 912*y**4 - 1399*y**3 + 744*y**2 - 155*y", "step_length": 6} {"cot_id": "3db459aa2675b525d9c752f1027e9047217fad74d031cfc0f8a8769ad471a2b5", "datapoint": {"question": "Simplify this expression: -16*y**3*(36 - 28*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "448*y**4 - 576*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 193, "polynomial_expr": "-16*y**3*(36 - 28*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -16*y**3*(36 - 28*y)\nExpanding the part (36 - 28*y) using the distributive property, and we got: (-28*y)*(-16*y**3) + 36*(-16*y**3)\n#Step 2:\nCurrent expression: (-28*y)*(-16*y**3) + 36*(-16*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 36*(-16*y**3) = -576*y**3\n (-28*y)*(-16*y**3) = 448*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 448*y**4 - 576*y**3\nNo more calculations needed.\n448*y**4 - 576*y**3", "generated_answer": "448*y**4 - 576*y**3", "step_length": 3} {"cot_id": "cfe0160d41d4f04ff693d7b1c147937f62aa1d6a97b3b8a7950fe5c1f9cec8a5", "datapoint": {"question": "Simplify this expression: (66 - 47*z)*(-33*z**3 - 24*z + 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1551*z**4 - 2178*z**3 + 1128*z**2 - 2242*z + 924", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 194, "polynomial_expr": "(66 - 47*z)*(-33*z**3 - 24*z + 14)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (66 - 47*z)*(-33*z**3 - 24*z + 14)\nExpanding the part (66 - 47*z) using the distributive property, and we got: (-47*z)*(-33*z**3 - 24*z + 14) + 66*(-33*z**3 - 24*z + 14)\n#Step 2:\nCurrent expression: (-47*z)*(-33*z**3 - 24*z + 14) + 66*(-33*z**3 - 24*z + 14)\nSimplifying the partial expression: 66*(-33*z**3 - 24*z + 14)\nExpanding the part (-33*z**3 - 24*z + 14) using the distributive property, and we got: -24*z*66 - 33*z**3*66 + 14*66\nReplacing 66*(-33*z**3 - 24*z + 14) with -24*z*66 - 33*z**3*66 + 14*66 in the overall expression.\n#Step 3:\nCurrent expression: (-47*z)*(-33*z**3 - 24*z + 14) - 24*z*66 - 33*z**3*66 + 924\nSimplifying the partial expression: (-47*z)*(-33*z**3 - 24*z + 14)\nExpanding the part (-33*z**3 - 24*z + 14) using the distributive property, and we got: (-47*z)*(-24*z) + (-47*z)*(-33*z**3) + 14*(-47*z)\nReplacing (-47*z)*(-33*z**3 - 24*z + 14) with (-47*z)*(-24*z) + (-47*z)*(-33*z**3) + 14*(-47*z) in the overall expression.\n#Step 4:\nCurrent expression: (-47*z)*(-24*z) + (-47*z)*(-33*z**3) - 24*z*66 + 14*(-47)*z - 33*z**3*66 + 924\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*z**3)*66 = -2178*z**3\n (-33*z**3)*(-47*z) = 1551*z**4\n (-24*z)*66 = -1584*z\n (-24*z)*(-47*z) = 1128*z**2\n 14*-47*z = -658*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1551*z**4 - 2178*z**3 + 1128*z**2 - 1584*z - 658*z + 924\nCombining like terms, got 1551*z**4 - 2178*z**3 + 1128*z**2 - 2242*z + 924\n#Step 6:\nCurrent expression: 1551*z**4 - 2178*z**3 + 1128*z**2 - 2242*z + 924\nNo more calculations needed.\n1551*z**4 - 2178*z**3 + 1128*z**2 - 2242*z + 924", "generated_answer": "1551*z**4 - 2178*z**3 + 1128*z**2 - 2242*z + 924", "step_length": 6} {"cot_id": "8170a0572c6dae2e839c63b4a4b9d806f6f4db433abfdce5f9b33f3825c3a0f0", "datapoint": {"question": "Calculate the following: -4*z**2*(17*z**3 - 31*z**2 - 45*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-68*z**5 + 124*z**4 + 180*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 195, "polynomial_expr": "-4*z**2*(17*z**3 - 31*z**2 - 45*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -4*z**2*(17*z**3 - 31*z**2 - 45*z)\nExpanding the part (17*z**3 - 31*z**2 - 45*z) using the distributive property, and we got: (-45*z)*(-4*z**2) + (-31*z**2)*(-4*z**2) + (-4*z**2)*(17*z**3)\n#Step 2:\nCurrent expression: (-45*z)*(-4*z**2) + (-31*z**2)*(-4*z**2) + (-4*z**2)*(17*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*z)*(-4*z**2) = 180*z**3\n (-31*z**2)*(-4*z**2) = 124*z**4\n (17*z**3)*(-4*z**2) = -68*z**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -68*z**5 + 124*z**4 + 180*z**3\nNo more calculations needed.\n-68*z**5 + 124*z**4 + 180*z**3", "generated_answer": "-68*z**5 + 124*z**4 + 180*z**3", "step_length": 3} {"cot_id": "2948dc5eccc83e305d21c4cb76ea9897d61784aa8610e0b97eb75af409ff0040", "datapoint": {"question": "Simplify this expression: -73*y**3*(-19*y**2 + 27*y + 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1387*y**5 - 1971*y**4 - 1241*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 196, "polynomial_expr": "-73*y**3*(-19*y**2 + 27*y + 17)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -73*y**3*(-19*y**2 + 27*y + 17)\nExpanding the part (-19*y**2 + 27*y + 17) using the distributive property, and we got: 17*(-73*y**3) + (27*y)*(-73*y**3) + (-19*y**2)*(-73*y**3)\n#Step 2:\nCurrent expression: 17*(-73*y**3) + (27*y)*(-73*y**3) + (-19*y**2)*(-73*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 17*(-73*y**3) = -1241*y**3\n (-19*y**2)*(-73*y**3) = 1387*y**5\n (27*y)*(-73*y**3) = -1971*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1387*y**5 - 1971*y**4 - 1241*y**3\nNo more calculations needed.\n1387*y**5 - 1971*y**4 - 1241*y**3", "generated_answer": "1387*y**5 - 1971*y**4 - 1241*y**3", "step_length": 3} {"cot_id": "51df4ba1ed929a28e52a1a8553d146c22c6656d707b239a891c0563e7727dda9", "datapoint": {"question": "Calculate the following: (16*x**2 - 36*x)*(-10*x**3 - 52*x**2 + 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-160*x**5 - 472*x**4 + 1872*x**3 + 784*x**2 - 1764*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 197, "polynomial_expr": "(16*x**2 - 36*x)*(-10*x**3 - 52*x**2 + 49)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (16*x**2 - 36*x)*(-10*x**3 - 52*x**2 + 49)\nExpanding the part (16*x**2 - 36*x) using the distributive property, and we got: (-36*x)*(-10*x**3 - 52*x**2 + 49) + (16*x**2)*(-10*x**3 - 52*x**2 + 49)\n#Step 2:\nCurrent expression: (-36*x)*(-10*x**3 - 52*x**2 + 49) + (16*x**2)*(-10*x**3 - 52*x**2 + 49)\nSimplifying the partial expression: (-36*x)*(-10*x**3 - 52*x**2 + 49)\nExpanding the part (-10*x**3 - 52*x**2 + 49) using the distributive property, and we got: (-36*x)*(-52*x**2) + (-36*x)*(-10*x**3) + 49*(-36*x)\nReplacing (-36*x)*(-10*x**3 - 52*x**2 + 49) with (-36*x)*(-52*x**2) + (-36*x)*(-10*x**3) + 49*(-36*x) in the overall expression.\n#Step 3:\nCurrent expression: (-36*x)*(-52*x**2) + (-36*x)*(-10*x**3) + 49*(-36)*x + (16*x**2)*(-10*x**3 - 52*x**2 + 49)\nSimplifying the partial expression: (16*x**2)*(-10*x**3 - 52*x**2 + 49)\nExpanding the part (-10*x**3 - 52*x**2 + 49) using the distributive property, and we got: 49*(16*x**2) + (-52*x**2)*(16*x**2) + (16*x**2)*(-10*x**3)\nReplacing (16*x**2)*(-10*x**3 - 52*x**2 + 49) with 49*(16*x**2) + (-52*x**2)*(16*x**2) + (16*x**2)*(-10*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-36*x)*(-52*x**2) + (-36*x)*(-10*x**3) + 49*16*x**2 + 49*(-36)*x + (-52*x**2)*(16*x**2) + (16*x**2)*(-10*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-52*x**2)*(-36*x) = 1872*x**3\n (-52*x**2)*(16*x**2) = -832*x**4\n (-10*x**3)*(-36*x) = 360*x**4\n (-10*x**3)*(16*x**2) = -160*x**5\n 49*-36*x = -1764*x\n 49*16*x**2 = 784*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -160*x**5 - 832*x**4 + 360*x**4 + 1872*x**3 + 784*x**2 - 1764*x\nCombining like terms, got -160*x**5 - 472*x**4 + 1872*x**3 + 784*x**2 - 1764*x\n#Step 6:\nCurrent expression: -160*x**5 - 472*x**4 + 1872*x**3 + 784*x**2 - 1764*x\nNo more calculations needed.\n-160*x**5 - 472*x**4 + 1872*x**3 + 784*x**2 - 1764*x", "generated_answer": "-160*x**5 - 472*x**4 + 1872*x**3 + 784*x**2 - 1764*x", "step_length": 6} {"cot_id": "1d42b759136fa64b437cb6e46bb45389ae3888037e571bc1a29f6c01bec9b901", "datapoint": {"question": "Simplify this expression: (21 - 34*z)*(16*z**3 + 30*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-544*z**4 + 336*z**3 - 1020*z**2 + 630*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 198, "polynomial_expr": "(21 - 34*z)*(16*z**3 + 30*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21 - 34*z)*(16*z**3 + 30*z)\nExpanding the part (21 - 34*z) using the distributive property, and we got: (-34*z)*(16*z**3 + 30*z) + 21*(16*z**3 + 30*z)\n#Step 2:\nCurrent expression: (-34*z)*(16*z**3 + 30*z) + 21*(16*z**3 + 30*z)\nSimplifying the partial expression: 21*(16*z**3 + 30*z)\nExpanding the part (16*z**3 + 30*z) using the distributive property, and we got: (30*z)*21 + (16*z**3)*21\nReplacing 21*(16*z**3 + 30*z) with (30*z)*21 + (16*z**3)*21 in the overall expression.\n#Step 3:\nCurrent expression: (-34*z)*(16*z**3 + 30*z) + (30*z)*21 + (16*z**3)*21\nSimplifying the partial expression: (-34*z)*(16*z**3 + 30*z)\nExpanding the part (16*z**3 + 30*z) using the distributive property, and we got: (-34*z)*(30*z) + (-34*z)*(16*z**3)\nReplacing (-34*z)*(16*z**3 + 30*z) with (-34*z)*(30*z) + (-34*z)*(16*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-34*z)*(30*z) + (-34*z)*(16*z**3) + (30*z)*21 + (16*z**3)*21\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (16*z**3)*21 = 336*z**3\n (16*z**3)*(-34*z) = -544*z**4\n (30*z)*21 = 630*z\n (30*z)*(-34*z) = -1020*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -544*z**4 + 336*z**3 - 1020*z**2 + 630*z\nNo more calculations needed.\n-544*z**4 + 336*z**3 - 1020*z**2 + 630*z", "generated_answer": "-544*z**4 + 336*z**3 - 1020*z**2 + 630*z", "step_length": 5} {"cot_id": "1ff11a679d7a0775520155282fc57dd917d5b18c6c1b30d669c80474b9c4a6c7", "datapoint": {"question": "Simplify this expression: (11*z**3 + 74)*(-45*z**3 + 18*z + 42)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-495*z**6 + 198*z**4 - 2868*z**3 + 1332*z + 3108", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 199, "polynomial_expr": "(11*z**3 + 74)*(-45*z**3 + 18*z + 42)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11*z**3 + 74)*(-45*z**3 + 18*z + 42)\nExpanding the part (11*z**3 + 74) using the distributive property, and we got: (11*z**3)*(-45*z**3 + 18*z + 42) + 74*(-45*z**3 + 18*z + 42)\n#Step 2:\nCurrent expression: (11*z**3)*(-45*z**3 + 18*z + 42) + 74*(-45*z**3 + 18*z + 42)\nSimplifying the partial expression: 74*(-45*z**3 + 18*z + 42)\nExpanding the part (-45*z**3 + 18*z + 42) using the distributive property, and we got: (18*z)*74 - 45*z**3*74 + 42*74\nReplacing 74*(-45*z**3 + 18*z + 42) with (18*z)*74 - 45*z**3*74 + 42*74 in the overall expression.\n#Step 3:\nCurrent expression: (18*z)*74 - 45*z**3*74 + (11*z**3)*(-45*z**3 + 18*z + 42) + 3108\nSimplifying the partial expression: (11*z**3)*(-45*z**3 + 18*z + 42)\nExpanding the part (-45*z**3 + 18*z + 42) using the distributive property, and we got: 42*(11*z**3) + (18*z)*(11*z**3) + (-45*z**3)*(11*z**3)\nReplacing (11*z**3)*(-45*z**3 + 18*z + 42) with 42*(11*z**3) + (18*z)*(11*z**3) + (-45*z**3)*(11*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 42*11*z**3 + (18*z)*(11*z**3) + (18*z)*74 + (-45*z**3)*(11*z**3) - 45*z**3*74 + 3108\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*z**3)*74 = -3330*z**3\n (-45*z**3)*(11*z**3) = -495*z**6\n (18*z)*74 = 1332*z\n (18*z)*(11*z**3) = 198*z**4\n 42*11*z**3 = 462*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -495*z**6 + 198*z**4 - 3330*z**3 + 462*z**3 + 1332*z + 3108\nCombining like terms, got -495*z**6 + 198*z**4 - 2868*z**3 + 1332*z + 3108\n#Step 6:\nCurrent expression: -495*z**6 + 198*z**4 - 2868*z**3 + 1332*z + 3108\nNo more calculations needed.\n-495*z**6 + 198*z**4 - 2868*z**3 + 1332*z + 3108", "generated_answer": "-495*z**6 + 198*z**4 - 2868*z**3 + 1332*z + 3108", "step_length": 6} {"cot_id": "b92baf47822bf4b7fe0232c6b401cd444df539900cf6aef22f78ab2b37295946", "datapoint": {"question": "Calculate the following: (34*y**2 - 67)*(28*y**3 + 9*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "952*y**5 + 306*y**4 - 1876*y**3 - 603*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 200, "polynomial_expr": "(34*y**2 - 67)*(28*y**3 + 9*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (34*y**2 - 67)*(28*y**3 + 9*y**2)\nExpanding the part (34*y**2 - 67) using the distributive property, and we got: (34*y**2)*(28*y**3 + 9*y**2) - 67*(28*y**3 + 9*y**2)\n#Step 2:\nCurrent expression: (34*y**2)*(28*y**3 + 9*y**2) - 67*(28*y**3 + 9*y**2)\nSimplifying the partial expression: -67*(28*y**3 + 9*y**2)\nExpanding the part (28*y**3 + 9*y**2) using the distributive property, and we got: (9*y**2)*(-67) + (28*y**3)*(-67)\nReplacing -67*(28*y**3 + 9*y**2) with (9*y**2)*(-67) + (28*y**3)*(-67) in the overall expression.\n#Step 3:\nCurrent expression: (9*y**2)*(-67) + (34*y**2)*(28*y**3 + 9*y**2) + (28*y**3)*(-67)\nSimplifying the partial expression: (34*y**2)*(28*y**3 + 9*y**2)\nExpanding the part (28*y**3 + 9*y**2) using the distributive property, and we got: (9*y**2)*(34*y**2) + (34*y**2)*(28*y**3)\nReplacing (34*y**2)*(28*y**3 + 9*y**2) with (9*y**2)*(34*y**2) + (34*y**2)*(28*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (9*y**2)*(34*y**2) + (9*y**2)*(-67) + (34*y**2)*(28*y**3) + (28*y**3)*(-67)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (9*y**2)*-67 = -603*y**2\n (9*y**2)*(34*y**2) = 306*y**4\n (28*y**3)*-67 = -1876*y**3\n (28*y**3)*(34*y**2) = 952*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 952*y**5 + 306*y**4 - 1876*y**3 - 603*y**2\nNo more calculations needed.\n952*y**5 + 306*y**4 - 1876*y**3 - 603*y**2", "generated_answer": "952*y**5 + 306*y**4 - 1876*y**3 - 603*y**2", "step_length": 5} {"cot_id": "91888f48398b9f7ea3b1b85834fd9710afb78084374d69bd76bed078079da673", "datapoint": {"question": "Simplify this expression: (4*z**2 - 4*z)*(-37*z**3 + 11*z - 40)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-148*z**5 + 148*z**4 + 44*z**3 - 204*z**2 + 160*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 201, "polynomial_expr": "(4*z**2 - 4*z)*(-37*z**3 + 11*z - 40)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (4*z**2 - 4*z)*(-37*z**3 + 11*z - 40)\nExpanding the part (4*z**2 - 4*z) using the distributive property, and we got: (-4*z)*(-37*z**3 + 11*z - 40) + (4*z**2)*(-37*z**3 + 11*z - 40)\n#Step 2:\nCurrent expression: (-4*z)*(-37*z**3 + 11*z - 40) + (4*z**2)*(-37*z**3 + 11*z - 40)\nSimplifying the partial expression: (-4*z)*(-37*z**3 + 11*z - 40)\nExpanding the part (-37*z**3 + 11*z - 40) using the distributive property, and we got: (-4*z)*(11*z) + (-4*z)*(-37*z**3) - (-1)*160*z\nReplacing (-4*z)*(-37*z**3 + 11*z - 40) with (-4*z)*(11*z) + (-4*z)*(-37*z**3) - (-1)*160*z in the overall expression.\n#Step 3:\nCurrent expression: (-4*z)*(11*z) + (-4*z)*(-37*z**3) - 40*(-4)*z + (4*z**2)*(-37*z**3 + 11*z - 40)\nSimplifying the partial expression: (4*z**2)*(-37*z**3 + 11*z - 40)\nExpanding the part (-37*z**3 + 11*z - 40) using the distributive property, and we got: -160*z**2 + (11*z)*(4*z**2) + (4*z**2)*(-37*z**3)\nReplacing (4*z**2)*(-37*z**3 + 11*z - 40) with -160*z**2 + (11*z)*(4*z**2) + (4*z**2)*(-37*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-4*z)*(11*z) + (-4*z)*(-37*z**3) - 40*4*z**2 - 40*(-4)*z + (11*z)*(4*z**2) + (4*z**2)*(-37*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*z**3)*(-4*z) = 148*z**4\n (-37*z**3)*(4*z**2) = -148*z**5\n (11*z)*(-4*z) = -44*z**2\n (11*z)*(4*z**2) = 44*z**3\n -40*-4*z = 160*z\n -40*4*z**2 = -160*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -148*z**5 + 148*z**4 + 44*z**3 - 160*z**2 - 44*z**2 + 160*z\nCombining like terms, got -148*z**5 + 148*z**4 + 44*z**3 - 204*z**2 + 160*z\n#Step 6:\nCurrent expression: -148*z**5 + 148*z**4 + 44*z**3 - 204*z**2 + 160*z\nNo more calculations needed.\n-148*z**5 + 148*z**4 + 44*z**3 - 204*z**2 + 160*z", "generated_answer": "-148*z**5 + 148*z**4 + 44*z**3 - 204*z**2 + 160*z", "step_length": 6} {"cot_id": "c3ea1d8401b9c89ebedeeaf1943b49cd486e3d7fb0e5b31afde21be7794d3cbb", "datapoint": {"question": "Calculate the following: (14 - 15*z**3)*(-38*z**2 + 18*z + 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "570*z**5 - 270*z**4 - 105*z**3 - 532*z**2 + 252*z + 98", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 202, "polynomial_expr": "(14 - 15*z**3)*(-38*z**2 + 18*z + 7)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14 - 15*z**3)*(-38*z**2 + 18*z + 7)\nExpanding the part (14 - 15*z**3) using the distributive property, and we got: (-15*z**3)*(-38*z**2 + 18*z + 7) + 14*(-38*z**2 + 18*z + 7)\n#Step 2:\nCurrent expression: (-15*z**3)*(-38*z**2 + 18*z + 7) + 14*(-38*z**2 + 18*z + 7)\nSimplifying the partial expression: 14*(-38*z**2 + 18*z + 7)\nExpanding the part (-38*z**2 + 18*z + 7) using the distributive property, and we got: (18*z)*14 - 38*z**2*14 + 7*14\nReplacing 14*(-38*z**2 + 18*z + 7) with (18*z)*14 - 38*z**2*14 + 7*14 in the overall expression.\n#Step 3:\nCurrent expression: (18*z)*14 - 38*z**2*14 + (-15*z**3)*(-38*z**2 + 18*z + 7) + 98\nSimplifying the partial expression: (-15*z**3)*(-38*z**2 + 18*z + 7)\nExpanding the part (-38*z**2 + 18*z + 7) using the distributive property, and we got: 7*(-15*z**3) + (18*z)*(-15*z**3) + (-38*z**2)*(-15*z**3)\nReplacing (-15*z**3)*(-38*z**2 + 18*z + 7) with 7*(-15*z**3) + (18*z)*(-15*z**3) + (-38*z**2)*(-15*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 7*(-15)*z**3 + (18*z)*(-15*z**3) + (18*z)*14 + (-38*z**2)*(-15*z**3) - 38*z**2*14 + 98\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*z**2)*14 = -532*z**2\n (-38*z**2)*(-15*z**3) = 570*z**5\n (18*z)*14 = 252*z\n (18*z)*(-15*z**3) = -270*z**4\n 7*-15*z**3 = -105*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 570*z**5 - 270*z**4 - 105*z**3 - 532*z**2 + 252*z + 98\nNo more calculations needed.\n570*z**5 - 270*z**4 - 105*z**3 - 532*z**2 + 252*z + 98", "generated_answer": "570*z**5 - 270*z**4 - 105*z**3 - 532*z**2 + 252*z + 98", "step_length": 5} {"cot_id": "cc356a4192131d53bf02e64bc35050a5ffaab89ed0384e1e2f2259fb374ab415", "datapoint": {"question": "Simplify this expression: (-31*x**2 + 13*x)*(43*x**3 + 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1333*x**5 + 559*x**4 - 1457*x**2 + 611*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 203, "polynomial_expr": "(-31*x**2 + 13*x)*(43*x**3 + 47)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-31*x**2 + 13*x)*(43*x**3 + 47)\nExpanding the part (43*x**3 + 47) using the distributive property, and we got: (43*x**3)*(-31*x**2 + 13*x) + 47*(-31*x**2 + 13*x)\n#Step 2:\nCurrent expression: (43*x**3)*(-31*x**2 + 13*x) + 47*(-31*x**2 + 13*x)\nSimplifying the partial expression: 47*(-31*x**2 + 13*x)\nExpanding the part (-31*x**2 + 13*x) using the distributive property, and we got: (13*x)*47 - 31*x**2*47\nReplacing 47*(-31*x**2 + 13*x) with (13*x)*47 - 31*x**2*47 in the overall expression.\n#Step 3:\nCurrent expression: (13*x)*47 - 31*x**2*47 + (43*x**3)*(-31*x**2 + 13*x)\nSimplifying the partial expression: (43*x**3)*(-31*x**2 + 13*x)\nExpanding the part (-31*x**2 + 13*x) using the distributive property, and we got: (13*x)*(43*x**3) + (-31*x**2)*(43*x**3)\nReplacing (43*x**3)*(-31*x**2 + 13*x) with (13*x)*(43*x**3) + (-31*x**2)*(43*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (13*x)*(43*x**3) + (13*x)*47 + (-31*x**2)*(43*x**3) - 31*x**2*47\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-31*x**2)*47 = -1457*x**2\n (-31*x**2)*(43*x**3) = -1333*x**5\n (13*x)*47 = 611*x\n (13*x)*(43*x**3) = 559*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1333*x**5 + 559*x**4 - 1457*x**2 + 611*x\nNo more calculations needed.\n-1333*x**5 + 559*x**4 - 1457*x**2 + 611*x", "generated_answer": "-1333*x**5 + 559*x**4 - 1457*x**2 + 611*x", "step_length": 5} {"cot_id": "e6259de3caa96b58d992e4e9e048dad0deaddd436086cba2a3143a48e26628be", "datapoint": {"question": "Calculate the following: (59*x + 11)*(-19*x**3 - 49*x + 29)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1121*x**4 - 209*x**3 - 2891*x**2 + 1172*x + 319", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 204, "polynomial_expr": "(59*x + 11)*(-19*x**3 - 49*x + 29)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (59*x + 11)*(-19*x**3 - 49*x + 29)\nExpanding the part (59*x + 11) using the distributive property, and we got: (59*x)*(-19*x**3 - 49*x + 29) + 11*(-19*x**3 - 49*x + 29)\n#Step 2:\nCurrent expression: (59*x)*(-19*x**3 - 49*x + 29) + 11*(-19*x**3 - 49*x + 29)\nSimplifying the partial expression: 11*(-19*x**3 - 49*x + 29)\nExpanding the part (-19*x**3 - 49*x + 29) using the distributive property, and we got: -49*x*11 - 19*x**3*11 + 29*11\nReplacing 11*(-19*x**3 - 49*x + 29) with -49*x*11 - 19*x**3*11 + 29*11 in the overall expression.\n#Step 3:\nCurrent expression: -49*x*11 + (59*x)*(-19*x**3 - 49*x + 29) - 19*x**3*11 + 319\nSimplifying the partial expression: (59*x)*(-19*x**3 - 49*x + 29)\nExpanding the part (-19*x**3 - 49*x + 29) using the distributive property, and we got: (-49*x)*(59*x) + 29*(59*x) + (59*x)*(-19*x**3)\nReplacing (59*x)*(-19*x**3 - 49*x + 29) with (-49*x)*(59*x) + 29*(59*x) + (59*x)*(-19*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-49*x)*(59*x) - 49*x*11 + 29*59*x + (59*x)*(-19*x**3) - 19*x**3*11 + 319\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*x)*11 = -539*x\n (-49*x)*(59*x) = -2891*x**2\n (-19*x**3)*11 = -209*x**3\n (-19*x**3)*(59*x) = -1121*x**4\n 29*59*x = 1711*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1121*x**4 - 209*x**3 - 2891*x**2 - 539*x + 1711*x + 319\nCombining like terms, got -1121*x**4 - 209*x**3 - 2891*x**2 + 1172*x + 319\n#Step 6:\nCurrent expression: -1121*x**4 - 209*x**3 - 2891*x**2 + 1172*x + 319\nNo more calculations needed.\n-1121*x**4 - 209*x**3 - 2891*x**2 + 1172*x + 319", "generated_answer": "-1121*x**4 - 209*x**3 - 2891*x**2 + 1172*x + 319", "step_length": 6} {"cot_id": "08318eb9c54fb737df17c6f3827413374741ee1be540d5e82cae6525ade69292", "datapoint": {"question": "Calculate the following: 713*y**2 - 124*y\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "713*y**2 - 124*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 205, "polynomial_expr": "713*y**2 - 124*y", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 713*y**2 - 124*y\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 713*y**2 - 124*y\nNo more calculations needed.\n713*y**2 - 124*y", "generated_answer": "713*y**2 - 124*y", "step_length": 2} {"cot_id": "f0023d7de8ada0bc4c703852d00c415e5fc1970fdb87a3180235b8b50e9949b8", "datapoint": {"question": "Calculate the following: (-26*y**2 + 21*y)*(18*y**2 - 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-468*y**4 + 378*y**3 + 832*y**2 - 672*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 206, "polynomial_expr": "(-26*y**2 + 21*y)*(18*y**2 - 32)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-26*y**2 + 21*y)*(18*y**2 - 32)\nExpanding the part (18*y**2 - 32) using the distributive property, and we got: (18*y**2)*(-26*y**2 + 21*y) - 32*(-26*y**2 + 21*y)\n#Step 2:\nCurrent expression: (18*y**2)*(-26*y**2 + 21*y) - 32*(-26*y**2 + 21*y)\nSimplifying the partial expression: -32*(-26*y**2 + 21*y)\nExpanding the part (-26*y**2 + 21*y) using the distributive property, and we got: (21*y)*(-32) - 26*y**2*(-32)\nReplacing -32*(-26*y**2 + 21*y) with (21*y)*(-32) - 26*y**2*(-32) in the overall expression.\n#Step 3:\nCurrent expression: (21*y)*(-32) - 26*y**2*(-32) + (18*y**2)*(-26*y**2 + 21*y)\nSimplifying the partial expression: (18*y**2)*(-26*y**2 + 21*y)\nExpanding the part (-26*y**2 + 21*y) using the distributive property, and we got: (21*y)*(18*y**2) + (-26*y**2)*(18*y**2)\nReplacing (18*y**2)*(-26*y**2 + 21*y) with (21*y)*(18*y**2) + (-26*y**2)*(18*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (21*y)*(18*y**2) + (21*y)*(-32) + (-26*y**2)*(18*y**2) - 26*y**2*(-32)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-26*y**2)*-32 = 832*y**2\n (-26*y**2)*(18*y**2) = -468*y**4\n (21*y)*-32 = -672*y\n (21*y)*(18*y**2) = 378*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -468*y**4 + 378*y**3 + 832*y**2 - 672*y\nNo more calculations needed.\n-468*y**4 + 378*y**3 + 832*y**2 - 672*y", "generated_answer": "-468*y**4 + 378*y**3 + 832*y**2 - 672*y", "step_length": 5} {"cot_id": "a51eb800a4c3ff86f4efb7c4a5a286a312bf8dca08358ea2c790d758c5ff1e83", "datapoint": {"question": "Calculate the following: (23*y - 29)*(23*y**3 + 69*y**2 - 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "529*y**4 + 920*y**3 - 2001*y**2 - 805*y + 1015", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 207, "polynomial_expr": "(23*y - 29)*(23*y**3 + 69*y**2 - 35)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (23*y - 29)*(23*y**3 + 69*y**2 - 35)\nExpanding the part (23*y - 29) using the distributive property, and we got: (23*y)*(23*y**3 + 69*y**2 - 35) - 29*(23*y**3 + 69*y**2 - 35)\n#Step 2:\nCurrent expression: (23*y)*(23*y**3 + 69*y**2 - 35) - 29*(23*y**3 + 69*y**2 - 35)\nSimplifying the partial expression: -29*(23*y**3 + 69*y**2 - 35)\nExpanding the part (23*y**3 + 69*y**2 - 35) using the distributive property, and we got: (69*y**2)*(-29) + (23*y**3)*(-29) - 35*(-29)\nReplacing -29*(23*y**3 + 69*y**2 - 35) with (69*y**2)*(-29) + (23*y**3)*(-29) - 35*(-29) in the overall expression.\n#Step 3:\nCurrent expression: (23*y)*(23*y**3 + 69*y**2 - 35) + (69*y**2)*(-29) + (23*y**3)*(-29) + 1015\nSimplifying the partial expression: (23*y)*(23*y**3 + 69*y**2 - 35)\nExpanding the part (23*y**3 + 69*y**2 - 35) using the distributive property, and we got: -805*y + (23*y)*(69*y**2) + (23*y)*(23*y**3)\nReplacing (23*y)*(23*y**3 + 69*y**2 - 35) with -805*y + (23*y)*(69*y**2) + (23*y)*(23*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -35*23*y + (23*y)*(69*y**2) + (23*y)*(23*y**3) + (69*y**2)*(-29) + (23*y**3)*(-29) + 1015\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (23*y**3)*-29 = -667*y**3\n (23*y**3)*(23*y) = 529*y**4\n (69*y**2)*-29 = -2001*y**2\n (69*y**2)*(23*y) = 1587*y**3\n -35*23*y = -805*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 529*y**4 - 667*y**3 + 1587*y**3 - 2001*y**2 - 805*y + 1015\nCombining like terms, got 529*y**4 + 920*y**3 - 2001*y**2 - 805*y + 1015\n#Step 6:\nCurrent expression: 529*y**4 + 920*y**3 - 2001*y**2 - 805*y + 1015\nNo more calculations needed.\n529*y**4 + 920*y**3 - 2001*y**2 - 805*y + 1015", "generated_answer": "529*y**4 + 920*y**3 - 2001*y**2 - 805*y + 1015", "step_length": 6} {"cot_id": "371efa258711a76d0b168fd680d12fa27b0616f857f51a71f3353e354517dd98", "datapoint": {"question": "Simplify this expression: (57*y + 37)*(36*y**3 + 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2052*y**4 + 1332*y**3 + 2052*y + 1332", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 208, "polynomial_expr": "(57*y + 37)*(36*y**3 + 36)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (57*y + 37)*(36*y**3 + 36)\nExpanding the part (36*y**3 + 36) using the distributive property, and we got: (36*y**3)*(57*y + 37) + 36*(57*y + 37)\n#Step 2:\nCurrent expression: (36*y**3)*(57*y + 37) + 36*(57*y + 37)\nSimplifying the partial expression: 36*(57*y + 37)\nExpanding the part (57*y + 37) using the distributive property, and we got: (57*y)*36 + 37*36\nReplacing 36*(57*y + 37) with (57*y)*36 + 37*36 in the overall expression.\n#Step 3:\nCurrent expression: (57*y)*36 + (36*y**3)*(57*y + 37) + 1332\nSimplifying the partial expression: (36*y**3)*(57*y + 37)\nExpanding the part (57*y + 37) using the distributive property, and we got: 37*(36*y**3) + (57*y)*(36*y**3)\nReplacing (36*y**3)*(57*y + 37) with 37*(36*y**3) + (57*y)*(36*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 37*36*y**3 + (57*y)*(36*y**3) + (57*y)*36 + 1332\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (57*y)*36 = 2052*y\n (57*y)*(36*y**3) = 2052*y**4\n 37*36*y**3 = 1332*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2052*y**4 + 1332*y**3 + 2052*y + 1332\nNo more calculations needed.\n2052*y**4 + 1332*y**3 + 2052*y + 1332", "generated_answer": "2052*y**4 + 1332*y**3 + 2052*y + 1332", "step_length": 5} {"cot_id": "e5027d752398f6369dee12e79c6ef5ec54e560f6d5ec543c5b5ac0f72b17c687", "datapoint": {"question": "Simplify this expression: (33 - 96*y**2)*(-57*y**3 + 13*y**2 - 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "5472*y**5 - 1248*y**4 - 1881*y**3 + 5133*y**2 - 1617", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 209, "polynomial_expr": "(33 - 96*y**2)*(-57*y**3 + 13*y**2 - 49)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (33 - 96*y**2)*(-57*y**3 + 13*y**2 - 49)\nExpanding the part (33 - 96*y**2) using the distributive property, and we got: (-96*y**2)*(-57*y**3 + 13*y**2 - 49) + 33*(-57*y**3 + 13*y**2 - 49)\n#Step 2:\nCurrent expression: (-96*y**2)*(-57*y**3 + 13*y**2 - 49) + 33*(-57*y**3 + 13*y**2 - 49)\nSimplifying the partial expression: 33*(-57*y**3 + 13*y**2 - 49)\nExpanding the part (-57*y**3 + 13*y**2 - 49) using the distributive property, and we got: (13*y**2)*33 - 57*y**3*33 - 49*33\nReplacing 33*(-57*y**3 + 13*y**2 - 49) with (13*y**2)*33 - 57*y**3*33 - 49*33 in the overall expression.\n#Step 3:\nCurrent expression: (-96*y**2)*(-57*y**3 + 13*y**2 - 49) + (13*y**2)*33 - 57*y**3*33 - 1617\nSimplifying the partial expression: (-96*y**2)*(-57*y**3 + 13*y**2 - 49)\nExpanding the part (-57*y**3 + 13*y**2 - 49) using the distributive property, and we got: -(-1)*4704*y**2 + (-96*y**2)*(13*y**2) + (-96*y**2)*(-57*y**3)\nReplacing (-96*y**2)*(-57*y**3 + 13*y**2 - 49) with -(-1)*4704*y**2 + (-96*y**2)*(13*y**2) + (-96*y**2)*(-57*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -49*(-96)*y**2 + (-96*y**2)*(13*y**2) + (-96*y**2)*(-57*y**3) + (13*y**2)*33 - 57*y**3*33 - 1617\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-57*y**3)*33 = -1881*y**3\n (-57*y**3)*(-96*y**2) = 5472*y**5\n (13*y**2)*33 = 429*y**2\n (13*y**2)*(-96*y**2) = -1248*y**4\n -49*-96*y**2 = 4704*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 5472*y**5 - 1248*y**4 - 1881*y**3 + 429*y**2 + 4704*y**2 - 1617\nCombining like terms, got 5472*y**5 - 1248*y**4 - 1881*y**3 + 5133*y**2 - 1617\n#Step 6:\nCurrent expression: 5472*y**5 - 1248*y**4 - 1881*y**3 + 5133*y**2 - 1617\nNo more calculations needed.\n5472*y**5 - 1248*y**4 - 1881*y**3 + 5133*y**2 - 1617", "generated_answer": "5472*y**5 - 1248*y**4 - 1881*y**3 + 5133*y**2 - 1617", "step_length": 6} {"cot_id": "17b8e08c8444386a9172be004b03ef1bd0fe9b35cb1dc798e91a717efc76fe8a", "datapoint": {"question": "Calculate the following: (-38*z**3 + 17*z**2 + 10*z)*(64*z**3 - 22*z + 19)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2432*z**6 + 1088*z**5 + 1476*z**4 - 1096*z**3 + 103*z**2 + 190*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 210, "polynomial_expr": "(-38*z**3 + 17*z**2 + 10*z)*(64*z**3 - 22*z + 19)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-38*z**3 + 17*z**2 + 10*z)*(64*z**3 - 22*z + 19)\nExpanding the part (64*z**3 - 22*z + 19) using the distributive property, and we got: (-22*z)*(-38*z**3 + 17*z**2 + 10*z) + (64*z**3)*(-38*z**3 + 17*z**2 + 10*z) + 19*(-38*z**3 + 17*z**2 + 10*z)\n#Step 2:\nCurrent expression: (-22*z)*(-38*z**3 + 17*z**2 + 10*z) + (64*z**3)*(-38*z**3 + 17*z**2 + 10*z) + 19*(-38*z**3 + 17*z**2 + 10*z)\nSimplifying the partial expression: 19*(-38*z**3 + 17*z**2 + 10*z)\nExpanding the part (-38*z**3 + 17*z**2 + 10*z) using the distributive property, and we got: (10*z)*19 + (17*z**2)*19 - 38*z**3*19\nReplacing 19*(-38*z**3 + 17*z**2 + 10*z) with (10*z)*19 + (17*z**2)*19 - 38*z**3*19 in the overall expression.\n#Step 3:\nCurrent expression: (-22*z)*(-38*z**3 + 17*z**2 + 10*z) + (10*z)*19 + (17*z**2)*19 - 38*z**3*19 + (64*z**3)*(-38*z**3 + 17*z**2 + 10*z)\nSimplifying the partial expression: (-22*z)*(-38*z**3 + 17*z**2 + 10*z)\nExpanding the part (-38*z**3 + 17*z**2 + 10*z) using the distributive property, and we got: (-22*z)*(10*z) + (-22*z)*(17*z**2) + (-22*z)*(-38*z**3)\nReplacing (-22*z)*(-38*z**3 + 17*z**2 + 10*z) with (-22*z)*(10*z) + (-22*z)*(17*z**2) + (-22*z)*(-38*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-22*z)*(10*z) + (-22*z)*(17*z**2) + (-22*z)*(-38*z**3) + (10*z)*19 + (17*z**2)*19 - 38*z**3*19 + (64*z**3)*(-38*z**3 + 17*z**2 + 10*z)\nSimplifying the partial expression: (64*z**3)*(-38*z**3 + 17*z**2 + 10*z)\nExpanding the part (-38*z**3 + 17*z**2 + 10*z) using the distributive property, and we got: (10*z)*(64*z**3) + (17*z**2)*(64*z**3) + (-38*z**3)*(64*z**3)\nReplacing (64*z**3)*(-38*z**3 + 17*z**2 + 10*z) with (10*z)*(64*z**3) + (17*z**2)*(64*z**3) + (-38*z**3)*(64*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-22*z)*(10*z) + (-22*z)*(17*z**2) + (-22*z)*(-38*z**3) + (10*z)*(64*z**3) + (10*z)*19 + (17*z**2)*(64*z**3) + (17*z**2)*19 + (-38*z**3)*(64*z**3) - 38*z**3*19\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*z**3)*19 = -722*z**3\n (-38*z**3)*(-22*z) = 836*z**4\n (-38*z**3)*(64*z**3) = -2432*z**6\n (10*z)*19 = 190*z\n (10*z)*(-22*z) = -220*z**2\n (10*z)*(64*z**3) = 640*z**4\n (17*z**2)*19 = 323*z**2\n (17*z**2)*(-22*z) = -374*z**3\n (17*z**2)*(64*z**3) = 1088*z**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -2432*z**6 + 1088*z**5 + 640*z**4 + 836*z**4 - 722*z**3 - 374*z**3 - 220*z**2 + 323*z**2 + 190*z\nCombining like terms, got -2432*z**6 + 1088*z**5 + 1476*z**4 - 1096*z**3 + 103*z**2 + 190*z\n#Step 7:\nCurrent expression: -2432*z**6 + 1088*z**5 + 1476*z**4 - 1096*z**3 + 103*z**2 + 190*z\nNo more calculations needed.\n-2432*z**6 + 1088*z**5 + 1476*z**4 - 1096*z**3 + 103*z**2 + 190*z", "generated_answer": "-2432*z**6 + 1088*z**5 + 1476*z**4 - 1096*z**3 + 103*z**2 + 190*z", "step_length": 7} {"cot_id": "0a9bdedacd55bee2f0a173e969c6311dbf5b2707a2208963a392e6feeb9573bf", "datapoint": {"question": "Simplify this expression: (-14*z**2 + 40*z)*(-29*z**3 + 32*z - 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "406*z**5 - 1160*z**4 - 448*z**3 + 1420*z**2 - 400*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 211, "polynomial_expr": "(-14*z**2 + 40*z)*(-29*z**3 + 32*z - 10)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-14*z**2 + 40*z)*(-29*z**3 + 32*z - 10)\nExpanding the part (-14*z**2 + 40*z) using the distributive property, and we got: (40*z)*(-29*z**3 + 32*z - 10) + (-14*z**2)*(-29*z**3 + 32*z - 10)\n#Step 2:\nCurrent expression: (40*z)*(-29*z**3 + 32*z - 10) + (-14*z**2)*(-29*z**3 + 32*z - 10)\nSimplifying the partial expression: (-14*z**2)*(-29*z**3 + 32*z - 10)\nExpanding the part (-29*z**3 + 32*z - 10) using the distributive property, and we got: -(-1)*140*z**2 + (32*z)*(-14*z**2) + (-14*z**2)*(-29*z**3)\nReplacing (-14*z**2)*(-29*z**3 + 32*z - 10) with -(-1)*140*z**2 + (32*z)*(-14*z**2) + (-14*z**2)*(-29*z**3) in the overall expression.\n#Step 3:\nCurrent expression: -10*(-14)*z**2 + (32*z)*(-14*z**2) + (40*z)*(-29*z**3 + 32*z - 10) + (-14*z**2)*(-29*z**3)\nSimplifying the partial expression: (40*z)*(-29*z**3 + 32*z - 10)\nExpanding the part (-29*z**3 + 32*z - 10) using the distributive property, and we got: -400*z + (32*z)*(40*z) + (40*z)*(-29*z**3)\nReplacing (40*z)*(-29*z**3 + 32*z - 10) with -400*z + (32*z)*(40*z) + (40*z)*(-29*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -10*(-14)*z**2 - 10*40*z + (32*z)*(40*z) + (32*z)*(-14*z**2) + (40*z)*(-29*z**3) + (-14*z**2)*(-29*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*z**3)*(-14*z**2) = 406*z**5\n (-29*z**3)*(40*z) = -1160*z**4\n (32*z)*(-14*z**2) = -448*z**3\n (32*z)*(40*z) = 1280*z**2\n -10*-14*z**2 = 140*z**2\n -10*40*z = -400*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 406*z**5 - 1160*z**4 - 448*z**3 + 140*z**2 + 1280*z**2 - 400*z\nCombining like terms, got 406*z**5 - 1160*z**4 - 448*z**3 + 1420*z**2 - 400*z\n#Step 6:\nCurrent expression: 406*z**5 - 1160*z**4 - 448*z**3 + 1420*z**2 - 400*z\nNo more calculations needed.\n406*z**5 - 1160*z**4 - 448*z**3 + 1420*z**2 - 400*z", "generated_answer": "406*z**5 - 1160*z**4 - 448*z**3 + 1420*z**2 - 400*z", "step_length": 6} {"cot_id": "ade5ef5d408884af061829ec72e2ba673efba89e9d9514dcb6ee441c3882b15d", "datapoint": {"question": "Calculate the following: (14 - 41*y)*(3*y - 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-123*y**2 + 1846*y - 616", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 212, "polynomial_expr": "(14 - 41*y)*(3*y - 44)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14 - 41*y)*(3*y - 44)\nExpanding the part (3*y - 44) using the distributive property, and we got: (3*y)*(14 - 41*y) - 44*(14 - 41*y)\n#Step 2:\nCurrent expression: (3*y)*(14 - 41*y) - 44*(14 - 41*y)\nSimplifying the partial expression: -44*(14 - 41*y)\nExpanding the part (14 - 41*y) using the distributive property, and we got: -41*y*(-44) + 14*(-44)\nReplacing -44*(14 - 41*y) with -41*y*(-44) + 14*(-44) in the overall expression.\n#Step 3:\nCurrent expression: -41*y*(-44) + (3*y)*(14 - 41*y) - 616\nSimplifying the partial expression: (3*y)*(14 - 41*y)\nExpanding the part (14 - 41*y) using the distributive property, and we got: (-41*y)*(3*y) + 14*(3*y)\nReplacing (3*y)*(14 - 41*y) with (-41*y)*(3*y) + 14*(3*y) in the overall expression.\n#Step 4:\nCurrent expression: (-41*y)*(3*y) - 41*y*(-44) + 14*3*y - 616\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*y)*-44 = 1804*y\n (-41*y)*(3*y) = -123*y**2\n 14*3*y = 42*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -123*y**2 + 42*y + 1804*y - 616\nCombining like terms, got -123*y**2 + 1846*y - 616\n#Step 6:\nCurrent expression: -123*y**2 + 1846*y - 616\nNo more calculations needed.\n-123*y**2 + 1846*y - 616", "generated_answer": "-123*y**2 + 1846*y - 616", "step_length": 6} {"cot_id": "5999ea49e50b0e1a8c0312973a62c4904d9187722f6cee0182fb660fce0fdff7", "datapoint": {"question": "Simplify this expression: (22*x**3 - 30*x**2 - 24)*(19*x**3 - 35*x**2 + 41*x + 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "418*x**6 - 1340*x**5 + 1952*x**4 - 1158*x**3 + 120*x**2 - 984*x - 576", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 213, "polynomial_expr": "(22*x**3 - 30*x**2 - 24)*(19*x**3 - 35*x**2 + 41*x + 24)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (22*x**3 - 30*x**2 - 24)*(19*x**3 - 35*x**2 + 41*x + 24)\nExpanding the part (22*x**3 - 30*x**2 - 24) using the distributive property, and we got: (-30*x**2)*(19*x**3 - 35*x**2 + 41*x + 24) + (22*x**3)*(19*x**3 - 35*x**2 + 41*x + 24) - 24*(19*x**3 - 35*x**2 + 41*x + 24)\n#Step 2:\nCurrent expression: (-30*x**2)*(19*x**3 - 35*x**2 + 41*x + 24) + (22*x**3)*(19*x**3 - 35*x**2 + 41*x + 24) - 24*(19*x**3 - 35*x**2 + 41*x + 24)\nSimplifying the partial expression: -24*(19*x**3 - 35*x**2 + 41*x + 24)\nExpanding the part (19*x**3 - 35*x**2 + 41*x + 24) using the distributive property, and we got: (41*x)*(-24) - 35*x**2*(-24) + (19*x**3)*(-24) + 24*(-24)\nReplacing -24*(19*x**3 - 35*x**2 + 41*x + 24) with (41*x)*(-24) - 35*x**2*(-24) + (19*x**3)*(-24) + 24*(-24) in the overall expression.\n#Step 3:\nCurrent expression: (41*x)*(-24) - 35*x**2*(-24) + (-30*x**2)*(19*x**3 - 35*x**2 + 41*x + 24) + (19*x**3)*(-24) + (22*x**3)*(19*x**3 - 35*x**2 + 41*x + 24) - 576\nSimplifying the partial expression: (-30*x**2)*(19*x**3 - 35*x**2 + 41*x + 24)\nExpanding the part (19*x**3 - 35*x**2 + 41*x + 24) using the distributive property, and we got: 24*(-30*x**2) + (41*x)*(-30*x**2) + (-35*x**2)*(-30*x**2) + (-30*x**2)*(19*x**3)\nReplacing (-30*x**2)*(19*x**3 - 35*x**2 + 41*x + 24) with 24*(-30*x**2) + (41*x)*(-30*x**2) + (-35*x**2)*(-30*x**2) + (-30*x**2)*(19*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 24*(-30)*x**2 + (41*x)*(-30*x**2) + (41*x)*(-24) + (-35*x**2)*(-30*x**2) - 35*x**2*(-24) + (-30*x**2)*(19*x**3) + (19*x**3)*(-24) + (22*x**3)*(19*x**3 - 35*x**2 + 41*x + 24) - 576\nSimplifying the partial expression: (22*x**3)*(19*x**3 - 35*x**2 + 41*x + 24)\nExpanding the part (19*x**3 - 35*x**2 + 41*x + 24) using the distributive property, and we got: 24*(22*x**3) + (41*x)*(22*x**3) + (-35*x**2)*(22*x**3) + (19*x**3)*(22*x**3)\nReplacing (22*x**3)*(19*x**3 - 35*x**2 + 41*x + 24) with 24*(22*x**3) + (41*x)*(22*x**3) + (-35*x**2)*(22*x**3) + (19*x**3)*(22*x**3) in the overall expression.\n#Step 5:\nCurrent expression: 24*22*x**3 + 24*(-30)*x**2 + (41*x)*(-30*x**2) + (41*x)*(22*x**3) + (41*x)*(-24) + (-35*x**2)*(-30*x**2) + (-35*x**2)*(22*x**3) - 35*x**2*(-24) + (-30*x**2)*(19*x**3) + (19*x**3)*(22*x**3) + (19*x**3)*(-24) - 576\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*x**2)*-24 = 840*x**2\n (-35*x**2)*(-30*x**2) = 1050*x**4\n (-35*x**2)*(22*x**3) = -770*x**5\n (19*x**3)*-24 = -456*x**3\n (19*x**3)*(-30*x**2) = -570*x**5\n (19*x**3)*(22*x**3) = 418*x**6\n (41*x)*-24 = -984*x\n (41*x)*(-30*x**2) = -1230*x**3\n (41*x)*(22*x**3) = 902*x**4\n 24*-30*x**2 = -720*x**2\n 24*22*x**3 = 528*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 418*x**6 - 770*x**5 - 570*x**5 + 902*x**4 + 1050*x**4 - 1230*x**3 - 456*x**3 + 528*x**3 - 720*x**2 + 840*x**2 - 984*x - 576\nCombining like terms, got 418*x**6 - 1340*x**5 + 1952*x**4 - 1158*x**3 + 120*x**2 - 984*x - 576\n#Step 7:\nCurrent expression: 418*x**6 - 1340*x**5 + 1952*x**4 - 1158*x**3 + 120*x**2 - 984*x - 576\nNo more calculations needed.\n418*x**6 - 1340*x**5 + 1952*x**4 - 1158*x**3 + 120*x**2 - 984*x - 576", "generated_answer": "418*x**6 - 1340*x**5 + 1952*x**4 - 1158*x**3 + 120*x**2 - 984*x - 576", "step_length": 7} {"cot_id": "3d100ff2e992c551524f99076adbe0ce445348cf226bdabd3005e28a24705930", "datapoint": {"question": "Simplify this expression: (-6*y**2 - 33)*(39*y**3 + 36*y + 19)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-234*y**5 - 1503*y**3 - 114*y**2 - 1188*y - 627", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 214, "polynomial_expr": "(-6*y**2 - 33)*(39*y**3 + 36*y + 19)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-6*y**2 - 33)*(39*y**3 + 36*y + 19)\nExpanding the part (-6*y**2 - 33) using the distributive property, and we got: (-6*y**2)*(39*y**3 + 36*y + 19) - 33*(39*y**3 + 36*y + 19)\n#Step 2:\nCurrent expression: (-6*y**2)*(39*y**3 + 36*y + 19) - 33*(39*y**3 + 36*y + 19)\nSimplifying the partial expression: -33*(39*y**3 + 36*y + 19)\nExpanding the part (39*y**3 + 36*y + 19) using the distributive property, and we got: (36*y)*(-33) + (39*y**3)*(-33) + 19*(-33)\nReplacing -33*(39*y**3 + 36*y + 19) with (36*y)*(-33) + (39*y**3)*(-33) + 19*(-33) in the overall expression.\n#Step 3:\nCurrent expression: (36*y)*(-33) + (-6*y**2)*(39*y**3 + 36*y + 19) + (39*y**3)*(-33) - 627\nSimplifying the partial expression: (-6*y**2)*(39*y**3 + 36*y + 19)\nExpanding the part (39*y**3 + 36*y + 19) using the distributive property, and we got: 19*(-6*y**2) + (36*y)*(-6*y**2) + (-6*y**2)*(39*y**3)\nReplacing (-6*y**2)*(39*y**3 + 36*y + 19) with 19*(-6*y**2) + (36*y)*(-6*y**2) + (-6*y**2)*(39*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 19*(-6)*y**2 + (36*y)*(-6*y**2) + (36*y)*(-33) + (-6*y**2)*(39*y**3) + (39*y**3)*(-33) - 627\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (36*y)*-33 = -1188*y\n (36*y)*(-6*y**2) = -216*y**3\n (39*y**3)*-33 = -1287*y**3\n (39*y**3)*(-6*y**2) = -234*y**5\n 19*-6*y**2 = -114*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -234*y**5 - 1287*y**3 - 216*y**3 - 114*y**2 - 1188*y - 627\nCombining like terms, got -234*y**5 - 1503*y**3 - 114*y**2 - 1188*y - 627\n#Step 6:\nCurrent expression: -234*y**5 - 1503*y**3 - 114*y**2 - 1188*y - 627\nNo more calculations needed.\n-234*y**5 - 1503*y**3 - 114*y**2 - 1188*y - 627", "generated_answer": "-234*y**5 - 1503*y**3 - 114*y**2 - 1188*y - 627", "step_length": 6} {"cot_id": "bea06a37ffa9e3b4ff04a779bcbdba31c98635d114fad82ffeec5cff122c937e", "datapoint": {"question": "Simplify this expression: (16*y + 31)*(y**2 - 18)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "16*y**3 + 31*y**2 - 288*y - 558", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 215, "polynomial_expr": "(16*y + 31)*(y**2 - 18)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (16*y + 31)*(y**2 - 18)\nExpanding the part (y**2 - 18) using the distributive property, and we got: y**2*(16*y + 31) - 18*(16*y + 31)\n#Step 2:\nCurrent expression: y**2*(16*y + 31) - 18*(16*y + 31)\nSimplifying the partial expression: -18*(16*y + 31)\nExpanding the part (16*y + 31) using the distributive property, and we got: (16*y)*(-18) + 31*(-18)\nReplacing -18*(16*y + 31) with (16*y)*(-18) + 31*(-18) in the overall expression.\n#Step 3:\nCurrent expression: y**2*(16*y + 31) + (16*y)*(-18) - 558\nSimplifying the partial expression: y**2*(16*y + 31)\nExpanding the part (16*y + 31) using the distributive property, and we got: (16*y)*y**2 + 31*y**2\nReplacing y**2*(16*y + 31) with (16*y)*y**2 + 31*y**2 in the overall expression.\n#Step 4:\nCurrent expression: (16*y)*y**2 + 31*y**2 + (16*y)*(-18) - 558\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (16*y)*-18 = -288*y\n (16*y)*y**2 = 16*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 16*y**3 + 31*y**2 - 288*y - 558\nNo more calculations needed.\n16*y**3 + 31*y**2 - 288*y - 558", "generated_answer": "16*y**3 + 31*y**2 - 288*y - 558", "step_length": 5} {"cot_id": "09207adaefb4b692e259f7eee1746e6c6c222b4eed2e396a9e710ce18cd119c4", "datapoint": {"question": "Simplify this expression: (43 - 35*z**2)*(-25*z - 19)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "875*z**3 + 665*z**2 - 1075*z - 817", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 216, "polynomial_expr": "(43 - 35*z**2)*(-25*z - 19)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (43 - 35*z**2)*(-25*z - 19)\nExpanding the part (-25*z - 19) using the distributive property, and we got: (-25*z)*(43 - 35*z**2) - 19*(43 - 35*z**2)\n#Step 2:\nCurrent expression: (-25*z)*(43 - 35*z**2) - 19*(43 - 35*z**2)\nSimplifying the partial expression: -19*(43 - 35*z**2)\nExpanding the part (43 - 35*z**2) using the distributive property, and we got: -35*z**2*(-19) + 43*(-19)\nReplacing -19*(43 - 35*z**2) with -35*z**2*(-19) + 43*(-19) in the overall expression.\n#Step 3:\nCurrent expression: (-25*z)*(43 - 35*z**2) - 35*z**2*(-19) - 817\nSimplifying the partial expression: (-25*z)*(43 - 35*z**2)\nExpanding the part (43 - 35*z**2) using the distributive property, and we got: (-25*z)*(-35*z**2) + 43*(-25*z)\nReplacing (-25*z)*(43 - 35*z**2) with (-25*z)*(-35*z**2) + 43*(-25*z) in the overall expression.\n#Step 4:\nCurrent expression: (-25*z)*(-35*z**2) + 43*(-25)*z - 35*z**2*(-19) - 817\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*z**2)*-19 = 665*z**2\n (-35*z**2)*(-25*z) = 875*z**3\n 43*-25*z = -1075*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 875*z**3 + 665*z**2 - 1075*z - 817\nNo more calculations needed.\n875*z**3 + 665*z**2 - 1075*z - 817", "generated_answer": "875*z**3 + 665*z**2 - 1075*z - 817", "step_length": 5} {"cot_id": "19f6f9432a841fefb715cacfee2b4ab2db12fc730f5b8fbe185d192a489798a9", "datapoint": {"question": "Simplify this expression: (37*x**2 - 9)*(39*x**3 + 4*x**2 + 16*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1443*x**5 + 148*x**4 + 241*x**3 - 36*x**2 - 144*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 217, "polynomial_expr": "(37*x**2 - 9)*(39*x**3 + 4*x**2 + 16*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (37*x**2 - 9)*(39*x**3 + 4*x**2 + 16*x)\nExpanding the part (37*x**2 - 9) using the distributive property, and we got: (37*x**2)*(39*x**3 + 4*x**2 + 16*x) - 9*(39*x**3 + 4*x**2 + 16*x)\n#Step 2:\nCurrent expression: (37*x**2)*(39*x**3 + 4*x**2 + 16*x) - 9*(39*x**3 + 4*x**2 + 16*x)\nSimplifying the partial expression: -9*(39*x**3 + 4*x**2 + 16*x)\nExpanding the part (39*x**3 + 4*x**2 + 16*x) using the distributive property, and we got: (16*x)*(-9) + (4*x**2)*(-9) + (39*x**3)*(-9)\nReplacing -9*(39*x**3 + 4*x**2 + 16*x) with (16*x)*(-9) + (4*x**2)*(-9) + (39*x**3)*(-9) in the overall expression.\n#Step 3:\nCurrent expression: (16*x)*(-9) + (4*x**2)*(-9) + (37*x**2)*(39*x**3 + 4*x**2 + 16*x) + (39*x**3)*(-9)\nSimplifying the partial expression: (37*x**2)*(39*x**3 + 4*x**2 + 16*x)\nExpanding the part (39*x**3 + 4*x**2 + 16*x) using the distributive property, and we got: (16*x)*(37*x**2) + (4*x**2)*(37*x**2) + (37*x**2)*(39*x**3)\nReplacing (37*x**2)*(39*x**3 + 4*x**2 + 16*x) with (16*x)*(37*x**2) + (4*x**2)*(37*x**2) + (37*x**2)*(39*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (16*x)*(37*x**2) + (16*x)*(-9) + (4*x**2)*(37*x**2) + (4*x**2)*(-9) + (37*x**2)*(39*x**3) + (39*x**3)*(-9)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (4*x**2)*-9 = -36*x**2\n (4*x**2)*(37*x**2) = 148*x**4\n (16*x)*-9 = -144*x\n (16*x)*(37*x**2) = 592*x**3\n (39*x**3)*-9 = -351*x**3\n (39*x**3)*(37*x**2) = 1443*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1443*x**5 + 148*x**4 - 351*x**3 + 592*x**3 - 36*x**2 - 144*x\nCombining like terms, got 1443*x**5 + 148*x**4 + 241*x**3 - 36*x**2 - 144*x\n#Step 6:\nCurrent expression: 1443*x**5 + 148*x**4 + 241*x**3 - 36*x**2 - 144*x\nNo more calculations needed.\n1443*x**5 + 148*x**4 + 241*x**3 - 36*x**2 - 144*x", "generated_answer": "1443*x**5 + 148*x**4 + 241*x**3 - 36*x**2 - 144*x", "step_length": 6} {"cot_id": "e4d12b7161c19bc1781e2773d543d6f51e999fe3863d997a09e2249dd4e1e010", "datapoint": {"question": "Calculate the following: (7*x**2 - 44)*(-37*x**3 + 9*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-259*x**5 + 63*x**4 + 1628*x**3 - 396*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 218, "polynomial_expr": "(7*x**2 - 44)*(-37*x**3 + 9*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7*x**2 - 44)*(-37*x**3 + 9*x**2)\nExpanding the part (7*x**2 - 44) using the distributive property, and we got: (7*x**2)*(-37*x**3 + 9*x**2) - 44*(-37*x**3 + 9*x**2)\n#Step 2:\nCurrent expression: (7*x**2)*(-37*x**3 + 9*x**2) - 44*(-37*x**3 + 9*x**2)\nSimplifying the partial expression: -44*(-37*x**3 + 9*x**2)\nExpanding the part (-37*x**3 + 9*x**2) using the distributive property, and we got: (9*x**2)*(-44) - 37*x**3*(-44)\nReplacing -44*(-37*x**3 + 9*x**2) with (9*x**2)*(-44) - 37*x**3*(-44) in the overall expression.\n#Step 3:\nCurrent expression: (7*x**2)*(-37*x**3 + 9*x**2) + (9*x**2)*(-44) - 37*x**3*(-44)\nSimplifying the partial expression: (7*x**2)*(-37*x**3 + 9*x**2)\nExpanding the part (-37*x**3 + 9*x**2) using the distributive property, and we got: (7*x**2)*(9*x**2) + (7*x**2)*(-37*x**3)\nReplacing (7*x**2)*(-37*x**3 + 9*x**2) with (7*x**2)*(9*x**2) + (7*x**2)*(-37*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (7*x**2)*(9*x**2) + (7*x**2)*(-37*x**3) + (9*x**2)*(-44) - 37*x**3*(-44)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*x**3)*-44 = 1628*x**3\n (-37*x**3)*(7*x**2) = -259*x**5\n (9*x**2)*-44 = -396*x**2\n (9*x**2)*(7*x**2) = 63*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -259*x**5 + 63*x**4 + 1628*x**3 - 396*x**2\nNo more calculations needed.\n-259*x**5 + 63*x**4 + 1628*x**3 - 396*x**2", "generated_answer": "-259*x**5 + 63*x**4 + 1628*x**3 - 396*x**2", "step_length": 5} {"cot_id": "8907db87052222753d5245c0b7b9232cbd08baae75b76f922cb4c1794c011445", "datapoint": {"question": "Simplify this expression: -47*y*(-17*y**2 - 6*y - 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "799*y**3 + 282*y**2 + 752*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 219, "polynomial_expr": "-47*y*(-17*y**2 - 6*y - 16)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -47*y*(-17*y**2 - 6*y - 16)\nExpanding the part (-17*y**2 - 6*y - 16) using the distributive property, and we got: (-47*y)*(-6*y) + (-47*y)*(-17*y**2) - (-1)*752*y\n#Step 2:\nCurrent expression: (-47*y)*(-6*y) + (-47*y)*(-17*y**2) - (-1)*752*y\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -16*(-47*y) = 752*y\n (-17*y**2)*(-47*y) = 799*y**3\n (-6*y)*(-47*y) = 282*y**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 799*y**3 + 282*y**2 + 752*y\nNo more calculations needed.\n799*y**3 + 282*y**2 + 752*y", "generated_answer": "799*y**3 + 282*y**2 + 752*y", "step_length": 3} {"cot_id": "30fc44a3ef0ce0a125300a831bf8e05aa688494f6ae4e96a73b7f07ae491143f", "datapoint": {"question": "Calculate the following: (10*y + 50)*(15*y**3 + 22*y + 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "150*y**4 + 750*y**3 + 220*y**2 + 1480*y + 1900", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 220, "polynomial_expr": "(10*y + 50)*(15*y**3 + 22*y + 38)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (10*y + 50)*(15*y**3 + 22*y + 38)\nExpanding the part (10*y + 50) using the distributive property, and we got: (10*y)*(15*y**3 + 22*y + 38) + 50*(15*y**3 + 22*y + 38)\n#Step 2:\nCurrent expression: (10*y)*(15*y**3 + 22*y + 38) + 50*(15*y**3 + 22*y + 38)\nSimplifying the partial expression: 50*(15*y**3 + 22*y + 38)\nExpanding the part (15*y**3 + 22*y + 38) using the distributive property, and we got: (22*y)*50 + (15*y**3)*50 + 38*50\nReplacing 50*(15*y**3 + 22*y + 38) with (22*y)*50 + (15*y**3)*50 + 38*50 in the overall expression.\n#Step 3:\nCurrent expression: (10*y)*(15*y**3 + 22*y + 38) + (22*y)*50 + (15*y**3)*50 + 1900\nSimplifying the partial expression: (10*y)*(15*y**3 + 22*y + 38)\nExpanding the part (15*y**3 + 22*y + 38) using the distributive property, and we got: 38*(10*y) + (10*y)*(22*y) + (10*y)*(15*y**3)\nReplacing (10*y)*(15*y**3 + 22*y + 38) with 38*(10*y) + (10*y)*(22*y) + (10*y)*(15*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 38*10*y + (10*y)*(22*y) + (10*y)*(15*y**3) + (22*y)*50 + (15*y**3)*50 + 1900\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (15*y**3)*50 = 750*y**3\n (15*y**3)*(10*y) = 150*y**4\n (22*y)*50 = 1100*y\n (22*y)*(10*y) = 220*y**2\n 38*10*y = 380*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 150*y**4 + 750*y**3 + 220*y**2 + 380*y + 1100*y + 1900\nCombining like terms, got 150*y**4 + 750*y**3 + 220*y**2 + 1480*y + 1900\n#Step 6:\nCurrent expression: 150*y**4 + 750*y**3 + 220*y**2 + 1480*y + 1900\nNo more calculations needed.\n150*y**4 + 750*y**3 + 220*y**2 + 1480*y + 1900", "generated_answer": "150*y**4 + 750*y**3 + 220*y**2 + 1480*y + 1900", "step_length": 6} {"cot_id": "ec70d2278dc0fc2ba16c2ede78ec5ab67b40172d85cc9e71381c768f94c93f22", "datapoint": {"question": "Simplify this expression: (51*z - 16)*(-48*z**3 + 30*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2448*z**4 + 2298*z**3 - 480*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 221, "polynomial_expr": "(51*z - 16)*(-48*z**3 + 30*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (51*z - 16)*(-48*z**3 + 30*z**2)\nExpanding the part (51*z - 16) using the distributive property, and we got: (51*z)*(-48*z**3 + 30*z**2) - 16*(-48*z**3 + 30*z**2)\n#Step 2:\nCurrent expression: (51*z)*(-48*z**3 + 30*z**2) - 16*(-48*z**3 + 30*z**2)\nSimplifying the partial expression: -16*(-48*z**3 + 30*z**2)\nExpanding the part (-48*z**3 + 30*z**2) using the distributive property, and we got: (30*z**2)*(-16) - 48*z**3*(-16)\nReplacing -16*(-48*z**3 + 30*z**2) with (30*z**2)*(-16) - 48*z**3*(-16) in the overall expression.\n#Step 3:\nCurrent expression: (51*z)*(-48*z**3 + 30*z**2) + (30*z**2)*(-16) - 48*z**3*(-16)\nSimplifying the partial expression: (51*z)*(-48*z**3 + 30*z**2)\nExpanding the part (-48*z**3 + 30*z**2) using the distributive property, and we got: (51*z)*(30*z**2) + (51*z)*(-48*z**3)\nReplacing (51*z)*(-48*z**3 + 30*z**2) with (51*z)*(30*z**2) + (51*z)*(-48*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (51*z)*(30*z**2) + (51*z)*(-48*z**3) + (30*z**2)*(-16) - 48*z**3*(-16)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*z**3)*-16 = 768*z**3\n (-48*z**3)*(51*z) = -2448*z**4\n (30*z**2)*-16 = -480*z**2\n (30*z**2)*(51*z) = 1530*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2448*z**4 + 768*z**3 + 1530*z**3 - 480*z**2\nCombining like terms, got -2448*z**4 + 2298*z**3 - 480*z**2\n#Step 6:\nCurrent expression: -2448*z**4 + 2298*z**3 - 480*z**2\nNo more calculations needed.\n-2448*z**4 + 2298*z**3 - 480*z**2", "generated_answer": "-2448*z**4 + 2298*z**3 - 480*z**2", "step_length": 6} {"cot_id": "ebcaf35e05fa9a25f179fdc4cd7490145a1a36209e8b24a4f5c88ad4778d3ad3", "datapoint": {"question": "Calculate the following: (11 - 2*z**2)*(68*z**3 - 24*z**2 - 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-136*z**5 + 48*z**4 + 748*z**3 - 238*z**2 - 143", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 222, "polynomial_expr": "(11 - 2*z**2)*(68*z**3 - 24*z**2 - 13)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11 - 2*z**2)*(68*z**3 - 24*z**2 - 13)\nExpanding the part (11 - 2*z**2) using the distributive property, and we got: (-2*z**2)*(68*z**3 - 24*z**2 - 13) + 11*(68*z**3 - 24*z**2 - 13)\n#Step 2:\nCurrent expression: (-2*z**2)*(68*z**3 - 24*z**2 - 13) + 11*(68*z**3 - 24*z**2 - 13)\nSimplifying the partial expression: 11*(68*z**3 - 24*z**2 - 13)\nExpanding the part (68*z**3 - 24*z**2 - 13) using the distributive property, and we got: -24*z**2*11 + (68*z**3)*11 - 13*11\nReplacing 11*(68*z**3 - 24*z**2 - 13) with -24*z**2*11 + (68*z**3)*11 - 13*11 in the overall expression.\n#Step 3:\nCurrent expression: -24*z**2*11 + (-2*z**2)*(68*z**3 - 24*z**2 - 13) + (68*z**3)*11 - 143\nSimplifying the partial expression: (-2*z**2)*(68*z**3 - 24*z**2 - 13)\nExpanding the part (68*z**3 - 24*z**2 - 13) using the distributive property, and we got: -(-1)*26*z**2 + (-24*z**2)*(-2*z**2) + (-2*z**2)*(68*z**3)\nReplacing (-2*z**2)*(68*z**3 - 24*z**2 - 13) with -(-1)*26*z**2 + (-24*z**2)*(-2*z**2) + (-2*z**2)*(68*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -13*(-2)*z**2 + (-24*z**2)*(-2*z**2) - 24*z**2*11 + (-2*z**2)*(68*z**3) + (68*z**3)*11 - 143\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-24*z**2)*11 = -264*z**2\n (-24*z**2)*(-2*z**2) = 48*z**4\n (68*z**3)*11 = 748*z**3\n (68*z**3)*(-2*z**2) = -136*z**5\n -13*-2*z**2 = 26*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -136*z**5 + 48*z**4 + 748*z**3 - 264*z**2 + 26*z**2 - 143\nCombining like terms, got -136*z**5 + 48*z**4 + 748*z**3 - 238*z**2 - 143\n#Step 6:\nCurrent expression: -136*z**5 + 48*z**4 + 748*z**3 - 238*z**2 - 143\nNo more calculations needed.\n-136*z**5 + 48*z**4 + 748*z**3 - 238*z**2 - 143", "generated_answer": "-136*z**5 + 48*z**4 + 748*z**3 - 238*z**2 - 143", "step_length": 6} {"cot_id": "b09565fe72270ec3016c689699a547207d02e7588cc97c80f5f1af59973e8a1d", "datapoint": {"question": "Calculate the following: 217*y - 196\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "217*y - 196", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 223, "polynomial_expr": "217*y - 196", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 217*y - 196\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 217*y - 196\nNo more calculations needed.\n217*y - 196", "generated_answer": "217*y - 196", "step_length": 2} {"cot_id": "78ab19dcbf668c947cf16a937111215069b97aef12128119128543ffd8339543", "datapoint": {"question": "Calculate the following: (20*x + 48)*(-39*x**3 - x**2 + 9*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-780*x**4 - 1892*x**3 + 132*x**2 + 432*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 224, "polynomial_expr": "(20*x + 48)*(-39*x**3 - x**2 + 9*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (20*x + 48)*(-39*x**3 - x**2 + 9*x)\nExpanding the part (20*x + 48) using the distributive property, and we got: (20*x)*(-39*x**3 - x**2 + 9*x) + 48*(-39*x**3 - x**2 + 9*x)\n#Step 2:\nCurrent expression: (20*x)*(-39*x**3 - x**2 + 9*x) + 48*(-39*x**3 - x**2 + 9*x)\nSimplifying the partial expression: 48*(-39*x**3 - x**2 + 9*x)\nExpanding the part (-39*x**3 - x**2 + 9*x) using the distributive property, and we got: (9*x)*48 - x**2*48 - 39*x**3*48\nReplacing 48*(-39*x**3 - x**2 + 9*x) with (9*x)*48 - x**2*48 - 39*x**3*48 in the overall expression.\n#Step 3:\nCurrent expression: (9*x)*48 + (20*x)*(-39*x**3 - x**2 + 9*x) - x**2*48 - 39*x**3*48\nSimplifying the partial expression: (20*x)*(-39*x**3 - x**2 + 9*x)\nExpanding the part (-39*x**3 - x**2 + 9*x) using the distributive property, and we got: (9*x)*(20*x) + (20*x)*(-x**2) + (20*x)*(-39*x**3)\nReplacing (20*x)*(-39*x**3 - x**2 + 9*x) with (9*x)*(20*x) + (20*x)*(-x**2) + (20*x)*(-39*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (9*x)*(20*x) + (9*x)*48 + (20*x)*(-x**2) + (20*x)*(-39*x**3) - x**2*48 - 39*x**3*48\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-x**2)*48 = -48*x**2\n (-x**2)*(20*x) = -20*x**3\n (-39*x**3)*48 = -1872*x**3\n (-39*x**3)*(20*x) = -780*x**4\n (9*x)*48 = 432*x\n (9*x)*(20*x) = 180*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -780*x**4 - 1872*x**3 - 20*x**3 - 48*x**2 + 180*x**2 + 432*x\nCombining like terms, got -780*x**4 - 1892*x**3 + 132*x**2 + 432*x\n#Step 6:\nCurrent expression: -780*x**4 - 1892*x**3 + 132*x**2 + 432*x\nNo more calculations needed.\n-780*x**4 - 1892*x**3 + 132*x**2 + 432*x", "generated_answer": "-780*x**4 - 1892*x**3 + 132*x**2 + 432*x", "step_length": 6} {"cot_id": "a3579888165bde65f5ba0026d02106c28914f0f6d7f1bb8b0e773907909dbc2d", "datapoint": {"question": "Calculate the following: 24*x*(34 - 36*x**3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-864*x**4 + 816*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 225, "polynomial_expr": "24*x*(34 - 36*x**3)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 24*x*(34 - 36*x**3)\nExpanding the part (34 - 36*x**3) using the distributive property, and we got: 34*(24*x) + (24*x)*(-36*x**3)\n#Step 2:\nCurrent expression: 34*(24*x) + (24*x)*(-36*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 34*(24*x) = 816*x\n (-36*x**3)*(24*x) = -864*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -864*x**4 + 816*x\nNo more calculations needed.\n-864*x**4 + 816*x", "generated_answer": "-864*x**4 + 816*x", "step_length": 3} {"cot_id": "06088cf2b16916613253ec69f48e8bae5415e45469b191c6664383c682cd669e", "datapoint": {"question": "Calculate the following: -1620*z**3 + 2220*z\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1620*z**3 + 2220*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 226, "polynomial_expr": "-1620*z**3 + 2220*z", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -1620*z**3 + 2220*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -1620*z**3 + 2220*z\nNo more calculations needed.\n-1620*z**3 + 2220*z", "generated_answer": "-1620*z**3 + 2220*z", "step_length": 2} {"cot_id": "b5deaa36b696733fff09e16597590146d6f26b7e41b14e8895a4df3f3d954db3", "datapoint": {"question": "Simplify this expression: 36*x**2*(-7*x**2 + 21*x + 5)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-252*x**4 + 756*x**3 + 180*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 227, "polynomial_expr": "36*x**2*(-7*x**2 + 21*x + 5)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 36*x**2*(-7*x**2 + 21*x + 5)\nExpanding the part (-7*x**2 + 21*x + 5) using the distributive property, and we got: 5*(36*x**2) + (21*x)*(36*x**2) + (-7*x**2)*(36*x**2)\n#Step 2:\nCurrent expression: 5*(36*x**2) + (21*x)*(36*x**2) + (-7*x**2)*(36*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 5*(36*x**2) = 180*x**2\n (-7*x**2)*(36*x**2) = -252*x**4\n (21*x)*(36*x**2) = 756*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -252*x**4 + 756*x**3 + 180*x**2\nNo more calculations needed.\n-252*x**4 + 756*x**3 + 180*x**2", "generated_answer": "-252*x**4 + 756*x**3 + 180*x**2", "step_length": 3} {"cot_id": "cc46cfb0d69259526333a7ea979a1edf73cb67a364a8081963ba63f83af1ddf3", "datapoint": {"question": "Simplify this expression: 35*x**2*(-47*x**2 - 42)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1645*x**4 - 1470*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 228, "polynomial_expr": "35*x**2*(-47*x**2 - 42)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 35*x**2*(-47*x**2 - 42)\nExpanding the part (-47*x**2 - 42) using the distributive property, and we got: -1470*x**2 + (-47*x**2)*(35*x**2)\n#Step 2:\nCurrent expression: -1470*x**2 + (-47*x**2)*(35*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -42*(35*x**2) = -1470*x**2\n (-47*x**2)*(35*x**2) = -1645*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1645*x**4 - 1470*x**2\nNo more calculations needed.\n-1645*x**4 - 1470*x**2", "generated_answer": "-1645*x**4 - 1470*x**2", "step_length": 3} {"cot_id": "6261550ebb1d6e71466b2a230bcf1a07e1b2456d555d40b9038859a984f1be90", "datapoint": {"question": "Calculate the following: (31*y**2 - 44)*(41*y**3 - 23*y**2 + 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1271*y**5 - 713*y**4 - 1804*y**3 + 1632*y**2 - 880", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 229, "polynomial_expr": "(31*y**2 - 44)*(41*y**3 - 23*y**2 + 20)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31*y**2 - 44)*(41*y**3 - 23*y**2 + 20)\nExpanding the part (31*y**2 - 44) using the distributive property, and we got: (31*y**2)*(41*y**3 - 23*y**2 + 20) - 44*(41*y**3 - 23*y**2 + 20)\n#Step 2:\nCurrent expression: (31*y**2)*(41*y**3 - 23*y**2 + 20) - 44*(41*y**3 - 23*y**2 + 20)\nSimplifying the partial expression: -44*(41*y**3 - 23*y**2 + 20)\nExpanding the part (41*y**3 - 23*y**2 + 20) using the distributive property, and we got: -23*y**2*(-44) + (41*y**3)*(-44) + 20*(-44)\nReplacing -44*(41*y**3 - 23*y**2 + 20) with -23*y**2*(-44) + (41*y**3)*(-44) + 20*(-44) in the overall expression.\n#Step 3:\nCurrent expression: -23*y**2*(-44) + (31*y**2)*(41*y**3 - 23*y**2 + 20) + (41*y**3)*(-44) - 880\nSimplifying the partial expression: (31*y**2)*(41*y**3 - 23*y**2 + 20)\nExpanding the part (41*y**3 - 23*y**2 + 20) using the distributive property, and we got: 20*(31*y**2) + (-23*y**2)*(31*y**2) + (31*y**2)*(41*y**3)\nReplacing (31*y**2)*(41*y**3 - 23*y**2 + 20) with 20*(31*y**2) + (-23*y**2)*(31*y**2) + (31*y**2)*(41*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 20*31*y**2 + (-23*y**2)*(31*y**2) - 23*y**2*(-44) + (31*y**2)*(41*y**3) + (41*y**3)*(-44) - 880\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*y**2)*-44 = 1012*y**2\n (-23*y**2)*(31*y**2) = -713*y**4\n (41*y**3)*-44 = -1804*y**3\n (41*y**3)*(31*y**2) = 1271*y**5\n 20*31*y**2 = 620*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1271*y**5 - 713*y**4 - 1804*y**3 + 620*y**2 + 1012*y**2 - 880\nCombining like terms, got 1271*y**5 - 713*y**4 - 1804*y**3 + 1632*y**2 - 880\n#Step 6:\nCurrent expression: 1271*y**5 - 713*y**4 - 1804*y**3 + 1632*y**2 - 880\nNo more calculations needed.\n1271*y**5 - 713*y**4 - 1804*y**3 + 1632*y**2 - 880", "generated_answer": "1271*y**5 - 713*y**4 - 1804*y**3 + 1632*y**2 - 880", "step_length": 6} {"cot_id": "e8ab008943c395f0808faacf0612b9faa5c6da92e2cbb7daae1b4fbf06d71760", "datapoint": {"question": "Simplify this expression: (-42*y**2 + 45*y)*(11*y**2 + 33*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-462*y**4 - 891*y**3 + 1485*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 230, "polynomial_expr": "(-42*y**2 + 45*y)*(11*y**2 + 33*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-42*y**2 + 45*y)*(11*y**2 + 33*y)\nExpanding the part (-42*y**2 + 45*y) using the distributive property, and we got: (45*y)*(11*y**2 + 33*y) + (-42*y**2)*(11*y**2 + 33*y)\n#Step 2:\nCurrent expression: (45*y)*(11*y**2 + 33*y) + (-42*y**2)*(11*y**2 + 33*y)\nSimplifying the partial expression: (-42*y**2)*(11*y**2 + 33*y)\nExpanding the part (11*y**2 + 33*y) using the distributive property, and we got: (33*y)*(-42*y**2) + (-42*y**2)*(11*y**2)\nReplacing (-42*y**2)*(11*y**2 + 33*y) with (33*y)*(-42*y**2) + (-42*y**2)*(11*y**2) in the overall expression.\n#Step 3:\nCurrent expression: (33*y)*(-42*y**2) + (45*y)*(11*y**2 + 33*y) + (-42*y**2)*(11*y**2)\nSimplifying the partial expression: (45*y)*(11*y**2 + 33*y)\nExpanding the part (11*y**2 + 33*y) using the distributive property, and we got: (33*y)*(45*y) + (45*y)*(11*y**2)\nReplacing (45*y)*(11*y**2 + 33*y) with (33*y)*(45*y) + (45*y)*(11*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (33*y)*(45*y) + (33*y)*(-42*y**2) + (45*y)*(11*y**2) + (-42*y**2)*(11*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (11*y**2)*(-42*y**2) = -462*y**4\n (11*y**2)*(45*y) = 495*y**3\n (33*y)*(-42*y**2) = -1386*y**3\n (33*y)*(45*y) = 1485*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -462*y**4 - 1386*y**3 + 495*y**3 + 1485*y**2\nCombining like terms, got -462*y**4 - 891*y**3 + 1485*y**2\n#Step 6:\nCurrent expression: -462*y**4 - 891*y**3 + 1485*y**2\nNo more calculations needed.\n-462*y**4 - 891*y**3 + 1485*y**2", "generated_answer": "-462*y**4 - 891*y**3 + 1485*y**2", "step_length": 6} {"cot_id": "d614e17119968aa44d294097713de789dbf1267de8eab4315b2fcdd3faaf280b", "datapoint": {"question": "Simplify this expression: (10*x**3 + 34*x**2 - 16)*(31*x**3 - 47*x**2 + 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "310*x**6 + 584*x**5 - 1598*x**4 - 436*x**3 + 956*x**2 - 96", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 231, "polynomial_expr": "(10*x**3 + 34*x**2 - 16)*(31*x**3 - 47*x**2 + 6)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (10*x**3 + 34*x**2 - 16)*(31*x**3 - 47*x**2 + 6)\nExpanding the part (10*x**3 + 34*x**2 - 16) using the distributive property, and we got: (34*x**2)*(31*x**3 - 47*x**2 + 6) + (10*x**3)*(31*x**3 - 47*x**2 + 6) - 16*(31*x**3 - 47*x**2 + 6)\n#Step 2:\nCurrent expression: (34*x**2)*(31*x**3 - 47*x**2 + 6) + (10*x**3)*(31*x**3 - 47*x**2 + 6) - 16*(31*x**3 - 47*x**2 + 6)\nSimplifying the partial expression: -16*(31*x**3 - 47*x**2 + 6)\nExpanding the part (31*x**3 - 47*x**2 + 6) using the distributive property, and we got: -47*x**2*(-16) + (31*x**3)*(-16) + 6*(-16)\nReplacing -16*(31*x**3 - 47*x**2 + 6) with -47*x**2*(-16) + (31*x**3)*(-16) + 6*(-16) in the overall expression.\n#Step 3:\nCurrent expression: -47*x**2*(-16) + (34*x**2)*(31*x**3 - 47*x**2 + 6) + (10*x**3)*(31*x**3 - 47*x**2 + 6) + (31*x**3)*(-16) - 96\nSimplifying the partial expression: (10*x**3)*(31*x**3 - 47*x**2 + 6)\nExpanding the part (31*x**3 - 47*x**2 + 6) using the distributive property, and we got: 6*(10*x**3) + (-47*x**2)*(10*x**3) + (10*x**3)*(31*x**3)\nReplacing (10*x**3)*(31*x**3 - 47*x**2 + 6) with 6*(10*x**3) + (-47*x**2)*(10*x**3) + (10*x**3)*(31*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 6*10*x**3 + (-47*x**2)*(10*x**3) - 47*x**2*(-16) + (34*x**2)*(31*x**3 - 47*x**2 + 6) + (10*x**3)*(31*x**3) + (31*x**3)*(-16) - 96\nSimplifying the partial expression: (34*x**2)*(31*x**3 - 47*x**2 + 6)\nExpanding the part (31*x**3 - 47*x**2 + 6) using the distributive property, and we got: 6*(34*x**2) + (-47*x**2)*(34*x**2) + (34*x**2)*(31*x**3)\nReplacing (34*x**2)*(31*x**3 - 47*x**2 + 6) with 6*(34*x**2) + (-47*x**2)*(34*x**2) + (34*x**2)*(31*x**3) in the overall expression.\n#Step 5:\nCurrent expression: 6*10*x**3 + 6*34*x**2 + (-47*x**2)*(34*x**2) + (-47*x**2)*(10*x**3) - 47*x**2*(-16) + (34*x**2)*(31*x**3) + (10*x**3)*(31*x**3) + (31*x**3)*(-16) - 96\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*x**2)*-16 = 752*x**2\n (-47*x**2)*(10*x**3) = -470*x**5\n (-47*x**2)*(34*x**2) = -1598*x**4\n (31*x**3)*-16 = -496*x**3\n (31*x**3)*(10*x**3) = 310*x**6\n (31*x**3)*(34*x**2) = 1054*x**5\n 6*10*x**3 = 60*x**3\n 6*34*x**2 = 204*x**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 310*x**6 - 470*x**5 + 1054*x**5 - 1598*x**4 - 496*x**3 + 60*x**3 + 204*x**2 + 752*x**2 - 96\nCombining like terms, got 310*x**6 + 584*x**5 - 1598*x**4 - 436*x**3 + 956*x**2 - 96\n#Step 7:\nCurrent expression: 310*x**6 + 584*x**5 - 1598*x**4 - 436*x**3 + 956*x**2 - 96\nNo more calculations needed.\n310*x**6 + 584*x**5 - 1598*x**4 - 436*x**3 + 956*x**2 - 96", "generated_answer": "310*x**6 + 584*x**5 - 1598*x**4 - 436*x**3 + 956*x**2 - 96", "step_length": 7} {"cot_id": "0e84cdbbf151aaf2f547778a74cf8171d05c6a54bbe539849137e00156481b40", "datapoint": {"question": "Simplify this expression: 32*x**2*(-2*x**2 + 27*x - 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-64*x**4 + 864*x**3 - 1600*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 232, "polynomial_expr": "32*x**2*(-2*x**2 + 27*x - 50)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 32*x**2*(-2*x**2 + 27*x - 50)\nExpanding the part (-2*x**2 + 27*x - 50) using the distributive property, and we got: -1600*x**2 + (27*x)*(32*x**2) + (-2*x**2)*(32*x**2)\n#Step 2:\nCurrent expression: -1600*x**2 + (27*x)*(32*x**2) + (-2*x**2)*(32*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -50*(32*x**2) = -1600*x**2\n (-2*x**2)*(32*x**2) = -64*x**4\n (27*x)*(32*x**2) = 864*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -64*x**4 + 864*x**3 - 1600*x**2\nNo more calculations needed.\n-64*x**4 + 864*x**3 - 1600*x**2", "generated_answer": "-64*x**4 + 864*x**3 - 1600*x**2", "step_length": 3} {"cot_id": "917a4a8e0948b528b124403cc3c20dbd26f112e476fa4cf9a3bc8dfe4f90d60a", "datapoint": {"question": "Simplify this expression: (-56*x**2 + 42*x - 50)*(13*x**3 - 19*x**2 + 22)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-728*x**5 + 1610*x**4 - 1448*x**3 - 282*x**2 + 924*x - 1100", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 233, "polynomial_expr": "(-56*x**2 + 42*x - 50)*(13*x**3 - 19*x**2 + 22)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-56*x**2 + 42*x - 50)*(13*x**3 - 19*x**2 + 22)\nExpanding the part (-56*x**2 + 42*x - 50) using the distributive property, and we got: (42*x)*(13*x**3 - 19*x**2 + 22) + (-56*x**2)*(13*x**3 - 19*x**2 + 22) - 50*(13*x**3 - 19*x**2 + 22)\n#Step 2:\nCurrent expression: (42*x)*(13*x**3 - 19*x**2 + 22) + (-56*x**2)*(13*x**3 - 19*x**2 + 22) - 50*(13*x**3 - 19*x**2 + 22)\nSimplifying the partial expression: -50*(13*x**3 - 19*x**2 + 22)\nExpanding the part (13*x**3 - 19*x**2 + 22) using the distributive property, and we got: -19*x**2*(-50) + (13*x**3)*(-50) + 22*(-50)\nReplacing -50*(13*x**3 - 19*x**2 + 22) with -19*x**2*(-50) + (13*x**3)*(-50) + 22*(-50) in the overall expression.\n#Step 3:\nCurrent expression: (42*x)*(13*x**3 - 19*x**2 + 22) + (-56*x**2)*(13*x**3 - 19*x**2 + 22) - 19*x**2*(-50) + (13*x**3)*(-50) - 1100\nSimplifying the partial expression: (-56*x**2)*(13*x**3 - 19*x**2 + 22)\nExpanding the part (13*x**3 - 19*x**2 + 22) using the distributive property, and we got: 22*(-56*x**2) + (-56*x**2)*(-19*x**2) + (-56*x**2)*(13*x**3)\nReplacing (-56*x**2)*(13*x**3 - 19*x**2 + 22) with 22*(-56*x**2) + (-56*x**2)*(-19*x**2) + (-56*x**2)*(13*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 22*(-56)*x**2 + (42*x)*(13*x**3 - 19*x**2 + 22) + (-56*x**2)*(-19*x**2) + (-56*x**2)*(13*x**3) - 19*x**2*(-50) + (13*x**3)*(-50) - 1100\nSimplifying the partial expression: (42*x)*(13*x**3 - 19*x**2 + 22)\nExpanding the part (13*x**3 - 19*x**2 + 22) using the distributive property, and we got: 22*(42*x) + (42*x)*(-19*x**2) + (42*x)*(13*x**3)\nReplacing (42*x)*(13*x**3 - 19*x**2 + 22) with 22*(42*x) + (42*x)*(-19*x**2) + (42*x)*(13*x**3) in the overall expression.\n#Step 5:\nCurrent expression: 22*(-56)*x**2 + 22*42*x + (42*x)*(-19*x**2) + (42*x)*(13*x**3) + (-56*x**2)*(-19*x**2) + (-56*x**2)*(13*x**3) - 19*x**2*(-50) + (13*x**3)*(-50) - 1100\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*x**2)*-50 = 950*x**2\n (-19*x**2)*(-56*x**2) = 1064*x**4\n (-19*x**2)*(42*x) = -798*x**3\n (13*x**3)*-50 = -650*x**3\n (13*x**3)*(-56*x**2) = -728*x**5\n (13*x**3)*(42*x) = 546*x**4\n 22*-56*x**2 = -1232*x**2\n 22*42*x = 924*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -728*x**5 + 546*x**4 + 1064*x**4 - 798*x**3 - 650*x**3 - 1232*x**2 + 950*x**2 + 924*x - 1100\nCombining like terms, got -728*x**5 + 1610*x**4 - 1448*x**3 - 282*x**2 + 924*x - 1100\n#Step 7:\nCurrent expression: -728*x**5 + 1610*x**4 - 1448*x**3 - 282*x**2 + 924*x - 1100\nNo more calculations needed.\n-728*x**5 + 1610*x**4 - 1448*x**3 - 282*x**2 + 924*x - 1100", "generated_answer": "-728*x**5 + 1610*x**4 - 1448*x**3 - 282*x**2 + 924*x - 1100", "step_length": 7} {"cot_id": "9b69c2429b3840212d25f9ae53e376ad4578e38bf26eaac38e24bb4f9016a693", "datapoint": {"question": "Simplify this expression: (-y**2 - 49*y)*(-25*y**3 - 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "25*y**5 + 1225*y**4 + 39*y**2 + 1911*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 234, "polynomial_expr": "(-y**2 - 49*y)*(-25*y**3 - 39)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-y**2 - 49*y)*(-25*y**3 - 39)\nExpanding the part (-25*y**3 - 39) using the distributive property, and we got: (-25*y**3)*(-y**2 - 49*y) - 39*(-y**2 - 49*y)\n#Step 2:\nCurrent expression: (-25*y**3)*(-y**2 - 49*y) - 39*(-y**2 - 49*y)\nSimplifying the partial expression: -39*(-y**2 - 49*y)\nExpanding the part (-y**2 - 49*y) using the distributive property, and we got: -49*y*(-39) - y**2*(-39)\nReplacing -39*(-y**2 - 49*y) with -49*y*(-39) - y**2*(-39) in the overall expression.\n#Step 3:\nCurrent expression: -49*y*(-39) - y**2*(-39) + (-25*y**3)*(-y**2 - 49*y)\nSimplifying the partial expression: (-25*y**3)*(-y**2 - 49*y)\nExpanding the part (-y**2 - 49*y) using the distributive property, and we got: (-49*y)*(-25*y**3) + (-y**2)*(-25*y**3)\nReplacing (-25*y**3)*(-y**2 - 49*y) with (-49*y)*(-25*y**3) + (-y**2)*(-25*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-49*y)*(-25*y**3) - 49*y*(-39) + (-y**2)*(-25*y**3) - y**2*(-39)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-y**2)*-39 = 39*y**2\n (-y**2)*(-25*y**3) = 25*y**5\n (-49*y)*-39 = 1911*y\n (-49*y)*(-25*y**3) = 1225*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 25*y**5 + 1225*y**4 + 39*y**2 + 1911*y\nNo more calculations needed.\n25*y**5 + 1225*y**4 + 39*y**2 + 1911*y", "generated_answer": "25*y**5 + 1225*y**4 + 39*y**2 + 1911*y", "step_length": 5} {"cot_id": "89ad3896d890a8f3c2c176b449c34615ebb8e01f52e3195c6477b135333a3efa", "datapoint": {"question": "Simplify this expression: (49 - 43*x)*(46*x**2 - 43)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1978*x**3 + 2254*x**2 + 1849*x - 2107", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 235, "polynomial_expr": "(49 - 43*x)*(46*x**2 - 43)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (49 - 43*x)*(46*x**2 - 43)\nExpanding the part (46*x**2 - 43) using the distributive property, and we got: (46*x**2)*(49 - 43*x) - 43*(49 - 43*x)\n#Step 2:\nCurrent expression: (46*x**2)*(49 - 43*x) - 43*(49 - 43*x)\nSimplifying the partial expression: -43*(49 - 43*x)\nExpanding the part (49 - 43*x) using the distributive property, and we got: -43*x*(-43) + 49*(-43)\nReplacing -43*(49 - 43*x) with -43*x*(-43) + 49*(-43) in the overall expression.\n#Step 3:\nCurrent expression: -43*x*(-43) + (46*x**2)*(49 - 43*x) - 2107\nSimplifying the partial expression: (46*x**2)*(49 - 43*x)\nExpanding the part (49 - 43*x) using the distributive property, and we got: (-43*x)*(46*x**2) + 49*(46*x**2)\nReplacing (46*x**2)*(49 - 43*x) with (-43*x)*(46*x**2) + 49*(46*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-43*x)*(46*x**2) - 43*x*(-43) + 49*46*x**2 - 2107\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-43*x)*-43 = 1849*x\n (-43*x)*(46*x**2) = -1978*x**3\n 49*46*x**2 = 2254*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1978*x**3 + 2254*x**2 + 1849*x - 2107\nNo more calculations needed.\n-1978*x**3 + 2254*x**2 + 1849*x - 2107", "generated_answer": "-1978*x**3 + 2254*x**2 + 1849*x - 2107", "step_length": 5} {"cot_id": "26cf217ef003a083dca22f4eff560fc17366e1ec051ab4e81a04dc364cc16a61", "datapoint": {"question": "Calculate the following: (-41*y**2 - 30)*(8*y**2 + 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-328*y**4 - 281*y**2 - 30", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 236, "polynomial_expr": "(-41*y**2 - 30)*(8*y**2 + 1)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-41*y**2 - 30)*(8*y**2 + 1)\nExpanding the part (8*y**2 + 1) using the distributive property, and we got: (8*y**2)*(-41*y**2 - 30) + 1*(-41*y**2 - 30)\n#Step 2:\nCurrent expression: (8*y**2)*(-41*y**2 - 30) + 1*(-41*y**2 - 30)\nSimplifying the partial expression: 1*(-41*y**2 - 30)\nExpanding the part (-41*y**2 - 30) using the distributive property, and we got: -41*y**2*1 - 30*1\nReplacing 1*(-41*y**2 - 30) with -41*y**2*1 - 30*1 in the overall expression.\n#Step 3:\nCurrent expression: -41*y**2*1 + (8*y**2)*(-41*y**2 - 30) - 30\nSimplifying the partial expression: (8*y**2)*(-41*y**2 - 30)\nExpanding the part (-41*y**2 - 30) using the distributive property, and we got: -240*y**2 + (-41*y**2)*(8*y**2)\nReplacing (8*y**2)*(-41*y**2 - 30) with -240*y**2 + (-41*y**2)*(8*y**2) in the overall expression.\n#Step 4:\nCurrent expression: -30*8*y**2 + (-41*y**2)*(8*y**2) - 41*y**2*1 - 30\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*y**2)*1 = -41*y**2\n (-41*y**2)*(8*y**2) = -328*y**4\n -30*8*y**2 = -240*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -328*y**4 - 240*y**2 - 41*y**2 - 30\nCombining like terms, got -328*y**4 - 281*y**2 - 30\n#Step 6:\nCurrent expression: -328*y**4 - 281*y**2 - 30\nNo more calculations needed.\n-328*y**4 - 281*y**2 - 30", "generated_answer": "-328*y**4 - 281*y**2 - 30", "step_length": 6} {"cot_id": "43b378299c202192ba7ce85d87ee798228a8dc3487ea5b660964fc4adb508322", "datapoint": {"question": "Simplify this expression: (32 - 22*y**3)*(14*y**2 - 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-308*y**5 + 154*y**3 + 448*y**2 - 224", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 237, "polynomial_expr": "(32 - 22*y**3)*(14*y**2 - 7)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (32 - 22*y**3)*(14*y**2 - 7)\nExpanding the part (14*y**2 - 7) using the distributive property, and we got: (14*y**2)*(32 - 22*y**3) - 7*(32 - 22*y**3)\n#Step 2:\nCurrent expression: (14*y**2)*(32 - 22*y**3) - 7*(32 - 22*y**3)\nSimplifying the partial expression: -7*(32 - 22*y**3)\nExpanding the part (32 - 22*y**3) using the distributive property, and we got: -22*y**3*(-7) + 32*(-7)\nReplacing -7*(32 - 22*y**3) with -22*y**3*(-7) + 32*(-7) in the overall expression.\n#Step 3:\nCurrent expression: (14*y**2)*(32 - 22*y**3) - 22*y**3*(-7) - 224\nSimplifying the partial expression: (14*y**2)*(32 - 22*y**3)\nExpanding the part (32 - 22*y**3) using the distributive property, and we got: 32*(14*y**2) + (14*y**2)*(-22*y**3)\nReplacing (14*y**2)*(32 - 22*y**3) with 32*(14*y**2) + (14*y**2)*(-22*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 32*14*y**2 + (14*y**2)*(-22*y**3) - 22*y**3*(-7) - 224\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*y**3)*-7 = 154*y**3\n (-22*y**3)*(14*y**2) = -308*y**5\n 32*14*y**2 = 448*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -308*y**5 + 154*y**3 + 448*y**2 - 224\nNo more calculations needed.\n-308*y**5 + 154*y**3 + 448*y**2 - 224", "generated_answer": "-308*y**5 + 154*y**3 + 448*y**2 - 224", "step_length": 5} {"cot_id": "1b2c06c321ad3a6bc9ead493f45d3d078c99e031f37d58d3dab27bf3bdbe7cca", "datapoint": {"question": "Calculate the following: (69*y**2 + 24*y)*(54*y**3 + 17*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "3726*y**5 + 2469*y**4 + 408*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 238, "polynomial_expr": "(69*y**2 + 24*y)*(54*y**3 + 17*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (69*y**2 + 24*y)*(54*y**3 + 17*y**2)\nExpanding the part (54*y**3 + 17*y**2) using the distributive property, and we got: (17*y**2)*(69*y**2 + 24*y) + (54*y**3)*(69*y**2 + 24*y)\n#Step 2:\nCurrent expression: (17*y**2)*(69*y**2 + 24*y) + (54*y**3)*(69*y**2 + 24*y)\nSimplifying the partial expression: (17*y**2)*(69*y**2 + 24*y)\nExpanding the part (69*y**2 + 24*y) using the distributive property, and we got: (24*y)*(17*y**2) + (17*y**2)*(69*y**2)\nReplacing (17*y**2)*(69*y**2 + 24*y) with (24*y)*(17*y**2) + (17*y**2)*(69*y**2) in the overall expression.\n#Step 3:\nCurrent expression: (24*y)*(17*y**2) + (17*y**2)*(69*y**2) + (54*y**3)*(69*y**2 + 24*y)\nSimplifying the partial expression: (54*y**3)*(69*y**2 + 24*y)\nExpanding the part (69*y**2 + 24*y) using the distributive property, and we got: (24*y)*(54*y**3) + (69*y**2)*(54*y**3)\nReplacing (54*y**3)*(69*y**2 + 24*y) with (24*y)*(54*y**3) + (69*y**2)*(54*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (24*y)*(17*y**2) + (24*y)*(54*y**3) + (17*y**2)*(69*y**2) + (69*y**2)*(54*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (24*y)*(17*y**2) = 408*y**3\n (24*y)*(54*y**3) = 1296*y**4\n (69*y**2)*(17*y**2) = 1173*y**4\n (69*y**2)*(54*y**3) = 3726*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 3726*y**5 + 1173*y**4 + 1296*y**4 + 408*y**3\nCombining like terms, got 3726*y**5 + 2469*y**4 + 408*y**3\n#Step 6:\nCurrent expression: 3726*y**5 + 2469*y**4 + 408*y**3\nNo more calculations needed.\n3726*y**5 + 2469*y**4 + 408*y**3", "generated_answer": "3726*y**5 + 2469*y**4 + 408*y**3", "step_length": 6} {"cot_id": "eb7f4b7a40a0b3ac1cf4ae37d592ee529f4910482f2ad49e90059d6fce227deb", "datapoint": {"question": "Simplify this expression: (27*x + 10)*(-8*x**3 + 3*x**2 + 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-216*x**4 + x**3 + 30*x**2 + 891*x + 330", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 239, "polynomial_expr": "(27*x + 10)*(-8*x**3 + 3*x**2 + 33)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*x + 10)*(-8*x**3 + 3*x**2 + 33)\nExpanding the part (27*x + 10) using the distributive property, and we got: (27*x)*(-8*x**3 + 3*x**2 + 33) + 10*(-8*x**3 + 3*x**2 + 33)\n#Step 2:\nCurrent expression: (27*x)*(-8*x**3 + 3*x**2 + 33) + 10*(-8*x**3 + 3*x**2 + 33)\nSimplifying the partial expression: 10*(-8*x**3 + 3*x**2 + 33)\nExpanding the part (-8*x**3 + 3*x**2 + 33) using the distributive property, and we got: (3*x**2)*10 - 8*x**3*10 + 33*10\nReplacing 10*(-8*x**3 + 3*x**2 + 33) with (3*x**2)*10 - 8*x**3*10 + 33*10 in the overall expression.\n#Step 3:\nCurrent expression: (27*x)*(-8*x**3 + 3*x**2 + 33) + (3*x**2)*10 - 8*x**3*10 + 330\nSimplifying the partial expression: (27*x)*(-8*x**3 + 3*x**2 + 33)\nExpanding the part (-8*x**3 + 3*x**2 + 33) using the distributive property, and we got: 33*(27*x) + (27*x)*(3*x**2) + (27*x)*(-8*x**3)\nReplacing (27*x)*(-8*x**3 + 3*x**2 + 33) with 33*(27*x) + (27*x)*(3*x**2) + (27*x)*(-8*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 33*27*x + (27*x)*(3*x**2) + (27*x)*(-8*x**3) + (3*x**2)*10 - 8*x**3*10 + 330\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-8*x**3)*10 = -80*x**3\n (-8*x**3)*(27*x) = -216*x**4\n (3*x**2)*10 = 30*x**2\n (3*x**2)*(27*x) = 81*x**3\n 33*27*x = 891*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -216*x**4 - 80*x**3 + 81*x**3 + 30*x**2 + 891*x + 330\nCombining like terms, got -216*x**4 + x**3 + 30*x**2 + 891*x + 330\n#Step 6:\nCurrent expression: -216*x**4 + x**3 + 30*x**2 + 891*x + 330\nNo more calculations needed.\n-216*x**4 + x**3 + 30*x**2 + 891*x + 330", "generated_answer": "-216*x**4 + x**3 + 30*x**2 + 891*x + 330", "step_length": 6} {"cot_id": "c92786671715e32d07bbe6816a5c004301dfea0ae03926578fd5b86d9793b762", "datapoint": {"question": "Calculate the following: (-61*z**2 - 50*z - 25)*(-10*z**3 + 73*z**2 + 21*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "610*z**5 - 3953*z**4 - 4681*z**3 - 2875*z**2 - 525*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 240, "polynomial_expr": "(-61*z**2 - 50*z - 25)*(-10*z**3 + 73*z**2 + 21*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-61*z**2 - 50*z - 25)*(-10*z**3 + 73*z**2 + 21*z)\nExpanding the part (-61*z**2 - 50*z - 25) using the distributive property, and we got: (-50*z)*(-10*z**3 + 73*z**2 + 21*z) + (-61*z**2)*(-10*z**3 + 73*z**2 + 21*z) - 25*(-10*z**3 + 73*z**2 + 21*z)\n#Step 2:\nCurrent expression: (-50*z)*(-10*z**3 + 73*z**2 + 21*z) + (-61*z**2)*(-10*z**3 + 73*z**2 + 21*z) - 25*(-10*z**3 + 73*z**2 + 21*z)\nSimplifying the partial expression: -25*(-10*z**3 + 73*z**2 + 21*z)\nExpanding the part (-10*z**3 + 73*z**2 + 21*z) using the distributive property, and we got: (21*z)*(-25) + (73*z**2)*(-25) - 10*z**3*(-25)\nReplacing -25*(-10*z**3 + 73*z**2 + 21*z) with (21*z)*(-25) + (73*z**2)*(-25) - 10*z**3*(-25) in the overall expression.\n#Step 3:\nCurrent expression: (-50*z)*(-10*z**3 + 73*z**2 + 21*z) + (21*z)*(-25) + (-61*z**2)*(-10*z**3 + 73*z**2 + 21*z) + (73*z**2)*(-25) - 10*z**3*(-25)\nSimplifying the partial expression: (-61*z**2)*(-10*z**3 + 73*z**2 + 21*z)\nExpanding the part (-10*z**3 + 73*z**2 + 21*z) using the distributive property, and we got: (21*z)*(-61*z**2) + (-61*z**2)*(73*z**2) + (-61*z**2)*(-10*z**3)\nReplacing (-61*z**2)*(-10*z**3 + 73*z**2 + 21*z) with (21*z)*(-61*z**2) + (-61*z**2)*(73*z**2) + (-61*z**2)*(-10*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-50*z)*(-10*z**3 + 73*z**2 + 21*z) + (21*z)*(-61*z**2) + (21*z)*(-25) + (-61*z**2)*(73*z**2) + (-61*z**2)*(-10*z**3) + (73*z**2)*(-25) - 10*z**3*(-25)\nSimplifying the partial expression: (-50*z)*(-10*z**3 + 73*z**2 + 21*z)\nExpanding the part (-10*z**3 + 73*z**2 + 21*z) using the distributive property, and we got: (-50*z)*(21*z) + (-50*z)*(73*z**2) + (-50*z)*(-10*z**3)\nReplacing (-50*z)*(-10*z**3 + 73*z**2 + 21*z) with (-50*z)*(21*z) + (-50*z)*(73*z**2) + (-50*z)*(-10*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-50*z)*(21*z) + (-50*z)*(73*z**2) + (-50*z)*(-10*z**3) + (21*z)*(-61*z**2) + (21*z)*(-25) + (-61*z**2)*(73*z**2) + (-61*z**2)*(-10*z**3) + (73*z**2)*(-25) - 10*z**3*(-25)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*z**3)*-25 = 250*z**3\n (-10*z**3)*(-61*z**2) = 610*z**5\n (-10*z**3)*(-50*z) = 500*z**4\n (21*z)*-25 = -525*z\n (21*z)*(-61*z**2) = -1281*z**3\n (21*z)*(-50*z) = -1050*z**2\n (73*z**2)*-25 = -1825*z**2\n (73*z**2)*(-61*z**2) = -4453*z**4\n (73*z**2)*(-50*z) = -3650*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 610*z**5 - 4453*z**4 + 500*z**4 - 3650*z**3 - 1281*z**3 + 250*z**3 - 1825*z**2 - 1050*z**2 - 525*z\nCombining like terms, got 610*z**5 - 3953*z**4 - 4681*z**3 - 2875*z**2 - 525*z\n#Step 7:\nCurrent expression: 610*z**5 - 3953*z**4 - 4681*z**3 - 2875*z**2 - 525*z\nNo more calculations needed.\n610*z**5 - 3953*z**4 - 4681*z**3 - 2875*z**2 - 525*z", "generated_answer": "610*z**5 - 3953*z**4 - 4681*z**3 - 2875*z**2 - 525*z", "step_length": 7} {"cot_id": "6f939c469b62f3061367528c2d2ea15d4face7f4db9073257678eff720b9032a", "datapoint": {"question": "Simplify this expression: (-30*z**2 + 34*z)*(27*z**2 + 73)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-810*z**4 + 918*z**3 - 2190*z**2 + 2482*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 241, "polynomial_expr": "(-30*z**2 + 34*z)*(27*z**2 + 73)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-30*z**2 + 34*z)*(27*z**2 + 73)\nExpanding the part (27*z**2 + 73) using the distributive property, and we got: (27*z**2)*(-30*z**2 + 34*z) + 73*(-30*z**2 + 34*z)\n#Step 2:\nCurrent expression: (27*z**2)*(-30*z**2 + 34*z) + 73*(-30*z**2 + 34*z)\nSimplifying the partial expression: 73*(-30*z**2 + 34*z)\nExpanding the part (-30*z**2 + 34*z) using the distributive property, and we got: (34*z)*73 - 30*z**2*73\nReplacing 73*(-30*z**2 + 34*z) with (34*z)*73 - 30*z**2*73 in the overall expression.\n#Step 3:\nCurrent expression: (34*z)*73 - 30*z**2*73 + (27*z**2)*(-30*z**2 + 34*z)\nSimplifying the partial expression: (27*z**2)*(-30*z**2 + 34*z)\nExpanding the part (-30*z**2 + 34*z) using the distributive property, and we got: (34*z)*(27*z**2) + (-30*z**2)*(27*z**2)\nReplacing (27*z**2)*(-30*z**2 + 34*z) with (34*z)*(27*z**2) + (-30*z**2)*(27*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (34*z)*(27*z**2) + (34*z)*73 + (-30*z**2)*(27*z**2) - 30*z**2*73\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*z**2)*73 = -2190*z**2\n (-30*z**2)*(27*z**2) = -810*z**4\n (34*z)*73 = 2482*z\n (34*z)*(27*z**2) = 918*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -810*z**4 + 918*z**3 - 2190*z**2 + 2482*z\nNo more calculations needed.\n-810*z**4 + 918*z**3 - 2190*z**2 + 2482*z", "generated_answer": "-810*z**4 + 918*z**3 - 2190*z**2 + 2482*z", "step_length": 5} {"cot_id": "1f7d4ecb009fd232580983e02f3ef9a636b2e7bbaac9cf02885f2658c997930c", "datapoint": {"question": "Simplify this expression: (21*x**2 - 4)*(-7*x**3 - 12*x - 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-147*x**5 - 224*x**3 - 693*x**2 + 48*x + 132", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 242, "polynomial_expr": "(21*x**2 - 4)*(-7*x**3 - 12*x - 33)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21*x**2 - 4)*(-7*x**3 - 12*x - 33)\nExpanding the part (21*x**2 - 4) using the distributive property, and we got: (21*x**2)*(-7*x**3 - 12*x - 33) - 4*(-7*x**3 - 12*x - 33)\n#Step 2:\nCurrent expression: (21*x**2)*(-7*x**3 - 12*x - 33) - 4*(-7*x**3 - 12*x - 33)\nSimplifying the partial expression: -4*(-7*x**3 - 12*x - 33)\nExpanding the part (-7*x**3 - 12*x - 33) using the distributive property, and we got: -12*x*(-4) - 7*x**3*(-4) - 33*(-4)\nReplacing -4*(-7*x**3 - 12*x - 33) with -12*x*(-4) - 7*x**3*(-4) - 33*(-4) in the overall expression.\n#Step 3:\nCurrent expression: -12*x*(-4) + (21*x**2)*(-7*x**3 - 12*x - 33) - 7*x**3*(-4) + 132\nSimplifying the partial expression: (21*x**2)*(-7*x**3 - 12*x - 33)\nExpanding the part (-7*x**3 - 12*x - 33) using the distributive property, and we got: (-12*x)*(21*x**2) - 693*x**2 + (21*x**2)*(-7*x**3)\nReplacing (21*x**2)*(-7*x**3 - 12*x - 33) with (-12*x)*(21*x**2) - 693*x**2 + (21*x**2)*(-7*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-12*x)*(21*x**2) - 12*x*(-4) - 33*21*x**2 + (21*x**2)*(-7*x**3) - 7*x**3*(-4) + 132\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*x)*-4 = 48*x\n (-12*x)*(21*x**2) = -252*x**3\n (-7*x**3)*-4 = 28*x**3\n (-7*x**3)*(21*x**2) = -147*x**5\n -33*21*x**2 = -693*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -147*x**5 - 252*x**3 + 28*x**3 - 693*x**2 + 48*x + 132\nCombining like terms, got -147*x**5 - 224*x**3 - 693*x**2 + 48*x + 132\n#Step 6:\nCurrent expression: -147*x**5 - 224*x**3 - 693*x**2 + 48*x + 132\nNo more calculations needed.\n-147*x**5 - 224*x**3 - 693*x**2 + 48*x + 132", "generated_answer": "-147*x**5 - 224*x**3 - 693*x**2 + 48*x + 132", "step_length": 6} {"cot_id": "ebee9e57f6095ee5b36d5307b57cac9d64305b981ba5f36d9a21729d1a047ac0", "datapoint": {"question": "Calculate the following: (-14*z**2 - 4*z)*(-z**3 - 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "14*z**5 + 4*z**4 + 574*z**2 + 164*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 243, "polynomial_expr": "(-14*z**2 - 4*z)*(-z**3 - 41)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-14*z**2 - 4*z)*(-z**3 - 41)\nExpanding the part (-z**3 - 41) using the distributive property, and we got: (-z**3)*(-14*z**2 - 4*z) - 41*(-14*z**2 - 4*z)\n#Step 2:\nCurrent expression: (-z**3)*(-14*z**2 - 4*z) - 41*(-14*z**2 - 4*z)\nSimplifying the partial expression: -41*(-14*z**2 - 4*z)\nExpanding the part (-14*z**2 - 4*z) using the distributive property, and we got: -4*z*(-41) - 14*z**2*(-41)\nReplacing -41*(-14*z**2 - 4*z) with -4*z*(-41) - 14*z**2*(-41) in the overall expression.\n#Step 3:\nCurrent expression: -4*z*(-41) - 14*z**2*(-41) + (-z**3)*(-14*z**2 - 4*z)\nSimplifying the partial expression: (-z**3)*(-14*z**2 - 4*z)\nExpanding the part (-14*z**2 - 4*z) using the distributive property, and we got: (-4*z)*(-z**3) + (-14*z**2)*(-z**3)\nReplacing (-z**3)*(-14*z**2 - 4*z) with (-4*z)*(-z**3) + (-14*z**2)*(-z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-4*z)*(-z**3) - 4*z*(-41) + (-14*z**2)*(-z**3) - 14*z**2*(-41)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-14*z**2)*-41 = 574*z**2\n (-14*z**2)*(-z**3) = 14*z**5\n (-4*z)*-41 = 164*z\n (-4*z)*(-z**3) = 4*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 14*z**5 + 4*z**4 + 574*z**2 + 164*z\nNo more calculations needed.\n14*z**5 + 4*z**4 + 574*z**2 + 164*z", "generated_answer": "14*z**5 + 4*z**4 + 574*z**2 + 164*z", "step_length": 5} {"cot_id": "e8237e8eae4d464b2125fca07ae4980ef7fa9943ca6c88227f2752aaa403306a", "datapoint": {"question": "Simplify this expression: (-45*y**3 - 27*y**2 + 10*y)*(-20*y**3 + 16*y**2 - 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "900*y**6 - 180*y**5 - 632*y**4 + 2365*y**3 + 1323*y**2 - 490*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 244, "polynomial_expr": "(-45*y**3 - 27*y**2 + 10*y)*(-20*y**3 + 16*y**2 - 49)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-45*y**3 - 27*y**2 + 10*y)*(-20*y**3 + 16*y**2 - 49)\nExpanding the part (-20*y**3 + 16*y**2 - 49) using the distributive property, and we got: (16*y**2)*(-45*y**3 - 27*y**2 + 10*y) + (-20*y**3)*(-45*y**3 - 27*y**2 + 10*y) - 49*(-45*y**3 - 27*y**2 + 10*y)\n#Step 2:\nCurrent expression: (16*y**2)*(-45*y**3 - 27*y**2 + 10*y) + (-20*y**3)*(-45*y**3 - 27*y**2 + 10*y) - 49*(-45*y**3 - 27*y**2 + 10*y)\nSimplifying the partial expression: -49*(-45*y**3 - 27*y**2 + 10*y)\nExpanding the part (-45*y**3 - 27*y**2 + 10*y) using the distributive property, and we got: (10*y)*(-49) - 27*y**2*(-49) - 45*y**3*(-49)\nReplacing -49*(-45*y**3 - 27*y**2 + 10*y) with (10*y)*(-49) - 27*y**2*(-49) - 45*y**3*(-49) in the overall expression.\n#Step 3:\nCurrent expression: (10*y)*(-49) - 27*y**2*(-49) + (16*y**2)*(-45*y**3 - 27*y**2 + 10*y) - 45*y**3*(-49) + (-20*y**3)*(-45*y**3 - 27*y**2 + 10*y)\nSimplifying the partial expression: (-20*y**3)*(-45*y**3 - 27*y**2 + 10*y)\nExpanding the part (-45*y**3 - 27*y**2 + 10*y) using the distributive property, and we got: (10*y)*(-20*y**3) + (-27*y**2)*(-20*y**3) + (-45*y**3)*(-20*y**3)\nReplacing (-20*y**3)*(-45*y**3 - 27*y**2 + 10*y) with (10*y)*(-20*y**3) + (-27*y**2)*(-20*y**3) + (-45*y**3)*(-20*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (10*y)*(-20*y**3) + (10*y)*(-49) + (-27*y**2)*(-20*y**3) - 27*y**2*(-49) + (16*y**2)*(-45*y**3 - 27*y**2 + 10*y) + (-45*y**3)*(-20*y**3) - 45*y**3*(-49)\nSimplifying the partial expression: (16*y**2)*(-45*y**3 - 27*y**2 + 10*y)\nExpanding the part (-45*y**3 - 27*y**2 + 10*y) using the distributive property, and we got: (10*y)*(16*y**2) + (-27*y**2)*(16*y**2) + (16*y**2)*(-45*y**3)\nReplacing (16*y**2)*(-45*y**3 - 27*y**2 + 10*y) with (10*y)*(16*y**2) + (-27*y**2)*(16*y**2) + (16*y**2)*(-45*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (10*y)*(16*y**2) + (10*y)*(-20*y**3) + (10*y)*(-49) + (-27*y**2)*(16*y**2) + (-27*y**2)*(-20*y**3) - 27*y**2*(-49) + (16*y**2)*(-45*y**3) + (-45*y**3)*(-20*y**3) - 45*y**3*(-49)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*y**3)*-49 = 2205*y**3\n (-45*y**3)*(-20*y**3) = 900*y**6\n (-45*y**3)*(16*y**2) = -720*y**5\n (-27*y**2)*-49 = 1323*y**2\n (-27*y**2)*(-20*y**3) = 540*y**5\n (-27*y**2)*(16*y**2) = -432*y**4\n (10*y)*-49 = -490*y\n (10*y)*(-20*y**3) = -200*y**4\n (10*y)*(16*y**2) = 160*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 900*y**6 - 720*y**5 + 540*y**5 - 432*y**4 - 200*y**4 + 160*y**3 + 2205*y**3 + 1323*y**2 - 490*y\nCombining like terms, got 900*y**6 - 180*y**5 - 632*y**4 + 2365*y**3 + 1323*y**2 - 490*y\n#Step 7:\nCurrent expression: 900*y**6 - 180*y**5 - 632*y**4 + 2365*y**3 + 1323*y**2 - 490*y\nNo more calculations needed.\n900*y**6 - 180*y**5 - 632*y**4 + 2365*y**3 + 1323*y**2 - 490*y", "generated_answer": "900*y**6 - 180*y**5 - 632*y**4 + 2365*y**3 + 1323*y**2 - 490*y", "step_length": 7} {"cot_id": "64581c6b789125c6b7445b73e599a1d9ba12c64b8bd96a1f57d0ecf516b77787", "datapoint": {"question": "Calculate the following: (-47*z**3 + 35*z + 32)*(17*z**3 - 22*z - 27)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-799*z**6 + 1629*z**4 + 1813*z**3 - 770*z**2 - 1649*z - 864", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 245, "polynomial_expr": "(-47*z**3 + 35*z + 32)*(17*z**3 - 22*z - 27)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-47*z**3 + 35*z + 32)*(17*z**3 - 22*z - 27)\nExpanding the part (17*z**3 - 22*z - 27) using the distributive property, and we got: (-22*z)*(-47*z**3 + 35*z + 32) + (17*z**3)*(-47*z**3 + 35*z + 32) - 27*(-47*z**3 + 35*z + 32)\n#Step 2:\nCurrent expression: (-22*z)*(-47*z**3 + 35*z + 32) + (17*z**3)*(-47*z**3 + 35*z + 32) - 27*(-47*z**3 + 35*z + 32)\nSimplifying the partial expression: -27*(-47*z**3 + 35*z + 32)\nExpanding the part (-47*z**3 + 35*z + 32) using the distributive property, and we got: (35*z)*(-27) - 47*z**3*(-27) + 32*(-27)\nReplacing -27*(-47*z**3 + 35*z + 32) with (35*z)*(-27) - 47*z**3*(-27) + 32*(-27) in the overall expression.\n#Step 3:\nCurrent expression: (-22*z)*(-47*z**3 + 35*z + 32) + (35*z)*(-27) - 47*z**3*(-27) + (17*z**3)*(-47*z**3 + 35*z + 32) - 864\nSimplifying the partial expression: (-22*z)*(-47*z**3 + 35*z + 32)\nExpanding the part (-47*z**3 + 35*z + 32) using the distributive property, and we got: (-22*z)*(35*z) + (-22*z)*(-47*z**3) + 32*(-22*z)\nReplacing (-22*z)*(-47*z**3 + 35*z + 32) with (-22*z)*(35*z) + (-22*z)*(-47*z**3) + 32*(-22*z) in the overall expression.\n#Step 4:\nCurrent expression: (-22*z)*(35*z) + (-22*z)*(-47*z**3) + 32*(-22)*z + (35*z)*(-27) - 47*z**3*(-27) + (17*z**3)*(-47*z**3 + 35*z + 32) - 864\nSimplifying the partial expression: (17*z**3)*(-47*z**3 + 35*z + 32)\nExpanding the part (-47*z**3 + 35*z + 32) using the distributive property, and we got: 32*(17*z**3) + (35*z)*(17*z**3) + (-47*z**3)*(17*z**3)\nReplacing (17*z**3)*(-47*z**3 + 35*z + 32) with 32*(17*z**3) + (35*z)*(17*z**3) + (-47*z**3)*(17*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-22*z)*(35*z) + (-22*z)*(-47*z**3) + 32*17*z**3 + 32*(-22)*z + (35*z)*(17*z**3) + (35*z)*(-27) + (-47*z**3)*(17*z**3) - 47*z**3*(-27) - 864\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*z**3)*-27 = 1269*z**3\n (-47*z**3)*(-22*z) = 1034*z**4\n (-47*z**3)*(17*z**3) = -799*z**6\n (35*z)*-27 = -945*z\n (35*z)*(-22*z) = -770*z**2\n (35*z)*(17*z**3) = 595*z**4\n 32*-22*z = -704*z\n 32*17*z**3 = 544*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -799*z**6 + 595*z**4 + 1034*z**4 + 544*z**3 + 1269*z**3 - 770*z**2 - 945*z - 704*z - 864\nCombining like terms, got -799*z**6 + 1629*z**4 + 1813*z**3 - 770*z**2 - 1649*z - 864\n#Step 7:\nCurrent expression: -799*z**6 + 1629*z**4 + 1813*z**3 - 770*z**2 - 1649*z - 864\nNo more calculations needed.\n-799*z**6 + 1629*z**4 + 1813*z**3 - 770*z**2 - 1649*z - 864", "generated_answer": "-799*z**6 + 1629*z**4 + 1813*z**3 - 770*z**2 - 1649*z - 864", "step_length": 7} {"cot_id": "f18fe58ab8a377451be3b3dcd3b1d6a44c338224727b2e8f73f1abc81153c2c9", "datapoint": {"question": "Calculate the following: (38*y**3 + 15*y)*(-28*y**3 - 80*y**2 - 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1064*y**6 - 3040*y**5 - 420*y**4 - 2378*y**3 - 465*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 246, "polynomial_expr": "(38*y**3 + 15*y)*(-28*y**3 - 80*y**2 - 31)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (38*y**3 + 15*y)*(-28*y**3 - 80*y**2 - 31)\nExpanding the part (38*y**3 + 15*y) using the distributive property, and we got: (15*y)*(-28*y**3 - 80*y**2 - 31) + (38*y**3)*(-28*y**3 - 80*y**2 - 31)\n#Step 2:\nCurrent expression: (15*y)*(-28*y**3 - 80*y**2 - 31) + (38*y**3)*(-28*y**3 - 80*y**2 - 31)\nSimplifying the partial expression: (15*y)*(-28*y**3 - 80*y**2 - 31)\nExpanding the part (-28*y**3 - 80*y**2 - 31) using the distributive property, and we got: -465*y + (15*y)*(-80*y**2) + (15*y)*(-28*y**3)\nReplacing (15*y)*(-28*y**3 - 80*y**2 - 31) with -465*y + (15*y)*(-80*y**2) + (15*y)*(-28*y**3) in the overall expression.\n#Step 3:\nCurrent expression: -31*15*y + (15*y)*(-80*y**2) + (15*y)*(-28*y**3) + (38*y**3)*(-28*y**3 - 80*y**2 - 31)\nSimplifying the partial expression: (38*y**3)*(-28*y**3 - 80*y**2 - 31)\nExpanding the part (-28*y**3 - 80*y**2 - 31) using the distributive property, and we got: -1178*y**3 + (-80*y**2)*(38*y**3) + (-28*y**3)*(38*y**3)\nReplacing (38*y**3)*(-28*y**3 - 80*y**2 - 31) with -1178*y**3 + (-80*y**2)*(38*y**3) + (-28*y**3)*(38*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -31*38*y**3 - 31*15*y + (15*y)*(-80*y**2) + (15*y)*(-28*y**3) + (-80*y**2)*(38*y**3) + (-28*y**3)*(38*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-80*y**2)*(15*y) = -1200*y**3\n (-80*y**2)*(38*y**3) = -3040*y**5\n (-28*y**3)*(15*y) = -420*y**4\n (-28*y**3)*(38*y**3) = -1064*y**6\n -31*15*y = -465*y\n -31*38*y**3 = -1178*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1064*y**6 - 3040*y**5 - 420*y**4 - 1200*y**3 - 1178*y**3 - 465*y\nCombining like terms, got -1064*y**6 - 3040*y**5 - 420*y**4 - 2378*y**3 - 465*y\n#Step 6:\nCurrent expression: -1064*y**6 - 3040*y**5 - 420*y**4 - 2378*y**3 - 465*y\nNo more calculations needed.\n-1064*y**6 - 3040*y**5 - 420*y**4 - 2378*y**3 - 465*y", "generated_answer": "-1064*y**6 - 3040*y**5 - 420*y**4 - 2378*y**3 - 465*y", "step_length": 6} {"cot_id": "3938105e640e3710d0543afb972967c00f72408ea109883f9af3da96311a769e", "datapoint": {"question": "Simplify this expression: (16*y**3 + 39*y**2)*(29*y**3 + 25*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "464*y**6 + 1531*y**5 + 975*y**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 247, "polynomial_expr": "(16*y**3 + 39*y**2)*(29*y**3 + 25*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (16*y**3 + 39*y**2)*(29*y**3 + 25*y**2)\nExpanding the part (16*y**3 + 39*y**2) using the distributive property, and we got: (39*y**2)*(29*y**3 + 25*y**2) + (16*y**3)*(29*y**3 + 25*y**2)\n#Step 2:\nCurrent expression: (39*y**2)*(29*y**3 + 25*y**2) + (16*y**3)*(29*y**3 + 25*y**2)\nSimplifying the partial expression: (16*y**3)*(29*y**3 + 25*y**2)\nExpanding the part (29*y**3 + 25*y**2) using the distributive property, and we got: (25*y**2)*(16*y**3) + (16*y**3)*(29*y**3)\nReplacing (16*y**3)*(29*y**3 + 25*y**2) with (25*y**2)*(16*y**3) + (16*y**3)*(29*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (25*y**2)*(16*y**3) + (39*y**2)*(29*y**3 + 25*y**2) + (16*y**3)*(29*y**3)\nSimplifying the partial expression: (39*y**2)*(29*y**3 + 25*y**2)\nExpanding the part (29*y**3 + 25*y**2) using the distributive property, and we got: (25*y**2)*(39*y**2) + (39*y**2)*(29*y**3)\nReplacing (39*y**2)*(29*y**3 + 25*y**2) with (25*y**2)*(39*y**2) + (39*y**2)*(29*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (25*y**2)*(39*y**2) + (25*y**2)*(16*y**3) + (39*y**2)*(29*y**3) + (16*y**3)*(29*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (25*y**2)*(16*y**3) = 400*y**5\n (25*y**2)*(39*y**2) = 975*y**4\n (29*y**3)*(16*y**3) = 464*y**6\n (29*y**3)*(39*y**2) = 1131*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 464*y**6 + 400*y**5 + 1131*y**5 + 975*y**4\nCombining like terms, got 464*y**6 + 1531*y**5 + 975*y**4\n#Step 6:\nCurrent expression: 464*y**6 + 1531*y**5 + 975*y**4\nNo more calculations needed.\n464*y**6 + 1531*y**5 + 975*y**4", "generated_answer": "464*y**6 + 1531*y**5 + 975*y**4", "step_length": 6} {"cot_id": "46699107d01f04a4522ca8e9b63be68cf9e853811f8a3a33f3d77f2b40bbfedb", "datapoint": {"question": "Calculate the following: -1520*z**3 - 440*z**2\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1520*z**3 - 440*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 248, "polynomial_expr": "-1520*z**3 - 440*z**2", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -1520*z**3 - 440*z**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -1520*z**3 - 440*z**2\nNo more calculations needed.\n-1520*z**3 - 440*z**2", "generated_answer": "-1520*z**3 - 440*z**2", "step_length": 2} {"cot_id": "e5bbbc116fc004c4d8e44423bffebb5b9dc9daf951525dd08d4de8e96399f124", "datapoint": {"question": "Calculate the following: (-91*z - 41)*(-41*z**3 - 43*z**2 + 51*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "3731*z**4 + 5594*z**3 - 2878*z**2 - 2091*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 249, "polynomial_expr": "(-91*z - 41)*(-41*z**3 - 43*z**2 + 51*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-91*z - 41)*(-41*z**3 - 43*z**2 + 51*z)\nExpanding the part (-91*z - 41) using the distributive property, and we got: (-91*z)*(-41*z**3 - 43*z**2 + 51*z) - 41*(-41*z**3 - 43*z**2 + 51*z)\n#Step 2:\nCurrent expression: (-91*z)*(-41*z**3 - 43*z**2 + 51*z) - 41*(-41*z**3 - 43*z**2 + 51*z)\nSimplifying the partial expression: -41*(-41*z**3 - 43*z**2 + 51*z)\nExpanding the part (-41*z**3 - 43*z**2 + 51*z) using the distributive property, and we got: (51*z)*(-41) - 43*z**2*(-41) - 41*z**3*(-41)\nReplacing -41*(-41*z**3 - 43*z**2 + 51*z) with (51*z)*(-41) - 43*z**2*(-41) - 41*z**3*(-41) in the overall expression.\n#Step 3:\nCurrent expression: (-91*z)*(-41*z**3 - 43*z**2 + 51*z) + (51*z)*(-41) - 43*z**2*(-41) - 41*z**3*(-41)\nSimplifying the partial expression: (-91*z)*(-41*z**3 - 43*z**2 + 51*z)\nExpanding the part (-41*z**3 - 43*z**2 + 51*z) using the distributive property, and we got: (-91*z)*(51*z) + (-91*z)*(-43*z**2) + (-91*z)*(-41*z**3)\nReplacing (-91*z)*(-41*z**3 - 43*z**2 + 51*z) with (-91*z)*(51*z) + (-91*z)*(-43*z**2) + (-91*z)*(-41*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-91*z)*(51*z) + (-91*z)*(-43*z**2) + (-91*z)*(-41*z**3) + (51*z)*(-41) - 43*z**2*(-41) - 41*z**3*(-41)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-43*z**2)*-41 = 1763*z**2\n (-43*z**2)*(-91*z) = 3913*z**3\n (-41*z**3)*-41 = 1681*z**3\n (-41*z**3)*(-91*z) = 3731*z**4\n (51*z)*-41 = -2091*z\n (51*z)*(-91*z) = -4641*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 3731*z**4 + 1681*z**3 + 3913*z**3 - 4641*z**2 + 1763*z**2 - 2091*z\nCombining like terms, got 3731*z**4 + 5594*z**3 - 2878*z**2 - 2091*z\n#Step 6:\nCurrent expression: 3731*z**4 + 5594*z**3 - 2878*z**2 - 2091*z\nNo more calculations needed.\n3731*z**4 + 5594*z**3 - 2878*z**2 - 2091*z", "generated_answer": "3731*z**4 + 5594*z**3 - 2878*z**2 - 2091*z", "step_length": 6} {"cot_id": "4f2c67e1a1cddd26b2047b23d8428a69547a3dccf011639c8216fe04b2320805", "datapoint": {"question": "Calculate the following: -79*x**2*(41*x**3 - 2*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-3239*x**5 + 158*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 250, "polynomial_expr": "-79*x**2*(41*x**3 - 2*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -79*x**2*(41*x**3 - 2*x)\nExpanding the part (41*x**3 - 2*x) using the distributive property, and we got: (-2*x)*(-79*x**2) + (-79*x**2)*(41*x**3)\n#Step 2:\nCurrent expression: (-2*x)*(-79*x**2) + (-79*x**2)*(41*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-2*x)*(-79*x**2) = 158*x**3\n (41*x**3)*(-79*x**2) = -3239*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -3239*x**5 + 158*x**3\nNo more calculations needed.\n-3239*x**5 + 158*x**3", "generated_answer": "-3239*x**5 + 158*x**3", "step_length": 3} {"cot_id": "5e37b33c4f01ff6bfcafbac8bb825a8756567ef86c48fe6cd7541b1a60d67ab1", "datapoint": {"question": "Calculate the following: -14*y**3*(-15*y**2 - 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "210*y**5 + 294*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 251, "polynomial_expr": "-14*y**3*(-15*y**2 - 21)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -14*y**3*(-15*y**2 - 21)\nExpanding the part (-15*y**2 - 21) using the distributive property, and we got: -(-1)*294*y**3 + (-15*y**2)*(-14*y**3)\n#Step 2:\nCurrent expression: -(-1)*294*y**3 + (-15*y**2)*(-14*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -21*(-14*y**3) = 294*y**3\n (-15*y**2)*(-14*y**3) = 210*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 210*y**5 + 294*y**3\nNo more calculations needed.\n210*y**5 + 294*y**3", "generated_answer": "210*y**5 + 294*y**3", "step_length": 3} {"cot_id": "21e5ce4f1c5fce3548b9e61f7efe8287932f64d1c2fc1e041b3d3d62068d182b", "datapoint": {"question": "Simplify this expression: (-81*x**3 - 13*x)*(-24*x**3 - 38*x**2 - 11)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1944*x**6 + 3078*x**5 + 312*x**4 + 1385*x**3 + 143*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 252, "polynomial_expr": "(-81*x**3 - 13*x)*(-24*x**3 - 38*x**2 - 11)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-81*x**3 - 13*x)*(-24*x**3 - 38*x**2 - 11)\nExpanding the part (-81*x**3 - 13*x) using the distributive property, and we got: (-13*x)*(-24*x**3 - 38*x**2 - 11) + (-81*x**3)*(-24*x**3 - 38*x**2 - 11)\n#Step 2:\nCurrent expression: (-13*x)*(-24*x**3 - 38*x**2 - 11) + (-81*x**3)*(-24*x**3 - 38*x**2 - 11)\nSimplifying the partial expression: (-81*x**3)*(-24*x**3 - 38*x**2 - 11)\nExpanding the part (-24*x**3 - 38*x**2 - 11) using the distributive property, and we got: -(-1)*891*x**3 + (-38*x**2)*(-81*x**3) + (-81*x**3)*(-24*x**3)\nReplacing (-81*x**3)*(-24*x**3 - 38*x**2 - 11) with -(-1)*891*x**3 + (-38*x**2)*(-81*x**3) + (-81*x**3)*(-24*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-13*x)*(-24*x**3 - 38*x**2 - 11) - 11*(-81)*x**3 + (-38*x**2)*(-81*x**3) + (-81*x**3)*(-24*x**3)\nSimplifying the partial expression: (-13*x)*(-24*x**3 - 38*x**2 - 11)\nExpanding the part (-24*x**3 - 38*x**2 - 11) using the distributive property, and we got: (-13*x)*(-38*x**2) + (-13*x)*(-24*x**3) - (-1)*143*x\nReplacing (-13*x)*(-24*x**3 - 38*x**2 - 11) with (-13*x)*(-38*x**2) + (-13*x)*(-24*x**3) - (-1)*143*x in the overall expression.\n#Step 4:\nCurrent expression: (-13*x)*(-38*x**2) + (-13*x)*(-24*x**3) - 11*(-81)*x**3 - 11*(-13)*x + (-38*x**2)*(-81*x**3) + (-81*x**3)*(-24*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*x**2)*(-81*x**3) = 3078*x**5\n (-38*x**2)*(-13*x) = 494*x**3\n (-24*x**3)*(-81*x**3) = 1944*x**6\n (-24*x**3)*(-13*x) = 312*x**4\n -11*-81*x**3 = 891*x**3\n -11*-13*x = 143*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1944*x**6 + 3078*x**5 + 312*x**4 + 494*x**3 + 891*x**3 + 143*x\nCombining like terms, got 1944*x**6 + 3078*x**5 + 312*x**4 + 1385*x**3 + 143*x\n#Step 6:\nCurrent expression: 1944*x**6 + 3078*x**5 + 312*x**4 + 1385*x**3 + 143*x\nNo more calculations needed.\n1944*x**6 + 3078*x**5 + 312*x**4 + 1385*x**3 + 143*x", "generated_answer": "1944*x**6 + 3078*x**5 + 312*x**4 + 1385*x**3 + 143*x", "step_length": 6} {"cot_id": "449d0412e944e4592b4e8ccd6bb8a600097d5bd4d87f8da806707714972de0ae", "datapoint": {"question": "Calculate the following: (21 - 38*y**2)*(-12*y**2 - 20*y - 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "456*y**4 + 760*y**3 + 1230*y**2 - 420*y - 819", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 253, "polynomial_expr": "(21 - 38*y**2)*(-12*y**2 - 20*y - 39)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21 - 38*y**2)*(-12*y**2 - 20*y - 39)\nExpanding the part (21 - 38*y**2) using the distributive property, and we got: (-38*y**2)*(-12*y**2 - 20*y - 39) + 21*(-12*y**2 - 20*y - 39)\n#Step 2:\nCurrent expression: (-38*y**2)*(-12*y**2 - 20*y - 39) + 21*(-12*y**2 - 20*y - 39)\nSimplifying the partial expression: 21*(-12*y**2 - 20*y - 39)\nExpanding the part (-12*y**2 - 20*y - 39) using the distributive property, and we got: -20*y*21 - 12*y**2*21 - 39*21\nReplacing 21*(-12*y**2 - 20*y - 39) with -20*y*21 - 12*y**2*21 - 39*21 in the overall expression.\n#Step 3:\nCurrent expression: -20*y*21 + (-38*y**2)*(-12*y**2 - 20*y - 39) - 12*y**2*21 - 819\nSimplifying the partial expression: (-38*y**2)*(-12*y**2 - 20*y - 39)\nExpanding the part (-12*y**2 - 20*y - 39) using the distributive property, and we got: (-20*y)*(-38*y**2) - (-1)*1482*y**2 + (-38*y**2)*(-12*y**2)\nReplacing (-38*y**2)*(-12*y**2 - 20*y - 39) with (-20*y)*(-38*y**2) - (-1)*1482*y**2 + (-38*y**2)*(-12*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-20*y)*(-38*y**2) - 20*y*21 - 39*(-38)*y**2 + (-38*y**2)*(-12*y**2) - 12*y**2*21 - 819\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*y)*21 = -420*y\n (-20*y)*(-38*y**2) = 760*y**3\n (-12*y**2)*21 = -252*y**2\n (-12*y**2)*(-38*y**2) = 456*y**4\n -39*-38*y**2 = 1482*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 456*y**4 + 760*y**3 - 252*y**2 + 1482*y**2 - 420*y - 819\nCombining like terms, got 456*y**4 + 760*y**3 + 1230*y**2 - 420*y - 819\n#Step 6:\nCurrent expression: 456*y**4 + 760*y**3 + 1230*y**2 - 420*y - 819\nNo more calculations needed.\n456*y**4 + 760*y**3 + 1230*y**2 - 420*y - 819", "generated_answer": "456*y**4 + 760*y**3 + 1230*y**2 - 420*y - 819", "step_length": 6} {"cot_id": "69986f1cdbe6a426acc8b16c2f7e382e3f845719a6839c30aa469b23424659a6", "datapoint": {"question": "Calculate the following: (x**3 + 48)*(37*x**3 + 25*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "37*x**6 + 25*x**4 + 1776*x**3 + 1200*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 254, "polynomial_expr": "(x**3 + 48)*(37*x**3 + 25*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (x**3 + 48)*(37*x**3 + 25*x)\nExpanding the part (x**3 + 48) using the distributive property, and we got: x**3*(37*x**3 + 25*x) + 48*(37*x**3 + 25*x)\n#Step 2:\nCurrent expression: x**3*(37*x**3 + 25*x) + 48*(37*x**3 + 25*x)\nSimplifying the partial expression: 48*(37*x**3 + 25*x)\nExpanding the part (37*x**3 + 25*x) using the distributive property, and we got: (25*x)*48 + (37*x**3)*48\nReplacing 48*(37*x**3 + 25*x) with (25*x)*48 + (37*x**3)*48 in the overall expression.\n#Step 3:\nCurrent expression: x**3*(37*x**3 + 25*x) + (25*x)*48 + (37*x**3)*48\nSimplifying the partial expression: x**3*(37*x**3 + 25*x)\nExpanding the part (37*x**3 + 25*x) using the distributive property, and we got: (25*x)*x**3 + x**3*(37*x**3)\nReplacing x**3*(37*x**3 + 25*x) with (25*x)*x**3 + x**3*(37*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (25*x)*x**3 + x**3*(37*x**3) + (25*x)*48 + (37*x**3)*48\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (25*x)*48 = 1200*x\n (25*x)*x**3 = 25*x**4\n (37*x**3)*48 = 1776*x**3\n (37*x**3)*x**3 = 37*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 37*x**6 + 25*x**4 + 1776*x**3 + 1200*x\nNo more calculations needed.\n37*x**6 + 25*x**4 + 1776*x**3 + 1200*x", "generated_answer": "37*x**6 + 25*x**4 + 1776*x**3 + 1200*x", "step_length": 5} {"cot_id": "32f9bc2c557abe42917593e29b8b255380fcb8221f9ca5593d65995331a04aa9", "datapoint": {"question": "Simplify this expression: (36*z**2 - 62*z)*(18*z**3 - 41*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "648*z**5 - 2592*z**4 + 2542*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 255, "polynomial_expr": "(36*z**2 - 62*z)*(18*z**3 - 41*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (36*z**2 - 62*z)*(18*z**3 - 41*z**2)\nExpanding the part (36*z**2 - 62*z) using the distributive property, and we got: (-62*z)*(18*z**3 - 41*z**2) + (36*z**2)*(18*z**3 - 41*z**2)\n#Step 2:\nCurrent expression: (-62*z)*(18*z**3 - 41*z**2) + (36*z**2)*(18*z**3 - 41*z**2)\nSimplifying the partial expression: (-62*z)*(18*z**3 - 41*z**2)\nExpanding the part (18*z**3 - 41*z**2) using the distributive property, and we got: (-62*z)*(-41*z**2) + (-62*z)*(18*z**3)\nReplacing (-62*z)*(18*z**3 - 41*z**2) with (-62*z)*(-41*z**2) + (-62*z)*(18*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-62*z)*(-41*z**2) + (-62*z)*(18*z**3) + (36*z**2)*(18*z**3 - 41*z**2)\nSimplifying the partial expression: (36*z**2)*(18*z**3 - 41*z**2)\nExpanding the part (18*z**3 - 41*z**2) using the distributive property, and we got: (-41*z**2)*(36*z**2) + (36*z**2)*(18*z**3)\nReplacing (36*z**2)*(18*z**3 - 41*z**2) with (-41*z**2)*(36*z**2) + (36*z**2)*(18*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-62*z)*(-41*z**2) + (-62*z)*(18*z**3) + (-41*z**2)*(36*z**2) + (36*z**2)*(18*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*z**2)*(-62*z) = 2542*z**3\n (-41*z**2)*(36*z**2) = -1476*z**4\n (18*z**3)*(-62*z) = -1116*z**4\n (18*z**3)*(36*z**2) = 648*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 648*z**5 - 1476*z**4 - 1116*z**4 + 2542*z**3\nCombining like terms, got 648*z**5 - 2592*z**4 + 2542*z**3\n#Step 6:\nCurrent expression: 648*z**5 - 2592*z**4 + 2542*z**3\nNo more calculations needed.\n648*z**5 - 2592*z**4 + 2542*z**3", "generated_answer": "648*z**5 - 2592*z**4 + 2542*z**3", "step_length": 6} {"cot_id": "2b0368c26094b886ed329983b9e03bf69e9b057d9fe10a4f628e99ed8f2ac3da", "datapoint": {"question": "Simplify this expression: (-36*x**3 - 43*x**2 - 42*x)*(-9*x**3 + 12*x**2 - 30*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "324*x**6 - 45*x**5 + 942*x**4 + 786*x**3 + 1260*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 256, "polynomial_expr": "(-36*x**3 - 43*x**2 - 42*x)*(-9*x**3 + 12*x**2 - 30*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-36*x**3 - 43*x**2 - 42*x)*(-9*x**3 + 12*x**2 - 30*x)\nExpanding the part (-36*x**3 - 43*x**2 - 42*x) using the distributive property, and we got: (-42*x)*(-9*x**3 + 12*x**2 - 30*x) + (-43*x**2)*(-9*x**3 + 12*x**2 - 30*x) + (-36*x**3)*(-9*x**3 + 12*x**2 - 30*x)\n#Step 2:\nCurrent expression: (-42*x)*(-9*x**3 + 12*x**2 - 30*x) + (-43*x**2)*(-9*x**3 + 12*x**2 - 30*x) + (-36*x**3)*(-9*x**3 + 12*x**2 - 30*x)\nSimplifying the partial expression: (-43*x**2)*(-9*x**3 + 12*x**2 - 30*x)\nExpanding the part (-9*x**3 + 12*x**2 - 30*x) using the distributive property, and we got: (-30*x)*(-43*x**2) + (-43*x**2)*(12*x**2) + (-43*x**2)*(-9*x**3)\nReplacing (-43*x**2)*(-9*x**3 + 12*x**2 - 30*x) with (-30*x)*(-43*x**2) + (-43*x**2)*(12*x**2) + (-43*x**2)*(-9*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-42*x)*(-9*x**3 + 12*x**2 - 30*x) + (-30*x)*(-43*x**2) + (-43*x**2)*(12*x**2) + (-43*x**2)*(-9*x**3) + (-36*x**3)*(-9*x**3 + 12*x**2 - 30*x)\nSimplifying the partial expression: (-42*x)*(-9*x**3 + 12*x**2 - 30*x)\nExpanding the part (-9*x**3 + 12*x**2 - 30*x) using the distributive property, and we got: (-42*x)*(-30*x) + (-42*x)*(12*x**2) + (-42*x)*(-9*x**3)\nReplacing (-42*x)*(-9*x**3 + 12*x**2 - 30*x) with (-42*x)*(-30*x) + (-42*x)*(12*x**2) + (-42*x)*(-9*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-42*x)*(-30*x) + (-42*x)*(12*x**2) + (-42*x)*(-9*x**3) + (-30*x)*(-43*x**2) + (-43*x**2)*(12*x**2) + (-43*x**2)*(-9*x**3) + (-36*x**3)*(-9*x**3 + 12*x**2 - 30*x)\nSimplifying the partial expression: (-36*x**3)*(-9*x**3 + 12*x**2 - 30*x)\nExpanding the part (-9*x**3 + 12*x**2 - 30*x) using the distributive property, and we got: (-30*x)*(-36*x**3) + (12*x**2)*(-36*x**3) + (-36*x**3)*(-9*x**3)\nReplacing (-36*x**3)*(-9*x**3 + 12*x**2 - 30*x) with (-30*x)*(-36*x**3) + (12*x**2)*(-36*x**3) + (-36*x**3)*(-9*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-42*x)*(-30*x) + (-42*x)*(12*x**2) + (-42*x)*(-9*x**3) + (-30*x)*(-43*x**2) + (-30*x)*(-36*x**3) + (-43*x**2)*(12*x**2) + (-43*x**2)*(-9*x**3) + (12*x**2)*(-36*x**3) + (-36*x**3)*(-9*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*x)*(-43*x**2) = 1290*x**3\n (-30*x)*(-42*x) = 1260*x**2\n (-30*x)*(-36*x**3) = 1080*x**4\n (-9*x**3)*(-43*x**2) = 387*x**5\n (-9*x**3)*(-42*x) = 378*x**4\n (-9*x**3)*(-36*x**3) = 324*x**6\n (12*x**2)*(-43*x**2) = -516*x**4\n (12*x**2)*(-42*x) = -504*x**3\n (12*x**2)*(-36*x**3) = -432*x**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 324*x**6 - 432*x**5 + 387*x**5 - 516*x**4 + 378*x**4 + 1080*x**4 - 504*x**3 + 1290*x**3 + 1260*x**2\nCombining like terms, got 324*x**6 - 45*x**5 + 942*x**4 + 786*x**3 + 1260*x**2\n#Step 7:\nCurrent expression: 324*x**6 - 45*x**5 + 942*x**4 + 786*x**3 + 1260*x**2\nNo more calculations needed.\n324*x**6 - 45*x**5 + 942*x**4 + 786*x**3 + 1260*x**2", "generated_answer": "324*x**6 - 45*x**5 + 942*x**4 + 786*x**3 + 1260*x**2", "step_length": 7} {"cot_id": "0aa3f075a535ab9a36b1a51af4dcafe1e0776e1354aa60a5e65bae9b1a7c4bf6", "datapoint": {"question": "Calculate the following: (39*y**3 + 30*y)*(26*y**2 + 31*y + 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1014*y**5 + 1209*y**4 + 2613*y**3 + 930*y**2 + 1410*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 257, "polynomial_expr": "(39*y**3 + 30*y)*(26*y**2 + 31*y + 47)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (39*y**3 + 30*y)*(26*y**2 + 31*y + 47)\nExpanding the part (39*y**3 + 30*y) using the distributive property, and we got: (30*y)*(26*y**2 + 31*y + 47) + (39*y**3)*(26*y**2 + 31*y + 47)\n#Step 2:\nCurrent expression: (30*y)*(26*y**2 + 31*y + 47) + (39*y**3)*(26*y**2 + 31*y + 47)\nSimplifying the partial expression: (30*y)*(26*y**2 + 31*y + 47)\nExpanding the part (26*y**2 + 31*y + 47) using the distributive property, and we got: 47*(30*y) + (30*y)*(31*y) + (30*y)*(26*y**2)\nReplacing (30*y)*(26*y**2 + 31*y + 47) with 47*(30*y) + (30*y)*(31*y) + (30*y)*(26*y**2) in the overall expression.\n#Step 3:\nCurrent expression: 47*30*y + (30*y)*(31*y) + (30*y)*(26*y**2) + (39*y**3)*(26*y**2 + 31*y + 47)\nSimplifying the partial expression: (39*y**3)*(26*y**2 + 31*y + 47)\nExpanding the part (26*y**2 + 31*y + 47) using the distributive property, and we got: 47*(39*y**3) + (31*y)*(39*y**3) + (26*y**2)*(39*y**3)\nReplacing (39*y**3)*(26*y**2 + 31*y + 47) with 47*(39*y**3) + (31*y)*(39*y**3) + (26*y**2)*(39*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 47*39*y**3 + 47*30*y + (30*y)*(31*y) + (30*y)*(26*y**2) + (31*y)*(39*y**3) + (26*y**2)*(39*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (26*y**2)*(30*y) = 780*y**3\n (26*y**2)*(39*y**3) = 1014*y**5\n (31*y)*(30*y) = 930*y**2\n (31*y)*(39*y**3) = 1209*y**4\n 47*30*y = 1410*y\n 47*39*y**3 = 1833*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1014*y**5 + 1209*y**4 + 780*y**3 + 1833*y**3 + 930*y**2 + 1410*y\nCombining like terms, got 1014*y**5 + 1209*y**4 + 2613*y**3 + 930*y**2 + 1410*y\n#Step 6:\nCurrent expression: 1014*y**5 + 1209*y**4 + 2613*y**3 + 930*y**2 + 1410*y\nNo more calculations needed.\n1014*y**5 + 1209*y**4 + 2613*y**3 + 930*y**2 + 1410*y", "generated_answer": "1014*y**5 + 1209*y**4 + 2613*y**3 + 930*y**2 + 1410*y", "step_length": 6} {"cot_id": "891fafedad8bbb3dfbc6fc97180c518c5cfc99ee666e04d1a33aba70f2f67564", "datapoint": {"question": "Calculate the following: (39*z**3 + 41)*(-z**2 - 28*z - 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-39*z**5 - 1092*z**4 - 1092*z**3 - 41*z**2 - 1148*z - 1148", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 258, "polynomial_expr": "(39*z**3 + 41)*(-z**2 - 28*z - 28)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (39*z**3 + 41)*(-z**2 - 28*z - 28)\nExpanding the part (39*z**3 + 41) using the distributive property, and we got: (39*z**3)*(-z**2 - 28*z - 28) + 41*(-z**2 - 28*z - 28)\n#Step 2:\nCurrent expression: (39*z**3)*(-z**2 - 28*z - 28) + 41*(-z**2 - 28*z - 28)\nSimplifying the partial expression: 41*(-z**2 - 28*z - 28)\nExpanding the part (-z**2 - 28*z - 28) using the distributive property, and we got: -28*z*41 - z**2*41 - 28*41\nReplacing 41*(-z**2 - 28*z - 28) with -28*z*41 - z**2*41 - 28*41 in the overall expression.\n#Step 3:\nCurrent expression: -28*z*41 - z**2*41 + (39*z**3)*(-z**2 - 28*z - 28) - 1148\nSimplifying the partial expression: (39*z**3)*(-z**2 - 28*z - 28)\nExpanding the part (-z**2 - 28*z - 28) using the distributive property, and we got: (-28*z)*(39*z**3) - 1092*z**3 + (-z**2)*(39*z**3)\nReplacing (39*z**3)*(-z**2 - 28*z - 28) with (-28*z)*(39*z**3) - 1092*z**3 + (-z**2)*(39*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-28*z)*(39*z**3) - 28*z*41 - 28*39*z**3 + (-z**2)*(39*z**3) - z**2*41 - 1148\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-z**2)*41 = -41*z**2\n (-z**2)*(39*z**3) = -39*z**5\n (-28*z)*41 = -1148*z\n (-28*z)*(39*z**3) = -1092*z**4\n -28*39*z**3 = -1092*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -39*z**5 - 1092*z**4 - 1092*z**3 - 41*z**2 - 1148*z - 1148\nNo more calculations needed.\n-39*z**5 - 1092*z**4 - 1092*z**3 - 41*z**2 - 1148*z - 1148", "generated_answer": "-39*z**5 - 1092*z**4 - 1092*z**3 - 41*z**2 - 1148*z - 1148", "step_length": 5} {"cot_id": "40b11d4fde55fa550239ab4c91972c1f2c900048f6e91f0bbcd9cfc197d01a94", "datapoint": {"question": "Simplify this expression: (14 - 69*y)*(2*y**3 + 15*y**2 + 36*y - 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-138*y**4 - 1007*y**3 - 2274*y**2 + 3816*y - 672", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 259, "polynomial_expr": "(14 - 69*y)*(2*y**3 + 15*y**2 + 36*y - 48)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14 - 69*y)*(2*y**3 + 15*y**2 + 36*y - 48)\nExpanding the part (14 - 69*y) using the distributive property, and we got: (-69*y)*(2*y**3 + 15*y**2 + 36*y - 48) + 14*(2*y**3 + 15*y**2 + 36*y - 48)\n#Step 2:\nCurrent expression: (-69*y)*(2*y**3 + 15*y**2 + 36*y - 48) + 14*(2*y**3 + 15*y**2 + 36*y - 48)\nSimplifying the partial expression: 14*(2*y**3 + 15*y**2 + 36*y - 48)\nExpanding the part (2*y**3 + 15*y**2 + 36*y - 48) using the distributive property, and we got: (36*y)*14 + (15*y**2)*14 + (2*y**3)*14 - 48*14\nReplacing 14*(2*y**3 + 15*y**2 + 36*y - 48) with (36*y)*14 + (15*y**2)*14 + (2*y**3)*14 - 48*14 in the overall expression.\n#Step 3:\nCurrent expression: (-69*y)*(2*y**3 + 15*y**2 + 36*y - 48) + (36*y)*14 + (15*y**2)*14 + (2*y**3)*14 - 672\nSimplifying the partial expression: (-69*y)*(2*y**3 + 15*y**2 + 36*y - 48)\nExpanding the part (2*y**3 + 15*y**2 + 36*y - 48) using the distributive property, and we got: (-69*y)*(36*y) + (-69*y)*(15*y**2) + (-69*y)*(2*y**3) - (-1)*3312*y\nReplacing (-69*y)*(2*y**3 + 15*y**2 + 36*y - 48) with (-69*y)*(36*y) + (-69*y)*(15*y**2) + (-69*y)*(2*y**3) - (-1)*3312*y in the overall expression.\n#Step 4:\nCurrent expression: (-69*y)*(36*y) + (-69*y)*(15*y**2) + (-69*y)*(2*y**3) - 48*(-69)*y + (36*y)*14 + (15*y**2)*14 + (2*y**3)*14 - 672\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (2*y**3)*14 = 28*y**3\n (2*y**3)*(-69*y) = -138*y**4\n (15*y**2)*14 = 210*y**2\n (15*y**2)*(-69*y) = -1035*y**3\n (36*y)*14 = 504*y\n (36*y)*(-69*y) = -2484*y**2\n -48*-69*y = 3312*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -138*y**4 - 1035*y**3 + 28*y**3 - 2484*y**2 + 210*y**2 + 504*y + 3312*y - 672\nCombining like terms, got -138*y**4 - 1007*y**3 - 2274*y**2 + 3816*y - 672\n#Step 6:\nCurrent expression: -138*y**4 - 1007*y**3 - 2274*y**2 + 3816*y - 672\nNo more calculations needed.\n-138*y**4 - 1007*y**3 - 2274*y**2 + 3816*y - 672", "generated_answer": "-138*y**4 - 1007*y**3 - 2274*y**2 + 3816*y - 672", "step_length": 6} {"cot_id": "74c9afdf1b85ab9a5d4c3f54c085ee9e48e7cd825993f0f0f212a4b1da124e8f", "datapoint": {"question": "Calculate the following: (29*z**3 - 13*z**2)*(69*z**3 + 49*z**2 + 2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2001*z**6 + 524*z**5 - 637*z**4 + 58*z**3 - 26*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 260, "polynomial_expr": "(29*z**3 - 13*z**2)*(69*z**3 + 49*z**2 + 2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29*z**3 - 13*z**2)*(69*z**3 + 49*z**2 + 2)\nExpanding the part (29*z**3 - 13*z**2) using the distributive property, and we got: (-13*z**2)*(69*z**3 + 49*z**2 + 2) + (29*z**3)*(69*z**3 + 49*z**2 + 2)\n#Step 2:\nCurrent expression: (-13*z**2)*(69*z**3 + 49*z**2 + 2) + (29*z**3)*(69*z**3 + 49*z**2 + 2)\nSimplifying the partial expression: (-13*z**2)*(69*z**3 + 49*z**2 + 2)\nExpanding the part (69*z**3 + 49*z**2 + 2) using the distributive property, and we got: 2*(-13*z**2) + (-13*z**2)*(49*z**2) + (-13*z**2)*(69*z**3)\nReplacing (-13*z**2)*(69*z**3 + 49*z**2 + 2) with 2*(-13*z**2) + (-13*z**2)*(49*z**2) + (-13*z**2)*(69*z**3) in the overall expression.\n#Step 3:\nCurrent expression: 2*(-13)*z**2 + (-13*z**2)*(49*z**2) + (-13*z**2)*(69*z**3) + (29*z**3)*(69*z**3 + 49*z**2 + 2)\nSimplifying the partial expression: (29*z**3)*(69*z**3 + 49*z**2 + 2)\nExpanding the part (69*z**3 + 49*z**2 + 2) using the distributive property, and we got: 2*(29*z**3) + (49*z**2)*(29*z**3) + (29*z**3)*(69*z**3)\nReplacing (29*z**3)*(69*z**3 + 49*z**2 + 2) with 2*(29*z**3) + (49*z**2)*(29*z**3) + (29*z**3)*(69*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 2*29*z**3 + 2*(-13)*z**2 + (-13*z**2)*(49*z**2) + (-13*z**2)*(69*z**3) + (49*z**2)*(29*z**3) + (29*z**3)*(69*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (49*z**2)*(-13*z**2) = -637*z**4\n (49*z**2)*(29*z**3) = 1421*z**5\n (69*z**3)*(-13*z**2) = -897*z**5\n (69*z**3)*(29*z**3) = 2001*z**6\n 2*-13*z**2 = -26*z**2\n 2*29*z**3 = 58*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2001*z**6 - 897*z**5 + 1421*z**5 - 637*z**4 + 58*z**3 - 26*z**2\nCombining like terms, got 2001*z**6 + 524*z**5 - 637*z**4 + 58*z**3 - 26*z**2\n#Step 6:\nCurrent expression: 2001*z**6 + 524*z**5 - 637*z**4 + 58*z**3 - 26*z**2\nNo more calculations needed.\n2001*z**6 + 524*z**5 - 637*z**4 + 58*z**3 - 26*z**2", "generated_answer": "2001*z**6 + 524*z**5 - 637*z**4 + 58*z**3 - 26*z**2", "step_length": 6} {"cot_id": "e44b6fd0b62025fcc7d8899707b26f14826ee6b26d0a16e2509856d0e09703ec", "datapoint": {"question": "Simplify this expression: (-52*x**3 + 69*x)*(40*x**2 - 25*x - 26)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2080*x**5 + 1300*x**4 + 4112*x**3 - 1725*x**2 - 1794*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 261, "polynomial_expr": "(-52*x**3 + 69*x)*(40*x**2 - 25*x - 26)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-52*x**3 + 69*x)*(40*x**2 - 25*x - 26)\nExpanding the part (-52*x**3 + 69*x) using the distributive property, and we got: (69*x)*(40*x**2 - 25*x - 26) + (-52*x**3)*(40*x**2 - 25*x - 26)\n#Step 2:\nCurrent expression: (69*x)*(40*x**2 - 25*x - 26) + (-52*x**3)*(40*x**2 - 25*x - 26)\nSimplifying the partial expression: (-52*x**3)*(40*x**2 - 25*x - 26)\nExpanding the part (40*x**2 - 25*x - 26) using the distributive property, and we got: (-25*x)*(-52*x**3) - (-1)*1352*x**3 + (40*x**2)*(-52*x**3)\nReplacing (-52*x**3)*(40*x**2 - 25*x - 26) with (-25*x)*(-52*x**3) - (-1)*1352*x**3 + (40*x**2)*(-52*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-25*x)*(-52*x**3) - 26*(-52)*x**3 + (69*x)*(40*x**2 - 25*x - 26) + (40*x**2)*(-52*x**3)\nSimplifying the partial expression: (69*x)*(40*x**2 - 25*x - 26)\nExpanding the part (40*x**2 - 25*x - 26) using the distributive property, and we got: (-25*x)*(69*x) - 1794*x + (69*x)*(40*x**2)\nReplacing (69*x)*(40*x**2 - 25*x - 26) with (-25*x)*(69*x) - 1794*x + (69*x)*(40*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-25*x)*(69*x) + (-25*x)*(-52*x**3) - 26*(-52)*x**3 - 26*69*x + (69*x)*(40*x**2) + (40*x**2)*(-52*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*x)*(-52*x**3) = 1300*x**4\n (-25*x)*(69*x) = -1725*x**2\n (40*x**2)*(-52*x**3) = -2080*x**5\n (40*x**2)*(69*x) = 2760*x**3\n -26*-52*x**3 = 1352*x**3\n -26*69*x = -1794*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2080*x**5 + 1300*x**4 + 1352*x**3 + 2760*x**3 - 1725*x**2 - 1794*x\nCombining like terms, got -2080*x**5 + 1300*x**4 + 4112*x**3 - 1725*x**2 - 1794*x\n#Step 6:\nCurrent expression: -2080*x**5 + 1300*x**4 + 4112*x**3 - 1725*x**2 - 1794*x\nNo more calculations needed.\n-2080*x**5 + 1300*x**4 + 4112*x**3 - 1725*x**2 - 1794*x", "generated_answer": "-2080*x**5 + 1300*x**4 + 4112*x**3 - 1725*x**2 - 1794*x", "step_length": 6} {"cot_id": "47dadeaadb27eda249e8eab11f17973212d683ad513c329516acc919db8b5e23", "datapoint": {"question": "Simplify this expression: (-4*x**2 - 44*x)*(-33*x**3 - 43*x**2 + 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "132*x**5 + 1624*x**4 + 1892*x**3 - 192*x**2 - 2112*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 262, "polynomial_expr": "(-4*x**2 - 44*x)*(-33*x**3 - 43*x**2 + 48)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-4*x**2 - 44*x)*(-33*x**3 - 43*x**2 + 48)\nExpanding the part (-4*x**2 - 44*x) using the distributive property, and we got: (-44*x)*(-33*x**3 - 43*x**2 + 48) + (-4*x**2)*(-33*x**3 - 43*x**2 + 48)\n#Step 2:\nCurrent expression: (-44*x)*(-33*x**3 - 43*x**2 + 48) + (-4*x**2)*(-33*x**3 - 43*x**2 + 48)\nSimplifying the partial expression: (-44*x)*(-33*x**3 - 43*x**2 + 48)\nExpanding the part (-33*x**3 - 43*x**2 + 48) using the distributive property, and we got: (-44*x)*(-43*x**2) + (-44*x)*(-33*x**3) + 48*(-44*x)\nReplacing (-44*x)*(-33*x**3 - 43*x**2 + 48) with (-44*x)*(-43*x**2) + (-44*x)*(-33*x**3) + 48*(-44*x) in the overall expression.\n#Step 3:\nCurrent expression: (-44*x)*(-43*x**2) + (-44*x)*(-33*x**3) + 48*(-44)*x + (-4*x**2)*(-33*x**3 - 43*x**2 + 48)\nSimplifying the partial expression: (-4*x**2)*(-33*x**3 - 43*x**2 + 48)\nExpanding the part (-33*x**3 - 43*x**2 + 48) using the distributive property, and we got: 48*(-4*x**2) + (-43*x**2)*(-4*x**2) + (-4*x**2)*(-33*x**3)\nReplacing (-4*x**2)*(-33*x**3 - 43*x**2 + 48) with 48*(-4*x**2) + (-43*x**2)*(-4*x**2) + (-4*x**2)*(-33*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-44*x)*(-43*x**2) + (-44*x)*(-33*x**3) + 48*(-4)*x**2 + 48*(-44)*x + (-43*x**2)*(-4*x**2) + (-4*x**2)*(-33*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-43*x**2)*(-44*x) = 1892*x**3\n (-43*x**2)*(-4*x**2) = 172*x**4\n (-33*x**3)*(-44*x) = 1452*x**4\n (-33*x**3)*(-4*x**2) = 132*x**5\n 48*-44*x = -2112*x\n 48*-4*x**2 = -192*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 132*x**5 + 172*x**4 + 1452*x**4 + 1892*x**3 - 192*x**2 - 2112*x\nCombining like terms, got 132*x**5 + 1624*x**4 + 1892*x**3 - 192*x**2 - 2112*x\n#Step 6:\nCurrent expression: 132*x**5 + 1624*x**4 + 1892*x**3 - 192*x**2 - 2112*x\nNo more calculations needed.\n132*x**5 + 1624*x**4 + 1892*x**3 - 192*x**2 - 2112*x", "generated_answer": "132*x**5 + 1624*x**4 + 1892*x**3 - 192*x**2 - 2112*x", "step_length": 6} {"cot_id": "53376fbd417734acf8e395ec68588fd02a205a73dc519efcd1d533c86052a1ba", "datapoint": {"question": "Calculate the following: (80*x**2 - 1)*(44*x**3 - 16*x**2 - 9*x - 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "3520*x**5 - 1280*x**4 - 764*x**3 - 2544*x**2 + 9*x + 32", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 263, "polynomial_expr": "(80*x**2 - 1)*(44*x**3 - 16*x**2 - 9*x - 32)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (80*x**2 - 1)*(44*x**3 - 16*x**2 - 9*x - 32)\nExpanding the part (80*x**2 - 1) using the distributive property, and we got: (80*x**2)*(44*x**3 - 16*x**2 - 9*x - 32) - (44*x**3 - 16*x**2 - 9*x - 32)\n#Step 2:\nCurrent expression: (80*x**2)*(44*x**3 - 16*x**2 - 9*x - 32) - (44*x**3 - 16*x**2 - 9*x - 32)\nSimplifying the partial expression: -(44*x**3 - 16*x**2 - 9*x - 32)\nExpanding the part (44*x**3 - 16*x**2 - 9*x - 32) using the distributive property, and we got: -9*x*(-1) - 16*x**2*(-1) + (44*x**3)*(-1) - 32*(-1)\nReplacing -(44*x**3 - 16*x**2 - 9*x - 32) with -9*x*(-1) - 16*x**2*(-1) + (44*x**3)*(-1) - 32*(-1) in the overall expression.\n#Step 3:\nCurrent expression: -9*x*(-1) - 16*x**2*(-1) + (80*x**2)*(44*x**3 - 16*x**2 - 9*x - 32) + (44*x**3)*(-1) + 32\nSimplifying the partial expression: (80*x**2)*(44*x**3 - 16*x**2 - 9*x - 32)\nExpanding the part (44*x**3 - 16*x**2 - 9*x - 32) using the distributive property, and we got: (-9*x)*(80*x**2) - 2560*x**2 + (-16*x**2)*(80*x**2) + (80*x**2)*(44*x**3)\nReplacing (80*x**2)*(44*x**3 - 16*x**2 - 9*x - 32) with (-9*x)*(80*x**2) - 2560*x**2 + (-16*x**2)*(80*x**2) + (80*x**2)*(44*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-9*x)*(80*x**2) - 9*x*(-1) - 32*80*x**2 + (-16*x**2)*(80*x**2) - 16*x**2*(-1) + (80*x**2)*(44*x**3) + (44*x**3)*(-1) + 32\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-16*x**2)*-1 = 16*x**2\n (-16*x**2)*(80*x**2) = -1280*x**4\n (-9*x)*-1 = 9*x\n (-9*x)*(80*x**2) = -720*x**3\n (44*x**3)*-1 = -44*x**3\n (44*x**3)*(80*x**2) = 3520*x**5\n -32*80*x**2 = -2560*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 3520*x**5 - 1280*x**4 - 720*x**3 - 44*x**3 - 2560*x**2 + 16*x**2 + 9*x + 32\nCombining like terms, got 3520*x**5 - 1280*x**4 - 764*x**3 - 2544*x**2 + 9*x + 32\n#Step 6:\nCurrent expression: 3520*x**5 - 1280*x**4 - 764*x**3 - 2544*x**2 + 9*x + 32\nNo more calculations needed.\n3520*x**5 - 1280*x**4 - 764*x**3 - 2544*x**2 + 9*x + 32", "generated_answer": "3520*x**5 - 1280*x**4 - 764*x**3 - 2544*x**2 + 9*x + 32", "step_length": 6} {"cot_id": "6d48b3f94f3b257ece861063d1af3cd5666eab26db3da8dc2960a128bc41cfa3", "datapoint": {"question": "Simplify this expression: (9*y + 27)*(64*y**3 - 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "576*y**4 + 1728*y**3 - 441*y - 1323", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 264, "polynomial_expr": "(9*y + 27)*(64*y**3 - 49)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9*y + 27)*(64*y**3 - 49)\nExpanding the part (64*y**3 - 49) using the distributive property, and we got: (64*y**3)*(9*y + 27) - 49*(9*y + 27)\n#Step 2:\nCurrent expression: (64*y**3)*(9*y + 27) - 49*(9*y + 27)\nSimplifying the partial expression: -49*(9*y + 27)\nExpanding the part (9*y + 27) using the distributive property, and we got: (9*y)*(-49) + 27*(-49)\nReplacing -49*(9*y + 27) with (9*y)*(-49) + 27*(-49) in the overall expression.\n#Step 3:\nCurrent expression: (9*y)*(-49) + (64*y**3)*(9*y + 27) - 1323\nSimplifying the partial expression: (64*y**3)*(9*y + 27)\nExpanding the part (9*y + 27) using the distributive property, and we got: 27*(64*y**3) + (9*y)*(64*y**3)\nReplacing (64*y**3)*(9*y + 27) with 27*(64*y**3) + (9*y)*(64*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 27*64*y**3 + (9*y)*(64*y**3) + (9*y)*(-49) - 1323\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (9*y)*-49 = -441*y\n (9*y)*(64*y**3) = 576*y**4\n 27*64*y**3 = 1728*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 576*y**4 + 1728*y**3 - 441*y - 1323\nNo more calculations needed.\n576*y**4 + 1728*y**3 - 441*y - 1323", "generated_answer": "576*y**4 + 1728*y**3 - 441*y - 1323", "step_length": 5} {"cot_id": "00618a293170203315295d7767e54f97be493a51fef2c6a8b34f80e9df2e490f", "datapoint": {"question": "Simplify this expression: (27*z**2 - 14*z)*(-46*z**3 - 12*z**2 + 43)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1242*z**5 + 320*z**4 + 168*z**3 + 1161*z**2 - 602*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 265, "polynomial_expr": "(27*z**2 - 14*z)*(-46*z**3 - 12*z**2 + 43)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*z**2 - 14*z)*(-46*z**3 - 12*z**2 + 43)\nExpanding the part (27*z**2 - 14*z) using the distributive property, and we got: (-14*z)*(-46*z**3 - 12*z**2 + 43) + (27*z**2)*(-46*z**3 - 12*z**2 + 43)\n#Step 2:\nCurrent expression: (-14*z)*(-46*z**3 - 12*z**2 + 43) + (27*z**2)*(-46*z**3 - 12*z**2 + 43)\nSimplifying the partial expression: (-14*z)*(-46*z**3 - 12*z**2 + 43)\nExpanding the part (-46*z**3 - 12*z**2 + 43) using the distributive property, and we got: (-14*z)*(-12*z**2) + (-14*z)*(-46*z**3) + 43*(-14*z)\nReplacing (-14*z)*(-46*z**3 - 12*z**2 + 43) with (-14*z)*(-12*z**2) + (-14*z)*(-46*z**3) + 43*(-14*z) in the overall expression.\n#Step 3:\nCurrent expression: (-14*z)*(-12*z**2) + (-14*z)*(-46*z**3) + 43*(-14)*z + (27*z**2)*(-46*z**3 - 12*z**2 + 43)\nSimplifying the partial expression: (27*z**2)*(-46*z**3 - 12*z**2 + 43)\nExpanding the part (-46*z**3 - 12*z**2 + 43) using the distributive property, and we got: 43*(27*z**2) + (-12*z**2)*(27*z**2) + (27*z**2)*(-46*z**3)\nReplacing (27*z**2)*(-46*z**3 - 12*z**2 + 43) with 43*(27*z**2) + (-12*z**2)*(27*z**2) + (27*z**2)*(-46*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-14*z)*(-12*z**2) + (-14*z)*(-46*z**3) + 43*27*z**2 + 43*(-14)*z + (-12*z**2)*(27*z**2) + (27*z**2)*(-46*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*z**3)*(-14*z) = 644*z**4\n (-46*z**3)*(27*z**2) = -1242*z**5\n (-12*z**2)*(-14*z) = 168*z**3\n (-12*z**2)*(27*z**2) = -324*z**4\n 43*-14*z = -602*z\n 43*27*z**2 = 1161*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1242*z**5 - 324*z**4 + 644*z**4 + 168*z**3 + 1161*z**2 - 602*z\nCombining like terms, got -1242*z**5 + 320*z**4 + 168*z**3 + 1161*z**2 - 602*z\n#Step 6:\nCurrent expression: -1242*z**5 + 320*z**4 + 168*z**3 + 1161*z**2 - 602*z\nNo more calculations needed.\n-1242*z**5 + 320*z**4 + 168*z**3 + 1161*z**2 - 602*z", "generated_answer": "-1242*z**5 + 320*z**4 + 168*z**3 + 1161*z**2 - 602*z", "step_length": 6} {"cot_id": "4b1d480445a7da5a79fa2496fe220397f223e53539977db8f09aa3f49b0aa37e", "datapoint": {"question": "Calculate the following: (8 - 6*x)*(48*x**3 + 23*x**2 - 18)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-288*x**4 + 246*x**3 + 184*x**2 + 108*x - 144", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 266, "polynomial_expr": "(8 - 6*x)*(48*x**3 + 23*x**2 - 18)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (8 - 6*x)*(48*x**3 + 23*x**2 - 18)\nExpanding the part (8 - 6*x) using the distributive property, and we got: (-6*x)*(48*x**3 + 23*x**2 - 18) + 8*(48*x**3 + 23*x**2 - 18)\n#Step 2:\nCurrent expression: (-6*x)*(48*x**3 + 23*x**2 - 18) + 8*(48*x**3 + 23*x**2 - 18)\nSimplifying the partial expression: 8*(48*x**3 + 23*x**2 - 18)\nExpanding the part (48*x**3 + 23*x**2 - 18) using the distributive property, and we got: (23*x**2)*8 + (48*x**3)*8 - 18*8\nReplacing 8*(48*x**3 + 23*x**2 - 18) with (23*x**2)*8 + (48*x**3)*8 - 18*8 in the overall expression.\n#Step 3:\nCurrent expression: (-6*x)*(48*x**3 + 23*x**2 - 18) + (23*x**2)*8 + (48*x**3)*8 - 144\nSimplifying the partial expression: (-6*x)*(48*x**3 + 23*x**2 - 18)\nExpanding the part (48*x**3 + 23*x**2 - 18) using the distributive property, and we got: (-6*x)*(23*x**2) + (-6*x)*(48*x**3) - (-1)*108*x\nReplacing (-6*x)*(48*x**3 + 23*x**2 - 18) with (-6*x)*(23*x**2) + (-6*x)*(48*x**3) - (-1)*108*x in the overall expression.\n#Step 4:\nCurrent expression: (-6*x)*(23*x**2) + (-6*x)*(48*x**3) - 18*(-6)*x + (23*x**2)*8 + (48*x**3)*8 - 144\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (23*x**2)*8 = 184*x**2\n (23*x**2)*(-6*x) = -138*x**3\n (48*x**3)*8 = 384*x**3\n (48*x**3)*(-6*x) = -288*x**4\n -18*-6*x = 108*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -288*x**4 - 138*x**3 + 384*x**3 + 184*x**2 + 108*x - 144\nCombining like terms, got -288*x**4 + 246*x**3 + 184*x**2 + 108*x - 144\n#Step 6:\nCurrent expression: -288*x**4 + 246*x**3 + 184*x**2 + 108*x - 144\nNo more calculations needed.\n-288*x**4 + 246*x**3 + 184*x**2 + 108*x - 144", "generated_answer": "-288*x**4 + 246*x**3 + 184*x**2 + 108*x - 144", "step_length": 6} {"cot_id": "8fc5d1b4aad2ff11be2ebd8865b82807d5a0e425e8b2c0c225bb31ab259b8bea", "datapoint": {"question": "Simplify this expression: 343*x**3 + 294*x**2 - 308*x + 245\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "343*x**3 + 294*x**2 - 308*x + 245", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 267, "polynomial_expr": "343*x**3 + 294*x**2 - 308*x + 245", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 343*x**3 + 294*x**2 - 308*x + 245\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 343*x**3 + 294*x**2 - 308*x + 245\nNo more calculations needed.\n343*x**3 + 294*x**2 - 308*x + 245", "generated_answer": "343*x**3 + 294*x**2 - 308*x + 245", "step_length": 2} {"cot_id": "ad03b43ef8087a296647119d9a59be491a62a9fad455976a2e6b73d405fcf474", "datapoint": {"question": "Calculate the following: 6480*z\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "6480*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 268, "polynomial_expr": "6480*z", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 6480*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 6480*z\nNo more calculations needed.\n6480*z", "generated_answer": "6480*z", "step_length": 2} {"cot_id": "91a96a4b3ea982f00f5d442e55a0b7706512585c967bf32a8454d0d4a708735e", "datapoint": {"question": "Simplify this expression: 85*y*(-40*y**2 - 11*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-3400*y**3 - 935*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 269, "polynomial_expr": "85*y*(-40*y**2 - 11*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 85*y*(-40*y**2 - 11*y)\nExpanding the part (-40*y**2 - 11*y) using the distributive property, and we got: (-11*y)*(85*y) + (85*y)*(-40*y**2)\n#Step 2:\nCurrent expression: (-11*y)*(85*y) + (85*y)*(-40*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*y**2)*(85*y) = -3400*y**3\n (-11*y)*(85*y) = -935*y**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -3400*y**3 - 935*y**2\nNo more calculations needed.\n-3400*y**3 - 935*y**2", "generated_answer": "-3400*y**3 - 935*y**2", "step_length": 3} {"cot_id": "9ec28cd857c5579e89634b7417d2d4e4ddf7c8a8161d9bfac68e0ff8315639fc", "datapoint": {"question": "Simplify this expression: (21*z + 49)*(25*z**3 - 44*z**2 + 20*z - 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "525*z**4 + 301*z**3 - 1736*z**2 + 539*z - 1029", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 270, "polynomial_expr": "(21*z + 49)*(25*z**3 - 44*z**2 + 20*z - 21)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21*z + 49)*(25*z**3 - 44*z**2 + 20*z - 21)\nExpanding the part (21*z + 49) using the distributive property, and we got: (21*z)*(25*z**3 - 44*z**2 + 20*z - 21) + 49*(25*z**3 - 44*z**2 + 20*z - 21)\n#Step 2:\nCurrent expression: (21*z)*(25*z**3 - 44*z**2 + 20*z - 21) + 49*(25*z**3 - 44*z**2 + 20*z - 21)\nSimplifying the partial expression: 49*(25*z**3 - 44*z**2 + 20*z - 21)\nExpanding the part (25*z**3 - 44*z**2 + 20*z - 21) using the distributive property, and we got: (20*z)*49 - 44*z**2*49 + (25*z**3)*49 - 21*49\nReplacing 49*(25*z**3 - 44*z**2 + 20*z - 21) with (20*z)*49 - 44*z**2*49 + (25*z**3)*49 - 21*49 in the overall expression.\n#Step 3:\nCurrent expression: (20*z)*49 + (21*z)*(25*z**3 - 44*z**2 + 20*z - 21) - 44*z**2*49 + (25*z**3)*49 - 1029\nSimplifying the partial expression: (21*z)*(25*z**3 - 44*z**2 + 20*z - 21)\nExpanding the part (25*z**3 - 44*z**2 + 20*z - 21) using the distributive property, and we got: -441*z + (20*z)*(21*z) + (21*z)*(-44*z**2) + (21*z)*(25*z**3)\nReplacing (21*z)*(25*z**3 - 44*z**2 + 20*z - 21) with -441*z + (20*z)*(21*z) + (21*z)*(-44*z**2) + (21*z)*(25*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -21*21*z + (20*z)*(21*z) + (20*z)*49 + (21*z)*(-44*z**2) + (21*z)*(25*z**3) - 44*z**2*49 + (25*z**3)*49 - 1029\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-44*z**2)*49 = -2156*z**2\n (-44*z**2)*(21*z) = -924*z**3\n (20*z)*49 = 980*z\n (20*z)*(21*z) = 420*z**2\n (25*z**3)*49 = 1225*z**3\n (25*z**3)*(21*z) = 525*z**4\n -21*21*z = -441*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 525*z**4 - 924*z**3 + 1225*z**3 - 2156*z**2 + 420*z**2 - 441*z + 980*z - 1029\nCombining like terms, got 525*z**4 + 301*z**3 - 1736*z**2 + 539*z - 1029\n#Step 6:\nCurrent expression: 525*z**4 + 301*z**3 - 1736*z**2 + 539*z - 1029\nNo more calculations needed.\n525*z**4 + 301*z**3 - 1736*z**2 + 539*z - 1029", "generated_answer": "525*z**4 + 301*z**3 - 1736*z**2 + 539*z - 1029", "step_length": 6} {"cot_id": "7998d3ad8c507d648358c0e567cb3aafbbf62adf1fb8e728abf25a16683c6484", "datapoint": {"question": "Calculate the following: (-22*z**3 + 54*z**2 - 13)*(33*z**3 - 13*z**2 - 9*z - 22)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-726*z**6 + 2068*z**5 - 504*z**4 - 431*z**3 - 1019*z**2 + 117*z + 286", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 271, "polynomial_expr": "(-22*z**3 + 54*z**2 - 13)*(33*z**3 - 13*z**2 - 9*z - 22)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-22*z**3 + 54*z**2 - 13)*(33*z**3 - 13*z**2 - 9*z - 22)\nExpanding the part (-22*z**3 + 54*z**2 - 13) using the distributive property, and we got: (54*z**2)*(33*z**3 - 13*z**2 - 9*z - 22) + (-22*z**3)*(33*z**3 - 13*z**2 - 9*z - 22) - 13*(33*z**3 - 13*z**2 - 9*z - 22)\n#Step 2:\nCurrent expression: (54*z**2)*(33*z**3 - 13*z**2 - 9*z - 22) + (-22*z**3)*(33*z**3 - 13*z**2 - 9*z - 22) - 13*(33*z**3 - 13*z**2 - 9*z - 22)\nSimplifying the partial expression: -13*(33*z**3 - 13*z**2 - 9*z - 22)\nExpanding the part (33*z**3 - 13*z**2 - 9*z - 22) using the distributive property, and we got: -9*z*(-13) - 13*z**2*(-13) + (33*z**3)*(-13) - 22*(-13)\nReplacing -13*(33*z**3 - 13*z**2 - 9*z - 22) with -9*z*(-13) - 13*z**2*(-13) + (33*z**3)*(-13) - 22*(-13) in the overall expression.\n#Step 3:\nCurrent expression: -9*z*(-13) - 13*z**2*(-13) + (54*z**2)*(33*z**3 - 13*z**2 - 9*z - 22) + (-22*z**3)*(33*z**3 - 13*z**2 - 9*z - 22) + (33*z**3)*(-13) + 286\nSimplifying the partial expression: (-22*z**3)*(33*z**3 - 13*z**2 - 9*z - 22)\nExpanding the part (33*z**3 - 13*z**2 - 9*z - 22) using the distributive property, and we got: (-9*z)*(-22*z**3) - (-1)*484*z**3 + (-13*z**2)*(-22*z**3) + (-22*z**3)*(33*z**3)\nReplacing (-22*z**3)*(33*z**3 - 13*z**2 - 9*z - 22) with (-9*z)*(-22*z**3) - (-1)*484*z**3 + (-13*z**2)*(-22*z**3) + (-22*z**3)*(33*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-9*z)*(-22*z**3) - 9*z*(-13) - 22*(-22)*z**3 + (-13*z**2)*(-22*z**3) - 13*z**2*(-13) + (54*z**2)*(33*z**3 - 13*z**2 - 9*z - 22) + (-22*z**3)*(33*z**3) + (33*z**3)*(-13) + 286\nSimplifying the partial expression: (54*z**2)*(33*z**3 - 13*z**2 - 9*z - 22)\nExpanding the part (33*z**3 - 13*z**2 - 9*z - 22) using the distributive property, and we got: (-9*z)*(54*z**2) - 1188*z**2 + (-13*z**2)*(54*z**2) + (54*z**2)*(33*z**3)\nReplacing (54*z**2)*(33*z**3 - 13*z**2 - 9*z - 22) with (-9*z)*(54*z**2) - 1188*z**2 + (-13*z**2)*(54*z**2) + (54*z**2)*(33*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-9*z)*(54*z**2) + (-9*z)*(-22*z**3) - 9*z*(-13) - 22*(-22)*z**3 - 22*54*z**2 + (-13*z**2)*(54*z**2) + (-13*z**2)*(-22*z**3) - 13*z**2*(-13) + (54*z**2)*(33*z**3) + (-22*z**3)*(33*z**3) + (33*z**3)*(-13) + 286\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*z**2)*-13 = 169*z**2\n (-13*z**2)*(-22*z**3) = 286*z**5\n (-13*z**2)*(54*z**2) = -702*z**4\n (-9*z)*-13 = 117*z\n (-9*z)*(-22*z**3) = 198*z**4\n (-9*z)*(54*z**2) = -486*z**3\n (33*z**3)*-13 = -429*z**3\n (33*z**3)*(-22*z**3) = -726*z**6\n (33*z**3)*(54*z**2) = 1782*z**5\n -22*-22*z**3 = 484*z**3\n -22*54*z**2 = -1188*z**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -726*z**6 + 286*z**5 + 1782*z**5 - 702*z**4 + 198*z**4 - 486*z**3 - 429*z**3 + 484*z**3 - 1188*z**2 + 169*z**2 + 117*z + 286\nCombining like terms, got -726*z**6 + 2068*z**5 - 504*z**4 - 431*z**3 - 1019*z**2 + 117*z + 286\n#Step 7:\nCurrent expression: -726*z**6 + 2068*z**5 - 504*z**4 - 431*z**3 - 1019*z**2 + 117*z + 286\nNo more calculations needed.\n-726*z**6 + 2068*z**5 - 504*z**4 - 431*z**3 - 1019*z**2 + 117*z + 286", "generated_answer": "-726*z**6 + 2068*z**5 - 504*z**4 - 431*z**3 - 1019*z**2 + 117*z + 286", "step_length": 7} {"cot_id": "65c119c1de74cd60608689b73bff85765df47982ea11c59c3335705fbb5e3f1a", "datapoint": {"question": "Calculate the following: (12*x - 19)*(-35*x**3 + 16*x - 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-420*x**4 + 665*x**3 + 192*x**2 - 796*x + 779", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 272, "polynomial_expr": "(12*x - 19)*(-35*x**3 + 16*x - 41)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (12*x - 19)*(-35*x**3 + 16*x - 41)\nExpanding the part (12*x - 19) using the distributive property, and we got: (12*x)*(-35*x**3 + 16*x - 41) - 19*(-35*x**3 + 16*x - 41)\n#Step 2:\nCurrent expression: (12*x)*(-35*x**3 + 16*x - 41) - 19*(-35*x**3 + 16*x - 41)\nSimplifying the partial expression: -19*(-35*x**3 + 16*x - 41)\nExpanding the part (-35*x**3 + 16*x - 41) using the distributive property, and we got: (16*x)*(-19) - 35*x**3*(-19) - 41*(-19)\nReplacing -19*(-35*x**3 + 16*x - 41) with (16*x)*(-19) - 35*x**3*(-19) - 41*(-19) in the overall expression.\n#Step 3:\nCurrent expression: (12*x)*(-35*x**3 + 16*x - 41) + (16*x)*(-19) - 35*x**3*(-19) + 779\nSimplifying the partial expression: (12*x)*(-35*x**3 + 16*x - 41)\nExpanding the part (-35*x**3 + 16*x - 41) using the distributive property, and we got: -492*x + (12*x)*(16*x) + (12*x)*(-35*x**3)\nReplacing (12*x)*(-35*x**3 + 16*x - 41) with -492*x + (12*x)*(16*x) + (12*x)*(-35*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -41*12*x + (12*x)*(16*x) + (12*x)*(-35*x**3) + (16*x)*(-19) - 35*x**3*(-19) + 779\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*x**3)*-19 = 665*x**3\n (-35*x**3)*(12*x) = -420*x**4\n (16*x)*-19 = -304*x\n (16*x)*(12*x) = 192*x**2\n -41*12*x = -492*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -420*x**4 + 665*x**3 + 192*x**2 - 492*x - 304*x + 779\nCombining like terms, got -420*x**4 + 665*x**3 + 192*x**2 - 796*x + 779\n#Step 6:\nCurrent expression: -420*x**4 + 665*x**3 + 192*x**2 - 796*x + 779\nNo more calculations needed.\n-420*x**4 + 665*x**3 + 192*x**2 - 796*x + 779", "generated_answer": "-420*x**4 + 665*x**3 + 192*x**2 - 796*x + 779", "step_length": 6} {"cot_id": "3080f91336f8a18f4d83462cb55344153af629af7099f964577b704c048c83e6", "datapoint": {"question": "Simplify this expression: (33*y**3 - 33)*(-4*y**3 + y + 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-132*y**6 + 33*y**4 + 693*y**3 - 33*y - 561", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 273, "polynomial_expr": "(33*y**3 - 33)*(-4*y**3 + y + 17)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (33*y**3 - 33)*(-4*y**3 + y + 17)\nExpanding the part (33*y**3 - 33) using the distributive property, and we got: (33*y**3)*(-4*y**3 + y + 17) - 33*(-4*y**3 + y + 17)\n#Step 2:\nCurrent expression: (33*y**3)*(-4*y**3 + y + 17) - 33*(-4*y**3 + y + 17)\nSimplifying the partial expression: -33*(-4*y**3 + y + 17)\nExpanding the part (-4*y**3 + y + 17) using the distributive property, and we got: y*(-33) - 4*y**3*(-33) + 17*(-33)\nReplacing -33*(-4*y**3 + y + 17) with y*(-33) - 4*y**3*(-33) + 17*(-33) in the overall expression.\n#Step 3:\nCurrent expression: y*(-33) - 4*y**3*(-33) + (33*y**3)*(-4*y**3 + y + 17) - 561\nSimplifying the partial expression: (33*y**3)*(-4*y**3 + y + 17)\nExpanding the part (-4*y**3 + y + 17) using the distributive property, and we got: 17*(33*y**3) + y*(33*y**3) + (-4*y**3)*(33*y**3)\nReplacing (33*y**3)*(-4*y**3 + y + 17) with 17*(33*y**3) + y*(33*y**3) + (-4*y**3)*(33*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 17*33*y**3 + y*(33*y**3) + y*(-33) + (-4*y**3)*(33*y**3) - 4*y**3*(-33) - 561\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n y*-33 = -33*y\n y*(33*y**3) = 33*y**4\n (-4*y**3)*-33 = 132*y**3\n (-4*y**3)*(33*y**3) = -132*y**6\n 17*33*y**3 = 561*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -132*y**6 + 33*y**4 + 132*y**3 + 561*y**3 - 33*y - 561\nCombining like terms, got -132*y**6 + 33*y**4 + 693*y**3 - 33*y - 561\n#Step 6:\nCurrent expression: -132*y**6 + 33*y**4 + 693*y**3 - 33*y - 561\nNo more calculations needed.\n-132*y**6 + 33*y**4 + 693*y**3 - 33*y - 561", "generated_answer": "-132*y**6 + 33*y**4 + 693*y**3 - 33*y - 561", "step_length": 6} {"cot_id": "b3fd9dba19b184fb43fb234f8c0d8e262d7cc8e48088e32529c004a18a370b4e", "datapoint": {"question": "Simplify this expression: (-30*x**3 + 10*x**2 - 41)*(5*x**3 - 49*x - 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-150*x**6 + 50*x**5 + 1470*x**4 - 665*x**3 - 10*x**2 + 2009*x + 41", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 274, "polynomial_expr": "(-30*x**3 + 10*x**2 - 41)*(5*x**3 - 49*x - 1)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-30*x**3 + 10*x**2 - 41)*(5*x**3 - 49*x - 1)\nExpanding the part (5*x**3 - 49*x - 1) using the distributive property, and we got: (-49*x)*(-30*x**3 + 10*x**2 - 41) + (5*x**3)*(-30*x**3 + 10*x**2 - 41) - (-30*x**3 + 10*x**2 - 41)\n#Step 2:\nCurrent expression: (-49*x)*(-30*x**3 + 10*x**2 - 41) + (5*x**3)*(-30*x**3 + 10*x**2 - 41) - (-30*x**3 + 10*x**2 - 41)\nSimplifying the partial expression: -(-30*x**3 + 10*x**2 - 41)\nExpanding the part (-30*x**3 + 10*x**2 - 41) using the distributive property, and we got: (10*x**2)*(-1) - 30*x**3*(-1) - 41*(-1)\nReplacing -(-30*x**3 + 10*x**2 - 41) with (10*x**2)*(-1) - 30*x**3*(-1) - 41*(-1) in the overall expression.\n#Step 3:\nCurrent expression: (-49*x)*(-30*x**3 + 10*x**2 - 41) + (10*x**2)*(-1) - 30*x**3*(-1) + (5*x**3)*(-30*x**3 + 10*x**2 - 41) + 41\nSimplifying the partial expression: (-49*x)*(-30*x**3 + 10*x**2 - 41)\nExpanding the part (-30*x**3 + 10*x**2 - 41) using the distributive property, and we got: (-49*x)*(10*x**2) + (-49*x)*(-30*x**3) - (-1)*2009*x\nReplacing (-49*x)*(-30*x**3 + 10*x**2 - 41) with (-49*x)*(10*x**2) + (-49*x)*(-30*x**3) - (-1)*2009*x in the overall expression.\n#Step 4:\nCurrent expression: (-49*x)*(10*x**2) + (-49*x)*(-30*x**3) - 41*(-49)*x + (10*x**2)*(-1) - 30*x**3*(-1) + (5*x**3)*(-30*x**3 + 10*x**2 - 41) + 41\nSimplifying the partial expression: (5*x**3)*(-30*x**3 + 10*x**2 - 41)\nExpanding the part (-30*x**3 + 10*x**2 - 41) using the distributive property, and we got: -205*x**3 + (10*x**2)*(5*x**3) + (-30*x**3)*(5*x**3)\nReplacing (5*x**3)*(-30*x**3 + 10*x**2 - 41) with -205*x**3 + (10*x**2)*(5*x**3) + (-30*x**3)*(5*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-49*x)*(10*x**2) + (-49*x)*(-30*x**3) - 41*5*x**3 - 41*(-49)*x + (10*x**2)*(5*x**3) + (10*x**2)*(-1) + (-30*x**3)*(5*x**3) - 30*x**3*(-1) + 41\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*x**3)*-1 = 30*x**3\n (-30*x**3)*(-49*x) = 1470*x**4\n (-30*x**3)*(5*x**3) = -150*x**6\n (10*x**2)*-1 = -10*x**2\n (10*x**2)*(-49*x) = -490*x**3\n (10*x**2)*(5*x**3) = 50*x**5\n -41*-49*x = 2009*x\n -41*5*x**3 = -205*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -150*x**6 + 50*x**5 + 1470*x**4 - 490*x**3 - 205*x**3 + 30*x**3 - 10*x**2 + 2009*x + 41\nCombining like terms, got -150*x**6 + 50*x**5 + 1470*x**4 - 665*x**3 - 10*x**2 + 2009*x + 41\n#Step 7:\nCurrent expression: -150*x**6 + 50*x**5 + 1470*x**4 - 665*x**3 - 10*x**2 + 2009*x + 41\nNo more calculations needed.\n-150*x**6 + 50*x**5 + 1470*x**4 - 665*x**3 - 10*x**2 + 2009*x + 41", "generated_answer": "-150*x**6 + 50*x**5 + 1470*x**4 - 665*x**3 - 10*x**2 + 2009*x + 41", "step_length": 7} {"cot_id": "f2abbbc8619b17fbc15fcd080d4aafc2f4f634183ca7bb141065ee0016ecbf60", "datapoint": {"question": "Simplify this expression: (-33*y**2 + 12*y)*(-65*y**3 + 33*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2145*y**5 - 1869*y**4 + 396*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 275, "polynomial_expr": "(-33*y**2 + 12*y)*(-65*y**3 + 33*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-33*y**2 + 12*y)*(-65*y**3 + 33*y**2)\nExpanding the part (-65*y**3 + 33*y**2) using the distributive property, and we got: (33*y**2)*(-33*y**2 + 12*y) + (-65*y**3)*(-33*y**2 + 12*y)\n#Step 2:\nCurrent expression: (33*y**2)*(-33*y**2 + 12*y) + (-65*y**3)*(-33*y**2 + 12*y)\nSimplifying the partial expression: (-65*y**3)*(-33*y**2 + 12*y)\nExpanding the part (-33*y**2 + 12*y) using the distributive property, and we got: (12*y)*(-65*y**3) + (-33*y**2)*(-65*y**3)\nReplacing (-65*y**3)*(-33*y**2 + 12*y) with (12*y)*(-65*y**3) + (-33*y**2)*(-65*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (12*y)*(-65*y**3) + (-33*y**2)*(-65*y**3) + (33*y**2)*(-33*y**2 + 12*y)\nSimplifying the partial expression: (33*y**2)*(-33*y**2 + 12*y)\nExpanding the part (-33*y**2 + 12*y) using the distributive property, and we got: (12*y)*(33*y**2) + (-33*y**2)*(33*y**2)\nReplacing (33*y**2)*(-33*y**2 + 12*y) with (12*y)*(33*y**2) + (-33*y**2)*(33*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (12*y)*(33*y**2) + (12*y)*(-65*y**3) + (-33*y**2)*(33*y**2) + (-33*y**2)*(-65*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*y**2)*(-65*y**3) = 2145*y**5\n (-33*y**2)*(33*y**2) = -1089*y**4\n (12*y)*(-65*y**3) = -780*y**4\n (12*y)*(33*y**2) = 396*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2145*y**5 - 1089*y**4 - 780*y**4 + 396*y**3\nCombining like terms, got 2145*y**5 - 1869*y**4 + 396*y**3\n#Step 6:\nCurrent expression: 2145*y**5 - 1869*y**4 + 396*y**3\nNo more calculations needed.\n2145*y**5 - 1869*y**4 + 396*y**3", "generated_answer": "2145*y**5 - 1869*y**4 + 396*y**3", "step_length": 6} {"cot_id": "5c7850c52eddeca83e7f2311c74a9c11b208c4e7b10af19e215e42320c342405", "datapoint": {"question": "Simplify this expression: (-72*z**2 - 43*z)*(-31*z**3 + 13*z**2 + 27*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2232*z**5 + 397*z**4 - 2503*z**3 - 1161*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 276, "polynomial_expr": "(-72*z**2 - 43*z)*(-31*z**3 + 13*z**2 + 27*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-72*z**2 - 43*z)*(-31*z**3 + 13*z**2 + 27*z)\nExpanding the part (-72*z**2 - 43*z) using the distributive property, and we got: (-43*z)*(-31*z**3 + 13*z**2 + 27*z) + (-72*z**2)*(-31*z**3 + 13*z**2 + 27*z)\n#Step 2:\nCurrent expression: (-43*z)*(-31*z**3 + 13*z**2 + 27*z) + (-72*z**2)*(-31*z**3 + 13*z**2 + 27*z)\nSimplifying the partial expression: (-72*z**2)*(-31*z**3 + 13*z**2 + 27*z)\nExpanding the part (-31*z**3 + 13*z**2 + 27*z) using the distributive property, and we got: (27*z)*(-72*z**2) + (-72*z**2)*(13*z**2) + (-72*z**2)*(-31*z**3)\nReplacing (-72*z**2)*(-31*z**3 + 13*z**2 + 27*z) with (27*z)*(-72*z**2) + (-72*z**2)*(13*z**2) + (-72*z**2)*(-31*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-43*z)*(-31*z**3 + 13*z**2 + 27*z) + (27*z)*(-72*z**2) + (-72*z**2)*(13*z**2) + (-72*z**2)*(-31*z**3)\nSimplifying the partial expression: (-43*z)*(-31*z**3 + 13*z**2 + 27*z)\nExpanding the part (-31*z**3 + 13*z**2 + 27*z) using the distributive property, and we got: (-43*z)*(27*z) + (-43*z)*(13*z**2) + (-43*z)*(-31*z**3)\nReplacing (-43*z)*(-31*z**3 + 13*z**2 + 27*z) with (-43*z)*(27*z) + (-43*z)*(13*z**2) + (-43*z)*(-31*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-43*z)*(27*z) + (-43*z)*(13*z**2) + (-43*z)*(-31*z**3) + (27*z)*(-72*z**2) + (-72*z**2)*(13*z**2) + (-72*z**2)*(-31*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-31*z**3)*(-72*z**2) = 2232*z**5\n (-31*z**3)*(-43*z) = 1333*z**4\n (13*z**2)*(-72*z**2) = -936*z**4\n (13*z**2)*(-43*z) = -559*z**3\n (27*z)*(-72*z**2) = -1944*z**3\n (27*z)*(-43*z) = -1161*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2232*z**5 - 936*z**4 + 1333*z**4 - 1944*z**3 - 559*z**3 - 1161*z**2\nCombining like terms, got 2232*z**5 + 397*z**4 - 2503*z**3 - 1161*z**2\n#Step 6:\nCurrent expression: 2232*z**5 + 397*z**4 - 2503*z**3 - 1161*z**2\nNo more calculations needed.\n2232*z**5 + 397*z**4 - 2503*z**3 - 1161*z**2", "generated_answer": "2232*z**5 + 397*z**4 - 2503*z**3 - 1161*z**2", "step_length": 6} {"cot_id": "739577b93f702a2d4313e420861716b0a4be5306a6c1da623f8ff546a20aca2f", "datapoint": {"question": "Calculate the following: (-25*x**2 + 32*x - 32)*(35*x**3 - 52*x**2 + 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-875*x**5 + 2420*x**4 - 2784*x**3 + 564*x**2 + 1408*x - 1408", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 277, "polynomial_expr": "(-25*x**2 + 32*x - 32)*(35*x**3 - 52*x**2 + 44)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-25*x**2 + 32*x - 32)*(35*x**3 - 52*x**2 + 44)\nExpanding the part (-25*x**2 + 32*x - 32) using the distributive property, and we got: (32*x)*(35*x**3 - 52*x**2 + 44) + (-25*x**2)*(35*x**3 - 52*x**2 + 44) - 32*(35*x**3 - 52*x**2 + 44)\n#Step 2:\nCurrent expression: (32*x)*(35*x**3 - 52*x**2 + 44) + (-25*x**2)*(35*x**3 - 52*x**2 + 44) - 32*(35*x**3 - 52*x**2 + 44)\nSimplifying the partial expression: -32*(35*x**3 - 52*x**2 + 44)\nExpanding the part (35*x**3 - 52*x**2 + 44) using the distributive property, and we got: -52*x**2*(-32) + (35*x**3)*(-32) + 44*(-32)\nReplacing -32*(35*x**3 - 52*x**2 + 44) with -52*x**2*(-32) + (35*x**3)*(-32) + 44*(-32) in the overall expression.\n#Step 3:\nCurrent expression: (32*x)*(35*x**3 - 52*x**2 + 44) - 52*x**2*(-32) + (-25*x**2)*(35*x**3 - 52*x**2 + 44) + (35*x**3)*(-32) - 1408\nSimplifying the partial expression: (-25*x**2)*(35*x**3 - 52*x**2 + 44)\nExpanding the part (35*x**3 - 52*x**2 + 44) using the distributive property, and we got: 44*(-25*x**2) + (-52*x**2)*(-25*x**2) + (-25*x**2)*(35*x**3)\nReplacing (-25*x**2)*(35*x**3 - 52*x**2 + 44) with 44*(-25*x**2) + (-52*x**2)*(-25*x**2) + (-25*x**2)*(35*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 44*(-25)*x**2 + (32*x)*(35*x**3 - 52*x**2 + 44) + (-52*x**2)*(-25*x**2) - 52*x**2*(-32) + (-25*x**2)*(35*x**3) + (35*x**3)*(-32) - 1408\nSimplifying the partial expression: (32*x)*(35*x**3 - 52*x**2 + 44)\nExpanding the part (35*x**3 - 52*x**2 + 44) using the distributive property, and we got: 44*(32*x) + (32*x)*(-52*x**2) + (32*x)*(35*x**3)\nReplacing (32*x)*(35*x**3 - 52*x**2 + 44) with 44*(32*x) + (32*x)*(-52*x**2) + (32*x)*(35*x**3) in the overall expression.\n#Step 5:\nCurrent expression: 44*(-25)*x**2 + 44*32*x + (32*x)*(-52*x**2) + (32*x)*(35*x**3) + (-52*x**2)*(-25*x**2) - 52*x**2*(-32) + (-25*x**2)*(35*x**3) + (35*x**3)*(-32) - 1408\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-52*x**2)*-32 = 1664*x**2\n (-52*x**2)*(-25*x**2) = 1300*x**4\n (-52*x**2)*(32*x) = -1664*x**3\n (35*x**3)*-32 = -1120*x**3\n (35*x**3)*(-25*x**2) = -875*x**5\n (35*x**3)*(32*x) = 1120*x**4\n 44*-25*x**2 = -1100*x**2\n 44*32*x = 1408*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -875*x**5 + 1120*x**4 + 1300*x**4 - 1664*x**3 - 1120*x**3 - 1100*x**2 + 1664*x**2 + 1408*x - 1408\nCombining like terms, got -875*x**5 + 2420*x**4 - 2784*x**3 + 564*x**2 + 1408*x - 1408\n#Step 7:\nCurrent expression: -875*x**5 + 2420*x**4 - 2784*x**3 + 564*x**2 + 1408*x - 1408\nNo more calculations needed.\n-875*x**5 + 2420*x**4 - 2784*x**3 + 564*x**2 + 1408*x - 1408", "generated_answer": "-875*x**5 + 2420*x**4 - 2784*x**3 + 564*x**2 + 1408*x - 1408", "step_length": 7} {"cot_id": "1375e58eb84350e29271f83954ef2f7fe0066de79dbb4e261217ea94e5fec89b", "datapoint": {"question": "Simplify this expression: 4*y**2*(18*y**3 + 11*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "72*y**5 + 44*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 278, "polynomial_expr": "4*y**2*(18*y**3 + 11*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 4*y**2*(18*y**3 + 11*y)\nExpanding the part (18*y**3 + 11*y) using the distributive property, and we got: (11*y)*(4*y**2) + (4*y**2)*(18*y**3)\n#Step 2:\nCurrent expression: (11*y)*(4*y**2) + (4*y**2)*(18*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (11*y)*(4*y**2) = 44*y**3\n (18*y**3)*(4*y**2) = 72*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 72*y**5 + 44*y**3\nNo more calculations needed.\n72*y**5 + 44*y**3", "generated_answer": "72*y**5 + 44*y**3", "step_length": 3} {"cot_id": "6514dafa131e09ce908e51d3bcaea1a1147fa645ac80aa4ce1bcb4c0bd36f78e", "datapoint": {"question": "Calculate the following: (47 - 24*y**2)*(-25*y**2 + y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "600*y**4 - 24*y**3 - 1175*y**2 + 47*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 279, "polynomial_expr": "(47 - 24*y**2)*(-25*y**2 + y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (47 - 24*y**2)*(-25*y**2 + y)\nExpanding the part (47 - 24*y**2) using the distributive property, and we got: (-24*y**2)*(-25*y**2 + y) + 47*(-25*y**2 + y)\n#Step 2:\nCurrent expression: (-24*y**2)*(-25*y**2 + y) + 47*(-25*y**2 + y)\nSimplifying the partial expression: 47*(-25*y**2 + y)\nExpanding the part (-25*y**2 + y) using the distributive property, and we got: y*47 - 25*y**2*47\nReplacing 47*(-25*y**2 + y) with y*47 - 25*y**2*47 in the overall expression.\n#Step 3:\nCurrent expression: y*47 - 25*y**2*47 + (-24*y**2)*(-25*y**2 + y)\nSimplifying the partial expression: (-24*y**2)*(-25*y**2 + y)\nExpanding the part (-25*y**2 + y) using the distributive property, and we got: y*(-24*y**2) + (-25*y**2)*(-24*y**2)\nReplacing (-24*y**2)*(-25*y**2 + y) with y*(-24*y**2) + (-25*y**2)*(-24*y**2) in the overall expression.\n#Step 4:\nCurrent expression: y*(-24*y**2) + y*47 + (-25*y**2)*(-24*y**2) - 25*y**2*47\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n y*47 = 47*y\n y*(-24*y**2) = -24*y**3\n (-25*y**2)*47 = -1175*y**2\n (-25*y**2)*(-24*y**2) = 600*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 600*y**4 - 24*y**3 - 1175*y**2 + 47*y\nNo more calculations needed.\n600*y**4 - 24*y**3 - 1175*y**2 + 47*y", "generated_answer": "600*y**4 - 24*y**3 - 1175*y**2 + 47*y", "step_length": 5} {"cot_id": "2e488acfe0a69d284a8620082eda983ba473558512b38b86b7f3ed42d7a18951", "datapoint": {"question": "Calculate the following: -1974*z**2 + 1512*z - 3192\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1974*z**2 + 1512*z - 3192", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 280, "polynomial_expr": "-1974*z**2 + 1512*z - 3192", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -1974*z**2 + 1512*z - 3192\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -1974*z**2 + 1512*z - 3192\nNo more calculations needed.\n-1974*z**2 + 1512*z - 3192", "generated_answer": "-1974*z**2 + 1512*z - 3192", "step_length": 2} {"cot_id": "60719fbf352151cf3679f8b734bb399c3541542556bb6539e090c965c2f35307", "datapoint": {"question": "Calculate the following: (43*z**2 - 40*z)*(32*z**3 - 30*z**2 - 39*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1376*z**5 - 2570*z**4 - 477*z**3 + 1560*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 281, "polynomial_expr": "(43*z**2 - 40*z)*(32*z**3 - 30*z**2 - 39*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (43*z**2 - 40*z)*(32*z**3 - 30*z**2 - 39*z)\nExpanding the part (43*z**2 - 40*z) using the distributive property, and we got: (-40*z)*(32*z**3 - 30*z**2 - 39*z) + (43*z**2)*(32*z**3 - 30*z**2 - 39*z)\n#Step 2:\nCurrent expression: (-40*z)*(32*z**3 - 30*z**2 - 39*z) + (43*z**2)*(32*z**3 - 30*z**2 - 39*z)\nSimplifying the partial expression: (-40*z)*(32*z**3 - 30*z**2 - 39*z)\nExpanding the part (32*z**3 - 30*z**2 - 39*z) using the distributive property, and we got: (-40*z)*(-39*z) + (-40*z)*(-30*z**2) + (-40*z)*(32*z**3)\nReplacing (-40*z)*(32*z**3 - 30*z**2 - 39*z) with (-40*z)*(-39*z) + (-40*z)*(-30*z**2) + (-40*z)*(32*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-40*z)*(-39*z) + (-40*z)*(-30*z**2) + (-40*z)*(32*z**3) + (43*z**2)*(32*z**3 - 30*z**2 - 39*z)\nSimplifying the partial expression: (43*z**2)*(32*z**3 - 30*z**2 - 39*z)\nExpanding the part (32*z**3 - 30*z**2 - 39*z) using the distributive property, and we got: (-39*z)*(43*z**2) + (-30*z**2)*(43*z**2) + (43*z**2)*(32*z**3)\nReplacing (43*z**2)*(32*z**3 - 30*z**2 - 39*z) with (-39*z)*(43*z**2) + (-30*z**2)*(43*z**2) + (43*z**2)*(32*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-40*z)*(-39*z) + (-40*z)*(-30*z**2) + (-40*z)*(32*z**3) + (-39*z)*(43*z**2) + (-30*z**2)*(43*z**2) + (43*z**2)*(32*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*z)*(-40*z) = 1560*z**2\n (-39*z)*(43*z**2) = -1677*z**3\n (-30*z**2)*(-40*z) = 1200*z**3\n (-30*z**2)*(43*z**2) = -1290*z**4\n (32*z**3)*(-40*z) = -1280*z**4\n (32*z**3)*(43*z**2) = 1376*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1376*z**5 - 1290*z**4 - 1280*z**4 - 1677*z**3 + 1200*z**3 + 1560*z**2\nCombining like terms, got 1376*z**5 - 2570*z**4 - 477*z**3 + 1560*z**2\n#Step 6:\nCurrent expression: 1376*z**5 - 2570*z**4 - 477*z**3 + 1560*z**2\nNo more calculations needed.\n1376*z**5 - 2570*z**4 - 477*z**3 + 1560*z**2", "generated_answer": "1376*z**5 - 2570*z**4 - 477*z**3 + 1560*z**2", "step_length": 6} {"cot_id": "4cabad4acb1a26677ebdde7ea8865426d6ebd6bed7af27a9f1f88b472aff7378", "datapoint": {"question": "Calculate the following: (-46*z**2 - 28*z + 6)*(-13*z**3 - 9*z**2 + 50*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "598*z**5 + 778*z**4 - 2126*z**3 - 1454*z**2 + 300*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 282, "polynomial_expr": "(-46*z**2 - 28*z + 6)*(-13*z**3 - 9*z**2 + 50*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-46*z**2 - 28*z + 6)*(-13*z**3 - 9*z**2 + 50*z)\nExpanding the part (-46*z**2 - 28*z + 6) using the distributive property, and we got: (-28*z)*(-13*z**3 - 9*z**2 + 50*z) + (-46*z**2)*(-13*z**3 - 9*z**2 + 50*z) + 6*(-13*z**3 - 9*z**2 + 50*z)\n#Step 2:\nCurrent expression: (-28*z)*(-13*z**3 - 9*z**2 + 50*z) + (-46*z**2)*(-13*z**3 - 9*z**2 + 50*z) + 6*(-13*z**3 - 9*z**2 + 50*z)\nSimplifying the partial expression: 6*(-13*z**3 - 9*z**2 + 50*z)\nExpanding the part (-13*z**3 - 9*z**2 + 50*z) using the distributive property, and we got: (50*z)*6 - 9*z**2*6 - 13*z**3*6\nReplacing 6*(-13*z**3 - 9*z**2 + 50*z) with (50*z)*6 - 9*z**2*6 - 13*z**3*6 in the overall expression.\n#Step 3:\nCurrent expression: (-28*z)*(-13*z**3 - 9*z**2 + 50*z) + (50*z)*6 + (-46*z**2)*(-13*z**3 - 9*z**2 + 50*z) - 9*z**2*6 - 13*z**3*6\nSimplifying the partial expression: (-46*z**2)*(-13*z**3 - 9*z**2 + 50*z)\nExpanding the part (-13*z**3 - 9*z**2 + 50*z) using the distributive property, and we got: (50*z)*(-46*z**2) + (-46*z**2)*(-9*z**2) + (-46*z**2)*(-13*z**3)\nReplacing (-46*z**2)*(-13*z**3 - 9*z**2 + 50*z) with (50*z)*(-46*z**2) + (-46*z**2)*(-9*z**2) + (-46*z**2)*(-13*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-28*z)*(-13*z**3 - 9*z**2 + 50*z) + (50*z)*(-46*z**2) + (50*z)*6 + (-46*z**2)*(-9*z**2) + (-46*z**2)*(-13*z**3) - 9*z**2*6 - 13*z**3*6\nSimplifying the partial expression: (-28*z)*(-13*z**3 - 9*z**2 + 50*z)\nExpanding the part (-13*z**3 - 9*z**2 + 50*z) using the distributive property, and we got: (-28*z)*(50*z) + (-28*z)*(-9*z**2) + (-28*z)*(-13*z**3)\nReplacing (-28*z)*(-13*z**3 - 9*z**2 + 50*z) with (-28*z)*(50*z) + (-28*z)*(-9*z**2) + (-28*z)*(-13*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-28*z)*(50*z) + (-28*z)*(-9*z**2) + (-28*z)*(-13*z**3) + (50*z)*(-46*z**2) + (50*z)*6 + (-46*z**2)*(-9*z**2) + (-46*z**2)*(-13*z**3) - 9*z**2*6 - 13*z**3*6\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*z**3)*6 = -78*z**3\n (-13*z**3)*(-46*z**2) = 598*z**5\n (-13*z**3)*(-28*z) = 364*z**4\n (-9*z**2)*6 = -54*z**2\n (-9*z**2)*(-46*z**2) = 414*z**4\n (-9*z**2)*(-28*z) = 252*z**3\n (50*z)*6 = 300*z\n (50*z)*(-46*z**2) = -2300*z**3\n (50*z)*(-28*z) = -1400*z**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 598*z**5 + 364*z**4 + 414*z**4 - 2300*z**3 - 78*z**3 + 252*z**3 - 1400*z**2 - 54*z**2 + 300*z\nCombining like terms, got 598*z**5 + 778*z**4 - 2126*z**3 - 1454*z**2 + 300*z\n#Step 7:\nCurrent expression: 598*z**5 + 778*z**4 - 2126*z**3 - 1454*z**2 + 300*z\nNo more calculations needed.\n598*z**5 + 778*z**4 - 2126*z**3 - 1454*z**2 + 300*z", "generated_answer": "598*z**5 + 778*z**4 - 2126*z**3 - 1454*z**2 + 300*z", "step_length": 7} {"cot_id": "2fc38ccdbbdb6d87ae824b77becf870ab0d6aaf648afd1c6cea75eda54cbcc77", "datapoint": {"question": "Calculate the following: (-13*z**3 - 36)*(33*z**3 - 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-429*z**6 - 980*z**3 + 576", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 283, "polynomial_expr": "(-13*z**3 - 36)*(33*z**3 - 16)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-13*z**3 - 36)*(33*z**3 - 16)\nExpanding the part (-13*z**3 - 36) using the distributive property, and we got: (-13*z**3)*(33*z**3 - 16) - 36*(33*z**3 - 16)\n#Step 2:\nCurrent expression: (-13*z**3)*(33*z**3 - 16) - 36*(33*z**3 - 16)\nSimplifying the partial expression: -36*(33*z**3 - 16)\nExpanding the part (33*z**3 - 16) using the distributive property, and we got: (33*z**3)*(-36) - 16*(-36)\nReplacing -36*(33*z**3 - 16) with (33*z**3)*(-36) - 16*(-36) in the overall expression.\n#Step 3:\nCurrent expression: (-13*z**3)*(33*z**3 - 16) + (33*z**3)*(-36) + 576\nSimplifying the partial expression: (-13*z**3)*(33*z**3 - 16)\nExpanding the part (33*z**3 - 16) using the distributive property, and we got: -(-1)*208*z**3 + (-13*z**3)*(33*z**3)\nReplacing (-13*z**3)*(33*z**3 - 16) with -(-1)*208*z**3 + (-13*z**3)*(33*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -16*(-13)*z**3 + (-13*z**3)*(33*z**3) + (33*z**3)*(-36) + 576\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (33*z**3)*-36 = -1188*z**3\n (33*z**3)*(-13*z**3) = -429*z**6\n -16*-13*z**3 = 208*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -429*z**6 - 1188*z**3 + 208*z**3 + 576\nCombining like terms, got -429*z**6 - 980*z**3 + 576\n#Step 6:\nCurrent expression: -429*z**6 - 980*z**3 + 576\nNo more calculations needed.\n-429*z**6 - 980*z**3 + 576", "generated_answer": "-429*z**6 - 980*z**3 + 576", "step_length": 6} {"cot_id": "167b021e600eef14d280bd191a239934dc0a7c16e18aab1db87868976fb6b556", "datapoint": {"question": "Calculate the following: -27*x*(-3*x**3 + 42*x - 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "81*x**4 - 1134*x**2 + 567*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 284, "polynomial_expr": "-27*x*(-3*x**3 + 42*x - 21)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -27*x*(-3*x**3 + 42*x - 21)\nExpanding the part (-3*x**3 + 42*x - 21) using the distributive property, and we got: (-27*x)*(42*x) + (-27*x)*(-3*x**3) - (-1)*567*x\n#Step 2:\nCurrent expression: (-27*x)*(42*x) + (-27*x)*(-3*x**3) - (-1)*567*x\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -21*(-27*x) = 567*x\n (-3*x**3)*(-27*x) = 81*x**4\n (42*x)*(-27*x) = -1134*x**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 81*x**4 - 1134*x**2 + 567*x\nNo more calculations needed.\n81*x**4 - 1134*x**2 + 567*x", "generated_answer": "81*x**4 - 1134*x**2 + 567*x", "step_length": 3} {"cot_id": "3fd5627ae06f5eb6fea2c1d819d227a29ddcaccabb90fcda4290aa12a560283a", "datapoint": {"question": "Calculate the following: (-12*x - 79)*(-30*x**2 - 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "360*x**3 + 2370*x**2 + 12*x + 79", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 285, "polynomial_expr": "(-12*x - 79)*(-30*x**2 - 1)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-12*x - 79)*(-30*x**2 - 1)\nExpanding the part (-30*x**2 - 1) using the distributive property, and we got: (-30*x**2)*(-12*x - 79) - (-12*x - 79)\n#Step 2:\nCurrent expression: (-30*x**2)*(-12*x - 79) - (-12*x - 79)\nSimplifying the partial expression: -(-12*x - 79)\nExpanding the part (-12*x - 79) using the distributive property, and we got: -12*x*(-1) - 79*(-1)\nReplacing -(-12*x - 79) with -12*x*(-1) - 79*(-1) in the overall expression.\n#Step 3:\nCurrent expression: -12*x*(-1) + (-30*x**2)*(-12*x - 79) + 79\nSimplifying the partial expression: (-30*x**2)*(-12*x - 79)\nExpanding the part (-12*x - 79) using the distributive property, and we got: (-12*x)*(-30*x**2) - (-1)*2370*x**2\nReplacing (-30*x**2)*(-12*x - 79) with (-12*x)*(-30*x**2) - (-1)*2370*x**2 in the overall expression.\n#Step 4:\nCurrent expression: (-12*x)*(-30*x**2) - 12*x*(-1) - 79*(-30)*x**2 + 79\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*x)*-1 = 12*x\n (-12*x)*(-30*x**2) = 360*x**3\n -79*-30*x**2 = 2370*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 360*x**3 + 2370*x**2 + 12*x + 79\nNo more calculations needed.\n360*x**3 + 2370*x**2 + 12*x + 79", "generated_answer": "360*x**3 + 2370*x**2 + 12*x + 79", "step_length": 5} {"cot_id": "89ce5fb3677ec27c8c9dced0404bdeea068315754559e95d2d1c4b96db69c243", "datapoint": {"question": "Simplify this expression: (21*z + 23)*(31*z**3 + 41*z**2 + 26)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "651*z**4 + 1574*z**3 + 943*z**2 + 546*z + 598", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 286, "polynomial_expr": "(21*z + 23)*(31*z**3 + 41*z**2 + 26)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21*z + 23)*(31*z**3 + 41*z**2 + 26)\nExpanding the part (21*z + 23) using the distributive property, and we got: (21*z)*(31*z**3 + 41*z**2 + 26) + 23*(31*z**3 + 41*z**2 + 26)\n#Step 2:\nCurrent expression: (21*z)*(31*z**3 + 41*z**2 + 26) + 23*(31*z**3 + 41*z**2 + 26)\nSimplifying the partial expression: 23*(31*z**3 + 41*z**2 + 26)\nExpanding the part (31*z**3 + 41*z**2 + 26) using the distributive property, and we got: (41*z**2)*23 + (31*z**3)*23 + 26*23\nReplacing 23*(31*z**3 + 41*z**2 + 26) with (41*z**2)*23 + (31*z**3)*23 + 26*23 in the overall expression.\n#Step 3:\nCurrent expression: (21*z)*(31*z**3 + 41*z**2 + 26) + (41*z**2)*23 + (31*z**3)*23 + 598\nSimplifying the partial expression: (21*z)*(31*z**3 + 41*z**2 + 26)\nExpanding the part (31*z**3 + 41*z**2 + 26) using the distributive property, and we got: 26*(21*z) + (21*z)*(41*z**2) + (21*z)*(31*z**3)\nReplacing (21*z)*(31*z**3 + 41*z**2 + 26) with 26*(21*z) + (21*z)*(41*z**2) + (21*z)*(31*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 26*21*z + (21*z)*(41*z**2) + (21*z)*(31*z**3) + (41*z**2)*23 + (31*z**3)*23 + 598\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (31*z**3)*23 = 713*z**3\n (31*z**3)*(21*z) = 651*z**4\n (41*z**2)*23 = 943*z**2\n (41*z**2)*(21*z) = 861*z**3\n 26*21*z = 546*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 651*z**4 + 713*z**3 + 861*z**3 + 943*z**2 + 546*z + 598\nCombining like terms, got 651*z**4 + 1574*z**3 + 943*z**2 + 546*z + 598\n#Step 6:\nCurrent expression: 651*z**4 + 1574*z**3 + 943*z**2 + 546*z + 598\nNo more calculations needed.\n651*z**4 + 1574*z**3 + 943*z**2 + 546*z + 598", "generated_answer": "651*z**4 + 1574*z**3 + 943*z**2 + 546*z + 598", "step_length": 6} {"cot_id": "e1cf9f5ff99ece18e739beaa4510aa78a55e4fbe2e7f38ae3454ba50df2ff9d9", "datapoint": {"question": "Simplify this expression: (-16*y**3 - 7*y**2 - 44)*(-14*y**3 - 27*y**2 - 22)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "224*y**6 + 530*y**5 + 189*y**4 + 968*y**3 + 1342*y**2 + 968", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 287, "polynomial_expr": "(-16*y**3 - 7*y**2 - 44)*(-14*y**3 - 27*y**2 - 22)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-16*y**3 - 7*y**2 - 44)*(-14*y**3 - 27*y**2 - 22)\nExpanding the part (-16*y**3 - 7*y**2 - 44) using the distributive property, and we got: (-7*y**2)*(-14*y**3 - 27*y**2 - 22) + (-16*y**3)*(-14*y**3 - 27*y**2 - 22) - 44*(-14*y**3 - 27*y**2 - 22)\n#Step 2:\nCurrent expression: (-7*y**2)*(-14*y**3 - 27*y**2 - 22) + (-16*y**3)*(-14*y**3 - 27*y**2 - 22) - 44*(-14*y**3 - 27*y**2 - 22)\nSimplifying the partial expression: -44*(-14*y**3 - 27*y**2 - 22)\nExpanding the part (-14*y**3 - 27*y**2 - 22) using the distributive property, and we got: -27*y**2*(-44) - 14*y**3*(-44) - 22*(-44)\nReplacing -44*(-14*y**3 - 27*y**2 - 22) with -27*y**2*(-44) - 14*y**3*(-44) - 22*(-44) in the overall expression.\n#Step 3:\nCurrent expression: -27*y**2*(-44) + (-7*y**2)*(-14*y**3 - 27*y**2 - 22) + (-16*y**3)*(-14*y**3 - 27*y**2 - 22) - 14*y**3*(-44) + 968\nSimplifying the partial expression: (-16*y**3)*(-14*y**3 - 27*y**2 - 22)\nExpanding the part (-14*y**3 - 27*y**2 - 22) using the distributive property, and we got: -(-1)*352*y**3 + (-27*y**2)*(-16*y**3) + (-16*y**3)*(-14*y**3)\nReplacing (-16*y**3)*(-14*y**3 - 27*y**2 - 22) with -(-1)*352*y**3 + (-27*y**2)*(-16*y**3) + (-16*y**3)*(-14*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -22*(-16)*y**3 + (-27*y**2)*(-16*y**3) - 27*y**2*(-44) + (-7*y**2)*(-14*y**3 - 27*y**2 - 22) + (-16*y**3)*(-14*y**3) - 14*y**3*(-44) + 968\nSimplifying the partial expression: (-7*y**2)*(-14*y**3 - 27*y**2 - 22)\nExpanding the part (-14*y**3 - 27*y**2 - 22) using the distributive property, and we got: -(-1)*154*y**2 + (-27*y**2)*(-7*y**2) + (-7*y**2)*(-14*y**3)\nReplacing (-7*y**2)*(-14*y**3 - 27*y**2 - 22) with -(-1)*154*y**2 + (-27*y**2)*(-7*y**2) + (-7*y**2)*(-14*y**3) in the overall expression.\n#Step 5:\nCurrent expression: -22*(-16)*y**3 - 22*(-7)*y**2 + (-27*y**2)*(-7*y**2) + (-27*y**2)*(-16*y**3) - 27*y**2*(-44) + (-7*y**2)*(-14*y**3) + (-16*y**3)*(-14*y**3) - 14*y**3*(-44) + 968\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*y**2)*-44 = 1188*y**2\n (-27*y**2)*(-16*y**3) = 432*y**5\n (-27*y**2)*(-7*y**2) = 189*y**4\n (-14*y**3)*-44 = 616*y**3\n (-14*y**3)*(-16*y**3) = 224*y**6\n (-14*y**3)*(-7*y**2) = 98*y**5\n -22*-16*y**3 = 352*y**3\n -22*-7*y**2 = 154*y**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 224*y**6 + 98*y**5 + 432*y**5 + 189*y**4 + 352*y**3 + 616*y**3 + 154*y**2 + 1188*y**2 + 968\nCombining like terms, got 224*y**6 + 530*y**5 + 189*y**4 + 968*y**3 + 1342*y**2 + 968\n#Step 7:\nCurrent expression: 224*y**6 + 530*y**5 + 189*y**4 + 968*y**3 + 1342*y**2 + 968\nNo more calculations needed.\n224*y**6 + 530*y**5 + 189*y**4 + 968*y**3 + 1342*y**2 + 968", "generated_answer": "224*y**6 + 530*y**5 + 189*y**4 + 968*y**3 + 1342*y**2 + 968", "step_length": 7} {"cot_id": "eb3f6f1733ffbf210db8e4153f191f9f62682b1392543d8e441d0b90f018a247", "datapoint": {"question": "Calculate the following: (-26*z**3 + 33*z)*(38*z**3 - 6*z**2 - 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-988*z**6 + 156*z**5 + 1254*z**4 + 868*z**3 - 1353*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 288, "polynomial_expr": "(-26*z**3 + 33*z)*(38*z**3 - 6*z**2 - 41)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-26*z**3 + 33*z)*(38*z**3 - 6*z**2 - 41)\nExpanding the part (-26*z**3 + 33*z) using the distributive property, and we got: (33*z)*(38*z**3 - 6*z**2 - 41) + (-26*z**3)*(38*z**3 - 6*z**2 - 41)\n#Step 2:\nCurrent expression: (33*z)*(38*z**3 - 6*z**2 - 41) + (-26*z**3)*(38*z**3 - 6*z**2 - 41)\nSimplifying the partial expression: (-26*z**3)*(38*z**3 - 6*z**2 - 41)\nExpanding the part (38*z**3 - 6*z**2 - 41) using the distributive property, and we got: -(-1)*1066*z**3 + (-6*z**2)*(-26*z**3) + (-26*z**3)*(38*z**3)\nReplacing (-26*z**3)*(38*z**3 - 6*z**2 - 41) with -(-1)*1066*z**3 + (-6*z**2)*(-26*z**3) + (-26*z**3)*(38*z**3) in the overall expression.\n#Step 3:\nCurrent expression: -41*(-26)*z**3 + (33*z)*(38*z**3 - 6*z**2 - 41) + (-6*z**2)*(-26*z**3) + (-26*z**3)*(38*z**3)\nSimplifying the partial expression: (33*z)*(38*z**3 - 6*z**2 - 41)\nExpanding the part (38*z**3 - 6*z**2 - 41) using the distributive property, and we got: -1353*z + (33*z)*(-6*z**2) + (33*z)*(38*z**3)\nReplacing (33*z)*(38*z**3 - 6*z**2 - 41) with -1353*z + (33*z)*(-6*z**2) + (33*z)*(38*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -41*(-26)*z**3 - 41*33*z + (33*z)*(-6*z**2) + (33*z)*(38*z**3) + (-6*z**2)*(-26*z**3) + (-26*z**3)*(38*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-6*z**2)*(-26*z**3) = 156*z**5\n (-6*z**2)*(33*z) = -198*z**3\n (38*z**3)*(-26*z**3) = -988*z**6\n (38*z**3)*(33*z) = 1254*z**4\n -41*-26*z**3 = 1066*z**3\n -41*33*z = -1353*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -988*z**6 + 156*z**5 + 1254*z**4 - 198*z**3 + 1066*z**3 - 1353*z\nCombining like terms, got -988*z**6 + 156*z**5 + 1254*z**4 + 868*z**3 - 1353*z\n#Step 6:\nCurrent expression: -988*z**6 + 156*z**5 + 1254*z**4 + 868*z**3 - 1353*z\nNo more calculations needed.\n-988*z**6 + 156*z**5 + 1254*z**4 + 868*z**3 - 1353*z", "generated_answer": "-988*z**6 + 156*z**5 + 1254*z**4 + 868*z**3 - 1353*z", "step_length": 6} {"cot_id": "bd1d88c5d4dc74c082cb1487ccbe07d51887f6d36857270f98c6977878409ee5", "datapoint": {"question": "Simplify this expression: (-19*z**2 + 82*z)*(16*z**3 + 30*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-304*z**5 + 1312*z**4 - 570*z**3 + 2460*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 289, "polynomial_expr": "(-19*z**2 + 82*z)*(16*z**3 + 30*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-19*z**2 + 82*z)*(16*z**3 + 30*z)\nExpanding the part (-19*z**2 + 82*z) using the distributive property, and we got: (82*z)*(16*z**3 + 30*z) + (-19*z**2)*(16*z**3 + 30*z)\n#Step 2:\nCurrent expression: (82*z)*(16*z**3 + 30*z) + (-19*z**2)*(16*z**3 + 30*z)\nSimplifying the partial expression: (-19*z**2)*(16*z**3 + 30*z)\nExpanding the part (16*z**3 + 30*z) using the distributive property, and we got: (30*z)*(-19*z**2) + (-19*z**2)*(16*z**3)\nReplacing (-19*z**2)*(16*z**3 + 30*z) with (30*z)*(-19*z**2) + (-19*z**2)*(16*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (30*z)*(-19*z**2) + (82*z)*(16*z**3 + 30*z) + (-19*z**2)*(16*z**3)\nSimplifying the partial expression: (82*z)*(16*z**3 + 30*z)\nExpanding the part (16*z**3 + 30*z) using the distributive property, and we got: (30*z)*(82*z) + (82*z)*(16*z**3)\nReplacing (82*z)*(16*z**3 + 30*z) with (30*z)*(82*z) + (82*z)*(16*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (30*z)*(82*z) + (30*z)*(-19*z**2) + (82*z)*(16*z**3) + (-19*z**2)*(16*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (16*z**3)*(-19*z**2) = -304*z**5\n (16*z**3)*(82*z) = 1312*z**4\n (30*z)*(-19*z**2) = -570*z**3\n (30*z)*(82*z) = 2460*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -304*z**5 + 1312*z**4 - 570*z**3 + 2460*z**2\nNo more calculations needed.\n-304*z**5 + 1312*z**4 - 570*z**3 + 2460*z**2", "generated_answer": "-304*z**5 + 1312*z**4 - 570*z**3 + 2460*z**2", "step_length": 5} {"cot_id": "09dcc66c3c7fd44aa8997d7655b178c2680fd2b2c3a2f6231372790f9e29a3ef", "datapoint": {"question": "Simplify this expression: (23 - 38*x**3)*(3*x**3 + 42*x - 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-114*x**6 - 1596*x**4 + 1399*x**3 + 966*x - 805", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 290, "polynomial_expr": "(23 - 38*x**3)*(3*x**3 + 42*x - 35)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (23 - 38*x**3)*(3*x**3 + 42*x - 35)\nExpanding the part (23 - 38*x**3) using the distributive property, and we got: (-38*x**3)*(3*x**3 + 42*x - 35) + 23*(3*x**3 + 42*x - 35)\n#Step 2:\nCurrent expression: (-38*x**3)*(3*x**3 + 42*x - 35) + 23*(3*x**3 + 42*x - 35)\nSimplifying the partial expression: 23*(3*x**3 + 42*x - 35)\nExpanding the part (3*x**3 + 42*x - 35) using the distributive property, and we got: (42*x)*23 + (3*x**3)*23 - 35*23\nReplacing 23*(3*x**3 + 42*x - 35) with (42*x)*23 + (3*x**3)*23 - 35*23 in the overall expression.\n#Step 3:\nCurrent expression: (42*x)*23 + (-38*x**3)*(3*x**3 + 42*x - 35) + (3*x**3)*23 - 805\nSimplifying the partial expression: (-38*x**3)*(3*x**3 + 42*x - 35)\nExpanding the part (3*x**3 + 42*x - 35) using the distributive property, and we got: -(-1)*1330*x**3 + (42*x)*(-38*x**3) + (-38*x**3)*(3*x**3)\nReplacing (-38*x**3)*(3*x**3 + 42*x - 35) with -(-1)*1330*x**3 + (42*x)*(-38*x**3) + (-38*x**3)*(3*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -35*(-38)*x**3 + (42*x)*(-38*x**3) + (42*x)*23 + (-38*x**3)*(3*x**3) + (3*x**3)*23 - 805\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (3*x**3)*23 = 69*x**3\n (3*x**3)*(-38*x**3) = -114*x**6\n (42*x)*23 = 966*x\n (42*x)*(-38*x**3) = -1596*x**4\n -35*-38*x**3 = 1330*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -114*x**6 - 1596*x**4 + 69*x**3 + 1330*x**3 + 966*x - 805\nCombining like terms, got -114*x**6 - 1596*x**4 + 1399*x**3 + 966*x - 805\n#Step 6:\nCurrent expression: -114*x**6 - 1596*x**4 + 1399*x**3 + 966*x - 805\nNo more calculations needed.\n-114*x**6 - 1596*x**4 + 1399*x**3 + 966*x - 805", "generated_answer": "-114*x**6 - 1596*x**4 + 1399*x**3 + 966*x - 805", "step_length": 6} {"cot_id": "31acf8ed8b3c317c50d8209d89906e0cecf503c7e44b2d41d3c19805bb4e5ba0", "datapoint": {"question": "Calculate the following: (-14*z**2 - 19*z)*(-28*z**3 + 17*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "392*z**5 + 294*z**4 - 323*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 291, "polynomial_expr": "(-14*z**2 - 19*z)*(-28*z**3 + 17*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-14*z**2 - 19*z)*(-28*z**3 + 17*z**2)\nExpanding the part (-28*z**3 + 17*z**2) using the distributive property, and we got: (17*z**2)*(-14*z**2 - 19*z) + (-28*z**3)*(-14*z**2 - 19*z)\n#Step 2:\nCurrent expression: (17*z**2)*(-14*z**2 - 19*z) + (-28*z**3)*(-14*z**2 - 19*z)\nSimplifying the partial expression: (-28*z**3)*(-14*z**2 - 19*z)\nExpanding the part (-14*z**2 - 19*z) using the distributive property, and we got: (-19*z)*(-28*z**3) + (-14*z**2)*(-28*z**3)\nReplacing (-28*z**3)*(-14*z**2 - 19*z) with (-19*z)*(-28*z**3) + (-14*z**2)*(-28*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-19*z)*(-28*z**3) + (-14*z**2)*(-28*z**3) + (17*z**2)*(-14*z**2 - 19*z)\nSimplifying the partial expression: (17*z**2)*(-14*z**2 - 19*z)\nExpanding the part (-14*z**2 - 19*z) using the distributive property, and we got: (-19*z)*(17*z**2) + (-14*z**2)*(17*z**2)\nReplacing (17*z**2)*(-14*z**2 - 19*z) with (-19*z)*(17*z**2) + (-14*z**2)*(17*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-19*z)*(17*z**2) + (-19*z)*(-28*z**3) + (-14*z**2)*(17*z**2) + (-14*z**2)*(-28*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*z)*(-28*z**3) = 532*z**4\n (-19*z)*(17*z**2) = -323*z**3\n (-14*z**2)*(-28*z**3) = 392*z**5\n (-14*z**2)*(17*z**2) = -238*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 392*z**5 - 238*z**4 + 532*z**4 - 323*z**3\nCombining like terms, got 392*z**5 + 294*z**4 - 323*z**3\n#Step 6:\nCurrent expression: 392*z**5 + 294*z**4 - 323*z**3\nNo more calculations needed.\n392*z**5 + 294*z**4 - 323*z**3", "generated_answer": "392*z**5 + 294*z**4 - 323*z**3", "step_length": 6} {"cot_id": "0cd0469a72f70afebea69389045d2f84b60e000ad3477358e368f7115da544db", "datapoint": {"question": "Calculate the following: (-6*x - 35)*(17*x**3 + 9*x**2 - 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-102*x**4 - 649*x**3 - 315*x**2 + 144*x + 840", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 292, "polynomial_expr": "(-6*x - 35)*(17*x**3 + 9*x**2 - 24)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-6*x - 35)*(17*x**3 + 9*x**2 - 24)\nExpanding the part (-6*x - 35) using the distributive property, and we got: (-6*x)*(17*x**3 + 9*x**2 - 24) - 35*(17*x**3 + 9*x**2 - 24)\n#Step 2:\nCurrent expression: (-6*x)*(17*x**3 + 9*x**2 - 24) - 35*(17*x**3 + 9*x**2 - 24)\nSimplifying the partial expression: -35*(17*x**3 + 9*x**2 - 24)\nExpanding the part (17*x**3 + 9*x**2 - 24) using the distributive property, and we got: (9*x**2)*(-35) + (17*x**3)*(-35) - 24*(-35)\nReplacing -35*(17*x**3 + 9*x**2 - 24) with (9*x**2)*(-35) + (17*x**3)*(-35) - 24*(-35) in the overall expression.\n#Step 3:\nCurrent expression: (-6*x)*(17*x**3 + 9*x**2 - 24) + (9*x**2)*(-35) + (17*x**3)*(-35) + 840\nSimplifying the partial expression: (-6*x)*(17*x**3 + 9*x**2 - 24)\nExpanding the part (17*x**3 + 9*x**2 - 24) using the distributive property, and we got: (-6*x)*(9*x**2) + (-6*x)*(17*x**3) - (-1)*144*x\nReplacing (-6*x)*(17*x**3 + 9*x**2 - 24) with (-6*x)*(9*x**2) + (-6*x)*(17*x**3) - (-1)*144*x in the overall expression.\n#Step 4:\nCurrent expression: (-6*x)*(9*x**2) + (-6*x)*(17*x**3) - 24*(-6)*x + (9*x**2)*(-35) + (17*x**3)*(-35) + 840\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (9*x**2)*-35 = -315*x**2\n (9*x**2)*(-6*x) = -54*x**3\n (17*x**3)*-35 = -595*x**3\n (17*x**3)*(-6*x) = -102*x**4\n -24*-6*x = 144*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -102*x**4 - 595*x**3 - 54*x**3 - 315*x**2 + 144*x + 840\nCombining like terms, got -102*x**4 - 649*x**3 - 315*x**2 + 144*x + 840\n#Step 6:\nCurrent expression: -102*x**4 - 649*x**3 - 315*x**2 + 144*x + 840\nNo more calculations needed.\n-102*x**4 - 649*x**3 - 315*x**2 + 144*x + 840", "generated_answer": "-102*x**4 - 649*x**3 - 315*x**2 + 144*x + 840", "step_length": 6} {"cot_id": "77b82eaba5438eb59712d11d5c40ce74cffca23d5896bddca637361f913d5186", "datapoint": {"question": "Calculate the following: (63*x**3 - 49*x)*(-30*x**3 - 15*x**2 + 22*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1890*x**6 - 945*x**5 + 2856*x**4 + 735*x**3 - 1078*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 293, "polynomial_expr": "(63*x**3 - 49*x)*(-30*x**3 - 15*x**2 + 22*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (63*x**3 - 49*x)*(-30*x**3 - 15*x**2 + 22*x)\nExpanding the part (63*x**3 - 49*x) using the distributive property, and we got: (-49*x)*(-30*x**3 - 15*x**2 + 22*x) + (63*x**3)*(-30*x**3 - 15*x**2 + 22*x)\n#Step 2:\nCurrent expression: (-49*x)*(-30*x**3 - 15*x**2 + 22*x) + (63*x**3)*(-30*x**3 - 15*x**2 + 22*x)\nSimplifying the partial expression: (-49*x)*(-30*x**3 - 15*x**2 + 22*x)\nExpanding the part (-30*x**3 - 15*x**2 + 22*x) using the distributive property, and we got: (-49*x)*(22*x) + (-49*x)*(-15*x**2) + (-49*x)*(-30*x**3)\nReplacing (-49*x)*(-30*x**3 - 15*x**2 + 22*x) with (-49*x)*(22*x) + (-49*x)*(-15*x**2) + (-49*x)*(-30*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-49*x)*(22*x) + (-49*x)*(-15*x**2) + (-49*x)*(-30*x**3) + (63*x**3)*(-30*x**3 - 15*x**2 + 22*x)\nSimplifying the partial expression: (63*x**3)*(-30*x**3 - 15*x**2 + 22*x)\nExpanding the part (-30*x**3 - 15*x**2 + 22*x) using the distributive property, and we got: (22*x)*(63*x**3) + (-15*x**2)*(63*x**3) + (-30*x**3)*(63*x**3)\nReplacing (63*x**3)*(-30*x**3 - 15*x**2 + 22*x) with (22*x)*(63*x**3) + (-15*x**2)*(63*x**3) + (-30*x**3)*(63*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-49*x)*(22*x) + (-49*x)*(-15*x**2) + (-49*x)*(-30*x**3) + (22*x)*(63*x**3) + (-15*x**2)*(63*x**3) + (-30*x**3)*(63*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*x**3)*(-49*x) = 1470*x**4\n (-30*x**3)*(63*x**3) = -1890*x**6\n (-15*x**2)*(-49*x) = 735*x**3\n (-15*x**2)*(63*x**3) = -945*x**5\n (22*x)*(-49*x) = -1078*x**2\n (22*x)*(63*x**3) = 1386*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1890*x**6 - 945*x**5 + 1386*x**4 + 1470*x**4 + 735*x**3 - 1078*x**2\nCombining like terms, got -1890*x**6 - 945*x**5 + 2856*x**4 + 735*x**3 - 1078*x**2\n#Step 6:\nCurrent expression: -1890*x**6 - 945*x**5 + 2856*x**4 + 735*x**3 - 1078*x**2\nNo more calculations needed.\n-1890*x**6 - 945*x**5 + 2856*x**4 + 735*x**3 - 1078*x**2", "generated_answer": "-1890*x**6 - 945*x**5 + 2856*x**4 + 735*x**3 - 1078*x**2", "step_length": 6} {"cot_id": "94995ed8740ac88d10167351b29c4b5c4335955fb7dc66757354c83d71867fc1", "datapoint": {"question": "Simplify this expression: (35*x**2 + 48)*(-3*x**3 - 69*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-105*x**5 - 2415*x**4 - 144*x**3 - 3312*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 294, "polynomial_expr": "(35*x**2 + 48)*(-3*x**3 - 69*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (35*x**2 + 48)*(-3*x**3 - 69*x**2)\nExpanding the part (35*x**2 + 48) using the distributive property, and we got: (35*x**2)*(-3*x**3 - 69*x**2) + 48*(-3*x**3 - 69*x**2)\n#Step 2:\nCurrent expression: (35*x**2)*(-3*x**3 - 69*x**2) + 48*(-3*x**3 - 69*x**2)\nSimplifying the partial expression: 48*(-3*x**3 - 69*x**2)\nExpanding the part (-3*x**3 - 69*x**2) using the distributive property, and we got: -69*x**2*48 - 3*x**3*48\nReplacing 48*(-3*x**3 - 69*x**2) with -69*x**2*48 - 3*x**3*48 in the overall expression.\n#Step 3:\nCurrent expression: -69*x**2*48 + (35*x**2)*(-3*x**3 - 69*x**2) - 3*x**3*48\nSimplifying the partial expression: (35*x**2)*(-3*x**3 - 69*x**2)\nExpanding the part (-3*x**3 - 69*x**2) using the distributive property, and we got: (-69*x**2)*(35*x**2) + (35*x**2)*(-3*x**3)\nReplacing (35*x**2)*(-3*x**3 - 69*x**2) with (-69*x**2)*(35*x**2) + (35*x**2)*(-3*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-69*x**2)*(35*x**2) - 69*x**2*48 + (35*x**2)*(-3*x**3) - 3*x**3*48\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-69*x**2)*48 = -3312*x**2\n (-69*x**2)*(35*x**2) = -2415*x**4\n (-3*x**3)*48 = -144*x**3\n (-3*x**3)*(35*x**2) = -105*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -105*x**5 - 2415*x**4 - 144*x**3 - 3312*x**2\nNo more calculations needed.\n-105*x**5 - 2415*x**4 - 144*x**3 - 3312*x**2", "generated_answer": "-105*x**5 - 2415*x**4 - 144*x**3 - 3312*x**2", "step_length": 5} {"cot_id": "c6abbff0589590cfcc93920a865b21fba10fb452805a9c695b96d4006d462083", "datapoint": {"question": "Calculate the following: 182*x**2 - 56*x\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "182*x**2 - 56*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 295, "polynomial_expr": "182*x**2 - 56*x", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 182*x**2 - 56*x\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 182*x**2 - 56*x\nNo more calculations needed.\n182*x**2 - 56*x", "generated_answer": "182*x**2 - 56*x", "step_length": 2} {"cot_id": "299edd0bd86c33977d253ff570ee55e88e8a6eb4a9892619231f23063d4e0eec", "datapoint": {"question": "Simplify this expression: (-34*x - 21)*(16*x**3 + 45*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-544*x**4 - 336*x**3 - 1530*x**2 - 945*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 296, "polynomial_expr": "(-34*x - 21)*(16*x**3 + 45*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-34*x - 21)*(16*x**3 + 45*x)\nExpanding the part (-34*x - 21) using the distributive property, and we got: (-34*x)*(16*x**3 + 45*x) - 21*(16*x**3 + 45*x)\n#Step 2:\nCurrent expression: (-34*x)*(16*x**3 + 45*x) - 21*(16*x**3 + 45*x)\nSimplifying the partial expression: -21*(16*x**3 + 45*x)\nExpanding the part (16*x**3 + 45*x) using the distributive property, and we got: (45*x)*(-21) + (16*x**3)*(-21)\nReplacing -21*(16*x**3 + 45*x) with (45*x)*(-21) + (16*x**3)*(-21) in the overall expression.\n#Step 3:\nCurrent expression: (-34*x)*(16*x**3 + 45*x) + (45*x)*(-21) + (16*x**3)*(-21)\nSimplifying the partial expression: (-34*x)*(16*x**3 + 45*x)\nExpanding the part (16*x**3 + 45*x) using the distributive property, and we got: (-34*x)*(45*x) + (-34*x)*(16*x**3)\nReplacing (-34*x)*(16*x**3 + 45*x) with (-34*x)*(45*x) + (-34*x)*(16*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-34*x)*(45*x) + (-34*x)*(16*x**3) + (45*x)*(-21) + (16*x**3)*(-21)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (16*x**3)*-21 = -336*x**3\n (16*x**3)*(-34*x) = -544*x**4\n (45*x)*-21 = -945*x\n (45*x)*(-34*x) = -1530*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -544*x**4 - 336*x**3 - 1530*x**2 - 945*x\nNo more calculations needed.\n-544*x**4 - 336*x**3 - 1530*x**2 - 945*x", "generated_answer": "-544*x**4 - 336*x**3 - 1530*x**2 - 945*x", "step_length": 5} {"cot_id": "0c077b1d960a870b19892ba88afff4b249262ea11873346e4229515920a30401", "datapoint": {"question": "Calculate the following: (-40*x**3 - 5*x**2)*(57*x**3 + 3*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2280*x**6 - 285*x**5 - 120*x**4 - 15*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 297, "polynomial_expr": "(-40*x**3 - 5*x**2)*(57*x**3 + 3*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-40*x**3 - 5*x**2)*(57*x**3 + 3*x)\nExpanding the part (-40*x**3 - 5*x**2) using the distributive property, and we got: (-5*x**2)*(57*x**3 + 3*x) + (-40*x**3)*(57*x**3 + 3*x)\n#Step 2:\nCurrent expression: (-5*x**2)*(57*x**3 + 3*x) + (-40*x**3)*(57*x**3 + 3*x)\nSimplifying the partial expression: (-40*x**3)*(57*x**3 + 3*x)\nExpanding the part (57*x**3 + 3*x) using the distributive property, and we got: (3*x)*(-40*x**3) + (-40*x**3)*(57*x**3)\nReplacing (-40*x**3)*(57*x**3 + 3*x) with (3*x)*(-40*x**3) + (-40*x**3)*(57*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (3*x)*(-40*x**3) + (-5*x**2)*(57*x**3 + 3*x) + (-40*x**3)*(57*x**3)\nSimplifying the partial expression: (-5*x**2)*(57*x**3 + 3*x)\nExpanding the part (57*x**3 + 3*x) using the distributive property, and we got: (3*x)*(-5*x**2) + (-5*x**2)*(57*x**3)\nReplacing (-5*x**2)*(57*x**3 + 3*x) with (3*x)*(-5*x**2) + (-5*x**2)*(57*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (3*x)*(-5*x**2) + (3*x)*(-40*x**3) + (-5*x**2)*(57*x**3) + (-40*x**3)*(57*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (3*x)*(-40*x**3) = -120*x**4\n (3*x)*(-5*x**2) = -15*x**3\n (57*x**3)*(-40*x**3) = -2280*x**6\n (57*x**3)*(-5*x**2) = -285*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2280*x**6 - 285*x**5 - 120*x**4 - 15*x**3\nNo more calculations needed.\n-2280*x**6 - 285*x**5 - 120*x**4 - 15*x**3", "generated_answer": "-2280*x**6 - 285*x**5 - 120*x**4 - 15*x**3", "step_length": 5} {"cot_id": "472fd9631ba7e56a24e4f1cf483d6b08094d3e8a7d10ead5a6886e031c32464a", "datapoint": {"question": "Calculate the following: (-18*y**3 - 12)*(35*y**3 + 36*y**2 - 46*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-630*y**6 - 648*y**5 + 828*y**4 - 420*y**3 - 432*y**2 + 552*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 298, "polynomial_expr": "(-18*y**3 - 12)*(35*y**3 + 36*y**2 - 46*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-18*y**3 - 12)*(35*y**3 + 36*y**2 - 46*y)\nExpanding the part (-18*y**3 - 12) using the distributive property, and we got: (-18*y**3)*(35*y**3 + 36*y**2 - 46*y) - 12*(35*y**3 + 36*y**2 - 46*y)\n#Step 2:\nCurrent expression: (-18*y**3)*(35*y**3 + 36*y**2 - 46*y) - 12*(35*y**3 + 36*y**2 - 46*y)\nSimplifying the partial expression: -12*(35*y**3 + 36*y**2 - 46*y)\nExpanding the part (35*y**3 + 36*y**2 - 46*y) using the distributive property, and we got: -46*y*(-12) + (36*y**2)*(-12) + (35*y**3)*(-12)\nReplacing -12*(35*y**3 + 36*y**2 - 46*y) with -46*y*(-12) + (36*y**2)*(-12) + (35*y**3)*(-12) in the overall expression.\n#Step 3:\nCurrent expression: -46*y*(-12) + (36*y**2)*(-12) + (-18*y**3)*(35*y**3 + 36*y**2 - 46*y) + (35*y**3)*(-12)\nSimplifying the partial expression: (-18*y**3)*(35*y**3 + 36*y**2 - 46*y)\nExpanding the part (35*y**3 + 36*y**2 - 46*y) using the distributive property, and we got: (-46*y)*(-18*y**3) + (36*y**2)*(-18*y**3) + (-18*y**3)*(35*y**3)\nReplacing (-18*y**3)*(35*y**3 + 36*y**2 - 46*y) with (-46*y)*(-18*y**3) + (36*y**2)*(-18*y**3) + (-18*y**3)*(35*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-46*y)*(-18*y**3) - 46*y*(-12) + (36*y**2)*(-18*y**3) + (36*y**2)*(-12) + (-18*y**3)*(35*y**3) + (35*y**3)*(-12)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*y)*-12 = 552*y\n (-46*y)*(-18*y**3) = 828*y**4\n (35*y**3)*-12 = -420*y**3\n (35*y**3)*(-18*y**3) = -630*y**6\n (36*y**2)*-12 = -432*y**2\n (36*y**2)*(-18*y**3) = -648*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -630*y**6 - 648*y**5 + 828*y**4 - 420*y**3 - 432*y**2 + 552*y\nNo more calculations needed.\n-630*y**6 - 648*y**5 + 828*y**4 - 420*y**3 - 432*y**2 + 552*y", "generated_answer": "-630*y**6 - 648*y**5 + 828*y**4 - 420*y**3 - 432*y**2 + 552*y", "step_length": 5} {"cot_id": "e06322a3175fa418f1ecc46dd526ed89b834f1ead296980f1fbcca65ca0581f0", "datapoint": {"question": "Simplify this expression: (-7*z**3 + 5*z)*(5*z**3 - 17*z**2 + 36*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-35*z**6 + 119*z**5 - 227*z**4 - 85*z**3 + 180*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 299, "polynomial_expr": "(-7*z**3 + 5*z)*(5*z**3 - 17*z**2 + 36*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-7*z**3 + 5*z)*(5*z**3 - 17*z**2 + 36*z)\nExpanding the part (-7*z**3 + 5*z) using the distributive property, and we got: (5*z)*(5*z**3 - 17*z**2 + 36*z) + (-7*z**3)*(5*z**3 - 17*z**2 + 36*z)\n#Step 2:\nCurrent expression: (5*z)*(5*z**3 - 17*z**2 + 36*z) + (-7*z**3)*(5*z**3 - 17*z**2 + 36*z)\nSimplifying the partial expression: (-7*z**3)*(5*z**3 - 17*z**2 + 36*z)\nExpanding the part (5*z**3 - 17*z**2 + 36*z) using the distributive property, and we got: (36*z)*(-7*z**3) + (-17*z**2)*(-7*z**3) + (-7*z**3)*(5*z**3)\nReplacing (-7*z**3)*(5*z**3 - 17*z**2 + 36*z) with (36*z)*(-7*z**3) + (-17*z**2)*(-7*z**3) + (-7*z**3)*(5*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (5*z)*(5*z**3 - 17*z**2 + 36*z) + (36*z)*(-7*z**3) + (-17*z**2)*(-7*z**3) + (-7*z**3)*(5*z**3)\nSimplifying the partial expression: (5*z)*(5*z**3 - 17*z**2 + 36*z)\nExpanding the part (5*z**3 - 17*z**2 + 36*z) using the distributive property, and we got: (5*z)*(36*z) + (5*z)*(-17*z**2) + (5*z)*(5*z**3)\nReplacing (5*z)*(5*z**3 - 17*z**2 + 36*z) with (5*z)*(36*z) + (5*z)*(-17*z**2) + (5*z)*(5*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (5*z)*(36*z) + (5*z)*(-17*z**2) + (5*z)*(5*z**3) + (36*z)*(-7*z**3) + (-17*z**2)*(-7*z**3) + (-7*z**3)*(5*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-17*z**2)*(-7*z**3) = 119*z**5\n (-17*z**2)*(5*z) = -85*z**3\n (5*z**3)*(-7*z**3) = -35*z**6\n (5*z**3)*(5*z) = 25*z**4\n (36*z)*(-7*z**3) = -252*z**4\n (36*z)*(5*z) = 180*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -35*z**6 + 119*z**5 - 252*z**4 + 25*z**4 - 85*z**3 + 180*z**2\nCombining like terms, got -35*z**6 + 119*z**5 - 227*z**4 - 85*z**3 + 180*z**2\n#Step 6:\nCurrent expression: -35*z**6 + 119*z**5 - 227*z**4 - 85*z**3 + 180*z**2\nNo more calculations needed.\n-35*z**6 + 119*z**5 - 227*z**4 - 85*z**3 + 180*z**2", "generated_answer": "-35*z**6 + 119*z**5 - 227*z**4 - 85*z**3 + 180*z**2", "step_length": 6} {"cot_id": "ae78fcaaaaa7c2308cb59c2cc8b351fa1b5206db8268be9bb6444803fbf91c8d", "datapoint": {"question": "Calculate the following: 1924*x**2 + 2288*x\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1924*x**2 + 2288*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 300, "polynomial_expr": "1924*x**2 + 2288*x", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 1924*x**2 + 2288*x\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 1924*x**2 + 2288*x\nNo more calculations needed.\n1924*x**2 + 2288*x", "generated_answer": "1924*x**2 + 2288*x", "step_length": 2} {"cot_id": "869f6ddb8f56a2846cd502774fce6b672a69cdb2a247258e14653a8419ded291", "datapoint": {"question": "Calculate the following: (18*x**2 + 2)*(-21*x**3 + 30*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-378*x**5 + 498*x**3 + 60*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 301, "polynomial_expr": "(18*x**2 + 2)*(-21*x**3 + 30*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (18*x**2 + 2)*(-21*x**3 + 30*x)\nExpanding the part (18*x**2 + 2) using the distributive property, and we got: (18*x**2)*(-21*x**3 + 30*x) + 2*(-21*x**3 + 30*x)\n#Step 2:\nCurrent expression: (18*x**2)*(-21*x**3 + 30*x) + 2*(-21*x**3 + 30*x)\nSimplifying the partial expression: 2*(-21*x**3 + 30*x)\nExpanding the part (-21*x**3 + 30*x) using the distributive property, and we got: (30*x)*2 - 21*x**3*2\nReplacing 2*(-21*x**3 + 30*x) with (30*x)*2 - 21*x**3*2 in the overall expression.\n#Step 3:\nCurrent expression: (30*x)*2 + (18*x**2)*(-21*x**3 + 30*x) - 21*x**3*2\nSimplifying the partial expression: (18*x**2)*(-21*x**3 + 30*x)\nExpanding the part (-21*x**3 + 30*x) using the distributive property, and we got: (30*x)*(18*x**2) + (18*x**2)*(-21*x**3)\nReplacing (18*x**2)*(-21*x**3 + 30*x) with (30*x)*(18*x**2) + (18*x**2)*(-21*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (30*x)*(18*x**2) + (30*x)*2 + (18*x**2)*(-21*x**3) - 21*x**3*2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-21*x**3)*2 = -42*x**3\n (-21*x**3)*(18*x**2) = -378*x**5\n (30*x)*2 = 60*x\n (30*x)*(18*x**2) = 540*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -378*x**5 - 42*x**3 + 540*x**3 + 60*x\nCombining like terms, got -378*x**5 + 498*x**3 + 60*x\n#Step 6:\nCurrent expression: -378*x**5 + 498*x**3 + 60*x\nNo more calculations needed.\n-378*x**5 + 498*x**3 + 60*x", "generated_answer": "-378*x**5 + 498*x**3 + 60*x", "step_length": 6} {"cot_id": "4a096412a46d9247da42962a87de18f0e217a86af175ad5ffc1da731a6d9fcfb", "datapoint": {"question": "Simplify this expression: -47*y*(21 - 42*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1974*y**3 - 987*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 302, "polynomial_expr": "-47*y*(21 - 42*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -47*y*(21 - 42*y**2)\nExpanding the part (21 - 42*y**2) using the distributive property, and we got: (-47*y)*(-42*y**2) + 21*(-47*y)\n#Step 2:\nCurrent expression: (-47*y)*(-42*y**2) + 21*(-47*y)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 21*(-47*y) = -987*y\n (-42*y**2)*(-47*y) = 1974*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1974*y**3 - 987*y\nNo more calculations needed.\n1974*y**3 - 987*y", "generated_answer": "1974*y**3 - 987*y", "step_length": 3} {"cot_id": "a78bf306b0c334df9377ab2126d4788f1662ae2bc0d9a5a49f7610afc35f0bef", "datapoint": {"question": "Simplify this expression: (45 - 27*y**3)*(-83*y - 22)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2241*y**4 + 594*y**3 - 3735*y - 990", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 303, "polynomial_expr": "(45 - 27*y**3)*(-83*y - 22)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (45 - 27*y**3)*(-83*y - 22)\nExpanding the part (-83*y - 22) using the distributive property, and we got: (-83*y)*(45 - 27*y**3) - 22*(45 - 27*y**3)\n#Step 2:\nCurrent expression: (-83*y)*(45 - 27*y**3) - 22*(45 - 27*y**3)\nSimplifying the partial expression: -22*(45 - 27*y**3)\nExpanding the part (45 - 27*y**3) using the distributive property, and we got: -27*y**3*(-22) + 45*(-22)\nReplacing -22*(45 - 27*y**3) with -27*y**3*(-22) + 45*(-22) in the overall expression.\n#Step 3:\nCurrent expression: (-83*y)*(45 - 27*y**3) - 27*y**3*(-22) - 990\nSimplifying the partial expression: (-83*y)*(45 - 27*y**3)\nExpanding the part (45 - 27*y**3) using the distributive property, and we got: (-83*y)*(-27*y**3) + 45*(-83*y)\nReplacing (-83*y)*(45 - 27*y**3) with (-83*y)*(-27*y**3) + 45*(-83*y) in the overall expression.\n#Step 4:\nCurrent expression: (-83*y)*(-27*y**3) + 45*(-83)*y - 27*y**3*(-22) - 990\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*y**3)*-22 = 594*y**3\n (-27*y**3)*(-83*y) = 2241*y**4\n 45*-83*y = -3735*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2241*y**4 + 594*y**3 - 3735*y - 990\nNo more calculations needed.\n2241*y**4 + 594*y**3 - 3735*y - 990", "generated_answer": "2241*y**4 + 594*y**3 - 3735*y - 990", "step_length": 5} {"cot_id": "51796da2e2fd22722394d455c3a6acac4c8b558560e400bf679ce7ad9cca0698", "datapoint": {"question": "Calculate the following: (-3*z**3 - 11*z**2)*(-18*z**3 + 26*z**2 + 33*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "54*z**6 + 120*z**5 - 385*z**4 - 363*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 304, "polynomial_expr": "(-3*z**3 - 11*z**2)*(-18*z**3 + 26*z**2 + 33*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-3*z**3 - 11*z**2)*(-18*z**3 + 26*z**2 + 33*z)\nExpanding the part (-3*z**3 - 11*z**2) using the distributive property, and we got: (-11*z**2)*(-18*z**3 + 26*z**2 + 33*z) + (-3*z**3)*(-18*z**3 + 26*z**2 + 33*z)\n#Step 2:\nCurrent expression: (-11*z**2)*(-18*z**3 + 26*z**2 + 33*z) + (-3*z**3)*(-18*z**3 + 26*z**2 + 33*z)\nSimplifying the partial expression: (-11*z**2)*(-18*z**3 + 26*z**2 + 33*z)\nExpanding the part (-18*z**3 + 26*z**2 + 33*z) using the distributive property, and we got: (33*z)*(-11*z**2) + (-11*z**2)*(26*z**2) + (-11*z**2)*(-18*z**3)\nReplacing (-11*z**2)*(-18*z**3 + 26*z**2 + 33*z) with (33*z)*(-11*z**2) + (-11*z**2)*(26*z**2) + (-11*z**2)*(-18*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (33*z)*(-11*z**2) + (-11*z**2)*(26*z**2) + (-11*z**2)*(-18*z**3) + (-3*z**3)*(-18*z**3 + 26*z**2 + 33*z)\nSimplifying the partial expression: (-3*z**3)*(-18*z**3 + 26*z**2 + 33*z)\nExpanding the part (-18*z**3 + 26*z**2 + 33*z) using the distributive property, and we got: (33*z)*(-3*z**3) + (26*z**2)*(-3*z**3) + (-18*z**3)*(-3*z**3)\nReplacing (-3*z**3)*(-18*z**3 + 26*z**2 + 33*z) with (33*z)*(-3*z**3) + (26*z**2)*(-3*z**3) + (-18*z**3)*(-3*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (33*z)*(-11*z**2) + (33*z)*(-3*z**3) + (-11*z**2)*(26*z**2) + (-11*z**2)*(-18*z**3) + (26*z**2)*(-3*z**3) + (-18*z**3)*(-3*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-18*z**3)*(-11*z**2) = 198*z**5\n (-18*z**3)*(-3*z**3) = 54*z**6\n (26*z**2)*(-11*z**2) = -286*z**4\n (26*z**2)*(-3*z**3) = -78*z**5\n (33*z)*(-11*z**2) = -363*z**3\n (33*z)*(-3*z**3) = -99*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 54*z**6 - 78*z**5 + 198*z**5 - 286*z**4 - 99*z**4 - 363*z**3\nCombining like terms, got 54*z**6 + 120*z**5 - 385*z**4 - 363*z**3\n#Step 6:\nCurrent expression: 54*z**6 + 120*z**5 - 385*z**4 - 363*z**3\nNo more calculations needed.\n54*z**6 + 120*z**5 - 385*z**4 - 363*z**3", "generated_answer": "54*z**6 + 120*z**5 - 385*z**4 - 363*z**3", "step_length": 6} {"cot_id": "f84b8a70c81d135246cb2e99ff51a60e32e5685b584fe1f9b71b256bfbca4fda", "datapoint": {"question": "Calculate the following: (49*y**2 + 9)*(-28*y**3 - 17*y**2 - 16*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1372*y**5 - 833*y**4 - 1036*y**3 - 153*y**2 - 144*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 305, "polynomial_expr": "(49*y**2 + 9)*(-28*y**3 - 17*y**2 - 16*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (49*y**2 + 9)*(-28*y**3 - 17*y**2 - 16*y)\nExpanding the part (49*y**2 + 9) using the distributive property, and we got: (49*y**2)*(-28*y**3 - 17*y**2 - 16*y) + 9*(-28*y**3 - 17*y**2 - 16*y)\n#Step 2:\nCurrent expression: (49*y**2)*(-28*y**3 - 17*y**2 - 16*y) + 9*(-28*y**3 - 17*y**2 - 16*y)\nSimplifying the partial expression: 9*(-28*y**3 - 17*y**2 - 16*y)\nExpanding the part (-28*y**3 - 17*y**2 - 16*y) using the distributive property, and we got: -16*y*9 - 17*y**2*9 - 28*y**3*9\nReplacing 9*(-28*y**3 - 17*y**2 - 16*y) with -16*y*9 - 17*y**2*9 - 28*y**3*9 in the overall expression.\n#Step 3:\nCurrent expression: -16*y*9 - 17*y**2*9 + (49*y**2)*(-28*y**3 - 17*y**2 - 16*y) - 28*y**3*9\nSimplifying the partial expression: (49*y**2)*(-28*y**3 - 17*y**2 - 16*y)\nExpanding the part (-28*y**3 - 17*y**2 - 16*y) using the distributive property, and we got: (-16*y)*(49*y**2) + (-17*y**2)*(49*y**2) + (49*y**2)*(-28*y**3)\nReplacing (49*y**2)*(-28*y**3 - 17*y**2 - 16*y) with (-16*y)*(49*y**2) + (-17*y**2)*(49*y**2) + (49*y**2)*(-28*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-16*y)*(49*y**2) - 16*y*9 + (-17*y**2)*(49*y**2) - 17*y**2*9 + (49*y**2)*(-28*y**3) - 28*y**3*9\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*y**3)*9 = -252*y**3\n (-28*y**3)*(49*y**2) = -1372*y**5\n (-17*y**2)*9 = -153*y**2\n (-17*y**2)*(49*y**2) = -833*y**4\n (-16*y)*9 = -144*y\n (-16*y)*(49*y**2) = -784*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1372*y**5 - 833*y**4 - 784*y**3 - 252*y**3 - 153*y**2 - 144*y\nCombining like terms, got -1372*y**5 - 833*y**4 - 1036*y**3 - 153*y**2 - 144*y\n#Step 6:\nCurrent expression: -1372*y**5 - 833*y**4 - 1036*y**3 - 153*y**2 - 144*y\nNo more calculations needed.\n-1372*y**5 - 833*y**4 - 1036*y**3 - 153*y**2 - 144*y", "generated_answer": "-1372*y**5 - 833*y**4 - 1036*y**3 - 153*y**2 - 144*y", "step_length": 6} {"cot_id": "ad3f7314e76d4acd8b12a540d8ea02715ef7adb897f46c8f7005d6e03ad81d73", "datapoint": {"question": "Calculate the following: (16*y**2 + 6)*(-23*y**3 + 29*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-368*y**5 + 326*y**3 + 174*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 306, "polynomial_expr": "(16*y**2 + 6)*(-23*y**3 + 29*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (16*y**2 + 6)*(-23*y**3 + 29*y)\nExpanding the part (16*y**2 + 6) using the distributive property, and we got: (16*y**2)*(-23*y**3 + 29*y) + 6*(-23*y**3 + 29*y)\n#Step 2:\nCurrent expression: (16*y**2)*(-23*y**3 + 29*y) + 6*(-23*y**3 + 29*y)\nSimplifying the partial expression: 6*(-23*y**3 + 29*y)\nExpanding the part (-23*y**3 + 29*y) using the distributive property, and we got: (29*y)*6 - 23*y**3*6\nReplacing 6*(-23*y**3 + 29*y) with (29*y)*6 - 23*y**3*6 in the overall expression.\n#Step 3:\nCurrent expression: (29*y)*6 + (16*y**2)*(-23*y**3 + 29*y) - 23*y**3*6\nSimplifying the partial expression: (16*y**2)*(-23*y**3 + 29*y)\nExpanding the part (-23*y**3 + 29*y) using the distributive property, and we got: (29*y)*(16*y**2) + (16*y**2)*(-23*y**3)\nReplacing (16*y**2)*(-23*y**3 + 29*y) with (29*y)*(16*y**2) + (16*y**2)*(-23*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (29*y)*(16*y**2) + (29*y)*6 + (16*y**2)*(-23*y**3) - 23*y**3*6\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*y**3)*6 = -138*y**3\n (-23*y**3)*(16*y**2) = -368*y**5\n (29*y)*6 = 174*y\n (29*y)*(16*y**2) = 464*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -368*y**5 - 138*y**3 + 464*y**3 + 174*y\nCombining like terms, got -368*y**5 + 326*y**3 + 174*y\n#Step 6:\nCurrent expression: -368*y**5 + 326*y**3 + 174*y\nNo more calculations needed.\n-368*y**5 + 326*y**3 + 174*y", "generated_answer": "-368*y**5 + 326*y**3 + 174*y", "step_length": 6} {"cot_id": "0da36c7ede8246473b10dc47b1bdc3c6efcdc5b8a7a9aeb87548a2adfc1ceb9e", "datapoint": {"question": "Simplify this expression: (-33*y - 48)*(-34*y**3 + 48*y**2 - 40*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1122*y**4 + 48*y**3 - 984*y**2 + 1920*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 307, "polynomial_expr": "(-33*y - 48)*(-34*y**3 + 48*y**2 - 40*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-33*y - 48)*(-34*y**3 + 48*y**2 - 40*y)\nExpanding the part (-33*y - 48) using the distributive property, and we got: (-33*y)*(-34*y**3 + 48*y**2 - 40*y) - 48*(-34*y**3 + 48*y**2 - 40*y)\n#Step 2:\nCurrent expression: (-33*y)*(-34*y**3 + 48*y**2 - 40*y) - 48*(-34*y**3 + 48*y**2 - 40*y)\nSimplifying the partial expression: -48*(-34*y**3 + 48*y**2 - 40*y)\nExpanding the part (-34*y**3 + 48*y**2 - 40*y) using the distributive property, and we got: -40*y*(-48) + (48*y**2)*(-48) - 34*y**3*(-48)\nReplacing -48*(-34*y**3 + 48*y**2 - 40*y) with -40*y*(-48) + (48*y**2)*(-48) - 34*y**3*(-48) in the overall expression.\n#Step 3:\nCurrent expression: -40*y*(-48) + (-33*y)*(-34*y**3 + 48*y**2 - 40*y) + (48*y**2)*(-48) - 34*y**3*(-48)\nSimplifying the partial expression: (-33*y)*(-34*y**3 + 48*y**2 - 40*y)\nExpanding the part (-34*y**3 + 48*y**2 - 40*y) using the distributive property, and we got: (-40*y)*(-33*y) + (-33*y)*(48*y**2) + (-33*y)*(-34*y**3)\nReplacing (-33*y)*(-34*y**3 + 48*y**2 - 40*y) with (-40*y)*(-33*y) + (-33*y)*(48*y**2) + (-33*y)*(-34*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-40*y)*(-33*y) - 40*y*(-48) + (-33*y)*(48*y**2) + (-33*y)*(-34*y**3) + (48*y**2)*(-48) - 34*y**3*(-48)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*y)*-48 = 1920*y\n (-40*y)*(-33*y) = 1320*y**2\n (-34*y**3)*-48 = 1632*y**3\n (-34*y**3)*(-33*y) = 1122*y**4\n (48*y**2)*-48 = -2304*y**2\n (48*y**2)*(-33*y) = -1584*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1122*y**4 - 1584*y**3 + 1632*y**3 - 2304*y**2 + 1320*y**2 + 1920*y\nCombining like terms, got 1122*y**4 + 48*y**3 - 984*y**2 + 1920*y\n#Step 6:\nCurrent expression: 1122*y**4 + 48*y**3 - 984*y**2 + 1920*y\nNo more calculations needed.\n1122*y**4 + 48*y**3 - 984*y**2 + 1920*y", "generated_answer": "1122*y**4 + 48*y**3 - 984*y**2 + 1920*y", "step_length": 6} {"cot_id": "01508f3f93eb1e3e36cc99894ae4c762a76f0c8e4710f6c56937dc4b6fd9930e", "datapoint": {"question": "Calculate the following: (43*y - 15)*(25*y**3 - 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1075*y**4 - 375*y**3 - 2107*y + 735", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 308, "polynomial_expr": "(43*y - 15)*(25*y**3 - 49)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (43*y - 15)*(25*y**3 - 49)\nExpanding the part (25*y**3 - 49) using the distributive property, and we got: (25*y**3)*(43*y - 15) - 49*(43*y - 15)\n#Step 2:\nCurrent expression: (25*y**3)*(43*y - 15) - 49*(43*y - 15)\nSimplifying the partial expression: -49*(43*y - 15)\nExpanding the part (43*y - 15) using the distributive property, and we got: (43*y)*(-49) - 15*(-49)\nReplacing -49*(43*y - 15) with (43*y)*(-49) - 15*(-49) in the overall expression.\n#Step 3:\nCurrent expression: (43*y)*(-49) + (25*y**3)*(43*y - 15) + 735\nSimplifying the partial expression: (25*y**3)*(43*y - 15)\nExpanding the part (43*y - 15) using the distributive property, and we got: -375*y**3 + (43*y)*(25*y**3)\nReplacing (25*y**3)*(43*y - 15) with -375*y**3 + (43*y)*(25*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -15*25*y**3 + (43*y)*(25*y**3) + (43*y)*(-49) + 735\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (43*y)*-49 = -2107*y\n (43*y)*(25*y**3) = 1075*y**4\n -15*25*y**3 = -375*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1075*y**4 - 375*y**3 - 2107*y + 735\nNo more calculations needed.\n1075*y**4 - 375*y**3 - 2107*y + 735", "generated_answer": "1075*y**4 - 375*y**3 - 2107*y + 735", "step_length": 5} {"cot_id": "f52a1943983db0b0352832c533131102372ef55b63864cd7f68bd5331f31699d", "datapoint": {"question": "Calculate the following: -1650*z\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1650*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 309, "polynomial_expr": "-1650*z", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -1650*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -1650*z\nNo more calculations needed.\n-1650*z", "generated_answer": "-1650*z", "step_length": 2} {"cot_id": "37495f1e60a2cd70c0d3cd93858a741e29ec6fcf4b11a066d15c8e0c921a5f08", "datapoint": {"question": "Simplify this expression: (4*y**3 + 19*y**2)*(-8*y**3 - 13*y**2 + 30*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-32*y**6 - 204*y**5 - 127*y**4 + 570*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 310, "polynomial_expr": "(4*y**3 + 19*y**2)*(-8*y**3 - 13*y**2 + 30*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (4*y**3 + 19*y**2)*(-8*y**3 - 13*y**2 + 30*y)\nExpanding the part (4*y**3 + 19*y**2) using the distributive property, and we got: (19*y**2)*(-8*y**3 - 13*y**2 + 30*y) + (4*y**3)*(-8*y**3 - 13*y**2 + 30*y)\n#Step 2:\nCurrent expression: (19*y**2)*(-8*y**3 - 13*y**2 + 30*y) + (4*y**3)*(-8*y**3 - 13*y**2 + 30*y)\nSimplifying the partial expression: (4*y**3)*(-8*y**3 - 13*y**2 + 30*y)\nExpanding the part (-8*y**3 - 13*y**2 + 30*y) using the distributive property, and we got: (30*y)*(4*y**3) + (-13*y**2)*(4*y**3) + (-8*y**3)*(4*y**3)\nReplacing (4*y**3)*(-8*y**3 - 13*y**2 + 30*y) with (30*y)*(4*y**3) + (-13*y**2)*(4*y**3) + (-8*y**3)*(4*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (30*y)*(4*y**3) + (-13*y**2)*(4*y**3) + (19*y**2)*(-8*y**3 - 13*y**2 + 30*y) + (-8*y**3)*(4*y**3)\nSimplifying the partial expression: (19*y**2)*(-8*y**3 - 13*y**2 + 30*y)\nExpanding the part (-8*y**3 - 13*y**2 + 30*y) using the distributive property, and we got: (30*y)*(19*y**2) + (-13*y**2)*(19*y**2) + (19*y**2)*(-8*y**3)\nReplacing (19*y**2)*(-8*y**3 - 13*y**2 + 30*y) with (30*y)*(19*y**2) + (-13*y**2)*(19*y**2) + (19*y**2)*(-8*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (30*y)*(19*y**2) + (30*y)*(4*y**3) + (-13*y**2)*(19*y**2) + (-13*y**2)*(4*y**3) + (19*y**2)*(-8*y**3) + (-8*y**3)*(4*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*y**2)*(4*y**3) = -52*y**5\n (-13*y**2)*(19*y**2) = -247*y**4\n (-8*y**3)*(4*y**3) = -32*y**6\n (-8*y**3)*(19*y**2) = -152*y**5\n (30*y)*(4*y**3) = 120*y**4\n (30*y)*(19*y**2) = 570*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -32*y**6 - 152*y**5 - 52*y**5 - 247*y**4 + 120*y**4 + 570*y**3\nCombining like terms, got -32*y**6 - 204*y**5 - 127*y**4 + 570*y**3\n#Step 6:\nCurrent expression: -32*y**6 - 204*y**5 - 127*y**4 + 570*y**3\nNo more calculations needed.\n-32*y**6 - 204*y**5 - 127*y**4 + 570*y**3", "generated_answer": "-32*y**6 - 204*y**5 - 127*y**4 + 570*y**3", "step_length": 6} {"cot_id": "b7f8462babfef08a1623d18c0dfe88dc132f6495e3f78ab0b03a8f43aa9a01d1", "datapoint": {"question": "Simplify this expression: (31*x**3 + 73*x)*(-40*x**3 - 6*x**2 - 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1240*x**6 - 186*x**5 - 2920*x**4 - 1957*x**3 - 3577*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 311, "polynomial_expr": "(31*x**3 + 73*x)*(-40*x**3 - 6*x**2 - 49)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31*x**3 + 73*x)*(-40*x**3 - 6*x**2 - 49)\nExpanding the part (31*x**3 + 73*x) using the distributive property, and we got: (73*x)*(-40*x**3 - 6*x**2 - 49) + (31*x**3)*(-40*x**3 - 6*x**2 - 49)\n#Step 2:\nCurrent expression: (73*x)*(-40*x**3 - 6*x**2 - 49) + (31*x**3)*(-40*x**3 - 6*x**2 - 49)\nSimplifying the partial expression: (31*x**3)*(-40*x**3 - 6*x**2 - 49)\nExpanding the part (-40*x**3 - 6*x**2 - 49) using the distributive property, and we got: -1519*x**3 + (-6*x**2)*(31*x**3) + (-40*x**3)*(31*x**3)\nReplacing (31*x**3)*(-40*x**3 - 6*x**2 - 49) with -1519*x**3 + (-6*x**2)*(31*x**3) + (-40*x**3)*(31*x**3) in the overall expression.\n#Step 3:\nCurrent expression: -49*31*x**3 + (73*x)*(-40*x**3 - 6*x**2 - 49) + (-6*x**2)*(31*x**3) + (-40*x**3)*(31*x**3)\nSimplifying the partial expression: (73*x)*(-40*x**3 - 6*x**2 - 49)\nExpanding the part (-40*x**3 - 6*x**2 - 49) using the distributive property, and we got: -3577*x + (73*x)*(-6*x**2) + (73*x)*(-40*x**3)\nReplacing (73*x)*(-40*x**3 - 6*x**2 - 49) with -3577*x + (73*x)*(-6*x**2) + (73*x)*(-40*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -49*31*x**3 - 49*73*x + (73*x)*(-6*x**2) + (73*x)*(-40*x**3) + (-6*x**2)*(31*x**3) + (-40*x**3)*(31*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*x**3)*(31*x**3) = -1240*x**6\n (-40*x**3)*(73*x) = -2920*x**4\n (-6*x**2)*(31*x**3) = -186*x**5\n (-6*x**2)*(73*x) = -438*x**3\n -49*31*x**3 = -1519*x**3\n -49*73*x = -3577*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1240*x**6 - 186*x**5 - 2920*x**4 - 1519*x**3 - 438*x**3 - 3577*x\nCombining like terms, got -1240*x**6 - 186*x**5 - 2920*x**4 - 1957*x**3 - 3577*x\n#Step 6:\nCurrent expression: -1240*x**6 - 186*x**5 - 2920*x**4 - 1957*x**3 - 3577*x\nNo more calculations needed.\n-1240*x**6 - 186*x**5 - 2920*x**4 - 1957*x**3 - 3577*x", "generated_answer": "-1240*x**6 - 186*x**5 - 2920*x**4 - 1957*x**3 - 3577*x", "step_length": 6} {"cot_id": "b0a6af4997e0e5cc48651f565b47343abb616d0a80a4072a0765e8a8593e7d83", "datapoint": {"question": "Simplify this expression: (43*x - 41)*(15*x**3 - 19*x**2 - 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "645*x**4 - 1432*x**3 + 779*x**2 - 1333*x + 1271", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 312, "polynomial_expr": "(43*x - 41)*(15*x**3 - 19*x**2 - 31)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (43*x - 41)*(15*x**3 - 19*x**2 - 31)\nExpanding the part (43*x - 41) using the distributive property, and we got: (43*x)*(15*x**3 - 19*x**2 - 31) - 41*(15*x**3 - 19*x**2 - 31)\n#Step 2:\nCurrent expression: (43*x)*(15*x**3 - 19*x**2 - 31) - 41*(15*x**3 - 19*x**2 - 31)\nSimplifying the partial expression: -41*(15*x**3 - 19*x**2 - 31)\nExpanding the part (15*x**3 - 19*x**2 - 31) using the distributive property, and we got: -19*x**2*(-41) + (15*x**3)*(-41) - 31*(-41)\nReplacing -41*(15*x**3 - 19*x**2 - 31) with -19*x**2*(-41) + (15*x**3)*(-41) - 31*(-41) in the overall expression.\n#Step 3:\nCurrent expression: (43*x)*(15*x**3 - 19*x**2 - 31) - 19*x**2*(-41) + (15*x**3)*(-41) + 1271\nSimplifying the partial expression: (43*x)*(15*x**3 - 19*x**2 - 31)\nExpanding the part (15*x**3 - 19*x**2 - 31) using the distributive property, and we got: -1333*x + (43*x)*(-19*x**2) + (43*x)*(15*x**3)\nReplacing (43*x)*(15*x**3 - 19*x**2 - 31) with -1333*x + (43*x)*(-19*x**2) + (43*x)*(15*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -31*43*x + (43*x)*(-19*x**2) + (43*x)*(15*x**3) - 19*x**2*(-41) + (15*x**3)*(-41) + 1271\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*x**2)*-41 = 779*x**2\n (-19*x**2)*(43*x) = -817*x**3\n (15*x**3)*-41 = -615*x**3\n (15*x**3)*(43*x) = 645*x**4\n -31*43*x = -1333*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 645*x**4 - 817*x**3 - 615*x**3 + 779*x**2 - 1333*x + 1271\nCombining like terms, got 645*x**4 - 1432*x**3 + 779*x**2 - 1333*x + 1271\n#Step 6:\nCurrent expression: 645*x**4 - 1432*x**3 + 779*x**2 - 1333*x + 1271\nNo more calculations needed.\n645*x**4 - 1432*x**3 + 779*x**2 - 1333*x + 1271", "generated_answer": "645*x**4 - 1432*x**3 + 779*x**2 - 1333*x + 1271", "step_length": 6} {"cot_id": "01ad25be3ed3d11781d36cdaf6d2154e0d9b160675df8534ff393acce4c39ae9", "datapoint": {"question": "Calculate the following: (-103*x**2 - 26*x)*(47*x**3 + 25*x**2 - 10*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-4841*x**5 - 3797*x**4 + 380*x**3 + 260*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 313, "polynomial_expr": "(-103*x**2 - 26*x)*(47*x**3 + 25*x**2 - 10*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-103*x**2 - 26*x)*(47*x**3 + 25*x**2 - 10*x)\nExpanding the part (-103*x**2 - 26*x) using the distributive property, and we got: (-26*x)*(47*x**3 + 25*x**2 - 10*x) + (-103*x**2)*(47*x**3 + 25*x**2 - 10*x)\n#Step 2:\nCurrent expression: (-26*x)*(47*x**3 + 25*x**2 - 10*x) + (-103*x**2)*(47*x**3 + 25*x**2 - 10*x)\nSimplifying the partial expression: (-103*x**2)*(47*x**3 + 25*x**2 - 10*x)\nExpanding the part (47*x**3 + 25*x**2 - 10*x) using the distributive property, and we got: (-10*x)*(-103*x**2) + (-103*x**2)*(25*x**2) + (-103*x**2)*(47*x**3)\nReplacing (-103*x**2)*(47*x**3 + 25*x**2 - 10*x) with (-10*x)*(-103*x**2) + (-103*x**2)*(25*x**2) + (-103*x**2)*(47*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-26*x)*(47*x**3 + 25*x**2 - 10*x) + (-10*x)*(-103*x**2) + (-103*x**2)*(25*x**2) + (-103*x**2)*(47*x**3)\nSimplifying the partial expression: (-26*x)*(47*x**3 + 25*x**2 - 10*x)\nExpanding the part (47*x**3 + 25*x**2 - 10*x) using the distributive property, and we got: (-26*x)*(-10*x) + (-26*x)*(25*x**2) + (-26*x)*(47*x**3)\nReplacing (-26*x)*(47*x**3 + 25*x**2 - 10*x) with (-26*x)*(-10*x) + (-26*x)*(25*x**2) + (-26*x)*(47*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-26*x)*(-10*x) + (-26*x)*(25*x**2) + (-26*x)*(47*x**3) + (-10*x)*(-103*x**2) + (-103*x**2)*(25*x**2) + (-103*x**2)*(47*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*x)*(-103*x**2) = 1030*x**3\n (-10*x)*(-26*x) = 260*x**2\n (25*x**2)*(-103*x**2) = -2575*x**4\n (25*x**2)*(-26*x) = -650*x**3\n (47*x**3)*(-103*x**2) = -4841*x**5\n (47*x**3)*(-26*x) = -1222*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -4841*x**5 - 2575*x**4 - 1222*x**4 - 650*x**3 + 1030*x**3 + 260*x**2\nCombining like terms, got -4841*x**5 - 3797*x**4 + 380*x**3 + 260*x**2\n#Step 6:\nCurrent expression: -4841*x**5 - 3797*x**4 + 380*x**3 + 260*x**2\nNo more calculations needed.\n-4841*x**5 - 3797*x**4 + 380*x**3 + 260*x**2", "generated_answer": "-4841*x**5 - 3797*x**4 + 380*x**3 + 260*x**2", "step_length": 6} {"cot_id": "20ac4cc552cb0c75ea2f4c82d662fc49648f8eb924650f90b9a14a38e9f24c58", "datapoint": {"question": "Simplify this expression: -68*z**2*(-34*z**2 - 26*z - 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2312*z**4 + 1768*z**3 + 1156*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 314, "polynomial_expr": "-68*z**2*(-34*z**2 - 26*z - 17)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -68*z**2*(-34*z**2 - 26*z - 17)\nExpanding the part (-34*z**2 - 26*z - 17) using the distributive property, and we got: (-26*z)*(-68*z**2) - (-1)*1156*z**2 + (-68*z**2)*(-34*z**2)\n#Step 2:\nCurrent expression: (-26*z)*(-68*z**2) - (-1)*1156*z**2 + (-68*z**2)*(-34*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -17*(-68*z**2) = 1156*z**2\n (-34*z**2)*(-68*z**2) = 2312*z**4\n (-26*z)*(-68*z**2) = 1768*z**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 2312*z**4 + 1768*z**3 + 1156*z**2\nNo more calculations needed.\n2312*z**4 + 1768*z**3 + 1156*z**2", "generated_answer": "2312*z**4 + 1768*z**3 + 1156*z**2", "step_length": 3} {"cot_id": "acb8c9cdad6ebbb9b6ab0527e92137490fe60ed22451217e928a0eb069161a9b", "datapoint": {"question": "Simplify this expression: (43*x**3 - 31*x)*(15*x**3 - 11*x + 23)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "645*x**6 - 938*x**4 + 989*x**3 + 341*x**2 - 713*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 315, "polynomial_expr": "(43*x**3 - 31*x)*(15*x**3 - 11*x + 23)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (43*x**3 - 31*x)*(15*x**3 - 11*x + 23)\nExpanding the part (43*x**3 - 31*x) using the distributive property, and we got: (-31*x)*(15*x**3 - 11*x + 23) + (43*x**3)*(15*x**3 - 11*x + 23)\n#Step 2:\nCurrent expression: (-31*x)*(15*x**3 - 11*x + 23) + (43*x**3)*(15*x**3 - 11*x + 23)\nSimplifying the partial expression: (-31*x)*(15*x**3 - 11*x + 23)\nExpanding the part (15*x**3 - 11*x + 23) using the distributive property, and we got: (-31*x)*(-11*x) + (-31*x)*(15*x**3) + 23*(-31*x)\nReplacing (-31*x)*(15*x**3 - 11*x + 23) with (-31*x)*(-11*x) + (-31*x)*(15*x**3) + 23*(-31*x) in the overall expression.\n#Step 3:\nCurrent expression: (-31*x)*(-11*x) + (-31*x)*(15*x**3) + 23*(-31)*x + (43*x**3)*(15*x**3 - 11*x + 23)\nSimplifying the partial expression: (43*x**3)*(15*x**3 - 11*x + 23)\nExpanding the part (15*x**3 - 11*x + 23) using the distributive property, and we got: (-11*x)*(43*x**3) + 23*(43*x**3) + (15*x**3)*(43*x**3)\nReplacing (43*x**3)*(15*x**3 - 11*x + 23) with (-11*x)*(43*x**3) + 23*(43*x**3) + (15*x**3)*(43*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-31*x)*(-11*x) + (-31*x)*(15*x**3) + (-11*x)*(43*x**3) + 23*43*x**3 + 23*(-31)*x + (15*x**3)*(43*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*x)*(-31*x) = 341*x**2\n (-11*x)*(43*x**3) = -473*x**4\n (15*x**3)*(-31*x) = -465*x**4\n (15*x**3)*(43*x**3) = 645*x**6\n 23*-31*x = -713*x\n 23*43*x**3 = 989*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 645*x**6 - 473*x**4 - 465*x**4 + 989*x**3 + 341*x**2 - 713*x\nCombining like terms, got 645*x**6 - 938*x**4 + 989*x**3 + 341*x**2 - 713*x\n#Step 6:\nCurrent expression: 645*x**6 - 938*x**4 + 989*x**3 + 341*x**2 - 713*x\nNo more calculations needed.\n645*x**6 - 938*x**4 + 989*x**3 + 341*x**2 - 713*x", "generated_answer": "645*x**6 - 938*x**4 + 989*x**3 + 341*x**2 - 713*x", "step_length": 6} {"cot_id": "5f605532dbcb0ab2d89b45b1635955bbcea6b6977a1e7a0072791b0e4b530829", "datapoint": {"question": "Simplify this expression: (48*x**2 - 46*x)*(32*x**3 - 62)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1536*x**5 - 1472*x**4 - 2976*x**2 + 2852*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 316, "polynomial_expr": "(48*x**2 - 46*x)*(32*x**3 - 62)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (48*x**2 - 46*x)*(32*x**3 - 62)\nExpanding the part (32*x**3 - 62) using the distributive property, and we got: (32*x**3)*(48*x**2 - 46*x) - 62*(48*x**2 - 46*x)\n#Step 2:\nCurrent expression: (32*x**3)*(48*x**2 - 46*x) - 62*(48*x**2 - 46*x)\nSimplifying the partial expression: -62*(48*x**2 - 46*x)\nExpanding the part (48*x**2 - 46*x) using the distributive property, and we got: -46*x*(-62) + (48*x**2)*(-62)\nReplacing -62*(48*x**2 - 46*x) with -46*x*(-62) + (48*x**2)*(-62) in the overall expression.\n#Step 3:\nCurrent expression: -46*x*(-62) + (48*x**2)*(-62) + (32*x**3)*(48*x**2 - 46*x)\nSimplifying the partial expression: (32*x**3)*(48*x**2 - 46*x)\nExpanding the part (48*x**2 - 46*x) using the distributive property, and we got: (-46*x)*(32*x**3) + (48*x**2)*(32*x**3)\nReplacing (32*x**3)*(48*x**2 - 46*x) with (-46*x)*(32*x**3) + (48*x**2)*(32*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-46*x)*(32*x**3) - 46*x*(-62) + (48*x**2)*(32*x**3) + (48*x**2)*(-62)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*x)*-62 = 2852*x\n (-46*x)*(32*x**3) = -1472*x**4\n (48*x**2)*-62 = -2976*x**2\n (48*x**2)*(32*x**3) = 1536*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1536*x**5 - 1472*x**4 - 2976*x**2 + 2852*x\nNo more calculations needed.\n1536*x**5 - 1472*x**4 - 2976*x**2 + 2852*x", "generated_answer": "1536*x**5 - 1472*x**4 - 2976*x**2 + 2852*x", "step_length": 5} {"cot_id": "d66e908323e7ecd1495f8a3c52c9bbfb479e4eb40ae072cd6cabb2693c28cb7b", "datapoint": {"question": "Simplify this expression: (32*x**2 + 43*x - 7)*(13*x**3 + 10*x - 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "416*x**5 + 559*x**4 + 229*x**3 - 1074*x**2 - 2091*x + 329", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 317, "polynomial_expr": "(32*x**2 + 43*x - 7)*(13*x**3 + 10*x - 47)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (32*x**2 + 43*x - 7)*(13*x**3 + 10*x - 47)\nExpanding the part (13*x**3 + 10*x - 47) using the distributive property, and we got: (10*x)*(32*x**2 + 43*x - 7) + (13*x**3)*(32*x**2 + 43*x - 7) - 47*(32*x**2 + 43*x - 7)\n#Step 2:\nCurrent expression: (10*x)*(32*x**2 + 43*x - 7) + (13*x**3)*(32*x**2 + 43*x - 7) - 47*(32*x**2 + 43*x - 7)\nSimplifying the partial expression: -47*(32*x**2 + 43*x - 7)\nExpanding the part (32*x**2 + 43*x - 7) using the distributive property, and we got: (43*x)*(-47) + (32*x**2)*(-47) - 7*(-47)\nReplacing -47*(32*x**2 + 43*x - 7) with (43*x)*(-47) + (32*x**2)*(-47) - 7*(-47) in the overall expression.\n#Step 3:\nCurrent expression: (10*x)*(32*x**2 + 43*x - 7) + (43*x)*(-47) + (32*x**2)*(-47) + (13*x**3)*(32*x**2 + 43*x - 7) + 329\nSimplifying the partial expression: (10*x)*(32*x**2 + 43*x - 7)\nExpanding the part (32*x**2 + 43*x - 7) using the distributive property, and we got: -70*x + (10*x)*(43*x) + (10*x)*(32*x**2)\nReplacing (10*x)*(32*x**2 + 43*x - 7) with -70*x + (10*x)*(43*x) + (10*x)*(32*x**2) in the overall expression.\n#Step 4:\nCurrent expression: -7*10*x + (10*x)*(43*x) + (10*x)*(32*x**2) + (43*x)*(-47) + (32*x**2)*(-47) + (13*x**3)*(32*x**2 + 43*x - 7) + 329\nSimplifying the partial expression: (13*x**3)*(32*x**2 + 43*x - 7)\nExpanding the part (32*x**2 + 43*x - 7) using the distributive property, and we got: -91*x**3 + (43*x)*(13*x**3) + (32*x**2)*(13*x**3)\nReplacing (13*x**3)*(32*x**2 + 43*x - 7) with -91*x**3 + (43*x)*(13*x**3) + (32*x**2)*(13*x**3) in the overall expression.\n#Step 5:\nCurrent expression: -7*13*x**3 - 7*10*x + (10*x)*(43*x) + (10*x)*(32*x**2) + (43*x)*(13*x**3) + (43*x)*(-47) + (32*x**2)*(13*x**3) + (32*x**2)*(-47) + 329\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (32*x**2)*-47 = -1504*x**2\n (32*x**2)*(10*x) = 320*x**3\n (32*x**2)*(13*x**3) = 416*x**5\n (43*x)*-47 = -2021*x\n (43*x)*(10*x) = 430*x**2\n (43*x)*(13*x**3) = 559*x**4\n -7*10*x = -70*x\n -7*13*x**3 = -91*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 416*x**5 + 559*x**4 - 91*x**3 + 320*x**3 - 1504*x**2 + 430*x**2 - 2021*x - 70*x + 329\nCombining like terms, got 416*x**5 + 559*x**4 + 229*x**3 - 1074*x**2 - 2091*x + 329\n#Step 7:\nCurrent expression: 416*x**5 + 559*x**4 + 229*x**3 - 1074*x**2 - 2091*x + 329\nNo more calculations needed.\n416*x**5 + 559*x**4 + 229*x**3 - 1074*x**2 - 2091*x + 329", "generated_answer": "416*x**5 + 559*x**4 + 229*x**3 - 1074*x**2 - 2091*x + 329", "step_length": 7} {"cot_id": "cfafd6f5e2393be128bd8f82235e9fd15b39bd114a9e22493f87e2a8f95dfa77", "datapoint": {"question": "Calculate the following: (43*x + 44)*(-8*x**2 - 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-344*x**3 - 352*x**2 - 258*x - 264", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 318, "polynomial_expr": "(43*x + 44)*(-8*x**2 - 6)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (43*x + 44)*(-8*x**2 - 6)\nExpanding the part (-8*x**2 - 6) using the distributive property, and we got: (-8*x**2)*(43*x + 44) - 6*(43*x + 44)\n#Step 2:\nCurrent expression: (-8*x**2)*(43*x + 44) - 6*(43*x + 44)\nSimplifying the partial expression: -6*(43*x + 44)\nExpanding the part (43*x + 44) using the distributive property, and we got: (43*x)*(-6) + 44*(-6)\nReplacing -6*(43*x + 44) with (43*x)*(-6) + 44*(-6) in the overall expression.\n#Step 3:\nCurrent expression: (43*x)*(-6) + (-8*x**2)*(43*x + 44) - 264\nSimplifying the partial expression: (-8*x**2)*(43*x + 44)\nExpanding the part (43*x + 44) using the distributive property, and we got: 44*(-8*x**2) + (43*x)*(-8*x**2)\nReplacing (-8*x**2)*(43*x + 44) with 44*(-8*x**2) + (43*x)*(-8*x**2) in the overall expression.\n#Step 4:\nCurrent expression: 44*(-8)*x**2 + (43*x)*(-8*x**2) + (43*x)*(-6) - 264\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (43*x)*-6 = -258*x\n (43*x)*(-8*x**2) = -344*x**3\n 44*-8*x**2 = -352*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -344*x**3 - 352*x**2 - 258*x - 264\nNo more calculations needed.\n-344*x**3 - 352*x**2 - 258*x - 264", "generated_answer": "-344*x**3 - 352*x**2 - 258*x - 264", "step_length": 5} {"cot_id": "a8f7c3f33bce111a1b7f811548ef69214a6bb5f0fb0a4e26027d8c6a9fcaa8a2", "datapoint": {"question": "Simplify this expression: -56*z**3*(-48*z**2 - 40*z + 9)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2688*z**5 + 2240*z**4 - 504*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 319, "polynomial_expr": "-56*z**3*(-48*z**2 - 40*z + 9)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -56*z**3*(-48*z**2 - 40*z + 9)\nExpanding the part (-48*z**2 - 40*z + 9) using the distributive property, and we got: (-40*z)*(-56*z**3) + 9*(-56*z**3) + (-48*z**2)*(-56*z**3)\n#Step 2:\nCurrent expression: (-40*z)*(-56*z**3) + 9*(-56*z**3) + (-48*z**2)*(-56*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 9*(-56*z**3) = -504*z**3\n (-48*z**2)*(-56*z**3) = 2688*z**5\n (-40*z)*(-56*z**3) = 2240*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 2688*z**5 + 2240*z**4 - 504*z**3\nNo more calculations needed.\n2688*z**5 + 2240*z**4 - 504*z**3", "generated_answer": "2688*z**5 + 2240*z**4 - 504*z**3", "step_length": 3} {"cot_id": "fe1d9c43f3783fff3de9fddc423dabbf6cc0e687599c7cc6cdcbd75ec32f0b9f", "datapoint": {"question": "Simplify this expression: -z*(29*z - 52)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-29*z**2 + 52*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 320, "polynomial_expr": "-z*(29*z - 52)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -z*(29*z - 52)\nExpanding the part (29*z - 52) using the distributive property, and we got: (-z)*(29*z) - (-1)*52*z\n#Step 2:\nCurrent expression: (-z)*(29*z) - (-1)*52*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -52*(-z) = 52*z\n (29*z)*(-z) = -29*z**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -29*z**2 + 52*z\nNo more calculations needed.\n-29*z**2 + 52*z", "generated_answer": "-29*z**2 + 52*z", "step_length": 3} {"cot_id": "5e6aba74af1b4bfb4f34a0a8b940f5122937c70de43b56e5a5bff836c554b491", "datapoint": {"question": "Calculate the following: -612*x**3 + 90*x**2 + 486\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-612*x**3 + 90*x**2 + 486", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 321, "polynomial_expr": "-612*x**3 + 90*x**2 + 486", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -612*x**3 + 90*x**2 + 486\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -612*x**3 + 90*x**2 + 486\nNo more calculations needed.\n-612*x**3 + 90*x**2 + 486", "generated_answer": "-612*x**3 + 90*x**2 + 486", "step_length": 2} {"cot_id": "d3c0b81c41db516f2dac13ddfbf54f6bd230d0856ce140ca389d9837d729730b", "datapoint": {"question": "Calculate the following: (57 - x)*(49*x + 25)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-49*x**2 + 2768*x + 1425", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 322, "polynomial_expr": "(57 - x)*(49*x + 25)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (57 - x)*(49*x + 25)\nExpanding the part (49*x + 25) using the distributive property, and we got: (49*x)*(57 - x) + 25*(57 - x)\n#Step 2:\nCurrent expression: (49*x)*(57 - x) + 25*(57 - x)\nSimplifying the partial expression: 25*(57 - x)\nExpanding the part (57 - x) using the distributive property, and we got: -x*25 + 57*25\nReplacing 25*(57 - x) with -x*25 + 57*25 in the overall expression.\n#Step 3:\nCurrent expression: -x*25 + (49*x)*(57 - x) + 1425\nSimplifying the partial expression: (49*x)*(57 - x)\nExpanding the part (57 - x) using the distributive property, and we got: (-x)*(49*x) + 57*(49*x)\nReplacing (49*x)*(57 - x) with (-x)*(49*x) + 57*(49*x) in the overall expression.\n#Step 4:\nCurrent expression: (-x)*(49*x) - x*25 + 57*49*x + 1425\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-x)*25 = -25*x\n (-x)*(49*x) = -49*x**2\n 57*49*x = 2793*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -49*x**2 - 25*x + 2793*x + 1425\nCombining like terms, got -49*x**2 + 2768*x + 1425\n#Step 6:\nCurrent expression: -49*x**2 + 2768*x + 1425\nNo more calculations needed.\n-49*x**2 + 2768*x + 1425", "generated_answer": "-49*x**2 + 2768*x + 1425", "step_length": 6} {"cot_id": "7e1ed048e5e72c4e4fc5155a07450c9588d8f1c2d8fafd9bd64c498ec4fd649e", "datapoint": {"question": "Calculate the following: (22*z**3 - 25*z)*(-49*z**3 + 13*z**2 - 92)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1078*z**6 + 286*z**5 + 1225*z**4 - 2349*z**3 + 2300*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 323, "polynomial_expr": "(22*z**3 - 25*z)*(-49*z**3 + 13*z**2 - 92)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (22*z**3 - 25*z)*(-49*z**3 + 13*z**2 - 92)\nExpanding the part (22*z**3 - 25*z) using the distributive property, and we got: (-25*z)*(-49*z**3 + 13*z**2 - 92) + (22*z**3)*(-49*z**3 + 13*z**2 - 92)\n#Step 2:\nCurrent expression: (-25*z)*(-49*z**3 + 13*z**2 - 92) + (22*z**3)*(-49*z**3 + 13*z**2 - 92)\nSimplifying the partial expression: (-25*z)*(-49*z**3 + 13*z**2 - 92)\nExpanding the part (-49*z**3 + 13*z**2 - 92) using the distributive property, and we got: (-25*z)*(13*z**2) + (-25*z)*(-49*z**3) - (-1)*2300*z\nReplacing (-25*z)*(-49*z**3 + 13*z**2 - 92) with (-25*z)*(13*z**2) + (-25*z)*(-49*z**3) - (-1)*2300*z in the overall expression.\n#Step 3:\nCurrent expression: (-25*z)*(13*z**2) + (-25*z)*(-49*z**3) - 92*(-25)*z + (22*z**3)*(-49*z**3 + 13*z**2 - 92)\nSimplifying the partial expression: (22*z**3)*(-49*z**3 + 13*z**2 - 92)\nExpanding the part (-49*z**3 + 13*z**2 - 92) using the distributive property, and we got: -2024*z**3 + (13*z**2)*(22*z**3) + (-49*z**3)*(22*z**3)\nReplacing (22*z**3)*(-49*z**3 + 13*z**2 - 92) with -2024*z**3 + (13*z**2)*(22*z**3) + (-49*z**3)*(22*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-25*z)*(13*z**2) + (-25*z)*(-49*z**3) - 92*22*z**3 - 92*(-25)*z + (13*z**2)*(22*z**3) + (-49*z**3)*(22*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*z**3)*(-25*z) = 1225*z**4\n (-49*z**3)*(22*z**3) = -1078*z**6\n (13*z**2)*(-25*z) = -325*z**3\n (13*z**2)*(22*z**3) = 286*z**5\n -92*-25*z = 2300*z\n -92*22*z**3 = -2024*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1078*z**6 + 286*z**5 + 1225*z**4 - 2024*z**3 - 325*z**3 + 2300*z\nCombining like terms, got -1078*z**6 + 286*z**5 + 1225*z**4 - 2349*z**3 + 2300*z\n#Step 6:\nCurrent expression: -1078*z**6 + 286*z**5 + 1225*z**4 - 2349*z**3 + 2300*z\nNo more calculations needed.\n-1078*z**6 + 286*z**5 + 1225*z**4 - 2349*z**3 + 2300*z", "generated_answer": "-1078*z**6 + 286*z**5 + 1225*z**4 - 2349*z**3 + 2300*z", "step_length": 6} {"cot_id": "a2ac012d5eb4ab43b934df58d1f71f276ab3415dc77863c58d44ba43d50cfcd9", "datapoint": {"question": "Simplify this expression: (-49*x**2 + 46*x)*(-25*x**3 - 90*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1225*x**5 - 1150*x**4 + 4410*x**3 - 4140*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 324, "polynomial_expr": "(-49*x**2 + 46*x)*(-25*x**3 - 90*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-49*x**2 + 46*x)*(-25*x**3 - 90*x)\nExpanding the part (-25*x**3 - 90*x) using the distributive property, and we got: (-90*x)*(-49*x**2 + 46*x) + (-25*x**3)*(-49*x**2 + 46*x)\n#Step 2:\nCurrent expression: (-90*x)*(-49*x**2 + 46*x) + (-25*x**3)*(-49*x**2 + 46*x)\nSimplifying the partial expression: (-90*x)*(-49*x**2 + 46*x)\nExpanding the part (-49*x**2 + 46*x) using the distributive property, and we got: (-90*x)*(46*x) + (-90*x)*(-49*x**2)\nReplacing (-90*x)*(-49*x**2 + 46*x) with (-90*x)*(46*x) + (-90*x)*(-49*x**2) in the overall expression.\n#Step 3:\nCurrent expression: (-90*x)*(46*x) + (-90*x)*(-49*x**2) + (-25*x**3)*(-49*x**2 + 46*x)\nSimplifying the partial expression: (-25*x**3)*(-49*x**2 + 46*x)\nExpanding the part (-49*x**2 + 46*x) using the distributive property, and we got: (46*x)*(-25*x**3) + (-49*x**2)*(-25*x**3)\nReplacing (-25*x**3)*(-49*x**2 + 46*x) with (46*x)*(-25*x**3) + (-49*x**2)*(-25*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-90*x)*(46*x) + (-90*x)*(-49*x**2) + (46*x)*(-25*x**3) + (-49*x**2)*(-25*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*x**2)*(-90*x) = 4410*x**3\n (-49*x**2)*(-25*x**3) = 1225*x**5\n (46*x)*(-90*x) = -4140*x**2\n (46*x)*(-25*x**3) = -1150*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1225*x**5 - 1150*x**4 + 4410*x**3 - 4140*x**2\nNo more calculations needed.\n1225*x**5 - 1150*x**4 + 4410*x**3 - 4140*x**2", "generated_answer": "1225*x**5 - 1150*x**4 + 4410*x**3 - 4140*x**2", "step_length": 5} {"cot_id": "4d082c0be00848639b1551c1881372a3bced9d2109cf6f95eedbf6afdea280d1", "datapoint": {"question": "Calculate the following: (-20*x**3 - 23)*(-16*x**3 - 39*x**2 - 43*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "320*x**6 + 780*x**5 + 860*x**4 + 368*x**3 + 897*x**2 + 989*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 325, "polynomial_expr": "(-20*x**3 - 23)*(-16*x**3 - 39*x**2 - 43*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-20*x**3 - 23)*(-16*x**3 - 39*x**2 - 43*x)\nExpanding the part (-20*x**3 - 23) using the distributive property, and we got: (-20*x**3)*(-16*x**3 - 39*x**2 - 43*x) - 23*(-16*x**3 - 39*x**2 - 43*x)\n#Step 2:\nCurrent expression: (-20*x**3)*(-16*x**3 - 39*x**2 - 43*x) - 23*(-16*x**3 - 39*x**2 - 43*x)\nSimplifying the partial expression: -23*(-16*x**3 - 39*x**2 - 43*x)\nExpanding the part (-16*x**3 - 39*x**2 - 43*x) using the distributive property, and we got: -43*x*(-23) - 39*x**2*(-23) - 16*x**3*(-23)\nReplacing -23*(-16*x**3 - 39*x**2 - 43*x) with -43*x*(-23) - 39*x**2*(-23) - 16*x**3*(-23) in the overall expression.\n#Step 3:\nCurrent expression: -43*x*(-23) - 39*x**2*(-23) + (-20*x**3)*(-16*x**3 - 39*x**2 - 43*x) - 16*x**3*(-23)\nSimplifying the partial expression: (-20*x**3)*(-16*x**3 - 39*x**2 - 43*x)\nExpanding the part (-16*x**3 - 39*x**2 - 43*x) using the distributive property, and we got: (-43*x)*(-20*x**3) + (-39*x**2)*(-20*x**3) + (-20*x**3)*(-16*x**3)\nReplacing (-20*x**3)*(-16*x**3 - 39*x**2 - 43*x) with (-43*x)*(-20*x**3) + (-39*x**2)*(-20*x**3) + (-20*x**3)*(-16*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-43*x)*(-20*x**3) - 43*x*(-23) + (-39*x**2)*(-20*x**3) - 39*x**2*(-23) + (-20*x**3)*(-16*x**3) - 16*x**3*(-23)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-43*x)*-23 = 989*x\n (-43*x)*(-20*x**3) = 860*x**4\n (-39*x**2)*-23 = 897*x**2\n (-39*x**2)*(-20*x**3) = 780*x**5\n (-16*x**3)*-23 = 368*x**3\n (-16*x**3)*(-20*x**3) = 320*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 320*x**6 + 780*x**5 + 860*x**4 + 368*x**3 + 897*x**2 + 989*x\nNo more calculations needed.\n320*x**6 + 780*x**5 + 860*x**4 + 368*x**3 + 897*x**2 + 989*x", "generated_answer": "320*x**6 + 780*x**5 + 860*x**4 + 368*x**3 + 897*x**2 + 989*x", "step_length": 5} {"cot_id": "fffa4bd6a6fa25d936e49b7c00be791563111d33156516deb19383316be88794", "datapoint": {"question": "Simplify this expression: -71*y**2*(-13*y**3 - 39*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "923*y**5 + 2769*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 326, "polynomial_expr": "-71*y**2*(-13*y**3 - 39*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -71*y**2*(-13*y**3 - 39*y)\nExpanding the part (-13*y**3 - 39*y) using the distributive property, and we got: (-39*y)*(-71*y**2) + (-71*y**2)*(-13*y**3)\n#Step 2:\nCurrent expression: (-39*y)*(-71*y**2) + (-71*y**2)*(-13*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*y)*(-71*y**2) = 2769*y**3\n (-13*y**3)*(-71*y**2) = 923*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 923*y**5 + 2769*y**3\nNo more calculations needed.\n923*y**5 + 2769*y**3", "generated_answer": "923*y**5 + 2769*y**3", "step_length": 3} {"cot_id": "90f20f542506a885c8fd3e4e86bb0d401e48debb0f7abb6a5ad5ea3fb7b565f4", "datapoint": {"question": "Calculate the following: (-47*y**3 + 47*y)*(-2*y**3 - 13*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "94*y**6 + 611*y**5 - 94*y**4 - 611*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 327, "polynomial_expr": "(-47*y**3 + 47*y)*(-2*y**3 - 13*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-47*y**3 + 47*y)*(-2*y**3 - 13*y**2)\nExpanding the part (-47*y**3 + 47*y) using the distributive property, and we got: (47*y)*(-2*y**3 - 13*y**2) + (-47*y**3)*(-2*y**3 - 13*y**2)\n#Step 2:\nCurrent expression: (47*y)*(-2*y**3 - 13*y**2) + (-47*y**3)*(-2*y**3 - 13*y**2)\nSimplifying the partial expression: (-47*y**3)*(-2*y**3 - 13*y**2)\nExpanding the part (-2*y**3 - 13*y**2) using the distributive property, and we got: (-13*y**2)*(-47*y**3) + (-47*y**3)*(-2*y**3)\nReplacing (-47*y**3)*(-2*y**3 - 13*y**2) with (-13*y**2)*(-47*y**3) + (-47*y**3)*(-2*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (47*y)*(-2*y**3 - 13*y**2) + (-13*y**2)*(-47*y**3) + (-47*y**3)*(-2*y**3)\nSimplifying the partial expression: (47*y)*(-2*y**3 - 13*y**2)\nExpanding the part (-2*y**3 - 13*y**2) using the distributive property, and we got: (47*y)*(-13*y**2) + (47*y)*(-2*y**3)\nReplacing (47*y)*(-2*y**3 - 13*y**2) with (47*y)*(-13*y**2) + (47*y)*(-2*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (47*y)*(-13*y**2) + (47*y)*(-2*y**3) + (-13*y**2)*(-47*y**3) + (-47*y**3)*(-2*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*y**2)*(-47*y**3) = 611*y**5\n (-13*y**2)*(47*y) = -611*y**3\n (-2*y**3)*(-47*y**3) = 94*y**6\n (-2*y**3)*(47*y) = -94*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 94*y**6 + 611*y**5 - 94*y**4 - 611*y**3\nNo more calculations needed.\n94*y**6 + 611*y**5 - 94*y**4 - 611*y**3", "generated_answer": "94*y**6 + 611*y**5 - 94*y**4 - 611*y**3", "step_length": 5} {"cot_id": "d5f7f6badc35b1744987b77ce9876b9b07d81c7ba03550eeece1b87a5fd366fb", "datapoint": {"question": "Calculate the following: (-47*x - 23)*(44*x**2 - 10*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2068*x**3 - 542*x**2 + 230*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 328, "polynomial_expr": "(-47*x - 23)*(44*x**2 - 10*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-47*x - 23)*(44*x**2 - 10*x)\nExpanding the part (-47*x - 23) using the distributive property, and we got: (-47*x)*(44*x**2 - 10*x) - 23*(44*x**2 - 10*x)\n#Step 2:\nCurrent expression: (-47*x)*(44*x**2 - 10*x) - 23*(44*x**2 - 10*x)\nSimplifying the partial expression: -23*(44*x**2 - 10*x)\nExpanding the part (44*x**2 - 10*x) using the distributive property, and we got: -10*x*(-23) + (44*x**2)*(-23)\nReplacing -23*(44*x**2 - 10*x) with -10*x*(-23) + (44*x**2)*(-23) in the overall expression.\n#Step 3:\nCurrent expression: (-47*x)*(44*x**2 - 10*x) - 10*x*(-23) + (44*x**2)*(-23)\nSimplifying the partial expression: (-47*x)*(44*x**2 - 10*x)\nExpanding the part (44*x**2 - 10*x) using the distributive property, and we got: (-47*x)*(-10*x) + (-47*x)*(44*x**2)\nReplacing (-47*x)*(44*x**2 - 10*x) with (-47*x)*(-10*x) + (-47*x)*(44*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-47*x)*(-10*x) + (-47*x)*(44*x**2) - 10*x*(-23) + (44*x**2)*(-23)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*x)*-23 = 230*x\n (-10*x)*(-47*x) = 470*x**2\n (44*x**2)*-23 = -1012*x**2\n (44*x**2)*(-47*x) = -2068*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2068*x**3 - 1012*x**2 + 470*x**2 + 230*x\nCombining like terms, got -2068*x**3 - 542*x**2 + 230*x\n#Step 6:\nCurrent expression: -2068*x**3 - 542*x**2 + 230*x\nNo more calculations needed.\n-2068*x**3 - 542*x**2 + 230*x", "generated_answer": "-2068*x**3 - 542*x**2 + 230*x", "step_length": 6} {"cot_id": "49ac69f0d58907e2a4aa90ea0d24e4cd25c5aee8bf7f5bba194631e506ca4b39", "datapoint": {"question": "Simplify this expression: (5*y**3 + 62)*(19*y**3 + 37)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "95*y**6 + 1363*y**3 + 2294", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 329, "polynomial_expr": "(5*y**3 + 62)*(19*y**3 + 37)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (5*y**3 + 62)*(19*y**3 + 37)\nExpanding the part (19*y**3 + 37) using the distributive property, and we got: (19*y**3)*(5*y**3 + 62) + 37*(5*y**3 + 62)\n#Step 2:\nCurrent expression: (19*y**3)*(5*y**3 + 62) + 37*(5*y**3 + 62)\nSimplifying the partial expression: 37*(5*y**3 + 62)\nExpanding the part (5*y**3 + 62) using the distributive property, and we got: (5*y**3)*37 + 62*37\nReplacing 37*(5*y**3 + 62) with (5*y**3)*37 + 62*37 in the overall expression.\n#Step 3:\nCurrent expression: (5*y**3)*37 + (19*y**3)*(5*y**3 + 62) + 2294\nSimplifying the partial expression: (19*y**3)*(5*y**3 + 62)\nExpanding the part (5*y**3 + 62) using the distributive property, and we got: 62*(19*y**3) + (5*y**3)*(19*y**3)\nReplacing (19*y**3)*(5*y**3 + 62) with 62*(19*y**3) + (5*y**3)*(19*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 62*19*y**3 + (5*y**3)*(19*y**3) + (5*y**3)*37 + 2294\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (5*y**3)*37 = 185*y**3\n (5*y**3)*(19*y**3) = 95*y**6\n 62*19*y**3 = 1178*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 95*y**6 + 185*y**3 + 1178*y**3 + 2294\nCombining like terms, got 95*y**6 + 1363*y**3 + 2294\n#Step 6:\nCurrent expression: 95*y**6 + 1363*y**3 + 2294\nNo more calculations needed.\n95*y**6 + 1363*y**3 + 2294", "generated_answer": "95*y**6 + 1363*y**3 + 2294", "step_length": 6} {"cot_id": "04f18c4e1bd61c77080b179c1ca3ce45886e9f6bcb6d505e9ac3dfea99b03e23", "datapoint": {"question": "Calculate the following: (30*x**3 + 6)*(-14*x**3 - 38*x**2 - 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-420*x**6 - 1140*x**5 - 564*x**3 - 228*x**2 - 96", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 330, "polynomial_expr": "(30*x**3 + 6)*(-14*x**3 - 38*x**2 - 16)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (30*x**3 + 6)*(-14*x**3 - 38*x**2 - 16)\nExpanding the part (30*x**3 + 6) using the distributive property, and we got: (30*x**3)*(-14*x**3 - 38*x**2 - 16) + 6*(-14*x**3 - 38*x**2 - 16)\n#Step 2:\nCurrent expression: (30*x**3)*(-14*x**3 - 38*x**2 - 16) + 6*(-14*x**3 - 38*x**2 - 16)\nSimplifying the partial expression: 6*(-14*x**3 - 38*x**2 - 16)\nExpanding the part (-14*x**3 - 38*x**2 - 16) using the distributive property, and we got: -38*x**2*6 - 14*x**3*6 - 16*6\nReplacing 6*(-14*x**3 - 38*x**2 - 16) with -38*x**2*6 - 14*x**3*6 - 16*6 in the overall expression.\n#Step 3:\nCurrent expression: -38*x**2*6 - 14*x**3*6 + (30*x**3)*(-14*x**3 - 38*x**2 - 16) - 96\nSimplifying the partial expression: (30*x**3)*(-14*x**3 - 38*x**2 - 16)\nExpanding the part (-14*x**3 - 38*x**2 - 16) using the distributive property, and we got: -480*x**3 + (-38*x**2)*(30*x**3) + (-14*x**3)*(30*x**3)\nReplacing (30*x**3)*(-14*x**3 - 38*x**2 - 16) with -480*x**3 + (-38*x**2)*(30*x**3) + (-14*x**3)*(30*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -16*30*x**3 + (-38*x**2)*(30*x**3) - 38*x**2*6 + (-14*x**3)*(30*x**3) - 14*x**3*6 - 96\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*x**2)*6 = -228*x**2\n (-38*x**2)*(30*x**3) = -1140*x**5\n (-14*x**3)*6 = -84*x**3\n (-14*x**3)*(30*x**3) = -420*x**6\n -16*30*x**3 = -480*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -420*x**6 - 1140*x**5 - 480*x**3 - 84*x**3 - 228*x**2 - 96\nCombining like terms, got -420*x**6 - 1140*x**5 - 564*x**3 - 228*x**2 - 96\n#Step 6:\nCurrent expression: -420*x**6 - 1140*x**5 - 564*x**3 - 228*x**2 - 96\nNo more calculations needed.\n-420*x**6 - 1140*x**5 - 564*x**3 - 228*x**2 - 96", "generated_answer": "-420*x**6 - 1140*x**5 - 564*x**3 - 228*x**2 - 96", "step_length": 6} {"cot_id": "4709980ae656dd85e545e0e2c78d5b06745306f7e8fd07d4dd9a1062c6b0536d", "datapoint": {"question": "Calculate the following: (11 - 57*x)*(-28*x**3 + 16*x**2 + 78*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1596*x**4 - 1220*x**3 - 4270*x**2 + 858*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 331, "polynomial_expr": "(11 - 57*x)*(-28*x**3 + 16*x**2 + 78*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11 - 57*x)*(-28*x**3 + 16*x**2 + 78*x)\nExpanding the part (11 - 57*x) using the distributive property, and we got: (-57*x)*(-28*x**3 + 16*x**2 + 78*x) + 11*(-28*x**3 + 16*x**2 + 78*x)\n#Step 2:\nCurrent expression: (-57*x)*(-28*x**3 + 16*x**2 + 78*x) + 11*(-28*x**3 + 16*x**2 + 78*x)\nSimplifying the partial expression: 11*(-28*x**3 + 16*x**2 + 78*x)\nExpanding the part (-28*x**3 + 16*x**2 + 78*x) using the distributive property, and we got: (78*x)*11 + (16*x**2)*11 - 28*x**3*11\nReplacing 11*(-28*x**3 + 16*x**2 + 78*x) with (78*x)*11 + (16*x**2)*11 - 28*x**3*11 in the overall expression.\n#Step 3:\nCurrent expression: (-57*x)*(-28*x**3 + 16*x**2 + 78*x) + (78*x)*11 + (16*x**2)*11 - 28*x**3*11\nSimplifying the partial expression: (-57*x)*(-28*x**3 + 16*x**2 + 78*x)\nExpanding the part (-28*x**3 + 16*x**2 + 78*x) using the distributive property, and we got: (-57*x)*(78*x) + (-57*x)*(16*x**2) + (-57*x)*(-28*x**3)\nReplacing (-57*x)*(-28*x**3 + 16*x**2 + 78*x) with (-57*x)*(78*x) + (-57*x)*(16*x**2) + (-57*x)*(-28*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-57*x)*(78*x) + (-57*x)*(16*x**2) + (-57*x)*(-28*x**3) + (78*x)*11 + (16*x**2)*11 - 28*x**3*11\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*x**3)*11 = -308*x**3\n (-28*x**3)*(-57*x) = 1596*x**4\n (16*x**2)*11 = 176*x**2\n (16*x**2)*(-57*x) = -912*x**3\n (78*x)*11 = 858*x\n (78*x)*(-57*x) = -4446*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1596*x**4 - 912*x**3 - 308*x**3 - 4446*x**2 + 176*x**2 + 858*x\nCombining like terms, got 1596*x**4 - 1220*x**3 - 4270*x**2 + 858*x\n#Step 6:\nCurrent expression: 1596*x**4 - 1220*x**3 - 4270*x**2 + 858*x\nNo more calculations needed.\n1596*x**4 - 1220*x**3 - 4270*x**2 + 858*x", "generated_answer": "1596*x**4 - 1220*x**3 - 4270*x**2 + 858*x", "step_length": 6} {"cot_id": "bb0c61c661c4bd5b5600a0af78064d40efe031872f53e67714e460ded6598c7b", "datapoint": {"question": "Calculate the following: (81*y + 14)*(32*y**2 + 35*y - 34)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2592*y**3 + 3283*y**2 - 2264*y - 476", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 332, "polynomial_expr": "(81*y + 14)*(32*y**2 + 35*y - 34)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (81*y + 14)*(32*y**2 + 35*y - 34)\nExpanding the part (81*y + 14) using the distributive property, and we got: (81*y)*(32*y**2 + 35*y - 34) + 14*(32*y**2 + 35*y - 34)\n#Step 2:\nCurrent expression: (81*y)*(32*y**2 + 35*y - 34) + 14*(32*y**2 + 35*y - 34)\nSimplifying the partial expression: 14*(32*y**2 + 35*y - 34)\nExpanding the part (32*y**2 + 35*y - 34) using the distributive property, and we got: (35*y)*14 + (32*y**2)*14 - 34*14\nReplacing 14*(32*y**2 + 35*y - 34) with (35*y)*14 + (32*y**2)*14 - 34*14 in the overall expression.\n#Step 3:\nCurrent expression: (35*y)*14 + (81*y)*(32*y**2 + 35*y - 34) + (32*y**2)*14 - 476\nSimplifying the partial expression: (81*y)*(32*y**2 + 35*y - 34)\nExpanding the part (32*y**2 + 35*y - 34) using the distributive property, and we got: -2754*y + (35*y)*(81*y) + (81*y)*(32*y**2)\nReplacing (81*y)*(32*y**2 + 35*y - 34) with -2754*y + (35*y)*(81*y) + (81*y)*(32*y**2) in the overall expression.\n#Step 4:\nCurrent expression: -34*81*y + (35*y)*(81*y) + (35*y)*14 + (81*y)*(32*y**2) + (32*y**2)*14 - 476\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (32*y**2)*14 = 448*y**2\n (32*y**2)*(81*y) = 2592*y**3\n (35*y)*14 = 490*y\n (35*y)*(81*y) = 2835*y**2\n -34*81*y = -2754*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2592*y**3 + 448*y**2 + 2835*y**2 - 2754*y + 490*y - 476\nCombining like terms, got 2592*y**3 + 3283*y**2 - 2264*y - 476\n#Step 6:\nCurrent expression: 2592*y**3 + 3283*y**2 - 2264*y - 476\nNo more calculations needed.\n2592*y**3 + 3283*y**2 - 2264*y - 476", "generated_answer": "2592*y**3 + 3283*y**2 - 2264*y - 476", "step_length": 6} {"cot_id": "92a460c2c81c37d68bd8c76087819cdbbc07fef56da1ded4ed92e12efbec15b9", "datapoint": {"question": "Calculate the following: (17 - 45*x**3)*(43 - 40*x**3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1800*x**6 - 2615*x**3 + 731", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 333, "polynomial_expr": "(17 - 45*x**3)*(43 - 40*x**3)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (17 - 45*x**3)*(43 - 40*x**3)\nExpanding the part (17 - 45*x**3) using the distributive property, and we got: (-45*x**3)*(43 - 40*x**3) + 17*(43 - 40*x**3)\n#Step 2:\nCurrent expression: (-45*x**3)*(43 - 40*x**3) + 17*(43 - 40*x**3)\nSimplifying the partial expression: 17*(43 - 40*x**3)\nExpanding the part (43 - 40*x**3) using the distributive property, and we got: -40*x**3*17 + 43*17\nReplacing 17*(43 - 40*x**3) with -40*x**3*17 + 43*17 in the overall expression.\n#Step 3:\nCurrent expression: (-45*x**3)*(43 - 40*x**3) - 40*x**3*17 + 731\nSimplifying the partial expression: (-45*x**3)*(43 - 40*x**3)\nExpanding the part (43 - 40*x**3) using the distributive property, and we got: 43*(-45*x**3) + (-45*x**3)*(-40*x**3)\nReplacing (-45*x**3)*(43 - 40*x**3) with 43*(-45*x**3) + (-45*x**3)*(-40*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 43*(-45)*x**3 + (-45*x**3)*(-40*x**3) - 40*x**3*17 + 731\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*x**3)*17 = -680*x**3\n (-40*x**3)*(-45*x**3) = 1800*x**6\n 43*-45*x**3 = -1935*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1800*x**6 - 1935*x**3 - 680*x**3 + 731\nCombining like terms, got 1800*x**6 - 2615*x**3 + 731\n#Step 6:\nCurrent expression: 1800*x**6 - 2615*x**3 + 731\nNo more calculations needed.\n1800*x**6 - 2615*x**3 + 731", "generated_answer": "1800*x**6 - 2615*x**3 + 731", "step_length": 6} {"cot_id": "5f56352bed82b49e053fbfa29d5c46efeb3d7ec672df8921458fc23f02508dd8", "datapoint": {"question": "Simplify this expression: (-20*z**3 - 6)*(-38*z**3 - 7*z**2 + 19)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "760*z**6 + 140*z**5 - 152*z**3 + 42*z**2 - 114", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 334, "polynomial_expr": "(-20*z**3 - 6)*(-38*z**3 - 7*z**2 + 19)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-20*z**3 - 6)*(-38*z**3 - 7*z**2 + 19)\nExpanding the part (-20*z**3 - 6) using the distributive property, and we got: (-20*z**3)*(-38*z**3 - 7*z**2 + 19) - 6*(-38*z**3 - 7*z**2 + 19)\n#Step 2:\nCurrent expression: (-20*z**3)*(-38*z**3 - 7*z**2 + 19) - 6*(-38*z**3 - 7*z**2 + 19)\nSimplifying the partial expression: -6*(-38*z**3 - 7*z**2 + 19)\nExpanding the part (-38*z**3 - 7*z**2 + 19) using the distributive property, and we got: -7*z**2*(-6) - 38*z**3*(-6) + 19*(-6)\nReplacing -6*(-38*z**3 - 7*z**2 + 19) with -7*z**2*(-6) - 38*z**3*(-6) + 19*(-6) in the overall expression.\n#Step 3:\nCurrent expression: -7*z**2*(-6) - 38*z**3*(-6) + (-20*z**3)*(-38*z**3 - 7*z**2 + 19) - 114\nSimplifying the partial expression: (-20*z**3)*(-38*z**3 - 7*z**2 + 19)\nExpanding the part (-38*z**3 - 7*z**2 + 19) using the distributive property, and we got: 19*(-20*z**3) + (-7*z**2)*(-20*z**3) + (-38*z**3)*(-20*z**3)\nReplacing (-20*z**3)*(-38*z**3 - 7*z**2 + 19) with 19*(-20*z**3) + (-7*z**2)*(-20*z**3) + (-38*z**3)*(-20*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 19*(-20)*z**3 + (-7*z**2)*(-20*z**3) - 7*z**2*(-6) + (-38*z**3)*(-20*z**3) - 38*z**3*(-6) - 114\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*z**3)*-6 = 228*z**3\n (-38*z**3)*(-20*z**3) = 760*z**6\n (-7*z**2)*-6 = 42*z**2\n (-7*z**2)*(-20*z**3) = 140*z**5\n 19*-20*z**3 = -380*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 760*z**6 + 140*z**5 - 380*z**3 + 228*z**3 + 42*z**2 - 114\nCombining like terms, got 760*z**6 + 140*z**5 - 152*z**3 + 42*z**2 - 114\n#Step 6:\nCurrent expression: 760*z**6 + 140*z**5 - 152*z**3 + 42*z**2 - 114\nNo more calculations needed.\n760*z**6 + 140*z**5 - 152*z**3 + 42*z**2 - 114", "generated_answer": "760*z**6 + 140*z**5 - 152*z**3 + 42*z**2 - 114", "step_length": 6} {"cot_id": "90ee367502836d9866ab3d2506b4d158780fe13f9eff507ccfd08c1beea3a3d9", "datapoint": {"question": "Simplify this expression: (18 - 33*x**2)*(22*x**3 + 12*x**2 - 33*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-726*x**5 - 396*x**4 + 1485*x**3 + 216*x**2 - 594*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 335, "polynomial_expr": "(18 - 33*x**2)*(22*x**3 + 12*x**2 - 33*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (18 - 33*x**2)*(22*x**3 + 12*x**2 - 33*x)\nExpanding the part (18 - 33*x**2) using the distributive property, and we got: (-33*x**2)*(22*x**3 + 12*x**2 - 33*x) + 18*(22*x**3 + 12*x**2 - 33*x)\n#Step 2:\nCurrent expression: (-33*x**2)*(22*x**3 + 12*x**2 - 33*x) + 18*(22*x**3 + 12*x**2 - 33*x)\nSimplifying the partial expression: 18*(22*x**3 + 12*x**2 - 33*x)\nExpanding the part (22*x**3 + 12*x**2 - 33*x) using the distributive property, and we got: -33*x*18 + (12*x**2)*18 + (22*x**3)*18\nReplacing 18*(22*x**3 + 12*x**2 - 33*x) with -33*x*18 + (12*x**2)*18 + (22*x**3)*18 in the overall expression.\n#Step 3:\nCurrent expression: -33*x*18 + (-33*x**2)*(22*x**3 + 12*x**2 - 33*x) + (12*x**2)*18 + (22*x**3)*18\nSimplifying the partial expression: (-33*x**2)*(22*x**3 + 12*x**2 - 33*x)\nExpanding the part (22*x**3 + 12*x**2 - 33*x) using the distributive property, and we got: (-33*x)*(-33*x**2) + (-33*x**2)*(12*x**2) + (-33*x**2)*(22*x**3)\nReplacing (-33*x**2)*(22*x**3 + 12*x**2 - 33*x) with (-33*x)*(-33*x**2) + (-33*x**2)*(12*x**2) + (-33*x**2)*(22*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-33*x)*(-33*x**2) - 33*x*18 + (-33*x**2)*(12*x**2) + (-33*x**2)*(22*x**3) + (12*x**2)*18 + (22*x**3)*18\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*x)*18 = -594*x\n (-33*x)*(-33*x**2) = 1089*x**3\n (12*x**2)*18 = 216*x**2\n (12*x**2)*(-33*x**2) = -396*x**4\n (22*x**3)*18 = 396*x**3\n (22*x**3)*(-33*x**2) = -726*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -726*x**5 - 396*x**4 + 396*x**3 + 1089*x**3 + 216*x**2 - 594*x\nCombining like terms, got -726*x**5 - 396*x**4 + 1485*x**3 + 216*x**2 - 594*x\n#Step 6:\nCurrent expression: -726*x**5 - 396*x**4 + 1485*x**3 + 216*x**2 - 594*x\nNo more calculations needed.\n-726*x**5 - 396*x**4 + 1485*x**3 + 216*x**2 - 594*x", "generated_answer": "-726*x**5 - 396*x**4 + 1485*x**3 + 216*x**2 - 594*x", "step_length": 6} {"cot_id": "ae4e71be886bd210668486e2bc36e547f7f4fb04d756982dd8f809f047b2d83e", "datapoint": {"question": "Simplify this expression: (64*x**3 + x)*(-73*x**3 + 22*x - 2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-4672*x**6 + 1335*x**4 - 128*x**3 + 22*x**2 - 2*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 336, "polynomial_expr": "(64*x**3 + x)*(-73*x**3 + 22*x - 2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (64*x**3 + x)*(-73*x**3 + 22*x - 2)\nExpanding the part (64*x**3 + x) using the distributive property, and we got: x*(-73*x**3 + 22*x - 2) + (64*x**3)*(-73*x**3 + 22*x - 2)\n#Step 2:\nCurrent expression: x*(-73*x**3 + 22*x - 2) + (64*x**3)*(-73*x**3 + 22*x - 2)\nSimplifying the partial expression: x*(-73*x**3 + 22*x - 2)\nExpanding the part (-73*x**3 + 22*x - 2) using the distributive property, and we got: x*(22*x) + x*(-73*x**3) - 2*x\nReplacing x*(-73*x**3 + 22*x - 2) with x*(22*x) + x*(-73*x**3) - 2*x in the overall expression.\n#Step 3:\nCurrent expression: x*(22*x) + x*(-73*x**3) - 2*x + (64*x**3)*(-73*x**3 + 22*x - 2)\nSimplifying the partial expression: (64*x**3)*(-73*x**3 + 22*x - 2)\nExpanding the part (-73*x**3 + 22*x - 2) using the distributive property, and we got: -128*x**3 + (22*x)*(64*x**3) + (-73*x**3)*(64*x**3)\nReplacing (64*x**3)*(-73*x**3 + 22*x - 2) with -128*x**3 + (22*x)*(64*x**3) + (-73*x**3)*(64*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -2*64*x**3 + x*(22*x) + x*(-73*x**3) - 2*x + (22*x)*(64*x**3) + (-73*x**3)*(64*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-73*x**3)*x = -73*x**4\n (-73*x**3)*(64*x**3) = -4672*x**6\n (22*x)*x = 22*x**2\n (22*x)*(64*x**3) = 1408*x**4\n -2*64*x**3 = -128*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -4672*x**6 - 73*x**4 + 1408*x**4 - 128*x**3 + 22*x**2 - 2*x\nCombining like terms, got -4672*x**6 + 1335*x**4 - 128*x**3 + 22*x**2 - 2*x\n#Step 6:\nCurrent expression: -4672*x**6 + 1335*x**4 - 128*x**3 + 22*x**2 - 2*x\nNo more calculations needed.\n-4672*x**6 + 1335*x**4 - 128*x**3 + 22*x**2 - 2*x", "generated_answer": "-4672*x**6 + 1335*x**4 - 128*x**3 + 22*x**2 - 2*x", "step_length": 6} {"cot_id": "c993e3b9d658190fffaca9a486f4c8050650be9893065d976b7e76053fc9a02c", "datapoint": {"question": "Simplify this expression: (14*x**2 - 48*x)*(43*x**3 + 33*x**2 - 41*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "602*x**5 - 1602*x**4 - 2158*x**3 + 1968*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 337, "polynomial_expr": "(14*x**2 - 48*x)*(43*x**3 + 33*x**2 - 41*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14*x**2 - 48*x)*(43*x**3 + 33*x**2 - 41*x)\nExpanding the part (14*x**2 - 48*x) using the distributive property, and we got: (-48*x)*(43*x**3 + 33*x**2 - 41*x) + (14*x**2)*(43*x**3 + 33*x**2 - 41*x)\n#Step 2:\nCurrent expression: (-48*x)*(43*x**3 + 33*x**2 - 41*x) + (14*x**2)*(43*x**3 + 33*x**2 - 41*x)\nSimplifying the partial expression: (-48*x)*(43*x**3 + 33*x**2 - 41*x)\nExpanding the part (43*x**3 + 33*x**2 - 41*x) using the distributive property, and we got: (-48*x)*(-41*x) + (-48*x)*(33*x**2) + (-48*x)*(43*x**3)\nReplacing (-48*x)*(43*x**3 + 33*x**2 - 41*x) with (-48*x)*(-41*x) + (-48*x)*(33*x**2) + (-48*x)*(43*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-48*x)*(-41*x) + (-48*x)*(33*x**2) + (-48*x)*(43*x**3) + (14*x**2)*(43*x**3 + 33*x**2 - 41*x)\nSimplifying the partial expression: (14*x**2)*(43*x**3 + 33*x**2 - 41*x)\nExpanding the part (43*x**3 + 33*x**2 - 41*x) using the distributive property, and we got: (-41*x)*(14*x**2) + (14*x**2)*(33*x**2) + (14*x**2)*(43*x**3)\nReplacing (14*x**2)*(43*x**3 + 33*x**2 - 41*x) with (-41*x)*(14*x**2) + (14*x**2)*(33*x**2) + (14*x**2)*(43*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-48*x)*(-41*x) + (-48*x)*(33*x**2) + (-48*x)*(43*x**3) + (-41*x)*(14*x**2) + (14*x**2)*(33*x**2) + (14*x**2)*(43*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*x)*(-48*x) = 1968*x**2\n (-41*x)*(14*x**2) = -574*x**3\n (33*x**2)*(-48*x) = -1584*x**3\n (33*x**2)*(14*x**2) = 462*x**4\n (43*x**3)*(-48*x) = -2064*x**4\n (43*x**3)*(14*x**2) = 602*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 602*x**5 - 2064*x**4 + 462*x**4 - 1584*x**3 - 574*x**3 + 1968*x**2\nCombining like terms, got 602*x**5 - 1602*x**4 - 2158*x**3 + 1968*x**2\n#Step 6:\nCurrent expression: 602*x**5 - 1602*x**4 - 2158*x**3 + 1968*x**2\nNo more calculations needed.\n602*x**5 - 1602*x**4 - 2158*x**3 + 1968*x**2", "generated_answer": "602*x**5 - 1602*x**4 - 2158*x**3 + 1968*x**2", "step_length": 6} {"cot_id": "36c1f6afb054a2a8fd82a3e9902546cb754cc10bcb3c0b1e65ee8d407e8941e1", "datapoint": {"question": "Simplify this expression: (63 - 41*x**3)*(-10*x**3 - 40*x**2 + 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "410*x**6 + 1640*x**5 - 2188*x**3 - 2520*x**2 + 2394", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 338, "polynomial_expr": "(63 - 41*x**3)*(-10*x**3 - 40*x**2 + 38)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (63 - 41*x**3)*(-10*x**3 - 40*x**2 + 38)\nExpanding the part (63 - 41*x**3) using the distributive property, and we got: (-41*x**3)*(-10*x**3 - 40*x**2 + 38) + 63*(-10*x**3 - 40*x**2 + 38)\n#Step 2:\nCurrent expression: (-41*x**3)*(-10*x**3 - 40*x**2 + 38) + 63*(-10*x**3 - 40*x**2 + 38)\nSimplifying the partial expression: 63*(-10*x**3 - 40*x**2 + 38)\nExpanding the part (-10*x**3 - 40*x**2 + 38) using the distributive property, and we got: -40*x**2*63 - 10*x**3*63 + 38*63\nReplacing 63*(-10*x**3 - 40*x**2 + 38) with -40*x**2*63 - 10*x**3*63 + 38*63 in the overall expression.\n#Step 3:\nCurrent expression: -40*x**2*63 + (-41*x**3)*(-10*x**3 - 40*x**2 + 38) - 10*x**3*63 + 2394\nSimplifying the partial expression: (-41*x**3)*(-10*x**3 - 40*x**2 + 38)\nExpanding the part (-10*x**3 - 40*x**2 + 38) using the distributive property, and we got: 38*(-41*x**3) + (-40*x**2)*(-41*x**3) + (-41*x**3)*(-10*x**3)\nReplacing (-41*x**3)*(-10*x**3 - 40*x**2 + 38) with 38*(-41*x**3) + (-40*x**2)*(-41*x**3) + (-41*x**3)*(-10*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 38*(-41)*x**3 + (-40*x**2)*(-41*x**3) - 40*x**2*63 + (-41*x**3)*(-10*x**3) - 10*x**3*63 + 2394\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*x**2)*63 = -2520*x**2\n (-40*x**2)*(-41*x**3) = 1640*x**5\n (-10*x**3)*63 = -630*x**3\n (-10*x**3)*(-41*x**3) = 410*x**6\n 38*-41*x**3 = -1558*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 410*x**6 + 1640*x**5 - 1558*x**3 - 630*x**3 - 2520*x**2 + 2394\nCombining like terms, got 410*x**6 + 1640*x**5 - 2188*x**3 - 2520*x**2 + 2394\n#Step 6:\nCurrent expression: 410*x**6 + 1640*x**5 - 2188*x**3 - 2520*x**2 + 2394\nNo more calculations needed.\n410*x**6 + 1640*x**5 - 2188*x**3 - 2520*x**2 + 2394", "generated_answer": "410*x**6 + 1640*x**5 - 2188*x**3 - 2520*x**2 + 2394", "step_length": 6} {"cot_id": "e1013a8cd408862b1fc6f514eee0c498489ae9d2d5bc12d37df918a59fa2c172", "datapoint": {"question": "Simplify this expression: (40*y + 46)*(-14*y**3 - y + 27)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-560*y**4 - 644*y**3 - 40*y**2 + 1034*y + 1242", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 339, "polynomial_expr": "(40*y + 46)*(-14*y**3 - y + 27)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (40*y + 46)*(-14*y**3 - y + 27)\nExpanding the part (40*y + 46) using the distributive property, and we got: (40*y)*(-14*y**3 - y + 27) + 46*(-14*y**3 - y + 27)\n#Step 2:\nCurrent expression: (40*y)*(-14*y**3 - y + 27) + 46*(-14*y**3 - y + 27)\nSimplifying the partial expression: 46*(-14*y**3 - y + 27)\nExpanding the part (-14*y**3 - y + 27) using the distributive property, and we got: -y*46 - 14*y**3*46 + 27*46\nReplacing 46*(-14*y**3 - y + 27) with -y*46 - 14*y**3*46 + 27*46 in the overall expression.\n#Step 3:\nCurrent expression: -y*46 + (40*y)*(-14*y**3 - y + 27) - 14*y**3*46 + 1242\nSimplifying the partial expression: (40*y)*(-14*y**3 - y + 27)\nExpanding the part (-14*y**3 - y + 27) using the distributive property, and we got: (-y)*(40*y) + 27*(40*y) + (40*y)*(-14*y**3)\nReplacing (40*y)*(-14*y**3 - y + 27) with (-y)*(40*y) + 27*(40*y) + (40*y)*(-14*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-y)*(40*y) - y*46 + 27*40*y + (40*y)*(-14*y**3) - 14*y**3*46 + 1242\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-y)*46 = -46*y\n (-y)*(40*y) = -40*y**2\n (-14*y**3)*46 = -644*y**3\n (-14*y**3)*(40*y) = -560*y**4\n 27*40*y = 1080*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -560*y**4 - 644*y**3 - 40*y**2 - 46*y + 1080*y + 1242\nCombining like terms, got -560*y**4 - 644*y**3 - 40*y**2 + 1034*y + 1242\n#Step 6:\nCurrent expression: -560*y**4 - 644*y**3 - 40*y**2 + 1034*y + 1242\nNo more calculations needed.\n-560*y**4 - 644*y**3 - 40*y**2 + 1034*y + 1242", "generated_answer": "-560*y**4 - 644*y**3 - 40*y**2 + 1034*y + 1242", "step_length": 6} {"cot_id": "616a84fb5d887351db231868676a1671a9387fda1b8a6c1aa547f353f8b147c8", "datapoint": {"question": "Simplify this expression: (21*x + 23)*(3*x**2 + 22)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "63*x**3 + 69*x**2 + 462*x + 506", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 340, "polynomial_expr": "(21*x + 23)*(3*x**2 + 22)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21*x + 23)*(3*x**2 + 22)\nExpanding the part (3*x**2 + 22) using the distributive property, and we got: (3*x**2)*(21*x + 23) + 22*(21*x + 23)\n#Step 2:\nCurrent expression: (3*x**2)*(21*x + 23) + 22*(21*x + 23)\nSimplifying the partial expression: 22*(21*x + 23)\nExpanding the part (21*x + 23) using the distributive property, and we got: (21*x)*22 + 23*22\nReplacing 22*(21*x + 23) with (21*x)*22 + 23*22 in the overall expression.\n#Step 3:\nCurrent expression: (21*x)*22 + (3*x**2)*(21*x + 23) + 506\nSimplifying the partial expression: (3*x**2)*(21*x + 23)\nExpanding the part (21*x + 23) using the distributive property, and we got: 23*(3*x**2) + (21*x)*(3*x**2)\nReplacing (3*x**2)*(21*x + 23) with 23*(3*x**2) + (21*x)*(3*x**2) in the overall expression.\n#Step 4:\nCurrent expression: 23*3*x**2 + (21*x)*(3*x**2) + (21*x)*22 + 506\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (21*x)*22 = 462*x\n (21*x)*(3*x**2) = 63*x**3\n 23*3*x**2 = 69*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 63*x**3 + 69*x**2 + 462*x + 506\nNo more calculations needed.\n63*x**3 + 69*x**2 + 462*x + 506", "generated_answer": "63*x**3 + 69*x**2 + 462*x + 506", "step_length": 5} {"cot_id": "e79740902e8bc0b79749588792ed41177083df4bfe23f636c0aad080ca8986c5", "datapoint": {"question": "Calculate the following: (-15*z**2 - 42*z)*(18*z**3 + 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-270*z**5 - 756*z**4 - 90*z**2 - 252*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 341, "polynomial_expr": "(-15*z**2 - 42*z)*(18*z**3 + 6)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-15*z**2 - 42*z)*(18*z**3 + 6)\nExpanding the part (18*z**3 + 6) using the distributive property, and we got: (18*z**3)*(-15*z**2 - 42*z) + 6*(-15*z**2 - 42*z)\n#Step 2:\nCurrent expression: (18*z**3)*(-15*z**2 - 42*z) + 6*(-15*z**2 - 42*z)\nSimplifying the partial expression: 6*(-15*z**2 - 42*z)\nExpanding the part (-15*z**2 - 42*z) using the distributive property, and we got: -42*z*6 - 15*z**2*6\nReplacing 6*(-15*z**2 - 42*z) with -42*z*6 - 15*z**2*6 in the overall expression.\n#Step 3:\nCurrent expression: -42*z*6 - 15*z**2*6 + (18*z**3)*(-15*z**2 - 42*z)\nSimplifying the partial expression: (18*z**3)*(-15*z**2 - 42*z)\nExpanding the part (-15*z**2 - 42*z) using the distributive property, and we got: (-42*z)*(18*z**3) + (-15*z**2)*(18*z**3)\nReplacing (18*z**3)*(-15*z**2 - 42*z) with (-42*z)*(18*z**3) + (-15*z**2)*(18*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-42*z)*(18*z**3) - 42*z*6 + (-15*z**2)*(18*z**3) - 15*z**2*6\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*z)*6 = -252*z\n (-42*z)*(18*z**3) = -756*z**4\n (-15*z**2)*6 = -90*z**2\n (-15*z**2)*(18*z**3) = -270*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -270*z**5 - 756*z**4 - 90*z**2 - 252*z\nNo more calculations needed.\n-270*z**5 - 756*z**4 - 90*z**2 - 252*z", "generated_answer": "-270*z**5 - 756*z**4 - 90*z**2 - 252*z", "step_length": 5} {"cot_id": "3a726302ed5f7be573224c1ccae2c2bf6cef8046ffc5de506c41a49096a60a36", "datapoint": {"question": "Calculate the following: (-19*z**3 - 45)*(35*z**3 - 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-665*z**6 - 1119*z**3 + 1080", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 342, "polynomial_expr": "(-19*z**3 - 45)*(35*z**3 - 24)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-19*z**3 - 45)*(35*z**3 - 24)\nExpanding the part (-19*z**3 - 45) using the distributive property, and we got: (-19*z**3)*(35*z**3 - 24) - 45*(35*z**3 - 24)\n#Step 2:\nCurrent expression: (-19*z**3)*(35*z**3 - 24) - 45*(35*z**3 - 24)\nSimplifying the partial expression: -45*(35*z**3 - 24)\nExpanding the part (35*z**3 - 24) using the distributive property, and we got: (35*z**3)*(-45) - 24*(-45)\nReplacing -45*(35*z**3 - 24) with (35*z**3)*(-45) - 24*(-45) in the overall expression.\n#Step 3:\nCurrent expression: (-19*z**3)*(35*z**3 - 24) + (35*z**3)*(-45) + 1080\nSimplifying the partial expression: (-19*z**3)*(35*z**3 - 24)\nExpanding the part (35*z**3 - 24) using the distributive property, and we got: -(-1)*456*z**3 + (-19*z**3)*(35*z**3)\nReplacing (-19*z**3)*(35*z**3 - 24) with -(-1)*456*z**3 + (-19*z**3)*(35*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -24*(-19)*z**3 + (-19*z**3)*(35*z**3) + (35*z**3)*(-45) + 1080\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (35*z**3)*-45 = -1575*z**3\n (35*z**3)*(-19*z**3) = -665*z**6\n -24*-19*z**3 = 456*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -665*z**6 - 1575*z**3 + 456*z**3 + 1080\nCombining like terms, got -665*z**6 - 1119*z**3 + 1080\n#Step 6:\nCurrent expression: -665*z**6 - 1119*z**3 + 1080\nNo more calculations needed.\n-665*z**6 - 1119*z**3 + 1080", "generated_answer": "-665*z**6 - 1119*z**3 + 1080", "step_length": 6} {"cot_id": "c08e629579cd8a784229a5bc4e2c520522da5dfefc54e762dd1a5fb81f566154", "datapoint": {"question": "Calculate the following: (49 - 34*x**2)*(x - 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-34*x**3 + 476*x**2 + 49*x - 686", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 343, "polynomial_expr": "(49 - 34*x**2)*(x - 14)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (49 - 34*x**2)*(x - 14)\nExpanding the part (x - 14) using the distributive property, and we got: x*(49 - 34*x**2) - 14*(49 - 34*x**2)\n#Step 2:\nCurrent expression: x*(49 - 34*x**2) - 14*(49 - 34*x**2)\nSimplifying the partial expression: -14*(49 - 34*x**2)\nExpanding the part (49 - 34*x**2) using the distributive property, and we got: -34*x**2*(-14) + 49*(-14)\nReplacing -14*(49 - 34*x**2) with -34*x**2*(-14) + 49*(-14) in the overall expression.\n#Step 3:\nCurrent expression: x*(49 - 34*x**2) - 34*x**2*(-14) - 686\nSimplifying the partial expression: x*(49 - 34*x**2)\nExpanding the part (49 - 34*x**2) using the distributive property, and we got: x*(-34*x**2) + 49*x\nReplacing x*(49 - 34*x**2) with x*(-34*x**2) + 49*x in the overall expression.\n#Step 4:\nCurrent expression: x*(-34*x**2) + 49*x - 34*x**2*(-14) - 686\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*x**2)*-14 = 476*x**2\n (-34*x**2)*x = -34*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -34*x**3 + 476*x**2 + 49*x - 686\nNo more calculations needed.\n-34*x**3 + 476*x**2 + 49*x - 686", "generated_answer": "-34*x**3 + 476*x**2 + 49*x - 686", "step_length": 5} {"cot_id": "813d3a108f15b08dd8d4e85196e9ebf1fb7e1d1020a68e55e89f34a1be41eca7", "datapoint": {"question": "Simplify this expression: (12*z**3 + 19*z**2 + 62)*(34*z**3 - 26*z**2 + 16*z + 45)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "408*z**6 + 334*z**5 - 302*z**4 + 2952*z**3 - 757*z**2 + 992*z + 2790", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 344, "polynomial_expr": "(12*z**3 + 19*z**2 + 62)*(34*z**3 - 26*z**2 + 16*z + 45)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (12*z**3 + 19*z**2 + 62)*(34*z**3 - 26*z**2 + 16*z + 45)\nExpanding the part (12*z**3 + 19*z**2 + 62) using the distributive property, and we got: (19*z**2)*(34*z**3 - 26*z**2 + 16*z + 45) + (12*z**3)*(34*z**3 - 26*z**2 + 16*z + 45) + 62*(34*z**3 - 26*z**2 + 16*z + 45)\n#Step 2:\nCurrent expression: (19*z**2)*(34*z**3 - 26*z**2 + 16*z + 45) + (12*z**3)*(34*z**3 - 26*z**2 + 16*z + 45) + 62*(34*z**3 - 26*z**2 + 16*z + 45)\nSimplifying the partial expression: 62*(34*z**3 - 26*z**2 + 16*z + 45)\nExpanding the part (34*z**3 - 26*z**2 + 16*z + 45) using the distributive property, and we got: (16*z)*62 - 26*z**2*62 + (34*z**3)*62 + 45*62\nReplacing 62*(34*z**3 - 26*z**2 + 16*z + 45) with (16*z)*62 - 26*z**2*62 + (34*z**3)*62 + 45*62 in the overall expression.\n#Step 3:\nCurrent expression: (16*z)*62 - 26*z**2*62 + (19*z**2)*(34*z**3 - 26*z**2 + 16*z + 45) + (12*z**3)*(34*z**3 - 26*z**2 + 16*z + 45) + (34*z**3)*62 + 2790\nSimplifying the partial expression: (12*z**3)*(34*z**3 - 26*z**2 + 16*z + 45)\nExpanding the part (34*z**3 - 26*z**2 + 16*z + 45) using the distributive property, and we got: 45*(12*z**3) + (16*z)*(12*z**3) + (-26*z**2)*(12*z**3) + (12*z**3)*(34*z**3)\nReplacing (12*z**3)*(34*z**3 - 26*z**2 + 16*z + 45) with 45*(12*z**3) + (16*z)*(12*z**3) + (-26*z**2)*(12*z**3) + (12*z**3)*(34*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 45*12*z**3 + (16*z)*(12*z**3) + (16*z)*62 + (-26*z**2)*(12*z**3) - 26*z**2*62 + (19*z**2)*(34*z**3 - 26*z**2 + 16*z + 45) + (12*z**3)*(34*z**3) + (34*z**3)*62 + 2790\nSimplifying the partial expression: (19*z**2)*(34*z**3 - 26*z**2 + 16*z + 45)\nExpanding the part (34*z**3 - 26*z**2 + 16*z + 45) using the distributive property, and we got: 45*(19*z**2) + (16*z)*(19*z**2) + (-26*z**2)*(19*z**2) + (19*z**2)*(34*z**3)\nReplacing (19*z**2)*(34*z**3 - 26*z**2 + 16*z + 45) with 45*(19*z**2) + (16*z)*(19*z**2) + (-26*z**2)*(19*z**2) + (19*z**2)*(34*z**3) in the overall expression.\n#Step 5:\nCurrent expression: 45*12*z**3 + 45*19*z**2 + (16*z)*(19*z**2) + (16*z)*(12*z**3) + (16*z)*62 + (-26*z**2)*(19*z**2) + (-26*z**2)*(12*z**3) - 26*z**2*62 + (19*z**2)*(34*z**3) + (12*z**3)*(34*z**3) + (34*z**3)*62 + 2790\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-26*z**2)*62 = -1612*z**2\n (-26*z**2)*(12*z**3) = -312*z**5\n (-26*z**2)*(19*z**2) = -494*z**4\n (16*z)*62 = 992*z\n (16*z)*(12*z**3) = 192*z**4\n (16*z)*(19*z**2) = 304*z**3\n (34*z**3)*62 = 2108*z**3\n (34*z**3)*(12*z**3) = 408*z**6\n (34*z**3)*(19*z**2) = 646*z**5\n 45*12*z**3 = 540*z**3\n 45*19*z**2 = 855*z**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 408*z**6 - 312*z**5 + 646*z**5 - 494*z**4 + 192*z**4 + 304*z**3 + 540*z**3 + 2108*z**3 - 1612*z**2 + 855*z**2 + 992*z + 2790\nCombining like terms, got 408*z**6 + 334*z**5 - 302*z**4 + 2952*z**3 - 757*z**2 + 992*z + 2790\n#Step 7:\nCurrent expression: 408*z**6 + 334*z**5 - 302*z**4 + 2952*z**3 - 757*z**2 + 992*z + 2790\nNo more calculations needed.\n408*z**6 + 334*z**5 - 302*z**4 + 2952*z**3 - 757*z**2 + 992*z + 2790", "generated_answer": "408*z**6 + 334*z**5 - 302*z**4 + 2952*z**3 - 757*z**2 + 992*z + 2790", "step_length": 7} {"cot_id": "f7d6cc19889b01cffd1ebd04618b24bb7fc42c9346bd21b094e4e48a191b0ae2", "datapoint": {"question": "Simplify this expression: (-6*y**3 - 27*y)*(18*y**3 - 12)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-108*y**6 - 486*y**4 + 72*y**3 + 324*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 345, "polynomial_expr": "(-6*y**3 - 27*y)*(18*y**3 - 12)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-6*y**3 - 27*y)*(18*y**3 - 12)\nExpanding the part (18*y**3 - 12) using the distributive property, and we got: (18*y**3)*(-6*y**3 - 27*y) - 12*(-6*y**3 - 27*y)\n#Step 2:\nCurrent expression: (18*y**3)*(-6*y**3 - 27*y) - 12*(-6*y**3 - 27*y)\nSimplifying the partial expression: -12*(-6*y**3 - 27*y)\nExpanding the part (-6*y**3 - 27*y) using the distributive property, and we got: -27*y*(-12) - 6*y**3*(-12)\nReplacing -12*(-6*y**3 - 27*y) with -27*y*(-12) - 6*y**3*(-12) in the overall expression.\n#Step 3:\nCurrent expression: -27*y*(-12) - 6*y**3*(-12) + (18*y**3)*(-6*y**3 - 27*y)\nSimplifying the partial expression: (18*y**3)*(-6*y**3 - 27*y)\nExpanding the part (-6*y**3 - 27*y) using the distributive property, and we got: (-27*y)*(18*y**3) + (-6*y**3)*(18*y**3)\nReplacing (18*y**3)*(-6*y**3 - 27*y) with (-27*y)*(18*y**3) + (-6*y**3)*(18*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-27*y)*(18*y**3) - 27*y*(-12) + (-6*y**3)*(18*y**3) - 6*y**3*(-12)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*y)*-12 = 324*y\n (-27*y)*(18*y**3) = -486*y**4\n (-6*y**3)*-12 = 72*y**3\n (-6*y**3)*(18*y**3) = -108*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -108*y**6 - 486*y**4 + 72*y**3 + 324*y\nNo more calculations needed.\n-108*y**6 - 486*y**4 + 72*y**3 + 324*y", "generated_answer": "-108*y**6 - 486*y**4 + 72*y**3 + 324*y", "step_length": 5} {"cot_id": "51d965421c44ef4e495157de82a3574534605f0a51f881be5c67fab5353c5303", "datapoint": {"question": "Simplify this expression: (15 - 16*y**2)*(-61*y**3 + 32*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "976*y**5 - 1427*y**3 + 480*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 346, "polynomial_expr": "(15 - 16*y**2)*(-61*y**3 + 32*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (15 - 16*y**2)*(-61*y**3 + 32*y)\nExpanding the part (15 - 16*y**2) using the distributive property, and we got: (-16*y**2)*(-61*y**3 + 32*y) + 15*(-61*y**3 + 32*y)\n#Step 2:\nCurrent expression: (-16*y**2)*(-61*y**3 + 32*y) + 15*(-61*y**3 + 32*y)\nSimplifying the partial expression: 15*(-61*y**3 + 32*y)\nExpanding the part (-61*y**3 + 32*y) using the distributive property, and we got: (32*y)*15 - 61*y**3*15\nReplacing 15*(-61*y**3 + 32*y) with (32*y)*15 - 61*y**3*15 in the overall expression.\n#Step 3:\nCurrent expression: (32*y)*15 + (-16*y**2)*(-61*y**3 + 32*y) - 61*y**3*15\nSimplifying the partial expression: (-16*y**2)*(-61*y**3 + 32*y)\nExpanding the part (-61*y**3 + 32*y) using the distributive property, and we got: (32*y)*(-16*y**2) + (-16*y**2)*(-61*y**3)\nReplacing (-16*y**2)*(-61*y**3 + 32*y) with (32*y)*(-16*y**2) + (-16*y**2)*(-61*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (32*y)*(-16*y**2) + (32*y)*15 + (-16*y**2)*(-61*y**3) - 61*y**3*15\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-61*y**3)*15 = -915*y**3\n (-61*y**3)*(-16*y**2) = 976*y**5\n (32*y)*15 = 480*y\n (32*y)*(-16*y**2) = -512*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 976*y**5 - 915*y**3 - 512*y**3 + 480*y\nCombining like terms, got 976*y**5 - 1427*y**3 + 480*y\n#Step 6:\nCurrent expression: 976*y**5 - 1427*y**3 + 480*y\nNo more calculations needed.\n976*y**5 - 1427*y**3 + 480*y", "generated_answer": "976*y**5 - 1427*y**3 + 480*y", "step_length": 6} {"cot_id": "b26fef91860ad2b775e8c02f1f6867c36aecd6b07bd45fd86f8c98655b3395b7", "datapoint": {"question": "Simplify this expression: (44*z**3 + 25*z**2)*(15*z**3 - 46*z**2 - 40)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "660*z**6 - 1649*z**5 - 1150*z**4 - 1760*z**3 - 1000*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 347, "polynomial_expr": "(44*z**3 + 25*z**2)*(15*z**3 - 46*z**2 - 40)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (44*z**3 + 25*z**2)*(15*z**3 - 46*z**2 - 40)\nExpanding the part (44*z**3 + 25*z**2) using the distributive property, and we got: (25*z**2)*(15*z**3 - 46*z**2 - 40) + (44*z**3)*(15*z**3 - 46*z**2 - 40)\n#Step 2:\nCurrent expression: (25*z**2)*(15*z**3 - 46*z**2 - 40) + (44*z**3)*(15*z**3 - 46*z**2 - 40)\nSimplifying the partial expression: (25*z**2)*(15*z**3 - 46*z**2 - 40)\nExpanding the part (15*z**3 - 46*z**2 - 40) using the distributive property, and we got: -1000*z**2 + (-46*z**2)*(25*z**2) + (25*z**2)*(15*z**3)\nReplacing (25*z**2)*(15*z**3 - 46*z**2 - 40) with -1000*z**2 + (-46*z**2)*(25*z**2) + (25*z**2)*(15*z**3) in the overall expression.\n#Step 3:\nCurrent expression: -40*25*z**2 + (-46*z**2)*(25*z**2) + (25*z**2)*(15*z**3) + (44*z**3)*(15*z**3 - 46*z**2 - 40)\nSimplifying the partial expression: (44*z**3)*(15*z**3 - 46*z**2 - 40)\nExpanding the part (15*z**3 - 46*z**2 - 40) using the distributive property, and we got: -1760*z**3 + (-46*z**2)*(44*z**3) + (15*z**3)*(44*z**3)\nReplacing (44*z**3)*(15*z**3 - 46*z**2 - 40) with -1760*z**3 + (-46*z**2)*(44*z**3) + (15*z**3)*(44*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -40*44*z**3 - 40*25*z**2 + (-46*z**2)*(25*z**2) + (-46*z**2)*(44*z**3) + (25*z**2)*(15*z**3) + (15*z**3)*(44*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*z**2)*(25*z**2) = -1150*z**4\n (-46*z**2)*(44*z**3) = -2024*z**5\n (15*z**3)*(25*z**2) = 375*z**5\n (15*z**3)*(44*z**3) = 660*z**6\n -40*25*z**2 = -1000*z**2\n -40*44*z**3 = -1760*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 660*z**6 - 2024*z**5 + 375*z**5 - 1150*z**4 - 1760*z**3 - 1000*z**2\nCombining like terms, got 660*z**6 - 1649*z**5 - 1150*z**4 - 1760*z**3 - 1000*z**2\n#Step 6:\nCurrent expression: 660*z**6 - 1649*z**5 - 1150*z**4 - 1760*z**3 - 1000*z**2\nNo more calculations needed.\n660*z**6 - 1649*z**5 - 1150*z**4 - 1760*z**3 - 1000*z**2", "generated_answer": "660*z**6 - 1649*z**5 - 1150*z**4 - 1760*z**3 - 1000*z**2", "step_length": 6} {"cot_id": "a024d3cade286028b37931dc732bbb3ba5541512922707891407332d5fcd71b2", "datapoint": {"question": "Simplify this expression: (44*z**2 - 13)*(17*z**3 - 35*z**2 + 49*z - 40)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "748*z**5 - 1540*z**4 + 1935*z**3 - 1305*z**2 - 637*z + 520", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 348, "polynomial_expr": "(44*z**2 - 13)*(17*z**3 - 35*z**2 + 49*z - 40)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (44*z**2 - 13)*(17*z**3 - 35*z**2 + 49*z - 40)\nExpanding the part (44*z**2 - 13) using the distributive property, and we got: (44*z**2)*(17*z**3 - 35*z**2 + 49*z - 40) - 13*(17*z**3 - 35*z**2 + 49*z - 40)\n#Step 2:\nCurrent expression: (44*z**2)*(17*z**3 - 35*z**2 + 49*z - 40) - 13*(17*z**3 - 35*z**2 + 49*z - 40)\nSimplifying the partial expression: -13*(17*z**3 - 35*z**2 + 49*z - 40)\nExpanding the part (17*z**3 - 35*z**2 + 49*z - 40) using the distributive property, and we got: (49*z)*(-13) - 35*z**2*(-13) + (17*z**3)*(-13) - 40*(-13)\nReplacing -13*(17*z**3 - 35*z**2 + 49*z - 40) with (49*z)*(-13) - 35*z**2*(-13) + (17*z**3)*(-13) - 40*(-13) in the overall expression.\n#Step 3:\nCurrent expression: (49*z)*(-13) - 35*z**2*(-13) + (44*z**2)*(17*z**3 - 35*z**2 + 49*z - 40) + (17*z**3)*(-13) + 520\nSimplifying the partial expression: (44*z**2)*(17*z**3 - 35*z**2 + 49*z - 40)\nExpanding the part (17*z**3 - 35*z**2 + 49*z - 40) using the distributive property, and we got: -1760*z**2 + (49*z)*(44*z**2) + (-35*z**2)*(44*z**2) + (44*z**2)*(17*z**3)\nReplacing (44*z**2)*(17*z**3 - 35*z**2 + 49*z - 40) with -1760*z**2 + (49*z)*(44*z**2) + (-35*z**2)*(44*z**2) + (44*z**2)*(17*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -40*44*z**2 + (49*z)*(44*z**2) + (49*z)*(-13) + (-35*z**2)*(44*z**2) - 35*z**2*(-13) + (44*z**2)*(17*z**3) + (17*z**3)*(-13) + 520\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*z**2)*-13 = 455*z**2\n (-35*z**2)*(44*z**2) = -1540*z**4\n (17*z**3)*-13 = -221*z**3\n (17*z**3)*(44*z**2) = 748*z**5\n (49*z)*-13 = -637*z\n (49*z)*(44*z**2) = 2156*z**3\n -40*44*z**2 = -1760*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 748*z**5 - 1540*z**4 - 221*z**3 + 2156*z**3 - 1760*z**2 + 455*z**2 - 637*z + 520\nCombining like terms, got 748*z**5 - 1540*z**4 + 1935*z**3 - 1305*z**2 - 637*z + 520\n#Step 6:\nCurrent expression: 748*z**5 - 1540*z**4 + 1935*z**3 - 1305*z**2 - 637*z + 520\nNo more calculations needed.\n748*z**5 - 1540*z**4 + 1935*z**3 - 1305*z**2 - 637*z + 520", "generated_answer": "748*z**5 - 1540*z**4 + 1935*z**3 - 1305*z**2 - 637*z + 520", "step_length": 6} {"cot_id": "03f4ee227837893c81ae8eae96b88c1ad36c1eeda76102f0f7d9f3a2a5cbaea9", "datapoint": {"question": "Calculate the following: (-42*y**3 - 47*y**2 - 27*y)*(-39*y**3 + 3*y**2 + 51)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1638*y**6 + 1707*y**5 + 912*y**4 - 2223*y**3 - 2397*y**2 - 1377*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 349, "polynomial_expr": "(-42*y**3 - 47*y**2 - 27*y)*(-39*y**3 + 3*y**2 + 51)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-42*y**3 - 47*y**2 - 27*y)*(-39*y**3 + 3*y**2 + 51)\nExpanding the part (-39*y**3 + 3*y**2 + 51) using the distributive property, and we got: (3*y**2)*(-42*y**3 - 47*y**2 - 27*y) + (-39*y**3)*(-42*y**3 - 47*y**2 - 27*y) + 51*(-42*y**3 - 47*y**2 - 27*y)\n#Step 2:\nCurrent expression: (3*y**2)*(-42*y**3 - 47*y**2 - 27*y) + (-39*y**3)*(-42*y**3 - 47*y**2 - 27*y) + 51*(-42*y**3 - 47*y**2 - 27*y)\nSimplifying the partial expression: 51*(-42*y**3 - 47*y**2 - 27*y)\nExpanding the part (-42*y**3 - 47*y**2 - 27*y) using the distributive property, and we got: -27*y*51 - 47*y**2*51 - 42*y**3*51\nReplacing 51*(-42*y**3 - 47*y**2 - 27*y) with -27*y*51 - 47*y**2*51 - 42*y**3*51 in the overall expression.\n#Step 3:\nCurrent expression: -27*y*51 - 47*y**2*51 + (3*y**2)*(-42*y**3 - 47*y**2 - 27*y) - 42*y**3*51 + (-39*y**3)*(-42*y**3 - 47*y**2 - 27*y)\nSimplifying the partial expression: (-39*y**3)*(-42*y**3 - 47*y**2 - 27*y)\nExpanding the part (-42*y**3 - 47*y**2 - 27*y) using the distributive property, and we got: (-27*y)*(-39*y**3) + (-47*y**2)*(-39*y**3) + (-42*y**3)*(-39*y**3)\nReplacing (-39*y**3)*(-42*y**3 - 47*y**2 - 27*y) with (-27*y)*(-39*y**3) + (-47*y**2)*(-39*y**3) + (-42*y**3)*(-39*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-27*y)*(-39*y**3) - 27*y*51 + (-47*y**2)*(-39*y**3) - 47*y**2*51 + (3*y**2)*(-42*y**3 - 47*y**2 - 27*y) + (-42*y**3)*(-39*y**3) - 42*y**3*51\nSimplifying the partial expression: (3*y**2)*(-42*y**3 - 47*y**2 - 27*y)\nExpanding the part (-42*y**3 - 47*y**2 - 27*y) using the distributive property, and we got: (-27*y)*(3*y**2) + (-47*y**2)*(3*y**2) + (3*y**2)*(-42*y**3)\nReplacing (3*y**2)*(-42*y**3 - 47*y**2 - 27*y) with (-27*y)*(3*y**2) + (-47*y**2)*(3*y**2) + (3*y**2)*(-42*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-27*y)*(3*y**2) + (-27*y)*(-39*y**3) - 27*y*51 + (-47*y**2)*(3*y**2) + (-47*y**2)*(-39*y**3) - 47*y**2*51 + (3*y**2)*(-42*y**3) + (-42*y**3)*(-39*y**3) - 42*y**3*51\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*y**2)*51 = -2397*y**2\n (-47*y**2)*(-39*y**3) = 1833*y**5\n (-47*y**2)*(3*y**2) = -141*y**4\n (-42*y**3)*51 = -2142*y**3\n (-42*y**3)*(-39*y**3) = 1638*y**6\n (-42*y**3)*(3*y**2) = -126*y**5\n (-27*y)*51 = -1377*y\n (-27*y)*(-39*y**3) = 1053*y**4\n (-27*y)*(3*y**2) = -81*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1638*y**6 - 126*y**5 + 1833*y**5 - 141*y**4 + 1053*y**4 - 2142*y**3 - 81*y**3 - 2397*y**2 - 1377*y\nCombining like terms, got 1638*y**6 + 1707*y**5 + 912*y**4 - 2223*y**3 - 2397*y**2 - 1377*y\n#Step 7:\nCurrent expression: 1638*y**6 + 1707*y**5 + 912*y**4 - 2223*y**3 - 2397*y**2 - 1377*y\nNo more calculations needed.\n1638*y**6 + 1707*y**5 + 912*y**4 - 2223*y**3 - 2397*y**2 - 1377*y", "generated_answer": "1638*y**6 + 1707*y**5 + 912*y**4 - 2223*y**3 - 2397*y**2 - 1377*y", "step_length": 7} {"cot_id": "ced8bc91eb2ffe0f46a16bdcb98767ebaf9688ecd1c7b59dd000bffb692b2ca7", "datapoint": {"question": "Simplify this expression: 16*z**3 - 44*z - 92\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "16*z**3 - 44*z - 92", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 350, "polynomial_expr": "16*z**3 - 44*z - 92", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 16*z**3 - 44*z - 92\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 16*z**3 - 44*z - 92\nNo more calculations needed.\n16*z**3 - 44*z - 92", "generated_answer": "16*z**3 - 44*z - 92", "step_length": 2} {"cot_id": "ae50a952c952c551ff8e2eace6380ef77ca7842dca9dbddd3553eebebe4b0b4d", "datapoint": {"question": "Calculate the following: (-9*y**3 - y**2)*(-y**3 - 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "9*y**6 + y**5 + 324*y**3 + 36*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 351, "polynomial_expr": "(-9*y**3 - y**2)*(-y**3 - 36)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-9*y**3 - y**2)*(-y**3 - 36)\nExpanding the part (-y**3 - 36) using the distributive property, and we got: (-y**3)*(-9*y**3 - y**2) - 36*(-9*y**3 - y**2)\n#Step 2:\nCurrent expression: (-y**3)*(-9*y**3 - y**2) - 36*(-9*y**3 - y**2)\nSimplifying the partial expression: -36*(-9*y**3 - y**2)\nExpanding the part (-9*y**3 - y**2) using the distributive property, and we got: -y**2*(-36) - 9*y**3*(-36)\nReplacing -36*(-9*y**3 - y**2) with -y**2*(-36) - 9*y**3*(-36) in the overall expression.\n#Step 3:\nCurrent expression: -y**2*(-36) - 9*y**3*(-36) + (-y**3)*(-9*y**3 - y**2)\nSimplifying the partial expression: (-y**3)*(-9*y**3 - y**2)\nExpanding the part (-9*y**3 - y**2) using the distributive property, and we got: (-y**2)*(-y**3) + (-9*y**3)*(-y**3)\nReplacing (-y**3)*(-9*y**3 - y**2) with (-y**2)*(-y**3) + (-9*y**3)*(-y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-y**2)*(-y**3) - y**2*(-36) + (-9*y**3)*(-y**3) - 9*y**3*(-36)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-y**2)*-36 = 36*y**2\n (-y**2)*(-y**3) = y**5\n (-9*y**3)*-36 = 324*y**3\n (-9*y**3)*(-y**3) = 9*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 9*y**6 + y**5 + 324*y**3 + 36*y**2\nNo more calculations needed.\n9*y**6 + y**5 + 324*y**3 + 36*y**2", "generated_answer": "9*y**6 + y**5 + 324*y**3 + 36*y**2", "step_length": 5} {"cot_id": "9d6058298ff412d5b59fc03bf86598f8c600f680dc408b21670972d55c313fce", "datapoint": {"question": "Calculate the following: (36*x**3 + 40*x - 24)*(41*x**3 - 22*x**2 - 45)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1476*x**6 - 792*x**5 + 1640*x**4 - 3484*x**3 + 528*x**2 - 1800*x + 1080", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 352, "polynomial_expr": "(36*x**3 + 40*x - 24)*(41*x**3 - 22*x**2 - 45)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (36*x**3 + 40*x - 24)*(41*x**3 - 22*x**2 - 45)\nExpanding the part (41*x**3 - 22*x**2 - 45) using the distributive property, and we got: (-22*x**2)*(36*x**3 + 40*x - 24) + (41*x**3)*(36*x**3 + 40*x - 24) - 45*(36*x**3 + 40*x - 24)\n#Step 2:\nCurrent expression: (-22*x**2)*(36*x**3 + 40*x - 24) + (41*x**3)*(36*x**3 + 40*x - 24) - 45*(36*x**3 + 40*x - 24)\nSimplifying the partial expression: -45*(36*x**3 + 40*x - 24)\nExpanding the part (36*x**3 + 40*x - 24) using the distributive property, and we got: (40*x)*(-45) + (36*x**3)*(-45) - 24*(-45)\nReplacing -45*(36*x**3 + 40*x - 24) with (40*x)*(-45) + (36*x**3)*(-45) - 24*(-45) in the overall expression.\n#Step 3:\nCurrent expression: (40*x)*(-45) + (-22*x**2)*(36*x**3 + 40*x - 24) + (36*x**3)*(-45) + (41*x**3)*(36*x**3 + 40*x - 24) + 1080\nSimplifying the partial expression: (-22*x**2)*(36*x**3 + 40*x - 24)\nExpanding the part (36*x**3 + 40*x - 24) using the distributive property, and we got: -(-1)*528*x**2 + (40*x)*(-22*x**2) + (-22*x**2)*(36*x**3)\nReplacing (-22*x**2)*(36*x**3 + 40*x - 24) with -(-1)*528*x**2 + (40*x)*(-22*x**2) + (-22*x**2)*(36*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -24*(-22)*x**2 + (40*x)*(-22*x**2) + (40*x)*(-45) + (-22*x**2)*(36*x**3) + (36*x**3)*(-45) + (41*x**3)*(36*x**3 + 40*x - 24) + 1080\nSimplifying the partial expression: (41*x**3)*(36*x**3 + 40*x - 24)\nExpanding the part (36*x**3 + 40*x - 24) using the distributive property, and we got: -984*x**3 + (40*x)*(41*x**3) + (36*x**3)*(41*x**3)\nReplacing (41*x**3)*(36*x**3 + 40*x - 24) with -984*x**3 + (40*x)*(41*x**3) + (36*x**3)*(41*x**3) in the overall expression.\n#Step 5:\nCurrent expression: -24*41*x**3 - 24*(-22)*x**2 + (40*x)*(-22*x**2) + (40*x)*(41*x**3) + (40*x)*(-45) + (-22*x**2)*(36*x**3) + (36*x**3)*(41*x**3) + (36*x**3)*(-45) + 1080\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (36*x**3)*-45 = -1620*x**3\n (36*x**3)*(-22*x**2) = -792*x**5\n (36*x**3)*(41*x**3) = 1476*x**6\n (40*x)*-45 = -1800*x\n (40*x)*(-22*x**2) = -880*x**3\n (40*x)*(41*x**3) = 1640*x**4\n -24*-22*x**2 = 528*x**2\n -24*41*x**3 = -984*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1476*x**6 - 792*x**5 + 1640*x**4 - 1620*x**3 - 984*x**3 - 880*x**3 + 528*x**2 - 1800*x + 1080\nCombining like terms, got 1476*x**6 - 792*x**5 + 1640*x**4 - 3484*x**3 + 528*x**2 - 1800*x + 1080\n#Step 7:\nCurrent expression: 1476*x**6 - 792*x**5 + 1640*x**4 - 3484*x**3 + 528*x**2 - 1800*x + 1080\nNo more calculations needed.\n1476*x**6 - 792*x**5 + 1640*x**4 - 3484*x**3 + 528*x**2 - 1800*x + 1080", "generated_answer": "1476*x**6 - 792*x**5 + 1640*x**4 - 3484*x**3 + 528*x**2 - 1800*x + 1080", "step_length": 7} {"cot_id": "f2353e10d6b5adda76a0cd1c22e833d620b58a1fbc528c4c646078971b6a62b2", "datapoint": {"question": "Calculate the following: (11*y**2 + 44*y)*(-9*y**3 + 49*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-99*y**5 - 396*y**4 + 539*y**3 + 2156*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 353, "polynomial_expr": "(11*y**2 + 44*y)*(-9*y**3 + 49*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11*y**2 + 44*y)*(-9*y**3 + 49*y)\nExpanding the part (-9*y**3 + 49*y) using the distributive property, and we got: (49*y)*(11*y**2 + 44*y) + (-9*y**3)*(11*y**2 + 44*y)\n#Step 2:\nCurrent expression: (49*y)*(11*y**2 + 44*y) + (-9*y**3)*(11*y**2 + 44*y)\nSimplifying the partial expression: (-9*y**3)*(11*y**2 + 44*y)\nExpanding the part (11*y**2 + 44*y) using the distributive property, and we got: (44*y)*(-9*y**3) + (11*y**2)*(-9*y**3)\nReplacing (-9*y**3)*(11*y**2 + 44*y) with (44*y)*(-9*y**3) + (11*y**2)*(-9*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (44*y)*(-9*y**3) + (49*y)*(11*y**2 + 44*y) + (11*y**2)*(-9*y**3)\nSimplifying the partial expression: (49*y)*(11*y**2 + 44*y)\nExpanding the part (11*y**2 + 44*y) using the distributive property, and we got: (44*y)*(49*y) + (49*y)*(11*y**2)\nReplacing (49*y)*(11*y**2 + 44*y) with (44*y)*(49*y) + (49*y)*(11*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (44*y)*(49*y) + (44*y)*(-9*y**3) + (49*y)*(11*y**2) + (11*y**2)*(-9*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (11*y**2)*(-9*y**3) = -99*y**5\n (11*y**2)*(49*y) = 539*y**3\n (44*y)*(-9*y**3) = -396*y**4\n (44*y)*(49*y) = 2156*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -99*y**5 - 396*y**4 + 539*y**3 + 2156*y**2\nNo more calculations needed.\n-99*y**5 - 396*y**4 + 539*y**3 + 2156*y**2", "generated_answer": "-99*y**5 - 396*y**4 + 539*y**3 + 2156*y**2", "step_length": 5} {"cot_id": "9a229e497bd83ed74510d4cea8fc679f1aa98efa56b37d022a7f9adf915560d5", "datapoint": {"question": "Calculate the following: (-19*x**2 - 31)*(6*x**3 + 39*x**2 - 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-114*x**5 - 741*x**4 - 186*x**3 - 886*x**2 + 527", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 354, "polynomial_expr": "(-19*x**2 - 31)*(6*x**3 + 39*x**2 - 17)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-19*x**2 - 31)*(6*x**3 + 39*x**2 - 17)\nExpanding the part (-19*x**2 - 31) using the distributive property, and we got: (-19*x**2)*(6*x**3 + 39*x**2 - 17) - 31*(6*x**3 + 39*x**2 - 17)\n#Step 2:\nCurrent expression: (-19*x**2)*(6*x**3 + 39*x**2 - 17) - 31*(6*x**3 + 39*x**2 - 17)\nSimplifying the partial expression: -31*(6*x**3 + 39*x**2 - 17)\nExpanding the part (6*x**3 + 39*x**2 - 17) using the distributive property, and we got: (39*x**2)*(-31) + (6*x**3)*(-31) - 17*(-31)\nReplacing -31*(6*x**3 + 39*x**2 - 17) with (39*x**2)*(-31) + (6*x**3)*(-31) - 17*(-31) in the overall expression.\n#Step 3:\nCurrent expression: (-19*x**2)*(6*x**3 + 39*x**2 - 17) + (39*x**2)*(-31) + (6*x**3)*(-31) + 527\nSimplifying the partial expression: (-19*x**2)*(6*x**3 + 39*x**2 - 17)\nExpanding the part (6*x**3 + 39*x**2 - 17) using the distributive property, and we got: -(-1)*323*x**2 + (-19*x**2)*(39*x**2) + (-19*x**2)*(6*x**3)\nReplacing (-19*x**2)*(6*x**3 + 39*x**2 - 17) with -(-1)*323*x**2 + (-19*x**2)*(39*x**2) + (-19*x**2)*(6*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -17*(-19)*x**2 + (-19*x**2)*(39*x**2) + (-19*x**2)*(6*x**3) + (39*x**2)*(-31) + (6*x**3)*(-31) + 527\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (6*x**3)*-31 = -186*x**3\n (6*x**3)*(-19*x**2) = -114*x**5\n (39*x**2)*-31 = -1209*x**2\n (39*x**2)*(-19*x**2) = -741*x**4\n -17*-19*x**2 = 323*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -114*x**5 - 741*x**4 - 186*x**3 - 1209*x**2 + 323*x**2 + 527\nCombining like terms, got -114*x**5 - 741*x**4 - 186*x**3 - 886*x**2 + 527\n#Step 6:\nCurrent expression: -114*x**5 - 741*x**4 - 186*x**3 - 886*x**2 + 527\nNo more calculations needed.\n-114*x**5 - 741*x**4 - 186*x**3 - 886*x**2 + 527", "generated_answer": "-114*x**5 - 741*x**4 - 186*x**3 - 886*x**2 + 527", "step_length": 6} {"cot_id": "3292ff6f1498a3ca2d805a90d5301b3bdea6b3f8814fe6d613b45e544e9dd28e", "datapoint": {"question": "Calculate the following: (66*x**3 - 47*x**2)*(-26*x**3 + 30*x - 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1716*x**6 + 1222*x**5 + 1980*x**4 - 3918*x**3 + 1786*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 355, "polynomial_expr": "(66*x**3 - 47*x**2)*(-26*x**3 + 30*x - 38)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (66*x**3 - 47*x**2)*(-26*x**3 + 30*x - 38)\nExpanding the part (66*x**3 - 47*x**2) using the distributive property, and we got: (-47*x**2)*(-26*x**3 + 30*x - 38) + (66*x**3)*(-26*x**3 + 30*x - 38)\n#Step 2:\nCurrent expression: (-47*x**2)*(-26*x**3 + 30*x - 38) + (66*x**3)*(-26*x**3 + 30*x - 38)\nSimplifying the partial expression: (-47*x**2)*(-26*x**3 + 30*x - 38)\nExpanding the part (-26*x**3 + 30*x - 38) using the distributive property, and we got: -(-1)*1786*x**2 + (30*x)*(-47*x**2) + (-47*x**2)*(-26*x**3)\nReplacing (-47*x**2)*(-26*x**3 + 30*x - 38) with -(-1)*1786*x**2 + (30*x)*(-47*x**2) + (-47*x**2)*(-26*x**3) in the overall expression.\n#Step 3:\nCurrent expression: -38*(-47)*x**2 + (30*x)*(-47*x**2) + (-47*x**2)*(-26*x**3) + (66*x**3)*(-26*x**3 + 30*x - 38)\nSimplifying the partial expression: (66*x**3)*(-26*x**3 + 30*x - 38)\nExpanding the part (-26*x**3 + 30*x - 38) using the distributive property, and we got: -2508*x**3 + (30*x)*(66*x**3) + (-26*x**3)*(66*x**3)\nReplacing (66*x**3)*(-26*x**3 + 30*x - 38) with -2508*x**3 + (30*x)*(66*x**3) + (-26*x**3)*(66*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -38*66*x**3 - 38*(-47)*x**2 + (30*x)*(-47*x**2) + (30*x)*(66*x**3) + (-47*x**2)*(-26*x**3) + (-26*x**3)*(66*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-26*x**3)*(-47*x**2) = 1222*x**5\n (-26*x**3)*(66*x**3) = -1716*x**6\n (30*x)*(-47*x**2) = -1410*x**3\n (30*x)*(66*x**3) = 1980*x**4\n -38*-47*x**2 = 1786*x**2\n -38*66*x**3 = -2508*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1716*x**6 + 1222*x**5 + 1980*x**4 - 2508*x**3 - 1410*x**3 + 1786*x**2\nCombining like terms, got -1716*x**6 + 1222*x**5 + 1980*x**4 - 3918*x**3 + 1786*x**2\n#Step 6:\nCurrent expression: -1716*x**6 + 1222*x**5 + 1980*x**4 - 3918*x**3 + 1786*x**2\nNo more calculations needed.\n-1716*x**6 + 1222*x**5 + 1980*x**4 - 3918*x**3 + 1786*x**2", "generated_answer": "-1716*x**6 + 1222*x**5 + 1980*x**4 - 3918*x**3 + 1786*x**2", "step_length": 6} {"cot_id": "249d72018f6b9e62af53d42d69e415fd40bd31bb68a0ce59d0f49525647785b6", "datapoint": {"question": "Simplify this expression: (46 - 39*y**2)*(27*y**2 - 31*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1053*y**4 + 1209*y**3 + 1242*y**2 - 1426*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 356, "polynomial_expr": "(46 - 39*y**2)*(27*y**2 - 31*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (46 - 39*y**2)*(27*y**2 - 31*y)\nExpanding the part (46 - 39*y**2) using the distributive property, and we got: (-39*y**2)*(27*y**2 - 31*y) + 46*(27*y**2 - 31*y)\n#Step 2:\nCurrent expression: (-39*y**2)*(27*y**2 - 31*y) + 46*(27*y**2 - 31*y)\nSimplifying the partial expression: 46*(27*y**2 - 31*y)\nExpanding the part (27*y**2 - 31*y) using the distributive property, and we got: -31*y*46 + (27*y**2)*46\nReplacing 46*(27*y**2 - 31*y) with -31*y*46 + (27*y**2)*46 in the overall expression.\n#Step 3:\nCurrent expression: -31*y*46 + (-39*y**2)*(27*y**2 - 31*y) + (27*y**2)*46\nSimplifying the partial expression: (-39*y**2)*(27*y**2 - 31*y)\nExpanding the part (27*y**2 - 31*y) using the distributive property, and we got: (-31*y)*(-39*y**2) + (-39*y**2)*(27*y**2)\nReplacing (-39*y**2)*(27*y**2 - 31*y) with (-31*y)*(-39*y**2) + (-39*y**2)*(27*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-31*y)*(-39*y**2) - 31*y*46 + (-39*y**2)*(27*y**2) + (27*y**2)*46\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-31*y)*46 = -1426*y\n (-31*y)*(-39*y**2) = 1209*y**3\n (27*y**2)*46 = 1242*y**2\n (27*y**2)*(-39*y**2) = -1053*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1053*y**4 + 1209*y**3 + 1242*y**2 - 1426*y\nNo more calculations needed.\n-1053*y**4 + 1209*y**3 + 1242*y**2 - 1426*y", "generated_answer": "-1053*y**4 + 1209*y**3 + 1242*y**2 - 1426*y", "step_length": 5} {"cot_id": "e8cfc00478466753dbf3d8269a0ec79f69492b15268ae92ae5756cf92b9281aa", "datapoint": {"question": "Simplify this expression: (39*x**3 + 50*x)*(-16*x**3 + 75*x + 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-624*x**6 + 2125*x**4 + 273*x**3 + 3750*x**2 + 350*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 357, "polynomial_expr": "(39*x**3 + 50*x)*(-16*x**3 + 75*x + 7)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (39*x**3 + 50*x)*(-16*x**3 + 75*x + 7)\nExpanding the part (39*x**3 + 50*x) using the distributive property, and we got: (50*x)*(-16*x**3 + 75*x + 7) + (39*x**3)*(-16*x**3 + 75*x + 7)\n#Step 2:\nCurrent expression: (50*x)*(-16*x**3 + 75*x + 7) + (39*x**3)*(-16*x**3 + 75*x + 7)\nSimplifying the partial expression: (39*x**3)*(-16*x**3 + 75*x + 7)\nExpanding the part (-16*x**3 + 75*x + 7) using the distributive property, and we got: 7*(39*x**3) + (75*x)*(39*x**3) + (-16*x**3)*(39*x**3)\nReplacing (39*x**3)*(-16*x**3 + 75*x + 7) with 7*(39*x**3) + (75*x)*(39*x**3) + (-16*x**3)*(39*x**3) in the overall expression.\n#Step 3:\nCurrent expression: 7*39*x**3 + (50*x)*(-16*x**3 + 75*x + 7) + (75*x)*(39*x**3) + (-16*x**3)*(39*x**3)\nSimplifying the partial expression: (50*x)*(-16*x**3 + 75*x + 7)\nExpanding the part (-16*x**3 + 75*x + 7) using the distributive property, and we got: 7*(50*x) + (50*x)*(75*x) + (50*x)*(-16*x**3)\nReplacing (50*x)*(-16*x**3 + 75*x + 7) with 7*(50*x) + (50*x)*(75*x) + (50*x)*(-16*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 7*39*x**3 + 7*50*x + (50*x)*(75*x) + (50*x)*(-16*x**3) + (75*x)*(39*x**3) + (-16*x**3)*(39*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-16*x**3)*(39*x**3) = -624*x**6\n (-16*x**3)*(50*x) = -800*x**4\n (75*x)*(39*x**3) = 2925*x**4\n (75*x)*(50*x) = 3750*x**2\n 7*39*x**3 = 273*x**3\n 7*50*x = 350*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -624*x**6 - 800*x**4 + 2925*x**4 + 273*x**3 + 3750*x**2 + 350*x\nCombining like terms, got -624*x**6 + 2125*x**4 + 273*x**3 + 3750*x**2 + 350*x\n#Step 6:\nCurrent expression: -624*x**6 + 2125*x**4 + 273*x**3 + 3750*x**2 + 350*x\nNo more calculations needed.\n-624*x**6 + 2125*x**4 + 273*x**3 + 3750*x**2 + 350*x", "generated_answer": "-624*x**6 + 2125*x**4 + 273*x**3 + 3750*x**2 + 350*x", "step_length": 6} {"cot_id": "490a2edc6c1292dc8549f490f9cbe67aac16a5436a98e1ed5231fc686e3b2a92", "datapoint": {"question": "Simplify this expression: 67*y**2*(-19*y**2 + 36*y + 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1273*y**4 + 2412*y**3 + 1876*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 358, "polynomial_expr": "67*y**2*(-19*y**2 + 36*y + 28)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 67*y**2*(-19*y**2 + 36*y + 28)\nExpanding the part (-19*y**2 + 36*y + 28) using the distributive property, and we got: 28*(67*y**2) + (36*y)*(67*y**2) + (-19*y**2)*(67*y**2)\n#Step 2:\nCurrent expression: 28*(67*y**2) + (36*y)*(67*y**2) + (-19*y**2)*(67*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 28*(67*y**2) = 1876*y**2\n (-19*y**2)*(67*y**2) = -1273*y**4\n (36*y)*(67*y**2) = 2412*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1273*y**4 + 2412*y**3 + 1876*y**2\nNo more calculations needed.\n-1273*y**4 + 2412*y**3 + 1876*y**2", "generated_answer": "-1273*y**4 + 2412*y**3 + 1876*y**2", "step_length": 3} {"cot_id": "335da12537c9b1bcb0796d91218aea3bba2d50fde93934c2ab68442b9da75d03", "datapoint": {"question": "Simplify this expression: (-61*y**2 - 21)*(61*y**3 + y**2 - 5*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-3721*y**5 - 61*y**4 - 976*y**3 - 21*y**2 + 105*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 359, "polynomial_expr": "(-61*y**2 - 21)*(61*y**3 + y**2 - 5*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-61*y**2 - 21)*(61*y**3 + y**2 - 5*y)\nExpanding the part (-61*y**2 - 21) using the distributive property, and we got: (-61*y**2)*(61*y**3 + y**2 - 5*y) - 21*(61*y**3 + y**2 - 5*y)\n#Step 2:\nCurrent expression: (-61*y**2)*(61*y**3 + y**2 - 5*y) - 21*(61*y**3 + y**2 - 5*y)\nSimplifying the partial expression: -21*(61*y**3 + y**2 - 5*y)\nExpanding the part (61*y**3 + y**2 - 5*y) using the distributive property, and we got: -5*y*(-21) + y**2*(-21) + (61*y**3)*(-21)\nReplacing -21*(61*y**3 + y**2 - 5*y) with -5*y*(-21) + y**2*(-21) + (61*y**3)*(-21) in the overall expression.\n#Step 3:\nCurrent expression: -5*y*(-21) + y**2*(-21) + (-61*y**2)*(61*y**3 + y**2 - 5*y) + (61*y**3)*(-21)\nSimplifying the partial expression: (-61*y**2)*(61*y**3 + y**2 - 5*y)\nExpanding the part (61*y**3 + y**2 - 5*y) using the distributive property, and we got: (-5*y)*(-61*y**2) + (-61*y**2)*y**2 + (-61*y**2)*(61*y**3)\nReplacing (-61*y**2)*(61*y**3 + y**2 - 5*y) with (-5*y)*(-61*y**2) + (-61*y**2)*y**2 + (-61*y**2)*(61*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-5*y)*(-61*y**2) - 5*y*(-21) + (-61*y**2)*y**2 + y**2*(-21) + (-61*y**2)*(61*y**3) + (61*y**3)*(-21)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n y**2*-21 = -21*y**2\n y**2*(-61*y**2) = -61*y**4\n (-5*y)*-21 = 105*y\n (-5*y)*(-61*y**2) = 305*y**3\n (61*y**3)*-21 = -1281*y**3\n (61*y**3)*(-61*y**2) = -3721*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -3721*y**5 - 61*y**4 - 1281*y**3 + 305*y**3 - 21*y**2 + 105*y\nCombining like terms, got -3721*y**5 - 61*y**4 - 976*y**3 - 21*y**2 + 105*y\n#Step 6:\nCurrent expression: -3721*y**5 - 61*y**4 - 976*y**3 - 21*y**2 + 105*y\nNo more calculations needed.\n-3721*y**5 - 61*y**4 - 976*y**3 - 21*y**2 + 105*y", "generated_answer": "-3721*y**5 - 61*y**4 - 976*y**3 - 21*y**2 + 105*y", "step_length": 6} {"cot_id": "db5e6bde6c15b941a0af47fb0a5989f161cf3a8b72545dce19e3f3f197bf5b43", "datapoint": {"question": "Calculate the following: (-109*y**2 - 26)*(-10*y**2 - 49*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1090*y**4 + 5341*y**3 + 260*y**2 + 1274*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 360, "polynomial_expr": "(-109*y**2 - 26)*(-10*y**2 - 49*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-109*y**2 - 26)*(-10*y**2 - 49*y)\nExpanding the part (-109*y**2 - 26) using the distributive property, and we got: (-109*y**2)*(-10*y**2 - 49*y) - 26*(-10*y**2 - 49*y)\n#Step 2:\nCurrent expression: (-109*y**2)*(-10*y**2 - 49*y) - 26*(-10*y**2 - 49*y)\nSimplifying the partial expression: -26*(-10*y**2 - 49*y)\nExpanding the part (-10*y**2 - 49*y) using the distributive property, and we got: -49*y*(-26) - 10*y**2*(-26)\nReplacing -26*(-10*y**2 - 49*y) with -49*y*(-26) - 10*y**2*(-26) in the overall expression.\n#Step 3:\nCurrent expression: -49*y*(-26) + (-109*y**2)*(-10*y**2 - 49*y) - 10*y**2*(-26)\nSimplifying the partial expression: (-109*y**2)*(-10*y**2 - 49*y)\nExpanding the part (-10*y**2 - 49*y) using the distributive property, and we got: (-49*y)*(-109*y**2) + (-109*y**2)*(-10*y**2)\nReplacing (-109*y**2)*(-10*y**2 - 49*y) with (-49*y)*(-109*y**2) + (-109*y**2)*(-10*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-49*y)*(-109*y**2) - 49*y*(-26) + (-109*y**2)*(-10*y**2) - 10*y**2*(-26)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*y)*-26 = 1274*y\n (-49*y)*(-109*y**2) = 5341*y**3\n (-10*y**2)*-26 = 260*y**2\n (-10*y**2)*(-109*y**2) = 1090*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1090*y**4 + 5341*y**3 + 260*y**2 + 1274*y\nNo more calculations needed.\n1090*y**4 + 5341*y**3 + 260*y**2 + 1274*y", "generated_answer": "1090*y**4 + 5341*y**3 + 260*y**2 + 1274*y", "step_length": 5} {"cot_id": "f0e0a21271bb86c8a9dd3ce13e877be1ef2bd876b4278ab8cfd786d3747f621c", "datapoint": {"question": "Simplify this expression: (-47*x**3 + 11*x**2)*(12*x**3 + 8*x**2 - 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-564*x**6 - 244*x**5 + 88*x**4 + 470*x**3 - 110*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 361, "polynomial_expr": "(-47*x**3 + 11*x**2)*(12*x**3 + 8*x**2 - 10)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-47*x**3 + 11*x**2)*(12*x**3 + 8*x**2 - 10)\nExpanding the part (-47*x**3 + 11*x**2) using the distributive property, and we got: (11*x**2)*(12*x**3 + 8*x**2 - 10) + (-47*x**3)*(12*x**3 + 8*x**2 - 10)\n#Step 2:\nCurrent expression: (11*x**2)*(12*x**3 + 8*x**2 - 10) + (-47*x**3)*(12*x**3 + 8*x**2 - 10)\nSimplifying the partial expression: (-47*x**3)*(12*x**3 + 8*x**2 - 10)\nExpanding the part (12*x**3 + 8*x**2 - 10) using the distributive property, and we got: -(-1)*470*x**3 + (8*x**2)*(-47*x**3) + (-47*x**3)*(12*x**3)\nReplacing (-47*x**3)*(12*x**3 + 8*x**2 - 10) with -(-1)*470*x**3 + (8*x**2)*(-47*x**3) + (-47*x**3)*(12*x**3) in the overall expression.\n#Step 3:\nCurrent expression: -10*(-47)*x**3 + (8*x**2)*(-47*x**3) + (11*x**2)*(12*x**3 + 8*x**2 - 10) + (-47*x**3)*(12*x**3)\nSimplifying the partial expression: (11*x**2)*(12*x**3 + 8*x**2 - 10)\nExpanding the part (12*x**3 + 8*x**2 - 10) using the distributive property, and we got: -110*x**2 + (8*x**2)*(11*x**2) + (11*x**2)*(12*x**3)\nReplacing (11*x**2)*(12*x**3 + 8*x**2 - 10) with -110*x**2 + (8*x**2)*(11*x**2) + (11*x**2)*(12*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -10*(-47)*x**3 - 10*11*x**2 + (8*x**2)*(11*x**2) + (8*x**2)*(-47*x**3) + (11*x**2)*(12*x**3) + (-47*x**3)*(12*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (8*x**2)*(-47*x**3) = -376*x**5\n (8*x**2)*(11*x**2) = 88*x**4\n (12*x**3)*(-47*x**3) = -564*x**6\n (12*x**3)*(11*x**2) = 132*x**5\n -10*-47*x**3 = 470*x**3\n -10*11*x**2 = -110*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -564*x**6 - 376*x**5 + 132*x**5 + 88*x**4 + 470*x**3 - 110*x**2\nCombining like terms, got -564*x**6 - 244*x**5 + 88*x**4 + 470*x**3 - 110*x**2\n#Step 6:\nCurrent expression: -564*x**6 - 244*x**5 + 88*x**4 + 470*x**3 - 110*x**2\nNo more calculations needed.\n-564*x**6 - 244*x**5 + 88*x**4 + 470*x**3 - 110*x**2", "generated_answer": "-564*x**6 - 244*x**5 + 88*x**4 + 470*x**3 - 110*x**2", "step_length": 6} {"cot_id": "1d518bfa1561aa6e6deccddb96aba61553bfe6a26a183fdd8a4de0ea4e32a890", "datapoint": {"question": "Simplify this expression: (1 - 2*x**3)*(-7*x**2 + 34*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "14*x**5 - 68*x**4 - 7*x**2 + 34*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 362, "polynomial_expr": "(1 - 2*x**3)*(-7*x**2 + 34*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (1 - 2*x**3)*(-7*x**2 + 34*x)\nExpanding the part (1 - 2*x**3) using the distributive property, and we got: (-2*x**3)*(-7*x**2 + 34*x) + 1*(-7*x**2 + 34*x)\n#Step 2:\nCurrent expression: (-2*x**3)*(-7*x**2 + 34*x) + 1*(-7*x**2 + 34*x)\nSimplifying the partial expression: 1*(-7*x**2 + 34*x)\nExpanding the part (-7*x**2 + 34*x) using the distributive property, and we got: (34*x)*1 - 7*x**2*1\nReplacing 1*(-7*x**2 + 34*x) with (34*x)*1 - 7*x**2*1 in the overall expression.\n#Step 3:\nCurrent expression: (34*x)*1 - 7*x**2*1 + (-2*x**3)*(-7*x**2 + 34*x)\nSimplifying the partial expression: (-2*x**3)*(-7*x**2 + 34*x)\nExpanding the part (-7*x**2 + 34*x) using the distributive property, and we got: (34*x)*(-2*x**3) + (-7*x**2)*(-2*x**3)\nReplacing (-2*x**3)*(-7*x**2 + 34*x) with (34*x)*(-2*x**3) + (-7*x**2)*(-2*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (34*x)*(-2*x**3) + (34*x)*1 + (-7*x**2)*(-2*x**3) - 7*x**2*1\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-7*x**2)*1 = -7*x**2\n (-7*x**2)*(-2*x**3) = 14*x**5\n (34*x)*1 = 34*x\n (34*x)*(-2*x**3) = -68*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 14*x**5 - 68*x**4 - 7*x**2 + 34*x\nNo more calculations needed.\n14*x**5 - 68*x**4 - 7*x**2 + 34*x", "generated_answer": "14*x**5 - 68*x**4 - 7*x**2 + 34*x", "step_length": 5} {"cot_id": "c59836b1804016fe146f74cbb302d4b016ffdeaccd14f957ccf08496cc1f4504", "datapoint": {"question": "Simplify this expression: (34*x**3 - 68*x**2)*(47*x**3 - 25*x**2 + 45*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1598*x**6 - 4046*x**5 + 3230*x**4 - 3060*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 363, "polynomial_expr": "(34*x**3 - 68*x**2)*(47*x**3 - 25*x**2 + 45*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (34*x**3 - 68*x**2)*(47*x**3 - 25*x**2 + 45*x)\nExpanding the part (34*x**3 - 68*x**2) using the distributive property, and we got: (-68*x**2)*(47*x**3 - 25*x**2 + 45*x) + (34*x**3)*(47*x**3 - 25*x**2 + 45*x)\n#Step 2:\nCurrent expression: (-68*x**2)*(47*x**3 - 25*x**2 + 45*x) + (34*x**3)*(47*x**3 - 25*x**2 + 45*x)\nSimplifying the partial expression: (-68*x**2)*(47*x**3 - 25*x**2 + 45*x)\nExpanding the part (47*x**3 - 25*x**2 + 45*x) using the distributive property, and we got: (45*x)*(-68*x**2) + (-68*x**2)*(-25*x**2) + (-68*x**2)*(47*x**3)\nReplacing (-68*x**2)*(47*x**3 - 25*x**2 + 45*x) with (45*x)*(-68*x**2) + (-68*x**2)*(-25*x**2) + (-68*x**2)*(47*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (45*x)*(-68*x**2) + (-68*x**2)*(-25*x**2) + (-68*x**2)*(47*x**3) + (34*x**3)*(47*x**3 - 25*x**2 + 45*x)\nSimplifying the partial expression: (34*x**3)*(47*x**3 - 25*x**2 + 45*x)\nExpanding the part (47*x**3 - 25*x**2 + 45*x) using the distributive property, and we got: (45*x)*(34*x**3) + (-25*x**2)*(34*x**3) + (34*x**3)*(47*x**3)\nReplacing (34*x**3)*(47*x**3 - 25*x**2 + 45*x) with (45*x)*(34*x**3) + (-25*x**2)*(34*x**3) + (34*x**3)*(47*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (45*x)*(-68*x**2) + (45*x)*(34*x**3) + (-68*x**2)*(-25*x**2) + (-68*x**2)*(47*x**3) + (-25*x**2)*(34*x**3) + (34*x**3)*(47*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*x**2)*(-68*x**2) = 1700*x**4\n (-25*x**2)*(34*x**3) = -850*x**5\n (45*x)*(-68*x**2) = -3060*x**3\n (45*x)*(34*x**3) = 1530*x**4\n (47*x**3)*(-68*x**2) = -3196*x**5\n (47*x**3)*(34*x**3) = 1598*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1598*x**6 - 3196*x**5 - 850*x**5 + 1530*x**4 + 1700*x**4 - 3060*x**3\nCombining like terms, got 1598*x**6 - 4046*x**5 + 3230*x**4 - 3060*x**3\n#Step 6:\nCurrent expression: 1598*x**6 - 4046*x**5 + 3230*x**4 - 3060*x**3\nNo more calculations needed.\n1598*x**6 - 4046*x**5 + 3230*x**4 - 3060*x**3", "generated_answer": "1598*x**6 - 4046*x**5 + 3230*x**4 - 3060*x**3", "step_length": 6} {"cot_id": "e09e309d10320c9c3476f6f243a1cb876550b61f3cea6692e4412051f06851f4", "datapoint": {"question": "Simplify this expression: (11 - 40*y**2)*(-30*y**3 + 37*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1200*y**5 - 1810*y**3 + 407*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 364, "polynomial_expr": "(11 - 40*y**2)*(-30*y**3 + 37*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11 - 40*y**2)*(-30*y**3 + 37*y)\nExpanding the part (11 - 40*y**2) using the distributive property, and we got: (-40*y**2)*(-30*y**3 + 37*y) + 11*(-30*y**3 + 37*y)\n#Step 2:\nCurrent expression: (-40*y**2)*(-30*y**3 + 37*y) + 11*(-30*y**3 + 37*y)\nSimplifying the partial expression: 11*(-30*y**3 + 37*y)\nExpanding the part (-30*y**3 + 37*y) using the distributive property, and we got: (37*y)*11 - 30*y**3*11\nReplacing 11*(-30*y**3 + 37*y) with (37*y)*11 - 30*y**3*11 in the overall expression.\n#Step 3:\nCurrent expression: (37*y)*11 + (-40*y**2)*(-30*y**3 + 37*y) - 30*y**3*11\nSimplifying the partial expression: (-40*y**2)*(-30*y**3 + 37*y)\nExpanding the part (-30*y**3 + 37*y) using the distributive property, and we got: (37*y)*(-40*y**2) + (-40*y**2)*(-30*y**3)\nReplacing (-40*y**2)*(-30*y**3 + 37*y) with (37*y)*(-40*y**2) + (-40*y**2)*(-30*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (37*y)*(-40*y**2) + (37*y)*11 + (-40*y**2)*(-30*y**3) - 30*y**3*11\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*y**3)*11 = -330*y**3\n (-30*y**3)*(-40*y**2) = 1200*y**5\n (37*y)*11 = 407*y\n (37*y)*(-40*y**2) = -1480*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1200*y**5 - 1480*y**3 - 330*y**3 + 407*y\nCombining like terms, got 1200*y**5 - 1810*y**3 + 407*y\n#Step 6:\nCurrent expression: 1200*y**5 - 1810*y**3 + 407*y\nNo more calculations needed.\n1200*y**5 - 1810*y**3 + 407*y", "generated_answer": "1200*y**5 - 1810*y**3 + 407*y", "step_length": 6} {"cot_id": "b683ca28e844ed665c5504c113d593b0fbff9794a44ecdfbc516310a505f7a69", "datapoint": {"question": "Calculate the following: -20*z**2*(-32*z**3 - 14*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "640*z**5 + 280*z**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 365, "polynomial_expr": "-20*z**2*(-32*z**3 - 14*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -20*z**2*(-32*z**3 - 14*z**2)\nExpanding the part (-32*z**3 - 14*z**2) using the distributive property, and we got: (-20*z**2)*(-14*z**2) + (-20*z**2)*(-32*z**3)\n#Step 2:\nCurrent expression: (-20*z**2)*(-14*z**2) + (-20*z**2)*(-32*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*z**3)*(-20*z**2) = 640*z**5\n (-14*z**2)*(-20*z**2) = 280*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 640*z**5 + 280*z**4\nNo more calculations needed.\n640*z**5 + 280*z**4", "generated_answer": "640*z**5 + 280*z**4", "step_length": 3} {"cot_id": "ac534a0ad1ed09092b75a78b19ded1b9b45da1b54f041eeb6db53bae666b93b8", "datapoint": {"question": "Simplify this expression: (12*z**2 + 36)*(30*z**3 + 17*z - 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "360*z**5 + 1284*z**3 - 468*z**2 + 612*z - 1404", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 366, "polynomial_expr": "(12*z**2 + 36)*(30*z**3 + 17*z - 39)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (12*z**2 + 36)*(30*z**3 + 17*z - 39)\nExpanding the part (12*z**2 + 36) using the distributive property, and we got: (12*z**2)*(30*z**3 + 17*z - 39) + 36*(30*z**3 + 17*z - 39)\n#Step 2:\nCurrent expression: (12*z**2)*(30*z**3 + 17*z - 39) + 36*(30*z**3 + 17*z - 39)\nSimplifying the partial expression: 36*(30*z**3 + 17*z - 39)\nExpanding the part (30*z**3 + 17*z - 39) using the distributive property, and we got: (17*z)*36 + (30*z**3)*36 - 39*36\nReplacing 36*(30*z**3 + 17*z - 39) with (17*z)*36 + (30*z**3)*36 - 39*36 in the overall expression.\n#Step 3:\nCurrent expression: (17*z)*36 + (12*z**2)*(30*z**3 + 17*z - 39) + (30*z**3)*36 - 1404\nSimplifying the partial expression: (12*z**2)*(30*z**3 + 17*z - 39)\nExpanding the part (30*z**3 + 17*z - 39) using the distributive property, and we got: -468*z**2 + (17*z)*(12*z**2) + (12*z**2)*(30*z**3)\nReplacing (12*z**2)*(30*z**3 + 17*z - 39) with -468*z**2 + (17*z)*(12*z**2) + (12*z**2)*(30*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -39*12*z**2 + (17*z)*(12*z**2) + (17*z)*36 + (12*z**2)*(30*z**3) + (30*z**3)*36 - 1404\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (17*z)*36 = 612*z\n (17*z)*(12*z**2) = 204*z**3\n (30*z**3)*36 = 1080*z**3\n (30*z**3)*(12*z**2) = 360*z**5\n -39*12*z**2 = -468*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 360*z**5 + 204*z**3 + 1080*z**3 - 468*z**2 + 612*z - 1404\nCombining like terms, got 360*z**5 + 1284*z**3 - 468*z**2 + 612*z - 1404\n#Step 6:\nCurrent expression: 360*z**5 + 1284*z**3 - 468*z**2 + 612*z - 1404\nNo more calculations needed.\n360*z**5 + 1284*z**3 - 468*z**2 + 612*z - 1404", "generated_answer": "360*z**5 + 1284*z**3 - 468*z**2 + 612*z - 1404", "step_length": 6} {"cot_id": "647620b051f2b6eafcf75c5ad428c8beb7e05fec473027531523c0bca13ba956", "datapoint": {"question": "Simplify this expression: (36*z**2 + 28)*(-69*z**3 - 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2484*z**5 - 1932*z**3 - 1260*z**2 - 980", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 367, "polynomial_expr": "(36*z**2 + 28)*(-69*z**3 - 35)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (36*z**2 + 28)*(-69*z**3 - 35)\nExpanding the part (-69*z**3 - 35) using the distributive property, and we got: (-69*z**3)*(36*z**2 + 28) - 35*(36*z**2 + 28)\n#Step 2:\nCurrent expression: (-69*z**3)*(36*z**2 + 28) - 35*(36*z**2 + 28)\nSimplifying the partial expression: -35*(36*z**2 + 28)\nExpanding the part (36*z**2 + 28) using the distributive property, and we got: (36*z**2)*(-35) + 28*(-35)\nReplacing -35*(36*z**2 + 28) with (36*z**2)*(-35) + 28*(-35) in the overall expression.\n#Step 3:\nCurrent expression: (36*z**2)*(-35) + (-69*z**3)*(36*z**2 + 28) - 980\nSimplifying the partial expression: (-69*z**3)*(36*z**2 + 28)\nExpanding the part (36*z**2 + 28) using the distributive property, and we got: 28*(-69*z**3) + (36*z**2)*(-69*z**3)\nReplacing (-69*z**3)*(36*z**2 + 28) with 28*(-69*z**3) + (36*z**2)*(-69*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 28*(-69)*z**3 + (36*z**2)*(-69*z**3) + (36*z**2)*(-35) - 980\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (36*z**2)*-35 = -1260*z**2\n (36*z**2)*(-69*z**3) = -2484*z**5\n 28*-69*z**3 = -1932*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2484*z**5 - 1932*z**3 - 1260*z**2 - 980\nNo more calculations needed.\n-2484*z**5 - 1932*z**3 - 1260*z**2 - 980", "generated_answer": "-2484*z**5 - 1932*z**3 - 1260*z**2 - 980", "step_length": 5} {"cot_id": "6e2235529387983f40ae7e43494009736a0d4af4b254f9eb017734b4d51a0ed1", "datapoint": {"question": "Simplify this expression: 4*x**3*(-20*x**3 - 44*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-80*x**6 - 176*x**5", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 368, "polynomial_expr": "4*x**3*(-20*x**3 - 44*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 4*x**3*(-20*x**3 - 44*x**2)\nExpanding the part (-20*x**3 - 44*x**2) using the distributive property, and we got: (-44*x**2)*(4*x**3) + (-20*x**3)*(4*x**3)\n#Step 2:\nCurrent expression: (-44*x**2)*(4*x**3) + (-20*x**3)*(4*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-44*x**2)*(4*x**3) = -176*x**5\n (-20*x**3)*(4*x**3) = -80*x**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -80*x**6 - 176*x**5\nNo more calculations needed.\n-80*x**6 - 176*x**5", "generated_answer": "-80*x**6 - 176*x**5", "step_length": 3} {"cot_id": "b7d7580604f7aced2ba5d81e689bd384d05a984822c953d81f805d9bc8aad7fe", "datapoint": {"question": "Simplify this expression: 50*x**2*(31*x**3 + x - 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1550*x**5 + 50*x**3 - 650*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 369, "polynomial_expr": "50*x**2*(31*x**3 + x - 13)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 50*x**2*(31*x**3 + x - 13)\nExpanding the part (31*x**3 + x - 13) using the distributive property, and we got: -650*x**2 + x*(50*x**2) + (50*x**2)*(31*x**3)\n#Step 2:\nCurrent expression: -650*x**2 + x*(50*x**2) + (50*x**2)*(31*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -13*(50*x**2) = -650*x**2\n x*(50*x**2) = 50*x**3\n (31*x**3)*(50*x**2) = 1550*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1550*x**5 + 50*x**3 - 650*x**2\nNo more calculations needed.\n1550*x**5 + 50*x**3 - 650*x**2", "generated_answer": "1550*x**5 + 50*x**3 - 650*x**2", "step_length": 3} {"cot_id": "b43e33749d0aa1064631e30b185eb6da36d3ffa0682e59f19dbb93b3bab70d76", "datapoint": {"question": "Calculate the following: (33*y - 5)*(-13*y**3 - 37)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-429*y**4 + 65*y**3 - 1221*y + 185", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 370, "polynomial_expr": "(33*y - 5)*(-13*y**3 - 37)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (33*y - 5)*(-13*y**3 - 37)\nExpanding the part (-13*y**3 - 37) using the distributive property, and we got: (-13*y**3)*(33*y - 5) - 37*(33*y - 5)\n#Step 2:\nCurrent expression: (-13*y**3)*(33*y - 5) - 37*(33*y - 5)\nSimplifying the partial expression: -37*(33*y - 5)\nExpanding the part (33*y - 5) using the distributive property, and we got: (33*y)*(-37) - 5*(-37)\nReplacing -37*(33*y - 5) with (33*y)*(-37) - 5*(-37) in the overall expression.\n#Step 3:\nCurrent expression: (33*y)*(-37) + (-13*y**3)*(33*y - 5) + 185\nSimplifying the partial expression: (-13*y**3)*(33*y - 5)\nExpanding the part (33*y - 5) using the distributive property, and we got: -(-1)*65*y**3 + (33*y)*(-13*y**3)\nReplacing (-13*y**3)*(33*y - 5) with -(-1)*65*y**3 + (33*y)*(-13*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -5*(-13)*y**3 + (33*y)*(-13*y**3) + (33*y)*(-37) + 185\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (33*y)*-37 = -1221*y\n (33*y)*(-13*y**3) = -429*y**4\n -5*-13*y**3 = 65*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -429*y**4 + 65*y**3 - 1221*y + 185\nNo more calculations needed.\n-429*y**4 + 65*y**3 - 1221*y + 185", "generated_answer": "-429*y**4 + 65*y**3 - 1221*y + 185", "step_length": 5} {"cot_id": "70a70544c375bdf4e64ba78009f2d419a1feb7eb40e625366fa36c9c8eecf690", "datapoint": {"question": "Simplify this expression: (-6*z - 36)*(-19*z**3 + 17*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "114*z**4 + 684*z**3 - 102*z**2 - 612*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 371, "polynomial_expr": "(-6*z - 36)*(-19*z**3 + 17*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-6*z - 36)*(-19*z**3 + 17*z)\nExpanding the part (-6*z - 36) using the distributive property, and we got: (-6*z)*(-19*z**3 + 17*z) - 36*(-19*z**3 + 17*z)\n#Step 2:\nCurrent expression: (-6*z)*(-19*z**3 + 17*z) - 36*(-19*z**3 + 17*z)\nSimplifying the partial expression: -36*(-19*z**3 + 17*z)\nExpanding the part (-19*z**3 + 17*z) using the distributive property, and we got: (17*z)*(-36) - 19*z**3*(-36)\nReplacing -36*(-19*z**3 + 17*z) with (17*z)*(-36) - 19*z**3*(-36) in the overall expression.\n#Step 3:\nCurrent expression: (-6*z)*(-19*z**3 + 17*z) + (17*z)*(-36) - 19*z**3*(-36)\nSimplifying the partial expression: (-6*z)*(-19*z**3 + 17*z)\nExpanding the part (-19*z**3 + 17*z) using the distributive property, and we got: (-6*z)*(17*z) + (-6*z)*(-19*z**3)\nReplacing (-6*z)*(-19*z**3 + 17*z) with (-6*z)*(17*z) + (-6*z)*(-19*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-6*z)*(17*z) + (-6*z)*(-19*z**3) + (17*z)*(-36) - 19*z**3*(-36)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*z**3)*-36 = 684*z**3\n (-19*z**3)*(-6*z) = 114*z**4\n (17*z)*-36 = -612*z\n (17*z)*(-6*z) = -102*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 114*z**4 + 684*z**3 - 102*z**2 - 612*z\nNo more calculations needed.\n114*z**4 + 684*z**3 - 102*z**2 - 612*z", "generated_answer": "114*z**4 + 684*z**3 - 102*z**2 - 612*z", "step_length": 5} {"cot_id": "2c1e67d8629885c15f784ded78a4849864c44f1f64dc70fb77593e362a38cb90", "datapoint": {"question": "Simplify this expression: (29 - y)*(19*y**3 + 58)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-19*y**4 + 551*y**3 - 58*y + 1682", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 372, "polynomial_expr": "(29 - y)*(19*y**3 + 58)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29 - y)*(19*y**3 + 58)\nExpanding the part (29 - y) using the distributive property, and we got: (-y)*(19*y**3 + 58) + 29*(19*y**3 + 58)\n#Step 2:\nCurrent expression: (-y)*(19*y**3 + 58) + 29*(19*y**3 + 58)\nSimplifying the partial expression: 29*(19*y**3 + 58)\nExpanding the part (19*y**3 + 58) using the distributive property, and we got: (19*y**3)*29 + 58*29\nReplacing 29*(19*y**3 + 58) with (19*y**3)*29 + 58*29 in the overall expression.\n#Step 3:\nCurrent expression: (-y)*(19*y**3 + 58) + (19*y**3)*29 + 1682\nSimplifying the partial expression: (-y)*(19*y**3 + 58)\nExpanding the part (19*y**3 + 58) using the distributive property, and we got: (-y)*(19*y**3) + 58*(-y)\nReplacing (-y)*(19*y**3 + 58) with (-y)*(19*y**3) + 58*(-y) in the overall expression.\n#Step 4:\nCurrent expression: (-y)*(19*y**3) + 58*(-1)*y + (19*y**3)*29 + 1682\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (19*y**3)*29 = 551*y**3\n (19*y**3)*(-y) = -19*y**4\n 58*-1*y = -58*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -19*y**4 + 551*y**3 - 58*y + 1682\nNo more calculations needed.\n-19*y**4 + 551*y**3 - 58*y + 1682", "generated_answer": "-19*y**4 + 551*y**3 - 58*y + 1682", "step_length": 5} {"cot_id": "405db52d6d625dcaa9ae63402fd3bc786d024d3884256ea73397e30bd35441a4", "datapoint": {"question": "Simplify this expression: (14*y**3 - 2*y)*(36*y**3 - 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "504*y**6 - 72*y**4 - 504*y**3 + 72*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 373, "polynomial_expr": "(14*y**3 - 2*y)*(36*y**3 - 36)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14*y**3 - 2*y)*(36*y**3 - 36)\nExpanding the part (36*y**3 - 36) using the distributive property, and we got: (36*y**3)*(14*y**3 - 2*y) - 36*(14*y**3 - 2*y)\n#Step 2:\nCurrent expression: (36*y**3)*(14*y**3 - 2*y) - 36*(14*y**3 - 2*y)\nSimplifying the partial expression: -36*(14*y**3 - 2*y)\nExpanding the part (14*y**3 - 2*y) using the distributive property, and we got: -2*y*(-36) + (14*y**3)*(-36)\nReplacing -36*(14*y**3 - 2*y) with -2*y*(-36) + (14*y**3)*(-36) in the overall expression.\n#Step 3:\nCurrent expression: -2*y*(-36) + (14*y**3)*(-36) + (36*y**3)*(14*y**3 - 2*y)\nSimplifying the partial expression: (36*y**3)*(14*y**3 - 2*y)\nExpanding the part (14*y**3 - 2*y) using the distributive property, and we got: (-2*y)*(36*y**3) + (14*y**3)*(36*y**3)\nReplacing (36*y**3)*(14*y**3 - 2*y) with (-2*y)*(36*y**3) + (14*y**3)*(36*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-2*y)*(36*y**3) - 2*y*(-36) + (14*y**3)*(36*y**3) + (14*y**3)*(-36)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-2*y)*-36 = 72*y\n (-2*y)*(36*y**3) = -72*y**4\n (14*y**3)*-36 = -504*y**3\n (14*y**3)*(36*y**3) = 504*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 504*y**6 - 72*y**4 - 504*y**3 + 72*y\nNo more calculations needed.\n504*y**6 - 72*y**4 - 504*y**3 + 72*y", "generated_answer": "504*y**6 - 72*y**4 - 504*y**3 + 72*y", "step_length": 5} {"cot_id": "854720889246d6ad069abeeb1eff6aec99a71982e4395d981c69f24a66bf0a19", "datapoint": {"question": "Simplify this expression: (25*y**3 - 52*y**2)*(62*y**3 + 46*y**2 + 38*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1550*y**6 - 2074*y**5 - 1442*y**4 - 1976*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 374, "polynomial_expr": "(25*y**3 - 52*y**2)*(62*y**3 + 46*y**2 + 38*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (25*y**3 - 52*y**2)*(62*y**3 + 46*y**2 + 38*y)\nExpanding the part (25*y**3 - 52*y**2) using the distributive property, and we got: (-52*y**2)*(62*y**3 + 46*y**2 + 38*y) + (25*y**3)*(62*y**3 + 46*y**2 + 38*y)\n#Step 2:\nCurrent expression: (-52*y**2)*(62*y**3 + 46*y**2 + 38*y) + (25*y**3)*(62*y**3 + 46*y**2 + 38*y)\nSimplifying the partial expression: (-52*y**2)*(62*y**3 + 46*y**2 + 38*y)\nExpanding the part (62*y**3 + 46*y**2 + 38*y) using the distributive property, and we got: (38*y)*(-52*y**2) + (-52*y**2)*(46*y**2) + (-52*y**2)*(62*y**3)\nReplacing (-52*y**2)*(62*y**3 + 46*y**2 + 38*y) with (38*y)*(-52*y**2) + (-52*y**2)*(46*y**2) + (-52*y**2)*(62*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (38*y)*(-52*y**2) + (-52*y**2)*(46*y**2) + (-52*y**2)*(62*y**3) + (25*y**3)*(62*y**3 + 46*y**2 + 38*y)\nSimplifying the partial expression: (25*y**3)*(62*y**3 + 46*y**2 + 38*y)\nExpanding the part (62*y**3 + 46*y**2 + 38*y) using the distributive property, and we got: (38*y)*(25*y**3) + (46*y**2)*(25*y**3) + (25*y**3)*(62*y**3)\nReplacing (25*y**3)*(62*y**3 + 46*y**2 + 38*y) with (38*y)*(25*y**3) + (46*y**2)*(25*y**3) + (25*y**3)*(62*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (38*y)*(-52*y**2) + (38*y)*(25*y**3) + (-52*y**2)*(46*y**2) + (-52*y**2)*(62*y**3) + (46*y**2)*(25*y**3) + (25*y**3)*(62*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (38*y)*(-52*y**2) = -1976*y**3\n (38*y)*(25*y**3) = 950*y**4\n (46*y**2)*(-52*y**2) = -2392*y**4\n (46*y**2)*(25*y**3) = 1150*y**5\n (62*y**3)*(-52*y**2) = -3224*y**5\n (62*y**3)*(25*y**3) = 1550*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1550*y**6 - 3224*y**5 + 1150*y**5 - 2392*y**4 + 950*y**4 - 1976*y**3\nCombining like terms, got 1550*y**6 - 2074*y**5 - 1442*y**4 - 1976*y**3\n#Step 6:\nCurrent expression: 1550*y**6 - 2074*y**5 - 1442*y**4 - 1976*y**3\nNo more calculations needed.\n1550*y**6 - 2074*y**5 - 1442*y**4 - 1976*y**3", "generated_answer": "1550*y**6 - 2074*y**5 - 1442*y**4 - 1976*y**3", "step_length": 6} {"cot_id": "7e4cf0a95a6fffec75ed96e2852ba5090d7864482fc03b464ac211155e5c61c8", "datapoint": {"question": "Calculate the following: (-48*z**2 - 3*z)*(-22*z**2 - 6*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1056*z**4 + 354*z**3 + 18*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 375, "polynomial_expr": "(-48*z**2 - 3*z)*(-22*z**2 - 6*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-48*z**2 - 3*z)*(-22*z**2 - 6*z)\nExpanding the part (-48*z**2 - 3*z) using the distributive property, and we got: (-3*z)*(-22*z**2 - 6*z) + (-48*z**2)*(-22*z**2 - 6*z)\n#Step 2:\nCurrent expression: (-3*z)*(-22*z**2 - 6*z) + (-48*z**2)*(-22*z**2 - 6*z)\nSimplifying the partial expression: (-48*z**2)*(-22*z**2 - 6*z)\nExpanding the part (-22*z**2 - 6*z) using the distributive property, and we got: (-6*z)*(-48*z**2) + (-48*z**2)*(-22*z**2)\nReplacing (-48*z**2)*(-22*z**2 - 6*z) with (-6*z)*(-48*z**2) + (-48*z**2)*(-22*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-6*z)*(-48*z**2) + (-3*z)*(-22*z**2 - 6*z) + (-48*z**2)*(-22*z**2)\nSimplifying the partial expression: (-3*z)*(-22*z**2 - 6*z)\nExpanding the part (-22*z**2 - 6*z) using the distributive property, and we got: (-6*z)*(-3*z) + (-3*z)*(-22*z**2)\nReplacing (-3*z)*(-22*z**2 - 6*z) with (-6*z)*(-3*z) + (-3*z)*(-22*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-6*z)*(-3*z) + (-6*z)*(-48*z**2) + (-3*z)*(-22*z**2) + (-48*z**2)*(-22*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*z**2)*(-48*z**2) = 1056*z**4\n (-22*z**2)*(-3*z) = 66*z**3\n (-6*z)*(-48*z**2) = 288*z**3\n (-6*z)*(-3*z) = 18*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1056*z**4 + 66*z**3 + 288*z**3 + 18*z**2\nCombining like terms, got 1056*z**4 + 354*z**3 + 18*z**2\n#Step 6:\nCurrent expression: 1056*z**4 + 354*z**3 + 18*z**2\nNo more calculations needed.\n1056*z**4 + 354*z**3 + 18*z**2", "generated_answer": "1056*z**4 + 354*z**3 + 18*z**2", "step_length": 6} {"cot_id": "ec0d3b35021bed7f1a8ebf1c99bdf5f757ba2534e251b7b7e6a9c7b13e04cef6", "datapoint": {"question": "Calculate the following: 583*y**2 + 1219\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "583*y**2 + 1219", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 376, "polynomial_expr": "583*y**2 + 1219", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 583*y**2 + 1219\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 583*y**2 + 1219\nNo more calculations needed.\n583*y**2 + 1219", "generated_answer": "583*y**2 + 1219", "step_length": 2} {"cot_id": "ffa07a48c12ff2c6ca0e786ed806879abc1e91117588e6c26ce9ea0c9be5178b", "datapoint": {"question": "Calculate the following: (6*z**3 + 19*z)*(-14*z**3 - 27*z**2 + 29*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-84*z**6 - 162*z**5 - 92*z**4 - 513*z**3 + 551*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 377, "polynomial_expr": "(6*z**3 + 19*z)*(-14*z**3 - 27*z**2 + 29*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6*z**3 + 19*z)*(-14*z**3 - 27*z**2 + 29*z)\nExpanding the part (6*z**3 + 19*z) using the distributive property, and we got: (19*z)*(-14*z**3 - 27*z**2 + 29*z) + (6*z**3)*(-14*z**3 - 27*z**2 + 29*z)\n#Step 2:\nCurrent expression: (19*z)*(-14*z**3 - 27*z**2 + 29*z) + (6*z**3)*(-14*z**3 - 27*z**2 + 29*z)\nSimplifying the partial expression: (6*z**3)*(-14*z**3 - 27*z**2 + 29*z)\nExpanding the part (-14*z**3 - 27*z**2 + 29*z) using the distributive property, and we got: (29*z)*(6*z**3) + (-27*z**2)*(6*z**3) + (-14*z**3)*(6*z**3)\nReplacing (6*z**3)*(-14*z**3 - 27*z**2 + 29*z) with (29*z)*(6*z**3) + (-27*z**2)*(6*z**3) + (-14*z**3)*(6*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (19*z)*(-14*z**3 - 27*z**2 + 29*z) + (29*z)*(6*z**3) + (-27*z**2)*(6*z**3) + (-14*z**3)*(6*z**3)\nSimplifying the partial expression: (19*z)*(-14*z**3 - 27*z**2 + 29*z)\nExpanding the part (-14*z**3 - 27*z**2 + 29*z) using the distributive property, and we got: (19*z)*(29*z) + (19*z)*(-27*z**2) + (19*z)*(-14*z**3)\nReplacing (19*z)*(-14*z**3 - 27*z**2 + 29*z) with (19*z)*(29*z) + (19*z)*(-27*z**2) + (19*z)*(-14*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (19*z)*(29*z) + (19*z)*(-27*z**2) + (19*z)*(-14*z**3) + (29*z)*(6*z**3) + (-27*z**2)*(6*z**3) + (-14*z**3)*(6*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*z**2)*(6*z**3) = -162*z**5\n (-27*z**2)*(19*z) = -513*z**3\n (-14*z**3)*(6*z**3) = -84*z**6\n (-14*z**3)*(19*z) = -266*z**4\n (29*z)*(6*z**3) = 174*z**4\n (29*z)*(19*z) = 551*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -84*z**6 - 162*z**5 - 266*z**4 + 174*z**4 - 513*z**3 + 551*z**2\nCombining like terms, got -84*z**6 - 162*z**5 - 92*z**4 - 513*z**3 + 551*z**2\n#Step 6:\nCurrent expression: -84*z**6 - 162*z**5 - 92*z**4 - 513*z**3 + 551*z**2\nNo more calculations needed.\n-84*z**6 - 162*z**5 - 92*z**4 - 513*z**3 + 551*z**2", "generated_answer": "-84*z**6 - 162*z**5 - 92*z**4 - 513*z**3 + 551*z**2", "step_length": 6} {"cot_id": "ee014c647426e58643cadbf1a8bab0a1795002c2956bd1434c3742d841086a05", "datapoint": {"question": "Calculate the following: (49 - 28*x**2)*(21*x**3 - 18*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-588*x**5 + 1533*x**3 - 882*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 378, "polynomial_expr": "(49 - 28*x**2)*(21*x**3 - 18*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (49 - 28*x**2)*(21*x**3 - 18*x)\nExpanding the part (49 - 28*x**2) using the distributive property, and we got: (-28*x**2)*(21*x**3 - 18*x) + 49*(21*x**3 - 18*x)\n#Step 2:\nCurrent expression: (-28*x**2)*(21*x**3 - 18*x) + 49*(21*x**3 - 18*x)\nSimplifying the partial expression: 49*(21*x**3 - 18*x)\nExpanding the part (21*x**3 - 18*x) using the distributive property, and we got: -18*x*49 + (21*x**3)*49\nReplacing 49*(21*x**3 - 18*x) with -18*x*49 + (21*x**3)*49 in the overall expression.\n#Step 3:\nCurrent expression: -18*x*49 + (-28*x**2)*(21*x**3 - 18*x) + (21*x**3)*49\nSimplifying the partial expression: (-28*x**2)*(21*x**3 - 18*x)\nExpanding the part (21*x**3 - 18*x) using the distributive property, and we got: (-18*x)*(-28*x**2) + (-28*x**2)*(21*x**3)\nReplacing (-28*x**2)*(21*x**3 - 18*x) with (-18*x)*(-28*x**2) + (-28*x**2)*(21*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-18*x)*(-28*x**2) - 18*x*49 + (-28*x**2)*(21*x**3) + (21*x**3)*49\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-18*x)*49 = -882*x\n (-18*x)*(-28*x**2) = 504*x**3\n (21*x**3)*49 = 1029*x**3\n (21*x**3)*(-28*x**2) = -588*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -588*x**5 + 504*x**3 + 1029*x**3 - 882*x\nCombining like terms, got -588*x**5 + 1533*x**3 - 882*x\n#Step 6:\nCurrent expression: -588*x**5 + 1533*x**3 - 882*x\nNo more calculations needed.\n-588*x**5 + 1533*x**3 - 882*x", "generated_answer": "-588*x**5 + 1533*x**3 - 882*x", "step_length": 6} {"cot_id": "b20ddd29f88af42dc371c0c39aba588faff3414869e2fb15165cc3bc8bf72390", "datapoint": {"question": "Calculate the following: -61*z**2*(-47*z**3 - 34*z**2 + 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2867*z**5 + 2074*z**4 - 1952*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 379, "polynomial_expr": "-61*z**2*(-47*z**3 - 34*z**2 + 32)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -61*z**2*(-47*z**3 - 34*z**2 + 32)\nExpanding the part (-47*z**3 - 34*z**2 + 32) using the distributive property, and we got: 32*(-61*z**2) + (-61*z**2)*(-34*z**2) + (-61*z**2)*(-47*z**3)\n#Step 2:\nCurrent expression: 32*(-61*z**2) + (-61*z**2)*(-34*z**2) + (-61*z**2)*(-47*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 32*(-61*z**2) = -1952*z**2\n (-47*z**3)*(-61*z**2) = 2867*z**5\n (-34*z**2)*(-61*z**2) = 2074*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 2867*z**5 + 2074*z**4 - 1952*z**2\nNo more calculations needed.\n2867*z**5 + 2074*z**4 - 1952*z**2", "generated_answer": "2867*z**5 + 2074*z**4 - 1952*z**2", "step_length": 3} {"cot_id": "ad49ded72cf3ec53c98bb392bde26d28353509c8b8309ec67529269c13d34cd7", "datapoint": {"question": "Simplify this expression: y**3*(-10*y**3 + 34*y**2 + 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-10*y**6 + 34*y**5 + 49*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 380, "polynomial_expr": "y**3*(-10*y**3 + 34*y**2 + 49)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: y**3*(-10*y**3 + 34*y**2 + 49)\nExpanding the part (-10*y**3 + 34*y**2 + 49) using the distributive property, and we got: (34*y**2)*y**3 + (-10*y**3)*y**3 + 49*y**3\n#Step 2:\nCurrent expression: (34*y**2)*y**3 + (-10*y**3)*y**3 + 49*y**3\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*y**3)*y**3 = -10*y**6\n (34*y**2)*y**3 = 34*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -10*y**6 + 34*y**5 + 49*y**3\nNo more calculations needed.\n-10*y**6 + 34*y**5 + 49*y**3", "generated_answer": "-10*y**6 + 34*y**5 + 49*y**3", "step_length": 3} {"cot_id": "05f1c4e686362886c966366a19d572f0a4e4eb9164299ce7b924967866d6e3c5", "datapoint": {"question": "Simplify this expression: (-53*y**3 + 34*y**2 + 41*y)*(48*y**3 - 41*y**2 + 30*y + 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2544*y**6 + 3805*y**5 - 1016*y**4 - 2569*y**3 + 2454*y**2 + 1476*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 381, "polynomial_expr": "(-53*y**3 + 34*y**2 + 41*y)*(48*y**3 - 41*y**2 + 30*y + 36)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-53*y**3 + 34*y**2 + 41*y)*(48*y**3 - 41*y**2 + 30*y + 36)\nExpanding the part (-53*y**3 + 34*y**2 + 41*y) using the distributive property, and we got: (41*y)*(48*y**3 - 41*y**2 + 30*y + 36) + (34*y**2)*(48*y**3 - 41*y**2 + 30*y + 36) + (-53*y**3)*(48*y**3 - 41*y**2 + 30*y + 36)\n#Step 2:\nCurrent expression: (41*y)*(48*y**3 - 41*y**2 + 30*y + 36) + (34*y**2)*(48*y**3 - 41*y**2 + 30*y + 36) + (-53*y**3)*(48*y**3 - 41*y**2 + 30*y + 36)\nSimplifying the partial expression: (-53*y**3)*(48*y**3 - 41*y**2 + 30*y + 36)\nExpanding the part (48*y**3 - 41*y**2 + 30*y + 36) using the distributive property, and we got: 36*(-53*y**3) + (30*y)*(-53*y**3) + (-41*y**2)*(-53*y**3) + (-53*y**3)*(48*y**3)\nReplacing (-53*y**3)*(48*y**3 - 41*y**2 + 30*y + 36) with 36*(-53*y**3) + (30*y)*(-53*y**3) + (-41*y**2)*(-53*y**3) + (-53*y**3)*(48*y**3) in the overall expression.\n#Step 3:\nCurrent expression: 36*(-53)*y**3 + (30*y)*(-53*y**3) + (41*y)*(48*y**3 - 41*y**2 + 30*y + 36) + (-41*y**2)*(-53*y**3) + (34*y**2)*(48*y**3 - 41*y**2 + 30*y + 36) + (-53*y**3)*(48*y**3)\nSimplifying the partial expression: (34*y**2)*(48*y**3 - 41*y**2 + 30*y + 36)\nExpanding the part (48*y**3 - 41*y**2 + 30*y + 36) using the distributive property, and we got: 36*(34*y**2) + (30*y)*(34*y**2) + (-41*y**2)*(34*y**2) + (34*y**2)*(48*y**3)\nReplacing (34*y**2)*(48*y**3 - 41*y**2 + 30*y + 36) with 36*(34*y**2) + (30*y)*(34*y**2) + (-41*y**2)*(34*y**2) + (34*y**2)*(48*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 36*(-53)*y**3 + 36*34*y**2 + (30*y)*(34*y**2) + (30*y)*(-53*y**3) + (41*y)*(48*y**3 - 41*y**2 + 30*y + 36) + (-41*y**2)*(34*y**2) + (-41*y**2)*(-53*y**3) + (34*y**2)*(48*y**3) + (-53*y**3)*(48*y**3)\nSimplifying the partial expression: (41*y)*(48*y**3 - 41*y**2 + 30*y + 36)\nExpanding the part (48*y**3 - 41*y**2 + 30*y + 36) using the distributive property, and we got: 36*(41*y) + (30*y)*(41*y) + (41*y)*(-41*y**2) + (41*y)*(48*y**3)\nReplacing (41*y)*(48*y**3 - 41*y**2 + 30*y + 36) with 36*(41*y) + (30*y)*(41*y) + (41*y)*(-41*y**2) + (41*y)*(48*y**3) in the overall expression.\n#Step 5:\nCurrent expression: 36*(-53)*y**3 + 36*34*y**2 + 36*41*y + (30*y)*(41*y) + (30*y)*(34*y**2) + (30*y)*(-53*y**3) + (41*y)*(-41*y**2) + (41*y)*(48*y**3) + (-41*y**2)*(34*y**2) + (-41*y**2)*(-53*y**3) + (34*y**2)*(48*y**3) + (-53*y**3)*(48*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*y**2)*(-53*y**3) = 2173*y**5\n (-41*y**2)*(34*y**2) = -1394*y**4\n (-41*y**2)*(41*y) = -1681*y**3\n (30*y)*(-53*y**3) = -1590*y**4\n (30*y)*(34*y**2) = 1020*y**3\n (30*y)*(41*y) = 1230*y**2\n (48*y**3)*(-53*y**3) = -2544*y**6\n (48*y**3)*(34*y**2) = 1632*y**5\n (48*y**3)*(41*y) = 1968*y**4\n 36*-53*y**3 = -1908*y**3\n 36*34*y**2 = 1224*y**2\n 36*41*y = 1476*y\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -2544*y**6 + 1632*y**5 + 2173*y**5 - 1590*y**4 - 1394*y**4 + 1968*y**4 - 1908*y**3 - 1681*y**3 + 1020*y**3 + 1224*y**2 + 1230*y**2 + 1476*y\nCombining like terms, got -2544*y**6 + 3805*y**5 - 1016*y**4 - 2569*y**3 + 2454*y**2 + 1476*y\n#Step 7:\nCurrent expression: -2544*y**6 + 3805*y**5 - 1016*y**4 - 2569*y**3 + 2454*y**2 + 1476*y\nNo more calculations needed.\n-2544*y**6 + 3805*y**5 - 1016*y**4 - 2569*y**3 + 2454*y**2 + 1476*y", "generated_answer": "-2544*y**6 + 3805*y**5 - 1016*y**4 - 2569*y**3 + 2454*y**2 + 1476*y", "step_length": 7} {"cot_id": "e217fffd654090d6325053bd3e59791f1bd40699a390a16e5e0db08b2575713a", "datapoint": {"question": "Calculate the following: (-15*z**2 - 14)*(11*z**3 + 3*z**2 - 46)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-165*z**5 - 45*z**4 - 154*z**3 + 648*z**2 + 644", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 382, "polynomial_expr": "(-15*z**2 - 14)*(11*z**3 + 3*z**2 - 46)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-15*z**2 - 14)*(11*z**3 + 3*z**2 - 46)\nExpanding the part (-15*z**2 - 14) using the distributive property, and we got: (-15*z**2)*(11*z**3 + 3*z**2 - 46) - 14*(11*z**3 + 3*z**2 - 46)\n#Step 2:\nCurrent expression: (-15*z**2)*(11*z**3 + 3*z**2 - 46) - 14*(11*z**3 + 3*z**2 - 46)\nSimplifying the partial expression: -14*(11*z**3 + 3*z**2 - 46)\nExpanding the part (11*z**3 + 3*z**2 - 46) using the distributive property, and we got: (3*z**2)*(-14) + (11*z**3)*(-14) - 46*(-14)\nReplacing -14*(11*z**3 + 3*z**2 - 46) with (3*z**2)*(-14) + (11*z**3)*(-14) - 46*(-14) in the overall expression.\n#Step 3:\nCurrent expression: (-15*z**2)*(11*z**3 + 3*z**2 - 46) + (3*z**2)*(-14) + (11*z**3)*(-14) + 644\nSimplifying the partial expression: (-15*z**2)*(11*z**3 + 3*z**2 - 46)\nExpanding the part (11*z**3 + 3*z**2 - 46) using the distributive property, and we got: -(-1)*690*z**2 + (-15*z**2)*(3*z**2) + (-15*z**2)*(11*z**3)\nReplacing (-15*z**2)*(11*z**3 + 3*z**2 - 46) with -(-1)*690*z**2 + (-15*z**2)*(3*z**2) + (-15*z**2)*(11*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -46*(-15)*z**2 + (-15*z**2)*(3*z**2) + (-15*z**2)*(11*z**3) + (3*z**2)*(-14) + (11*z**3)*(-14) + 644\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (3*z**2)*-14 = -42*z**2\n (3*z**2)*(-15*z**2) = -45*z**4\n (11*z**3)*-14 = -154*z**3\n (11*z**3)*(-15*z**2) = -165*z**5\n -46*-15*z**2 = 690*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -165*z**5 - 45*z**4 - 154*z**3 - 42*z**2 + 690*z**2 + 644\nCombining like terms, got -165*z**5 - 45*z**4 - 154*z**3 + 648*z**2 + 644\n#Step 6:\nCurrent expression: -165*z**5 - 45*z**4 - 154*z**3 + 648*z**2 + 644\nNo more calculations needed.\n-165*z**5 - 45*z**4 - 154*z**3 + 648*z**2 + 644", "generated_answer": "-165*z**5 - 45*z**4 - 154*z**3 + 648*z**2 + 644", "step_length": 6} {"cot_id": "d1f6daa4168233686deda6eaf1193d65754e8d48946c6e2d50ab9f2be2f7d1e4", "datapoint": {"question": "Calculate the following: (23*y**3 + 36)*(39*y**3 - 24*y**2 - 15*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "897*y**6 - 552*y**5 - 345*y**4 + 1404*y**3 - 864*y**2 - 540*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 383, "polynomial_expr": "(23*y**3 + 36)*(39*y**3 - 24*y**2 - 15*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (23*y**3 + 36)*(39*y**3 - 24*y**2 - 15*y)\nExpanding the part (23*y**3 + 36) using the distributive property, and we got: (23*y**3)*(39*y**3 - 24*y**2 - 15*y) + 36*(39*y**3 - 24*y**2 - 15*y)\n#Step 2:\nCurrent expression: (23*y**3)*(39*y**3 - 24*y**2 - 15*y) + 36*(39*y**3 - 24*y**2 - 15*y)\nSimplifying the partial expression: 36*(39*y**3 - 24*y**2 - 15*y)\nExpanding the part (39*y**3 - 24*y**2 - 15*y) using the distributive property, and we got: -15*y*36 - 24*y**2*36 + (39*y**3)*36\nReplacing 36*(39*y**3 - 24*y**2 - 15*y) with -15*y*36 - 24*y**2*36 + (39*y**3)*36 in the overall expression.\n#Step 3:\nCurrent expression: -15*y*36 - 24*y**2*36 + (23*y**3)*(39*y**3 - 24*y**2 - 15*y) + (39*y**3)*36\nSimplifying the partial expression: (23*y**3)*(39*y**3 - 24*y**2 - 15*y)\nExpanding the part (39*y**3 - 24*y**2 - 15*y) using the distributive property, and we got: (-15*y)*(23*y**3) + (-24*y**2)*(23*y**3) + (23*y**3)*(39*y**3)\nReplacing (23*y**3)*(39*y**3 - 24*y**2 - 15*y) with (-15*y)*(23*y**3) + (-24*y**2)*(23*y**3) + (23*y**3)*(39*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-15*y)*(23*y**3) - 15*y*36 + (-24*y**2)*(23*y**3) - 24*y**2*36 + (23*y**3)*(39*y**3) + (39*y**3)*36\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-24*y**2)*36 = -864*y**2\n (-24*y**2)*(23*y**3) = -552*y**5\n (-15*y)*36 = -540*y\n (-15*y)*(23*y**3) = -345*y**4\n (39*y**3)*36 = 1404*y**3\n (39*y**3)*(23*y**3) = 897*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 897*y**6 - 552*y**5 - 345*y**4 + 1404*y**3 - 864*y**2 - 540*y\nNo more calculations needed.\n897*y**6 - 552*y**5 - 345*y**4 + 1404*y**3 - 864*y**2 - 540*y", "generated_answer": "897*y**6 - 552*y**5 - 345*y**4 + 1404*y**3 - 864*y**2 - 540*y", "step_length": 5} {"cot_id": "4716ecc6b1a349b2eabdda5a0ab283bb17963920c8d8c43704f1f19de724de11", "datapoint": {"question": "Simplify this expression: (-41*x**3 + 6*x**2)*(40*x**3 - 22*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1640*x**6 + 1142*x**5 - 132*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 384, "polynomial_expr": "(-41*x**3 + 6*x**2)*(40*x**3 - 22*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-41*x**3 + 6*x**2)*(40*x**3 - 22*x**2)\nExpanding the part (-41*x**3 + 6*x**2) using the distributive property, and we got: (6*x**2)*(40*x**3 - 22*x**2) + (-41*x**3)*(40*x**3 - 22*x**2)\n#Step 2:\nCurrent expression: (6*x**2)*(40*x**3 - 22*x**2) + (-41*x**3)*(40*x**3 - 22*x**2)\nSimplifying the partial expression: (-41*x**3)*(40*x**3 - 22*x**2)\nExpanding the part (40*x**3 - 22*x**2) using the distributive property, and we got: (-22*x**2)*(-41*x**3) + (-41*x**3)*(40*x**3)\nReplacing (-41*x**3)*(40*x**3 - 22*x**2) with (-22*x**2)*(-41*x**3) + (-41*x**3)*(40*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-22*x**2)*(-41*x**3) + (6*x**2)*(40*x**3 - 22*x**2) + (-41*x**3)*(40*x**3)\nSimplifying the partial expression: (6*x**2)*(40*x**3 - 22*x**2)\nExpanding the part (40*x**3 - 22*x**2) using the distributive property, and we got: (-22*x**2)*(6*x**2) + (6*x**2)*(40*x**3)\nReplacing (6*x**2)*(40*x**3 - 22*x**2) with (-22*x**2)*(6*x**2) + (6*x**2)*(40*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-22*x**2)*(6*x**2) + (-22*x**2)*(-41*x**3) + (6*x**2)*(40*x**3) + (-41*x**3)*(40*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*x**2)*(-41*x**3) = 902*x**5\n (-22*x**2)*(6*x**2) = -132*x**4\n (40*x**3)*(-41*x**3) = -1640*x**6\n (40*x**3)*(6*x**2) = 240*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1640*x**6 + 240*x**5 + 902*x**5 - 132*x**4\nCombining like terms, got -1640*x**6 + 1142*x**5 - 132*x**4\n#Step 6:\nCurrent expression: -1640*x**6 + 1142*x**5 - 132*x**4\nNo more calculations needed.\n-1640*x**6 + 1142*x**5 - 132*x**4", "generated_answer": "-1640*x**6 + 1142*x**5 - 132*x**4", "step_length": 6} {"cot_id": "0aadc36033c9452c312ad27e00f0bd315f1c45db6390ee4858300beb4c9c1cbb", "datapoint": {"question": "Simplify this expression: -2*x**2*(46*x**3 + 44*x - 3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-92*x**5 - 88*x**3 + 6*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 385, "polynomial_expr": "-2*x**2*(46*x**3 + 44*x - 3)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -2*x**2*(46*x**3 + 44*x - 3)\nExpanding the part (46*x**3 + 44*x - 3) using the distributive property, and we got: -(-1)*6*x**2 + (44*x)*(-2*x**2) + (-2*x**2)*(46*x**3)\n#Step 2:\nCurrent expression: -(-1)*6*x**2 + (44*x)*(-2*x**2) + (-2*x**2)*(46*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -3*(-2*x**2) = 6*x**2\n (44*x)*(-2*x**2) = -88*x**3\n (46*x**3)*(-2*x**2) = -92*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -92*x**5 - 88*x**3 + 6*x**2\nNo more calculations needed.\n-92*x**5 - 88*x**3 + 6*x**2", "generated_answer": "-92*x**5 - 88*x**3 + 6*x**2", "step_length": 3} {"cot_id": "4902c0fd49b11a1fd9f10c5a306d88de4a578947943bb331e8a32736f0a756de", "datapoint": {"question": "Calculate the following: (-41*y**2 + 11*y)*(29*y**3 + 56*y**2 + 17*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1189*y**5 - 1977*y**4 - 81*y**3 + 187*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 386, "polynomial_expr": "(-41*y**2 + 11*y)*(29*y**3 + 56*y**2 + 17*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-41*y**2 + 11*y)*(29*y**3 + 56*y**2 + 17*y)\nExpanding the part (-41*y**2 + 11*y) using the distributive property, and we got: (11*y)*(29*y**3 + 56*y**2 + 17*y) + (-41*y**2)*(29*y**3 + 56*y**2 + 17*y)\n#Step 2:\nCurrent expression: (11*y)*(29*y**3 + 56*y**2 + 17*y) + (-41*y**2)*(29*y**3 + 56*y**2 + 17*y)\nSimplifying the partial expression: (-41*y**2)*(29*y**3 + 56*y**2 + 17*y)\nExpanding the part (29*y**3 + 56*y**2 + 17*y) using the distributive property, and we got: (17*y)*(-41*y**2) + (-41*y**2)*(56*y**2) + (-41*y**2)*(29*y**3)\nReplacing (-41*y**2)*(29*y**3 + 56*y**2 + 17*y) with (17*y)*(-41*y**2) + (-41*y**2)*(56*y**2) + (-41*y**2)*(29*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (11*y)*(29*y**3 + 56*y**2 + 17*y) + (17*y)*(-41*y**2) + (-41*y**2)*(56*y**2) + (-41*y**2)*(29*y**3)\nSimplifying the partial expression: (11*y)*(29*y**3 + 56*y**2 + 17*y)\nExpanding the part (29*y**3 + 56*y**2 + 17*y) using the distributive property, and we got: (11*y)*(17*y) + (11*y)*(56*y**2) + (11*y)*(29*y**3)\nReplacing (11*y)*(29*y**3 + 56*y**2 + 17*y) with (11*y)*(17*y) + (11*y)*(56*y**2) + (11*y)*(29*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (11*y)*(17*y) + (11*y)*(56*y**2) + (11*y)*(29*y**3) + (17*y)*(-41*y**2) + (-41*y**2)*(56*y**2) + (-41*y**2)*(29*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (17*y)*(-41*y**2) = -697*y**3\n (17*y)*(11*y) = 187*y**2\n (29*y**3)*(-41*y**2) = -1189*y**5\n (29*y**3)*(11*y) = 319*y**4\n (56*y**2)*(-41*y**2) = -2296*y**4\n (56*y**2)*(11*y) = 616*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1189*y**5 - 2296*y**4 + 319*y**4 - 697*y**3 + 616*y**3 + 187*y**2\nCombining like terms, got -1189*y**5 - 1977*y**4 - 81*y**3 + 187*y**2\n#Step 6:\nCurrent expression: -1189*y**5 - 1977*y**4 - 81*y**3 + 187*y**2\nNo more calculations needed.\n-1189*y**5 - 1977*y**4 - 81*y**3 + 187*y**2", "generated_answer": "-1189*y**5 - 1977*y**4 - 81*y**3 + 187*y**2", "step_length": 6} {"cot_id": "56071ed0274fdddb118c6def399375d262f2c30b27e85280f8e3d6422324f459", "datapoint": {"question": "Simplify this expression: (-22*z**3 - 25)*(27*z**3 - 36*z**2 + 35*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-594*z**6 + 792*z**5 - 770*z**4 - 675*z**3 + 900*z**2 - 875*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 387, "polynomial_expr": "(-22*z**3 - 25)*(27*z**3 - 36*z**2 + 35*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-22*z**3 - 25)*(27*z**3 - 36*z**2 + 35*z)\nExpanding the part (-22*z**3 - 25) using the distributive property, and we got: (-22*z**3)*(27*z**3 - 36*z**2 + 35*z) - 25*(27*z**3 - 36*z**2 + 35*z)\n#Step 2:\nCurrent expression: (-22*z**3)*(27*z**3 - 36*z**2 + 35*z) - 25*(27*z**3 - 36*z**2 + 35*z)\nSimplifying the partial expression: -25*(27*z**3 - 36*z**2 + 35*z)\nExpanding the part (27*z**3 - 36*z**2 + 35*z) using the distributive property, and we got: (35*z)*(-25) - 36*z**2*(-25) + (27*z**3)*(-25)\nReplacing -25*(27*z**3 - 36*z**2 + 35*z) with (35*z)*(-25) - 36*z**2*(-25) + (27*z**3)*(-25) in the overall expression.\n#Step 3:\nCurrent expression: (35*z)*(-25) - 36*z**2*(-25) + (-22*z**3)*(27*z**3 - 36*z**2 + 35*z) + (27*z**3)*(-25)\nSimplifying the partial expression: (-22*z**3)*(27*z**3 - 36*z**2 + 35*z)\nExpanding the part (27*z**3 - 36*z**2 + 35*z) using the distributive property, and we got: (35*z)*(-22*z**3) + (-36*z**2)*(-22*z**3) + (-22*z**3)*(27*z**3)\nReplacing (-22*z**3)*(27*z**3 - 36*z**2 + 35*z) with (35*z)*(-22*z**3) + (-36*z**2)*(-22*z**3) + (-22*z**3)*(27*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (35*z)*(-22*z**3) + (35*z)*(-25) + (-36*z**2)*(-22*z**3) - 36*z**2*(-25) + (-22*z**3)*(27*z**3) + (27*z**3)*(-25)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*z**2)*-25 = 900*z**2\n (-36*z**2)*(-22*z**3) = 792*z**5\n (27*z**3)*-25 = -675*z**3\n (27*z**3)*(-22*z**3) = -594*z**6\n (35*z)*-25 = -875*z\n (35*z)*(-22*z**3) = -770*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -594*z**6 + 792*z**5 - 770*z**4 - 675*z**3 + 900*z**2 - 875*z\nNo more calculations needed.\n-594*z**6 + 792*z**5 - 770*z**4 - 675*z**3 + 900*z**2 - 875*z", "generated_answer": "-594*z**6 + 792*z**5 - 770*z**4 - 675*z**3 + 900*z**2 - 875*z", "step_length": 5} {"cot_id": "42edfc1837d45e1fc18ffc77b9a8dff83576ed4c738764d32a23aba9d3d62170", "datapoint": {"question": "Calculate the following: (-50*y - 10)*(-37*y**2 - 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1850*y**3 + 370*y**2 + 500*y + 100", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 388, "polynomial_expr": "(-50*y - 10)*(-37*y**2 - 10)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-50*y - 10)*(-37*y**2 - 10)\nExpanding the part (-50*y - 10) using the distributive property, and we got: (-50*y)*(-37*y**2 - 10) - 10*(-37*y**2 - 10)\n#Step 2:\nCurrent expression: (-50*y)*(-37*y**2 - 10) - 10*(-37*y**2 - 10)\nSimplifying the partial expression: -10*(-37*y**2 - 10)\nExpanding the part (-37*y**2 - 10) using the distributive property, and we got: -37*y**2*(-10) - 10*(-10)\nReplacing -10*(-37*y**2 - 10) with -37*y**2*(-10) - 10*(-10) in the overall expression.\n#Step 3:\nCurrent expression: (-50*y)*(-37*y**2 - 10) - 37*y**2*(-10) + 100\nSimplifying the partial expression: (-50*y)*(-37*y**2 - 10)\nExpanding the part (-37*y**2 - 10) using the distributive property, and we got: (-50*y)*(-37*y**2) - (-1)*500*y\nReplacing (-50*y)*(-37*y**2 - 10) with (-50*y)*(-37*y**2) - (-1)*500*y in the overall expression.\n#Step 4:\nCurrent expression: (-50*y)*(-37*y**2) - 10*(-50)*y - 37*y**2*(-10) + 100\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*y**2)*-10 = 370*y**2\n (-37*y**2)*(-50*y) = 1850*y**3\n -10*-50*y = 500*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1850*y**3 + 370*y**2 + 500*y + 100\nNo more calculations needed.\n1850*y**3 + 370*y**2 + 500*y + 100", "generated_answer": "1850*y**3 + 370*y**2 + 500*y + 100", "step_length": 5} {"cot_id": "db03f42dddb22b273aeb4e060e4cce8e9775d1d189e4e410eb0d625a2d780712", "datapoint": {"question": "Calculate the following: (5*y**3 - 35)*(26*y**3 + 13*y**2 - 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "130*y**6 + 65*y**5 - 1115*y**3 - 455*y**2 + 1435", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 389, "polynomial_expr": "(5*y**3 - 35)*(26*y**3 + 13*y**2 - 41)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (5*y**3 - 35)*(26*y**3 + 13*y**2 - 41)\nExpanding the part (5*y**3 - 35) using the distributive property, and we got: (5*y**3)*(26*y**3 + 13*y**2 - 41) - 35*(26*y**3 + 13*y**2 - 41)\n#Step 2:\nCurrent expression: (5*y**3)*(26*y**3 + 13*y**2 - 41) - 35*(26*y**3 + 13*y**2 - 41)\nSimplifying the partial expression: -35*(26*y**3 + 13*y**2 - 41)\nExpanding the part (26*y**3 + 13*y**2 - 41) using the distributive property, and we got: (13*y**2)*(-35) + (26*y**3)*(-35) - 41*(-35)\nReplacing -35*(26*y**3 + 13*y**2 - 41) with (13*y**2)*(-35) + (26*y**3)*(-35) - 41*(-35) in the overall expression.\n#Step 3:\nCurrent expression: (13*y**2)*(-35) + (5*y**3)*(26*y**3 + 13*y**2 - 41) + (26*y**3)*(-35) + 1435\nSimplifying the partial expression: (5*y**3)*(26*y**3 + 13*y**2 - 41)\nExpanding the part (26*y**3 + 13*y**2 - 41) using the distributive property, and we got: -205*y**3 + (13*y**2)*(5*y**3) + (5*y**3)*(26*y**3)\nReplacing (5*y**3)*(26*y**3 + 13*y**2 - 41) with -205*y**3 + (13*y**2)*(5*y**3) + (5*y**3)*(26*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -41*5*y**3 + (13*y**2)*(5*y**3) + (13*y**2)*(-35) + (5*y**3)*(26*y**3) + (26*y**3)*(-35) + 1435\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (13*y**2)*-35 = -455*y**2\n (13*y**2)*(5*y**3) = 65*y**5\n (26*y**3)*-35 = -910*y**3\n (26*y**3)*(5*y**3) = 130*y**6\n -41*5*y**3 = -205*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 130*y**6 + 65*y**5 - 910*y**3 - 205*y**3 - 455*y**2 + 1435\nCombining like terms, got 130*y**6 + 65*y**5 - 1115*y**3 - 455*y**2 + 1435\n#Step 6:\nCurrent expression: 130*y**6 + 65*y**5 - 1115*y**3 - 455*y**2 + 1435\nNo more calculations needed.\n130*y**6 + 65*y**5 - 1115*y**3 - 455*y**2 + 1435", "generated_answer": "130*y**6 + 65*y**5 - 1115*y**3 - 455*y**2 + 1435", "step_length": 6} {"cot_id": "c91b0d84821892384a571b15f4dc74068b10eec69f066d6314058f5acd9ed5c4", "datapoint": {"question": "Calculate the following: (12 - 50*z**2)*(11*z**2 + 49*z - 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-550*z**4 - 2450*z**3 + 1682*z**2 + 588*z - 372", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 390, "polynomial_expr": "(12 - 50*z**2)*(11*z**2 + 49*z - 31)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (12 - 50*z**2)*(11*z**2 + 49*z - 31)\nExpanding the part (12 - 50*z**2) using the distributive property, and we got: (-50*z**2)*(11*z**2 + 49*z - 31) + 12*(11*z**2 + 49*z - 31)\n#Step 2:\nCurrent expression: (-50*z**2)*(11*z**2 + 49*z - 31) + 12*(11*z**2 + 49*z - 31)\nSimplifying the partial expression: 12*(11*z**2 + 49*z - 31)\nExpanding the part (11*z**2 + 49*z - 31) using the distributive property, and we got: (49*z)*12 + (11*z**2)*12 - 31*12\nReplacing 12*(11*z**2 + 49*z - 31) with (49*z)*12 + (11*z**2)*12 - 31*12 in the overall expression.\n#Step 3:\nCurrent expression: (49*z)*12 + (-50*z**2)*(11*z**2 + 49*z - 31) + (11*z**2)*12 - 372\nSimplifying the partial expression: (-50*z**2)*(11*z**2 + 49*z - 31)\nExpanding the part (11*z**2 + 49*z - 31) using the distributive property, and we got: -(-1)*1550*z**2 + (49*z)*(-50*z**2) + (-50*z**2)*(11*z**2)\nReplacing (-50*z**2)*(11*z**2 + 49*z - 31) with -(-1)*1550*z**2 + (49*z)*(-50*z**2) + (-50*z**2)*(11*z**2) in the overall expression.\n#Step 4:\nCurrent expression: -31*(-50)*z**2 + (49*z)*(-50*z**2) + (49*z)*12 + (-50*z**2)*(11*z**2) + (11*z**2)*12 - 372\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (11*z**2)*12 = 132*z**2\n (11*z**2)*(-50*z**2) = -550*z**4\n (49*z)*12 = 588*z\n (49*z)*(-50*z**2) = -2450*z**3\n -31*-50*z**2 = 1550*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -550*z**4 - 2450*z**3 + 132*z**2 + 1550*z**2 + 588*z - 372\nCombining like terms, got -550*z**4 - 2450*z**3 + 1682*z**2 + 588*z - 372\n#Step 6:\nCurrent expression: -550*z**4 - 2450*z**3 + 1682*z**2 + 588*z - 372\nNo more calculations needed.\n-550*z**4 - 2450*z**3 + 1682*z**2 + 588*z - 372", "generated_answer": "-550*z**4 - 2450*z**3 + 1682*z**2 + 588*z - 372", "step_length": 6} {"cot_id": "3b04bc37775ef27b82013a11a13e614d91d753e525a02a2fcf54a9c3c93405c9", "datapoint": {"question": "Simplify this expression: (3*x**3 + 20*x)*(4*x**3 + 18*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "12*x**6 + 134*x**4 + 360*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 391, "polynomial_expr": "(3*x**3 + 20*x)*(4*x**3 + 18*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (3*x**3 + 20*x)*(4*x**3 + 18*x)\nExpanding the part (3*x**3 + 20*x) using the distributive property, and we got: (20*x)*(4*x**3 + 18*x) + (3*x**3)*(4*x**3 + 18*x)\n#Step 2:\nCurrent expression: (20*x)*(4*x**3 + 18*x) + (3*x**3)*(4*x**3 + 18*x)\nSimplifying the partial expression: (3*x**3)*(4*x**3 + 18*x)\nExpanding the part (4*x**3 + 18*x) using the distributive property, and we got: (18*x)*(3*x**3) + (3*x**3)*(4*x**3)\nReplacing (3*x**3)*(4*x**3 + 18*x) with (18*x)*(3*x**3) + (3*x**3)*(4*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (18*x)*(3*x**3) + (20*x)*(4*x**3 + 18*x) + (3*x**3)*(4*x**3)\nSimplifying the partial expression: (20*x)*(4*x**3 + 18*x)\nExpanding the part (4*x**3 + 18*x) using the distributive property, and we got: (18*x)*(20*x) + (20*x)*(4*x**3)\nReplacing (20*x)*(4*x**3 + 18*x) with (18*x)*(20*x) + (20*x)*(4*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (18*x)*(20*x) + (18*x)*(3*x**3) + (20*x)*(4*x**3) + (3*x**3)*(4*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (4*x**3)*(3*x**3) = 12*x**6\n (4*x**3)*(20*x) = 80*x**4\n (18*x)*(3*x**3) = 54*x**4\n (18*x)*(20*x) = 360*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 12*x**6 + 54*x**4 + 80*x**4 + 360*x**2\nCombining like terms, got 12*x**6 + 134*x**4 + 360*x**2\n#Step 6:\nCurrent expression: 12*x**6 + 134*x**4 + 360*x**2\nNo more calculations needed.\n12*x**6 + 134*x**4 + 360*x**2", "generated_answer": "12*x**6 + 134*x**4 + 360*x**2", "step_length": 6} {"cot_id": "bbc11a3d375b578ab67095d16ce363758b686dfd0959f8b56ac6117954acd229", "datapoint": {"question": "Calculate the following: -34*y**3*(5*y**3 - 34*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-170*y**6 + 1156*y**5", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 392, "polynomial_expr": "-34*y**3*(5*y**3 - 34*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -34*y**3*(5*y**3 - 34*y**2)\nExpanding the part (5*y**3 - 34*y**2) using the distributive property, and we got: (-34*y**2)*(-34*y**3) + (-34*y**3)*(5*y**3)\n#Step 2:\nCurrent expression: (-34*y**2)*(-34*y**3) + (-34*y**3)*(5*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*y**2)*(-34*y**3) = 1156*y**5\n (5*y**3)*(-34*y**3) = -170*y**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -170*y**6 + 1156*y**5\nNo more calculations needed.\n-170*y**6 + 1156*y**5", "generated_answer": "-170*y**6 + 1156*y**5", "step_length": 3} {"cot_id": "245abeb0e1431c916c41a340fb3fdb17185b61df4cc343e978d78eff7c11d29c", "datapoint": {"question": "Simplify this expression: (-42*x**3 - 4*x)*(-4*x**3 - 36*x**2 - 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "168*x**6 + 1512*x**5 + 16*x**4 + 1614*x**3 + 140*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 393, "polynomial_expr": "(-42*x**3 - 4*x)*(-4*x**3 - 36*x**2 - 35)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-42*x**3 - 4*x)*(-4*x**3 - 36*x**2 - 35)\nExpanding the part (-42*x**3 - 4*x) using the distributive property, and we got: (-4*x)*(-4*x**3 - 36*x**2 - 35) + (-42*x**3)*(-4*x**3 - 36*x**2 - 35)\n#Step 2:\nCurrent expression: (-4*x)*(-4*x**3 - 36*x**2 - 35) + (-42*x**3)*(-4*x**3 - 36*x**2 - 35)\nSimplifying the partial expression: (-42*x**3)*(-4*x**3 - 36*x**2 - 35)\nExpanding the part (-4*x**3 - 36*x**2 - 35) using the distributive property, and we got: -(-1)*1470*x**3 + (-36*x**2)*(-42*x**3) + (-42*x**3)*(-4*x**3)\nReplacing (-42*x**3)*(-4*x**3 - 36*x**2 - 35) with -(-1)*1470*x**3 + (-36*x**2)*(-42*x**3) + (-42*x**3)*(-4*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-4*x)*(-4*x**3 - 36*x**2 - 35) - 35*(-42)*x**3 + (-36*x**2)*(-42*x**3) + (-42*x**3)*(-4*x**3)\nSimplifying the partial expression: (-4*x)*(-4*x**3 - 36*x**2 - 35)\nExpanding the part (-4*x**3 - 36*x**2 - 35) using the distributive property, and we got: (-4*x)*(-36*x**2) + (-4*x)*(-4*x**3) - (-1)*140*x\nReplacing (-4*x)*(-4*x**3 - 36*x**2 - 35) with (-4*x)*(-36*x**2) + (-4*x)*(-4*x**3) - (-1)*140*x in the overall expression.\n#Step 4:\nCurrent expression: (-4*x)*(-36*x**2) + (-4*x)*(-4*x**3) - 35*(-42)*x**3 - 35*(-4)*x + (-36*x**2)*(-42*x**3) + (-42*x**3)*(-4*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*x**2)*(-42*x**3) = 1512*x**5\n (-36*x**2)*(-4*x) = 144*x**3\n (-4*x**3)*(-42*x**3) = 168*x**6\n (-4*x**3)*(-4*x) = 16*x**4\n -35*-42*x**3 = 1470*x**3\n -35*-4*x = 140*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 168*x**6 + 1512*x**5 + 16*x**4 + 144*x**3 + 1470*x**3 + 140*x\nCombining like terms, got 168*x**6 + 1512*x**5 + 16*x**4 + 1614*x**3 + 140*x\n#Step 6:\nCurrent expression: 168*x**6 + 1512*x**5 + 16*x**4 + 1614*x**3 + 140*x\nNo more calculations needed.\n168*x**6 + 1512*x**5 + 16*x**4 + 1614*x**3 + 140*x", "generated_answer": "168*x**6 + 1512*x**5 + 16*x**4 + 1614*x**3 + 140*x", "step_length": 6} {"cot_id": "059270f79df6564c9e8b439b736dc37ce83fb875ac3447ad174d5a0030696161", "datapoint": {"question": "Calculate the following: (21*y**3 + 15)*(-29*y**3 - 20*y**2 + 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-609*y**6 - 420*y**5 + 258*y**3 - 300*y**2 + 495", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 394, "polynomial_expr": "(21*y**3 + 15)*(-29*y**3 - 20*y**2 + 33)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21*y**3 + 15)*(-29*y**3 - 20*y**2 + 33)\nExpanding the part (21*y**3 + 15) using the distributive property, and we got: (21*y**3)*(-29*y**3 - 20*y**2 + 33) + 15*(-29*y**3 - 20*y**2 + 33)\n#Step 2:\nCurrent expression: (21*y**3)*(-29*y**3 - 20*y**2 + 33) + 15*(-29*y**3 - 20*y**2 + 33)\nSimplifying the partial expression: 15*(-29*y**3 - 20*y**2 + 33)\nExpanding the part (-29*y**3 - 20*y**2 + 33) using the distributive property, and we got: -20*y**2*15 - 29*y**3*15 + 33*15\nReplacing 15*(-29*y**3 - 20*y**2 + 33) with -20*y**2*15 - 29*y**3*15 + 33*15 in the overall expression.\n#Step 3:\nCurrent expression: -20*y**2*15 - 29*y**3*15 + (21*y**3)*(-29*y**3 - 20*y**2 + 33) + 495\nSimplifying the partial expression: (21*y**3)*(-29*y**3 - 20*y**2 + 33)\nExpanding the part (-29*y**3 - 20*y**2 + 33) using the distributive property, and we got: 33*(21*y**3) + (-20*y**2)*(21*y**3) + (-29*y**3)*(21*y**3)\nReplacing (21*y**3)*(-29*y**3 - 20*y**2 + 33) with 33*(21*y**3) + (-20*y**2)*(21*y**3) + (-29*y**3)*(21*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 33*21*y**3 + (-20*y**2)*(21*y**3) - 20*y**2*15 + (-29*y**3)*(21*y**3) - 29*y**3*15 + 495\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*y**3)*15 = -435*y**3\n (-29*y**3)*(21*y**3) = -609*y**6\n (-20*y**2)*15 = -300*y**2\n (-20*y**2)*(21*y**3) = -420*y**5\n 33*21*y**3 = 693*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -609*y**6 - 420*y**5 - 435*y**3 + 693*y**3 - 300*y**2 + 495\nCombining like terms, got -609*y**6 - 420*y**5 + 258*y**3 - 300*y**2 + 495\n#Step 6:\nCurrent expression: -609*y**6 - 420*y**5 + 258*y**3 - 300*y**2 + 495\nNo more calculations needed.\n-609*y**6 - 420*y**5 + 258*y**3 - 300*y**2 + 495", "generated_answer": "-609*y**6 - 420*y**5 + 258*y**3 - 300*y**2 + 495", "step_length": 6} {"cot_id": "f8fb039d9ec8dd4212bc5b834ad9fbf813426bdaa8c61df32a6b65b4e03d6243", "datapoint": {"question": "Calculate the following: (17*z**2 - 2)*(17*z**3 + 19*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "289*z**5 + 289*z**3 - 38*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 395, "polynomial_expr": "(17*z**2 - 2)*(17*z**3 + 19*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (17*z**2 - 2)*(17*z**3 + 19*z)\nExpanding the part (17*z**2 - 2) using the distributive property, and we got: (17*z**2)*(17*z**3 + 19*z) - 2*(17*z**3 + 19*z)\n#Step 2:\nCurrent expression: (17*z**2)*(17*z**3 + 19*z) - 2*(17*z**3 + 19*z)\nSimplifying the partial expression: -2*(17*z**3 + 19*z)\nExpanding the part (17*z**3 + 19*z) using the distributive property, and we got: (19*z)*(-2) + (17*z**3)*(-2)\nReplacing -2*(17*z**3 + 19*z) with (19*z)*(-2) + (17*z**3)*(-2) in the overall expression.\n#Step 3:\nCurrent expression: (19*z)*(-2) + (17*z**2)*(17*z**3 + 19*z) + (17*z**3)*(-2)\nSimplifying the partial expression: (17*z**2)*(17*z**3 + 19*z)\nExpanding the part (17*z**3 + 19*z) using the distributive property, and we got: (19*z)*(17*z**2) + (17*z**2)*(17*z**3)\nReplacing (17*z**2)*(17*z**3 + 19*z) with (19*z)*(17*z**2) + (17*z**2)*(17*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (19*z)*(17*z**2) + (19*z)*(-2) + (17*z**2)*(17*z**3) + (17*z**3)*(-2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (17*z**3)*-2 = -34*z**3\n (17*z**3)*(17*z**2) = 289*z**5\n (19*z)*-2 = -38*z\n (19*z)*(17*z**2) = 323*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 289*z**5 - 34*z**3 + 323*z**3 - 38*z\nCombining like terms, got 289*z**5 + 289*z**3 - 38*z\n#Step 6:\nCurrent expression: 289*z**5 + 289*z**3 - 38*z\nNo more calculations needed.\n289*z**5 + 289*z**3 - 38*z", "generated_answer": "289*z**5 + 289*z**3 - 38*z", "step_length": 6} {"cot_id": "f86d3b684e6b4fbe7341107bba4e1e39c2bfbe0efce75e750ad79fb36a013392", "datapoint": {"question": "Calculate the following: (-19*x**3 - 26)*(22*x**3 - 18*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-418*x**6 + 342*x**4 - 572*x**3 + 468*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 396, "polynomial_expr": "(-19*x**3 - 26)*(22*x**3 - 18*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-19*x**3 - 26)*(22*x**3 - 18*x)\nExpanding the part (-19*x**3 - 26) using the distributive property, and we got: (-19*x**3)*(22*x**3 - 18*x) - 26*(22*x**3 - 18*x)\n#Step 2:\nCurrent expression: (-19*x**3)*(22*x**3 - 18*x) - 26*(22*x**3 - 18*x)\nSimplifying the partial expression: -26*(22*x**3 - 18*x)\nExpanding the part (22*x**3 - 18*x) using the distributive property, and we got: -18*x*(-26) + (22*x**3)*(-26)\nReplacing -26*(22*x**3 - 18*x) with -18*x*(-26) + (22*x**3)*(-26) in the overall expression.\n#Step 3:\nCurrent expression: -18*x*(-26) + (-19*x**3)*(22*x**3 - 18*x) + (22*x**3)*(-26)\nSimplifying the partial expression: (-19*x**3)*(22*x**3 - 18*x)\nExpanding the part (22*x**3 - 18*x) using the distributive property, and we got: (-18*x)*(-19*x**3) + (-19*x**3)*(22*x**3)\nReplacing (-19*x**3)*(22*x**3 - 18*x) with (-18*x)*(-19*x**3) + (-19*x**3)*(22*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-18*x)*(-19*x**3) - 18*x*(-26) + (-19*x**3)*(22*x**3) + (22*x**3)*(-26)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-18*x)*-26 = 468*x\n (-18*x)*(-19*x**3) = 342*x**4\n (22*x**3)*-26 = -572*x**3\n (22*x**3)*(-19*x**3) = -418*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -418*x**6 + 342*x**4 - 572*x**3 + 468*x\nNo more calculations needed.\n-418*x**6 + 342*x**4 - 572*x**3 + 468*x", "generated_answer": "-418*x**6 + 342*x**4 - 572*x**3 + 468*x", "step_length": 5} {"cot_id": "445d36ffab14d11746d906460b7c77474516db64297011aad08124c16227f47d", "datapoint": {"question": "Calculate the following: (27*y**2 + 55*y)*(39*y**3 + 20*y**2 + 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1053*y**5 + 2685*y**4 + 1100*y**3 + 567*y**2 + 1155*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 397, "polynomial_expr": "(27*y**2 + 55*y)*(39*y**3 + 20*y**2 + 21)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*y**2 + 55*y)*(39*y**3 + 20*y**2 + 21)\nExpanding the part (27*y**2 + 55*y) using the distributive property, and we got: (55*y)*(39*y**3 + 20*y**2 + 21) + (27*y**2)*(39*y**3 + 20*y**2 + 21)\n#Step 2:\nCurrent expression: (55*y)*(39*y**3 + 20*y**2 + 21) + (27*y**2)*(39*y**3 + 20*y**2 + 21)\nSimplifying the partial expression: (27*y**2)*(39*y**3 + 20*y**2 + 21)\nExpanding the part (39*y**3 + 20*y**2 + 21) using the distributive property, and we got: 21*(27*y**2) + (20*y**2)*(27*y**2) + (27*y**2)*(39*y**3)\nReplacing (27*y**2)*(39*y**3 + 20*y**2 + 21) with 21*(27*y**2) + (20*y**2)*(27*y**2) + (27*y**2)*(39*y**3) in the overall expression.\n#Step 3:\nCurrent expression: 21*27*y**2 + (55*y)*(39*y**3 + 20*y**2 + 21) + (20*y**2)*(27*y**2) + (27*y**2)*(39*y**3)\nSimplifying the partial expression: (55*y)*(39*y**3 + 20*y**2 + 21)\nExpanding the part (39*y**3 + 20*y**2 + 21) using the distributive property, and we got: 21*(55*y) + (55*y)*(20*y**2) + (55*y)*(39*y**3)\nReplacing (55*y)*(39*y**3 + 20*y**2 + 21) with 21*(55*y) + (55*y)*(20*y**2) + (55*y)*(39*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 21*27*y**2 + 21*55*y + (55*y)*(20*y**2) + (55*y)*(39*y**3) + (20*y**2)*(27*y**2) + (27*y**2)*(39*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (20*y**2)*(27*y**2) = 540*y**4\n (20*y**2)*(55*y) = 1100*y**3\n (39*y**3)*(27*y**2) = 1053*y**5\n (39*y**3)*(55*y) = 2145*y**4\n 21*27*y**2 = 567*y**2\n 21*55*y = 1155*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1053*y**5 + 540*y**4 + 2145*y**4 + 1100*y**3 + 567*y**2 + 1155*y\nCombining like terms, got 1053*y**5 + 2685*y**4 + 1100*y**3 + 567*y**2 + 1155*y\n#Step 6:\nCurrent expression: 1053*y**5 + 2685*y**4 + 1100*y**3 + 567*y**2 + 1155*y\nNo more calculations needed.\n1053*y**5 + 2685*y**4 + 1100*y**3 + 567*y**2 + 1155*y", "generated_answer": "1053*y**5 + 2685*y**4 + 1100*y**3 + 567*y**2 + 1155*y", "step_length": 6} {"cot_id": "f239c37469c02410a9aab56f06a4ae1fc22dba16ae05bf414e8dc4d09d8bf6f6", "datapoint": {"question": "Calculate the following: (4*x**2 + 18)*(-7*x**3 + 24*x + 9)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-28*x**5 - 30*x**3 + 36*x**2 + 432*x + 162", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 398, "polynomial_expr": "(4*x**2 + 18)*(-7*x**3 + 24*x + 9)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (4*x**2 + 18)*(-7*x**3 + 24*x + 9)\nExpanding the part (4*x**2 + 18) using the distributive property, and we got: (4*x**2)*(-7*x**3 + 24*x + 9) + 18*(-7*x**3 + 24*x + 9)\n#Step 2:\nCurrent expression: (4*x**2)*(-7*x**3 + 24*x + 9) + 18*(-7*x**3 + 24*x + 9)\nSimplifying the partial expression: 18*(-7*x**3 + 24*x + 9)\nExpanding the part (-7*x**3 + 24*x + 9) using the distributive property, and we got: (24*x)*18 - 7*x**3*18 + 9*18\nReplacing 18*(-7*x**3 + 24*x + 9) with (24*x)*18 - 7*x**3*18 + 9*18 in the overall expression.\n#Step 3:\nCurrent expression: (24*x)*18 + (4*x**2)*(-7*x**3 + 24*x + 9) - 7*x**3*18 + 162\nSimplifying the partial expression: (4*x**2)*(-7*x**3 + 24*x + 9)\nExpanding the part (-7*x**3 + 24*x + 9) using the distributive property, and we got: 9*(4*x**2) + (24*x)*(4*x**2) + (4*x**2)*(-7*x**3)\nReplacing (4*x**2)*(-7*x**3 + 24*x + 9) with 9*(4*x**2) + (24*x)*(4*x**2) + (4*x**2)*(-7*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 9*4*x**2 + (24*x)*(4*x**2) + (24*x)*18 + (4*x**2)*(-7*x**3) - 7*x**3*18 + 162\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-7*x**3)*18 = -126*x**3\n (-7*x**3)*(4*x**2) = -28*x**5\n (24*x)*18 = 432*x\n (24*x)*(4*x**2) = 96*x**3\n 9*4*x**2 = 36*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -28*x**5 - 126*x**3 + 96*x**3 + 36*x**2 + 432*x + 162\nCombining like terms, got -28*x**5 - 30*x**3 + 36*x**2 + 432*x + 162\n#Step 6:\nCurrent expression: -28*x**5 - 30*x**3 + 36*x**2 + 432*x + 162\nNo more calculations needed.\n-28*x**5 - 30*x**3 + 36*x**2 + 432*x + 162", "generated_answer": "-28*x**5 - 30*x**3 + 36*x**2 + 432*x + 162", "step_length": 6} {"cot_id": "15750eec0a5500ace41aa08c3a3adef6afa32b8126e9e818109253278bb63715", "datapoint": {"question": "Calculate the following: (-9*x**3 - 34*x**2 + 34*x - 10)*(14*x**3 + 7*x**2 - 20*x - 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-126*x**6 - 539*x**5 + 418*x**4 + 1219*x**3 + 916*x**2 - 1466*x + 490", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 399, "polynomial_expr": "(-9*x**3 - 34*x**2 + 34*x - 10)*(14*x**3 + 7*x**2 - 20*x - 49)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-9*x**3 - 34*x**2 + 34*x - 10)*(14*x**3 + 7*x**2 - 20*x - 49)\nExpanding the part (14*x**3 + 7*x**2 - 20*x - 49) using the distributive property, and we got: (-20*x)*(-9*x**3 - 34*x**2 + 34*x - 10) + (7*x**2)*(-9*x**3 - 34*x**2 + 34*x - 10) + (14*x**3)*(-9*x**3 - 34*x**2 + 34*x - 10) - 49*(-9*x**3 - 34*x**2 + 34*x - 10)\n#Step 2:\nCurrent expression: (-20*x)*(-9*x**3 - 34*x**2 + 34*x - 10) + (7*x**2)*(-9*x**3 - 34*x**2 + 34*x - 10) + (14*x**3)*(-9*x**3 - 34*x**2 + 34*x - 10) - 49*(-9*x**3 - 34*x**2 + 34*x - 10)\nSimplifying the partial expression: -49*(-9*x**3 - 34*x**2 + 34*x - 10)\nExpanding the part (-9*x**3 - 34*x**2 + 34*x - 10) using the distributive property, and we got: (34*x)*(-49) - 34*x**2*(-49) - 9*x**3*(-49) - 10*(-49)\nReplacing -49*(-9*x**3 - 34*x**2 + 34*x - 10) with (34*x)*(-49) - 34*x**2*(-49) - 9*x**3*(-49) - 10*(-49) in the overall expression.\n#Step 3:\nCurrent expression: (-20*x)*(-9*x**3 - 34*x**2 + 34*x - 10) + (34*x)*(-49) - 34*x**2*(-49) + (7*x**2)*(-9*x**3 - 34*x**2 + 34*x - 10) - 9*x**3*(-49) + (14*x**3)*(-9*x**3 - 34*x**2 + 34*x - 10) + 490\nSimplifying the partial expression: (-20*x)*(-9*x**3 - 34*x**2 + 34*x - 10)\nExpanding the part (-9*x**3 - 34*x**2 + 34*x - 10) using the distributive property, and we got: (-20*x)*(34*x) + (-20*x)*(-34*x**2) + (-20*x)*(-9*x**3) - (-1)*200*x\nReplacing (-20*x)*(-9*x**3 - 34*x**2 + 34*x - 10) with (-20*x)*(34*x) + (-20*x)*(-34*x**2) + (-20*x)*(-9*x**3) - (-1)*200*x in the overall expression.\n#Step 4:\nCurrent expression: (-20*x)*(34*x) + (-20*x)*(-34*x**2) + (-20*x)*(-9*x**3) - 10*(-20)*x + (34*x)*(-49) - 34*x**2*(-49) + (7*x**2)*(-9*x**3 - 34*x**2 + 34*x - 10) - 9*x**3*(-49) + (14*x**3)*(-9*x**3 - 34*x**2 + 34*x - 10) + 490\nSimplifying the partial expression: (7*x**2)*(-9*x**3 - 34*x**2 + 34*x - 10)\nExpanding the part (-9*x**3 - 34*x**2 + 34*x - 10) using the distributive property, and we got: -70*x**2 + (34*x)*(7*x**2) + (-34*x**2)*(7*x**2) + (7*x**2)*(-9*x**3)\nReplacing (7*x**2)*(-9*x**3 - 34*x**2 + 34*x - 10) with -70*x**2 + (34*x)*(7*x**2) + (-34*x**2)*(7*x**2) + (7*x**2)*(-9*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-20*x)*(34*x) + (-20*x)*(-34*x**2) + (-20*x)*(-9*x**3) - 10*7*x**2 - 10*(-20)*x + (34*x)*(7*x**2) + (34*x)*(-49) + (-34*x**2)*(7*x**2) - 34*x**2*(-49) + (7*x**2)*(-9*x**3) - 9*x**3*(-49) + (14*x**3)*(-9*x**3 - 34*x**2 + 34*x - 10) + 490\nSimplifying the partial expression: (14*x**3)*(-9*x**3 - 34*x**2 + 34*x - 10)\nExpanding the part (-9*x**3 - 34*x**2 + 34*x - 10) using the distributive property, and we got: -140*x**3 + (34*x)*(14*x**3) + (-34*x**2)*(14*x**3) + (-9*x**3)*(14*x**3)\nReplacing (14*x**3)*(-9*x**3 - 34*x**2 + 34*x - 10) with -140*x**3 + (34*x)*(14*x**3) + (-34*x**2)*(14*x**3) + (-9*x**3)*(14*x**3) in the overall expression.\n#Step 6:\nCurrent expression: (-20*x)*(34*x) + (-20*x)*(-34*x**2) + (-20*x)*(-9*x**3) - 10*14*x**3 - 10*7*x**2 - 10*(-20)*x + (34*x)*(7*x**2) + (34*x)*(14*x**3) + (34*x)*(-49) + (-34*x**2)*(7*x**2) + (-34*x**2)*(14*x**3) - 34*x**2*(-49) + (7*x**2)*(-9*x**3) + (-9*x**3)*(14*x**3) - 9*x**3*(-49) + 490\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*x**2)*-49 = 1666*x**2\n (-34*x**2)*(-20*x) = 680*x**3\n (-34*x**2)*(7*x**2) = -238*x**4\n (-34*x**2)*(14*x**3) = -476*x**5\n (-9*x**3)*-49 = 441*x**3\n (-9*x**3)*(-20*x) = 180*x**4\n (-9*x**3)*(7*x**2) = -63*x**5\n (-9*x**3)*(14*x**3) = -126*x**6\n (34*x)*-49 = -1666*x\n (34*x)*(-20*x) = -680*x**2\n (34*x)*(7*x**2) = 238*x**3\n (34*x)*(14*x**3) = 476*x**4\n -10*-20*x = 200*x\n -10*7*x**2 = -70*x**2\n -10*14*x**3 = -140*x**3\nReplacing them in the overall expression.\n#Step 7:\nCurrent expression: -126*x**6 - 476*x**5 - 63*x**5 - 238*x**4 + 180*x**4 + 476*x**4 - 140*x**3 + 238*x**3 + 441*x**3 + 680*x**3 - 680*x**2 - 70*x**2 + 1666*x**2 - 1666*x + 200*x + 490\nCombining like terms, got -126*x**6 - 539*x**5 + 418*x**4 + 1219*x**3 + 916*x**2 - 1466*x + 490\n#Step 8:\nCurrent expression: -126*x**6 - 539*x**5 + 418*x**4 + 1219*x**3 + 916*x**2 - 1466*x + 490\nNo more calculations needed.\n-126*x**6 - 539*x**5 + 418*x**4 + 1219*x**3 + 916*x**2 - 1466*x + 490", "generated_answer": "-126*x**6 - 539*x**5 + 418*x**4 + 1219*x**3 + 916*x**2 - 1466*x + 490", "step_length": 8} {"cot_id": "ab66e355247ac01fd5f2b793adf85e1b1c05dc93550b09371d46f19295b89f24", "datapoint": {"question": "Simplify this expression: 60*y**2*(-29*y**2 - 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1740*y**4 - 360*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 400, "polynomial_expr": "60*y**2*(-29*y**2 - 6)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 60*y**2*(-29*y**2 - 6)\nExpanding the part (-29*y**2 - 6) using the distributive property, and we got: -360*y**2 + (-29*y**2)*(60*y**2)\n#Step 2:\nCurrent expression: -360*y**2 + (-29*y**2)*(60*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -6*(60*y**2) = -360*y**2\n (-29*y**2)*(60*y**2) = -1740*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1740*y**4 - 360*y**2\nNo more calculations needed.\n-1740*y**4 - 360*y**2", "generated_answer": "-1740*y**4 - 360*y**2", "step_length": 3} {"cot_id": "ba0310c48d3e8f287f53f55f2d8e780790222420263883901e501ad4d9b03751", "datapoint": {"question": "Calculate the following: (-49*x**2 - 23*x + 30)*(-32*x**3 + 2*x**2 + 43)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1568*x**5 + 638*x**4 - 1006*x**3 - 2047*x**2 - 989*x + 1290", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 401, "polynomial_expr": "(-49*x**2 - 23*x + 30)*(-32*x**3 + 2*x**2 + 43)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-49*x**2 - 23*x + 30)*(-32*x**3 + 2*x**2 + 43)\nExpanding the part (-49*x**2 - 23*x + 30) using the distributive property, and we got: (-23*x)*(-32*x**3 + 2*x**2 + 43) + (-49*x**2)*(-32*x**3 + 2*x**2 + 43) + 30*(-32*x**3 + 2*x**2 + 43)\n#Step 2:\nCurrent expression: (-23*x)*(-32*x**3 + 2*x**2 + 43) + (-49*x**2)*(-32*x**3 + 2*x**2 + 43) + 30*(-32*x**3 + 2*x**2 + 43)\nSimplifying the partial expression: 30*(-32*x**3 + 2*x**2 + 43)\nExpanding the part (-32*x**3 + 2*x**2 + 43) using the distributive property, and we got: (2*x**2)*30 - 32*x**3*30 + 43*30\nReplacing 30*(-32*x**3 + 2*x**2 + 43) with (2*x**2)*30 - 32*x**3*30 + 43*30 in the overall expression.\n#Step 3:\nCurrent expression: (-23*x)*(-32*x**3 + 2*x**2 + 43) + (-49*x**2)*(-32*x**3 + 2*x**2 + 43) + (2*x**2)*30 - 32*x**3*30 + 1290\nSimplifying the partial expression: (-49*x**2)*(-32*x**3 + 2*x**2 + 43)\nExpanding the part (-32*x**3 + 2*x**2 + 43) using the distributive property, and we got: 43*(-49*x**2) + (-49*x**2)*(2*x**2) + (-49*x**2)*(-32*x**3)\nReplacing (-49*x**2)*(-32*x**3 + 2*x**2 + 43) with 43*(-49*x**2) + (-49*x**2)*(2*x**2) + (-49*x**2)*(-32*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-23*x)*(-32*x**3 + 2*x**2 + 43) + 43*(-49)*x**2 + (-49*x**2)*(2*x**2) + (-49*x**2)*(-32*x**3) + (2*x**2)*30 - 32*x**3*30 + 1290\nSimplifying the partial expression: (-23*x)*(-32*x**3 + 2*x**2 + 43)\nExpanding the part (-32*x**3 + 2*x**2 + 43) using the distributive property, and we got: (-23*x)*(2*x**2) + (-23*x)*(-32*x**3) + 43*(-23*x)\nReplacing (-23*x)*(-32*x**3 + 2*x**2 + 43) with (-23*x)*(2*x**2) + (-23*x)*(-32*x**3) + 43*(-23*x) in the overall expression.\n#Step 5:\nCurrent expression: (-23*x)*(2*x**2) + (-23*x)*(-32*x**3) + 43*(-49)*x**2 + 43*(-23)*x + (-49*x**2)*(2*x**2) + (-49*x**2)*(-32*x**3) + (2*x**2)*30 - 32*x**3*30 + 1290\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*x**3)*30 = -960*x**3\n (-32*x**3)*(-49*x**2) = 1568*x**5\n (-32*x**3)*(-23*x) = 736*x**4\n (2*x**2)*30 = 60*x**2\n (2*x**2)*(-49*x**2) = -98*x**4\n (2*x**2)*(-23*x) = -46*x**3\n 43*-49*x**2 = -2107*x**2\n 43*-23*x = -989*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1568*x**5 - 98*x**4 + 736*x**4 - 960*x**3 - 46*x**3 - 2107*x**2 + 60*x**2 - 989*x + 1290\nCombining like terms, got 1568*x**5 + 638*x**4 - 1006*x**3 - 2047*x**2 - 989*x + 1290\n#Step 7:\nCurrent expression: 1568*x**5 + 638*x**4 - 1006*x**3 - 2047*x**2 - 989*x + 1290\nNo more calculations needed.\n1568*x**5 + 638*x**4 - 1006*x**3 - 2047*x**2 - 989*x + 1290", "generated_answer": "1568*x**5 + 638*x**4 - 1006*x**3 - 2047*x**2 - 989*x + 1290", "step_length": 7} {"cot_id": "cf3c508f5b1609ba03734a269a682dfdc1f841902bac23105f03d841988683ae", "datapoint": {"question": "Simplify this expression: 0\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "0", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 402, "polynomial_expr": "0", "variables": [], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 0\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 0\nNo more calculations needed.\n0", "generated_answer": "0", "step_length": 2} {"cot_id": "5c40f5f3fda839007b1c5d4f9606ea6184ed681236decded3933041b2452e96a", "datapoint": {"question": "Simplify this expression: 23*z**2*(-39*z**2 - 28*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-897*z**4 - 644*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 403, "polynomial_expr": "23*z**2*(-39*z**2 - 28*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 23*z**2*(-39*z**2 - 28*z)\nExpanding the part (-39*z**2 - 28*z) using the distributive property, and we got: (-28*z)*(23*z**2) + (-39*z**2)*(23*z**2)\n#Step 2:\nCurrent expression: (-28*z)*(23*z**2) + (-39*z**2)*(23*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*z**2)*(23*z**2) = -897*z**4\n (-28*z)*(23*z**2) = -644*z**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -897*z**4 - 644*z**3\nNo more calculations needed.\n-897*z**4 - 644*z**3", "generated_answer": "-897*z**4 - 644*z**3", "step_length": 3} {"cot_id": "b31f8b53af4d7ccc2aaf70e09534d9940197e3a94ff08cd1bf07bfbe4cfcdf43", "datapoint": {"question": "Calculate the following: (7 - 9*y**3)*(25*y**3 + 9*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-225*y**6 - 81*y**5 + 175*y**3 + 63*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 404, "polynomial_expr": "(7 - 9*y**3)*(25*y**3 + 9*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7 - 9*y**3)*(25*y**3 + 9*y**2)\nExpanding the part (7 - 9*y**3) using the distributive property, and we got: (-9*y**3)*(25*y**3 + 9*y**2) + 7*(25*y**3 + 9*y**2)\n#Step 2:\nCurrent expression: (-9*y**3)*(25*y**3 + 9*y**2) + 7*(25*y**3 + 9*y**2)\nSimplifying the partial expression: 7*(25*y**3 + 9*y**2)\nExpanding the part (25*y**3 + 9*y**2) using the distributive property, and we got: (9*y**2)*7 + (25*y**3)*7\nReplacing 7*(25*y**3 + 9*y**2) with (9*y**2)*7 + (25*y**3)*7 in the overall expression.\n#Step 3:\nCurrent expression: (9*y**2)*7 + (-9*y**3)*(25*y**3 + 9*y**2) + (25*y**3)*7\nSimplifying the partial expression: (-9*y**3)*(25*y**3 + 9*y**2)\nExpanding the part (25*y**3 + 9*y**2) using the distributive property, and we got: (9*y**2)*(-9*y**3) + (-9*y**3)*(25*y**3)\nReplacing (-9*y**3)*(25*y**3 + 9*y**2) with (9*y**2)*(-9*y**3) + (-9*y**3)*(25*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (9*y**2)*(-9*y**3) + (9*y**2)*7 + (-9*y**3)*(25*y**3) + (25*y**3)*7\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (9*y**2)*7 = 63*y**2\n (9*y**2)*(-9*y**3) = -81*y**5\n (25*y**3)*7 = 175*y**3\n (25*y**3)*(-9*y**3) = -225*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -225*y**6 - 81*y**5 + 175*y**3 + 63*y**2\nNo more calculations needed.\n-225*y**6 - 81*y**5 + 175*y**3 + 63*y**2", "generated_answer": "-225*y**6 - 81*y**5 + 175*y**3 + 63*y**2", "step_length": 5} {"cot_id": "0126ae4e7fbc427e54212d3411fafb68ff95dc7654a1208307ff759a2f718c9b", "datapoint": {"question": "Calculate the following: 550*y**3 + 748*y**2 - 1100*y\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "550*y**3 + 748*y**2 - 1100*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 405, "polynomial_expr": "550*y**3 + 748*y**2 - 1100*y", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 550*y**3 + 748*y**2 - 1100*y\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 550*y**3 + 748*y**2 - 1100*y\nNo more calculations needed.\n550*y**3 + 748*y**2 - 1100*y", "generated_answer": "550*y**3 + 748*y**2 - 1100*y", "step_length": 2} {"cot_id": "eb5e824a48b4e3ff3bcf4d29fca08c1799cb7a3e49db8ad31393f0cb3a3071cc", "datapoint": {"question": "Simplify this expression: (-38*y - 19)*(21*y + 8)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-798*y**2 - 703*y - 152", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 406, "polynomial_expr": "(-38*y - 19)*(21*y + 8)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-38*y - 19)*(21*y + 8)\nExpanding the part (-38*y - 19) using the distributive property, and we got: (-38*y)*(21*y + 8) - 19*(21*y + 8)\n#Step 2:\nCurrent expression: (-38*y)*(21*y + 8) - 19*(21*y + 8)\nSimplifying the partial expression: -19*(21*y + 8)\nExpanding the part (21*y + 8) using the distributive property, and we got: (21*y)*(-19) + 8*(-19)\nReplacing -19*(21*y + 8) with (21*y)*(-19) + 8*(-19) in the overall expression.\n#Step 3:\nCurrent expression: (-38*y)*(21*y + 8) + (21*y)*(-19) - 152\nSimplifying the partial expression: (-38*y)*(21*y + 8)\nExpanding the part (21*y + 8) using the distributive property, and we got: (-38*y)*(21*y) + 8*(-38*y)\nReplacing (-38*y)*(21*y + 8) with (-38*y)*(21*y) + 8*(-38*y) in the overall expression.\n#Step 4:\nCurrent expression: (-38*y)*(21*y) + 8*(-38)*y + (21*y)*(-19) - 152\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (21*y)*-19 = -399*y\n (21*y)*(-38*y) = -798*y**2\n 8*-38*y = -304*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -798*y**2 - 399*y - 304*y - 152\nCombining like terms, got -798*y**2 - 703*y - 152\n#Step 6:\nCurrent expression: -798*y**2 - 703*y - 152\nNo more calculations needed.\n-798*y**2 - 703*y - 152", "generated_answer": "-798*y**2 - 703*y - 152", "step_length": 6} {"cot_id": "b0b668f5f729bd14df9ef7397b19e3888d2f16df4caaac084d647ac4ef3b8d83", "datapoint": {"question": "Calculate the following: (-46*x**3 - 39)*(-x**3 + 6*x**2 - 35*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "46*x**6 - 276*x**5 + 1610*x**4 + 39*x**3 - 234*x**2 + 1365*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 407, "polynomial_expr": "(-46*x**3 - 39)*(-x**3 + 6*x**2 - 35*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-46*x**3 - 39)*(-x**3 + 6*x**2 - 35*x)\nExpanding the part (-46*x**3 - 39) using the distributive property, and we got: (-46*x**3)*(-x**3 + 6*x**2 - 35*x) - 39*(-x**3 + 6*x**2 - 35*x)\n#Step 2:\nCurrent expression: (-46*x**3)*(-x**3 + 6*x**2 - 35*x) - 39*(-x**3 + 6*x**2 - 35*x)\nSimplifying the partial expression: -39*(-x**3 + 6*x**2 - 35*x)\nExpanding the part (-x**3 + 6*x**2 - 35*x) using the distributive property, and we got: -35*x*(-39) + (6*x**2)*(-39) - x**3*(-39)\nReplacing -39*(-x**3 + 6*x**2 - 35*x) with -35*x*(-39) + (6*x**2)*(-39) - x**3*(-39) in the overall expression.\n#Step 3:\nCurrent expression: -35*x*(-39) + (6*x**2)*(-39) + (-46*x**3)*(-x**3 + 6*x**2 - 35*x) - x**3*(-39)\nSimplifying the partial expression: (-46*x**3)*(-x**3 + 6*x**2 - 35*x)\nExpanding the part (-x**3 + 6*x**2 - 35*x) using the distributive property, and we got: (-35*x)*(-46*x**3) + (6*x**2)*(-46*x**3) + (-46*x**3)*(-x**3)\nReplacing (-46*x**3)*(-x**3 + 6*x**2 - 35*x) with (-35*x)*(-46*x**3) + (6*x**2)*(-46*x**3) + (-46*x**3)*(-x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-35*x)*(-46*x**3) - 35*x*(-39) + (6*x**2)*(-46*x**3) + (6*x**2)*(-39) + (-46*x**3)*(-x**3) - x**3*(-39)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-x**3)*-39 = 39*x**3\n (-x**3)*(-46*x**3) = 46*x**6\n (-35*x)*-39 = 1365*x\n (-35*x)*(-46*x**3) = 1610*x**4\n (6*x**2)*-39 = -234*x**2\n (6*x**2)*(-46*x**3) = -276*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 46*x**6 - 276*x**5 + 1610*x**4 + 39*x**3 - 234*x**2 + 1365*x\nNo more calculations needed.\n46*x**6 - 276*x**5 + 1610*x**4 + 39*x**3 - 234*x**2 + 1365*x", "generated_answer": "46*x**6 - 276*x**5 + 1610*x**4 + 39*x**3 - 234*x**2 + 1365*x", "step_length": 5} {"cot_id": "ef4eac972ebd332b4e36bd9bb883e4c945bc3c9c76480bbdfb89934474a063b3", "datapoint": {"question": "Calculate the following: (8 - 10*x**2)*(18*x**3 - 92*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-180*x**5 + 1064*x**3 - 736*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 408, "polynomial_expr": "(8 - 10*x**2)*(18*x**3 - 92*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (8 - 10*x**2)*(18*x**3 - 92*x)\nExpanding the part (8 - 10*x**2) using the distributive property, and we got: (-10*x**2)*(18*x**3 - 92*x) + 8*(18*x**3 - 92*x)\n#Step 2:\nCurrent expression: (-10*x**2)*(18*x**3 - 92*x) + 8*(18*x**3 - 92*x)\nSimplifying the partial expression: 8*(18*x**3 - 92*x)\nExpanding the part (18*x**3 - 92*x) using the distributive property, and we got: -92*x*8 + (18*x**3)*8\nReplacing 8*(18*x**3 - 92*x) with -92*x*8 + (18*x**3)*8 in the overall expression.\n#Step 3:\nCurrent expression: -92*x*8 + (-10*x**2)*(18*x**3 - 92*x) + (18*x**3)*8\nSimplifying the partial expression: (-10*x**2)*(18*x**3 - 92*x)\nExpanding the part (18*x**3 - 92*x) using the distributive property, and we got: (-92*x)*(-10*x**2) + (-10*x**2)*(18*x**3)\nReplacing (-10*x**2)*(18*x**3 - 92*x) with (-92*x)*(-10*x**2) + (-10*x**2)*(18*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-92*x)*(-10*x**2) - 92*x*8 + (-10*x**2)*(18*x**3) + (18*x**3)*8\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-92*x)*8 = -736*x\n (-92*x)*(-10*x**2) = 920*x**3\n (18*x**3)*8 = 144*x**3\n (18*x**3)*(-10*x**2) = -180*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -180*x**5 + 144*x**3 + 920*x**3 - 736*x\nCombining like terms, got -180*x**5 + 1064*x**3 - 736*x\n#Step 6:\nCurrent expression: -180*x**5 + 1064*x**3 - 736*x\nNo more calculations needed.\n-180*x**5 + 1064*x**3 - 736*x", "generated_answer": "-180*x**5 + 1064*x**3 - 736*x", "step_length": 6} {"cot_id": "e40f240550a7b1217f89c2ff03dcd37e8e4e5d9cb1b58369b401dd6863caf435", "datapoint": {"question": "Calculate the following: (21*x**3 - 15)*(-48*x**2 + 7*x - 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1008*x**5 + 147*x**4 - 420*x**3 + 720*x**2 - 105*x + 300", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 409, "polynomial_expr": "(21*x**3 - 15)*(-48*x**2 + 7*x - 20)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21*x**3 - 15)*(-48*x**2 + 7*x - 20)\nExpanding the part (21*x**3 - 15) using the distributive property, and we got: (21*x**3)*(-48*x**2 + 7*x - 20) - 15*(-48*x**2 + 7*x - 20)\n#Step 2:\nCurrent expression: (21*x**3)*(-48*x**2 + 7*x - 20) - 15*(-48*x**2 + 7*x - 20)\nSimplifying the partial expression: -15*(-48*x**2 + 7*x - 20)\nExpanding the part (-48*x**2 + 7*x - 20) using the distributive property, and we got: (7*x)*(-15) - 48*x**2*(-15) - 20*(-15)\nReplacing -15*(-48*x**2 + 7*x - 20) with (7*x)*(-15) - 48*x**2*(-15) - 20*(-15) in the overall expression.\n#Step 3:\nCurrent expression: (7*x)*(-15) - 48*x**2*(-15) + (21*x**3)*(-48*x**2 + 7*x - 20) + 300\nSimplifying the partial expression: (21*x**3)*(-48*x**2 + 7*x - 20)\nExpanding the part (-48*x**2 + 7*x - 20) using the distributive property, and we got: -420*x**3 + (7*x)*(21*x**3) + (-48*x**2)*(21*x**3)\nReplacing (21*x**3)*(-48*x**2 + 7*x - 20) with -420*x**3 + (7*x)*(21*x**3) + (-48*x**2)*(21*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -20*21*x**3 + (7*x)*(21*x**3) + (7*x)*(-15) + (-48*x**2)*(21*x**3) - 48*x**2*(-15) + 300\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*x**2)*-15 = 720*x**2\n (-48*x**2)*(21*x**3) = -1008*x**5\n (7*x)*-15 = -105*x\n (7*x)*(21*x**3) = 147*x**4\n -20*21*x**3 = -420*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1008*x**5 + 147*x**4 - 420*x**3 + 720*x**2 - 105*x + 300\nNo more calculations needed.\n-1008*x**5 + 147*x**4 - 420*x**3 + 720*x**2 - 105*x + 300", "generated_answer": "-1008*x**5 + 147*x**4 - 420*x**3 + 720*x**2 - 105*x + 300", "step_length": 5} {"cot_id": "bc4d9a2f03dd054f3fb094c8676babc0956a5241eedb593766f4e15f763f6345", "datapoint": {"question": "Calculate the following: (-8*y**2 - 10*y + 49)*(20*y**3 - 51*y**2 - 43*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-160*y**5 + 208*y**4 + 1834*y**3 - 2069*y**2 - 2107*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 410, "polynomial_expr": "(-8*y**2 - 10*y + 49)*(20*y**3 - 51*y**2 - 43*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-8*y**2 - 10*y + 49)*(20*y**3 - 51*y**2 - 43*y)\nExpanding the part (-8*y**2 - 10*y + 49) using the distributive property, and we got: (-10*y)*(20*y**3 - 51*y**2 - 43*y) + (-8*y**2)*(20*y**3 - 51*y**2 - 43*y) + 49*(20*y**3 - 51*y**2 - 43*y)\n#Step 2:\nCurrent expression: (-10*y)*(20*y**3 - 51*y**2 - 43*y) + (-8*y**2)*(20*y**3 - 51*y**2 - 43*y) + 49*(20*y**3 - 51*y**2 - 43*y)\nSimplifying the partial expression: 49*(20*y**3 - 51*y**2 - 43*y)\nExpanding the part (20*y**3 - 51*y**2 - 43*y) using the distributive property, and we got: -43*y*49 - 51*y**2*49 + (20*y**3)*49\nReplacing 49*(20*y**3 - 51*y**2 - 43*y) with -43*y*49 - 51*y**2*49 + (20*y**3)*49 in the overall expression.\n#Step 3:\nCurrent expression: -43*y*49 + (-10*y)*(20*y**3 - 51*y**2 - 43*y) - 51*y**2*49 + (-8*y**2)*(20*y**3 - 51*y**2 - 43*y) + (20*y**3)*49\nSimplifying the partial expression: (-10*y)*(20*y**3 - 51*y**2 - 43*y)\nExpanding the part (20*y**3 - 51*y**2 - 43*y) using the distributive property, and we got: (-43*y)*(-10*y) + (-10*y)*(-51*y**2) + (-10*y)*(20*y**3)\nReplacing (-10*y)*(20*y**3 - 51*y**2 - 43*y) with (-43*y)*(-10*y) + (-10*y)*(-51*y**2) + (-10*y)*(20*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-43*y)*(-10*y) - 43*y*49 + (-10*y)*(-51*y**2) + (-10*y)*(20*y**3) - 51*y**2*49 + (-8*y**2)*(20*y**3 - 51*y**2 - 43*y) + (20*y**3)*49\nSimplifying the partial expression: (-8*y**2)*(20*y**3 - 51*y**2 - 43*y)\nExpanding the part (20*y**3 - 51*y**2 - 43*y) using the distributive property, and we got: (-43*y)*(-8*y**2) + (-51*y**2)*(-8*y**2) + (-8*y**2)*(20*y**3)\nReplacing (-8*y**2)*(20*y**3 - 51*y**2 - 43*y) with (-43*y)*(-8*y**2) + (-51*y**2)*(-8*y**2) + (-8*y**2)*(20*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-43*y)*(-10*y) + (-43*y)*(-8*y**2) - 43*y*49 + (-10*y)*(-51*y**2) + (-10*y)*(20*y**3) + (-51*y**2)*(-8*y**2) - 51*y**2*49 + (-8*y**2)*(20*y**3) + (20*y**3)*49\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-51*y**2)*49 = -2499*y**2\n (-51*y**2)*(-10*y) = 510*y**3\n (-51*y**2)*(-8*y**2) = 408*y**4\n (-43*y)*49 = -2107*y\n (-43*y)*(-10*y) = 430*y**2\n (-43*y)*(-8*y**2) = 344*y**3\n (20*y**3)*49 = 980*y**3\n (20*y**3)*(-10*y) = -200*y**4\n (20*y**3)*(-8*y**2) = -160*y**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -160*y**5 - 200*y**4 + 408*y**4 + 344*y**3 + 510*y**3 + 980*y**3 - 2499*y**2 + 430*y**2 - 2107*y\nCombining like terms, got -160*y**5 + 208*y**4 + 1834*y**3 - 2069*y**2 - 2107*y\n#Step 7:\nCurrent expression: -160*y**5 + 208*y**4 + 1834*y**3 - 2069*y**2 - 2107*y\nNo more calculations needed.\n-160*y**5 + 208*y**4 + 1834*y**3 - 2069*y**2 - 2107*y", "generated_answer": "-160*y**5 + 208*y**4 + 1834*y**3 - 2069*y**2 - 2107*y", "step_length": 7} {"cot_id": "7c2f1cac2765def49720ad607f0c8049ae108cfa8931f5270213b31037e9da4d", "datapoint": {"question": "Calculate the following: 57*x**3*(4*x**3 + 6*x - 11)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "228*x**6 + 342*x**4 - 627*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 411, "polynomial_expr": "57*x**3*(4*x**3 + 6*x - 11)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 57*x**3*(4*x**3 + 6*x - 11)\nExpanding the part (4*x**3 + 6*x - 11) using the distributive property, and we got: -627*x**3 + (6*x)*(57*x**3) + (4*x**3)*(57*x**3)\n#Step 2:\nCurrent expression: -627*x**3 + (6*x)*(57*x**3) + (4*x**3)*(57*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -11*(57*x**3) = -627*x**3\n (4*x**3)*(57*x**3) = 228*x**6\n (6*x)*(57*x**3) = 342*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 228*x**6 + 342*x**4 - 627*x**3\nNo more calculations needed.\n228*x**6 + 342*x**4 - 627*x**3", "generated_answer": "228*x**6 + 342*x**4 - 627*x**3", "step_length": 3} {"cot_id": "06814754a37d08ff282061b178dd49c7c85a54335da6133812f3a180e955ff25", "datapoint": {"question": "Simplify this expression: (17*y**2 + 11*y)*(41*y**3 + 14*y**2 + 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "697*y**5 + 689*y**4 + 154*y**3 + 238*y**2 + 154*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 412, "polynomial_expr": "(17*y**2 + 11*y)*(41*y**3 + 14*y**2 + 14)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (17*y**2 + 11*y)*(41*y**3 + 14*y**2 + 14)\nExpanding the part (17*y**2 + 11*y) using the distributive property, and we got: (11*y)*(41*y**3 + 14*y**2 + 14) + (17*y**2)*(41*y**3 + 14*y**2 + 14)\n#Step 2:\nCurrent expression: (11*y)*(41*y**3 + 14*y**2 + 14) + (17*y**2)*(41*y**3 + 14*y**2 + 14)\nSimplifying the partial expression: (11*y)*(41*y**3 + 14*y**2 + 14)\nExpanding the part (41*y**3 + 14*y**2 + 14) using the distributive property, and we got: 14*(11*y) + (11*y)*(14*y**2) + (11*y)*(41*y**3)\nReplacing (11*y)*(41*y**3 + 14*y**2 + 14) with 14*(11*y) + (11*y)*(14*y**2) + (11*y)*(41*y**3) in the overall expression.\n#Step 3:\nCurrent expression: 14*11*y + (11*y)*(14*y**2) + (11*y)*(41*y**3) + (17*y**2)*(41*y**3 + 14*y**2 + 14)\nSimplifying the partial expression: (17*y**2)*(41*y**3 + 14*y**2 + 14)\nExpanding the part (41*y**3 + 14*y**2 + 14) using the distributive property, and we got: 14*(17*y**2) + (14*y**2)*(17*y**2) + (17*y**2)*(41*y**3)\nReplacing (17*y**2)*(41*y**3 + 14*y**2 + 14) with 14*(17*y**2) + (14*y**2)*(17*y**2) + (17*y**2)*(41*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 14*17*y**2 + 14*11*y + (11*y)*(14*y**2) + (11*y)*(41*y**3) + (14*y**2)*(17*y**2) + (17*y**2)*(41*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (14*y**2)*(11*y) = 154*y**3\n (14*y**2)*(17*y**2) = 238*y**4\n (41*y**3)*(11*y) = 451*y**4\n (41*y**3)*(17*y**2) = 697*y**5\n 14*11*y = 154*y\n 14*17*y**2 = 238*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 697*y**5 + 238*y**4 + 451*y**4 + 154*y**3 + 238*y**2 + 154*y\nCombining like terms, got 697*y**5 + 689*y**4 + 154*y**3 + 238*y**2 + 154*y\n#Step 6:\nCurrent expression: 697*y**5 + 689*y**4 + 154*y**3 + 238*y**2 + 154*y\nNo more calculations needed.\n697*y**5 + 689*y**4 + 154*y**3 + 238*y**2 + 154*y", "generated_answer": "697*y**5 + 689*y**4 + 154*y**3 + 238*y**2 + 154*y", "step_length": 6} {"cot_id": "644b08dd809423778957ed3d2c681fad08d2ffec5de8ad327e9ea9da0d55b22b", "datapoint": {"question": "Simplify this expression: (-34*z**2 - 5*z)*(9*z**3 + 25)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-306*z**5 - 45*z**4 - 850*z**2 - 125*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 413, "polynomial_expr": "(-34*z**2 - 5*z)*(9*z**3 + 25)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-34*z**2 - 5*z)*(9*z**3 + 25)\nExpanding the part (9*z**3 + 25) using the distributive property, and we got: (9*z**3)*(-34*z**2 - 5*z) + 25*(-34*z**2 - 5*z)\n#Step 2:\nCurrent expression: (9*z**3)*(-34*z**2 - 5*z) + 25*(-34*z**2 - 5*z)\nSimplifying the partial expression: 25*(-34*z**2 - 5*z)\nExpanding the part (-34*z**2 - 5*z) using the distributive property, and we got: -5*z*25 - 34*z**2*25\nReplacing 25*(-34*z**2 - 5*z) with -5*z*25 - 34*z**2*25 in the overall expression.\n#Step 3:\nCurrent expression: -5*z*25 - 34*z**2*25 + (9*z**3)*(-34*z**2 - 5*z)\nSimplifying the partial expression: (9*z**3)*(-34*z**2 - 5*z)\nExpanding the part (-34*z**2 - 5*z) using the distributive property, and we got: (-5*z)*(9*z**3) + (-34*z**2)*(9*z**3)\nReplacing (9*z**3)*(-34*z**2 - 5*z) with (-5*z)*(9*z**3) + (-34*z**2)*(9*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-5*z)*(9*z**3) - 5*z*25 + (-34*z**2)*(9*z**3) - 34*z**2*25\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*z**2)*25 = -850*z**2\n (-34*z**2)*(9*z**3) = -306*z**5\n (-5*z)*25 = -125*z\n (-5*z)*(9*z**3) = -45*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -306*z**5 - 45*z**4 - 850*z**2 - 125*z\nNo more calculations needed.\n-306*z**5 - 45*z**4 - 850*z**2 - 125*z", "generated_answer": "-306*z**5 - 45*z**4 - 850*z**2 - 125*z", "step_length": 5} {"cot_id": "ec6f0a58c1ba7d63bb56e486aa6aca7f78796ec16006538223f6f24894be3369", "datapoint": {"question": "Simplify this expression: (6*z**2 - 3*z)*(8*z**3 + 28*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "48*z**5 + 144*z**4 - 84*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 414, "polynomial_expr": "(6*z**2 - 3*z)*(8*z**3 + 28*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6*z**2 - 3*z)*(8*z**3 + 28*z**2)\nExpanding the part (6*z**2 - 3*z) using the distributive property, and we got: (-3*z)*(8*z**3 + 28*z**2) + (6*z**2)*(8*z**3 + 28*z**2)\n#Step 2:\nCurrent expression: (-3*z)*(8*z**3 + 28*z**2) + (6*z**2)*(8*z**3 + 28*z**2)\nSimplifying the partial expression: (-3*z)*(8*z**3 + 28*z**2)\nExpanding the part (8*z**3 + 28*z**2) using the distributive property, and we got: (-3*z)*(28*z**2) + (-3*z)*(8*z**3)\nReplacing (-3*z)*(8*z**3 + 28*z**2) with (-3*z)*(28*z**2) + (-3*z)*(8*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-3*z)*(28*z**2) + (-3*z)*(8*z**3) + (6*z**2)*(8*z**3 + 28*z**2)\nSimplifying the partial expression: (6*z**2)*(8*z**3 + 28*z**2)\nExpanding the part (8*z**3 + 28*z**2) using the distributive property, and we got: (6*z**2)*(28*z**2) + (6*z**2)*(8*z**3)\nReplacing (6*z**2)*(8*z**3 + 28*z**2) with (6*z**2)*(28*z**2) + (6*z**2)*(8*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-3*z)*(28*z**2) + (-3*z)*(8*z**3) + (6*z**2)*(28*z**2) + (6*z**2)*(8*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (8*z**3)*(-3*z) = -24*z**4\n (8*z**3)*(6*z**2) = 48*z**5\n (28*z**2)*(-3*z) = -84*z**3\n (28*z**2)*(6*z**2) = 168*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 48*z**5 - 24*z**4 + 168*z**4 - 84*z**3\nCombining like terms, got 48*z**5 + 144*z**4 - 84*z**3\n#Step 6:\nCurrent expression: 48*z**5 + 144*z**4 - 84*z**3\nNo more calculations needed.\n48*z**5 + 144*z**4 - 84*z**3", "generated_answer": "48*z**5 + 144*z**4 - 84*z**3", "step_length": 6} {"cot_id": "780a3f5edca52893fd549246c69d52a334eaef36471a4ed38802ae3f6fde6e9b", "datapoint": {"question": "Calculate the following: (-5*x**3 - 45*x)*(18*x**3 - 22*x + 56)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-90*x**6 - 700*x**4 - 280*x**3 + 990*x**2 - 2520*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 415, "polynomial_expr": "(-5*x**3 - 45*x)*(18*x**3 - 22*x + 56)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-5*x**3 - 45*x)*(18*x**3 - 22*x + 56)\nExpanding the part (-5*x**3 - 45*x) using the distributive property, and we got: (-45*x)*(18*x**3 - 22*x + 56) + (-5*x**3)*(18*x**3 - 22*x + 56)\n#Step 2:\nCurrent expression: (-45*x)*(18*x**3 - 22*x + 56) + (-5*x**3)*(18*x**3 - 22*x + 56)\nSimplifying the partial expression: (-45*x)*(18*x**3 - 22*x + 56)\nExpanding the part (18*x**3 - 22*x + 56) using the distributive property, and we got: (-45*x)*(-22*x) + (-45*x)*(18*x**3) + 56*(-45*x)\nReplacing (-45*x)*(18*x**3 - 22*x + 56) with (-45*x)*(-22*x) + (-45*x)*(18*x**3) + 56*(-45*x) in the overall expression.\n#Step 3:\nCurrent expression: (-45*x)*(-22*x) + (-45*x)*(18*x**3) + 56*(-45)*x + (-5*x**3)*(18*x**3 - 22*x + 56)\nSimplifying the partial expression: (-5*x**3)*(18*x**3 - 22*x + 56)\nExpanding the part (18*x**3 - 22*x + 56) using the distributive property, and we got: (-22*x)*(-5*x**3) + 56*(-5*x**3) + (-5*x**3)*(18*x**3)\nReplacing (-5*x**3)*(18*x**3 - 22*x + 56) with (-22*x)*(-5*x**3) + 56*(-5*x**3) + (-5*x**3)*(18*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-45*x)*(-22*x) + (-45*x)*(18*x**3) + (-22*x)*(-5*x**3) + 56*(-5)*x**3 + 56*(-45)*x + (-5*x**3)*(18*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*x)*(-45*x) = 990*x**2\n (-22*x)*(-5*x**3) = 110*x**4\n (18*x**3)*(-45*x) = -810*x**4\n (18*x**3)*(-5*x**3) = -90*x**6\n 56*-45*x = -2520*x\n 56*-5*x**3 = -280*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -90*x**6 - 810*x**4 + 110*x**4 - 280*x**3 + 990*x**2 - 2520*x\nCombining like terms, got -90*x**6 - 700*x**4 - 280*x**3 + 990*x**2 - 2520*x\n#Step 6:\nCurrent expression: -90*x**6 - 700*x**4 - 280*x**3 + 990*x**2 - 2520*x\nNo more calculations needed.\n-90*x**6 - 700*x**4 - 280*x**3 + 990*x**2 - 2520*x", "generated_answer": "-90*x**6 - 700*x**4 - 280*x**3 + 990*x**2 - 2520*x", "step_length": 6} {"cot_id": "37aabd952e8ddae410480ac916979c684c7434e9f0cb4e8082d237f415e5192c", "datapoint": {"question": "Calculate the following: (-33*x**2 + 37*x)*(-43*x**3 + 6*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1419*x**5 - 1789*x**4 + 222*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 416, "polynomial_expr": "(-33*x**2 + 37*x)*(-43*x**3 + 6*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-33*x**2 + 37*x)*(-43*x**3 + 6*x**2)\nExpanding the part (-43*x**3 + 6*x**2) using the distributive property, and we got: (6*x**2)*(-33*x**2 + 37*x) + (-43*x**3)*(-33*x**2 + 37*x)\n#Step 2:\nCurrent expression: (6*x**2)*(-33*x**2 + 37*x) + (-43*x**3)*(-33*x**2 + 37*x)\nSimplifying the partial expression: (-43*x**3)*(-33*x**2 + 37*x)\nExpanding the part (-33*x**2 + 37*x) using the distributive property, and we got: (37*x)*(-43*x**3) + (-33*x**2)*(-43*x**3)\nReplacing (-43*x**3)*(-33*x**2 + 37*x) with (37*x)*(-43*x**3) + (-33*x**2)*(-43*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (37*x)*(-43*x**3) + (-33*x**2)*(-43*x**3) + (6*x**2)*(-33*x**2 + 37*x)\nSimplifying the partial expression: (6*x**2)*(-33*x**2 + 37*x)\nExpanding the part (-33*x**2 + 37*x) using the distributive property, and we got: (37*x)*(6*x**2) + (-33*x**2)*(6*x**2)\nReplacing (6*x**2)*(-33*x**2 + 37*x) with (37*x)*(6*x**2) + (-33*x**2)*(6*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (37*x)*(6*x**2) + (37*x)*(-43*x**3) + (-33*x**2)*(6*x**2) + (-33*x**2)*(-43*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*x**2)*(-43*x**3) = 1419*x**5\n (-33*x**2)*(6*x**2) = -198*x**4\n (37*x)*(-43*x**3) = -1591*x**4\n (37*x)*(6*x**2) = 222*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1419*x**5 - 1591*x**4 - 198*x**4 + 222*x**3\nCombining like terms, got 1419*x**5 - 1789*x**4 + 222*x**3\n#Step 6:\nCurrent expression: 1419*x**5 - 1789*x**4 + 222*x**3\nNo more calculations needed.\n1419*x**5 - 1789*x**4 + 222*x**3", "generated_answer": "1419*x**5 - 1789*x**4 + 222*x**3", "step_length": 6} {"cot_id": "326cdefda085dbead9c6e88db15d3272f4962870f638e753b95fcead793c7d0b", "datapoint": {"question": "Simplify this expression: (-28*z**3 + 29*z**2)*(16*z**3 - 35*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-448*z**6 + 1444*z**5 - 1015*z**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 417, "polynomial_expr": "(-28*z**3 + 29*z**2)*(16*z**3 - 35*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-28*z**3 + 29*z**2)*(16*z**3 - 35*z**2)\nExpanding the part (16*z**3 - 35*z**2) using the distributive property, and we got: (-35*z**2)*(-28*z**3 + 29*z**2) + (16*z**3)*(-28*z**3 + 29*z**2)\n#Step 2:\nCurrent expression: (-35*z**2)*(-28*z**3 + 29*z**2) + (16*z**3)*(-28*z**3 + 29*z**2)\nSimplifying the partial expression: (-35*z**2)*(-28*z**3 + 29*z**2)\nExpanding the part (-28*z**3 + 29*z**2) using the distributive property, and we got: (-35*z**2)*(29*z**2) + (-35*z**2)*(-28*z**3)\nReplacing (-35*z**2)*(-28*z**3 + 29*z**2) with (-35*z**2)*(29*z**2) + (-35*z**2)*(-28*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-35*z**2)*(29*z**2) + (-35*z**2)*(-28*z**3) + (16*z**3)*(-28*z**3 + 29*z**2)\nSimplifying the partial expression: (16*z**3)*(-28*z**3 + 29*z**2)\nExpanding the part (-28*z**3 + 29*z**2) using the distributive property, and we got: (29*z**2)*(16*z**3) + (-28*z**3)*(16*z**3)\nReplacing (16*z**3)*(-28*z**3 + 29*z**2) with (29*z**2)*(16*z**3) + (-28*z**3)*(16*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-35*z**2)*(29*z**2) + (-35*z**2)*(-28*z**3) + (29*z**2)*(16*z**3) + (-28*z**3)*(16*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*z**3)*(-35*z**2) = 980*z**5\n (-28*z**3)*(16*z**3) = -448*z**6\n (29*z**2)*(-35*z**2) = -1015*z**4\n (29*z**2)*(16*z**3) = 464*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -448*z**6 + 464*z**5 + 980*z**5 - 1015*z**4\nCombining like terms, got -448*z**6 + 1444*z**5 - 1015*z**4\n#Step 6:\nCurrent expression: -448*z**6 + 1444*z**5 - 1015*z**4\nNo more calculations needed.\n-448*z**6 + 1444*z**5 - 1015*z**4", "generated_answer": "-448*z**6 + 1444*z**5 - 1015*z**4", "step_length": 6} {"cot_id": "f37b55a65a5358847abff3b4fa9249ef1f23973967857b48e785af3f59dbfc55", "datapoint": {"question": "Calculate the following: 2226*y**3 + 1537*y**2\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2226*y**3 + 1537*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 418, "polynomial_expr": "2226*y**3 + 1537*y**2", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 2226*y**3 + 1537*y**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 2226*y**3 + 1537*y**2\nNo more calculations needed.\n2226*y**3 + 1537*y**2", "generated_answer": "2226*y**3 + 1537*y**2", "step_length": 2} {"cot_id": "50d4a1f810058d14c9a5c3196509207041552a062eecadeafcb004d8a2f39197", "datapoint": {"question": "Simplify this expression: (37*z**2 - 40)*(-10*z**3 - 38*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-370*z**5 - 1406*z**4 + 400*z**3 + 1520*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 419, "polynomial_expr": "(37*z**2 - 40)*(-10*z**3 - 38*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (37*z**2 - 40)*(-10*z**3 - 38*z**2)\nExpanding the part (37*z**2 - 40) using the distributive property, and we got: (37*z**2)*(-10*z**3 - 38*z**2) - 40*(-10*z**3 - 38*z**2)\n#Step 2:\nCurrent expression: (37*z**2)*(-10*z**3 - 38*z**2) - 40*(-10*z**3 - 38*z**2)\nSimplifying the partial expression: -40*(-10*z**3 - 38*z**2)\nExpanding the part (-10*z**3 - 38*z**2) using the distributive property, and we got: -38*z**2*(-40) - 10*z**3*(-40)\nReplacing -40*(-10*z**3 - 38*z**2) with -38*z**2*(-40) - 10*z**3*(-40) in the overall expression.\n#Step 3:\nCurrent expression: -38*z**2*(-40) + (37*z**2)*(-10*z**3 - 38*z**2) - 10*z**3*(-40)\nSimplifying the partial expression: (37*z**2)*(-10*z**3 - 38*z**2)\nExpanding the part (-10*z**3 - 38*z**2) using the distributive property, and we got: (-38*z**2)*(37*z**2) + (37*z**2)*(-10*z**3)\nReplacing (37*z**2)*(-10*z**3 - 38*z**2) with (-38*z**2)*(37*z**2) + (37*z**2)*(-10*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-38*z**2)*(37*z**2) - 38*z**2*(-40) + (37*z**2)*(-10*z**3) - 10*z**3*(-40)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*z**2)*-40 = 1520*z**2\n (-38*z**2)*(37*z**2) = -1406*z**4\n (-10*z**3)*-40 = 400*z**3\n (-10*z**3)*(37*z**2) = -370*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -370*z**5 - 1406*z**4 + 400*z**3 + 1520*z**2\nNo more calculations needed.\n-370*z**5 - 1406*z**4 + 400*z**3 + 1520*z**2", "generated_answer": "-370*z**5 - 1406*z**4 + 400*z**3 + 1520*z**2", "step_length": 5} {"cot_id": "3a49508ab3bc56ef7c3ee2de7451e6f2e98a14f7c25741e1c1ccd53edd9b633d", "datapoint": {"question": "Calculate the following: (-45*z - 48)*(13*z**3 + 25*z - 4)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-585*z**4 - 624*z**3 - 1125*z**2 - 1020*z + 192", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 420, "polynomial_expr": "(-45*z - 48)*(13*z**3 + 25*z - 4)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-45*z - 48)*(13*z**3 + 25*z - 4)\nExpanding the part (-45*z - 48) using the distributive property, and we got: (-45*z)*(13*z**3 + 25*z - 4) - 48*(13*z**3 + 25*z - 4)\n#Step 2:\nCurrent expression: (-45*z)*(13*z**3 + 25*z - 4) - 48*(13*z**3 + 25*z - 4)\nSimplifying the partial expression: -48*(13*z**3 + 25*z - 4)\nExpanding the part (13*z**3 + 25*z - 4) using the distributive property, and we got: (25*z)*(-48) + (13*z**3)*(-48) - 4*(-48)\nReplacing -48*(13*z**3 + 25*z - 4) with (25*z)*(-48) + (13*z**3)*(-48) - 4*(-48) in the overall expression.\n#Step 3:\nCurrent expression: (-45*z)*(13*z**3 + 25*z - 4) + (25*z)*(-48) + (13*z**3)*(-48) + 192\nSimplifying the partial expression: (-45*z)*(13*z**3 + 25*z - 4)\nExpanding the part (13*z**3 + 25*z - 4) using the distributive property, and we got: (-45*z)*(25*z) + (-45*z)*(13*z**3) - (-1)*180*z\nReplacing (-45*z)*(13*z**3 + 25*z - 4) with (-45*z)*(25*z) + (-45*z)*(13*z**3) - (-1)*180*z in the overall expression.\n#Step 4:\nCurrent expression: (-45*z)*(25*z) + (-45*z)*(13*z**3) - 4*(-45)*z + (25*z)*(-48) + (13*z**3)*(-48) + 192\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (13*z**3)*-48 = -624*z**3\n (13*z**3)*(-45*z) = -585*z**4\n (25*z)*-48 = -1200*z\n (25*z)*(-45*z) = -1125*z**2\n -4*-45*z = 180*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -585*z**4 - 624*z**3 - 1125*z**2 - 1200*z + 180*z + 192\nCombining like terms, got -585*z**4 - 624*z**3 - 1125*z**2 - 1020*z + 192\n#Step 6:\nCurrent expression: -585*z**4 - 624*z**3 - 1125*z**2 - 1020*z + 192\nNo more calculations needed.\n-585*z**4 - 624*z**3 - 1125*z**2 - 1020*z + 192", "generated_answer": "-585*z**4 - 624*z**3 - 1125*z**2 - 1020*z + 192", "step_length": 6} {"cot_id": "223cf2ebd0bd168f9bbee0097a47786e92b47851ecec8dcffa4cc68ebbc8db89", "datapoint": {"question": "Simplify this expression: (43*x**3 + 12)*(-33*x**3 + 35*x - 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1419*x**6 + 1505*x**4 - 1686*x**3 + 420*x - 360", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 421, "polynomial_expr": "(43*x**3 + 12)*(-33*x**3 + 35*x - 30)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (43*x**3 + 12)*(-33*x**3 + 35*x - 30)\nExpanding the part (43*x**3 + 12) using the distributive property, and we got: (43*x**3)*(-33*x**3 + 35*x - 30) + 12*(-33*x**3 + 35*x - 30)\n#Step 2:\nCurrent expression: (43*x**3)*(-33*x**3 + 35*x - 30) + 12*(-33*x**3 + 35*x - 30)\nSimplifying the partial expression: 12*(-33*x**3 + 35*x - 30)\nExpanding the part (-33*x**3 + 35*x - 30) using the distributive property, and we got: (35*x)*12 - 33*x**3*12 - 30*12\nReplacing 12*(-33*x**3 + 35*x - 30) with (35*x)*12 - 33*x**3*12 - 30*12 in the overall expression.\n#Step 3:\nCurrent expression: (35*x)*12 - 33*x**3*12 + (43*x**3)*(-33*x**3 + 35*x - 30) - 360\nSimplifying the partial expression: (43*x**3)*(-33*x**3 + 35*x - 30)\nExpanding the part (-33*x**3 + 35*x - 30) using the distributive property, and we got: -1290*x**3 + (35*x)*(43*x**3) + (-33*x**3)*(43*x**3)\nReplacing (43*x**3)*(-33*x**3 + 35*x - 30) with -1290*x**3 + (35*x)*(43*x**3) + (-33*x**3)*(43*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -30*43*x**3 + (35*x)*(43*x**3) + (35*x)*12 + (-33*x**3)*(43*x**3) - 33*x**3*12 - 360\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*x**3)*12 = -396*x**3\n (-33*x**3)*(43*x**3) = -1419*x**6\n (35*x)*12 = 420*x\n (35*x)*(43*x**3) = 1505*x**4\n -30*43*x**3 = -1290*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1419*x**6 + 1505*x**4 - 1290*x**3 - 396*x**3 + 420*x - 360\nCombining like terms, got -1419*x**6 + 1505*x**4 - 1686*x**3 + 420*x - 360\n#Step 6:\nCurrent expression: -1419*x**6 + 1505*x**4 - 1686*x**3 + 420*x - 360\nNo more calculations needed.\n-1419*x**6 + 1505*x**4 - 1686*x**3 + 420*x - 360", "generated_answer": "-1419*x**6 + 1505*x**4 - 1686*x**3 + 420*x - 360", "step_length": 6} {"cot_id": "3161179f7b3e70626005413b554d0febe1f5fe387ee86da9fbf11a2650e8d8c9", "datapoint": {"question": "Simplify this expression: (9*y**2 - 38)*(-34*y**3 + 49*y**2 - 22)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-306*y**5 + 441*y**4 + 1292*y**3 - 2060*y**2 + 836", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 422, "polynomial_expr": "(9*y**2 - 38)*(-34*y**3 + 49*y**2 - 22)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9*y**2 - 38)*(-34*y**3 + 49*y**2 - 22)\nExpanding the part (9*y**2 - 38) using the distributive property, and we got: (9*y**2)*(-34*y**3 + 49*y**2 - 22) - 38*(-34*y**3 + 49*y**2 - 22)\n#Step 2:\nCurrent expression: (9*y**2)*(-34*y**3 + 49*y**2 - 22) - 38*(-34*y**3 + 49*y**2 - 22)\nSimplifying the partial expression: -38*(-34*y**3 + 49*y**2 - 22)\nExpanding the part (-34*y**3 + 49*y**2 - 22) using the distributive property, and we got: (49*y**2)*(-38) - 34*y**3*(-38) - 22*(-38)\nReplacing -38*(-34*y**3 + 49*y**2 - 22) with (49*y**2)*(-38) - 34*y**3*(-38) - 22*(-38) in the overall expression.\n#Step 3:\nCurrent expression: (9*y**2)*(-34*y**3 + 49*y**2 - 22) + (49*y**2)*(-38) - 34*y**3*(-38) + 836\nSimplifying the partial expression: (9*y**2)*(-34*y**3 + 49*y**2 - 22)\nExpanding the part (-34*y**3 + 49*y**2 - 22) using the distributive property, and we got: -198*y**2 + (9*y**2)*(49*y**2) + (9*y**2)*(-34*y**3)\nReplacing (9*y**2)*(-34*y**3 + 49*y**2 - 22) with -198*y**2 + (9*y**2)*(49*y**2) + (9*y**2)*(-34*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -22*9*y**2 + (9*y**2)*(49*y**2) + (9*y**2)*(-34*y**3) + (49*y**2)*(-38) - 34*y**3*(-38) + 836\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*y**3)*-38 = 1292*y**3\n (-34*y**3)*(9*y**2) = -306*y**5\n (49*y**2)*-38 = -1862*y**2\n (49*y**2)*(9*y**2) = 441*y**4\n -22*9*y**2 = -198*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -306*y**5 + 441*y**4 + 1292*y**3 - 1862*y**2 - 198*y**2 + 836\nCombining like terms, got -306*y**5 + 441*y**4 + 1292*y**3 - 2060*y**2 + 836\n#Step 6:\nCurrent expression: -306*y**5 + 441*y**4 + 1292*y**3 - 2060*y**2 + 836\nNo more calculations needed.\n-306*y**5 + 441*y**4 + 1292*y**3 - 2060*y**2 + 836", "generated_answer": "-306*y**5 + 441*y**4 + 1292*y**3 - 2060*y**2 + 836", "step_length": 6} {"cot_id": "6ddc620a0f5aa1fcae2d14781c95fd7febe64718732bfc12f897e16e139f743f", "datapoint": {"question": "Simplify this expression: (-42*x - 36)*(41*x**3 + 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1722*x**4 - 1476*x**3 - 672*x - 576", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 423, "polynomial_expr": "(-42*x - 36)*(41*x**3 + 16)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-42*x - 36)*(41*x**3 + 16)\nExpanding the part (-42*x - 36) using the distributive property, and we got: (-42*x)*(41*x**3 + 16) - 36*(41*x**3 + 16)\n#Step 2:\nCurrent expression: (-42*x)*(41*x**3 + 16) - 36*(41*x**3 + 16)\nSimplifying the partial expression: -36*(41*x**3 + 16)\nExpanding the part (41*x**3 + 16) using the distributive property, and we got: (41*x**3)*(-36) + 16*(-36)\nReplacing -36*(41*x**3 + 16) with (41*x**3)*(-36) + 16*(-36) in the overall expression.\n#Step 3:\nCurrent expression: (-42*x)*(41*x**3 + 16) + (41*x**3)*(-36) - 576\nSimplifying the partial expression: (-42*x)*(41*x**3 + 16)\nExpanding the part (41*x**3 + 16) using the distributive property, and we got: (-42*x)*(41*x**3) + 16*(-42*x)\nReplacing (-42*x)*(41*x**3 + 16) with (-42*x)*(41*x**3) + 16*(-42*x) in the overall expression.\n#Step 4:\nCurrent expression: (-42*x)*(41*x**3) + 16*(-42)*x + (41*x**3)*(-36) - 576\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (41*x**3)*-36 = -1476*x**3\n (41*x**3)*(-42*x) = -1722*x**4\n 16*-42*x = -672*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1722*x**4 - 1476*x**3 - 672*x - 576\nNo more calculations needed.\n-1722*x**4 - 1476*x**3 - 672*x - 576", "generated_answer": "-1722*x**4 - 1476*x**3 - 672*x - 576", "step_length": 5} {"cot_id": "41042d98f8a268141401ea3493c1f437553fcee7ceac1012653c57b2c944158a", "datapoint": {"question": "Simplify this expression: (19*x**2 - 10*x)*(15*x**3 - 46*x**2 + 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "285*x**5 - 1024*x**4 + 460*x**3 + 247*x**2 - 130*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 424, "polynomial_expr": "(19*x**2 - 10*x)*(15*x**3 - 46*x**2 + 13)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (19*x**2 - 10*x)*(15*x**3 - 46*x**2 + 13)\nExpanding the part (19*x**2 - 10*x) using the distributive property, and we got: (-10*x)*(15*x**3 - 46*x**2 + 13) + (19*x**2)*(15*x**3 - 46*x**2 + 13)\n#Step 2:\nCurrent expression: (-10*x)*(15*x**3 - 46*x**2 + 13) + (19*x**2)*(15*x**3 - 46*x**2 + 13)\nSimplifying the partial expression: (-10*x)*(15*x**3 - 46*x**2 + 13)\nExpanding the part (15*x**3 - 46*x**2 + 13) using the distributive property, and we got: (-10*x)*(-46*x**2) + (-10*x)*(15*x**3) + 13*(-10*x)\nReplacing (-10*x)*(15*x**3 - 46*x**2 + 13) with (-10*x)*(-46*x**2) + (-10*x)*(15*x**3) + 13*(-10*x) in the overall expression.\n#Step 3:\nCurrent expression: (-10*x)*(-46*x**2) + (-10*x)*(15*x**3) + 13*(-10)*x + (19*x**2)*(15*x**3 - 46*x**2 + 13)\nSimplifying the partial expression: (19*x**2)*(15*x**3 - 46*x**2 + 13)\nExpanding the part (15*x**3 - 46*x**2 + 13) using the distributive property, and we got: 13*(19*x**2) + (-46*x**2)*(19*x**2) + (19*x**2)*(15*x**3)\nReplacing (19*x**2)*(15*x**3 - 46*x**2 + 13) with 13*(19*x**2) + (-46*x**2)*(19*x**2) + (19*x**2)*(15*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-10*x)*(-46*x**2) + (-10*x)*(15*x**3) + 13*19*x**2 + 13*(-10)*x + (-46*x**2)*(19*x**2) + (19*x**2)*(15*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*x**2)*(-10*x) = 460*x**3\n (-46*x**2)*(19*x**2) = -874*x**4\n (15*x**3)*(-10*x) = -150*x**4\n (15*x**3)*(19*x**2) = 285*x**5\n 13*-10*x = -130*x\n 13*19*x**2 = 247*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 285*x**5 - 874*x**4 - 150*x**4 + 460*x**3 + 247*x**2 - 130*x\nCombining like terms, got 285*x**5 - 1024*x**4 + 460*x**3 + 247*x**2 - 130*x\n#Step 6:\nCurrent expression: 285*x**5 - 1024*x**4 + 460*x**3 + 247*x**2 - 130*x\nNo more calculations needed.\n285*x**5 - 1024*x**4 + 460*x**3 + 247*x**2 - 130*x", "generated_answer": "285*x**5 - 1024*x**4 + 460*x**3 + 247*x**2 - 130*x", "step_length": 6} {"cot_id": "d351eca9defe6e6c62487371bdd07f7599940f0177202b3ab9ec1585260606ab", "datapoint": {"question": "Simplify this expression: (-15*y**2 - 7)*(22*y**3 + 7*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-330*y**5 - 259*y**3 - 49*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 425, "polynomial_expr": "(-15*y**2 - 7)*(22*y**3 + 7*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-15*y**2 - 7)*(22*y**3 + 7*y)\nExpanding the part (-15*y**2 - 7) using the distributive property, and we got: (-15*y**2)*(22*y**3 + 7*y) - 7*(22*y**3 + 7*y)\n#Step 2:\nCurrent expression: (-15*y**2)*(22*y**3 + 7*y) - 7*(22*y**3 + 7*y)\nSimplifying the partial expression: -7*(22*y**3 + 7*y)\nExpanding the part (22*y**3 + 7*y) using the distributive property, and we got: (7*y)*(-7) + (22*y**3)*(-7)\nReplacing -7*(22*y**3 + 7*y) with (7*y)*(-7) + (22*y**3)*(-7) in the overall expression.\n#Step 3:\nCurrent expression: (7*y)*(-7) + (-15*y**2)*(22*y**3 + 7*y) + (22*y**3)*(-7)\nSimplifying the partial expression: (-15*y**2)*(22*y**3 + 7*y)\nExpanding the part (22*y**3 + 7*y) using the distributive property, and we got: (7*y)*(-15*y**2) + (-15*y**2)*(22*y**3)\nReplacing (-15*y**2)*(22*y**3 + 7*y) with (7*y)*(-15*y**2) + (-15*y**2)*(22*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (7*y)*(-15*y**2) + (7*y)*(-7) + (-15*y**2)*(22*y**3) + (22*y**3)*(-7)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (7*y)*-7 = -49*y\n (7*y)*(-15*y**2) = -105*y**3\n (22*y**3)*-7 = -154*y**3\n (22*y**3)*(-15*y**2) = -330*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -330*y**5 - 154*y**3 - 105*y**3 - 49*y\nCombining like terms, got -330*y**5 - 259*y**3 - 49*y\n#Step 6:\nCurrent expression: -330*y**5 - 259*y**3 - 49*y\nNo more calculations needed.\n-330*y**5 - 259*y**3 - 49*y", "generated_answer": "-330*y**5 - 259*y**3 - 49*y", "step_length": 6} {"cot_id": "732bf9e50b75bf6d47f468b5c765d3445522ff72b80eecc41499eb0f4030f2cd", "datapoint": {"question": "Calculate the following: (-42*x**3 - 38*x)*(30*x**3 + 19*x - 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1260*x**6 - 1938*x**4 + 2058*x**3 - 722*x**2 + 1862*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 426, "polynomial_expr": "(-42*x**3 - 38*x)*(30*x**3 + 19*x - 49)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-42*x**3 - 38*x)*(30*x**3 + 19*x - 49)\nExpanding the part (-42*x**3 - 38*x) using the distributive property, and we got: (-38*x)*(30*x**3 + 19*x - 49) + (-42*x**3)*(30*x**3 + 19*x - 49)\n#Step 2:\nCurrent expression: (-38*x)*(30*x**3 + 19*x - 49) + (-42*x**3)*(30*x**3 + 19*x - 49)\nSimplifying the partial expression: (-42*x**3)*(30*x**3 + 19*x - 49)\nExpanding the part (30*x**3 + 19*x - 49) using the distributive property, and we got: -(-1)*2058*x**3 + (19*x)*(-42*x**3) + (-42*x**3)*(30*x**3)\nReplacing (-42*x**3)*(30*x**3 + 19*x - 49) with -(-1)*2058*x**3 + (19*x)*(-42*x**3) + (-42*x**3)*(30*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-38*x)*(30*x**3 + 19*x - 49) - 49*(-42)*x**3 + (19*x)*(-42*x**3) + (-42*x**3)*(30*x**3)\nSimplifying the partial expression: (-38*x)*(30*x**3 + 19*x - 49)\nExpanding the part (30*x**3 + 19*x - 49) using the distributive property, and we got: (-38*x)*(19*x) + (-38*x)*(30*x**3) - (-1)*1862*x\nReplacing (-38*x)*(30*x**3 + 19*x - 49) with (-38*x)*(19*x) + (-38*x)*(30*x**3) - (-1)*1862*x in the overall expression.\n#Step 4:\nCurrent expression: (-38*x)*(19*x) + (-38*x)*(30*x**3) - 49*(-42)*x**3 - 49*(-38)*x + (19*x)*(-42*x**3) + (-42*x**3)*(30*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (19*x)*(-42*x**3) = -798*x**4\n (19*x)*(-38*x) = -722*x**2\n (30*x**3)*(-42*x**3) = -1260*x**6\n (30*x**3)*(-38*x) = -1140*x**4\n -49*-42*x**3 = 2058*x**3\n -49*-38*x = 1862*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1260*x**6 - 1140*x**4 - 798*x**4 + 2058*x**3 - 722*x**2 + 1862*x\nCombining like terms, got -1260*x**6 - 1938*x**4 + 2058*x**3 - 722*x**2 + 1862*x\n#Step 6:\nCurrent expression: -1260*x**6 - 1938*x**4 + 2058*x**3 - 722*x**2 + 1862*x\nNo more calculations needed.\n-1260*x**6 - 1938*x**4 + 2058*x**3 - 722*x**2 + 1862*x", "generated_answer": "-1260*x**6 - 1938*x**4 + 2058*x**3 - 722*x**2 + 1862*x", "step_length": 6} {"cot_id": "503e7e2fc8cd864e32d5b9892f60d8ddf16074ebabe29cb5be98a2a6237918d0", "datapoint": {"question": "Calculate the following: (41*y**2 + 13*y)*(-59*y**3 + 17*y**2 - 34)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2419*y**5 - 70*y**4 + 221*y**3 - 1394*y**2 - 442*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 427, "polynomial_expr": "(41*y**2 + 13*y)*(-59*y**3 + 17*y**2 - 34)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (41*y**2 + 13*y)*(-59*y**3 + 17*y**2 - 34)\nExpanding the part (41*y**2 + 13*y) using the distributive property, and we got: (13*y)*(-59*y**3 + 17*y**2 - 34) + (41*y**2)*(-59*y**3 + 17*y**2 - 34)\n#Step 2:\nCurrent expression: (13*y)*(-59*y**3 + 17*y**2 - 34) + (41*y**2)*(-59*y**3 + 17*y**2 - 34)\nSimplifying the partial expression: (13*y)*(-59*y**3 + 17*y**2 - 34)\nExpanding the part (-59*y**3 + 17*y**2 - 34) using the distributive property, and we got: -442*y + (13*y)*(17*y**2) + (13*y)*(-59*y**3)\nReplacing (13*y)*(-59*y**3 + 17*y**2 - 34) with -442*y + (13*y)*(17*y**2) + (13*y)*(-59*y**3) in the overall expression.\n#Step 3:\nCurrent expression: -34*13*y + (13*y)*(17*y**2) + (13*y)*(-59*y**3) + (41*y**2)*(-59*y**3 + 17*y**2 - 34)\nSimplifying the partial expression: (41*y**2)*(-59*y**3 + 17*y**2 - 34)\nExpanding the part (-59*y**3 + 17*y**2 - 34) using the distributive property, and we got: -1394*y**2 + (17*y**2)*(41*y**2) + (41*y**2)*(-59*y**3)\nReplacing (41*y**2)*(-59*y**3 + 17*y**2 - 34) with -1394*y**2 + (17*y**2)*(41*y**2) + (41*y**2)*(-59*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -34*41*y**2 - 34*13*y + (13*y)*(17*y**2) + (13*y)*(-59*y**3) + (17*y**2)*(41*y**2) + (41*y**2)*(-59*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-59*y**3)*(13*y) = -767*y**4\n (-59*y**3)*(41*y**2) = -2419*y**5\n (17*y**2)*(13*y) = 221*y**3\n (17*y**2)*(41*y**2) = 697*y**4\n -34*13*y = -442*y\n -34*41*y**2 = -1394*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2419*y**5 - 767*y**4 + 697*y**4 + 221*y**3 - 1394*y**2 - 442*y\nCombining like terms, got -2419*y**5 - 70*y**4 + 221*y**3 - 1394*y**2 - 442*y\n#Step 6:\nCurrent expression: -2419*y**5 - 70*y**4 + 221*y**3 - 1394*y**2 - 442*y\nNo more calculations needed.\n-2419*y**5 - 70*y**4 + 221*y**3 - 1394*y**2 - 442*y", "generated_answer": "-2419*y**5 - 70*y**4 + 221*y**3 - 1394*y**2 - 442*y", "step_length": 6} {"cot_id": "726747d4757c14c4513a80e65cbd6bff5703a638bc83e4187fb1ba4f9b503753", "datapoint": {"question": "Simplify this expression: 54*x**3*(-48*x**2 + 21*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2592*x**5 + 1134*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 428, "polynomial_expr": "54*x**3*(-48*x**2 + 21*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 54*x**3*(-48*x**2 + 21*x)\nExpanding the part (-48*x**2 + 21*x) using the distributive property, and we got: (21*x)*(54*x**3) + (-48*x**2)*(54*x**3)\n#Step 2:\nCurrent expression: (21*x)*(54*x**3) + (-48*x**2)*(54*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*x**2)*(54*x**3) = -2592*x**5\n (21*x)*(54*x**3) = 1134*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -2592*x**5 + 1134*x**4\nNo more calculations needed.\n-2592*x**5 + 1134*x**4", "generated_answer": "-2592*x**5 + 1134*x**4", "step_length": 3} {"cot_id": "9a1fecc96884afc1c23626fb55c6fec18f44d1659fba44fa8bccd37f1add04f2", "datapoint": {"question": "Simplify this expression: (-46*z**3 + 20*z**2 + 4*z + 23)*(17*z**3 - 28*z**2 + 14*z - 18)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-782*z**6 + 1628*z**5 - 1136*z**4 + 1387*z**3 - 948*z**2 + 250*z - 414", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 429, "polynomial_expr": "(-46*z**3 + 20*z**2 + 4*z + 23)*(17*z**3 - 28*z**2 + 14*z - 18)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-46*z**3 + 20*z**2 + 4*z + 23)*(17*z**3 - 28*z**2 + 14*z - 18)\nExpanding the part (17*z**3 - 28*z**2 + 14*z - 18) using the distributive property, and we got: (14*z)*(-46*z**3 + 20*z**2 + 4*z + 23) + (-28*z**2)*(-46*z**3 + 20*z**2 + 4*z + 23) + (17*z**3)*(-46*z**3 + 20*z**2 + 4*z + 23) - 18*(-46*z**3 + 20*z**2 + 4*z + 23)\n#Step 2:\nCurrent expression: (14*z)*(-46*z**3 + 20*z**2 + 4*z + 23) + (-28*z**2)*(-46*z**3 + 20*z**2 + 4*z + 23) + (17*z**3)*(-46*z**3 + 20*z**2 + 4*z + 23) - 18*(-46*z**3 + 20*z**2 + 4*z + 23)\nSimplifying the partial expression: -18*(-46*z**3 + 20*z**2 + 4*z + 23)\nExpanding the part (-46*z**3 + 20*z**2 + 4*z + 23) using the distributive property, and we got: (4*z)*(-18) + (20*z**2)*(-18) - 46*z**3*(-18) + 23*(-18)\nReplacing -18*(-46*z**3 + 20*z**2 + 4*z + 23) with (4*z)*(-18) + (20*z**2)*(-18) - 46*z**3*(-18) + 23*(-18) in the overall expression.\n#Step 3:\nCurrent expression: (4*z)*(-18) + (14*z)*(-46*z**3 + 20*z**2 + 4*z + 23) + (-28*z**2)*(-46*z**3 + 20*z**2 + 4*z + 23) + (20*z**2)*(-18) - 46*z**3*(-18) + (17*z**3)*(-46*z**3 + 20*z**2 + 4*z + 23) - 414\nSimplifying the partial expression: (-28*z**2)*(-46*z**3 + 20*z**2 + 4*z + 23)\nExpanding the part (-46*z**3 + 20*z**2 + 4*z + 23) using the distributive property, and we got: 23*(-28*z**2) + (4*z)*(-28*z**2) + (-28*z**2)*(20*z**2) + (-28*z**2)*(-46*z**3)\nReplacing (-28*z**2)*(-46*z**3 + 20*z**2 + 4*z + 23) with 23*(-28*z**2) + (4*z)*(-28*z**2) + (-28*z**2)*(20*z**2) + (-28*z**2)*(-46*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 23*(-28)*z**2 + (4*z)*(-28*z**2) + (4*z)*(-18) + (14*z)*(-46*z**3 + 20*z**2 + 4*z + 23) + (-28*z**2)*(20*z**2) + (-28*z**2)*(-46*z**3) + (20*z**2)*(-18) - 46*z**3*(-18) + (17*z**3)*(-46*z**3 + 20*z**2 + 4*z + 23) - 414\nSimplifying the partial expression: (14*z)*(-46*z**3 + 20*z**2 + 4*z + 23)\nExpanding the part (-46*z**3 + 20*z**2 + 4*z + 23) using the distributive property, and we got: 23*(14*z) + (4*z)*(14*z) + (14*z)*(20*z**2) + (14*z)*(-46*z**3)\nReplacing (14*z)*(-46*z**3 + 20*z**2 + 4*z + 23) with 23*(14*z) + (4*z)*(14*z) + (14*z)*(20*z**2) + (14*z)*(-46*z**3) in the overall expression.\n#Step 5:\nCurrent expression: 23*(-28)*z**2 + 23*14*z + (4*z)*(14*z) + (4*z)*(-28*z**2) + (4*z)*(-18) + (14*z)*(20*z**2) + (14*z)*(-46*z**3) + (-28*z**2)*(20*z**2) + (-28*z**2)*(-46*z**3) + (20*z**2)*(-18) - 46*z**3*(-18) + (17*z**3)*(-46*z**3 + 20*z**2 + 4*z + 23) - 414\nSimplifying the partial expression: (17*z**3)*(-46*z**3 + 20*z**2 + 4*z + 23)\nExpanding the part (-46*z**3 + 20*z**2 + 4*z + 23) using the distributive property, and we got: 23*(17*z**3) + (4*z)*(17*z**3) + (20*z**2)*(17*z**3) + (-46*z**3)*(17*z**3)\nReplacing (17*z**3)*(-46*z**3 + 20*z**2 + 4*z + 23) with 23*(17*z**3) + (4*z)*(17*z**3) + (20*z**2)*(17*z**3) + (-46*z**3)*(17*z**3) in the overall expression.\n#Step 6:\nCurrent expression: 23*17*z**3 + 23*(-28)*z**2 + 23*14*z + (4*z)*(14*z) + (4*z)*(-28*z**2) + (4*z)*(17*z**3) + (4*z)*(-18) + (14*z)*(20*z**2) + (14*z)*(-46*z**3) + (-28*z**2)*(20*z**2) + (-28*z**2)*(-46*z**3) + (20*z**2)*(17*z**3) + (20*z**2)*(-18) + (-46*z**3)*(17*z**3) - 46*z**3*(-18) - 414\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*z**3)*-18 = 828*z**3\n (-46*z**3)*(-28*z**2) = 1288*z**5\n (-46*z**3)*(14*z) = -644*z**4\n (-46*z**3)*(17*z**3) = -782*z**6\n (4*z)*-18 = -72*z\n (4*z)*(-28*z**2) = -112*z**3\n (4*z)*(14*z) = 56*z**2\n (4*z)*(17*z**3) = 68*z**4\n (20*z**2)*-18 = -360*z**2\n (20*z**2)*(-28*z**2) = -560*z**4\n (20*z**2)*(14*z) = 280*z**3\n (20*z**2)*(17*z**3) = 340*z**5\n 23*-28*z**2 = -644*z**2\n 23*14*z = 322*z\n 23*17*z**3 = 391*z**3\nReplacing them in the overall expression.\n#Step 7:\nCurrent expression: -782*z**6 + 340*z**5 + 1288*z**5 - 644*z**4 - 560*z**4 + 68*z**4 - 112*z**3 + 280*z**3 + 391*z**3 + 828*z**3 - 644*z**2 - 360*z**2 + 56*z**2 - 72*z + 322*z - 414\nCombining like terms, got -782*z**6 + 1628*z**5 - 1136*z**4 + 1387*z**3 - 948*z**2 + 250*z - 414\n#Step 8:\nCurrent expression: -782*z**6 + 1628*z**5 - 1136*z**4 + 1387*z**3 - 948*z**2 + 250*z - 414\nNo more calculations needed.\n-782*z**6 + 1628*z**5 - 1136*z**4 + 1387*z**3 - 948*z**2 + 250*z - 414", "generated_answer": "-782*z**6 + 1628*z**5 - 1136*z**4 + 1387*z**3 - 948*z**2 + 250*z - 414", "step_length": 8} {"cot_id": "df5c2c8d4b054e954b41aac6143a8d639230c7ac0464470f3bccbba306ac6749", "datapoint": {"question": "Calculate the following: (8*x**2 - 20)*(8*x**3 + 10*x**2 + 30*x + 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "64*x**5 + 80*x**4 + 80*x**3 - 120*x**2 - 600*x - 200", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 430, "polynomial_expr": "(8*x**2 - 20)*(8*x**3 + 10*x**2 + 30*x + 10)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (8*x**2 - 20)*(8*x**3 + 10*x**2 + 30*x + 10)\nExpanding the part (8*x**2 - 20) using the distributive property, and we got: (8*x**2)*(8*x**3 + 10*x**2 + 30*x + 10) - 20*(8*x**3 + 10*x**2 + 30*x + 10)\n#Step 2:\nCurrent expression: (8*x**2)*(8*x**3 + 10*x**2 + 30*x + 10) - 20*(8*x**3 + 10*x**2 + 30*x + 10)\nSimplifying the partial expression: -20*(8*x**3 + 10*x**2 + 30*x + 10)\nExpanding the part (8*x**3 + 10*x**2 + 30*x + 10) using the distributive property, and we got: (30*x)*(-20) + (10*x**2)*(-20) + (8*x**3)*(-20) + 10*(-20)\nReplacing -20*(8*x**3 + 10*x**2 + 30*x + 10) with (30*x)*(-20) + (10*x**2)*(-20) + (8*x**3)*(-20) + 10*(-20) in the overall expression.\n#Step 3:\nCurrent expression: (30*x)*(-20) + (8*x**2)*(8*x**3 + 10*x**2 + 30*x + 10) + (10*x**2)*(-20) + (8*x**3)*(-20) - 200\nSimplifying the partial expression: (8*x**2)*(8*x**3 + 10*x**2 + 30*x + 10)\nExpanding the part (8*x**3 + 10*x**2 + 30*x + 10) using the distributive property, and we got: 10*(8*x**2) + (30*x)*(8*x**2) + (8*x**2)*(10*x**2) + (8*x**2)*(8*x**3)\nReplacing (8*x**2)*(8*x**3 + 10*x**2 + 30*x + 10) with 10*(8*x**2) + (30*x)*(8*x**2) + (8*x**2)*(10*x**2) + (8*x**2)*(8*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 10*8*x**2 + (30*x)*(8*x**2) + (30*x)*(-20) + (8*x**2)*(10*x**2) + (8*x**2)*(8*x**3) + (10*x**2)*(-20) + (8*x**3)*(-20) - 200\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (8*x**3)*-20 = -160*x**3\n (8*x**3)*(8*x**2) = 64*x**5\n (10*x**2)*-20 = -200*x**2\n (10*x**2)*(8*x**2) = 80*x**4\n (30*x)*-20 = -600*x\n (30*x)*(8*x**2) = 240*x**3\n 10*8*x**2 = 80*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 64*x**5 + 80*x**4 - 160*x**3 + 240*x**3 - 200*x**2 + 80*x**2 - 600*x - 200\nCombining like terms, got 64*x**5 + 80*x**4 + 80*x**3 - 120*x**2 - 600*x - 200\n#Step 6:\nCurrent expression: 64*x**5 + 80*x**4 + 80*x**3 - 120*x**2 - 600*x - 200\nNo more calculations needed.\n64*x**5 + 80*x**4 + 80*x**3 - 120*x**2 - 600*x - 200", "generated_answer": "64*x**5 + 80*x**4 + 80*x**3 - 120*x**2 - 600*x - 200", "step_length": 6} {"cot_id": "f2ec089fb75849e2a9ded516177dfcf40a4f815ef7bece25482fb571c8d28a9e", "datapoint": {"question": "Calculate the following: -46*y*(38*y**2 - 12*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1748*y**3 + 552*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 431, "polynomial_expr": "-46*y*(38*y**2 - 12*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -46*y*(38*y**2 - 12*y)\nExpanding the part (38*y**2 - 12*y) using the distributive property, and we got: (-46*y)*(-12*y) + (-46*y)*(38*y**2)\n#Step 2:\nCurrent expression: (-46*y)*(-12*y) + (-46*y)*(38*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*y)*(-46*y) = 552*y**2\n (38*y**2)*(-46*y) = -1748*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1748*y**3 + 552*y**2\nNo more calculations needed.\n-1748*y**3 + 552*y**2", "generated_answer": "-1748*y**3 + 552*y**2", "step_length": 3} {"cot_id": "0f30906f8a48eedadc84a0c679b01966d5a16686875db2a0d21a7b2bfb1f6c23", "datapoint": {"question": "Calculate the following: (3 - 16*x)*(33*x**2 - 11*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-528*x**3 + 275*x**2 - 33*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 432, "polynomial_expr": "(3 - 16*x)*(33*x**2 - 11*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (3 - 16*x)*(33*x**2 - 11*x)\nExpanding the part (3 - 16*x) using the distributive property, and we got: (-16*x)*(33*x**2 - 11*x) + 3*(33*x**2 - 11*x)\n#Step 2:\nCurrent expression: (-16*x)*(33*x**2 - 11*x) + 3*(33*x**2 - 11*x)\nSimplifying the partial expression: 3*(33*x**2 - 11*x)\nExpanding the part (33*x**2 - 11*x) using the distributive property, and we got: -11*x*3 + (33*x**2)*3\nReplacing 3*(33*x**2 - 11*x) with -11*x*3 + (33*x**2)*3 in the overall expression.\n#Step 3:\nCurrent expression: (-16*x)*(33*x**2 - 11*x) - 11*x*3 + (33*x**2)*3\nSimplifying the partial expression: (-16*x)*(33*x**2 - 11*x)\nExpanding the part (33*x**2 - 11*x) using the distributive property, and we got: (-16*x)*(-11*x) + (-16*x)*(33*x**2)\nReplacing (-16*x)*(33*x**2 - 11*x) with (-16*x)*(-11*x) + (-16*x)*(33*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-16*x)*(-11*x) + (-16*x)*(33*x**2) - 11*x*3 + (33*x**2)*3\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*x)*3 = -33*x\n (-11*x)*(-16*x) = 176*x**2\n (33*x**2)*3 = 99*x**2\n (33*x**2)*(-16*x) = -528*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -528*x**3 + 99*x**2 + 176*x**2 - 33*x\nCombining like terms, got -528*x**3 + 275*x**2 - 33*x\n#Step 6:\nCurrent expression: -528*x**3 + 275*x**2 - 33*x\nNo more calculations needed.\n-528*x**3 + 275*x**2 - 33*x", "generated_answer": "-528*x**3 + 275*x**2 - 33*x", "step_length": 6} {"cot_id": "7aa714c180a01f8863ec1a5bc91ac345decd9e78e4d88133fdb0acb14804647d", "datapoint": {"question": "Simplify this expression: (21*x**2 + 23*x)*(36*x**3 + 43*x**2 - 17*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "756*x**5 + 1731*x**4 + 632*x**3 - 391*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 433, "polynomial_expr": "(21*x**2 + 23*x)*(36*x**3 + 43*x**2 - 17*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21*x**2 + 23*x)*(36*x**3 + 43*x**2 - 17*x)\nExpanding the part (21*x**2 + 23*x) using the distributive property, and we got: (23*x)*(36*x**3 + 43*x**2 - 17*x) + (21*x**2)*(36*x**3 + 43*x**2 - 17*x)\n#Step 2:\nCurrent expression: (23*x)*(36*x**3 + 43*x**2 - 17*x) + (21*x**2)*(36*x**3 + 43*x**2 - 17*x)\nSimplifying the partial expression: (21*x**2)*(36*x**3 + 43*x**2 - 17*x)\nExpanding the part (36*x**3 + 43*x**2 - 17*x) using the distributive property, and we got: (-17*x)*(21*x**2) + (21*x**2)*(43*x**2) + (21*x**2)*(36*x**3)\nReplacing (21*x**2)*(36*x**3 + 43*x**2 - 17*x) with (-17*x)*(21*x**2) + (21*x**2)*(43*x**2) + (21*x**2)*(36*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-17*x)*(21*x**2) + (23*x)*(36*x**3 + 43*x**2 - 17*x) + (21*x**2)*(43*x**2) + (21*x**2)*(36*x**3)\nSimplifying the partial expression: (23*x)*(36*x**3 + 43*x**2 - 17*x)\nExpanding the part (36*x**3 + 43*x**2 - 17*x) using the distributive property, and we got: (-17*x)*(23*x) + (23*x)*(43*x**2) + (23*x)*(36*x**3)\nReplacing (23*x)*(36*x**3 + 43*x**2 - 17*x) with (-17*x)*(23*x) + (23*x)*(43*x**2) + (23*x)*(36*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-17*x)*(23*x) + (-17*x)*(21*x**2) + (23*x)*(43*x**2) + (23*x)*(36*x**3) + (21*x**2)*(43*x**2) + (21*x**2)*(36*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-17*x)*(21*x**2) = -357*x**3\n (-17*x)*(23*x) = -391*x**2\n (36*x**3)*(21*x**2) = 756*x**5\n (36*x**3)*(23*x) = 828*x**4\n (43*x**2)*(21*x**2) = 903*x**4\n (43*x**2)*(23*x) = 989*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 756*x**5 + 828*x**4 + 903*x**4 - 357*x**3 + 989*x**3 - 391*x**2\nCombining like terms, got 756*x**5 + 1731*x**4 + 632*x**3 - 391*x**2\n#Step 6:\nCurrent expression: 756*x**5 + 1731*x**4 + 632*x**3 - 391*x**2\nNo more calculations needed.\n756*x**5 + 1731*x**4 + 632*x**3 - 391*x**2", "generated_answer": "756*x**5 + 1731*x**4 + 632*x**3 - 391*x**2", "step_length": 6} {"cot_id": "04a55f1bdb213280e3dc34c01e950af24734295a1a489e3f76d48a7e8aeec6ef", "datapoint": {"question": "Calculate the following: (62*y**2 + 39*y)*(-21*y**2 - 38*y + 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1302*y**4 - 3175*y**3 + 1246*y**2 + 1716*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 434, "polynomial_expr": "(62*y**2 + 39*y)*(-21*y**2 - 38*y + 44)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (62*y**2 + 39*y)*(-21*y**2 - 38*y + 44)\nExpanding the part (62*y**2 + 39*y) using the distributive property, and we got: (39*y)*(-21*y**2 - 38*y + 44) + (62*y**2)*(-21*y**2 - 38*y + 44)\n#Step 2:\nCurrent expression: (39*y)*(-21*y**2 - 38*y + 44) + (62*y**2)*(-21*y**2 - 38*y + 44)\nSimplifying the partial expression: (39*y)*(-21*y**2 - 38*y + 44)\nExpanding the part (-21*y**2 - 38*y + 44) using the distributive property, and we got: (-38*y)*(39*y) + 44*(39*y) + (39*y)*(-21*y**2)\nReplacing (39*y)*(-21*y**2 - 38*y + 44) with (-38*y)*(39*y) + 44*(39*y) + (39*y)*(-21*y**2) in the overall expression.\n#Step 3:\nCurrent expression: (-38*y)*(39*y) + 44*39*y + (39*y)*(-21*y**2) + (62*y**2)*(-21*y**2 - 38*y + 44)\nSimplifying the partial expression: (62*y**2)*(-21*y**2 - 38*y + 44)\nExpanding the part (-21*y**2 - 38*y + 44) using the distributive property, and we got: (-38*y)*(62*y**2) + 44*(62*y**2) + (-21*y**2)*(62*y**2)\nReplacing (62*y**2)*(-21*y**2 - 38*y + 44) with (-38*y)*(62*y**2) + 44*(62*y**2) + (-21*y**2)*(62*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-38*y)*(39*y) + (-38*y)*(62*y**2) + 44*62*y**2 + 44*39*y + (39*y)*(-21*y**2) + (-21*y**2)*(62*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*y)*(39*y) = -1482*y**2\n (-38*y)*(62*y**2) = -2356*y**3\n (-21*y**2)*(39*y) = -819*y**3\n (-21*y**2)*(62*y**2) = -1302*y**4\n 44*39*y = 1716*y\n 44*62*y**2 = 2728*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1302*y**4 - 2356*y**3 - 819*y**3 - 1482*y**2 + 2728*y**2 + 1716*y\nCombining like terms, got -1302*y**4 - 3175*y**3 + 1246*y**2 + 1716*y\n#Step 6:\nCurrent expression: -1302*y**4 - 3175*y**3 + 1246*y**2 + 1716*y\nNo more calculations needed.\n-1302*y**4 - 3175*y**3 + 1246*y**2 + 1716*y", "generated_answer": "-1302*y**4 - 3175*y**3 + 1246*y**2 + 1716*y", "step_length": 6} {"cot_id": "b61ad4aa76b3cd028cce20bea35f4bec2e45ef38c38c1aea4cebc59f76e571e8", "datapoint": {"question": "Simplify this expression: 203*z**2 + 133\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "203*z**2 + 133", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 435, "polynomial_expr": "203*z**2 + 133", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 203*z**2 + 133\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 203*z**2 + 133\nNo more calculations needed.\n203*z**2 + 133", "generated_answer": "203*z**2 + 133", "step_length": 2} {"cot_id": "c3308927858c3841dbee3c355af437b77f81233eef3344a98784d88fa4cd6a9b", "datapoint": {"question": "Simplify this expression: -13*y**3*(-49*y**3 - 24*y**2 + 20*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "637*y**6 + 312*y**5 - 260*y**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 436, "polynomial_expr": "-13*y**3*(-49*y**3 - 24*y**2 + 20*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -13*y**3*(-49*y**3 - 24*y**2 + 20*y)\nExpanding the part (-49*y**3 - 24*y**2 + 20*y) using the distributive property, and we got: (20*y)*(-13*y**3) + (-24*y**2)*(-13*y**3) + (-49*y**3)*(-13*y**3)\n#Step 2:\nCurrent expression: (20*y)*(-13*y**3) + (-24*y**2)*(-13*y**3) + (-49*y**3)*(-13*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*y**3)*(-13*y**3) = 637*y**6\n (-24*y**2)*(-13*y**3) = 312*y**5\n (20*y)*(-13*y**3) = -260*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 637*y**6 + 312*y**5 - 260*y**4\nNo more calculations needed.\n637*y**6 + 312*y**5 - 260*y**4", "generated_answer": "637*y**6 + 312*y**5 - 260*y**4", "step_length": 3} {"cot_id": "19c08bfc6ae5b3f4f53ee569690fa96241010fe48b5ebede9bc7c05f065f3632", "datapoint": {"question": "Calculate the following: (42*y**2 + 38*y)*(42*y**3 - 145)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1764*y**5 + 1596*y**4 - 6090*y**2 - 5510*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 437, "polynomial_expr": "(42*y**2 + 38*y)*(42*y**3 - 145)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (42*y**2 + 38*y)*(42*y**3 - 145)\nExpanding the part (42*y**3 - 145) using the distributive property, and we got: (42*y**3)*(42*y**2 + 38*y) - 145*(42*y**2 + 38*y)\n#Step 2:\nCurrent expression: (42*y**3)*(42*y**2 + 38*y) - 145*(42*y**2 + 38*y)\nSimplifying the partial expression: -145*(42*y**2 + 38*y)\nExpanding the part (42*y**2 + 38*y) using the distributive property, and we got: (38*y)*(-145) + (42*y**2)*(-145)\nReplacing -145*(42*y**2 + 38*y) with (38*y)*(-145) + (42*y**2)*(-145) in the overall expression.\n#Step 3:\nCurrent expression: (38*y)*(-145) + (42*y**2)*(-145) + (42*y**3)*(42*y**2 + 38*y)\nSimplifying the partial expression: (42*y**3)*(42*y**2 + 38*y)\nExpanding the part (42*y**2 + 38*y) using the distributive property, and we got: (38*y)*(42*y**3) + (42*y**2)*(42*y**3)\nReplacing (42*y**3)*(42*y**2 + 38*y) with (38*y)*(42*y**3) + (42*y**2)*(42*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (38*y)*(42*y**3) + (38*y)*(-145) + (42*y**2)*(42*y**3) + (42*y**2)*(-145)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (38*y)*-145 = -5510*y\n (38*y)*(42*y**3) = 1596*y**4\n (42*y**2)*-145 = -6090*y**2\n (42*y**2)*(42*y**3) = 1764*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1764*y**5 + 1596*y**4 - 6090*y**2 - 5510*y\nNo more calculations needed.\n1764*y**5 + 1596*y**4 - 6090*y**2 - 5510*y", "generated_answer": "1764*y**5 + 1596*y**4 - 6090*y**2 - 5510*y", "step_length": 5} {"cot_id": "6a3c41e1b2768df29184d1ae15f3ff61a404337175e86e3de66023940537ba64", "datapoint": {"question": "Simplify this expression: -30*y**3*(-43*y**2 + 44*y - 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1290*y**5 - 1320*y**4 + 900*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 438, "polynomial_expr": "-30*y**3*(-43*y**2 + 44*y - 30)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -30*y**3*(-43*y**2 + 44*y - 30)\nExpanding the part (-43*y**2 + 44*y - 30) using the distributive property, and we got: -(-1)*900*y**3 + (44*y)*(-30*y**3) + (-43*y**2)*(-30*y**3)\n#Step 2:\nCurrent expression: -(-1)*900*y**3 + (44*y)*(-30*y**3) + (-43*y**2)*(-30*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -30*(-30*y**3) = 900*y**3\n (-43*y**2)*(-30*y**3) = 1290*y**5\n (44*y)*(-30*y**3) = -1320*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1290*y**5 - 1320*y**4 + 900*y**3\nNo more calculations needed.\n1290*y**5 - 1320*y**4 + 900*y**3", "generated_answer": "1290*y**5 - 1320*y**4 + 900*y**3", "step_length": 3} {"cot_id": "472b10821ca29fdea05112afaa1117da7788fdeafab59cea3928b88bf0afde27", "datapoint": {"question": "Calculate the following: (-20*z**2 - 18*z)*(20*z**2 - 8*z - 43)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-400*z**4 - 200*z**3 + 1004*z**2 + 774*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 439, "polynomial_expr": "(-20*z**2 - 18*z)*(20*z**2 - 8*z - 43)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-20*z**2 - 18*z)*(20*z**2 - 8*z - 43)\nExpanding the part (-20*z**2 - 18*z) using the distributive property, and we got: (-18*z)*(20*z**2 - 8*z - 43) + (-20*z**2)*(20*z**2 - 8*z - 43)\n#Step 2:\nCurrent expression: (-18*z)*(20*z**2 - 8*z - 43) + (-20*z**2)*(20*z**2 - 8*z - 43)\nSimplifying the partial expression: (-20*z**2)*(20*z**2 - 8*z - 43)\nExpanding the part (20*z**2 - 8*z - 43) using the distributive property, and we got: (-8*z)*(-20*z**2) - (-1)*860*z**2 + (-20*z**2)*(20*z**2)\nReplacing (-20*z**2)*(20*z**2 - 8*z - 43) with (-8*z)*(-20*z**2) - (-1)*860*z**2 + (-20*z**2)*(20*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-18*z)*(20*z**2 - 8*z - 43) + (-8*z)*(-20*z**2) - 43*(-20)*z**2 + (-20*z**2)*(20*z**2)\nSimplifying the partial expression: (-18*z)*(20*z**2 - 8*z - 43)\nExpanding the part (20*z**2 - 8*z - 43) using the distributive property, and we got: (-18*z)*(-8*z) + (-18*z)*(20*z**2) - (-1)*774*z\nReplacing (-18*z)*(20*z**2 - 8*z - 43) with (-18*z)*(-8*z) + (-18*z)*(20*z**2) - (-1)*774*z in the overall expression.\n#Step 4:\nCurrent expression: (-18*z)*(-8*z) + (-18*z)*(20*z**2) + (-8*z)*(-20*z**2) - 43*(-20)*z**2 - 43*(-18)*z + (-20*z**2)*(20*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-8*z)*(-20*z**2) = 160*z**3\n (-8*z)*(-18*z) = 144*z**2\n (20*z**2)*(-20*z**2) = -400*z**4\n (20*z**2)*(-18*z) = -360*z**3\n -43*-20*z**2 = 860*z**2\n -43*-18*z = 774*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -400*z**4 - 360*z**3 + 160*z**3 + 144*z**2 + 860*z**2 + 774*z\nCombining like terms, got -400*z**4 - 200*z**3 + 1004*z**2 + 774*z\n#Step 6:\nCurrent expression: -400*z**4 - 200*z**3 + 1004*z**2 + 774*z\nNo more calculations needed.\n-400*z**4 - 200*z**3 + 1004*z**2 + 774*z", "generated_answer": "-400*z**4 - 200*z**3 + 1004*z**2 + 774*z", "step_length": 6} {"cot_id": "dbba094af4388d6ea7f8e528879ac27213febf0d4a609dfa5370ac4f88bac4e9", "datapoint": {"question": "Calculate the following: -3*z*(42*z**3 - 35*z - 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-126*z**4 + 105*z**2 + 114*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 440, "polynomial_expr": "-3*z*(42*z**3 - 35*z - 38)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -3*z*(42*z**3 - 35*z - 38)\nExpanding the part (42*z**3 - 35*z - 38) using the distributive property, and we got: (-35*z)*(-3*z) + (-3*z)*(42*z**3) - (-1)*114*z\n#Step 2:\nCurrent expression: (-35*z)*(-3*z) + (-3*z)*(42*z**3) - (-1)*114*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -38*(-3*z) = 114*z\n (-35*z)*(-3*z) = 105*z**2\n (42*z**3)*(-3*z) = -126*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -126*z**4 + 105*z**2 + 114*z\nNo more calculations needed.\n-126*z**4 + 105*z**2 + 114*z", "generated_answer": "-126*z**4 + 105*z**2 + 114*z", "step_length": 3} {"cot_id": "be521dece960011f7b523829258e43c3cfc25673b7c335822b6d2a0ee55ee575", "datapoint": {"question": "Simplify this expression: (-6*z**3 - 24)*(20*z**3 + 19*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-120*z**6 - 114*z**4 - 480*z**3 - 456*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 441, "polynomial_expr": "(-6*z**3 - 24)*(20*z**3 + 19*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-6*z**3 - 24)*(20*z**3 + 19*z)\nExpanding the part (-6*z**3 - 24) using the distributive property, and we got: (-6*z**3)*(20*z**3 + 19*z) - 24*(20*z**3 + 19*z)\n#Step 2:\nCurrent expression: (-6*z**3)*(20*z**3 + 19*z) - 24*(20*z**3 + 19*z)\nSimplifying the partial expression: -24*(20*z**3 + 19*z)\nExpanding the part (20*z**3 + 19*z) using the distributive property, and we got: (19*z)*(-24) + (20*z**3)*(-24)\nReplacing -24*(20*z**3 + 19*z) with (19*z)*(-24) + (20*z**3)*(-24) in the overall expression.\n#Step 3:\nCurrent expression: (19*z)*(-24) + (-6*z**3)*(20*z**3 + 19*z) + (20*z**3)*(-24)\nSimplifying the partial expression: (-6*z**3)*(20*z**3 + 19*z)\nExpanding the part (20*z**3 + 19*z) using the distributive property, and we got: (19*z)*(-6*z**3) + (-6*z**3)*(20*z**3)\nReplacing (-6*z**3)*(20*z**3 + 19*z) with (19*z)*(-6*z**3) + (-6*z**3)*(20*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (19*z)*(-6*z**3) + (19*z)*(-24) + (-6*z**3)*(20*z**3) + (20*z**3)*(-24)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (19*z)*-24 = -456*z\n (19*z)*(-6*z**3) = -114*z**4\n (20*z**3)*-24 = -480*z**3\n (20*z**3)*(-6*z**3) = -120*z**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -120*z**6 - 114*z**4 - 480*z**3 - 456*z\nNo more calculations needed.\n-120*z**6 - 114*z**4 - 480*z**3 - 456*z", "generated_answer": "-120*z**6 - 114*z**4 - 480*z**3 - 456*z", "step_length": 5} {"cot_id": "5ae8903884b0f9115e515c1fb91c3f24015dc925a7b416102ab9126568d66485", "datapoint": {"question": "Calculate the following: (-36*z**2 - 26)*(21*z**3 + 43*z + 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-756*z**5 - 2094*z**3 - 1080*z**2 - 1118*z - 780", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 442, "polynomial_expr": "(-36*z**2 - 26)*(21*z**3 + 43*z + 30)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-36*z**2 - 26)*(21*z**3 + 43*z + 30)\nExpanding the part (-36*z**2 - 26) using the distributive property, and we got: (-36*z**2)*(21*z**3 + 43*z + 30) - 26*(21*z**3 + 43*z + 30)\n#Step 2:\nCurrent expression: (-36*z**2)*(21*z**3 + 43*z + 30) - 26*(21*z**3 + 43*z + 30)\nSimplifying the partial expression: -26*(21*z**3 + 43*z + 30)\nExpanding the part (21*z**3 + 43*z + 30) using the distributive property, and we got: (43*z)*(-26) + (21*z**3)*(-26) + 30*(-26)\nReplacing -26*(21*z**3 + 43*z + 30) with (43*z)*(-26) + (21*z**3)*(-26) + 30*(-26) in the overall expression.\n#Step 3:\nCurrent expression: (43*z)*(-26) + (-36*z**2)*(21*z**3 + 43*z + 30) + (21*z**3)*(-26) - 780\nSimplifying the partial expression: (-36*z**2)*(21*z**3 + 43*z + 30)\nExpanding the part (21*z**3 + 43*z + 30) using the distributive property, and we got: 30*(-36*z**2) + (43*z)*(-36*z**2) + (-36*z**2)*(21*z**3)\nReplacing (-36*z**2)*(21*z**3 + 43*z + 30) with 30*(-36*z**2) + (43*z)*(-36*z**2) + (-36*z**2)*(21*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 30*(-36)*z**2 + (43*z)*(-36*z**2) + (43*z)*(-26) + (-36*z**2)*(21*z**3) + (21*z**3)*(-26) - 780\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (21*z**3)*-26 = -546*z**3\n (21*z**3)*(-36*z**2) = -756*z**5\n (43*z)*-26 = -1118*z\n (43*z)*(-36*z**2) = -1548*z**3\n 30*-36*z**2 = -1080*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -756*z**5 - 1548*z**3 - 546*z**3 - 1080*z**2 - 1118*z - 780\nCombining like terms, got -756*z**5 - 2094*z**3 - 1080*z**2 - 1118*z - 780\n#Step 6:\nCurrent expression: -756*z**5 - 2094*z**3 - 1080*z**2 - 1118*z - 780\nNo more calculations needed.\n-756*z**5 - 2094*z**3 - 1080*z**2 - 1118*z - 780", "generated_answer": "-756*z**5 - 2094*z**3 - 1080*z**2 - 1118*z - 780", "step_length": 6} {"cot_id": "13faf1b46f17ae78e76c1d04342336f08a8009441cc6ee54001fbcacc600f78c", "datapoint": {"question": "Calculate the following: (50*x - 12)*(31*x**3 - 31*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1550*x**4 - 1922*x**3 + 372*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 443, "polynomial_expr": "(50*x - 12)*(31*x**3 - 31*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (50*x - 12)*(31*x**3 - 31*x**2)\nExpanding the part (50*x - 12) using the distributive property, and we got: (50*x)*(31*x**3 - 31*x**2) - 12*(31*x**3 - 31*x**2)\n#Step 2:\nCurrent expression: (50*x)*(31*x**3 - 31*x**2) - 12*(31*x**3 - 31*x**2)\nSimplifying the partial expression: -12*(31*x**3 - 31*x**2)\nExpanding the part (31*x**3 - 31*x**2) using the distributive property, and we got: -31*x**2*(-12) + (31*x**3)*(-12)\nReplacing -12*(31*x**3 - 31*x**2) with -31*x**2*(-12) + (31*x**3)*(-12) in the overall expression.\n#Step 3:\nCurrent expression: (50*x)*(31*x**3 - 31*x**2) - 31*x**2*(-12) + (31*x**3)*(-12)\nSimplifying the partial expression: (50*x)*(31*x**3 - 31*x**2)\nExpanding the part (31*x**3 - 31*x**2) using the distributive property, and we got: (50*x)*(-31*x**2) + (50*x)*(31*x**3)\nReplacing (50*x)*(31*x**3 - 31*x**2) with (50*x)*(-31*x**2) + (50*x)*(31*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (50*x)*(-31*x**2) + (50*x)*(31*x**3) - 31*x**2*(-12) + (31*x**3)*(-12)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-31*x**2)*-12 = 372*x**2\n (-31*x**2)*(50*x) = -1550*x**3\n (31*x**3)*-12 = -372*x**3\n (31*x**3)*(50*x) = 1550*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1550*x**4 - 1550*x**3 - 372*x**3 + 372*x**2\nCombining like terms, got 1550*x**4 - 1922*x**3 + 372*x**2\n#Step 6:\nCurrent expression: 1550*x**4 - 1922*x**3 + 372*x**2\nNo more calculations needed.\n1550*x**4 - 1922*x**3 + 372*x**2", "generated_answer": "1550*x**4 - 1922*x**3 + 372*x**2", "step_length": 6} {"cot_id": "cefb971b8d14d978571cac70ff74c1f9e2dcb451cc00c60c50d1b848bf76509d", "datapoint": {"question": "Simplify this expression: (-64*x**2 - 17)*(6*x**3 - 23*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-384*x**5 + 1472*x**4 - 102*x**3 + 391*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 444, "polynomial_expr": "(-64*x**2 - 17)*(6*x**3 - 23*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-64*x**2 - 17)*(6*x**3 - 23*x**2)\nExpanding the part (-64*x**2 - 17) using the distributive property, and we got: (-64*x**2)*(6*x**3 - 23*x**2) - 17*(6*x**3 - 23*x**2)\n#Step 2:\nCurrent expression: (-64*x**2)*(6*x**3 - 23*x**2) - 17*(6*x**3 - 23*x**2)\nSimplifying the partial expression: -17*(6*x**3 - 23*x**2)\nExpanding the part (6*x**3 - 23*x**2) using the distributive property, and we got: -23*x**2*(-17) + (6*x**3)*(-17)\nReplacing -17*(6*x**3 - 23*x**2) with -23*x**2*(-17) + (6*x**3)*(-17) in the overall expression.\n#Step 3:\nCurrent expression: (-64*x**2)*(6*x**3 - 23*x**2) - 23*x**2*(-17) + (6*x**3)*(-17)\nSimplifying the partial expression: (-64*x**2)*(6*x**3 - 23*x**2)\nExpanding the part (6*x**3 - 23*x**2) using the distributive property, and we got: (-64*x**2)*(-23*x**2) + (-64*x**2)*(6*x**3)\nReplacing (-64*x**2)*(6*x**3 - 23*x**2) with (-64*x**2)*(-23*x**2) + (-64*x**2)*(6*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-64*x**2)*(-23*x**2) + (-64*x**2)*(6*x**3) - 23*x**2*(-17) + (6*x**3)*(-17)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*x**2)*-17 = 391*x**2\n (-23*x**2)*(-64*x**2) = 1472*x**4\n (6*x**3)*-17 = -102*x**3\n (6*x**3)*(-64*x**2) = -384*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -384*x**5 + 1472*x**4 - 102*x**3 + 391*x**2\nNo more calculations needed.\n-384*x**5 + 1472*x**4 - 102*x**3 + 391*x**2", "generated_answer": "-384*x**5 + 1472*x**4 - 102*x**3 + 391*x**2", "step_length": 5} {"cot_id": "10c25590d8b156892b3f6b6b85a6ca51eeebcf506af2997ba8b4fac8474f69c5", "datapoint": {"question": "Calculate the following: (18 - 21*z**2)*(-14*z**3 + 14*z + 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "294*z**5 - 546*z**3 - 336*z**2 + 252*z + 288", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 445, "polynomial_expr": "(18 - 21*z**2)*(-14*z**3 + 14*z + 16)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (18 - 21*z**2)*(-14*z**3 + 14*z + 16)\nExpanding the part (18 - 21*z**2) using the distributive property, and we got: (-21*z**2)*(-14*z**3 + 14*z + 16) + 18*(-14*z**3 + 14*z + 16)\n#Step 2:\nCurrent expression: (-21*z**2)*(-14*z**3 + 14*z + 16) + 18*(-14*z**3 + 14*z + 16)\nSimplifying the partial expression: 18*(-14*z**3 + 14*z + 16)\nExpanding the part (-14*z**3 + 14*z + 16) using the distributive property, and we got: (14*z)*18 - 14*z**3*18 + 16*18\nReplacing 18*(-14*z**3 + 14*z + 16) with (14*z)*18 - 14*z**3*18 + 16*18 in the overall expression.\n#Step 3:\nCurrent expression: (14*z)*18 + (-21*z**2)*(-14*z**3 + 14*z + 16) - 14*z**3*18 + 288\nSimplifying the partial expression: (-21*z**2)*(-14*z**3 + 14*z + 16)\nExpanding the part (-14*z**3 + 14*z + 16) using the distributive property, and we got: 16*(-21*z**2) + (14*z)*(-21*z**2) + (-21*z**2)*(-14*z**3)\nReplacing (-21*z**2)*(-14*z**3 + 14*z + 16) with 16*(-21*z**2) + (14*z)*(-21*z**2) + (-21*z**2)*(-14*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 16*(-21)*z**2 + (14*z)*(-21*z**2) + (14*z)*18 + (-21*z**2)*(-14*z**3) - 14*z**3*18 + 288\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-14*z**3)*18 = -252*z**3\n (-14*z**3)*(-21*z**2) = 294*z**5\n (14*z)*18 = 252*z\n (14*z)*(-21*z**2) = -294*z**3\n 16*-21*z**2 = -336*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 294*z**5 - 294*z**3 - 252*z**3 - 336*z**2 + 252*z + 288\nCombining like terms, got 294*z**5 - 546*z**3 - 336*z**2 + 252*z + 288\n#Step 6:\nCurrent expression: 294*z**5 - 546*z**3 - 336*z**2 + 252*z + 288\nNo more calculations needed.\n294*z**5 - 546*z**3 - 336*z**2 + 252*z + 288", "generated_answer": "294*z**5 - 546*z**3 - 336*z**2 + 252*z + 288", "step_length": 6} {"cot_id": "4e1a5ad4c737a9748132e4eb42bcf8b28651f0dba3280d92d82ef80c41ba17ca", "datapoint": {"question": "Simplify this expression: (19*x**2 - 18*x - 40)*(-37*x**3 - 25*x**2 + 17*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-703*x**5 + 191*x**4 + 2253*x**3 + 694*x**2 - 680*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 446, "polynomial_expr": "(19*x**2 - 18*x - 40)*(-37*x**3 - 25*x**2 + 17*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (19*x**2 - 18*x - 40)*(-37*x**3 - 25*x**2 + 17*x)\nExpanding the part (19*x**2 - 18*x - 40) using the distributive property, and we got: (-18*x)*(-37*x**3 - 25*x**2 + 17*x) + (19*x**2)*(-37*x**3 - 25*x**2 + 17*x) - 40*(-37*x**3 - 25*x**2 + 17*x)\n#Step 2:\nCurrent expression: (-18*x)*(-37*x**3 - 25*x**2 + 17*x) + (19*x**2)*(-37*x**3 - 25*x**2 + 17*x) - 40*(-37*x**3 - 25*x**2 + 17*x)\nSimplifying the partial expression: -40*(-37*x**3 - 25*x**2 + 17*x)\nExpanding the part (-37*x**3 - 25*x**2 + 17*x) using the distributive property, and we got: (17*x)*(-40) - 25*x**2*(-40) - 37*x**3*(-40)\nReplacing -40*(-37*x**3 - 25*x**2 + 17*x) with (17*x)*(-40) - 25*x**2*(-40) - 37*x**3*(-40) in the overall expression.\n#Step 3:\nCurrent expression: (-18*x)*(-37*x**3 - 25*x**2 + 17*x) + (17*x)*(-40) - 25*x**2*(-40) + (19*x**2)*(-37*x**3 - 25*x**2 + 17*x) - 37*x**3*(-40)\nSimplifying the partial expression: (-18*x)*(-37*x**3 - 25*x**2 + 17*x)\nExpanding the part (-37*x**3 - 25*x**2 + 17*x) using the distributive property, and we got: (-18*x)*(17*x) + (-18*x)*(-25*x**2) + (-18*x)*(-37*x**3)\nReplacing (-18*x)*(-37*x**3 - 25*x**2 + 17*x) with (-18*x)*(17*x) + (-18*x)*(-25*x**2) + (-18*x)*(-37*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-18*x)*(17*x) + (-18*x)*(-25*x**2) + (-18*x)*(-37*x**3) + (17*x)*(-40) - 25*x**2*(-40) + (19*x**2)*(-37*x**3 - 25*x**2 + 17*x) - 37*x**3*(-40)\nSimplifying the partial expression: (19*x**2)*(-37*x**3 - 25*x**2 + 17*x)\nExpanding the part (-37*x**3 - 25*x**2 + 17*x) using the distributive property, and we got: (17*x)*(19*x**2) + (-25*x**2)*(19*x**2) + (19*x**2)*(-37*x**3)\nReplacing (19*x**2)*(-37*x**3 - 25*x**2 + 17*x) with (17*x)*(19*x**2) + (-25*x**2)*(19*x**2) + (19*x**2)*(-37*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-18*x)*(17*x) + (-18*x)*(-25*x**2) + (-18*x)*(-37*x**3) + (17*x)*(19*x**2) + (17*x)*(-40) + (-25*x**2)*(19*x**2) - 25*x**2*(-40) + (19*x**2)*(-37*x**3) - 37*x**3*(-40)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*x**3)*-40 = 1480*x**3\n (-37*x**3)*(-18*x) = 666*x**4\n (-37*x**3)*(19*x**2) = -703*x**5\n (-25*x**2)*-40 = 1000*x**2\n (-25*x**2)*(-18*x) = 450*x**3\n (-25*x**2)*(19*x**2) = -475*x**4\n (17*x)*-40 = -680*x\n (17*x)*(-18*x) = -306*x**2\n (17*x)*(19*x**2) = 323*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -703*x**5 - 475*x**4 + 666*x**4 + 323*x**3 + 450*x**3 + 1480*x**3 - 306*x**2 + 1000*x**2 - 680*x\nCombining like terms, got -703*x**5 + 191*x**4 + 2253*x**3 + 694*x**2 - 680*x\n#Step 7:\nCurrent expression: -703*x**5 + 191*x**4 + 2253*x**3 + 694*x**2 - 680*x\nNo more calculations needed.\n-703*x**5 + 191*x**4 + 2253*x**3 + 694*x**2 - 680*x", "generated_answer": "-703*x**5 + 191*x**4 + 2253*x**3 + 694*x**2 - 680*x", "step_length": 7} {"cot_id": "1420e68226c184dea3de453e1f14fdfdefb6dc278e7dd4f65cf71e2cac78fbe1", "datapoint": {"question": "Simplify this expression: (x**3 + 48*x)*(6*x**3 + x - 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "6*x**6 + 289*x**4 - 14*x**3 + 48*x**2 - 672*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 447, "polynomial_expr": "(x**3 + 48*x)*(6*x**3 + x - 14)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (x**3 + 48*x)*(6*x**3 + x - 14)\nExpanding the part (x**3 + 48*x) using the distributive property, and we got: x**3*(6*x**3 + x - 14) + (48*x)*(6*x**3 + x - 14)\n#Step 2:\nCurrent expression: x**3*(6*x**3 + x - 14) + (48*x)*(6*x**3 + x - 14)\nSimplifying the partial expression: x**3*(6*x**3 + x - 14)\nExpanding the part (6*x**3 + x - 14) using the distributive property, and we got: x**3*(6*x**3) - 14*x**3 + x*x**3\nReplacing x**3*(6*x**3 + x - 14) with x**3*(6*x**3) - 14*x**3 + x*x**3 in the overall expression.\n#Step 3:\nCurrent expression: x**3*(6*x**3) - 14*x**3 + x*x**3 + (48*x)*(6*x**3 + x - 14)\nSimplifying the partial expression: (48*x)*(6*x**3 + x - 14)\nExpanding the part (6*x**3 + x - 14) using the distributive property, and we got: x*(48*x) - 672*x + (48*x)*(6*x**3)\nReplacing (48*x)*(6*x**3 + x - 14) with x*(48*x) - 672*x + (48*x)*(6*x**3) in the overall expression.\n#Step 4:\nCurrent expression: x**3*(6*x**3) - 14*x**3 + x*x**3 + x*(48*x) - 14*48*x + (48*x)*(6*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n x*x**3 = x**4\n x*(48*x) = 48*x**2\n (6*x**3)*x**3 = 6*x**6\n (6*x**3)*(48*x) = 288*x**4\n -14*48*x = -672*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 6*x**6 + x**4 + 288*x**4 - 14*x**3 + 48*x**2 - 672*x\nCombining like terms, got 6*x**6 + 289*x**4 - 14*x**3 + 48*x**2 - 672*x\n#Step 6:\nCurrent expression: 6*x**6 + 289*x**4 - 14*x**3 + 48*x**2 - 672*x\nNo more calculations needed.\n6*x**6 + 289*x**4 - 14*x**3 + 48*x**2 - 672*x", "generated_answer": "6*x**6 + 289*x**4 - 14*x**3 + 48*x**2 - 672*x", "step_length": 6} {"cot_id": "887ca3c7219182d69867f7fd0480d3b946f5fe97f73e2e390fbcfb1502d30631", "datapoint": {"question": "Calculate the following: (9*z**3 - 4)*(31*z**3 - 61*z**2 - 41*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "279*z**6 - 549*z**5 - 369*z**4 - 124*z**3 + 244*z**2 + 164*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 448, "polynomial_expr": "(9*z**3 - 4)*(31*z**3 - 61*z**2 - 41*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9*z**3 - 4)*(31*z**3 - 61*z**2 - 41*z)\nExpanding the part (9*z**3 - 4) using the distributive property, and we got: (9*z**3)*(31*z**3 - 61*z**2 - 41*z) - 4*(31*z**3 - 61*z**2 - 41*z)\n#Step 2:\nCurrent expression: (9*z**3)*(31*z**3 - 61*z**2 - 41*z) - 4*(31*z**3 - 61*z**2 - 41*z)\nSimplifying the partial expression: -4*(31*z**3 - 61*z**2 - 41*z)\nExpanding the part (31*z**3 - 61*z**2 - 41*z) using the distributive property, and we got: -41*z*(-4) - 61*z**2*(-4) + (31*z**3)*(-4)\nReplacing -4*(31*z**3 - 61*z**2 - 41*z) with -41*z*(-4) - 61*z**2*(-4) + (31*z**3)*(-4) in the overall expression.\n#Step 3:\nCurrent expression: -41*z*(-4) - 61*z**2*(-4) + (9*z**3)*(31*z**3 - 61*z**2 - 41*z) + (31*z**3)*(-4)\nSimplifying the partial expression: (9*z**3)*(31*z**3 - 61*z**2 - 41*z)\nExpanding the part (31*z**3 - 61*z**2 - 41*z) using the distributive property, and we got: (-41*z)*(9*z**3) + (-61*z**2)*(9*z**3) + (9*z**3)*(31*z**3)\nReplacing (9*z**3)*(31*z**3 - 61*z**2 - 41*z) with (-41*z)*(9*z**3) + (-61*z**2)*(9*z**3) + (9*z**3)*(31*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-41*z)*(9*z**3) - 41*z*(-4) + (-61*z**2)*(9*z**3) - 61*z**2*(-4) + (9*z**3)*(31*z**3) + (31*z**3)*(-4)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-61*z**2)*-4 = 244*z**2\n (-61*z**2)*(9*z**3) = -549*z**5\n (-41*z)*-4 = 164*z\n (-41*z)*(9*z**3) = -369*z**4\n (31*z**3)*-4 = -124*z**3\n (31*z**3)*(9*z**3) = 279*z**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 279*z**6 - 549*z**5 - 369*z**4 - 124*z**3 + 244*z**2 + 164*z\nNo more calculations needed.\n279*z**6 - 549*z**5 - 369*z**4 - 124*z**3 + 244*z**2 + 164*z", "generated_answer": "279*z**6 - 549*z**5 - 369*z**4 - 124*z**3 + 244*z**2 + 164*z", "step_length": 5} {"cot_id": "f2ca4f22f8a174848cc878ed7a6e8f546e1dc1fd131044e0994e4d4a940007e6", "datapoint": {"question": "Simplify this expression: (-49*y - 1)*(-24*y**3 - 5*y + 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1176*y**4 + 24*y**3 + 245*y**2 - 1857*y - 38", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 449, "polynomial_expr": "(-49*y - 1)*(-24*y**3 - 5*y + 38)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-49*y - 1)*(-24*y**3 - 5*y + 38)\nExpanding the part (-49*y - 1) using the distributive property, and we got: (-49*y)*(-24*y**3 - 5*y + 38) - (-24*y**3 - 5*y + 38)\n#Step 2:\nCurrent expression: (-49*y)*(-24*y**3 - 5*y + 38) - (-24*y**3 - 5*y + 38)\nSimplifying the partial expression: -(-24*y**3 - 5*y + 38)\nExpanding the part (-24*y**3 - 5*y + 38) using the distributive property, and we got: -5*y*(-1) - 24*y**3*(-1) + 38*(-1)\nReplacing -(-24*y**3 - 5*y + 38) with -5*y*(-1) - 24*y**3*(-1) + 38*(-1) in the overall expression.\n#Step 3:\nCurrent expression: (-49*y)*(-24*y**3 - 5*y + 38) - 5*y*(-1) - 24*y**3*(-1) - 38\nSimplifying the partial expression: (-49*y)*(-24*y**3 - 5*y + 38)\nExpanding the part (-24*y**3 - 5*y + 38) using the distributive property, and we got: (-49*y)*(-5*y) + (-49*y)*(-24*y**3) + 38*(-49*y)\nReplacing (-49*y)*(-24*y**3 - 5*y + 38) with (-49*y)*(-5*y) + (-49*y)*(-24*y**3) + 38*(-49*y) in the overall expression.\n#Step 4:\nCurrent expression: (-49*y)*(-5*y) + (-49*y)*(-24*y**3) - 5*y*(-1) + 38*(-49)*y - 24*y**3*(-1) - 38\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-24*y**3)*-1 = 24*y**3\n (-24*y**3)*(-49*y) = 1176*y**4\n (-5*y)*-1 = 5*y\n (-5*y)*(-49*y) = 245*y**2\n 38*-49*y = -1862*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1176*y**4 + 24*y**3 + 245*y**2 - 1862*y + 5*y - 38\nCombining like terms, got 1176*y**4 + 24*y**3 + 245*y**2 - 1857*y - 38\n#Step 6:\nCurrent expression: 1176*y**4 + 24*y**3 + 245*y**2 - 1857*y - 38\nNo more calculations needed.\n1176*y**4 + 24*y**3 + 245*y**2 - 1857*y - 38", "generated_answer": "1176*y**4 + 24*y**3 + 245*y**2 - 1857*y - 38", "step_length": 6} {"cot_id": "1706545c04c7a64bbb86e8bbaac1d7bcadb489992be1d0ef8ba4258d98e40dd3", "datapoint": {"question": "Calculate the following: (-38*z**3 - 1)*(-4*z**3 + 4*z - 19)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "152*z**6 - 152*z**4 + 726*z**3 - 4*z + 19", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 450, "polynomial_expr": "(-38*z**3 - 1)*(-4*z**3 + 4*z - 19)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-38*z**3 - 1)*(-4*z**3 + 4*z - 19)\nExpanding the part (-38*z**3 - 1) using the distributive property, and we got: (-38*z**3)*(-4*z**3 + 4*z - 19) - (-4*z**3 + 4*z - 19)\n#Step 2:\nCurrent expression: (-38*z**3)*(-4*z**3 + 4*z - 19) - (-4*z**3 + 4*z - 19)\nSimplifying the partial expression: -(-4*z**3 + 4*z - 19)\nExpanding the part (-4*z**3 + 4*z - 19) using the distributive property, and we got: (4*z)*(-1) - 4*z**3*(-1) - 19*(-1)\nReplacing -(-4*z**3 + 4*z - 19) with (4*z)*(-1) - 4*z**3*(-1) - 19*(-1) in the overall expression.\n#Step 3:\nCurrent expression: (4*z)*(-1) + (-38*z**3)*(-4*z**3 + 4*z - 19) - 4*z**3*(-1) + 19\nSimplifying the partial expression: (-38*z**3)*(-4*z**3 + 4*z - 19)\nExpanding the part (-4*z**3 + 4*z - 19) using the distributive property, and we got: -(-1)*722*z**3 + (4*z)*(-38*z**3) + (-38*z**3)*(-4*z**3)\nReplacing (-38*z**3)*(-4*z**3 + 4*z - 19) with -(-1)*722*z**3 + (4*z)*(-38*z**3) + (-38*z**3)*(-4*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -19*(-38)*z**3 + (4*z)*(-38*z**3) + (4*z)*(-1) + (-38*z**3)*(-4*z**3) - 4*z**3*(-1) + 19\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-4*z**3)*-1 = 4*z**3\n (-4*z**3)*(-38*z**3) = 152*z**6\n (4*z)*-1 = -4*z\n (4*z)*(-38*z**3) = -152*z**4\n -19*-38*z**3 = 722*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 152*z**6 - 152*z**4 + 4*z**3 + 722*z**3 - 4*z + 19\nCombining like terms, got 152*z**6 - 152*z**4 + 726*z**3 - 4*z + 19\n#Step 6:\nCurrent expression: 152*z**6 - 152*z**4 + 726*z**3 - 4*z + 19\nNo more calculations needed.\n152*z**6 - 152*z**4 + 726*z**3 - 4*z + 19", "generated_answer": "152*z**6 - 152*z**4 + 726*z**3 - 4*z + 19", "step_length": 6} {"cot_id": "8bf0fa764be31cd4b60f9bebddbd17b0c9d34ef1bb7b34693323653fa5d8a6b0", "datapoint": {"question": "Calculate the following: 20*y*(40*y**3 + 33*y**2 - 58)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "800*y**4 + 660*y**3 - 1160*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 451, "polynomial_expr": "20*y*(40*y**3 + 33*y**2 - 58)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 20*y*(40*y**3 + 33*y**2 - 58)\nExpanding the part (40*y**3 + 33*y**2 - 58) using the distributive property, and we got: -1160*y + (20*y)*(33*y**2) + (20*y)*(40*y**3)\n#Step 2:\nCurrent expression: -1160*y + (20*y)*(33*y**2) + (20*y)*(40*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -58*(20*y) = -1160*y\n (33*y**2)*(20*y) = 660*y**3\n (40*y**3)*(20*y) = 800*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 800*y**4 + 660*y**3 - 1160*y\nNo more calculations needed.\n800*y**4 + 660*y**3 - 1160*y", "generated_answer": "800*y**4 + 660*y**3 - 1160*y", "step_length": 3} {"cot_id": "e5acde4d9b70ee4b863aa76a41830d659964a17ff5c88c3b259e7570c0b2eb7a", "datapoint": {"question": "Calculate the following: 380*z**4\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "380*z**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 452, "polynomial_expr": "380*z**4", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 380*z**4\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 380*z**4\nNo more calculations needed.\n380*z**4", "generated_answer": "380*z**4", "step_length": 2} {"cot_id": "d7f4f0174217c18e759f9adf7846f88c1d605590c43a9334072997867f0860e3", "datapoint": {"question": "Calculate the following: (35*z**3 + 14*z)*(49*z**3 - 2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1715*z**6 + 686*z**4 - 70*z**3 - 28*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 453, "polynomial_expr": "(35*z**3 + 14*z)*(49*z**3 - 2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (35*z**3 + 14*z)*(49*z**3 - 2)\nExpanding the part (49*z**3 - 2) using the distributive property, and we got: (49*z**3)*(35*z**3 + 14*z) - 2*(35*z**3 + 14*z)\n#Step 2:\nCurrent expression: (49*z**3)*(35*z**3 + 14*z) - 2*(35*z**3 + 14*z)\nSimplifying the partial expression: -2*(35*z**3 + 14*z)\nExpanding the part (35*z**3 + 14*z) using the distributive property, and we got: (14*z)*(-2) + (35*z**3)*(-2)\nReplacing -2*(35*z**3 + 14*z) with (14*z)*(-2) + (35*z**3)*(-2) in the overall expression.\n#Step 3:\nCurrent expression: (14*z)*(-2) + (35*z**3)*(-2) + (49*z**3)*(35*z**3 + 14*z)\nSimplifying the partial expression: (49*z**3)*(35*z**3 + 14*z)\nExpanding the part (35*z**3 + 14*z) using the distributive property, and we got: (14*z)*(49*z**3) + (35*z**3)*(49*z**3)\nReplacing (49*z**3)*(35*z**3 + 14*z) with (14*z)*(49*z**3) + (35*z**3)*(49*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (14*z)*(49*z**3) + (14*z)*(-2) + (35*z**3)*(49*z**3) + (35*z**3)*(-2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (14*z)*-2 = -28*z\n (14*z)*(49*z**3) = 686*z**4\n (35*z**3)*-2 = -70*z**3\n (35*z**3)*(49*z**3) = 1715*z**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1715*z**6 + 686*z**4 - 70*z**3 - 28*z\nNo more calculations needed.\n1715*z**6 + 686*z**4 - 70*z**3 - 28*z", "generated_answer": "1715*z**6 + 686*z**4 - 70*z**3 - 28*z", "step_length": 5} {"cot_id": "042dc7f12df98f0d0ef9864daa7f27e28d68fbb7cf4fffd89aacbf4619bcd734", "datapoint": {"question": "Calculate the following: (8*z + 64)*(-45*z**3 - 21*z**2 + 49*z + 15)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-360*z**4 - 3048*z**3 - 952*z**2 + 3256*z + 960", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 454, "polynomial_expr": "(8*z + 64)*(-45*z**3 - 21*z**2 + 49*z + 15)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (8*z + 64)*(-45*z**3 - 21*z**2 + 49*z + 15)\nExpanding the part (8*z + 64) using the distributive property, and we got: (8*z)*(-45*z**3 - 21*z**2 + 49*z + 15) + 64*(-45*z**3 - 21*z**2 + 49*z + 15)\n#Step 2:\nCurrent expression: (8*z)*(-45*z**3 - 21*z**2 + 49*z + 15) + 64*(-45*z**3 - 21*z**2 + 49*z + 15)\nSimplifying the partial expression: 64*(-45*z**3 - 21*z**2 + 49*z + 15)\nExpanding the part (-45*z**3 - 21*z**2 + 49*z + 15) using the distributive property, and we got: (49*z)*64 - 21*z**2*64 - 45*z**3*64 + 15*64\nReplacing 64*(-45*z**3 - 21*z**2 + 49*z + 15) with (49*z)*64 - 21*z**2*64 - 45*z**3*64 + 15*64 in the overall expression.\n#Step 3:\nCurrent expression: (8*z)*(-45*z**3 - 21*z**2 + 49*z + 15) + (49*z)*64 - 21*z**2*64 - 45*z**3*64 + 960\nSimplifying the partial expression: (8*z)*(-45*z**3 - 21*z**2 + 49*z + 15)\nExpanding the part (-45*z**3 - 21*z**2 + 49*z + 15) using the distributive property, and we got: 15*(8*z) + (8*z)*(49*z) + (8*z)*(-21*z**2) + (8*z)*(-45*z**3)\nReplacing (8*z)*(-45*z**3 - 21*z**2 + 49*z + 15) with 15*(8*z) + (8*z)*(49*z) + (8*z)*(-21*z**2) + (8*z)*(-45*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 15*8*z + (8*z)*(49*z) + (8*z)*(-21*z**2) + (8*z)*(-45*z**3) + (49*z)*64 - 21*z**2*64 - 45*z**3*64 + 960\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*z**3)*64 = -2880*z**3\n (-45*z**3)*(8*z) = -360*z**4\n (-21*z**2)*64 = -1344*z**2\n (-21*z**2)*(8*z) = -168*z**3\n (49*z)*64 = 3136*z\n (49*z)*(8*z) = 392*z**2\n 15*8*z = 120*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -360*z**4 - 2880*z**3 - 168*z**3 - 1344*z**2 + 392*z**2 + 120*z + 3136*z + 960\nCombining like terms, got -360*z**4 - 3048*z**3 - 952*z**2 + 3256*z + 960\n#Step 6:\nCurrent expression: -360*z**4 - 3048*z**3 - 952*z**2 + 3256*z + 960\nNo more calculations needed.\n-360*z**4 - 3048*z**3 - 952*z**2 + 3256*z + 960", "generated_answer": "-360*z**4 - 3048*z**3 - 952*z**2 + 3256*z + 960", "step_length": 6} {"cot_id": "2839e1f1bf10f7243a21e9e0e802065346b33098689bbb9576dba06438bcd490", "datapoint": {"question": "Simplify this expression: (-9*y**3 - 7*y**2)*(7*y**3 + 7*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-63*y**6 - 49*y**5 - 63*y**4 - 49*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 455, "polynomial_expr": "(-9*y**3 - 7*y**2)*(7*y**3 + 7*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-9*y**3 - 7*y**2)*(7*y**3 + 7*y)\nExpanding the part (-9*y**3 - 7*y**2) using the distributive property, and we got: (-7*y**2)*(7*y**3 + 7*y) + (-9*y**3)*(7*y**3 + 7*y)\n#Step 2:\nCurrent expression: (-7*y**2)*(7*y**3 + 7*y) + (-9*y**3)*(7*y**3 + 7*y)\nSimplifying the partial expression: (-9*y**3)*(7*y**3 + 7*y)\nExpanding the part (7*y**3 + 7*y) using the distributive property, and we got: (7*y)*(-9*y**3) + (-9*y**3)*(7*y**3)\nReplacing (-9*y**3)*(7*y**3 + 7*y) with (7*y)*(-9*y**3) + (-9*y**3)*(7*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (7*y)*(-9*y**3) + (-7*y**2)*(7*y**3 + 7*y) + (-9*y**3)*(7*y**3)\nSimplifying the partial expression: (-7*y**2)*(7*y**3 + 7*y)\nExpanding the part (7*y**3 + 7*y) using the distributive property, and we got: (7*y)*(-7*y**2) + (-7*y**2)*(7*y**3)\nReplacing (-7*y**2)*(7*y**3 + 7*y) with (7*y)*(-7*y**2) + (-7*y**2)*(7*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (7*y)*(-7*y**2) + (7*y)*(-9*y**3) + (-7*y**2)*(7*y**3) + (-9*y**3)*(7*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (7*y)*(-9*y**3) = -63*y**4\n (7*y)*(-7*y**2) = -49*y**3\n (7*y**3)*(-9*y**3) = -63*y**6\n (7*y**3)*(-7*y**2) = -49*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -63*y**6 - 49*y**5 - 63*y**4 - 49*y**3\nNo more calculations needed.\n-63*y**6 - 49*y**5 - 63*y**4 - 49*y**3", "generated_answer": "-63*y**6 - 49*y**5 - 63*y**4 - 49*y**3", "step_length": 5} {"cot_id": "902a15aba5e020a2b9d19a3f3805ff8ddbfa80c84f56df576a9f51b25b10adc4", "datapoint": {"question": "Simplify this expression: (-45*y**2 - 24)*(25*y**3 + 39*y + 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1125*y**5 - 2355*y**3 - 1260*y**2 - 936*y - 672", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 456, "polynomial_expr": "(-45*y**2 - 24)*(25*y**3 + 39*y + 28)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-45*y**2 - 24)*(25*y**3 + 39*y + 28)\nExpanding the part (-45*y**2 - 24) using the distributive property, and we got: (-45*y**2)*(25*y**3 + 39*y + 28) - 24*(25*y**3 + 39*y + 28)\n#Step 2:\nCurrent expression: (-45*y**2)*(25*y**3 + 39*y + 28) - 24*(25*y**3 + 39*y + 28)\nSimplifying the partial expression: -24*(25*y**3 + 39*y + 28)\nExpanding the part (25*y**3 + 39*y + 28) using the distributive property, and we got: (39*y)*(-24) + (25*y**3)*(-24) + 28*(-24)\nReplacing -24*(25*y**3 + 39*y + 28) with (39*y)*(-24) + (25*y**3)*(-24) + 28*(-24) in the overall expression.\n#Step 3:\nCurrent expression: (39*y)*(-24) + (-45*y**2)*(25*y**3 + 39*y + 28) + (25*y**3)*(-24) - 672\nSimplifying the partial expression: (-45*y**2)*(25*y**3 + 39*y + 28)\nExpanding the part (25*y**3 + 39*y + 28) using the distributive property, and we got: 28*(-45*y**2) + (39*y)*(-45*y**2) + (-45*y**2)*(25*y**3)\nReplacing (-45*y**2)*(25*y**3 + 39*y + 28) with 28*(-45*y**2) + (39*y)*(-45*y**2) + (-45*y**2)*(25*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 28*(-45)*y**2 + (39*y)*(-45*y**2) + (39*y)*(-24) + (-45*y**2)*(25*y**3) + (25*y**3)*(-24) - 672\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (25*y**3)*-24 = -600*y**3\n (25*y**3)*(-45*y**2) = -1125*y**5\n (39*y)*-24 = -936*y\n (39*y)*(-45*y**2) = -1755*y**3\n 28*-45*y**2 = -1260*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1125*y**5 - 1755*y**3 - 600*y**3 - 1260*y**2 - 936*y - 672\nCombining like terms, got -1125*y**5 - 2355*y**3 - 1260*y**2 - 936*y - 672\n#Step 6:\nCurrent expression: -1125*y**5 - 2355*y**3 - 1260*y**2 - 936*y - 672\nNo more calculations needed.\n-1125*y**5 - 2355*y**3 - 1260*y**2 - 936*y - 672", "generated_answer": "-1125*y**5 - 2355*y**3 - 1260*y**2 - 936*y - 672", "step_length": 6} {"cot_id": "9aa8535b7d4754c5b39840a06833bf6ff972ca70907e2e3c5284acd44d75833b", "datapoint": {"question": "Simplify this expression: (29*x**2 + 6)*(-20*x**3 + 20*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-580*x**5 + 580*x**4 - 120*x**3 + 120*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 457, "polynomial_expr": "(29*x**2 + 6)*(-20*x**3 + 20*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29*x**2 + 6)*(-20*x**3 + 20*x**2)\nExpanding the part (29*x**2 + 6) using the distributive property, and we got: (29*x**2)*(-20*x**3 + 20*x**2) + 6*(-20*x**3 + 20*x**2)\n#Step 2:\nCurrent expression: (29*x**2)*(-20*x**3 + 20*x**2) + 6*(-20*x**3 + 20*x**2)\nSimplifying the partial expression: 6*(-20*x**3 + 20*x**2)\nExpanding the part (-20*x**3 + 20*x**2) using the distributive property, and we got: (20*x**2)*6 - 20*x**3*6\nReplacing 6*(-20*x**3 + 20*x**2) with (20*x**2)*6 - 20*x**3*6 in the overall expression.\n#Step 3:\nCurrent expression: (20*x**2)*6 + (29*x**2)*(-20*x**3 + 20*x**2) - 20*x**3*6\nSimplifying the partial expression: (29*x**2)*(-20*x**3 + 20*x**2)\nExpanding the part (-20*x**3 + 20*x**2) using the distributive property, and we got: (20*x**2)*(29*x**2) + (29*x**2)*(-20*x**3)\nReplacing (29*x**2)*(-20*x**3 + 20*x**2) with (20*x**2)*(29*x**2) + (29*x**2)*(-20*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (20*x**2)*(29*x**2) + (20*x**2)*6 + (29*x**2)*(-20*x**3) - 20*x**3*6\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*x**3)*6 = -120*x**3\n (-20*x**3)*(29*x**2) = -580*x**5\n (20*x**2)*6 = 120*x**2\n (20*x**2)*(29*x**2) = 580*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -580*x**5 + 580*x**4 - 120*x**3 + 120*x**2\nNo more calculations needed.\n-580*x**5 + 580*x**4 - 120*x**3 + 120*x**2", "generated_answer": "-580*x**5 + 580*x**4 - 120*x**3 + 120*x**2", "step_length": 5} {"cot_id": "8de6c585d813af53c8d987a3fdb6163df55710d35580e76f845225fe2525a861", "datapoint": {"question": "Calculate the following: (-48*y**3 - 41*y**2 + 7*y)*(-4*y**3 + 15*y**2 - 40*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "192*y**6 - 556*y**5 + 1277*y**4 + 1745*y**3 - 280*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 458, "polynomial_expr": "(-48*y**3 - 41*y**2 + 7*y)*(-4*y**3 + 15*y**2 - 40*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-48*y**3 - 41*y**2 + 7*y)*(-4*y**3 + 15*y**2 - 40*y)\nExpanding the part (-48*y**3 - 41*y**2 + 7*y) using the distributive property, and we got: (7*y)*(-4*y**3 + 15*y**2 - 40*y) + (-41*y**2)*(-4*y**3 + 15*y**2 - 40*y) + (-48*y**3)*(-4*y**3 + 15*y**2 - 40*y)\n#Step 2:\nCurrent expression: (7*y)*(-4*y**3 + 15*y**2 - 40*y) + (-41*y**2)*(-4*y**3 + 15*y**2 - 40*y) + (-48*y**3)*(-4*y**3 + 15*y**2 - 40*y)\nSimplifying the partial expression: (-48*y**3)*(-4*y**3 + 15*y**2 - 40*y)\nExpanding the part (-4*y**3 + 15*y**2 - 40*y) using the distributive property, and we got: (-40*y)*(-48*y**3) + (15*y**2)*(-48*y**3) + (-48*y**3)*(-4*y**3)\nReplacing (-48*y**3)*(-4*y**3 + 15*y**2 - 40*y) with (-40*y)*(-48*y**3) + (15*y**2)*(-48*y**3) + (-48*y**3)*(-4*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-40*y)*(-48*y**3) + (7*y)*(-4*y**3 + 15*y**2 - 40*y) + (-41*y**2)*(-4*y**3 + 15*y**2 - 40*y) + (15*y**2)*(-48*y**3) + (-48*y**3)*(-4*y**3)\nSimplifying the partial expression: (-41*y**2)*(-4*y**3 + 15*y**2 - 40*y)\nExpanding the part (-4*y**3 + 15*y**2 - 40*y) using the distributive property, and we got: (-40*y)*(-41*y**2) + (-41*y**2)*(15*y**2) + (-41*y**2)*(-4*y**3)\nReplacing (-41*y**2)*(-4*y**3 + 15*y**2 - 40*y) with (-40*y)*(-41*y**2) + (-41*y**2)*(15*y**2) + (-41*y**2)*(-4*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-40*y)*(-41*y**2) + (-40*y)*(-48*y**3) + (7*y)*(-4*y**3 + 15*y**2 - 40*y) + (-41*y**2)*(15*y**2) + (-41*y**2)*(-4*y**3) + (15*y**2)*(-48*y**3) + (-48*y**3)*(-4*y**3)\nSimplifying the partial expression: (7*y)*(-4*y**3 + 15*y**2 - 40*y)\nExpanding the part (-4*y**3 + 15*y**2 - 40*y) using the distributive property, and we got: (-40*y)*(7*y) + (7*y)*(15*y**2) + (7*y)*(-4*y**3)\nReplacing (7*y)*(-4*y**3 + 15*y**2 - 40*y) with (-40*y)*(7*y) + (7*y)*(15*y**2) + (7*y)*(-4*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-40*y)*(7*y) + (-40*y)*(-41*y**2) + (-40*y)*(-48*y**3) + (7*y)*(15*y**2) + (7*y)*(-4*y**3) + (-41*y**2)*(15*y**2) + (-41*y**2)*(-4*y**3) + (15*y**2)*(-48*y**3) + (-48*y**3)*(-4*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*y)*(-48*y**3) = 1920*y**4\n (-40*y)*(-41*y**2) = 1640*y**3\n (-40*y)*(7*y) = -280*y**2\n (-4*y**3)*(-48*y**3) = 192*y**6\n (-4*y**3)*(-41*y**2) = 164*y**5\n (-4*y**3)*(7*y) = -28*y**4\n (15*y**2)*(-48*y**3) = -720*y**5\n (15*y**2)*(-41*y**2) = -615*y**4\n (15*y**2)*(7*y) = 105*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 192*y**6 - 720*y**5 + 164*y**5 - 615*y**4 - 28*y**4 + 1920*y**4 + 105*y**3 + 1640*y**3 - 280*y**2\nCombining like terms, got 192*y**6 - 556*y**5 + 1277*y**4 + 1745*y**3 - 280*y**2\n#Step 7:\nCurrent expression: 192*y**6 - 556*y**5 + 1277*y**4 + 1745*y**3 - 280*y**2\nNo more calculations needed.\n192*y**6 - 556*y**5 + 1277*y**4 + 1745*y**3 - 280*y**2", "generated_answer": "192*y**6 - 556*y**5 + 1277*y**4 + 1745*y**3 - 280*y**2", "step_length": 7} {"cot_id": "c2e356057acf2e7e3e1ab3d3b76549e44716b2ac56b4a57dd7b0e93f24fdf32c", "datapoint": {"question": "Simplify this expression: (-47*z**2 + 10*z + 23)*(-30*z**3 - 13*z**2 - 2*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1410*z**5 + 311*z**4 - 726*z**3 - 319*z**2 - 46*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 459, "polynomial_expr": "(-47*z**2 + 10*z + 23)*(-30*z**3 - 13*z**2 - 2*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-47*z**2 + 10*z + 23)*(-30*z**3 - 13*z**2 - 2*z)\nExpanding the part (-47*z**2 + 10*z + 23) using the distributive property, and we got: (10*z)*(-30*z**3 - 13*z**2 - 2*z) + (-47*z**2)*(-30*z**3 - 13*z**2 - 2*z) + 23*(-30*z**3 - 13*z**2 - 2*z)\n#Step 2:\nCurrent expression: (10*z)*(-30*z**3 - 13*z**2 - 2*z) + (-47*z**2)*(-30*z**3 - 13*z**2 - 2*z) + 23*(-30*z**3 - 13*z**2 - 2*z)\nSimplifying the partial expression: 23*(-30*z**3 - 13*z**2 - 2*z)\nExpanding the part (-30*z**3 - 13*z**2 - 2*z) using the distributive property, and we got: -2*z*23 - 13*z**2*23 - 30*z**3*23\nReplacing 23*(-30*z**3 - 13*z**2 - 2*z) with -2*z*23 - 13*z**2*23 - 30*z**3*23 in the overall expression.\n#Step 3:\nCurrent expression: -2*z*23 + (10*z)*(-30*z**3 - 13*z**2 - 2*z) + (-47*z**2)*(-30*z**3 - 13*z**2 - 2*z) - 13*z**2*23 - 30*z**3*23\nSimplifying the partial expression: (-47*z**2)*(-30*z**3 - 13*z**2 - 2*z)\nExpanding the part (-30*z**3 - 13*z**2 - 2*z) using the distributive property, and we got: (-2*z)*(-47*z**2) + (-47*z**2)*(-13*z**2) + (-47*z**2)*(-30*z**3)\nReplacing (-47*z**2)*(-30*z**3 - 13*z**2 - 2*z) with (-2*z)*(-47*z**2) + (-47*z**2)*(-13*z**2) + (-47*z**2)*(-30*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-2*z)*(-47*z**2) - 2*z*23 + (10*z)*(-30*z**3 - 13*z**2 - 2*z) + (-47*z**2)*(-13*z**2) + (-47*z**2)*(-30*z**3) - 13*z**2*23 - 30*z**3*23\nSimplifying the partial expression: (10*z)*(-30*z**3 - 13*z**2 - 2*z)\nExpanding the part (-30*z**3 - 13*z**2 - 2*z) using the distributive property, and we got: (-2*z)*(10*z) + (10*z)*(-13*z**2) + (10*z)*(-30*z**3)\nReplacing (10*z)*(-30*z**3 - 13*z**2 - 2*z) with (-2*z)*(10*z) + (10*z)*(-13*z**2) + (10*z)*(-30*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-2*z)*(10*z) + (-2*z)*(-47*z**2) - 2*z*23 + (10*z)*(-13*z**2) + (10*z)*(-30*z**3) + (-47*z**2)*(-13*z**2) + (-47*z**2)*(-30*z**3) - 13*z**2*23 - 30*z**3*23\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*z**3)*23 = -690*z**3\n (-30*z**3)*(-47*z**2) = 1410*z**5\n (-30*z**3)*(10*z) = -300*z**4\n (-13*z**2)*23 = -299*z**2\n (-13*z**2)*(-47*z**2) = 611*z**4\n (-13*z**2)*(10*z) = -130*z**3\n (-2*z)*23 = -46*z\n (-2*z)*(-47*z**2) = 94*z**3\n (-2*z)*(10*z) = -20*z**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1410*z**5 - 300*z**4 + 611*z**4 - 690*z**3 - 130*z**3 + 94*z**3 - 299*z**2 - 20*z**2 - 46*z\nCombining like terms, got 1410*z**5 + 311*z**4 - 726*z**3 - 319*z**2 - 46*z\n#Step 7:\nCurrent expression: 1410*z**5 + 311*z**4 - 726*z**3 - 319*z**2 - 46*z\nNo more calculations needed.\n1410*z**5 + 311*z**4 - 726*z**3 - 319*z**2 - 46*z", "generated_answer": "1410*z**5 + 311*z**4 - 726*z**3 - 319*z**2 - 46*z", "step_length": 7} {"cot_id": "0e3c645f51aa3ff0e2b1cec51ba14f2ff43dd02bc0fe84bd7925caa57edd785c", "datapoint": {"question": "Simplify this expression: 34*z**3*(41*z + 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1394*z**4 + 1632*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 460, "polynomial_expr": "34*z**3*(41*z + 48)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 34*z**3*(41*z + 48)\nExpanding the part (41*z + 48) using the distributive property, and we got: 48*(34*z**3) + (41*z)*(34*z**3)\n#Step 2:\nCurrent expression: 48*(34*z**3) + (41*z)*(34*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 48*(34*z**3) = 1632*z**3\n (41*z)*(34*z**3) = 1394*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1394*z**4 + 1632*z**3\nNo more calculations needed.\n1394*z**4 + 1632*z**3", "generated_answer": "1394*z**4 + 1632*z**3", "step_length": 3} {"cot_id": "02b73ef5794821fd50b94a46babb2ac9a596dbe883ba230d69292a76b30148aa", "datapoint": {"question": "Calculate the following: (-37*x - 47)*(-48*x**3 + 47*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1776*x**4 + 2256*x**3 - 1739*x**2 - 2209*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 461, "polynomial_expr": "(-37*x - 47)*(-48*x**3 + 47*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-37*x - 47)*(-48*x**3 + 47*x)\nExpanding the part (-37*x - 47) using the distributive property, and we got: (-37*x)*(-48*x**3 + 47*x) - 47*(-48*x**3 + 47*x)\n#Step 2:\nCurrent expression: (-37*x)*(-48*x**3 + 47*x) - 47*(-48*x**3 + 47*x)\nSimplifying the partial expression: -47*(-48*x**3 + 47*x)\nExpanding the part (-48*x**3 + 47*x) using the distributive property, and we got: (47*x)*(-47) - 48*x**3*(-47)\nReplacing -47*(-48*x**3 + 47*x) with (47*x)*(-47) - 48*x**3*(-47) in the overall expression.\n#Step 3:\nCurrent expression: (-37*x)*(-48*x**3 + 47*x) + (47*x)*(-47) - 48*x**3*(-47)\nSimplifying the partial expression: (-37*x)*(-48*x**3 + 47*x)\nExpanding the part (-48*x**3 + 47*x) using the distributive property, and we got: (-37*x)*(47*x) + (-37*x)*(-48*x**3)\nReplacing (-37*x)*(-48*x**3 + 47*x) with (-37*x)*(47*x) + (-37*x)*(-48*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-37*x)*(47*x) + (-37*x)*(-48*x**3) + (47*x)*(-47) - 48*x**3*(-47)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*x**3)*-47 = 2256*x**3\n (-48*x**3)*(-37*x) = 1776*x**4\n (47*x)*-47 = -2209*x\n (47*x)*(-37*x) = -1739*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1776*x**4 + 2256*x**3 - 1739*x**2 - 2209*x\nNo more calculations needed.\n1776*x**4 + 2256*x**3 - 1739*x**2 - 2209*x", "generated_answer": "1776*x**4 + 2256*x**3 - 1739*x**2 - 2209*x", "step_length": 5} {"cot_id": "1eac73a99b18e5f5812e6708c2e98ff6848773c1a311e12ecfed5461dc70678e", "datapoint": {"question": "Calculate the following: (12*y - 49)*(44*y**3 - 16*y**2 - 37*y + 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "528*y**4 - 2348*y**3 + 340*y**2 + 1933*y - 490", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 462, "polynomial_expr": "(12*y - 49)*(44*y**3 - 16*y**2 - 37*y + 10)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (12*y - 49)*(44*y**3 - 16*y**2 - 37*y + 10)\nExpanding the part (12*y - 49) using the distributive property, and we got: (12*y)*(44*y**3 - 16*y**2 - 37*y + 10) - 49*(44*y**3 - 16*y**2 - 37*y + 10)\n#Step 2:\nCurrent expression: (12*y)*(44*y**3 - 16*y**2 - 37*y + 10) - 49*(44*y**3 - 16*y**2 - 37*y + 10)\nSimplifying the partial expression: -49*(44*y**3 - 16*y**2 - 37*y + 10)\nExpanding the part (44*y**3 - 16*y**2 - 37*y + 10) using the distributive property, and we got: -37*y*(-49) - 16*y**2*(-49) + (44*y**3)*(-49) + 10*(-49)\nReplacing -49*(44*y**3 - 16*y**2 - 37*y + 10) with -37*y*(-49) - 16*y**2*(-49) + (44*y**3)*(-49) + 10*(-49) in the overall expression.\n#Step 3:\nCurrent expression: -37*y*(-49) + (12*y)*(44*y**3 - 16*y**2 - 37*y + 10) - 16*y**2*(-49) + (44*y**3)*(-49) - 490\nSimplifying the partial expression: (12*y)*(44*y**3 - 16*y**2 - 37*y + 10)\nExpanding the part (44*y**3 - 16*y**2 - 37*y + 10) using the distributive property, and we got: (-37*y)*(12*y) + 10*(12*y) + (12*y)*(-16*y**2) + (12*y)*(44*y**3)\nReplacing (12*y)*(44*y**3 - 16*y**2 - 37*y + 10) with (-37*y)*(12*y) + 10*(12*y) + (12*y)*(-16*y**2) + (12*y)*(44*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-37*y)*(12*y) - 37*y*(-49) + 10*12*y + (12*y)*(-16*y**2) + (12*y)*(44*y**3) - 16*y**2*(-49) + (44*y**3)*(-49) - 490\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*y)*-49 = 1813*y\n (-37*y)*(12*y) = -444*y**2\n (-16*y**2)*-49 = 784*y**2\n (-16*y**2)*(12*y) = -192*y**3\n (44*y**3)*-49 = -2156*y**3\n (44*y**3)*(12*y) = 528*y**4\n 10*12*y = 120*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 528*y**4 - 2156*y**3 - 192*y**3 - 444*y**2 + 784*y**2 + 120*y + 1813*y - 490\nCombining like terms, got 528*y**4 - 2348*y**3 + 340*y**2 + 1933*y - 490\n#Step 6:\nCurrent expression: 528*y**4 - 2348*y**3 + 340*y**2 + 1933*y - 490\nNo more calculations needed.\n528*y**4 - 2348*y**3 + 340*y**2 + 1933*y - 490", "generated_answer": "528*y**4 - 2348*y**3 + 340*y**2 + 1933*y - 490", "step_length": 6} {"cot_id": "67a4988d178847036625e9174eca224cac59030f03f86cbbbd4c1d5e6635ff26", "datapoint": {"question": "Calculate the following: (40*x**3 - x**2)*(-22*x**3 - 2*x**2 + 61*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-880*x**6 - 58*x**5 + 2442*x**4 - 61*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 463, "polynomial_expr": "(40*x**3 - x**2)*(-22*x**3 - 2*x**2 + 61*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (40*x**3 - x**2)*(-22*x**3 - 2*x**2 + 61*x)\nExpanding the part (40*x**3 - x**2) using the distributive property, and we got: (-x**2)*(-22*x**3 - 2*x**2 + 61*x) + (40*x**3)*(-22*x**3 - 2*x**2 + 61*x)\n#Step 2:\nCurrent expression: (-x**2)*(-22*x**3 - 2*x**2 + 61*x) + (40*x**3)*(-22*x**3 - 2*x**2 + 61*x)\nSimplifying the partial expression: (-x**2)*(-22*x**3 - 2*x**2 + 61*x)\nExpanding the part (-22*x**3 - 2*x**2 + 61*x) using the distributive property, and we got: (61*x)*(-x**2) + (-2*x**2)*(-x**2) + (-x**2)*(-22*x**3)\nReplacing (-x**2)*(-22*x**3 - 2*x**2 + 61*x) with (61*x)*(-x**2) + (-2*x**2)*(-x**2) + (-x**2)*(-22*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (61*x)*(-x**2) + (-2*x**2)*(-x**2) + (-x**2)*(-22*x**3) + (40*x**3)*(-22*x**3 - 2*x**2 + 61*x)\nSimplifying the partial expression: (40*x**3)*(-22*x**3 - 2*x**2 + 61*x)\nExpanding the part (-22*x**3 - 2*x**2 + 61*x) using the distributive property, and we got: (61*x)*(40*x**3) + (-2*x**2)*(40*x**3) + (-22*x**3)*(40*x**3)\nReplacing (40*x**3)*(-22*x**3 - 2*x**2 + 61*x) with (61*x)*(40*x**3) + (-2*x**2)*(40*x**3) + (-22*x**3)*(40*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (61*x)*(-x**2) + (61*x)*(40*x**3) + (-2*x**2)*(-x**2) + (-2*x**2)*(40*x**3) + (-x**2)*(-22*x**3) + (-22*x**3)*(40*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*x**3)*(-x**2) = 22*x**5\n (-22*x**3)*(40*x**3) = -880*x**6\n (-2*x**2)*(-x**2) = 2*x**4\n (-2*x**2)*(40*x**3) = -80*x**5\n (61*x)*(-x**2) = -61*x**3\n (61*x)*(40*x**3) = 2440*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -880*x**6 - 80*x**5 + 22*x**5 + 2*x**4 + 2440*x**4 - 61*x**3\nCombining like terms, got -880*x**6 - 58*x**5 + 2442*x**4 - 61*x**3\n#Step 6:\nCurrent expression: -880*x**6 - 58*x**5 + 2442*x**4 - 61*x**3\nNo more calculations needed.\n-880*x**6 - 58*x**5 + 2442*x**4 - 61*x**3", "generated_answer": "-880*x**6 - 58*x**5 + 2442*x**4 - 61*x**3", "step_length": 6} {"cot_id": "441336a907cf9d9aef7cba3c0131c1c9ad5c88d05683cd334f91841a7fe897f9", "datapoint": {"question": "Simplify this expression: (7*y**3 - 25)*(37*y**2 + 28*y + 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "259*y**5 + 196*y**4 + 112*y**3 - 925*y**2 - 700*y - 400", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 464, "polynomial_expr": "(7*y**3 - 25)*(37*y**2 + 28*y + 16)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7*y**3 - 25)*(37*y**2 + 28*y + 16)\nExpanding the part (7*y**3 - 25) using the distributive property, and we got: (7*y**3)*(37*y**2 + 28*y + 16) - 25*(37*y**2 + 28*y + 16)\n#Step 2:\nCurrent expression: (7*y**3)*(37*y**2 + 28*y + 16) - 25*(37*y**2 + 28*y + 16)\nSimplifying the partial expression: -25*(37*y**2 + 28*y + 16)\nExpanding the part (37*y**2 + 28*y + 16) using the distributive property, and we got: (28*y)*(-25) + (37*y**2)*(-25) + 16*(-25)\nReplacing -25*(37*y**2 + 28*y + 16) with (28*y)*(-25) + (37*y**2)*(-25) + 16*(-25) in the overall expression.\n#Step 3:\nCurrent expression: (28*y)*(-25) + (37*y**2)*(-25) + (7*y**3)*(37*y**2 + 28*y + 16) - 400\nSimplifying the partial expression: (7*y**3)*(37*y**2 + 28*y + 16)\nExpanding the part (37*y**2 + 28*y + 16) using the distributive property, and we got: 16*(7*y**3) + (28*y)*(7*y**3) + (37*y**2)*(7*y**3)\nReplacing (7*y**3)*(37*y**2 + 28*y + 16) with 16*(7*y**3) + (28*y)*(7*y**3) + (37*y**2)*(7*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 16*7*y**3 + (28*y)*(7*y**3) + (28*y)*(-25) + (37*y**2)*(7*y**3) + (37*y**2)*(-25) - 400\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (28*y)*-25 = -700*y\n (28*y)*(7*y**3) = 196*y**4\n (37*y**2)*-25 = -925*y**2\n (37*y**2)*(7*y**3) = 259*y**5\n 16*7*y**3 = 112*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 259*y**5 + 196*y**4 + 112*y**3 - 925*y**2 - 700*y - 400\nNo more calculations needed.\n259*y**5 + 196*y**4 + 112*y**3 - 925*y**2 - 700*y - 400", "generated_answer": "259*y**5 + 196*y**4 + 112*y**3 - 925*y**2 - 700*y - 400", "step_length": 5} {"cot_id": "15cd3b4136ff32ef25ec5ff5f2744f965b1e56ad38ffdcb67a08de00f28546e6", "datapoint": {"question": "Calculate the following: 93 - 1302*y**3\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "93 - 1302*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 465, "polynomial_expr": "93 - 1302*y**3", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 93 - 1302*y**3\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 93 - 1302*y**3\nNo more calculations needed.\n93 - 1302*y**3", "generated_answer": "93 - 1302*y**3", "step_length": 2} {"cot_id": "562a43ba3c050ce1030402cc6e0221c1b2111f0e16d885a667fc81c07902dbd7", "datapoint": {"question": "Simplify this expression: (-48*z**2 - 46*z)*(38*z**3 + 34*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1824*z**5 - 1748*z**4 - 1632*z**3 - 1564*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 466, "polynomial_expr": "(-48*z**2 - 46*z)*(38*z**3 + 34*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-48*z**2 - 46*z)*(38*z**3 + 34*z)\nExpanding the part (-48*z**2 - 46*z) using the distributive property, and we got: (-46*z)*(38*z**3 + 34*z) + (-48*z**2)*(38*z**3 + 34*z)\n#Step 2:\nCurrent expression: (-46*z)*(38*z**3 + 34*z) + (-48*z**2)*(38*z**3 + 34*z)\nSimplifying the partial expression: (-48*z**2)*(38*z**3 + 34*z)\nExpanding the part (38*z**3 + 34*z) using the distributive property, and we got: (34*z)*(-48*z**2) + (-48*z**2)*(38*z**3)\nReplacing (-48*z**2)*(38*z**3 + 34*z) with (34*z)*(-48*z**2) + (-48*z**2)*(38*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-46*z)*(38*z**3 + 34*z) + (34*z)*(-48*z**2) + (-48*z**2)*(38*z**3)\nSimplifying the partial expression: (-46*z)*(38*z**3 + 34*z)\nExpanding the part (38*z**3 + 34*z) using the distributive property, and we got: (-46*z)*(34*z) + (-46*z)*(38*z**3)\nReplacing (-46*z)*(38*z**3 + 34*z) with (-46*z)*(34*z) + (-46*z)*(38*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-46*z)*(34*z) + (-46*z)*(38*z**3) + (34*z)*(-48*z**2) + (-48*z**2)*(38*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (34*z)*(-48*z**2) = -1632*z**3\n (34*z)*(-46*z) = -1564*z**2\n (38*z**3)*(-48*z**2) = -1824*z**5\n (38*z**3)*(-46*z) = -1748*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1824*z**5 - 1748*z**4 - 1632*z**3 - 1564*z**2\nNo more calculations needed.\n-1824*z**5 - 1748*z**4 - 1632*z**3 - 1564*z**2", "generated_answer": "-1824*z**5 - 1748*z**4 - 1632*z**3 - 1564*z**2", "step_length": 5} {"cot_id": "3b7d4e24acf9b42ae2197cd92c5264f71b77f43140a9d2954f48768321250702", "datapoint": {"question": "Calculate the following: (-18*z - 11)*(-21*z**3 - 38*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "378*z**4 + 231*z**3 + 684*z**2 + 418*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 467, "polynomial_expr": "(-18*z - 11)*(-21*z**3 - 38*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-18*z - 11)*(-21*z**3 - 38*z)\nExpanding the part (-18*z - 11) using the distributive property, and we got: (-18*z)*(-21*z**3 - 38*z) - 11*(-21*z**3 - 38*z)\n#Step 2:\nCurrent expression: (-18*z)*(-21*z**3 - 38*z) - 11*(-21*z**3 - 38*z)\nSimplifying the partial expression: -11*(-21*z**3 - 38*z)\nExpanding the part (-21*z**3 - 38*z) using the distributive property, and we got: -38*z*(-11) - 21*z**3*(-11)\nReplacing -11*(-21*z**3 - 38*z) with -38*z*(-11) - 21*z**3*(-11) in the overall expression.\n#Step 3:\nCurrent expression: -38*z*(-11) + (-18*z)*(-21*z**3 - 38*z) - 21*z**3*(-11)\nSimplifying the partial expression: (-18*z)*(-21*z**3 - 38*z)\nExpanding the part (-21*z**3 - 38*z) using the distributive property, and we got: (-38*z)*(-18*z) + (-18*z)*(-21*z**3)\nReplacing (-18*z)*(-21*z**3 - 38*z) with (-38*z)*(-18*z) + (-18*z)*(-21*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-38*z)*(-18*z) - 38*z*(-11) + (-18*z)*(-21*z**3) - 21*z**3*(-11)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*z)*-11 = 418*z\n (-38*z)*(-18*z) = 684*z**2\n (-21*z**3)*-11 = 231*z**3\n (-21*z**3)*(-18*z) = 378*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 378*z**4 + 231*z**3 + 684*z**2 + 418*z\nNo more calculations needed.\n378*z**4 + 231*z**3 + 684*z**2 + 418*z", "generated_answer": "378*z**4 + 231*z**3 + 684*z**2 + 418*z", "step_length": 5} {"cot_id": "8f0d6bcd7816c433b1cbb9c1bcb9e56b384ec2fa04df7bf8166242ac44c22b1e", "datapoint": {"question": "Calculate the following: (24*z - 27)*(27*z**3 + 10*z + 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "648*z**4 - 729*z**3 + 240*z**2 + 714*z - 1107", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 468, "polynomial_expr": "(24*z - 27)*(27*z**3 + 10*z + 41)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (24*z - 27)*(27*z**3 + 10*z + 41)\nExpanding the part (24*z - 27) using the distributive property, and we got: (24*z)*(27*z**3 + 10*z + 41) - 27*(27*z**3 + 10*z + 41)\n#Step 2:\nCurrent expression: (24*z)*(27*z**3 + 10*z + 41) - 27*(27*z**3 + 10*z + 41)\nSimplifying the partial expression: -27*(27*z**3 + 10*z + 41)\nExpanding the part (27*z**3 + 10*z + 41) using the distributive property, and we got: (10*z)*(-27) + (27*z**3)*(-27) + 41*(-27)\nReplacing -27*(27*z**3 + 10*z + 41) with (10*z)*(-27) + (27*z**3)*(-27) + 41*(-27) in the overall expression.\n#Step 3:\nCurrent expression: (10*z)*(-27) + (24*z)*(27*z**3 + 10*z + 41) + (27*z**3)*(-27) - 1107\nSimplifying the partial expression: (24*z)*(27*z**3 + 10*z + 41)\nExpanding the part (27*z**3 + 10*z + 41) using the distributive property, and we got: 41*(24*z) + (10*z)*(24*z) + (24*z)*(27*z**3)\nReplacing (24*z)*(27*z**3 + 10*z + 41) with 41*(24*z) + (10*z)*(24*z) + (24*z)*(27*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 41*24*z + (10*z)*(24*z) + (10*z)*(-27) + (24*z)*(27*z**3) + (27*z**3)*(-27) - 1107\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (10*z)*-27 = -270*z\n (10*z)*(24*z) = 240*z**2\n (27*z**3)*-27 = -729*z**3\n (27*z**3)*(24*z) = 648*z**4\n 41*24*z = 984*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 648*z**4 - 729*z**3 + 240*z**2 - 270*z + 984*z - 1107\nCombining like terms, got 648*z**4 - 729*z**3 + 240*z**2 + 714*z - 1107\n#Step 6:\nCurrent expression: 648*z**4 - 729*z**3 + 240*z**2 + 714*z - 1107\nNo more calculations needed.\n648*z**4 - 729*z**3 + 240*z**2 + 714*z - 1107", "generated_answer": "648*z**4 - 729*z**3 + 240*z**2 + 714*z - 1107", "step_length": 6} {"cot_id": "e785dc2db3f290a04a54256d63b34c434be5cef88b8b99be2b221976b76a7ccf", "datapoint": {"question": "Calculate the following: 1470*x**3 + 70*x**2 + 280*x + 315\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1470*x**3 + 70*x**2 + 280*x + 315", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 469, "polynomial_expr": "1470*x**3 + 70*x**2 + 280*x + 315", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 1470*x**3 + 70*x**2 + 280*x + 315\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 1470*x**3 + 70*x**2 + 280*x + 315\nNo more calculations needed.\n1470*x**3 + 70*x**2 + 280*x + 315", "generated_answer": "1470*x**3 + 70*x**2 + 280*x + 315", "step_length": 2} {"cot_id": "22da0307eb6f1d3b1044b71bf3f5e85a43d16713eb9fa0b5b1fe7540987ff792", "datapoint": {"question": "Calculate the following: 18*x**3*(-48*x - 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-864*x**4 - 288*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 470, "polynomial_expr": "18*x**3*(-48*x - 16)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 18*x**3*(-48*x - 16)\nExpanding the part (-48*x - 16) using the distributive property, and we got: (-48*x)*(18*x**3) - 288*x**3\n#Step 2:\nCurrent expression: (-48*x)*(18*x**3) - 288*x**3\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -16*(18*x**3) = -288*x**3\n (-48*x)*(18*x**3) = -864*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -864*x**4 - 288*x**3\nNo more calculations needed.\n-864*x**4 - 288*x**3", "generated_answer": "-864*x**4 - 288*x**3", "step_length": 3} {"cot_id": "2a0d6ab647d73873f0b440eca3db368b639d324208a82f7f0801c76ac0d123db", "datapoint": {"question": "Calculate the following: (40 - 38*x**2)*(50*x**3 + 37)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1900*x**5 + 2000*x**3 - 1406*x**2 + 1480", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 471, "polynomial_expr": "(40 - 38*x**2)*(50*x**3 + 37)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (40 - 38*x**2)*(50*x**3 + 37)\nExpanding the part (50*x**3 + 37) using the distributive property, and we got: (50*x**3)*(40 - 38*x**2) + 37*(40 - 38*x**2)\n#Step 2:\nCurrent expression: (50*x**3)*(40 - 38*x**2) + 37*(40 - 38*x**2)\nSimplifying the partial expression: 37*(40 - 38*x**2)\nExpanding the part (40 - 38*x**2) using the distributive property, and we got: -38*x**2*37 + 40*37\nReplacing 37*(40 - 38*x**2) with -38*x**2*37 + 40*37 in the overall expression.\n#Step 3:\nCurrent expression: -38*x**2*37 + (50*x**3)*(40 - 38*x**2) + 1480\nSimplifying the partial expression: (50*x**3)*(40 - 38*x**2)\nExpanding the part (40 - 38*x**2) using the distributive property, and we got: 40*(50*x**3) + (-38*x**2)*(50*x**3)\nReplacing (50*x**3)*(40 - 38*x**2) with 40*(50*x**3) + (-38*x**2)*(50*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 40*50*x**3 + (-38*x**2)*(50*x**3) - 38*x**2*37 + 1480\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*x**2)*37 = -1406*x**2\n (-38*x**2)*(50*x**3) = -1900*x**5\n 40*50*x**3 = 2000*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1900*x**5 + 2000*x**3 - 1406*x**2 + 1480\nNo more calculations needed.\n-1900*x**5 + 2000*x**3 - 1406*x**2 + 1480", "generated_answer": "-1900*x**5 + 2000*x**3 - 1406*x**2 + 1480", "step_length": 5} {"cot_id": "0f9c2379292711126c2668152dc2551cdc6c93e57510cab7034d68a1a09ea8f5", "datapoint": {"question": "Simplify this expression: (44*y**3 - 7*y)*(21*y**2 - 64*y - 42)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "924*y**5 - 2816*y**4 - 1995*y**3 + 448*y**2 + 294*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 472, "polynomial_expr": "(44*y**3 - 7*y)*(21*y**2 - 64*y - 42)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (44*y**3 - 7*y)*(21*y**2 - 64*y - 42)\nExpanding the part (44*y**3 - 7*y) using the distributive property, and we got: (-7*y)*(21*y**2 - 64*y - 42) + (44*y**3)*(21*y**2 - 64*y - 42)\n#Step 2:\nCurrent expression: (-7*y)*(21*y**2 - 64*y - 42) + (44*y**3)*(21*y**2 - 64*y - 42)\nSimplifying the partial expression: (-7*y)*(21*y**2 - 64*y - 42)\nExpanding the part (21*y**2 - 64*y - 42) using the distributive property, and we got: (-64*y)*(-7*y) + (-7*y)*(21*y**2) - (-1)*294*y\nReplacing (-7*y)*(21*y**2 - 64*y - 42) with (-64*y)*(-7*y) + (-7*y)*(21*y**2) - (-1)*294*y in the overall expression.\n#Step 3:\nCurrent expression: (-64*y)*(-7*y) + (-7*y)*(21*y**2) - 42*(-7)*y + (44*y**3)*(21*y**2 - 64*y - 42)\nSimplifying the partial expression: (44*y**3)*(21*y**2 - 64*y - 42)\nExpanding the part (21*y**2 - 64*y - 42) using the distributive property, and we got: (-64*y)*(44*y**3) - 1848*y**3 + (21*y**2)*(44*y**3)\nReplacing (44*y**3)*(21*y**2 - 64*y - 42) with (-64*y)*(44*y**3) - 1848*y**3 + (21*y**2)*(44*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-64*y)*(-7*y) + (-64*y)*(44*y**3) + (-7*y)*(21*y**2) - 42*44*y**3 - 42*(-7)*y + (21*y**2)*(44*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-64*y)*(-7*y) = 448*y**2\n (-64*y)*(44*y**3) = -2816*y**4\n (21*y**2)*(-7*y) = -147*y**3\n (21*y**2)*(44*y**3) = 924*y**5\n -42*-7*y = 294*y\n -42*44*y**3 = -1848*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 924*y**5 - 2816*y**4 - 1848*y**3 - 147*y**3 + 448*y**2 + 294*y\nCombining like terms, got 924*y**5 - 2816*y**4 - 1995*y**3 + 448*y**2 + 294*y\n#Step 6:\nCurrent expression: 924*y**5 - 2816*y**4 - 1995*y**3 + 448*y**2 + 294*y\nNo more calculations needed.\n924*y**5 - 2816*y**4 - 1995*y**3 + 448*y**2 + 294*y", "generated_answer": "924*y**5 - 2816*y**4 - 1995*y**3 + 448*y**2 + 294*y", "step_length": 6} {"cot_id": "f79c2ef4e52e98ce894488ee8137b44cb1a742ca641d3b8d3df53c03d8f5bb95", "datapoint": {"question": "Simplify this expression: 11*x**3*(x**3 + 42*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "11*x**6 + 462*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 473, "polynomial_expr": "11*x**3*(x**3 + 42*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 11*x**3*(x**3 + 42*x)\nExpanding the part (x**3 + 42*x) using the distributive property, and we got: x**3*(11*x**3) + (42*x)*(11*x**3)\n#Step 2:\nCurrent expression: x**3*(11*x**3) + (42*x)*(11*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n x**3*(11*x**3) = 11*x**6\n (42*x)*(11*x**3) = 462*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 11*x**6 + 462*x**4\nNo more calculations needed.\n11*x**6 + 462*x**4", "generated_answer": "11*x**6 + 462*x**4", "step_length": 3} {"cot_id": "b59f9854b9c1d46912c9c02827a98837ae4ad6df3bc46b97c50d95dcc0a18cd3", "datapoint": {"question": "Calculate the following: (-50*z**3 - 62*z)*(-10*z**3 - 6*z**2 - 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "500*z**6 + 300*z**5 + 620*z**4 + 672*z**3 + 372*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 474, "polynomial_expr": "(-50*z**3 - 62*z)*(-10*z**3 - 6*z**2 - 6)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-50*z**3 - 62*z)*(-10*z**3 - 6*z**2 - 6)\nExpanding the part (-50*z**3 - 62*z) using the distributive property, and we got: (-62*z)*(-10*z**3 - 6*z**2 - 6) + (-50*z**3)*(-10*z**3 - 6*z**2 - 6)\n#Step 2:\nCurrent expression: (-62*z)*(-10*z**3 - 6*z**2 - 6) + (-50*z**3)*(-10*z**3 - 6*z**2 - 6)\nSimplifying the partial expression: (-62*z)*(-10*z**3 - 6*z**2 - 6)\nExpanding the part (-10*z**3 - 6*z**2 - 6) using the distributive property, and we got: (-62*z)*(-6*z**2) + (-62*z)*(-10*z**3) - (-1)*372*z\nReplacing (-62*z)*(-10*z**3 - 6*z**2 - 6) with (-62*z)*(-6*z**2) + (-62*z)*(-10*z**3) - (-1)*372*z in the overall expression.\n#Step 3:\nCurrent expression: (-62*z)*(-6*z**2) + (-62*z)*(-10*z**3) - 6*(-62)*z + (-50*z**3)*(-10*z**3 - 6*z**2 - 6)\nSimplifying the partial expression: (-50*z**3)*(-10*z**3 - 6*z**2 - 6)\nExpanding the part (-10*z**3 - 6*z**2 - 6) using the distributive property, and we got: -(-1)*300*z**3 + (-6*z**2)*(-50*z**3) + (-50*z**3)*(-10*z**3)\nReplacing (-50*z**3)*(-10*z**3 - 6*z**2 - 6) with -(-1)*300*z**3 + (-6*z**2)*(-50*z**3) + (-50*z**3)*(-10*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-62*z)*(-6*z**2) + (-62*z)*(-10*z**3) - 6*(-50)*z**3 - 6*(-62)*z + (-6*z**2)*(-50*z**3) + (-50*z**3)*(-10*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*z**3)*(-62*z) = 620*z**4\n (-10*z**3)*(-50*z**3) = 500*z**6\n (-6*z**2)*(-62*z) = 372*z**3\n (-6*z**2)*(-50*z**3) = 300*z**5\n -6*-62*z = 372*z\n -6*-50*z**3 = 300*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 500*z**6 + 300*z**5 + 620*z**4 + 300*z**3 + 372*z**3 + 372*z\nCombining like terms, got 500*z**6 + 300*z**5 + 620*z**4 + 672*z**3 + 372*z\n#Step 6:\nCurrent expression: 500*z**6 + 300*z**5 + 620*z**4 + 672*z**3 + 372*z\nNo more calculations needed.\n500*z**6 + 300*z**5 + 620*z**4 + 672*z**3 + 372*z", "generated_answer": "500*z**6 + 300*z**5 + 620*z**4 + 672*z**3 + 372*z", "step_length": 6} {"cot_id": "dc11ef65fbe2a57cfc8c357f12a01573ef04d1005dee1f023255eb1aded0db80", "datapoint": {"question": "Calculate the following: (49*y**2 + 32*y)*(51*y**3 - 26*y**2 + 33*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2499*y**5 + 358*y**4 + 785*y**3 + 1056*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 475, "polynomial_expr": "(49*y**2 + 32*y)*(51*y**3 - 26*y**2 + 33*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (49*y**2 + 32*y)*(51*y**3 - 26*y**2 + 33*y)\nExpanding the part (49*y**2 + 32*y) using the distributive property, and we got: (32*y)*(51*y**3 - 26*y**2 + 33*y) + (49*y**2)*(51*y**3 - 26*y**2 + 33*y)\n#Step 2:\nCurrent expression: (32*y)*(51*y**3 - 26*y**2 + 33*y) + (49*y**2)*(51*y**3 - 26*y**2 + 33*y)\nSimplifying the partial expression: (32*y)*(51*y**3 - 26*y**2 + 33*y)\nExpanding the part (51*y**3 - 26*y**2 + 33*y) using the distributive property, and we got: (32*y)*(33*y) + (32*y)*(-26*y**2) + (32*y)*(51*y**3)\nReplacing (32*y)*(51*y**3 - 26*y**2 + 33*y) with (32*y)*(33*y) + (32*y)*(-26*y**2) + (32*y)*(51*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (32*y)*(33*y) + (32*y)*(-26*y**2) + (32*y)*(51*y**3) + (49*y**2)*(51*y**3 - 26*y**2 + 33*y)\nSimplifying the partial expression: (49*y**2)*(51*y**3 - 26*y**2 + 33*y)\nExpanding the part (51*y**3 - 26*y**2 + 33*y) using the distributive property, and we got: (33*y)*(49*y**2) + (-26*y**2)*(49*y**2) + (49*y**2)*(51*y**3)\nReplacing (49*y**2)*(51*y**3 - 26*y**2 + 33*y) with (33*y)*(49*y**2) + (-26*y**2)*(49*y**2) + (49*y**2)*(51*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (32*y)*(33*y) + (32*y)*(-26*y**2) + (32*y)*(51*y**3) + (33*y)*(49*y**2) + (-26*y**2)*(49*y**2) + (49*y**2)*(51*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-26*y**2)*(32*y) = -832*y**3\n (-26*y**2)*(49*y**2) = -1274*y**4\n (33*y)*(32*y) = 1056*y**2\n (33*y)*(49*y**2) = 1617*y**3\n (51*y**3)*(32*y) = 1632*y**4\n (51*y**3)*(49*y**2) = 2499*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2499*y**5 - 1274*y**4 + 1632*y**4 - 832*y**3 + 1617*y**3 + 1056*y**2\nCombining like terms, got 2499*y**5 + 358*y**4 + 785*y**3 + 1056*y**2\n#Step 6:\nCurrent expression: 2499*y**5 + 358*y**4 + 785*y**3 + 1056*y**2\nNo more calculations needed.\n2499*y**5 + 358*y**4 + 785*y**3 + 1056*y**2", "generated_answer": "2499*y**5 + 358*y**4 + 785*y**3 + 1056*y**2", "step_length": 6} {"cot_id": "031fc6f6fcbd5596f3eef670d1735abe98b76f565fc1160447496e2e0c7607eb", "datapoint": {"question": "Calculate the following: (13*y**2 + 37*y)*(-37*y**3 - 35*y**2 - 9*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-481*y**5 - 1824*y**4 - 1412*y**3 - 333*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 476, "polynomial_expr": "(13*y**2 + 37*y)*(-37*y**3 - 35*y**2 - 9*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (13*y**2 + 37*y)*(-37*y**3 - 35*y**2 - 9*y)\nExpanding the part (13*y**2 + 37*y) using the distributive property, and we got: (37*y)*(-37*y**3 - 35*y**2 - 9*y) + (13*y**2)*(-37*y**3 - 35*y**2 - 9*y)\n#Step 2:\nCurrent expression: (37*y)*(-37*y**3 - 35*y**2 - 9*y) + (13*y**2)*(-37*y**3 - 35*y**2 - 9*y)\nSimplifying the partial expression: (13*y**2)*(-37*y**3 - 35*y**2 - 9*y)\nExpanding the part (-37*y**3 - 35*y**2 - 9*y) using the distributive property, and we got: (-9*y)*(13*y**2) + (-35*y**2)*(13*y**2) + (13*y**2)*(-37*y**3)\nReplacing (13*y**2)*(-37*y**3 - 35*y**2 - 9*y) with (-9*y)*(13*y**2) + (-35*y**2)*(13*y**2) + (13*y**2)*(-37*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-9*y)*(13*y**2) + (37*y)*(-37*y**3 - 35*y**2 - 9*y) + (-35*y**2)*(13*y**2) + (13*y**2)*(-37*y**3)\nSimplifying the partial expression: (37*y)*(-37*y**3 - 35*y**2 - 9*y)\nExpanding the part (-37*y**3 - 35*y**2 - 9*y) using the distributive property, and we got: (-9*y)*(37*y) + (37*y)*(-35*y**2) + (37*y)*(-37*y**3)\nReplacing (37*y)*(-37*y**3 - 35*y**2 - 9*y) with (-9*y)*(37*y) + (37*y)*(-35*y**2) + (37*y)*(-37*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-9*y)*(37*y) + (-9*y)*(13*y**2) + (37*y)*(-35*y**2) + (37*y)*(-37*y**3) + (-35*y**2)*(13*y**2) + (13*y**2)*(-37*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*y**3)*(13*y**2) = -481*y**5\n (-37*y**3)*(37*y) = -1369*y**4\n (-35*y**2)*(13*y**2) = -455*y**4\n (-35*y**2)*(37*y) = -1295*y**3\n (-9*y)*(13*y**2) = -117*y**3\n (-9*y)*(37*y) = -333*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -481*y**5 - 1369*y**4 - 455*y**4 - 1295*y**3 - 117*y**3 - 333*y**2\nCombining like terms, got -481*y**5 - 1824*y**4 - 1412*y**3 - 333*y**2\n#Step 6:\nCurrent expression: -481*y**5 - 1824*y**4 - 1412*y**3 - 333*y**2\nNo more calculations needed.\n-481*y**5 - 1824*y**4 - 1412*y**3 - 333*y**2", "generated_answer": "-481*y**5 - 1824*y**4 - 1412*y**3 - 333*y**2", "step_length": 6} {"cot_id": "fbc8ca214037cfa3672eda1ec0a47a0f7d6d867b30c2edc0e7957cb3ccc2bc1b", "datapoint": {"question": "Simplify this expression: 280*z**3 + 644*z**2 - 350\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "280*z**3 + 644*z**2 - 350", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 477, "polynomial_expr": "280*z**3 + 644*z**2 - 350", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 280*z**3 + 644*z**2 - 350\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 280*z**3 + 644*z**2 - 350\nNo more calculations needed.\n280*z**3 + 644*z**2 - 350", "generated_answer": "280*z**3 + 644*z**2 - 350", "step_length": 2} {"cot_id": "d183704b33a5148c7e58a1ebe7517f75d8c74b948d7922e34b9ffbb067098bbe", "datapoint": {"question": "Calculate the following: (-17*x - 50)*(33*x**3 - 26)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-561*x**4 - 1650*x**3 + 442*x + 1300", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 478, "polynomial_expr": "(-17*x - 50)*(33*x**3 - 26)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-17*x - 50)*(33*x**3 - 26)\nExpanding the part (-17*x - 50) using the distributive property, and we got: (-17*x)*(33*x**3 - 26) - 50*(33*x**3 - 26)\n#Step 2:\nCurrent expression: (-17*x)*(33*x**3 - 26) - 50*(33*x**3 - 26)\nSimplifying the partial expression: -50*(33*x**3 - 26)\nExpanding the part (33*x**3 - 26) using the distributive property, and we got: (33*x**3)*(-50) - 26*(-50)\nReplacing -50*(33*x**3 - 26) with (33*x**3)*(-50) - 26*(-50) in the overall expression.\n#Step 3:\nCurrent expression: (-17*x)*(33*x**3 - 26) + (33*x**3)*(-50) + 1300\nSimplifying the partial expression: (-17*x)*(33*x**3 - 26)\nExpanding the part (33*x**3 - 26) using the distributive property, and we got: (-17*x)*(33*x**3) - (-1)*442*x\nReplacing (-17*x)*(33*x**3 - 26) with (-17*x)*(33*x**3) - (-1)*442*x in the overall expression.\n#Step 4:\nCurrent expression: (-17*x)*(33*x**3) - 26*(-17)*x + (33*x**3)*(-50) + 1300\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (33*x**3)*-50 = -1650*x**3\n (33*x**3)*(-17*x) = -561*x**4\n -26*-17*x = 442*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -561*x**4 - 1650*x**3 + 442*x + 1300\nNo more calculations needed.\n-561*x**4 - 1650*x**3 + 442*x + 1300", "generated_answer": "-561*x**4 - 1650*x**3 + 442*x + 1300", "step_length": 5} {"cot_id": "5f7c310138d40f2212f2106f4d5e6ab9e8132c54cae8379ebca6845b9a2d41c1", "datapoint": {"question": "Calculate the following: (3*x**3 + 18*x**2 - 22)*(17*x**3 + 23*x + 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "51*x**6 + 306*x**5 + 69*x**4 + 190*x**3 + 900*x**2 - 506*x - 1100", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 479, "polynomial_expr": "(3*x**3 + 18*x**2 - 22)*(17*x**3 + 23*x + 50)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (3*x**3 + 18*x**2 - 22)*(17*x**3 + 23*x + 50)\nExpanding the part (3*x**3 + 18*x**2 - 22) using the distributive property, and we got: (18*x**2)*(17*x**3 + 23*x + 50) + (3*x**3)*(17*x**3 + 23*x + 50) - 22*(17*x**3 + 23*x + 50)\n#Step 2:\nCurrent expression: (18*x**2)*(17*x**3 + 23*x + 50) + (3*x**3)*(17*x**3 + 23*x + 50) - 22*(17*x**3 + 23*x + 50)\nSimplifying the partial expression: -22*(17*x**3 + 23*x + 50)\nExpanding the part (17*x**3 + 23*x + 50) using the distributive property, and we got: (23*x)*(-22) + (17*x**3)*(-22) + 50*(-22)\nReplacing -22*(17*x**3 + 23*x + 50) with (23*x)*(-22) + (17*x**3)*(-22) + 50*(-22) in the overall expression.\n#Step 3:\nCurrent expression: (23*x)*(-22) + (18*x**2)*(17*x**3 + 23*x + 50) + (3*x**3)*(17*x**3 + 23*x + 50) + (17*x**3)*(-22) - 1100\nSimplifying the partial expression: (3*x**3)*(17*x**3 + 23*x + 50)\nExpanding the part (17*x**3 + 23*x + 50) using the distributive property, and we got: 50*(3*x**3) + (23*x)*(3*x**3) + (3*x**3)*(17*x**3)\nReplacing (3*x**3)*(17*x**3 + 23*x + 50) with 50*(3*x**3) + (23*x)*(3*x**3) + (3*x**3)*(17*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 50*3*x**3 + (23*x)*(3*x**3) + (23*x)*(-22) + (18*x**2)*(17*x**3 + 23*x + 50) + (3*x**3)*(17*x**3) + (17*x**3)*(-22) - 1100\nSimplifying the partial expression: (18*x**2)*(17*x**3 + 23*x + 50)\nExpanding the part (17*x**3 + 23*x + 50) using the distributive property, and we got: 50*(18*x**2) + (23*x)*(18*x**2) + (18*x**2)*(17*x**3)\nReplacing (18*x**2)*(17*x**3 + 23*x + 50) with 50*(18*x**2) + (23*x)*(18*x**2) + (18*x**2)*(17*x**3) in the overall expression.\n#Step 5:\nCurrent expression: 50*3*x**3 + 50*18*x**2 + (23*x)*(18*x**2) + (23*x)*(3*x**3) + (23*x)*(-22) + (18*x**2)*(17*x**3) + (3*x**3)*(17*x**3) + (17*x**3)*(-22) - 1100\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (17*x**3)*-22 = -374*x**3\n (17*x**3)*(3*x**3) = 51*x**6\n (17*x**3)*(18*x**2) = 306*x**5\n (23*x)*-22 = -506*x\n (23*x)*(3*x**3) = 69*x**4\n (23*x)*(18*x**2) = 414*x**3\n 50*3*x**3 = 150*x**3\n 50*18*x**2 = 900*x**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 51*x**6 + 306*x**5 + 69*x**4 - 374*x**3 + 150*x**3 + 414*x**3 + 900*x**2 - 506*x - 1100\nCombining like terms, got 51*x**6 + 306*x**5 + 69*x**4 + 190*x**3 + 900*x**2 - 506*x - 1100\n#Step 7:\nCurrent expression: 51*x**6 + 306*x**5 + 69*x**4 + 190*x**3 + 900*x**2 - 506*x - 1100\nNo more calculations needed.\n51*x**6 + 306*x**5 + 69*x**4 + 190*x**3 + 900*x**2 - 506*x - 1100", "generated_answer": "51*x**6 + 306*x**5 + 69*x**4 + 190*x**3 + 900*x**2 - 506*x - 1100", "step_length": 7} {"cot_id": "a7115d2e74a75f52e98b29dc5d8e30f639bbff7f7259e0c3ec138ae6ca567684", "datapoint": {"question": "Calculate the following: (6 - 2*x)*(16*x**3 + 37*x**2 - 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-32*x**4 + 22*x**3 + 222*x**2 + 62*x - 186", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 480, "polynomial_expr": "(6 - 2*x)*(16*x**3 + 37*x**2 - 31)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6 - 2*x)*(16*x**3 + 37*x**2 - 31)\nExpanding the part (6 - 2*x) using the distributive property, and we got: (-2*x)*(16*x**3 + 37*x**2 - 31) + 6*(16*x**3 + 37*x**2 - 31)\n#Step 2:\nCurrent expression: (-2*x)*(16*x**3 + 37*x**2 - 31) + 6*(16*x**3 + 37*x**2 - 31)\nSimplifying the partial expression: 6*(16*x**3 + 37*x**2 - 31)\nExpanding the part (16*x**3 + 37*x**2 - 31) using the distributive property, and we got: (37*x**2)*6 + (16*x**3)*6 - 31*6\nReplacing 6*(16*x**3 + 37*x**2 - 31) with (37*x**2)*6 + (16*x**3)*6 - 31*6 in the overall expression.\n#Step 3:\nCurrent expression: (-2*x)*(16*x**3 + 37*x**2 - 31) + (37*x**2)*6 + (16*x**3)*6 - 186\nSimplifying the partial expression: (-2*x)*(16*x**3 + 37*x**2 - 31)\nExpanding the part (16*x**3 + 37*x**2 - 31) using the distributive property, and we got: (-2*x)*(37*x**2) + (-2*x)*(16*x**3) - (-1)*62*x\nReplacing (-2*x)*(16*x**3 + 37*x**2 - 31) with (-2*x)*(37*x**2) + (-2*x)*(16*x**3) - (-1)*62*x in the overall expression.\n#Step 4:\nCurrent expression: (-2*x)*(37*x**2) + (-2*x)*(16*x**3) - 31*(-2)*x + (37*x**2)*6 + (16*x**3)*6 - 186\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (16*x**3)*6 = 96*x**3\n (16*x**3)*(-2*x) = -32*x**4\n (37*x**2)*6 = 222*x**2\n (37*x**2)*(-2*x) = -74*x**3\n -31*-2*x = 62*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -32*x**4 - 74*x**3 + 96*x**3 + 222*x**2 + 62*x - 186\nCombining like terms, got -32*x**4 + 22*x**3 + 222*x**2 + 62*x - 186\n#Step 6:\nCurrent expression: -32*x**4 + 22*x**3 + 222*x**2 + 62*x - 186\nNo more calculations needed.\n-32*x**4 + 22*x**3 + 222*x**2 + 62*x - 186", "generated_answer": "-32*x**4 + 22*x**3 + 222*x**2 + 62*x - 186", "step_length": 6} {"cot_id": "2b1d5f8de96a06660acdc0b71e3d1d7a5c85bfb2013c17d0f675ffd036421bc0", "datapoint": {"question": "Calculate the following: 1584*z**3 - 2904*z**2 + 1100\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1584*z**3 - 2904*z**2 + 1100", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 481, "polynomial_expr": "1584*z**3 - 2904*z**2 + 1100", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 1584*z**3 - 2904*z**2 + 1100\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 1584*z**3 - 2904*z**2 + 1100\nNo more calculations needed.\n1584*z**3 - 2904*z**2 + 1100", "generated_answer": "1584*z**3 - 2904*z**2 + 1100", "step_length": 2} {"cot_id": "b6a4359a6c468d6e4e2297e0aba751323bd1f94e80841d4eb4df10ba2a0ac903", "datapoint": {"question": "Calculate the following: (-x**2 - 37)*(-18*x**3 - 30*x**2 - 6*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "18*x**5 + 30*x**4 + 672*x**3 + 1110*x**2 + 222*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 482, "polynomial_expr": "(-x**2 - 37)*(-18*x**3 - 30*x**2 - 6*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-x**2 - 37)*(-18*x**3 - 30*x**2 - 6*x)\nExpanding the part (-x**2 - 37) using the distributive property, and we got: (-x**2)*(-18*x**3 - 30*x**2 - 6*x) - 37*(-18*x**3 - 30*x**2 - 6*x)\n#Step 2:\nCurrent expression: (-x**2)*(-18*x**3 - 30*x**2 - 6*x) - 37*(-18*x**3 - 30*x**2 - 6*x)\nSimplifying the partial expression: -37*(-18*x**3 - 30*x**2 - 6*x)\nExpanding the part (-18*x**3 - 30*x**2 - 6*x) using the distributive property, and we got: -6*x*(-37) - 30*x**2*(-37) - 18*x**3*(-37)\nReplacing -37*(-18*x**3 - 30*x**2 - 6*x) with -6*x*(-37) - 30*x**2*(-37) - 18*x**3*(-37) in the overall expression.\n#Step 3:\nCurrent expression: -6*x*(-37) - 30*x**2*(-37) + (-x**2)*(-18*x**3 - 30*x**2 - 6*x) - 18*x**3*(-37)\nSimplifying the partial expression: (-x**2)*(-18*x**3 - 30*x**2 - 6*x)\nExpanding the part (-18*x**3 - 30*x**2 - 6*x) using the distributive property, and we got: (-6*x)*(-x**2) + (-30*x**2)*(-x**2) + (-x**2)*(-18*x**3)\nReplacing (-x**2)*(-18*x**3 - 30*x**2 - 6*x) with (-6*x)*(-x**2) + (-30*x**2)*(-x**2) + (-x**2)*(-18*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-6*x)*(-x**2) - 6*x*(-37) + (-30*x**2)*(-x**2) - 30*x**2*(-37) + (-x**2)*(-18*x**3) - 18*x**3*(-37)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*x**2)*-37 = 1110*x**2\n (-30*x**2)*(-x**2) = 30*x**4\n (-18*x**3)*-37 = 666*x**3\n (-18*x**3)*(-x**2) = 18*x**5\n (-6*x)*-37 = 222*x\n (-6*x)*(-x**2) = 6*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 18*x**5 + 30*x**4 + 6*x**3 + 666*x**3 + 1110*x**2 + 222*x\nCombining like terms, got 18*x**5 + 30*x**4 + 672*x**3 + 1110*x**2 + 222*x\n#Step 6:\nCurrent expression: 18*x**5 + 30*x**4 + 672*x**3 + 1110*x**2 + 222*x\nNo more calculations needed.\n18*x**5 + 30*x**4 + 672*x**3 + 1110*x**2 + 222*x", "generated_answer": "18*x**5 + 30*x**4 + 672*x**3 + 1110*x**2 + 222*x", "step_length": 6} {"cot_id": "d252a5d91c681fa4f135bdc019606f699e98e2198f726535d6da9e7f570d7078", "datapoint": {"question": "Simplify this expression: (29 - 50*z**2)*(35*z**3 + 10*z + 11)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1750*z**5 + 515*z**3 - 550*z**2 + 290*z + 319", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 483, "polynomial_expr": "(29 - 50*z**2)*(35*z**3 + 10*z + 11)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29 - 50*z**2)*(35*z**3 + 10*z + 11)\nExpanding the part (29 - 50*z**2) using the distributive property, and we got: (-50*z**2)*(35*z**3 + 10*z + 11) + 29*(35*z**3 + 10*z + 11)\n#Step 2:\nCurrent expression: (-50*z**2)*(35*z**3 + 10*z + 11) + 29*(35*z**3 + 10*z + 11)\nSimplifying the partial expression: 29*(35*z**3 + 10*z + 11)\nExpanding the part (35*z**3 + 10*z + 11) using the distributive property, and we got: (10*z)*29 + (35*z**3)*29 + 11*29\nReplacing 29*(35*z**3 + 10*z + 11) with (10*z)*29 + (35*z**3)*29 + 11*29 in the overall expression.\n#Step 3:\nCurrent expression: (10*z)*29 + (-50*z**2)*(35*z**3 + 10*z + 11) + (35*z**3)*29 + 319\nSimplifying the partial expression: (-50*z**2)*(35*z**3 + 10*z + 11)\nExpanding the part (35*z**3 + 10*z + 11) using the distributive property, and we got: 11*(-50*z**2) + (10*z)*(-50*z**2) + (-50*z**2)*(35*z**3)\nReplacing (-50*z**2)*(35*z**3 + 10*z + 11) with 11*(-50*z**2) + (10*z)*(-50*z**2) + (-50*z**2)*(35*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 11*(-50)*z**2 + (10*z)*(-50*z**2) + (10*z)*29 + (-50*z**2)*(35*z**3) + (35*z**3)*29 + 319\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (10*z)*29 = 290*z\n (10*z)*(-50*z**2) = -500*z**3\n (35*z**3)*29 = 1015*z**3\n (35*z**3)*(-50*z**2) = -1750*z**5\n 11*-50*z**2 = -550*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1750*z**5 - 500*z**3 + 1015*z**3 - 550*z**2 + 290*z + 319\nCombining like terms, got -1750*z**5 + 515*z**3 - 550*z**2 + 290*z + 319\n#Step 6:\nCurrent expression: -1750*z**5 + 515*z**3 - 550*z**2 + 290*z + 319\nNo more calculations needed.\n-1750*z**5 + 515*z**3 - 550*z**2 + 290*z + 319", "generated_answer": "-1750*z**5 + 515*z**3 - 550*z**2 + 290*z + 319", "step_length": 6} {"cot_id": "1e1c839d851f834afac58dacced26467a8e986d8ebdcaa50aa56377baf947a45", "datapoint": {"question": "Simplify this expression: (16*x**2 + 3)*(26*x**3 - 4*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "416*x**5 - 64*x**4 + 78*x**3 - 12*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 484, "polynomial_expr": "(16*x**2 + 3)*(26*x**3 - 4*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (16*x**2 + 3)*(26*x**3 - 4*x**2)\nExpanding the part (16*x**2 + 3) using the distributive property, and we got: (16*x**2)*(26*x**3 - 4*x**2) + 3*(26*x**3 - 4*x**2)\n#Step 2:\nCurrent expression: (16*x**2)*(26*x**3 - 4*x**2) + 3*(26*x**3 - 4*x**2)\nSimplifying the partial expression: 3*(26*x**3 - 4*x**2)\nExpanding the part (26*x**3 - 4*x**2) using the distributive property, and we got: -4*x**2*3 + (26*x**3)*3\nReplacing 3*(26*x**3 - 4*x**2) with -4*x**2*3 + (26*x**3)*3 in the overall expression.\n#Step 3:\nCurrent expression: -4*x**2*3 + (16*x**2)*(26*x**3 - 4*x**2) + (26*x**3)*3\nSimplifying the partial expression: (16*x**2)*(26*x**3 - 4*x**2)\nExpanding the part (26*x**3 - 4*x**2) using the distributive property, and we got: (-4*x**2)*(16*x**2) + (16*x**2)*(26*x**3)\nReplacing (16*x**2)*(26*x**3 - 4*x**2) with (-4*x**2)*(16*x**2) + (16*x**2)*(26*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-4*x**2)*(16*x**2) - 4*x**2*3 + (16*x**2)*(26*x**3) + (26*x**3)*3\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-4*x**2)*3 = -12*x**2\n (-4*x**2)*(16*x**2) = -64*x**4\n (26*x**3)*3 = 78*x**3\n (26*x**3)*(16*x**2) = 416*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 416*x**5 - 64*x**4 + 78*x**3 - 12*x**2\nNo more calculations needed.\n416*x**5 - 64*x**4 + 78*x**3 - 12*x**2", "generated_answer": "416*x**5 - 64*x**4 + 78*x**3 - 12*x**2", "step_length": 5} {"cot_id": "fa284ebea854330f5c4ece1f492361cbad85aa69b6bad9d342d463262e9ca794", "datapoint": {"question": "Simplify this expression: (-24*y**3 + 85*y**2 + 23)*(3*y**3 + 64*y - 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-72*y**6 + 255*y**5 - 1536*y**4 + 6685*y**3 - 4165*y**2 + 1472*y - 1127", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 485, "polynomial_expr": "(-24*y**3 + 85*y**2 + 23)*(3*y**3 + 64*y - 49)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-24*y**3 + 85*y**2 + 23)*(3*y**3 + 64*y - 49)\nExpanding the part (3*y**3 + 64*y - 49) using the distributive property, and we got: (64*y)*(-24*y**3 + 85*y**2 + 23) + (3*y**3)*(-24*y**3 + 85*y**2 + 23) - 49*(-24*y**3 + 85*y**2 + 23)\n#Step 2:\nCurrent expression: (64*y)*(-24*y**3 + 85*y**2 + 23) + (3*y**3)*(-24*y**3 + 85*y**2 + 23) - 49*(-24*y**3 + 85*y**2 + 23)\nSimplifying the partial expression: -49*(-24*y**3 + 85*y**2 + 23)\nExpanding the part (-24*y**3 + 85*y**2 + 23) using the distributive property, and we got: (85*y**2)*(-49) - 24*y**3*(-49) + 23*(-49)\nReplacing -49*(-24*y**3 + 85*y**2 + 23) with (85*y**2)*(-49) - 24*y**3*(-49) + 23*(-49) in the overall expression.\n#Step 3:\nCurrent expression: (64*y)*(-24*y**3 + 85*y**2 + 23) + (85*y**2)*(-49) - 24*y**3*(-49) + (3*y**3)*(-24*y**3 + 85*y**2 + 23) - 1127\nSimplifying the partial expression: (3*y**3)*(-24*y**3 + 85*y**2 + 23)\nExpanding the part (-24*y**3 + 85*y**2 + 23) using the distributive property, and we got: 23*(3*y**3) + (85*y**2)*(3*y**3) + (-24*y**3)*(3*y**3)\nReplacing (3*y**3)*(-24*y**3 + 85*y**2 + 23) with 23*(3*y**3) + (85*y**2)*(3*y**3) + (-24*y**3)*(3*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 23*3*y**3 + (64*y)*(-24*y**3 + 85*y**2 + 23) + (85*y**2)*(3*y**3) + (85*y**2)*(-49) + (-24*y**3)*(3*y**3) - 24*y**3*(-49) - 1127\nSimplifying the partial expression: (64*y)*(-24*y**3 + 85*y**2 + 23)\nExpanding the part (-24*y**3 + 85*y**2 + 23) using the distributive property, and we got: 23*(64*y) + (64*y)*(85*y**2) + (64*y)*(-24*y**3)\nReplacing (64*y)*(-24*y**3 + 85*y**2 + 23) with 23*(64*y) + (64*y)*(85*y**2) + (64*y)*(-24*y**3) in the overall expression.\n#Step 5:\nCurrent expression: 23*3*y**3 + 23*64*y + (64*y)*(85*y**2) + (64*y)*(-24*y**3) + (85*y**2)*(3*y**3) + (85*y**2)*(-49) + (-24*y**3)*(3*y**3) - 24*y**3*(-49) - 1127\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-24*y**3)*-49 = 1176*y**3\n (-24*y**3)*(3*y**3) = -72*y**6\n (-24*y**3)*(64*y) = -1536*y**4\n (85*y**2)*-49 = -4165*y**2\n (85*y**2)*(3*y**3) = 255*y**5\n (85*y**2)*(64*y) = 5440*y**3\n 23*3*y**3 = 69*y**3\n 23*64*y = 1472*y\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -72*y**6 + 255*y**5 - 1536*y**4 + 69*y**3 + 1176*y**3 + 5440*y**3 - 4165*y**2 + 1472*y - 1127\nCombining like terms, got -72*y**6 + 255*y**5 - 1536*y**4 + 6685*y**3 - 4165*y**2 + 1472*y - 1127\n#Step 7:\nCurrent expression: -72*y**6 + 255*y**5 - 1536*y**4 + 6685*y**3 - 4165*y**2 + 1472*y - 1127\nNo more calculations needed.\n-72*y**6 + 255*y**5 - 1536*y**4 + 6685*y**3 - 4165*y**2 + 1472*y - 1127", "generated_answer": "-72*y**6 + 255*y**5 - 1536*y**4 + 6685*y**3 - 4165*y**2 + 1472*y - 1127", "step_length": 7} {"cot_id": "cb861e1c245d44604d1f4a3eb48355a5f78bb669fe7bea0cf17e72e76a3f0fc8", "datapoint": {"question": "Simplify this expression: (-12*x**3 - 10)*(31*x**3 + 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-372*x**6 - 766*x**3 - 380", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 486, "polynomial_expr": "(-12*x**3 - 10)*(31*x**3 + 38)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-12*x**3 - 10)*(31*x**3 + 38)\nExpanding the part (-12*x**3 - 10) using the distributive property, and we got: (-12*x**3)*(31*x**3 + 38) - 10*(31*x**3 + 38)\n#Step 2:\nCurrent expression: (-12*x**3)*(31*x**3 + 38) - 10*(31*x**3 + 38)\nSimplifying the partial expression: -10*(31*x**3 + 38)\nExpanding the part (31*x**3 + 38) using the distributive property, and we got: (31*x**3)*(-10) + 38*(-10)\nReplacing -10*(31*x**3 + 38) with (31*x**3)*(-10) + 38*(-10) in the overall expression.\n#Step 3:\nCurrent expression: (-12*x**3)*(31*x**3 + 38) + (31*x**3)*(-10) - 380\nSimplifying the partial expression: (-12*x**3)*(31*x**3 + 38)\nExpanding the part (31*x**3 + 38) using the distributive property, and we got: 38*(-12*x**3) + (-12*x**3)*(31*x**3)\nReplacing (-12*x**3)*(31*x**3 + 38) with 38*(-12*x**3) + (-12*x**3)*(31*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 38*(-12)*x**3 + (-12*x**3)*(31*x**3) + (31*x**3)*(-10) - 380\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (31*x**3)*-10 = -310*x**3\n (31*x**3)*(-12*x**3) = -372*x**6\n 38*-12*x**3 = -456*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -372*x**6 - 456*x**3 - 310*x**3 - 380\nCombining like terms, got -372*x**6 - 766*x**3 - 380\n#Step 6:\nCurrent expression: -372*x**6 - 766*x**3 - 380\nNo more calculations needed.\n-372*x**6 - 766*x**3 - 380", "generated_answer": "-372*x**6 - 766*x**3 - 380", "step_length": 6} {"cot_id": "746968b610d3b4a252d7212480159b8d68c63e3d83e27cb2816fb042309987b2", "datapoint": {"question": "Calculate the following: (38*z**2 - 11*z)*(71*z**2 + 78)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2698*z**4 - 781*z**3 + 2964*z**2 - 858*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 487, "polynomial_expr": "(38*z**2 - 11*z)*(71*z**2 + 78)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (38*z**2 - 11*z)*(71*z**2 + 78)\nExpanding the part (71*z**2 + 78) using the distributive property, and we got: (71*z**2)*(38*z**2 - 11*z) + 78*(38*z**2 - 11*z)\n#Step 2:\nCurrent expression: (71*z**2)*(38*z**2 - 11*z) + 78*(38*z**2 - 11*z)\nSimplifying the partial expression: 78*(38*z**2 - 11*z)\nExpanding the part (38*z**2 - 11*z) using the distributive property, and we got: -11*z*78 + (38*z**2)*78\nReplacing 78*(38*z**2 - 11*z) with -11*z*78 + (38*z**2)*78 in the overall expression.\n#Step 3:\nCurrent expression: -11*z*78 + (38*z**2)*78 + (71*z**2)*(38*z**2 - 11*z)\nSimplifying the partial expression: (71*z**2)*(38*z**2 - 11*z)\nExpanding the part (38*z**2 - 11*z) using the distributive property, and we got: (-11*z)*(71*z**2) + (38*z**2)*(71*z**2)\nReplacing (71*z**2)*(38*z**2 - 11*z) with (-11*z)*(71*z**2) + (38*z**2)*(71*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-11*z)*(71*z**2) - 11*z*78 + (38*z**2)*(71*z**2) + (38*z**2)*78\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*z)*78 = -858*z\n (-11*z)*(71*z**2) = -781*z**3\n (38*z**2)*78 = 2964*z**2\n (38*z**2)*(71*z**2) = 2698*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2698*z**4 - 781*z**3 + 2964*z**2 - 858*z\nNo more calculations needed.\n2698*z**4 - 781*z**3 + 2964*z**2 - 858*z", "generated_answer": "2698*z**4 - 781*z**3 + 2964*z**2 - 858*z", "step_length": 5} {"cot_id": "282ea3774f947269ad6674a08573abff2289e4f081bb5f3d7fb9852ac85ab196", "datapoint": {"question": "Simplify this expression: (11*y**2 - 53*y)*(32*y**3 + 41*y + 11)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "352*y**5 - 1696*y**4 + 451*y**3 - 2052*y**2 - 583*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 488, "polynomial_expr": "(11*y**2 - 53*y)*(32*y**3 + 41*y + 11)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11*y**2 - 53*y)*(32*y**3 + 41*y + 11)\nExpanding the part (11*y**2 - 53*y) using the distributive property, and we got: (-53*y)*(32*y**3 + 41*y + 11) + (11*y**2)*(32*y**3 + 41*y + 11)\n#Step 2:\nCurrent expression: (-53*y)*(32*y**3 + 41*y + 11) + (11*y**2)*(32*y**3 + 41*y + 11)\nSimplifying the partial expression: (-53*y)*(32*y**3 + 41*y + 11)\nExpanding the part (32*y**3 + 41*y + 11) using the distributive property, and we got: (-53*y)*(41*y) + (-53*y)*(32*y**3) + 11*(-53*y)\nReplacing (-53*y)*(32*y**3 + 41*y + 11) with (-53*y)*(41*y) + (-53*y)*(32*y**3) + 11*(-53*y) in the overall expression.\n#Step 3:\nCurrent expression: (-53*y)*(41*y) + (-53*y)*(32*y**3) + 11*(-53)*y + (11*y**2)*(32*y**3 + 41*y + 11)\nSimplifying the partial expression: (11*y**2)*(32*y**3 + 41*y + 11)\nExpanding the part (32*y**3 + 41*y + 11) using the distributive property, and we got: 11*(11*y**2) + (41*y)*(11*y**2) + (11*y**2)*(32*y**3)\nReplacing (11*y**2)*(32*y**3 + 41*y + 11) with 11*(11*y**2) + (41*y)*(11*y**2) + (11*y**2)*(32*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-53*y)*(41*y) + (-53*y)*(32*y**3) + 11*11*y**2 + 11*(-53)*y + (41*y)*(11*y**2) + (11*y**2)*(32*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (32*y**3)*(-53*y) = -1696*y**4\n (32*y**3)*(11*y**2) = 352*y**5\n (41*y)*(-53*y) = -2173*y**2\n (41*y)*(11*y**2) = 451*y**3\n 11*-53*y = -583*y\n 11*11*y**2 = 121*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 352*y**5 - 1696*y**4 + 451*y**3 - 2173*y**2 + 121*y**2 - 583*y\nCombining like terms, got 352*y**5 - 1696*y**4 + 451*y**3 - 2052*y**2 - 583*y\n#Step 6:\nCurrent expression: 352*y**5 - 1696*y**4 + 451*y**3 - 2052*y**2 - 583*y\nNo more calculations needed.\n352*y**5 - 1696*y**4 + 451*y**3 - 2052*y**2 - 583*y", "generated_answer": "352*y**5 - 1696*y**4 + 451*y**3 - 2052*y**2 - 583*y", "step_length": 6} {"cot_id": "4a2f5588f431a86d81025a5b5966b61b6de7b6d891c6b212d4017fb3fb49e3d6", "datapoint": {"question": "Calculate the following: (-44*z**3 - 37*z - 40)*(-3*z**3 + 26*z**2 - 45*z + 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "132*z**6 - 1144*z**5 + 2091*z**4 - 1282*z**3 + 625*z**2 + 1430*z - 400", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 489, "polynomial_expr": "(-44*z**3 - 37*z - 40)*(-3*z**3 + 26*z**2 - 45*z + 10)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-44*z**3 - 37*z - 40)*(-3*z**3 + 26*z**2 - 45*z + 10)\nExpanding the part (-44*z**3 - 37*z - 40) using the distributive property, and we got: (-37*z)*(-3*z**3 + 26*z**2 - 45*z + 10) + (-44*z**3)*(-3*z**3 + 26*z**2 - 45*z + 10) - 40*(-3*z**3 + 26*z**2 - 45*z + 10)\n#Step 2:\nCurrent expression: (-37*z)*(-3*z**3 + 26*z**2 - 45*z + 10) + (-44*z**3)*(-3*z**3 + 26*z**2 - 45*z + 10) - 40*(-3*z**3 + 26*z**2 - 45*z + 10)\nSimplifying the partial expression: -40*(-3*z**3 + 26*z**2 - 45*z + 10)\nExpanding the part (-3*z**3 + 26*z**2 - 45*z + 10) using the distributive property, and we got: -45*z*(-40) + (26*z**2)*(-40) - 3*z**3*(-40) + 10*(-40)\nReplacing -40*(-3*z**3 + 26*z**2 - 45*z + 10) with -45*z*(-40) + (26*z**2)*(-40) - 3*z**3*(-40) + 10*(-40) in the overall expression.\n#Step 3:\nCurrent expression: -45*z*(-40) + (-37*z)*(-3*z**3 + 26*z**2 - 45*z + 10) + (26*z**2)*(-40) + (-44*z**3)*(-3*z**3 + 26*z**2 - 45*z + 10) - 3*z**3*(-40) - 400\nSimplifying the partial expression: (-44*z**3)*(-3*z**3 + 26*z**2 - 45*z + 10)\nExpanding the part (-3*z**3 + 26*z**2 - 45*z + 10) using the distributive property, and we got: (-45*z)*(-44*z**3) + 10*(-44*z**3) + (26*z**2)*(-44*z**3) + (-44*z**3)*(-3*z**3)\nReplacing (-44*z**3)*(-3*z**3 + 26*z**2 - 45*z + 10) with (-45*z)*(-44*z**3) + 10*(-44*z**3) + (26*z**2)*(-44*z**3) + (-44*z**3)*(-3*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-45*z)*(-44*z**3) - 45*z*(-40) + (-37*z)*(-3*z**3 + 26*z**2 - 45*z + 10) + 10*(-44)*z**3 + (26*z**2)*(-44*z**3) + (26*z**2)*(-40) + (-44*z**3)*(-3*z**3) - 3*z**3*(-40) - 400\nSimplifying the partial expression: (-37*z)*(-3*z**3 + 26*z**2 - 45*z + 10)\nExpanding the part (-3*z**3 + 26*z**2 - 45*z + 10) using the distributive property, and we got: (-45*z)*(-37*z) + (-37*z)*(26*z**2) + (-37*z)*(-3*z**3) + 10*(-37*z)\nReplacing (-37*z)*(-3*z**3 + 26*z**2 - 45*z + 10) with (-45*z)*(-37*z) + (-37*z)*(26*z**2) + (-37*z)*(-3*z**3) + 10*(-37*z) in the overall expression.\n#Step 5:\nCurrent expression: (-45*z)*(-37*z) + (-45*z)*(-44*z**3) - 45*z*(-40) + (-37*z)*(26*z**2) + (-37*z)*(-3*z**3) + 10*(-44)*z**3 + 10*(-37)*z + (26*z**2)*(-44*z**3) + (26*z**2)*(-40) + (-44*z**3)*(-3*z**3) - 3*z**3*(-40) - 400\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*z)*-40 = 1800*z\n (-45*z)*(-44*z**3) = 1980*z**4\n (-45*z)*(-37*z) = 1665*z**2\n (-3*z**3)*-40 = 120*z**3\n (-3*z**3)*(-44*z**3) = 132*z**6\n (-3*z**3)*(-37*z) = 111*z**4\n (26*z**2)*-40 = -1040*z**2\n (26*z**2)*(-44*z**3) = -1144*z**5\n (26*z**2)*(-37*z) = -962*z**3\n 10*-44*z**3 = -440*z**3\n 10*-37*z = -370*z\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 132*z**6 - 1144*z**5 + 111*z**4 + 1980*z**4 - 962*z**3 - 440*z**3 + 120*z**3 - 1040*z**2 + 1665*z**2 - 370*z + 1800*z - 400\nCombining like terms, got 132*z**6 - 1144*z**5 + 2091*z**4 - 1282*z**3 + 625*z**2 + 1430*z - 400\n#Step 7:\nCurrent expression: 132*z**6 - 1144*z**5 + 2091*z**4 - 1282*z**3 + 625*z**2 + 1430*z - 400\nNo more calculations needed.\n132*z**6 - 1144*z**5 + 2091*z**4 - 1282*z**3 + 625*z**2 + 1430*z - 400", "generated_answer": "132*z**6 - 1144*z**5 + 2091*z**4 - 1282*z**3 + 625*z**2 + 1430*z - 400", "step_length": 7} {"cot_id": "148806983b78924b4cfe4238e41af2bba1e910e375b7f54e3c2f4063e28be53a", "datapoint": {"question": "Calculate the following: (23*x**2 - 12)*(32*x**2 - 42*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "736*x**4 - 966*x**3 - 384*x**2 + 504*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 490, "polynomial_expr": "(23*x**2 - 12)*(32*x**2 - 42*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (23*x**2 - 12)*(32*x**2 - 42*x)\nExpanding the part (23*x**2 - 12) using the distributive property, and we got: (23*x**2)*(32*x**2 - 42*x) - 12*(32*x**2 - 42*x)\n#Step 2:\nCurrent expression: (23*x**2)*(32*x**2 - 42*x) - 12*(32*x**2 - 42*x)\nSimplifying the partial expression: -12*(32*x**2 - 42*x)\nExpanding the part (32*x**2 - 42*x) using the distributive property, and we got: -42*x*(-12) + (32*x**2)*(-12)\nReplacing -12*(32*x**2 - 42*x) with -42*x*(-12) + (32*x**2)*(-12) in the overall expression.\n#Step 3:\nCurrent expression: -42*x*(-12) + (23*x**2)*(32*x**2 - 42*x) + (32*x**2)*(-12)\nSimplifying the partial expression: (23*x**2)*(32*x**2 - 42*x)\nExpanding the part (32*x**2 - 42*x) using the distributive property, and we got: (-42*x)*(23*x**2) + (23*x**2)*(32*x**2)\nReplacing (23*x**2)*(32*x**2 - 42*x) with (-42*x)*(23*x**2) + (23*x**2)*(32*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-42*x)*(23*x**2) - 42*x*(-12) + (23*x**2)*(32*x**2) + (32*x**2)*(-12)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*x)*-12 = 504*x\n (-42*x)*(23*x**2) = -966*x**3\n (32*x**2)*-12 = -384*x**2\n (32*x**2)*(23*x**2) = 736*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 736*x**4 - 966*x**3 - 384*x**2 + 504*x\nNo more calculations needed.\n736*x**4 - 966*x**3 - 384*x**2 + 504*x", "generated_answer": "736*x**4 - 966*x**3 - 384*x**2 + 504*x", "step_length": 5} {"cot_id": "c2676535272663a4ed35214f25c21a2706ce3779fc032b39bed7df69cd140c24", "datapoint": {"question": "Calculate the following: (33 - 20*y**3)*(-52*y**3 + 24*y + 19)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1040*y**6 - 480*y**4 - 2096*y**3 + 792*y + 627", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 491, "polynomial_expr": "(33 - 20*y**3)*(-52*y**3 + 24*y + 19)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (33 - 20*y**3)*(-52*y**3 + 24*y + 19)\nExpanding the part (33 - 20*y**3) using the distributive property, and we got: (-20*y**3)*(-52*y**3 + 24*y + 19) + 33*(-52*y**3 + 24*y + 19)\n#Step 2:\nCurrent expression: (-20*y**3)*(-52*y**3 + 24*y + 19) + 33*(-52*y**3 + 24*y + 19)\nSimplifying the partial expression: 33*(-52*y**3 + 24*y + 19)\nExpanding the part (-52*y**3 + 24*y + 19) using the distributive property, and we got: (24*y)*33 - 52*y**3*33 + 19*33\nReplacing 33*(-52*y**3 + 24*y + 19) with (24*y)*33 - 52*y**3*33 + 19*33 in the overall expression.\n#Step 3:\nCurrent expression: (24*y)*33 - 52*y**3*33 + (-20*y**3)*(-52*y**3 + 24*y + 19) + 627\nSimplifying the partial expression: (-20*y**3)*(-52*y**3 + 24*y + 19)\nExpanding the part (-52*y**3 + 24*y + 19) using the distributive property, and we got: 19*(-20*y**3) + (24*y)*(-20*y**3) + (-52*y**3)*(-20*y**3)\nReplacing (-20*y**3)*(-52*y**3 + 24*y + 19) with 19*(-20*y**3) + (24*y)*(-20*y**3) + (-52*y**3)*(-20*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 19*(-20)*y**3 + (24*y)*(-20*y**3) + (24*y)*33 + (-52*y**3)*(-20*y**3) - 52*y**3*33 + 627\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-52*y**3)*33 = -1716*y**3\n (-52*y**3)*(-20*y**3) = 1040*y**6\n (24*y)*33 = 792*y\n (24*y)*(-20*y**3) = -480*y**4\n 19*-20*y**3 = -380*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1040*y**6 - 480*y**4 - 1716*y**3 - 380*y**3 + 792*y + 627\nCombining like terms, got 1040*y**6 - 480*y**4 - 2096*y**3 + 792*y + 627\n#Step 6:\nCurrent expression: 1040*y**6 - 480*y**4 - 2096*y**3 + 792*y + 627\nNo more calculations needed.\n1040*y**6 - 480*y**4 - 2096*y**3 + 792*y + 627", "generated_answer": "1040*y**6 - 480*y**4 - 2096*y**3 + 792*y + 627", "step_length": 6} {"cot_id": "2dff7b8d68be792a05a7d17b042b77c9153479ac394f57c18599f0676a187a00", "datapoint": {"question": "Simplify this expression: (-6*y**2 - 12*y)*(-28*y**3 - 12*y - 34)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "168*y**5 + 336*y**4 + 72*y**3 + 348*y**2 + 408*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 492, "polynomial_expr": "(-6*y**2 - 12*y)*(-28*y**3 - 12*y - 34)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-6*y**2 - 12*y)*(-28*y**3 - 12*y - 34)\nExpanding the part (-6*y**2 - 12*y) using the distributive property, and we got: (-12*y)*(-28*y**3 - 12*y - 34) + (-6*y**2)*(-28*y**3 - 12*y - 34)\n#Step 2:\nCurrent expression: (-12*y)*(-28*y**3 - 12*y - 34) + (-6*y**2)*(-28*y**3 - 12*y - 34)\nSimplifying the partial expression: (-12*y)*(-28*y**3 - 12*y - 34)\nExpanding the part (-28*y**3 - 12*y - 34) using the distributive property, and we got: (-12*y)*(-28*y**3) + (-12*y)*(-12*y) - (-1)*408*y\nReplacing (-12*y)*(-28*y**3 - 12*y - 34) with (-12*y)*(-28*y**3) + (-12*y)*(-12*y) - (-1)*408*y in the overall expression.\n#Step 3:\nCurrent expression: (-12*y)*(-28*y**3) + (-12*y)*(-12*y) - 34*(-12)*y + (-6*y**2)*(-28*y**3 - 12*y - 34)\nSimplifying the partial expression: (-6*y**2)*(-28*y**3 - 12*y - 34)\nExpanding the part (-28*y**3 - 12*y - 34) using the distributive property, and we got: (-12*y)*(-6*y**2) - (-1)*204*y**2 + (-6*y**2)*(-28*y**3)\nReplacing (-6*y**2)*(-28*y**3 - 12*y - 34) with (-12*y)*(-6*y**2) - (-1)*204*y**2 + (-6*y**2)*(-28*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-12*y)*(-6*y**2) + (-12*y)*(-28*y**3) + (-12*y)*(-12*y) - 34*(-6)*y**2 - 34*(-12)*y + (-6*y**2)*(-28*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*y**3)*(-12*y) = 336*y**4\n (-28*y**3)*(-6*y**2) = 168*y**5\n (-12*y)*(-12*y) = 144*y**2\n (-12*y)*(-6*y**2) = 72*y**3\n -34*-12*y = 408*y\n -34*-6*y**2 = 204*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 168*y**5 + 336*y**4 + 72*y**3 + 144*y**2 + 204*y**2 + 408*y\nCombining like terms, got 168*y**5 + 336*y**4 + 72*y**3 + 348*y**2 + 408*y\n#Step 6:\nCurrent expression: 168*y**5 + 336*y**4 + 72*y**3 + 348*y**2 + 408*y\nNo more calculations needed.\n168*y**5 + 336*y**4 + 72*y**3 + 348*y**2 + 408*y", "generated_answer": "168*y**5 + 336*y**4 + 72*y**3 + 348*y**2 + 408*y", "step_length": 6} {"cot_id": "a0f6766d968f7985c83712ed6272ce0c04e3aa36445984fe06d53b9bb5376d65", "datapoint": {"question": "Calculate the following: (-34*x**3 + 15*x)*(12*x**3 + 45*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-408*x**6 - 1350*x**4 + 675*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 493, "polynomial_expr": "(-34*x**3 + 15*x)*(12*x**3 + 45*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-34*x**3 + 15*x)*(12*x**3 + 45*x)\nExpanding the part (-34*x**3 + 15*x) using the distributive property, and we got: (15*x)*(12*x**3 + 45*x) + (-34*x**3)*(12*x**3 + 45*x)\n#Step 2:\nCurrent expression: (15*x)*(12*x**3 + 45*x) + (-34*x**3)*(12*x**3 + 45*x)\nSimplifying the partial expression: (-34*x**3)*(12*x**3 + 45*x)\nExpanding the part (12*x**3 + 45*x) using the distributive property, and we got: (45*x)*(-34*x**3) + (-34*x**3)*(12*x**3)\nReplacing (-34*x**3)*(12*x**3 + 45*x) with (45*x)*(-34*x**3) + (-34*x**3)*(12*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (15*x)*(12*x**3 + 45*x) + (45*x)*(-34*x**3) + (-34*x**3)*(12*x**3)\nSimplifying the partial expression: (15*x)*(12*x**3 + 45*x)\nExpanding the part (12*x**3 + 45*x) using the distributive property, and we got: (15*x)*(45*x) + (15*x)*(12*x**3)\nReplacing (15*x)*(12*x**3 + 45*x) with (15*x)*(45*x) + (15*x)*(12*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (15*x)*(45*x) + (15*x)*(12*x**3) + (45*x)*(-34*x**3) + (-34*x**3)*(12*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (12*x**3)*(-34*x**3) = -408*x**6\n (12*x**3)*(15*x) = 180*x**4\n (45*x)*(-34*x**3) = -1530*x**4\n (45*x)*(15*x) = 675*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -408*x**6 - 1530*x**4 + 180*x**4 + 675*x**2\nCombining like terms, got -408*x**6 - 1350*x**4 + 675*x**2\n#Step 6:\nCurrent expression: -408*x**6 - 1350*x**4 + 675*x**2\nNo more calculations needed.\n-408*x**6 - 1350*x**4 + 675*x**2", "generated_answer": "-408*x**6 - 1350*x**4 + 675*x**2", "step_length": 6} {"cot_id": "6829da0729735731c8cd0dc28220d55217c506bf1428d97468ad8b3d0c79c637", "datapoint": {"question": "Simplify this expression: (35*z**3 - 44*z**2)*(-25*z**3 + 36*z**2 - 50*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-875*z**6 + 2360*z**5 - 3334*z**4 + 2200*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 494, "polynomial_expr": "(35*z**3 - 44*z**2)*(-25*z**3 + 36*z**2 - 50*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (35*z**3 - 44*z**2)*(-25*z**3 + 36*z**2 - 50*z)\nExpanding the part (35*z**3 - 44*z**2) using the distributive property, and we got: (-44*z**2)*(-25*z**3 + 36*z**2 - 50*z) + (35*z**3)*(-25*z**3 + 36*z**2 - 50*z)\n#Step 2:\nCurrent expression: (-44*z**2)*(-25*z**3 + 36*z**2 - 50*z) + (35*z**3)*(-25*z**3 + 36*z**2 - 50*z)\nSimplifying the partial expression: (-44*z**2)*(-25*z**3 + 36*z**2 - 50*z)\nExpanding the part (-25*z**3 + 36*z**2 - 50*z) using the distributive property, and we got: (-50*z)*(-44*z**2) + (-44*z**2)*(36*z**2) + (-44*z**2)*(-25*z**3)\nReplacing (-44*z**2)*(-25*z**3 + 36*z**2 - 50*z) with (-50*z)*(-44*z**2) + (-44*z**2)*(36*z**2) + (-44*z**2)*(-25*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-50*z)*(-44*z**2) + (-44*z**2)*(36*z**2) + (-44*z**2)*(-25*z**3) + (35*z**3)*(-25*z**3 + 36*z**2 - 50*z)\nSimplifying the partial expression: (35*z**3)*(-25*z**3 + 36*z**2 - 50*z)\nExpanding the part (-25*z**3 + 36*z**2 - 50*z) using the distributive property, and we got: (-50*z)*(35*z**3) + (36*z**2)*(35*z**3) + (-25*z**3)*(35*z**3)\nReplacing (35*z**3)*(-25*z**3 + 36*z**2 - 50*z) with (-50*z)*(35*z**3) + (36*z**2)*(35*z**3) + (-25*z**3)*(35*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-50*z)*(-44*z**2) + (-50*z)*(35*z**3) + (-44*z**2)*(36*z**2) + (-44*z**2)*(-25*z**3) + (36*z**2)*(35*z**3) + (-25*z**3)*(35*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-50*z)*(-44*z**2) = 2200*z**3\n (-50*z)*(35*z**3) = -1750*z**4\n (-25*z**3)*(-44*z**2) = 1100*z**5\n (-25*z**3)*(35*z**3) = -875*z**6\n (36*z**2)*(-44*z**2) = -1584*z**4\n (36*z**2)*(35*z**3) = 1260*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -875*z**6 + 1100*z**5 + 1260*z**5 - 1750*z**4 - 1584*z**4 + 2200*z**3\nCombining like terms, got -875*z**6 + 2360*z**5 - 3334*z**4 + 2200*z**3\n#Step 6:\nCurrent expression: -875*z**6 + 2360*z**5 - 3334*z**4 + 2200*z**3\nNo more calculations needed.\n-875*z**6 + 2360*z**5 - 3334*z**4 + 2200*z**3", "generated_answer": "-875*z**6 + 2360*z**5 - 3334*z**4 + 2200*z**3", "step_length": 6} {"cot_id": "fc402a22e52df8103f73a9eea21fd09bd0ea4244bc96ef7544d70c2807e0c4e8", "datapoint": {"question": "Simplify this expression: (-15*z**3 - 46*z**2)*(3*z**3 - 27*z**2 + 18*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-45*z**6 + 267*z**5 + 972*z**4 - 828*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 495, "polynomial_expr": "(-15*z**3 - 46*z**2)*(3*z**3 - 27*z**2 + 18*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-15*z**3 - 46*z**2)*(3*z**3 - 27*z**2 + 18*z)\nExpanding the part (-15*z**3 - 46*z**2) using the distributive property, and we got: (-46*z**2)*(3*z**3 - 27*z**2 + 18*z) + (-15*z**3)*(3*z**3 - 27*z**2 + 18*z)\n#Step 2:\nCurrent expression: (-46*z**2)*(3*z**3 - 27*z**2 + 18*z) + (-15*z**3)*(3*z**3 - 27*z**2 + 18*z)\nSimplifying the partial expression: (-46*z**2)*(3*z**3 - 27*z**2 + 18*z)\nExpanding the part (3*z**3 - 27*z**2 + 18*z) using the distributive property, and we got: (18*z)*(-46*z**2) + (-46*z**2)*(-27*z**2) + (-46*z**2)*(3*z**3)\nReplacing (-46*z**2)*(3*z**3 - 27*z**2 + 18*z) with (18*z)*(-46*z**2) + (-46*z**2)*(-27*z**2) + (-46*z**2)*(3*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (18*z)*(-46*z**2) + (-46*z**2)*(-27*z**2) + (-46*z**2)*(3*z**3) + (-15*z**3)*(3*z**3 - 27*z**2 + 18*z)\nSimplifying the partial expression: (-15*z**3)*(3*z**3 - 27*z**2 + 18*z)\nExpanding the part (3*z**3 - 27*z**2 + 18*z) using the distributive property, and we got: (18*z)*(-15*z**3) + (-27*z**2)*(-15*z**3) + (-15*z**3)*(3*z**3)\nReplacing (-15*z**3)*(3*z**3 - 27*z**2 + 18*z) with (18*z)*(-15*z**3) + (-27*z**2)*(-15*z**3) + (-15*z**3)*(3*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (18*z)*(-46*z**2) + (18*z)*(-15*z**3) + (-46*z**2)*(-27*z**2) + (-46*z**2)*(3*z**3) + (-27*z**2)*(-15*z**3) + (-15*z**3)*(3*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*z**2)*(-46*z**2) = 1242*z**4\n (-27*z**2)*(-15*z**3) = 405*z**5\n (3*z**3)*(-46*z**2) = -138*z**5\n (3*z**3)*(-15*z**3) = -45*z**6\n (18*z)*(-46*z**2) = -828*z**3\n (18*z)*(-15*z**3) = -270*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -45*z**6 - 138*z**5 + 405*z**5 - 270*z**4 + 1242*z**4 - 828*z**3\nCombining like terms, got -45*z**6 + 267*z**5 + 972*z**4 - 828*z**3\n#Step 6:\nCurrent expression: -45*z**6 + 267*z**5 + 972*z**4 - 828*z**3\nNo more calculations needed.\n-45*z**6 + 267*z**5 + 972*z**4 - 828*z**3", "generated_answer": "-45*z**6 + 267*z**5 + 972*z**4 - 828*z**3", "step_length": 6} {"cot_id": "21e78b4b1c328b023a04a15c61bbe86f02e03d93a30dba75b8caf42c12bb36c1", "datapoint": {"question": "Calculate the following: -5*y**3*(27*y**2 - 10*y - 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-135*y**5 + 50*y**4 + 250*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 496, "polynomial_expr": "-5*y**3*(27*y**2 - 10*y - 50)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -5*y**3*(27*y**2 - 10*y - 50)\nExpanding the part (27*y**2 - 10*y - 50) using the distributive property, and we got: (-10*y)*(-5*y**3) - (-1)*250*y**3 + (27*y**2)*(-5*y**3)\n#Step 2:\nCurrent expression: (-10*y)*(-5*y**3) - (-1)*250*y**3 + (27*y**2)*(-5*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -50*(-5*y**3) = 250*y**3\n (-10*y)*(-5*y**3) = 50*y**4\n (27*y**2)*(-5*y**3) = -135*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -135*y**5 + 50*y**4 + 250*y**3\nNo more calculations needed.\n-135*y**5 + 50*y**4 + 250*y**3", "generated_answer": "-135*y**5 + 50*y**4 + 250*y**3", "step_length": 3} {"cot_id": "d5e715a7d3eaf32d14e154720b0bc806e9f945cf8723c31d49f3c79624b1d61d", "datapoint": {"question": "Calculate the following: (-49*y**3 + 43*y**2)*(12*y**3 - 45*y - 5)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-588*y**6 + 516*y**5 + 2205*y**4 - 1690*y**3 - 215*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 497, "polynomial_expr": "(-49*y**3 + 43*y**2)*(12*y**3 - 45*y - 5)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-49*y**3 + 43*y**2)*(12*y**3 - 45*y - 5)\nExpanding the part (-49*y**3 + 43*y**2) using the distributive property, and we got: (43*y**2)*(12*y**3 - 45*y - 5) + (-49*y**3)*(12*y**3 - 45*y - 5)\n#Step 2:\nCurrent expression: (43*y**2)*(12*y**3 - 45*y - 5) + (-49*y**3)*(12*y**3 - 45*y - 5)\nSimplifying the partial expression: (-49*y**3)*(12*y**3 - 45*y - 5)\nExpanding the part (12*y**3 - 45*y - 5) using the distributive property, and we got: (-45*y)*(-49*y**3) - (-1)*245*y**3 + (-49*y**3)*(12*y**3)\nReplacing (-49*y**3)*(12*y**3 - 45*y - 5) with (-45*y)*(-49*y**3) - (-1)*245*y**3 + (-49*y**3)*(12*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-45*y)*(-49*y**3) - 5*(-49)*y**3 + (43*y**2)*(12*y**3 - 45*y - 5) + (-49*y**3)*(12*y**3)\nSimplifying the partial expression: (43*y**2)*(12*y**3 - 45*y - 5)\nExpanding the part (12*y**3 - 45*y - 5) using the distributive property, and we got: (-45*y)*(43*y**2) - 215*y**2 + (43*y**2)*(12*y**3)\nReplacing (43*y**2)*(12*y**3 - 45*y - 5) with (-45*y)*(43*y**2) - 215*y**2 + (43*y**2)*(12*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-45*y)*(43*y**2) + (-45*y)*(-49*y**3) - 5*(-49)*y**3 - 5*43*y**2 + (43*y**2)*(12*y**3) + (-49*y**3)*(12*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*y)*(-49*y**3) = 2205*y**4\n (-45*y)*(43*y**2) = -1935*y**3\n (12*y**3)*(-49*y**3) = -588*y**6\n (12*y**3)*(43*y**2) = 516*y**5\n -5*-49*y**3 = 245*y**3\n -5*43*y**2 = -215*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -588*y**6 + 516*y**5 + 2205*y**4 - 1935*y**3 + 245*y**3 - 215*y**2\nCombining like terms, got -588*y**6 + 516*y**5 + 2205*y**4 - 1690*y**3 - 215*y**2\n#Step 6:\nCurrent expression: -588*y**6 + 516*y**5 + 2205*y**4 - 1690*y**3 - 215*y**2\nNo more calculations needed.\n-588*y**6 + 516*y**5 + 2205*y**4 - 1690*y**3 - 215*y**2", "generated_answer": "-588*y**6 + 516*y**5 + 2205*y**4 - 1690*y**3 - 215*y**2", "step_length": 6} {"cot_id": "8235f4ae5d1b71db1fb8d10e98bdc27a242c36b3c07f47476bb61c8bbe599554", "datapoint": {"question": "Calculate the following: (37 - 34*z**3)*(-38*z**2 + 30*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1292*z**5 - 1020*z**4 - 1406*z**2 + 1110*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 498, "polynomial_expr": "(37 - 34*z**3)*(-38*z**2 + 30*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (37 - 34*z**3)*(-38*z**2 + 30*z)\nExpanding the part (37 - 34*z**3) using the distributive property, and we got: (-34*z**3)*(-38*z**2 + 30*z) + 37*(-38*z**2 + 30*z)\n#Step 2:\nCurrent expression: (-34*z**3)*(-38*z**2 + 30*z) + 37*(-38*z**2 + 30*z)\nSimplifying the partial expression: 37*(-38*z**2 + 30*z)\nExpanding the part (-38*z**2 + 30*z) using the distributive property, and we got: (30*z)*37 - 38*z**2*37\nReplacing 37*(-38*z**2 + 30*z) with (30*z)*37 - 38*z**2*37 in the overall expression.\n#Step 3:\nCurrent expression: (30*z)*37 - 38*z**2*37 + (-34*z**3)*(-38*z**2 + 30*z)\nSimplifying the partial expression: (-34*z**3)*(-38*z**2 + 30*z)\nExpanding the part (-38*z**2 + 30*z) using the distributive property, and we got: (30*z)*(-34*z**3) + (-38*z**2)*(-34*z**3)\nReplacing (-34*z**3)*(-38*z**2 + 30*z) with (30*z)*(-34*z**3) + (-38*z**2)*(-34*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (30*z)*(-34*z**3) + (30*z)*37 + (-38*z**2)*(-34*z**3) - 38*z**2*37\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*z**2)*37 = -1406*z**2\n (-38*z**2)*(-34*z**3) = 1292*z**5\n (30*z)*37 = 1110*z\n (30*z)*(-34*z**3) = -1020*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1292*z**5 - 1020*z**4 - 1406*z**2 + 1110*z\nNo more calculations needed.\n1292*z**5 - 1020*z**4 - 1406*z**2 + 1110*z", "generated_answer": "1292*z**5 - 1020*z**4 - 1406*z**2 + 1110*z", "step_length": 5} {"cot_id": "a9033641e72a708a629af0cc217ff80de915073f4b4e03db92e491c87ae8fbe6", "datapoint": {"question": "Calculate the following: (49*y**3 - 35*y + 25)*(-39*y**3 - 47*y**2 + y + 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1911*y**6 - 2303*y**5 + 1414*y**4 + 2973*y**3 - 1210*y**2 - 1620*y + 1175", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 499, "polynomial_expr": "(49*y**3 - 35*y + 25)*(-39*y**3 - 47*y**2 + y + 47)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (49*y**3 - 35*y + 25)*(-39*y**3 - 47*y**2 + y + 47)\nExpanding the part (49*y**3 - 35*y + 25) using the distributive property, and we got: (-35*y)*(-39*y**3 - 47*y**2 + y + 47) + (49*y**3)*(-39*y**3 - 47*y**2 + y + 47) + 25*(-39*y**3 - 47*y**2 + y + 47)\n#Step 2:\nCurrent expression: (-35*y)*(-39*y**3 - 47*y**2 + y + 47) + (49*y**3)*(-39*y**3 - 47*y**2 + y + 47) + 25*(-39*y**3 - 47*y**2 + y + 47)\nSimplifying the partial expression: 25*(-39*y**3 - 47*y**2 + y + 47)\nExpanding the part (-39*y**3 - 47*y**2 + y + 47) using the distributive property, and we got: y*25 - 47*y**2*25 - 39*y**3*25 + 47*25\nReplacing 25*(-39*y**3 - 47*y**2 + y + 47) with y*25 - 47*y**2*25 - 39*y**3*25 + 47*25 in the overall expression.\n#Step 3:\nCurrent expression: (-35*y)*(-39*y**3 - 47*y**2 + y + 47) + y*25 - 47*y**2*25 - 39*y**3*25 + (49*y**3)*(-39*y**3 - 47*y**2 + y + 47) + 1175\nSimplifying the partial expression: (-35*y)*(-39*y**3 - 47*y**2 + y + 47)\nExpanding the part (-39*y**3 - 47*y**2 + y + 47) using the distributive property, and we got: (-35*y)*y + (-35*y)*(-47*y**2) + (-35*y)*(-39*y**3) + 47*(-35*y)\nReplacing (-35*y)*(-39*y**3 - 47*y**2 + y + 47) with (-35*y)*y + (-35*y)*(-47*y**2) + (-35*y)*(-39*y**3) + 47*(-35*y) in the overall expression.\n#Step 4:\nCurrent expression: (-35*y)*y + (-35*y)*(-47*y**2) + (-35*y)*(-39*y**3) + 47*(-35)*y + y*25 - 47*y**2*25 - 39*y**3*25 + (49*y**3)*(-39*y**3 - 47*y**2 + y + 47) + 1175\nSimplifying the partial expression: (49*y**3)*(-39*y**3 - 47*y**2 + y + 47)\nExpanding the part (-39*y**3 - 47*y**2 + y + 47) using the distributive property, and we got: 47*(49*y**3) + y*(49*y**3) + (-47*y**2)*(49*y**3) + (-39*y**3)*(49*y**3)\nReplacing (49*y**3)*(-39*y**3 - 47*y**2 + y + 47) with 47*(49*y**3) + y*(49*y**3) + (-47*y**2)*(49*y**3) + (-39*y**3)*(49*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-35*y)*y + (-35*y)*(-47*y**2) + (-35*y)*(-39*y**3) + 47*49*y**3 + y*(49*y**3) + 47*(-35)*y + y*25 + (-47*y**2)*(49*y**3) - 47*y**2*25 + (-39*y**3)*(49*y**3) - 39*y**3*25 + 1175\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n y*25 = 25*y\n y*(-35*y) = -35*y**2\n y*(49*y**3) = 49*y**4\n (-47*y**2)*25 = -1175*y**2\n (-47*y**2)*(-35*y) = 1645*y**3\n (-47*y**2)*(49*y**3) = -2303*y**5\n (-39*y**3)*25 = -975*y**3\n (-39*y**3)*(-35*y) = 1365*y**4\n (-39*y**3)*(49*y**3) = -1911*y**6\n 47*-35*y = -1645*y\n 47*49*y**3 = 2303*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1911*y**6 - 2303*y**5 + 49*y**4 + 1365*y**4 - 975*y**3 + 1645*y**3 + 2303*y**3 - 1175*y**2 - 35*y**2 - 1645*y + 25*y + 1175\nCombining like terms, got -1911*y**6 - 2303*y**5 + 1414*y**4 + 2973*y**3 - 1210*y**2 - 1620*y + 1175\n#Step 7:\nCurrent expression: -1911*y**6 - 2303*y**5 + 1414*y**4 + 2973*y**3 - 1210*y**2 - 1620*y + 1175\nNo more calculations needed.\n-1911*y**6 - 2303*y**5 + 1414*y**4 + 2973*y**3 - 1210*y**2 - 1620*y + 1175", "generated_answer": "-1911*y**6 - 2303*y**5 + 1414*y**4 + 2973*y**3 - 1210*y**2 - 1620*y + 1175", "step_length": 7} {"cot_id": "0813b3cad07004640dae3945acb451dd8b15bd15364e81d7f444196825fb3ed5", "datapoint": {"question": "Simplify this expression: (-40*y - 27)*(25*y**3 - 46)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1000*y**4 - 675*y**3 + 1840*y + 1242", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 500, "polynomial_expr": "(-40*y - 27)*(25*y**3 - 46)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-40*y - 27)*(25*y**3 - 46)\nExpanding the part (25*y**3 - 46) using the distributive property, and we got: (25*y**3)*(-40*y - 27) - 46*(-40*y - 27)\n#Step 2:\nCurrent expression: (25*y**3)*(-40*y - 27) - 46*(-40*y - 27)\nSimplifying the partial expression: -46*(-40*y - 27)\nExpanding the part (-40*y - 27) using the distributive property, and we got: -40*y*(-46) - 27*(-46)\nReplacing -46*(-40*y - 27) with -40*y*(-46) - 27*(-46) in the overall expression.\n#Step 3:\nCurrent expression: -40*y*(-46) + (25*y**3)*(-40*y - 27) + 1242\nSimplifying the partial expression: (25*y**3)*(-40*y - 27)\nExpanding the part (-40*y - 27) using the distributive property, and we got: (-40*y)*(25*y**3) - 675*y**3\nReplacing (25*y**3)*(-40*y - 27) with (-40*y)*(25*y**3) - 675*y**3 in the overall expression.\n#Step 4:\nCurrent expression: (-40*y)*(25*y**3) - 40*y*(-46) - 27*25*y**3 + 1242\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*y)*-46 = 1840*y\n (-40*y)*(25*y**3) = -1000*y**4\n -27*25*y**3 = -675*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1000*y**4 - 675*y**3 + 1840*y + 1242\nNo more calculations needed.\n-1000*y**4 - 675*y**3 + 1840*y + 1242", "generated_answer": "-1000*y**4 - 675*y**3 + 1840*y + 1242", "step_length": 5} {"cot_id": "a9ccf5cd72079ebf66c42f723b0b2ce55a0ae061390877addfba6473fdaf981d", "datapoint": {"question": "Calculate the following: (40*z**2 + 3*z)*(6*z**3 + 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "240*z**5 + 18*z**4 + 1200*z**2 + 90*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 501, "polynomial_expr": "(40*z**2 + 3*z)*(6*z**3 + 30)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (40*z**2 + 3*z)*(6*z**3 + 30)\nExpanding the part (6*z**3 + 30) using the distributive property, and we got: (6*z**3)*(40*z**2 + 3*z) + 30*(40*z**2 + 3*z)\n#Step 2:\nCurrent expression: (6*z**3)*(40*z**2 + 3*z) + 30*(40*z**2 + 3*z)\nSimplifying the partial expression: 30*(40*z**2 + 3*z)\nExpanding the part (40*z**2 + 3*z) using the distributive property, and we got: (3*z)*30 + (40*z**2)*30\nReplacing 30*(40*z**2 + 3*z) with (3*z)*30 + (40*z**2)*30 in the overall expression.\n#Step 3:\nCurrent expression: (3*z)*30 + (40*z**2)*30 + (6*z**3)*(40*z**2 + 3*z)\nSimplifying the partial expression: (6*z**3)*(40*z**2 + 3*z)\nExpanding the part (40*z**2 + 3*z) using the distributive property, and we got: (3*z)*(6*z**3) + (40*z**2)*(6*z**3)\nReplacing (6*z**3)*(40*z**2 + 3*z) with (3*z)*(6*z**3) + (40*z**2)*(6*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (3*z)*(6*z**3) + (3*z)*30 + (40*z**2)*(6*z**3) + (40*z**2)*30\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (3*z)*30 = 90*z\n (3*z)*(6*z**3) = 18*z**4\n (40*z**2)*30 = 1200*z**2\n (40*z**2)*(6*z**3) = 240*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 240*z**5 + 18*z**4 + 1200*z**2 + 90*z\nNo more calculations needed.\n240*z**5 + 18*z**4 + 1200*z**2 + 90*z", "generated_answer": "240*z**5 + 18*z**4 + 1200*z**2 + 90*z", "step_length": 5} {"cot_id": "5d1b94c484d0c90c6e002eec51560127ee579cc0a048b34bbf4e2c9916c11b45", "datapoint": {"question": "Simplify this expression: -30*z**2*(45*z**3 + 20*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1350*z**5 - 600*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 502, "polynomial_expr": "-30*z**2*(45*z**3 + 20*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -30*z**2*(45*z**3 + 20*z)\nExpanding the part (45*z**3 + 20*z) using the distributive property, and we got: (20*z)*(-30*z**2) + (-30*z**2)*(45*z**3)\n#Step 2:\nCurrent expression: (20*z)*(-30*z**2) + (-30*z**2)*(45*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (20*z)*(-30*z**2) = -600*z**3\n (45*z**3)*(-30*z**2) = -1350*z**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1350*z**5 - 600*z**3\nNo more calculations needed.\n-1350*z**5 - 600*z**3", "generated_answer": "-1350*z**5 - 600*z**3", "step_length": 3} {"cot_id": "213f8808d01fef0c065ad76477255113f0f067aa77afcafd66be41205680af9a", "datapoint": {"question": "Simplify this expression: -54*x*(-5*x**3 - 8*x**2 + 8)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "270*x**4 + 432*x**3 - 432*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 503, "polynomial_expr": "-54*x*(-5*x**3 - 8*x**2 + 8)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -54*x*(-5*x**3 - 8*x**2 + 8)\nExpanding the part (-5*x**3 - 8*x**2 + 8) using the distributive property, and we got: (-54*x)*(-8*x**2) + (-54*x)*(-5*x**3) + 8*(-54*x)\n#Step 2:\nCurrent expression: (-54*x)*(-8*x**2) + (-54*x)*(-5*x**3) + 8*(-54*x)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 8*(-54*x) = -432*x\n (-8*x**2)*(-54*x) = 432*x**3\n (-5*x**3)*(-54*x) = 270*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 270*x**4 + 432*x**3 - 432*x\nNo more calculations needed.\n270*x**4 + 432*x**3 - 432*x", "generated_answer": "270*x**4 + 432*x**3 - 432*x", "step_length": 3} {"cot_id": "48e7b3f5e8fd1ede9216c79f1beadeff8d0d1aa0b627fdcbf0cf7a981bb43774", "datapoint": {"question": "Simplify this expression: (21*x**2 + 4*x)*(14*x**2 + 26*x - 25)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "294*x**4 + 602*x**3 - 421*x**2 - 100*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 504, "polynomial_expr": "(21*x**2 + 4*x)*(14*x**2 + 26*x - 25)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21*x**2 + 4*x)*(14*x**2 + 26*x - 25)\nExpanding the part (21*x**2 + 4*x) using the distributive property, and we got: (4*x)*(14*x**2 + 26*x - 25) + (21*x**2)*(14*x**2 + 26*x - 25)\n#Step 2:\nCurrent expression: (4*x)*(14*x**2 + 26*x - 25) + (21*x**2)*(14*x**2 + 26*x - 25)\nSimplifying the partial expression: (4*x)*(14*x**2 + 26*x - 25)\nExpanding the part (14*x**2 + 26*x - 25) using the distributive property, and we got: -100*x + (4*x)*(26*x) + (4*x)*(14*x**2)\nReplacing (4*x)*(14*x**2 + 26*x - 25) with -100*x + (4*x)*(26*x) + (4*x)*(14*x**2) in the overall expression.\n#Step 3:\nCurrent expression: -25*4*x + (4*x)*(26*x) + (4*x)*(14*x**2) + (21*x**2)*(14*x**2 + 26*x - 25)\nSimplifying the partial expression: (21*x**2)*(14*x**2 + 26*x - 25)\nExpanding the part (14*x**2 + 26*x - 25) using the distributive property, and we got: -525*x**2 + (26*x)*(21*x**2) + (14*x**2)*(21*x**2)\nReplacing (21*x**2)*(14*x**2 + 26*x - 25) with -525*x**2 + (26*x)*(21*x**2) + (14*x**2)*(21*x**2) in the overall expression.\n#Step 4:\nCurrent expression: -25*21*x**2 - 25*4*x + (4*x)*(26*x) + (4*x)*(14*x**2) + (26*x)*(21*x**2) + (14*x**2)*(21*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (14*x**2)*(4*x) = 56*x**3\n (14*x**2)*(21*x**2) = 294*x**4\n (26*x)*(4*x) = 104*x**2\n (26*x)*(21*x**2) = 546*x**3\n -25*4*x = -100*x\n -25*21*x**2 = -525*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 294*x**4 + 56*x**3 + 546*x**3 - 525*x**2 + 104*x**2 - 100*x\nCombining like terms, got 294*x**4 + 602*x**3 - 421*x**2 - 100*x\n#Step 6:\nCurrent expression: 294*x**4 + 602*x**3 - 421*x**2 - 100*x\nNo more calculations needed.\n294*x**4 + 602*x**3 - 421*x**2 - 100*x", "generated_answer": "294*x**4 + 602*x**3 - 421*x**2 - 100*x", "step_length": 6} {"cot_id": "52007baa970d24d0bf26395e87112dbc74d8a5907b3ba5be9fa914b86101935c", "datapoint": {"question": "Simplify this expression: (5*x**3 + 18*x**2)*(39*x**3 - 37*x**2 - 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "195*x**6 + 517*x**5 - 666*x**4 - 65*x**3 - 234*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 505, "polynomial_expr": "(5*x**3 + 18*x**2)*(39*x**3 - 37*x**2 - 13)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (5*x**3 + 18*x**2)*(39*x**3 - 37*x**2 - 13)\nExpanding the part (5*x**3 + 18*x**2) using the distributive property, and we got: (18*x**2)*(39*x**3 - 37*x**2 - 13) + (5*x**3)*(39*x**3 - 37*x**2 - 13)\n#Step 2:\nCurrent expression: (18*x**2)*(39*x**3 - 37*x**2 - 13) + (5*x**3)*(39*x**3 - 37*x**2 - 13)\nSimplifying the partial expression: (5*x**3)*(39*x**3 - 37*x**2 - 13)\nExpanding the part (39*x**3 - 37*x**2 - 13) using the distributive property, and we got: -65*x**3 + (-37*x**2)*(5*x**3) + (5*x**3)*(39*x**3)\nReplacing (5*x**3)*(39*x**3 - 37*x**2 - 13) with -65*x**3 + (-37*x**2)*(5*x**3) + (5*x**3)*(39*x**3) in the overall expression.\n#Step 3:\nCurrent expression: -13*5*x**3 + (-37*x**2)*(5*x**3) + (18*x**2)*(39*x**3 - 37*x**2 - 13) + (5*x**3)*(39*x**3)\nSimplifying the partial expression: (18*x**2)*(39*x**3 - 37*x**2 - 13)\nExpanding the part (39*x**3 - 37*x**2 - 13) using the distributive property, and we got: -234*x**2 + (-37*x**2)*(18*x**2) + (18*x**2)*(39*x**3)\nReplacing (18*x**2)*(39*x**3 - 37*x**2 - 13) with -234*x**2 + (-37*x**2)*(18*x**2) + (18*x**2)*(39*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -13*5*x**3 - 13*18*x**2 + (-37*x**2)*(18*x**2) + (-37*x**2)*(5*x**3) + (18*x**2)*(39*x**3) + (5*x**3)*(39*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*x**2)*(5*x**3) = -185*x**5\n (-37*x**2)*(18*x**2) = -666*x**4\n (39*x**3)*(5*x**3) = 195*x**6\n (39*x**3)*(18*x**2) = 702*x**5\n -13*5*x**3 = -65*x**3\n -13*18*x**2 = -234*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 195*x**6 - 185*x**5 + 702*x**5 - 666*x**4 - 65*x**3 - 234*x**2\nCombining like terms, got 195*x**6 + 517*x**5 - 666*x**4 - 65*x**3 - 234*x**2\n#Step 6:\nCurrent expression: 195*x**6 + 517*x**5 - 666*x**4 - 65*x**3 - 234*x**2\nNo more calculations needed.\n195*x**6 + 517*x**5 - 666*x**4 - 65*x**3 - 234*x**2", "generated_answer": "195*x**6 + 517*x**5 - 666*x**4 - 65*x**3 - 234*x**2", "step_length": 6} {"cot_id": "118811fad63e3dbe39e881a9a1e0080f7f979b249584b4d8580ec7a190fd4076", "datapoint": {"question": "Calculate the following: (x**3 - 39*x**2)*(-46*x**2 + 10*x + 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-46*x**5 + 1804*x**4 - 351*x**3 - 1521*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 506, "polynomial_expr": "(x**3 - 39*x**2)*(-46*x**2 + 10*x + 39)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (x**3 - 39*x**2)*(-46*x**2 + 10*x + 39)\nExpanding the part (x**3 - 39*x**2) using the distributive property, and we got: x**3*(-46*x**2 + 10*x + 39) + (-39*x**2)*(-46*x**2 + 10*x + 39)\n#Step 2:\nCurrent expression: x**3*(-46*x**2 + 10*x + 39) + (-39*x**2)*(-46*x**2 + 10*x + 39)\nSimplifying the partial expression: x**3*(-46*x**2 + 10*x + 39)\nExpanding the part (-46*x**2 + 10*x + 39) using the distributive property, and we got: (10*x)*x**3 + (-46*x**2)*x**3 + 39*x**3\nReplacing x**3*(-46*x**2 + 10*x + 39) with (10*x)*x**3 + (-46*x**2)*x**3 + 39*x**3 in the overall expression.\n#Step 3:\nCurrent expression: (10*x)*x**3 + (-46*x**2)*x**3 + 39*x**3 + (-39*x**2)*(-46*x**2 + 10*x + 39)\nSimplifying the partial expression: (-39*x**2)*(-46*x**2 + 10*x + 39)\nExpanding the part (-46*x**2 + 10*x + 39) using the distributive property, and we got: 39*(-39*x**2) + (10*x)*(-39*x**2) + (-46*x**2)*(-39*x**2)\nReplacing (-39*x**2)*(-46*x**2 + 10*x + 39) with 39*(-39*x**2) + (10*x)*(-39*x**2) + (-46*x**2)*(-39*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (10*x)*x**3 + (-46*x**2)*x**3 + 39*x**3 + 39*(-39)*x**2 + (10*x)*(-39*x**2) + (-46*x**2)*(-39*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*x**2)*x**3 = -46*x**5\n (-46*x**2)*(-39*x**2) = 1794*x**4\n (10*x)*x**3 = 10*x**4\n (10*x)*(-39*x**2) = -390*x**3\n 39*-39*x**2 = -1521*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -46*x**5 + 10*x**4 + 1794*x**4 - 390*x**3 + 39*x**3 - 1521*x**2\nCombining like terms, got -46*x**5 + 1804*x**4 - 351*x**3 - 1521*x**2\n#Step 6:\nCurrent expression: -46*x**5 + 1804*x**4 - 351*x**3 - 1521*x**2\nNo more calculations needed.\n-46*x**5 + 1804*x**4 - 351*x**3 - 1521*x**2", "generated_answer": "-46*x**5 + 1804*x**4 - 351*x**3 - 1521*x**2", "step_length": 6} {"cot_id": "186ee2be3a84fad8364b95e05dbfe4dcfa5f3b1bb7b28325caeb5ae4de20285f", "datapoint": {"question": "Simplify this expression: (14 - 33*z**3)*(25*z**3 - 11*z**2 + 21*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-825*z**6 + 363*z**5 - 693*z**4 + 350*z**3 - 154*z**2 + 294*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 507, "polynomial_expr": "(14 - 33*z**3)*(25*z**3 - 11*z**2 + 21*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14 - 33*z**3)*(25*z**3 - 11*z**2 + 21*z)\nExpanding the part (14 - 33*z**3) using the distributive property, and we got: (-33*z**3)*(25*z**3 - 11*z**2 + 21*z) + 14*(25*z**3 - 11*z**2 + 21*z)\n#Step 2:\nCurrent expression: (-33*z**3)*(25*z**3 - 11*z**2 + 21*z) + 14*(25*z**3 - 11*z**2 + 21*z)\nSimplifying the partial expression: 14*(25*z**3 - 11*z**2 + 21*z)\nExpanding the part (25*z**3 - 11*z**2 + 21*z) using the distributive property, and we got: (21*z)*14 - 11*z**2*14 + (25*z**3)*14\nReplacing 14*(25*z**3 - 11*z**2 + 21*z) with (21*z)*14 - 11*z**2*14 + (25*z**3)*14 in the overall expression.\n#Step 3:\nCurrent expression: (21*z)*14 - 11*z**2*14 + (-33*z**3)*(25*z**3 - 11*z**2 + 21*z) + (25*z**3)*14\nSimplifying the partial expression: (-33*z**3)*(25*z**3 - 11*z**2 + 21*z)\nExpanding the part (25*z**3 - 11*z**2 + 21*z) using the distributive property, and we got: (21*z)*(-33*z**3) + (-11*z**2)*(-33*z**3) + (-33*z**3)*(25*z**3)\nReplacing (-33*z**3)*(25*z**3 - 11*z**2 + 21*z) with (21*z)*(-33*z**3) + (-11*z**2)*(-33*z**3) + (-33*z**3)*(25*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (21*z)*(-33*z**3) + (21*z)*14 + (-11*z**2)*(-33*z**3) - 11*z**2*14 + (-33*z**3)*(25*z**3) + (25*z**3)*14\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*z**2)*14 = -154*z**2\n (-11*z**2)*(-33*z**3) = 363*z**5\n (21*z)*14 = 294*z\n (21*z)*(-33*z**3) = -693*z**4\n (25*z**3)*14 = 350*z**3\n (25*z**3)*(-33*z**3) = -825*z**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -825*z**6 + 363*z**5 - 693*z**4 + 350*z**3 - 154*z**2 + 294*z\nNo more calculations needed.\n-825*z**6 + 363*z**5 - 693*z**4 + 350*z**3 - 154*z**2 + 294*z", "generated_answer": "-825*z**6 + 363*z**5 - 693*z**4 + 350*z**3 - 154*z**2 + 294*z", "step_length": 5} {"cot_id": "e135e0ffa421dbeaec743a6356a9922199acaee2faedb7b824aebb0cf1caf6bb", "datapoint": {"question": "Calculate the following: (7*y**2 - 46*y)*(-54*y**3 - 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-378*y**5 + 2484*y**4 - 231*y**2 + 1518*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 508, "polynomial_expr": "(7*y**2 - 46*y)*(-54*y**3 - 33)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7*y**2 - 46*y)*(-54*y**3 - 33)\nExpanding the part (-54*y**3 - 33) using the distributive property, and we got: (-54*y**3)*(7*y**2 - 46*y) - 33*(7*y**2 - 46*y)\n#Step 2:\nCurrent expression: (-54*y**3)*(7*y**2 - 46*y) - 33*(7*y**2 - 46*y)\nSimplifying the partial expression: -33*(7*y**2 - 46*y)\nExpanding the part (7*y**2 - 46*y) using the distributive property, and we got: -46*y*(-33) + (7*y**2)*(-33)\nReplacing -33*(7*y**2 - 46*y) with -46*y*(-33) + (7*y**2)*(-33) in the overall expression.\n#Step 3:\nCurrent expression: -46*y*(-33) + (7*y**2)*(-33) + (-54*y**3)*(7*y**2 - 46*y)\nSimplifying the partial expression: (-54*y**3)*(7*y**2 - 46*y)\nExpanding the part (7*y**2 - 46*y) using the distributive property, and we got: (-46*y)*(-54*y**3) + (7*y**2)*(-54*y**3)\nReplacing (-54*y**3)*(7*y**2 - 46*y) with (-46*y)*(-54*y**3) + (7*y**2)*(-54*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-46*y)*(-54*y**3) - 46*y*(-33) + (7*y**2)*(-54*y**3) + (7*y**2)*(-33)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*y)*-33 = 1518*y\n (-46*y)*(-54*y**3) = 2484*y**4\n (7*y**2)*-33 = -231*y**2\n (7*y**2)*(-54*y**3) = -378*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -378*y**5 + 2484*y**4 - 231*y**2 + 1518*y\nNo more calculations needed.\n-378*y**5 + 2484*y**4 - 231*y**2 + 1518*y", "generated_answer": "-378*y**5 + 2484*y**4 - 231*y**2 + 1518*y", "step_length": 5} {"cot_id": "c08e7365de03913e5f79ce505228ad744861a37dd86bb1167de26dbf9b192d6a", "datapoint": {"question": "Calculate the following: (27*z**2 - 14)*(-28*z**3 + 17*z - 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-756*z**5 + 851*z**3 - 837*z**2 - 238*z + 434", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 509, "polynomial_expr": "(27*z**2 - 14)*(-28*z**3 + 17*z - 31)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*z**2 - 14)*(-28*z**3 + 17*z - 31)\nExpanding the part (27*z**2 - 14) using the distributive property, and we got: (27*z**2)*(-28*z**3 + 17*z - 31) - 14*(-28*z**3 + 17*z - 31)\n#Step 2:\nCurrent expression: (27*z**2)*(-28*z**3 + 17*z - 31) - 14*(-28*z**3 + 17*z - 31)\nSimplifying the partial expression: -14*(-28*z**3 + 17*z - 31)\nExpanding the part (-28*z**3 + 17*z - 31) using the distributive property, and we got: (17*z)*(-14) - 28*z**3*(-14) - 31*(-14)\nReplacing -14*(-28*z**3 + 17*z - 31) with (17*z)*(-14) - 28*z**3*(-14) - 31*(-14) in the overall expression.\n#Step 3:\nCurrent expression: (17*z)*(-14) + (27*z**2)*(-28*z**3 + 17*z - 31) - 28*z**3*(-14) + 434\nSimplifying the partial expression: (27*z**2)*(-28*z**3 + 17*z - 31)\nExpanding the part (-28*z**3 + 17*z - 31) using the distributive property, and we got: -837*z**2 + (17*z)*(27*z**2) + (27*z**2)*(-28*z**3)\nReplacing (27*z**2)*(-28*z**3 + 17*z - 31) with -837*z**2 + (17*z)*(27*z**2) + (27*z**2)*(-28*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -31*27*z**2 + (17*z)*(27*z**2) + (17*z)*(-14) + (27*z**2)*(-28*z**3) - 28*z**3*(-14) + 434\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*z**3)*-14 = 392*z**3\n (-28*z**3)*(27*z**2) = -756*z**5\n (17*z)*-14 = -238*z\n (17*z)*(27*z**2) = 459*z**3\n -31*27*z**2 = -837*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -756*z**5 + 392*z**3 + 459*z**3 - 837*z**2 - 238*z + 434\nCombining like terms, got -756*z**5 + 851*z**3 - 837*z**2 - 238*z + 434\n#Step 6:\nCurrent expression: -756*z**5 + 851*z**3 - 837*z**2 - 238*z + 434\nNo more calculations needed.\n-756*z**5 + 851*z**3 - 837*z**2 - 238*z + 434", "generated_answer": "-756*z**5 + 851*z**3 - 837*z**2 - 238*z + 434", "step_length": 6} {"cot_id": "87e38e25c091654eb757be77ca56b55285329dad9bdbc7be70a98732fcbdfb5e", "datapoint": {"question": "Simplify this expression: (70*x**3 + 52)*(49*x**3 + 24*x**2 - 56*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "3430*x**6 + 1680*x**5 - 3920*x**4 + 2548*x**3 + 1248*x**2 - 2912*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 510, "polynomial_expr": "(70*x**3 + 52)*(49*x**3 + 24*x**2 - 56*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (70*x**3 + 52)*(49*x**3 + 24*x**2 - 56*x)\nExpanding the part (70*x**3 + 52) using the distributive property, and we got: (70*x**3)*(49*x**3 + 24*x**2 - 56*x) + 52*(49*x**3 + 24*x**2 - 56*x)\n#Step 2:\nCurrent expression: (70*x**3)*(49*x**3 + 24*x**2 - 56*x) + 52*(49*x**3 + 24*x**2 - 56*x)\nSimplifying the partial expression: 52*(49*x**3 + 24*x**2 - 56*x)\nExpanding the part (49*x**3 + 24*x**2 - 56*x) using the distributive property, and we got: -56*x*52 + (24*x**2)*52 + (49*x**3)*52\nReplacing 52*(49*x**3 + 24*x**2 - 56*x) with -56*x*52 + (24*x**2)*52 + (49*x**3)*52 in the overall expression.\n#Step 3:\nCurrent expression: -56*x*52 + (24*x**2)*52 + (49*x**3)*52 + (70*x**3)*(49*x**3 + 24*x**2 - 56*x)\nSimplifying the partial expression: (70*x**3)*(49*x**3 + 24*x**2 - 56*x)\nExpanding the part (49*x**3 + 24*x**2 - 56*x) using the distributive property, and we got: (-56*x)*(70*x**3) + (24*x**2)*(70*x**3) + (49*x**3)*(70*x**3)\nReplacing (70*x**3)*(49*x**3 + 24*x**2 - 56*x) with (-56*x)*(70*x**3) + (24*x**2)*(70*x**3) + (49*x**3)*(70*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-56*x)*(70*x**3) - 56*x*52 + (24*x**2)*(70*x**3) + (24*x**2)*52 + (49*x**3)*(70*x**3) + (49*x**3)*52\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-56*x)*52 = -2912*x\n (-56*x)*(70*x**3) = -3920*x**4\n (24*x**2)*52 = 1248*x**2\n (24*x**2)*(70*x**3) = 1680*x**5\n (49*x**3)*52 = 2548*x**3\n (49*x**3)*(70*x**3) = 3430*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 3430*x**6 + 1680*x**5 - 3920*x**4 + 2548*x**3 + 1248*x**2 - 2912*x\nNo more calculations needed.\n3430*x**6 + 1680*x**5 - 3920*x**4 + 2548*x**3 + 1248*x**2 - 2912*x", "generated_answer": "3430*x**6 + 1680*x**5 - 3920*x**4 + 2548*x**3 + 1248*x**2 - 2912*x", "step_length": 5} {"cot_id": "01f38a63df3e39d1337be5412fe70f1069335a7bc24e1e5d8eb9f179f0393b1b", "datapoint": {"question": "Calculate the following: (-30*y**3 - 34*y**2)*(-44*y**2 + y - 27)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1320*y**5 + 1466*y**4 + 776*y**3 + 918*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 511, "polynomial_expr": "(-30*y**3 - 34*y**2)*(-44*y**2 + y - 27)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-30*y**3 - 34*y**2)*(-44*y**2 + y - 27)\nExpanding the part (-30*y**3 - 34*y**2) using the distributive property, and we got: (-34*y**2)*(-44*y**2 + y - 27) + (-30*y**3)*(-44*y**2 + y - 27)\n#Step 2:\nCurrent expression: (-34*y**2)*(-44*y**2 + y - 27) + (-30*y**3)*(-44*y**2 + y - 27)\nSimplifying the partial expression: (-34*y**2)*(-44*y**2 + y - 27)\nExpanding the part (-44*y**2 + y - 27) using the distributive property, and we got: -(-1)*918*y**2 + y*(-34*y**2) + (-44*y**2)*(-34*y**2)\nReplacing (-34*y**2)*(-44*y**2 + y - 27) with -(-1)*918*y**2 + y*(-34*y**2) + (-44*y**2)*(-34*y**2) in the overall expression.\n#Step 3:\nCurrent expression: -27*(-34)*y**2 + y*(-34*y**2) + (-44*y**2)*(-34*y**2) + (-30*y**3)*(-44*y**2 + y - 27)\nSimplifying the partial expression: (-30*y**3)*(-44*y**2 + y - 27)\nExpanding the part (-44*y**2 + y - 27) using the distributive property, and we got: -(-1)*810*y**3 + y*(-30*y**3) + (-44*y**2)*(-30*y**3)\nReplacing (-30*y**3)*(-44*y**2 + y - 27) with -(-1)*810*y**3 + y*(-30*y**3) + (-44*y**2)*(-30*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -27*(-30)*y**3 - 27*(-34)*y**2 + y*(-34*y**2) + y*(-30*y**3) + (-44*y**2)*(-34*y**2) + (-44*y**2)*(-30*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n y*(-34*y**2) = -34*y**3\n y*(-30*y**3) = -30*y**4\n (-44*y**2)*(-34*y**2) = 1496*y**4\n (-44*y**2)*(-30*y**3) = 1320*y**5\n -27*-34*y**2 = 918*y**2\n -27*-30*y**3 = 810*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1320*y**5 - 30*y**4 + 1496*y**4 - 34*y**3 + 810*y**3 + 918*y**2\nCombining like terms, got 1320*y**5 + 1466*y**4 + 776*y**3 + 918*y**2\n#Step 6:\nCurrent expression: 1320*y**5 + 1466*y**4 + 776*y**3 + 918*y**2\nNo more calculations needed.\n1320*y**5 + 1466*y**4 + 776*y**3 + 918*y**2", "generated_answer": "1320*y**5 + 1466*y**4 + 776*y**3 + 918*y**2", "step_length": 6} {"cot_id": "e833c007a822eeb1f18cc9c864de0786090565d87eb11c30450f68ceb23446ae", "datapoint": {"question": "Simplify this expression: -1300*z**3 + 1235*z - 260\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1300*z**3 + 1235*z - 260", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 512, "polynomial_expr": "-1300*z**3 + 1235*z - 260", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -1300*z**3 + 1235*z - 260\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -1300*z**3 + 1235*z - 260\nNo more calculations needed.\n-1300*z**3 + 1235*z - 260", "generated_answer": "-1300*z**3 + 1235*z - 260", "step_length": 2} {"cot_id": "848996d40b7e70408974c39cf5008f699cf40def5dbd4c7f2b2b9ba0d9bbaac6", "datapoint": {"question": "Simplify this expression: (27 - 9*x)*(-39*x**3 - 20*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "351*x**4 - 1053*x**3 + 180*x**2 - 540*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 513, "polynomial_expr": "(27 - 9*x)*(-39*x**3 - 20*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27 - 9*x)*(-39*x**3 - 20*x)\nExpanding the part (27 - 9*x) using the distributive property, and we got: (-9*x)*(-39*x**3 - 20*x) + 27*(-39*x**3 - 20*x)\n#Step 2:\nCurrent expression: (-9*x)*(-39*x**3 - 20*x) + 27*(-39*x**3 - 20*x)\nSimplifying the partial expression: 27*(-39*x**3 - 20*x)\nExpanding the part (-39*x**3 - 20*x) using the distributive property, and we got: -20*x*27 - 39*x**3*27\nReplacing 27*(-39*x**3 - 20*x) with -20*x*27 - 39*x**3*27 in the overall expression.\n#Step 3:\nCurrent expression: -20*x*27 + (-9*x)*(-39*x**3 - 20*x) - 39*x**3*27\nSimplifying the partial expression: (-9*x)*(-39*x**3 - 20*x)\nExpanding the part (-39*x**3 - 20*x) using the distributive property, and we got: (-20*x)*(-9*x) + (-9*x)*(-39*x**3)\nReplacing (-9*x)*(-39*x**3 - 20*x) with (-20*x)*(-9*x) + (-9*x)*(-39*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-20*x)*(-9*x) - 20*x*27 + (-9*x)*(-39*x**3) - 39*x**3*27\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*x**3)*27 = -1053*x**3\n (-39*x**3)*(-9*x) = 351*x**4\n (-20*x)*27 = -540*x\n (-20*x)*(-9*x) = 180*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 351*x**4 - 1053*x**3 + 180*x**2 - 540*x\nNo more calculations needed.\n351*x**4 - 1053*x**3 + 180*x**2 - 540*x", "generated_answer": "351*x**4 - 1053*x**3 + 180*x**2 - 540*x", "step_length": 5} {"cot_id": "44492a858dddf6f63e568b3a29279c0520b71114d06c55af5233f50493bbabdb", "datapoint": {"question": "Calculate the following: (41*z**2 - 46*z)*(12*z**3 + 26)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "492*z**5 - 552*z**4 + 1066*z**2 - 1196*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 514, "polynomial_expr": "(41*z**2 - 46*z)*(12*z**3 + 26)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (41*z**2 - 46*z)*(12*z**3 + 26)\nExpanding the part (12*z**3 + 26) using the distributive property, and we got: (12*z**3)*(41*z**2 - 46*z) + 26*(41*z**2 - 46*z)\n#Step 2:\nCurrent expression: (12*z**3)*(41*z**2 - 46*z) + 26*(41*z**2 - 46*z)\nSimplifying the partial expression: 26*(41*z**2 - 46*z)\nExpanding the part (41*z**2 - 46*z) using the distributive property, and we got: -46*z*26 + (41*z**2)*26\nReplacing 26*(41*z**2 - 46*z) with -46*z*26 + (41*z**2)*26 in the overall expression.\n#Step 3:\nCurrent expression: -46*z*26 + (41*z**2)*26 + (12*z**3)*(41*z**2 - 46*z)\nSimplifying the partial expression: (12*z**3)*(41*z**2 - 46*z)\nExpanding the part (41*z**2 - 46*z) using the distributive property, and we got: (-46*z)*(12*z**3) + (41*z**2)*(12*z**3)\nReplacing (12*z**3)*(41*z**2 - 46*z) with (-46*z)*(12*z**3) + (41*z**2)*(12*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-46*z)*(12*z**3) - 46*z*26 + (41*z**2)*(12*z**3) + (41*z**2)*26\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*z)*26 = -1196*z\n (-46*z)*(12*z**3) = -552*z**4\n (41*z**2)*26 = 1066*z**2\n (41*z**2)*(12*z**3) = 492*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 492*z**5 - 552*z**4 + 1066*z**2 - 1196*z\nNo more calculations needed.\n492*z**5 - 552*z**4 + 1066*z**2 - 1196*z", "generated_answer": "492*z**5 - 552*z**4 + 1066*z**2 - 1196*z", "step_length": 5} {"cot_id": "c6e47d2f33e8925fd26e1572bd2d79df9e8b3c4ee5c12c6510a02888d0916573", "datapoint": {"question": "Calculate the following: (16 - 2*x**3)*(-36*x**2 + 9*x - 5)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "72*x**5 - 18*x**4 + 10*x**3 - 576*x**2 + 144*x - 80", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 515, "polynomial_expr": "(16 - 2*x**3)*(-36*x**2 + 9*x - 5)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (16 - 2*x**3)*(-36*x**2 + 9*x - 5)\nExpanding the part (16 - 2*x**3) using the distributive property, and we got: (-2*x**3)*(-36*x**2 + 9*x - 5) + 16*(-36*x**2 + 9*x - 5)\n#Step 2:\nCurrent expression: (-2*x**3)*(-36*x**2 + 9*x - 5) + 16*(-36*x**2 + 9*x - 5)\nSimplifying the partial expression: 16*(-36*x**2 + 9*x - 5)\nExpanding the part (-36*x**2 + 9*x - 5) using the distributive property, and we got: (9*x)*16 - 36*x**2*16 - 5*16\nReplacing 16*(-36*x**2 + 9*x - 5) with (9*x)*16 - 36*x**2*16 - 5*16 in the overall expression.\n#Step 3:\nCurrent expression: (9*x)*16 - 36*x**2*16 + (-2*x**3)*(-36*x**2 + 9*x - 5) - 80\nSimplifying the partial expression: (-2*x**3)*(-36*x**2 + 9*x - 5)\nExpanding the part (-36*x**2 + 9*x - 5) using the distributive property, and we got: -(-1)*10*x**3 + (9*x)*(-2*x**3) + (-36*x**2)*(-2*x**3)\nReplacing (-2*x**3)*(-36*x**2 + 9*x - 5) with -(-1)*10*x**3 + (9*x)*(-2*x**3) + (-36*x**2)*(-2*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -5*(-2)*x**3 + (9*x)*(-2*x**3) + (9*x)*16 + (-36*x**2)*(-2*x**3) - 36*x**2*16 - 80\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*x**2)*16 = -576*x**2\n (-36*x**2)*(-2*x**3) = 72*x**5\n (9*x)*16 = 144*x\n (9*x)*(-2*x**3) = -18*x**4\n -5*-2*x**3 = 10*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 72*x**5 - 18*x**4 + 10*x**3 - 576*x**2 + 144*x - 80\nNo more calculations needed.\n72*x**5 - 18*x**4 + 10*x**3 - 576*x**2 + 144*x - 80", "generated_answer": "72*x**5 - 18*x**4 + 10*x**3 - 576*x**2 + 144*x - 80", "step_length": 5} {"cot_id": "df60d6335f5da227012c860941971c1b39151d13f4e511e01bcfd06ad6578d67", "datapoint": {"question": "Calculate the following: (49 - 34*y)*(14*y**3 + 12*y**2 + 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-476*y**4 + 278*y**3 + 588*y**2 - 1292*y + 1862", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 516, "polynomial_expr": "(49 - 34*y)*(14*y**3 + 12*y**2 + 38)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (49 - 34*y)*(14*y**3 + 12*y**2 + 38)\nExpanding the part (49 - 34*y) using the distributive property, and we got: (-34*y)*(14*y**3 + 12*y**2 + 38) + 49*(14*y**3 + 12*y**2 + 38)\n#Step 2:\nCurrent expression: (-34*y)*(14*y**3 + 12*y**2 + 38) + 49*(14*y**3 + 12*y**2 + 38)\nSimplifying the partial expression: 49*(14*y**3 + 12*y**2 + 38)\nExpanding the part (14*y**3 + 12*y**2 + 38) using the distributive property, and we got: (12*y**2)*49 + (14*y**3)*49 + 38*49\nReplacing 49*(14*y**3 + 12*y**2 + 38) with (12*y**2)*49 + (14*y**3)*49 + 38*49 in the overall expression.\n#Step 3:\nCurrent expression: (-34*y)*(14*y**3 + 12*y**2 + 38) + (12*y**2)*49 + (14*y**3)*49 + 1862\nSimplifying the partial expression: (-34*y)*(14*y**3 + 12*y**2 + 38)\nExpanding the part (14*y**3 + 12*y**2 + 38) using the distributive property, and we got: (-34*y)*(12*y**2) + (-34*y)*(14*y**3) + 38*(-34*y)\nReplacing (-34*y)*(14*y**3 + 12*y**2 + 38) with (-34*y)*(12*y**2) + (-34*y)*(14*y**3) + 38*(-34*y) in the overall expression.\n#Step 4:\nCurrent expression: (-34*y)*(12*y**2) + (-34*y)*(14*y**3) + 38*(-34)*y + (12*y**2)*49 + (14*y**3)*49 + 1862\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (12*y**2)*49 = 588*y**2\n (12*y**2)*(-34*y) = -408*y**3\n (14*y**3)*49 = 686*y**3\n (14*y**3)*(-34*y) = -476*y**4\n 38*-34*y = -1292*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -476*y**4 - 408*y**3 + 686*y**3 + 588*y**2 - 1292*y + 1862\nCombining like terms, got -476*y**4 + 278*y**3 + 588*y**2 - 1292*y + 1862\n#Step 6:\nCurrent expression: -476*y**4 + 278*y**3 + 588*y**2 - 1292*y + 1862\nNo more calculations needed.\n-476*y**4 + 278*y**3 + 588*y**2 - 1292*y + 1862", "generated_answer": "-476*y**4 + 278*y**3 + 588*y**2 - 1292*y + 1862", "step_length": 6} {"cot_id": "cff4d3e75518b6e185c57b00029d2ca4ba86c3522c1448408898201435970c3d", "datapoint": {"question": "Calculate the following: (17*x**3 - 46)*(34*x**3 - 17*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "578*x**6 - 289*x**4 - 1564*x**3 + 782*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 517, "polynomial_expr": "(17*x**3 - 46)*(34*x**3 - 17*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (17*x**3 - 46)*(34*x**3 - 17*x)\nExpanding the part (17*x**3 - 46) using the distributive property, and we got: (17*x**3)*(34*x**3 - 17*x) - 46*(34*x**3 - 17*x)\n#Step 2:\nCurrent expression: (17*x**3)*(34*x**3 - 17*x) - 46*(34*x**3 - 17*x)\nSimplifying the partial expression: -46*(34*x**3 - 17*x)\nExpanding the part (34*x**3 - 17*x) using the distributive property, and we got: -17*x*(-46) + (34*x**3)*(-46)\nReplacing -46*(34*x**3 - 17*x) with -17*x*(-46) + (34*x**3)*(-46) in the overall expression.\n#Step 3:\nCurrent expression: -17*x*(-46) + (17*x**3)*(34*x**3 - 17*x) + (34*x**3)*(-46)\nSimplifying the partial expression: (17*x**3)*(34*x**3 - 17*x)\nExpanding the part (34*x**3 - 17*x) using the distributive property, and we got: (-17*x)*(17*x**3) + (17*x**3)*(34*x**3)\nReplacing (17*x**3)*(34*x**3 - 17*x) with (-17*x)*(17*x**3) + (17*x**3)*(34*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-17*x)*(17*x**3) - 17*x*(-46) + (17*x**3)*(34*x**3) + (34*x**3)*(-46)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-17*x)*-46 = 782*x\n (-17*x)*(17*x**3) = -289*x**4\n (34*x**3)*-46 = -1564*x**3\n (34*x**3)*(17*x**3) = 578*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 578*x**6 - 289*x**4 - 1564*x**3 + 782*x\nNo more calculations needed.\n578*x**6 - 289*x**4 - 1564*x**3 + 782*x", "generated_answer": "578*x**6 - 289*x**4 - 1564*x**3 + 782*x", "step_length": 5} {"cot_id": "c07e616993a087c40b0fb24a0aa3a82a9b80f1a8ff047d36a0d42fda5ef9f840", "datapoint": {"question": "Calculate the following: -210*z**2 - 336\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-210*z**2 - 336", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 518, "polynomial_expr": "-210*z**2 - 336", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -210*z**2 - 336\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -210*z**2 - 336\nNo more calculations needed.\n-210*z**2 - 336", "generated_answer": "-210*z**2 - 336", "step_length": 2} {"cot_id": "754767f7e1bc7329bc67ba3c5ca5ca72d27448c0bf0095bd9bea21e1dd1103e5", "datapoint": {"question": "Simplify this expression: -21*z*(54*z**2 - 5)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1134*z**3 + 105*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 519, "polynomial_expr": "-21*z*(54*z**2 - 5)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -21*z*(54*z**2 - 5)\nExpanding the part (54*z**2 - 5) using the distributive property, and we got: (-21*z)*(54*z**2) - (-1)*105*z\n#Step 2:\nCurrent expression: (-21*z)*(54*z**2) - (-1)*105*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -5*(-21*z) = 105*z\n (54*z**2)*(-21*z) = -1134*z**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1134*z**3 + 105*z\nNo more calculations needed.\n-1134*z**3 + 105*z", "generated_answer": "-1134*z**3 + 105*z", "step_length": 3} {"cot_id": "5f8b7df6c089a498b69413de5ad766c196c197503a99219e9d55e3c211d47cd1", "datapoint": {"question": "Simplify this expression: (6*z**3 + 35*z**2)*(-79*z**3 + 8*z**2 - 12*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-474*z**6 - 2717*z**5 + 208*z**4 - 420*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 520, "polynomial_expr": "(6*z**3 + 35*z**2)*(-79*z**3 + 8*z**2 - 12*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6*z**3 + 35*z**2)*(-79*z**3 + 8*z**2 - 12*z)\nExpanding the part (6*z**3 + 35*z**2) using the distributive property, and we got: (35*z**2)*(-79*z**3 + 8*z**2 - 12*z) + (6*z**3)*(-79*z**3 + 8*z**2 - 12*z)\n#Step 2:\nCurrent expression: (35*z**2)*(-79*z**3 + 8*z**2 - 12*z) + (6*z**3)*(-79*z**3 + 8*z**2 - 12*z)\nSimplifying the partial expression: (6*z**3)*(-79*z**3 + 8*z**2 - 12*z)\nExpanding the part (-79*z**3 + 8*z**2 - 12*z) using the distributive property, and we got: (-12*z)*(6*z**3) + (8*z**2)*(6*z**3) + (-79*z**3)*(6*z**3)\nReplacing (6*z**3)*(-79*z**3 + 8*z**2 - 12*z) with (-12*z)*(6*z**3) + (8*z**2)*(6*z**3) + (-79*z**3)*(6*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-12*z)*(6*z**3) + (8*z**2)*(6*z**3) + (35*z**2)*(-79*z**3 + 8*z**2 - 12*z) + (-79*z**3)*(6*z**3)\nSimplifying the partial expression: (35*z**2)*(-79*z**3 + 8*z**2 - 12*z)\nExpanding the part (-79*z**3 + 8*z**2 - 12*z) using the distributive property, and we got: (-12*z)*(35*z**2) + (8*z**2)*(35*z**2) + (35*z**2)*(-79*z**3)\nReplacing (35*z**2)*(-79*z**3 + 8*z**2 - 12*z) with (-12*z)*(35*z**2) + (8*z**2)*(35*z**2) + (35*z**2)*(-79*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-12*z)*(35*z**2) + (-12*z)*(6*z**3) + (8*z**2)*(35*z**2) + (8*z**2)*(6*z**3) + (35*z**2)*(-79*z**3) + (-79*z**3)*(6*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-79*z**3)*(6*z**3) = -474*z**6\n (-79*z**3)*(35*z**2) = -2765*z**5\n (-12*z)*(6*z**3) = -72*z**4\n (-12*z)*(35*z**2) = -420*z**3\n (8*z**2)*(6*z**3) = 48*z**5\n (8*z**2)*(35*z**2) = 280*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -474*z**6 - 2765*z**5 + 48*z**5 - 72*z**4 + 280*z**4 - 420*z**3\nCombining like terms, got -474*z**6 - 2717*z**5 + 208*z**4 - 420*z**3\n#Step 6:\nCurrent expression: -474*z**6 - 2717*z**5 + 208*z**4 - 420*z**3\nNo more calculations needed.\n-474*z**6 - 2717*z**5 + 208*z**4 - 420*z**3", "generated_answer": "-474*z**6 - 2717*z**5 + 208*z**4 - 420*z**3", "step_length": 6} {"cot_id": "2c8b9621065356079077c8a85e73c8ec0e6d17b06afad999f2bcb9a6b956a4cc", "datapoint": {"question": "Simplify this expression: 30*z**2*(31 - 44*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1320*z**3 + 930*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 521, "polynomial_expr": "30*z**2*(31 - 44*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 30*z**2*(31 - 44*z)\nExpanding the part (31 - 44*z) using the distributive property, and we got: (-44*z)*(30*z**2) + 31*(30*z**2)\n#Step 2:\nCurrent expression: (-44*z)*(30*z**2) + 31*(30*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 31*(30*z**2) = 930*z**2\n (-44*z)*(30*z**2) = -1320*z**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1320*z**3 + 930*z**2\nNo more calculations needed.\n-1320*z**3 + 930*z**2", "generated_answer": "-1320*z**3 + 930*z**2", "step_length": 3} {"cot_id": "12406aff137700e0d65e7241e06e0cc3334f210f6dc680c741989627d707824b", "datapoint": {"question": "Calculate the following: (45 - 33*y)*(-34*y**3 - 46*y - 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1122*y**4 - 1530*y**3 + 1518*y**2 - 1047*y - 1395", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 522, "polynomial_expr": "(45 - 33*y)*(-34*y**3 - 46*y - 31)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (45 - 33*y)*(-34*y**3 - 46*y - 31)\nExpanding the part (45 - 33*y) using the distributive property, and we got: (-33*y)*(-34*y**3 - 46*y - 31) + 45*(-34*y**3 - 46*y - 31)\n#Step 2:\nCurrent expression: (-33*y)*(-34*y**3 - 46*y - 31) + 45*(-34*y**3 - 46*y - 31)\nSimplifying the partial expression: 45*(-34*y**3 - 46*y - 31)\nExpanding the part (-34*y**3 - 46*y - 31) using the distributive property, and we got: -46*y*45 - 34*y**3*45 - 31*45\nReplacing 45*(-34*y**3 - 46*y - 31) with -46*y*45 - 34*y**3*45 - 31*45 in the overall expression.\n#Step 3:\nCurrent expression: -46*y*45 + (-33*y)*(-34*y**3 - 46*y - 31) - 34*y**3*45 - 1395\nSimplifying the partial expression: (-33*y)*(-34*y**3 - 46*y - 31)\nExpanding the part (-34*y**3 - 46*y - 31) using the distributive property, and we got: (-46*y)*(-33*y) + (-33*y)*(-34*y**3) - (-1)*1023*y\nReplacing (-33*y)*(-34*y**3 - 46*y - 31) with (-46*y)*(-33*y) + (-33*y)*(-34*y**3) - (-1)*1023*y in the overall expression.\n#Step 4:\nCurrent expression: (-46*y)*(-33*y) - 46*y*45 + (-33*y)*(-34*y**3) - 31*(-33)*y - 34*y**3*45 - 1395\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*y)*45 = -2070*y\n (-46*y)*(-33*y) = 1518*y**2\n (-34*y**3)*45 = -1530*y**3\n (-34*y**3)*(-33*y) = 1122*y**4\n -31*-33*y = 1023*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1122*y**4 - 1530*y**3 + 1518*y**2 - 2070*y + 1023*y - 1395\nCombining like terms, got 1122*y**4 - 1530*y**3 + 1518*y**2 - 1047*y - 1395\n#Step 6:\nCurrent expression: 1122*y**4 - 1530*y**3 + 1518*y**2 - 1047*y - 1395\nNo more calculations needed.\n1122*y**4 - 1530*y**3 + 1518*y**2 - 1047*y - 1395", "generated_answer": "1122*y**4 - 1530*y**3 + 1518*y**2 - 1047*y - 1395", "step_length": 6} {"cot_id": "dc54f636db9c329289c8de54d7574b559a5639d5fc08127d51cdc5922dba40ac", "datapoint": {"question": "Calculate the following: (-33*z - 45)*(-10*z**3 - 25*z**2 - 44*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "330*z**4 + 1275*z**3 + 2577*z**2 + 1980*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 523, "polynomial_expr": "(-33*z - 45)*(-10*z**3 - 25*z**2 - 44*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-33*z - 45)*(-10*z**3 - 25*z**2 - 44*z)\nExpanding the part (-33*z - 45) using the distributive property, and we got: (-33*z)*(-10*z**3 - 25*z**2 - 44*z) - 45*(-10*z**3 - 25*z**2 - 44*z)\n#Step 2:\nCurrent expression: (-33*z)*(-10*z**3 - 25*z**2 - 44*z) - 45*(-10*z**3 - 25*z**2 - 44*z)\nSimplifying the partial expression: -45*(-10*z**3 - 25*z**2 - 44*z)\nExpanding the part (-10*z**3 - 25*z**2 - 44*z) using the distributive property, and we got: -44*z*(-45) - 25*z**2*(-45) - 10*z**3*(-45)\nReplacing -45*(-10*z**3 - 25*z**2 - 44*z) with -44*z*(-45) - 25*z**2*(-45) - 10*z**3*(-45) in the overall expression.\n#Step 3:\nCurrent expression: -44*z*(-45) + (-33*z)*(-10*z**3 - 25*z**2 - 44*z) - 25*z**2*(-45) - 10*z**3*(-45)\nSimplifying the partial expression: (-33*z)*(-10*z**3 - 25*z**2 - 44*z)\nExpanding the part (-10*z**3 - 25*z**2 - 44*z) using the distributive property, and we got: (-44*z)*(-33*z) + (-33*z)*(-25*z**2) + (-33*z)*(-10*z**3)\nReplacing (-33*z)*(-10*z**3 - 25*z**2 - 44*z) with (-44*z)*(-33*z) + (-33*z)*(-25*z**2) + (-33*z)*(-10*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-44*z)*(-33*z) - 44*z*(-45) + (-33*z)*(-25*z**2) + (-33*z)*(-10*z**3) - 25*z**2*(-45) - 10*z**3*(-45)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-44*z)*-45 = 1980*z\n (-44*z)*(-33*z) = 1452*z**2\n (-25*z**2)*-45 = 1125*z**2\n (-25*z**2)*(-33*z) = 825*z**3\n (-10*z**3)*-45 = 450*z**3\n (-10*z**3)*(-33*z) = 330*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 330*z**4 + 450*z**3 + 825*z**3 + 1125*z**2 + 1452*z**2 + 1980*z\nCombining like terms, got 330*z**4 + 1275*z**3 + 2577*z**2 + 1980*z\n#Step 6:\nCurrent expression: 330*z**4 + 1275*z**3 + 2577*z**2 + 1980*z\nNo more calculations needed.\n330*z**4 + 1275*z**3 + 2577*z**2 + 1980*z", "generated_answer": "330*z**4 + 1275*z**3 + 2577*z**2 + 1980*z", "step_length": 6} {"cot_id": "df35770de45d012f6399323234eeee4af7ac5ab47b802481f6c251b2c9832137", "datapoint": {"question": "Simplify this expression: (8*y + 24)*(-28*y**3 - 33*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-224*y**4 - 672*y**3 - 264*y**2 - 792*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 524, "polynomial_expr": "(8*y + 24)*(-28*y**3 - 33*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (8*y + 24)*(-28*y**3 - 33*y)\nExpanding the part (8*y + 24) using the distributive property, and we got: (8*y)*(-28*y**3 - 33*y) + 24*(-28*y**3 - 33*y)\n#Step 2:\nCurrent expression: (8*y)*(-28*y**3 - 33*y) + 24*(-28*y**3 - 33*y)\nSimplifying the partial expression: 24*(-28*y**3 - 33*y)\nExpanding the part (-28*y**3 - 33*y) using the distributive property, and we got: -33*y*24 - 28*y**3*24\nReplacing 24*(-28*y**3 - 33*y) with -33*y*24 - 28*y**3*24 in the overall expression.\n#Step 3:\nCurrent expression: -33*y*24 + (8*y)*(-28*y**3 - 33*y) - 28*y**3*24\nSimplifying the partial expression: (8*y)*(-28*y**3 - 33*y)\nExpanding the part (-28*y**3 - 33*y) using the distributive property, and we got: (-33*y)*(8*y) + (8*y)*(-28*y**3)\nReplacing (8*y)*(-28*y**3 - 33*y) with (-33*y)*(8*y) + (8*y)*(-28*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-33*y)*(8*y) - 33*y*24 + (8*y)*(-28*y**3) - 28*y**3*24\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*y)*24 = -792*y\n (-33*y)*(8*y) = -264*y**2\n (-28*y**3)*24 = -672*y**3\n (-28*y**3)*(8*y) = -224*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -224*y**4 - 672*y**3 - 264*y**2 - 792*y\nNo more calculations needed.\n-224*y**4 - 672*y**3 - 264*y**2 - 792*y", "generated_answer": "-224*y**4 - 672*y**3 - 264*y**2 - 792*y", "step_length": 5} {"cot_id": "f65670318080928019c46e5615c683782c3f5804ab97aaff88ece6f09271b7ec", "datapoint": {"question": "Simplify this expression: (15*x**2 + 48*x)*(77*x**3 + 26)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1155*x**5 + 3696*x**4 + 390*x**2 + 1248*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 525, "polynomial_expr": "(15*x**2 + 48*x)*(77*x**3 + 26)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (15*x**2 + 48*x)*(77*x**3 + 26)\nExpanding the part (77*x**3 + 26) using the distributive property, and we got: (77*x**3)*(15*x**2 + 48*x) + 26*(15*x**2 + 48*x)\n#Step 2:\nCurrent expression: (77*x**3)*(15*x**2 + 48*x) + 26*(15*x**2 + 48*x)\nSimplifying the partial expression: 26*(15*x**2 + 48*x)\nExpanding the part (15*x**2 + 48*x) using the distributive property, and we got: (48*x)*26 + (15*x**2)*26\nReplacing 26*(15*x**2 + 48*x) with (48*x)*26 + (15*x**2)*26 in the overall expression.\n#Step 3:\nCurrent expression: (48*x)*26 + (15*x**2)*26 + (77*x**3)*(15*x**2 + 48*x)\nSimplifying the partial expression: (77*x**3)*(15*x**2 + 48*x)\nExpanding the part (15*x**2 + 48*x) using the distributive property, and we got: (48*x)*(77*x**3) + (15*x**2)*(77*x**3)\nReplacing (77*x**3)*(15*x**2 + 48*x) with (48*x)*(77*x**3) + (15*x**2)*(77*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (48*x)*(77*x**3) + (48*x)*26 + (15*x**2)*(77*x**3) + (15*x**2)*26\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (15*x**2)*26 = 390*x**2\n (15*x**2)*(77*x**3) = 1155*x**5\n (48*x)*26 = 1248*x\n (48*x)*(77*x**3) = 3696*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1155*x**5 + 3696*x**4 + 390*x**2 + 1248*x\nNo more calculations needed.\n1155*x**5 + 3696*x**4 + 390*x**2 + 1248*x", "generated_answer": "1155*x**5 + 3696*x**4 + 390*x**2 + 1248*x", "step_length": 5} {"cot_id": "f081ec0e21a1cc10592c0f387ef5874aacdc6b311725e5faf7dcda28912b1daf", "datapoint": {"question": "Calculate the following: (-4*x**2 - 68*x)*(-x**2 - 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "4*x**4 + 68*x**3 + 120*x**2 + 2040*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 526, "polynomial_expr": "(-4*x**2 - 68*x)*(-x**2 - 30)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-4*x**2 - 68*x)*(-x**2 - 30)\nExpanding the part (-x**2 - 30) using the distributive property, and we got: (-x**2)*(-4*x**2 - 68*x) - 30*(-4*x**2 - 68*x)\n#Step 2:\nCurrent expression: (-x**2)*(-4*x**2 - 68*x) - 30*(-4*x**2 - 68*x)\nSimplifying the partial expression: -30*(-4*x**2 - 68*x)\nExpanding the part (-4*x**2 - 68*x) using the distributive property, and we got: -68*x*(-30) - 4*x**2*(-30)\nReplacing -30*(-4*x**2 - 68*x) with -68*x*(-30) - 4*x**2*(-30) in the overall expression.\n#Step 3:\nCurrent expression: -68*x*(-30) - 4*x**2*(-30) + (-x**2)*(-4*x**2 - 68*x)\nSimplifying the partial expression: (-x**2)*(-4*x**2 - 68*x)\nExpanding the part (-4*x**2 - 68*x) using the distributive property, and we got: (-68*x)*(-x**2) + (-4*x**2)*(-x**2)\nReplacing (-x**2)*(-4*x**2 - 68*x) with (-68*x)*(-x**2) + (-4*x**2)*(-x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-68*x)*(-x**2) - 68*x*(-30) + (-4*x**2)*(-x**2) - 4*x**2*(-30)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-68*x)*-30 = 2040*x\n (-68*x)*(-x**2) = 68*x**3\n (-4*x**2)*-30 = 120*x**2\n (-4*x**2)*(-x**2) = 4*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 4*x**4 + 68*x**3 + 120*x**2 + 2040*x\nNo more calculations needed.\n4*x**4 + 68*x**3 + 120*x**2 + 2040*x", "generated_answer": "4*x**4 + 68*x**3 + 120*x**2 + 2040*x", "step_length": 5} {"cot_id": "4b93f81359b01e00ce2d29712fbd1677d54002ba864bd631100793a12401d67a", "datapoint": {"question": "Simplify this expression: (43*z**2 + 39*z)*(9*z**2 - 22*z + 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "387*z**4 - 595*z**3 + 647*z**2 + 1365*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 527, "polynomial_expr": "(43*z**2 + 39*z)*(9*z**2 - 22*z + 35)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (43*z**2 + 39*z)*(9*z**2 - 22*z + 35)\nExpanding the part (43*z**2 + 39*z) using the distributive property, and we got: (39*z)*(9*z**2 - 22*z + 35) + (43*z**2)*(9*z**2 - 22*z + 35)\n#Step 2:\nCurrent expression: (39*z)*(9*z**2 - 22*z + 35) + (43*z**2)*(9*z**2 - 22*z + 35)\nSimplifying the partial expression: (39*z)*(9*z**2 - 22*z + 35)\nExpanding the part (9*z**2 - 22*z + 35) using the distributive property, and we got: (-22*z)*(39*z) + 35*(39*z) + (39*z)*(9*z**2)\nReplacing (39*z)*(9*z**2 - 22*z + 35) with (-22*z)*(39*z) + 35*(39*z) + (39*z)*(9*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-22*z)*(39*z) + 35*39*z + (39*z)*(9*z**2) + (43*z**2)*(9*z**2 - 22*z + 35)\nSimplifying the partial expression: (43*z**2)*(9*z**2 - 22*z + 35)\nExpanding the part (9*z**2 - 22*z + 35) using the distributive property, and we got: (-22*z)*(43*z**2) + 35*(43*z**2) + (9*z**2)*(43*z**2)\nReplacing (43*z**2)*(9*z**2 - 22*z + 35) with (-22*z)*(43*z**2) + 35*(43*z**2) + (9*z**2)*(43*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-22*z)*(39*z) + (-22*z)*(43*z**2) + 35*43*z**2 + 35*39*z + (39*z)*(9*z**2) + (9*z**2)*(43*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*z)*(39*z) = -858*z**2\n (-22*z)*(43*z**2) = -946*z**3\n (9*z**2)*(39*z) = 351*z**3\n (9*z**2)*(43*z**2) = 387*z**4\n 35*39*z = 1365*z\n 35*43*z**2 = 1505*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 387*z**4 - 946*z**3 + 351*z**3 - 858*z**2 + 1505*z**2 + 1365*z\nCombining like terms, got 387*z**4 - 595*z**3 + 647*z**2 + 1365*z\n#Step 6:\nCurrent expression: 387*z**4 - 595*z**3 + 647*z**2 + 1365*z\nNo more calculations needed.\n387*z**4 - 595*z**3 + 647*z**2 + 1365*z", "generated_answer": "387*z**4 - 595*z**3 + 647*z**2 + 1365*z", "step_length": 6} {"cot_id": "1c74badc47510936435c21a60942b87fe831dd1d78a17f563207ae6195c9b9e1", "datapoint": {"question": "Calculate the following: (17*x**2 - 22*x)*(2*x**3 - 15*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "34*x**5 - 299*x**4 + 330*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 528, "polynomial_expr": "(17*x**2 - 22*x)*(2*x**3 - 15*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (17*x**2 - 22*x)*(2*x**3 - 15*x**2)\nExpanding the part (17*x**2 - 22*x) using the distributive property, and we got: (-22*x)*(2*x**3 - 15*x**2) + (17*x**2)*(2*x**3 - 15*x**2)\n#Step 2:\nCurrent expression: (-22*x)*(2*x**3 - 15*x**2) + (17*x**2)*(2*x**3 - 15*x**2)\nSimplifying the partial expression: (-22*x)*(2*x**3 - 15*x**2)\nExpanding the part (2*x**3 - 15*x**2) using the distributive property, and we got: (-22*x)*(-15*x**2) + (-22*x)*(2*x**3)\nReplacing (-22*x)*(2*x**3 - 15*x**2) with (-22*x)*(-15*x**2) + (-22*x)*(2*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-22*x)*(-15*x**2) + (-22*x)*(2*x**3) + (17*x**2)*(2*x**3 - 15*x**2)\nSimplifying the partial expression: (17*x**2)*(2*x**3 - 15*x**2)\nExpanding the part (2*x**3 - 15*x**2) using the distributive property, and we got: (-15*x**2)*(17*x**2) + (17*x**2)*(2*x**3)\nReplacing (17*x**2)*(2*x**3 - 15*x**2) with (-15*x**2)*(17*x**2) + (17*x**2)*(2*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-22*x)*(-15*x**2) + (-22*x)*(2*x**3) + (-15*x**2)*(17*x**2) + (17*x**2)*(2*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-15*x**2)*(-22*x) = 330*x**3\n (-15*x**2)*(17*x**2) = -255*x**4\n (2*x**3)*(-22*x) = -44*x**4\n (2*x**3)*(17*x**2) = 34*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 34*x**5 - 255*x**4 - 44*x**4 + 330*x**3\nCombining like terms, got 34*x**5 - 299*x**4 + 330*x**3\n#Step 6:\nCurrent expression: 34*x**5 - 299*x**4 + 330*x**3\nNo more calculations needed.\n34*x**5 - 299*x**4 + 330*x**3", "generated_answer": "34*x**5 - 299*x**4 + 330*x**3", "step_length": 6} {"cot_id": "b680fabec22fb54056ee28922d3ba81db2dde6b9643ff9e0681c0d86ada614f1", "datapoint": {"question": "Calculate the following: (35*x - 34)*(-40*x**3 + 9*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1400*x**4 + 1360*x**3 + 315*x**2 - 306*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 529, "polynomial_expr": "(35*x - 34)*(-40*x**3 + 9*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (35*x - 34)*(-40*x**3 + 9*x)\nExpanding the part (35*x - 34) using the distributive property, and we got: (35*x)*(-40*x**3 + 9*x) - 34*(-40*x**3 + 9*x)\n#Step 2:\nCurrent expression: (35*x)*(-40*x**3 + 9*x) - 34*(-40*x**3 + 9*x)\nSimplifying the partial expression: -34*(-40*x**3 + 9*x)\nExpanding the part (-40*x**3 + 9*x) using the distributive property, and we got: (9*x)*(-34) - 40*x**3*(-34)\nReplacing -34*(-40*x**3 + 9*x) with (9*x)*(-34) - 40*x**3*(-34) in the overall expression.\n#Step 3:\nCurrent expression: (9*x)*(-34) + (35*x)*(-40*x**3 + 9*x) - 40*x**3*(-34)\nSimplifying the partial expression: (35*x)*(-40*x**3 + 9*x)\nExpanding the part (-40*x**3 + 9*x) using the distributive property, and we got: (9*x)*(35*x) + (35*x)*(-40*x**3)\nReplacing (35*x)*(-40*x**3 + 9*x) with (9*x)*(35*x) + (35*x)*(-40*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (9*x)*(35*x) + (9*x)*(-34) + (35*x)*(-40*x**3) - 40*x**3*(-34)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*x**3)*-34 = 1360*x**3\n (-40*x**3)*(35*x) = -1400*x**4\n (9*x)*-34 = -306*x\n (9*x)*(35*x) = 315*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1400*x**4 + 1360*x**3 + 315*x**2 - 306*x\nNo more calculations needed.\n-1400*x**4 + 1360*x**3 + 315*x**2 - 306*x", "generated_answer": "-1400*x**4 + 1360*x**3 + 315*x**2 - 306*x", "step_length": 5} {"cot_id": "386de4d6341f33e15bc636ce2eefa47f6656629bf419029f64899523671c2ad7", "datapoint": {"question": "Simplify this expression: (-29*x**2 - 15)*(18*x**2 - 48*x - 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-522*x**4 + 1392*x**3 + 1180*x**2 + 720*x + 750", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 530, "polynomial_expr": "(-29*x**2 - 15)*(18*x**2 - 48*x - 50)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-29*x**2 - 15)*(18*x**2 - 48*x - 50)\nExpanding the part (-29*x**2 - 15) using the distributive property, and we got: (-29*x**2)*(18*x**2 - 48*x - 50) - 15*(18*x**2 - 48*x - 50)\n#Step 2:\nCurrent expression: (-29*x**2)*(18*x**2 - 48*x - 50) - 15*(18*x**2 - 48*x - 50)\nSimplifying the partial expression: -15*(18*x**2 - 48*x - 50)\nExpanding the part (18*x**2 - 48*x - 50) using the distributive property, and we got: -48*x*(-15) + (18*x**2)*(-15) - 50*(-15)\nReplacing -15*(18*x**2 - 48*x - 50) with -48*x*(-15) + (18*x**2)*(-15) - 50*(-15) in the overall expression.\n#Step 3:\nCurrent expression: -48*x*(-15) + (-29*x**2)*(18*x**2 - 48*x - 50) + (18*x**2)*(-15) + 750\nSimplifying the partial expression: (-29*x**2)*(18*x**2 - 48*x - 50)\nExpanding the part (18*x**2 - 48*x - 50) using the distributive property, and we got: (-48*x)*(-29*x**2) - (-1)*1450*x**2 + (-29*x**2)*(18*x**2)\nReplacing (-29*x**2)*(18*x**2 - 48*x - 50) with (-48*x)*(-29*x**2) - (-1)*1450*x**2 + (-29*x**2)*(18*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-48*x)*(-29*x**2) - 48*x*(-15) - 50*(-29)*x**2 + (-29*x**2)*(18*x**2) + (18*x**2)*(-15) + 750\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*x)*-15 = 720*x\n (-48*x)*(-29*x**2) = 1392*x**3\n (18*x**2)*-15 = -270*x**2\n (18*x**2)*(-29*x**2) = -522*x**4\n -50*-29*x**2 = 1450*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -522*x**4 + 1392*x**3 - 270*x**2 + 1450*x**2 + 720*x + 750\nCombining like terms, got -522*x**4 + 1392*x**3 + 1180*x**2 + 720*x + 750\n#Step 6:\nCurrent expression: -522*x**4 + 1392*x**3 + 1180*x**2 + 720*x + 750\nNo more calculations needed.\n-522*x**4 + 1392*x**3 + 1180*x**2 + 720*x + 750", "generated_answer": "-522*x**4 + 1392*x**3 + 1180*x**2 + 720*x + 750", "step_length": 6} {"cot_id": "21750bd10e7817a687de2bff4438f071a13057e1d1901bee70c5b64aa4781ce3", "datapoint": {"question": "Calculate the following: 38*z**2*(40*z**3 - 18*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1520*z**5 - 684*z**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 531, "polynomial_expr": "38*z**2*(40*z**3 - 18*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 38*z**2*(40*z**3 - 18*z**2)\nExpanding the part (40*z**3 - 18*z**2) using the distributive property, and we got: (-18*z**2)*(38*z**2) + (38*z**2)*(40*z**3)\n#Step 2:\nCurrent expression: (-18*z**2)*(38*z**2) + (38*z**2)*(40*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-18*z**2)*(38*z**2) = -684*z**4\n (40*z**3)*(38*z**2) = 1520*z**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1520*z**5 - 684*z**4\nNo more calculations needed.\n1520*z**5 - 684*z**4", "generated_answer": "1520*z**5 - 684*z**4", "step_length": 3} {"cot_id": "2e02c9d89c8af02d6761db87dfc158a8a810d13a00380f8fa5b6f1d47331a917", "datapoint": {"question": "Simplify this expression: (-10*y**2 - 44)*(-34*y**3 - 3*y**2 - 37*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "340*y**5 + 30*y**4 + 1866*y**3 + 132*y**2 + 1628*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 532, "polynomial_expr": "(-10*y**2 - 44)*(-34*y**3 - 3*y**2 - 37*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-10*y**2 - 44)*(-34*y**3 - 3*y**2 - 37*y)\nExpanding the part (-10*y**2 - 44) using the distributive property, and we got: (-10*y**2)*(-34*y**3 - 3*y**2 - 37*y) - 44*(-34*y**3 - 3*y**2 - 37*y)\n#Step 2:\nCurrent expression: (-10*y**2)*(-34*y**3 - 3*y**2 - 37*y) - 44*(-34*y**3 - 3*y**2 - 37*y)\nSimplifying the partial expression: -44*(-34*y**3 - 3*y**2 - 37*y)\nExpanding the part (-34*y**3 - 3*y**2 - 37*y) using the distributive property, and we got: -37*y*(-44) - 3*y**2*(-44) - 34*y**3*(-44)\nReplacing -44*(-34*y**3 - 3*y**2 - 37*y) with -37*y*(-44) - 3*y**2*(-44) - 34*y**3*(-44) in the overall expression.\n#Step 3:\nCurrent expression: -37*y*(-44) + (-10*y**2)*(-34*y**3 - 3*y**2 - 37*y) - 3*y**2*(-44) - 34*y**3*(-44)\nSimplifying the partial expression: (-10*y**2)*(-34*y**3 - 3*y**2 - 37*y)\nExpanding the part (-34*y**3 - 3*y**2 - 37*y) using the distributive property, and we got: (-37*y)*(-10*y**2) + (-10*y**2)*(-3*y**2) + (-10*y**2)*(-34*y**3)\nReplacing (-10*y**2)*(-34*y**3 - 3*y**2 - 37*y) with (-37*y)*(-10*y**2) + (-10*y**2)*(-3*y**2) + (-10*y**2)*(-34*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-37*y)*(-10*y**2) - 37*y*(-44) + (-10*y**2)*(-3*y**2) + (-10*y**2)*(-34*y**3) - 3*y**2*(-44) - 34*y**3*(-44)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*y)*-44 = 1628*y\n (-37*y)*(-10*y**2) = 370*y**3\n (-34*y**3)*-44 = 1496*y**3\n (-34*y**3)*(-10*y**2) = 340*y**5\n (-3*y**2)*-44 = 132*y**2\n (-3*y**2)*(-10*y**2) = 30*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 340*y**5 + 30*y**4 + 370*y**3 + 1496*y**3 + 132*y**2 + 1628*y\nCombining like terms, got 340*y**5 + 30*y**4 + 1866*y**3 + 132*y**2 + 1628*y\n#Step 6:\nCurrent expression: 340*y**5 + 30*y**4 + 1866*y**3 + 132*y**2 + 1628*y\nNo more calculations needed.\n340*y**5 + 30*y**4 + 1866*y**3 + 132*y**2 + 1628*y", "generated_answer": "340*y**5 + 30*y**4 + 1866*y**3 + 132*y**2 + 1628*y", "step_length": 6} {"cot_id": "caab1e47fb94794ef26048abe1e6891864c79b2b8992efa204dbc986d1595a2c", "datapoint": {"question": "Calculate the following: (-8*y**2 - 42*y + 29)*(2*y**2 + 47*y + 3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-16*y**4 - 460*y**3 - 1940*y**2 + 1237*y + 87", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 533, "polynomial_expr": "(-8*y**2 - 42*y + 29)*(2*y**2 + 47*y + 3)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-8*y**2 - 42*y + 29)*(2*y**2 + 47*y + 3)\nExpanding the part (2*y**2 + 47*y + 3) using the distributive property, and we got: (47*y)*(-8*y**2 - 42*y + 29) + (2*y**2)*(-8*y**2 - 42*y + 29) + 3*(-8*y**2 - 42*y + 29)\n#Step 2:\nCurrent expression: (47*y)*(-8*y**2 - 42*y + 29) + (2*y**2)*(-8*y**2 - 42*y + 29) + 3*(-8*y**2 - 42*y + 29)\nSimplifying the partial expression: 3*(-8*y**2 - 42*y + 29)\nExpanding the part (-8*y**2 - 42*y + 29) using the distributive property, and we got: -42*y*3 - 8*y**2*3 + 29*3\nReplacing 3*(-8*y**2 - 42*y + 29) with -42*y*3 - 8*y**2*3 + 29*3 in the overall expression.\n#Step 3:\nCurrent expression: -42*y*3 + (47*y)*(-8*y**2 - 42*y + 29) - 8*y**2*3 + (2*y**2)*(-8*y**2 - 42*y + 29) + 87\nSimplifying the partial expression: (2*y**2)*(-8*y**2 - 42*y + 29)\nExpanding the part (-8*y**2 - 42*y + 29) using the distributive property, and we got: (-42*y)*(2*y**2) + 29*(2*y**2) + (-8*y**2)*(2*y**2)\nReplacing (2*y**2)*(-8*y**2 - 42*y + 29) with (-42*y)*(2*y**2) + 29*(2*y**2) + (-8*y**2)*(2*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-42*y)*(2*y**2) - 42*y*3 + 29*2*y**2 + (47*y)*(-8*y**2 - 42*y + 29) + (-8*y**2)*(2*y**2) - 8*y**2*3 + 87\nSimplifying the partial expression: (47*y)*(-8*y**2 - 42*y + 29)\nExpanding the part (-8*y**2 - 42*y + 29) using the distributive property, and we got: (-42*y)*(47*y) + 29*(47*y) + (47*y)*(-8*y**2)\nReplacing (47*y)*(-8*y**2 - 42*y + 29) with (-42*y)*(47*y) + 29*(47*y) + (47*y)*(-8*y**2) in the overall expression.\n#Step 5:\nCurrent expression: (-42*y)*(47*y) + (-42*y)*(2*y**2) - 42*y*3 + 29*2*y**2 + 29*47*y + (47*y)*(-8*y**2) + (-8*y**2)*(2*y**2) - 8*y**2*3 + 87\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*y)*3 = -126*y\n (-42*y)*(2*y**2) = -84*y**3\n (-42*y)*(47*y) = -1974*y**2\n (-8*y**2)*3 = -24*y**2\n (-8*y**2)*(2*y**2) = -16*y**4\n (-8*y**2)*(47*y) = -376*y**3\n 29*2*y**2 = 58*y**2\n 29*47*y = 1363*y\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -16*y**4 - 376*y**3 - 84*y**3 - 1974*y**2 - 24*y**2 + 58*y**2 - 126*y + 1363*y + 87\nCombining like terms, got -16*y**4 - 460*y**3 - 1940*y**2 + 1237*y + 87\n#Step 7:\nCurrent expression: -16*y**4 - 460*y**3 - 1940*y**2 + 1237*y + 87\nNo more calculations needed.\n-16*y**4 - 460*y**3 - 1940*y**2 + 1237*y + 87", "generated_answer": "-16*y**4 - 460*y**3 - 1940*y**2 + 1237*y + 87", "step_length": 7} {"cot_id": "becaf5eaa3ee6ce9e84ab71e52ce81a1abe7f1a35d1a6ebc30a9e85ccc86ec68", "datapoint": {"question": "Calculate the following: (6 - z)*(43*z**2 + 45*z - 19)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-43*z**3 + 213*z**2 + 289*z - 114", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 534, "polynomial_expr": "(6 - z)*(43*z**2 + 45*z - 19)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6 - z)*(43*z**2 + 45*z - 19)\nExpanding the part (6 - z) using the distributive property, and we got: (-z)*(43*z**2 + 45*z - 19) + 6*(43*z**2 + 45*z - 19)\n#Step 2:\nCurrent expression: (-z)*(43*z**2 + 45*z - 19) + 6*(43*z**2 + 45*z - 19)\nSimplifying the partial expression: 6*(43*z**2 + 45*z - 19)\nExpanding the part (43*z**2 + 45*z - 19) using the distributive property, and we got: (45*z)*6 + (43*z**2)*6 - 19*6\nReplacing 6*(43*z**2 + 45*z - 19) with (45*z)*6 + (43*z**2)*6 - 19*6 in the overall expression.\n#Step 3:\nCurrent expression: (-z)*(43*z**2 + 45*z - 19) + (45*z)*6 + (43*z**2)*6 - 114\nSimplifying the partial expression: (-z)*(43*z**2 + 45*z - 19)\nExpanding the part (43*z**2 + 45*z - 19) using the distributive property, and we got: (-z)*(45*z) + (-z)*(43*z**2) - (-1)*19*z\nReplacing (-z)*(43*z**2 + 45*z - 19) with (-z)*(45*z) + (-z)*(43*z**2) - (-1)*19*z in the overall expression.\n#Step 4:\nCurrent expression: (-z)*(45*z) + (-z)*(43*z**2) - 19*(-1)*z + (45*z)*6 + (43*z**2)*6 - 114\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (43*z**2)*6 = 258*z**2\n (43*z**2)*(-z) = -43*z**3\n (45*z)*6 = 270*z\n (45*z)*(-z) = -45*z**2\n -19*-1*z = 19*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -43*z**3 - 45*z**2 + 258*z**2 + 19*z + 270*z - 114\nCombining like terms, got -43*z**3 + 213*z**2 + 289*z - 114\n#Step 6:\nCurrent expression: -43*z**3 + 213*z**2 + 289*z - 114\nNo more calculations needed.\n-43*z**3 + 213*z**2 + 289*z - 114", "generated_answer": "-43*z**3 + 213*z**2 + 289*z - 114", "step_length": 6} {"cot_id": "02f5988603b2f57a5ee790dd0cd8352fa4962b2623f1ae7e5529a48a2f1fefa8", "datapoint": {"question": "Simplify this expression: (-16*y**2 - 13*y - 8)*(y**3 + 9*y**2 - 6*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-16*y**5 - 157*y**4 - 29*y**3 + 6*y**2 + 48*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 535, "polynomial_expr": "(-16*y**2 - 13*y - 8)*(y**3 + 9*y**2 - 6*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-16*y**2 - 13*y - 8)*(y**3 + 9*y**2 - 6*y)\nExpanding the part (-16*y**2 - 13*y - 8) using the distributive property, and we got: (-13*y)*(y**3 + 9*y**2 - 6*y) + (-16*y**2)*(y**3 + 9*y**2 - 6*y) - 8*(y**3 + 9*y**2 - 6*y)\n#Step 2:\nCurrent expression: (-13*y)*(y**3 + 9*y**2 - 6*y) + (-16*y**2)*(y**3 + 9*y**2 - 6*y) - 8*(y**3 + 9*y**2 - 6*y)\nSimplifying the partial expression: -8*(y**3 + 9*y**2 - 6*y)\nExpanding the part (y**3 + 9*y**2 - 6*y) using the distributive property, and we got: -6*y*(-8) + y**3*(-8) + (9*y**2)*(-8)\nReplacing -8*(y**3 + 9*y**2 - 6*y) with -6*y*(-8) + y**3*(-8) + (9*y**2)*(-8) in the overall expression.\n#Step 3:\nCurrent expression: (-13*y)*(y**3 + 9*y**2 - 6*y) - 6*y*(-8) + y**3*(-8) + (-16*y**2)*(y**3 + 9*y**2 - 6*y) + (9*y**2)*(-8)\nSimplifying the partial expression: (-16*y**2)*(y**3 + 9*y**2 - 6*y)\nExpanding the part (y**3 + 9*y**2 - 6*y) using the distributive property, and we got: (-6*y)*(-16*y**2) + (-16*y**2)*y**3 + (-16*y**2)*(9*y**2)\nReplacing (-16*y**2)*(y**3 + 9*y**2 - 6*y) with (-6*y)*(-16*y**2) + (-16*y**2)*y**3 + (-16*y**2)*(9*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-13*y)*(y**3 + 9*y**2 - 6*y) + (-6*y)*(-16*y**2) - 6*y*(-8) + (-16*y**2)*y**3 + y**3*(-8) + (-16*y**2)*(9*y**2) + (9*y**2)*(-8)\nSimplifying the partial expression: (-13*y)*(y**3 + 9*y**2 - 6*y)\nExpanding the part (y**3 + 9*y**2 - 6*y) using the distributive property, and we got: (-13*y)*(-6*y) + (-13*y)*y**3 + (-13*y)*(9*y**2)\nReplacing (-13*y)*(y**3 + 9*y**2 - 6*y) with (-13*y)*(-6*y) + (-13*y)*y**3 + (-13*y)*(9*y**2) in the overall expression.\n#Step 5:\nCurrent expression: (-13*y)*(-6*y) + (-13*y)*y**3 + (-13*y)*(9*y**2) + (-6*y)*(-16*y**2) - 6*y*(-8) + (-16*y**2)*y**3 + y**3*(-8) + (-16*y**2)*(9*y**2) + (9*y**2)*(-8)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n y**3*-8 = -8*y**3\n y**3*(-16*y**2) = -16*y**5\n y**3*(-13*y) = -13*y**4\n (-6*y)*-8 = 48*y\n (-6*y)*(-16*y**2) = 96*y**3\n (-6*y)*(-13*y) = 78*y**2\n (9*y**2)*-8 = -72*y**2\n (9*y**2)*(-16*y**2) = -144*y**4\n (9*y**2)*(-13*y) = -117*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -16*y**5 - 144*y**4 - 13*y**4 - 117*y**3 - 8*y**3 + 96*y**3 - 72*y**2 + 78*y**2 + 48*y\nCombining like terms, got -16*y**5 - 157*y**4 - 29*y**3 + 6*y**2 + 48*y\n#Step 7:\nCurrent expression: -16*y**5 - 157*y**4 - 29*y**3 + 6*y**2 + 48*y\nNo more calculations needed.\n-16*y**5 - 157*y**4 - 29*y**3 + 6*y**2 + 48*y", "generated_answer": "-16*y**5 - 157*y**4 - 29*y**3 + 6*y**2 + 48*y", "step_length": 7} {"cot_id": "a5ee40d74c7140940108944d598acdcbcdf8eceffcea66d89989778b94e00606", "datapoint": {"question": "Simplify this expression: (-41*y**3 - 5*y**2 + 2*y)*(50*y**3 - 37*y**2 + 11*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2050*y**6 + 1267*y**5 - 166*y**4 - 129*y**3 + 22*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 536, "polynomial_expr": "(-41*y**3 - 5*y**2 + 2*y)*(50*y**3 - 37*y**2 + 11*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-41*y**3 - 5*y**2 + 2*y)*(50*y**3 - 37*y**2 + 11*y)\nExpanding the part (-41*y**3 - 5*y**2 + 2*y) using the distributive property, and we got: (2*y)*(50*y**3 - 37*y**2 + 11*y) + (-5*y**2)*(50*y**3 - 37*y**2 + 11*y) + (-41*y**3)*(50*y**3 - 37*y**2 + 11*y)\n#Step 2:\nCurrent expression: (2*y)*(50*y**3 - 37*y**2 + 11*y) + (-5*y**2)*(50*y**3 - 37*y**2 + 11*y) + (-41*y**3)*(50*y**3 - 37*y**2 + 11*y)\nSimplifying the partial expression: (-41*y**3)*(50*y**3 - 37*y**2 + 11*y)\nExpanding the part (50*y**3 - 37*y**2 + 11*y) using the distributive property, and we got: (11*y)*(-41*y**3) + (-37*y**2)*(-41*y**3) + (-41*y**3)*(50*y**3)\nReplacing (-41*y**3)*(50*y**3 - 37*y**2 + 11*y) with (11*y)*(-41*y**3) + (-37*y**2)*(-41*y**3) + (-41*y**3)*(50*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (2*y)*(50*y**3 - 37*y**2 + 11*y) + (11*y)*(-41*y**3) + (-37*y**2)*(-41*y**3) + (-5*y**2)*(50*y**3 - 37*y**2 + 11*y) + (-41*y**3)*(50*y**3)\nSimplifying the partial expression: (-5*y**2)*(50*y**3 - 37*y**2 + 11*y)\nExpanding the part (50*y**3 - 37*y**2 + 11*y) using the distributive property, and we got: (11*y)*(-5*y**2) + (-37*y**2)*(-5*y**2) + (-5*y**2)*(50*y**3)\nReplacing (-5*y**2)*(50*y**3 - 37*y**2 + 11*y) with (11*y)*(-5*y**2) + (-37*y**2)*(-5*y**2) + (-5*y**2)*(50*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (2*y)*(50*y**3 - 37*y**2 + 11*y) + (11*y)*(-5*y**2) + (11*y)*(-41*y**3) + (-37*y**2)*(-5*y**2) + (-37*y**2)*(-41*y**3) + (-5*y**2)*(50*y**3) + (-41*y**3)*(50*y**3)\nSimplifying the partial expression: (2*y)*(50*y**3 - 37*y**2 + 11*y)\nExpanding the part (50*y**3 - 37*y**2 + 11*y) using the distributive property, and we got: (2*y)*(11*y) + (2*y)*(-37*y**2) + (2*y)*(50*y**3)\nReplacing (2*y)*(50*y**3 - 37*y**2 + 11*y) with (2*y)*(11*y) + (2*y)*(-37*y**2) + (2*y)*(50*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (2*y)*(11*y) + (2*y)*(-37*y**2) + (2*y)*(50*y**3) + (11*y)*(-5*y**2) + (11*y)*(-41*y**3) + (-37*y**2)*(-5*y**2) + (-37*y**2)*(-41*y**3) + (-5*y**2)*(50*y**3) + (-41*y**3)*(50*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*y**2)*(-41*y**3) = 1517*y**5\n (-37*y**2)*(-5*y**2) = 185*y**4\n (-37*y**2)*(2*y) = -74*y**3\n (11*y)*(-41*y**3) = -451*y**4\n (11*y)*(-5*y**2) = -55*y**3\n (11*y)*(2*y) = 22*y**2\n (50*y**3)*(-41*y**3) = -2050*y**6\n (50*y**3)*(-5*y**2) = -250*y**5\n (50*y**3)*(2*y) = 100*y**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -2050*y**6 - 250*y**5 + 1517*y**5 - 451*y**4 + 100*y**4 + 185*y**4 - 74*y**3 - 55*y**3 + 22*y**2\nCombining like terms, got -2050*y**6 + 1267*y**5 - 166*y**4 - 129*y**3 + 22*y**2\n#Step 7:\nCurrent expression: -2050*y**6 + 1267*y**5 - 166*y**4 - 129*y**3 + 22*y**2\nNo more calculations needed.\n-2050*y**6 + 1267*y**5 - 166*y**4 - 129*y**3 + 22*y**2", "generated_answer": "-2050*y**6 + 1267*y**5 - 166*y**4 - 129*y**3 + 22*y**2", "step_length": 7} {"cot_id": "e285f2382a9dd2620d659b4a50ec6b0c55d2509705a9e4ca5ef62b7452029674", "datapoint": {"question": "Calculate the following: (30*y**2 + 46*y - 14)*(49*y**2 - 3*y + 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1470*y**4 + 2164*y**3 + 586*y**2 + 2204*y - 658", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 537, "polynomial_expr": "(30*y**2 + 46*y - 14)*(49*y**2 - 3*y + 47)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (30*y**2 + 46*y - 14)*(49*y**2 - 3*y + 47)\nExpanding the part (30*y**2 + 46*y - 14) using the distributive property, and we got: (46*y)*(49*y**2 - 3*y + 47) + (30*y**2)*(49*y**2 - 3*y + 47) - 14*(49*y**2 - 3*y + 47)\n#Step 2:\nCurrent expression: (46*y)*(49*y**2 - 3*y + 47) + (30*y**2)*(49*y**2 - 3*y + 47) - 14*(49*y**2 - 3*y + 47)\nSimplifying the partial expression: -14*(49*y**2 - 3*y + 47)\nExpanding the part (49*y**2 - 3*y + 47) using the distributive property, and we got: -3*y*(-14) + (49*y**2)*(-14) + 47*(-14)\nReplacing -14*(49*y**2 - 3*y + 47) with -3*y*(-14) + (49*y**2)*(-14) + 47*(-14) in the overall expression.\n#Step 3:\nCurrent expression: -3*y*(-14) + (46*y)*(49*y**2 - 3*y + 47) + (30*y**2)*(49*y**2 - 3*y + 47) + (49*y**2)*(-14) - 658\nSimplifying the partial expression: (30*y**2)*(49*y**2 - 3*y + 47)\nExpanding the part (49*y**2 - 3*y + 47) using the distributive property, and we got: (-3*y)*(30*y**2) + 47*(30*y**2) + (30*y**2)*(49*y**2)\nReplacing (30*y**2)*(49*y**2 - 3*y + 47) with (-3*y)*(30*y**2) + 47*(30*y**2) + (30*y**2)*(49*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-3*y)*(30*y**2) - 3*y*(-14) + 47*30*y**2 + (46*y)*(49*y**2 - 3*y + 47) + (30*y**2)*(49*y**2) + (49*y**2)*(-14) - 658\nSimplifying the partial expression: (46*y)*(49*y**2 - 3*y + 47)\nExpanding the part (49*y**2 - 3*y + 47) using the distributive property, and we got: (-3*y)*(46*y) + 47*(46*y) + (46*y)*(49*y**2)\nReplacing (46*y)*(49*y**2 - 3*y + 47) with (-3*y)*(46*y) + 47*(46*y) + (46*y)*(49*y**2) in the overall expression.\n#Step 5:\nCurrent expression: (-3*y)*(46*y) + (-3*y)*(30*y**2) - 3*y*(-14) + 47*30*y**2 + 47*46*y + (46*y)*(49*y**2) + (30*y**2)*(49*y**2) + (49*y**2)*(-14) - 658\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-3*y)*-14 = 42*y\n (-3*y)*(30*y**2) = -90*y**3\n (-3*y)*(46*y) = -138*y**2\n (49*y**2)*-14 = -686*y**2\n (49*y**2)*(30*y**2) = 1470*y**4\n (49*y**2)*(46*y) = 2254*y**3\n 47*30*y**2 = 1410*y**2\n 47*46*y = 2162*y\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1470*y**4 - 90*y**3 + 2254*y**3 - 686*y**2 - 138*y**2 + 1410*y**2 + 42*y + 2162*y - 658\nCombining like terms, got 1470*y**4 + 2164*y**3 + 586*y**2 + 2204*y - 658\n#Step 7:\nCurrent expression: 1470*y**4 + 2164*y**3 + 586*y**2 + 2204*y - 658\nNo more calculations needed.\n1470*y**4 + 2164*y**3 + 586*y**2 + 2204*y - 658", "generated_answer": "1470*y**4 + 2164*y**3 + 586*y**2 + 2204*y - 658", "step_length": 7} {"cot_id": "2bbb001a8a3198cfc2d3558921fcf20d49e50d18b36ccb6221cf27ac56b9a1da", "datapoint": {"question": "Calculate the following: 16*z*(48*z - 43)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "768*z**2 - 688*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 538, "polynomial_expr": "16*z*(48*z - 43)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 16*z*(48*z - 43)\nExpanding the part (48*z - 43) using the distributive property, and we got: -688*z + (16*z)*(48*z)\n#Step 2:\nCurrent expression: -688*z + (16*z)*(48*z)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -43*(16*z) = -688*z\n (48*z)*(16*z) = 768*z**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 768*z**2 - 688*z\nNo more calculations needed.\n768*z**2 - 688*z", "generated_answer": "768*z**2 - 688*z", "step_length": 3} {"cot_id": "a6928fe54be1493c8217eb4cbd8b84ec308c2601a1ebc606be8eb18c3b430a4b", "datapoint": {"question": "Simplify this expression: (47*z**3 + 19*z)*(30*z**3 - 37*z**2 - 20*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1410*z**6 - 1739*z**5 - 370*z**4 - 703*z**3 - 380*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 539, "polynomial_expr": "(47*z**3 + 19*z)*(30*z**3 - 37*z**2 - 20*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (47*z**3 + 19*z)*(30*z**3 - 37*z**2 - 20*z)\nExpanding the part (47*z**3 + 19*z) using the distributive property, and we got: (19*z)*(30*z**3 - 37*z**2 - 20*z) + (47*z**3)*(30*z**3 - 37*z**2 - 20*z)\n#Step 2:\nCurrent expression: (19*z)*(30*z**3 - 37*z**2 - 20*z) + (47*z**3)*(30*z**3 - 37*z**2 - 20*z)\nSimplifying the partial expression: (19*z)*(30*z**3 - 37*z**2 - 20*z)\nExpanding the part (30*z**3 - 37*z**2 - 20*z) using the distributive property, and we got: (-20*z)*(19*z) + (19*z)*(-37*z**2) + (19*z)*(30*z**3)\nReplacing (19*z)*(30*z**3 - 37*z**2 - 20*z) with (-20*z)*(19*z) + (19*z)*(-37*z**2) + (19*z)*(30*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-20*z)*(19*z) + (19*z)*(-37*z**2) + (19*z)*(30*z**3) + (47*z**3)*(30*z**3 - 37*z**2 - 20*z)\nSimplifying the partial expression: (47*z**3)*(30*z**3 - 37*z**2 - 20*z)\nExpanding the part (30*z**3 - 37*z**2 - 20*z) using the distributive property, and we got: (-20*z)*(47*z**3) + (-37*z**2)*(47*z**3) + (30*z**3)*(47*z**3)\nReplacing (47*z**3)*(30*z**3 - 37*z**2 - 20*z) with (-20*z)*(47*z**3) + (-37*z**2)*(47*z**3) + (30*z**3)*(47*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-20*z)*(19*z) + (-20*z)*(47*z**3) + (19*z)*(-37*z**2) + (19*z)*(30*z**3) + (-37*z**2)*(47*z**3) + (30*z**3)*(47*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*z**2)*(19*z) = -703*z**3\n (-37*z**2)*(47*z**3) = -1739*z**5\n (-20*z)*(19*z) = -380*z**2\n (-20*z)*(47*z**3) = -940*z**4\n (30*z**3)*(19*z) = 570*z**4\n (30*z**3)*(47*z**3) = 1410*z**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1410*z**6 - 1739*z**5 - 940*z**4 + 570*z**4 - 703*z**3 - 380*z**2\nCombining like terms, got 1410*z**6 - 1739*z**5 - 370*z**4 - 703*z**3 - 380*z**2\n#Step 6:\nCurrent expression: 1410*z**6 - 1739*z**5 - 370*z**4 - 703*z**3 - 380*z**2\nNo more calculations needed.\n1410*z**6 - 1739*z**5 - 370*z**4 - 703*z**3 - 380*z**2", "generated_answer": "1410*z**6 - 1739*z**5 - 370*z**4 - 703*z**3 - 380*z**2", "step_length": 6} {"cot_id": "2bf3d918432d0e6a84fa8ccbba107f7ffea9e6586488156f48fbfbde0e6af249", "datapoint": {"question": "Simplify this expression: (43*x - 30)*(46*x**3 - 9*x**2 - 58)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1978*x**4 - 1767*x**3 + 270*x**2 - 2494*x + 1740", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 540, "polynomial_expr": "(43*x - 30)*(46*x**3 - 9*x**2 - 58)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (43*x - 30)*(46*x**3 - 9*x**2 - 58)\nExpanding the part (43*x - 30) using the distributive property, and we got: (43*x)*(46*x**3 - 9*x**2 - 58) - 30*(46*x**3 - 9*x**2 - 58)\n#Step 2:\nCurrent expression: (43*x)*(46*x**3 - 9*x**2 - 58) - 30*(46*x**3 - 9*x**2 - 58)\nSimplifying the partial expression: -30*(46*x**3 - 9*x**2 - 58)\nExpanding the part (46*x**3 - 9*x**2 - 58) using the distributive property, and we got: -9*x**2*(-30) + (46*x**3)*(-30) - 58*(-30)\nReplacing -30*(46*x**3 - 9*x**2 - 58) with -9*x**2*(-30) + (46*x**3)*(-30) - 58*(-30) in the overall expression.\n#Step 3:\nCurrent expression: (43*x)*(46*x**3 - 9*x**2 - 58) - 9*x**2*(-30) + (46*x**3)*(-30) + 1740\nSimplifying the partial expression: (43*x)*(46*x**3 - 9*x**2 - 58)\nExpanding the part (46*x**3 - 9*x**2 - 58) using the distributive property, and we got: -2494*x + (43*x)*(-9*x**2) + (43*x)*(46*x**3)\nReplacing (43*x)*(46*x**3 - 9*x**2 - 58) with -2494*x + (43*x)*(-9*x**2) + (43*x)*(46*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -58*43*x + (43*x)*(-9*x**2) + (43*x)*(46*x**3) - 9*x**2*(-30) + (46*x**3)*(-30) + 1740\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-9*x**2)*-30 = 270*x**2\n (-9*x**2)*(43*x) = -387*x**3\n (46*x**3)*-30 = -1380*x**3\n (46*x**3)*(43*x) = 1978*x**4\n -58*43*x = -2494*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1978*x**4 - 1380*x**3 - 387*x**3 + 270*x**2 - 2494*x + 1740\nCombining like terms, got 1978*x**4 - 1767*x**3 + 270*x**2 - 2494*x + 1740\n#Step 6:\nCurrent expression: 1978*x**4 - 1767*x**3 + 270*x**2 - 2494*x + 1740\nNo more calculations needed.\n1978*x**4 - 1767*x**3 + 270*x**2 - 2494*x + 1740", "generated_answer": "1978*x**4 - 1767*x**3 + 270*x**2 - 2494*x + 1740", "step_length": 6} {"cot_id": "06047a8e4bd3ec9bd3fd81651cea217272a565d9797b79d53e068e37620ae6d7", "datapoint": {"question": "Simplify this expression: (3*z + 45)*(-42*z**3 + 33*z - 46)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-126*z**4 - 1890*z**3 + 99*z**2 + 1347*z - 2070", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 541, "polynomial_expr": "(3*z + 45)*(-42*z**3 + 33*z - 46)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (3*z + 45)*(-42*z**3 + 33*z - 46)\nExpanding the part (3*z + 45) using the distributive property, and we got: (3*z)*(-42*z**3 + 33*z - 46) + 45*(-42*z**3 + 33*z - 46)\n#Step 2:\nCurrent expression: (3*z)*(-42*z**3 + 33*z - 46) + 45*(-42*z**3 + 33*z - 46)\nSimplifying the partial expression: 45*(-42*z**3 + 33*z - 46)\nExpanding the part (-42*z**3 + 33*z - 46) using the distributive property, and we got: (33*z)*45 - 42*z**3*45 - 46*45\nReplacing 45*(-42*z**3 + 33*z - 46) with (33*z)*45 - 42*z**3*45 - 46*45 in the overall expression.\n#Step 3:\nCurrent expression: (3*z)*(-42*z**3 + 33*z - 46) + (33*z)*45 - 42*z**3*45 - 2070\nSimplifying the partial expression: (3*z)*(-42*z**3 + 33*z - 46)\nExpanding the part (-42*z**3 + 33*z - 46) using the distributive property, and we got: -138*z + (3*z)*(33*z) + (3*z)*(-42*z**3)\nReplacing (3*z)*(-42*z**3 + 33*z - 46) with -138*z + (3*z)*(33*z) + (3*z)*(-42*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -46*3*z + (3*z)*(33*z) + (3*z)*(-42*z**3) + (33*z)*45 - 42*z**3*45 - 2070\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*z**3)*45 = -1890*z**3\n (-42*z**3)*(3*z) = -126*z**4\n (33*z)*45 = 1485*z\n (33*z)*(3*z) = 99*z**2\n -46*3*z = -138*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -126*z**4 - 1890*z**3 + 99*z**2 - 138*z + 1485*z - 2070\nCombining like terms, got -126*z**4 - 1890*z**3 + 99*z**2 + 1347*z - 2070\n#Step 6:\nCurrent expression: -126*z**4 - 1890*z**3 + 99*z**2 + 1347*z - 2070\nNo more calculations needed.\n-126*z**4 - 1890*z**3 + 99*z**2 + 1347*z - 2070", "generated_answer": "-126*z**4 - 1890*z**3 + 99*z**2 + 1347*z - 2070", "step_length": 6} {"cot_id": "3a3731ba2e76ecc1504fa8c1a9851d788e070f18e3a4ce2e5e6dcc3298013ec1", "datapoint": {"question": "Calculate the following: (38*z**2 + 16*z)*(-8*z**3 - 5*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-304*z**5 - 318*z**4 - 80*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 542, "polynomial_expr": "(38*z**2 + 16*z)*(-8*z**3 - 5*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (38*z**2 + 16*z)*(-8*z**3 - 5*z**2)\nExpanding the part (-8*z**3 - 5*z**2) using the distributive property, and we got: (-5*z**2)*(38*z**2 + 16*z) + (-8*z**3)*(38*z**2 + 16*z)\n#Step 2:\nCurrent expression: (-5*z**2)*(38*z**2 + 16*z) + (-8*z**3)*(38*z**2 + 16*z)\nSimplifying the partial expression: (-8*z**3)*(38*z**2 + 16*z)\nExpanding the part (38*z**2 + 16*z) using the distributive property, and we got: (16*z)*(-8*z**3) + (38*z**2)*(-8*z**3)\nReplacing (-8*z**3)*(38*z**2 + 16*z) with (16*z)*(-8*z**3) + (38*z**2)*(-8*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (16*z)*(-8*z**3) + (-5*z**2)*(38*z**2 + 16*z) + (38*z**2)*(-8*z**3)\nSimplifying the partial expression: (-5*z**2)*(38*z**2 + 16*z)\nExpanding the part (38*z**2 + 16*z) using the distributive property, and we got: (16*z)*(-5*z**2) + (-5*z**2)*(38*z**2)\nReplacing (-5*z**2)*(38*z**2 + 16*z) with (16*z)*(-5*z**2) + (-5*z**2)*(38*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (16*z)*(-5*z**2) + (16*z)*(-8*z**3) + (-5*z**2)*(38*z**2) + (38*z**2)*(-8*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (16*z)*(-8*z**3) = -128*z**4\n (16*z)*(-5*z**2) = -80*z**3\n (38*z**2)*(-8*z**3) = -304*z**5\n (38*z**2)*(-5*z**2) = -190*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -304*z**5 - 190*z**4 - 128*z**4 - 80*z**3\nCombining like terms, got -304*z**5 - 318*z**4 - 80*z**3\n#Step 6:\nCurrent expression: -304*z**5 - 318*z**4 - 80*z**3\nNo more calculations needed.\n-304*z**5 - 318*z**4 - 80*z**3", "generated_answer": "-304*z**5 - 318*z**4 - 80*z**3", "step_length": 6} {"cot_id": "f1443636ec026b81ea82c2fa44a73be0cc00e5ac5ce0d48dd7aa7fd08a0dfa9b", "datapoint": {"question": "Calculate the following: (-32*x**3 + 38*x)*(-11*x**3 - x**2 - 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "352*x**6 + 32*x**5 - 418*x**4 + 1274*x**3 - 1558*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 543, "polynomial_expr": "(-32*x**3 + 38*x)*(-11*x**3 - x**2 - 41)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-32*x**3 + 38*x)*(-11*x**3 - x**2 - 41)\nExpanding the part (-32*x**3 + 38*x) using the distributive property, and we got: (38*x)*(-11*x**3 - x**2 - 41) + (-32*x**3)*(-11*x**3 - x**2 - 41)\n#Step 2:\nCurrent expression: (38*x)*(-11*x**3 - x**2 - 41) + (-32*x**3)*(-11*x**3 - x**2 - 41)\nSimplifying the partial expression: (-32*x**3)*(-11*x**3 - x**2 - 41)\nExpanding the part (-11*x**3 - x**2 - 41) using the distributive property, and we got: -(-1)*1312*x**3 + (-x**2)*(-32*x**3) + (-32*x**3)*(-11*x**3)\nReplacing (-32*x**3)*(-11*x**3 - x**2 - 41) with -(-1)*1312*x**3 + (-x**2)*(-32*x**3) + (-32*x**3)*(-11*x**3) in the overall expression.\n#Step 3:\nCurrent expression: -41*(-32)*x**3 + (38*x)*(-11*x**3 - x**2 - 41) + (-x**2)*(-32*x**3) + (-32*x**3)*(-11*x**3)\nSimplifying the partial expression: (38*x)*(-11*x**3 - x**2 - 41)\nExpanding the part (-11*x**3 - x**2 - 41) using the distributive property, and we got: -1558*x + (38*x)*(-x**2) + (38*x)*(-11*x**3)\nReplacing (38*x)*(-11*x**3 - x**2 - 41) with -1558*x + (38*x)*(-x**2) + (38*x)*(-11*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -41*(-32)*x**3 - 41*38*x + (38*x)*(-x**2) + (38*x)*(-11*x**3) + (-x**2)*(-32*x**3) + (-32*x**3)*(-11*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-x**2)*(-32*x**3) = 32*x**5\n (-x**2)*(38*x) = -38*x**3\n (-11*x**3)*(-32*x**3) = 352*x**6\n (-11*x**3)*(38*x) = -418*x**4\n -41*-32*x**3 = 1312*x**3\n -41*38*x = -1558*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 352*x**6 + 32*x**5 - 418*x**4 - 38*x**3 + 1312*x**3 - 1558*x\nCombining like terms, got 352*x**6 + 32*x**5 - 418*x**4 + 1274*x**3 - 1558*x\n#Step 6:\nCurrent expression: 352*x**6 + 32*x**5 - 418*x**4 + 1274*x**3 - 1558*x\nNo more calculations needed.\n352*x**6 + 32*x**5 - 418*x**4 + 1274*x**3 - 1558*x", "generated_answer": "352*x**6 + 32*x**5 - 418*x**4 + 1274*x**3 - 1558*x", "step_length": 6} {"cot_id": "884300be22ca8ecae228c4eeca5c90c0a2e93bdaea400273ace23944491a7607", "datapoint": {"question": "Simplify this expression: (-50*z**2 - 49*z)*(-13*z**2 + 26*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "650*z**4 - 663*z**3 - 1274*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 544, "polynomial_expr": "(-50*z**2 - 49*z)*(-13*z**2 + 26*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-50*z**2 - 49*z)*(-13*z**2 + 26*z)\nExpanding the part (-50*z**2 - 49*z) using the distributive property, and we got: (-49*z)*(-13*z**2 + 26*z) + (-50*z**2)*(-13*z**2 + 26*z)\n#Step 2:\nCurrent expression: (-49*z)*(-13*z**2 + 26*z) + (-50*z**2)*(-13*z**2 + 26*z)\nSimplifying the partial expression: (-50*z**2)*(-13*z**2 + 26*z)\nExpanding the part (-13*z**2 + 26*z) using the distributive property, and we got: (26*z)*(-50*z**2) + (-50*z**2)*(-13*z**2)\nReplacing (-50*z**2)*(-13*z**2 + 26*z) with (26*z)*(-50*z**2) + (-50*z**2)*(-13*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-49*z)*(-13*z**2 + 26*z) + (26*z)*(-50*z**2) + (-50*z**2)*(-13*z**2)\nSimplifying the partial expression: (-49*z)*(-13*z**2 + 26*z)\nExpanding the part (-13*z**2 + 26*z) using the distributive property, and we got: (-49*z)*(26*z) + (-49*z)*(-13*z**2)\nReplacing (-49*z)*(-13*z**2 + 26*z) with (-49*z)*(26*z) + (-49*z)*(-13*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-49*z)*(26*z) + (-49*z)*(-13*z**2) + (26*z)*(-50*z**2) + (-50*z**2)*(-13*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*z**2)*(-50*z**2) = 650*z**4\n (-13*z**2)*(-49*z) = 637*z**3\n (26*z)*(-50*z**2) = -1300*z**3\n (26*z)*(-49*z) = -1274*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 650*z**4 - 1300*z**3 + 637*z**3 - 1274*z**2\nCombining like terms, got 650*z**4 - 663*z**3 - 1274*z**2\n#Step 6:\nCurrent expression: 650*z**4 - 663*z**3 - 1274*z**2\nNo more calculations needed.\n650*z**4 - 663*z**3 - 1274*z**2", "generated_answer": "650*z**4 - 663*z**3 - 1274*z**2", "step_length": 6} {"cot_id": "8274b28d31b8e30bdca102906ed5aa8a565736e37fdf7bdebbd516912f7f52b5", "datapoint": {"question": "Calculate the following: (26 - 25*z**2)*(43*z**2 - 42*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1075*z**4 + 1050*z**3 + 1118*z**2 - 1092*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 545, "polynomial_expr": "(26 - 25*z**2)*(43*z**2 - 42*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (26 - 25*z**2)*(43*z**2 - 42*z)\nExpanding the part (26 - 25*z**2) using the distributive property, and we got: (-25*z**2)*(43*z**2 - 42*z) + 26*(43*z**2 - 42*z)\n#Step 2:\nCurrent expression: (-25*z**2)*(43*z**2 - 42*z) + 26*(43*z**2 - 42*z)\nSimplifying the partial expression: 26*(43*z**2 - 42*z)\nExpanding the part (43*z**2 - 42*z) using the distributive property, and we got: -42*z*26 + (43*z**2)*26\nReplacing 26*(43*z**2 - 42*z) with -42*z*26 + (43*z**2)*26 in the overall expression.\n#Step 3:\nCurrent expression: -42*z*26 + (-25*z**2)*(43*z**2 - 42*z) + (43*z**2)*26\nSimplifying the partial expression: (-25*z**2)*(43*z**2 - 42*z)\nExpanding the part (43*z**2 - 42*z) using the distributive property, and we got: (-42*z)*(-25*z**2) + (-25*z**2)*(43*z**2)\nReplacing (-25*z**2)*(43*z**2 - 42*z) with (-42*z)*(-25*z**2) + (-25*z**2)*(43*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-42*z)*(-25*z**2) - 42*z*26 + (-25*z**2)*(43*z**2) + (43*z**2)*26\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*z)*26 = -1092*z\n (-42*z)*(-25*z**2) = 1050*z**3\n (43*z**2)*26 = 1118*z**2\n (43*z**2)*(-25*z**2) = -1075*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1075*z**4 + 1050*z**3 + 1118*z**2 - 1092*z\nNo more calculations needed.\n-1075*z**4 + 1050*z**3 + 1118*z**2 - 1092*z", "generated_answer": "-1075*z**4 + 1050*z**3 + 1118*z**2 - 1092*z", "step_length": 5} {"cot_id": "68adede2bd51fa4703c559b6436506da4f3d88520692db78b2f1fe1b8ed54349", "datapoint": {"question": "Calculate the following: 83*z**3*(83*z**3 - 49*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "6889*z**6 - 4067*z**5", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 546, "polynomial_expr": "83*z**3*(83*z**3 - 49*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 83*z**3*(83*z**3 - 49*z**2)\nExpanding the part (83*z**3 - 49*z**2) using the distributive property, and we got: (-49*z**2)*(83*z**3) + (83*z**3)*(83*z**3)\n#Step 2:\nCurrent expression: (-49*z**2)*(83*z**3) + (83*z**3)*(83*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*z**2)*(83*z**3) = -4067*z**5\n (83*z**3)*(83*z**3) = 6889*z**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 6889*z**6 - 4067*z**5\nNo more calculations needed.\n6889*z**6 - 4067*z**5", "generated_answer": "6889*z**6 - 4067*z**5", "step_length": 3} {"cot_id": "14b295aae1c32dfb7098381b05f4ebd37b3018fecd561746d184f820824b54cc", "datapoint": {"question": "Simplify this expression: (-26*x**3 - 38*x)*(-41*x**3 + 20*x**2 + 32*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1066*x**6 - 520*x**5 + 726*x**4 - 760*x**3 - 1216*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 547, "polynomial_expr": "(-26*x**3 - 38*x)*(-41*x**3 + 20*x**2 + 32*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-26*x**3 - 38*x)*(-41*x**3 + 20*x**2 + 32*x)\nExpanding the part (-26*x**3 - 38*x) using the distributive property, and we got: (-38*x)*(-41*x**3 + 20*x**2 + 32*x) + (-26*x**3)*(-41*x**3 + 20*x**2 + 32*x)\n#Step 2:\nCurrent expression: (-38*x)*(-41*x**3 + 20*x**2 + 32*x) + (-26*x**3)*(-41*x**3 + 20*x**2 + 32*x)\nSimplifying the partial expression: (-38*x)*(-41*x**3 + 20*x**2 + 32*x)\nExpanding the part (-41*x**3 + 20*x**2 + 32*x) using the distributive property, and we got: (-38*x)*(32*x) + (-38*x)*(20*x**2) + (-38*x)*(-41*x**3)\nReplacing (-38*x)*(-41*x**3 + 20*x**2 + 32*x) with (-38*x)*(32*x) + (-38*x)*(20*x**2) + (-38*x)*(-41*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-38*x)*(32*x) + (-38*x)*(20*x**2) + (-38*x)*(-41*x**3) + (-26*x**3)*(-41*x**3 + 20*x**2 + 32*x)\nSimplifying the partial expression: (-26*x**3)*(-41*x**3 + 20*x**2 + 32*x)\nExpanding the part (-41*x**3 + 20*x**2 + 32*x) using the distributive property, and we got: (32*x)*(-26*x**3) + (20*x**2)*(-26*x**3) + (-41*x**3)*(-26*x**3)\nReplacing (-26*x**3)*(-41*x**3 + 20*x**2 + 32*x) with (32*x)*(-26*x**3) + (20*x**2)*(-26*x**3) + (-41*x**3)*(-26*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-38*x)*(32*x) + (-38*x)*(20*x**2) + (-38*x)*(-41*x**3) + (32*x)*(-26*x**3) + (20*x**2)*(-26*x**3) + (-41*x**3)*(-26*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*x**3)*(-38*x) = 1558*x**4\n (-41*x**3)*(-26*x**3) = 1066*x**6\n (20*x**2)*(-38*x) = -760*x**3\n (20*x**2)*(-26*x**3) = -520*x**5\n (32*x)*(-38*x) = -1216*x**2\n (32*x)*(-26*x**3) = -832*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1066*x**6 - 520*x**5 - 832*x**4 + 1558*x**4 - 760*x**3 - 1216*x**2\nCombining like terms, got 1066*x**6 - 520*x**5 + 726*x**4 - 760*x**3 - 1216*x**2\n#Step 6:\nCurrent expression: 1066*x**6 - 520*x**5 + 726*x**4 - 760*x**3 - 1216*x**2\nNo more calculations needed.\n1066*x**6 - 520*x**5 + 726*x**4 - 760*x**3 - 1216*x**2", "generated_answer": "1066*x**6 - 520*x**5 + 726*x**4 - 760*x**3 - 1216*x**2", "step_length": 6} {"cot_id": "c46f00efa81d858350e36e355d8911cafd52c956358b865b7bcf0e931e58a549", "datapoint": {"question": "Simplify this expression: 3640*x**3 - 2632*x**2 + 1512*x\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "3640*x**3 - 2632*x**2 + 1512*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 548, "polynomial_expr": "3640*x**3 - 2632*x**2 + 1512*x", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 3640*x**3 - 2632*x**2 + 1512*x\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 3640*x**3 - 2632*x**2 + 1512*x\nNo more calculations needed.\n3640*x**3 - 2632*x**2 + 1512*x", "generated_answer": "3640*x**3 - 2632*x**2 + 1512*x", "step_length": 2} {"cot_id": "4241a1105df30e02ebbabdc8cc4ea768c0ab23cfb138a0d1fc2f47558f3b90bb", "datapoint": {"question": "Calculate the following: (-34*z**3 - 23*z**2)*(13*z**3 + 8*z**2 - 17*z - 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-442*z**6 - 571*z**5 + 394*z**4 + 595*z**3 + 138*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 549, "polynomial_expr": "(-34*z**3 - 23*z**2)*(13*z**3 + 8*z**2 - 17*z - 6)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-34*z**3 - 23*z**2)*(13*z**3 + 8*z**2 - 17*z - 6)\nExpanding the part (-34*z**3 - 23*z**2) using the distributive property, and we got: (-23*z**2)*(13*z**3 + 8*z**2 - 17*z - 6) + (-34*z**3)*(13*z**3 + 8*z**2 - 17*z - 6)\n#Step 2:\nCurrent expression: (-23*z**2)*(13*z**3 + 8*z**2 - 17*z - 6) + (-34*z**3)*(13*z**3 + 8*z**2 - 17*z - 6)\nSimplifying the partial expression: (-34*z**3)*(13*z**3 + 8*z**2 - 17*z - 6)\nExpanding the part (13*z**3 + 8*z**2 - 17*z - 6) using the distributive property, and we got: (-17*z)*(-34*z**3) - (-1)*204*z**3 + (8*z**2)*(-34*z**3) + (-34*z**3)*(13*z**3)\nReplacing (-34*z**3)*(13*z**3 + 8*z**2 - 17*z - 6) with (-17*z)*(-34*z**3) - (-1)*204*z**3 + (8*z**2)*(-34*z**3) + (-34*z**3)*(13*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-17*z)*(-34*z**3) - 6*(-34)*z**3 + (-23*z**2)*(13*z**3 + 8*z**2 - 17*z - 6) + (8*z**2)*(-34*z**3) + (-34*z**3)*(13*z**3)\nSimplifying the partial expression: (-23*z**2)*(13*z**3 + 8*z**2 - 17*z - 6)\nExpanding the part (13*z**3 + 8*z**2 - 17*z - 6) using the distributive property, and we got: (-17*z)*(-23*z**2) - (-1)*138*z**2 + (-23*z**2)*(8*z**2) + (-23*z**2)*(13*z**3)\nReplacing (-23*z**2)*(13*z**3 + 8*z**2 - 17*z - 6) with (-17*z)*(-23*z**2) - (-1)*138*z**2 + (-23*z**2)*(8*z**2) + (-23*z**2)*(13*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-17*z)*(-23*z**2) + (-17*z)*(-34*z**3) - 6*(-34)*z**3 - 6*(-23)*z**2 + (-23*z**2)*(8*z**2) + (-23*z**2)*(13*z**3) + (8*z**2)*(-34*z**3) + (-34*z**3)*(13*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-17*z)*(-34*z**3) = 578*z**4\n (-17*z)*(-23*z**2) = 391*z**3\n (8*z**2)*(-34*z**3) = -272*z**5\n (8*z**2)*(-23*z**2) = -184*z**4\n (13*z**3)*(-34*z**3) = -442*z**6\n (13*z**3)*(-23*z**2) = -299*z**5\n -6*-34*z**3 = 204*z**3\n -6*-23*z**2 = 138*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -442*z**6 - 299*z**5 - 272*z**5 - 184*z**4 + 578*z**4 + 204*z**3 + 391*z**3 + 138*z**2\nCombining like terms, got -442*z**6 - 571*z**5 + 394*z**4 + 595*z**3 + 138*z**2\n#Step 6:\nCurrent expression: -442*z**6 - 571*z**5 + 394*z**4 + 595*z**3 + 138*z**2\nNo more calculations needed.\n-442*z**6 - 571*z**5 + 394*z**4 + 595*z**3 + 138*z**2", "generated_answer": "-442*z**6 - 571*z**5 + 394*z**4 + 595*z**3 + 138*z**2", "step_length": 6} {"cot_id": "0e922e3511367c536403c6491bc346e6ebe111815e6e351be8ffa47340ddab15", "datapoint": {"question": "Calculate the following: (-23*x**2 - 11*x - 3)*(21*x**3 + 8*x**2 + 49*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-483*x**5 - 415*x**4 - 1278*x**3 - 563*x**2 - 147*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 550, "polynomial_expr": "(-23*x**2 - 11*x - 3)*(21*x**3 + 8*x**2 + 49*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-23*x**2 - 11*x - 3)*(21*x**3 + 8*x**2 + 49*x)\nExpanding the part (-23*x**2 - 11*x - 3) using the distributive property, and we got: (-11*x)*(21*x**3 + 8*x**2 + 49*x) + (-23*x**2)*(21*x**3 + 8*x**2 + 49*x) - 3*(21*x**3 + 8*x**2 + 49*x)\n#Step 2:\nCurrent expression: (-11*x)*(21*x**3 + 8*x**2 + 49*x) + (-23*x**2)*(21*x**3 + 8*x**2 + 49*x) - 3*(21*x**3 + 8*x**2 + 49*x)\nSimplifying the partial expression: -3*(21*x**3 + 8*x**2 + 49*x)\nExpanding the part (21*x**3 + 8*x**2 + 49*x) using the distributive property, and we got: (49*x)*(-3) + (8*x**2)*(-3) + (21*x**3)*(-3)\nReplacing -3*(21*x**3 + 8*x**2 + 49*x) with (49*x)*(-3) + (8*x**2)*(-3) + (21*x**3)*(-3) in the overall expression.\n#Step 3:\nCurrent expression: (-11*x)*(21*x**3 + 8*x**2 + 49*x) + (49*x)*(-3) + (-23*x**2)*(21*x**3 + 8*x**2 + 49*x) + (8*x**2)*(-3) + (21*x**3)*(-3)\nSimplifying the partial expression: (-23*x**2)*(21*x**3 + 8*x**2 + 49*x)\nExpanding the part (21*x**3 + 8*x**2 + 49*x) using the distributive property, and we got: (49*x)*(-23*x**2) + (-23*x**2)*(8*x**2) + (-23*x**2)*(21*x**3)\nReplacing (-23*x**2)*(21*x**3 + 8*x**2 + 49*x) with (49*x)*(-23*x**2) + (-23*x**2)*(8*x**2) + (-23*x**2)*(21*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-11*x)*(21*x**3 + 8*x**2 + 49*x) + (49*x)*(-23*x**2) + (49*x)*(-3) + (-23*x**2)*(8*x**2) + (-23*x**2)*(21*x**3) + (8*x**2)*(-3) + (21*x**3)*(-3)\nSimplifying the partial expression: (-11*x)*(21*x**3 + 8*x**2 + 49*x)\nExpanding the part (21*x**3 + 8*x**2 + 49*x) using the distributive property, and we got: (-11*x)*(49*x) + (-11*x)*(8*x**2) + (-11*x)*(21*x**3)\nReplacing (-11*x)*(21*x**3 + 8*x**2 + 49*x) with (-11*x)*(49*x) + (-11*x)*(8*x**2) + (-11*x)*(21*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-11*x)*(49*x) + (-11*x)*(8*x**2) + (-11*x)*(21*x**3) + (49*x)*(-23*x**2) + (49*x)*(-3) + (-23*x**2)*(8*x**2) + (-23*x**2)*(21*x**3) + (8*x**2)*(-3) + (21*x**3)*(-3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (8*x**2)*-3 = -24*x**2\n (8*x**2)*(-23*x**2) = -184*x**4\n (8*x**2)*(-11*x) = -88*x**3\n (21*x**3)*-3 = -63*x**3\n (21*x**3)*(-23*x**2) = -483*x**5\n (21*x**3)*(-11*x) = -231*x**4\n (49*x)*-3 = -147*x\n (49*x)*(-23*x**2) = -1127*x**3\n (49*x)*(-11*x) = -539*x**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -483*x**5 - 231*x**4 - 184*x**4 - 1127*x**3 - 88*x**3 - 63*x**3 - 539*x**2 - 24*x**2 - 147*x\nCombining like terms, got -483*x**5 - 415*x**4 - 1278*x**3 - 563*x**2 - 147*x\n#Step 7:\nCurrent expression: -483*x**5 - 415*x**4 - 1278*x**3 - 563*x**2 - 147*x\nNo more calculations needed.\n-483*x**5 - 415*x**4 - 1278*x**3 - 563*x**2 - 147*x", "generated_answer": "-483*x**5 - 415*x**4 - 1278*x**3 - 563*x**2 - 147*x", "step_length": 7} {"cot_id": "10eafea914dd1946affece0e6728d16292e70d604c36462d788c497667fedc04", "datapoint": {"question": "Simplify this expression: 17*y**3*(16*y**3 + 32*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "272*y**6 + 544*y**5", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 551, "polynomial_expr": "17*y**3*(16*y**3 + 32*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 17*y**3*(16*y**3 + 32*y**2)\nExpanding the part (16*y**3 + 32*y**2) using the distributive property, and we got: (32*y**2)*(17*y**3) + (16*y**3)*(17*y**3)\n#Step 2:\nCurrent expression: (32*y**2)*(17*y**3) + (16*y**3)*(17*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (16*y**3)*(17*y**3) = 272*y**6\n (32*y**2)*(17*y**3) = 544*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 272*y**6 + 544*y**5\nNo more calculations needed.\n272*y**6 + 544*y**5", "generated_answer": "272*y**6 + 544*y**5", "step_length": 3} {"cot_id": "dd4c803bf4a113de34aa0eda1dd4c5f80c4c8a0442369f09d5b472c1722ab326", "datapoint": {"question": "Simplify this expression: (33*x**3 - 47*x**2)*(15*x**3 - x - 40)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "495*x**6 - 705*x**5 - 33*x**4 - 1273*x**3 + 1880*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 552, "polynomial_expr": "(33*x**3 - 47*x**2)*(15*x**3 - x - 40)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (33*x**3 - 47*x**2)*(15*x**3 - x - 40)\nExpanding the part (33*x**3 - 47*x**2) using the distributive property, and we got: (-47*x**2)*(15*x**3 - x - 40) + (33*x**3)*(15*x**3 - x - 40)\n#Step 2:\nCurrent expression: (-47*x**2)*(15*x**3 - x - 40) + (33*x**3)*(15*x**3 - x - 40)\nSimplifying the partial expression: (-47*x**2)*(15*x**3 - x - 40)\nExpanding the part (15*x**3 - x - 40) using the distributive property, and we got: (-x)*(-47*x**2) - (-1)*1880*x**2 + (-47*x**2)*(15*x**3)\nReplacing (-47*x**2)*(15*x**3 - x - 40) with (-x)*(-47*x**2) - (-1)*1880*x**2 + (-47*x**2)*(15*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-x)*(-47*x**2) - 40*(-47)*x**2 + (-47*x**2)*(15*x**3) + (33*x**3)*(15*x**3 - x - 40)\nSimplifying the partial expression: (33*x**3)*(15*x**3 - x - 40)\nExpanding the part (15*x**3 - x - 40) using the distributive property, and we got: (-x)*(33*x**3) - 1320*x**3 + (15*x**3)*(33*x**3)\nReplacing (33*x**3)*(15*x**3 - x - 40) with (-x)*(33*x**3) - 1320*x**3 + (15*x**3)*(33*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-x)*(-47*x**2) + (-x)*(33*x**3) - 40*33*x**3 - 40*(-47)*x**2 + (-47*x**2)*(15*x**3) + (15*x**3)*(33*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-x)*(-47*x**2) = 47*x**3\n (-x)*(33*x**3) = -33*x**4\n (15*x**3)*(-47*x**2) = -705*x**5\n (15*x**3)*(33*x**3) = 495*x**6\n -40*-47*x**2 = 1880*x**2\n -40*33*x**3 = -1320*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 495*x**6 - 705*x**5 - 33*x**4 - 1320*x**3 + 47*x**3 + 1880*x**2\nCombining like terms, got 495*x**6 - 705*x**5 - 33*x**4 - 1273*x**3 + 1880*x**2\n#Step 6:\nCurrent expression: 495*x**6 - 705*x**5 - 33*x**4 - 1273*x**3 + 1880*x**2\nNo more calculations needed.\n495*x**6 - 705*x**5 - 33*x**4 - 1273*x**3 + 1880*x**2", "generated_answer": "495*x**6 - 705*x**5 - 33*x**4 - 1273*x**3 + 1880*x**2", "step_length": 6} {"cot_id": "eefe835d1fae01847a80f71cd20ac57aa17ede770d670f7e5308505a0cb40580", "datapoint": {"question": "Simplify this expression: (21 - 65*y**2)*(45 - 5*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "325*y**3 - 2925*y**2 - 105*y + 945", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 553, "polynomial_expr": "(21 - 65*y**2)*(45 - 5*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21 - 65*y**2)*(45 - 5*y)\nExpanding the part (21 - 65*y**2) using the distributive property, and we got: (-65*y**2)*(45 - 5*y) + 21*(45 - 5*y)\n#Step 2:\nCurrent expression: (-65*y**2)*(45 - 5*y) + 21*(45 - 5*y)\nSimplifying the partial expression: 21*(45 - 5*y)\nExpanding the part (45 - 5*y) using the distributive property, and we got: -5*y*21 + 45*21\nReplacing 21*(45 - 5*y) with -5*y*21 + 45*21 in the overall expression.\n#Step 3:\nCurrent expression: -5*y*21 + (-65*y**2)*(45 - 5*y) + 945\nSimplifying the partial expression: (-65*y**2)*(45 - 5*y)\nExpanding the part (45 - 5*y) using the distributive property, and we got: (-5*y)*(-65*y**2) + 45*(-65*y**2)\nReplacing (-65*y**2)*(45 - 5*y) with (-5*y)*(-65*y**2) + 45*(-65*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-5*y)*(-65*y**2) - 5*y*21 + 45*(-65)*y**2 + 945\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-5*y)*21 = -105*y\n (-5*y)*(-65*y**2) = 325*y**3\n 45*-65*y**2 = -2925*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 325*y**3 - 2925*y**2 - 105*y + 945\nNo more calculations needed.\n325*y**3 - 2925*y**2 - 105*y + 945", "generated_answer": "325*y**3 - 2925*y**2 - 105*y + 945", "step_length": 5} {"cot_id": "b1713292d4d0e5057d9b7fdc7a2abb1d2cadc097cf2421c17e8532587e348c86", "datapoint": {"question": "Calculate the following: -1856*y**3 - 192*y\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1856*y**3 - 192*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 554, "polynomial_expr": "-1856*y**3 - 192*y", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -1856*y**3 - 192*y\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -1856*y**3 - 192*y\nNo more calculations needed.\n-1856*y**3 - 192*y", "generated_answer": "-1856*y**3 - 192*y", "step_length": 2} {"cot_id": "42f5a59c87ff43eb0307237cfb44c5979358bc0abc7ec5141529d1381140bd35", "datapoint": {"question": "Simplify this expression: (33*x**3 - 35*x**2)*(-39*x**3 - 18*x**2 + 28*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1287*x**6 + 771*x**5 + 1554*x**4 - 980*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 555, "polynomial_expr": "(33*x**3 - 35*x**2)*(-39*x**3 - 18*x**2 + 28*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (33*x**3 - 35*x**2)*(-39*x**3 - 18*x**2 + 28*x)\nExpanding the part (33*x**3 - 35*x**2) using the distributive property, and we got: (-35*x**2)*(-39*x**3 - 18*x**2 + 28*x) + (33*x**3)*(-39*x**3 - 18*x**2 + 28*x)\n#Step 2:\nCurrent expression: (-35*x**2)*(-39*x**3 - 18*x**2 + 28*x) + (33*x**3)*(-39*x**3 - 18*x**2 + 28*x)\nSimplifying the partial expression: (-35*x**2)*(-39*x**3 - 18*x**2 + 28*x)\nExpanding the part (-39*x**3 - 18*x**2 + 28*x) using the distributive property, and we got: (28*x)*(-35*x**2) + (-35*x**2)*(-18*x**2) + (-35*x**2)*(-39*x**3)\nReplacing (-35*x**2)*(-39*x**3 - 18*x**2 + 28*x) with (28*x)*(-35*x**2) + (-35*x**2)*(-18*x**2) + (-35*x**2)*(-39*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (28*x)*(-35*x**2) + (-35*x**2)*(-18*x**2) + (-35*x**2)*(-39*x**3) + (33*x**3)*(-39*x**3 - 18*x**2 + 28*x)\nSimplifying the partial expression: (33*x**3)*(-39*x**3 - 18*x**2 + 28*x)\nExpanding the part (-39*x**3 - 18*x**2 + 28*x) using the distributive property, and we got: (28*x)*(33*x**3) + (-18*x**2)*(33*x**3) + (-39*x**3)*(33*x**3)\nReplacing (33*x**3)*(-39*x**3 - 18*x**2 + 28*x) with (28*x)*(33*x**3) + (-18*x**2)*(33*x**3) + (-39*x**3)*(33*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (28*x)*(-35*x**2) + (28*x)*(33*x**3) + (-35*x**2)*(-18*x**2) + (-35*x**2)*(-39*x**3) + (-18*x**2)*(33*x**3) + (-39*x**3)*(33*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*x**3)*(-35*x**2) = 1365*x**5\n (-39*x**3)*(33*x**3) = -1287*x**6\n (-18*x**2)*(-35*x**2) = 630*x**4\n (-18*x**2)*(33*x**3) = -594*x**5\n (28*x)*(-35*x**2) = -980*x**3\n (28*x)*(33*x**3) = 924*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1287*x**6 - 594*x**5 + 1365*x**5 + 630*x**4 + 924*x**4 - 980*x**3\nCombining like terms, got -1287*x**6 + 771*x**5 + 1554*x**4 - 980*x**3\n#Step 6:\nCurrent expression: -1287*x**6 + 771*x**5 + 1554*x**4 - 980*x**3\nNo more calculations needed.\n-1287*x**6 + 771*x**5 + 1554*x**4 - 980*x**3", "generated_answer": "-1287*x**6 + 771*x**5 + 1554*x**4 - 980*x**3", "step_length": 6} {"cot_id": "1640d1d72e349404636c0c840248d944bbedb7468c0235e4774c725814d326b5", "datapoint": {"question": "Calculate the following: (31*x**2 - 105*x)*(23*x**2 - 47*x + 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "713*x**4 - 3872*x**3 + 5679*x**2 - 2520*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 556, "polynomial_expr": "(31*x**2 - 105*x)*(23*x**2 - 47*x + 24)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31*x**2 - 105*x)*(23*x**2 - 47*x + 24)\nExpanding the part (31*x**2 - 105*x) using the distributive property, and we got: (-105*x)*(23*x**2 - 47*x + 24) + (31*x**2)*(23*x**2 - 47*x + 24)\n#Step 2:\nCurrent expression: (-105*x)*(23*x**2 - 47*x + 24) + (31*x**2)*(23*x**2 - 47*x + 24)\nSimplifying the partial expression: (-105*x)*(23*x**2 - 47*x + 24)\nExpanding the part (23*x**2 - 47*x + 24) using the distributive property, and we got: (-105*x)*(-47*x) + (-105*x)*(23*x**2) + 24*(-105*x)\nReplacing (-105*x)*(23*x**2 - 47*x + 24) with (-105*x)*(-47*x) + (-105*x)*(23*x**2) + 24*(-105*x) in the overall expression.\n#Step 3:\nCurrent expression: (-105*x)*(-47*x) + (-105*x)*(23*x**2) + 24*(-105)*x + (31*x**2)*(23*x**2 - 47*x + 24)\nSimplifying the partial expression: (31*x**2)*(23*x**2 - 47*x + 24)\nExpanding the part (23*x**2 - 47*x + 24) using the distributive property, and we got: (-47*x)*(31*x**2) + 24*(31*x**2) + (23*x**2)*(31*x**2)\nReplacing (31*x**2)*(23*x**2 - 47*x + 24) with (-47*x)*(31*x**2) + 24*(31*x**2) + (23*x**2)*(31*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-105*x)*(-47*x) + (-105*x)*(23*x**2) + (-47*x)*(31*x**2) + 24*31*x**2 + 24*(-105)*x + (23*x**2)*(31*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*x)*(-105*x) = 4935*x**2\n (-47*x)*(31*x**2) = -1457*x**3\n (23*x**2)*(-105*x) = -2415*x**3\n (23*x**2)*(31*x**2) = 713*x**4\n 24*-105*x = -2520*x\n 24*31*x**2 = 744*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 713*x**4 - 2415*x**3 - 1457*x**3 + 744*x**2 + 4935*x**2 - 2520*x\nCombining like terms, got 713*x**4 - 3872*x**3 + 5679*x**2 - 2520*x\n#Step 6:\nCurrent expression: 713*x**4 - 3872*x**3 + 5679*x**2 - 2520*x\nNo more calculations needed.\n713*x**4 - 3872*x**3 + 5679*x**2 - 2520*x", "generated_answer": "713*x**4 - 3872*x**3 + 5679*x**2 - 2520*x", "step_length": 6} {"cot_id": "ad749c24318f2714a0be1cef90b57953d783bffa913cd7e748ca5d4b8cae8900", "datapoint": {"question": "Calculate the following: (-21*z**3 - 46*z)*(-17*z**3 + 8*z**2 - 41*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "357*z**6 - 168*z**5 + 1643*z**4 - 368*z**3 + 1886*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 557, "polynomial_expr": "(-21*z**3 - 46*z)*(-17*z**3 + 8*z**2 - 41*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-21*z**3 - 46*z)*(-17*z**3 + 8*z**2 - 41*z)\nExpanding the part (-21*z**3 - 46*z) using the distributive property, and we got: (-46*z)*(-17*z**3 + 8*z**2 - 41*z) + (-21*z**3)*(-17*z**3 + 8*z**2 - 41*z)\n#Step 2:\nCurrent expression: (-46*z)*(-17*z**3 + 8*z**2 - 41*z) + (-21*z**3)*(-17*z**3 + 8*z**2 - 41*z)\nSimplifying the partial expression: (-46*z)*(-17*z**3 + 8*z**2 - 41*z)\nExpanding the part (-17*z**3 + 8*z**2 - 41*z) using the distributive property, and we got: (-46*z)*(-41*z) + (-46*z)*(8*z**2) + (-46*z)*(-17*z**3)\nReplacing (-46*z)*(-17*z**3 + 8*z**2 - 41*z) with (-46*z)*(-41*z) + (-46*z)*(8*z**2) + (-46*z)*(-17*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-46*z)*(-41*z) + (-46*z)*(8*z**2) + (-46*z)*(-17*z**3) + (-21*z**3)*(-17*z**3 + 8*z**2 - 41*z)\nSimplifying the partial expression: (-21*z**3)*(-17*z**3 + 8*z**2 - 41*z)\nExpanding the part (-17*z**3 + 8*z**2 - 41*z) using the distributive property, and we got: (-41*z)*(-21*z**3) + (8*z**2)*(-21*z**3) + (-21*z**3)*(-17*z**3)\nReplacing (-21*z**3)*(-17*z**3 + 8*z**2 - 41*z) with (-41*z)*(-21*z**3) + (8*z**2)*(-21*z**3) + (-21*z**3)*(-17*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-46*z)*(-41*z) + (-46*z)*(8*z**2) + (-46*z)*(-17*z**3) + (-41*z)*(-21*z**3) + (8*z**2)*(-21*z**3) + (-21*z**3)*(-17*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*z)*(-46*z) = 1886*z**2\n (-41*z)*(-21*z**3) = 861*z**4\n (-17*z**3)*(-46*z) = 782*z**4\n (-17*z**3)*(-21*z**3) = 357*z**6\n (8*z**2)*(-46*z) = -368*z**3\n (8*z**2)*(-21*z**3) = -168*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 357*z**6 - 168*z**5 + 782*z**4 + 861*z**4 - 368*z**3 + 1886*z**2\nCombining like terms, got 357*z**6 - 168*z**5 + 1643*z**4 - 368*z**3 + 1886*z**2\n#Step 6:\nCurrent expression: 357*z**6 - 168*z**5 + 1643*z**4 - 368*z**3 + 1886*z**2\nNo more calculations needed.\n357*z**6 - 168*z**5 + 1643*z**4 - 368*z**3 + 1886*z**2", "generated_answer": "357*z**6 - 168*z**5 + 1643*z**4 - 368*z**3 + 1886*z**2", "step_length": 6} {"cot_id": "864f59b51f05d691fe9d122c91daa03ebfd347397c84298211ca54b2eb8797bc", "datapoint": {"question": "Simplify this expression: (-11*y**3 - 41*y - 47)*(64*y**3 - 7*y**2 + 29)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-704*y**6 + 77*y**5 - 2624*y**4 - 3040*y**3 + 329*y**2 - 1189*y - 1363", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 558, "polynomial_expr": "(-11*y**3 - 41*y - 47)*(64*y**3 - 7*y**2 + 29)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-11*y**3 - 41*y - 47)*(64*y**3 - 7*y**2 + 29)\nExpanding the part (-11*y**3 - 41*y - 47) using the distributive property, and we got: (-41*y)*(64*y**3 - 7*y**2 + 29) + (-11*y**3)*(64*y**3 - 7*y**2 + 29) - 47*(64*y**3 - 7*y**2 + 29)\n#Step 2:\nCurrent expression: (-41*y)*(64*y**3 - 7*y**2 + 29) + (-11*y**3)*(64*y**3 - 7*y**2 + 29) - 47*(64*y**3 - 7*y**2 + 29)\nSimplifying the partial expression: -47*(64*y**3 - 7*y**2 + 29)\nExpanding the part (64*y**3 - 7*y**2 + 29) using the distributive property, and we got: -7*y**2*(-47) + (64*y**3)*(-47) + 29*(-47)\nReplacing -47*(64*y**3 - 7*y**2 + 29) with -7*y**2*(-47) + (64*y**3)*(-47) + 29*(-47) in the overall expression.\n#Step 3:\nCurrent expression: (-41*y)*(64*y**3 - 7*y**2 + 29) - 7*y**2*(-47) + (-11*y**3)*(64*y**3 - 7*y**2 + 29) + (64*y**3)*(-47) - 1363\nSimplifying the partial expression: (-41*y)*(64*y**3 - 7*y**2 + 29)\nExpanding the part (64*y**3 - 7*y**2 + 29) using the distributive property, and we got: (-41*y)*(-7*y**2) + (-41*y)*(64*y**3) + 29*(-41*y)\nReplacing (-41*y)*(64*y**3 - 7*y**2 + 29) with (-41*y)*(-7*y**2) + (-41*y)*(64*y**3) + 29*(-41*y) in the overall expression.\n#Step 4:\nCurrent expression: (-41*y)*(-7*y**2) + (-41*y)*(64*y**3) + 29*(-41)*y - 7*y**2*(-47) + (-11*y**3)*(64*y**3 - 7*y**2 + 29) + (64*y**3)*(-47) - 1363\nSimplifying the partial expression: (-11*y**3)*(64*y**3 - 7*y**2 + 29)\nExpanding the part (64*y**3 - 7*y**2 + 29) using the distributive property, and we got: 29*(-11*y**3) + (-7*y**2)*(-11*y**3) + (-11*y**3)*(64*y**3)\nReplacing (-11*y**3)*(64*y**3 - 7*y**2 + 29) with 29*(-11*y**3) + (-7*y**2)*(-11*y**3) + (-11*y**3)*(64*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-41*y)*(-7*y**2) + (-41*y)*(64*y**3) + 29*(-11)*y**3 + 29*(-41)*y + (-7*y**2)*(-11*y**3) - 7*y**2*(-47) + (-11*y**3)*(64*y**3) + (64*y**3)*(-47) - 1363\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-7*y**2)*-47 = 329*y**2\n (-7*y**2)*(-41*y) = 287*y**3\n (-7*y**2)*(-11*y**3) = 77*y**5\n (64*y**3)*-47 = -3008*y**3\n (64*y**3)*(-41*y) = -2624*y**4\n (64*y**3)*(-11*y**3) = -704*y**6\n 29*-41*y = -1189*y\n 29*-11*y**3 = -319*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -704*y**6 + 77*y**5 - 2624*y**4 - 3008*y**3 - 319*y**3 + 287*y**3 + 329*y**2 - 1189*y - 1363\nCombining like terms, got -704*y**6 + 77*y**5 - 2624*y**4 - 3040*y**3 + 329*y**2 - 1189*y - 1363\n#Step 7:\nCurrent expression: -704*y**6 + 77*y**5 - 2624*y**4 - 3040*y**3 + 329*y**2 - 1189*y - 1363\nNo more calculations needed.\n-704*y**6 + 77*y**5 - 2624*y**4 - 3040*y**3 + 329*y**2 - 1189*y - 1363", "generated_answer": "-704*y**6 + 77*y**5 - 2624*y**4 - 3040*y**3 + 329*y**2 - 1189*y - 1363", "step_length": 7} {"cot_id": "ef5fd25a717898be45b83a21954ddf27915d6d6c75da752da0ca02656525c362", "datapoint": {"question": "Calculate the following: (18*x**2 + 1)*(-30*x**3 - 3*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-540*x**5 - 54*x**4 - 30*x**3 - 3*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 559, "polynomial_expr": "(18*x**2 + 1)*(-30*x**3 - 3*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (18*x**2 + 1)*(-30*x**3 - 3*x**2)\nExpanding the part (18*x**2 + 1) using the distributive property, and we got: (18*x**2)*(-30*x**3 - 3*x**2) + 1*(-30*x**3 - 3*x**2)\n#Step 2:\nCurrent expression: (18*x**2)*(-30*x**3 - 3*x**2) + 1*(-30*x**3 - 3*x**2)\nSimplifying the partial expression: 1*(-30*x**3 - 3*x**2)\nExpanding the part (-30*x**3 - 3*x**2) using the distributive property, and we got: -3*x**2*1 - 30*x**3*1\nReplacing 1*(-30*x**3 - 3*x**2) with -3*x**2*1 - 30*x**3*1 in the overall expression.\n#Step 3:\nCurrent expression: -3*x**2*1 + (18*x**2)*(-30*x**3 - 3*x**2) - 30*x**3*1\nSimplifying the partial expression: (18*x**2)*(-30*x**3 - 3*x**2)\nExpanding the part (-30*x**3 - 3*x**2) using the distributive property, and we got: (-3*x**2)*(18*x**2) + (18*x**2)*(-30*x**3)\nReplacing (18*x**2)*(-30*x**3 - 3*x**2) with (-3*x**2)*(18*x**2) + (18*x**2)*(-30*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-3*x**2)*(18*x**2) - 3*x**2*1 + (18*x**2)*(-30*x**3) - 30*x**3*1\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*x**3)*1 = -30*x**3\n (-30*x**3)*(18*x**2) = -540*x**5\n (-3*x**2)*1 = -3*x**2\n (-3*x**2)*(18*x**2) = -54*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -540*x**5 - 54*x**4 - 30*x**3 - 3*x**2\nNo more calculations needed.\n-540*x**5 - 54*x**4 - 30*x**3 - 3*x**2", "generated_answer": "-540*x**5 - 54*x**4 - 30*x**3 - 3*x**2", "step_length": 5} {"cot_id": "5fd774a140dd7733e1957d5e3216cdedc9b3982ed9c857f423d606ffc255b2dc", "datapoint": {"question": "Simplify this expression: (-40*y**2 + 42*y - 33)*(-7*y**3 - 39*y**2 - 34*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "280*y**5 + 1266*y**4 - 47*y**3 - 141*y**2 + 1122*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 560, "polynomial_expr": "(-40*y**2 + 42*y - 33)*(-7*y**3 - 39*y**2 - 34*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-40*y**2 + 42*y - 33)*(-7*y**3 - 39*y**2 - 34*y)\nExpanding the part (-40*y**2 + 42*y - 33) using the distributive property, and we got: (42*y)*(-7*y**3 - 39*y**2 - 34*y) + (-40*y**2)*(-7*y**3 - 39*y**2 - 34*y) - 33*(-7*y**3 - 39*y**2 - 34*y)\n#Step 2:\nCurrent expression: (42*y)*(-7*y**3 - 39*y**2 - 34*y) + (-40*y**2)*(-7*y**3 - 39*y**2 - 34*y) - 33*(-7*y**3 - 39*y**2 - 34*y)\nSimplifying the partial expression: -33*(-7*y**3 - 39*y**2 - 34*y)\nExpanding the part (-7*y**3 - 39*y**2 - 34*y) using the distributive property, and we got: -34*y*(-33) - 39*y**2*(-33) - 7*y**3*(-33)\nReplacing -33*(-7*y**3 - 39*y**2 - 34*y) with -34*y*(-33) - 39*y**2*(-33) - 7*y**3*(-33) in the overall expression.\n#Step 3:\nCurrent expression: -34*y*(-33) + (42*y)*(-7*y**3 - 39*y**2 - 34*y) + (-40*y**2)*(-7*y**3 - 39*y**2 - 34*y) - 39*y**2*(-33) - 7*y**3*(-33)\nSimplifying the partial expression: (-40*y**2)*(-7*y**3 - 39*y**2 - 34*y)\nExpanding the part (-7*y**3 - 39*y**2 - 34*y) using the distributive property, and we got: (-34*y)*(-40*y**2) + (-40*y**2)*(-39*y**2) + (-40*y**2)*(-7*y**3)\nReplacing (-40*y**2)*(-7*y**3 - 39*y**2 - 34*y) with (-34*y)*(-40*y**2) + (-40*y**2)*(-39*y**2) + (-40*y**2)*(-7*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-34*y)*(-40*y**2) - 34*y*(-33) + (42*y)*(-7*y**3 - 39*y**2 - 34*y) + (-40*y**2)*(-39*y**2) + (-40*y**2)*(-7*y**3) - 39*y**2*(-33) - 7*y**3*(-33)\nSimplifying the partial expression: (42*y)*(-7*y**3 - 39*y**2 - 34*y)\nExpanding the part (-7*y**3 - 39*y**2 - 34*y) using the distributive property, and we got: (-34*y)*(42*y) + (42*y)*(-39*y**2) + (42*y)*(-7*y**3)\nReplacing (42*y)*(-7*y**3 - 39*y**2 - 34*y) with (-34*y)*(42*y) + (42*y)*(-39*y**2) + (42*y)*(-7*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-34*y)*(42*y) + (-34*y)*(-40*y**2) - 34*y*(-33) + (42*y)*(-39*y**2) + (42*y)*(-7*y**3) + (-40*y**2)*(-39*y**2) + (-40*y**2)*(-7*y**3) - 39*y**2*(-33) - 7*y**3*(-33)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*y**2)*-33 = 1287*y**2\n (-39*y**2)*(-40*y**2) = 1560*y**4\n (-39*y**2)*(42*y) = -1638*y**3\n (-34*y)*-33 = 1122*y\n (-34*y)*(-40*y**2) = 1360*y**3\n (-34*y)*(42*y) = -1428*y**2\n (-7*y**3)*-33 = 231*y**3\n (-7*y**3)*(-40*y**2) = 280*y**5\n (-7*y**3)*(42*y) = -294*y**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 280*y**5 - 294*y**4 + 1560*y**4 - 1638*y**3 + 231*y**3 + 1360*y**3 - 1428*y**2 + 1287*y**2 + 1122*y\nCombining like terms, got 280*y**5 + 1266*y**4 - 47*y**3 - 141*y**2 + 1122*y\n#Step 7:\nCurrent expression: 280*y**5 + 1266*y**4 - 47*y**3 - 141*y**2 + 1122*y\nNo more calculations needed.\n280*y**5 + 1266*y**4 - 47*y**3 - 141*y**2 + 1122*y", "generated_answer": "280*y**5 + 1266*y**4 - 47*y**3 - 141*y**2 + 1122*y", "step_length": 7} {"cot_id": "2657e0178d89b3f37d2122e7ff2f119edbc6d896ee805e88de6a121935726f34", "datapoint": {"question": "Calculate the following: 861*x**3 + 651*x\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "861*x**3 + 651*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 561, "polynomial_expr": "861*x**3 + 651*x", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 861*x**3 + 651*x\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 861*x**3 + 651*x\nNo more calculations needed.\n861*x**3 + 651*x", "generated_answer": "861*x**3 + 651*x", "step_length": 2} {"cot_id": "d1f6cb27d67d112255b5c092468a8fa483cd7a7195bd5f37a9b562a38b7c0073", "datapoint": {"question": "Calculate the following: 1755*x**4\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1755*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 562, "polynomial_expr": "1755*x**4", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 1755*x**4\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 1755*x**4\nNo more calculations needed.\n1755*x**4", "generated_answer": "1755*x**4", "step_length": 2} {"cot_id": "3c6c76bfb7a3d02c59b6c45bdbc48d18b332618a23f050b31a7bae2a0ea22ca6", "datapoint": {"question": "Calculate the following: -59*x**3*(-19*x**3 - 32*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1121*x**6 + 1888*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 563, "polynomial_expr": "-59*x**3*(-19*x**3 - 32*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -59*x**3*(-19*x**3 - 32*x)\nExpanding the part (-19*x**3 - 32*x) using the distributive property, and we got: (-32*x)*(-59*x**3) + (-59*x**3)*(-19*x**3)\n#Step 2:\nCurrent expression: (-32*x)*(-59*x**3) + (-59*x**3)*(-19*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*x)*(-59*x**3) = 1888*x**4\n (-19*x**3)*(-59*x**3) = 1121*x**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1121*x**6 + 1888*x**4\nNo more calculations needed.\n1121*x**6 + 1888*x**4", "generated_answer": "1121*x**6 + 1888*x**4", "step_length": 3} {"cot_id": "329b25f95a6e021be9b6c713b5d70c6a583bd7398ee53648ce21ea806f010719", "datapoint": {"question": "Simplify this expression: (-7*z**2 - 49*z)*(34*z**2 + 11)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-238*z**4 - 1666*z**3 - 77*z**2 - 539*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 564, "polynomial_expr": "(-7*z**2 - 49*z)*(34*z**2 + 11)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-7*z**2 - 49*z)*(34*z**2 + 11)\nExpanding the part (34*z**2 + 11) using the distributive property, and we got: (34*z**2)*(-7*z**2 - 49*z) + 11*(-7*z**2 - 49*z)\n#Step 2:\nCurrent expression: (34*z**2)*(-7*z**2 - 49*z) + 11*(-7*z**2 - 49*z)\nSimplifying the partial expression: 11*(-7*z**2 - 49*z)\nExpanding the part (-7*z**2 - 49*z) using the distributive property, and we got: -49*z*11 - 7*z**2*11\nReplacing 11*(-7*z**2 - 49*z) with -49*z*11 - 7*z**2*11 in the overall expression.\n#Step 3:\nCurrent expression: -49*z*11 - 7*z**2*11 + (34*z**2)*(-7*z**2 - 49*z)\nSimplifying the partial expression: (34*z**2)*(-7*z**2 - 49*z)\nExpanding the part (-7*z**2 - 49*z) using the distributive property, and we got: (-49*z)*(34*z**2) + (-7*z**2)*(34*z**2)\nReplacing (34*z**2)*(-7*z**2 - 49*z) with (-49*z)*(34*z**2) + (-7*z**2)*(34*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-49*z)*(34*z**2) - 49*z*11 + (-7*z**2)*(34*z**2) - 7*z**2*11\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*z)*11 = -539*z\n (-49*z)*(34*z**2) = -1666*z**3\n (-7*z**2)*11 = -77*z**2\n (-7*z**2)*(34*z**2) = -238*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -238*z**4 - 1666*z**3 - 77*z**2 - 539*z\nNo more calculations needed.\n-238*z**4 - 1666*z**3 - 77*z**2 - 539*z", "generated_answer": "-238*z**4 - 1666*z**3 - 77*z**2 - 539*z", "step_length": 5} {"cot_id": "72127e09961edbdc4c51368f01692f8427401ec6d5ebf84a8a3afc465f1ad7a6", "datapoint": {"question": "Simplify this expression: (11 - 9*z)*(26*z**3 + 29*z**2 - 27)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-234*z**4 + 25*z**3 + 319*z**2 + 243*z - 297", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 565, "polynomial_expr": "(11 - 9*z)*(26*z**3 + 29*z**2 - 27)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11 - 9*z)*(26*z**3 + 29*z**2 - 27)\nExpanding the part (11 - 9*z) using the distributive property, and we got: (-9*z)*(26*z**3 + 29*z**2 - 27) + 11*(26*z**3 + 29*z**2 - 27)\n#Step 2:\nCurrent expression: (-9*z)*(26*z**3 + 29*z**2 - 27) + 11*(26*z**3 + 29*z**2 - 27)\nSimplifying the partial expression: 11*(26*z**3 + 29*z**2 - 27)\nExpanding the part (26*z**3 + 29*z**2 - 27) using the distributive property, and we got: (29*z**2)*11 + (26*z**3)*11 - 27*11\nReplacing 11*(26*z**3 + 29*z**2 - 27) with (29*z**2)*11 + (26*z**3)*11 - 27*11 in the overall expression.\n#Step 3:\nCurrent expression: (-9*z)*(26*z**3 + 29*z**2 - 27) + (29*z**2)*11 + (26*z**3)*11 - 297\nSimplifying the partial expression: (-9*z)*(26*z**3 + 29*z**2 - 27)\nExpanding the part (26*z**3 + 29*z**2 - 27) using the distributive property, and we got: (-9*z)*(29*z**2) + (-9*z)*(26*z**3) - (-1)*243*z\nReplacing (-9*z)*(26*z**3 + 29*z**2 - 27) with (-9*z)*(29*z**2) + (-9*z)*(26*z**3) - (-1)*243*z in the overall expression.\n#Step 4:\nCurrent expression: (-9*z)*(29*z**2) + (-9*z)*(26*z**3) - 27*(-9)*z + (29*z**2)*11 + (26*z**3)*11 - 297\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (26*z**3)*11 = 286*z**3\n (26*z**3)*(-9*z) = -234*z**4\n (29*z**2)*11 = 319*z**2\n (29*z**2)*(-9*z) = -261*z**3\n -27*-9*z = 243*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -234*z**4 - 261*z**3 + 286*z**3 + 319*z**2 + 243*z - 297\nCombining like terms, got -234*z**4 + 25*z**3 + 319*z**2 + 243*z - 297\n#Step 6:\nCurrent expression: -234*z**4 + 25*z**3 + 319*z**2 + 243*z - 297\nNo more calculations needed.\n-234*z**4 + 25*z**3 + 319*z**2 + 243*z - 297", "generated_answer": "-234*z**4 + 25*z**3 + 319*z**2 + 243*z - 297", "step_length": 6} {"cot_id": "b756efea2bce3988729f274a79ba98ce5222053c25a4c43bbeb52501fb5ef678", "datapoint": {"question": "Calculate the following: 49*x**3*(55*x**3 - 43)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2695*x**6 - 2107*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 566, "polynomial_expr": "49*x**3*(55*x**3 - 43)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 49*x**3*(55*x**3 - 43)\nExpanding the part (55*x**3 - 43) using the distributive property, and we got: -2107*x**3 + (49*x**3)*(55*x**3)\n#Step 2:\nCurrent expression: -2107*x**3 + (49*x**3)*(55*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -43*(49*x**3) = -2107*x**3\n (55*x**3)*(49*x**3) = 2695*x**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 2695*x**6 - 2107*x**3\nNo more calculations needed.\n2695*x**6 - 2107*x**3", "generated_answer": "2695*x**6 - 2107*x**3", "step_length": 3} {"cot_id": "55c490329d5090504da967ed177b0d9cad42ba49d74b48ca3f89f6a0a122001e", "datapoint": {"question": "Simplify this expression: (11*z - 12)*(-10*z**3 - 30*z**2 - 11*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-110*z**4 - 210*z**3 + 239*z**2 + 132*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 567, "polynomial_expr": "(11*z - 12)*(-10*z**3 - 30*z**2 - 11*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11*z - 12)*(-10*z**3 - 30*z**2 - 11*z)\nExpanding the part (11*z - 12) using the distributive property, and we got: (11*z)*(-10*z**3 - 30*z**2 - 11*z) - 12*(-10*z**3 - 30*z**2 - 11*z)\n#Step 2:\nCurrent expression: (11*z)*(-10*z**3 - 30*z**2 - 11*z) - 12*(-10*z**3 - 30*z**2 - 11*z)\nSimplifying the partial expression: -12*(-10*z**3 - 30*z**2 - 11*z)\nExpanding the part (-10*z**3 - 30*z**2 - 11*z) using the distributive property, and we got: -11*z*(-12) - 30*z**2*(-12) - 10*z**3*(-12)\nReplacing -12*(-10*z**3 - 30*z**2 - 11*z) with -11*z*(-12) - 30*z**2*(-12) - 10*z**3*(-12) in the overall expression.\n#Step 3:\nCurrent expression: -11*z*(-12) + (11*z)*(-10*z**3 - 30*z**2 - 11*z) - 30*z**2*(-12) - 10*z**3*(-12)\nSimplifying the partial expression: (11*z)*(-10*z**3 - 30*z**2 - 11*z)\nExpanding the part (-10*z**3 - 30*z**2 - 11*z) using the distributive property, and we got: (-11*z)*(11*z) + (11*z)*(-30*z**2) + (11*z)*(-10*z**3)\nReplacing (11*z)*(-10*z**3 - 30*z**2 - 11*z) with (-11*z)*(11*z) + (11*z)*(-30*z**2) + (11*z)*(-10*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-11*z)*(11*z) - 11*z*(-12) + (11*z)*(-30*z**2) + (11*z)*(-10*z**3) - 30*z**2*(-12) - 10*z**3*(-12)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*z**2)*-12 = 360*z**2\n (-30*z**2)*(11*z) = -330*z**3\n (-11*z)*-12 = 132*z\n (-11*z)*(11*z) = -121*z**2\n (-10*z**3)*-12 = 120*z**3\n (-10*z**3)*(11*z) = -110*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -110*z**4 - 330*z**3 + 120*z**3 - 121*z**2 + 360*z**2 + 132*z\nCombining like terms, got -110*z**4 - 210*z**3 + 239*z**2 + 132*z\n#Step 6:\nCurrent expression: -110*z**4 - 210*z**3 + 239*z**2 + 132*z\nNo more calculations needed.\n-110*z**4 - 210*z**3 + 239*z**2 + 132*z", "generated_answer": "-110*z**4 - 210*z**3 + 239*z**2 + 132*z", "step_length": 6} {"cot_id": "19a1f2429b83bc140f2c2da938d958a55d315f404cb9eaaac8f993b03de168c6", "datapoint": {"question": "Calculate the following: 0\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "0", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 568, "polynomial_expr": "0", "variables": [], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 0\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 0\nNo more calculations needed.\n0", "generated_answer": "0", "step_length": 2} {"cot_id": "cd5c20bcc18cc9ff282e7620bc63d2ef745b5c2159ddb326d4e074624e72103c", "datapoint": {"question": "Calculate the following: (-40*z**2 + 9*z - 74)*(-5*z**3 - 48*z**2 - 92)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "200*z**5 + 1875*z**4 - 62*z**3 + 7232*z**2 - 828*z + 6808", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 569, "polynomial_expr": "(-40*z**2 + 9*z - 74)*(-5*z**3 - 48*z**2 - 92)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-40*z**2 + 9*z - 74)*(-5*z**3 - 48*z**2 - 92)\nExpanding the part (-5*z**3 - 48*z**2 - 92) using the distributive property, and we got: (-48*z**2)*(-40*z**2 + 9*z - 74) + (-5*z**3)*(-40*z**2 + 9*z - 74) - 92*(-40*z**2 + 9*z - 74)\n#Step 2:\nCurrent expression: (-48*z**2)*(-40*z**2 + 9*z - 74) + (-5*z**3)*(-40*z**2 + 9*z - 74) - 92*(-40*z**2 + 9*z - 74)\nSimplifying the partial expression: -92*(-40*z**2 + 9*z - 74)\nExpanding the part (-40*z**2 + 9*z - 74) using the distributive property, and we got: (9*z)*(-92) - 40*z**2*(-92) - 74*(-92)\nReplacing -92*(-40*z**2 + 9*z - 74) with (9*z)*(-92) - 40*z**2*(-92) - 74*(-92) in the overall expression.\n#Step 3:\nCurrent expression: (9*z)*(-92) + (-48*z**2)*(-40*z**2 + 9*z - 74) - 40*z**2*(-92) + (-5*z**3)*(-40*z**2 + 9*z - 74) + 6808\nSimplifying the partial expression: (-48*z**2)*(-40*z**2 + 9*z - 74)\nExpanding the part (-40*z**2 + 9*z - 74) using the distributive property, and we got: -(-1)*3552*z**2 + (9*z)*(-48*z**2) + (-48*z**2)*(-40*z**2)\nReplacing (-48*z**2)*(-40*z**2 + 9*z - 74) with -(-1)*3552*z**2 + (9*z)*(-48*z**2) + (-48*z**2)*(-40*z**2) in the overall expression.\n#Step 4:\nCurrent expression: -74*(-48)*z**2 + (9*z)*(-48*z**2) + (9*z)*(-92) + (-48*z**2)*(-40*z**2) - 40*z**2*(-92) + (-5*z**3)*(-40*z**2 + 9*z - 74) + 6808\nSimplifying the partial expression: (-5*z**3)*(-40*z**2 + 9*z - 74)\nExpanding the part (-40*z**2 + 9*z - 74) using the distributive property, and we got: -(-1)*370*z**3 + (9*z)*(-5*z**3) + (-40*z**2)*(-5*z**3)\nReplacing (-5*z**3)*(-40*z**2 + 9*z - 74) with -(-1)*370*z**3 + (9*z)*(-5*z**3) + (-40*z**2)*(-5*z**3) in the overall expression.\n#Step 5:\nCurrent expression: -74*(-5)*z**3 - 74*(-48)*z**2 + (9*z)*(-48*z**2) + (9*z)*(-5*z**3) + (9*z)*(-92) + (-48*z**2)*(-40*z**2) + (-40*z**2)*(-5*z**3) - 40*z**2*(-92) + 6808\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*z**2)*-92 = 3680*z**2\n (-40*z**2)*(-48*z**2) = 1920*z**4\n (-40*z**2)*(-5*z**3) = 200*z**5\n (9*z)*-92 = -828*z\n (9*z)*(-48*z**2) = -432*z**3\n (9*z)*(-5*z**3) = -45*z**4\n -74*-48*z**2 = 3552*z**2\n -74*-5*z**3 = 370*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 200*z**5 - 45*z**4 + 1920*z**4 - 432*z**3 + 370*z**3 + 3552*z**2 + 3680*z**2 - 828*z + 6808\nCombining like terms, got 200*z**5 + 1875*z**4 - 62*z**3 + 7232*z**2 - 828*z + 6808\n#Step 7:\nCurrent expression: 200*z**5 + 1875*z**4 - 62*z**3 + 7232*z**2 - 828*z + 6808\nNo more calculations needed.\n200*z**5 + 1875*z**4 - 62*z**3 + 7232*z**2 - 828*z + 6808", "generated_answer": "200*z**5 + 1875*z**4 - 62*z**3 + 7232*z**2 - 828*z + 6808", "step_length": 7} {"cot_id": "6c95b914489511476df7c0e5a0fe42b0d7c18772087842603e5781628e1e72ee", "datapoint": {"question": "Calculate the following: (23*x**2 + 21*x + 39)*(33*x**2 + 50*x + 15)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "759*x**4 + 1843*x**3 + 2682*x**2 + 2265*x + 585", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 570, "polynomial_expr": "(23*x**2 + 21*x + 39)*(33*x**2 + 50*x + 15)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (23*x**2 + 21*x + 39)*(33*x**2 + 50*x + 15)\nExpanding the part (33*x**2 + 50*x + 15) using the distributive property, and we got: (50*x)*(23*x**2 + 21*x + 39) + (33*x**2)*(23*x**2 + 21*x + 39) + 15*(23*x**2 + 21*x + 39)\n#Step 2:\nCurrent expression: (50*x)*(23*x**2 + 21*x + 39) + (33*x**2)*(23*x**2 + 21*x + 39) + 15*(23*x**2 + 21*x + 39)\nSimplifying the partial expression: 15*(23*x**2 + 21*x + 39)\nExpanding the part (23*x**2 + 21*x + 39) using the distributive property, and we got: (21*x)*15 + (23*x**2)*15 + 39*15\nReplacing 15*(23*x**2 + 21*x + 39) with (21*x)*15 + (23*x**2)*15 + 39*15 in the overall expression.\n#Step 3:\nCurrent expression: (21*x)*15 + (50*x)*(23*x**2 + 21*x + 39) + (23*x**2)*15 + (33*x**2)*(23*x**2 + 21*x + 39) + 585\nSimplifying the partial expression: (33*x**2)*(23*x**2 + 21*x + 39)\nExpanding the part (23*x**2 + 21*x + 39) using the distributive property, and we got: 39*(33*x**2) + (21*x)*(33*x**2) + (23*x**2)*(33*x**2)\nReplacing (33*x**2)*(23*x**2 + 21*x + 39) with 39*(33*x**2) + (21*x)*(33*x**2) + (23*x**2)*(33*x**2) in the overall expression.\n#Step 4:\nCurrent expression: 39*33*x**2 + (21*x)*(33*x**2) + (21*x)*15 + (50*x)*(23*x**2 + 21*x + 39) + (23*x**2)*(33*x**2) + (23*x**2)*15 + 585\nSimplifying the partial expression: (50*x)*(23*x**2 + 21*x + 39)\nExpanding the part (23*x**2 + 21*x + 39) using the distributive property, and we got: 39*(50*x) + (21*x)*(50*x) + (50*x)*(23*x**2)\nReplacing (50*x)*(23*x**2 + 21*x + 39) with 39*(50*x) + (21*x)*(50*x) + (50*x)*(23*x**2) in the overall expression.\n#Step 5:\nCurrent expression: 39*33*x**2 + 39*50*x + (21*x)*(50*x) + (21*x)*(33*x**2) + (21*x)*15 + (50*x)*(23*x**2) + (23*x**2)*(33*x**2) + (23*x**2)*15 + 585\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (21*x)*15 = 315*x\n (21*x)*(33*x**2) = 693*x**3\n (21*x)*(50*x) = 1050*x**2\n (23*x**2)*15 = 345*x**2\n (23*x**2)*(33*x**2) = 759*x**4\n (23*x**2)*(50*x) = 1150*x**3\n 39*33*x**2 = 1287*x**2\n 39*50*x = 1950*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 759*x**4 + 693*x**3 + 1150*x**3 + 345*x**2 + 1050*x**2 + 1287*x**2 + 315*x + 1950*x + 585\nCombining like terms, got 759*x**4 + 1843*x**3 + 2682*x**2 + 2265*x + 585\n#Step 7:\nCurrent expression: 759*x**4 + 1843*x**3 + 2682*x**2 + 2265*x + 585\nNo more calculations needed.\n759*x**4 + 1843*x**3 + 2682*x**2 + 2265*x + 585", "generated_answer": "759*x**4 + 1843*x**3 + 2682*x**2 + 2265*x + 585", "step_length": 7} {"cot_id": "7b2d7b3b690717bc5d70526b7205cf3c11f682610d8d4ae2323a3599cc3aef98", "datapoint": {"question": "Simplify this expression: -29*y**2*(31*y**3 + 50*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-899*y**5 - 1450*y**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 571, "polynomial_expr": "-29*y**2*(31*y**3 + 50*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -29*y**2*(31*y**3 + 50*y**2)\nExpanding the part (31*y**3 + 50*y**2) using the distributive property, and we got: (-29*y**2)*(50*y**2) + (-29*y**2)*(31*y**3)\n#Step 2:\nCurrent expression: (-29*y**2)*(50*y**2) + (-29*y**2)*(31*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (31*y**3)*(-29*y**2) = -899*y**5\n (50*y**2)*(-29*y**2) = -1450*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -899*y**5 - 1450*y**4\nNo more calculations needed.\n-899*y**5 - 1450*y**4", "generated_answer": "-899*y**5 - 1450*y**4", "step_length": 3} {"cot_id": "1b67613b033b5ad4558aa1f33c1e084ee5127d01d9c27dbeed9e02a04c84a5fc", "datapoint": {"question": "Simplify this expression: (-13*y**2 - 26*y)*(-8*y**3 - 71)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "104*y**5 + 208*y**4 + 923*y**2 + 1846*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 572, "polynomial_expr": "(-13*y**2 - 26*y)*(-8*y**3 - 71)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-13*y**2 - 26*y)*(-8*y**3 - 71)\nExpanding the part (-8*y**3 - 71) using the distributive property, and we got: (-8*y**3)*(-13*y**2 - 26*y) - 71*(-13*y**2 - 26*y)\n#Step 2:\nCurrent expression: (-8*y**3)*(-13*y**2 - 26*y) - 71*(-13*y**2 - 26*y)\nSimplifying the partial expression: -71*(-13*y**2 - 26*y)\nExpanding the part (-13*y**2 - 26*y) using the distributive property, and we got: -26*y*(-71) - 13*y**2*(-71)\nReplacing -71*(-13*y**2 - 26*y) with -26*y*(-71) - 13*y**2*(-71) in the overall expression.\n#Step 3:\nCurrent expression: -26*y*(-71) - 13*y**2*(-71) + (-8*y**3)*(-13*y**2 - 26*y)\nSimplifying the partial expression: (-8*y**3)*(-13*y**2 - 26*y)\nExpanding the part (-13*y**2 - 26*y) using the distributive property, and we got: (-26*y)*(-8*y**3) + (-13*y**2)*(-8*y**3)\nReplacing (-8*y**3)*(-13*y**2 - 26*y) with (-26*y)*(-8*y**3) + (-13*y**2)*(-8*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-26*y)*(-8*y**3) - 26*y*(-71) + (-13*y**2)*(-8*y**3) - 13*y**2*(-71)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-26*y)*-71 = 1846*y\n (-26*y)*(-8*y**3) = 208*y**4\n (-13*y**2)*-71 = 923*y**2\n (-13*y**2)*(-8*y**3) = 104*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 104*y**5 + 208*y**4 + 923*y**2 + 1846*y\nNo more calculations needed.\n104*y**5 + 208*y**4 + 923*y**2 + 1846*y", "generated_answer": "104*y**5 + 208*y**4 + 923*y**2 + 1846*y", "step_length": 5} {"cot_id": "fc1a3be68098eae95aa0935a1b71f836b5deb8d617f29e0faf70981c3325e7fd", "datapoint": {"question": "Simplify this expression: 49*x**2*(-19*x**2 - 43)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-931*x**4 - 2107*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 573, "polynomial_expr": "49*x**2*(-19*x**2 - 43)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 49*x**2*(-19*x**2 - 43)\nExpanding the part (-19*x**2 - 43) using the distributive property, and we got: -2107*x**2 + (-19*x**2)*(49*x**2)\n#Step 2:\nCurrent expression: -2107*x**2 + (-19*x**2)*(49*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -43*(49*x**2) = -2107*x**2\n (-19*x**2)*(49*x**2) = -931*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -931*x**4 - 2107*x**2\nNo more calculations needed.\n-931*x**4 - 2107*x**2", "generated_answer": "-931*x**4 - 2107*x**2", "step_length": 3} {"cot_id": "b65e7acacf771fcbdcbd199e92fb1ba3b50913064d9e63607aaf278952fa5470", "datapoint": {"question": "Simplify this expression: (9*x**2 - 63)*(13*x**2 + 8*x + 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "117*x**4 + 72*x**3 - 468*x**2 - 504*x - 2457", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 574, "polynomial_expr": "(9*x**2 - 63)*(13*x**2 + 8*x + 39)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9*x**2 - 63)*(13*x**2 + 8*x + 39)\nExpanding the part (9*x**2 - 63) using the distributive property, and we got: (9*x**2)*(13*x**2 + 8*x + 39) - 63*(13*x**2 + 8*x + 39)\n#Step 2:\nCurrent expression: (9*x**2)*(13*x**2 + 8*x + 39) - 63*(13*x**2 + 8*x + 39)\nSimplifying the partial expression: -63*(13*x**2 + 8*x + 39)\nExpanding the part (13*x**2 + 8*x + 39) using the distributive property, and we got: (8*x)*(-63) + (13*x**2)*(-63) + 39*(-63)\nReplacing -63*(13*x**2 + 8*x + 39) with (8*x)*(-63) + (13*x**2)*(-63) + 39*(-63) in the overall expression.\n#Step 3:\nCurrent expression: (8*x)*(-63) + (9*x**2)*(13*x**2 + 8*x + 39) + (13*x**2)*(-63) - 2457\nSimplifying the partial expression: (9*x**2)*(13*x**2 + 8*x + 39)\nExpanding the part (13*x**2 + 8*x + 39) using the distributive property, and we got: 39*(9*x**2) + (8*x)*(9*x**2) + (9*x**2)*(13*x**2)\nReplacing (9*x**2)*(13*x**2 + 8*x + 39) with 39*(9*x**2) + (8*x)*(9*x**2) + (9*x**2)*(13*x**2) in the overall expression.\n#Step 4:\nCurrent expression: 39*9*x**2 + (8*x)*(9*x**2) + (8*x)*(-63) + (9*x**2)*(13*x**2) + (13*x**2)*(-63) - 2457\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (8*x)*-63 = -504*x\n (8*x)*(9*x**2) = 72*x**3\n (13*x**2)*-63 = -819*x**2\n (13*x**2)*(9*x**2) = 117*x**4\n 39*9*x**2 = 351*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 117*x**4 + 72*x**3 - 819*x**2 + 351*x**2 - 504*x - 2457\nCombining like terms, got 117*x**4 + 72*x**3 - 468*x**2 - 504*x - 2457\n#Step 6:\nCurrent expression: 117*x**4 + 72*x**3 - 468*x**2 - 504*x - 2457\nNo more calculations needed.\n117*x**4 + 72*x**3 - 468*x**2 - 504*x - 2457", "generated_answer": "117*x**4 + 72*x**3 - 468*x**2 - 504*x - 2457", "step_length": 6} {"cot_id": "152293ae89365c67fe501b2504965575d6d9c2516a93e2e221d57ff713e3ac2f", "datapoint": {"question": "Simplify this expression: (-24*z - 29)*(40*z**2 - 9*z + 40)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-960*z**3 - 944*z**2 - 699*z - 1160", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 575, "polynomial_expr": "(-24*z - 29)*(40*z**2 - 9*z + 40)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-24*z - 29)*(40*z**2 - 9*z + 40)\nExpanding the part (-24*z - 29) using the distributive property, and we got: (-24*z)*(40*z**2 - 9*z + 40) - 29*(40*z**2 - 9*z + 40)\n#Step 2:\nCurrent expression: (-24*z)*(40*z**2 - 9*z + 40) - 29*(40*z**2 - 9*z + 40)\nSimplifying the partial expression: -29*(40*z**2 - 9*z + 40)\nExpanding the part (40*z**2 - 9*z + 40) using the distributive property, and we got: -9*z*(-29) + (40*z**2)*(-29) + 40*(-29)\nReplacing -29*(40*z**2 - 9*z + 40) with -9*z*(-29) + (40*z**2)*(-29) + 40*(-29) in the overall expression.\n#Step 3:\nCurrent expression: (-24*z)*(40*z**2 - 9*z + 40) - 9*z*(-29) + (40*z**2)*(-29) - 1160\nSimplifying the partial expression: (-24*z)*(40*z**2 - 9*z + 40)\nExpanding the part (40*z**2 - 9*z + 40) using the distributive property, and we got: (-24*z)*(-9*z) + (-24*z)*(40*z**2) + 40*(-24*z)\nReplacing (-24*z)*(40*z**2 - 9*z + 40) with (-24*z)*(-9*z) + (-24*z)*(40*z**2) + 40*(-24*z) in the overall expression.\n#Step 4:\nCurrent expression: (-24*z)*(-9*z) + (-24*z)*(40*z**2) - 9*z*(-29) + 40*(-24)*z + (40*z**2)*(-29) - 1160\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-9*z)*-29 = 261*z\n (-9*z)*(-24*z) = 216*z**2\n (40*z**2)*-29 = -1160*z**2\n (40*z**2)*(-24*z) = -960*z**3\n 40*-24*z = -960*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -960*z**3 - 1160*z**2 + 216*z**2 - 960*z + 261*z - 1160\nCombining like terms, got -960*z**3 - 944*z**2 - 699*z - 1160\n#Step 6:\nCurrent expression: -960*z**3 - 944*z**2 - 699*z - 1160\nNo more calculations needed.\n-960*z**3 - 944*z**2 - 699*z - 1160", "generated_answer": "-960*z**3 - 944*z**2 - 699*z - 1160", "step_length": 6} {"cot_id": "503b0a1d5fa52fa48fb3dbc5c5969c066a9ae825e2701e69994b5250d81c19ad", "datapoint": {"question": "Calculate the following: -10*y*(45*y**3 + 19*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-450*y**4 - 190*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 576, "polynomial_expr": "-10*y*(45*y**3 + 19*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -10*y*(45*y**3 + 19*y)\nExpanding the part (45*y**3 + 19*y) using the distributive property, and we got: (-10*y)*(19*y) + (-10*y)*(45*y**3)\n#Step 2:\nCurrent expression: (-10*y)*(19*y) + (-10*y)*(45*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (19*y)*(-10*y) = -190*y**2\n (45*y**3)*(-10*y) = -450*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -450*y**4 - 190*y**2\nNo more calculations needed.\n-450*y**4 - 190*y**2", "generated_answer": "-450*y**4 - 190*y**2", "step_length": 3} {"cot_id": "5d1805ab674f773a3371a7e6632f04cb8f5841d6f5f83db123318ff1876958be", "datapoint": {"question": "Calculate the following: (-2*z**3 + 10*z**2)*(-30*z**3 - 21*z**2 + 22*z + 4)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "60*z**6 - 258*z**5 - 254*z**4 + 212*z**3 + 40*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 577, "polynomial_expr": "(-2*z**3 + 10*z**2)*(-30*z**3 - 21*z**2 + 22*z + 4)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-2*z**3 + 10*z**2)*(-30*z**3 - 21*z**2 + 22*z + 4)\nExpanding the part (-2*z**3 + 10*z**2) using the distributive property, and we got: (10*z**2)*(-30*z**3 - 21*z**2 + 22*z + 4) + (-2*z**3)*(-30*z**3 - 21*z**2 + 22*z + 4)\n#Step 2:\nCurrent expression: (10*z**2)*(-30*z**3 - 21*z**2 + 22*z + 4) + (-2*z**3)*(-30*z**3 - 21*z**2 + 22*z + 4)\nSimplifying the partial expression: (-2*z**3)*(-30*z**3 - 21*z**2 + 22*z + 4)\nExpanding the part (-30*z**3 - 21*z**2 + 22*z + 4) using the distributive property, and we got: 4*(-2*z**3) + (22*z)*(-2*z**3) + (-21*z**2)*(-2*z**3) + (-30*z**3)*(-2*z**3)\nReplacing (-2*z**3)*(-30*z**3 - 21*z**2 + 22*z + 4) with 4*(-2*z**3) + (22*z)*(-2*z**3) + (-21*z**2)*(-2*z**3) + (-30*z**3)*(-2*z**3) in the overall expression.\n#Step 3:\nCurrent expression: 4*(-2)*z**3 + (22*z)*(-2*z**3) + (-21*z**2)*(-2*z**3) + (10*z**2)*(-30*z**3 - 21*z**2 + 22*z + 4) + (-30*z**3)*(-2*z**3)\nSimplifying the partial expression: (10*z**2)*(-30*z**3 - 21*z**2 + 22*z + 4)\nExpanding the part (-30*z**3 - 21*z**2 + 22*z + 4) using the distributive property, and we got: 4*(10*z**2) + (22*z)*(10*z**2) + (-21*z**2)*(10*z**2) + (10*z**2)*(-30*z**3)\nReplacing (10*z**2)*(-30*z**3 - 21*z**2 + 22*z + 4) with 4*(10*z**2) + (22*z)*(10*z**2) + (-21*z**2)*(10*z**2) + (10*z**2)*(-30*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 4*(-2)*z**3 + 4*10*z**2 + (22*z)*(10*z**2) + (22*z)*(-2*z**3) + (-21*z**2)*(10*z**2) + (-21*z**2)*(-2*z**3) + (10*z**2)*(-30*z**3) + (-30*z**3)*(-2*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*z**3)*(-2*z**3) = 60*z**6\n (-30*z**3)*(10*z**2) = -300*z**5\n (-21*z**2)*(-2*z**3) = 42*z**5\n (-21*z**2)*(10*z**2) = -210*z**4\n (22*z)*(-2*z**3) = -44*z**4\n (22*z)*(10*z**2) = 220*z**3\n 4*-2*z**3 = -8*z**3\n 4*10*z**2 = 40*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 60*z**6 - 300*z**5 + 42*z**5 - 210*z**4 - 44*z**4 - 8*z**3 + 220*z**3 + 40*z**2\nCombining like terms, got 60*z**6 - 258*z**5 - 254*z**4 + 212*z**3 + 40*z**2\n#Step 6:\nCurrent expression: 60*z**6 - 258*z**5 - 254*z**4 + 212*z**3 + 40*z**2\nNo more calculations needed.\n60*z**6 - 258*z**5 - 254*z**4 + 212*z**3 + 40*z**2", "generated_answer": "60*z**6 - 258*z**5 - 254*z**4 + 212*z**3 + 40*z**2", "step_length": 6} {"cot_id": "64120372db831bbf3ae701f80c72cd2c0b4ebef19cf809ff6fa325160a1719d7", "datapoint": {"question": "Calculate the following: (2 - 43*x)*(-58*x**3 + 31*x - 4)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2494*x**4 - 116*x**3 - 1333*x**2 + 234*x - 8", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 578, "polynomial_expr": "(2 - 43*x)*(-58*x**3 + 31*x - 4)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2 - 43*x)*(-58*x**3 + 31*x - 4)\nExpanding the part (2 - 43*x) using the distributive property, and we got: (-43*x)*(-58*x**3 + 31*x - 4) + 2*(-58*x**3 + 31*x - 4)\n#Step 2:\nCurrent expression: (-43*x)*(-58*x**3 + 31*x - 4) + 2*(-58*x**3 + 31*x - 4)\nSimplifying the partial expression: 2*(-58*x**3 + 31*x - 4)\nExpanding the part (-58*x**3 + 31*x - 4) using the distributive property, and we got: (31*x)*2 - 58*x**3*2 - 4*2\nReplacing 2*(-58*x**3 + 31*x - 4) with (31*x)*2 - 58*x**3*2 - 4*2 in the overall expression.\n#Step 3:\nCurrent expression: (-43*x)*(-58*x**3 + 31*x - 4) + (31*x)*2 - 58*x**3*2 - 8\nSimplifying the partial expression: (-43*x)*(-58*x**3 + 31*x - 4)\nExpanding the part (-58*x**3 + 31*x - 4) using the distributive property, and we got: (-43*x)*(31*x) + (-43*x)*(-58*x**3) - (-1)*172*x\nReplacing (-43*x)*(-58*x**3 + 31*x - 4) with (-43*x)*(31*x) + (-43*x)*(-58*x**3) - (-1)*172*x in the overall expression.\n#Step 4:\nCurrent expression: (-43*x)*(31*x) + (-43*x)*(-58*x**3) - 4*(-43)*x + (31*x)*2 - 58*x**3*2 - 8\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-58*x**3)*2 = -116*x**3\n (-58*x**3)*(-43*x) = 2494*x**4\n (31*x)*2 = 62*x\n (31*x)*(-43*x) = -1333*x**2\n -4*-43*x = 172*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2494*x**4 - 116*x**3 - 1333*x**2 + 62*x + 172*x - 8\nCombining like terms, got 2494*x**4 - 116*x**3 - 1333*x**2 + 234*x - 8\n#Step 6:\nCurrent expression: 2494*x**4 - 116*x**3 - 1333*x**2 + 234*x - 8\nNo more calculations needed.\n2494*x**4 - 116*x**3 - 1333*x**2 + 234*x - 8", "generated_answer": "2494*x**4 - 116*x**3 - 1333*x**2 + 234*x - 8", "step_length": 6} {"cot_id": "1981c3858725ff7e09798f21d7919832714b4ecdb8b0110372ee88dddb28447e", "datapoint": {"question": "Calculate the following: (-67*y**2 + 26*y)*(34*y**3 - 46)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2278*y**5 + 884*y**4 + 3082*y**2 - 1196*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 579, "polynomial_expr": "(-67*y**2 + 26*y)*(34*y**3 - 46)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-67*y**2 + 26*y)*(34*y**3 - 46)\nExpanding the part (34*y**3 - 46) using the distributive property, and we got: (34*y**3)*(-67*y**2 + 26*y) - 46*(-67*y**2 + 26*y)\n#Step 2:\nCurrent expression: (34*y**3)*(-67*y**2 + 26*y) - 46*(-67*y**2 + 26*y)\nSimplifying the partial expression: -46*(-67*y**2 + 26*y)\nExpanding the part (-67*y**2 + 26*y) using the distributive property, and we got: (26*y)*(-46) - 67*y**2*(-46)\nReplacing -46*(-67*y**2 + 26*y) with (26*y)*(-46) - 67*y**2*(-46) in the overall expression.\n#Step 3:\nCurrent expression: (26*y)*(-46) - 67*y**2*(-46) + (34*y**3)*(-67*y**2 + 26*y)\nSimplifying the partial expression: (34*y**3)*(-67*y**2 + 26*y)\nExpanding the part (-67*y**2 + 26*y) using the distributive property, and we got: (26*y)*(34*y**3) + (-67*y**2)*(34*y**3)\nReplacing (34*y**3)*(-67*y**2 + 26*y) with (26*y)*(34*y**3) + (-67*y**2)*(34*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (26*y)*(34*y**3) + (26*y)*(-46) + (-67*y**2)*(34*y**3) - 67*y**2*(-46)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-67*y**2)*-46 = 3082*y**2\n (-67*y**2)*(34*y**3) = -2278*y**5\n (26*y)*-46 = -1196*y\n (26*y)*(34*y**3) = 884*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2278*y**5 + 884*y**4 + 3082*y**2 - 1196*y\nNo more calculations needed.\n-2278*y**5 + 884*y**4 + 3082*y**2 - 1196*y", "generated_answer": "-2278*y**5 + 884*y**4 + 3082*y**2 - 1196*y", "step_length": 5} {"cot_id": "32f653262cb40215eafe4861c37466b9f0fb98630e6817669a4a44c0567a155d", "datapoint": {"question": "Simplify this expression: (39*y**2 - 68*y)*(60*y**3 - 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2340*y**5 - 4080*y**4 - 1248*y**2 + 2176*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 580, "polynomial_expr": "(39*y**2 - 68*y)*(60*y**3 - 32)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (39*y**2 - 68*y)*(60*y**3 - 32)\nExpanding the part (60*y**3 - 32) using the distributive property, and we got: (60*y**3)*(39*y**2 - 68*y) - 32*(39*y**2 - 68*y)\n#Step 2:\nCurrent expression: (60*y**3)*(39*y**2 - 68*y) - 32*(39*y**2 - 68*y)\nSimplifying the partial expression: -32*(39*y**2 - 68*y)\nExpanding the part (39*y**2 - 68*y) using the distributive property, and we got: -68*y*(-32) + (39*y**2)*(-32)\nReplacing -32*(39*y**2 - 68*y) with -68*y*(-32) + (39*y**2)*(-32) in the overall expression.\n#Step 3:\nCurrent expression: -68*y*(-32) + (39*y**2)*(-32) + (60*y**3)*(39*y**2 - 68*y)\nSimplifying the partial expression: (60*y**3)*(39*y**2 - 68*y)\nExpanding the part (39*y**2 - 68*y) using the distributive property, and we got: (-68*y)*(60*y**3) + (39*y**2)*(60*y**3)\nReplacing (60*y**3)*(39*y**2 - 68*y) with (-68*y)*(60*y**3) + (39*y**2)*(60*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-68*y)*(60*y**3) - 68*y*(-32) + (39*y**2)*(60*y**3) + (39*y**2)*(-32)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-68*y)*-32 = 2176*y\n (-68*y)*(60*y**3) = -4080*y**4\n (39*y**2)*-32 = -1248*y**2\n (39*y**2)*(60*y**3) = 2340*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2340*y**5 - 4080*y**4 - 1248*y**2 + 2176*y\nNo more calculations needed.\n2340*y**5 - 4080*y**4 - 1248*y**2 + 2176*y", "generated_answer": "2340*y**5 - 4080*y**4 - 1248*y**2 + 2176*y", "step_length": 5} {"cot_id": "6c8472126e989b9b87e722695f43d90dd63d906fab46316c21aa51613a96eafc", "datapoint": {"question": "Simplify this expression: 12*x*(43*x**2 + 45*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "516*x**3 + 540*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 581, "polynomial_expr": "12*x*(43*x**2 + 45*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 12*x*(43*x**2 + 45*x)\nExpanding the part (43*x**2 + 45*x) using the distributive property, and we got: (12*x)*(45*x) + (12*x)*(43*x**2)\n#Step 2:\nCurrent expression: (12*x)*(45*x) + (12*x)*(43*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (43*x**2)*(12*x) = 516*x**3\n (45*x)*(12*x) = 540*x**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 516*x**3 + 540*x**2\nNo more calculations needed.\n516*x**3 + 540*x**2", "generated_answer": "516*x**3 + 540*x**2", "step_length": 3} {"cot_id": "130cf984545f548e03467637fc0e76202932aa3054e64395624d2917a3f09690", "datapoint": {"question": "Simplify this expression: -4*x**2*(21*x**3 + 43*x**2 + 42*x + 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-84*x**5 - 172*x**4 - 168*x**3 - 200*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 582, "polynomial_expr": "-4*x**2*(21*x**3 + 43*x**2 + 42*x + 50)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -4*x**2*(21*x**3 + 43*x**2 + 42*x + 50)\nExpanding the part (21*x**3 + 43*x**2 + 42*x + 50) using the distributive property, and we got: 50*(-4*x**2) + (42*x)*(-4*x**2) + (-4*x**2)*(43*x**2) + (-4*x**2)*(21*x**3)\n#Step 2:\nCurrent expression: 50*(-4*x**2) + (42*x)*(-4*x**2) + (-4*x**2)*(43*x**2) + (-4*x**2)*(21*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 50*(-4*x**2) = -200*x**2\n (21*x**3)*(-4*x**2) = -84*x**5\n (42*x)*(-4*x**2) = -168*x**3\n (43*x**2)*(-4*x**2) = -172*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -84*x**5 - 172*x**4 - 168*x**3 - 200*x**2\nNo more calculations needed.\n-84*x**5 - 172*x**4 - 168*x**3 - 200*x**2", "generated_answer": "-84*x**5 - 172*x**4 - 168*x**3 - 200*x**2", "step_length": 3} {"cot_id": "47e837daf96eac009c2b6576d709be9e0d37a7cdbaa9cf9d13de4acf2e84a0c3", "datapoint": {"question": "Simplify this expression: (-28*y**3 + 21*y**2 - 46*y)*(38*y**3 + 79*y**2 + 15)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1064*y**6 - 1414*y**5 - 89*y**4 - 4054*y**3 + 315*y**2 - 690*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 583, "polynomial_expr": "(-28*y**3 + 21*y**2 - 46*y)*(38*y**3 + 79*y**2 + 15)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-28*y**3 + 21*y**2 - 46*y)*(38*y**3 + 79*y**2 + 15)\nExpanding the part (38*y**3 + 79*y**2 + 15) using the distributive property, and we got: (79*y**2)*(-28*y**3 + 21*y**2 - 46*y) + (38*y**3)*(-28*y**3 + 21*y**2 - 46*y) + 15*(-28*y**3 + 21*y**2 - 46*y)\n#Step 2:\nCurrent expression: (79*y**2)*(-28*y**3 + 21*y**2 - 46*y) + (38*y**3)*(-28*y**3 + 21*y**2 - 46*y) + 15*(-28*y**3 + 21*y**2 - 46*y)\nSimplifying the partial expression: 15*(-28*y**3 + 21*y**2 - 46*y)\nExpanding the part (-28*y**3 + 21*y**2 - 46*y) using the distributive property, and we got: -46*y*15 + (21*y**2)*15 - 28*y**3*15\nReplacing 15*(-28*y**3 + 21*y**2 - 46*y) with -46*y*15 + (21*y**2)*15 - 28*y**3*15 in the overall expression.\n#Step 3:\nCurrent expression: -46*y*15 + (21*y**2)*15 + (79*y**2)*(-28*y**3 + 21*y**2 - 46*y) - 28*y**3*15 + (38*y**3)*(-28*y**3 + 21*y**2 - 46*y)\nSimplifying the partial expression: (38*y**3)*(-28*y**3 + 21*y**2 - 46*y)\nExpanding the part (-28*y**3 + 21*y**2 - 46*y) using the distributive property, and we got: (-46*y)*(38*y**3) + (21*y**2)*(38*y**3) + (-28*y**3)*(38*y**3)\nReplacing (38*y**3)*(-28*y**3 + 21*y**2 - 46*y) with (-46*y)*(38*y**3) + (21*y**2)*(38*y**3) + (-28*y**3)*(38*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-46*y)*(38*y**3) - 46*y*15 + (21*y**2)*(38*y**3) + (21*y**2)*15 + (79*y**2)*(-28*y**3 + 21*y**2 - 46*y) + (-28*y**3)*(38*y**3) - 28*y**3*15\nSimplifying the partial expression: (79*y**2)*(-28*y**3 + 21*y**2 - 46*y)\nExpanding the part (-28*y**3 + 21*y**2 - 46*y) using the distributive property, and we got: (-46*y)*(79*y**2) + (21*y**2)*(79*y**2) + (79*y**2)*(-28*y**3)\nReplacing (79*y**2)*(-28*y**3 + 21*y**2 - 46*y) with (-46*y)*(79*y**2) + (21*y**2)*(79*y**2) + (79*y**2)*(-28*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-46*y)*(79*y**2) + (-46*y)*(38*y**3) - 46*y*15 + (21*y**2)*(79*y**2) + (21*y**2)*(38*y**3) + (21*y**2)*15 + (79*y**2)*(-28*y**3) + (-28*y**3)*(38*y**3) - 28*y**3*15\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*y)*15 = -690*y\n (-46*y)*(38*y**3) = -1748*y**4\n (-46*y)*(79*y**2) = -3634*y**3\n (-28*y**3)*15 = -420*y**3\n (-28*y**3)*(38*y**3) = -1064*y**6\n (-28*y**3)*(79*y**2) = -2212*y**5\n (21*y**2)*15 = 315*y**2\n (21*y**2)*(38*y**3) = 798*y**5\n (21*y**2)*(79*y**2) = 1659*y**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1064*y**6 - 2212*y**5 + 798*y**5 - 1748*y**4 + 1659*y**4 - 3634*y**3 - 420*y**3 + 315*y**2 - 690*y\nCombining like terms, got -1064*y**6 - 1414*y**5 - 89*y**4 - 4054*y**3 + 315*y**2 - 690*y\n#Step 7:\nCurrent expression: -1064*y**6 - 1414*y**5 - 89*y**4 - 4054*y**3 + 315*y**2 - 690*y\nNo more calculations needed.\n-1064*y**6 - 1414*y**5 - 89*y**4 - 4054*y**3 + 315*y**2 - 690*y", "generated_answer": "-1064*y**6 - 1414*y**5 - 89*y**4 - 4054*y**3 + 315*y**2 - 690*y", "step_length": 7} {"cot_id": "6e8890736b08b4b83a5784295d633ac1e0f59ad0d2c3169363582ff7a08239fb", "datapoint": {"question": "Calculate the following: (y**2 + 16*y)*(21*y**2 + 2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "21*y**4 + 336*y**3 + 2*y**2 + 32*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 584, "polynomial_expr": "(y**2 + 16*y)*(21*y**2 + 2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (y**2 + 16*y)*(21*y**2 + 2)\nExpanding the part (21*y**2 + 2) using the distributive property, and we got: (21*y**2)*(y**2 + 16*y) + 2*(y**2 + 16*y)\n#Step 2:\nCurrent expression: (21*y**2)*(y**2 + 16*y) + 2*(y**2 + 16*y)\nSimplifying the partial expression: 2*(y**2 + 16*y)\nExpanding the part (y**2 + 16*y) using the distributive property, and we got: y**2*2 + (16*y)*2\nReplacing 2*(y**2 + 16*y) with y**2*2 + (16*y)*2 in the overall expression.\n#Step 3:\nCurrent expression: y**2*2 + (16*y)*2 + (21*y**2)*(y**2 + 16*y)\nSimplifying the partial expression: (21*y**2)*(y**2 + 16*y)\nExpanding the part (y**2 + 16*y) using the distributive property, and we got: y**2*(21*y**2) + (16*y)*(21*y**2)\nReplacing (21*y**2)*(y**2 + 16*y) with y**2*(21*y**2) + (16*y)*(21*y**2) in the overall expression.\n#Step 4:\nCurrent expression: y**2*(21*y**2) + y**2*2 + (16*y)*(21*y**2) + (16*y)*2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n y**2*2 = 2*y**2\n y**2*(21*y**2) = 21*y**4\n (16*y)*2 = 32*y\n (16*y)*(21*y**2) = 336*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 21*y**4 + 336*y**3 + 2*y**2 + 32*y\nNo more calculations needed.\n21*y**4 + 336*y**3 + 2*y**2 + 32*y", "generated_answer": "21*y**4 + 336*y**3 + 2*y**2 + 32*y", "step_length": 5} {"cot_id": "173f74dc3f789034ac4ca2c739f4dc622fcf2be1a684e51f6cd0bb2f5f69b4b0", "datapoint": {"question": "Simplify this expression: (-15*y**3 - 27)*(35*y**2 + 34*y - 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-525*y**5 - 510*y**4 + 720*y**3 - 945*y**2 - 918*y + 1296", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 585, "polynomial_expr": "(-15*y**3 - 27)*(35*y**2 + 34*y - 48)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-15*y**3 - 27)*(35*y**2 + 34*y - 48)\nExpanding the part (-15*y**3 - 27) using the distributive property, and we got: (-15*y**3)*(35*y**2 + 34*y - 48) - 27*(35*y**2 + 34*y - 48)\n#Step 2:\nCurrent expression: (-15*y**3)*(35*y**2 + 34*y - 48) - 27*(35*y**2 + 34*y - 48)\nSimplifying the partial expression: -27*(35*y**2 + 34*y - 48)\nExpanding the part (35*y**2 + 34*y - 48) using the distributive property, and we got: (34*y)*(-27) + (35*y**2)*(-27) - 48*(-27)\nReplacing -27*(35*y**2 + 34*y - 48) with (34*y)*(-27) + (35*y**2)*(-27) - 48*(-27) in the overall expression.\n#Step 3:\nCurrent expression: (34*y)*(-27) + (35*y**2)*(-27) + (-15*y**3)*(35*y**2 + 34*y - 48) + 1296\nSimplifying the partial expression: (-15*y**3)*(35*y**2 + 34*y - 48)\nExpanding the part (35*y**2 + 34*y - 48) using the distributive property, and we got: -(-1)*720*y**3 + (34*y)*(-15*y**3) + (35*y**2)*(-15*y**3)\nReplacing (-15*y**3)*(35*y**2 + 34*y - 48) with -(-1)*720*y**3 + (34*y)*(-15*y**3) + (35*y**2)*(-15*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -48*(-15)*y**3 + (34*y)*(-15*y**3) + (34*y)*(-27) + (35*y**2)*(-15*y**3) + (35*y**2)*(-27) + 1296\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (34*y)*-27 = -918*y\n (34*y)*(-15*y**3) = -510*y**4\n (35*y**2)*-27 = -945*y**2\n (35*y**2)*(-15*y**3) = -525*y**5\n -48*-15*y**3 = 720*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -525*y**5 - 510*y**4 + 720*y**3 - 945*y**2 - 918*y + 1296\nNo more calculations needed.\n-525*y**5 - 510*y**4 + 720*y**3 - 945*y**2 - 918*y + 1296", "generated_answer": "-525*y**5 - 510*y**4 + 720*y**3 - 945*y**2 - 918*y + 1296", "step_length": 5} {"cot_id": "e0039d7dc4a9de4812d9fcd51a2f880e0ecdd11054b6b99940b367e6bb0a6b8d", "datapoint": {"question": "Calculate the following: (-20*y**2 - 30*y + 38)*(-36*y**3 + 11*y**2 + 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "720*y**5 + 860*y**4 - 1698*y**3 + 218*y**2 - 300*y + 380", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 586, "polynomial_expr": "(-20*y**2 - 30*y + 38)*(-36*y**3 + 11*y**2 + 10)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-20*y**2 - 30*y + 38)*(-36*y**3 + 11*y**2 + 10)\nExpanding the part (-36*y**3 + 11*y**2 + 10) using the distributive property, and we got: (11*y**2)*(-20*y**2 - 30*y + 38) + (-36*y**3)*(-20*y**2 - 30*y + 38) + 10*(-20*y**2 - 30*y + 38)\n#Step 2:\nCurrent expression: (11*y**2)*(-20*y**2 - 30*y + 38) + (-36*y**3)*(-20*y**2 - 30*y + 38) + 10*(-20*y**2 - 30*y + 38)\nSimplifying the partial expression: 10*(-20*y**2 - 30*y + 38)\nExpanding the part (-20*y**2 - 30*y + 38) using the distributive property, and we got: -30*y*10 - 20*y**2*10 + 38*10\nReplacing 10*(-20*y**2 - 30*y + 38) with -30*y*10 - 20*y**2*10 + 38*10 in the overall expression.\n#Step 3:\nCurrent expression: -30*y*10 - 20*y**2*10 + (11*y**2)*(-20*y**2 - 30*y + 38) + (-36*y**3)*(-20*y**2 - 30*y + 38) + 380\nSimplifying the partial expression: (-36*y**3)*(-20*y**2 - 30*y + 38)\nExpanding the part (-20*y**2 - 30*y + 38) using the distributive property, and we got: (-30*y)*(-36*y**3) + 38*(-36*y**3) + (-20*y**2)*(-36*y**3)\nReplacing (-36*y**3)*(-20*y**2 - 30*y + 38) with (-30*y)*(-36*y**3) + 38*(-36*y**3) + (-20*y**2)*(-36*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-30*y)*(-36*y**3) - 30*y*10 + 38*(-36)*y**3 + (-20*y**2)*(-36*y**3) - 20*y**2*10 + (11*y**2)*(-20*y**2 - 30*y + 38) + 380\nSimplifying the partial expression: (11*y**2)*(-20*y**2 - 30*y + 38)\nExpanding the part (-20*y**2 - 30*y + 38) using the distributive property, and we got: (-30*y)*(11*y**2) + 38*(11*y**2) + (-20*y**2)*(11*y**2)\nReplacing (11*y**2)*(-20*y**2 - 30*y + 38) with (-30*y)*(11*y**2) + 38*(11*y**2) + (-20*y**2)*(11*y**2) in the overall expression.\n#Step 5:\nCurrent expression: (-30*y)*(11*y**2) + (-30*y)*(-36*y**3) - 30*y*10 + 38*(-36)*y**3 + 38*11*y**2 + (-20*y**2)*(11*y**2) + (-20*y**2)*(-36*y**3) - 20*y**2*10 + 380\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*y)*10 = -300*y\n (-30*y)*(-36*y**3) = 1080*y**4\n (-30*y)*(11*y**2) = -330*y**3\n (-20*y**2)*10 = -200*y**2\n (-20*y**2)*(-36*y**3) = 720*y**5\n (-20*y**2)*(11*y**2) = -220*y**4\n 38*-36*y**3 = -1368*y**3\n 38*11*y**2 = 418*y**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 720*y**5 - 220*y**4 + 1080*y**4 - 1368*y**3 - 330*y**3 - 200*y**2 + 418*y**2 - 300*y + 380\nCombining like terms, got 720*y**5 + 860*y**4 - 1698*y**3 + 218*y**2 - 300*y + 380\n#Step 7:\nCurrent expression: 720*y**5 + 860*y**4 - 1698*y**3 + 218*y**2 - 300*y + 380\nNo more calculations needed.\n720*y**5 + 860*y**4 - 1698*y**3 + 218*y**2 - 300*y + 380", "generated_answer": "720*y**5 + 860*y**4 - 1698*y**3 + 218*y**2 - 300*y + 380", "step_length": 7} {"cot_id": "7fb82f32fc48197802b75836b08674db1931577d5e92afa1283f44c4bfc3b862", "datapoint": {"question": "Calculate the following: (x**3 - x)*(-38*x**2 + 48*x - 5)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-38*x**5 + 48*x**4 + 33*x**3 - 48*x**2 + 5*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 587, "polynomial_expr": "(x**3 - x)*(-38*x**2 + 48*x - 5)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (x**3 - x)*(-38*x**2 + 48*x - 5)\nExpanding the part (x**3 - x) using the distributive property, and we got: (-x)*(-38*x**2 + 48*x - 5) + x**3*(-38*x**2 + 48*x - 5)\n#Step 2:\nCurrent expression: (-x)*(-38*x**2 + 48*x - 5) + x**3*(-38*x**2 + 48*x - 5)\nSimplifying the partial expression: x**3*(-38*x**2 + 48*x - 5)\nExpanding the part (-38*x**2 + 48*x - 5) using the distributive property, and we got: (48*x)*x**3 + (-38*x**2)*x**3 - 5*x**3\nReplacing x**3*(-38*x**2 + 48*x - 5) with (48*x)*x**3 + (-38*x**2)*x**3 - 5*x**3 in the overall expression.\n#Step 3:\nCurrent expression: (-x)*(-38*x**2 + 48*x - 5) + (48*x)*x**3 + (-38*x**2)*x**3 - 5*x**3\nSimplifying the partial expression: (-x)*(-38*x**2 + 48*x - 5)\nExpanding the part (-38*x**2 + 48*x - 5) using the distributive property, and we got: (-x)*(48*x) + (-x)*(-38*x**2) - (-1)*5*x\nReplacing (-x)*(-38*x**2 + 48*x - 5) with (-x)*(48*x) + (-x)*(-38*x**2) - (-1)*5*x in the overall expression.\n#Step 4:\nCurrent expression: (-x)*(48*x) + (-x)*(-38*x**2) + (48*x)*x**3 + (-38*x**2)*x**3 - 5*x**3 - 5*(-1)*x\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*x**2)*x**3 = -38*x**5\n (-38*x**2)*(-x) = 38*x**3\n (48*x)*x**3 = 48*x**4\n (48*x)*(-x) = -48*x**2\n -5*-1*x = 5*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -38*x**5 + 48*x**4 - 5*x**3 + 38*x**3 - 48*x**2 + 5*x\nCombining like terms, got -38*x**5 + 48*x**4 + 33*x**3 - 48*x**2 + 5*x\n#Step 6:\nCurrent expression: -38*x**5 + 48*x**4 + 33*x**3 - 48*x**2 + 5*x\nNo more calculations needed.\n-38*x**5 + 48*x**4 + 33*x**3 - 48*x**2 + 5*x", "generated_answer": "-38*x**5 + 48*x**4 + 33*x**3 - 48*x**2 + 5*x", "step_length": 6} {"cot_id": "b4a0afa3790f0778af3aa182272f2a7852fa1c1beaae30740f3684d9513385dc", "datapoint": {"question": "Calculate the following: (14*y**2 + 33*y)*(25*y**2 - 6*y + 61)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "350*y**4 + 741*y**3 + 656*y**2 + 2013*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 588, "polynomial_expr": "(14*y**2 + 33*y)*(25*y**2 - 6*y + 61)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14*y**2 + 33*y)*(25*y**2 - 6*y + 61)\nExpanding the part (14*y**2 + 33*y) using the distributive property, and we got: (33*y)*(25*y**2 - 6*y + 61) + (14*y**2)*(25*y**2 - 6*y + 61)\n#Step 2:\nCurrent expression: (33*y)*(25*y**2 - 6*y + 61) + (14*y**2)*(25*y**2 - 6*y + 61)\nSimplifying the partial expression: (14*y**2)*(25*y**2 - 6*y + 61)\nExpanding the part (25*y**2 - 6*y + 61) using the distributive property, and we got: (-6*y)*(14*y**2) + 61*(14*y**2) + (14*y**2)*(25*y**2)\nReplacing (14*y**2)*(25*y**2 - 6*y + 61) with (-6*y)*(14*y**2) + 61*(14*y**2) + (14*y**2)*(25*y**2) in the overall expression.\n#Step 3:\nCurrent expression: (-6*y)*(14*y**2) + 61*14*y**2 + (33*y)*(25*y**2 - 6*y + 61) + (14*y**2)*(25*y**2)\nSimplifying the partial expression: (33*y)*(25*y**2 - 6*y + 61)\nExpanding the part (25*y**2 - 6*y + 61) using the distributive property, and we got: (-6*y)*(33*y) + 61*(33*y) + (33*y)*(25*y**2)\nReplacing (33*y)*(25*y**2 - 6*y + 61) with (-6*y)*(33*y) + 61*(33*y) + (33*y)*(25*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-6*y)*(33*y) + (-6*y)*(14*y**2) + 61*14*y**2 + 61*33*y + (33*y)*(25*y**2) + (14*y**2)*(25*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-6*y)*(14*y**2) = -84*y**3\n (-6*y)*(33*y) = -198*y**2\n (25*y**2)*(14*y**2) = 350*y**4\n (25*y**2)*(33*y) = 825*y**3\n 61*14*y**2 = 854*y**2\n 61*33*y = 2013*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 350*y**4 - 84*y**3 + 825*y**3 - 198*y**2 + 854*y**2 + 2013*y\nCombining like terms, got 350*y**4 + 741*y**3 + 656*y**2 + 2013*y\n#Step 6:\nCurrent expression: 350*y**4 + 741*y**3 + 656*y**2 + 2013*y\nNo more calculations needed.\n350*y**4 + 741*y**3 + 656*y**2 + 2013*y", "generated_answer": "350*y**4 + 741*y**3 + 656*y**2 + 2013*y", "step_length": 6} {"cot_id": "5a0fbecac7dae970db719771b3854b4d2ae37e4c9fa81eb9ff14abb269967eb4", "datapoint": {"question": "Calculate the following: -510*y**3 + 2856*y\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-510*y**3 + 2856*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 589, "polynomial_expr": "-510*y**3 + 2856*y", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -510*y**3 + 2856*y\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -510*y**3 + 2856*y\nNo more calculations needed.\n-510*y**3 + 2856*y", "generated_answer": "-510*y**3 + 2856*y", "step_length": 2} {"cot_id": "3a3bbd1434bb65b7ea3226eb5003e3e8f5273a259951f83e1b2cc66359f5ebf1", "datapoint": {"question": "Calculate the following: (-40*y**3 + 26*y**2 - 42*y)*(-3*y**3 + 30*y**2 - 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "120*y**6 - 1278*y**5 + 906*y**4 - 580*y**3 - 442*y**2 + 714*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 590, "polynomial_expr": "(-40*y**3 + 26*y**2 - 42*y)*(-3*y**3 + 30*y**2 - 17)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-40*y**3 + 26*y**2 - 42*y)*(-3*y**3 + 30*y**2 - 17)\nExpanding the part (-3*y**3 + 30*y**2 - 17) using the distributive property, and we got: (30*y**2)*(-40*y**3 + 26*y**2 - 42*y) + (-3*y**3)*(-40*y**3 + 26*y**2 - 42*y) - 17*(-40*y**3 + 26*y**2 - 42*y)\n#Step 2:\nCurrent expression: (30*y**2)*(-40*y**3 + 26*y**2 - 42*y) + (-3*y**3)*(-40*y**3 + 26*y**2 - 42*y) - 17*(-40*y**3 + 26*y**2 - 42*y)\nSimplifying the partial expression: -17*(-40*y**3 + 26*y**2 - 42*y)\nExpanding the part (-40*y**3 + 26*y**2 - 42*y) using the distributive property, and we got: -42*y*(-17) + (26*y**2)*(-17) - 40*y**3*(-17)\nReplacing -17*(-40*y**3 + 26*y**2 - 42*y) with -42*y*(-17) + (26*y**2)*(-17) - 40*y**3*(-17) in the overall expression.\n#Step 3:\nCurrent expression: -42*y*(-17) + (26*y**2)*(-17) + (30*y**2)*(-40*y**3 + 26*y**2 - 42*y) - 40*y**3*(-17) + (-3*y**3)*(-40*y**3 + 26*y**2 - 42*y)\nSimplifying the partial expression: (-3*y**3)*(-40*y**3 + 26*y**2 - 42*y)\nExpanding the part (-40*y**3 + 26*y**2 - 42*y) using the distributive property, and we got: (-42*y)*(-3*y**3) + (26*y**2)*(-3*y**3) + (-40*y**3)*(-3*y**3)\nReplacing (-3*y**3)*(-40*y**3 + 26*y**2 - 42*y) with (-42*y)*(-3*y**3) + (26*y**2)*(-3*y**3) + (-40*y**3)*(-3*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-42*y)*(-3*y**3) - 42*y*(-17) + (26*y**2)*(-3*y**3) + (26*y**2)*(-17) + (30*y**2)*(-40*y**3 + 26*y**2 - 42*y) + (-40*y**3)*(-3*y**3) - 40*y**3*(-17)\nSimplifying the partial expression: (30*y**2)*(-40*y**3 + 26*y**2 - 42*y)\nExpanding the part (-40*y**3 + 26*y**2 - 42*y) using the distributive property, and we got: (-42*y)*(30*y**2) + (26*y**2)*(30*y**2) + (30*y**2)*(-40*y**3)\nReplacing (30*y**2)*(-40*y**3 + 26*y**2 - 42*y) with (-42*y)*(30*y**2) + (26*y**2)*(30*y**2) + (30*y**2)*(-40*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-42*y)*(30*y**2) + (-42*y)*(-3*y**3) - 42*y*(-17) + (26*y**2)*(30*y**2) + (26*y**2)*(-3*y**3) + (26*y**2)*(-17) + (30*y**2)*(-40*y**3) + (-40*y**3)*(-3*y**3) - 40*y**3*(-17)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*y)*-17 = 714*y\n (-42*y)*(-3*y**3) = 126*y**4\n (-42*y)*(30*y**2) = -1260*y**3\n (-40*y**3)*-17 = 680*y**3\n (-40*y**3)*(-3*y**3) = 120*y**6\n (-40*y**3)*(30*y**2) = -1200*y**5\n (26*y**2)*-17 = -442*y**2\n (26*y**2)*(-3*y**3) = -78*y**5\n (26*y**2)*(30*y**2) = 780*y**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 120*y**6 - 1200*y**5 - 78*y**5 + 126*y**4 + 780*y**4 - 1260*y**3 + 680*y**3 - 442*y**2 + 714*y\nCombining like terms, got 120*y**6 - 1278*y**5 + 906*y**4 - 580*y**3 - 442*y**2 + 714*y\n#Step 7:\nCurrent expression: 120*y**6 - 1278*y**5 + 906*y**4 - 580*y**3 - 442*y**2 + 714*y\nNo more calculations needed.\n120*y**6 - 1278*y**5 + 906*y**4 - 580*y**3 - 442*y**2 + 714*y", "generated_answer": "120*y**6 - 1278*y**5 + 906*y**4 - 580*y**3 - 442*y**2 + 714*y", "step_length": 7} {"cot_id": "d4384c76964d54f6385051575cafbfc0b938bf5e6380503f710868c4e8f41446", "datapoint": {"question": "Calculate the following: (24 - 23*x)*(-49*x**3 - 6*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1127*x**4 - 1038*x**3 - 144*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 591, "polynomial_expr": "(24 - 23*x)*(-49*x**3 - 6*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (24 - 23*x)*(-49*x**3 - 6*x**2)\nExpanding the part (24 - 23*x) using the distributive property, and we got: (-23*x)*(-49*x**3 - 6*x**2) + 24*(-49*x**3 - 6*x**2)\n#Step 2:\nCurrent expression: (-23*x)*(-49*x**3 - 6*x**2) + 24*(-49*x**3 - 6*x**2)\nSimplifying the partial expression: 24*(-49*x**3 - 6*x**2)\nExpanding the part (-49*x**3 - 6*x**2) using the distributive property, and we got: -6*x**2*24 - 49*x**3*24\nReplacing 24*(-49*x**3 - 6*x**2) with -6*x**2*24 - 49*x**3*24 in the overall expression.\n#Step 3:\nCurrent expression: (-23*x)*(-49*x**3 - 6*x**2) - 6*x**2*24 - 49*x**3*24\nSimplifying the partial expression: (-23*x)*(-49*x**3 - 6*x**2)\nExpanding the part (-49*x**3 - 6*x**2) using the distributive property, and we got: (-23*x)*(-6*x**2) + (-23*x)*(-49*x**3)\nReplacing (-23*x)*(-49*x**3 - 6*x**2) with (-23*x)*(-6*x**2) + (-23*x)*(-49*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-23*x)*(-6*x**2) + (-23*x)*(-49*x**3) - 6*x**2*24 - 49*x**3*24\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*x**3)*24 = -1176*x**3\n (-49*x**3)*(-23*x) = 1127*x**4\n (-6*x**2)*24 = -144*x**2\n (-6*x**2)*(-23*x) = 138*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1127*x**4 - 1176*x**3 + 138*x**3 - 144*x**2\nCombining like terms, got 1127*x**4 - 1038*x**3 - 144*x**2\n#Step 6:\nCurrent expression: 1127*x**4 - 1038*x**3 - 144*x**2\nNo more calculations needed.\n1127*x**4 - 1038*x**3 - 144*x**2", "generated_answer": "1127*x**4 - 1038*x**3 - 144*x**2", "step_length": 6} {"cot_id": "47cef603230ba2e16e948a6aef346ab50db05f0d0ac6a759f92ef91d44b7e983", "datapoint": {"question": "Simplify this expression: -21*x**2*(25*x**2 + 48*x + 84)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-525*x**4 - 1008*x**3 - 1764*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 592, "polynomial_expr": "-21*x**2*(25*x**2 + 48*x + 84)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -21*x**2*(25*x**2 + 48*x + 84)\nExpanding the part (25*x**2 + 48*x + 84) using the distributive property, and we got: 84*(-21*x**2) + (48*x)*(-21*x**2) + (-21*x**2)*(25*x**2)\n#Step 2:\nCurrent expression: 84*(-21*x**2) + (48*x)*(-21*x**2) + (-21*x**2)*(25*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 84*(-21*x**2) = -1764*x**2\n (25*x**2)*(-21*x**2) = -525*x**4\n (48*x)*(-21*x**2) = -1008*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -525*x**4 - 1008*x**3 - 1764*x**2\nNo more calculations needed.\n-525*x**4 - 1008*x**3 - 1764*x**2", "generated_answer": "-525*x**4 - 1008*x**3 - 1764*x**2", "step_length": 3} {"cot_id": "6fe315e05ec3901f18ab5035607478f49cc25a4d8783be8989aceadbbf9f5712", "datapoint": {"question": "Calculate the following: -38*y*(42 - 13*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "494*y**2 - 1596*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 593, "polynomial_expr": "-38*y*(42 - 13*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -38*y*(42 - 13*y)\nExpanding the part (42 - 13*y) using the distributive property, and we got: (-38*y)*(-13*y) + 42*(-38*y)\n#Step 2:\nCurrent expression: (-38*y)*(-13*y) + 42*(-38*y)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 42*(-38*y) = -1596*y\n (-13*y)*(-38*y) = 494*y**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 494*y**2 - 1596*y\nNo more calculations needed.\n494*y**2 - 1596*y", "generated_answer": "494*y**2 - 1596*y", "step_length": 3} {"cot_id": "be4dbb729e0b0aac1eb597921d8dee792e9b2349a94d0eb5c63126588da2d7de", "datapoint": {"question": "Calculate the following: (-16*x - 10)*(-44*x**3 - 50*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "704*x**4 + 1240*x**3 + 500*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 594, "polynomial_expr": "(-16*x - 10)*(-44*x**3 - 50*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-16*x - 10)*(-44*x**3 - 50*x**2)\nExpanding the part (-16*x - 10) using the distributive property, and we got: (-16*x)*(-44*x**3 - 50*x**2) - 10*(-44*x**3 - 50*x**2)\n#Step 2:\nCurrent expression: (-16*x)*(-44*x**3 - 50*x**2) - 10*(-44*x**3 - 50*x**2)\nSimplifying the partial expression: -10*(-44*x**3 - 50*x**2)\nExpanding the part (-44*x**3 - 50*x**2) using the distributive property, and we got: -50*x**2*(-10) - 44*x**3*(-10)\nReplacing -10*(-44*x**3 - 50*x**2) with -50*x**2*(-10) - 44*x**3*(-10) in the overall expression.\n#Step 3:\nCurrent expression: (-16*x)*(-44*x**3 - 50*x**2) - 50*x**2*(-10) - 44*x**3*(-10)\nSimplifying the partial expression: (-16*x)*(-44*x**3 - 50*x**2)\nExpanding the part (-44*x**3 - 50*x**2) using the distributive property, and we got: (-16*x)*(-50*x**2) + (-16*x)*(-44*x**3)\nReplacing (-16*x)*(-44*x**3 - 50*x**2) with (-16*x)*(-50*x**2) + (-16*x)*(-44*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-16*x)*(-50*x**2) + (-16*x)*(-44*x**3) - 50*x**2*(-10) - 44*x**3*(-10)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-50*x**2)*-10 = 500*x**2\n (-50*x**2)*(-16*x) = 800*x**3\n (-44*x**3)*-10 = 440*x**3\n (-44*x**3)*(-16*x) = 704*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 704*x**4 + 440*x**3 + 800*x**3 + 500*x**2\nCombining like terms, got 704*x**4 + 1240*x**3 + 500*x**2\n#Step 6:\nCurrent expression: 704*x**4 + 1240*x**3 + 500*x**2\nNo more calculations needed.\n704*x**4 + 1240*x**3 + 500*x**2", "generated_answer": "704*x**4 + 1240*x**3 + 500*x**2", "step_length": 6} {"cot_id": "280fcc3f5d73b6a0dd55262be8d2dc7bef709084ef265a8ded343e2768602ada", "datapoint": {"question": "Simplify this expression: (-53*y**3 - 46)*(25*y**3 + 78*y + 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1325*y**6 - 4134*y**4 - 1998*y**3 - 3588*y - 736", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 595, "polynomial_expr": "(-53*y**3 - 46)*(25*y**3 + 78*y + 16)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-53*y**3 - 46)*(25*y**3 + 78*y + 16)\nExpanding the part (-53*y**3 - 46) using the distributive property, and we got: (-53*y**3)*(25*y**3 + 78*y + 16) - 46*(25*y**3 + 78*y + 16)\n#Step 2:\nCurrent expression: (-53*y**3)*(25*y**3 + 78*y + 16) - 46*(25*y**3 + 78*y + 16)\nSimplifying the partial expression: -46*(25*y**3 + 78*y + 16)\nExpanding the part (25*y**3 + 78*y + 16) using the distributive property, and we got: (78*y)*(-46) + (25*y**3)*(-46) + 16*(-46)\nReplacing -46*(25*y**3 + 78*y + 16) with (78*y)*(-46) + (25*y**3)*(-46) + 16*(-46) in the overall expression.\n#Step 3:\nCurrent expression: (78*y)*(-46) + (-53*y**3)*(25*y**3 + 78*y + 16) + (25*y**3)*(-46) - 736\nSimplifying the partial expression: (-53*y**3)*(25*y**3 + 78*y + 16)\nExpanding the part (25*y**3 + 78*y + 16) using the distributive property, and we got: 16*(-53*y**3) + (78*y)*(-53*y**3) + (-53*y**3)*(25*y**3)\nReplacing (-53*y**3)*(25*y**3 + 78*y + 16) with 16*(-53*y**3) + (78*y)*(-53*y**3) + (-53*y**3)*(25*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 16*(-53)*y**3 + (78*y)*(-53*y**3) + (78*y)*(-46) + (-53*y**3)*(25*y**3) + (25*y**3)*(-46) - 736\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (25*y**3)*-46 = -1150*y**3\n (25*y**3)*(-53*y**3) = -1325*y**6\n (78*y)*-46 = -3588*y\n (78*y)*(-53*y**3) = -4134*y**4\n 16*-53*y**3 = -848*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1325*y**6 - 4134*y**4 - 1150*y**3 - 848*y**3 - 3588*y - 736\nCombining like terms, got -1325*y**6 - 4134*y**4 - 1998*y**3 - 3588*y - 736\n#Step 6:\nCurrent expression: -1325*y**6 - 4134*y**4 - 1998*y**3 - 3588*y - 736\nNo more calculations needed.\n-1325*y**6 - 4134*y**4 - 1998*y**3 - 3588*y - 736", "generated_answer": "-1325*y**6 - 4134*y**4 - 1998*y**3 - 3588*y - 736", "step_length": 6} {"cot_id": "afa39cf1872503b08ecabdb5fa3b477405efa922fa9783a4cd0fce110b9502cc", "datapoint": {"question": "Simplify this expression: (50*z - 6)*(-46*z**2 - 46*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2300*z**3 - 2024*z**2 + 276*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 596, "polynomial_expr": "(50*z - 6)*(-46*z**2 - 46*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (50*z - 6)*(-46*z**2 - 46*z)\nExpanding the part (50*z - 6) using the distributive property, and we got: (50*z)*(-46*z**2 - 46*z) - 6*(-46*z**2 - 46*z)\n#Step 2:\nCurrent expression: (50*z)*(-46*z**2 - 46*z) - 6*(-46*z**2 - 46*z)\nSimplifying the partial expression: -6*(-46*z**2 - 46*z)\nExpanding the part (-46*z**2 - 46*z) using the distributive property, and we got: -46*z*(-6) - 46*z**2*(-6)\nReplacing -6*(-46*z**2 - 46*z) with -46*z*(-6) - 46*z**2*(-6) in the overall expression.\n#Step 3:\nCurrent expression: -46*z*(-6) + (50*z)*(-46*z**2 - 46*z) - 46*z**2*(-6)\nSimplifying the partial expression: (50*z)*(-46*z**2 - 46*z)\nExpanding the part (-46*z**2 - 46*z) using the distributive property, and we got: (-46*z)*(50*z) + (50*z)*(-46*z**2)\nReplacing (50*z)*(-46*z**2 - 46*z) with (-46*z)*(50*z) + (50*z)*(-46*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-46*z)*(50*z) - 46*z*(-6) + (50*z)*(-46*z**2) - 46*z**2*(-6)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*z)*-6 = 276*z\n (-46*z)*(50*z) = -2300*z**2\n (-46*z**2)*-6 = 276*z**2\n (-46*z**2)*(50*z) = -2300*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2300*z**3 - 2300*z**2 + 276*z**2 + 276*z\nCombining like terms, got -2300*z**3 - 2024*z**2 + 276*z\n#Step 6:\nCurrent expression: -2300*z**3 - 2024*z**2 + 276*z\nNo more calculations needed.\n-2300*z**3 - 2024*z**2 + 276*z", "generated_answer": "-2300*z**3 - 2024*z**2 + 276*z", "step_length": 6} {"cot_id": "3920bda37731ab061e7ce21bdd16e1cb5d0b807211258a58fa2fbd5bd6fec17d", "datapoint": {"question": "Simplify this expression: (-33*z - 15)*(-13*z**2 + 2*z - 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "429*z**3 + 129*z**2 + 168*z + 90", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 597, "polynomial_expr": "(-33*z - 15)*(-13*z**2 + 2*z - 6)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-33*z - 15)*(-13*z**2 + 2*z - 6)\nExpanding the part (-33*z - 15) using the distributive property, and we got: (-33*z)*(-13*z**2 + 2*z - 6) - 15*(-13*z**2 + 2*z - 6)\n#Step 2:\nCurrent expression: (-33*z)*(-13*z**2 + 2*z - 6) - 15*(-13*z**2 + 2*z - 6)\nSimplifying the partial expression: -15*(-13*z**2 + 2*z - 6)\nExpanding the part (-13*z**2 + 2*z - 6) using the distributive property, and we got: (2*z)*(-15) - 13*z**2*(-15) - 6*(-15)\nReplacing -15*(-13*z**2 + 2*z - 6) with (2*z)*(-15) - 13*z**2*(-15) - 6*(-15) in the overall expression.\n#Step 3:\nCurrent expression: (-33*z)*(-13*z**2 + 2*z - 6) + (2*z)*(-15) - 13*z**2*(-15) + 90\nSimplifying the partial expression: (-33*z)*(-13*z**2 + 2*z - 6)\nExpanding the part (-13*z**2 + 2*z - 6) using the distributive property, and we got: (-33*z)*(2*z) + (-33*z)*(-13*z**2) - (-1)*198*z\nReplacing (-33*z)*(-13*z**2 + 2*z - 6) with (-33*z)*(2*z) + (-33*z)*(-13*z**2) - (-1)*198*z in the overall expression.\n#Step 4:\nCurrent expression: (-33*z)*(2*z) + (-33*z)*(-13*z**2) - 6*(-33)*z + (2*z)*(-15) - 13*z**2*(-15) + 90\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*z**2)*-15 = 195*z**2\n (-13*z**2)*(-33*z) = 429*z**3\n (2*z)*-15 = -30*z\n (2*z)*(-33*z) = -66*z**2\n -6*-33*z = 198*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 429*z**3 - 66*z**2 + 195*z**2 - 30*z + 198*z + 90\nCombining like terms, got 429*z**3 + 129*z**2 + 168*z + 90\n#Step 6:\nCurrent expression: 429*z**3 + 129*z**2 + 168*z + 90\nNo more calculations needed.\n429*z**3 + 129*z**2 + 168*z + 90", "generated_answer": "429*z**3 + 129*z**2 + 168*z + 90", "step_length": 6} {"cot_id": "0eb322c01d96654436f5840e5a34cabc531c6c6386a7e7231c0a79a1bf3cb518", "datapoint": {"question": "Simplify this expression: -6*x**3*(4*x**2 + 43)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-24*x**5 - 258*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 598, "polynomial_expr": "-6*x**3*(4*x**2 + 43)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -6*x**3*(4*x**2 + 43)\nExpanding the part (4*x**2 + 43) using the distributive property, and we got: 43*(-6*x**3) + (4*x**2)*(-6*x**3)\n#Step 2:\nCurrent expression: 43*(-6*x**3) + (4*x**2)*(-6*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 43*(-6*x**3) = -258*x**3\n (4*x**2)*(-6*x**3) = -24*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -24*x**5 - 258*x**3\nNo more calculations needed.\n-24*x**5 - 258*x**3", "generated_answer": "-24*x**5 - 258*x**3", "step_length": 3} {"cot_id": "45656c0075a92c1319694c7652003551769ae5473b658e4f2d831f37c4b3eb4f", "datapoint": {"question": "Calculate the following: (28*y**2 + 64)*(47*y**2 + 49*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1316*y**4 + 1372*y**3 + 3008*y**2 + 3136*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 599, "polynomial_expr": "(28*y**2 + 64)*(47*y**2 + 49*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28*y**2 + 64)*(47*y**2 + 49*y)\nExpanding the part (28*y**2 + 64) using the distributive property, and we got: (28*y**2)*(47*y**2 + 49*y) + 64*(47*y**2 + 49*y)\n#Step 2:\nCurrent expression: (28*y**2)*(47*y**2 + 49*y) + 64*(47*y**2 + 49*y)\nSimplifying the partial expression: 64*(47*y**2 + 49*y)\nExpanding the part (47*y**2 + 49*y) using the distributive property, and we got: (49*y)*64 + (47*y**2)*64\nReplacing 64*(47*y**2 + 49*y) with (49*y)*64 + (47*y**2)*64 in the overall expression.\n#Step 3:\nCurrent expression: (49*y)*64 + (28*y**2)*(47*y**2 + 49*y) + (47*y**2)*64\nSimplifying the partial expression: (28*y**2)*(47*y**2 + 49*y)\nExpanding the part (47*y**2 + 49*y) using the distributive property, and we got: (49*y)*(28*y**2) + (28*y**2)*(47*y**2)\nReplacing (28*y**2)*(47*y**2 + 49*y) with (49*y)*(28*y**2) + (28*y**2)*(47*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (49*y)*(28*y**2) + (49*y)*64 + (28*y**2)*(47*y**2) + (47*y**2)*64\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (47*y**2)*64 = 3008*y**2\n (47*y**2)*(28*y**2) = 1316*y**4\n (49*y)*64 = 3136*y\n (49*y)*(28*y**2) = 1372*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1316*y**4 + 1372*y**3 + 3008*y**2 + 3136*y\nNo more calculations needed.\n1316*y**4 + 1372*y**3 + 3008*y**2 + 3136*y", "generated_answer": "1316*y**4 + 1372*y**3 + 3008*y**2 + 3136*y", "step_length": 5} {"cot_id": "bb357322487f73e8b604019ed15487d72291092fbc4e28ee47516558e48b9682", "datapoint": {"question": "Simplify this expression: (-47*z**3 + 33*z**2 - 19*z)*(55*z**3 + 5*z**2 - 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2585*z**6 + 1580*z**5 - 880*z**4 + 187*z**3 - 198*z**2 + 114*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 600, "polynomial_expr": "(-47*z**3 + 33*z**2 - 19*z)*(55*z**3 + 5*z**2 - 6)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-47*z**3 + 33*z**2 - 19*z)*(55*z**3 + 5*z**2 - 6)\nExpanding the part (55*z**3 + 5*z**2 - 6) using the distributive property, and we got: (5*z**2)*(-47*z**3 + 33*z**2 - 19*z) + (55*z**3)*(-47*z**3 + 33*z**2 - 19*z) - 6*(-47*z**3 + 33*z**2 - 19*z)\n#Step 2:\nCurrent expression: (5*z**2)*(-47*z**3 + 33*z**2 - 19*z) + (55*z**3)*(-47*z**3 + 33*z**2 - 19*z) - 6*(-47*z**3 + 33*z**2 - 19*z)\nSimplifying the partial expression: -6*(-47*z**3 + 33*z**2 - 19*z)\nExpanding the part (-47*z**3 + 33*z**2 - 19*z) using the distributive property, and we got: -19*z*(-6) + (33*z**2)*(-6) - 47*z**3*(-6)\nReplacing -6*(-47*z**3 + 33*z**2 - 19*z) with -19*z*(-6) + (33*z**2)*(-6) - 47*z**3*(-6) in the overall expression.\n#Step 3:\nCurrent expression: -19*z*(-6) + (5*z**2)*(-47*z**3 + 33*z**2 - 19*z) + (33*z**2)*(-6) - 47*z**3*(-6) + (55*z**3)*(-47*z**3 + 33*z**2 - 19*z)\nSimplifying the partial expression: (5*z**2)*(-47*z**3 + 33*z**2 - 19*z)\nExpanding the part (-47*z**3 + 33*z**2 - 19*z) using the distributive property, and we got: (-19*z)*(5*z**2) + (5*z**2)*(33*z**2) + (5*z**2)*(-47*z**3)\nReplacing (5*z**2)*(-47*z**3 + 33*z**2 - 19*z) with (-19*z)*(5*z**2) + (5*z**2)*(33*z**2) + (5*z**2)*(-47*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-19*z)*(5*z**2) - 19*z*(-6) + (5*z**2)*(33*z**2) + (5*z**2)*(-47*z**3) + (33*z**2)*(-6) - 47*z**3*(-6) + (55*z**3)*(-47*z**3 + 33*z**2 - 19*z)\nSimplifying the partial expression: (55*z**3)*(-47*z**3 + 33*z**2 - 19*z)\nExpanding the part (-47*z**3 + 33*z**2 - 19*z) using the distributive property, and we got: (-19*z)*(55*z**3) + (33*z**2)*(55*z**3) + (-47*z**3)*(55*z**3)\nReplacing (55*z**3)*(-47*z**3 + 33*z**2 - 19*z) with (-19*z)*(55*z**3) + (33*z**2)*(55*z**3) + (-47*z**3)*(55*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-19*z)*(5*z**2) + (-19*z)*(55*z**3) - 19*z*(-6) + (5*z**2)*(33*z**2) + (5*z**2)*(-47*z**3) + (33*z**2)*(55*z**3) + (33*z**2)*(-6) + (-47*z**3)*(55*z**3) - 47*z**3*(-6)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*z**3)*-6 = 282*z**3\n (-47*z**3)*(5*z**2) = -235*z**5\n (-47*z**3)*(55*z**3) = -2585*z**6\n (-19*z)*-6 = 114*z\n (-19*z)*(5*z**2) = -95*z**3\n (-19*z)*(55*z**3) = -1045*z**4\n (33*z**2)*-6 = -198*z**2\n (33*z**2)*(5*z**2) = 165*z**4\n (33*z**2)*(55*z**3) = 1815*z**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -2585*z**6 - 235*z**5 + 1815*z**5 - 1045*z**4 + 165*z**4 - 95*z**3 + 282*z**3 - 198*z**2 + 114*z\nCombining like terms, got -2585*z**6 + 1580*z**5 - 880*z**4 + 187*z**3 - 198*z**2 + 114*z\n#Step 7:\nCurrent expression: -2585*z**6 + 1580*z**5 - 880*z**4 + 187*z**3 - 198*z**2 + 114*z\nNo more calculations needed.\n-2585*z**6 + 1580*z**5 - 880*z**4 + 187*z**3 - 198*z**2 + 114*z", "generated_answer": "-2585*z**6 + 1580*z**5 - 880*z**4 + 187*z**3 - 198*z**2 + 114*z", "step_length": 7} {"cot_id": "a0ccb10f30590fa05324b2f1b43c64ae1b2bb9372fdb25d070b27b2e12add5fa", "datapoint": {"question": "Simplify this expression: (28 - 30*z**3)*(-15*z**3 + 11*z + 26)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "450*z**6 - 330*z**4 - 1200*z**3 + 308*z + 728", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 601, "polynomial_expr": "(28 - 30*z**3)*(-15*z**3 + 11*z + 26)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28 - 30*z**3)*(-15*z**3 + 11*z + 26)\nExpanding the part (28 - 30*z**3) using the distributive property, and we got: (-30*z**3)*(-15*z**3 + 11*z + 26) + 28*(-15*z**3 + 11*z + 26)\n#Step 2:\nCurrent expression: (-30*z**3)*(-15*z**3 + 11*z + 26) + 28*(-15*z**3 + 11*z + 26)\nSimplifying the partial expression: 28*(-15*z**3 + 11*z + 26)\nExpanding the part (-15*z**3 + 11*z + 26) using the distributive property, and we got: (11*z)*28 - 15*z**3*28 + 26*28\nReplacing 28*(-15*z**3 + 11*z + 26) with (11*z)*28 - 15*z**3*28 + 26*28 in the overall expression.\n#Step 3:\nCurrent expression: (11*z)*28 + (-30*z**3)*(-15*z**3 + 11*z + 26) - 15*z**3*28 + 728\nSimplifying the partial expression: (-30*z**3)*(-15*z**3 + 11*z + 26)\nExpanding the part (-15*z**3 + 11*z + 26) using the distributive property, and we got: 26*(-30*z**3) + (11*z)*(-30*z**3) + (-30*z**3)*(-15*z**3)\nReplacing (-30*z**3)*(-15*z**3 + 11*z + 26) with 26*(-30*z**3) + (11*z)*(-30*z**3) + (-30*z**3)*(-15*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 26*(-30)*z**3 + (11*z)*(-30*z**3) + (11*z)*28 + (-30*z**3)*(-15*z**3) - 15*z**3*28 + 728\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-15*z**3)*28 = -420*z**3\n (-15*z**3)*(-30*z**3) = 450*z**6\n (11*z)*28 = 308*z\n (11*z)*(-30*z**3) = -330*z**4\n 26*-30*z**3 = -780*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 450*z**6 - 330*z**4 - 780*z**3 - 420*z**3 + 308*z + 728\nCombining like terms, got 450*z**6 - 330*z**4 - 1200*z**3 + 308*z + 728\n#Step 6:\nCurrent expression: 450*z**6 - 330*z**4 - 1200*z**3 + 308*z + 728\nNo more calculations needed.\n450*z**6 - 330*z**4 - 1200*z**3 + 308*z + 728", "generated_answer": "450*z**6 - 330*z**4 - 1200*z**3 + 308*z + 728", "step_length": 6} {"cot_id": "6bbf9db7a34710899bb03bdbb24e797a14f47bd32f8565a228631a44c6d0e0c4", "datapoint": {"question": "Simplify this expression: (31*y**2 - 36)*(67*y**3 + 44*y**2 + 12)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2077*y**5 + 1364*y**4 - 2412*y**3 - 1212*y**2 - 432", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 602, "polynomial_expr": "(31*y**2 - 36)*(67*y**3 + 44*y**2 + 12)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31*y**2 - 36)*(67*y**3 + 44*y**2 + 12)\nExpanding the part (31*y**2 - 36) using the distributive property, and we got: (31*y**2)*(67*y**3 + 44*y**2 + 12) - 36*(67*y**3 + 44*y**2 + 12)\n#Step 2:\nCurrent expression: (31*y**2)*(67*y**3 + 44*y**2 + 12) - 36*(67*y**3 + 44*y**2 + 12)\nSimplifying the partial expression: -36*(67*y**3 + 44*y**2 + 12)\nExpanding the part (67*y**3 + 44*y**2 + 12) using the distributive property, and we got: (44*y**2)*(-36) + (67*y**3)*(-36) + 12*(-36)\nReplacing -36*(67*y**3 + 44*y**2 + 12) with (44*y**2)*(-36) + (67*y**3)*(-36) + 12*(-36) in the overall expression.\n#Step 3:\nCurrent expression: (31*y**2)*(67*y**3 + 44*y**2 + 12) + (44*y**2)*(-36) + (67*y**3)*(-36) - 432\nSimplifying the partial expression: (31*y**2)*(67*y**3 + 44*y**2 + 12)\nExpanding the part (67*y**3 + 44*y**2 + 12) using the distributive property, and we got: 12*(31*y**2) + (31*y**2)*(44*y**2) + (31*y**2)*(67*y**3)\nReplacing (31*y**2)*(67*y**3 + 44*y**2 + 12) with 12*(31*y**2) + (31*y**2)*(44*y**2) + (31*y**2)*(67*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 12*31*y**2 + (31*y**2)*(44*y**2) + (31*y**2)*(67*y**3) + (44*y**2)*(-36) + (67*y**3)*(-36) - 432\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (44*y**2)*-36 = -1584*y**2\n (44*y**2)*(31*y**2) = 1364*y**4\n (67*y**3)*-36 = -2412*y**3\n (67*y**3)*(31*y**2) = 2077*y**5\n 12*31*y**2 = 372*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2077*y**5 + 1364*y**4 - 2412*y**3 - 1584*y**2 + 372*y**2 - 432\nCombining like terms, got 2077*y**5 + 1364*y**4 - 2412*y**3 - 1212*y**2 - 432\n#Step 6:\nCurrent expression: 2077*y**5 + 1364*y**4 - 2412*y**3 - 1212*y**2 - 432\nNo more calculations needed.\n2077*y**5 + 1364*y**4 - 2412*y**3 - 1212*y**2 - 432", "generated_answer": "2077*y**5 + 1364*y**4 - 2412*y**3 - 1212*y**2 - 432", "step_length": 6} {"cot_id": "d50ccbe12ab19ac3c5cd049bac0487ef50244961dc530f0be3b63b485af7ef4d", "datapoint": {"question": "Simplify this expression: (31 - 32*x)*(-67*x**2 - 44*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2144*x**3 - 669*x**2 - 1364*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 603, "polynomial_expr": "(31 - 32*x)*(-67*x**2 - 44*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31 - 32*x)*(-67*x**2 - 44*x)\nExpanding the part (31 - 32*x) using the distributive property, and we got: (-32*x)*(-67*x**2 - 44*x) + 31*(-67*x**2 - 44*x)\n#Step 2:\nCurrent expression: (-32*x)*(-67*x**2 - 44*x) + 31*(-67*x**2 - 44*x)\nSimplifying the partial expression: 31*(-67*x**2 - 44*x)\nExpanding the part (-67*x**2 - 44*x) using the distributive property, and we got: -44*x*31 - 67*x**2*31\nReplacing 31*(-67*x**2 - 44*x) with -44*x*31 - 67*x**2*31 in the overall expression.\n#Step 3:\nCurrent expression: -44*x*31 + (-32*x)*(-67*x**2 - 44*x) - 67*x**2*31\nSimplifying the partial expression: (-32*x)*(-67*x**2 - 44*x)\nExpanding the part (-67*x**2 - 44*x) using the distributive property, and we got: (-44*x)*(-32*x) + (-32*x)*(-67*x**2)\nReplacing (-32*x)*(-67*x**2 - 44*x) with (-44*x)*(-32*x) + (-32*x)*(-67*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-44*x)*(-32*x) - 44*x*31 + (-32*x)*(-67*x**2) - 67*x**2*31\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-67*x**2)*31 = -2077*x**2\n (-67*x**2)*(-32*x) = 2144*x**3\n (-44*x)*31 = -1364*x\n (-44*x)*(-32*x) = 1408*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2144*x**3 - 2077*x**2 + 1408*x**2 - 1364*x\nCombining like terms, got 2144*x**3 - 669*x**2 - 1364*x\n#Step 6:\nCurrent expression: 2144*x**3 - 669*x**2 - 1364*x\nNo more calculations needed.\n2144*x**3 - 669*x**2 - 1364*x", "generated_answer": "2144*x**3 - 669*x**2 - 1364*x", "step_length": 6} {"cot_id": "27a7a114e45b5f1fe284493e416081e440cf30823b74cf42db6bec653c7bb8e5", "datapoint": {"question": "Simplify this expression: (11*z**2 - 36*z + 34)*(18*z**3 + 18*z**2 - 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "198*z**5 - 450*z**4 - 36*z**3 + 62*z**2 + 1800*z - 1700", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 604, "polynomial_expr": "(11*z**2 - 36*z + 34)*(18*z**3 + 18*z**2 - 50)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11*z**2 - 36*z + 34)*(18*z**3 + 18*z**2 - 50)\nExpanding the part (18*z**3 + 18*z**2 - 50) using the distributive property, and we got: (18*z**2)*(11*z**2 - 36*z + 34) + (18*z**3)*(11*z**2 - 36*z + 34) - 50*(11*z**2 - 36*z + 34)\n#Step 2:\nCurrent expression: (18*z**2)*(11*z**2 - 36*z + 34) + (18*z**3)*(11*z**2 - 36*z + 34) - 50*(11*z**2 - 36*z + 34)\nSimplifying the partial expression: -50*(11*z**2 - 36*z + 34)\nExpanding the part (11*z**2 - 36*z + 34) using the distributive property, and we got: -36*z*(-50) + (11*z**2)*(-50) + 34*(-50)\nReplacing -50*(11*z**2 - 36*z + 34) with -36*z*(-50) + (11*z**2)*(-50) + 34*(-50) in the overall expression.\n#Step 3:\nCurrent expression: -36*z*(-50) + (11*z**2)*(-50) + (18*z**2)*(11*z**2 - 36*z + 34) + (18*z**3)*(11*z**2 - 36*z + 34) - 1700\nSimplifying the partial expression: (18*z**2)*(11*z**2 - 36*z + 34)\nExpanding the part (11*z**2 - 36*z + 34) using the distributive property, and we got: (-36*z)*(18*z**2) + 34*(18*z**2) + (11*z**2)*(18*z**2)\nReplacing (18*z**2)*(11*z**2 - 36*z + 34) with (-36*z)*(18*z**2) + 34*(18*z**2) + (11*z**2)*(18*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-36*z)*(18*z**2) - 36*z*(-50) + 34*18*z**2 + (11*z**2)*(18*z**2) + (11*z**2)*(-50) + (18*z**3)*(11*z**2 - 36*z + 34) - 1700\nSimplifying the partial expression: (18*z**3)*(11*z**2 - 36*z + 34)\nExpanding the part (11*z**2 - 36*z + 34) using the distributive property, and we got: (-36*z)*(18*z**3) + 34*(18*z**3) + (11*z**2)*(18*z**3)\nReplacing (18*z**3)*(11*z**2 - 36*z + 34) with (-36*z)*(18*z**3) + 34*(18*z**3) + (11*z**2)*(18*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-36*z)*(18*z**2) + (-36*z)*(18*z**3) - 36*z*(-50) + 34*18*z**3 + 34*18*z**2 + (11*z**2)*(18*z**2) + (11*z**2)*(18*z**3) + (11*z**2)*(-50) - 1700\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*z)*-50 = 1800*z\n (-36*z)*(18*z**2) = -648*z**3\n (-36*z)*(18*z**3) = -648*z**4\n (11*z**2)*-50 = -550*z**2\n (11*z**2)*(18*z**2) = 198*z**4\n (11*z**2)*(18*z**3) = 198*z**5\n 34*18*z**2 = 612*z**2\n 34*18*z**3 = 612*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 198*z**5 - 648*z**4 + 198*z**4 - 648*z**3 + 612*z**3 - 550*z**2 + 612*z**2 + 1800*z - 1700\nCombining like terms, got 198*z**5 - 450*z**4 - 36*z**3 + 62*z**2 + 1800*z - 1700\n#Step 7:\nCurrent expression: 198*z**5 - 450*z**4 - 36*z**3 + 62*z**2 + 1800*z - 1700\nNo more calculations needed.\n198*z**5 - 450*z**4 - 36*z**3 + 62*z**2 + 1800*z - 1700", "generated_answer": "198*z**5 - 450*z**4 - 36*z**3 + 62*z**2 + 1800*z - 1700", "step_length": 7} {"cot_id": "a87a8220af319cd96fdbea69ffc8d0907b94328b8410afbc4236e2db74552f72", "datapoint": {"question": "Calculate the following: (-22*z**3 - 5*z**2 + z)*(-17*z**3 + 7*z**2 + 11*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "374*z**6 - 69*z**5 - 294*z**4 - 48*z**3 + 11*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 605, "polynomial_expr": "(-22*z**3 - 5*z**2 + z)*(-17*z**3 + 7*z**2 + 11*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-22*z**3 - 5*z**2 + z)*(-17*z**3 + 7*z**2 + 11*z)\nExpanding the part (-22*z**3 - 5*z**2 + z) using the distributive property, and we got: z*(-17*z**3 + 7*z**2 + 11*z) + (-5*z**2)*(-17*z**3 + 7*z**2 + 11*z) + (-22*z**3)*(-17*z**3 + 7*z**2 + 11*z)\n#Step 2:\nCurrent expression: z*(-17*z**3 + 7*z**2 + 11*z) + (-5*z**2)*(-17*z**3 + 7*z**2 + 11*z) + (-22*z**3)*(-17*z**3 + 7*z**2 + 11*z)\nSimplifying the partial expression: z*(-17*z**3 + 7*z**2 + 11*z)\nExpanding the part (-17*z**3 + 7*z**2 + 11*z) using the distributive property, and we got: z*(11*z) + z*(7*z**2) + z*(-17*z**3)\nReplacing z*(-17*z**3 + 7*z**2 + 11*z) with z*(11*z) + z*(7*z**2) + z*(-17*z**3) in the overall expression.\n#Step 3:\nCurrent expression: z*(11*z) + z*(7*z**2) + z*(-17*z**3) + (-5*z**2)*(-17*z**3 + 7*z**2 + 11*z) + (-22*z**3)*(-17*z**3 + 7*z**2 + 11*z)\nSimplifying the partial expression: (-22*z**3)*(-17*z**3 + 7*z**2 + 11*z)\nExpanding the part (-17*z**3 + 7*z**2 + 11*z) using the distributive property, and we got: (11*z)*(-22*z**3) + (7*z**2)*(-22*z**3) + (-22*z**3)*(-17*z**3)\nReplacing (-22*z**3)*(-17*z**3 + 7*z**2 + 11*z) with (11*z)*(-22*z**3) + (7*z**2)*(-22*z**3) + (-22*z**3)*(-17*z**3) in the overall expression.\n#Step 4:\nCurrent expression: z*(11*z) + z*(7*z**2) + z*(-17*z**3) + (11*z)*(-22*z**3) + (-5*z**2)*(-17*z**3 + 7*z**2 + 11*z) + (7*z**2)*(-22*z**3) + (-22*z**3)*(-17*z**3)\nSimplifying the partial expression: (-5*z**2)*(-17*z**3 + 7*z**2 + 11*z)\nExpanding the part (-17*z**3 + 7*z**2 + 11*z) using the distributive property, and we got: (11*z)*(-5*z**2) + (-5*z**2)*(7*z**2) + (-5*z**2)*(-17*z**3)\nReplacing (-5*z**2)*(-17*z**3 + 7*z**2 + 11*z) with (11*z)*(-5*z**2) + (-5*z**2)*(7*z**2) + (-5*z**2)*(-17*z**3) in the overall expression.\n#Step 5:\nCurrent expression: z*(11*z) + z*(7*z**2) + z*(-17*z**3) + (11*z)*(-5*z**2) + (11*z)*(-22*z**3) + (-5*z**2)*(7*z**2) + (-5*z**2)*(-17*z**3) + (7*z**2)*(-22*z**3) + (-22*z**3)*(-17*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-17*z**3)*z = -17*z**4\n (-17*z**3)*(-22*z**3) = 374*z**6\n (-17*z**3)*(-5*z**2) = 85*z**5\n (7*z**2)*z = 7*z**3\n (7*z**2)*(-22*z**3) = -154*z**5\n (7*z**2)*(-5*z**2) = -35*z**4\n (11*z)*z = 11*z**2\n (11*z)*(-22*z**3) = -242*z**4\n (11*z)*(-5*z**2) = -55*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 374*z**6 - 154*z**5 + 85*z**5 - 242*z**4 - 35*z**4 - 17*z**4 - 55*z**3 + 7*z**3 + 11*z**2\nCombining like terms, got 374*z**6 - 69*z**5 - 294*z**4 - 48*z**3 + 11*z**2\n#Step 7:\nCurrent expression: 374*z**6 - 69*z**5 - 294*z**4 - 48*z**3 + 11*z**2\nNo more calculations needed.\n374*z**6 - 69*z**5 - 294*z**4 - 48*z**3 + 11*z**2", "generated_answer": "374*z**6 - 69*z**5 - 294*z**4 - 48*z**3 + 11*z**2", "step_length": 7} {"cot_id": "0e249ab3c83b1edc2d084faac17aab2403649f7dc48a6d474f1f3245cc1ecea6", "datapoint": {"question": "Simplify this expression: (-9*z**3 + 27*z)*(-7*z**3 + 37*z**2 - 46*z - 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "63*z**6 - 333*z**5 + 225*z**4 + 1188*z**3 - 1242*z**2 - 567*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 606, "polynomial_expr": "(-9*z**3 + 27*z)*(-7*z**3 + 37*z**2 - 46*z - 21)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-9*z**3 + 27*z)*(-7*z**3 + 37*z**2 - 46*z - 21)\nExpanding the part (-9*z**3 + 27*z) using the distributive property, and we got: (27*z)*(-7*z**3 + 37*z**2 - 46*z - 21) + (-9*z**3)*(-7*z**3 + 37*z**2 - 46*z - 21)\n#Step 2:\nCurrent expression: (27*z)*(-7*z**3 + 37*z**2 - 46*z - 21) + (-9*z**3)*(-7*z**3 + 37*z**2 - 46*z - 21)\nSimplifying the partial expression: (-9*z**3)*(-7*z**3 + 37*z**2 - 46*z - 21)\nExpanding the part (-7*z**3 + 37*z**2 - 46*z - 21) using the distributive property, and we got: (-46*z)*(-9*z**3) - (-1)*189*z**3 + (37*z**2)*(-9*z**3) + (-9*z**3)*(-7*z**3)\nReplacing (-9*z**3)*(-7*z**3 + 37*z**2 - 46*z - 21) with (-46*z)*(-9*z**3) - (-1)*189*z**3 + (37*z**2)*(-9*z**3) + (-9*z**3)*(-7*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-46*z)*(-9*z**3) - 21*(-9)*z**3 + (27*z)*(-7*z**3 + 37*z**2 - 46*z - 21) + (37*z**2)*(-9*z**3) + (-9*z**3)*(-7*z**3)\nSimplifying the partial expression: (27*z)*(-7*z**3 + 37*z**2 - 46*z - 21)\nExpanding the part (-7*z**3 + 37*z**2 - 46*z - 21) using the distributive property, and we got: (-46*z)*(27*z) - 567*z + (27*z)*(37*z**2) + (27*z)*(-7*z**3)\nReplacing (27*z)*(-7*z**3 + 37*z**2 - 46*z - 21) with (-46*z)*(27*z) - 567*z + (27*z)*(37*z**2) + (27*z)*(-7*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-46*z)*(27*z) + (-46*z)*(-9*z**3) - 21*(-9)*z**3 - 21*27*z + (27*z)*(37*z**2) + (27*z)*(-7*z**3) + (37*z**2)*(-9*z**3) + (-9*z**3)*(-7*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*z)*(-9*z**3) = 414*z**4\n (-46*z)*(27*z) = -1242*z**2\n (-7*z**3)*(-9*z**3) = 63*z**6\n (-7*z**3)*(27*z) = -189*z**4\n (37*z**2)*(-9*z**3) = -333*z**5\n (37*z**2)*(27*z) = 999*z**3\n -21*-9*z**3 = 189*z**3\n -21*27*z = -567*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 63*z**6 - 333*z**5 - 189*z**4 + 414*z**4 + 189*z**3 + 999*z**3 - 1242*z**2 - 567*z\nCombining like terms, got 63*z**6 - 333*z**5 + 225*z**4 + 1188*z**3 - 1242*z**2 - 567*z\n#Step 6:\nCurrent expression: 63*z**6 - 333*z**5 + 225*z**4 + 1188*z**3 - 1242*z**2 - 567*z\nNo more calculations needed.\n63*z**6 - 333*z**5 + 225*z**4 + 1188*z**3 - 1242*z**2 - 567*z", "generated_answer": "63*z**6 - 333*z**5 + 225*z**4 + 1188*z**3 - 1242*z**2 - 567*z", "step_length": 6} {"cot_id": "d88ad8eaf890576f527489939cb0dba71a834f63ee6d61a62785d723271575fd", "datapoint": {"question": "Calculate the following: (10*y**3 + 19*y**2)*(-28*y**3 + 20*y - 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-280*y**6 - 532*y**5 + 200*y**4 + 210*y**3 - 323*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 607, "polynomial_expr": "(10*y**3 + 19*y**2)*(-28*y**3 + 20*y - 17)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (10*y**3 + 19*y**2)*(-28*y**3 + 20*y - 17)\nExpanding the part (10*y**3 + 19*y**2) using the distributive property, and we got: (19*y**2)*(-28*y**3 + 20*y - 17) + (10*y**3)*(-28*y**3 + 20*y - 17)\n#Step 2:\nCurrent expression: (19*y**2)*(-28*y**3 + 20*y - 17) + (10*y**3)*(-28*y**3 + 20*y - 17)\nSimplifying the partial expression: (10*y**3)*(-28*y**3 + 20*y - 17)\nExpanding the part (-28*y**3 + 20*y - 17) using the distributive property, and we got: -170*y**3 + (20*y)*(10*y**3) + (-28*y**3)*(10*y**3)\nReplacing (10*y**3)*(-28*y**3 + 20*y - 17) with -170*y**3 + (20*y)*(10*y**3) + (-28*y**3)*(10*y**3) in the overall expression.\n#Step 3:\nCurrent expression: -17*10*y**3 + (20*y)*(10*y**3) + (19*y**2)*(-28*y**3 + 20*y - 17) + (-28*y**3)*(10*y**3)\nSimplifying the partial expression: (19*y**2)*(-28*y**3 + 20*y - 17)\nExpanding the part (-28*y**3 + 20*y - 17) using the distributive property, and we got: -323*y**2 + (20*y)*(19*y**2) + (19*y**2)*(-28*y**3)\nReplacing (19*y**2)*(-28*y**3 + 20*y - 17) with -323*y**2 + (20*y)*(19*y**2) + (19*y**2)*(-28*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -17*10*y**3 - 17*19*y**2 + (20*y)*(19*y**2) + (20*y)*(10*y**3) + (19*y**2)*(-28*y**3) + (-28*y**3)*(10*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*y**3)*(10*y**3) = -280*y**6\n (-28*y**3)*(19*y**2) = -532*y**5\n (20*y)*(10*y**3) = 200*y**4\n (20*y)*(19*y**2) = 380*y**3\n -17*10*y**3 = -170*y**3\n -17*19*y**2 = -323*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -280*y**6 - 532*y**5 + 200*y**4 - 170*y**3 + 380*y**3 - 323*y**2\nCombining like terms, got -280*y**6 - 532*y**5 + 200*y**4 + 210*y**3 - 323*y**2\n#Step 6:\nCurrent expression: -280*y**6 - 532*y**5 + 200*y**4 + 210*y**3 - 323*y**2\nNo more calculations needed.\n-280*y**6 - 532*y**5 + 200*y**4 + 210*y**3 - 323*y**2", "generated_answer": "-280*y**6 - 532*y**5 + 200*y**4 + 210*y**3 - 323*y**2", "step_length": 6} {"cot_id": "b058331659a365640b841776c3cd404f46073ef181727d2f4c521213d5f3eb2f", "datapoint": {"question": "Simplify this expression: (29*y**2 + 4)*(-38*y**3 - 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1102*y**5 - 152*y**3 - 290*y**2 - 40", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 608, "polynomial_expr": "(29*y**2 + 4)*(-38*y**3 - 10)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29*y**2 + 4)*(-38*y**3 - 10)\nExpanding the part (-38*y**3 - 10) using the distributive property, and we got: (-38*y**3)*(29*y**2 + 4) - 10*(29*y**2 + 4)\n#Step 2:\nCurrent expression: (-38*y**3)*(29*y**2 + 4) - 10*(29*y**2 + 4)\nSimplifying the partial expression: -10*(29*y**2 + 4)\nExpanding the part (29*y**2 + 4) using the distributive property, and we got: (29*y**2)*(-10) + 4*(-10)\nReplacing -10*(29*y**2 + 4) with (29*y**2)*(-10) + 4*(-10) in the overall expression.\n#Step 3:\nCurrent expression: (29*y**2)*(-10) + (-38*y**3)*(29*y**2 + 4) - 40\nSimplifying the partial expression: (-38*y**3)*(29*y**2 + 4)\nExpanding the part (29*y**2 + 4) using the distributive property, and we got: 4*(-38*y**3) + (29*y**2)*(-38*y**3)\nReplacing (-38*y**3)*(29*y**2 + 4) with 4*(-38*y**3) + (29*y**2)*(-38*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 4*(-38)*y**3 + (29*y**2)*(-38*y**3) + (29*y**2)*(-10) - 40\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (29*y**2)*-10 = -290*y**2\n (29*y**2)*(-38*y**3) = -1102*y**5\n 4*-38*y**3 = -152*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1102*y**5 - 152*y**3 - 290*y**2 - 40\nNo more calculations needed.\n-1102*y**5 - 152*y**3 - 290*y**2 - 40", "generated_answer": "-1102*y**5 - 152*y**3 - 290*y**2 - 40", "step_length": 5} {"cot_id": "09c0a4ebf678c78a7fde60000d311ef1af78bc62c1562ecd554bcba822034b2c", "datapoint": {"question": "Simplify this expression: (53*x + 19)*(6*x**3 + 23*x**2 + 10*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "318*x**4 + 1333*x**3 + 967*x**2 + 190*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 609, "polynomial_expr": "(53*x + 19)*(6*x**3 + 23*x**2 + 10*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (53*x + 19)*(6*x**3 + 23*x**2 + 10*x)\nExpanding the part (53*x + 19) using the distributive property, and we got: (53*x)*(6*x**3 + 23*x**2 + 10*x) + 19*(6*x**3 + 23*x**2 + 10*x)\n#Step 2:\nCurrent expression: (53*x)*(6*x**3 + 23*x**2 + 10*x) + 19*(6*x**3 + 23*x**2 + 10*x)\nSimplifying the partial expression: 19*(6*x**3 + 23*x**2 + 10*x)\nExpanding the part (6*x**3 + 23*x**2 + 10*x) using the distributive property, and we got: (10*x)*19 + (23*x**2)*19 + (6*x**3)*19\nReplacing 19*(6*x**3 + 23*x**2 + 10*x) with (10*x)*19 + (23*x**2)*19 + (6*x**3)*19 in the overall expression.\n#Step 3:\nCurrent expression: (10*x)*19 + (53*x)*(6*x**3 + 23*x**2 + 10*x) + (23*x**2)*19 + (6*x**3)*19\nSimplifying the partial expression: (53*x)*(6*x**3 + 23*x**2 + 10*x)\nExpanding the part (6*x**3 + 23*x**2 + 10*x) using the distributive property, and we got: (10*x)*(53*x) + (53*x)*(23*x**2) + (53*x)*(6*x**3)\nReplacing (53*x)*(6*x**3 + 23*x**2 + 10*x) with (10*x)*(53*x) + (53*x)*(23*x**2) + (53*x)*(6*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (10*x)*(53*x) + (10*x)*19 + (53*x)*(23*x**2) + (53*x)*(6*x**3) + (23*x**2)*19 + (6*x**3)*19\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (6*x**3)*19 = 114*x**3\n (6*x**3)*(53*x) = 318*x**4\n (10*x)*19 = 190*x\n (10*x)*(53*x) = 530*x**2\n (23*x**2)*19 = 437*x**2\n (23*x**2)*(53*x) = 1219*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 318*x**4 + 114*x**3 + 1219*x**3 + 437*x**2 + 530*x**2 + 190*x\nCombining like terms, got 318*x**4 + 1333*x**3 + 967*x**2 + 190*x\n#Step 6:\nCurrent expression: 318*x**4 + 1333*x**3 + 967*x**2 + 190*x\nNo more calculations needed.\n318*x**4 + 1333*x**3 + 967*x**2 + 190*x", "generated_answer": "318*x**4 + 1333*x**3 + 967*x**2 + 190*x", "step_length": 6} {"cot_id": "ad8bcfdb2307bc877dda3ea4fb234c112cc1fe57907e2b4a7a1a0bb4661de628", "datapoint": {"question": "Calculate the following: (-49*x**3 - 4*x**2 - 46*x)*(-43*x**3 + 29*x**2 - 23*x - 46)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2107*x**6 - 1249*x**5 + 2989*x**4 + 1012*x**3 + 1242*x**2 + 2116*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 610, "polynomial_expr": "(-49*x**3 - 4*x**2 - 46*x)*(-43*x**3 + 29*x**2 - 23*x - 46)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-49*x**3 - 4*x**2 - 46*x)*(-43*x**3 + 29*x**2 - 23*x - 46)\nExpanding the part (-49*x**3 - 4*x**2 - 46*x) using the distributive property, and we got: (-46*x)*(-43*x**3 + 29*x**2 - 23*x - 46) + (-4*x**2)*(-43*x**3 + 29*x**2 - 23*x - 46) + (-49*x**3)*(-43*x**3 + 29*x**2 - 23*x - 46)\n#Step 2:\nCurrent expression: (-46*x)*(-43*x**3 + 29*x**2 - 23*x - 46) + (-4*x**2)*(-43*x**3 + 29*x**2 - 23*x - 46) + (-49*x**3)*(-43*x**3 + 29*x**2 - 23*x - 46)\nSimplifying the partial expression: (-49*x**3)*(-43*x**3 + 29*x**2 - 23*x - 46)\nExpanding the part (-43*x**3 + 29*x**2 - 23*x - 46) using the distributive property, and we got: (-23*x)*(-49*x**3) - (-1)*2254*x**3 + (29*x**2)*(-49*x**3) + (-49*x**3)*(-43*x**3)\nReplacing (-49*x**3)*(-43*x**3 + 29*x**2 - 23*x - 46) with (-23*x)*(-49*x**3) - (-1)*2254*x**3 + (29*x**2)*(-49*x**3) + (-49*x**3)*(-43*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-46*x)*(-43*x**3 + 29*x**2 - 23*x - 46) + (-23*x)*(-49*x**3) - 46*(-49)*x**3 + (-4*x**2)*(-43*x**3 + 29*x**2 - 23*x - 46) + (29*x**2)*(-49*x**3) + (-49*x**3)*(-43*x**3)\nSimplifying the partial expression: (-46*x)*(-43*x**3 + 29*x**2 - 23*x - 46)\nExpanding the part (-43*x**3 + 29*x**2 - 23*x - 46) using the distributive property, and we got: (-46*x)*(-23*x) + (-46*x)*(29*x**2) + (-46*x)*(-43*x**3) - (-1)*2116*x\nReplacing (-46*x)*(-43*x**3 + 29*x**2 - 23*x - 46) with (-46*x)*(-23*x) + (-46*x)*(29*x**2) + (-46*x)*(-43*x**3) - (-1)*2116*x in the overall expression.\n#Step 4:\nCurrent expression: (-46*x)*(-23*x) + (-46*x)*(29*x**2) + (-46*x)*(-43*x**3) + (-23*x)*(-49*x**3) - 46*(-49)*x**3 - 46*(-46)*x + (-4*x**2)*(-43*x**3 + 29*x**2 - 23*x - 46) + (29*x**2)*(-49*x**3) + (-49*x**3)*(-43*x**3)\nSimplifying the partial expression: (-4*x**2)*(-43*x**3 + 29*x**2 - 23*x - 46)\nExpanding the part (-43*x**3 + 29*x**2 - 23*x - 46) using the distributive property, and we got: (-23*x)*(-4*x**2) - (-1)*184*x**2 + (-4*x**2)*(29*x**2) + (-4*x**2)*(-43*x**3)\nReplacing (-4*x**2)*(-43*x**3 + 29*x**2 - 23*x - 46) with (-23*x)*(-4*x**2) - (-1)*184*x**2 + (-4*x**2)*(29*x**2) + (-4*x**2)*(-43*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-46*x)*(-23*x) + (-46*x)*(29*x**2) + (-46*x)*(-43*x**3) + (-23*x)*(-4*x**2) + (-23*x)*(-49*x**3) - 46*(-49)*x**3 - 46*(-4)*x**2 - 46*(-46)*x + (-4*x**2)*(29*x**2) + (-4*x**2)*(-43*x**3) + (29*x**2)*(-49*x**3) + (-49*x**3)*(-43*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-43*x**3)*(-49*x**3) = 2107*x**6\n (-43*x**3)*(-46*x) = 1978*x**4\n (-43*x**3)*(-4*x**2) = 172*x**5\n (-23*x)*(-49*x**3) = 1127*x**4\n (-23*x)*(-46*x) = 1058*x**2\n (-23*x)*(-4*x**2) = 92*x**3\n (29*x**2)*(-49*x**3) = -1421*x**5\n (29*x**2)*(-46*x) = -1334*x**3\n (29*x**2)*(-4*x**2) = -116*x**4\n -46*-49*x**3 = 2254*x**3\n -46*-46*x = 2116*x\n -46*-4*x**2 = 184*x**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 2107*x**6 - 1421*x**5 + 172*x**5 - 116*x**4 + 1127*x**4 + 1978*x**4 - 1334*x**3 + 92*x**3 + 2254*x**3 + 184*x**2 + 1058*x**2 + 2116*x\nCombining like terms, got 2107*x**6 - 1249*x**5 + 2989*x**4 + 1012*x**3 + 1242*x**2 + 2116*x\n#Step 7:\nCurrent expression: 2107*x**6 - 1249*x**5 + 2989*x**4 + 1012*x**3 + 1242*x**2 + 2116*x\nNo more calculations needed.\n2107*x**6 - 1249*x**5 + 2989*x**4 + 1012*x**3 + 1242*x**2 + 2116*x", "generated_answer": "2107*x**6 - 1249*x**5 + 2989*x**4 + 1012*x**3 + 1242*x**2 + 2116*x", "step_length": 7} {"cot_id": "2824e3fc0624e83296047ba8dd9a1cb2622211d72646584cb5461f662b66ffd0", "datapoint": {"question": "Calculate the following: (-29*z**3 + 25*z**2)*(25*z**3 + 18*z**2 - 42*z + 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-725*z**6 + 103*z**5 + 1668*z**4 - 1253*z**3 + 175*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 611, "polynomial_expr": "(-29*z**3 + 25*z**2)*(25*z**3 + 18*z**2 - 42*z + 7)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-29*z**3 + 25*z**2)*(25*z**3 + 18*z**2 - 42*z + 7)\nExpanding the part (-29*z**3 + 25*z**2) using the distributive property, and we got: (25*z**2)*(25*z**3 + 18*z**2 - 42*z + 7) + (-29*z**3)*(25*z**3 + 18*z**2 - 42*z + 7)\n#Step 2:\nCurrent expression: (25*z**2)*(25*z**3 + 18*z**2 - 42*z + 7) + (-29*z**3)*(25*z**3 + 18*z**2 - 42*z + 7)\nSimplifying the partial expression: (-29*z**3)*(25*z**3 + 18*z**2 - 42*z + 7)\nExpanding the part (25*z**3 + 18*z**2 - 42*z + 7) using the distributive property, and we got: (-42*z)*(-29*z**3) + 7*(-29*z**3) + (18*z**2)*(-29*z**3) + (-29*z**3)*(25*z**3)\nReplacing (-29*z**3)*(25*z**3 + 18*z**2 - 42*z + 7) with (-42*z)*(-29*z**3) + 7*(-29*z**3) + (18*z**2)*(-29*z**3) + (-29*z**3)*(25*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-42*z)*(-29*z**3) + 7*(-29)*z**3 + (18*z**2)*(-29*z**3) + (25*z**2)*(25*z**3 + 18*z**2 - 42*z + 7) + (-29*z**3)*(25*z**3)\nSimplifying the partial expression: (25*z**2)*(25*z**3 + 18*z**2 - 42*z + 7)\nExpanding the part (25*z**3 + 18*z**2 - 42*z + 7) using the distributive property, and we got: (-42*z)*(25*z**2) + 7*(25*z**2) + (18*z**2)*(25*z**2) + (25*z**2)*(25*z**3)\nReplacing (25*z**2)*(25*z**3 + 18*z**2 - 42*z + 7) with (-42*z)*(25*z**2) + 7*(25*z**2) + (18*z**2)*(25*z**2) + (25*z**2)*(25*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-42*z)*(25*z**2) + (-42*z)*(-29*z**3) + 7*(-29)*z**3 + 7*25*z**2 + (18*z**2)*(25*z**2) + (18*z**2)*(-29*z**3) + (25*z**2)*(25*z**3) + (-29*z**3)*(25*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*z)*(-29*z**3) = 1218*z**4\n (-42*z)*(25*z**2) = -1050*z**3\n (18*z**2)*(-29*z**3) = -522*z**5\n (18*z**2)*(25*z**2) = 450*z**4\n (25*z**3)*(-29*z**3) = -725*z**6\n (25*z**3)*(25*z**2) = 625*z**5\n 7*-29*z**3 = -203*z**3\n 7*25*z**2 = 175*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -725*z**6 - 522*z**5 + 625*z**5 + 450*z**4 + 1218*z**4 - 1050*z**3 - 203*z**3 + 175*z**2\nCombining like terms, got -725*z**6 + 103*z**5 + 1668*z**4 - 1253*z**3 + 175*z**2\n#Step 6:\nCurrent expression: -725*z**6 + 103*z**5 + 1668*z**4 - 1253*z**3 + 175*z**2\nNo more calculations needed.\n-725*z**6 + 103*z**5 + 1668*z**4 - 1253*z**3 + 175*z**2", "generated_answer": "-725*z**6 + 103*z**5 + 1668*z**4 - 1253*z**3 + 175*z**2", "step_length": 6} {"cot_id": "f6dc972581decb7216ad83660e1f3156b2e271dd3fa3582612a24ece3afb2a85", "datapoint": {"question": "Calculate the following: (40*z**3 + 62*z)*(-47*z**3 - 21*z**2 - 9*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1880*z**6 - 840*z**5 - 3274*z**4 - 1302*z**3 - 558*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 612, "polynomial_expr": "(40*z**3 + 62*z)*(-47*z**3 - 21*z**2 - 9*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (40*z**3 + 62*z)*(-47*z**3 - 21*z**2 - 9*z)\nExpanding the part (40*z**3 + 62*z) using the distributive property, and we got: (62*z)*(-47*z**3 - 21*z**2 - 9*z) + (40*z**3)*(-47*z**3 - 21*z**2 - 9*z)\n#Step 2:\nCurrent expression: (62*z)*(-47*z**3 - 21*z**2 - 9*z) + (40*z**3)*(-47*z**3 - 21*z**2 - 9*z)\nSimplifying the partial expression: (40*z**3)*(-47*z**3 - 21*z**2 - 9*z)\nExpanding the part (-47*z**3 - 21*z**2 - 9*z) using the distributive property, and we got: (-9*z)*(40*z**3) + (-21*z**2)*(40*z**3) + (-47*z**3)*(40*z**3)\nReplacing (40*z**3)*(-47*z**3 - 21*z**2 - 9*z) with (-9*z)*(40*z**3) + (-21*z**2)*(40*z**3) + (-47*z**3)*(40*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-9*z)*(40*z**3) + (62*z)*(-47*z**3 - 21*z**2 - 9*z) + (-21*z**2)*(40*z**3) + (-47*z**3)*(40*z**3)\nSimplifying the partial expression: (62*z)*(-47*z**3 - 21*z**2 - 9*z)\nExpanding the part (-47*z**3 - 21*z**2 - 9*z) using the distributive property, and we got: (-9*z)*(62*z) + (62*z)*(-21*z**2) + (62*z)*(-47*z**3)\nReplacing (62*z)*(-47*z**3 - 21*z**2 - 9*z) with (-9*z)*(62*z) + (62*z)*(-21*z**2) + (62*z)*(-47*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-9*z)*(62*z) + (-9*z)*(40*z**3) + (62*z)*(-21*z**2) + (62*z)*(-47*z**3) + (-21*z**2)*(40*z**3) + (-47*z**3)*(40*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*z**3)*(40*z**3) = -1880*z**6\n (-47*z**3)*(62*z) = -2914*z**4\n (-21*z**2)*(40*z**3) = -840*z**5\n (-21*z**2)*(62*z) = -1302*z**3\n (-9*z)*(40*z**3) = -360*z**4\n (-9*z)*(62*z) = -558*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1880*z**6 - 840*z**5 - 2914*z**4 - 360*z**4 - 1302*z**3 - 558*z**2\nCombining like terms, got -1880*z**6 - 840*z**5 - 3274*z**4 - 1302*z**3 - 558*z**2\n#Step 6:\nCurrent expression: -1880*z**6 - 840*z**5 - 3274*z**4 - 1302*z**3 - 558*z**2\nNo more calculations needed.\n-1880*z**6 - 840*z**5 - 3274*z**4 - 1302*z**3 - 558*z**2", "generated_answer": "-1880*z**6 - 840*z**5 - 3274*z**4 - 1302*z**3 - 558*z**2", "step_length": 6} {"cot_id": "53d17420a6051f5d2ce74701ad4de03f284efde332d7fd9145ad7e147df06e69", "datapoint": {"question": "Calculate the following: 14*x*(35*x**2 + 30*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "490*x**3 + 420*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 613, "polynomial_expr": "14*x*(35*x**2 + 30*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 14*x*(35*x**2 + 30*x)\nExpanding the part (35*x**2 + 30*x) using the distributive property, and we got: (14*x)*(30*x) + (14*x)*(35*x**2)\n#Step 2:\nCurrent expression: (14*x)*(30*x) + (14*x)*(35*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (30*x)*(14*x) = 420*x**2\n (35*x**2)*(14*x) = 490*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 490*x**3 + 420*x**2\nNo more calculations needed.\n490*x**3 + 420*x**2", "generated_answer": "490*x**3 + 420*x**2", "step_length": 3} {"cot_id": "f0c600b2b6d2030dd7d2c9793f6ee2c6c431789e673b3277fed33e2fb95556cd", "datapoint": {"question": "Simplify this expression: (2*z**3 + 42)*(37*z**3 - 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "74*z**6 + 1472*z**3 - 1722", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 614, "polynomial_expr": "(2*z**3 + 42)*(37*z**3 - 41)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2*z**3 + 42)*(37*z**3 - 41)\nExpanding the part (37*z**3 - 41) using the distributive property, and we got: (37*z**3)*(2*z**3 + 42) - 41*(2*z**3 + 42)\n#Step 2:\nCurrent expression: (37*z**3)*(2*z**3 + 42) - 41*(2*z**3 + 42)\nSimplifying the partial expression: -41*(2*z**3 + 42)\nExpanding the part (2*z**3 + 42) using the distributive property, and we got: (2*z**3)*(-41) + 42*(-41)\nReplacing -41*(2*z**3 + 42) with (2*z**3)*(-41) + 42*(-41) in the overall expression.\n#Step 3:\nCurrent expression: (2*z**3)*(-41) + (37*z**3)*(2*z**3 + 42) - 1722\nSimplifying the partial expression: (37*z**3)*(2*z**3 + 42)\nExpanding the part (2*z**3 + 42) using the distributive property, and we got: 42*(37*z**3) + (2*z**3)*(37*z**3)\nReplacing (37*z**3)*(2*z**3 + 42) with 42*(37*z**3) + (2*z**3)*(37*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 42*37*z**3 + (2*z**3)*(37*z**3) + (2*z**3)*(-41) - 1722\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (2*z**3)*-41 = -82*z**3\n (2*z**3)*(37*z**3) = 74*z**6\n 42*37*z**3 = 1554*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 74*z**6 - 82*z**3 + 1554*z**3 - 1722\nCombining like terms, got 74*z**6 + 1472*z**3 - 1722\n#Step 6:\nCurrent expression: 74*z**6 + 1472*z**3 - 1722\nNo more calculations needed.\n74*z**6 + 1472*z**3 - 1722", "generated_answer": "74*z**6 + 1472*z**3 - 1722", "step_length": 6} {"cot_id": "0f4a865ff4f0f8958948f660be27da7b8173ed595818fda8d0060019768c5b48", "datapoint": {"question": "Calculate the following: 33*z**3*(28*z**3 - 47*z**2 + 21*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "924*z**6 - 1551*z**5 + 693*z**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 615, "polynomial_expr": "33*z**3*(28*z**3 - 47*z**2 + 21*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 33*z**3*(28*z**3 - 47*z**2 + 21*z)\nExpanding the part (28*z**3 - 47*z**2 + 21*z) using the distributive property, and we got: (21*z)*(33*z**3) + (-47*z**2)*(33*z**3) + (28*z**3)*(33*z**3)\n#Step 2:\nCurrent expression: (21*z)*(33*z**3) + (-47*z**2)*(33*z**3) + (28*z**3)*(33*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*z**2)*(33*z**3) = -1551*z**5\n (21*z)*(33*z**3) = 693*z**4\n (28*z**3)*(33*z**3) = 924*z**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 924*z**6 - 1551*z**5 + 693*z**4\nNo more calculations needed.\n924*z**6 - 1551*z**5 + 693*z**4", "generated_answer": "924*z**6 - 1551*z**5 + 693*z**4", "step_length": 3} {"cot_id": "4e00727dfb157b1109262c526d75b9a5c617f036be56beea3fe0f03aa51e37e9", "datapoint": {"question": "Simplify this expression: 2120*x**4\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2120*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 616, "polynomial_expr": "2120*x**4", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 2120*x**4\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 2120*x**4\nNo more calculations needed.\n2120*x**4", "generated_answer": "2120*x**4", "step_length": 2} {"cot_id": "d882d123474dd4368458a0a2511b6d9755fd06d2296444a73ead877990085fa5", "datapoint": {"question": "Simplify this expression: (13*z**3 - 36*z)*(13*z**3 - 30*z + 42)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "169*z**6 - 858*z**4 + 546*z**3 + 1080*z**2 - 1512*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 617, "polynomial_expr": "(13*z**3 - 36*z)*(13*z**3 - 30*z + 42)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (13*z**3 - 36*z)*(13*z**3 - 30*z + 42)\nExpanding the part (13*z**3 - 36*z) using the distributive property, and we got: (-36*z)*(13*z**3 - 30*z + 42) + (13*z**3)*(13*z**3 - 30*z + 42)\n#Step 2:\nCurrent expression: (-36*z)*(13*z**3 - 30*z + 42) + (13*z**3)*(13*z**3 - 30*z + 42)\nSimplifying the partial expression: (-36*z)*(13*z**3 - 30*z + 42)\nExpanding the part (13*z**3 - 30*z + 42) using the distributive property, and we got: (-36*z)*(-30*z) + (-36*z)*(13*z**3) + 42*(-36*z)\nReplacing (-36*z)*(13*z**3 - 30*z + 42) with (-36*z)*(-30*z) + (-36*z)*(13*z**3) + 42*(-36*z) in the overall expression.\n#Step 3:\nCurrent expression: (-36*z)*(-30*z) + (-36*z)*(13*z**3) + 42*(-36)*z + (13*z**3)*(13*z**3 - 30*z + 42)\nSimplifying the partial expression: (13*z**3)*(13*z**3 - 30*z + 42)\nExpanding the part (13*z**3 - 30*z + 42) using the distributive property, and we got: (-30*z)*(13*z**3) + 42*(13*z**3) + (13*z**3)*(13*z**3)\nReplacing (13*z**3)*(13*z**3 - 30*z + 42) with (-30*z)*(13*z**3) + 42*(13*z**3) + (13*z**3)*(13*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-36*z)*(-30*z) + (-36*z)*(13*z**3) + (-30*z)*(13*z**3) + 42*13*z**3 + 42*(-36)*z + (13*z**3)*(13*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*z)*(-36*z) = 1080*z**2\n (-30*z)*(13*z**3) = -390*z**4\n (13*z**3)*(-36*z) = -468*z**4\n (13*z**3)*(13*z**3) = 169*z**6\n 42*-36*z = -1512*z\n 42*13*z**3 = 546*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 169*z**6 - 468*z**4 - 390*z**4 + 546*z**3 + 1080*z**2 - 1512*z\nCombining like terms, got 169*z**6 - 858*z**4 + 546*z**3 + 1080*z**2 - 1512*z\n#Step 6:\nCurrent expression: 169*z**6 - 858*z**4 + 546*z**3 + 1080*z**2 - 1512*z\nNo more calculations needed.\n169*z**6 - 858*z**4 + 546*z**3 + 1080*z**2 - 1512*z", "generated_answer": "169*z**6 - 858*z**4 + 546*z**3 + 1080*z**2 - 1512*z", "step_length": 6} {"cot_id": "56f1afedadc2ee182445b9616cfb6e216b5fe498ccc066ddf3b97b2e635eb749", "datapoint": {"question": "Calculate the following: (68*x + 6)*(47*x**2 - 37*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "3196*x**3 - 2234*x**2 - 222*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 618, "polynomial_expr": "(68*x + 6)*(47*x**2 - 37*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (68*x + 6)*(47*x**2 - 37*x)\nExpanding the part (68*x + 6) using the distributive property, and we got: (68*x)*(47*x**2 - 37*x) + 6*(47*x**2 - 37*x)\n#Step 2:\nCurrent expression: (68*x)*(47*x**2 - 37*x) + 6*(47*x**2 - 37*x)\nSimplifying the partial expression: 6*(47*x**2 - 37*x)\nExpanding the part (47*x**2 - 37*x) using the distributive property, and we got: -37*x*6 + (47*x**2)*6\nReplacing 6*(47*x**2 - 37*x) with -37*x*6 + (47*x**2)*6 in the overall expression.\n#Step 3:\nCurrent expression: -37*x*6 + (68*x)*(47*x**2 - 37*x) + (47*x**2)*6\nSimplifying the partial expression: (68*x)*(47*x**2 - 37*x)\nExpanding the part (47*x**2 - 37*x) using the distributive property, and we got: (-37*x)*(68*x) + (68*x)*(47*x**2)\nReplacing (68*x)*(47*x**2 - 37*x) with (-37*x)*(68*x) + (68*x)*(47*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-37*x)*(68*x) - 37*x*6 + (68*x)*(47*x**2) + (47*x**2)*6\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*x)*6 = -222*x\n (-37*x)*(68*x) = -2516*x**2\n (47*x**2)*6 = 282*x**2\n (47*x**2)*(68*x) = 3196*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 3196*x**3 - 2516*x**2 + 282*x**2 - 222*x\nCombining like terms, got 3196*x**3 - 2234*x**2 - 222*x\n#Step 6:\nCurrent expression: 3196*x**3 - 2234*x**2 - 222*x\nNo more calculations needed.\n3196*x**3 - 2234*x**2 - 222*x", "generated_answer": "3196*x**3 - 2234*x**2 - 222*x", "step_length": 6} {"cot_id": "c61701c1b5dd3492572177603ad27d04b649db3a66c86f4ddc7532e6a1a96e41", "datapoint": {"question": "Calculate the following: (34*x**3 - 5*x**2 - 23*x)*(40*x**3 + 29*x - 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1360*x**6 - 200*x**5 + 66*x**4 - 349*x**3 - 637*x**2 + 138*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 619, "polynomial_expr": "(34*x**3 - 5*x**2 - 23*x)*(40*x**3 + 29*x - 6)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (34*x**3 - 5*x**2 - 23*x)*(40*x**3 + 29*x - 6)\nExpanding the part (40*x**3 + 29*x - 6) using the distributive property, and we got: (29*x)*(34*x**3 - 5*x**2 - 23*x) + (40*x**3)*(34*x**3 - 5*x**2 - 23*x) - 6*(34*x**3 - 5*x**2 - 23*x)\n#Step 2:\nCurrent expression: (29*x)*(34*x**3 - 5*x**2 - 23*x) + (40*x**3)*(34*x**3 - 5*x**2 - 23*x) - 6*(34*x**3 - 5*x**2 - 23*x)\nSimplifying the partial expression: -6*(34*x**3 - 5*x**2 - 23*x)\nExpanding the part (34*x**3 - 5*x**2 - 23*x) using the distributive property, and we got: -23*x*(-6) - 5*x**2*(-6) + (34*x**3)*(-6)\nReplacing -6*(34*x**3 - 5*x**2 - 23*x) with -23*x*(-6) - 5*x**2*(-6) + (34*x**3)*(-6) in the overall expression.\n#Step 3:\nCurrent expression: -23*x*(-6) + (29*x)*(34*x**3 - 5*x**2 - 23*x) - 5*x**2*(-6) + (34*x**3)*(-6) + (40*x**3)*(34*x**3 - 5*x**2 - 23*x)\nSimplifying the partial expression: (29*x)*(34*x**3 - 5*x**2 - 23*x)\nExpanding the part (34*x**3 - 5*x**2 - 23*x) using the distributive property, and we got: (-23*x)*(29*x) + (29*x)*(-5*x**2) + (29*x)*(34*x**3)\nReplacing (29*x)*(34*x**3 - 5*x**2 - 23*x) with (-23*x)*(29*x) + (29*x)*(-5*x**2) + (29*x)*(34*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-23*x)*(29*x) - 23*x*(-6) + (29*x)*(-5*x**2) + (29*x)*(34*x**3) - 5*x**2*(-6) + (34*x**3)*(-6) + (40*x**3)*(34*x**3 - 5*x**2 - 23*x)\nSimplifying the partial expression: (40*x**3)*(34*x**3 - 5*x**2 - 23*x)\nExpanding the part (34*x**3 - 5*x**2 - 23*x) using the distributive property, and we got: (-23*x)*(40*x**3) + (-5*x**2)*(40*x**3) + (34*x**3)*(40*x**3)\nReplacing (40*x**3)*(34*x**3 - 5*x**2 - 23*x) with (-23*x)*(40*x**3) + (-5*x**2)*(40*x**3) + (34*x**3)*(40*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-23*x)*(29*x) + (-23*x)*(40*x**3) - 23*x*(-6) + (29*x)*(-5*x**2) + (29*x)*(34*x**3) + (-5*x**2)*(40*x**3) - 5*x**2*(-6) + (34*x**3)*(40*x**3) + (34*x**3)*(-6)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*x)*-6 = 138*x\n (-23*x)*(29*x) = -667*x**2\n (-23*x)*(40*x**3) = -920*x**4\n (-5*x**2)*-6 = 30*x**2\n (-5*x**2)*(29*x) = -145*x**3\n (-5*x**2)*(40*x**3) = -200*x**5\n (34*x**3)*-6 = -204*x**3\n (34*x**3)*(29*x) = 986*x**4\n (34*x**3)*(40*x**3) = 1360*x**6\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1360*x**6 - 200*x**5 - 920*x**4 + 986*x**4 - 204*x**3 - 145*x**3 - 667*x**2 + 30*x**2 + 138*x\nCombining like terms, got 1360*x**6 - 200*x**5 + 66*x**4 - 349*x**3 - 637*x**2 + 138*x\n#Step 7:\nCurrent expression: 1360*x**6 - 200*x**5 + 66*x**4 - 349*x**3 - 637*x**2 + 138*x\nNo more calculations needed.\n1360*x**6 - 200*x**5 + 66*x**4 - 349*x**3 - 637*x**2 + 138*x", "generated_answer": "1360*x**6 - 200*x**5 + 66*x**4 - 349*x**3 - 637*x**2 + 138*x", "step_length": 7} {"cot_id": "1fbdbe79c1ba05af38a92fdb8f4d953080d461b8d817e5ce04cb7e2eef363757", "datapoint": {"question": "Calculate the following: (18*z**2 - 16*z)*(-33*z**3 + 52*z**2 - 23*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-594*z**5 + 1464*z**4 - 1246*z**3 + 368*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 620, "polynomial_expr": "(18*z**2 - 16*z)*(-33*z**3 + 52*z**2 - 23*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (18*z**2 - 16*z)*(-33*z**3 + 52*z**2 - 23*z)\nExpanding the part (18*z**2 - 16*z) using the distributive property, and we got: (-16*z)*(-33*z**3 + 52*z**2 - 23*z) + (18*z**2)*(-33*z**3 + 52*z**2 - 23*z)\n#Step 2:\nCurrent expression: (-16*z)*(-33*z**3 + 52*z**2 - 23*z) + (18*z**2)*(-33*z**3 + 52*z**2 - 23*z)\nSimplifying the partial expression: (-16*z)*(-33*z**3 + 52*z**2 - 23*z)\nExpanding the part (-33*z**3 + 52*z**2 - 23*z) using the distributive property, and we got: (-23*z)*(-16*z) + (-16*z)*(52*z**2) + (-16*z)*(-33*z**3)\nReplacing (-16*z)*(-33*z**3 + 52*z**2 - 23*z) with (-23*z)*(-16*z) + (-16*z)*(52*z**2) + (-16*z)*(-33*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-23*z)*(-16*z) + (-16*z)*(52*z**2) + (-16*z)*(-33*z**3) + (18*z**2)*(-33*z**3 + 52*z**2 - 23*z)\nSimplifying the partial expression: (18*z**2)*(-33*z**3 + 52*z**2 - 23*z)\nExpanding the part (-33*z**3 + 52*z**2 - 23*z) using the distributive property, and we got: (-23*z)*(18*z**2) + (18*z**2)*(52*z**2) + (18*z**2)*(-33*z**3)\nReplacing (18*z**2)*(-33*z**3 + 52*z**2 - 23*z) with (-23*z)*(18*z**2) + (18*z**2)*(52*z**2) + (18*z**2)*(-33*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-23*z)*(-16*z) + (-23*z)*(18*z**2) + (-16*z)*(52*z**2) + (-16*z)*(-33*z**3) + (18*z**2)*(52*z**2) + (18*z**2)*(-33*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*z**3)*(-16*z) = 528*z**4\n (-33*z**3)*(18*z**2) = -594*z**5\n (-23*z)*(-16*z) = 368*z**2\n (-23*z)*(18*z**2) = -414*z**3\n (52*z**2)*(-16*z) = -832*z**3\n (52*z**2)*(18*z**2) = 936*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -594*z**5 + 528*z**4 + 936*z**4 - 832*z**3 - 414*z**3 + 368*z**2\nCombining like terms, got -594*z**5 + 1464*z**4 - 1246*z**3 + 368*z**2\n#Step 6:\nCurrent expression: -594*z**5 + 1464*z**4 - 1246*z**3 + 368*z**2\nNo more calculations needed.\n-594*z**5 + 1464*z**4 - 1246*z**3 + 368*z**2", "generated_answer": "-594*z**5 + 1464*z**4 - 1246*z**3 + 368*z**2", "step_length": 6} {"cot_id": "d2bf945e85a4faa4bc2d2a7018bf2a0d2d9f09c1dd700464721aa08a2f3b3a8c", "datapoint": {"question": "Simplify this expression: (-11*z**3 + 38*z)*(42*z**2 - 7*z + 45)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-462*z**5 + 77*z**4 + 1101*z**3 - 266*z**2 + 1710*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 621, "polynomial_expr": "(-11*z**3 + 38*z)*(42*z**2 - 7*z + 45)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-11*z**3 + 38*z)*(42*z**2 - 7*z + 45)\nExpanding the part (-11*z**3 + 38*z) using the distributive property, and we got: (38*z)*(42*z**2 - 7*z + 45) + (-11*z**3)*(42*z**2 - 7*z + 45)\n#Step 2:\nCurrent expression: (38*z)*(42*z**2 - 7*z + 45) + (-11*z**3)*(42*z**2 - 7*z + 45)\nSimplifying the partial expression: (-11*z**3)*(42*z**2 - 7*z + 45)\nExpanding the part (42*z**2 - 7*z + 45) using the distributive property, and we got: (-7*z)*(-11*z**3) + 45*(-11*z**3) + (42*z**2)*(-11*z**3)\nReplacing (-11*z**3)*(42*z**2 - 7*z + 45) with (-7*z)*(-11*z**3) + 45*(-11*z**3) + (42*z**2)*(-11*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-7*z)*(-11*z**3) + 45*(-11)*z**3 + (38*z)*(42*z**2 - 7*z + 45) + (42*z**2)*(-11*z**3)\nSimplifying the partial expression: (38*z)*(42*z**2 - 7*z + 45)\nExpanding the part (42*z**2 - 7*z + 45) using the distributive property, and we got: (-7*z)*(38*z) + 45*(38*z) + (38*z)*(42*z**2)\nReplacing (38*z)*(42*z**2 - 7*z + 45) with (-7*z)*(38*z) + 45*(38*z) + (38*z)*(42*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-7*z)*(38*z) + (-7*z)*(-11*z**3) + 45*(-11)*z**3 + 45*38*z + (38*z)*(42*z**2) + (42*z**2)*(-11*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-7*z)*(-11*z**3) = 77*z**4\n (-7*z)*(38*z) = -266*z**2\n (42*z**2)*(-11*z**3) = -462*z**5\n (42*z**2)*(38*z) = 1596*z**3\n 45*-11*z**3 = -495*z**3\n 45*38*z = 1710*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -462*z**5 + 77*z**4 - 495*z**3 + 1596*z**3 - 266*z**2 + 1710*z\nCombining like terms, got -462*z**5 + 77*z**4 + 1101*z**3 - 266*z**2 + 1710*z\n#Step 6:\nCurrent expression: -462*z**5 + 77*z**4 + 1101*z**3 - 266*z**2 + 1710*z\nNo more calculations needed.\n-462*z**5 + 77*z**4 + 1101*z**3 - 266*z**2 + 1710*z", "generated_answer": "-462*z**5 + 77*z**4 + 1101*z**3 - 266*z**2 + 1710*z", "step_length": 6} {"cot_id": "728ad01c18d351abf272d88e7f878eb974a5f555d517bf9e828dba8293e2a9c9", "datapoint": {"question": "Calculate the following: (41*z**2 + 59)*(15*z**2 - 37*z - 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "615*z**4 - 1517*z**3 - 1083*z**2 - 2183*z - 2832", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 622, "polynomial_expr": "(41*z**2 + 59)*(15*z**2 - 37*z - 48)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (41*z**2 + 59)*(15*z**2 - 37*z - 48)\nExpanding the part (41*z**2 + 59) using the distributive property, and we got: (41*z**2)*(15*z**2 - 37*z - 48) + 59*(15*z**2 - 37*z - 48)\n#Step 2:\nCurrent expression: (41*z**2)*(15*z**2 - 37*z - 48) + 59*(15*z**2 - 37*z - 48)\nSimplifying the partial expression: 59*(15*z**2 - 37*z - 48)\nExpanding the part (15*z**2 - 37*z - 48) using the distributive property, and we got: -37*z*59 + (15*z**2)*59 - 48*59\nReplacing 59*(15*z**2 - 37*z - 48) with -37*z*59 + (15*z**2)*59 - 48*59 in the overall expression.\n#Step 3:\nCurrent expression: -37*z*59 + (15*z**2)*59 + (41*z**2)*(15*z**2 - 37*z - 48) - 2832\nSimplifying the partial expression: (41*z**2)*(15*z**2 - 37*z - 48)\nExpanding the part (15*z**2 - 37*z - 48) using the distributive property, and we got: (-37*z)*(41*z**2) - 1968*z**2 + (15*z**2)*(41*z**2)\nReplacing (41*z**2)*(15*z**2 - 37*z - 48) with (-37*z)*(41*z**2) - 1968*z**2 + (15*z**2)*(41*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-37*z)*(41*z**2) - 37*z*59 - 48*41*z**2 + (15*z**2)*(41*z**2) + (15*z**2)*59 - 2832\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*z)*59 = -2183*z\n (-37*z)*(41*z**2) = -1517*z**3\n (15*z**2)*59 = 885*z**2\n (15*z**2)*(41*z**2) = 615*z**4\n -48*41*z**2 = -1968*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 615*z**4 - 1517*z**3 - 1968*z**2 + 885*z**2 - 2183*z - 2832\nCombining like terms, got 615*z**4 - 1517*z**3 - 1083*z**2 - 2183*z - 2832\n#Step 6:\nCurrent expression: 615*z**4 - 1517*z**3 - 1083*z**2 - 2183*z - 2832\nNo more calculations needed.\n615*z**4 - 1517*z**3 - 1083*z**2 - 2183*z - 2832", "generated_answer": "615*z**4 - 1517*z**3 - 1083*z**2 - 2183*z - 2832", "step_length": 6} {"cot_id": "eafbb7c57b6aa8e9fe95a0d3a554da03041e56bfc9e57cc5b9bc1d0f6be3a895", "datapoint": {"question": "Simplify this expression: -87*z**2*(31*z**3 - 70*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2697*z**5 + 6090*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 623, "polynomial_expr": "-87*z**2*(31*z**3 - 70*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -87*z**2*(31*z**3 - 70*z)\nExpanding the part (31*z**3 - 70*z) using the distributive property, and we got: (-70*z)*(-87*z**2) + (-87*z**2)*(31*z**3)\n#Step 2:\nCurrent expression: (-70*z)*(-87*z**2) + (-87*z**2)*(31*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-70*z)*(-87*z**2) = 6090*z**3\n (31*z**3)*(-87*z**2) = -2697*z**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -2697*z**5 + 6090*z**3\nNo more calculations needed.\n-2697*z**5 + 6090*z**3", "generated_answer": "-2697*z**5 + 6090*z**3", "step_length": 3} {"cot_id": "bb3ff78da91b291935659d4f554ac039e71e2d24d64e6fd659e68eabb621ce45", "datapoint": {"question": "Calculate the following: (-18*y**3 - 48)*(19*y**3 + 10*y**2 - 36*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-342*y**6 - 180*y**5 + 648*y**4 - 912*y**3 - 480*y**2 + 1728*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 624, "polynomial_expr": "(-18*y**3 - 48)*(19*y**3 + 10*y**2 - 36*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-18*y**3 - 48)*(19*y**3 + 10*y**2 - 36*y)\nExpanding the part (-18*y**3 - 48) using the distributive property, and we got: (-18*y**3)*(19*y**3 + 10*y**2 - 36*y) - 48*(19*y**3 + 10*y**2 - 36*y)\n#Step 2:\nCurrent expression: (-18*y**3)*(19*y**3 + 10*y**2 - 36*y) - 48*(19*y**3 + 10*y**2 - 36*y)\nSimplifying the partial expression: -48*(19*y**3 + 10*y**2 - 36*y)\nExpanding the part (19*y**3 + 10*y**2 - 36*y) using the distributive property, and we got: -36*y*(-48) + (10*y**2)*(-48) + (19*y**3)*(-48)\nReplacing -48*(19*y**3 + 10*y**2 - 36*y) with -36*y*(-48) + (10*y**2)*(-48) + (19*y**3)*(-48) in the overall expression.\n#Step 3:\nCurrent expression: -36*y*(-48) + (10*y**2)*(-48) + (-18*y**3)*(19*y**3 + 10*y**2 - 36*y) + (19*y**3)*(-48)\nSimplifying the partial expression: (-18*y**3)*(19*y**3 + 10*y**2 - 36*y)\nExpanding the part (19*y**3 + 10*y**2 - 36*y) using the distributive property, and we got: (-36*y)*(-18*y**3) + (10*y**2)*(-18*y**3) + (-18*y**3)*(19*y**3)\nReplacing (-18*y**3)*(19*y**3 + 10*y**2 - 36*y) with (-36*y)*(-18*y**3) + (10*y**2)*(-18*y**3) + (-18*y**3)*(19*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-36*y)*(-18*y**3) - 36*y*(-48) + (10*y**2)*(-18*y**3) + (10*y**2)*(-48) + (-18*y**3)*(19*y**3) + (19*y**3)*(-48)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*y)*-48 = 1728*y\n (-36*y)*(-18*y**3) = 648*y**4\n (10*y**2)*-48 = -480*y**2\n (10*y**2)*(-18*y**3) = -180*y**5\n (19*y**3)*-48 = -912*y**3\n (19*y**3)*(-18*y**3) = -342*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -342*y**6 - 180*y**5 + 648*y**4 - 912*y**3 - 480*y**2 + 1728*y\nNo more calculations needed.\n-342*y**6 - 180*y**5 + 648*y**4 - 912*y**3 - 480*y**2 + 1728*y", "generated_answer": "-342*y**6 - 180*y**5 + 648*y**4 - 912*y**3 - 480*y**2 + 1728*y", "step_length": 5} {"cot_id": "faf513bfa4a618cf2a24b671509d438c8b1fa71af3080b6c29f40a6b869ed1f8", "datapoint": {"question": "Simplify this expression: (-47*x**3 + 47*x - 4)*(44*x**3 - 59*x**2 - 11*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2068*x**6 + 2773*x**5 + 2585*x**4 - 2949*x**3 - 281*x**2 + 44*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 625, "polynomial_expr": "(-47*x**3 + 47*x - 4)*(44*x**3 - 59*x**2 - 11*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-47*x**3 + 47*x - 4)*(44*x**3 - 59*x**2 - 11*x)\nExpanding the part (-47*x**3 + 47*x - 4) using the distributive property, and we got: (47*x)*(44*x**3 - 59*x**2 - 11*x) + (-47*x**3)*(44*x**3 - 59*x**2 - 11*x) - 4*(44*x**3 - 59*x**2 - 11*x)\n#Step 2:\nCurrent expression: (47*x)*(44*x**3 - 59*x**2 - 11*x) + (-47*x**3)*(44*x**3 - 59*x**2 - 11*x) - 4*(44*x**3 - 59*x**2 - 11*x)\nSimplifying the partial expression: -4*(44*x**3 - 59*x**2 - 11*x)\nExpanding the part (44*x**3 - 59*x**2 - 11*x) using the distributive property, and we got: -11*x*(-4) - 59*x**2*(-4) + (44*x**3)*(-4)\nReplacing -4*(44*x**3 - 59*x**2 - 11*x) with -11*x*(-4) - 59*x**2*(-4) + (44*x**3)*(-4) in the overall expression.\n#Step 3:\nCurrent expression: -11*x*(-4) + (47*x)*(44*x**3 - 59*x**2 - 11*x) - 59*x**2*(-4) + (-47*x**3)*(44*x**3 - 59*x**2 - 11*x) + (44*x**3)*(-4)\nSimplifying the partial expression: (-47*x**3)*(44*x**3 - 59*x**2 - 11*x)\nExpanding the part (44*x**3 - 59*x**2 - 11*x) using the distributive property, and we got: (-11*x)*(-47*x**3) + (-59*x**2)*(-47*x**3) + (-47*x**3)*(44*x**3)\nReplacing (-47*x**3)*(44*x**3 - 59*x**2 - 11*x) with (-11*x)*(-47*x**3) + (-59*x**2)*(-47*x**3) + (-47*x**3)*(44*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-11*x)*(-47*x**3) - 11*x*(-4) + (47*x)*(44*x**3 - 59*x**2 - 11*x) + (-59*x**2)*(-47*x**3) - 59*x**2*(-4) + (-47*x**3)*(44*x**3) + (44*x**3)*(-4)\nSimplifying the partial expression: (47*x)*(44*x**3 - 59*x**2 - 11*x)\nExpanding the part (44*x**3 - 59*x**2 - 11*x) using the distributive property, and we got: (-11*x)*(47*x) + (47*x)*(-59*x**2) + (47*x)*(44*x**3)\nReplacing (47*x)*(44*x**3 - 59*x**2 - 11*x) with (-11*x)*(47*x) + (47*x)*(-59*x**2) + (47*x)*(44*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-11*x)*(47*x) + (-11*x)*(-47*x**3) - 11*x*(-4) + (47*x)*(-59*x**2) + (47*x)*(44*x**3) + (-59*x**2)*(-47*x**3) - 59*x**2*(-4) + (-47*x**3)*(44*x**3) + (44*x**3)*(-4)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-59*x**2)*-4 = 236*x**2\n (-59*x**2)*(-47*x**3) = 2773*x**5\n (-59*x**2)*(47*x) = -2773*x**3\n (-11*x)*-4 = 44*x\n (-11*x)*(-47*x**3) = 517*x**4\n (-11*x)*(47*x) = -517*x**2\n (44*x**3)*-4 = -176*x**3\n (44*x**3)*(-47*x**3) = -2068*x**6\n (44*x**3)*(47*x) = 2068*x**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -2068*x**6 + 2773*x**5 + 517*x**4 + 2068*x**4 - 2773*x**3 - 176*x**3 - 517*x**2 + 236*x**2 + 44*x\nCombining like terms, got -2068*x**6 + 2773*x**5 + 2585*x**4 - 2949*x**3 - 281*x**2 + 44*x\n#Step 7:\nCurrent expression: -2068*x**6 + 2773*x**5 + 2585*x**4 - 2949*x**3 - 281*x**2 + 44*x\nNo more calculations needed.\n-2068*x**6 + 2773*x**5 + 2585*x**4 - 2949*x**3 - 281*x**2 + 44*x", "generated_answer": "-2068*x**6 + 2773*x**5 + 2585*x**4 - 2949*x**3 - 281*x**2 + 44*x", "step_length": 7} {"cot_id": "27a410c9576273aebe47f20e2970fff0a931240b8ae3f5e75d4493872436b6e3", "datapoint": {"question": "Simplify this expression: (12*y**3 - 28)*(48*y**3 + 45*y**2 + 46*y + 27)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "576*y**6 + 540*y**5 + 552*y**4 - 1020*y**3 - 1260*y**2 - 1288*y - 756", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 626, "polynomial_expr": "(12*y**3 - 28)*(48*y**3 + 45*y**2 + 46*y + 27)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (12*y**3 - 28)*(48*y**3 + 45*y**2 + 46*y + 27)\nExpanding the part (12*y**3 - 28) using the distributive property, and we got: (12*y**3)*(48*y**3 + 45*y**2 + 46*y + 27) - 28*(48*y**3 + 45*y**2 + 46*y + 27)\n#Step 2:\nCurrent expression: (12*y**3)*(48*y**3 + 45*y**2 + 46*y + 27) - 28*(48*y**3 + 45*y**2 + 46*y + 27)\nSimplifying the partial expression: -28*(48*y**3 + 45*y**2 + 46*y + 27)\nExpanding the part (48*y**3 + 45*y**2 + 46*y + 27) using the distributive property, and we got: (46*y)*(-28) + (45*y**2)*(-28) + (48*y**3)*(-28) + 27*(-28)\nReplacing -28*(48*y**3 + 45*y**2 + 46*y + 27) with (46*y)*(-28) + (45*y**2)*(-28) + (48*y**3)*(-28) + 27*(-28) in the overall expression.\n#Step 3:\nCurrent expression: (46*y)*(-28) + (45*y**2)*(-28) + (12*y**3)*(48*y**3 + 45*y**2 + 46*y + 27) + (48*y**3)*(-28) - 756\nSimplifying the partial expression: (12*y**3)*(48*y**3 + 45*y**2 + 46*y + 27)\nExpanding the part (48*y**3 + 45*y**2 + 46*y + 27) using the distributive property, and we got: 27*(12*y**3) + (46*y)*(12*y**3) + (45*y**2)*(12*y**3) + (12*y**3)*(48*y**3)\nReplacing (12*y**3)*(48*y**3 + 45*y**2 + 46*y + 27) with 27*(12*y**3) + (46*y)*(12*y**3) + (45*y**2)*(12*y**3) + (12*y**3)*(48*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 27*12*y**3 + (46*y)*(12*y**3) + (46*y)*(-28) + (45*y**2)*(12*y**3) + (45*y**2)*(-28) + (12*y**3)*(48*y**3) + (48*y**3)*(-28) - 756\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (45*y**2)*-28 = -1260*y**2\n (45*y**2)*(12*y**3) = 540*y**5\n (46*y)*-28 = -1288*y\n (46*y)*(12*y**3) = 552*y**4\n (48*y**3)*-28 = -1344*y**3\n (48*y**3)*(12*y**3) = 576*y**6\n 27*12*y**3 = 324*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 576*y**6 + 540*y**5 + 552*y**4 - 1344*y**3 + 324*y**3 - 1260*y**2 - 1288*y - 756\nCombining like terms, got 576*y**6 + 540*y**5 + 552*y**4 - 1020*y**3 - 1260*y**2 - 1288*y - 756\n#Step 6:\nCurrent expression: 576*y**6 + 540*y**5 + 552*y**4 - 1020*y**3 - 1260*y**2 - 1288*y - 756\nNo more calculations needed.\n576*y**6 + 540*y**5 + 552*y**4 - 1020*y**3 - 1260*y**2 - 1288*y - 756", "generated_answer": "576*y**6 + 540*y**5 + 552*y**4 - 1020*y**3 - 1260*y**2 - 1288*y - 756", "step_length": 6} {"cot_id": "2b882c271e8f31c1907fbf95d0bb4652aca8d67a24b9dccfb7353977e125fad5", "datapoint": {"question": "Calculate the following: (28*y**2 - 34*y)*(41*y**2 - 37*y + 46)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1148*y**4 - 2430*y**3 + 2546*y**2 - 1564*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 627, "polynomial_expr": "(28*y**2 - 34*y)*(41*y**2 - 37*y + 46)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28*y**2 - 34*y)*(41*y**2 - 37*y + 46)\nExpanding the part (28*y**2 - 34*y) using the distributive property, and we got: (-34*y)*(41*y**2 - 37*y + 46) + (28*y**2)*(41*y**2 - 37*y + 46)\n#Step 2:\nCurrent expression: (-34*y)*(41*y**2 - 37*y + 46) + (28*y**2)*(41*y**2 - 37*y + 46)\nSimplifying the partial expression: (-34*y)*(41*y**2 - 37*y + 46)\nExpanding the part (41*y**2 - 37*y + 46) using the distributive property, and we got: (-37*y)*(-34*y) + (-34*y)*(41*y**2) + 46*(-34*y)\nReplacing (-34*y)*(41*y**2 - 37*y + 46) with (-37*y)*(-34*y) + (-34*y)*(41*y**2) + 46*(-34*y) in the overall expression.\n#Step 3:\nCurrent expression: (-37*y)*(-34*y) + (-34*y)*(41*y**2) + 46*(-34)*y + (28*y**2)*(41*y**2 - 37*y + 46)\nSimplifying the partial expression: (28*y**2)*(41*y**2 - 37*y + 46)\nExpanding the part (41*y**2 - 37*y + 46) using the distributive property, and we got: (-37*y)*(28*y**2) + 46*(28*y**2) + (28*y**2)*(41*y**2)\nReplacing (28*y**2)*(41*y**2 - 37*y + 46) with (-37*y)*(28*y**2) + 46*(28*y**2) + (28*y**2)*(41*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-37*y)*(-34*y) + (-37*y)*(28*y**2) + (-34*y)*(41*y**2) + 46*28*y**2 + 46*(-34)*y + (28*y**2)*(41*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*y)*(-34*y) = 1258*y**2\n (-37*y)*(28*y**2) = -1036*y**3\n (41*y**2)*(-34*y) = -1394*y**3\n (41*y**2)*(28*y**2) = 1148*y**4\n 46*-34*y = -1564*y\n 46*28*y**2 = 1288*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1148*y**4 - 1394*y**3 - 1036*y**3 + 1258*y**2 + 1288*y**2 - 1564*y\nCombining like terms, got 1148*y**4 - 2430*y**3 + 2546*y**2 - 1564*y\n#Step 6:\nCurrent expression: 1148*y**4 - 2430*y**3 + 2546*y**2 - 1564*y\nNo more calculations needed.\n1148*y**4 - 2430*y**3 + 2546*y**2 - 1564*y", "generated_answer": "1148*y**4 - 2430*y**3 + 2546*y**2 - 1564*y", "step_length": 6} {"cot_id": "61da3ade060dde64faa646c7c6bf742ff81f86e0455d2967904beb5af9f3367f", "datapoint": {"question": "Simplify this expression: (-36*z**2 - 30*z)*(-31*z**2 + 26*z + 8)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1116*z**4 - 6*z**3 - 1068*z**2 - 240*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 628, "polynomial_expr": "(-36*z**2 - 30*z)*(-31*z**2 + 26*z + 8)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-36*z**2 - 30*z)*(-31*z**2 + 26*z + 8)\nExpanding the part (-36*z**2 - 30*z) using the distributive property, and we got: (-30*z)*(-31*z**2 + 26*z + 8) + (-36*z**2)*(-31*z**2 + 26*z + 8)\n#Step 2:\nCurrent expression: (-30*z)*(-31*z**2 + 26*z + 8) + (-36*z**2)*(-31*z**2 + 26*z + 8)\nSimplifying the partial expression: (-36*z**2)*(-31*z**2 + 26*z + 8)\nExpanding the part (-31*z**2 + 26*z + 8) using the distributive property, and we got: 8*(-36*z**2) + (26*z)*(-36*z**2) + (-36*z**2)*(-31*z**2)\nReplacing (-36*z**2)*(-31*z**2 + 26*z + 8) with 8*(-36*z**2) + (26*z)*(-36*z**2) + (-36*z**2)*(-31*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-30*z)*(-31*z**2 + 26*z + 8) + 8*(-36)*z**2 + (26*z)*(-36*z**2) + (-36*z**2)*(-31*z**2)\nSimplifying the partial expression: (-30*z)*(-31*z**2 + 26*z + 8)\nExpanding the part (-31*z**2 + 26*z + 8) using the distributive property, and we got: (-30*z)*(26*z) + (-30*z)*(-31*z**2) + 8*(-30*z)\nReplacing (-30*z)*(-31*z**2 + 26*z + 8) with (-30*z)*(26*z) + (-30*z)*(-31*z**2) + 8*(-30*z) in the overall expression.\n#Step 4:\nCurrent expression: (-30*z)*(26*z) + (-30*z)*(-31*z**2) + 8*(-36)*z**2 + 8*(-30)*z + (26*z)*(-36*z**2) + (-36*z**2)*(-31*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-31*z**2)*(-36*z**2) = 1116*z**4\n (-31*z**2)*(-30*z) = 930*z**3\n (26*z)*(-36*z**2) = -936*z**3\n (26*z)*(-30*z) = -780*z**2\n 8*-36*z**2 = -288*z**2\n 8*-30*z = -240*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1116*z**4 - 936*z**3 + 930*z**3 - 780*z**2 - 288*z**2 - 240*z\nCombining like terms, got 1116*z**4 - 6*z**3 - 1068*z**2 - 240*z\n#Step 6:\nCurrent expression: 1116*z**4 - 6*z**3 - 1068*z**2 - 240*z\nNo more calculations needed.\n1116*z**4 - 6*z**3 - 1068*z**2 - 240*z", "generated_answer": "1116*z**4 - 6*z**3 - 1068*z**2 - 240*z", "step_length": 6} {"cot_id": "33490c456e02a283153aff83fe3a3578a05458dd0701e02c6f1862e6433a0d35", "datapoint": {"question": "Calculate the following: (-46*z**2 + 2*z)*(41*z**2 - 36*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1886*z**4 + 1738*z**3 - 72*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 629, "polynomial_expr": "(-46*z**2 + 2*z)*(41*z**2 - 36*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-46*z**2 + 2*z)*(41*z**2 - 36*z)\nExpanding the part (-46*z**2 + 2*z) using the distributive property, and we got: (2*z)*(41*z**2 - 36*z) + (-46*z**2)*(41*z**2 - 36*z)\n#Step 2:\nCurrent expression: (2*z)*(41*z**2 - 36*z) + (-46*z**2)*(41*z**2 - 36*z)\nSimplifying the partial expression: (-46*z**2)*(41*z**2 - 36*z)\nExpanding the part (41*z**2 - 36*z) using the distributive property, and we got: (-36*z)*(-46*z**2) + (-46*z**2)*(41*z**2)\nReplacing (-46*z**2)*(41*z**2 - 36*z) with (-36*z)*(-46*z**2) + (-46*z**2)*(41*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-36*z)*(-46*z**2) + (2*z)*(41*z**2 - 36*z) + (-46*z**2)*(41*z**2)\nSimplifying the partial expression: (2*z)*(41*z**2 - 36*z)\nExpanding the part (41*z**2 - 36*z) using the distributive property, and we got: (-36*z)*(2*z) + (2*z)*(41*z**2)\nReplacing (2*z)*(41*z**2 - 36*z) with (-36*z)*(2*z) + (2*z)*(41*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-36*z)*(2*z) + (-36*z)*(-46*z**2) + (2*z)*(41*z**2) + (-46*z**2)*(41*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*z)*(-46*z**2) = 1656*z**3\n (-36*z)*(2*z) = -72*z**2\n (41*z**2)*(-46*z**2) = -1886*z**4\n (41*z**2)*(2*z) = 82*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1886*z**4 + 82*z**3 + 1656*z**3 - 72*z**2\nCombining like terms, got -1886*z**4 + 1738*z**3 - 72*z**2\n#Step 6:\nCurrent expression: -1886*z**4 + 1738*z**3 - 72*z**2\nNo more calculations needed.\n-1886*z**4 + 1738*z**3 - 72*z**2", "generated_answer": "-1886*z**4 + 1738*z**3 - 72*z**2", "step_length": 6} {"cot_id": "d24e0b840313157cbfe1e490fe7654fb3343616d8fe7e1129a1de2a6c3623a20", "datapoint": {"question": "Simplify this expression: (42 - 38*x**2)*(-12*x**3 + 17*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "456*x**5 - 1150*x**3 + 714*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 630, "polynomial_expr": "(42 - 38*x**2)*(-12*x**3 + 17*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (42 - 38*x**2)*(-12*x**3 + 17*x)\nExpanding the part (42 - 38*x**2) using the distributive property, and we got: (-38*x**2)*(-12*x**3 + 17*x) + 42*(-12*x**3 + 17*x)\n#Step 2:\nCurrent expression: (-38*x**2)*(-12*x**3 + 17*x) + 42*(-12*x**3 + 17*x)\nSimplifying the partial expression: 42*(-12*x**3 + 17*x)\nExpanding the part (-12*x**3 + 17*x) using the distributive property, and we got: (17*x)*42 - 12*x**3*42\nReplacing 42*(-12*x**3 + 17*x) with (17*x)*42 - 12*x**3*42 in the overall expression.\n#Step 3:\nCurrent expression: (17*x)*42 + (-38*x**2)*(-12*x**3 + 17*x) - 12*x**3*42\nSimplifying the partial expression: (-38*x**2)*(-12*x**3 + 17*x)\nExpanding the part (-12*x**3 + 17*x) using the distributive property, and we got: (17*x)*(-38*x**2) + (-38*x**2)*(-12*x**3)\nReplacing (-38*x**2)*(-12*x**3 + 17*x) with (17*x)*(-38*x**2) + (-38*x**2)*(-12*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (17*x)*(-38*x**2) + (17*x)*42 + (-38*x**2)*(-12*x**3) - 12*x**3*42\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*x**3)*42 = -504*x**3\n (-12*x**3)*(-38*x**2) = 456*x**5\n (17*x)*42 = 714*x\n (17*x)*(-38*x**2) = -646*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 456*x**5 - 646*x**3 - 504*x**3 + 714*x\nCombining like terms, got 456*x**5 - 1150*x**3 + 714*x\n#Step 6:\nCurrent expression: 456*x**5 - 1150*x**3 + 714*x\nNo more calculations needed.\n456*x**5 - 1150*x**3 + 714*x", "generated_answer": "456*x**5 - 1150*x**3 + 714*x", "step_length": 6} {"cot_id": "59c78e3fe8e3469a6e4848f7cc6787aee9a806317439c342feb2ed5327ea3586", "datapoint": {"question": "Simplify this expression: (-24*z - 40)*(14*z**3 + 49*z**2 - 23*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-336*z**4 - 1736*z**3 - 1408*z**2 + 920*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 631, "polynomial_expr": "(-24*z - 40)*(14*z**3 + 49*z**2 - 23*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-24*z - 40)*(14*z**3 + 49*z**2 - 23*z)\nExpanding the part (-24*z - 40) using the distributive property, and we got: (-24*z)*(14*z**3 + 49*z**2 - 23*z) - 40*(14*z**3 + 49*z**2 - 23*z)\n#Step 2:\nCurrent expression: (-24*z)*(14*z**3 + 49*z**2 - 23*z) - 40*(14*z**3 + 49*z**2 - 23*z)\nSimplifying the partial expression: -40*(14*z**3 + 49*z**2 - 23*z)\nExpanding the part (14*z**3 + 49*z**2 - 23*z) using the distributive property, and we got: -23*z*(-40) + (49*z**2)*(-40) + (14*z**3)*(-40)\nReplacing -40*(14*z**3 + 49*z**2 - 23*z) with -23*z*(-40) + (49*z**2)*(-40) + (14*z**3)*(-40) in the overall expression.\n#Step 3:\nCurrent expression: (-24*z)*(14*z**3 + 49*z**2 - 23*z) - 23*z*(-40) + (49*z**2)*(-40) + (14*z**3)*(-40)\nSimplifying the partial expression: (-24*z)*(14*z**3 + 49*z**2 - 23*z)\nExpanding the part (14*z**3 + 49*z**2 - 23*z) using the distributive property, and we got: (-24*z)*(-23*z) + (-24*z)*(49*z**2) + (-24*z)*(14*z**3)\nReplacing (-24*z)*(14*z**3 + 49*z**2 - 23*z) with (-24*z)*(-23*z) + (-24*z)*(49*z**2) + (-24*z)*(14*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-24*z)*(-23*z) + (-24*z)*(49*z**2) + (-24*z)*(14*z**3) - 23*z*(-40) + (49*z**2)*(-40) + (14*z**3)*(-40)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*z)*-40 = 920*z\n (-23*z)*(-24*z) = 552*z**2\n (14*z**3)*-40 = -560*z**3\n (14*z**3)*(-24*z) = -336*z**4\n (49*z**2)*-40 = -1960*z**2\n (49*z**2)*(-24*z) = -1176*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -336*z**4 - 1176*z**3 - 560*z**3 - 1960*z**2 + 552*z**2 + 920*z\nCombining like terms, got -336*z**4 - 1736*z**3 - 1408*z**2 + 920*z\n#Step 6:\nCurrent expression: -336*z**4 - 1736*z**3 - 1408*z**2 + 920*z\nNo more calculations needed.\n-336*z**4 - 1736*z**3 - 1408*z**2 + 920*z", "generated_answer": "-336*z**4 - 1736*z**3 - 1408*z**2 + 920*z", "step_length": 6} {"cot_id": "c1c195ee6840641085fec40e9dd1043114828c1ba9e563a994a25ef305abaf7a", "datapoint": {"question": "Simplify this expression: 355 - 85*y**2\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "355 - 85*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 632, "polynomial_expr": "355 - 85*y**2", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 355 - 85*y**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 355 - 85*y**2\nNo more calculations needed.\n355 - 85*y**2", "generated_answer": "355 - 85*y**2", "step_length": 2} {"cot_id": "32762f2996f55df4e7eae8aafd96b119ee700cfeb281ea744a42dfda38c13ffc", "datapoint": {"question": "Calculate the following: (15*x + 25)*(17*x**2 + 25*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "255*x**3 + 800*x**2 + 625*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 633, "polynomial_expr": "(15*x + 25)*(17*x**2 + 25*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (15*x + 25)*(17*x**2 + 25*x)\nExpanding the part (15*x + 25) using the distributive property, and we got: (15*x)*(17*x**2 + 25*x) + 25*(17*x**2 + 25*x)\n#Step 2:\nCurrent expression: (15*x)*(17*x**2 + 25*x) + 25*(17*x**2 + 25*x)\nSimplifying the partial expression: 25*(17*x**2 + 25*x)\nExpanding the part (17*x**2 + 25*x) using the distributive property, and we got: (25*x)*25 + (17*x**2)*25\nReplacing 25*(17*x**2 + 25*x) with (25*x)*25 + (17*x**2)*25 in the overall expression.\n#Step 3:\nCurrent expression: (15*x)*(17*x**2 + 25*x) + (25*x)*25 + (17*x**2)*25\nSimplifying the partial expression: (15*x)*(17*x**2 + 25*x)\nExpanding the part (17*x**2 + 25*x) using the distributive property, and we got: (15*x)*(25*x) + (15*x)*(17*x**2)\nReplacing (15*x)*(17*x**2 + 25*x) with (15*x)*(25*x) + (15*x)*(17*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (15*x)*(25*x) + (15*x)*(17*x**2) + (25*x)*25 + (17*x**2)*25\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (17*x**2)*25 = 425*x**2\n (17*x**2)*(15*x) = 255*x**3\n (25*x)*25 = 625*x\n (25*x)*(15*x) = 375*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 255*x**3 + 375*x**2 + 425*x**2 + 625*x\nCombining like terms, got 255*x**3 + 800*x**2 + 625*x\n#Step 6:\nCurrent expression: 255*x**3 + 800*x**2 + 625*x\nNo more calculations needed.\n255*x**3 + 800*x**2 + 625*x", "generated_answer": "255*x**3 + 800*x**2 + 625*x", "step_length": 6} {"cot_id": "92372cb1b76a7436260ebef9d0c4330076bcdca45ae3da8d284c7fde3b8c865f", "datapoint": {"question": "Calculate the following: -10*x**2*(15*x**3 + 46*x**2 - 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-150*x**5 - 460*x**4 + 310*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 634, "polynomial_expr": "-10*x**2*(15*x**3 + 46*x**2 - 31)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -10*x**2*(15*x**3 + 46*x**2 - 31)\nExpanding the part (15*x**3 + 46*x**2 - 31) using the distributive property, and we got: -(-1)*310*x**2 + (-10*x**2)*(46*x**2) + (-10*x**2)*(15*x**3)\n#Step 2:\nCurrent expression: -(-1)*310*x**2 + (-10*x**2)*(46*x**2) + (-10*x**2)*(15*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -31*(-10*x**2) = 310*x**2\n (15*x**3)*(-10*x**2) = -150*x**5\n (46*x**2)*(-10*x**2) = -460*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -150*x**5 - 460*x**4 + 310*x**2\nNo more calculations needed.\n-150*x**5 - 460*x**4 + 310*x**2", "generated_answer": "-150*x**5 - 460*x**4 + 310*x**2", "step_length": 3} {"cot_id": "76738a3c6c78540667e62d24ea825c4a070c9750f84e9cfd0b1755096f290d28", "datapoint": {"question": "Calculate the following: (6*z + 40)*(-30*z**3 + 26*z + 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-180*z**4 - 1200*z**3 + 156*z**2 + 1304*z + 1760", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 635, "polynomial_expr": "(6*z + 40)*(-30*z**3 + 26*z + 44)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6*z + 40)*(-30*z**3 + 26*z + 44)\nExpanding the part (6*z + 40) using the distributive property, and we got: (6*z)*(-30*z**3 + 26*z + 44) + 40*(-30*z**3 + 26*z + 44)\n#Step 2:\nCurrent expression: (6*z)*(-30*z**3 + 26*z + 44) + 40*(-30*z**3 + 26*z + 44)\nSimplifying the partial expression: 40*(-30*z**3 + 26*z + 44)\nExpanding the part (-30*z**3 + 26*z + 44) using the distributive property, and we got: (26*z)*40 - 30*z**3*40 + 44*40\nReplacing 40*(-30*z**3 + 26*z + 44) with (26*z)*40 - 30*z**3*40 + 44*40 in the overall expression.\n#Step 3:\nCurrent expression: (6*z)*(-30*z**3 + 26*z + 44) + (26*z)*40 - 30*z**3*40 + 1760\nSimplifying the partial expression: (6*z)*(-30*z**3 + 26*z + 44)\nExpanding the part (-30*z**3 + 26*z + 44) using the distributive property, and we got: 44*(6*z) + (6*z)*(26*z) + (6*z)*(-30*z**3)\nReplacing (6*z)*(-30*z**3 + 26*z + 44) with 44*(6*z) + (6*z)*(26*z) + (6*z)*(-30*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 44*6*z + (6*z)*(26*z) + (6*z)*(-30*z**3) + (26*z)*40 - 30*z**3*40 + 1760\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*z**3)*40 = -1200*z**3\n (-30*z**3)*(6*z) = -180*z**4\n (26*z)*40 = 1040*z\n (26*z)*(6*z) = 156*z**2\n 44*6*z = 264*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -180*z**4 - 1200*z**3 + 156*z**2 + 264*z + 1040*z + 1760\nCombining like terms, got -180*z**4 - 1200*z**3 + 156*z**2 + 1304*z + 1760\n#Step 6:\nCurrent expression: -180*z**4 - 1200*z**3 + 156*z**2 + 1304*z + 1760\nNo more calculations needed.\n-180*z**4 - 1200*z**3 + 156*z**2 + 1304*z + 1760", "generated_answer": "-180*z**4 - 1200*z**3 + 156*z**2 + 1304*z + 1760", "step_length": 6} {"cot_id": "4025f1f53705e82d9f5f0e33ce52247578074a20ac932c94fff156819551286b", "datapoint": {"question": "Calculate the following: 26*x*(3*x**3 + 9*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "78*x**4 + 234*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 636, "polynomial_expr": "26*x*(3*x**3 + 9*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 26*x*(3*x**3 + 9*x)\nExpanding the part (3*x**3 + 9*x) using the distributive property, and we got: (9*x)*(26*x) + (26*x)*(3*x**3)\n#Step 2:\nCurrent expression: (9*x)*(26*x) + (26*x)*(3*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (3*x**3)*(26*x) = 78*x**4\n (9*x)*(26*x) = 234*x**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 78*x**4 + 234*x**2\nNo more calculations needed.\n78*x**4 + 234*x**2", "generated_answer": "78*x**4 + 234*x**2", "step_length": 3} {"cot_id": "a3d7fad36f9eee92bd3a8c160327f6310c6602d8fd6c98c01cab78249c4263c8", "datapoint": {"question": "Simplify this expression: (-3*z**2 - 23*z)*(6*z**3 - 14*z**2 - 45*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-18*z**5 - 96*z**4 + 457*z**3 + 1035*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 637, "polynomial_expr": "(-3*z**2 - 23*z)*(6*z**3 - 14*z**2 - 45*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-3*z**2 - 23*z)*(6*z**3 - 14*z**2 - 45*z)\nExpanding the part (-3*z**2 - 23*z) using the distributive property, and we got: (-23*z)*(6*z**3 - 14*z**2 - 45*z) + (-3*z**2)*(6*z**3 - 14*z**2 - 45*z)\n#Step 2:\nCurrent expression: (-23*z)*(6*z**3 - 14*z**2 - 45*z) + (-3*z**2)*(6*z**3 - 14*z**2 - 45*z)\nSimplifying the partial expression: (-23*z)*(6*z**3 - 14*z**2 - 45*z)\nExpanding the part (6*z**3 - 14*z**2 - 45*z) using the distributive property, and we got: (-45*z)*(-23*z) + (-23*z)*(-14*z**2) + (-23*z)*(6*z**3)\nReplacing (-23*z)*(6*z**3 - 14*z**2 - 45*z) with (-45*z)*(-23*z) + (-23*z)*(-14*z**2) + (-23*z)*(6*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-45*z)*(-23*z) + (-23*z)*(-14*z**2) + (-23*z)*(6*z**3) + (-3*z**2)*(6*z**3 - 14*z**2 - 45*z)\nSimplifying the partial expression: (-3*z**2)*(6*z**3 - 14*z**2 - 45*z)\nExpanding the part (6*z**3 - 14*z**2 - 45*z) using the distributive property, and we got: (-45*z)*(-3*z**2) + (-14*z**2)*(-3*z**2) + (-3*z**2)*(6*z**3)\nReplacing (-3*z**2)*(6*z**3 - 14*z**2 - 45*z) with (-45*z)*(-3*z**2) + (-14*z**2)*(-3*z**2) + (-3*z**2)*(6*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-45*z)*(-23*z) + (-45*z)*(-3*z**2) + (-23*z)*(-14*z**2) + (-23*z)*(6*z**3) + (-14*z**2)*(-3*z**2) + (-3*z**2)*(6*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*z)*(-23*z) = 1035*z**2\n (-45*z)*(-3*z**2) = 135*z**3\n (-14*z**2)*(-23*z) = 322*z**3\n (-14*z**2)*(-3*z**2) = 42*z**4\n (6*z**3)*(-23*z) = -138*z**4\n (6*z**3)*(-3*z**2) = -18*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -18*z**5 - 138*z**4 + 42*z**4 + 135*z**3 + 322*z**3 + 1035*z**2\nCombining like terms, got -18*z**5 - 96*z**4 + 457*z**3 + 1035*z**2\n#Step 6:\nCurrent expression: -18*z**5 - 96*z**4 + 457*z**3 + 1035*z**2\nNo more calculations needed.\n-18*z**5 - 96*z**4 + 457*z**3 + 1035*z**2", "generated_answer": "-18*z**5 - 96*z**4 + 457*z**3 + 1035*z**2", "step_length": 6} {"cot_id": "bf5395fa050142e51f661e61aef821e32bfa336179e3acaac405ebc7921684c8", "datapoint": {"question": "Simplify this expression: (50*z**2 + 9*z)*(9*z**3 + 40*z**2 - 11*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "450*z**5 + 2081*z**4 - 190*z**3 - 99*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 638, "polynomial_expr": "(50*z**2 + 9*z)*(9*z**3 + 40*z**2 - 11*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (50*z**2 + 9*z)*(9*z**3 + 40*z**2 - 11*z)\nExpanding the part (50*z**2 + 9*z) using the distributive property, and we got: (9*z)*(9*z**3 + 40*z**2 - 11*z) + (50*z**2)*(9*z**3 + 40*z**2 - 11*z)\n#Step 2:\nCurrent expression: (9*z)*(9*z**3 + 40*z**2 - 11*z) + (50*z**2)*(9*z**3 + 40*z**2 - 11*z)\nSimplifying the partial expression: (9*z)*(9*z**3 + 40*z**2 - 11*z)\nExpanding the part (9*z**3 + 40*z**2 - 11*z) using the distributive property, and we got: (-11*z)*(9*z) + (9*z)*(40*z**2) + (9*z)*(9*z**3)\nReplacing (9*z)*(9*z**3 + 40*z**2 - 11*z) with (-11*z)*(9*z) + (9*z)*(40*z**2) + (9*z)*(9*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-11*z)*(9*z) + (9*z)*(40*z**2) + (9*z)*(9*z**3) + (50*z**2)*(9*z**3 + 40*z**2 - 11*z)\nSimplifying the partial expression: (50*z**2)*(9*z**3 + 40*z**2 - 11*z)\nExpanding the part (9*z**3 + 40*z**2 - 11*z) using the distributive property, and we got: (-11*z)*(50*z**2) + (40*z**2)*(50*z**2) + (50*z**2)*(9*z**3)\nReplacing (50*z**2)*(9*z**3 + 40*z**2 - 11*z) with (-11*z)*(50*z**2) + (40*z**2)*(50*z**2) + (50*z**2)*(9*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-11*z)*(9*z) + (-11*z)*(50*z**2) + (9*z)*(40*z**2) + (9*z)*(9*z**3) + (40*z**2)*(50*z**2) + (50*z**2)*(9*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*z)*(9*z) = -99*z**2\n (-11*z)*(50*z**2) = -550*z**3\n (9*z**3)*(9*z) = 81*z**4\n (9*z**3)*(50*z**2) = 450*z**5\n (40*z**2)*(9*z) = 360*z**3\n (40*z**2)*(50*z**2) = 2000*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 450*z**5 + 81*z**4 + 2000*z**4 - 550*z**3 + 360*z**3 - 99*z**2\nCombining like terms, got 450*z**5 + 2081*z**4 - 190*z**3 - 99*z**2\n#Step 6:\nCurrent expression: 450*z**5 + 2081*z**4 - 190*z**3 - 99*z**2\nNo more calculations needed.\n450*z**5 + 2081*z**4 - 190*z**3 - 99*z**2", "generated_answer": "450*z**5 + 2081*z**4 - 190*z**3 - 99*z**2", "step_length": 6} {"cot_id": "5f258db64d4df98fa46fb6781d01ebb598e5b6f5aaaa14cdfd2c0e33df168c2a", "datapoint": {"question": "Calculate the following: -2190*y**2 + 2263*y\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2190*y**2 + 2263*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 639, "polynomial_expr": "-2190*y**2 + 2263*y", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -2190*y**2 + 2263*y\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -2190*y**2 + 2263*y\nNo more calculations needed.\n-2190*y**2 + 2263*y", "generated_answer": "-2190*y**2 + 2263*y", "step_length": 2} {"cot_id": "31e69d5134aa9be9cbf6c73e2475b1f311ef0d750122284708f1a9897ef47730", "datapoint": {"question": "Simplify this expression: (13*z**2 + 11*z)*(-38*z**3 - 50*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-494*z**5 - 1068*z**4 - 550*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 640, "polynomial_expr": "(13*z**2 + 11*z)*(-38*z**3 - 50*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (13*z**2 + 11*z)*(-38*z**3 - 50*z**2)\nExpanding the part (-38*z**3 - 50*z**2) using the distributive property, and we got: (-50*z**2)*(13*z**2 + 11*z) + (-38*z**3)*(13*z**2 + 11*z)\n#Step 2:\nCurrent expression: (-50*z**2)*(13*z**2 + 11*z) + (-38*z**3)*(13*z**2 + 11*z)\nSimplifying the partial expression: (-50*z**2)*(13*z**2 + 11*z)\nExpanding the part (13*z**2 + 11*z) using the distributive property, and we got: (11*z)*(-50*z**2) + (-50*z**2)*(13*z**2)\nReplacing (-50*z**2)*(13*z**2 + 11*z) with (11*z)*(-50*z**2) + (-50*z**2)*(13*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (11*z)*(-50*z**2) + (-50*z**2)*(13*z**2) + (-38*z**3)*(13*z**2 + 11*z)\nSimplifying the partial expression: (-38*z**3)*(13*z**2 + 11*z)\nExpanding the part (13*z**2 + 11*z) using the distributive property, and we got: (11*z)*(-38*z**3) + (13*z**2)*(-38*z**3)\nReplacing (-38*z**3)*(13*z**2 + 11*z) with (11*z)*(-38*z**3) + (13*z**2)*(-38*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (11*z)*(-50*z**2) + (11*z)*(-38*z**3) + (-50*z**2)*(13*z**2) + (13*z**2)*(-38*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (11*z)*(-50*z**2) = -550*z**3\n (11*z)*(-38*z**3) = -418*z**4\n (13*z**2)*(-50*z**2) = -650*z**4\n (13*z**2)*(-38*z**3) = -494*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -494*z**5 - 650*z**4 - 418*z**4 - 550*z**3\nCombining like terms, got -494*z**5 - 1068*z**4 - 550*z**3\n#Step 6:\nCurrent expression: -494*z**5 - 1068*z**4 - 550*z**3\nNo more calculations needed.\n-494*z**5 - 1068*z**4 - 550*z**3", "generated_answer": "-494*z**5 - 1068*z**4 - 550*z**3", "step_length": 6} {"cot_id": "ace463497b18aa052284d90fc8128107ba4a252e643d5b2c9b4826c88082543b", "datapoint": {"question": "Calculate the following: (50*y**2 - 9)*(27*y**3 + 9*y**2 + 37)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1350*y**5 + 450*y**4 - 243*y**3 + 1769*y**2 - 333", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 641, "polynomial_expr": "(50*y**2 - 9)*(27*y**3 + 9*y**2 + 37)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (50*y**2 - 9)*(27*y**3 + 9*y**2 + 37)\nExpanding the part (50*y**2 - 9) using the distributive property, and we got: (50*y**2)*(27*y**3 + 9*y**2 + 37) - 9*(27*y**3 + 9*y**2 + 37)\n#Step 2:\nCurrent expression: (50*y**2)*(27*y**3 + 9*y**2 + 37) - 9*(27*y**3 + 9*y**2 + 37)\nSimplifying the partial expression: -9*(27*y**3 + 9*y**2 + 37)\nExpanding the part (27*y**3 + 9*y**2 + 37) using the distributive property, and we got: (9*y**2)*(-9) + (27*y**3)*(-9) + 37*(-9)\nReplacing -9*(27*y**3 + 9*y**2 + 37) with (9*y**2)*(-9) + (27*y**3)*(-9) + 37*(-9) in the overall expression.\n#Step 3:\nCurrent expression: (9*y**2)*(-9) + (50*y**2)*(27*y**3 + 9*y**2 + 37) + (27*y**3)*(-9) - 333\nSimplifying the partial expression: (50*y**2)*(27*y**3 + 9*y**2 + 37)\nExpanding the part (27*y**3 + 9*y**2 + 37) using the distributive property, and we got: 37*(50*y**2) + (9*y**2)*(50*y**2) + (50*y**2)*(27*y**3)\nReplacing (50*y**2)*(27*y**3 + 9*y**2 + 37) with 37*(50*y**2) + (9*y**2)*(50*y**2) + (50*y**2)*(27*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 37*50*y**2 + (9*y**2)*(50*y**2) + (9*y**2)*(-9) + (50*y**2)*(27*y**3) + (27*y**3)*(-9) - 333\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (9*y**2)*-9 = -81*y**2\n (9*y**2)*(50*y**2) = 450*y**4\n (27*y**3)*-9 = -243*y**3\n (27*y**3)*(50*y**2) = 1350*y**5\n 37*50*y**2 = 1850*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1350*y**5 + 450*y**4 - 243*y**3 - 81*y**2 + 1850*y**2 - 333\nCombining like terms, got 1350*y**5 + 450*y**4 - 243*y**3 + 1769*y**2 - 333\n#Step 6:\nCurrent expression: 1350*y**5 + 450*y**4 - 243*y**3 + 1769*y**2 - 333\nNo more calculations needed.\n1350*y**5 + 450*y**4 - 243*y**3 + 1769*y**2 - 333", "generated_answer": "1350*y**5 + 450*y**4 - 243*y**3 + 1769*y**2 - 333", "step_length": 6} {"cot_id": "ea36cd20abc94fe1c3bfa92857a01f850042a96c151e7dba0be3f627277a00d2", "datapoint": {"question": "Calculate the following: (67*y**2 - 13)*(-26*y**3 - 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1742*y**5 + 338*y**3 - 3283*y**2 + 637", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 642, "polynomial_expr": "(67*y**2 - 13)*(-26*y**3 - 49)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (67*y**2 - 13)*(-26*y**3 - 49)\nExpanding the part (-26*y**3 - 49) using the distributive property, and we got: (-26*y**3)*(67*y**2 - 13) - 49*(67*y**2 - 13)\n#Step 2:\nCurrent expression: (-26*y**3)*(67*y**2 - 13) - 49*(67*y**2 - 13)\nSimplifying the partial expression: -49*(67*y**2 - 13)\nExpanding the part (67*y**2 - 13) using the distributive property, and we got: (67*y**2)*(-49) - 13*(-49)\nReplacing -49*(67*y**2 - 13) with (67*y**2)*(-49) - 13*(-49) in the overall expression.\n#Step 3:\nCurrent expression: (67*y**2)*(-49) + (-26*y**3)*(67*y**2 - 13) + 637\nSimplifying the partial expression: (-26*y**3)*(67*y**2 - 13)\nExpanding the part (67*y**2 - 13) using the distributive property, and we got: -(-1)*338*y**3 + (67*y**2)*(-26*y**3)\nReplacing (-26*y**3)*(67*y**2 - 13) with -(-1)*338*y**3 + (67*y**2)*(-26*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -13*(-26)*y**3 + (67*y**2)*(-26*y**3) + (67*y**2)*(-49) + 637\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (67*y**2)*-49 = -3283*y**2\n (67*y**2)*(-26*y**3) = -1742*y**5\n -13*-26*y**3 = 338*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1742*y**5 + 338*y**3 - 3283*y**2 + 637\nNo more calculations needed.\n-1742*y**5 + 338*y**3 - 3283*y**2 + 637", "generated_answer": "-1742*y**5 + 338*y**3 - 3283*y**2 + 637", "step_length": 5} {"cot_id": "f4000ccfe6a5bdc31b93dd34aec378e99de685c672afca8e22056839161a7954", "datapoint": {"question": "Simplify this expression: (y + 10)*(-38*y**3 - 11*y**2 - 46)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-38*y**4 - 391*y**3 - 110*y**2 - 46*y - 460", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 643, "polynomial_expr": "(y + 10)*(-38*y**3 - 11*y**2 - 46)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (y + 10)*(-38*y**3 - 11*y**2 - 46)\nExpanding the part (y + 10) using the distributive property, and we got: y*(-38*y**3 - 11*y**2 - 46) + 10*(-38*y**3 - 11*y**2 - 46)\n#Step 2:\nCurrent expression: y*(-38*y**3 - 11*y**2 - 46) + 10*(-38*y**3 - 11*y**2 - 46)\nSimplifying the partial expression: 10*(-38*y**3 - 11*y**2 - 46)\nExpanding the part (-38*y**3 - 11*y**2 - 46) using the distributive property, and we got: -11*y**2*10 - 38*y**3*10 - 46*10\nReplacing 10*(-38*y**3 - 11*y**2 - 46) with -11*y**2*10 - 38*y**3*10 - 46*10 in the overall expression.\n#Step 3:\nCurrent expression: y*(-38*y**3 - 11*y**2 - 46) - 11*y**2*10 - 38*y**3*10 - 460\nSimplifying the partial expression: y*(-38*y**3 - 11*y**2 - 46)\nExpanding the part (-38*y**3 - 11*y**2 - 46) using the distributive property, and we got: y*(-11*y**2) + y*(-38*y**3) - 46*y\nReplacing y*(-38*y**3 - 11*y**2 - 46) with y*(-11*y**2) + y*(-38*y**3) - 46*y in the overall expression.\n#Step 4:\nCurrent expression: y*(-11*y**2) + y*(-38*y**3) - 46*y - 11*y**2*10 - 38*y**3*10 - 460\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*y**3)*10 = -380*y**3\n (-38*y**3)*y = -38*y**4\n (-11*y**2)*10 = -110*y**2\n (-11*y**2)*y = -11*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -38*y**4 - 380*y**3 - 11*y**3 - 110*y**2 - 46*y - 460\nCombining like terms, got -38*y**4 - 391*y**3 - 110*y**2 - 46*y - 460\n#Step 6:\nCurrent expression: -38*y**4 - 391*y**3 - 110*y**2 - 46*y - 460\nNo more calculations needed.\n-38*y**4 - 391*y**3 - 110*y**2 - 46*y - 460", "generated_answer": "-38*y**4 - 391*y**3 - 110*y**2 - 46*y - 460", "step_length": 6} {"cot_id": "5de26415deb6e1da304d3de60fc6fdf0ca4a84127ad5d017a6ed9425b1c0a8be", "datapoint": {"question": "Simplify this expression: -64*z*(-52*z**3 - 43*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "3328*z**4 + 2752*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 644, "polynomial_expr": "-64*z*(-52*z**3 - 43*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -64*z*(-52*z**3 - 43*z**2)\nExpanding the part (-52*z**3 - 43*z**2) using the distributive property, and we got: (-64*z)*(-43*z**2) + (-64*z)*(-52*z**3)\n#Step 2:\nCurrent expression: (-64*z)*(-43*z**2) + (-64*z)*(-52*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-52*z**3)*(-64*z) = 3328*z**4\n (-43*z**2)*(-64*z) = 2752*z**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 3328*z**4 + 2752*z**3\nNo more calculations needed.\n3328*z**4 + 2752*z**3", "generated_answer": "3328*z**4 + 2752*z**3", "step_length": 3} {"cot_id": "3a90ba13e8d92e50fd0fea5e35a086f47e48394a81c423500f24898b18c79a70", "datapoint": {"question": "Calculate the following: (-47*y**3 + 49*y**2)*(-22*y**3 - 18*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1034*y**6 - 1078*y**5 + 846*y**4 - 882*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 645, "polynomial_expr": "(-47*y**3 + 49*y**2)*(-22*y**3 - 18*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-47*y**3 + 49*y**2)*(-22*y**3 - 18*y)\nExpanding the part (-47*y**3 + 49*y**2) using the distributive property, and we got: (49*y**2)*(-22*y**3 - 18*y) + (-47*y**3)*(-22*y**3 - 18*y)\n#Step 2:\nCurrent expression: (49*y**2)*(-22*y**3 - 18*y) + (-47*y**3)*(-22*y**3 - 18*y)\nSimplifying the partial expression: (-47*y**3)*(-22*y**3 - 18*y)\nExpanding the part (-22*y**3 - 18*y) using the distributive property, and we got: (-18*y)*(-47*y**3) + (-47*y**3)*(-22*y**3)\nReplacing (-47*y**3)*(-22*y**3 - 18*y) with (-18*y)*(-47*y**3) + (-47*y**3)*(-22*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-18*y)*(-47*y**3) + (49*y**2)*(-22*y**3 - 18*y) + (-47*y**3)*(-22*y**3)\nSimplifying the partial expression: (49*y**2)*(-22*y**3 - 18*y)\nExpanding the part (-22*y**3 - 18*y) using the distributive property, and we got: (-18*y)*(49*y**2) + (49*y**2)*(-22*y**3)\nReplacing (49*y**2)*(-22*y**3 - 18*y) with (-18*y)*(49*y**2) + (49*y**2)*(-22*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-18*y)*(49*y**2) + (-18*y)*(-47*y**3) + (49*y**2)*(-22*y**3) + (-47*y**3)*(-22*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*y**3)*(-47*y**3) = 1034*y**6\n (-22*y**3)*(49*y**2) = -1078*y**5\n (-18*y)*(-47*y**3) = 846*y**4\n (-18*y)*(49*y**2) = -882*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1034*y**6 - 1078*y**5 + 846*y**4 - 882*y**3\nNo more calculations needed.\n1034*y**6 - 1078*y**5 + 846*y**4 - 882*y**3", "generated_answer": "1034*y**6 - 1078*y**5 + 846*y**4 - 882*y**3", "step_length": 5} {"cot_id": "d607960e9814219d6788916bd3d671f2bd1510d074ff9e0468e91e11bef514ad", "datapoint": {"question": "Calculate the following: z**2*(-5*z**3 - 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-5*z**5 - 24*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 646, "polynomial_expr": "z**2*(-5*z**3 - 24)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: z**2*(-5*z**3 - 24)\nExpanding the part (-5*z**3 - 24) using the distributive property, and we got: z**2*(-5*z**3) - 24*z**2\n#Step 2:\nCurrent expression: z**2*(-5*z**3) - 24*z**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-5*z**3)*z**2 = -5*z**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -5*z**5 - 24*z**2\nNo more calculations needed.\n-5*z**5 - 24*z**2", "generated_answer": "-5*z**5 - 24*z**2", "step_length": 3} {"cot_id": "d4ddb12315f5b2f825236f3951c972559d701ff45d65b9f8d093b6acfa8e4472", "datapoint": {"question": "Calculate the following: (81*z**3 + 26*z**2)*(14*z**3 + z**2 + 38*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1134*z**6 + 445*z**5 + 3104*z**4 + 988*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 647, "polynomial_expr": "(81*z**3 + 26*z**2)*(14*z**3 + z**2 + 38*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (81*z**3 + 26*z**2)*(14*z**3 + z**2 + 38*z)\nExpanding the part (81*z**3 + 26*z**2) using the distributive property, and we got: (26*z**2)*(14*z**3 + z**2 + 38*z) + (81*z**3)*(14*z**3 + z**2 + 38*z)\n#Step 2:\nCurrent expression: (26*z**2)*(14*z**3 + z**2 + 38*z) + (81*z**3)*(14*z**3 + z**2 + 38*z)\nSimplifying the partial expression: (26*z**2)*(14*z**3 + z**2 + 38*z)\nExpanding the part (14*z**3 + z**2 + 38*z) using the distributive property, and we got: z**2*(26*z**2) + (38*z)*(26*z**2) + (26*z**2)*(14*z**3)\nReplacing (26*z**2)*(14*z**3 + z**2 + 38*z) with z**2*(26*z**2) + (38*z)*(26*z**2) + (26*z**2)*(14*z**3) in the overall expression.\n#Step 3:\nCurrent expression: z**2*(26*z**2) + (38*z)*(26*z**2) + (26*z**2)*(14*z**3) + (81*z**3)*(14*z**3 + z**2 + 38*z)\nSimplifying the partial expression: (81*z**3)*(14*z**3 + z**2 + 38*z)\nExpanding the part (14*z**3 + z**2 + 38*z) using the distributive property, and we got: z**2*(81*z**3) + (38*z)*(81*z**3) + (14*z**3)*(81*z**3)\nReplacing (81*z**3)*(14*z**3 + z**2 + 38*z) with z**2*(81*z**3) + (38*z)*(81*z**3) + (14*z**3)*(81*z**3) in the overall expression.\n#Step 4:\nCurrent expression: z**2*(26*z**2) + z**2*(81*z**3) + (38*z)*(26*z**2) + (38*z)*(81*z**3) + (26*z**2)*(14*z**3) + (14*z**3)*(81*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n z**2*(26*z**2) = 26*z**4\n z**2*(81*z**3) = 81*z**5\n (14*z**3)*(26*z**2) = 364*z**5\n (14*z**3)*(81*z**3) = 1134*z**6\n (38*z)*(26*z**2) = 988*z**3\n (38*z)*(81*z**3) = 3078*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1134*z**6 + 81*z**5 + 364*z**5 + 26*z**4 + 3078*z**4 + 988*z**3\nCombining like terms, got 1134*z**6 + 445*z**5 + 3104*z**4 + 988*z**3\n#Step 6:\nCurrent expression: 1134*z**6 + 445*z**5 + 3104*z**4 + 988*z**3\nNo more calculations needed.\n1134*z**6 + 445*z**5 + 3104*z**4 + 988*z**3", "generated_answer": "1134*z**6 + 445*z**5 + 3104*z**4 + 988*z**3", "step_length": 6} {"cot_id": "93af1c07c67dac39e7f3ab9c9c5687ff855bc0f6bab97f00f23d9b58092aedd2", "datapoint": {"question": "Simplify this expression: (-7*y**3 - 51*y**2)*(31*y**3 + 38*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-217*y**6 - 1581*y**5 - 266*y**4 - 1938*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 648, "polynomial_expr": "(-7*y**3 - 51*y**2)*(31*y**3 + 38*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-7*y**3 - 51*y**2)*(31*y**3 + 38*y)\nExpanding the part (-7*y**3 - 51*y**2) using the distributive property, and we got: (-51*y**2)*(31*y**3 + 38*y) + (-7*y**3)*(31*y**3 + 38*y)\n#Step 2:\nCurrent expression: (-51*y**2)*(31*y**3 + 38*y) + (-7*y**3)*(31*y**3 + 38*y)\nSimplifying the partial expression: (-51*y**2)*(31*y**3 + 38*y)\nExpanding the part (31*y**3 + 38*y) using the distributive property, and we got: (38*y)*(-51*y**2) + (-51*y**2)*(31*y**3)\nReplacing (-51*y**2)*(31*y**3 + 38*y) with (38*y)*(-51*y**2) + (-51*y**2)*(31*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (38*y)*(-51*y**2) + (-51*y**2)*(31*y**3) + (-7*y**3)*(31*y**3 + 38*y)\nSimplifying the partial expression: (-7*y**3)*(31*y**3 + 38*y)\nExpanding the part (31*y**3 + 38*y) using the distributive property, and we got: (38*y)*(-7*y**3) + (-7*y**3)*(31*y**3)\nReplacing (-7*y**3)*(31*y**3 + 38*y) with (38*y)*(-7*y**3) + (-7*y**3)*(31*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (38*y)*(-51*y**2) + (38*y)*(-7*y**3) + (-51*y**2)*(31*y**3) + (-7*y**3)*(31*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (31*y**3)*(-51*y**2) = -1581*y**5\n (31*y**3)*(-7*y**3) = -217*y**6\n (38*y)*(-51*y**2) = -1938*y**3\n (38*y)*(-7*y**3) = -266*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -217*y**6 - 1581*y**5 - 266*y**4 - 1938*y**3\nNo more calculations needed.\n-217*y**6 - 1581*y**5 - 266*y**4 - 1938*y**3", "generated_answer": "-217*y**6 - 1581*y**5 - 266*y**4 - 1938*y**3", "step_length": 5} {"cot_id": "96018e6a3c249726bac2a58fa1018045ff3491aea35051bfda9349aec9e6a7ea", "datapoint": {"question": "Calculate the following: (7*z**2 + 21)*(42*z**3 - 23*z**2 - 3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "294*z**5 - 161*z**4 + 882*z**3 - 504*z**2 - 63", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 649, "polynomial_expr": "(7*z**2 + 21)*(42*z**3 - 23*z**2 - 3)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7*z**2 + 21)*(42*z**3 - 23*z**2 - 3)\nExpanding the part (7*z**2 + 21) using the distributive property, and we got: (7*z**2)*(42*z**3 - 23*z**2 - 3) + 21*(42*z**3 - 23*z**2 - 3)\n#Step 2:\nCurrent expression: (7*z**2)*(42*z**3 - 23*z**2 - 3) + 21*(42*z**3 - 23*z**2 - 3)\nSimplifying the partial expression: 21*(42*z**3 - 23*z**2 - 3)\nExpanding the part (42*z**3 - 23*z**2 - 3) using the distributive property, and we got: -23*z**2*21 + (42*z**3)*21 - 3*21\nReplacing 21*(42*z**3 - 23*z**2 - 3) with -23*z**2*21 + (42*z**3)*21 - 3*21 in the overall expression.\n#Step 3:\nCurrent expression: -23*z**2*21 + (7*z**2)*(42*z**3 - 23*z**2 - 3) + (42*z**3)*21 - 63\nSimplifying the partial expression: (7*z**2)*(42*z**3 - 23*z**2 - 3)\nExpanding the part (42*z**3 - 23*z**2 - 3) using the distributive property, and we got: -21*z**2 + (-23*z**2)*(7*z**2) + (7*z**2)*(42*z**3)\nReplacing (7*z**2)*(42*z**3 - 23*z**2 - 3) with -21*z**2 + (-23*z**2)*(7*z**2) + (7*z**2)*(42*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -3*7*z**2 + (-23*z**2)*(7*z**2) - 23*z**2*21 + (7*z**2)*(42*z**3) + (42*z**3)*21 - 63\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*z**2)*21 = -483*z**2\n (-23*z**2)*(7*z**2) = -161*z**4\n (42*z**3)*21 = 882*z**3\n (42*z**3)*(7*z**2) = 294*z**5\n -3*7*z**2 = -21*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 294*z**5 - 161*z**4 + 882*z**3 - 483*z**2 - 21*z**2 - 63\nCombining like terms, got 294*z**5 - 161*z**4 + 882*z**3 - 504*z**2 - 63\n#Step 6:\nCurrent expression: 294*z**5 - 161*z**4 + 882*z**3 - 504*z**2 - 63\nNo more calculations needed.\n294*z**5 - 161*z**4 + 882*z**3 - 504*z**2 - 63", "generated_answer": "294*z**5 - 161*z**4 + 882*z**3 - 504*z**2 - 63", "step_length": 6} {"cot_id": "64d4261fa8c7fb701073353c88e206056c9aca7a7df586b9fe9c48925c66fa85", "datapoint": {"question": "Calculate the following: (-14*x**3 - 7*x**2)*(15*x**2 - 3*x + 9)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-210*x**5 - 63*x**4 - 105*x**3 - 63*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 650, "polynomial_expr": "(-14*x**3 - 7*x**2)*(15*x**2 - 3*x + 9)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-14*x**3 - 7*x**2)*(15*x**2 - 3*x + 9)\nExpanding the part (-14*x**3 - 7*x**2) using the distributive property, and we got: (-7*x**2)*(15*x**2 - 3*x + 9) + (-14*x**3)*(15*x**2 - 3*x + 9)\n#Step 2:\nCurrent expression: (-7*x**2)*(15*x**2 - 3*x + 9) + (-14*x**3)*(15*x**2 - 3*x + 9)\nSimplifying the partial expression: (-14*x**3)*(15*x**2 - 3*x + 9)\nExpanding the part (15*x**2 - 3*x + 9) using the distributive property, and we got: (-3*x)*(-14*x**3) + 9*(-14*x**3) + (15*x**2)*(-14*x**3)\nReplacing (-14*x**3)*(15*x**2 - 3*x + 9) with (-3*x)*(-14*x**3) + 9*(-14*x**3) + (15*x**2)*(-14*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-3*x)*(-14*x**3) + 9*(-14)*x**3 + (-7*x**2)*(15*x**2 - 3*x + 9) + (15*x**2)*(-14*x**3)\nSimplifying the partial expression: (-7*x**2)*(15*x**2 - 3*x + 9)\nExpanding the part (15*x**2 - 3*x + 9) using the distributive property, and we got: (-3*x)*(-7*x**2) + 9*(-7*x**2) + (-7*x**2)*(15*x**2)\nReplacing (-7*x**2)*(15*x**2 - 3*x + 9) with (-3*x)*(-7*x**2) + 9*(-7*x**2) + (-7*x**2)*(15*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-3*x)*(-7*x**2) + (-3*x)*(-14*x**3) + 9*(-14)*x**3 + 9*(-7)*x**2 + (-7*x**2)*(15*x**2) + (15*x**2)*(-14*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-3*x)*(-14*x**3) = 42*x**4\n (-3*x)*(-7*x**2) = 21*x**3\n (15*x**2)*(-14*x**3) = -210*x**5\n (15*x**2)*(-7*x**2) = -105*x**4\n 9*-14*x**3 = -126*x**3\n 9*-7*x**2 = -63*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -210*x**5 - 105*x**4 + 42*x**4 - 126*x**3 + 21*x**3 - 63*x**2\nCombining like terms, got -210*x**5 - 63*x**4 - 105*x**3 - 63*x**2\n#Step 6:\nCurrent expression: -210*x**5 - 63*x**4 - 105*x**3 - 63*x**2\nNo more calculations needed.\n-210*x**5 - 63*x**4 - 105*x**3 - 63*x**2", "generated_answer": "-210*x**5 - 63*x**4 - 105*x**3 - 63*x**2", "step_length": 6} {"cot_id": "0373991f9087895678dbed147df70ff915d4da8c909dbc43221b810e4473bb8c", "datapoint": {"question": "Calculate the following: (6 - 88*y**2)*(-27*y**3 + 47*y**2 - 43*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2376*y**5 - 4136*y**4 + 3622*y**3 + 282*y**2 - 258*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 651, "polynomial_expr": "(6 - 88*y**2)*(-27*y**3 + 47*y**2 - 43*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6 - 88*y**2)*(-27*y**3 + 47*y**2 - 43*y)\nExpanding the part (6 - 88*y**2) using the distributive property, and we got: (-88*y**2)*(-27*y**3 + 47*y**2 - 43*y) + 6*(-27*y**3 + 47*y**2 - 43*y)\n#Step 2:\nCurrent expression: (-88*y**2)*(-27*y**3 + 47*y**2 - 43*y) + 6*(-27*y**3 + 47*y**2 - 43*y)\nSimplifying the partial expression: 6*(-27*y**3 + 47*y**2 - 43*y)\nExpanding the part (-27*y**3 + 47*y**2 - 43*y) using the distributive property, and we got: -43*y*6 + (47*y**2)*6 - 27*y**3*6\nReplacing 6*(-27*y**3 + 47*y**2 - 43*y) with -43*y*6 + (47*y**2)*6 - 27*y**3*6 in the overall expression.\n#Step 3:\nCurrent expression: -43*y*6 + (-88*y**2)*(-27*y**3 + 47*y**2 - 43*y) + (47*y**2)*6 - 27*y**3*6\nSimplifying the partial expression: (-88*y**2)*(-27*y**3 + 47*y**2 - 43*y)\nExpanding the part (-27*y**3 + 47*y**2 - 43*y) using the distributive property, and we got: (-43*y)*(-88*y**2) + (-88*y**2)*(47*y**2) + (-88*y**2)*(-27*y**3)\nReplacing (-88*y**2)*(-27*y**3 + 47*y**2 - 43*y) with (-43*y)*(-88*y**2) + (-88*y**2)*(47*y**2) + (-88*y**2)*(-27*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-43*y)*(-88*y**2) - 43*y*6 + (-88*y**2)*(47*y**2) + (-88*y**2)*(-27*y**3) + (47*y**2)*6 - 27*y**3*6\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-43*y)*6 = -258*y\n (-43*y)*(-88*y**2) = 3784*y**3\n (-27*y**3)*6 = -162*y**3\n (-27*y**3)*(-88*y**2) = 2376*y**5\n (47*y**2)*6 = 282*y**2\n (47*y**2)*(-88*y**2) = -4136*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2376*y**5 - 4136*y**4 - 162*y**3 + 3784*y**3 + 282*y**2 - 258*y\nCombining like terms, got 2376*y**5 - 4136*y**4 + 3622*y**3 + 282*y**2 - 258*y\n#Step 6:\nCurrent expression: 2376*y**5 - 4136*y**4 + 3622*y**3 + 282*y**2 - 258*y\nNo more calculations needed.\n2376*y**5 - 4136*y**4 + 3622*y**3 + 282*y**2 - 258*y", "generated_answer": "2376*y**5 - 4136*y**4 + 3622*y**3 + 282*y**2 - 258*y", "step_length": 6} {"cot_id": "ff8b9fcb0e662eb69fe9e50a9e1f5524820cd6312b6fa151364c9e41928836d9", "datapoint": {"question": "Calculate the following: (-46*z**3 - 28*z)*(32*z**3 - 24*z**2 - 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1472*z**6 + 1104*z**5 - 896*z**4 + 2420*z**3 + 1064*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 652, "polynomial_expr": "(-46*z**3 - 28*z)*(32*z**3 - 24*z**2 - 38)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-46*z**3 - 28*z)*(32*z**3 - 24*z**2 - 38)\nExpanding the part (-46*z**3 - 28*z) using the distributive property, and we got: (-28*z)*(32*z**3 - 24*z**2 - 38) + (-46*z**3)*(32*z**3 - 24*z**2 - 38)\n#Step 2:\nCurrent expression: (-28*z)*(32*z**3 - 24*z**2 - 38) + (-46*z**3)*(32*z**3 - 24*z**2 - 38)\nSimplifying the partial expression: (-46*z**3)*(32*z**3 - 24*z**2 - 38)\nExpanding the part (32*z**3 - 24*z**2 - 38) using the distributive property, and we got: -(-1)*1748*z**3 + (-24*z**2)*(-46*z**3) + (-46*z**3)*(32*z**3)\nReplacing (-46*z**3)*(32*z**3 - 24*z**2 - 38) with -(-1)*1748*z**3 + (-24*z**2)*(-46*z**3) + (-46*z**3)*(32*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-28*z)*(32*z**3 - 24*z**2 - 38) - 38*(-46)*z**3 + (-24*z**2)*(-46*z**3) + (-46*z**3)*(32*z**3)\nSimplifying the partial expression: (-28*z)*(32*z**3 - 24*z**2 - 38)\nExpanding the part (32*z**3 - 24*z**2 - 38) using the distributive property, and we got: (-28*z)*(-24*z**2) + (-28*z)*(32*z**3) - (-1)*1064*z\nReplacing (-28*z)*(32*z**3 - 24*z**2 - 38) with (-28*z)*(-24*z**2) + (-28*z)*(32*z**3) - (-1)*1064*z in the overall expression.\n#Step 4:\nCurrent expression: (-28*z)*(-24*z**2) + (-28*z)*(32*z**3) - 38*(-46)*z**3 - 38*(-28)*z + (-24*z**2)*(-46*z**3) + (-46*z**3)*(32*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-24*z**2)*(-46*z**3) = 1104*z**5\n (-24*z**2)*(-28*z) = 672*z**3\n (32*z**3)*(-46*z**3) = -1472*z**6\n (32*z**3)*(-28*z) = -896*z**4\n -38*-46*z**3 = 1748*z**3\n -38*-28*z = 1064*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1472*z**6 + 1104*z**5 - 896*z**4 + 672*z**3 + 1748*z**3 + 1064*z\nCombining like terms, got -1472*z**6 + 1104*z**5 - 896*z**4 + 2420*z**3 + 1064*z\n#Step 6:\nCurrent expression: -1472*z**6 + 1104*z**5 - 896*z**4 + 2420*z**3 + 1064*z\nNo more calculations needed.\n-1472*z**6 + 1104*z**5 - 896*z**4 + 2420*z**3 + 1064*z", "generated_answer": "-1472*z**6 + 1104*z**5 - 896*z**4 + 2420*z**3 + 1064*z", "step_length": 6} {"cot_id": "d6d37d7b1293ef7863a9bbdb3a2bd6ed64e676a6b8126e4f236982f7b48e00f4", "datapoint": {"question": "Simplify this expression: (23*y**2 - 17)*(-18*y**3 - 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-414*y**5 + 306*y**3 - 1081*y**2 + 799", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 653, "polynomial_expr": "(23*y**2 - 17)*(-18*y**3 - 47)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (23*y**2 - 17)*(-18*y**3 - 47)\nExpanding the part (-18*y**3 - 47) using the distributive property, and we got: (-18*y**3)*(23*y**2 - 17) - 47*(23*y**2 - 17)\n#Step 2:\nCurrent expression: (-18*y**3)*(23*y**2 - 17) - 47*(23*y**2 - 17)\nSimplifying the partial expression: -47*(23*y**2 - 17)\nExpanding the part (23*y**2 - 17) using the distributive property, and we got: (23*y**2)*(-47) - 17*(-47)\nReplacing -47*(23*y**2 - 17) with (23*y**2)*(-47) - 17*(-47) in the overall expression.\n#Step 3:\nCurrent expression: (23*y**2)*(-47) + (-18*y**3)*(23*y**2 - 17) + 799\nSimplifying the partial expression: (-18*y**3)*(23*y**2 - 17)\nExpanding the part (23*y**2 - 17) using the distributive property, and we got: -(-1)*306*y**3 + (23*y**2)*(-18*y**3)\nReplacing (-18*y**3)*(23*y**2 - 17) with -(-1)*306*y**3 + (23*y**2)*(-18*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -17*(-18)*y**3 + (23*y**2)*(-18*y**3) + (23*y**2)*(-47) + 799\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (23*y**2)*-47 = -1081*y**2\n (23*y**2)*(-18*y**3) = -414*y**5\n -17*-18*y**3 = 306*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -414*y**5 + 306*y**3 - 1081*y**2 + 799\nNo more calculations needed.\n-414*y**5 + 306*y**3 - 1081*y**2 + 799", "generated_answer": "-414*y**5 + 306*y**3 - 1081*y**2 + 799", "step_length": 5} {"cot_id": "2d81c6412dd6db87fd8e29cb59c466c2506ea93afe164193080745a9b0460384", "datapoint": {"question": "Simplify this expression: (-6*x**3 - 24*x)*(-41*x**3 + 21*x**2 - 29)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "246*x**6 - 126*x**5 + 984*x**4 - 330*x**3 + 696*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 654, "polynomial_expr": "(-6*x**3 - 24*x)*(-41*x**3 + 21*x**2 - 29)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-6*x**3 - 24*x)*(-41*x**3 + 21*x**2 - 29)\nExpanding the part (-6*x**3 - 24*x) using the distributive property, and we got: (-24*x)*(-41*x**3 + 21*x**2 - 29) + (-6*x**3)*(-41*x**3 + 21*x**2 - 29)\n#Step 2:\nCurrent expression: (-24*x)*(-41*x**3 + 21*x**2 - 29) + (-6*x**3)*(-41*x**3 + 21*x**2 - 29)\nSimplifying the partial expression: (-24*x)*(-41*x**3 + 21*x**2 - 29)\nExpanding the part (-41*x**3 + 21*x**2 - 29) using the distributive property, and we got: (-24*x)*(21*x**2) + (-24*x)*(-41*x**3) - (-1)*696*x\nReplacing (-24*x)*(-41*x**3 + 21*x**2 - 29) with (-24*x)*(21*x**2) + (-24*x)*(-41*x**3) - (-1)*696*x in the overall expression.\n#Step 3:\nCurrent expression: (-24*x)*(21*x**2) + (-24*x)*(-41*x**3) - 29*(-24)*x + (-6*x**3)*(-41*x**3 + 21*x**2 - 29)\nSimplifying the partial expression: (-6*x**3)*(-41*x**3 + 21*x**2 - 29)\nExpanding the part (-41*x**3 + 21*x**2 - 29) using the distributive property, and we got: -(-1)*174*x**3 + (21*x**2)*(-6*x**3) + (-41*x**3)*(-6*x**3)\nReplacing (-6*x**3)*(-41*x**3 + 21*x**2 - 29) with -(-1)*174*x**3 + (21*x**2)*(-6*x**3) + (-41*x**3)*(-6*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-24*x)*(21*x**2) + (-24*x)*(-41*x**3) - 29*(-6)*x**3 - 29*(-24)*x + (21*x**2)*(-6*x**3) + (-41*x**3)*(-6*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*x**3)*(-24*x) = 984*x**4\n (-41*x**3)*(-6*x**3) = 246*x**6\n (21*x**2)*(-24*x) = -504*x**3\n (21*x**2)*(-6*x**3) = -126*x**5\n -29*-24*x = 696*x\n -29*-6*x**3 = 174*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 246*x**6 - 126*x**5 + 984*x**4 - 504*x**3 + 174*x**3 + 696*x\nCombining like terms, got 246*x**6 - 126*x**5 + 984*x**4 - 330*x**3 + 696*x\n#Step 6:\nCurrent expression: 246*x**6 - 126*x**5 + 984*x**4 - 330*x**3 + 696*x\nNo more calculations needed.\n246*x**6 - 126*x**5 + 984*x**4 - 330*x**3 + 696*x", "generated_answer": "246*x**6 - 126*x**5 + 984*x**4 - 330*x**3 + 696*x", "step_length": 6} {"cot_id": "7e45936c1ebc1c01eb5f244bcc127183d6af89ad7d9a393473039a9d8bcd75f1", "datapoint": {"question": "Calculate the following: (-74*x - 17)*(-19*x**3 - 2*x**2 - 43)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1406*x**4 + 471*x**3 + 34*x**2 + 3182*x + 731", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 655, "polynomial_expr": "(-74*x - 17)*(-19*x**3 - 2*x**2 - 43)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-74*x - 17)*(-19*x**3 - 2*x**2 - 43)\nExpanding the part (-74*x - 17) using the distributive property, and we got: (-74*x)*(-19*x**3 - 2*x**2 - 43) - 17*(-19*x**3 - 2*x**2 - 43)\n#Step 2:\nCurrent expression: (-74*x)*(-19*x**3 - 2*x**2 - 43) - 17*(-19*x**3 - 2*x**2 - 43)\nSimplifying the partial expression: -17*(-19*x**3 - 2*x**2 - 43)\nExpanding the part (-19*x**3 - 2*x**2 - 43) using the distributive property, and we got: -2*x**2*(-17) - 19*x**3*(-17) - 43*(-17)\nReplacing -17*(-19*x**3 - 2*x**2 - 43) with -2*x**2*(-17) - 19*x**3*(-17) - 43*(-17) in the overall expression.\n#Step 3:\nCurrent expression: (-74*x)*(-19*x**3 - 2*x**2 - 43) - 2*x**2*(-17) - 19*x**3*(-17) + 731\nSimplifying the partial expression: (-74*x)*(-19*x**3 - 2*x**2 - 43)\nExpanding the part (-19*x**3 - 2*x**2 - 43) using the distributive property, and we got: (-74*x)*(-2*x**2) + (-74*x)*(-19*x**3) - (-1)*3182*x\nReplacing (-74*x)*(-19*x**3 - 2*x**2 - 43) with (-74*x)*(-2*x**2) + (-74*x)*(-19*x**3) - (-1)*3182*x in the overall expression.\n#Step 4:\nCurrent expression: (-74*x)*(-2*x**2) + (-74*x)*(-19*x**3) - 43*(-74)*x - 2*x**2*(-17) - 19*x**3*(-17) + 731\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*x**3)*-17 = 323*x**3\n (-19*x**3)*(-74*x) = 1406*x**4\n (-2*x**2)*-17 = 34*x**2\n (-2*x**2)*(-74*x) = 148*x**3\n -43*-74*x = 3182*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1406*x**4 + 148*x**3 + 323*x**3 + 34*x**2 + 3182*x + 731\nCombining like terms, got 1406*x**4 + 471*x**3 + 34*x**2 + 3182*x + 731\n#Step 6:\nCurrent expression: 1406*x**4 + 471*x**3 + 34*x**2 + 3182*x + 731\nNo more calculations needed.\n1406*x**4 + 471*x**3 + 34*x**2 + 3182*x + 731", "generated_answer": "1406*x**4 + 471*x**3 + 34*x**2 + 3182*x + 731", "step_length": 6} {"cot_id": "66378fc8b3d87931a3a55cfb59ba417a7f07233be7a998a1af90d51bc5758501", "datapoint": {"question": "Calculate the following: -924*y - 880\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-924*y - 880", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 656, "polynomial_expr": "-924*y - 880", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -924*y - 880\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -924*y - 880\nNo more calculations needed.\n-924*y - 880", "generated_answer": "-924*y - 880", "step_length": 2} {"cot_id": "c56ffcb0c34edada671cd8bf480fd4717e1ac9bc694460a0beebaa3f582c9f8e", "datapoint": {"question": "Calculate the following: (-49*y**3 + 40*y**2)*(-38*y**3 - 47*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1862*y**6 + 783*y**5 - 1880*y**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 657, "polynomial_expr": "(-49*y**3 + 40*y**2)*(-38*y**3 - 47*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-49*y**3 + 40*y**2)*(-38*y**3 - 47*y**2)\nExpanding the part (-49*y**3 + 40*y**2) using the distributive property, and we got: (40*y**2)*(-38*y**3 - 47*y**2) + (-49*y**3)*(-38*y**3 - 47*y**2)\n#Step 2:\nCurrent expression: (40*y**2)*(-38*y**3 - 47*y**2) + (-49*y**3)*(-38*y**3 - 47*y**2)\nSimplifying the partial expression: (-49*y**3)*(-38*y**3 - 47*y**2)\nExpanding the part (-38*y**3 - 47*y**2) using the distributive property, and we got: (-47*y**2)*(-49*y**3) + (-49*y**3)*(-38*y**3)\nReplacing (-49*y**3)*(-38*y**3 - 47*y**2) with (-47*y**2)*(-49*y**3) + (-49*y**3)*(-38*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-47*y**2)*(-49*y**3) + (40*y**2)*(-38*y**3 - 47*y**2) + (-49*y**3)*(-38*y**3)\nSimplifying the partial expression: (40*y**2)*(-38*y**3 - 47*y**2)\nExpanding the part (-38*y**3 - 47*y**2) using the distributive property, and we got: (-47*y**2)*(40*y**2) + (40*y**2)*(-38*y**3)\nReplacing (40*y**2)*(-38*y**3 - 47*y**2) with (-47*y**2)*(40*y**2) + (40*y**2)*(-38*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-47*y**2)*(40*y**2) + (-47*y**2)*(-49*y**3) + (40*y**2)*(-38*y**3) + (-49*y**3)*(-38*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*y**2)*(-49*y**3) = 2303*y**5\n (-47*y**2)*(40*y**2) = -1880*y**4\n (-38*y**3)*(-49*y**3) = 1862*y**6\n (-38*y**3)*(40*y**2) = -1520*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1862*y**6 - 1520*y**5 + 2303*y**5 - 1880*y**4\nCombining like terms, got 1862*y**6 + 783*y**5 - 1880*y**4\n#Step 6:\nCurrent expression: 1862*y**6 + 783*y**5 - 1880*y**4\nNo more calculations needed.\n1862*y**6 + 783*y**5 - 1880*y**4", "generated_answer": "1862*y**6 + 783*y**5 - 1880*y**4", "step_length": 6} {"cot_id": "20963d973b9c7d3bc483c4e975a5debc8505b239f2aabbb2824c85b03d3da4f3", "datapoint": {"question": "Calculate the following: -62*x**2*(40*x**2 + 39*x + 45)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2480*x**4 - 2418*x**3 - 2790*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 658, "polynomial_expr": "-62*x**2*(40*x**2 + 39*x + 45)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -62*x**2*(40*x**2 + 39*x + 45)\nExpanding the part (40*x**2 + 39*x + 45) using the distributive property, and we got: 45*(-62*x**2) + (39*x)*(-62*x**2) + (-62*x**2)*(40*x**2)\n#Step 2:\nCurrent expression: 45*(-62*x**2) + (39*x)*(-62*x**2) + (-62*x**2)*(40*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 45*(-62*x**2) = -2790*x**2\n (39*x)*(-62*x**2) = -2418*x**3\n (40*x**2)*(-62*x**2) = -2480*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -2480*x**4 - 2418*x**3 - 2790*x**2\nNo more calculations needed.\n-2480*x**4 - 2418*x**3 - 2790*x**2", "generated_answer": "-2480*x**4 - 2418*x**3 - 2790*x**2", "step_length": 3} {"cot_id": "d1ebe509ed3f208138b49d5f6079b5b132c48c42eb1615b6714d3fd1ba9bd78f", "datapoint": {"question": "Simplify this expression: 189*z**3 + 405*z**2 + 1026\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "189*z**3 + 405*z**2 + 1026", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 659, "polynomial_expr": "189*z**3 + 405*z**2 + 1026", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 189*z**3 + 405*z**2 + 1026\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 189*z**3 + 405*z**2 + 1026\nNo more calculations needed.\n189*z**3 + 405*z**2 + 1026", "generated_answer": "189*z**3 + 405*z**2 + 1026", "step_length": 2} {"cot_id": "378761e6af1d1ccc9df1bc7de5cf9fe460375aaf8d6dd2612b0f805161a77f26", "datapoint": {"question": "Simplify this expression: 96*x**2*(-25*x**3 - 37*x + 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2400*x**5 - 3552*x**3 + 1536*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 660, "polynomial_expr": "96*x**2*(-25*x**3 - 37*x + 16)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 96*x**2*(-25*x**3 - 37*x + 16)\nExpanding the part (-25*x**3 - 37*x + 16) using the distributive property, and we got: (-37*x)*(96*x**2) + 16*(96*x**2) + (96*x**2)*(-25*x**3)\n#Step 2:\nCurrent expression: (-37*x)*(96*x**2) + 16*(96*x**2) + (96*x**2)*(-25*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 16*(96*x**2) = 1536*x**2\n (-37*x)*(96*x**2) = -3552*x**3\n (-25*x**3)*(96*x**2) = -2400*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -2400*x**5 - 3552*x**3 + 1536*x**2\nNo more calculations needed.\n-2400*x**5 - 3552*x**3 + 1536*x**2", "generated_answer": "-2400*x**5 - 3552*x**3 + 1536*x**2", "step_length": 3} {"cot_id": "ddb8c304905c5940b9f207abfdfe6b93f48fa47a652d6c33393eef5c46d13c0f", "datapoint": {"question": "Simplify this expression: 5*x**2*(-22*x - 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-110*x**3 - 155*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 661, "polynomial_expr": "5*x**2*(-22*x - 31)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 5*x**2*(-22*x - 31)\nExpanding the part (-22*x - 31) using the distributive property, and we got: (-22*x)*(5*x**2) - 155*x**2\n#Step 2:\nCurrent expression: (-22*x)*(5*x**2) - 155*x**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -31*(5*x**2) = -155*x**2\n (-22*x)*(5*x**2) = -110*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -110*x**3 - 155*x**2\nNo more calculations needed.\n-110*x**3 - 155*x**2", "generated_answer": "-110*x**3 - 155*x**2", "step_length": 3} {"cot_id": "453655841d3110ff2d862e3d63e0f9381913f1b1b44de48bfcf70e7b71e44456", "datapoint": {"question": "Calculate the following: (-43*z**2 + 14*z)*(2*z**3 + 48*z - 51)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-86*z**5 + 28*z**4 - 2064*z**3 + 2865*z**2 - 714*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 662, "polynomial_expr": "(-43*z**2 + 14*z)*(2*z**3 + 48*z - 51)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-43*z**2 + 14*z)*(2*z**3 + 48*z - 51)\nExpanding the part (-43*z**2 + 14*z) using the distributive property, and we got: (14*z)*(2*z**3 + 48*z - 51) + (-43*z**2)*(2*z**3 + 48*z - 51)\n#Step 2:\nCurrent expression: (14*z)*(2*z**3 + 48*z - 51) + (-43*z**2)*(2*z**3 + 48*z - 51)\nSimplifying the partial expression: (-43*z**2)*(2*z**3 + 48*z - 51)\nExpanding the part (2*z**3 + 48*z - 51) using the distributive property, and we got: -(-1)*2193*z**2 + (48*z)*(-43*z**2) + (-43*z**2)*(2*z**3)\nReplacing (-43*z**2)*(2*z**3 + 48*z - 51) with -(-1)*2193*z**2 + (48*z)*(-43*z**2) + (-43*z**2)*(2*z**3) in the overall expression.\n#Step 3:\nCurrent expression: -51*(-43)*z**2 + (14*z)*(2*z**3 + 48*z - 51) + (48*z)*(-43*z**2) + (-43*z**2)*(2*z**3)\nSimplifying the partial expression: (14*z)*(2*z**3 + 48*z - 51)\nExpanding the part (2*z**3 + 48*z - 51) using the distributive property, and we got: -714*z + (14*z)*(48*z) + (14*z)*(2*z**3)\nReplacing (14*z)*(2*z**3 + 48*z - 51) with -714*z + (14*z)*(48*z) + (14*z)*(2*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -51*(-43)*z**2 - 51*14*z + (14*z)*(48*z) + (14*z)*(2*z**3) + (48*z)*(-43*z**2) + (-43*z**2)*(2*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (2*z**3)*(-43*z**2) = -86*z**5\n (2*z**3)*(14*z) = 28*z**4\n (48*z)*(-43*z**2) = -2064*z**3\n (48*z)*(14*z) = 672*z**2\n -51*-43*z**2 = 2193*z**2\n -51*14*z = -714*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -86*z**5 + 28*z**4 - 2064*z**3 + 672*z**2 + 2193*z**2 - 714*z\nCombining like terms, got -86*z**5 + 28*z**4 - 2064*z**3 + 2865*z**2 - 714*z\n#Step 6:\nCurrent expression: -86*z**5 + 28*z**4 - 2064*z**3 + 2865*z**2 - 714*z\nNo more calculations needed.\n-86*z**5 + 28*z**4 - 2064*z**3 + 2865*z**2 - 714*z", "generated_answer": "-86*z**5 + 28*z**4 - 2064*z**3 + 2865*z**2 - 714*z", "step_length": 6} {"cot_id": "942bd06d266f156029e3175da6664e2f8cc9094d6eae164b7195add367456c67", "datapoint": {"question": "Calculate the following: (10*y**2 + 21)*(-22*y**3 - 20*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-220*y**5 - 200*y**4 - 462*y**3 - 420*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 663, "polynomial_expr": "(10*y**2 + 21)*(-22*y**3 - 20*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (10*y**2 + 21)*(-22*y**3 - 20*y**2)\nExpanding the part (10*y**2 + 21) using the distributive property, and we got: (10*y**2)*(-22*y**3 - 20*y**2) + 21*(-22*y**3 - 20*y**2)\n#Step 2:\nCurrent expression: (10*y**2)*(-22*y**3 - 20*y**2) + 21*(-22*y**3 - 20*y**2)\nSimplifying the partial expression: 21*(-22*y**3 - 20*y**2)\nExpanding the part (-22*y**3 - 20*y**2) using the distributive property, and we got: -20*y**2*21 - 22*y**3*21\nReplacing 21*(-22*y**3 - 20*y**2) with -20*y**2*21 - 22*y**3*21 in the overall expression.\n#Step 3:\nCurrent expression: -20*y**2*21 + (10*y**2)*(-22*y**3 - 20*y**2) - 22*y**3*21\nSimplifying the partial expression: (10*y**2)*(-22*y**3 - 20*y**2)\nExpanding the part (-22*y**3 - 20*y**2) using the distributive property, and we got: (-20*y**2)*(10*y**2) + (10*y**2)*(-22*y**3)\nReplacing (10*y**2)*(-22*y**3 - 20*y**2) with (-20*y**2)*(10*y**2) + (10*y**2)*(-22*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-20*y**2)*(10*y**2) - 20*y**2*21 + (10*y**2)*(-22*y**3) - 22*y**3*21\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*y**3)*21 = -462*y**3\n (-22*y**3)*(10*y**2) = -220*y**5\n (-20*y**2)*21 = -420*y**2\n (-20*y**2)*(10*y**2) = -200*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -220*y**5 - 200*y**4 - 462*y**3 - 420*y**2\nNo more calculations needed.\n-220*y**5 - 200*y**4 - 462*y**3 - 420*y**2", "generated_answer": "-220*y**5 - 200*y**4 - 462*y**3 - 420*y**2", "step_length": 5} {"cot_id": "b181bf1f594747f0a36bd0f9db4713c7744c312b41acc5358610aea1ee18a979", "datapoint": {"question": "Simplify this expression: (45 - 38*z**2)*(-16*z**3 - 79*z**2 - 24*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "608*z**5 + 3002*z**4 + 192*z**3 - 3555*z**2 - 1080*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 664, "polynomial_expr": "(45 - 38*z**2)*(-16*z**3 - 79*z**2 - 24*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (45 - 38*z**2)*(-16*z**3 - 79*z**2 - 24*z)\nExpanding the part (45 - 38*z**2) using the distributive property, and we got: (-38*z**2)*(-16*z**3 - 79*z**2 - 24*z) + 45*(-16*z**3 - 79*z**2 - 24*z)\n#Step 2:\nCurrent expression: (-38*z**2)*(-16*z**3 - 79*z**2 - 24*z) + 45*(-16*z**3 - 79*z**2 - 24*z)\nSimplifying the partial expression: 45*(-16*z**3 - 79*z**2 - 24*z)\nExpanding the part (-16*z**3 - 79*z**2 - 24*z) using the distributive property, and we got: -24*z*45 - 79*z**2*45 - 16*z**3*45\nReplacing 45*(-16*z**3 - 79*z**2 - 24*z) with -24*z*45 - 79*z**2*45 - 16*z**3*45 in the overall expression.\n#Step 3:\nCurrent expression: -24*z*45 - 79*z**2*45 + (-38*z**2)*(-16*z**3 - 79*z**2 - 24*z) - 16*z**3*45\nSimplifying the partial expression: (-38*z**2)*(-16*z**3 - 79*z**2 - 24*z)\nExpanding the part (-16*z**3 - 79*z**2 - 24*z) using the distributive property, and we got: (-24*z)*(-38*z**2) + (-79*z**2)*(-38*z**2) + (-38*z**2)*(-16*z**3)\nReplacing (-38*z**2)*(-16*z**3 - 79*z**2 - 24*z) with (-24*z)*(-38*z**2) + (-79*z**2)*(-38*z**2) + (-38*z**2)*(-16*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-24*z)*(-38*z**2) - 24*z*45 + (-79*z**2)*(-38*z**2) - 79*z**2*45 + (-38*z**2)*(-16*z**3) - 16*z**3*45\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-79*z**2)*45 = -3555*z**2\n (-79*z**2)*(-38*z**2) = 3002*z**4\n (-24*z)*45 = -1080*z\n (-24*z)*(-38*z**2) = 912*z**3\n (-16*z**3)*45 = -720*z**3\n (-16*z**3)*(-38*z**2) = 608*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 608*z**5 + 3002*z**4 - 720*z**3 + 912*z**3 - 3555*z**2 - 1080*z\nCombining like terms, got 608*z**5 + 3002*z**4 + 192*z**3 - 3555*z**2 - 1080*z\n#Step 6:\nCurrent expression: 608*z**5 + 3002*z**4 + 192*z**3 - 3555*z**2 - 1080*z\nNo more calculations needed.\n608*z**5 + 3002*z**4 + 192*z**3 - 3555*z**2 - 1080*z", "generated_answer": "608*z**5 + 3002*z**4 + 192*z**3 - 3555*z**2 - 1080*z", "step_length": 6} {"cot_id": "8572d53917dd6ab183040b083ae8e3eb840c59d74ced455c3f6e55957a88cbb2", "datapoint": {"question": "Calculate the following: (-30*x**3 + 99*x**2)*(30*x**3 - 33*x**2 + 30*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-900*x**6 + 3960*x**5 - 4167*x**4 + 2970*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 665, "polynomial_expr": "(-30*x**3 + 99*x**2)*(30*x**3 - 33*x**2 + 30*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-30*x**3 + 99*x**2)*(30*x**3 - 33*x**2 + 30*x)\nExpanding the part (-30*x**3 + 99*x**2) using the distributive property, and we got: (99*x**2)*(30*x**3 - 33*x**2 + 30*x) + (-30*x**3)*(30*x**3 - 33*x**2 + 30*x)\n#Step 2:\nCurrent expression: (99*x**2)*(30*x**3 - 33*x**2 + 30*x) + (-30*x**3)*(30*x**3 - 33*x**2 + 30*x)\nSimplifying the partial expression: (-30*x**3)*(30*x**3 - 33*x**2 + 30*x)\nExpanding the part (30*x**3 - 33*x**2 + 30*x) using the distributive property, and we got: (30*x)*(-30*x**3) + (-33*x**2)*(-30*x**3) + (-30*x**3)*(30*x**3)\nReplacing (-30*x**3)*(30*x**3 - 33*x**2 + 30*x) with (30*x)*(-30*x**3) + (-33*x**2)*(-30*x**3) + (-30*x**3)*(30*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (30*x)*(-30*x**3) + (-33*x**2)*(-30*x**3) + (99*x**2)*(30*x**3 - 33*x**2 + 30*x) + (-30*x**3)*(30*x**3)\nSimplifying the partial expression: (99*x**2)*(30*x**3 - 33*x**2 + 30*x)\nExpanding the part (30*x**3 - 33*x**2 + 30*x) using the distributive property, and we got: (30*x)*(99*x**2) + (-33*x**2)*(99*x**2) + (99*x**2)*(30*x**3)\nReplacing (99*x**2)*(30*x**3 - 33*x**2 + 30*x) with (30*x)*(99*x**2) + (-33*x**2)*(99*x**2) + (99*x**2)*(30*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (30*x)*(99*x**2) + (30*x)*(-30*x**3) + (-33*x**2)*(99*x**2) + (-33*x**2)*(-30*x**3) + (99*x**2)*(30*x**3) + (-30*x**3)*(30*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*x**2)*(-30*x**3) = 990*x**5\n (-33*x**2)*(99*x**2) = -3267*x**4\n (30*x)*(-30*x**3) = -900*x**4\n (30*x)*(99*x**2) = 2970*x**3\n (30*x**3)*(-30*x**3) = -900*x**6\n (30*x**3)*(99*x**2) = 2970*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -900*x**6 + 990*x**5 + 2970*x**5 - 3267*x**4 - 900*x**4 + 2970*x**3\nCombining like terms, got -900*x**6 + 3960*x**5 - 4167*x**4 + 2970*x**3\n#Step 6:\nCurrent expression: -900*x**6 + 3960*x**5 - 4167*x**4 + 2970*x**3\nNo more calculations needed.\n-900*x**6 + 3960*x**5 - 4167*x**4 + 2970*x**3", "generated_answer": "-900*x**6 + 3960*x**5 - 4167*x**4 + 2970*x**3", "step_length": 6} {"cot_id": "29a751a3de2c875b59179377fdb1fb20f6ce151f5445739cad2d83065e2f8677", "datapoint": {"question": "Simplify this expression: (3 - 28*x**3)*(-39*x**3 + 48*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1092*x**6 - 1344*x**5 - 117*x**3 + 144*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 666, "polynomial_expr": "(3 - 28*x**3)*(-39*x**3 + 48*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (3 - 28*x**3)*(-39*x**3 + 48*x**2)\nExpanding the part (3 - 28*x**3) using the distributive property, and we got: (-28*x**3)*(-39*x**3 + 48*x**2) + 3*(-39*x**3 + 48*x**2)\n#Step 2:\nCurrent expression: (-28*x**3)*(-39*x**3 + 48*x**2) + 3*(-39*x**3 + 48*x**2)\nSimplifying the partial expression: 3*(-39*x**3 + 48*x**2)\nExpanding the part (-39*x**3 + 48*x**2) using the distributive property, and we got: (48*x**2)*3 - 39*x**3*3\nReplacing 3*(-39*x**3 + 48*x**2) with (48*x**2)*3 - 39*x**3*3 in the overall expression.\n#Step 3:\nCurrent expression: (48*x**2)*3 - 39*x**3*3 + (-28*x**3)*(-39*x**3 + 48*x**2)\nSimplifying the partial expression: (-28*x**3)*(-39*x**3 + 48*x**2)\nExpanding the part (-39*x**3 + 48*x**2) using the distributive property, and we got: (48*x**2)*(-28*x**3) + (-39*x**3)*(-28*x**3)\nReplacing (-28*x**3)*(-39*x**3 + 48*x**2) with (48*x**2)*(-28*x**3) + (-39*x**3)*(-28*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (48*x**2)*(-28*x**3) + (48*x**2)*3 + (-39*x**3)*(-28*x**3) - 39*x**3*3\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*x**3)*3 = -117*x**3\n (-39*x**3)*(-28*x**3) = 1092*x**6\n (48*x**2)*3 = 144*x**2\n (48*x**2)*(-28*x**3) = -1344*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1092*x**6 - 1344*x**5 - 117*x**3 + 144*x**2\nNo more calculations needed.\n1092*x**6 - 1344*x**5 - 117*x**3 + 144*x**2", "generated_answer": "1092*x**6 - 1344*x**5 - 117*x**3 + 144*x**2", "step_length": 5} {"cot_id": "8acd8f4031e4a32d9b9b67886e14f3d7100049d8a4d42b1dc8bc308b3dbfd79d", "datapoint": {"question": "Simplify this expression: (5*z + 27)*(-16*z**3 + 32*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-80*z**4 - 272*z**3 + 864*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 667, "polynomial_expr": "(5*z + 27)*(-16*z**3 + 32*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (5*z + 27)*(-16*z**3 + 32*z**2)\nExpanding the part (5*z + 27) using the distributive property, and we got: (5*z)*(-16*z**3 + 32*z**2) + 27*(-16*z**3 + 32*z**2)\n#Step 2:\nCurrent expression: (5*z)*(-16*z**3 + 32*z**2) + 27*(-16*z**3 + 32*z**2)\nSimplifying the partial expression: 27*(-16*z**3 + 32*z**2)\nExpanding the part (-16*z**3 + 32*z**2) using the distributive property, and we got: (32*z**2)*27 - 16*z**3*27\nReplacing 27*(-16*z**3 + 32*z**2) with (32*z**2)*27 - 16*z**3*27 in the overall expression.\n#Step 3:\nCurrent expression: (5*z)*(-16*z**3 + 32*z**2) + (32*z**2)*27 - 16*z**3*27\nSimplifying the partial expression: (5*z)*(-16*z**3 + 32*z**2)\nExpanding the part (-16*z**3 + 32*z**2) using the distributive property, and we got: (5*z)*(32*z**2) + (5*z)*(-16*z**3)\nReplacing (5*z)*(-16*z**3 + 32*z**2) with (5*z)*(32*z**2) + (5*z)*(-16*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (5*z)*(32*z**2) + (5*z)*(-16*z**3) + (32*z**2)*27 - 16*z**3*27\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-16*z**3)*27 = -432*z**3\n (-16*z**3)*(5*z) = -80*z**4\n (32*z**2)*27 = 864*z**2\n (32*z**2)*(5*z) = 160*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -80*z**4 - 432*z**3 + 160*z**3 + 864*z**2\nCombining like terms, got -80*z**4 - 272*z**3 + 864*z**2\n#Step 6:\nCurrent expression: -80*z**4 - 272*z**3 + 864*z**2\nNo more calculations needed.\n-80*z**4 - 272*z**3 + 864*z**2", "generated_answer": "-80*z**4 - 272*z**3 + 864*z**2", "step_length": 6} {"cot_id": "29112ac97b99bab1f54de18a405e5758370d3bbe622e9fd8fb581c3f38b25f77", "datapoint": {"question": "Simplify this expression: (93*y**3 - 27*y)*(14*y**2 - 3*y + 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1302*y**5 - 279*y**4 + 2505*y**3 + 81*y**2 - 837*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 668, "polynomial_expr": "(93*y**3 - 27*y)*(14*y**2 - 3*y + 31)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (93*y**3 - 27*y)*(14*y**2 - 3*y + 31)\nExpanding the part (93*y**3 - 27*y) using the distributive property, and we got: (-27*y)*(14*y**2 - 3*y + 31) + (93*y**3)*(14*y**2 - 3*y + 31)\n#Step 2:\nCurrent expression: (-27*y)*(14*y**2 - 3*y + 31) + (93*y**3)*(14*y**2 - 3*y + 31)\nSimplifying the partial expression: (-27*y)*(14*y**2 - 3*y + 31)\nExpanding the part (14*y**2 - 3*y + 31) using the distributive property, and we got: (-27*y)*(-3*y) + (-27*y)*(14*y**2) + 31*(-27*y)\nReplacing (-27*y)*(14*y**2 - 3*y + 31) with (-27*y)*(-3*y) + (-27*y)*(14*y**2) + 31*(-27*y) in the overall expression.\n#Step 3:\nCurrent expression: (-27*y)*(-3*y) + (-27*y)*(14*y**2) + 31*(-27)*y + (93*y**3)*(14*y**2 - 3*y + 31)\nSimplifying the partial expression: (93*y**3)*(14*y**2 - 3*y + 31)\nExpanding the part (14*y**2 - 3*y + 31) using the distributive property, and we got: (-3*y)*(93*y**3) + 31*(93*y**3) + (14*y**2)*(93*y**3)\nReplacing (93*y**3)*(14*y**2 - 3*y + 31) with (-3*y)*(93*y**3) + 31*(93*y**3) + (14*y**2)*(93*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-27*y)*(-3*y) + (-27*y)*(14*y**2) + (-3*y)*(93*y**3) + 31*93*y**3 + 31*(-27)*y + (14*y**2)*(93*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-3*y)*(-27*y) = 81*y**2\n (-3*y)*(93*y**3) = -279*y**4\n (14*y**2)*(-27*y) = -378*y**3\n (14*y**2)*(93*y**3) = 1302*y**5\n 31*-27*y = -837*y\n 31*93*y**3 = 2883*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1302*y**5 - 279*y**4 - 378*y**3 + 2883*y**3 + 81*y**2 - 837*y\nCombining like terms, got 1302*y**5 - 279*y**4 + 2505*y**3 + 81*y**2 - 837*y\n#Step 6:\nCurrent expression: 1302*y**5 - 279*y**4 + 2505*y**3 + 81*y**2 - 837*y\nNo more calculations needed.\n1302*y**5 - 279*y**4 + 2505*y**3 + 81*y**2 - 837*y", "generated_answer": "1302*y**5 - 279*y**4 + 2505*y**3 + 81*y**2 - 837*y", "step_length": 6} {"cot_id": "b3ad48ef4ed4f98d0e61afd34b430260e2e7c29174c071294a1b63fa637ec808", "datapoint": {"question": "Simplify this expression: (-27*z**2 - 28)*(-7*z**3 + 29*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "189*z**5 - 783*z**4 + 196*z**3 - 812*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 669, "polynomial_expr": "(-27*z**2 - 28)*(-7*z**3 + 29*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-27*z**2 - 28)*(-7*z**3 + 29*z**2)\nExpanding the part (-27*z**2 - 28) using the distributive property, and we got: (-27*z**2)*(-7*z**3 + 29*z**2) - 28*(-7*z**3 + 29*z**2)\n#Step 2:\nCurrent expression: (-27*z**2)*(-7*z**3 + 29*z**2) - 28*(-7*z**3 + 29*z**2)\nSimplifying the partial expression: -28*(-7*z**3 + 29*z**2)\nExpanding the part (-7*z**3 + 29*z**2) using the distributive property, and we got: (29*z**2)*(-28) - 7*z**3*(-28)\nReplacing -28*(-7*z**3 + 29*z**2) with (29*z**2)*(-28) - 7*z**3*(-28) in the overall expression.\n#Step 3:\nCurrent expression: (-27*z**2)*(-7*z**3 + 29*z**2) + (29*z**2)*(-28) - 7*z**3*(-28)\nSimplifying the partial expression: (-27*z**2)*(-7*z**3 + 29*z**2)\nExpanding the part (-7*z**3 + 29*z**2) using the distributive property, and we got: (-27*z**2)*(29*z**2) + (-27*z**2)*(-7*z**3)\nReplacing (-27*z**2)*(-7*z**3 + 29*z**2) with (-27*z**2)*(29*z**2) + (-27*z**2)*(-7*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-27*z**2)*(29*z**2) + (-27*z**2)*(-7*z**3) + (29*z**2)*(-28) - 7*z**3*(-28)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-7*z**3)*-28 = 196*z**3\n (-7*z**3)*(-27*z**2) = 189*z**5\n (29*z**2)*-28 = -812*z**2\n (29*z**2)*(-27*z**2) = -783*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 189*z**5 - 783*z**4 + 196*z**3 - 812*z**2\nNo more calculations needed.\n189*z**5 - 783*z**4 + 196*z**3 - 812*z**2", "generated_answer": "189*z**5 - 783*z**4 + 196*z**3 - 812*z**2", "step_length": 5} {"cot_id": "4c4bd4c87872c681ceb9a56127669a2fee6c698c38f4f75d2c154a858caa830b", "datapoint": {"question": "Calculate the following: (2*y**2 - 9*y)*(-6*y**2 - 42*y + 18)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-12*y**4 - 30*y**3 + 414*y**2 - 162*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 670, "polynomial_expr": "(2*y**2 - 9*y)*(-6*y**2 - 42*y + 18)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2*y**2 - 9*y)*(-6*y**2 - 42*y + 18)\nExpanding the part (2*y**2 - 9*y) using the distributive property, and we got: (-9*y)*(-6*y**2 - 42*y + 18) + (2*y**2)*(-6*y**2 - 42*y + 18)\n#Step 2:\nCurrent expression: (-9*y)*(-6*y**2 - 42*y + 18) + (2*y**2)*(-6*y**2 - 42*y + 18)\nSimplifying the partial expression: (-9*y)*(-6*y**2 - 42*y + 18)\nExpanding the part (-6*y**2 - 42*y + 18) using the distributive property, and we got: (-42*y)*(-9*y) + (-9*y)*(-6*y**2) + 18*(-9*y)\nReplacing (-9*y)*(-6*y**2 - 42*y + 18) with (-42*y)*(-9*y) + (-9*y)*(-6*y**2) + 18*(-9*y) in the overall expression.\n#Step 3:\nCurrent expression: (-42*y)*(-9*y) + (-9*y)*(-6*y**2) + 18*(-9)*y + (2*y**2)*(-6*y**2 - 42*y + 18)\nSimplifying the partial expression: (2*y**2)*(-6*y**2 - 42*y + 18)\nExpanding the part (-6*y**2 - 42*y + 18) using the distributive property, and we got: (-42*y)*(2*y**2) + 18*(2*y**2) + (-6*y**2)*(2*y**2)\nReplacing (2*y**2)*(-6*y**2 - 42*y + 18) with (-42*y)*(2*y**2) + 18*(2*y**2) + (-6*y**2)*(2*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-42*y)*(-9*y) + (-42*y)*(2*y**2) + (-9*y)*(-6*y**2) + 18*2*y**2 + 18*(-9)*y + (-6*y**2)*(2*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*y)*(-9*y) = 378*y**2\n (-42*y)*(2*y**2) = -84*y**3\n (-6*y**2)*(-9*y) = 54*y**3\n (-6*y**2)*(2*y**2) = -12*y**4\n 18*-9*y = -162*y\n 18*2*y**2 = 36*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -12*y**4 - 84*y**3 + 54*y**3 + 36*y**2 + 378*y**2 - 162*y\nCombining like terms, got -12*y**4 - 30*y**3 + 414*y**2 - 162*y\n#Step 6:\nCurrent expression: -12*y**4 - 30*y**3 + 414*y**2 - 162*y\nNo more calculations needed.\n-12*y**4 - 30*y**3 + 414*y**2 - 162*y", "generated_answer": "-12*y**4 - 30*y**3 + 414*y**2 - 162*y", "step_length": 6} {"cot_id": "629f8786cbf929e58c2d9ac5cdffd3d522dc7e827c37cb501daa9d5b0fca30df", "datapoint": {"question": "Calculate the following: (-15*y**3 - 8*y**2)*(44*y**3 + 48*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-660*y**6 - 1072*y**5 - 384*y**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 671, "polynomial_expr": "(-15*y**3 - 8*y**2)*(44*y**3 + 48*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-15*y**3 - 8*y**2)*(44*y**3 + 48*y**2)\nExpanding the part (-15*y**3 - 8*y**2) using the distributive property, and we got: (-8*y**2)*(44*y**3 + 48*y**2) + (-15*y**3)*(44*y**3 + 48*y**2)\n#Step 2:\nCurrent expression: (-8*y**2)*(44*y**3 + 48*y**2) + (-15*y**3)*(44*y**3 + 48*y**2)\nSimplifying the partial expression: (-15*y**3)*(44*y**3 + 48*y**2)\nExpanding the part (44*y**3 + 48*y**2) using the distributive property, and we got: (48*y**2)*(-15*y**3) + (-15*y**3)*(44*y**3)\nReplacing (-15*y**3)*(44*y**3 + 48*y**2) with (48*y**2)*(-15*y**3) + (-15*y**3)*(44*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-8*y**2)*(44*y**3 + 48*y**2) + (48*y**2)*(-15*y**3) + (-15*y**3)*(44*y**3)\nSimplifying the partial expression: (-8*y**2)*(44*y**3 + 48*y**2)\nExpanding the part (44*y**3 + 48*y**2) using the distributive property, and we got: (-8*y**2)*(48*y**2) + (-8*y**2)*(44*y**3)\nReplacing (-8*y**2)*(44*y**3 + 48*y**2) with (-8*y**2)*(48*y**2) + (-8*y**2)*(44*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-8*y**2)*(48*y**2) + (-8*y**2)*(44*y**3) + (48*y**2)*(-15*y**3) + (-15*y**3)*(44*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (44*y**3)*(-15*y**3) = -660*y**6\n (44*y**3)*(-8*y**2) = -352*y**5\n (48*y**2)*(-15*y**3) = -720*y**5\n (48*y**2)*(-8*y**2) = -384*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -660*y**6 - 720*y**5 - 352*y**5 - 384*y**4\nCombining like terms, got -660*y**6 - 1072*y**5 - 384*y**4\n#Step 6:\nCurrent expression: -660*y**6 - 1072*y**5 - 384*y**4\nNo more calculations needed.\n-660*y**6 - 1072*y**5 - 384*y**4", "generated_answer": "-660*y**6 - 1072*y**5 - 384*y**4", "step_length": 6} {"cot_id": "0c9e7f196eb3704ff969a46eb73745754f032638c97df672795f9a96cba66a12", "datapoint": {"question": "Simplify this expression: (-10*x**3 - 86*x)*(-8*x**2 + 47*x - 4)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "80*x**5 - 470*x**4 + 728*x**3 - 4042*x**2 + 344*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 672, "polynomial_expr": "(-10*x**3 - 86*x)*(-8*x**2 + 47*x - 4)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-10*x**3 - 86*x)*(-8*x**2 + 47*x - 4)\nExpanding the part (-10*x**3 - 86*x) using the distributive property, and we got: (-86*x)*(-8*x**2 + 47*x - 4) + (-10*x**3)*(-8*x**2 + 47*x - 4)\n#Step 2:\nCurrent expression: (-86*x)*(-8*x**2 + 47*x - 4) + (-10*x**3)*(-8*x**2 + 47*x - 4)\nSimplifying the partial expression: (-86*x)*(-8*x**2 + 47*x - 4)\nExpanding the part (-8*x**2 + 47*x - 4) using the distributive property, and we got: (-86*x)*(47*x) + (-86*x)*(-8*x**2) - (-1)*344*x\nReplacing (-86*x)*(-8*x**2 + 47*x - 4) with (-86*x)*(47*x) + (-86*x)*(-8*x**2) - (-1)*344*x in the overall expression.\n#Step 3:\nCurrent expression: (-86*x)*(47*x) + (-86*x)*(-8*x**2) - 4*(-86)*x + (-10*x**3)*(-8*x**2 + 47*x - 4)\nSimplifying the partial expression: (-10*x**3)*(-8*x**2 + 47*x - 4)\nExpanding the part (-8*x**2 + 47*x - 4) using the distributive property, and we got: -(-1)*40*x**3 + (47*x)*(-10*x**3) + (-8*x**2)*(-10*x**3)\nReplacing (-10*x**3)*(-8*x**2 + 47*x - 4) with -(-1)*40*x**3 + (47*x)*(-10*x**3) + (-8*x**2)*(-10*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-86*x)*(47*x) + (-86*x)*(-8*x**2) - 4*(-10)*x**3 - 4*(-86)*x + (47*x)*(-10*x**3) + (-8*x**2)*(-10*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-8*x**2)*(-86*x) = 688*x**3\n (-8*x**2)*(-10*x**3) = 80*x**5\n (47*x)*(-86*x) = -4042*x**2\n (47*x)*(-10*x**3) = -470*x**4\n -4*-86*x = 344*x\n -4*-10*x**3 = 40*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 80*x**5 - 470*x**4 + 40*x**3 + 688*x**3 - 4042*x**2 + 344*x\nCombining like terms, got 80*x**5 - 470*x**4 + 728*x**3 - 4042*x**2 + 344*x\n#Step 6:\nCurrent expression: 80*x**5 - 470*x**4 + 728*x**3 - 4042*x**2 + 344*x\nNo more calculations needed.\n80*x**5 - 470*x**4 + 728*x**3 - 4042*x**2 + 344*x", "generated_answer": "80*x**5 - 470*x**4 + 728*x**3 - 4042*x**2 + 344*x", "step_length": 6} {"cot_id": "ba8404ca4e4b6107513e1d6e5679a39ea6f6862e480dafcbe9a4e6273dbad1af", "datapoint": {"question": "Calculate the following: (-16*z**3 + 9*z)*(7*z**3 - 46*z**2 + 36*z + 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-112*z**6 + 736*z**5 - 513*z**4 - 1022*z**3 + 324*z**2 + 342*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 673, "polynomial_expr": "(-16*z**3 + 9*z)*(7*z**3 - 46*z**2 + 36*z + 38)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-16*z**3 + 9*z)*(7*z**3 - 46*z**2 + 36*z + 38)\nExpanding the part (-16*z**3 + 9*z) using the distributive property, and we got: (9*z)*(7*z**3 - 46*z**2 + 36*z + 38) + (-16*z**3)*(7*z**3 - 46*z**2 + 36*z + 38)\n#Step 2:\nCurrent expression: (9*z)*(7*z**3 - 46*z**2 + 36*z + 38) + (-16*z**3)*(7*z**3 - 46*z**2 + 36*z + 38)\nSimplifying the partial expression: (-16*z**3)*(7*z**3 - 46*z**2 + 36*z + 38)\nExpanding the part (7*z**3 - 46*z**2 + 36*z + 38) using the distributive property, and we got: 38*(-16*z**3) + (36*z)*(-16*z**3) + (-46*z**2)*(-16*z**3) + (-16*z**3)*(7*z**3)\nReplacing (-16*z**3)*(7*z**3 - 46*z**2 + 36*z + 38) with 38*(-16*z**3) + (36*z)*(-16*z**3) + (-46*z**2)*(-16*z**3) + (-16*z**3)*(7*z**3) in the overall expression.\n#Step 3:\nCurrent expression: 38*(-16)*z**3 + (9*z)*(7*z**3 - 46*z**2 + 36*z + 38) + (36*z)*(-16*z**3) + (-46*z**2)*(-16*z**3) + (-16*z**3)*(7*z**3)\nSimplifying the partial expression: (9*z)*(7*z**3 - 46*z**2 + 36*z + 38)\nExpanding the part (7*z**3 - 46*z**2 + 36*z + 38) using the distributive property, and we got: 38*(9*z) + (9*z)*(36*z) + (9*z)*(-46*z**2) + (9*z)*(7*z**3)\nReplacing (9*z)*(7*z**3 - 46*z**2 + 36*z + 38) with 38*(9*z) + (9*z)*(36*z) + (9*z)*(-46*z**2) + (9*z)*(7*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 38*(-16)*z**3 + 38*9*z + (9*z)*(36*z) + (9*z)*(-46*z**2) + (9*z)*(7*z**3) + (36*z)*(-16*z**3) + (-46*z**2)*(-16*z**3) + (-16*z**3)*(7*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*z**2)*(-16*z**3) = 736*z**5\n (-46*z**2)*(9*z) = -414*z**3\n (7*z**3)*(-16*z**3) = -112*z**6\n (7*z**3)*(9*z) = 63*z**4\n (36*z)*(-16*z**3) = -576*z**4\n (36*z)*(9*z) = 324*z**2\n 38*-16*z**3 = -608*z**3\n 38*9*z = 342*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -112*z**6 + 736*z**5 - 576*z**4 + 63*z**4 - 608*z**3 - 414*z**3 + 324*z**2 + 342*z\nCombining like terms, got -112*z**6 + 736*z**5 - 513*z**4 - 1022*z**3 + 324*z**2 + 342*z\n#Step 6:\nCurrent expression: -112*z**6 + 736*z**5 - 513*z**4 - 1022*z**3 + 324*z**2 + 342*z\nNo more calculations needed.\n-112*z**6 + 736*z**5 - 513*z**4 - 1022*z**3 + 324*z**2 + 342*z", "generated_answer": "-112*z**6 + 736*z**5 - 513*z**4 - 1022*z**3 + 324*z**2 + 342*z", "step_length": 6} {"cot_id": "abf8db16f5125e1fec04866083d9249311f1fc649d9ca5806c4d245c5ed49137", "datapoint": {"question": "Simplify this expression: (16 - 71*x**3)*(78 - 10*x**3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "710*x**6 - 5698*x**3 + 1248", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 674, "polynomial_expr": "(16 - 71*x**3)*(78 - 10*x**3)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (16 - 71*x**3)*(78 - 10*x**3)\nExpanding the part (16 - 71*x**3) using the distributive property, and we got: (-71*x**3)*(78 - 10*x**3) + 16*(78 - 10*x**3)\n#Step 2:\nCurrent expression: (-71*x**3)*(78 - 10*x**3) + 16*(78 - 10*x**3)\nSimplifying the partial expression: 16*(78 - 10*x**3)\nExpanding the part (78 - 10*x**3) using the distributive property, and we got: -10*x**3*16 + 78*16\nReplacing 16*(78 - 10*x**3) with -10*x**3*16 + 78*16 in the overall expression.\n#Step 3:\nCurrent expression: (-71*x**3)*(78 - 10*x**3) - 10*x**3*16 + 1248\nSimplifying the partial expression: (-71*x**3)*(78 - 10*x**3)\nExpanding the part (78 - 10*x**3) using the distributive property, and we got: 78*(-71*x**3) + (-71*x**3)*(-10*x**3)\nReplacing (-71*x**3)*(78 - 10*x**3) with 78*(-71*x**3) + (-71*x**3)*(-10*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 78*(-71)*x**3 + (-71*x**3)*(-10*x**3) - 10*x**3*16 + 1248\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*x**3)*16 = -160*x**3\n (-10*x**3)*(-71*x**3) = 710*x**6\n 78*-71*x**3 = -5538*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 710*x**6 - 5538*x**3 - 160*x**3 + 1248\nCombining like terms, got 710*x**6 - 5698*x**3 + 1248\n#Step 6:\nCurrent expression: 710*x**6 - 5698*x**3 + 1248\nNo more calculations needed.\n710*x**6 - 5698*x**3 + 1248", "generated_answer": "710*x**6 - 5698*x**3 + 1248", "step_length": 6} {"cot_id": "d9aed25668c1bfa81c28ee88e06b1d9997ef98f1e19093f4a9738e2caf40c40a", "datapoint": {"question": "Calculate the following: 17*x**3*(57*x**3 + 28*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "969*x**6 + 476*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 675, "polynomial_expr": "17*x**3*(57*x**3 + 28*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 17*x**3*(57*x**3 + 28*x)\nExpanding the part (57*x**3 + 28*x) using the distributive property, and we got: (28*x)*(17*x**3) + (17*x**3)*(57*x**3)\n#Step 2:\nCurrent expression: (28*x)*(17*x**3) + (17*x**3)*(57*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (28*x)*(17*x**3) = 476*x**4\n (57*x**3)*(17*x**3) = 969*x**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 969*x**6 + 476*x**4\nNo more calculations needed.\n969*x**6 + 476*x**4", "generated_answer": "969*x**6 + 476*x**4", "step_length": 3} {"cot_id": "8c7cec136804df2bb25bc99d0a384005a7d2a5db93e4151f8125fbafb41ed5a6", "datapoint": {"question": "Calculate the following: (-9*y**2 + 37*y)*(64*y**2 + 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-576*y**4 + 2368*y**3 - 252*y**2 + 1036*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 676, "polynomial_expr": "(-9*y**2 + 37*y)*(64*y**2 + 28)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-9*y**2 + 37*y)*(64*y**2 + 28)\nExpanding the part (64*y**2 + 28) using the distributive property, and we got: (64*y**2)*(-9*y**2 + 37*y) + 28*(-9*y**2 + 37*y)\n#Step 2:\nCurrent expression: (64*y**2)*(-9*y**2 + 37*y) + 28*(-9*y**2 + 37*y)\nSimplifying the partial expression: 28*(-9*y**2 + 37*y)\nExpanding the part (-9*y**2 + 37*y) using the distributive property, and we got: (37*y)*28 - 9*y**2*28\nReplacing 28*(-9*y**2 + 37*y) with (37*y)*28 - 9*y**2*28 in the overall expression.\n#Step 3:\nCurrent expression: (37*y)*28 - 9*y**2*28 + (64*y**2)*(-9*y**2 + 37*y)\nSimplifying the partial expression: (64*y**2)*(-9*y**2 + 37*y)\nExpanding the part (-9*y**2 + 37*y) using the distributive property, and we got: (37*y)*(64*y**2) + (-9*y**2)*(64*y**2)\nReplacing (64*y**2)*(-9*y**2 + 37*y) with (37*y)*(64*y**2) + (-9*y**2)*(64*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (37*y)*(64*y**2) + (37*y)*28 + (-9*y**2)*(64*y**2) - 9*y**2*28\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-9*y**2)*28 = -252*y**2\n (-9*y**2)*(64*y**2) = -576*y**4\n (37*y)*28 = 1036*y\n (37*y)*(64*y**2) = 2368*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -576*y**4 + 2368*y**3 - 252*y**2 + 1036*y\nNo more calculations needed.\n-576*y**4 + 2368*y**3 - 252*y**2 + 1036*y", "generated_answer": "-576*y**4 + 2368*y**3 - 252*y**2 + 1036*y", "step_length": 5} {"cot_id": "984f3a1631dda39eb64ccb07d99c06733aac890bb830587d1c1ed01e1943aa2c", "datapoint": {"question": "Simplify this expression: (-2*y - 10)*(82*y**2 + 54*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-164*y**3 - 928*y**2 - 540*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 677, "polynomial_expr": "(-2*y - 10)*(82*y**2 + 54*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-2*y - 10)*(82*y**2 + 54*y)\nExpanding the part (-2*y - 10) using the distributive property, and we got: (-2*y)*(82*y**2 + 54*y) - 10*(82*y**2 + 54*y)\n#Step 2:\nCurrent expression: (-2*y)*(82*y**2 + 54*y) - 10*(82*y**2 + 54*y)\nSimplifying the partial expression: -10*(82*y**2 + 54*y)\nExpanding the part (82*y**2 + 54*y) using the distributive property, and we got: (54*y)*(-10) + (82*y**2)*(-10)\nReplacing -10*(82*y**2 + 54*y) with (54*y)*(-10) + (82*y**2)*(-10) in the overall expression.\n#Step 3:\nCurrent expression: (-2*y)*(82*y**2 + 54*y) + (54*y)*(-10) + (82*y**2)*(-10)\nSimplifying the partial expression: (-2*y)*(82*y**2 + 54*y)\nExpanding the part (82*y**2 + 54*y) using the distributive property, and we got: (-2*y)*(54*y) + (-2*y)*(82*y**2)\nReplacing (-2*y)*(82*y**2 + 54*y) with (-2*y)*(54*y) + (-2*y)*(82*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-2*y)*(54*y) + (-2*y)*(82*y**2) + (54*y)*(-10) + (82*y**2)*(-10)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (54*y)*-10 = -540*y\n (54*y)*(-2*y) = -108*y**2\n (82*y**2)*-10 = -820*y**2\n (82*y**2)*(-2*y) = -164*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -164*y**3 - 820*y**2 - 108*y**2 - 540*y\nCombining like terms, got -164*y**3 - 928*y**2 - 540*y\n#Step 6:\nCurrent expression: -164*y**3 - 928*y**2 - 540*y\nNo more calculations needed.\n-164*y**3 - 928*y**2 - 540*y", "generated_answer": "-164*y**3 - 928*y**2 - 540*y", "step_length": 6} {"cot_id": "a110cbeeb924b7e874e2fe11b04ed59bdc4584f044797f56b8d89d3871d67518", "datapoint": {"question": "Calculate the following: (48 - 29*z**2)*(39*z**2 - 28*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1131*z**4 + 812*z**3 + 1872*z**2 - 1344*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 678, "polynomial_expr": "(48 - 29*z**2)*(39*z**2 - 28*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (48 - 29*z**2)*(39*z**2 - 28*z)\nExpanding the part (48 - 29*z**2) using the distributive property, and we got: (-29*z**2)*(39*z**2 - 28*z) + 48*(39*z**2 - 28*z)\n#Step 2:\nCurrent expression: (-29*z**2)*(39*z**2 - 28*z) + 48*(39*z**2 - 28*z)\nSimplifying the partial expression: 48*(39*z**2 - 28*z)\nExpanding the part (39*z**2 - 28*z) using the distributive property, and we got: -28*z*48 + (39*z**2)*48\nReplacing 48*(39*z**2 - 28*z) with -28*z*48 + (39*z**2)*48 in the overall expression.\n#Step 3:\nCurrent expression: -28*z*48 + (-29*z**2)*(39*z**2 - 28*z) + (39*z**2)*48\nSimplifying the partial expression: (-29*z**2)*(39*z**2 - 28*z)\nExpanding the part (39*z**2 - 28*z) using the distributive property, and we got: (-28*z)*(-29*z**2) + (-29*z**2)*(39*z**2)\nReplacing (-29*z**2)*(39*z**2 - 28*z) with (-28*z)*(-29*z**2) + (-29*z**2)*(39*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-28*z)*(-29*z**2) - 28*z*48 + (-29*z**2)*(39*z**2) + (39*z**2)*48\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*z)*48 = -1344*z\n (-28*z)*(-29*z**2) = 812*z**3\n (39*z**2)*48 = 1872*z**2\n (39*z**2)*(-29*z**2) = -1131*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1131*z**4 + 812*z**3 + 1872*z**2 - 1344*z\nNo more calculations needed.\n-1131*z**4 + 812*z**3 + 1872*z**2 - 1344*z", "generated_answer": "-1131*z**4 + 812*z**3 + 1872*z**2 - 1344*z", "step_length": 5} {"cot_id": "45f617bca0e42f51f924251bdcb9cd0c146cf4a8e3ed0c206e51f5fc018cc79e", "datapoint": {"question": "Calculate the following: -2829*x**3 + 3381*x**2\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2829*x**3 + 3381*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 679, "polynomial_expr": "-2829*x**3 + 3381*x**2", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -2829*x**3 + 3381*x**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -2829*x**3 + 3381*x**2\nNo more calculations needed.\n-2829*x**3 + 3381*x**2", "generated_answer": "-2829*x**3 + 3381*x**2", "step_length": 2} {"cot_id": "55f488b0378a8e1b1c3dd265bffead6fd313967b7dfa0d2dd6497c1b2f9c5861", "datapoint": {"question": "Calculate the following: (18 - 20*z**2)*(-90*z**3 - 31*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1800*z**5 - 1000*z**3 - 558*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 680, "polynomial_expr": "(18 - 20*z**2)*(-90*z**3 - 31*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (18 - 20*z**2)*(-90*z**3 - 31*z)\nExpanding the part (18 - 20*z**2) using the distributive property, and we got: (-20*z**2)*(-90*z**3 - 31*z) + 18*(-90*z**3 - 31*z)\n#Step 2:\nCurrent expression: (-20*z**2)*(-90*z**3 - 31*z) + 18*(-90*z**3 - 31*z)\nSimplifying the partial expression: 18*(-90*z**3 - 31*z)\nExpanding the part (-90*z**3 - 31*z) using the distributive property, and we got: -31*z*18 - 90*z**3*18\nReplacing 18*(-90*z**3 - 31*z) with -31*z*18 - 90*z**3*18 in the overall expression.\n#Step 3:\nCurrent expression: -31*z*18 + (-20*z**2)*(-90*z**3 - 31*z) - 90*z**3*18\nSimplifying the partial expression: (-20*z**2)*(-90*z**3 - 31*z)\nExpanding the part (-90*z**3 - 31*z) using the distributive property, and we got: (-31*z)*(-20*z**2) + (-20*z**2)*(-90*z**3)\nReplacing (-20*z**2)*(-90*z**3 - 31*z) with (-31*z)*(-20*z**2) + (-20*z**2)*(-90*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-31*z)*(-20*z**2) - 31*z*18 + (-20*z**2)*(-90*z**3) - 90*z**3*18\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-90*z**3)*18 = -1620*z**3\n (-90*z**3)*(-20*z**2) = 1800*z**5\n (-31*z)*18 = -558*z\n (-31*z)*(-20*z**2) = 620*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1800*z**5 - 1620*z**3 + 620*z**3 - 558*z\nCombining like terms, got 1800*z**5 - 1000*z**3 - 558*z\n#Step 6:\nCurrent expression: 1800*z**5 - 1000*z**3 - 558*z\nNo more calculations needed.\n1800*z**5 - 1000*z**3 - 558*z", "generated_answer": "1800*z**5 - 1000*z**3 - 558*z", "step_length": 6} {"cot_id": "49e902f7249ce86e6540818a6413730b7b92609dff05aee01f3aea46cc5ba18b", "datapoint": {"question": "Calculate the following: -37*z**2*(46*z**3 + 13*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1702*z**5 - 481*z**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 682, "polynomial_expr": "-37*z**2*(46*z**3 + 13*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -37*z**2*(46*z**3 + 13*z**2)\nExpanding the part (46*z**3 + 13*z**2) using the distributive property, and we got: (-37*z**2)*(13*z**2) + (-37*z**2)*(46*z**3)\n#Step 2:\nCurrent expression: (-37*z**2)*(13*z**2) + (-37*z**2)*(46*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (13*z**2)*(-37*z**2) = -481*z**4\n (46*z**3)*(-37*z**2) = -1702*z**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1702*z**5 - 481*z**4\nNo more calculations needed.\n-1702*z**5 - 481*z**4", "generated_answer": "-1702*z**5 - 481*z**4", "step_length": 3} {"cot_id": "ece7497aaa30917e48ac3064a18a8a4d25929b8bc4a6ff2884918bcc2daaf2c5", "datapoint": {"question": "Simplify this expression: (21 - 29*x)*(x**2 - 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-29*x**3 + 21*x**2 + 1276*x - 924", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 683, "polynomial_expr": "(21 - 29*x)*(x**2 - 44)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21 - 29*x)*(x**2 - 44)\nExpanding the part (x**2 - 44) using the distributive property, and we got: x**2*(21 - 29*x) - 44*(21 - 29*x)\n#Step 2:\nCurrent expression: x**2*(21 - 29*x) - 44*(21 - 29*x)\nSimplifying the partial expression: -44*(21 - 29*x)\nExpanding the part (21 - 29*x) using the distributive property, and we got: -29*x*(-44) + 21*(-44)\nReplacing -44*(21 - 29*x) with -29*x*(-44) + 21*(-44) in the overall expression.\n#Step 3:\nCurrent expression: -29*x*(-44) + x**2*(21 - 29*x) - 924\nSimplifying the partial expression: x**2*(21 - 29*x)\nExpanding the part (21 - 29*x) using the distributive property, and we got: (-29*x)*x**2 + 21*x**2\nReplacing x**2*(21 - 29*x) with (-29*x)*x**2 + 21*x**2 in the overall expression.\n#Step 4:\nCurrent expression: (-29*x)*x**2 - 29*x*(-44) + 21*x**2 - 924\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*x)*-44 = 1276*x\n (-29*x)*x**2 = -29*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -29*x**3 + 21*x**2 + 1276*x - 924\nNo more calculations needed.\n-29*x**3 + 21*x**2 + 1276*x - 924", "generated_answer": "-29*x**3 + 21*x**2 + 1276*x - 924", "step_length": 5} {"cot_id": "f6203c0b5165769c4845e624950b68469c5e785705e24bddfb37ff3c5c25ad93", "datapoint": {"question": "Simplify this expression: (53*y**2 + 35)*(31*y**3 + 5*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1643*y**5 + 265*y**4 + 1085*y**3 + 175*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 684, "polynomial_expr": "(53*y**2 + 35)*(31*y**3 + 5*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (53*y**2 + 35)*(31*y**3 + 5*y**2)\nExpanding the part (53*y**2 + 35) using the distributive property, and we got: (53*y**2)*(31*y**3 + 5*y**2) + 35*(31*y**3 + 5*y**2)\n#Step 2:\nCurrent expression: (53*y**2)*(31*y**3 + 5*y**2) + 35*(31*y**3 + 5*y**2)\nSimplifying the partial expression: 35*(31*y**3 + 5*y**2)\nExpanding the part (31*y**3 + 5*y**2) using the distributive property, and we got: (5*y**2)*35 + (31*y**3)*35\nReplacing 35*(31*y**3 + 5*y**2) with (5*y**2)*35 + (31*y**3)*35 in the overall expression.\n#Step 3:\nCurrent expression: (5*y**2)*35 + (53*y**2)*(31*y**3 + 5*y**2) + (31*y**3)*35\nSimplifying the partial expression: (53*y**2)*(31*y**3 + 5*y**2)\nExpanding the part (31*y**3 + 5*y**2) using the distributive property, and we got: (5*y**2)*(53*y**2) + (53*y**2)*(31*y**3)\nReplacing (53*y**2)*(31*y**3 + 5*y**2) with (5*y**2)*(53*y**2) + (53*y**2)*(31*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (5*y**2)*(53*y**2) + (5*y**2)*35 + (53*y**2)*(31*y**3) + (31*y**3)*35\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (5*y**2)*35 = 175*y**2\n (5*y**2)*(53*y**2) = 265*y**4\n (31*y**3)*35 = 1085*y**3\n (31*y**3)*(53*y**2) = 1643*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1643*y**5 + 265*y**4 + 1085*y**3 + 175*y**2\nNo more calculations needed.\n1643*y**5 + 265*y**4 + 1085*y**3 + 175*y**2", "generated_answer": "1643*y**5 + 265*y**4 + 1085*y**3 + 175*y**2", "step_length": 5} {"cot_id": "f447b088e5b504cdf1a7e0804f3909288ca952215c8cbe0b182a9a2abb95505b", "datapoint": {"question": "Simplify this expression: -1209*z**3 - 124*z**2 + 2232\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1209*z**3 - 124*z**2 + 2232", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 685, "polynomial_expr": "-1209*z**3 - 124*z**2 + 2232", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -1209*z**3 - 124*z**2 + 2232\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -1209*z**3 - 124*z**2 + 2232\nNo more calculations needed.\n-1209*z**3 - 124*z**2 + 2232", "generated_answer": "-1209*z**3 - 124*z**2 + 2232", "step_length": 2} {"cot_id": "f54c0393e704379317427119d4e37d6c98fc508a6e9fe8446c802f764fa2a4af", "datapoint": {"question": "Simplify this expression: (-17*x**2 + 69*x)*(-15*x**3 - 3*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "255*x**5 - 984*x**4 - 207*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 686, "polynomial_expr": "(-17*x**2 + 69*x)*(-15*x**3 - 3*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-17*x**2 + 69*x)*(-15*x**3 - 3*x**2)\nExpanding the part (-17*x**2 + 69*x) using the distributive property, and we got: (69*x)*(-15*x**3 - 3*x**2) + (-17*x**2)*(-15*x**3 - 3*x**2)\n#Step 2:\nCurrent expression: (69*x)*(-15*x**3 - 3*x**2) + (-17*x**2)*(-15*x**3 - 3*x**2)\nSimplifying the partial expression: (-17*x**2)*(-15*x**3 - 3*x**2)\nExpanding the part (-15*x**3 - 3*x**2) using the distributive property, and we got: (-17*x**2)*(-3*x**2) + (-17*x**2)*(-15*x**3)\nReplacing (-17*x**2)*(-15*x**3 - 3*x**2) with (-17*x**2)*(-3*x**2) + (-17*x**2)*(-15*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (69*x)*(-15*x**3 - 3*x**2) + (-17*x**2)*(-3*x**2) + (-17*x**2)*(-15*x**3)\nSimplifying the partial expression: (69*x)*(-15*x**3 - 3*x**2)\nExpanding the part (-15*x**3 - 3*x**2) using the distributive property, and we got: (69*x)*(-3*x**2) + (69*x)*(-15*x**3)\nReplacing (69*x)*(-15*x**3 - 3*x**2) with (69*x)*(-3*x**2) + (69*x)*(-15*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (69*x)*(-3*x**2) + (69*x)*(-15*x**3) + (-17*x**2)*(-3*x**2) + (-17*x**2)*(-15*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-15*x**3)*(-17*x**2) = 255*x**5\n (-15*x**3)*(69*x) = -1035*x**4\n (-3*x**2)*(-17*x**2) = 51*x**4\n (-3*x**2)*(69*x) = -207*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 255*x**5 - 1035*x**4 + 51*x**4 - 207*x**3\nCombining like terms, got 255*x**5 - 984*x**4 - 207*x**3\n#Step 6:\nCurrent expression: 255*x**5 - 984*x**4 - 207*x**3\nNo more calculations needed.\n255*x**5 - 984*x**4 - 207*x**3", "generated_answer": "255*x**5 - 984*x**4 - 207*x**3", "step_length": 6} {"cot_id": "8a438fac294d663d6064e9484bae19c1934e05717f1417417a0eb1ce9479f84a", "datapoint": {"question": "Simplify this expression: (19*z**3 + 43)*(37*z**3 + 6*z**2 - 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "703*z**6 + 114*z**5 + 869*z**3 + 258*z**2 - 1634", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 687, "polynomial_expr": "(19*z**3 + 43)*(37*z**3 + 6*z**2 - 38)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (19*z**3 + 43)*(37*z**3 + 6*z**2 - 38)\nExpanding the part (19*z**3 + 43) using the distributive property, and we got: (19*z**3)*(37*z**3 + 6*z**2 - 38) + 43*(37*z**3 + 6*z**2 - 38)\n#Step 2:\nCurrent expression: (19*z**3)*(37*z**3 + 6*z**2 - 38) + 43*(37*z**3 + 6*z**2 - 38)\nSimplifying the partial expression: 43*(37*z**3 + 6*z**2 - 38)\nExpanding the part (37*z**3 + 6*z**2 - 38) using the distributive property, and we got: (6*z**2)*43 + (37*z**3)*43 - 38*43\nReplacing 43*(37*z**3 + 6*z**2 - 38) with (6*z**2)*43 + (37*z**3)*43 - 38*43 in the overall expression.\n#Step 3:\nCurrent expression: (6*z**2)*43 + (19*z**3)*(37*z**3 + 6*z**2 - 38) + (37*z**3)*43 - 1634\nSimplifying the partial expression: (19*z**3)*(37*z**3 + 6*z**2 - 38)\nExpanding the part (37*z**3 + 6*z**2 - 38) using the distributive property, and we got: -722*z**3 + (6*z**2)*(19*z**3) + (19*z**3)*(37*z**3)\nReplacing (19*z**3)*(37*z**3 + 6*z**2 - 38) with -722*z**3 + (6*z**2)*(19*z**3) + (19*z**3)*(37*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -38*19*z**3 + (6*z**2)*(19*z**3) + (6*z**2)*43 + (19*z**3)*(37*z**3) + (37*z**3)*43 - 1634\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (6*z**2)*43 = 258*z**2\n (6*z**2)*(19*z**3) = 114*z**5\n (37*z**3)*43 = 1591*z**3\n (37*z**3)*(19*z**3) = 703*z**6\n -38*19*z**3 = -722*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 703*z**6 + 114*z**5 - 722*z**3 + 1591*z**3 + 258*z**2 - 1634\nCombining like terms, got 703*z**6 + 114*z**5 + 869*z**3 + 258*z**2 - 1634\n#Step 6:\nCurrent expression: 703*z**6 + 114*z**5 + 869*z**3 + 258*z**2 - 1634\nNo more calculations needed.\n703*z**6 + 114*z**5 + 869*z**3 + 258*z**2 - 1634", "generated_answer": "703*z**6 + 114*z**5 + 869*z**3 + 258*z**2 - 1634", "step_length": 6} {"cot_id": "69610d6d529585f716836ec52ff7dc9fc0852daecbfcd24e82d48ae594fe19a8", "datapoint": {"question": "Simplify this expression: (27*y**2 - 8*y + 18)*(-44*y**3 + 27*y**2 + 19*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1188*y**5 + 1081*y**4 - 495*y**3 + 334*y**2 + 342*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 688, "polynomial_expr": "(27*y**2 - 8*y + 18)*(-44*y**3 + 27*y**2 + 19*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*y**2 - 8*y + 18)*(-44*y**3 + 27*y**2 + 19*y)\nExpanding the part (27*y**2 - 8*y + 18) using the distributive property, and we got: (-8*y)*(-44*y**3 + 27*y**2 + 19*y) + (27*y**2)*(-44*y**3 + 27*y**2 + 19*y) + 18*(-44*y**3 + 27*y**2 + 19*y)\n#Step 2:\nCurrent expression: (-8*y)*(-44*y**3 + 27*y**2 + 19*y) + (27*y**2)*(-44*y**3 + 27*y**2 + 19*y) + 18*(-44*y**3 + 27*y**2 + 19*y)\nSimplifying the partial expression: 18*(-44*y**3 + 27*y**2 + 19*y)\nExpanding the part (-44*y**3 + 27*y**2 + 19*y) using the distributive property, and we got: (19*y)*18 + (27*y**2)*18 - 44*y**3*18\nReplacing 18*(-44*y**3 + 27*y**2 + 19*y) with (19*y)*18 + (27*y**2)*18 - 44*y**3*18 in the overall expression.\n#Step 3:\nCurrent expression: (-8*y)*(-44*y**3 + 27*y**2 + 19*y) + (19*y)*18 + (27*y**2)*(-44*y**3 + 27*y**2 + 19*y) + (27*y**2)*18 - 44*y**3*18\nSimplifying the partial expression: (-8*y)*(-44*y**3 + 27*y**2 + 19*y)\nExpanding the part (-44*y**3 + 27*y**2 + 19*y) using the distributive property, and we got: (-8*y)*(19*y) + (-8*y)*(27*y**2) + (-8*y)*(-44*y**3)\nReplacing (-8*y)*(-44*y**3 + 27*y**2 + 19*y) with (-8*y)*(19*y) + (-8*y)*(27*y**2) + (-8*y)*(-44*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-8*y)*(19*y) + (-8*y)*(27*y**2) + (-8*y)*(-44*y**3) + (19*y)*18 + (27*y**2)*(-44*y**3 + 27*y**2 + 19*y) + (27*y**2)*18 - 44*y**3*18\nSimplifying the partial expression: (27*y**2)*(-44*y**3 + 27*y**2 + 19*y)\nExpanding the part (-44*y**3 + 27*y**2 + 19*y) using the distributive property, and we got: (19*y)*(27*y**2) + (27*y**2)*(-44*y**3) + (27*y**2)*(27*y**2)\nReplacing (27*y**2)*(-44*y**3 + 27*y**2 + 19*y) with (19*y)*(27*y**2) + (27*y**2)*(-44*y**3) + (27*y**2)*(27*y**2) in the overall expression.\n#Step 5:\nCurrent expression: (-8*y)*(19*y) + (-8*y)*(27*y**2) + (-8*y)*(-44*y**3) + (19*y)*(27*y**2) + (19*y)*18 + (27*y**2)*(-44*y**3) + (27*y**2)*(27*y**2) + (27*y**2)*18 - 44*y**3*18\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-44*y**3)*18 = -792*y**3\n (-44*y**3)*(-8*y) = 352*y**4\n (-44*y**3)*(27*y**2) = -1188*y**5\n (19*y)*18 = 342*y\n (19*y)*(-8*y) = -152*y**2\n (19*y)*(27*y**2) = 513*y**3\n (27*y**2)*18 = 486*y**2\n (27*y**2)*(-8*y) = -216*y**3\n (27*y**2)*(27*y**2) = 729*y**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1188*y**5 + 352*y**4 + 729*y**4 - 792*y**3 - 216*y**3 + 513*y**3 - 152*y**2 + 486*y**2 + 342*y\nCombining like terms, got -1188*y**5 + 1081*y**4 - 495*y**3 + 334*y**2 + 342*y\n#Step 7:\nCurrent expression: -1188*y**5 + 1081*y**4 - 495*y**3 + 334*y**2 + 342*y\nNo more calculations needed.\n-1188*y**5 + 1081*y**4 - 495*y**3 + 334*y**2 + 342*y", "generated_answer": "-1188*y**5 + 1081*y**4 - 495*y**3 + 334*y**2 + 342*y", "step_length": 7} {"cot_id": "bd13bcad5b0afde7f8c61e386cd7a7724748acc72bd86f318b3ed523046a2a51", "datapoint": {"question": "Calculate the following: (-41*z**2 - 30)*(35*z**3 + 43*z**2 - 34*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1435*z**5 - 1763*z**4 + 344*z**3 - 1290*z**2 + 1020*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 689, "polynomial_expr": "(-41*z**2 - 30)*(35*z**3 + 43*z**2 - 34*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-41*z**2 - 30)*(35*z**3 + 43*z**2 - 34*z)\nExpanding the part (-41*z**2 - 30) using the distributive property, and we got: (-41*z**2)*(35*z**3 + 43*z**2 - 34*z) - 30*(35*z**3 + 43*z**2 - 34*z)\n#Step 2:\nCurrent expression: (-41*z**2)*(35*z**3 + 43*z**2 - 34*z) - 30*(35*z**3 + 43*z**2 - 34*z)\nSimplifying the partial expression: -30*(35*z**3 + 43*z**2 - 34*z)\nExpanding the part (35*z**3 + 43*z**2 - 34*z) using the distributive property, and we got: -34*z*(-30) + (43*z**2)*(-30) + (35*z**3)*(-30)\nReplacing -30*(35*z**3 + 43*z**2 - 34*z) with -34*z*(-30) + (43*z**2)*(-30) + (35*z**3)*(-30) in the overall expression.\n#Step 3:\nCurrent expression: -34*z*(-30) + (-41*z**2)*(35*z**3 + 43*z**2 - 34*z) + (43*z**2)*(-30) + (35*z**3)*(-30)\nSimplifying the partial expression: (-41*z**2)*(35*z**3 + 43*z**2 - 34*z)\nExpanding the part (35*z**3 + 43*z**2 - 34*z) using the distributive property, and we got: (-34*z)*(-41*z**2) + (-41*z**2)*(43*z**2) + (-41*z**2)*(35*z**3)\nReplacing (-41*z**2)*(35*z**3 + 43*z**2 - 34*z) with (-34*z)*(-41*z**2) + (-41*z**2)*(43*z**2) + (-41*z**2)*(35*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-34*z)*(-41*z**2) - 34*z*(-30) + (-41*z**2)*(43*z**2) + (-41*z**2)*(35*z**3) + (43*z**2)*(-30) + (35*z**3)*(-30)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*z)*-30 = 1020*z\n (-34*z)*(-41*z**2) = 1394*z**3\n (35*z**3)*-30 = -1050*z**3\n (35*z**3)*(-41*z**2) = -1435*z**5\n (43*z**2)*-30 = -1290*z**2\n (43*z**2)*(-41*z**2) = -1763*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1435*z**5 - 1763*z**4 - 1050*z**3 + 1394*z**3 - 1290*z**2 + 1020*z\nCombining like terms, got -1435*z**5 - 1763*z**4 + 344*z**3 - 1290*z**2 + 1020*z\n#Step 6:\nCurrent expression: -1435*z**5 - 1763*z**4 + 344*z**3 - 1290*z**2 + 1020*z\nNo more calculations needed.\n-1435*z**5 - 1763*z**4 + 344*z**3 - 1290*z**2 + 1020*z", "generated_answer": "-1435*z**5 - 1763*z**4 + 344*z**3 - 1290*z**2 + 1020*z", "step_length": 6} {"cot_id": "366bb2f85eac8f02b0029b41ba7c3965c27be86286076e388e99aef3991c649e", "datapoint": {"question": "Calculate the following: (-20*z**3 - 43)*(37*z**3 - 42)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-740*z**6 - 751*z**3 + 1806", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 690, "polynomial_expr": "(-20*z**3 - 43)*(37*z**3 - 42)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-20*z**3 - 43)*(37*z**3 - 42)\nExpanding the part (-20*z**3 - 43) using the distributive property, and we got: (-20*z**3)*(37*z**3 - 42) - 43*(37*z**3 - 42)\n#Step 2:\nCurrent expression: (-20*z**3)*(37*z**3 - 42) - 43*(37*z**3 - 42)\nSimplifying the partial expression: -43*(37*z**3 - 42)\nExpanding the part (37*z**3 - 42) using the distributive property, and we got: (37*z**3)*(-43) - 42*(-43)\nReplacing -43*(37*z**3 - 42) with (37*z**3)*(-43) - 42*(-43) in the overall expression.\n#Step 3:\nCurrent expression: (-20*z**3)*(37*z**3 - 42) + (37*z**3)*(-43) + 1806\nSimplifying the partial expression: (-20*z**3)*(37*z**3 - 42)\nExpanding the part (37*z**3 - 42) using the distributive property, and we got: -(-1)*840*z**3 + (-20*z**3)*(37*z**3)\nReplacing (-20*z**3)*(37*z**3 - 42) with -(-1)*840*z**3 + (-20*z**3)*(37*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -42*(-20)*z**3 + (-20*z**3)*(37*z**3) + (37*z**3)*(-43) + 1806\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (37*z**3)*-43 = -1591*z**3\n (37*z**3)*(-20*z**3) = -740*z**6\n -42*-20*z**3 = 840*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -740*z**6 - 1591*z**3 + 840*z**3 + 1806\nCombining like terms, got -740*z**6 - 751*z**3 + 1806\n#Step 6:\nCurrent expression: -740*z**6 - 751*z**3 + 1806\nNo more calculations needed.\n-740*z**6 - 751*z**3 + 1806", "generated_answer": "-740*z**6 - 751*z**3 + 1806", "step_length": 6} {"cot_id": "7aec9d83adf7c277771c39e8544fb5be3d70030784e7c365f379e36aa47b384a", "datapoint": {"question": "Calculate the following: (50 - 48*y**2)*(14*y**2 + 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-672*y**4 - 260*y**2 + 1000", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 691, "polynomial_expr": "(50 - 48*y**2)*(14*y**2 + 20)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (50 - 48*y**2)*(14*y**2 + 20)\nExpanding the part (14*y**2 + 20) using the distributive property, and we got: (14*y**2)*(50 - 48*y**2) + 20*(50 - 48*y**2)\n#Step 2:\nCurrent expression: (14*y**2)*(50 - 48*y**2) + 20*(50 - 48*y**2)\nSimplifying the partial expression: 20*(50 - 48*y**2)\nExpanding the part (50 - 48*y**2) using the distributive property, and we got: -48*y**2*20 + 50*20\nReplacing 20*(50 - 48*y**2) with -48*y**2*20 + 50*20 in the overall expression.\n#Step 3:\nCurrent expression: -48*y**2*20 + (14*y**2)*(50 - 48*y**2) + 1000\nSimplifying the partial expression: (14*y**2)*(50 - 48*y**2)\nExpanding the part (50 - 48*y**2) using the distributive property, and we got: 50*(14*y**2) + (-48*y**2)*(14*y**2)\nReplacing (14*y**2)*(50 - 48*y**2) with 50*(14*y**2) + (-48*y**2)*(14*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 50*14*y**2 + (-48*y**2)*(14*y**2) - 48*y**2*20 + 1000\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*y**2)*20 = -960*y**2\n (-48*y**2)*(14*y**2) = -672*y**4\n 50*14*y**2 = 700*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -672*y**4 - 960*y**2 + 700*y**2 + 1000\nCombining like terms, got -672*y**4 - 260*y**2 + 1000\n#Step 6:\nCurrent expression: -672*y**4 - 260*y**2 + 1000\nNo more calculations needed.\n-672*y**4 - 260*y**2 + 1000", "generated_answer": "-672*y**4 - 260*y**2 + 1000", "step_length": 6} {"cot_id": "cf57c7de0de524d7d8e9fcae61d406052550dba5d966b993a91c66f3f17c660a", "datapoint": {"question": "Simplify this expression: (7*z**2 - 31*z)*(59*z**3 + 44*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "413*z**5 - 1829*z**4 + 308*z**3 - 1364*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 692, "polynomial_expr": "(7*z**2 - 31*z)*(59*z**3 + 44*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7*z**2 - 31*z)*(59*z**3 + 44*z)\nExpanding the part (7*z**2 - 31*z) using the distributive property, and we got: (-31*z)*(59*z**3 + 44*z) + (7*z**2)*(59*z**3 + 44*z)\n#Step 2:\nCurrent expression: (-31*z)*(59*z**3 + 44*z) + (7*z**2)*(59*z**3 + 44*z)\nSimplifying the partial expression: (-31*z)*(59*z**3 + 44*z)\nExpanding the part (59*z**3 + 44*z) using the distributive property, and we got: (-31*z)*(44*z) + (-31*z)*(59*z**3)\nReplacing (-31*z)*(59*z**3 + 44*z) with (-31*z)*(44*z) + (-31*z)*(59*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-31*z)*(44*z) + (-31*z)*(59*z**3) + (7*z**2)*(59*z**3 + 44*z)\nSimplifying the partial expression: (7*z**2)*(59*z**3 + 44*z)\nExpanding the part (59*z**3 + 44*z) using the distributive property, and we got: (44*z)*(7*z**2) + (7*z**2)*(59*z**3)\nReplacing (7*z**2)*(59*z**3 + 44*z) with (44*z)*(7*z**2) + (7*z**2)*(59*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-31*z)*(44*z) + (-31*z)*(59*z**3) + (44*z)*(7*z**2) + (7*z**2)*(59*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (44*z)*(-31*z) = -1364*z**2\n (44*z)*(7*z**2) = 308*z**3\n (59*z**3)*(-31*z) = -1829*z**4\n (59*z**3)*(7*z**2) = 413*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 413*z**5 - 1829*z**4 + 308*z**3 - 1364*z**2\nNo more calculations needed.\n413*z**5 - 1829*z**4 + 308*z**3 - 1364*z**2", "generated_answer": "413*z**5 - 1829*z**4 + 308*z**3 - 1364*z**2", "step_length": 5} {"cot_id": "cf1319a09ffc14798a55f4c3a72b2fb3acbff6e454a5b66f6a6a8d61551ea63a", "datapoint": {"question": "Simplify this expression: (-13*y**3 + 35*y**2)*(6*y**3 - 25*y**2 + 27)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-78*y**6 + 535*y**5 - 875*y**4 - 351*y**3 + 945*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 693, "polynomial_expr": "(-13*y**3 + 35*y**2)*(6*y**3 - 25*y**2 + 27)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-13*y**3 + 35*y**2)*(6*y**3 - 25*y**2 + 27)\nExpanding the part (-13*y**3 + 35*y**2) using the distributive property, and we got: (35*y**2)*(6*y**3 - 25*y**2 + 27) + (-13*y**3)*(6*y**3 - 25*y**2 + 27)\n#Step 2:\nCurrent expression: (35*y**2)*(6*y**3 - 25*y**2 + 27) + (-13*y**3)*(6*y**3 - 25*y**2 + 27)\nSimplifying the partial expression: (-13*y**3)*(6*y**3 - 25*y**2 + 27)\nExpanding the part (6*y**3 - 25*y**2 + 27) using the distributive property, and we got: 27*(-13*y**3) + (-25*y**2)*(-13*y**3) + (-13*y**3)*(6*y**3)\nReplacing (-13*y**3)*(6*y**3 - 25*y**2 + 27) with 27*(-13*y**3) + (-25*y**2)*(-13*y**3) + (-13*y**3)*(6*y**3) in the overall expression.\n#Step 3:\nCurrent expression: 27*(-13)*y**3 + (-25*y**2)*(-13*y**3) + (35*y**2)*(6*y**3 - 25*y**2 + 27) + (-13*y**3)*(6*y**3)\nSimplifying the partial expression: (35*y**2)*(6*y**3 - 25*y**2 + 27)\nExpanding the part (6*y**3 - 25*y**2 + 27) using the distributive property, and we got: 27*(35*y**2) + (-25*y**2)*(35*y**2) + (35*y**2)*(6*y**3)\nReplacing (35*y**2)*(6*y**3 - 25*y**2 + 27) with 27*(35*y**2) + (-25*y**2)*(35*y**2) + (35*y**2)*(6*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 27*(-13)*y**3 + 27*35*y**2 + (-25*y**2)*(35*y**2) + (-25*y**2)*(-13*y**3) + (35*y**2)*(6*y**3) + (-13*y**3)*(6*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*y**2)*(-13*y**3) = 325*y**5\n (-25*y**2)*(35*y**2) = -875*y**4\n (6*y**3)*(-13*y**3) = -78*y**6\n (6*y**3)*(35*y**2) = 210*y**5\n 27*-13*y**3 = -351*y**3\n 27*35*y**2 = 945*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -78*y**6 + 210*y**5 + 325*y**5 - 875*y**4 - 351*y**3 + 945*y**2\nCombining like terms, got -78*y**6 + 535*y**5 - 875*y**4 - 351*y**3 + 945*y**2\n#Step 6:\nCurrent expression: -78*y**6 + 535*y**5 - 875*y**4 - 351*y**3 + 945*y**2\nNo more calculations needed.\n-78*y**6 + 535*y**5 - 875*y**4 - 351*y**3 + 945*y**2", "generated_answer": "-78*y**6 + 535*y**5 - 875*y**4 - 351*y**3 + 945*y**2", "step_length": 6} {"cot_id": "13564ff7c181a99141f385dbd4d0538d536b41986bb06379000516f7e4cf3965", "datapoint": {"question": "Simplify this expression: (34*y**3 - 3*y**2)*(76*y**3 + 10*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2584*y**6 - 228*y**5 + 340*y**4 - 30*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 694, "polynomial_expr": "(34*y**3 - 3*y**2)*(76*y**3 + 10*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (34*y**3 - 3*y**2)*(76*y**3 + 10*y)\nExpanding the part (34*y**3 - 3*y**2) using the distributive property, and we got: (-3*y**2)*(76*y**3 + 10*y) + (34*y**3)*(76*y**3 + 10*y)\n#Step 2:\nCurrent expression: (-3*y**2)*(76*y**3 + 10*y) + (34*y**3)*(76*y**3 + 10*y)\nSimplifying the partial expression: (-3*y**2)*(76*y**3 + 10*y)\nExpanding the part (76*y**3 + 10*y) using the distributive property, and we got: (10*y)*(-3*y**2) + (-3*y**2)*(76*y**3)\nReplacing (-3*y**2)*(76*y**3 + 10*y) with (10*y)*(-3*y**2) + (-3*y**2)*(76*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (10*y)*(-3*y**2) + (-3*y**2)*(76*y**3) + (34*y**3)*(76*y**3 + 10*y)\nSimplifying the partial expression: (34*y**3)*(76*y**3 + 10*y)\nExpanding the part (76*y**3 + 10*y) using the distributive property, and we got: (10*y)*(34*y**3) + (34*y**3)*(76*y**3)\nReplacing (34*y**3)*(76*y**3 + 10*y) with (10*y)*(34*y**3) + (34*y**3)*(76*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (10*y)*(-3*y**2) + (10*y)*(34*y**3) + (-3*y**2)*(76*y**3) + (34*y**3)*(76*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (10*y)*(-3*y**2) = -30*y**3\n (10*y)*(34*y**3) = 340*y**4\n (76*y**3)*(-3*y**2) = -228*y**5\n (76*y**3)*(34*y**3) = 2584*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2584*y**6 - 228*y**5 + 340*y**4 - 30*y**3\nNo more calculations needed.\n2584*y**6 - 228*y**5 + 340*y**4 - 30*y**3", "generated_answer": "2584*y**6 - 228*y**5 + 340*y**4 - 30*y**3", "step_length": 5} {"cot_id": "b57922ba0c5ebf02d13befee917ace5d98a0904b7e74cd53d77f58bbd30c21a9", "datapoint": {"question": "Simplify this expression: (-7*x - 1)*(47*x**2 + 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-329*x**3 - 47*x**2 - 91*x - 13", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 695, "polynomial_expr": "(-7*x - 1)*(47*x**2 + 13)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-7*x - 1)*(47*x**2 + 13)\nExpanding the part (-7*x - 1) using the distributive property, and we got: (-7*x)*(47*x**2 + 13) - (47*x**2 + 13)\n#Step 2:\nCurrent expression: (-7*x)*(47*x**2 + 13) - (47*x**2 + 13)\nSimplifying the partial expression: -(47*x**2 + 13)\nExpanding the part (47*x**2 + 13) using the distributive property, and we got: (47*x**2)*(-1) + 13*(-1)\nReplacing -(47*x**2 + 13) with (47*x**2)*(-1) + 13*(-1) in the overall expression.\n#Step 3:\nCurrent expression: (-7*x)*(47*x**2 + 13) + (47*x**2)*(-1) - 13\nSimplifying the partial expression: (-7*x)*(47*x**2 + 13)\nExpanding the part (47*x**2 + 13) using the distributive property, and we got: (-7*x)*(47*x**2) + 13*(-7*x)\nReplacing (-7*x)*(47*x**2 + 13) with (-7*x)*(47*x**2) + 13*(-7*x) in the overall expression.\n#Step 4:\nCurrent expression: (-7*x)*(47*x**2) + 13*(-7)*x + (47*x**2)*(-1) - 13\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (47*x**2)*-1 = -47*x**2\n (47*x**2)*(-7*x) = -329*x**3\n 13*-7*x = -91*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -329*x**3 - 47*x**2 - 91*x - 13\nNo more calculations needed.\n-329*x**3 - 47*x**2 - 91*x - 13", "generated_answer": "-329*x**3 - 47*x**2 - 91*x - 13", "step_length": 5} {"cot_id": "a1e27f106b6435df5c98b2f8a1d579539a446b974d2fd4bd0fd3b819ba409ca3", "datapoint": {"question": "Simplify this expression: (-7*x**2 - 10*x + 36)*(41*x**2 - 37*x - 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-287*x**4 - 151*x**3 + 2182*x**2 - 852*x - 1728", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 696, "polynomial_expr": "(-7*x**2 - 10*x + 36)*(41*x**2 - 37*x - 48)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-7*x**2 - 10*x + 36)*(41*x**2 - 37*x - 48)\nExpanding the part (41*x**2 - 37*x - 48) using the distributive property, and we got: (-37*x)*(-7*x**2 - 10*x + 36) + (41*x**2)*(-7*x**2 - 10*x + 36) - 48*(-7*x**2 - 10*x + 36)\n#Step 2:\nCurrent expression: (-37*x)*(-7*x**2 - 10*x + 36) + (41*x**2)*(-7*x**2 - 10*x + 36) - 48*(-7*x**2 - 10*x + 36)\nSimplifying the partial expression: -48*(-7*x**2 - 10*x + 36)\nExpanding the part (-7*x**2 - 10*x + 36) using the distributive property, and we got: -10*x*(-48) - 7*x**2*(-48) + 36*(-48)\nReplacing -48*(-7*x**2 - 10*x + 36) with -10*x*(-48) - 7*x**2*(-48) + 36*(-48) in the overall expression.\n#Step 3:\nCurrent expression: (-37*x)*(-7*x**2 - 10*x + 36) - 10*x*(-48) - 7*x**2*(-48) + (41*x**2)*(-7*x**2 - 10*x + 36) - 1728\nSimplifying the partial expression: (-37*x)*(-7*x**2 - 10*x + 36)\nExpanding the part (-7*x**2 - 10*x + 36) using the distributive property, and we got: (-37*x)*(-10*x) + (-37*x)*(-7*x**2) + 36*(-37*x)\nReplacing (-37*x)*(-7*x**2 - 10*x + 36) with (-37*x)*(-10*x) + (-37*x)*(-7*x**2) + 36*(-37*x) in the overall expression.\n#Step 4:\nCurrent expression: (-37*x)*(-10*x) + (-37*x)*(-7*x**2) - 10*x*(-48) + 36*(-37)*x - 7*x**2*(-48) + (41*x**2)*(-7*x**2 - 10*x + 36) - 1728\nSimplifying the partial expression: (41*x**2)*(-7*x**2 - 10*x + 36)\nExpanding the part (-7*x**2 - 10*x + 36) using the distributive property, and we got: (-10*x)*(41*x**2) + 36*(41*x**2) + (-7*x**2)*(41*x**2)\nReplacing (41*x**2)*(-7*x**2 - 10*x + 36) with (-10*x)*(41*x**2) + 36*(41*x**2) + (-7*x**2)*(41*x**2) in the overall expression.\n#Step 5:\nCurrent expression: (-37*x)*(-10*x) + (-37*x)*(-7*x**2) + (-10*x)*(41*x**2) - 10*x*(-48) + 36*41*x**2 + 36*(-37)*x + (-7*x**2)*(41*x**2) - 7*x**2*(-48) - 1728\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*x)*-48 = 480*x\n (-10*x)*(-37*x) = 370*x**2\n (-10*x)*(41*x**2) = -410*x**3\n (-7*x**2)*-48 = 336*x**2\n (-7*x**2)*(-37*x) = 259*x**3\n (-7*x**2)*(41*x**2) = -287*x**4\n 36*-37*x = -1332*x\n 36*41*x**2 = 1476*x**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -287*x**4 - 410*x**3 + 259*x**3 + 336*x**2 + 370*x**2 + 1476*x**2 - 1332*x + 480*x - 1728\nCombining like terms, got -287*x**4 - 151*x**3 + 2182*x**2 - 852*x - 1728\n#Step 7:\nCurrent expression: -287*x**4 - 151*x**3 + 2182*x**2 - 852*x - 1728\nNo more calculations needed.\n-287*x**4 - 151*x**3 + 2182*x**2 - 852*x - 1728", "generated_answer": "-287*x**4 - 151*x**3 + 2182*x**2 - 852*x - 1728", "step_length": 7} {"cot_id": "a9109681e52589b8b04669714904b23557f8fdab756a54aacaaeed1587b51a04", "datapoint": {"question": "Calculate the following: (60 - 3*x)*(-49*x**2 - 6*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "147*x**3 - 2922*x**2 - 360*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 697, "polynomial_expr": "(60 - 3*x)*(-49*x**2 - 6*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (60 - 3*x)*(-49*x**2 - 6*x)\nExpanding the part (60 - 3*x) using the distributive property, and we got: (-3*x)*(-49*x**2 - 6*x) + 60*(-49*x**2 - 6*x)\n#Step 2:\nCurrent expression: (-3*x)*(-49*x**2 - 6*x) + 60*(-49*x**2 - 6*x)\nSimplifying the partial expression: 60*(-49*x**2 - 6*x)\nExpanding the part (-49*x**2 - 6*x) using the distributive property, and we got: -6*x*60 - 49*x**2*60\nReplacing 60*(-49*x**2 - 6*x) with -6*x*60 - 49*x**2*60 in the overall expression.\n#Step 3:\nCurrent expression: -6*x*60 + (-3*x)*(-49*x**2 - 6*x) - 49*x**2*60\nSimplifying the partial expression: (-3*x)*(-49*x**2 - 6*x)\nExpanding the part (-49*x**2 - 6*x) using the distributive property, and we got: (-6*x)*(-3*x) + (-3*x)*(-49*x**2)\nReplacing (-3*x)*(-49*x**2 - 6*x) with (-6*x)*(-3*x) + (-3*x)*(-49*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-6*x)*(-3*x) - 6*x*60 + (-3*x)*(-49*x**2) - 49*x**2*60\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*x**2)*60 = -2940*x**2\n (-49*x**2)*(-3*x) = 147*x**3\n (-6*x)*60 = -360*x\n (-6*x)*(-3*x) = 18*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 147*x**3 - 2940*x**2 + 18*x**2 - 360*x\nCombining like terms, got 147*x**3 - 2922*x**2 - 360*x\n#Step 6:\nCurrent expression: 147*x**3 - 2922*x**2 - 360*x\nNo more calculations needed.\n147*x**3 - 2922*x**2 - 360*x", "generated_answer": "147*x**3 - 2922*x**2 - 360*x", "step_length": 6} {"cot_id": "dcb24217e3bb9618b360a65b7bf5154070e0079a83f908e18e9a8fa2a24d29f6", "datapoint": {"question": "Simplify this expression: (11*z - 23)*(45*z + 34)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "495*z**2 - 661*z - 782", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 698, "polynomial_expr": "(11*z - 23)*(45*z + 34)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11*z - 23)*(45*z + 34)\nExpanding the part (11*z - 23) using the distributive property, and we got: (11*z)*(45*z + 34) - 23*(45*z + 34)\n#Step 2:\nCurrent expression: (11*z)*(45*z + 34) - 23*(45*z + 34)\nSimplifying the partial expression: -23*(45*z + 34)\nExpanding the part (45*z + 34) using the distributive property, and we got: (45*z)*(-23) + 34*(-23)\nReplacing -23*(45*z + 34) with (45*z)*(-23) + 34*(-23) in the overall expression.\n#Step 3:\nCurrent expression: (11*z)*(45*z + 34) + (45*z)*(-23) - 782\nSimplifying the partial expression: (11*z)*(45*z + 34)\nExpanding the part (45*z + 34) using the distributive property, and we got: 34*(11*z) + (11*z)*(45*z)\nReplacing (11*z)*(45*z + 34) with 34*(11*z) + (11*z)*(45*z) in the overall expression.\n#Step 4:\nCurrent expression: 34*11*z + (11*z)*(45*z) + (45*z)*(-23) - 782\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (45*z)*-23 = -1035*z\n (45*z)*(11*z) = 495*z**2\n 34*11*z = 374*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 495*z**2 - 1035*z + 374*z - 782\nCombining like terms, got 495*z**2 - 661*z - 782\n#Step 6:\nCurrent expression: 495*z**2 - 661*z - 782\nNo more calculations needed.\n495*z**2 - 661*z - 782", "generated_answer": "495*z**2 - 661*z - 782", "step_length": 6} {"cot_id": "e9cb8b972839545566a256116a4253b48a68fef2a7e3c7a7fd1ed03d0007a510", "datapoint": {"question": "Calculate the following: (13 - 8*x**3)*(49*x**2 - 6*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-392*x**5 + 48*x**4 + 637*x**2 - 78*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 699, "polynomial_expr": "(13 - 8*x**3)*(49*x**2 - 6*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (13 - 8*x**3)*(49*x**2 - 6*x)\nExpanding the part (13 - 8*x**3) using the distributive property, and we got: (-8*x**3)*(49*x**2 - 6*x) + 13*(49*x**2 - 6*x)\n#Step 2:\nCurrent expression: (-8*x**3)*(49*x**2 - 6*x) + 13*(49*x**2 - 6*x)\nSimplifying the partial expression: 13*(49*x**2 - 6*x)\nExpanding the part (49*x**2 - 6*x) using the distributive property, and we got: -6*x*13 + (49*x**2)*13\nReplacing 13*(49*x**2 - 6*x) with -6*x*13 + (49*x**2)*13 in the overall expression.\n#Step 3:\nCurrent expression: -6*x*13 + (49*x**2)*13 + (-8*x**3)*(49*x**2 - 6*x)\nSimplifying the partial expression: (-8*x**3)*(49*x**2 - 6*x)\nExpanding the part (49*x**2 - 6*x) using the distributive property, and we got: (-6*x)*(-8*x**3) + (49*x**2)*(-8*x**3)\nReplacing (-8*x**3)*(49*x**2 - 6*x) with (-6*x)*(-8*x**3) + (49*x**2)*(-8*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-6*x)*(-8*x**3) - 6*x*13 + (49*x**2)*(-8*x**3) + (49*x**2)*13\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-6*x)*13 = -78*x\n (-6*x)*(-8*x**3) = 48*x**4\n (49*x**2)*13 = 637*x**2\n (49*x**2)*(-8*x**3) = -392*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -392*x**5 + 48*x**4 + 637*x**2 - 78*x\nNo more calculations needed.\n-392*x**5 + 48*x**4 + 637*x**2 - 78*x", "generated_answer": "-392*x**5 + 48*x**4 + 637*x**2 - 78*x", "step_length": 5} {"cot_id": "712453c212d47255e174a704a79bb39ae4d45644d3bf6fa6c641e87aa4f4fb29", "datapoint": {"question": "Calculate the following: -y**3*(28*y**3 - 10*y + 23)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-28*y**6 + 10*y**4 - 23*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 700, "polynomial_expr": "-y**3*(28*y**3 - 10*y + 23)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -y**3*(28*y**3 - 10*y + 23)\nExpanding the part (28*y**3 - 10*y + 23) using the distributive property, and we got: (-10*y)*(-y**3) + 23*(-y**3) + (-y**3)*(28*y**3)\n#Step 2:\nCurrent expression: (-10*y)*(-y**3) + 23*(-y**3) + (-y**3)*(28*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 23*(-y**3) = -23*y**3\n (-10*y)*(-y**3) = 10*y**4\n (28*y**3)*(-y**3) = -28*y**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -28*y**6 + 10*y**4 - 23*y**3\nNo more calculations needed.\n-28*y**6 + 10*y**4 - 23*y**3", "generated_answer": "-28*y**6 + 10*y**4 - 23*y**3", "step_length": 3} {"cot_id": "35cdf15bf8b438992a45ea81b08276631c8bd97dd6f2006493cebe133be9ba41", "datapoint": {"question": "Simplify this expression: (47*z**2 - 19)*(36*z**3 - 27*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1692*z**5 - 1953*z**3 + 513*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 701, "polynomial_expr": "(47*z**2 - 19)*(36*z**3 - 27*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (47*z**2 - 19)*(36*z**3 - 27*z)\nExpanding the part (47*z**2 - 19) using the distributive property, and we got: (47*z**2)*(36*z**3 - 27*z) - 19*(36*z**3 - 27*z)\n#Step 2:\nCurrent expression: (47*z**2)*(36*z**3 - 27*z) - 19*(36*z**3 - 27*z)\nSimplifying the partial expression: -19*(36*z**3 - 27*z)\nExpanding the part (36*z**3 - 27*z) using the distributive property, and we got: -27*z*(-19) + (36*z**3)*(-19)\nReplacing -19*(36*z**3 - 27*z) with -27*z*(-19) + (36*z**3)*(-19) in the overall expression.\n#Step 3:\nCurrent expression: -27*z*(-19) + (47*z**2)*(36*z**3 - 27*z) + (36*z**3)*(-19)\nSimplifying the partial expression: (47*z**2)*(36*z**3 - 27*z)\nExpanding the part (36*z**3 - 27*z) using the distributive property, and we got: (-27*z)*(47*z**2) + (47*z**2)*(36*z**3)\nReplacing (47*z**2)*(36*z**3 - 27*z) with (-27*z)*(47*z**2) + (47*z**2)*(36*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-27*z)*(47*z**2) - 27*z*(-19) + (47*z**2)*(36*z**3) + (36*z**3)*(-19)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*z)*-19 = 513*z\n (-27*z)*(47*z**2) = -1269*z**3\n (36*z**3)*-19 = -684*z**3\n (36*z**3)*(47*z**2) = 1692*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1692*z**5 - 1269*z**3 - 684*z**3 + 513*z\nCombining like terms, got 1692*z**5 - 1953*z**3 + 513*z\n#Step 6:\nCurrent expression: 1692*z**5 - 1953*z**3 + 513*z\nNo more calculations needed.\n1692*z**5 - 1953*z**3 + 513*z", "generated_answer": "1692*z**5 - 1953*z**3 + 513*z", "step_length": 6} {"cot_id": "56b448ff1a464c60afddd4ffaae4dd679681371c1392f57e33877dd4acbfefab", "datapoint": {"question": "Calculate the following: (-20*y**2 - 31)*(-7*y**3 - 11*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "140*y**5 + 437*y**3 + 341*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 702, "polynomial_expr": "(-20*y**2 - 31)*(-7*y**3 - 11*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-20*y**2 - 31)*(-7*y**3 - 11*y)\nExpanding the part (-20*y**2 - 31) using the distributive property, and we got: (-20*y**2)*(-7*y**3 - 11*y) - 31*(-7*y**3 - 11*y)\n#Step 2:\nCurrent expression: (-20*y**2)*(-7*y**3 - 11*y) - 31*(-7*y**3 - 11*y)\nSimplifying the partial expression: -31*(-7*y**3 - 11*y)\nExpanding the part (-7*y**3 - 11*y) using the distributive property, and we got: -11*y*(-31) - 7*y**3*(-31)\nReplacing -31*(-7*y**3 - 11*y) with -11*y*(-31) - 7*y**3*(-31) in the overall expression.\n#Step 3:\nCurrent expression: -11*y*(-31) + (-20*y**2)*(-7*y**3 - 11*y) - 7*y**3*(-31)\nSimplifying the partial expression: (-20*y**2)*(-7*y**3 - 11*y)\nExpanding the part (-7*y**3 - 11*y) using the distributive property, and we got: (-11*y)*(-20*y**2) + (-20*y**2)*(-7*y**3)\nReplacing (-20*y**2)*(-7*y**3 - 11*y) with (-11*y)*(-20*y**2) + (-20*y**2)*(-7*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-11*y)*(-20*y**2) - 11*y*(-31) + (-20*y**2)*(-7*y**3) - 7*y**3*(-31)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*y)*-31 = 341*y\n (-11*y)*(-20*y**2) = 220*y**3\n (-7*y**3)*-31 = 217*y**3\n (-7*y**3)*(-20*y**2) = 140*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 140*y**5 + 217*y**3 + 220*y**3 + 341*y\nCombining like terms, got 140*y**5 + 437*y**3 + 341*y\n#Step 6:\nCurrent expression: 140*y**5 + 437*y**3 + 341*y\nNo more calculations needed.\n140*y**5 + 437*y**3 + 341*y", "generated_answer": "140*y**5 + 437*y**3 + 341*y", "step_length": 6} {"cot_id": "417b0844ed8aebc703a734924e1084184c986b4c5a1222220e4724c2ddb87a54", "datapoint": {"question": "Calculate the following: 28*x**3*(37*x**3 - 38*x + 15)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1036*x**6 - 1064*x**4 + 420*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 703, "polynomial_expr": "28*x**3*(37*x**3 - 38*x + 15)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 28*x**3*(37*x**3 - 38*x + 15)\nExpanding the part (37*x**3 - 38*x + 15) using the distributive property, and we got: (-38*x)*(28*x**3) + 15*(28*x**3) + (28*x**3)*(37*x**3)\n#Step 2:\nCurrent expression: (-38*x)*(28*x**3) + 15*(28*x**3) + (28*x**3)*(37*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 15*(28*x**3) = 420*x**3\n (-38*x)*(28*x**3) = -1064*x**4\n (37*x**3)*(28*x**3) = 1036*x**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1036*x**6 - 1064*x**4 + 420*x**3\nNo more calculations needed.\n1036*x**6 - 1064*x**4 + 420*x**3", "generated_answer": "1036*x**6 - 1064*x**4 + 420*x**3", "step_length": 3} {"cot_id": "ad6f1f7d974daa942a14b0018fc5588c1f0f8146b686215314d3cd515af49891", "datapoint": {"question": "Calculate the following: (75 - 49*y)*(-33*y**3 + 30*y**2 + 34*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1617*y**4 - 3945*y**3 + 584*y**2 + 2550*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 704, "polynomial_expr": "(75 - 49*y)*(-33*y**3 + 30*y**2 + 34*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (75 - 49*y)*(-33*y**3 + 30*y**2 + 34*y)\nExpanding the part (75 - 49*y) using the distributive property, and we got: (-49*y)*(-33*y**3 + 30*y**2 + 34*y) + 75*(-33*y**3 + 30*y**2 + 34*y)\n#Step 2:\nCurrent expression: (-49*y)*(-33*y**3 + 30*y**2 + 34*y) + 75*(-33*y**3 + 30*y**2 + 34*y)\nSimplifying the partial expression: 75*(-33*y**3 + 30*y**2 + 34*y)\nExpanding the part (-33*y**3 + 30*y**2 + 34*y) using the distributive property, and we got: (34*y)*75 + (30*y**2)*75 - 33*y**3*75\nReplacing 75*(-33*y**3 + 30*y**2 + 34*y) with (34*y)*75 + (30*y**2)*75 - 33*y**3*75 in the overall expression.\n#Step 3:\nCurrent expression: (-49*y)*(-33*y**3 + 30*y**2 + 34*y) + (34*y)*75 + (30*y**2)*75 - 33*y**3*75\nSimplifying the partial expression: (-49*y)*(-33*y**3 + 30*y**2 + 34*y)\nExpanding the part (-33*y**3 + 30*y**2 + 34*y) using the distributive property, and we got: (-49*y)*(34*y) + (-49*y)*(30*y**2) + (-49*y)*(-33*y**3)\nReplacing (-49*y)*(-33*y**3 + 30*y**2 + 34*y) with (-49*y)*(34*y) + (-49*y)*(30*y**2) + (-49*y)*(-33*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-49*y)*(34*y) + (-49*y)*(30*y**2) + (-49*y)*(-33*y**3) + (34*y)*75 + (30*y**2)*75 - 33*y**3*75\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*y**3)*75 = -2475*y**3\n (-33*y**3)*(-49*y) = 1617*y**4\n (30*y**2)*75 = 2250*y**2\n (30*y**2)*(-49*y) = -1470*y**3\n (34*y)*75 = 2550*y\n (34*y)*(-49*y) = -1666*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1617*y**4 - 2475*y**3 - 1470*y**3 - 1666*y**2 + 2250*y**2 + 2550*y\nCombining like terms, got 1617*y**4 - 3945*y**3 + 584*y**2 + 2550*y\n#Step 6:\nCurrent expression: 1617*y**4 - 3945*y**3 + 584*y**2 + 2550*y\nNo more calculations needed.\n1617*y**4 - 3945*y**3 + 584*y**2 + 2550*y", "generated_answer": "1617*y**4 - 3945*y**3 + 584*y**2 + 2550*y", "step_length": 6} {"cot_id": "287ab84a43b55e407f93587ac6fe1edfc08c7dac805291fc13eb52933c91fc7b", "datapoint": {"question": "Simplify this expression: (31 - 40*y)*(12*y + 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-480*y**2 - 748*y + 868", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 705, "polynomial_expr": "(31 - 40*y)*(12*y + 28)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31 - 40*y)*(12*y + 28)\nExpanding the part (12*y + 28) using the distributive property, and we got: (12*y)*(31 - 40*y) + 28*(31 - 40*y)\n#Step 2:\nCurrent expression: (12*y)*(31 - 40*y) + 28*(31 - 40*y)\nSimplifying the partial expression: 28*(31 - 40*y)\nExpanding the part (31 - 40*y) using the distributive property, and we got: -40*y*28 + 31*28\nReplacing 28*(31 - 40*y) with -40*y*28 + 31*28 in the overall expression.\n#Step 3:\nCurrent expression: -40*y*28 + (12*y)*(31 - 40*y) + 868\nSimplifying the partial expression: (12*y)*(31 - 40*y)\nExpanding the part (31 - 40*y) using the distributive property, and we got: (-40*y)*(12*y) + 31*(12*y)\nReplacing (12*y)*(31 - 40*y) with (-40*y)*(12*y) + 31*(12*y) in the overall expression.\n#Step 4:\nCurrent expression: (-40*y)*(12*y) - 40*y*28 + 31*12*y + 868\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*y)*28 = -1120*y\n (-40*y)*(12*y) = -480*y**2\n 31*12*y = 372*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -480*y**2 - 1120*y + 372*y + 868\nCombining like terms, got -480*y**2 - 748*y + 868\n#Step 6:\nCurrent expression: -480*y**2 - 748*y + 868\nNo more calculations needed.\n-480*y**2 - 748*y + 868", "generated_answer": "-480*y**2 - 748*y + 868", "step_length": 6} {"cot_id": "a0e6b41176e5fddbe5a6129ba43d13eb25281a55bfa787c94b65570f01e73242", "datapoint": {"question": "Calculate the following: (-21*x**2 - 46*x)*(-20*x**3 + 29*x**2 + 43*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "420*x**5 + 311*x**4 - 2237*x**3 - 1978*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 706, "polynomial_expr": "(-21*x**2 - 46*x)*(-20*x**3 + 29*x**2 + 43*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-21*x**2 - 46*x)*(-20*x**3 + 29*x**2 + 43*x)\nExpanding the part (-21*x**2 - 46*x) using the distributive property, and we got: (-46*x)*(-20*x**3 + 29*x**2 + 43*x) + (-21*x**2)*(-20*x**3 + 29*x**2 + 43*x)\n#Step 2:\nCurrent expression: (-46*x)*(-20*x**3 + 29*x**2 + 43*x) + (-21*x**2)*(-20*x**3 + 29*x**2 + 43*x)\nSimplifying the partial expression: (-46*x)*(-20*x**3 + 29*x**2 + 43*x)\nExpanding the part (-20*x**3 + 29*x**2 + 43*x) using the distributive property, and we got: (-46*x)*(43*x) + (-46*x)*(29*x**2) + (-46*x)*(-20*x**3)\nReplacing (-46*x)*(-20*x**3 + 29*x**2 + 43*x) with (-46*x)*(43*x) + (-46*x)*(29*x**2) + (-46*x)*(-20*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-46*x)*(43*x) + (-46*x)*(29*x**2) + (-46*x)*(-20*x**3) + (-21*x**2)*(-20*x**3 + 29*x**2 + 43*x)\nSimplifying the partial expression: (-21*x**2)*(-20*x**3 + 29*x**2 + 43*x)\nExpanding the part (-20*x**3 + 29*x**2 + 43*x) using the distributive property, and we got: (43*x)*(-21*x**2) + (-21*x**2)*(29*x**2) + (-21*x**2)*(-20*x**3)\nReplacing (-21*x**2)*(-20*x**3 + 29*x**2 + 43*x) with (43*x)*(-21*x**2) + (-21*x**2)*(29*x**2) + (-21*x**2)*(-20*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-46*x)*(43*x) + (-46*x)*(29*x**2) + (-46*x)*(-20*x**3) + (43*x)*(-21*x**2) + (-21*x**2)*(29*x**2) + (-21*x**2)*(-20*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*x**3)*(-46*x) = 920*x**4\n (-20*x**3)*(-21*x**2) = 420*x**5\n (29*x**2)*(-46*x) = -1334*x**3\n (29*x**2)*(-21*x**2) = -609*x**4\n (43*x)*(-46*x) = -1978*x**2\n (43*x)*(-21*x**2) = -903*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 420*x**5 - 609*x**4 + 920*x**4 - 1334*x**3 - 903*x**3 - 1978*x**2\nCombining like terms, got 420*x**5 + 311*x**4 - 2237*x**3 - 1978*x**2\n#Step 6:\nCurrent expression: 420*x**5 + 311*x**4 - 2237*x**3 - 1978*x**2\nNo more calculations needed.\n420*x**5 + 311*x**4 - 2237*x**3 - 1978*x**2", "generated_answer": "420*x**5 + 311*x**4 - 2237*x**3 - 1978*x**2", "step_length": 6} {"cot_id": "5a7d1fef1e0cfa2f7c47bcdf3831d464e858e93fe0b0d3d185a5be7f42965584", "datapoint": {"question": "Calculate the following: (-39*y**2 + 21*y)*(61*y**3 + 38*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2379*y**5 - 201*y**4 + 798*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 707, "polynomial_expr": "(-39*y**2 + 21*y)*(61*y**3 + 38*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-39*y**2 + 21*y)*(61*y**3 + 38*y**2)\nExpanding the part (-39*y**2 + 21*y) using the distributive property, and we got: (21*y)*(61*y**3 + 38*y**2) + (-39*y**2)*(61*y**3 + 38*y**2)\n#Step 2:\nCurrent expression: (21*y)*(61*y**3 + 38*y**2) + (-39*y**2)*(61*y**3 + 38*y**2)\nSimplifying the partial expression: (-39*y**2)*(61*y**3 + 38*y**2)\nExpanding the part (61*y**3 + 38*y**2) using the distributive property, and we got: (-39*y**2)*(38*y**2) + (-39*y**2)*(61*y**3)\nReplacing (-39*y**2)*(61*y**3 + 38*y**2) with (-39*y**2)*(38*y**2) + (-39*y**2)*(61*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (21*y)*(61*y**3 + 38*y**2) + (-39*y**2)*(38*y**2) + (-39*y**2)*(61*y**3)\nSimplifying the partial expression: (21*y)*(61*y**3 + 38*y**2)\nExpanding the part (61*y**3 + 38*y**2) using the distributive property, and we got: (21*y)*(38*y**2) + (21*y)*(61*y**3)\nReplacing (21*y)*(61*y**3 + 38*y**2) with (21*y)*(38*y**2) + (21*y)*(61*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (21*y)*(38*y**2) + (21*y)*(61*y**3) + (-39*y**2)*(38*y**2) + (-39*y**2)*(61*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (38*y**2)*(-39*y**2) = -1482*y**4\n (38*y**2)*(21*y) = 798*y**3\n (61*y**3)*(-39*y**2) = -2379*y**5\n (61*y**3)*(21*y) = 1281*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2379*y**5 - 1482*y**4 + 1281*y**4 + 798*y**3\nCombining like terms, got -2379*y**5 - 201*y**4 + 798*y**3\n#Step 6:\nCurrent expression: -2379*y**5 - 201*y**4 + 798*y**3\nNo more calculations needed.\n-2379*y**5 - 201*y**4 + 798*y**3", "generated_answer": "-2379*y**5 - 201*y**4 + 798*y**3", "step_length": 6} {"cot_id": "224e3c722d2072d318a6028420ff50238ad12fad8b81a8a08f851d8da8ee8a0c", "datapoint": {"question": "Simplify this expression: (-23*y**2 - 40*y)*(3*y**3 + 16*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-69*y**5 - 488*y**4 - 640*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 708, "polynomial_expr": "(-23*y**2 - 40*y)*(3*y**3 + 16*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-23*y**2 - 40*y)*(3*y**3 + 16*y**2)\nExpanding the part (-23*y**2 - 40*y) using the distributive property, and we got: (-40*y)*(3*y**3 + 16*y**2) + (-23*y**2)*(3*y**3 + 16*y**2)\n#Step 2:\nCurrent expression: (-40*y)*(3*y**3 + 16*y**2) + (-23*y**2)*(3*y**3 + 16*y**2)\nSimplifying the partial expression: (-40*y)*(3*y**3 + 16*y**2)\nExpanding the part (3*y**3 + 16*y**2) using the distributive property, and we got: (-40*y)*(16*y**2) + (-40*y)*(3*y**3)\nReplacing (-40*y)*(3*y**3 + 16*y**2) with (-40*y)*(16*y**2) + (-40*y)*(3*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-40*y)*(16*y**2) + (-40*y)*(3*y**3) + (-23*y**2)*(3*y**3 + 16*y**2)\nSimplifying the partial expression: (-23*y**2)*(3*y**3 + 16*y**2)\nExpanding the part (3*y**3 + 16*y**2) using the distributive property, and we got: (-23*y**2)*(16*y**2) + (-23*y**2)*(3*y**3)\nReplacing (-23*y**2)*(3*y**3 + 16*y**2) with (-23*y**2)*(16*y**2) + (-23*y**2)*(3*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-40*y)*(16*y**2) + (-40*y)*(3*y**3) + (-23*y**2)*(16*y**2) + (-23*y**2)*(3*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (3*y**3)*(-40*y) = -120*y**4\n (3*y**3)*(-23*y**2) = -69*y**5\n (16*y**2)*(-40*y) = -640*y**3\n (16*y**2)*(-23*y**2) = -368*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -69*y**5 - 368*y**4 - 120*y**4 - 640*y**3\nCombining like terms, got -69*y**5 - 488*y**4 - 640*y**3\n#Step 6:\nCurrent expression: -69*y**5 - 488*y**4 - 640*y**3\nNo more calculations needed.\n-69*y**5 - 488*y**4 - 640*y**3", "generated_answer": "-69*y**5 - 488*y**4 - 640*y**3", "step_length": 6} {"cot_id": "7f17194b9046cc3bb66bae74cf7e1d5260a015050718edcb1790539b1681b715", "datapoint": {"question": "Simplify this expression: (27*z**2 - 5*z + 18)*(48*z**3 + 28*z - 8)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1296*z**5 - 240*z**4 + 1620*z**3 - 356*z**2 + 544*z - 144", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 709, "polynomial_expr": "(27*z**2 - 5*z + 18)*(48*z**3 + 28*z - 8)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*z**2 - 5*z + 18)*(48*z**3 + 28*z - 8)\nExpanding the part (48*z**3 + 28*z - 8) using the distributive property, and we got: (28*z)*(27*z**2 - 5*z + 18) + (48*z**3)*(27*z**2 - 5*z + 18) - 8*(27*z**2 - 5*z + 18)\n#Step 2:\nCurrent expression: (28*z)*(27*z**2 - 5*z + 18) + (48*z**3)*(27*z**2 - 5*z + 18) - 8*(27*z**2 - 5*z + 18)\nSimplifying the partial expression: -8*(27*z**2 - 5*z + 18)\nExpanding the part (27*z**2 - 5*z + 18) using the distributive property, and we got: -5*z*(-8) + (27*z**2)*(-8) + 18*(-8)\nReplacing -8*(27*z**2 - 5*z + 18) with -5*z*(-8) + (27*z**2)*(-8) + 18*(-8) in the overall expression.\n#Step 3:\nCurrent expression: -5*z*(-8) + (28*z)*(27*z**2 - 5*z + 18) + (27*z**2)*(-8) + (48*z**3)*(27*z**2 - 5*z + 18) - 144\nSimplifying the partial expression: (28*z)*(27*z**2 - 5*z + 18)\nExpanding the part (27*z**2 - 5*z + 18) using the distributive property, and we got: (-5*z)*(28*z) + 18*(28*z) + (28*z)*(27*z**2)\nReplacing (28*z)*(27*z**2 - 5*z + 18) with (-5*z)*(28*z) + 18*(28*z) + (28*z)*(27*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-5*z)*(28*z) - 5*z*(-8) + 18*28*z + (28*z)*(27*z**2) + (27*z**2)*(-8) + (48*z**3)*(27*z**2 - 5*z + 18) - 144\nSimplifying the partial expression: (48*z**3)*(27*z**2 - 5*z + 18)\nExpanding the part (27*z**2 - 5*z + 18) using the distributive property, and we got: (-5*z)*(48*z**3) + 18*(48*z**3) + (27*z**2)*(48*z**3)\nReplacing (48*z**3)*(27*z**2 - 5*z + 18) with (-5*z)*(48*z**3) + 18*(48*z**3) + (27*z**2)*(48*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-5*z)*(28*z) + (-5*z)*(48*z**3) - 5*z*(-8) + 18*48*z**3 + 18*28*z + (28*z)*(27*z**2) + (27*z**2)*(48*z**3) + (27*z**2)*(-8) - 144\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-5*z)*-8 = 40*z\n (-5*z)*(28*z) = -140*z**2\n (-5*z)*(48*z**3) = -240*z**4\n (27*z**2)*-8 = -216*z**2\n (27*z**2)*(28*z) = 756*z**3\n (27*z**2)*(48*z**3) = 1296*z**5\n 18*28*z = 504*z\n 18*48*z**3 = 864*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1296*z**5 - 240*z**4 + 756*z**3 + 864*z**3 - 216*z**2 - 140*z**2 + 40*z + 504*z - 144\nCombining like terms, got 1296*z**5 - 240*z**4 + 1620*z**3 - 356*z**2 + 544*z - 144\n#Step 7:\nCurrent expression: 1296*z**5 - 240*z**4 + 1620*z**3 - 356*z**2 + 544*z - 144\nNo more calculations needed.\n1296*z**5 - 240*z**4 + 1620*z**3 - 356*z**2 + 544*z - 144", "generated_answer": "1296*z**5 - 240*z**4 + 1620*z**3 - 356*z**2 + 544*z - 144", "step_length": 7} {"cot_id": "23a6752e5feaf7a060263ec3e4c5b6feb74c5a4c7082bf54659a782544b6a6b3", "datapoint": {"question": "Simplify this expression: (-3*z**2 - 20*z + 27)*(26*z**3 - 20*z**2 + 47*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-78*z**5 - 460*z**4 + 961*z**3 - 1480*z**2 + 1269*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 710, "polynomial_expr": "(-3*z**2 - 20*z + 27)*(26*z**3 - 20*z**2 + 47*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-3*z**2 - 20*z + 27)*(26*z**3 - 20*z**2 + 47*z)\nExpanding the part (-3*z**2 - 20*z + 27) using the distributive property, and we got: (-20*z)*(26*z**3 - 20*z**2 + 47*z) + (-3*z**2)*(26*z**3 - 20*z**2 + 47*z) + 27*(26*z**3 - 20*z**2 + 47*z)\n#Step 2:\nCurrent expression: (-20*z)*(26*z**3 - 20*z**2 + 47*z) + (-3*z**2)*(26*z**3 - 20*z**2 + 47*z) + 27*(26*z**3 - 20*z**2 + 47*z)\nSimplifying the partial expression: 27*(26*z**3 - 20*z**2 + 47*z)\nExpanding the part (26*z**3 - 20*z**2 + 47*z) using the distributive property, and we got: (47*z)*27 - 20*z**2*27 + (26*z**3)*27\nReplacing 27*(26*z**3 - 20*z**2 + 47*z) with (47*z)*27 - 20*z**2*27 + (26*z**3)*27 in the overall expression.\n#Step 3:\nCurrent expression: (-20*z)*(26*z**3 - 20*z**2 + 47*z) + (47*z)*27 - 20*z**2*27 + (-3*z**2)*(26*z**3 - 20*z**2 + 47*z) + (26*z**3)*27\nSimplifying the partial expression: (-20*z)*(26*z**3 - 20*z**2 + 47*z)\nExpanding the part (26*z**3 - 20*z**2 + 47*z) using the distributive property, and we got: (-20*z)*(47*z) + (-20*z)*(-20*z**2) + (-20*z)*(26*z**3)\nReplacing (-20*z)*(26*z**3 - 20*z**2 + 47*z) with (-20*z)*(47*z) + (-20*z)*(-20*z**2) + (-20*z)*(26*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-20*z)*(47*z) + (-20*z)*(-20*z**2) + (-20*z)*(26*z**3) + (47*z)*27 - 20*z**2*27 + (-3*z**2)*(26*z**3 - 20*z**2 + 47*z) + (26*z**3)*27\nSimplifying the partial expression: (-3*z**2)*(26*z**3 - 20*z**2 + 47*z)\nExpanding the part (26*z**3 - 20*z**2 + 47*z) using the distributive property, and we got: (47*z)*(-3*z**2) + (-20*z**2)*(-3*z**2) + (-3*z**2)*(26*z**3)\nReplacing (-3*z**2)*(26*z**3 - 20*z**2 + 47*z) with (47*z)*(-3*z**2) + (-20*z**2)*(-3*z**2) + (-3*z**2)*(26*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-20*z)*(47*z) + (-20*z)*(-20*z**2) + (-20*z)*(26*z**3) + (47*z)*(-3*z**2) + (47*z)*27 + (-20*z**2)*(-3*z**2) - 20*z**2*27 + (-3*z**2)*(26*z**3) + (26*z**3)*27\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*z**2)*27 = -540*z**2\n (-20*z**2)*(-20*z) = 400*z**3\n (-20*z**2)*(-3*z**2) = 60*z**4\n (26*z**3)*27 = 702*z**3\n (26*z**3)*(-20*z) = -520*z**4\n (26*z**3)*(-3*z**2) = -78*z**5\n (47*z)*27 = 1269*z\n (47*z)*(-20*z) = -940*z**2\n (47*z)*(-3*z**2) = -141*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -78*z**5 - 520*z**4 + 60*z**4 - 141*z**3 + 400*z**3 + 702*z**3 - 940*z**2 - 540*z**2 + 1269*z\nCombining like terms, got -78*z**5 - 460*z**4 + 961*z**3 - 1480*z**2 + 1269*z\n#Step 7:\nCurrent expression: -78*z**5 - 460*z**4 + 961*z**3 - 1480*z**2 + 1269*z\nNo more calculations needed.\n-78*z**5 - 460*z**4 + 961*z**3 - 1480*z**2 + 1269*z", "generated_answer": "-78*z**5 - 460*z**4 + 961*z**3 - 1480*z**2 + 1269*z", "step_length": 7} {"cot_id": "c33df0812b2444b214f52db29ccf072b5ff2b2167882609c305eb5917a1d7c52", "datapoint": {"question": "Simplify this expression: (-43*y**3 - 27*y**2 - 43)*(-2*y**3 + 54*y**2 + 38*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "86*y**6 - 2268*y**5 - 3092*y**4 - 940*y**3 - 2322*y**2 - 1634*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 711, "polynomial_expr": "(-43*y**3 - 27*y**2 - 43)*(-2*y**3 + 54*y**2 + 38*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-43*y**3 - 27*y**2 - 43)*(-2*y**3 + 54*y**2 + 38*y)\nExpanding the part (-43*y**3 - 27*y**2 - 43) using the distributive property, and we got: (-27*y**2)*(-2*y**3 + 54*y**2 + 38*y) + (-43*y**3)*(-2*y**3 + 54*y**2 + 38*y) - 43*(-2*y**3 + 54*y**2 + 38*y)\n#Step 2:\nCurrent expression: (-27*y**2)*(-2*y**3 + 54*y**2 + 38*y) + (-43*y**3)*(-2*y**3 + 54*y**2 + 38*y) - 43*(-2*y**3 + 54*y**2 + 38*y)\nSimplifying the partial expression: -43*(-2*y**3 + 54*y**2 + 38*y)\nExpanding the part (-2*y**3 + 54*y**2 + 38*y) using the distributive property, and we got: (38*y)*(-43) + (54*y**2)*(-43) - 2*y**3*(-43)\nReplacing -43*(-2*y**3 + 54*y**2 + 38*y) with (38*y)*(-43) + (54*y**2)*(-43) - 2*y**3*(-43) in the overall expression.\n#Step 3:\nCurrent expression: (38*y)*(-43) + (-27*y**2)*(-2*y**3 + 54*y**2 + 38*y) + (54*y**2)*(-43) + (-43*y**3)*(-2*y**3 + 54*y**2 + 38*y) - 2*y**3*(-43)\nSimplifying the partial expression: (-43*y**3)*(-2*y**3 + 54*y**2 + 38*y)\nExpanding the part (-2*y**3 + 54*y**2 + 38*y) using the distributive property, and we got: (38*y)*(-43*y**3) + (54*y**2)*(-43*y**3) + (-43*y**3)*(-2*y**3)\nReplacing (-43*y**3)*(-2*y**3 + 54*y**2 + 38*y) with (38*y)*(-43*y**3) + (54*y**2)*(-43*y**3) + (-43*y**3)*(-2*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (38*y)*(-43*y**3) + (38*y)*(-43) + (-27*y**2)*(-2*y**3 + 54*y**2 + 38*y) + (54*y**2)*(-43*y**3) + (54*y**2)*(-43) + (-43*y**3)*(-2*y**3) - 2*y**3*(-43)\nSimplifying the partial expression: (-27*y**2)*(-2*y**3 + 54*y**2 + 38*y)\nExpanding the part (-2*y**3 + 54*y**2 + 38*y) using the distributive property, and we got: (38*y)*(-27*y**2) + (-27*y**2)*(54*y**2) + (-27*y**2)*(-2*y**3)\nReplacing (-27*y**2)*(-2*y**3 + 54*y**2 + 38*y) with (38*y)*(-27*y**2) + (-27*y**2)*(54*y**2) + (-27*y**2)*(-2*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (38*y)*(-27*y**2) + (38*y)*(-43*y**3) + (38*y)*(-43) + (-27*y**2)*(54*y**2) + (-27*y**2)*(-2*y**3) + (54*y**2)*(-43*y**3) + (54*y**2)*(-43) + (-43*y**3)*(-2*y**3) - 2*y**3*(-43)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-2*y**3)*-43 = 86*y**3\n (-2*y**3)*(-43*y**3) = 86*y**6\n (-2*y**3)*(-27*y**2) = 54*y**5\n (38*y)*-43 = -1634*y\n (38*y)*(-43*y**3) = -1634*y**4\n (38*y)*(-27*y**2) = -1026*y**3\n (54*y**2)*-43 = -2322*y**2\n (54*y**2)*(-43*y**3) = -2322*y**5\n (54*y**2)*(-27*y**2) = -1458*y**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 86*y**6 - 2322*y**5 + 54*y**5 - 1634*y**4 - 1458*y**4 - 1026*y**3 + 86*y**3 - 2322*y**2 - 1634*y\nCombining like terms, got 86*y**6 - 2268*y**5 - 3092*y**4 - 940*y**3 - 2322*y**2 - 1634*y\n#Step 7:\nCurrent expression: 86*y**6 - 2268*y**5 - 3092*y**4 - 940*y**3 - 2322*y**2 - 1634*y\nNo more calculations needed.\n86*y**6 - 2268*y**5 - 3092*y**4 - 940*y**3 - 2322*y**2 - 1634*y", "generated_answer": "86*y**6 - 2268*y**5 - 3092*y**4 - 940*y**3 - 2322*y**2 - 1634*y", "step_length": 7} {"cot_id": "e26fb6d68d771909b9b667326134514bd688f9724a271c52c50262cb6c051ce9", "datapoint": {"question": "Calculate the following: (-8*x - 41)*(-10*x**2 - 108*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "80*x**3 + 1274*x**2 + 4428*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 712, "polynomial_expr": "(-8*x - 41)*(-10*x**2 - 108*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-8*x - 41)*(-10*x**2 - 108*x)\nExpanding the part (-8*x - 41) using the distributive property, and we got: (-8*x)*(-10*x**2 - 108*x) - 41*(-10*x**2 - 108*x)\n#Step 2:\nCurrent expression: (-8*x)*(-10*x**2 - 108*x) - 41*(-10*x**2 - 108*x)\nSimplifying the partial expression: -41*(-10*x**2 - 108*x)\nExpanding the part (-10*x**2 - 108*x) using the distributive property, and we got: -108*x*(-41) - 10*x**2*(-41)\nReplacing -41*(-10*x**2 - 108*x) with -108*x*(-41) - 10*x**2*(-41) in the overall expression.\n#Step 3:\nCurrent expression: -108*x*(-41) + (-8*x)*(-10*x**2 - 108*x) - 10*x**2*(-41)\nSimplifying the partial expression: (-8*x)*(-10*x**2 - 108*x)\nExpanding the part (-10*x**2 - 108*x) using the distributive property, and we got: (-108*x)*(-8*x) + (-8*x)*(-10*x**2)\nReplacing (-8*x)*(-10*x**2 - 108*x) with (-108*x)*(-8*x) + (-8*x)*(-10*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-108*x)*(-8*x) - 108*x*(-41) + (-8*x)*(-10*x**2) - 10*x**2*(-41)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-108*x)*-41 = 4428*x\n (-108*x)*(-8*x) = 864*x**2\n (-10*x**2)*-41 = 410*x**2\n (-10*x**2)*(-8*x) = 80*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 80*x**3 + 410*x**2 + 864*x**2 + 4428*x\nCombining like terms, got 80*x**3 + 1274*x**2 + 4428*x\n#Step 6:\nCurrent expression: 80*x**3 + 1274*x**2 + 4428*x\nNo more calculations needed.\n80*x**3 + 1274*x**2 + 4428*x", "generated_answer": "80*x**3 + 1274*x**2 + 4428*x", "step_length": 6} {"cot_id": "1ff9d20b69d9aef89b6a6df7a96f5d16f3ca2b7d597c695fe3d13848aa5778c4", "datapoint": {"question": "Calculate the following: (-27*z**2 - 77*z + 30)*(-20*z**3 + z - 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "540*z**5 + 1540*z**4 - 627*z**3 + 571*z**2 + 1878*z - 720", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 713, "polynomial_expr": "(-27*z**2 - 77*z + 30)*(-20*z**3 + z - 24)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-27*z**2 - 77*z + 30)*(-20*z**3 + z - 24)\nExpanding the part (-20*z**3 + z - 24) using the distributive property, and we got: z*(-27*z**2 - 77*z + 30) + (-20*z**3)*(-27*z**2 - 77*z + 30) - 24*(-27*z**2 - 77*z + 30)\n#Step 2:\nCurrent expression: z*(-27*z**2 - 77*z + 30) + (-20*z**3)*(-27*z**2 - 77*z + 30) - 24*(-27*z**2 - 77*z + 30)\nSimplifying the partial expression: -24*(-27*z**2 - 77*z + 30)\nExpanding the part (-27*z**2 - 77*z + 30) using the distributive property, and we got: -77*z*(-24) - 27*z**2*(-24) + 30*(-24)\nReplacing -24*(-27*z**2 - 77*z + 30) with -77*z*(-24) - 27*z**2*(-24) + 30*(-24) in the overall expression.\n#Step 3:\nCurrent expression: -77*z*(-24) + z*(-27*z**2 - 77*z + 30) - 27*z**2*(-24) + (-20*z**3)*(-27*z**2 - 77*z + 30) - 720\nSimplifying the partial expression: z*(-27*z**2 - 77*z + 30)\nExpanding the part (-27*z**2 - 77*z + 30) using the distributive property, and we got: (-77*z)*z + z*(-27*z**2) + 30*z\nReplacing z*(-27*z**2 - 77*z + 30) with (-77*z)*z + z*(-27*z**2) + 30*z in the overall expression.\n#Step 4:\nCurrent expression: (-77*z)*z - 77*z*(-24) + z*(-27*z**2) + 30*z - 27*z**2*(-24) + (-20*z**3)*(-27*z**2 - 77*z + 30) - 720\nSimplifying the partial expression: (-20*z**3)*(-27*z**2 - 77*z + 30)\nExpanding the part (-27*z**2 - 77*z + 30) using the distributive property, and we got: (-77*z)*(-20*z**3) + 30*(-20*z**3) + (-27*z**2)*(-20*z**3)\nReplacing (-20*z**3)*(-27*z**2 - 77*z + 30) with (-77*z)*(-20*z**3) + 30*(-20*z**3) + (-27*z**2)*(-20*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-77*z)*z + (-77*z)*(-20*z**3) - 77*z*(-24) + 30*(-20)*z**3 + z*(-27*z**2) + 30*z + (-27*z**2)*(-20*z**3) - 27*z**2*(-24) - 720\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-77*z)*-24 = 1848*z\n (-77*z)*z = -77*z**2\n (-77*z)*(-20*z**3) = 1540*z**4\n (-27*z**2)*-24 = 648*z**2\n (-27*z**2)*z = -27*z**3\n (-27*z**2)*(-20*z**3) = 540*z**5\n 30*-20*z**3 = -600*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 540*z**5 + 1540*z**4 - 600*z**3 - 27*z**3 - 77*z**2 + 648*z**2 + 30*z + 1848*z - 720\nCombining like terms, got 540*z**5 + 1540*z**4 - 627*z**3 + 571*z**2 + 1878*z - 720\n#Step 7:\nCurrent expression: 540*z**5 + 1540*z**4 - 627*z**3 + 571*z**2 + 1878*z - 720\nNo more calculations needed.\n540*z**5 + 1540*z**4 - 627*z**3 + 571*z**2 + 1878*z - 720", "generated_answer": "540*z**5 + 1540*z**4 - 627*z**3 + 571*z**2 + 1878*z - 720", "step_length": 7} {"cot_id": "54bd9bd00544f91558e2760facd3adda0457d5c84308a620e347f8ebf99ac776", "datapoint": {"question": "Calculate the following: (51*y - 9)*(30*y**2 + 34*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1530*y**3 + 1464*y**2 - 306*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 714, "polynomial_expr": "(51*y - 9)*(30*y**2 + 34*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (51*y - 9)*(30*y**2 + 34*y)\nExpanding the part (51*y - 9) using the distributive property, and we got: (51*y)*(30*y**2 + 34*y) - 9*(30*y**2 + 34*y)\n#Step 2:\nCurrent expression: (51*y)*(30*y**2 + 34*y) - 9*(30*y**2 + 34*y)\nSimplifying the partial expression: -9*(30*y**2 + 34*y)\nExpanding the part (30*y**2 + 34*y) using the distributive property, and we got: (34*y)*(-9) + (30*y**2)*(-9)\nReplacing -9*(30*y**2 + 34*y) with (34*y)*(-9) + (30*y**2)*(-9) in the overall expression.\n#Step 3:\nCurrent expression: (34*y)*(-9) + (51*y)*(30*y**2 + 34*y) + (30*y**2)*(-9)\nSimplifying the partial expression: (51*y)*(30*y**2 + 34*y)\nExpanding the part (30*y**2 + 34*y) using the distributive property, and we got: (34*y)*(51*y) + (51*y)*(30*y**2)\nReplacing (51*y)*(30*y**2 + 34*y) with (34*y)*(51*y) + (51*y)*(30*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (34*y)*(51*y) + (34*y)*(-9) + (51*y)*(30*y**2) + (30*y**2)*(-9)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (30*y**2)*-9 = -270*y**2\n (30*y**2)*(51*y) = 1530*y**3\n (34*y)*-9 = -306*y\n (34*y)*(51*y) = 1734*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1530*y**3 - 270*y**2 + 1734*y**2 - 306*y\nCombining like terms, got 1530*y**3 + 1464*y**2 - 306*y\n#Step 6:\nCurrent expression: 1530*y**3 + 1464*y**2 - 306*y\nNo more calculations needed.\n1530*y**3 + 1464*y**2 - 306*y", "generated_answer": "1530*y**3 + 1464*y**2 - 306*y", "step_length": 6} {"cot_id": "c2718a4c1fb563c6923ab44a5a5ffb12ea46406524a91d627fadd1e6cfd705dc", "datapoint": {"question": "Calculate the following: -208*y**2 + 784*y - 432\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-208*y**2 + 784*y - 432", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 715, "polynomial_expr": "-208*y**2 + 784*y - 432", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -208*y**2 + 784*y - 432\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -208*y**2 + 784*y - 432\nNo more calculations needed.\n-208*y**2 + 784*y - 432", "generated_answer": "-208*y**2 + 784*y - 432", "step_length": 2} {"cot_id": "a515c4d5f743c0b864693d59297fa2cb3a98316fec6fc1e9ad47327ee1ae447f", "datapoint": {"question": "Simplify this expression: (44*y**3 + 15)*(-47*y**3 + 32*y**2 + 44*y + 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2068*y**6 + 1408*y**5 + 1936*y**4 + 659*y**3 + 480*y**2 + 660*y + 465", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 716, "polynomial_expr": "(44*y**3 + 15)*(-47*y**3 + 32*y**2 + 44*y + 31)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (44*y**3 + 15)*(-47*y**3 + 32*y**2 + 44*y + 31)\nExpanding the part (44*y**3 + 15) using the distributive property, and we got: (44*y**3)*(-47*y**3 + 32*y**2 + 44*y + 31) + 15*(-47*y**3 + 32*y**2 + 44*y + 31)\n#Step 2:\nCurrent expression: (44*y**3)*(-47*y**3 + 32*y**2 + 44*y + 31) + 15*(-47*y**3 + 32*y**2 + 44*y + 31)\nSimplifying the partial expression: 15*(-47*y**3 + 32*y**2 + 44*y + 31)\nExpanding the part (-47*y**3 + 32*y**2 + 44*y + 31) using the distributive property, and we got: (44*y)*15 + (32*y**2)*15 - 47*y**3*15 + 31*15\nReplacing 15*(-47*y**3 + 32*y**2 + 44*y + 31) with (44*y)*15 + (32*y**2)*15 - 47*y**3*15 + 31*15 in the overall expression.\n#Step 3:\nCurrent expression: (44*y)*15 + (32*y**2)*15 - 47*y**3*15 + (44*y**3)*(-47*y**3 + 32*y**2 + 44*y + 31) + 465\nSimplifying the partial expression: (44*y**3)*(-47*y**3 + 32*y**2 + 44*y + 31)\nExpanding the part (-47*y**3 + 32*y**2 + 44*y + 31) using the distributive property, and we got: 31*(44*y**3) + (44*y)*(44*y**3) + (32*y**2)*(44*y**3) + (-47*y**3)*(44*y**3)\nReplacing (44*y**3)*(-47*y**3 + 32*y**2 + 44*y + 31) with 31*(44*y**3) + (44*y)*(44*y**3) + (32*y**2)*(44*y**3) + (-47*y**3)*(44*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 31*44*y**3 + (44*y)*(44*y**3) + (44*y)*15 + (32*y**2)*(44*y**3) + (32*y**2)*15 + (-47*y**3)*(44*y**3) - 47*y**3*15 + 465\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*y**3)*15 = -705*y**3\n (-47*y**3)*(44*y**3) = -2068*y**6\n (32*y**2)*15 = 480*y**2\n (32*y**2)*(44*y**3) = 1408*y**5\n (44*y)*15 = 660*y\n (44*y)*(44*y**3) = 1936*y**4\n 31*44*y**3 = 1364*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2068*y**6 + 1408*y**5 + 1936*y**4 - 705*y**3 + 1364*y**3 + 480*y**2 + 660*y + 465\nCombining like terms, got -2068*y**6 + 1408*y**5 + 1936*y**4 + 659*y**3 + 480*y**2 + 660*y + 465\n#Step 6:\nCurrent expression: -2068*y**6 + 1408*y**5 + 1936*y**4 + 659*y**3 + 480*y**2 + 660*y + 465\nNo more calculations needed.\n-2068*y**6 + 1408*y**5 + 1936*y**4 + 659*y**3 + 480*y**2 + 660*y + 465", "generated_answer": "-2068*y**6 + 1408*y**5 + 1936*y**4 + 659*y**3 + 480*y**2 + 660*y + 465", "step_length": 6} {"cot_id": "30689c457e03e3ab0d9b34418887a85d74dbf8d6ca3ec3becda63b4b556dfe6b", "datapoint": {"question": "Calculate the following: (-29*x**2 - 22*x)*(8*x**3 + 38*x - 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-232*x**5 - 176*x**4 - 1102*x**3 + 614*x**2 + 1100*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 717, "polynomial_expr": "(-29*x**2 - 22*x)*(8*x**3 + 38*x - 50)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-29*x**2 - 22*x)*(8*x**3 + 38*x - 50)\nExpanding the part (-29*x**2 - 22*x) using the distributive property, and we got: (-22*x)*(8*x**3 + 38*x - 50) + (-29*x**2)*(8*x**3 + 38*x - 50)\n#Step 2:\nCurrent expression: (-22*x)*(8*x**3 + 38*x - 50) + (-29*x**2)*(8*x**3 + 38*x - 50)\nSimplifying the partial expression: (-29*x**2)*(8*x**3 + 38*x - 50)\nExpanding the part (8*x**3 + 38*x - 50) using the distributive property, and we got: -(-1)*1450*x**2 + (38*x)*(-29*x**2) + (-29*x**2)*(8*x**3)\nReplacing (-29*x**2)*(8*x**3 + 38*x - 50) with -(-1)*1450*x**2 + (38*x)*(-29*x**2) + (-29*x**2)*(8*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-22*x)*(8*x**3 + 38*x - 50) - 50*(-29)*x**2 + (38*x)*(-29*x**2) + (-29*x**2)*(8*x**3)\nSimplifying the partial expression: (-22*x)*(8*x**3 + 38*x - 50)\nExpanding the part (8*x**3 + 38*x - 50) using the distributive property, and we got: (-22*x)*(38*x) + (-22*x)*(8*x**3) - (-1)*1100*x\nReplacing (-22*x)*(8*x**3 + 38*x - 50) with (-22*x)*(38*x) + (-22*x)*(8*x**3) - (-1)*1100*x in the overall expression.\n#Step 4:\nCurrent expression: (-22*x)*(38*x) + (-22*x)*(8*x**3) - 50*(-29)*x**2 - 50*(-22)*x + (38*x)*(-29*x**2) + (-29*x**2)*(8*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (8*x**3)*(-29*x**2) = -232*x**5\n (8*x**3)*(-22*x) = -176*x**4\n (38*x)*(-29*x**2) = -1102*x**3\n (38*x)*(-22*x) = -836*x**2\n -50*-29*x**2 = 1450*x**2\n -50*-22*x = 1100*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -232*x**5 - 176*x**4 - 1102*x**3 - 836*x**2 + 1450*x**2 + 1100*x\nCombining like terms, got -232*x**5 - 176*x**4 - 1102*x**3 + 614*x**2 + 1100*x\n#Step 6:\nCurrent expression: -232*x**5 - 176*x**4 - 1102*x**3 + 614*x**2 + 1100*x\nNo more calculations needed.\n-232*x**5 - 176*x**4 - 1102*x**3 + 614*x**2 + 1100*x", "generated_answer": "-232*x**5 - 176*x**4 - 1102*x**3 + 614*x**2 + 1100*x", "step_length": 6} {"cot_id": "985877565ea20699e5fdd5da310911bf6727cdc2aacb7aa7d2101c0cd605f43d", "datapoint": {"question": "Calculate the following: (-35*x**3 - 56*x - 42)*(-35*x**3 + 42*x**2 - 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1225*x**6 - 1470*x**5 + 1960*x**4 - 637*x**3 - 1764*x**2 + 392*x + 294", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 718, "polynomial_expr": "(-35*x**3 - 56*x - 42)*(-35*x**3 + 42*x**2 - 7)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-35*x**3 - 56*x - 42)*(-35*x**3 + 42*x**2 - 7)\nExpanding the part (-35*x**3 - 56*x - 42) using the distributive property, and we got: (-56*x)*(-35*x**3 + 42*x**2 - 7) + (-35*x**3)*(-35*x**3 + 42*x**2 - 7) - 42*(-35*x**3 + 42*x**2 - 7)\n#Step 2:\nCurrent expression: (-56*x)*(-35*x**3 + 42*x**2 - 7) + (-35*x**3)*(-35*x**3 + 42*x**2 - 7) - 42*(-35*x**3 + 42*x**2 - 7)\nSimplifying the partial expression: -42*(-35*x**3 + 42*x**2 - 7)\nExpanding the part (-35*x**3 + 42*x**2 - 7) using the distributive property, and we got: (42*x**2)*(-42) - 35*x**3*(-42) - 7*(-42)\nReplacing -42*(-35*x**3 + 42*x**2 - 7) with (42*x**2)*(-42) - 35*x**3*(-42) - 7*(-42) in the overall expression.\n#Step 3:\nCurrent expression: (-56*x)*(-35*x**3 + 42*x**2 - 7) + (42*x**2)*(-42) + (-35*x**3)*(-35*x**3 + 42*x**2 - 7) - 35*x**3*(-42) + 294\nSimplifying the partial expression: (-56*x)*(-35*x**3 + 42*x**2 - 7)\nExpanding the part (-35*x**3 + 42*x**2 - 7) using the distributive property, and we got: (-56*x)*(42*x**2) + (-56*x)*(-35*x**3) - (-1)*392*x\nReplacing (-56*x)*(-35*x**3 + 42*x**2 - 7) with (-56*x)*(42*x**2) + (-56*x)*(-35*x**3) - (-1)*392*x in the overall expression.\n#Step 4:\nCurrent expression: (-56*x)*(42*x**2) + (-56*x)*(-35*x**3) - 7*(-56)*x + (42*x**2)*(-42) + (-35*x**3)*(-35*x**3 + 42*x**2 - 7) - 35*x**3*(-42) + 294\nSimplifying the partial expression: (-35*x**3)*(-35*x**3 + 42*x**2 - 7)\nExpanding the part (-35*x**3 + 42*x**2 - 7) using the distributive property, and we got: -(-1)*245*x**3 + (42*x**2)*(-35*x**3) + (-35*x**3)*(-35*x**3)\nReplacing (-35*x**3)*(-35*x**3 + 42*x**2 - 7) with -(-1)*245*x**3 + (42*x**2)*(-35*x**3) + (-35*x**3)*(-35*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-56*x)*(42*x**2) + (-56*x)*(-35*x**3) - 7*(-35)*x**3 - 7*(-56)*x + (42*x**2)*(-35*x**3) + (42*x**2)*(-42) - 35*x**3*(-42) + (-35*x**3)*(-35*x**3) + 294\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*x**3)*-42 = 1470*x**3\n (-35*x**3)*(-56*x) = 1960*x**4\n (-35*x**3)*(-35*x**3) = 1225*x**6\n (42*x**2)*-42 = -1764*x**2\n (42*x**2)*(-56*x) = -2352*x**3\n (42*x**2)*(-35*x**3) = -1470*x**5\n -7*-56*x = 392*x\n -7*-35*x**3 = 245*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1225*x**6 - 1470*x**5 + 1960*x**4 - 2352*x**3 + 245*x**3 + 1470*x**3 - 1764*x**2 + 392*x + 294\nCombining like terms, got 1225*x**6 - 1470*x**5 + 1960*x**4 - 637*x**3 - 1764*x**2 + 392*x + 294\n#Step 7:\nCurrent expression: 1225*x**6 - 1470*x**5 + 1960*x**4 - 637*x**3 - 1764*x**2 + 392*x + 294\nNo more calculations needed.\n1225*x**6 - 1470*x**5 + 1960*x**4 - 637*x**3 - 1764*x**2 + 392*x + 294", "generated_answer": "1225*x**6 - 1470*x**5 + 1960*x**4 - 637*x**3 - 1764*x**2 + 392*x + 294", "step_length": 7} {"cot_id": "43f27a95d9e50b137212c3b76f0e76e3a67ac293362a86a50f4b0df6a05acbd2", "datapoint": {"question": "Simplify this expression: (25*x**2 + x)*(14*x**3 - 26)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "350*x**5 + 14*x**4 - 650*x**2 - 26*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 719, "polynomial_expr": "(25*x**2 + x)*(14*x**3 - 26)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (25*x**2 + x)*(14*x**3 - 26)\nExpanding the part (14*x**3 - 26) using the distributive property, and we got: (14*x**3)*(25*x**2 + x) - 26*(25*x**2 + x)\n#Step 2:\nCurrent expression: (14*x**3)*(25*x**2 + x) - 26*(25*x**2 + x)\nSimplifying the partial expression: -26*(25*x**2 + x)\nExpanding the part (25*x**2 + x) using the distributive property, and we got: x*(-26) + (25*x**2)*(-26)\nReplacing -26*(25*x**2 + x) with x*(-26) + (25*x**2)*(-26) in the overall expression.\n#Step 3:\nCurrent expression: x*(-26) + (25*x**2)*(-26) + (14*x**3)*(25*x**2 + x)\nSimplifying the partial expression: (14*x**3)*(25*x**2 + x)\nExpanding the part (25*x**2 + x) using the distributive property, and we got: x*(14*x**3) + (25*x**2)*(14*x**3)\nReplacing (14*x**3)*(25*x**2 + x) with x*(14*x**3) + (25*x**2)*(14*x**3) in the overall expression.\n#Step 4:\nCurrent expression: x*(14*x**3) + x*(-26) + (25*x**2)*(14*x**3) + (25*x**2)*(-26)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n x*-26 = -26*x\n x*(14*x**3) = 14*x**4\n (25*x**2)*-26 = -650*x**2\n (25*x**2)*(14*x**3) = 350*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 350*x**5 + 14*x**4 - 650*x**2 - 26*x\nNo more calculations needed.\n350*x**5 + 14*x**4 - 650*x**2 - 26*x", "generated_answer": "350*x**5 + 14*x**4 - 650*x**2 - 26*x", "step_length": 5} {"cot_id": "624bea1d0d9fbb52445c3b2517e79137ded2cc44a51e8d68bedf01f5284618f8", "datapoint": {"question": "Calculate the following: -2867*z**3\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2867*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 720, "polynomial_expr": "-2867*z**3", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -2867*z**3\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -2867*z**3\nNo more calculations needed.\n-2867*z**3", "generated_answer": "-2867*z**3", "step_length": 2} {"cot_id": "9d7c72795d3415b87f8b789938b3f8aa3e4667bb973735cb753976ada8f3d030", "datapoint": {"question": "Calculate the following: (13*z**2 + 39*z + 41)*(8*z**3 + 7*z + 46)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "104*z**5 + 312*z**4 + 419*z**3 + 871*z**2 + 2081*z + 1886", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 721, "polynomial_expr": "(13*z**2 + 39*z + 41)*(8*z**3 + 7*z + 46)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (13*z**2 + 39*z + 41)*(8*z**3 + 7*z + 46)\nExpanding the part (13*z**2 + 39*z + 41) using the distributive property, and we got: (39*z)*(8*z**3 + 7*z + 46) + (13*z**2)*(8*z**3 + 7*z + 46) + 41*(8*z**3 + 7*z + 46)\n#Step 2:\nCurrent expression: (39*z)*(8*z**3 + 7*z + 46) + (13*z**2)*(8*z**3 + 7*z + 46) + 41*(8*z**3 + 7*z + 46)\nSimplifying the partial expression: 41*(8*z**3 + 7*z + 46)\nExpanding the part (8*z**3 + 7*z + 46) using the distributive property, and we got: (7*z)*41 + (8*z**3)*41 + 46*41\nReplacing 41*(8*z**3 + 7*z + 46) with (7*z)*41 + (8*z**3)*41 + 46*41 in the overall expression.\n#Step 3:\nCurrent expression: (7*z)*41 + (39*z)*(8*z**3 + 7*z + 46) + (13*z**2)*(8*z**3 + 7*z + 46) + (8*z**3)*41 + 1886\nSimplifying the partial expression: (13*z**2)*(8*z**3 + 7*z + 46)\nExpanding the part (8*z**3 + 7*z + 46) using the distributive property, and we got: 46*(13*z**2) + (7*z)*(13*z**2) + (13*z**2)*(8*z**3)\nReplacing (13*z**2)*(8*z**3 + 7*z + 46) with 46*(13*z**2) + (7*z)*(13*z**2) + (13*z**2)*(8*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 46*13*z**2 + (7*z)*(13*z**2) + (7*z)*41 + (39*z)*(8*z**3 + 7*z + 46) + (13*z**2)*(8*z**3) + (8*z**3)*41 + 1886\nSimplifying the partial expression: (39*z)*(8*z**3 + 7*z + 46)\nExpanding the part (8*z**3 + 7*z + 46) using the distributive property, and we got: 46*(39*z) + (7*z)*(39*z) + (39*z)*(8*z**3)\nReplacing (39*z)*(8*z**3 + 7*z + 46) with 46*(39*z) + (7*z)*(39*z) + (39*z)*(8*z**3) in the overall expression.\n#Step 5:\nCurrent expression: 46*13*z**2 + 46*39*z + (7*z)*(39*z) + (7*z)*(13*z**2) + (7*z)*41 + (39*z)*(8*z**3) + (13*z**2)*(8*z**3) + (8*z**3)*41 + 1886\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (7*z)*41 = 287*z\n (7*z)*(13*z**2) = 91*z**3\n (7*z)*(39*z) = 273*z**2\n (8*z**3)*41 = 328*z**3\n (8*z**3)*(13*z**2) = 104*z**5\n (8*z**3)*(39*z) = 312*z**4\n 46*13*z**2 = 598*z**2\n 46*39*z = 1794*z\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 104*z**5 + 312*z**4 + 91*z**3 + 328*z**3 + 273*z**2 + 598*z**2 + 287*z + 1794*z + 1886\nCombining like terms, got 104*z**5 + 312*z**4 + 419*z**3 + 871*z**2 + 2081*z + 1886\n#Step 7:\nCurrent expression: 104*z**5 + 312*z**4 + 419*z**3 + 871*z**2 + 2081*z + 1886\nNo more calculations needed.\n104*z**5 + 312*z**4 + 419*z**3 + 871*z**2 + 2081*z + 1886", "generated_answer": "104*z**5 + 312*z**4 + 419*z**3 + 871*z**2 + 2081*z + 1886", "step_length": 7} {"cot_id": "ede4fe3b9cb331d82b2dad244e2280a0a9d69f3bb741a2f62454f18df65c88f7", "datapoint": {"question": "Simplify this expression: (27*z**2 + 9*z)*(27*z**3 + 50*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "729*z**5 + 1593*z**4 + 450*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 722, "polynomial_expr": "(27*z**2 + 9*z)*(27*z**3 + 50*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*z**2 + 9*z)*(27*z**3 + 50*z**2)\nExpanding the part (27*z**2 + 9*z) using the distributive property, and we got: (9*z)*(27*z**3 + 50*z**2) + (27*z**2)*(27*z**3 + 50*z**2)\n#Step 2:\nCurrent expression: (9*z)*(27*z**3 + 50*z**2) + (27*z**2)*(27*z**3 + 50*z**2)\nSimplifying the partial expression: (9*z)*(27*z**3 + 50*z**2)\nExpanding the part (27*z**3 + 50*z**2) using the distributive property, and we got: (9*z)*(50*z**2) + (9*z)*(27*z**3)\nReplacing (9*z)*(27*z**3 + 50*z**2) with (9*z)*(50*z**2) + (9*z)*(27*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (9*z)*(50*z**2) + (9*z)*(27*z**3) + (27*z**2)*(27*z**3 + 50*z**2)\nSimplifying the partial expression: (27*z**2)*(27*z**3 + 50*z**2)\nExpanding the part (27*z**3 + 50*z**2) using the distributive property, and we got: (27*z**2)*(50*z**2) + (27*z**2)*(27*z**3)\nReplacing (27*z**2)*(27*z**3 + 50*z**2) with (27*z**2)*(50*z**2) + (27*z**2)*(27*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (9*z)*(50*z**2) + (9*z)*(27*z**3) + (27*z**2)*(50*z**2) + (27*z**2)*(27*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (27*z**3)*(9*z) = 243*z**4\n (27*z**3)*(27*z**2) = 729*z**5\n (50*z**2)*(9*z) = 450*z**3\n (50*z**2)*(27*z**2) = 1350*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 729*z**5 + 243*z**4 + 1350*z**4 + 450*z**3\nCombining like terms, got 729*z**5 + 1593*z**4 + 450*z**3\n#Step 6:\nCurrent expression: 729*z**5 + 1593*z**4 + 450*z**3\nNo more calculations needed.\n729*z**5 + 1593*z**4 + 450*z**3", "generated_answer": "729*z**5 + 1593*z**4 + 450*z**3", "step_length": 6} {"cot_id": "325fb4d8007d508db8cfcaea44fe7f83b3ef938e30dbae3e120cadad6fc3d824", "datapoint": {"question": "Calculate the following: (-27*x**2 + 12*x)*(26*x**3 + 12*x**2 + 76*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-702*x**5 - 12*x**4 - 1908*x**3 + 912*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 723, "polynomial_expr": "(-27*x**2 + 12*x)*(26*x**3 + 12*x**2 + 76*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-27*x**2 + 12*x)*(26*x**3 + 12*x**2 + 76*x)\nExpanding the part (-27*x**2 + 12*x) using the distributive property, and we got: (12*x)*(26*x**3 + 12*x**2 + 76*x) + (-27*x**2)*(26*x**3 + 12*x**2 + 76*x)\n#Step 2:\nCurrent expression: (12*x)*(26*x**3 + 12*x**2 + 76*x) + (-27*x**2)*(26*x**3 + 12*x**2 + 76*x)\nSimplifying the partial expression: (-27*x**2)*(26*x**3 + 12*x**2 + 76*x)\nExpanding the part (26*x**3 + 12*x**2 + 76*x) using the distributive property, and we got: (76*x)*(-27*x**2) + (-27*x**2)*(12*x**2) + (-27*x**2)*(26*x**3)\nReplacing (-27*x**2)*(26*x**3 + 12*x**2 + 76*x) with (76*x)*(-27*x**2) + (-27*x**2)*(12*x**2) + (-27*x**2)*(26*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (12*x)*(26*x**3 + 12*x**2 + 76*x) + (76*x)*(-27*x**2) + (-27*x**2)*(12*x**2) + (-27*x**2)*(26*x**3)\nSimplifying the partial expression: (12*x)*(26*x**3 + 12*x**2 + 76*x)\nExpanding the part (26*x**3 + 12*x**2 + 76*x) using the distributive property, and we got: (12*x)*(76*x) + (12*x)*(12*x**2) + (12*x)*(26*x**3)\nReplacing (12*x)*(26*x**3 + 12*x**2 + 76*x) with (12*x)*(76*x) + (12*x)*(12*x**2) + (12*x)*(26*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (12*x)*(76*x) + (12*x)*(12*x**2) + (12*x)*(26*x**3) + (76*x)*(-27*x**2) + (-27*x**2)*(12*x**2) + (-27*x**2)*(26*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (12*x**2)*(-27*x**2) = -324*x**4\n (12*x**2)*(12*x) = 144*x**3\n (26*x**3)*(-27*x**2) = -702*x**5\n (26*x**3)*(12*x) = 312*x**4\n (76*x)*(-27*x**2) = -2052*x**3\n (76*x)*(12*x) = 912*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -702*x**5 - 324*x**4 + 312*x**4 - 2052*x**3 + 144*x**3 + 912*x**2\nCombining like terms, got -702*x**5 - 12*x**4 - 1908*x**3 + 912*x**2\n#Step 6:\nCurrent expression: -702*x**5 - 12*x**4 - 1908*x**3 + 912*x**2\nNo more calculations needed.\n-702*x**5 - 12*x**4 - 1908*x**3 + 912*x**2", "generated_answer": "-702*x**5 - 12*x**4 - 1908*x**3 + 912*x**2", "step_length": 6} {"cot_id": "ac83af26ce701157db5c8ed3fccb3a5511295161312b61974ca4317de8be3d37", "datapoint": {"question": "Simplify this expression: (32*y**2 - 3)*(-33*y**3 + 28*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1056*y**5 + 995*y**3 - 84*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 724, "polynomial_expr": "(32*y**2 - 3)*(-33*y**3 + 28*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (32*y**2 - 3)*(-33*y**3 + 28*y)\nExpanding the part (32*y**2 - 3) using the distributive property, and we got: (32*y**2)*(-33*y**3 + 28*y) - 3*(-33*y**3 + 28*y)\n#Step 2:\nCurrent expression: (32*y**2)*(-33*y**3 + 28*y) - 3*(-33*y**3 + 28*y)\nSimplifying the partial expression: -3*(-33*y**3 + 28*y)\nExpanding the part (-33*y**3 + 28*y) using the distributive property, and we got: (28*y)*(-3) - 33*y**3*(-3)\nReplacing -3*(-33*y**3 + 28*y) with (28*y)*(-3) - 33*y**3*(-3) in the overall expression.\n#Step 3:\nCurrent expression: (28*y)*(-3) + (32*y**2)*(-33*y**3 + 28*y) - 33*y**3*(-3)\nSimplifying the partial expression: (32*y**2)*(-33*y**3 + 28*y)\nExpanding the part (-33*y**3 + 28*y) using the distributive property, and we got: (28*y)*(32*y**2) + (32*y**2)*(-33*y**3)\nReplacing (32*y**2)*(-33*y**3 + 28*y) with (28*y)*(32*y**2) + (32*y**2)*(-33*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (28*y)*(32*y**2) + (28*y)*(-3) + (32*y**2)*(-33*y**3) - 33*y**3*(-3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*y**3)*-3 = 99*y**3\n (-33*y**3)*(32*y**2) = -1056*y**5\n (28*y)*-3 = -84*y\n (28*y)*(32*y**2) = 896*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1056*y**5 + 99*y**3 + 896*y**3 - 84*y\nCombining like terms, got -1056*y**5 + 995*y**3 - 84*y\n#Step 6:\nCurrent expression: -1056*y**5 + 995*y**3 - 84*y\nNo more calculations needed.\n-1056*y**5 + 995*y**3 - 84*y", "generated_answer": "-1056*y**5 + 995*y**3 - 84*y", "step_length": 6} {"cot_id": "b951835e4199d1a02fd8547a51ddd85f2008a44b12db4bff4bf06b506c4f1993", "datapoint": {"question": "Simplify this expression: (-41*z**2 + 30*z)*(38*z**2 + 22*z + 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1558*z**4 + 238*z**3 - 37*z**2 + 510*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 725, "polynomial_expr": "(-41*z**2 + 30*z)*(38*z**2 + 22*z + 17)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-41*z**2 + 30*z)*(38*z**2 + 22*z + 17)\nExpanding the part (-41*z**2 + 30*z) using the distributive property, and we got: (30*z)*(38*z**2 + 22*z + 17) + (-41*z**2)*(38*z**2 + 22*z + 17)\n#Step 2:\nCurrent expression: (30*z)*(38*z**2 + 22*z + 17) + (-41*z**2)*(38*z**2 + 22*z + 17)\nSimplifying the partial expression: (-41*z**2)*(38*z**2 + 22*z + 17)\nExpanding the part (38*z**2 + 22*z + 17) using the distributive property, and we got: 17*(-41*z**2) + (22*z)*(-41*z**2) + (-41*z**2)*(38*z**2)\nReplacing (-41*z**2)*(38*z**2 + 22*z + 17) with 17*(-41*z**2) + (22*z)*(-41*z**2) + (-41*z**2)*(38*z**2) in the overall expression.\n#Step 3:\nCurrent expression: 17*(-41)*z**2 + (22*z)*(-41*z**2) + (30*z)*(38*z**2 + 22*z + 17) + (-41*z**2)*(38*z**2)\nSimplifying the partial expression: (30*z)*(38*z**2 + 22*z + 17)\nExpanding the part (38*z**2 + 22*z + 17) using the distributive property, and we got: 17*(30*z) + (22*z)*(30*z) + (30*z)*(38*z**2)\nReplacing (30*z)*(38*z**2 + 22*z + 17) with 17*(30*z) + (22*z)*(30*z) + (30*z)*(38*z**2) in the overall expression.\n#Step 4:\nCurrent expression: 17*(-41)*z**2 + 17*30*z + (22*z)*(30*z) + (22*z)*(-41*z**2) + (30*z)*(38*z**2) + (-41*z**2)*(38*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (22*z)*(-41*z**2) = -902*z**3\n (22*z)*(30*z) = 660*z**2\n (38*z**2)*(-41*z**2) = -1558*z**4\n (38*z**2)*(30*z) = 1140*z**3\n 17*-41*z**2 = -697*z**2\n 17*30*z = 510*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1558*z**4 - 902*z**3 + 1140*z**3 - 697*z**2 + 660*z**2 + 510*z\nCombining like terms, got -1558*z**4 + 238*z**3 - 37*z**2 + 510*z\n#Step 6:\nCurrent expression: -1558*z**4 + 238*z**3 - 37*z**2 + 510*z\nNo more calculations needed.\n-1558*z**4 + 238*z**3 - 37*z**2 + 510*z", "generated_answer": "-1558*z**4 + 238*z**3 - 37*z**2 + 510*z", "step_length": 6} {"cot_id": "3342899ad6aee474e916beea70d461cd56f4406eeac6430bfa8e7e70324fa4cf", "datapoint": {"question": "Simplify this expression: (-3*x**2 + 10*x + 19)*(34*x**2 - 23*x + 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-102*x**4 + 409*x**3 + 317*x**2 - 107*x + 627", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 726, "polynomial_expr": "(-3*x**2 + 10*x + 19)*(34*x**2 - 23*x + 33)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-3*x**2 + 10*x + 19)*(34*x**2 - 23*x + 33)\nExpanding the part (-3*x**2 + 10*x + 19) using the distributive property, and we got: (10*x)*(34*x**2 - 23*x + 33) + (-3*x**2)*(34*x**2 - 23*x + 33) + 19*(34*x**2 - 23*x + 33)\n#Step 2:\nCurrent expression: (10*x)*(34*x**2 - 23*x + 33) + (-3*x**2)*(34*x**2 - 23*x + 33) + 19*(34*x**2 - 23*x + 33)\nSimplifying the partial expression: 19*(34*x**2 - 23*x + 33)\nExpanding the part (34*x**2 - 23*x + 33) using the distributive property, and we got: -23*x*19 + (34*x**2)*19 + 33*19\nReplacing 19*(34*x**2 - 23*x + 33) with -23*x*19 + (34*x**2)*19 + 33*19 in the overall expression.\n#Step 3:\nCurrent expression: -23*x*19 + (10*x)*(34*x**2 - 23*x + 33) + (-3*x**2)*(34*x**2 - 23*x + 33) + (34*x**2)*19 + 627\nSimplifying the partial expression: (-3*x**2)*(34*x**2 - 23*x + 33)\nExpanding the part (34*x**2 - 23*x + 33) using the distributive property, and we got: (-23*x)*(-3*x**2) + 33*(-3*x**2) + (-3*x**2)*(34*x**2)\nReplacing (-3*x**2)*(34*x**2 - 23*x + 33) with (-23*x)*(-3*x**2) + 33*(-3*x**2) + (-3*x**2)*(34*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-23*x)*(-3*x**2) - 23*x*19 + 33*(-3)*x**2 + (10*x)*(34*x**2 - 23*x + 33) + (-3*x**2)*(34*x**2) + (34*x**2)*19 + 627\nSimplifying the partial expression: (10*x)*(34*x**2 - 23*x + 33)\nExpanding the part (34*x**2 - 23*x + 33) using the distributive property, and we got: (-23*x)*(10*x) + 33*(10*x) + (10*x)*(34*x**2)\nReplacing (10*x)*(34*x**2 - 23*x + 33) with (-23*x)*(10*x) + 33*(10*x) + (10*x)*(34*x**2) in the overall expression.\n#Step 5:\nCurrent expression: (-23*x)*(10*x) + (-23*x)*(-3*x**2) - 23*x*19 + 33*(-3)*x**2 + 33*10*x + (10*x)*(34*x**2) + (-3*x**2)*(34*x**2) + (34*x**2)*19 + 627\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*x)*19 = -437*x\n (-23*x)*(-3*x**2) = 69*x**3\n (-23*x)*(10*x) = -230*x**2\n (34*x**2)*19 = 646*x**2\n (34*x**2)*(-3*x**2) = -102*x**4\n (34*x**2)*(10*x) = 340*x**3\n 33*-3*x**2 = -99*x**2\n 33*10*x = 330*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -102*x**4 + 69*x**3 + 340*x**3 - 230*x**2 - 99*x**2 + 646*x**2 - 437*x + 330*x + 627\nCombining like terms, got -102*x**4 + 409*x**3 + 317*x**2 - 107*x + 627\n#Step 7:\nCurrent expression: -102*x**4 + 409*x**3 + 317*x**2 - 107*x + 627\nNo more calculations needed.\n-102*x**4 + 409*x**3 + 317*x**2 - 107*x + 627", "generated_answer": "-102*x**4 + 409*x**3 + 317*x**2 - 107*x + 627", "step_length": 7} {"cot_id": "cd85327d61517e28fa0617fea6cbec4fc5c6bd97330a089278aad9b5171d8678", "datapoint": {"question": "Calculate the following: (14*x**3 + 64*x + 33)*(17*x**3 - 37*x**2 - 78)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "238*x**6 - 518*x**5 + 1088*x**4 - 2899*x**3 - 1221*x**2 - 4992*x - 2574", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 727, "polynomial_expr": "(14*x**3 + 64*x + 33)*(17*x**3 - 37*x**2 - 78)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14*x**3 + 64*x + 33)*(17*x**3 - 37*x**2 - 78)\nExpanding the part (17*x**3 - 37*x**2 - 78) using the distributive property, and we got: (-37*x**2)*(14*x**3 + 64*x + 33) + (17*x**3)*(14*x**3 + 64*x + 33) - 78*(14*x**3 + 64*x + 33)\n#Step 2:\nCurrent expression: (-37*x**2)*(14*x**3 + 64*x + 33) + (17*x**3)*(14*x**3 + 64*x + 33) - 78*(14*x**3 + 64*x + 33)\nSimplifying the partial expression: -78*(14*x**3 + 64*x + 33)\nExpanding the part (14*x**3 + 64*x + 33) using the distributive property, and we got: (64*x)*(-78) + (14*x**3)*(-78) + 33*(-78)\nReplacing -78*(14*x**3 + 64*x + 33) with (64*x)*(-78) + (14*x**3)*(-78) + 33*(-78) in the overall expression.\n#Step 3:\nCurrent expression: (64*x)*(-78) + (-37*x**2)*(14*x**3 + 64*x + 33) + (14*x**3)*(-78) + (17*x**3)*(14*x**3 + 64*x + 33) - 2574\nSimplifying the partial expression: (-37*x**2)*(14*x**3 + 64*x + 33)\nExpanding the part (14*x**3 + 64*x + 33) using the distributive property, and we got: 33*(-37*x**2) + (64*x)*(-37*x**2) + (-37*x**2)*(14*x**3)\nReplacing (-37*x**2)*(14*x**3 + 64*x + 33) with 33*(-37*x**2) + (64*x)*(-37*x**2) + (-37*x**2)*(14*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 33*(-37)*x**2 + (64*x)*(-37*x**2) + (64*x)*(-78) + (-37*x**2)*(14*x**3) + (14*x**3)*(-78) + (17*x**3)*(14*x**3 + 64*x + 33) - 2574\nSimplifying the partial expression: (17*x**3)*(14*x**3 + 64*x + 33)\nExpanding the part (14*x**3 + 64*x + 33) using the distributive property, and we got: 33*(17*x**3) + (64*x)*(17*x**3) + (14*x**3)*(17*x**3)\nReplacing (17*x**3)*(14*x**3 + 64*x + 33) with 33*(17*x**3) + (64*x)*(17*x**3) + (14*x**3)*(17*x**3) in the overall expression.\n#Step 5:\nCurrent expression: 33*17*x**3 + 33*(-37)*x**2 + (64*x)*(-37*x**2) + (64*x)*(17*x**3) + (64*x)*(-78) + (-37*x**2)*(14*x**3) + (14*x**3)*(17*x**3) + (14*x**3)*(-78) - 2574\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (14*x**3)*-78 = -1092*x**3\n (14*x**3)*(-37*x**2) = -518*x**5\n (14*x**3)*(17*x**3) = 238*x**6\n (64*x)*-78 = -4992*x\n (64*x)*(-37*x**2) = -2368*x**3\n (64*x)*(17*x**3) = 1088*x**4\n 33*-37*x**2 = -1221*x**2\n 33*17*x**3 = 561*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 238*x**6 - 518*x**5 + 1088*x**4 - 2368*x**3 - 1092*x**3 + 561*x**3 - 1221*x**2 - 4992*x - 2574\nCombining like terms, got 238*x**6 - 518*x**5 + 1088*x**4 - 2899*x**3 - 1221*x**2 - 4992*x - 2574\n#Step 7:\nCurrent expression: 238*x**6 - 518*x**5 + 1088*x**4 - 2899*x**3 - 1221*x**2 - 4992*x - 2574\nNo more calculations needed.\n238*x**6 - 518*x**5 + 1088*x**4 - 2899*x**3 - 1221*x**2 - 4992*x - 2574", "generated_answer": "238*x**6 - 518*x**5 + 1088*x**4 - 2899*x**3 - 1221*x**2 - 4992*x - 2574", "step_length": 7} {"cot_id": "7a48c554a34be59c7582e611d8bcde0fa1efd79044aeb2363ebed9bd7025e2e4", "datapoint": {"question": "Calculate the following: (22*y**3 + 8)*(35*y**3 + 3*y**2 - 48*y + 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "770*y**6 + 66*y**5 - 1056*y**4 + 654*y**3 + 24*y**2 - 384*y + 136", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 728, "polynomial_expr": "(22*y**3 + 8)*(35*y**3 + 3*y**2 - 48*y + 17)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (22*y**3 + 8)*(35*y**3 + 3*y**2 - 48*y + 17)\nExpanding the part (22*y**3 + 8) using the distributive property, and we got: (22*y**3)*(35*y**3 + 3*y**2 - 48*y + 17) + 8*(35*y**3 + 3*y**2 - 48*y + 17)\n#Step 2:\nCurrent expression: (22*y**3)*(35*y**3 + 3*y**2 - 48*y + 17) + 8*(35*y**3 + 3*y**2 - 48*y + 17)\nSimplifying the partial expression: 8*(35*y**3 + 3*y**2 - 48*y + 17)\nExpanding the part (35*y**3 + 3*y**2 - 48*y + 17) using the distributive property, and we got: -48*y*8 + (3*y**2)*8 + (35*y**3)*8 + 17*8\nReplacing 8*(35*y**3 + 3*y**2 - 48*y + 17) with -48*y*8 + (3*y**2)*8 + (35*y**3)*8 + 17*8 in the overall expression.\n#Step 3:\nCurrent expression: -48*y*8 + (3*y**2)*8 + (22*y**3)*(35*y**3 + 3*y**2 - 48*y + 17) + (35*y**3)*8 + 136\nSimplifying the partial expression: (22*y**3)*(35*y**3 + 3*y**2 - 48*y + 17)\nExpanding the part (35*y**3 + 3*y**2 - 48*y + 17) using the distributive property, and we got: (-48*y)*(22*y**3) + 17*(22*y**3) + (3*y**2)*(22*y**3) + (22*y**3)*(35*y**3)\nReplacing (22*y**3)*(35*y**3 + 3*y**2 - 48*y + 17) with (-48*y)*(22*y**3) + 17*(22*y**3) + (3*y**2)*(22*y**3) + (22*y**3)*(35*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-48*y)*(22*y**3) - 48*y*8 + 17*22*y**3 + (3*y**2)*(22*y**3) + (3*y**2)*8 + (22*y**3)*(35*y**3) + (35*y**3)*8 + 136\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*y)*8 = -384*y\n (-48*y)*(22*y**3) = -1056*y**4\n (3*y**2)*8 = 24*y**2\n (3*y**2)*(22*y**3) = 66*y**5\n (35*y**3)*8 = 280*y**3\n (35*y**3)*(22*y**3) = 770*y**6\n 17*22*y**3 = 374*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 770*y**6 + 66*y**5 - 1056*y**4 + 280*y**3 + 374*y**3 + 24*y**2 - 384*y + 136\nCombining like terms, got 770*y**6 + 66*y**5 - 1056*y**4 + 654*y**3 + 24*y**2 - 384*y + 136\n#Step 6:\nCurrent expression: 770*y**6 + 66*y**5 - 1056*y**4 + 654*y**3 + 24*y**2 - 384*y + 136\nNo more calculations needed.\n770*y**6 + 66*y**5 - 1056*y**4 + 654*y**3 + 24*y**2 - 384*y + 136", "generated_answer": "770*y**6 + 66*y**5 - 1056*y**4 + 654*y**3 + 24*y**2 - 384*y + 136", "step_length": 6} {"cot_id": "b481d3819568a5cd9064fa8cb2abce423d085e194388825c0a7734300ed99868", "datapoint": {"question": "Calculate the following: (20 - 30*y**2)*(40*y**3 + 31*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1200*y**5 - 130*y**3 + 620*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 729, "polynomial_expr": "(20 - 30*y**2)*(40*y**3 + 31*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (20 - 30*y**2)*(40*y**3 + 31*y)\nExpanding the part (20 - 30*y**2) using the distributive property, and we got: (-30*y**2)*(40*y**3 + 31*y) + 20*(40*y**3 + 31*y)\n#Step 2:\nCurrent expression: (-30*y**2)*(40*y**3 + 31*y) + 20*(40*y**3 + 31*y)\nSimplifying the partial expression: 20*(40*y**3 + 31*y)\nExpanding the part (40*y**3 + 31*y) using the distributive property, and we got: (31*y)*20 + (40*y**3)*20\nReplacing 20*(40*y**3 + 31*y) with (31*y)*20 + (40*y**3)*20 in the overall expression.\n#Step 3:\nCurrent expression: (31*y)*20 + (-30*y**2)*(40*y**3 + 31*y) + (40*y**3)*20\nSimplifying the partial expression: (-30*y**2)*(40*y**3 + 31*y)\nExpanding the part (40*y**3 + 31*y) using the distributive property, and we got: (31*y)*(-30*y**2) + (-30*y**2)*(40*y**3)\nReplacing (-30*y**2)*(40*y**3 + 31*y) with (31*y)*(-30*y**2) + (-30*y**2)*(40*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (31*y)*(-30*y**2) + (31*y)*20 + (-30*y**2)*(40*y**3) + (40*y**3)*20\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (31*y)*20 = 620*y\n (31*y)*(-30*y**2) = -930*y**3\n (40*y**3)*20 = 800*y**3\n (40*y**3)*(-30*y**2) = -1200*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1200*y**5 - 930*y**3 + 800*y**3 + 620*y\nCombining like terms, got -1200*y**5 - 130*y**3 + 620*y\n#Step 6:\nCurrent expression: -1200*y**5 - 130*y**3 + 620*y\nNo more calculations needed.\n-1200*y**5 - 130*y**3 + 620*y", "generated_answer": "-1200*y**5 - 130*y**3 + 620*y", "step_length": 6} {"cot_id": "48535355b8055cecc25c389672bc1ec0a40349eae96b11576d4890cb53aeda43", "datapoint": {"question": "Calculate the following: (25*x**2 + 44*x - 4)*(-7*x**3 - 29*x**2 + 61)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-175*x**5 - 1033*x**4 - 1248*x**3 + 1641*x**2 + 2684*x - 244", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 730, "polynomial_expr": "(25*x**2 + 44*x - 4)*(-7*x**3 - 29*x**2 + 61)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (25*x**2 + 44*x - 4)*(-7*x**3 - 29*x**2 + 61)\nExpanding the part (25*x**2 + 44*x - 4) using the distributive property, and we got: (44*x)*(-7*x**3 - 29*x**2 + 61) + (25*x**2)*(-7*x**3 - 29*x**2 + 61) - 4*(-7*x**3 - 29*x**2 + 61)\n#Step 2:\nCurrent expression: (44*x)*(-7*x**3 - 29*x**2 + 61) + (25*x**2)*(-7*x**3 - 29*x**2 + 61) - 4*(-7*x**3 - 29*x**2 + 61)\nSimplifying the partial expression: -4*(-7*x**3 - 29*x**2 + 61)\nExpanding the part (-7*x**3 - 29*x**2 + 61) using the distributive property, and we got: -29*x**2*(-4) - 7*x**3*(-4) + 61*(-4)\nReplacing -4*(-7*x**3 - 29*x**2 + 61) with -29*x**2*(-4) - 7*x**3*(-4) + 61*(-4) in the overall expression.\n#Step 3:\nCurrent expression: (44*x)*(-7*x**3 - 29*x**2 + 61) - 29*x**2*(-4) + (25*x**2)*(-7*x**3 - 29*x**2 + 61) - 7*x**3*(-4) - 244\nSimplifying the partial expression: (25*x**2)*(-7*x**3 - 29*x**2 + 61)\nExpanding the part (-7*x**3 - 29*x**2 + 61) using the distributive property, and we got: 61*(25*x**2) + (-29*x**2)*(25*x**2) + (25*x**2)*(-7*x**3)\nReplacing (25*x**2)*(-7*x**3 - 29*x**2 + 61) with 61*(25*x**2) + (-29*x**2)*(25*x**2) + (25*x**2)*(-7*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 61*25*x**2 + (44*x)*(-7*x**3 - 29*x**2 + 61) + (-29*x**2)*(25*x**2) - 29*x**2*(-4) + (25*x**2)*(-7*x**3) - 7*x**3*(-4) - 244\nSimplifying the partial expression: (44*x)*(-7*x**3 - 29*x**2 + 61)\nExpanding the part (-7*x**3 - 29*x**2 + 61) using the distributive property, and we got: 61*(44*x) + (44*x)*(-29*x**2) + (44*x)*(-7*x**3)\nReplacing (44*x)*(-7*x**3 - 29*x**2 + 61) with 61*(44*x) + (44*x)*(-29*x**2) + (44*x)*(-7*x**3) in the overall expression.\n#Step 5:\nCurrent expression: 61*25*x**2 + 61*44*x + (44*x)*(-29*x**2) + (44*x)*(-7*x**3) + (-29*x**2)*(25*x**2) - 29*x**2*(-4) + (25*x**2)*(-7*x**3) - 7*x**3*(-4) - 244\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*x**2)*-4 = 116*x**2\n (-29*x**2)*(25*x**2) = -725*x**4\n (-29*x**2)*(44*x) = -1276*x**3\n (-7*x**3)*-4 = 28*x**3\n (-7*x**3)*(25*x**2) = -175*x**5\n (-7*x**3)*(44*x) = -308*x**4\n 61*25*x**2 = 1525*x**2\n 61*44*x = 2684*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -175*x**5 - 725*x**4 - 308*x**4 - 1276*x**3 + 28*x**3 + 116*x**2 + 1525*x**2 + 2684*x - 244\nCombining like terms, got -175*x**5 - 1033*x**4 - 1248*x**3 + 1641*x**2 + 2684*x - 244\n#Step 7:\nCurrent expression: -175*x**5 - 1033*x**4 - 1248*x**3 + 1641*x**2 + 2684*x - 244\nNo more calculations needed.\n-175*x**5 - 1033*x**4 - 1248*x**3 + 1641*x**2 + 2684*x - 244", "generated_answer": "-175*x**5 - 1033*x**4 - 1248*x**3 + 1641*x**2 + 2684*x - 244", "step_length": 7} {"cot_id": "8edacedffa79d11f8d250aa4f140d543d9d47cdd12585766e5845891852564be", "datapoint": {"question": "Calculate the following: (8*x**3 + 35*x + 49)*(54*x**3 + 24*x**2 + 40*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "432*x**6 + 192*x**5 + 2210*x**4 + 3486*x**3 + 2576*x**2 + 1960*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 731, "polynomial_expr": "(8*x**3 + 35*x + 49)*(54*x**3 + 24*x**2 + 40*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (8*x**3 + 35*x + 49)*(54*x**3 + 24*x**2 + 40*x)\nExpanding the part (8*x**3 + 35*x + 49) using the distributive property, and we got: (35*x)*(54*x**3 + 24*x**2 + 40*x) + (8*x**3)*(54*x**3 + 24*x**2 + 40*x) + 49*(54*x**3 + 24*x**2 + 40*x)\n#Step 2:\nCurrent expression: (35*x)*(54*x**3 + 24*x**2 + 40*x) + (8*x**3)*(54*x**3 + 24*x**2 + 40*x) + 49*(54*x**3 + 24*x**2 + 40*x)\nSimplifying the partial expression: 49*(54*x**3 + 24*x**2 + 40*x)\nExpanding the part (54*x**3 + 24*x**2 + 40*x) using the distributive property, and we got: (40*x)*49 + (24*x**2)*49 + (54*x**3)*49\nReplacing 49*(54*x**3 + 24*x**2 + 40*x) with (40*x)*49 + (24*x**2)*49 + (54*x**3)*49 in the overall expression.\n#Step 3:\nCurrent expression: (35*x)*(54*x**3 + 24*x**2 + 40*x) + (40*x)*49 + (24*x**2)*49 + (8*x**3)*(54*x**3 + 24*x**2 + 40*x) + (54*x**3)*49\nSimplifying the partial expression: (8*x**3)*(54*x**3 + 24*x**2 + 40*x)\nExpanding the part (54*x**3 + 24*x**2 + 40*x) using the distributive property, and we got: (40*x)*(8*x**3) + (24*x**2)*(8*x**3) + (8*x**3)*(54*x**3)\nReplacing (8*x**3)*(54*x**3 + 24*x**2 + 40*x) with (40*x)*(8*x**3) + (24*x**2)*(8*x**3) + (8*x**3)*(54*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (35*x)*(54*x**3 + 24*x**2 + 40*x) + (40*x)*(8*x**3) + (40*x)*49 + (24*x**2)*(8*x**3) + (24*x**2)*49 + (8*x**3)*(54*x**3) + (54*x**3)*49\nSimplifying the partial expression: (35*x)*(54*x**3 + 24*x**2 + 40*x)\nExpanding the part (54*x**3 + 24*x**2 + 40*x) using the distributive property, and we got: (35*x)*(40*x) + (35*x)*(24*x**2) + (35*x)*(54*x**3)\nReplacing (35*x)*(54*x**3 + 24*x**2 + 40*x) with (35*x)*(40*x) + (35*x)*(24*x**2) + (35*x)*(54*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (35*x)*(40*x) + (35*x)*(24*x**2) + (35*x)*(54*x**3) + (40*x)*(8*x**3) + (40*x)*49 + (24*x**2)*(8*x**3) + (24*x**2)*49 + (8*x**3)*(54*x**3) + (54*x**3)*49\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (24*x**2)*49 = 1176*x**2\n (24*x**2)*(8*x**3) = 192*x**5\n (24*x**2)*(35*x) = 840*x**3\n (40*x)*49 = 1960*x\n (40*x)*(8*x**3) = 320*x**4\n (40*x)*(35*x) = 1400*x**2\n (54*x**3)*49 = 2646*x**3\n (54*x**3)*(8*x**3) = 432*x**6\n (54*x**3)*(35*x) = 1890*x**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 432*x**6 + 192*x**5 + 320*x**4 + 1890*x**4 + 840*x**3 + 2646*x**3 + 1176*x**2 + 1400*x**2 + 1960*x\nCombining like terms, got 432*x**6 + 192*x**5 + 2210*x**4 + 3486*x**3 + 2576*x**2 + 1960*x\n#Step 7:\nCurrent expression: 432*x**6 + 192*x**5 + 2210*x**4 + 3486*x**3 + 2576*x**2 + 1960*x\nNo more calculations needed.\n432*x**6 + 192*x**5 + 2210*x**4 + 3486*x**3 + 2576*x**2 + 1960*x", "generated_answer": "432*x**6 + 192*x**5 + 2210*x**4 + 3486*x**3 + 2576*x**2 + 1960*x", "step_length": 7} {"cot_id": "f9423d51aaf981718753c2d71197dac8ec2830e7cae93a8fc0d7e42cbebded69", "datapoint": {"question": "Simplify this expression: (37*y**2 - 46)*(63*y**2 + 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2331*y**4 - 2639*y**2 - 322", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 732, "polynomial_expr": "(37*y**2 - 46)*(63*y**2 + 7)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (37*y**2 - 46)*(63*y**2 + 7)\nExpanding the part (37*y**2 - 46) using the distributive property, and we got: (37*y**2)*(63*y**2 + 7) - 46*(63*y**2 + 7)\n#Step 2:\nCurrent expression: (37*y**2)*(63*y**2 + 7) - 46*(63*y**2 + 7)\nSimplifying the partial expression: -46*(63*y**2 + 7)\nExpanding the part (63*y**2 + 7) using the distributive property, and we got: (63*y**2)*(-46) + 7*(-46)\nReplacing -46*(63*y**2 + 7) with (63*y**2)*(-46) + 7*(-46) in the overall expression.\n#Step 3:\nCurrent expression: (37*y**2)*(63*y**2 + 7) + (63*y**2)*(-46) - 322\nSimplifying the partial expression: (37*y**2)*(63*y**2 + 7)\nExpanding the part (63*y**2 + 7) using the distributive property, and we got: 7*(37*y**2) + (37*y**2)*(63*y**2)\nReplacing (37*y**2)*(63*y**2 + 7) with 7*(37*y**2) + (37*y**2)*(63*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 7*37*y**2 + (37*y**2)*(63*y**2) + (63*y**2)*(-46) - 322\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (63*y**2)*-46 = -2898*y**2\n (63*y**2)*(37*y**2) = 2331*y**4\n 7*37*y**2 = 259*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2331*y**4 - 2898*y**2 + 259*y**2 - 322\nCombining like terms, got 2331*y**4 - 2639*y**2 - 322\n#Step 6:\nCurrent expression: 2331*y**4 - 2639*y**2 - 322\nNo more calculations needed.\n2331*y**4 - 2639*y**2 - 322", "generated_answer": "2331*y**4 - 2639*y**2 - 322", "step_length": 6} {"cot_id": "43a43b28aca7e2e851a3fab0153bcb8b072774f43f7dc253043425db32c86d33", "datapoint": {"question": "Calculate the following: (-27*y**3 + 41*y**2)*(-28*y**3 - 19*y**2 - 11*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "756*y**6 - 635*y**5 - 482*y**4 - 451*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 733, "polynomial_expr": "(-27*y**3 + 41*y**2)*(-28*y**3 - 19*y**2 - 11*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-27*y**3 + 41*y**2)*(-28*y**3 - 19*y**2 - 11*y)\nExpanding the part (-27*y**3 + 41*y**2) using the distributive property, and we got: (41*y**2)*(-28*y**3 - 19*y**2 - 11*y) + (-27*y**3)*(-28*y**3 - 19*y**2 - 11*y)\n#Step 2:\nCurrent expression: (41*y**2)*(-28*y**3 - 19*y**2 - 11*y) + (-27*y**3)*(-28*y**3 - 19*y**2 - 11*y)\nSimplifying the partial expression: (-27*y**3)*(-28*y**3 - 19*y**2 - 11*y)\nExpanding the part (-28*y**3 - 19*y**2 - 11*y) using the distributive property, and we got: (-11*y)*(-27*y**3) + (-19*y**2)*(-27*y**3) + (-28*y**3)*(-27*y**3)\nReplacing (-27*y**3)*(-28*y**3 - 19*y**2 - 11*y) with (-11*y)*(-27*y**3) + (-19*y**2)*(-27*y**3) + (-28*y**3)*(-27*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-11*y)*(-27*y**3) + (-19*y**2)*(-27*y**3) + (41*y**2)*(-28*y**3 - 19*y**2 - 11*y) + (-28*y**3)*(-27*y**3)\nSimplifying the partial expression: (41*y**2)*(-28*y**3 - 19*y**2 - 11*y)\nExpanding the part (-28*y**3 - 19*y**2 - 11*y) using the distributive property, and we got: (-11*y)*(41*y**2) + (-19*y**2)*(41*y**2) + (41*y**2)*(-28*y**3)\nReplacing (41*y**2)*(-28*y**3 - 19*y**2 - 11*y) with (-11*y)*(41*y**2) + (-19*y**2)*(41*y**2) + (41*y**2)*(-28*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-11*y)*(41*y**2) + (-11*y)*(-27*y**3) + (-19*y**2)*(41*y**2) + (-19*y**2)*(-27*y**3) + (41*y**2)*(-28*y**3) + (-28*y**3)*(-27*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*y**3)*(-27*y**3) = 756*y**6\n (-28*y**3)*(41*y**2) = -1148*y**5\n (-19*y**2)*(-27*y**3) = 513*y**5\n (-19*y**2)*(41*y**2) = -779*y**4\n (-11*y)*(-27*y**3) = 297*y**4\n (-11*y)*(41*y**2) = -451*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 756*y**6 - 1148*y**5 + 513*y**5 - 779*y**4 + 297*y**4 - 451*y**3\nCombining like terms, got 756*y**6 - 635*y**5 - 482*y**4 - 451*y**3\n#Step 6:\nCurrent expression: 756*y**6 - 635*y**5 - 482*y**4 - 451*y**3\nNo more calculations needed.\n756*y**6 - 635*y**5 - 482*y**4 - 451*y**3", "generated_answer": "756*y**6 - 635*y**5 - 482*y**4 - 451*y**3", "step_length": 6} {"cot_id": "92a443f3adc30367d8a57fb8239bcda0b4789fca0f0819da2ff7dfe2dbcababf", "datapoint": {"question": "Simplify this expression: (31*y**3 + 30*y**2)*(-4*y**3 + 11*y + 26)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-124*y**6 - 120*y**5 + 341*y**4 + 1136*y**3 + 780*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 734, "polynomial_expr": "(31*y**3 + 30*y**2)*(-4*y**3 + 11*y + 26)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31*y**3 + 30*y**2)*(-4*y**3 + 11*y + 26)\nExpanding the part (31*y**3 + 30*y**2) using the distributive property, and we got: (30*y**2)*(-4*y**3 + 11*y + 26) + (31*y**3)*(-4*y**3 + 11*y + 26)\n#Step 2:\nCurrent expression: (30*y**2)*(-4*y**3 + 11*y + 26) + (31*y**3)*(-4*y**3 + 11*y + 26)\nSimplifying the partial expression: (30*y**2)*(-4*y**3 + 11*y + 26)\nExpanding the part (-4*y**3 + 11*y + 26) using the distributive property, and we got: 26*(30*y**2) + (11*y)*(30*y**2) + (30*y**2)*(-4*y**3)\nReplacing (30*y**2)*(-4*y**3 + 11*y + 26) with 26*(30*y**2) + (11*y)*(30*y**2) + (30*y**2)*(-4*y**3) in the overall expression.\n#Step 3:\nCurrent expression: 26*30*y**2 + (11*y)*(30*y**2) + (30*y**2)*(-4*y**3) + (31*y**3)*(-4*y**3 + 11*y + 26)\nSimplifying the partial expression: (31*y**3)*(-4*y**3 + 11*y + 26)\nExpanding the part (-4*y**3 + 11*y + 26) using the distributive property, and we got: 26*(31*y**3) + (11*y)*(31*y**3) + (-4*y**3)*(31*y**3)\nReplacing (31*y**3)*(-4*y**3 + 11*y + 26) with 26*(31*y**3) + (11*y)*(31*y**3) + (-4*y**3)*(31*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 26*31*y**3 + 26*30*y**2 + (11*y)*(30*y**2) + (11*y)*(31*y**3) + (30*y**2)*(-4*y**3) + (-4*y**3)*(31*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-4*y**3)*(30*y**2) = -120*y**5\n (-4*y**3)*(31*y**3) = -124*y**6\n (11*y)*(30*y**2) = 330*y**3\n (11*y)*(31*y**3) = 341*y**4\n 26*30*y**2 = 780*y**2\n 26*31*y**3 = 806*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -124*y**6 - 120*y**5 + 341*y**4 + 330*y**3 + 806*y**3 + 780*y**2\nCombining like terms, got -124*y**6 - 120*y**5 + 341*y**4 + 1136*y**3 + 780*y**2\n#Step 6:\nCurrent expression: -124*y**6 - 120*y**5 + 341*y**4 + 1136*y**3 + 780*y**2\nNo more calculations needed.\n-124*y**6 - 120*y**5 + 341*y**4 + 1136*y**3 + 780*y**2", "generated_answer": "-124*y**6 - 120*y**5 + 341*y**4 + 1136*y**3 + 780*y**2", "step_length": 6} {"cot_id": "b29ead824d0c6c472cb36643e1d12133f2aa1531567c94d1dd7f5bbb92c1a09e", "datapoint": {"question": "Calculate the following: 15*x*(43*x**3 + 24*x**2 + 35*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "645*x**4 + 360*x**3 + 525*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 735, "polynomial_expr": "15*x*(43*x**3 + 24*x**2 + 35*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 15*x*(43*x**3 + 24*x**2 + 35*x)\nExpanding the part (43*x**3 + 24*x**2 + 35*x) using the distributive property, and we got: (15*x)*(35*x) + (15*x)*(24*x**2) + (15*x)*(43*x**3)\n#Step 2:\nCurrent expression: (15*x)*(35*x) + (15*x)*(24*x**2) + (15*x)*(43*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (24*x**2)*(15*x) = 360*x**3\n (35*x)*(15*x) = 525*x**2\n (43*x**3)*(15*x) = 645*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 645*x**4 + 360*x**3 + 525*x**2\nNo more calculations needed.\n645*x**4 + 360*x**3 + 525*x**2", "generated_answer": "645*x**4 + 360*x**3 + 525*x**2", "step_length": 3} {"cot_id": "04d92efedffbc5451d27334c276cb2727ff9f967951b4e6842aaa157d79d5aa2", "datapoint": {"question": "Simplify this expression: (2*x + 43)*(14*x**3 + 49*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "28*x**4 + 700*x**3 + 2107*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 736, "polynomial_expr": "(2*x + 43)*(14*x**3 + 49*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2*x + 43)*(14*x**3 + 49*x**2)\nExpanding the part (2*x + 43) using the distributive property, and we got: (2*x)*(14*x**3 + 49*x**2) + 43*(14*x**3 + 49*x**2)\n#Step 2:\nCurrent expression: (2*x)*(14*x**3 + 49*x**2) + 43*(14*x**3 + 49*x**2)\nSimplifying the partial expression: 43*(14*x**3 + 49*x**2)\nExpanding the part (14*x**3 + 49*x**2) using the distributive property, and we got: (49*x**2)*43 + (14*x**3)*43\nReplacing 43*(14*x**3 + 49*x**2) with (49*x**2)*43 + (14*x**3)*43 in the overall expression.\n#Step 3:\nCurrent expression: (2*x)*(14*x**3 + 49*x**2) + (49*x**2)*43 + (14*x**3)*43\nSimplifying the partial expression: (2*x)*(14*x**3 + 49*x**2)\nExpanding the part (14*x**3 + 49*x**2) using the distributive property, and we got: (2*x)*(49*x**2) + (2*x)*(14*x**3)\nReplacing (2*x)*(14*x**3 + 49*x**2) with (2*x)*(49*x**2) + (2*x)*(14*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (2*x)*(49*x**2) + (2*x)*(14*x**3) + (49*x**2)*43 + (14*x**3)*43\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (14*x**3)*43 = 602*x**3\n (14*x**3)*(2*x) = 28*x**4\n (49*x**2)*43 = 2107*x**2\n (49*x**2)*(2*x) = 98*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 28*x**4 + 98*x**3 + 602*x**3 + 2107*x**2\nCombining like terms, got 28*x**4 + 700*x**3 + 2107*x**2\n#Step 6:\nCurrent expression: 28*x**4 + 700*x**3 + 2107*x**2\nNo more calculations needed.\n28*x**4 + 700*x**3 + 2107*x**2", "generated_answer": "28*x**4 + 700*x**3 + 2107*x**2", "step_length": 6} {"cot_id": "5e3f67abfd4b7704de5dd91e0311d5cd1d09ed26adf1fa67681b9a2f339aea16", "datapoint": {"question": "Simplify this expression: -946*z**2 + 220*z + 902\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-946*z**2 + 220*z + 902", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 737, "polynomial_expr": "-946*z**2 + 220*z + 902", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -946*z**2 + 220*z + 902\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -946*z**2 + 220*z + 902\nNo more calculations needed.\n-946*z**2 + 220*z + 902", "generated_answer": "-946*z**2 + 220*z + 902", "step_length": 2} {"cot_id": "f6dc41ffb44f50c4d39aa3f644990e9bd12bc3d5cc135b54833af62801029b0c", "datapoint": {"question": "Simplify this expression: (-5*x**2 - 35)*(-14*x**3 - 75*x - 45)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "70*x**5 + 865*x**3 + 225*x**2 + 2625*x + 1575", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 738, "polynomial_expr": "(-5*x**2 - 35)*(-14*x**3 - 75*x - 45)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-5*x**2 - 35)*(-14*x**3 - 75*x - 45)\nExpanding the part (-5*x**2 - 35) using the distributive property, and we got: (-5*x**2)*(-14*x**3 - 75*x - 45) - 35*(-14*x**3 - 75*x - 45)\n#Step 2:\nCurrent expression: (-5*x**2)*(-14*x**3 - 75*x - 45) - 35*(-14*x**3 - 75*x - 45)\nSimplifying the partial expression: -35*(-14*x**3 - 75*x - 45)\nExpanding the part (-14*x**3 - 75*x - 45) using the distributive property, and we got: -75*x*(-35) - 14*x**3*(-35) - 45*(-35)\nReplacing -35*(-14*x**3 - 75*x - 45) with -75*x*(-35) - 14*x**3*(-35) - 45*(-35) in the overall expression.\n#Step 3:\nCurrent expression: -75*x*(-35) + (-5*x**2)*(-14*x**3 - 75*x - 45) - 14*x**3*(-35) + 1575\nSimplifying the partial expression: (-5*x**2)*(-14*x**3 - 75*x - 45)\nExpanding the part (-14*x**3 - 75*x - 45) using the distributive property, and we got: (-75*x)*(-5*x**2) - (-1)*225*x**2 + (-5*x**2)*(-14*x**3)\nReplacing (-5*x**2)*(-14*x**3 - 75*x - 45) with (-75*x)*(-5*x**2) - (-1)*225*x**2 + (-5*x**2)*(-14*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-75*x)*(-5*x**2) - 75*x*(-35) - 45*(-5)*x**2 + (-5*x**2)*(-14*x**3) - 14*x**3*(-35) + 1575\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-75*x)*-35 = 2625*x\n (-75*x)*(-5*x**2) = 375*x**3\n (-14*x**3)*-35 = 490*x**3\n (-14*x**3)*(-5*x**2) = 70*x**5\n -45*-5*x**2 = 225*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 70*x**5 + 375*x**3 + 490*x**3 + 225*x**2 + 2625*x + 1575\nCombining like terms, got 70*x**5 + 865*x**3 + 225*x**2 + 2625*x + 1575\n#Step 6:\nCurrent expression: 70*x**5 + 865*x**3 + 225*x**2 + 2625*x + 1575\nNo more calculations needed.\n70*x**5 + 865*x**3 + 225*x**2 + 2625*x + 1575", "generated_answer": "70*x**5 + 865*x**3 + 225*x**2 + 2625*x + 1575", "step_length": 6} {"cot_id": "934dff8104a3edd93fe14aa2710713760be6dd593574a0c63d407f7a33c11de3", "datapoint": {"question": "Simplify this expression: (-29*x**2 + 20*x - 39)*(47*x**3 - 10*x**2 + 18*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1363*x**5 + 1230*x**4 - 2555*x**3 + 750*x**2 - 702*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 739, "polynomial_expr": "(-29*x**2 + 20*x - 39)*(47*x**3 - 10*x**2 + 18*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-29*x**2 + 20*x - 39)*(47*x**3 - 10*x**2 + 18*x)\nExpanding the part (-29*x**2 + 20*x - 39) using the distributive property, and we got: (20*x)*(47*x**3 - 10*x**2 + 18*x) + (-29*x**2)*(47*x**3 - 10*x**2 + 18*x) - 39*(47*x**3 - 10*x**2 + 18*x)\n#Step 2:\nCurrent expression: (20*x)*(47*x**3 - 10*x**2 + 18*x) + (-29*x**2)*(47*x**3 - 10*x**2 + 18*x) - 39*(47*x**3 - 10*x**2 + 18*x)\nSimplifying the partial expression: -39*(47*x**3 - 10*x**2 + 18*x)\nExpanding the part (47*x**3 - 10*x**2 + 18*x) using the distributive property, and we got: (18*x)*(-39) - 10*x**2*(-39) + (47*x**3)*(-39)\nReplacing -39*(47*x**3 - 10*x**2 + 18*x) with (18*x)*(-39) - 10*x**2*(-39) + (47*x**3)*(-39) in the overall expression.\n#Step 3:\nCurrent expression: (18*x)*(-39) + (20*x)*(47*x**3 - 10*x**2 + 18*x) + (-29*x**2)*(47*x**3 - 10*x**2 + 18*x) - 10*x**2*(-39) + (47*x**3)*(-39)\nSimplifying the partial expression: (-29*x**2)*(47*x**3 - 10*x**2 + 18*x)\nExpanding the part (47*x**3 - 10*x**2 + 18*x) using the distributive property, and we got: (18*x)*(-29*x**2) + (-29*x**2)*(-10*x**2) + (-29*x**2)*(47*x**3)\nReplacing (-29*x**2)*(47*x**3 - 10*x**2 + 18*x) with (18*x)*(-29*x**2) + (-29*x**2)*(-10*x**2) + (-29*x**2)*(47*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (18*x)*(-29*x**2) + (18*x)*(-39) + (20*x)*(47*x**3 - 10*x**2 + 18*x) + (-29*x**2)*(-10*x**2) + (-29*x**2)*(47*x**3) - 10*x**2*(-39) + (47*x**3)*(-39)\nSimplifying the partial expression: (20*x)*(47*x**3 - 10*x**2 + 18*x)\nExpanding the part (47*x**3 - 10*x**2 + 18*x) using the distributive property, and we got: (18*x)*(20*x) + (20*x)*(-10*x**2) + (20*x)*(47*x**3)\nReplacing (20*x)*(47*x**3 - 10*x**2 + 18*x) with (18*x)*(20*x) + (20*x)*(-10*x**2) + (20*x)*(47*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (18*x)*(20*x) + (18*x)*(-29*x**2) + (18*x)*(-39) + (20*x)*(-10*x**2) + (20*x)*(47*x**3) + (-29*x**2)*(-10*x**2) + (-29*x**2)*(47*x**3) - 10*x**2*(-39) + (47*x**3)*(-39)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*x**2)*-39 = 390*x**2\n (-10*x**2)*(-29*x**2) = 290*x**4\n (-10*x**2)*(20*x) = -200*x**3\n (18*x)*-39 = -702*x\n (18*x)*(-29*x**2) = -522*x**3\n (18*x)*(20*x) = 360*x**2\n (47*x**3)*-39 = -1833*x**3\n (47*x**3)*(-29*x**2) = -1363*x**5\n (47*x**3)*(20*x) = 940*x**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1363*x**5 + 290*x**4 + 940*x**4 - 1833*x**3 - 522*x**3 - 200*x**3 + 360*x**2 + 390*x**2 - 702*x\nCombining like terms, got -1363*x**5 + 1230*x**4 - 2555*x**3 + 750*x**2 - 702*x\n#Step 7:\nCurrent expression: -1363*x**5 + 1230*x**4 - 2555*x**3 + 750*x**2 - 702*x\nNo more calculations needed.\n-1363*x**5 + 1230*x**4 - 2555*x**3 + 750*x**2 - 702*x", "generated_answer": "-1363*x**5 + 1230*x**4 - 2555*x**3 + 750*x**2 - 702*x", "step_length": 7} {"cot_id": "69edfcb57ab75006e2ef1f48b1391dc480b269e68e82ecc67c1df974116e0c75", "datapoint": {"question": "Simplify this expression: (50 - 42*z**2)*(-38*z - 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1596*z**3 + 1260*z**2 - 1900*z - 1500", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 740, "polynomial_expr": "(50 - 42*z**2)*(-38*z - 30)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (50 - 42*z**2)*(-38*z - 30)\nExpanding the part (-38*z - 30) using the distributive property, and we got: (-38*z)*(50 - 42*z**2) - 30*(50 - 42*z**2)\n#Step 2:\nCurrent expression: (-38*z)*(50 - 42*z**2) - 30*(50 - 42*z**2)\nSimplifying the partial expression: -30*(50 - 42*z**2)\nExpanding the part (50 - 42*z**2) using the distributive property, and we got: -42*z**2*(-30) + 50*(-30)\nReplacing -30*(50 - 42*z**2) with -42*z**2*(-30) + 50*(-30) in the overall expression.\n#Step 3:\nCurrent expression: (-38*z)*(50 - 42*z**2) - 42*z**2*(-30) - 1500\nSimplifying the partial expression: (-38*z)*(50 - 42*z**2)\nExpanding the part (50 - 42*z**2) using the distributive property, and we got: (-38*z)*(-42*z**2) + 50*(-38*z)\nReplacing (-38*z)*(50 - 42*z**2) with (-38*z)*(-42*z**2) + 50*(-38*z) in the overall expression.\n#Step 4:\nCurrent expression: (-38*z)*(-42*z**2) + 50*(-38)*z - 42*z**2*(-30) - 1500\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*z**2)*-30 = 1260*z**2\n (-42*z**2)*(-38*z) = 1596*z**3\n 50*-38*z = -1900*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1596*z**3 + 1260*z**2 - 1900*z - 1500\nNo more calculations needed.\n1596*z**3 + 1260*z**2 - 1900*z - 1500", "generated_answer": "1596*z**3 + 1260*z**2 - 1900*z - 1500", "step_length": 5} {"cot_id": "4911517716b6ef67634813a30d50389a61783a1f206686b0914e48c78eee45b3", "datapoint": {"question": "Simplify this expression: (13*z**3 - 30*z**2)*(46*z**3 - 17*z**2 + 31*z + 5)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "598*z**6 - 1601*z**5 + 913*z**4 - 865*z**3 - 150*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 741, "polynomial_expr": "(13*z**3 - 30*z**2)*(46*z**3 - 17*z**2 + 31*z + 5)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (13*z**3 - 30*z**2)*(46*z**3 - 17*z**2 + 31*z + 5)\nExpanding the part (13*z**3 - 30*z**2) using the distributive property, and we got: (-30*z**2)*(46*z**3 - 17*z**2 + 31*z + 5) + (13*z**3)*(46*z**3 - 17*z**2 + 31*z + 5)\n#Step 2:\nCurrent expression: (-30*z**2)*(46*z**3 - 17*z**2 + 31*z + 5) + (13*z**3)*(46*z**3 - 17*z**2 + 31*z + 5)\nSimplifying the partial expression: (-30*z**2)*(46*z**3 - 17*z**2 + 31*z + 5)\nExpanding the part (46*z**3 - 17*z**2 + 31*z + 5) using the distributive property, and we got: 5*(-30*z**2) + (31*z)*(-30*z**2) + (-30*z**2)*(-17*z**2) + (-30*z**2)*(46*z**3)\nReplacing (-30*z**2)*(46*z**3 - 17*z**2 + 31*z + 5) with 5*(-30*z**2) + (31*z)*(-30*z**2) + (-30*z**2)*(-17*z**2) + (-30*z**2)*(46*z**3) in the overall expression.\n#Step 3:\nCurrent expression: 5*(-30)*z**2 + (31*z)*(-30*z**2) + (-30*z**2)*(-17*z**2) + (-30*z**2)*(46*z**3) + (13*z**3)*(46*z**3 - 17*z**2 + 31*z + 5)\nSimplifying the partial expression: (13*z**3)*(46*z**3 - 17*z**2 + 31*z + 5)\nExpanding the part (46*z**3 - 17*z**2 + 31*z + 5) using the distributive property, and we got: 5*(13*z**3) + (31*z)*(13*z**3) + (-17*z**2)*(13*z**3) + (13*z**3)*(46*z**3)\nReplacing (13*z**3)*(46*z**3 - 17*z**2 + 31*z + 5) with 5*(13*z**3) + (31*z)*(13*z**3) + (-17*z**2)*(13*z**3) + (13*z**3)*(46*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 5*13*z**3 + 5*(-30)*z**2 + (31*z)*(-30*z**2) + (31*z)*(13*z**3) + (-30*z**2)*(-17*z**2) + (-30*z**2)*(46*z**3) + (-17*z**2)*(13*z**3) + (13*z**3)*(46*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-17*z**2)*(-30*z**2) = 510*z**4\n (-17*z**2)*(13*z**3) = -221*z**5\n (31*z)*(-30*z**2) = -930*z**3\n (31*z)*(13*z**3) = 403*z**4\n (46*z**3)*(-30*z**2) = -1380*z**5\n (46*z**3)*(13*z**3) = 598*z**6\n 5*-30*z**2 = -150*z**2\n 5*13*z**3 = 65*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 598*z**6 - 1380*z**5 - 221*z**5 + 403*z**4 + 510*z**4 - 930*z**3 + 65*z**3 - 150*z**2\nCombining like terms, got 598*z**6 - 1601*z**5 + 913*z**4 - 865*z**3 - 150*z**2\n#Step 6:\nCurrent expression: 598*z**6 - 1601*z**5 + 913*z**4 - 865*z**3 - 150*z**2\nNo more calculations needed.\n598*z**6 - 1601*z**5 + 913*z**4 - 865*z**3 - 150*z**2", "generated_answer": "598*z**6 - 1601*z**5 + 913*z**4 - 865*z**3 - 150*z**2", "step_length": 6} {"cot_id": "11063a76660f3d5de68ce090d018b7cbf0093fe2528d2171b4052eacf1be2259", "datapoint": {"question": "Calculate the following: (-24*y**2 - 3*y)*(16*y**3 + 22*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-384*y**5 - 576*y**4 - 66*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 742, "polynomial_expr": "(-24*y**2 - 3*y)*(16*y**3 + 22*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-24*y**2 - 3*y)*(16*y**3 + 22*y**2)\nExpanding the part (-24*y**2 - 3*y) using the distributive property, and we got: (-3*y)*(16*y**3 + 22*y**2) + (-24*y**2)*(16*y**3 + 22*y**2)\n#Step 2:\nCurrent expression: (-3*y)*(16*y**3 + 22*y**2) + (-24*y**2)*(16*y**3 + 22*y**2)\nSimplifying the partial expression: (-24*y**2)*(16*y**3 + 22*y**2)\nExpanding the part (16*y**3 + 22*y**2) using the distributive property, and we got: (-24*y**2)*(22*y**2) + (-24*y**2)*(16*y**3)\nReplacing (-24*y**2)*(16*y**3 + 22*y**2) with (-24*y**2)*(22*y**2) + (-24*y**2)*(16*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-3*y)*(16*y**3 + 22*y**2) + (-24*y**2)*(22*y**2) + (-24*y**2)*(16*y**3)\nSimplifying the partial expression: (-3*y)*(16*y**3 + 22*y**2)\nExpanding the part (16*y**3 + 22*y**2) using the distributive property, and we got: (-3*y)*(22*y**2) + (-3*y)*(16*y**3)\nReplacing (-3*y)*(16*y**3 + 22*y**2) with (-3*y)*(22*y**2) + (-3*y)*(16*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-3*y)*(22*y**2) + (-3*y)*(16*y**3) + (-24*y**2)*(22*y**2) + (-24*y**2)*(16*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (16*y**3)*(-24*y**2) = -384*y**5\n (16*y**3)*(-3*y) = -48*y**4\n (22*y**2)*(-24*y**2) = -528*y**4\n (22*y**2)*(-3*y) = -66*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -384*y**5 - 528*y**4 - 48*y**4 - 66*y**3\nCombining like terms, got -384*y**5 - 576*y**4 - 66*y**3\n#Step 6:\nCurrent expression: -384*y**5 - 576*y**4 - 66*y**3\nNo more calculations needed.\n-384*y**5 - 576*y**4 - 66*y**3", "generated_answer": "-384*y**5 - 576*y**4 - 66*y**3", "step_length": 6} {"cot_id": "1b1982fa7c5ff808fd86c75172c50d1263b2340ca2549550983bf7c92d078816", "datapoint": {"question": "Calculate the following: (-26*z**3 - 46*z**2)*(-4*z**3 - 19*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "104*z**6 + 184*z**5 + 494*z**4 + 874*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 743, "polynomial_expr": "(-26*z**3 - 46*z**2)*(-4*z**3 - 19*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-26*z**3 - 46*z**2)*(-4*z**3 - 19*z)\nExpanding the part (-26*z**3 - 46*z**2) using the distributive property, and we got: (-46*z**2)*(-4*z**3 - 19*z) + (-26*z**3)*(-4*z**3 - 19*z)\n#Step 2:\nCurrent expression: (-46*z**2)*(-4*z**3 - 19*z) + (-26*z**3)*(-4*z**3 - 19*z)\nSimplifying the partial expression: (-46*z**2)*(-4*z**3 - 19*z)\nExpanding the part (-4*z**3 - 19*z) using the distributive property, and we got: (-19*z)*(-46*z**2) + (-46*z**2)*(-4*z**3)\nReplacing (-46*z**2)*(-4*z**3 - 19*z) with (-19*z)*(-46*z**2) + (-46*z**2)*(-4*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-19*z)*(-46*z**2) + (-46*z**2)*(-4*z**3) + (-26*z**3)*(-4*z**3 - 19*z)\nSimplifying the partial expression: (-26*z**3)*(-4*z**3 - 19*z)\nExpanding the part (-4*z**3 - 19*z) using the distributive property, and we got: (-19*z)*(-26*z**3) + (-26*z**3)*(-4*z**3)\nReplacing (-26*z**3)*(-4*z**3 - 19*z) with (-19*z)*(-26*z**3) + (-26*z**3)*(-4*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-19*z)*(-46*z**2) + (-19*z)*(-26*z**3) + (-46*z**2)*(-4*z**3) + (-26*z**3)*(-4*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*z)*(-46*z**2) = 874*z**3\n (-19*z)*(-26*z**3) = 494*z**4\n (-4*z**3)*(-46*z**2) = 184*z**5\n (-4*z**3)*(-26*z**3) = 104*z**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 104*z**6 + 184*z**5 + 494*z**4 + 874*z**3\nNo more calculations needed.\n104*z**6 + 184*z**5 + 494*z**4 + 874*z**3", "generated_answer": "104*z**6 + 184*z**5 + 494*z**4 + 874*z**3", "step_length": 5} {"cot_id": "7c4f4305a19db840fb6760f52ab0f9ace2349a8e35c9c399268f9eacd9438738", "datapoint": {"question": "Simplify this expression: (68*y**3 + 18)*(y**2 + 53*y - 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "68*y**5 + 3604*y**4 - 1632*y**3 + 18*y**2 + 954*y - 432", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 744, "polynomial_expr": "(68*y**3 + 18)*(y**2 + 53*y - 24)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (68*y**3 + 18)*(y**2 + 53*y - 24)\nExpanding the part (68*y**3 + 18) using the distributive property, and we got: (68*y**3)*(y**2 + 53*y - 24) + 18*(y**2 + 53*y - 24)\n#Step 2:\nCurrent expression: (68*y**3)*(y**2 + 53*y - 24) + 18*(y**2 + 53*y - 24)\nSimplifying the partial expression: 18*(y**2 + 53*y - 24)\nExpanding the part (y**2 + 53*y - 24) using the distributive property, and we got: y**2*18 + (53*y)*18 - 24*18\nReplacing 18*(y**2 + 53*y - 24) with y**2*18 + (53*y)*18 - 24*18 in the overall expression.\n#Step 3:\nCurrent expression: y**2*18 + (53*y)*18 + (68*y**3)*(y**2 + 53*y - 24) - 432\nSimplifying the partial expression: (68*y**3)*(y**2 + 53*y - 24)\nExpanding the part (y**2 + 53*y - 24) using the distributive property, and we got: -1632*y**3 + y**2*(68*y**3) + (53*y)*(68*y**3)\nReplacing (68*y**3)*(y**2 + 53*y - 24) with -1632*y**3 + y**2*(68*y**3) + (53*y)*(68*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -24*68*y**3 + y**2*(68*y**3) + y**2*18 + (53*y)*(68*y**3) + (53*y)*18 - 432\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n y**2*18 = 18*y**2\n y**2*(68*y**3) = 68*y**5\n (53*y)*18 = 954*y\n (53*y)*(68*y**3) = 3604*y**4\n -24*68*y**3 = -1632*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 68*y**5 + 3604*y**4 - 1632*y**3 + 18*y**2 + 954*y - 432\nNo more calculations needed.\n68*y**5 + 3604*y**4 - 1632*y**3 + 18*y**2 + 954*y - 432", "generated_answer": "68*y**5 + 3604*y**4 - 1632*y**3 + 18*y**2 + 954*y - 432", "step_length": 5} {"cot_id": "275ec26f96d8582ec6d8b9e84553e7bc59da57b86935e19f4d74ca0b7b74171f", "datapoint": {"question": "Calculate the following: (26*y**3 + 47*y**2)*(-25*y**2 + 6*y - 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-650*y**5 - 1019*y**4 - 550*y**3 - 1504*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 745, "polynomial_expr": "(26*y**3 + 47*y**2)*(-25*y**2 + 6*y - 32)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (26*y**3 + 47*y**2)*(-25*y**2 + 6*y - 32)\nExpanding the part (26*y**3 + 47*y**2) using the distributive property, and we got: (47*y**2)*(-25*y**2 + 6*y - 32) + (26*y**3)*(-25*y**2 + 6*y - 32)\n#Step 2:\nCurrent expression: (47*y**2)*(-25*y**2 + 6*y - 32) + (26*y**3)*(-25*y**2 + 6*y - 32)\nSimplifying the partial expression: (26*y**3)*(-25*y**2 + 6*y - 32)\nExpanding the part (-25*y**2 + 6*y - 32) using the distributive property, and we got: -832*y**3 + (6*y)*(26*y**3) + (-25*y**2)*(26*y**3)\nReplacing (26*y**3)*(-25*y**2 + 6*y - 32) with -832*y**3 + (6*y)*(26*y**3) + (-25*y**2)*(26*y**3) in the overall expression.\n#Step 3:\nCurrent expression: -32*26*y**3 + (6*y)*(26*y**3) + (-25*y**2)*(26*y**3) + (47*y**2)*(-25*y**2 + 6*y - 32)\nSimplifying the partial expression: (47*y**2)*(-25*y**2 + 6*y - 32)\nExpanding the part (-25*y**2 + 6*y - 32) using the distributive property, and we got: -1504*y**2 + (6*y)*(47*y**2) + (-25*y**2)*(47*y**2)\nReplacing (47*y**2)*(-25*y**2 + 6*y - 32) with -1504*y**2 + (6*y)*(47*y**2) + (-25*y**2)*(47*y**2) in the overall expression.\n#Step 4:\nCurrent expression: -32*26*y**3 - 32*47*y**2 + (6*y)*(47*y**2) + (6*y)*(26*y**3) + (-25*y**2)*(47*y**2) + (-25*y**2)*(26*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*y**2)*(26*y**3) = -650*y**5\n (-25*y**2)*(47*y**2) = -1175*y**4\n (6*y)*(26*y**3) = 156*y**4\n (6*y)*(47*y**2) = 282*y**3\n -32*26*y**3 = -832*y**3\n -32*47*y**2 = -1504*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -650*y**5 - 1175*y**4 + 156*y**4 - 832*y**3 + 282*y**3 - 1504*y**2\nCombining like terms, got -650*y**5 - 1019*y**4 - 550*y**3 - 1504*y**2\n#Step 6:\nCurrent expression: -650*y**5 - 1019*y**4 - 550*y**3 - 1504*y**2\nNo more calculations needed.\n-650*y**5 - 1019*y**4 - 550*y**3 - 1504*y**2", "generated_answer": "-650*y**5 - 1019*y**4 - 550*y**3 - 1504*y**2", "step_length": 6} {"cot_id": "569f594af48a715f8166898a86e58158f1cc178d012979829a1633a0f688be77", "datapoint": {"question": "Simplify this expression: 2516*z**3 + 1020*z**2 + 748*z - 2788\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2516*z**3 + 1020*z**2 + 748*z - 2788", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 746, "polynomial_expr": "2516*z**3 + 1020*z**2 + 748*z - 2788", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 2516*z**3 + 1020*z**2 + 748*z - 2788\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 2516*z**3 + 1020*z**2 + 748*z - 2788\nNo more calculations needed.\n2516*z**3 + 1020*z**2 + 748*z - 2788", "generated_answer": "2516*z**3 + 1020*z**2 + 748*z - 2788", "step_length": 2} {"cot_id": "0ad7d89fb73c8b9165d9d55bd3c55b1a04d1fb35178eb17cef27878f33e111d8", "datapoint": {"question": "Simplify this expression: (9*y**2 + 48*y)*(-15*y**2 + 20*y - 42)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-135*y**4 - 540*y**3 + 582*y**2 - 2016*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 747, "polynomial_expr": "(9*y**2 + 48*y)*(-15*y**2 + 20*y - 42)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9*y**2 + 48*y)*(-15*y**2 + 20*y - 42)\nExpanding the part (9*y**2 + 48*y) using the distributive property, and we got: (48*y)*(-15*y**2 + 20*y - 42) + (9*y**2)*(-15*y**2 + 20*y - 42)\n#Step 2:\nCurrent expression: (48*y)*(-15*y**2 + 20*y - 42) + (9*y**2)*(-15*y**2 + 20*y - 42)\nSimplifying the partial expression: (9*y**2)*(-15*y**2 + 20*y - 42)\nExpanding the part (-15*y**2 + 20*y - 42) using the distributive property, and we got: -378*y**2 + (20*y)*(9*y**2) + (-15*y**2)*(9*y**2)\nReplacing (9*y**2)*(-15*y**2 + 20*y - 42) with -378*y**2 + (20*y)*(9*y**2) + (-15*y**2)*(9*y**2) in the overall expression.\n#Step 3:\nCurrent expression: -42*9*y**2 + (20*y)*(9*y**2) + (48*y)*(-15*y**2 + 20*y - 42) + (-15*y**2)*(9*y**2)\nSimplifying the partial expression: (48*y)*(-15*y**2 + 20*y - 42)\nExpanding the part (-15*y**2 + 20*y - 42) using the distributive property, and we got: -2016*y + (20*y)*(48*y) + (48*y)*(-15*y**2)\nReplacing (48*y)*(-15*y**2 + 20*y - 42) with -2016*y + (20*y)*(48*y) + (48*y)*(-15*y**2) in the overall expression.\n#Step 4:\nCurrent expression: -42*9*y**2 - 42*48*y + (20*y)*(48*y) + (20*y)*(9*y**2) + (48*y)*(-15*y**2) + (-15*y**2)*(9*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-15*y**2)*(9*y**2) = -135*y**4\n (-15*y**2)*(48*y) = -720*y**3\n (20*y)*(9*y**2) = 180*y**3\n (20*y)*(48*y) = 960*y**2\n -42*9*y**2 = -378*y**2\n -42*48*y = -2016*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -135*y**4 - 720*y**3 + 180*y**3 - 378*y**2 + 960*y**2 - 2016*y\nCombining like terms, got -135*y**4 - 540*y**3 + 582*y**2 - 2016*y\n#Step 6:\nCurrent expression: -135*y**4 - 540*y**3 + 582*y**2 - 2016*y\nNo more calculations needed.\n-135*y**4 - 540*y**3 + 582*y**2 - 2016*y", "generated_answer": "-135*y**4 - 540*y**3 + 582*y**2 - 2016*y", "step_length": 6} {"cot_id": "754dac2ced8c1ed1c2b3eeb540f644680b97afd18253e15ce16c93b6c01badc2", "datapoint": {"question": "Simplify this expression: (30*z**3 - 18*z)*(-48*z**3 - 3*z - 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1440*z**6 + 774*z**4 - 1140*z**3 + 54*z**2 + 684*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 748, "polynomial_expr": "(30*z**3 - 18*z)*(-48*z**3 - 3*z - 38)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (30*z**3 - 18*z)*(-48*z**3 - 3*z - 38)\nExpanding the part (30*z**3 - 18*z) using the distributive property, and we got: (-18*z)*(-48*z**3 - 3*z - 38) + (30*z**3)*(-48*z**3 - 3*z - 38)\n#Step 2:\nCurrent expression: (-18*z)*(-48*z**3 - 3*z - 38) + (30*z**3)*(-48*z**3 - 3*z - 38)\nSimplifying the partial expression: (-18*z)*(-48*z**3 - 3*z - 38)\nExpanding the part (-48*z**3 - 3*z - 38) using the distributive property, and we got: (-18*z)*(-3*z) + (-18*z)*(-48*z**3) - (-1)*684*z\nReplacing (-18*z)*(-48*z**3 - 3*z - 38) with (-18*z)*(-3*z) + (-18*z)*(-48*z**3) - (-1)*684*z in the overall expression.\n#Step 3:\nCurrent expression: (-18*z)*(-3*z) + (-18*z)*(-48*z**3) - 38*(-18)*z + (30*z**3)*(-48*z**3 - 3*z - 38)\nSimplifying the partial expression: (30*z**3)*(-48*z**3 - 3*z - 38)\nExpanding the part (-48*z**3 - 3*z - 38) using the distributive property, and we got: (-3*z)*(30*z**3) - 1140*z**3 + (-48*z**3)*(30*z**3)\nReplacing (30*z**3)*(-48*z**3 - 3*z - 38) with (-3*z)*(30*z**3) - 1140*z**3 + (-48*z**3)*(30*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-18*z)*(-3*z) + (-18*z)*(-48*z**3) + (-3*z)*(30*z**3) - 38*30*z**3 - 38*(-18)*z + (-48*z**3)*(30*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*z**3)*(-18*z) = 864*z**4\n (-48*z**3)*(30*z**3) = -1440*z**6\n (-3*z)*(-18*z) = 54*z**2\n (-3*z)*(30*z**3) = -90*z**4\n -38*-18*z = 684*z\n -38*30*z**3 = -1140*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1440*z**6 - 90*z**4 + 864*z**4 - 1140*z**3 + 54*z**2 + 684*z\nCombining like terms, got -1440*z**6 + 774*z**4 - 1140*z**3 + 54*z**2 + 684*z\n#Step 6:\nCurrent expression: -1440*z**6 + 774*z**4 - 1140*z**3 + 54*z**2 + 684*z\nNo more calculations needed.\n-1440*z**6 + 774*z**4 - 1140*z**3 + 54*z**2 + 684*z", "generated_answer": "-1440*z**6 + 774*z**4 - 1140*z**3 + 54*z**2 + 684*z", "step_length": 6} {"cot_id": "f96b5bd8bdc586cfaf8390473e682321cf993cbe9c1bf5e60b83b2b174dcf301", "datapoint": {"question": "Calculate the following: (17*z**2 - 5*z)*(11*z**2 - 41*z + 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "187*z**4 - 752*z**3 + 222*z**2 - 5*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 749, "polynomial_expr": "(17*z**2 - 5*z)*(11*z**2 - 41*z + 1)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (17*z**2 - 5*z)*(11*z**2 - 41*z + 1)\nExpanding the part (17*z**2 - 5*z) using the distributive property, and we got: (-5*z)*(11*z**2 - 41*z + 1) + (17*z**2)*(11*z**2 - 41*z + 1)\n#Step 2:\nCurrent expression: (-5*z)*(11*z**2 - 41*z + 1) + (17*z**2)*(11*z**2 - 41*z + 1)\nSimplifying the partial expression: (-5*z)*(11*z**2 - 41*z + 1)\nExpanding the part (11*z**2 - 41*z + 1) using the distributive property, and we got: (-41*z)*(-5*z) + (-5*z)*(11*z**2) + 1*(-5*z)\nReplacing (-5*z)*(11*z**2 - 41*z + 1) with (-41*z)*(-5*z) + (-5*z)*(11*z**2) + 1*(-5*z) in the overall expression.\n#Step 3:\nCurrent expression: (-41*z)*(-5*z) + (-5*z)*(11*z**2) - 5*z + (17*z**2)*(11*z**2 - 41*z + 1)\nSimplifying the partial expression: (17*z**2)*(11*z**2 - 41*z + 1)\nExpanding the part (11*z**2 - 41*z + 1) using the distributive property, and we got: (-41*z)*(17*z**2) + 1*(17*z**2) + (11*z**2)*(17*z**2)\nReplacing (17*z**2)*(11*z**2 - 41*z + 1) with (-41*z)*(17*z**2) + 1*(17*z**2) + (11*z**2)*(17*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-41*z)*(-5*z) + (-41*z)*(17*z**2) + (-5*z)*(11*z**2) + 17*z**2 - 5*z + (11*z**2)*(17*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*z)*(-5*z) = 205*z**2\n (-41*z)*(17*z**2) = -697*z**3\n (11*z**2)*(-5*z) = -55*z**3\n (11*z**2)*(17*z**2) = 187*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 187*z**4 - 697*z**3 - 55*z**3 + 17*z**2 + 205*z**2 - 5*z\nCombining like terms, got 187*z**4 - 752*z**3 + 222*z**2 - 5*z\n#Step 6:\nCurrent expression: 187*z**4 - 752*z**3 + 222*z**2 - 5*z\nNo more calculations needed.\n187*z**4 - 752*z**3 + 222*z**2 - 5*z", "generated_answer": "187*z**4 - 752*z**3 + 222*z**2 - 5*z", "step_length": 6} {"cot_id": "1cfb24d9f8b850f84cf37cc9599943ea19b55117b8b76164972178dbac5acfc1", "datapoint": {"question": "Calculate the following: (-33*z**3 - 30*z - 4)*(46*z**3 - 37*z - 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1518*z**6 - 159*z**4 + 971*z**3 + 1110*z**2 + 1198*z + 140", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 750, "polynomial_expr": "(-33*z**3 - 30*z - 4)*(46*z**3 - 37*z - 35)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-33*z**3 - 30*z - 4)*(46*z**3 - 37*z - 35)\nExpanding the part (46*z**3 - 37*z - 35) using the distributive property, and we got: (-37*z)*(-33*z**3 - 30*z - 4) + (46*z**3)*(-33*z**3 - 30*z - 4) - 35*(-33*z**3 - 30*z - 4)\n#Step 2:\nCurrent expression: (-37*z)*(-33*z**3 - 30*z - 4) + (46*z**3)*(-33*z**3 - 30*z - 4) - 35*(-33*z**3 - 30*z - 4)\nSimplifying the partial expression: -35*(-33*z**3 - 30*z - 4)\nExpanding the part (-33*z**3 - 30*z - 4) using the distributive property, and we got: -30*z*(-35) - 33*z**3*(-35) - 4*(-35)\nReplacing -35*(-33*z**3 - 30*z - 4) with -30*z*(-35) - 33*z**3*(-35) - 4*(-35) in the overall expression.\n#Step 3:\nCurrent expression: (-37*z)*(-33*z**3 - 30*z - 4) - 30*z*(-35) - 33*z**3*(-35) + (46*z**3)*(-33*z**3 - 30*z - 4) + 140\nSimplifying the partial expression: (-37*z)*(-33*z**3 - 30*z - 4)\nExpanding the part (-33*z**3 - 30*z - 4) using the distributive property, and we got: (-37*z)*(-30*z) + (-37*z)*(-33*z**3) - (-1)*148*z\nReplacing (-37*z)*(-33*z**3 - 30*z - 4) with (-37*z)*(-30*z) + (-37*z)*(-33*z**3) - (-1)*148*z in the overall expression.\n#Step 4:\nCurrent expression: (-37*z)*(-30*z) + (-37*z)*(-33*z**3) - 30*z*(-35) - 4*(-37)*z - 33*z**3*(-35) + (46*z**3)*(-33*z**3 - 30*z - 4) + 140\nSimplifying the partial expression: (46*z**3)*(-33*z**3 - 30*z - 4)\nExpanding the part (-33*z**3 - 30*z - 4) using the distributive property, and we got: (-30*z)*(46*z**3) - 184*z**3 + (-33*z**3)*(46*z**3)\nReplacing (46*z**3)*(-33*z**3 - 30*z - 4) with (-30*z)*(46*z**3) - 184*z**3 + (-33*z**3)*(46*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-37*z)*(-30*z) + (-37*z)*(-33*z**3) + (-30*z)*(46*z**3) - 30*z*(-35) - 4*46*z**3 - 4*(-37)*z + (-33*z**3)*(46*z**3) - 33*z**3*(-35) + 140\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*z**3)*-35 = 1155*z**3\n (-33*z**3)*(-37*z) = 1221*z**4\n (-33*z**3)*(46*z**3) = -1518*z**6\n (-30*z)*-35 = 1050*z\n (-30*z)*(-37*z) = 1110*z**2\n (-30*z)*(46*z**3) = -1380*z**4\n -4*-37*z = 148*z\n -4*46*z**3 = -184*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1518*z**6 - 1380*z**4 + 1221*z**4 - 184*z**3 + 1155*z**3 + 1110*z**2 + 148*z + 1050*z + 140\nCombining like terms, got -1518*z**6 - 159*z**4 + 971*z**3 + 1110*z**2 + 1198*z + 140\n#Step 7:\nCurrent expression: -1518*z**6 - 159*z**4 + 971*z**3 + 1110*z**2 + 1198*z + 140\nNo more calculations needed.\n-1518*z**6 - 159*z**4 + 971*z**3 + 1110*z**2 + 1198*z + 140", "generated_answer": "-1518*z**6 - 159*z**4 + 971*z**3 + 1110*z**2 + 1198*z + 140", "step_length": 7} {"cot_id": "75796a1a0aee03057829a0bda14a8e102b03df46fc18086f5181173bdab901de", "datapoint": {"question": "Calculate the following: (35*z**3 + 17*z**2)*(66*z**3 + 36*z - 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2310*z**6 + 1122*z**5 + 1260*z**4 + 157*z**3 - 221*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 751, "polynomial_expr": "(35*z**3 + 17*z**2)*(66*z**3 + 36*z - 13)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (35*z**3 + 17*z**2)*(66*z**3 + 36*z - 13)\nExpanding the part (35*z**3 + 17*z**2) using the distributive property, and we got: (17*z**2)*(66*z**3 + 36*z - 13) + (35*z**3)*(66*z**3 + 36*z - 13)\n#Step 2:\nCurrent expression: (17*z**2)*(66*z**3 + 36*z - 13) + (35*z**3)*(66*z**3 + 36*z - 13)\nSimplifying the partial expression: (17*z**2)*(66*z**3 + 36*z - 13)\nExpanding the part (66*z**3 + 36*z - 13) using the distributive property, and we got: -221*z**2 + (36*z)*(17*z**2) + (17*z**2)*(66*z**3)\nReplacing (17*z**2)*(66*z**3 + 36*z - 13) with -221*z**2 + (36*z)*(17*z**2) + (17*z**2)*(66*z**3) in the overall expression.\n#Step 3:\nCurrent expression: -13*17*z**2 + (36*z)*(17*z**2) + (17*z**2)*(66*z**3) + (35*z**3)*(66*z**3 + 36*z - 13)\nSimplifying the partial expression: (35*z**3)*(66*z**3 + 36*z - 13)\nExpanding the part (66*z**3 + 36*z - 13) using the distributive property, and we got: -455*z**3 + (36*z)*(35*z**3) + (35*z**3)*(66*z**3)\nReplacing (35*z**3)*(66*z**3 + 36*z - 13) with -455*z**3 + (36*z)*(35*z**3) + (35*z**3)*(66*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -13*35*z**3 - 13*17*z**2 + (36*z)*(17*z**2) + (36*z)*(35*z**3) + (17*z**2)*(66*z**3) + (35*z**3)*(66*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (36*z)*(17*z**2) = 612*z**3\n (36*z)*(35*z**3) = 1260*z**4\n (66*z**3)*(17*z**2) = 1122*z**5\n (66*z**3)*(35*z**3) = 2310*z**6\n -13*17*z**2 = -221*z**2\n -13*35*z**3 = -455*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2310*z**6 + 1122*z**5 + 1260*z**4 - 455*z**3 + 612*z**3 - 221*z**2\nCombining like terms, got 2310*z**6 + 1122*z**5 + 1260*z**4 + 157*z**3 - 221*z**2\n#Step 6:\nCurrent expression: 2310*z**6 + 1122*z**5 + 1260*z**4 + 157*z**3 - 221*z**2\nNo more calculations needed.\n2310*z**6 + 1122*z**5 + 1260*z**4 + 157*z**3 - 221*z**2", "generated_answer": "2310*z**6 + 1122*z**5 + 1260*z**4 + 157*z**3 - 221*z**2", "step_length": 6} {"cot_id": "77f9ec717bd54a6fe42d01b091f9fd26f3813973ec5a28307856c14e1ec38d37", "datapoint": {"question": "Calculate the following: (5*y + 39)*(46*y**3 - 27*y**2 + 6*y + 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "230*y**4 + 1659*y**3 - 1023*y**2 + 239*y + 39", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 752, "polynomial_expr": "(5*y + 39)*(46*y**3 - 27*y**2 + 6*y + 1)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (5*y + 39)*(46*y**3 - 27*y**2 + 6*y + 1)\nExpanding the part (5*y + 39) using the distributive property, and we got: (5*y)*(46*y**3 - 27*y**2 + 6*y + 1) + 39*(46*y**3 - 27*y**2 + 6*y + 1)\n#Step 2:\nCurrent expression: (5*y)*(46*y**3 - 27*y**2 + 6*y + 1) + 39*(46*y**3 - 27*y**2 + 6*y + 1)\nSimplifying the partial expression: 39*(46*y**3 - 27*y**2 + 6*y + 1)\nExpanding the part (46*y**3 - 27*y**2 + 6*y + 1) using the distributive property, and we got: (6*y)*39 - 27*y**2*39 + (46*y**3)*39 + 1*39\nReplacing 39*(46*y**3 - 27*y**2 + 6*y + 1) with (6*y)*39 - 27*y**2*39 + (46*y**3)*39 + 1*39 in the overall expression.\n#Step 3:\nCurrent expression: (5*y)*(46*y**3 - 27*y**2 + 6*y + 1) + (6*y)*39 - 27*y**2*39 + (46*y**3)*39 + 39\nSimplifying the partial expression: (5*y)*(46*y**3 - 27*y**2 + 6*y + 1)\nExpanding the part (46*y**3 - 27*y**2 + 6*y + 1) using the distributive property, and we got: 1*(5*y) + (5*y)*(6*y) + (5*y)*(-27*y**2) + (5*y)*(46*y**3)\nReplacing (5*y)*(46*y**3 - 27*y**2 + 6*y + 1) with 1*(5*y) + (5*y)*(6*y) + (5*y)*(-27*y**2) + (5*y)*(46*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 5*y + (5*y)*(6*y) + (5*y)*(-27*y**2) + (5*y)*(46*y**3) + (6*y)*39 - 27*y**2*39 + (46*y**3)*39 + 39\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*y**2)*39 = -1053*y**2\n (-27*y**2)*(5*y) = -135*y**3\n (6*y)*39 = 234*y\n (6*y)*(5*y) = 30*y**2\n (46*y**3)*39 = 1794*y**3\n (46*y**3)*(5*y) = 230*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 230*y**4 - 135*y**3 + 1794*y**3 - 1053*y**2 + 30*y**2 + 5*y + 234*y + 39\nCombining like terms, got 230*y**4 + 1659*y**3 - 1023*y**2 + 239*y + 39\n#Step 6:\nCurrent expression: 230*y**4 + 1659*y**3 - 1023*y**2 + 239*y + 39\nNo more calculations needed.\n230*y**4 + 1659*y**3 - 1023*y**2 + 239*y + 39", "generated_answer": "230*y**4 + 1659*y**3 - 1023*y**2 + 239*y + 39", "step_length": 6} {"cot_id": "3107a79d52cd27142b0a2aa14a6ed046911d7fef7600f8ff7adb574eb125aeee", "datapoint": {"question": "Calculate the following: 61*y**3*(-39*y**3 - 24*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2379*y**6 - 1464*y**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 753, "polynomial_expr": "61*y**3*(-39*y**3 - 24*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 61*y**3*(-39*y**3 - 24*y)\nExpanding the part (-39*y**3 - 24*y) using the distributive property, and we got: (-24*y)*(61*y**3) + (-39*y**3)*(61*y**3)\n#Step 2:\nCurrent expression: (-24*y)*(61*y**3) + (-39*y**3)*(61*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*y**3)*(61*y**3) = -2379*y**6\n (-24*y)*(61*y**3) = -1464*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -2379*y**6 - 1464*y**4\nNo more calculations needed.\n-2379*y**6 - 1464*y**4", "generated_answer": "-2379*y**6 - 1464*y**4", "step_length": 3} {"cot_id": "3dd083c53aac5cddfa0604d032ba21fcba53cc91385bdac184d8f321694037a7", "datapoint": {"question": "Calculate the following: (2*z**3 - 7*z**2)*(8*z**3 + 49*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "16*z**6 - 56*z**5 + 98*z**4 - 343*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 754, "polynomial_expr": "(2*z**3 - 7*z**2)*(8*z**3 + 49*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2*z**3 - 7*z**2)*(8*z**3 + 49*z)\nExpanding the part (2*z**3 - 7*z**2) using the distributive property, and we got: (-7*z**2)*(8*z**3 + 49*z) + (2*z**3)*(8*z**3 + 49*z)\n#Step 2:\nCurrent expression: (-7*z**2)*(8*z**3 + 49*z) + (2*z**3)*(8*z**3 + 49*z)\nSimplifying the partial expression: (-7*z**2)*(8*z**3 + 49*z)\nExpanding the part (8*z**3 + 49*z) using the distributive property, and we got: (49*z)*(-7*z**2) + (-7*z**2)*(8*z**3)\nReplacing (-7*z**2)*(8*z**3 + 49*z) with (49*z)*(-7*z**2) + (-7*z**2)*(8*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (49*z)*(-7*z**2) + (-7*z**2)*(8*z**3) + (2*z**3)*(8*z**3 + 49*z)\nSimplifying the partial expression: (2*z**3)*(8*z**3 + 49*z)\nExpanding the part (8*z**3 + 49*z) using the distributive property, and we got: (49*z)*(2*z**3) + (2*z**3)*(8*z**3)\nReplacing (2*z**3)*(8*z**3 + 49*z) with (49*z)*(2*z**3) + (2*z**3)*(8*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (49*z)*(-7*z**2) + (49*z)*(2*z**3) + (-7*z**2)*(8*z**3) + (2*z**3)*(8*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (8*z**3)*(-7*z**2) = -56*z**5\n (8*z**3)*(2*z**3) = 16*z**6\n (49*z)*(-7*z**2) = -343*z**3\n (49*z)*(2*z**3) = 98*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 16*z**6 - 56*z**5 + 98*z**4 - 343*z**3\nNo more calculations needed.\n16*z**6 - 56*z**5 + 98*z**4 - 343*z**3", "generated_answer": "16*z**6 - 56*z**5 + 98*z**4 - 343*z**3", "step_length": 5} {"cot_id": "86b4cc3a4b456b0dbbff09d01ef2f6ed80c4525dc623c0cbeff86c3ef460fefd", "datapoint": {"question": "Simplify this expression: (33*z**3 + 6*z**2)*(33*z**3 + 23*z**2 + 8*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1089*z**6 + 957*z**5 + 402*z**4 + 48*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 755, "polynomial_expr": "(33*z**3 + 6*z**2)*(33*z**3 + 23*z**2 + 8*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (33*z**3 + 6*z**2)*(33*z**3 + 23*z**2 + 8*z)\nExpanding the part (33*z**3 + 6*z**2) using the distributive property, and we got: (6*z**2)*(33*z**3 + 23*z**2 + 8*z) + (33*z**3)*(33*z**3 + 23*z**2 + 8*z)\n#Step 2:\nCurrent expression: (6*z**2)*(33*z**3 + 23*z**2 + 8*z) + (33*z**3)*(33*z**3 + 23*z**2 + 8*z)\nSimplifying the partial expression: (6*z**2)*(33*z**3 + 23*z**2 + 8*z)\nExpanding the part (33*z**3 + 23*z**2 + 8*z) using the distributive property, and we got: (8*z)*(6*z**2) + (6*z**2)*(23*z**2) + (6*z**2)*(33*z**3)\nReplacing (6*z**2)*(33*z**3 + 23*z**2 + 8*z) with (8*z)*(6*z**2) + (6*z**2)*(23*z**2) + (6*z**2)*(33*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (8*z)*(6*z**2) + (6*z**2)*(23*z**2) + (6*z**2)*(33*z**3) + (33*z**3)*(33*z**3 + 23*z**2 + 8*z)\nSimplifying the partial expression: (33*z**3)*(33*z**3 + 23*z**2 + 8*z)\nExpanding the part (33*z**3 + 23*z**2 + 8*z) using the distributive property, and we got: (8*z)*(33*z**3) + (23*z**2)*(33*z**3) + (33*z**3)*(33*z**3)\nReplacing (33*z**3)*(33*z**3 + 23*z**2 + 8*z) with (8*z)*(33*z**3) + (23*z**2)*(33*z**3) + (33*z**3)*(33*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (8*z)*(6*z**2) + (8*z)*(33*z**3) + (6*z**2)*(23*z**2) + (6*z**2)*(33*z**3) + (23*z**2)*(33*z**3) + (33*z**3)*(33*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (8*z)*(6*z**2) = 48*z**3\n (8*z)*(33*z**3) = 264*z**4\n (23*z**2)*(6*z**2) = 138*z**4\n (23*z**2)*(33*z**3) = 759*z**5\n (33*z**3)*(6*z**2) = 198*z**5\n (33*z**3)*(33*z**3) = 1089*z**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1089*z**6 + 198*z**5 + 759*z**5 + 138*z**4 + 264*z**4 + 48*z**3\nCombining like terms, got 1089*z**6 + 957*z**5 + 402*z**4 + 48*z**3\n#Step 6:\nCurrent expression: 1089*z**6 + 957*z**5 + 402*z**4 + 48*z**3\nNo more calculations needed.\n1089*z**6 + 957*z**5 + 402*z**4 + 48*z**3", "generated_answer": "1089*z**6 + 957*z**5 + 402*z**4 + 48*z**3", "step_length": 6} {"cot_id": "7053c9ea685804fc1fa894f218208b5232d630e85845ad1543d9dceae714fe3f", "datapoint": {"question": "Simplify this expression: -56*y**2*(50*y**3 - 40*y + 12)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2800*y**5 + 2240*y**3 - 672*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 756, "polynomial_expr": "-56*y**2*(50*y**3 - 40*y + 12)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -56*y**2*(50*y**3 - 40*y + 12)\nExpanding the part (50*y**3 - 40*y + 12) using the distributive property, and we got: (-40*y)*(-56*y**2) + 12*(-56*y**2) + (-56*y**2)*(50*y**3)\n#Step 2:\nCurrent expression: (-40*y)*(-56*y**2) + 12*(-56*y**2) + (-56*y**2)*(50*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 12*(-56*y**2) = -672*y**2\n (-40*y)*(-56*y**2) = 2240*y**3\n (50*y**3)*(-56*y**2) = -2800*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -2800*y**5 + 2240*y**3 - 672*y**2\nNo more calculations needed.\n-2800*y**5 + 2240*y**3 - 672*y**2", "generated_answer": "-2800*y**5 + 2240*y**3 - 672*y**2", "step_length": 3} {"cot_id": "35bc71b02f0c8d9295ab97f1c3a7998601c76ae2826a4e8e0a6801055bfb155c", "datapoint": {"question": "Calculate the following: (14*x**3 + x)*(-4*x**2 + 12*x - 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-56*x**5 + 168*x**4 - 18*x**3 + 12*x**2 - x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 757, "polynomial_expr": "(14*x**3 + x)*(-4*x**2 + 12*x - 1)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14*x**3 + x)*(-4*x**2 + 12*x - 1)\nExpanding the part (14*x**3 + x) using the distributive property, and we got: x*(-4*x**2 + 12*x - 1) + (14*x**3)*(-4*x**2 + 12*x - 1)\n#Step 2:\nCurrent expression: x*(-4*x**2 + 12*x - 1) + (14*x**3)*(-4*x**2 + 12*x - 1)\nSimplifying the partial expression: x*(-4*x**2 + 12*x - 1)\nExpanding the part (-4*x**2 + 12*x - 1) using the distributive property, and we got: x*(12*x) + x*(-4*x**2) - x\nReplacing x*(-4*x**2 + 12*x - 1) with x*(12*x) + x*(-4*x**2) - x in the overall expression.\n#Step 3:\nCurrent expression: x*(12*x) + x*(-4*x**2) - x + (14*x**3)*(-4*x**2 + 12*x - 1)\nSimplifying the partial expression: (14*x**3)*(-4*x**2 + 12*x - 1)\nExpanding the part (-4*x**2 + 12*x - 1) using the distributive property, and we got: -14*x**3 + (12*x)*(14*x**3) + (-4*x**2)*(14*x**3)\nReplacing (14*x**3)*(-4*x**2 + 12*x - 1) with -14*x**3 + (12*x)*(14*x**3) + (-4*x**2)*(14*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -1*14*x**3 + x*(12*x) + x*(-4*x**2) - x + (12*x)*(14*x**3) + (-4*x**2)*(14*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-4*x**2)*x = -4*x**3\n (-4*x**2)*(14*x**3) = -56*x**5\n (12*x)*x = 12*x**2\n (12*x)*(14*x**3) = 168*x**4\n -1*14*x**3 = -14*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -56*x**5 + 168*x**4 - 14*x**3 - 4*x**3 + 12*x**2 - x\nCombining like terms, got -56*x**5 + 168*x**4 - 18*x**3 + 12*x**2 - x\n#Step 6:\nCurrent expression: -56*x**5 + 168*x**4 - 18*x**3 + 12*x**2 - x\nNo more calculations needed.\n-56*x**5 + 168*x**4 - 18*x**3 + 12*x**2 - x", "generated_answer": "-56*x**5 + 168*x**4 - 18*x**3 + 12*x**2 - x", "step_length": 6} {"cot_id": "d4ebee2303fb5a28cf53deb5c2fe8c09144b52978e80619f423c0f292d10db68", "datapoint": {"question": "Simplify this expression: (-4*z**2 + 33*z + 36)*(11*z**2 - 21*z - 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-44*z**4 + 447*z**3 - 185*z**2 - 1680*z - 1008", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 758, "polynomial_expr": "(-4*z**2 + 33*z + 36)*(11*z**2 - 21*z - 28)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-4*z**2 + 33*z + 36)*(11*z**2 - 21*z - 28)\nExpanding the part (11*z**2 - 21*z - 28) using the distributive property, and we got: (-21*z)*(-4*z**2 + 33*z + 36) + (11*z**2)*(-4*z**2 + 33*z + 36) - 28*(-4*z**2 + 33*z + 36)\n#Step 2:\nCurrent expression: (-21*z)*(-4*z**2 + 33*z + 36) + (11*z**2)*(-4*z**2 + 33*z + 36) - 28*(-4*z**2 + 33*z + 36)\nSimplifying the partial expression: -28*(-4*z**2 + 33*z + 36)\nExpanding the part (-4*z**2 + 33*z + 36) using the distributive property, and we got: (33*z)*(-28) - 4*z**2*(-28) + 36*(-28)\nReplacing -28*(-4*z**2 + 33*z + 36) with (33*z)*(-28) - 4*z**2*(-28) + 36*(-28) in the overall expression.\n#Step 3:\nCurrent expression: (-21*z)*(-4*z**2 + 33*z + 36) + (33*z)*(-28) - 4*z**2*(-28) + (11*z**2)*(-4*z**2 + 33*z + 36) - 1008\nSimplifying the partial expression: (-21*z)*(-4*z**2 + 33*z + 36)\nExpanding the part (-4*z**2 + 33*z + 36) using the distributive property, and we got: (-21*z)*(33*z) + (-21*z)*(-4*z**2) + 36*(-21*z)\nReplacing (-21*z)*(-4*z**2 + 33*z + 36) with (-21*z)*(33*z) + (-21*z)*(-4*z**2) + 36*(-21*z) in the overall expression.\n#Step 4:\nCurrent expression: (-21*z)*(33*z) + (-21*z)*(-4*z**2) + 36*(-21)*z + (33*z)*(-28) - 4*z**2*(-28) + (11*z**2)*(-4*z**2 + 33*z + 36) - 1008\nSimplifying the partial expression: (11*z**2)*(-4*z**2 + 33*z + 36)\nExpanding the part (-4*z**2 + 33*z + 36) using the distributive property, and we got: 36*(11*z**2) + (33*z)*(11*z**2) + (-4*z**2)*(11*z**2)\nReplacing (11*z**2)*(-4*z**2 + 33*z + 36) with 36*(11*z**2) + (33*z)*(11*z**2) + (-4*z**2)*(11*z**2) in the overall expression.\n#Step 5:\nCurrent expression: (-21*z)*(33*z) + (-21*z)*(-4*z**2) + 36*11*z**2 + 36*(-21)*z + (33*z)*(11*z**2) + (33*z)*(-28) + (-4*z**2)*(11*z**2) - 4*z**2*(-28) - 1008\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-4*z**2)*-28 = 112*z**2\n (-4*z**2)*(-21*z) = 84*z**3\n (-4*z**2)*(11*z**2) = -44*z**4\n (33*z)*-28 = -924*z\n (33*z)*(-21*z) = -693*z**2\n (33*z)*(11*z**2) = 363*z**3\n 36*-21*z = -756*z\n 36*11*z**2 = 396*z**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -44*z**4 + 84*z**3 + 363*z**3 - 693*z**2 + 112*z**2 + 396*z**2 - 924*z - 756*z - 1008\nCombining like terms, got -44*z**4 + 447*z**3 - 185*z**2 - 1680*z - 1008\n#Step 7:\nCurrent expression: -44*z**4 + 447*z**3 - 185*z**2 - 1680*z - 1008\nNo more calculations needed.\n-44*z**4 + 447*z**3 - 185*z**2 - 1680*z - 1008", "generated_answer": "-44*z**4 + 447*z**3 - 185*z**2 - 1680*z - 1008", "step_length": 7} {"cot_id": "dde1f659e87487466b621fad8c9bab419c12f7b321243c9a6ab4d29daa1a04b9", "datapoint": {"question": "Calculate the following: (21*x**2 + 19*x)*(-8*x**3 - 40*x + 22)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-168*x**5 - 152*x**4 - 840*x**3 - 298*x**2 + 418*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 759, "polynomial_expr": "(21*x**2 + 19*x)*(-8*x**3 - 40*x + 22)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21*x**2 + 19*x)*(-8*x**3 - 40*x + 22)\nExpanding the part (21*x**2 + 19*x) using the distributive property, and we got: (19*x)*(-8*x**3 - 40*x + 22) + (21*x**2)*(-8*x**3 - 40*x + 22)\n#Step 2:\nCurrent expression: (19*x)*(-8*x**3 - 40*x + 22) + (21*x**2)*(-8*x**3 - 40*x + 22)\nSimplifying the partial expression: (19*x)*(-8*x**3 - 40*x + 22)\nExpanding the part (-8*x**3 - 40*x + 22) using the distributive property, and we got: (-40*x)*(19*x) + 22*(19*x) + (19*x)*(-8*x**3)\nReplacing (19*x)*(-8*x**3 - 40*x + 22) with (-40*x)*(19*x) + 22*(19*x) + (19*x)*(-8*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-40*x)*(19*x) + 22*19*x + (19*x)*(-8*x**3) + (21*x**2)*(-8*x**3 - 40*x + 22)\nSimplifying the partial expression: (21*x**2)*(-8*x**3 - 40*x + 22)\nExpanding the part (-8*x**3 - 40*x + 22) using the distributive property, and we got: (-40*x)*(21*x**2) + 22*(21*x**2) + (21*x**2)*(-8*x**3)\nReplacing (21*x**2)*(-8*x**3 - 40*x + 22) with (-40*x)*(21*x**2) + 22*(21*x**2) + (21*x**2)*(-8*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-40*x)*(19*x) + (-40*x)*(21*x**2) + 22*21*x**2 + 22*19*x + (19*x)*(-8*x**3) + (21*x**2)*(-8*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*x)*(19*x) = -760*x**2\n (-40*x)*(21*x**2) = -840*x**3\n (-8*x**3)*(19*x) = -152*x**4\n (-8*x**3)*(21*x**2) = -168*x**5\n 22*19*x = 418*x\n 22*21*x**2 = 462*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -168*x**5 - 152*x**4 - 840*x**3 - 760*x**2 + 462*x**2 + 418*x\nCombining like terms, got -168*x**5 - 152*x**4 - 840*x**3 - 298*x**2 + 418*x\n#Step 6:\nCurrent expression: -168*x**5 - 152*x**4 - 840*x**3 - 298*x**2 + 418*x\nNo more calculations needed.\n-168*x**5 - 152*x**4 - 840*x**3 - 298*x**2 + 418*x", "generated_answer": "-168*x**5 - 152*x**4 - 840*x**3 - 298*x**2 + 418*x", "step_length": 6} {"cot_id": "82526515e08d48320994c952c73da1975263e4934b012898835483455854e8e1", "datapoint": {"question": "Simplify this expression: (67*z**2 + 35*z)*(33*z**3 + 21*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2211*z**5 + 1155*z**4 + 1407*z**3 + 735*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 760, "polynomial_expr": "(67*z**2 + 35*z)*(33*z**3 + 21*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (67*z**2 + 35*z)*(33*z**3 + 21*z)\nExpanding the part (33*z**3 + 21*z) using the distributive property, and we got: (21*z)*(67*z**2 + 35*z) + (33*z**3)*(67*z**2 + 35*z)\n#Step 2:\nCurrent expression: (21*z)*(67*z**2 + 35*z) + (33*z**3)*(67*z**2 + 35*z)\nSimplifying the partial expression: (21*z)*(67*z**2 + 35*z)\nExpanding the part (67*z**2 + 35*z) using the distributive property, and we got: (21*z)*(35*z) + (21*z)*(67*z**2)\nReplacing (21*z)*(67*z**2 + 35*z) with (21*z)*(35*z) + (21*z)*(67*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (21*z)*(35*z) + (21*z)*(67*z**2) + (33*z**3)*(67*z**2 + 35*z)\nSimplifying the partial expression: (33*z**3)*(67*z**2 + 35*z)\nExpanding the part (67*z**2 + 35*z) using the distributive property, and we got: (35*z)*(33*z**3) + (67*z**2)*(33*z**3)\nReplacing (33*z**3)*(67*z**2 + 35*z) with (35*z)*(33*z**3) + (67*z**2)*(33*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (21*z)*(35*z) + (21*z)*(67*z**2) + (35*z)*(33*z**3) + (67*z**2)*(33*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (35*z)*(21*z) = 735*z**2\n (35*z)*(33*z**3) = 1155*z**4\n (67*z**2)*(21*z) = 1407*z**3\n (67*z**2)*(33*z**3) = 2211*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2211*z**5 + 1155*z**4 + 1407*z**3 + 735*z**2\nNo more calculations needed.\n2211*z**5 + 1155*z**4 + 1407*z**3 + 735*z**2", "generated_answer": "2211*z**5 + 1155*z**4 + 1407*z**3 + 735*z**2", "step_length": 5} {"cot_id": "54de65ae14dd981df4a6270e8ff8115984bf1db272d43d7ef0b95a2d9fe10297", "datapoint": {"question": "Calculate the following: (-34*x**3 - 9)*(50*x**2 - 23*x - 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1700*x**5 + 782*x**4 + 714*x**3 - 450*x**2 + 207*x + 189", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 761, "polynomial_expr": "(-34*x**3 - 9)*(50*x**2 - 23*x - 21)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-34*x**3 - 9)*(50*x**2 - 23*x - 21)\nExpanding the part (-34*x**3 - 9) using the distributive property, and we got: (-34*x**3)*(50*x**2 - 23*x - 21) - 9*(50*x**2 - 23*x - 21)\n#Step 2:\nCurrent expression: (-34*x**3)*(50*x**2 - 23*x - 21) - 9*(50*x**2 - 23*x - 21)\nSimplifying the partial expression: -9*(50*x**2 - 23*x - 21)\nExpanding the part (50*x**2 - 23*x - 21) using the distributive property, and we got: -23*x*(-9) + (50*x**2)*(-9) - 21*(-9)\nReplacing -9*(50*x**2 - 23*x - 21) with -23*x*(-9) + (50*x**2)*(-9) - 21*(-9) in the overall expression.\n#Step 3:\nCurrent expression: -23*x*(-9) + (50*x**2)*(-9) + (-34*x**3)*(50*x**2 - 23*x - 21) + 189\nSimplifying the partial expression: (-34*x**3)*(50*x**2 - 23*x - 21)\nExpanding the part (50*x**2 - 23*x - 21) using the distributive property, and we got: (-23*x)*(-34*x**3) - (-1)*714*x**3 + (50*x**2)*(-34*x**3)\nReplacing (-34*x**3)*(50*x**2 - 23*x - 21) with (-23*x)*(-34*x**3) - (-1)*714*x**3 + (50*x**2)*(-34*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-23*x)*(-34*x**3) - 23*x*(-9) - 21*(-34)*x**3 + (50*x**2)*(-34*x**3) + (50*x**2)*(-9) + 189\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*x)*-9 = 207*x\n (-23*x)*(-34*x**3) = 782*x**4\n (50*x**2)*-9 = -450*x**2\n (50*x**2)*(-34*x**3) = -1700*x**5\n -21*-34*x**3 = 714*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1700*x**5 + 782*x**4 + 714*x**3 - 450*x**2 + 207*x + 189\nNo more calculations needed.\n-1700*x**5 + 782*x**4 + 714*x**3 - 450*x**2 + 207*x + 189", "generated_answer": "-1700*x**5 + 782*x**4 + 714*x**3 - 450*x**2 + 207*x + 189", "step_length": 5} {"cot_id": "9e51bca6f1446b058a09c94c9b8857635066205bc17b88dbc05a3a8755f6da87", "datapoint": {"question": "Calculate the following: (44 - 39*y)*(-22*y**3 - 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "858*y**4 - 968*y**3 + 1950*y - 2200", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 762, "polynomial_expr": "(44 - 39*y)*(-22*y**3 - 50)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (44 - 39*y)*(-22*y**3 - 50)\nExpanding the part (-22*y**3 - 50) using the distributive property, and we got: (-22*y**3)*(44 - 39*y) - 50*(44 - 39*y)\n#Step 2:\nCurrent expression: (-22*y**3)*(44 - 39*y) - 50*(44 - 39*y)\nSimplifying the partial expression: -50*(44 - 39*y)\nExpanding the part (44 - 39*y) using the distributive property, and we got: -39*y*(-50) + 44*(-50)\nReplacing -50*(44 - 39*y) with -39*y*(-50) + 44*(-50) in the overall expression.\n#Step 3:\nCurrent expression: -39*y*(-50) + (-22*y**3)*(44 - 39*y) - 2200\nSimplifying the partial expression: (-22*y**3)*(44 - 39*y)\nExpanding the part (44 - 39*y) using the distributive property, and we got: (-39*y)*(-22*y**3) + 44*(-22*y**3)\nReplacing (-22*y**3)*(44 - 39*y) with (-39*y)*(-22*y**3) + 44*(-22*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-39*y)*(-22*y**3) - 39*y*(-50) + 44*(-22)*y**3 - 2200\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*y)*-50 = 1950*y\n (-39*y)*(-22*y**3) = 858*y**4\n 44*-22*y**3 = -968*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 858*y**4 - 968*y**3 + 1950*y - 2200\nNo more calculations needed.\n858*y**4 - 968*y**3 + 1950*y - 2200", "generated_answer": "858*y**4 - 968*y**3 + 1950*y - 2200", "step_length": 5} {"cot_id": "a4c55accea581bc3e314830eb744b59b8e3ee158d9684c256c73af91cb4de310", "datapoint": {"question": "Simplify this expression: (30*y**2 - 46*y)*(47*y**3 + 41*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1410*y**5 - 932*y**4 - 1886*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 763, "polynomial_expr": "(30*y**2 - 46*y)*(47*y**3 + 41*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (30*y**2 - 46*y)*(47*y**3 + 41*y**2)\nExpanding the part (30*y**2 - 46*y) using the distributive property, and we got: (-46*y)*(47*y**3 + 41*y**2) + (30*y**2)*(47*y**3 + 41*y**2)\n#Step 2:\nCurrent expression: (-46*y)*(47*y**3 + 41*y**2) + (30*y**2)*(47*y**3 + 41*y**2)\nSimplifying the partial expression: (-46*y)*(47*y**3 + 41*y**2)\nExpanding the part (47*y**3 + 41*y**2) using the distributive property, and we got: (-46*y)*(41*y**2) + (-46*y)*(47*y**3)\nReplacing (-46*y)*(47*y**3 + 41*y**2) with (-46*y)*(41*y**2) + (-46*y)*(47*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-46*y)*(41*y**2) + (-46*y)*(47*y**3) + (30*y**2)*(47*y**3 + 41*y**2)\nSimplifying the partial expression: (30*y**2)*(47*y**3 + 41*y**2)\nExpanding the part (47*y**3 + 41*y**2) using the distributive property, and we got: (30*y**2)*(41*y**2) + (30*y**2)*(47*y**3)\nReplacing (30*y**2)*(47*y**3 + 41*y**2) with (30*y**2)*(41*y**2) + (30*y**2)*(47*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-46*y)*(41*y**2) + (-46*y)*(47*y**3) + (30*y**2)*(41*y**2) + (30*y**2)*(47*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (41*y**2)*(-46*y) = -1886*y**3\n (41*y**2)*(30*y**2) = 1230*y**4\n (47*y**3)*(-46*y) = -2162*y**4\n (47*y**3)*(30*y**2) = 1410*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1410*y**5 - 2162*y**4 + 1230*y**4 - 1886*y**3\nCombining like terms, got 1410*y**5 - 932*y**4 - 1886*y**3\n#Step 6:\nCurrent expression: 1410*y**5 - 932*y**4 - 1886*y**3\nNo more calculations needed.\n1410*y**5 - 932*y**4 - 1886*y**3", "generated_answer": "1410*y**5 - 932*y**4 - 1886*y**3", "step_length": 6} {"cot_id": "f2a4efc182ace4d4a7082be972cd8d3c8f2a2b64e75b9d66c1b0cd6a36cece59", "datapoint": {"question": "Simplify this expression: 6*y**3*(6*y**2 - 11*y - 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "36*y**5 - 66*y**4 - 120*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 764, "polynomial_expr": "6*y**3*(6*y**2 - 11*y - 20)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 6*y**3*(6*y**2 - 11*y - 20)\nExpanding the part (6*y**2 - 11*y - 20) using the distributive property, and we got: (-11*y)*(6*y**3) - 120*y**3 + (6*y**2)*(6*y**3)\n#Step 2:\nCurrent expression: (-11*y)*(6*y**3) - 120*y**3 + (6*y**2)*(6*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -20*(6*y**3) = -120*y**3\n (-11*y)*(6*y**3) = -66*y**4\n (6*y**2)*(6*y**3) = 36*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 36*y**5 - 66*y**4 - 120*y**3\nNo more calculations needed.\n36*y**5 - 66*y**4 - 120*y**3", "generated_answer": "36*y**5 - 66*y**4 - 120*y**3", "step_length": 3} {"cot_id": "0ebc7db9227cbb79964aa0035a1fb26736670924d469d068e61f02e4aaceafcb", "datapoint": {"question": "Simplify this expression: (16 - 35*y)*(-10*y**3 - 15*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "350*y**4 - 160*y**3 + 525*y**2 - 240*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 765, "polynomial_expr": "(16 - 35*y)*(-10*y**3 - 15*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (16 - 35*y)*(-10*y**3 - 15*y)\nExpanding the part (16 - 35*y) using the distributive property, and we got: (-35*y)*(-10*y**3 - 15*y) + 16*(-10*y**3 - 15*y)\n#Step 2:\nCurrent expression: (-35*y)*(-10*y**3 - 15*y) + 16*(-10*y**3 - 15*y)\nSimplifying the partial expression: 16*(-10*y**3 - 15*y)\nExpanding the part (-10*y**3 - 15*y) using the distributive property, and we got: -15*y*16 - 10*y**3*16\nReplacing 16*(-10*y**3 - 15*y) with -15*y*16 - 10*y**3*16 in the overall expression.\n#Step 3:\nCurrent expression: (-35*y)*(-10*y**3 - 15*y) - 15*y*16 - 10*y**3*16\nSimplifying the partial expression: (-35*y)*(-10*y**3 - 15*y)\nExpanding the part (-10*y**3 - 15*y) using the distributive property, and we got: (-35*y)*(-15*y) + (-35*y)*(-10*y**3)\nReplacing (-35*y)*(-10*y**3 - 15*y) with (-35*y)*(-15*y) + (-35*y)*(-10*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-35*y)*(-15*y) + (-35*y)*(-10*y**3) - 15*y*16 - 10*y**3*16\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-15*y)*16 = -240*y\n (-15*y)*(-35*y) = 525*y**2\n (-10*y**3)*16 = -160*y**3\n (-10*y**3)*(-35*y) = 350*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 350*y**4 - 160*y**3 + 525*y**2 - 240*y\nNo more calculations needed.\n350*y**4 - 160*y**3 + 525*y**2 - 240*y", "generated_answer": "350*y**4 - 160*y**3 + 525*y**2 - 240*y", "step_length": 5} {"cot_id": "55e41c8d49d9798a671ea2bb8c0f0f786e157a9d92f146724657bbfe76209aea", "datapoint": {"question": "Simplify this expression: (7 - 45*y)*(25*y**2 - 5)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1125*y**3 + 175*y**2 + 225*y - 35", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 766, "polynomial_expr": "(7 - 45*y)*(25*y**2 - 5)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7 - 45*y)*(25*y**2 - 5)\nExpanding the part (25*y**2 - 5) using the distributive property, and we got: (25*y**2)*(7 - 45*y) - 5*(7 - 45*y)\n#Step 2:\nCurrent expression: (25*y**2)*(7 - 45*y) - 5*(7 - 45*y)\nSimplifying the partial expression: -5*(7 - 45*y)\nExpanding the part (7 - 45*y) using the distributive property, and we got: -45*y*(-5) + 7*(-5)\nReplacing -5*(7 - 45*y) with -45*y*(-5) + 7*(-5) in the overall expression.\n#Step 3:\nCurrent expression: -45*y*(-5) + (25*y**2)*(7 - 45*y) - 35\nSimplifying the partial expression: (25*y**2)*(7 - 45*y)\nExpanding the part (7 - 45*y) using the distributive property, and we got: (-45*y)*(25*y**2) + 7*(25*y**2)\nReplacing (25*y**2)*(7 - 45*y) with (-45*y)*(25*y**2) + 7*(25*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-45*y)*(25*y**2) - 45*y*(-5) + 7*25*y**2 - 35\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*y)*-5 = 225*y\n (-45*y)*(25*y**2) = -1125*y**3\n 7*25*y**2 = 175*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1125*y**3 + 175*y**2 + 225*y - 35\nNo more calculations needed.\n-1125*y**3 + 175*y**2 + 225*y - 35", "generated_answer": "-1125*y**3 + 175*y**2 + 225*y - 35", "step_length": 5} {"cot_id": "a32763effe216aedf6ef43e2848be646f760ef931f551870d3e5b572d8a4d115", "datapoint": {"question": "Calculate the following: (39*x**2 - 30)*(-15*x**3 - 18)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-585*x**5 + 450*x**3 - 702*x**2 + 540", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 767, "polynomial_expr": "(39*x**2 - 30)*(-15*x**3 - 18)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (39*x**2 - 30)*(-15*x**3 - 18)\nExpanding the part (39*x**2 - 30) using the distributive property, and we got: (39*x**2)*(-15*x**3 - 18) - 30*(-15*x**3 - 18)\n#Step 2:\nCurrent expression: (39*x**2)*(-15*x**3 - 18) - 30*(-15*x**3 - 18)\nSimplifying the partial expression: -30*(-15*x**3 - 18)\nExpanding the part (-15*x**3 - 18) using the distributive property, and we got: -15*x**3*(-30) - 18*(-30)\nReplacing -30*(-15*x**3 - 18) with -15*x**3*(-30) - 18*(-30) in the overall expression.\n#Step 3:\nCurrent expression: (39*x**2)*(-15*x**3 - 18) - 15*x**3*(-30) + 540\nSimplifying the partial expression: (39*x**2)*(-15*x**3 - 18)\nExpanding the part (-15*x**3 - 18) using the distributive property, and we got: -702*x**2 + (39*x**2)*(-15*x**3)\nReplacing (39*x**2)*(-15*x**3 - 18) with -702*x**2 + (39*x**2)*(-15*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -18*39*x**2 + (39*x**2)*(-15*x**3) - 15*x**3*(-30) + 540\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-15*x**3)*-30 = 450*x**3\n (-15*x**3)*(39*x**2) = -585*x**5\n -18*39*x**2 = -702*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -585*x**5 + 450*x**3 - 702*x**2 + 540\nNo more calculations needed.\n-585*x**5 + 450*x**3 - 702*x**2 + 540", "generated_answer": "-585*x**5 + 450*x**3 - 702*x**2 + 540", "step_length": 5} {"cot_id": "fb0d0cff148f15c0be75f4539d7b4c4e6084f77d300f011d7e8bf8ee61b87b45", "datapoint": {"question": "Calculate the following: (31*z**2 + 29*z)*(42*z**2 - 11*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1302*z**4 + 877*z**3 - 319*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 768, "polynomial_expr": "(31*z**2 + 29*z)*(42*z**2 - 11*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31*z**2 + 29*z)*(42*z**2 - 11*z)\nExpanding the part (42*z**2 - 11*z) using the distributive property, and we got: (-11*z)*(31*z**2 + 29*z) + (42*z**2)*(31*z**2 + 29*z)\n#Step 2:\nCurrent expression: (-11*z)*(31*z**2 + 29*z) + (42*z**2)*(31*z**2 + 29*z)\nSimplifying the partial expression: (-11*z)*(31*z**2 + 29*z)\nExpanding the part (31*z**2 + 29*z) using the distributive property, and we got: (-11*z)*(29*z) + (-11*z)*(31*z**2)\nReplacing (-11*z)*(31*z**2 + 29*z) with (-11*z)*(29*z) + (-11*z)*(31*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-11*z)*(29*z) + (-11*z)*(31*z**2) + (42*z**2)*(31*z**2 + 29*z)\nSimplifying the partial expression: (42*z**2)*(31*z**2 + 29*z)\nExpanding the part (31*z**2 + 29*z) using the distributive property, and we got: (29*z)*(42*z**2) + (31*z**2)*(42*z**2)\nReplacing (42*z**2)*(31*z**2 + 29*z) with (29*z)*(42*z**2) + (31*z**2)*(42*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-11*z)*(29*z) + (-11*z)*(31*z**2) + (29*z)*(42*z**2) + (31*z**2)*(42*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (29*z)*(-11*z) = -319*z**2\n (29*z)*(42*z**2) = 1218*z**3\n (31*z**2)*(-11*z) = -341*z**3\n (31*z**2)*(42*z**2) = 1302*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1302*z**4 - 341*z**3 + 1218*z**3 - 319*z**2\nCombining like terms, got 1302*z**4 + 877*z**3 - 319*z**2\n#Step 6:\nCurrent expression: 1302*z**4 + 877*z**3 - 319*z**2\nNo more calculations needed.\n1302*z**4 + 877*z**3 - 319*z**2", "generated_answer": "1302*z**4 + 877*z**3 - 319*z**2", "step_length": 6} {"cot_id": "4ae16b741ad1366dd42c9b5f658a550ec4a2c3a0908321c2e1e55ed44713ca90", "datapoint": {"question": "Simplify this expression: (-25*x**3 - 7*x)*(-34*x**3 - 28*x**2 + 16*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "850*x**6 + 700*x**5 - 162*x**4 + 196*x**3 - 112*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 769, "polynomial_expr": "(-25*x**3 - 7*x)*(-34*x**3 - 28*x**2 + 16*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-25*x**3 - 7*x)*(-34*x**3 - 28*x**2 + 16*x)\nExpanding the part (-25*x**3 - 7*x) using the distributive property, and we got: (-7*x)*(-34*x**3 - 28*x**2 + 16*x) + (-25*x**3)*(-34*x**3 - 28*x**2 + 16*x)\n#Step 2:\nCurrent expression: (-7*x)*(-34*x**3 - 28*x**2 + 16*x) + (-25*x**3)*(-34*x**3 - 28*x**2 + 16*x)\nSimplifying the partial expression: (-25*x**3)*(-34*x**3 - 28*x**2 + 16*x)\nExpanding the part (-34*x**3 - 28*x**2 + 16*x) using the distributive property, and we got: (16*x)*(-25*x**3) + (-28*x**2)*(-25*x**3) + (-34*x**3)*(-25*x**3)\nReplacing (-25*x**3)*(-34*x**3 - 28*x**2 + 16*x) with (16*x)*(-25*x**3) + (-28*x**2)*(-25*x**3) + (-34*x**3)*(-25*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-7*x)*(-34*x**3 - 28*x**2 + 16*x) + (16*x)*(-25*x**3) + (-28*x**2)*(-25*x**3) + (-34*x**3)*(-25*x**3)\nSimplifying the partial expression: (-7*x)*(-34*x**3 - 28*x**2 + 16*x)\nExpanding the part (-34*x**3 - 28*x**2 + 16*x) using the distributive property, and we got: (-7*x)*(16*x) + (-7*x)*(-28*x**2) + (-7*x)*(-34*x**3)\nReplacing (-7*x)*(-34*x**3 - 28*x**2 + 16*x) with (-7*x)*(16*x) + (-7*x)*(-28*x**2) + (-7*x)*(-34*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-7*x)*(16*x) + (-7*x)*(-28*x**2) + (-7*x)*(-34*x**3) + (16*x)*(-25*x**3) + (-28*x**2)*(-25*x**3) + (-34*x**3)*(-25*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*x**3)*(-25*x**3) = 850*x**6\n (-34*x**3)*(-7*x) = 238*x**4\n (-28*x**2)*(-25*x**3) = 700*x**5\n (-28*x**2)*(-7*x) = 196*x**3\n (16*x)*(-25*x**3) = -400*x**4\n (16*x)*(-7*x) = -112*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 850*x**6 + 700*x**5 - 400*x**4 + 238*x**4 + 196*x**3 - 112*x**2\nCombining like terms, got 850*x**6 + 700*x**5 - 162*x**4 + 196*x**3 - 112*x**2\n#Step 6:\nCurrent expression: 850*x**6 + 700*x**5 - 162*x**4 + 196*x**3 - 112*x**2\nNo more calculations needed.\n850*x**6 + 700*x**5 - 162*x**4 + 196*x**3 - 112*x**2", "generated_answer": "850*x**6 + 700*x**5 - 162*x**4 + 196*x**3 - 112*x**2", "step_length": 6} {"cot_id": "c4bcf364bdd07c8e3145e931204e824eec9023f593de2d9b2f712304e53cd3b2", "datapoint": {"question": "Simplify this expression: (-88*x**2 - 14)*(33*x**2 - 58*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2904*x**4 + 5104*x**3 - 462*x**2 + 812*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 770, "polynomial_expr": "(-88*x**2 - 14)*(33*x**2 - 58*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-88*x**2 - 14)*(33*x**2 - 58*x)\nExpanding the part (-88*x**2 - 14) using the distributive property, and we got: (-88*x**2)*(33*x**2 - 58*x) - 14*(33*x**2 - 58*x)\n#Step 2:\nCurrent expression: (-88*x**2)*(33*x**2 - 58*x) - 14*(33*x**2 - 58*x)\nSimplifying the partial expression: -14*(33*x**2 - 58*x)\nExpanding the part (33*x**2 - 58*x) using the distributive property, and we got: -58*x*(-14) + (33*x**2)*(-14)\nReplacing -14*(33*x**2 - 58*x) with -58*x*(-14) + (33*x**2)*(-14) in the overall expression.\n#Step 3:\nCurrent expression: -58*x*(-14) + (-88*x**2)*(33*x**2 - 58*x) + (33*x**2)*(-14)\nSimplifying the partial expression: (-88*x**2)*(33*x**2 - 58*x)\nExpanding the part (33*x**2 - 58*x) using the distributive property, and we got: (-58*x)*(-88*x**2) + (-88*x**2)*(33*x**2)\nReplacing (-88*x**2)*(33*x**2 - 58*x) with (-58*x)*(-88*x**2) + (-88*x**2)*(33*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-58*x)*(-88*x**2) - 58*x*(-14) + (-88*x**2)*(33*x**2) + (33*x**2)*(-14)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-58*x)*-14 = 812*x\n (-58*x)*(-88*x**2) = 5104*x**3\n (33*x**2)*-14 = -462*x**2\n (33*x**2)*(-88*x**2) = -2904*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2904*x**4 + 5104*x**3 - 462*x**2 + 812*x\nNo more calculations needed.\n-2904*x**4 + 5104*x**3 - 462*x**2 + 812*x", "generated_answer": "-2904*x**4 + 5104*x**3 - 462*x**2 + 812*x", "step_length": 5} {"cot_id": "0da00ea0bae238a1219bf0eb0315dbb6ee192c8057641a3f56e7b0d9ff552b6e", "datapoint": {"question": "Simplify this expression: (-x**2 + 18*x + 41)*(-48*x**3 + 46*x**2 - 11*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "48*x**5 - 910*x**4 - 1129*x**3 + 1688*x**2 - 451*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 771, "polynomial_expr": "(-x**2 + 18*x + 41)*(-48*x**3 + 46*x**2 - 11*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-x**2 + 18*x + 41)*(-48*x**3 + 46*x**2 - 11*x)\nExpanding the part (-x**2 + 18*x + 41) using the distributive property, and we got: (18*x)*(-48*x**3 + 46*x**2 - 11*x) + (-x**2)*(-48*x**3 + 46*x**2 - 11*x) + 41*(-48*x**3 + 46*x**2 - 11*x)\n#Step 2:\nCurrent expression: (18*x)*(-48*x**3 + 46*x**2 - 11*x) + (-x**2)*(-48*x**3 + 46*x**2 - 11*x) + 41*(-48*x**3 + 46*x**2 - 11*x)\nSimplifying the partial expression: 41*(-48*x**3 + 46*x**2 - 11*x)\nExpanding the part (-48*x**3 + 46*x**2 - 11*x) using the distributive property, and we got: -11*x*41 + (46*x**2)*41 - 48*x**3*41\nReplacing 41*(-48*x**3 + 46*x**2 - 11*x) with -11*x*41 + (46*x**2)*41 - 48*x**3*41 in the overall expression.\n#Step 3:\nCurrent expression: -11*x*41 + (18*x)*(-48*x**3 + 46*x**2 - 11*x) + (-x**2)*(-48*x**3 + 46*x**2 - 11*x) + (46*x**2)*41 - 48*x**3*41\nSimplifying the partial expression: (-x**2)*(-48*x**3 + 46*x**2 - 11*x)\nExpanding the part (-48*x**3 + 46*x**2 - 11*x) using the distributive property, and we got: (-11*x)*(-x**2) + (-x**2)*(46*x**2) + (-x**2)*(-48*x**3)\nReplacing (-x**2)*(-48*x**3 + 46*x**2 - 11*x) with (-11*x)*(-x**2) + (-x**2)*(46*x**2) + (-x**2)*(-48*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-11*x)*(-x**2) - 11*x*41 + (18*x)*(-48*x**3 + 46*x**2 - 11*x) + (-x**2)*(46*x**2) + (-x**2)*(-48*x**3) + (46*x**2)*41 - 48*x**3*41\nSimplifying the partial expression: (18*x)*(-48*x**3 + 46*x**2 - 11*x)\nExpanding the part (-48*x**3 + 46*x**2 - 11*x) using the distributive property, and we got: (-11*x)*(18*x) + (18*x)*(46*x**2) + (18*x)*(-48*x**3)\nReplacing (18*x)*(-48*x**3 + 46*x**2 - 11*x) with (-11*x)*(18*x) + (18*x)*(46*x**2) + (18*x)*(-48*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-11*x)*(18*x) + (-11*x)*(-x**2) - 11*x*41 + (18*x)*(46*x**2) + (18*x)*(-48*x**3) + (-x**2)*(46*x**2) + (-x**2)*(-48*x**3) + (46*x**2)*41 - 48*x**3*41\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*x**3)*41 = -1968*x**3\n (-48*x**3)*(-x**2) = 48*x**5\n (-48*x**3)*(18*x) = -864*x**4\n (-11*x)*41 = -451*x\n (-11*x)*(-x**2) = 11*x**3\n (-11*x)*(18*x) = -198*x**2\n (46*x**2)*41 = 1886*x**2\n (46*x**2)*(-x**2) = -46*x**4\n (46*x**2)*(18*x) = 828*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 48*x**5 - 864*x**4 - 46*x**4 - 1968*x**3 + 11*x**3 + 828*x**3 - 198*x**2 + 1886*x**2 - 451*x\nCombining like terms, got 48*x**5 - 910*x**4 - 1129*x**3 + 1688*x**2 - 451*x\n#Step 7:\nCurrent expression: 48*x**5 - 910*x**4 - 1129*x**3 + 1688*x**2 - 451*x\nNo more calculations needed.\n48*x**5 - 910*x**4 - 1129*x**3 + 1688*x**2 - 451*x", "generated_answer": "48*x**5 - 910*x**4 - 1129*x**3 + 1688*x**2 - 451*x", "step_length": 7} {"cot_id": "e3c5e2f1ec1287214658fcad5e63484d562c5a512f9b5e12279b5163aa3ee54b", "datapoint": {"question": "Calculate the following: (-16*z**3 - 11*z**2)*(-13*z**3 + 6*z**2 + 28*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "208*z**6 + 47*z**5 - 514*z**4 - 308*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 772, "polynomial_expr": "(-16*z**3 - 11*z**2)*(-13*z**3 + 6*z**2 + 28*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-16*z**3 - 11*z**2)*(-13*z**3 + 6*z**2 + 28*z)\nExpanding the part (-16*z**3 - 11*z**2) using the distributive property, and we got: (-11*z**2)*(-13*z**3 + 6*z**2 + 28*z) + (-16*z**3)*(-13*z**3 + 6*z**2 + 28*z)\n#Step 2:\nCurrent expression: (-11*z**2)*(-13*z**3 + 6*z**2 + 28*z) + (-16*z**3)*(-13*z**3 + 6*z**2 + 28*z)\nSimplifying the partial expression: (-16*z**3)*(-13*z**3 + 6*z**2 + 28*z)\nExpanding the part (-13*z**3 + 6*z**2 + 28*z) using the distributive property, and we got: (28*z)*(-16*z**3) + (6*z**2)*(-16*z**3) + (-16*z**3)*(-13*z**3)\nReplacing (-16*z**3)*(-13*z**3 + 6*z**2 + 28*z) with (28*z)*(-16*z**3) + (6*z**2)*(-16*z**3) + (-16*z**3)*(-13*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (28*z)*(-16*z**3) + (-11*z**2)*(-13*z**3 + 6*z**2 + 28*z) + (6*z**2)*(-16*z**3) + (-16*z**3)*(-13*z**3)\nSimplifying the partial expression: (-11*z**2)*(-13*z**3 + 6*z**2 + 28*z)\nExpanding the part (-13*z**3 + 6*z**2 + 28*z) using the distributive property, and we got: (28*z)*(-11*z**2) + (-11*z**2)*(6*z**2) + (-11*z**2)*(-13*z**3)\nReplacing (-11*z**2)*(-13*z**3 + 6*z**2 + 28*z) with (28*z)*(-11*z**2) + (-11*z**2)*(6*z**2) + (-11*z**2)*(-13*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (28*z)*(-11*z**2) + (28*z)*(-16*z**3) + (-11*z**2)*(6*z**2) + (-11*z**2)*(-13*z**3) + (6*z**2)*(-16*z**3) + (-16*z**3)*(-13*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*z**3)*(-16*z**3) = 208*z**6\n (-13*z**3)*(-11*z**2) = 143*z**5\n (6*z**2)*(-16*z**3) = -96*z**5\n (6*z**2)*(-11*z**2) = -66*z**4\n (28*z)*(-16*z**3) = -448*z**4\n (28*z)*(-11*z**2) = -308*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 208*z**6 - 96*z**5 + 143*z**5 - 448*z**4 - 66*z**4 - 308*z**3\nCombining like terms, got 208*z**6 + 47*z**5 - 514*z**4 - 308*z**3\n#Step 6:\nCurrent expression: 208*z**6 + 47*z**5 - 514*z**4 - 308*z**3\nNo more calculations needed.\n208*z**6 + 47*z**5 - 514*z**4 - 308*z**3", "generated_answer": "208*z**6 + 47*z**5 - 514*z**4 - 308*z**3", "step_length": 6} {"cot_id": "1d2b1e18ff1a6194a1a23552980664316e327e54451bf019249aaa44cef9f763", "datapoint": {"question": "Simplify this expression: (-40*x**2 + 8*x)*(-13*x**2 - 12*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "520*x**4 + 376*x**3 - 96*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 773, "polynomial_expr": "(-40*x**2 + 8*x)*(-13*x**2 - 12*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-40*x**2 + 8*x)*(-13*x**2 - 12*x)\nExpanding the part (-40*x**2 + 8*x) using the distributive property, and we got: (8*x)*(-13*x**2 - 12*x) + (-40*x**2)*(-13*x**2 - 12*x)\n#Step 2:\nCurrent expression: (8*x)*(-13*x**2 - 12*x) + (-40*x**2)*(-13*x**2 - 12*x)\nSimplifying the partial expression: (-40*x**2)*(-13*x**2 - 12*x)\nExpanding the part (-13*x**2 - 12*x) using the distributive property, and we got: (-12*x)*(-40*x**2) + (-40*x**2)*(-13*x**2)\nReplacing (-40*x**2)*(-13*x**2 - 12*x) with (-12*x)*(-40*x**2) + (-40*x**2)*(-13*x**2) in the overall expression.\n#Step 3:\nCurrent expression: (-12*x)*(-40*x**2) + (8*x)*(-13*x**2 - 12*x) + (-40*x**2)*(-13*x**2)\nSimplifying the partial expression: (8*x)*(-13*x**2 - 12*x)\nExpanding the part (-13*x**2 - 12*x) using the distributive property, and we got: (-12*x)*(8*x) + (8*x)*(-13*x**2)\nReplacing (8*x)*(-13*x**2 - 12*x) with (-12*x)*(8*x) + (8*x)*(-13*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-12*x)*(8*x) + (-12*x)*(-40*x**2) + (8*x)*(-13*x**2) + (-40*x**2)*(-13*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*x**2)*(-40*x**2) = 520*x**4\n (-13*x**2)*(8*x) = -104*x**3\n (-12*x)*(-40*x**2) = 480*x**3\n (-12*x)*(8*x) = -96*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 520*x**4 - 104*x**3 + 480*x**3 - 96*x**2\nCombining like terms, got 520*x**4 + 376*x**3 - 96*x**2\n#Step 6:\nCurrent expression: 520*x**4 + 376*x**3 - 96*x**2\nNo more calculations needed.\n520*x**4 + 376*x**3 - 96*x**2", "generated_answer": "520*x**4 + 376*x**3 - 96*x**2", "step_length": 6} {"cot_id": "7cff6f41f2654d6c258751d7e4d8ce46091feafa0ebf4c6b0d7f8f49f0505e2a", "datapoint": {"question": "Simplify this expression: (-48*x**3 - 3*x**2 - 38*x)*(-18*x**3 - 20*x**2 - 31*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "864*x**6 + 1014*x**5 + 2232*x**4 + 853*x**3 + 1178*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 774, "polynomial_expr": "(-48*x**3 - 3*x**2 - 38*x)*(-18*x**3 - 20*x**2 - 31*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-48*x**3 - 3*x**2 - 38*x)*(-18*x**3 - 20*x**2 - 31*x)\nExpanding the part (-48*x**3 - 3*x**2 - 38*x) using the distributive property, and we got: (-38*x)*(-18*x**3 - 20*x**2 - 31*x) + (-3*x**2)*(-18*x**3 - 20*x**2 - 31*x) + (-48*x**3)*(-18*x**3 - 20*x**2 - 31*x)\n#Step 2:\nCurrent expression: (-38*x)*(-18*x**3 - 20*x**2 - 31*x) + (-3*x**2)*(-18*x**3 - 20*x**2 - 31*x) + (-48*x**3)*(-18*x**3 - 20*x**2 - 31*x)\nSimplifying the partial expression: (-48*x**3)*(-18*x**3 - 20*x**2 - 31*x)\nExpanding the part (-18*x**3 - 20*x**2 - 31*x) using the distributive property, and we got: (-31*x)*(-48*x**3) + (-20*x**2)*(-48*x**3) + (-48*x**3)*(-18*x**3)\nReplacing (-48*x**3)*(-18*x**3 - 20*x**2 - 31*x) with (-31*x)*(-48*x**3) + (-20*x**2)*(-48*x**3) + (-48*x**3)*(-18*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-38*x)*(-18*x**3 - 20*x**2 - 31*x) + (-31*x)*(-48*x**3) + (-20*x**2)*(-48*x**3) + (-3*x**2)*(-18*x**3 - 20*x**2 - 31*x) + (-48*x**3)*(-18*x**3)\nSimplifying the partial expression: (-38*x)*(-18*x**3 - 20*x**2 - 31*x)\nExpanding the part (-18*x**3 - 20*x**2 - 31*x) using the distributive property, and we got: (-38*x)*(-31*x) + (-38*x)*(-20*x**2) + (-38*x)*(-18*x**3)\nReplacing (-38*x)*(-18*x**3 - 20*x**2 - 31*x) with (-38*x)*(-31*x) + (-38*x)*(-20*x**2) + (-38*x)*(-18*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-38*x)*(-31*x) + (-38*x)*(-20*x**2) + (-38*x)*(-18*x**3) + (-31*x)*(-48*x**3) + (-20*x**2)*(-48*x**3) + (-3*x**2)*(-18*x**3 - 20*x**2 - 31*x) + (-48*x**3)*(-18*x**3)\nSimplifying the partial expression: (-3*x**2)*(-18*x**3 - 20*x**2 - 31*x)\nExpanding the part (-18*x**3 - 20*x**2 - 31*x) using the distributive property, and we got: (-31*x)*(-3*x**2) + (-20*x**2)*(-3*x**2) + (-3*x**2)*(-18*x**3)\nReplacing (-3*x**2)*(-18*x**3 - 20*x**2 - 31*x) with (-31*x)*(-3*x**2) + (-20*x**2)*(-3*x**2) + (-3*x**2)*(-18*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-38*x)*(-31*x) + (-38*x)*(-20*x**2) + (-38*x)*(-18*x**3) + (-31*x)*(-3*x**2) + (-31*x)*(-48*x**3) + (-20*x**2)*(-3*x**2) + (-20*x**2)*(-48*x**3) + (-3*x**2)*(-18*x**3) + (-48*x**3)*(-18*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-31*x)*(-48*x**3) = 1488*x**4\n (-31*x)*(-38*x) = 1178*x**2\n (-31*x)*(-3*x**2) = 93*x**3\n (-20*x**2)*(-48*x**3) = 960*x**5\n (-20*x**2)*(-38*x) = 760*x**3\n (-20*x**2)*(-3*x**2) = 60*x**4\n (-18*x**3)*(-48*x**3) = 864*x**6\n (-18*x**3)*(-38*x) = 684*x**4\n (-18*x**3)*(-3*x**2) = 54*x**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 864*x**6 + 54*x**5 + 960*x**5 + 60*x**4 + 684*x**4 + 1488*x**4 + 93*x**3 + 760*x**3 + 1178*x**2\nCombining like terms, got 864*x**6 + 1014*x**5 + 2232*x**4 + 853*x**3 + 1178*x**2\n#Step 7:\nCurrent expression: 864*x**6 + 1014*x**5 + 2232*x**4 + 853*x**3 + 1178*x**2\nNo more calculations needed.\n864*x**6 + 1014*x**5 + 2232*x**4 + 853*x**3 + 1178*x**2", "generated_answer": "864*x**6 + 1014*x**5 + 2232*x**4 + 853*x**3 + 1178*x**2", "step_length": 7} {"cot_id": "994191688a472a20b5c2d9a1a7de12a6ba222152f842a92e558365f8747fd44c", "datapoint": {"question": "Calculate the following: (-33*x**2 - 9)*(-25*x**2 - 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "825*x**4 + 1215*x**2 + 270", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 775, "polynomial_expr": "(-33*x**2 - 9)*(-25*x**2 - 30)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-33*x**2 - 9)*(-25*x**2 - 30)\nExpanding the part (-25*x**2 - 30) using the distributive property, and we got: (-25*x**2)*(-33*x**2 - 9) - 30*(-33*x**2 - 9)\n#Step 2:\nCurrent expression: (-25*x**2)*(-33*x**2 - 9) - 30*(-33*x**2 - 9)\nSimplifying the partial expression: -30*(-33*x**2 - 9)\nExpanding the part (-33*x**2 - 9) using the distributive property, and we got: -33*x**2*(-30) - 9*(-30)\nReplacing -30*(-33*x**2 - 9) with -33*x**2*(-30) - 9*(-30) in the overall expression.\n#Step 3:\nCurrent expression: -33*x**2*(-30) + (-25*x**2)*(-33*x**2 - 9) + 270\nSimplifying the partial expression: (-25*x**2)*(-33*x**2 - 9)\nExpanding the part (-33*x**2 - 9) using the distributive property, and we got: -(-1)*225*x**2 + (-33*x**2)*(-25*x**2)\nReplacing (-25*x**2)*(-33*x**2 - 9) with -(-1)*225*x**2 + (-33*x**2)*(-25*x**2) in the overall expression.\n#Step 4:\nCurrent expression: -9*(-25)*x**2 + (-33*x**2)*(-25*x**2) - 33*x**2*(-30) + 270\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*x**2)*-30 = 990*x**2\n (-33*x**2)*(-25*x**2) = 825*x**4\n -9*-25*x**2 = 225*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 825*x**4 + 225*x**2 + 990*x**2 + 270\nCombining like terms, got 825*x**4 + 1215*x**2 + 270\n#Step 6:\nCurrent expression: 825*x**4 + 1215*x**2 + 270\nNo more calculations needed.\n825*x**4 + 1215*x**2 + 270", "generated_answer": "825*x**4 + 1215*x**2 + 270", "step_length": 6} {"cot_id": "400573d1f4ad86f1bd7d4ea9eb9ceffb7bc988ca3a3fa6ae66afa69fdd27bd3f", "datapoint": {"question": "Simplify this expression: (-25*y**3 + 8*y + 43)*(62*y**3 - 17*y + 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1550*y**6 + 921*y**4 + 1966*y**3 - 136*y**2 - 507*y + 1204", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 776, "polynomial_expr": "(-25*y**3 + 8*y + 43)*(62*y**3 - 17*y + 28)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-25*y**3 + 8*y + 43)*(62*y**3 - 17*y + 28)\nExpanding the part (62*y**3 - 17*y + 28) using the distributive property, and we got: (-17*y)*(-25*y**3 + 8*y + 43) + (62*y**3)*(-25*y**3 + 8*y + 43) + 28*(-25*y**3 + 8*y + 43)\n#Step 2:\nCurrent expression: (-17*y)*(-25*y**3 + 8*y + 43) + (62*y**3)*(-25*y**3 + 8*y + 43) + 28*(-25*y**3 + 8*y + 43)\nSimplifying the partial expression: 28*(-25*y**3 + 8*y + 43)\nExpanding the part (-25*y**3 + 8*y + 43) using the distributive property, and we got: (8*y)*28 - 25*y**3*28 + 43*28\nReplacing 28*(-25*y**3 + 8*y + 43) with (8*y)*28 - 25*y**3*28 + 43*28 in the overall expression.\n#Step 3:\nCurrent expression: (-17*y)*(-25*y**3 + 8*y + 43) + (8*y)*28 - 25*y**3*28 + (62*y**3)*(-25*y**3 + 8*y + 43) + 1204\nSimplifying the partial expression: (-17*y)*(-25*y**3 + 8*y + 43)\nExpanding the part (-25*y**3 + 8*y + 43) using the distributive property, and we got: (-17*y)*(8*y) + (-17*y)*(-25*y**3) + 43*(-17*y)\nReplacing (-17*y)*(-25*y**3 + 8*y + 43) with (-17*y)*(8*y) + (-17*y)*(-25*y**3) + 43*(-17*y) in the overall expression.\n#Step 4:\nCurrent expression: (-17*y)*(8*y) + (-17*y)*(-25*y**3) + 43*(-17)*y + (8*y)*28 - 25*y**3*28 + (62*y**3)*(-25*y**3 + 8*y + 43) + 1204\nSimplifying the partial expression: (62*y**3)*(-25*y**3 + 8*y + 43)\nExpanding the part (-25*y**3 + 8*y + 43) using the distributive property, and we got: 43*(62*y**3) + (8*y)*(62*y**3) + (-25*y**3)*(62*y**3)\nReplacing (62*y**3)*(-25*y**3 + 8*y + 43) with 43*(62*y**3) + (8*y)*(62*y**3) + (-25*y**3)*(62*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-17*y)*(8*y) + (-17*y)*(-25*y**3) + 43*62*y**3 + 43*(-17)*y + (8*y)*(62*y**3) + (8*y)*28 + (-25*y**3)*(62*y**3) - 25*y**3*28 + 1204\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*y**3)*28 = -700*y**3\n (-25*y**3)*(-17*y) = 425*y**4\n (-25*y**3)*(62*y**3) = -1550*y**6\n (8*y)*28 = 224*y\n (8*y)*(-17*y) = -136*y**2\n (8*y)*(62*y**3) = 496*y**4\n 43*-17*y = -731*y\n 43*62*y**3 = 2666*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1550*y**6 + 425*y**4 + 496*y**4 - 700*y**3 + 2666*y**3 - 136*y**2 - 731*y + 224*y + 1204\nCombining like terms, got -1550*y**6 + 921*y**4 + 1966*y**3 - 136*y**2 - 507*y + 1204\n#Step 7:\nCurrent expression: -1550*y**6 + 921*y**4 + 1966*y**3 - 136*y**2 - 507*y + 1204\nNo more calculations needed.\n-1550*y**6 + 921*y**4 + 1966*y**3 - 136*y**2 - 507*y + 1204", "generated_answer": "-1550*y**6 + 921*y**4 + 1966*y**3 - 136*y**2 - 507*y + 1204", "step_length": 7} {"cot_id": "fb35e36d3e9e8c6dd81c50d268d8ee2f4ca693bd76987376e41b3be0196fd418", "datapoint": {"question": "Calculate the following: (-14*x**2 + 69*x + 13)*(-36*x**3 - 20*x**2 + x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "504*x**5 - 2204*x**4 - 1862*x**3 - 191*x**2 + 13*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 778, "polynomial_expr": "(-14*x**2 + 69*x + 13)*(-36*x**3 - 20*x**2 + x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-14*x**2 + 69*x + 13)*(-36*x**3 - 20*x**2 + x)\nExpanding the part (-14*x**2 + 69*x + 13) using the distributive property, and we got: (69*x)*(-36*x**3 - 20*x**2 + x) + (-14*x**2)*(-36*x**3 - 20*x**2 + x) + 13*(-36*x**3 - 20*x**2 + x)\n#Step 2:\nCurrent expression: (69*x)*(-36*x**3 - 20*x**2 + x) + (-14*x**2)*(-36*x**3 - 20*x**2 + x) + 13*(-36*x**3 - 20*x**2 + x)\nSimplifying the partial expression: 13*(-36*x**3 - 20*x**2 + x)\nExpanding the part (-36*x**3 - 20*x**2 + x) using the distributive property, and we got: x*13 - 20*x**2*13 - 36*x**3*13\nReplacing 13*(-36*x**3 - 20*x**2 + x) with x*13 - 20*x**2*13 - 36*x**3*13 in the overall expression.\n#Step 3:\nCurrent expression: x*13 + (69*x)*(-36*x**3 - 20*x**2 + x) - 20*x**2*13 + (-14*x**2)*(-36*x**3 - 20*x**2 + x) - 36*x**3*13\nSimplifying the partial expression: (-14*x**2)*(-36*x**3 - 20*x**2 + x)\nExpanding the part (-36*x**3 - 20*x**2 + x) using the distributive property, and we got: x*(-14*x**2) + (-20*x**2)*(-14*x**2) + (-14*x**2)*(-36*x**3)\nReplacing (-14*x**2)*(-36*x**3 - 20*x**2 + x) with x*(-14*x**2) + (-20*x**2)*(-14*x**2) + (-14*x**2)*(-36*x**3) in the overall expression.\n#Step 4:\nCurrent expression: x*(-14*x**2) + x*13 + (69*x)*(-36*x**3 - 20*x**2 + x) + (-20*x**2)*(-14*x**2) - 20*x**2*13 + (-14*x**2)*(-36*x**3) - 36*x**3*13\nSimplifying the partial expression: (69*x)*(-36*x**3 - 20*x**2 + x)\nExpanding the part (-36*x**3 - 20*x**2 + x) using the distributive property, and we got: x*(69*x) + (69*x)*(-20*x**2) + (69*x)*(-36*x**3)\nReplacing (69*x)*(-36*x**3 - 20*x**2 + x) with x*(69*x) + (69*x)*(-20*x**2) + (69*x)*(-36*x**3) in the overall expression.\n#Step 5:\nCurrent expression: x*(69*x) + x*(-14*x**2) + x*13 + (69*x)*(-20*x**2) + (69*x)*(-36*x**3) + (-20*x**2)*(-14*x**2) - 20*x**2*13 + (-14*x**2)*(-36*x**3) - 36*x**3*13\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n x*13 = 13*x\n x*(-14*x**2) = -14*x**3\n x*(69*x) = 69*x**2\n (-36*x**3)*13 = -468*x**3\n (-36*x**3)*(-14*x**2) = 504*x**5\n (-36*x**3)*(69*x) = -2484*x**4\n (-20*x**2)*13 = -260*x**2\n (-20*x**2)*(-14*x**2) = 280*x**4\n (-20*x**2)*(69*x) = -1380*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 504*x**5 - 2484*x**4 + 280*x**4 - 1380*x**3 - 468*x**3 - 14*x**3 - 260*x**2 + 69*x**2 + 13*x\nCombining like terms, got 504*x**5 - 2204*x**4 - 1862*x**3 - 191*x**2 + 13*x\n#Step 7:\nCurrent expression: 504*x**5 - 2204*x**4 - 1862*x**3 - 191*x**2 + 13*x\nNo more calculations needed.\n504*x**5 - 2204*x**4 - 1862*x**3 - 191*x**2 + 13*x", "generated_answer": "504*x**5 - 2204*x**4 - 1862*x**3 - 191*x**2 + 13*x", "step_length": 7} {"cot_id": "048b7070f4411890b51c0aeceb0e39382b4bfe1b71deefcd6ab7fc26b628f8eb", "datapoint": {"question": "Calculate the following: (-7*z**3 + 3*z)*(18*z**3 + 42*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-126*z**6 - 240*z**4 + 126*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 779, "polynomial_expr": "(-7*z**3 + 3*z)*(18*z**3 + 42*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-7*z**3 + 3*z)*(18*z**3 + 42*z)\nExpanding the part (-7*z**3 + 3*z) using the distributive property, and we got: (3*z)*(18*z**3 + 42*z) + (-7*z**3)*(18*z**3 + 42*z)\n#Step 2:\nCurrent expression: (3*z)*(18*z**3 + 42*z) + (-7*z**3)*(18*z**3 + 42*z)\nSimplifying the partial expression: (-7*z**3)*(18*z**3 + 42*z)\nExpanding the part (18*z**3 + 42*z) using the distributive property, and we got: (42*z)*(-7*z**3) + (-7*z**3)*(18*z**3)\nReplacing (-7*z**3)*(18*z**3 + 42*z) with (42*z)*(-7*z**3) + (-7*z**3)*(18*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (3*z)*(18*z**3 + 42*z) + (42*z)*(-7*z**3) + (-7*z**3)*(18*z**3)\nSimplifying the partial expression: (3*z)*(18*z**3 + 42*z)\nExpanding the part (18*z**3 + 42*z) using the distributive property, and we got: (3*z)*(42*z) + (3*z)*(18*z**3)\nReplacing (3*z)*(18*z**3 + 42*z) with (3*z)*(42*z) + (3*z)*(18*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (3*z)*(42*z) + (3*z)*(18*z**3) + (42*z)*(-7*z**3) + (-7*z**3)*(18*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (18*z**3)*(-7*z**3) = -126*z**6\n (18*z**3)*(3*z) = 54*z**4\n (42*z)*(-7*z**3) = -294*z**4\n (42*z)*(3*z) = 126*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -126*z**6 - 294*z**4 + 54*z**4 + 126*z**2\nCombining like terms, got -126*z**6 - 240*z**4 + 126*z**2\n#Step 6:\nCurrent expression: -126*z**6 - 240*z**4 + 126*z**2\nNo more calculations needed.\n-126*z**6 - 240*z**4 + 126*z**2", "generated_answer": "-126*z**6 - 240*z**4 + 126*z**2", "step_length": 6} {"cot_id": "aecb9c90e13b39bdf6eed5e48b14ec0031ac9018a24a4137f78992a4950b58c8", "datapoint": {"question": "Calculate the following: (-11*x**3 + 20*x)*(28*x**3 + 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-308*x**6 + 560*x**4 - 451*x**3 + 820*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 780, "polynomial_expr": "(-11*x**3 + 20*x)*(28*x**3 + 41)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-11*x**3 + 20*x)*(28*x**3 + 41)\nExpanding the part (28*x**3 + 41) using the distributive property, and we got: (28*x**3)*(-11*x**3 + 20*x) + 41*(-11*x**3 + 20*x)\n#Step 2:\nCurrent expression: (28*x**3)*(-11*x**3 + 20*x) + 41*(-11*x**3 + 20*x)\nSimplifying the partial expression: 41*(-11*x**3 + 20*x)\nExpanding the part (-11*x**3 + 20*x) using the distributive property, and we got: (20*x)*41 - 11*x**3*41\nReplacing 41*(-11*x**3 + 20*x) with (20*x)*41 - 11*x**3*41 in the overall expression.\n#Step 3:\nCurrent expression: (20*x)*41 - 11*x**3*41 + (28*x**3)*(-11*x**3 + 20*x)\nSimplifying the partial expression: (28*x**3)*(-11*x**3 + 20*x)\nExpanding the part (-11*x**3 + 20*x) using the distributive property, and we got: (20*x)*(28*x**3) + (-11*x**3)*(28*x**3)\nReplacing (28*x**3)*(-11*x**3 + 20*x) with (20*x)*(28*x**3) + (-11*x**3)*(28*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (20*x)*(28*x**3) + (20*x)*41 + (-11*x**3)*(28*x**3) - 11*x**3*41\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*x**3)*41 = -451*x**3\n (-11*x**3)*(28*x**3) = -308*x**6\n (20*x)*41 = 820*x\n (20*x)*(28*x**3) = 560*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -308*x**6 + 560*x**4 - 451*x**3 + 820*x\nNo more calculations needed.\n-308*x**6 + 560*x**4 - 451*x**3 + 820*x", "generated_answer": "-308*x**6 + 560*x**4 - 451*x**3 + 820*x", "step_length": 5} {"cot_id": "da97ad5ea0a4525a19fe9b92c4e43a23dd01f1cfccc451a39e0a229c81a85923", "datapoint": {"question": "Simplify this expression: (24 - 6*y)*(-71*y**3 + 50*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "426*y**4 - 2004*y**3 + 1200*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 781, "polynomial_expr": "(24 - 6*y)*(-71*y**3 + 50*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (24 - 6*y)*(-71*y**3 + 50*y**2)\nExpanding the part (24 - 6*y) using the distributive property, and we got: (-6*y)*(-71*y**3 + 50*y**2) + 24*(-71*y**3 + 50*y**2)\n#Step 2:\nCurrent expression: (-6*y)*(-71*y**3 + 50*y**2) + 24*(-71*y**3 + 50*y**2)\nSimplifying the partial expression: 24*(-71*y**3 + 50*y**2)\nExpanding the part (-71*y**3 + 50*y**2) using the distributive property, and we got: (50*y**2)*24 - 71*y**3*24\nReplacing 24*(-71*y**3 + 50*y**2) with (50*y**2)*24 - 71*y**3*24 in the overall expression.\n#Step 3:\nCurrent expression: (-6*y)*(-71*y**3 + 50*y**2) + (50*y**2)*24 - 71*y**3*24\nSimplifying the partial expression: (-6*y)*(-71*y**3 + 50*y**2)\nExpanding the part (-71*y**3 + 50*y**2) using the distributive property, and we got: (-6*y)*(50*y**2) + (-6*y)*(-71*y**3)\nReplacing (-6*y)*(-71*y**3 + 50*y**2) with (-6*y)*(50*y**2) + (-6*y)*(-71*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-6*y)*(50*y**2) + (-6*y)*(-71*y**3) + (50*y**2)*24 - 71*y**3*24\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-71*y**3)*24 = -1704*y**3\n (-71*y**3)*(-6*y) = 426*y**4\n (50*y**2)*24 = 1200*y**2\n (50*y**2)*(-6*y) = -300*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 426*y**4 - 1704*y**3 - 300*y**3 + 1200*y**2\nCombining like terms, got 426*y**4 - 2004*y**3 + 1200*y**2\n#Step 6:\nCurrent expression: 426*y**4 - 2004*y**3 + 1200*y**2\nNo more calculations needed.\n426*y**4 - 2004*y**3 + 1200*y**2", "generated_answer": "426*y**4 - 2004*y**3 + 1200*y**2", "step_length": 6} {"cot_id": "f22910560b439eec0e35193f8215018c0368229cfd016731e0d93bf25d57bc61", "datapoint": {"question": "Calculate the following: 13*z*(-27*z**3 + 6*z + 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-351*z**4 + 78*z**2 + 455*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 782, "polynomial_expr": "13*z*(-27*z**3 + 6*z + 35)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 13*z*(-27*z**3 + 6*z + 35)\nExpanding the part (-27*z**3 + 6*z + 35) using the distributive property, and we got: 35*(13*z) + (6*z)*(13*z) + (13*z)*(-27*z**3)\n#Step 2:\nCurrent expression: 35*(13*z) + (6*z)*(13*z) + (13*z)*(-27*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 35*(13*z) = 455*z\n (-27*z**3)*(13*z) = -351*z**4\n (6*z)*(13*z) = 78*z**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -351*z**4 + 78*z**2 + 455*z\nNo more calculations needed.\n-351*z**4 + 78*z**2 + 455*z", "generated_answer": "-351*z**4 + 78*z**2 + 455*z", "step_length": 3} {"cot_id": "88d35b8c833f63c28c70e077037f08c75283cd6f3916df251c9fe54fdb306775", "datapoint": {"question": "Simplify this expression: (-34*y**3 - 5*y - 1)*(-13*y**3 - 22*y + 8)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "442*y**6 + 813*y**4 - 259*y**3 + 110*y**2 - 18*y - 8", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 783, "polynomial_expr": "(-34*y**3 - 5*y - 1)*(-13*y**3 - 22*y + 8)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-34*y**3 - 5*y - 1)*(-13*y**3 - 22*y + 8)\nExpanding the part (-34*y**3 - 5*y - 1) using the distributive property, and we got: (-5*y)*(-13*y**3 - 22*y + 8) + (-34*y**3)*(-13*y**3 - 22*y + 8) - (-13*y**3 - 22*y + 8)\n#Step 2:\nCurrent expression: (-5*y)*(-13*y**3 - 22*y + 8) + (-34*y**3)*(-13*y**3 - 22*y + 8) - (-13*y**3 - 22*y + 8)\nSimplifying the partial expression: -(-13*y**3 - 22*y + 8)\nExpanding the part (-13*y**3 - 22*y + 8) using the distributive property, and we got: -22*y*(-1) - 13*y**3*(-1) + 8*(-1)\nReplacing -(-13*y**3 - 22*y + 8) with -22*y*(-1) - 13*y**3*(-1) + 8*(-1) in the overall expression.\n#Step 3:\nCurrent expression: -22*y*(-1) + (-5*y)*(-13*y**3 - 22*y + 8) + (-34*y**3)*(-13*y**3 - 22*y + 8) - 13*y**3*(-1) - 8\nSimplifying the partial expression: (-34*y**3)*(-13*y**3 - 22*y + 8)\nExpanding the part (-13*y**3 - 22*y + 8) using the distributive property, and we got: (-22*y)*(-34*y**3) + 8*(-34*y**3) + (-34*y**3)*(-13*y**3)\nReplacing (-34*y**3)*(-13*y**3 - 22*y + 8) with (-22*y)*(-34*y**3) + 8*(-34*y**3) + (-34*y**3)*(-13*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-22*y)*(-34*y**3) - 22*y*(-1) + (-5*y)*(-13*y**3 - 22*y + 8) + 8*(-34)*y**3 + (-34*y**3)*(-13*y**3) - 13*y**3*(-1) - 8\nSimplifying the partial expression: (-5*y)*(-13*y**3 - 22*y + 8)\nExpanding the part (-13*y**3 - 22*y + 8) using the distributive property, and we got: (-22*y)*(-5*y) + (-5*y)*(-13*y**3) + 8*(-5*y)\nReplacing (-5*y)*(-13*y**3 - 22*y + 8) with (-22*y)*(-5*y) + (-5*y)*(-13*y**3) + 8*(-5*y) in the overall expression.\n#Step 5:\nCurrent expression: (-22*y)*(-5*y) + (-22*y)*(-34*y**3) - 22*y*(-1) + (-5*y)*(-13*y**3) + 8*(-34)*y**3 + 8*(-5)*y + (-34*y**3)*(-13*y**3) - 13*y**3*(-1) - 8\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*y)*-1 = 22*y\n (-22*y)*(-34*y**3) = 748*y**4\n (-22*y)*(-5*y) = 110*y**2\n (-13*y**3)*-1 = 13*y**3\n (-13*y**3)*(-34*y**3) = 442*y**6\n (-13*y**3)*(-5*y) = 65*y**4\n 8*-34*y**3 = -272*y**3\n 8*-5*y = -40*y\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 442*y**6 + 65*y**4 + 748*y**4 - 272*y**3 + 13*y**3 + 110*y**2 - 40*y + 22*y - 8\nCombining like terms, got 442*y**6 + 813*y**4 - 259*y**3 + 110*y**2 - 18*y - 8\n#Step 7:\nCurrent expression: 442*y**6 + 813*y**4 - 259*y**3 + 110*y**2 - 18*y - 8\nNo more calculations needed.\n442*y**6 + 813*y**4 - 259*y**3 + 110*y**2 - 18*y - 8", "generated_answer": "442*y**6 + 813*y**4 - 259*y**3 + 110*y**2 - 18*y - 8", "step_length": 7} {"cot_id": "ff02ad170627585e59b7235d76917f243b9b05be38df558199ab6eb2d1aee596", "datapoint": {"question": "Simplify this expression: 126*z + 99\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "126*z + 99", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 784, "polynomial_expr": "126*z + 99", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 126*z + 99\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 126*z + 99\nNo more calculations needed.\n126*z + 99", "generated_answer": "126*z + 99", "step_length": 2} {"cot_id": "ee8a162b220b28ac0de227748073bc38db67ef1d2cf38633d1cad0c9bc0397da", "datapoint": {"question": "Simplify this expression: 36*y**3*(48*y**3 - 43*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1728*y**6 - 1548*y**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 785, "polynomial_expr": "36*y**3*(48*y**3 - 43*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 36*y**3*(48*y**3 - 43*y)\nExpanding the part (48*y**3 - 43*y) using the distributive property, and we got: (-43*y)*(36*y**3) + (36*y**3)*(48*y**3)\n#Step 2:\nCurrent expression: (-43*y)*(36*y**3) + (36*y**3)*(48*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-43*y)*(36*y**3) = -1548*y**4\n (48*y**3)*(36*y**3) = 1728*y**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1728*y**6 - 1548*y**4\nNo more calculations needed.\n1728*y**6 - 1548*y**4", "generated_answer": "1728*y**6 - 1548*y**4", "step_length": 3} {"cot_id": "c4b8299f378246b170fdfb3dfdb6d56252629e7b7107a103dd1ffa884155d74a", "datapoint": {"question": "Simplify this expression: (-16*x**3 + 8*x)*(-24*x**3 + 9*x**2 - 30*x + 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "384*x**6 - 144*x**5 + 288*x**4 - 24*x**3 - 240*x**2 + 48*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 786, "polynomial_expr": "(-16*x**3 + 8*x)*(-24*x**3 + 9*x**2 - 30*x + 6)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-16*x**3 + 8*x)*(-24*x**3 + 9*x**2 - 30*x + 6)\nExpanding the part (-16*x**3 + 8*x) using the distributive property, and we got: (8*x)*(-24*x**3 + 9*x**2 - 30*x + 6) + (-16*x**3)*(-24*x**3 + 9*x**2 - 30*x + 6)\n#Step 2:\nCurrent expression: (8*x)*(-24*x**3 + 9*x**2 - 30*x + 6) + (-16*x**3)*(-24*x**3 + 9*x**2 - 30*x + 6)\nSimplifying the partial expression: (-16*x**3)*(-24*x**3 + 9*x**2 - 30*x + 6)\nExpanding the part (-24*x**3 + 9*x**2 - 30*x + 6) using the distributive property, and we got: (-30*x)*(-16*x**3) + 6*(-16*x**3) + (9*x**2)*(-16*x**3) + (-24*x**3)*(-16*x**3)\nReplacing (-16*x**3)*(-24*x**3 + 9*x**2 - 30*x + 6) with (-30*x)*(-16*x**3) + 6*(-16*x**3) + (9*x**2)*(-16*x**3) + (-24*x**3)*(-16*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-30*x)*(-16*x**3) + 6*(-16)*x**3 + (8*x)*(-24*x**3 + 9*x**2 - 30*x + 6) + (9*x**2)*(-16*x**3) + (-24*x**3)*(-16*x**3)\nSimplifying the partial expression: (8*x)*(-24*x**3 + 9*x**2 - 30*x + 6)\nExpanding the part (-24*x**3 + 9*x**2 - 30*x + 6) using the distributive property, and we got: (-30*x)*(8*x) + 6*(8*x) + (8*x)*(9*x**2) + (8*x)*(-24*x**3)\nReplacing (8*x)*(-24*x**3 + 9*x**2 - 30*x + 6) with (-30*x)*(8*x) + 6*(8*x) + (8*x)*(9*x**2) + (8*x)*(-24*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-30*x)*(8*x) + (-30*x)*(-16*x**3) + 6*(-16)*x**3 + 6*8*x + (8*x)*(9*x**2) + (8*x)*(-24*x**3) + (9*x**2)*(-16*x**3) + (-24*x**3)*(-16*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*x)*(-16*x**3) = 480*x**4\n (-30*x)*(8*x) = -240*x**2\n (-24*x**3)*(-16*x**3) = 384*x**6\n (-24*x**3)*(8*x) = -192*x**4\n (9*x**2)*(-16*x**3) = -144*x**5\n (9*x**2)*(8*x) = 72*x**3\n 6*-16*x**3 = -96*x**3\n 6*8*x = 48*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 384*x**6 - 144*x**5 - 192*x**4 + 480*x**4 - 96*x**3 + 72*x**3 - 240*x**2 + 48*x\nCombining like terms, got 384*x**6 - 144*x**5 + 288*x**4 - 24*x**3 - 240*x**2 + 48*x\n#Step 6:\nCurrent expression: 384*x**6 - 144*x**5 + 288*x**4 - 24*x**3 - 240*x**2 + 48*x\nNo more calculations needed.\n384*x**6 - 144*x**5 + 288*x**4 - 24*x**3 - 240*x**2 + 48*x", "generated_answer": "384*x**6 - 144*x**5 + 288*x**4 - 24*x**3 - 240*x**2 + 48*x", "step_length": 6} {"cot_id": "224e386c52fbb6bfac1df536ce7fe2ac5dee533bf664f4f0267c2805a4d5bc28", "datapoint": {"question": "Simplify this expression: (50*x**3 + 20*x)*(-14*x**3 + 50*x**2 - 26*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-700*x**6 + 2500*x**5 - 1580*x**4 + 1000*x**3 - 520*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 787, "polynomial_expr": "(50*x**3 + 20*x)*(-14*x**3 + 50*x**2 - 26*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (50*x**3 + 20*x)*(-14*x**3 + 50*x**2 - 26*x)\nExpanding the part (50*x**3 + 20*x) using the distributive property, and we got: (20*x)*(-14*x**3 + 50*x**2 - 26*x) + (50*x**3)*(-14*x**3 + 50*x**2 - 26*x)\n#Step 2:\nCurrent expression: (20*x)*(-14*x**3 + 50*x**2 - 26*x) + (50*x**3)*(-14*x**3 + 50*x**2 - 26*x)\nSimplifying the partial expression: (20*x)*(-14*x**3 + 50*x**2 - 26*x)\nExpanding the part (-14*x**3 + 50*x**2 - 26*x) using the distributive property, and we got: (-26*x)*(20*x) + (20*x)*(50*x**2) + (20*x)*(-14*x**3)\nReplacing (20*x)*(-14*x**3 + 50*x**2 - 26*x) with (-26*x)*(20*x) + (20*x)*(50*x**2) + (20*x)*(-14*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-26*x)*(20*x) + (20*x)*(50*x**2) + (20*x)*(-14*x**3) + (50*x**3)*(-14*x**3 + 50*x**2 - 26*x)\nSimplifying the partial expression: (50*x**3)*(-14*x**3 + 50*x**2 - 26*x)\nExpanding the part (-14*x**3 + 50*x**2 - 26*x) using the distributive property, and we got: (-26*x)*(50*x**3) + (50*x**2)*(50*x**3) + (-14*x**3)*(50*x**3)\nReplacing (50*x**3)*(-14*x**3 + 50*x**2 - 26*x) with (-26*x)*(50*x**3) + (50*x**2)*(50*x**3) + (-14*x**3)*(50*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-26*x)*(20*x) + (-26*x)*(50*x**3) + (20*x)*(50*x**2) + (20*x)*(-14*x**3) + (50*x**2)*(50*x**3) + (-14*x**3)*(50*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-26*x)*(20*x) = -520*x**2\n (-26*x)*(50*x**3) = -1300*x**4\n (-14*x**3)*(20*x) = -280*x**4\n (-14*x**3)*(50*x**3) = -700*x**6\n (50*x**2)*(20*x) = 1000*x**3\n (50*x**2)*(50*x**3) = 2500*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -700*x**6 + 2500*x**5 - 1300*x**4 - 280*x**4 + 1000*x**3 - 520*x**2\nCombining like terms, got -700*x**6 + 2500*x**5 - 1580*x**4 + 1000*x**3 - 520*x**2\n#Step 6:\nCurrent expression: -700*x**6 + 2500*x**5 - 1580*x**4 + 1000*x**3 - 520*x**2\nNo more calculations needed.\n-700*x**6 + 2500*x**5 - 1580*x**4 + 1000*x**3 - 520*x**2", "generated_answer": "-700*x**6 + 2500*x**5 - 1580*x**4 + 1000*x**3 - 520*x**2", "step_length": 6} {"cot_id": "7fa868dc7d3853fb6b1abcfa47b8ef5277ad29d6014d87aaf04cefda0d49020b", "datapoint": {"question": "Calculate the following: (2*x**3 + 47*x)*(18*x**3 + 5*x**2 - 47*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "36*x**6 + 10*x**5 + 752*x**4 + 235*x**3 - 2209*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 788, "polynomial_expr": "(2*x**3 + 47*x)*(18*x**3 + 5*x**2 - 47*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2*x**3 + 47*x)*(18*x**3 + 5*x**2 - 47*x)\nExpanding the part (2*x**3 + 47*x) using the distributive property, and we got: (47*x)*(18*x**3 + 5*x**2 - 47*x) + (2*x**3)*(18*x**3 + 5*x**2 - 47*x)\n#Step 2:\nCurrent expression: (47*x)*(18*x**3 + 5*x**2 - 47*x) + (2*x**3)*(18*x**3 + 5*x**2 - 47*x)\nSimplifying the partial expression: (2*x**3)*(18*x**3 + 5*x**2 - 47*x)\nExpanding the part (18*x**3 + 5*x**2 - 47*x) using the distributive property, and we got: (-47*x)*(2*x**3) + (5*x**2)*(2*x**3) + (2*x**3)*(18*x**3)\nReplacing (2*x**3)*(18*x**3 + 5*x**2 - 47*x) with (-47*x)*(2*x**3) + (5*x**2)*(2*x**3) + (2*x**3)*(18*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-47*x)*(2*x**3) + (47*x)*(18*x**3 + 5*x**2 - 47*x) + (5*x**2)*(2*x**3) + (2*x**3)*(18*x**3)\nSimplifying the partial expression: (47*x)*(18*x**3 + 5*x**2 - 47*x)\nExpanding the part (18*x**3 + 5*x**2 - 47*x) using the distributive property, and we got: (-47*x)*(47*x) + (47*x)*(5*x**2) + (47*x)*(18*x**3)\nReplacing (47*x)*(18*x**3 + 5*x**2 - 47*x) with (-47*x)*(47*x) + (47*x)*(5*x**2) + (47*x)*(18*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-47*x)*(47*x) + (-47*x)*(2*x**3) + (47*x)*(5*x**2) + (47*x)*(18*x**3) + (5*x**2)*(2*x**3) + (2*x**3)*(18*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*x)*(2*x**3) = -94*x**4\n (-47*x)*(47*x) = -2209*x**2\n (5*x**2)*(2*x**3) = 10*x**5\n (5*x**2)*(47*x) = 235*x**3\n (18*x**3)*(2*x**3) = 36*x**6\n (18*x**3)*(47*x) = 846*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 36*x**6 + 10*x**5 - 94*x**4 + 846*x**4 + 235*x**3 - 2209*x**2\nCombining like terms, got 36*x**6 + 10*x**5 + 752*x**4 + 235*x**3 - 2209*x**2\n#Step 6:\nCurrent expression: 36*x**6 + 10*x**5 + 752*x**4 + 235*x**3 - 2209*x**2\nNo more calculations needed.\n36*x**6 + 10*x**5 + 752*x**4 + 235*x**3 - 2209*x**2", "generated_answer": "36*x**6 + 10*x**5 + 752*x**4 + 235*x**3 - 2209*x**2", "step_length": 6} {"cot_id": "a805e63a6f2c79b71c0d9fa11eb0a2b29d584a6cf6c0013c4ae13b054b40feeb", "datapoint": {"question": "Simplify this expression: -420*x**3\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-420*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 789, "polynomial_expr": "-420*x**3", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -420*x**3\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -420*x**3\nNo more calculations needed.\n-420*x**3", "generated_answer": "-420*x**3", "step_length": 2} {"cot_id": "1038ce46407933c356665f721e4ccb15422facdfe44c6a9698539197985fe03a", "datapoint": {"question": "Simplify this expression: (21 - 21*z**3)*(-25*z**3 + 33*z**2 - 39*z - 37)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "525*z**6 - 693*z**5 + 819*z**4 + 252*z**3 + 693*z**2 - 819*z - 777", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 790, "polynomial_expr": "(21 - 21*z**3)*(-25*z**3 + 33*z**2 - 39*z - 37)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21 - 21*z**3)*(-25*z**3 + 33*z**2 - 39*z - 37)\nExpanding the part (21 - 21*z**3) using the distributive property, and we got: (-21*z**3)*(-25*z**3 + 33*z**2 - 39*z - 37) + 21*(-25*z**3 + 33*z**2 - 39*z - 37)\n#Step 2:\nCurrent expression: (-21*z**3)*(-25*z**3 + 33*z**2 - 39*z - 37) + 21*(-25*z**3 + 33*z**2 - 39*z - 37)\nSimplifying the partial expression: 21*(-25*z**3 + 33*z**2 - 39*z - 37)\nExpanding the part (-25*z**3 + 33*z**2 - 39*z - 37) using the distributive property, and we got: -39*z*21 + (33*z**2)*21 - 25*z**3*21 - 37*21\nReplacing 21*(-25*z**3 + 33*z**2 - 39*z - 37) with -39*z*21 + (33*z**2)*21 - 25*z**3*21 - 37*21 in the overall expression.\n#Step 3:\nCurrent expression: -39*z*21 + (33*z**2)*21 - 25*z**3*21 + (-21*z**3)*(-25*z**3 + 33*z**2 - 39*z - 37) - 777\nSimplifying the partial expression: (-21*z**3)*(-25*z**3 + 33*z**2 - 39*z - 37)\nExpanding the part (-25*z**3 + 33*z**2 - 39*z - 37) using the distributive property, and we got: (-39*z)*(-21*z**3) - (-1)*777*z**3 + (33*z**2)*(-21*z**3) + (-25*z**3)*(-21*z**3)\nReplacing (-21*z**3)*(-25*z**3 + 33*z**2 - 39*z - 37) with (-39*z)*(-21*z**3) - (-1)*777*z**3 + (33*z**2)*(-21*z**3) + (-25*z**3)*(-21*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-39*z)*(-21*z**3) - 39*z*21 - 37*(-21)*z**3 + (33*z**2)*(-21*z**3) + (33*z**2)*21 + (-25*z**3)*(-21*z**3) - 25*z**3*21 - 777\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*z)*21 = -819*z\n (-39*z)*(-21*z**3) = 819*z**4\n (-25*z**3)*21 = -525*z**3\n (-25*z**3)*(-21*z**3) = 525*z**6\n (33*z**2)*21 = 693*z**2\n (33*z**2)*(-21*z**3) = -693*z**5\n -37*-21*z**3 = 777*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 525*z**6 - 693*z**5 + 819*z**4 - 525*z**3 + 777*z**3 + 693*z**2 - 819*z - 777\nCombining like terms, got 525*z**6 - 693*z**5 + 819*z**4 + 252*z**3 + 693*z**2 - 819*z - 777\n#Step 6:\nCurrent expression: 525*z**6 - 693*z**5 + 819*z**4 + 252*z**3 + 693*z**2 - 819*z - 777\nNo more calculations needed.\n525*z**6 - 693*z**5 + 819*z**4 + 252*z**3 + 693*z**2 - 819*z - 777", "generated_answer": "525*z**6 - 693*z**5 + 819*z**4 + 252*z**3 + 693*z**2 - 819*z - 777", "step_length": 6} {"cot_id": "ffc9b3b6ddcfdddb388c355803a4e1b62ae5aeea5c584cb5d21d4794aef9232f", "datapoint": {"question": "Simplify this expression: (32*z**2 - 10)*(-24*z**2 + 20*z + 11)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-768*z**4 + 640*z**3 + 592*z**2 - 200*z - 110", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 791, "polynomial_expr": "(32*z**2 - 10)*(-24*z**2 + 20*z + 11)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (32*z**2 - 10)*(-24*z**2 + 20*z + 11)\nExpanding the part (32*z**2 - 10) using the distributive property, and we got: (32*z**2)*(-24*z**2 + 20*z + 11) - 10*(-24*z**2 + 20*z + 11)\n#Step 2:\nCurrent expression: (32*z**2)*(-24*z**2 + 20*z + 11) - 10*(-24*z**2 + 20*z + 11)\nSimplifying the partial expression: -10*(-24*z**2 + 20*z + 11)\nExpanding the part (-24*z**2 + 20*z + 11) using the distributive property, and we got: (20*z)*(-10) - 24*z**2*(-10) + 11*(-10)\nReplacing -10*(-24*z**2 + 20*z + 11) with (20*z)*(-10) - 24*z**2*(-10) + 11*(-10) in the overall expression.\n#Step 3:\nCurrent expression: (20*z)*(-10) - 24*z**2*(-10) + (32*z**2)*(-24*z**2 + 20*z + 11) - 110\nSimplifying the partial expression: (32*z**2)*(-24*z**2 + 20*z + 11)\nExpanding the part (-24*z**2 + 20*z + 11) using the distributive property, and we got: 11*(32*z**2) + (20*z)*(32*z**2) + (-24*z**2)*(32*z**2)\nReplacing (32*z**2)*(-24*z**2 + 20*z + 11) with 11*(32*z**2) + (20*z)*(32*z**2) + (-24*z**2)*(32*z**2) in the overall expression.\n#Step 4:\nCurrent expression: 11*32*z**2 + (20*z)*(32*z**2) + (20*z)*(-10) + (-24*z**2)*(32*z**2) - 24*z**2*(-10) - 110\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-24*z**2)*-10 = 240*z**2\n (-24*z**2)*(32*z**2) = -768*z**4\n (20*z)*-10 = -200*z\n (20*z)*(32*z**2) = 640*z**3\n 11*32*z**2 = 352*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -768*z**4 + 640*z**3 + 240*z**2 + 352*z**2 - 200*z - 110\nCombining like terms, got -768*z**4 + 640*z**3 + 592*z**2 - 200*z - 110\n#Step 6:\nCurrent expression: -768*z**4 + 640*z**3 + 592*z**2 - 200*z - 110\nNo more calculations needed.\n-768*z**4 + 640*z**3 + 592*z**2 - 200*z - 110", "generated_answer": "-768*z**4 + 640*z**3 + 592*z**2 - 200*z - 110", "step_length": 6} {"cot_id": "183b94fd8c9e867ca119db2382ad30d10f2410f53fc2bd705866a19efc171331", "datapoint": {"question": "Calculate the following: (8*y + 37)*(2*y**2 - 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "16*y**3 + 74*y**2 - 224*y - 1036", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 792, "polynomial_expr": "(8*y + 37)*(2*y**2 - 28)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (8*y + 37)*(2*y**2 - 28)\nExpanding the part (2*y**2 - 28) using the distributive property, and we got: (2*y**2)*(8*y + 37) - 28*(8*y + 37)\n#Step 2:\nCurrent expression: (2*y**2)*(8*y + 37) - 28*(8*y + 37)\nSimplifying the partial expression: -28*(8*y + 37)\nExpanding the part (8*y + 37) using the distributive property, and we got: (8*y)*(-28) + 37*(-28)\nReplacing -28*(8*y + 37) with (8*y)*(-28) + 37*(-28) in the overall expression.\n#Step 3:\nCurrent expression: (8*y)*(-28) + (2*y**2)*(8*y + 37) - 1036\nSimplifying the partial expression: (2*y**2)*(8*y + 37)\nExpanding the part (8*y + 37) using the distributive property, and we got: 37*(2*y**2) + (8*y)*(2*y**2)\nReplacing (2*y**2)*(8*y + 37) with 37*(2*y**2) + (8*y)*(2*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 37*2*y**2 + (8*y)*(2*y**2) + (8*y)*(-28) - 1036\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (8*y)*-28 = -224*y\n (8*y)*(2*y**2) = 16*y**3\n 37*2*y**2 = 74*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 16*y**3 + 74*y**2 - 224*y - 1036\nNo more calculations needed.\n16*y**3 + 74*y**2 - 224*y - 1036", "generated_answer": "16*y**3 + 74*y**2 - 224*y - 1036", "step_length": 5} {"cot_id": "74188fa23b658a590bba0fcb91cc27dd083ee2f96b0ba95d41d6b7987293a730", "datapoint": {"question": "Simplify this expression: (38*z**2 - 30*z)*(-30*z**3 - 6*z**2 + 22*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1140*z**5 + 672*z**4 + 1016*z**3 - 660*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 793, "polynomial_expr": "(38*z**2 - 30*z)*(-30*z**3 - 6*z**2 + 22*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (38*z**2 - 30*z)*(-30*z**3 - 6*z**2 + 22*z)\nExpanding the part (38*z**2 - 30*z) using the distributive property, and we got: (-30*z)*(-30*z**3 - 6*z**2 + 22*z) + (38*z**2)*(-30*z**3 - 6*z**2 + 22*z)\n#Step 2:\nCurrent expression: (-30*z)*(-30*z**3 - 6*z**2 + 22*z) + (38*z**2)*(-30*z**3 - 6*z**2 + 22*z)\nSimplifying the partial expression: (-30*z)*(-30*z**3 - 6*z**2 + 22*z)\nExpanding the part (-30*z**3 - 6*z**2 + 22*z) using the distributive property, and we got: (-30*z)*(22*z) + (-30*z)*(-6*z**2) + (-30*z)*(-30*z**3)\nReplacing (-30*z)*(-30*z**3 - 6*z**2 + 22*z) with (-30*z)*(22*z) + (-30*z)*(-6*z**2) + (-30*z)*(-30*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-30*z)*(22*z) + (-30*z)*(-6*z**2) + (-30*z)*(-30*z**3) + (38*z**2)*(-30*z**3 - 6*z**2 + 22*z)\nSimplifying the partial expression: (38*z**2)*(-30*z**3 - 6*z**2 + 22*z)\nExpanding the part (-30*z**3 - 6*z**2 + 22*z) using the distributive property, and we got: (22*z)*(38*z**2) + (-6*z**2)*(38*z**2) + (38*z**2)*(-30*z**3)\nReplacing (38*z**2)*(-30*z**3 - 6*z**2 + 22*z) with (22*z)*(38*z**2) + (-6*z**2)*(38*z**2) + (38*z**2)*(-30*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-30*z)*(22*z) + (-30*z)*(-6*z**2) + (-30*z)*(-30*z**3) + (22*z)*(38*z**2) + (-6*z**2)*(38*z**2) + (38*z**2)*(-30*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*z**3)*(-30*z) = 900*z**4\n (-30*z**3)*(38*z**2) = -1140*z**5\n (-6*z**2)*(-30*z) = 180*z**3\n (-6*z**2)*(38*z**2) = -228*z**4\n (22*z)*(-30*z) = -660*z**2\n (22*z)*(38*z**2) = 836*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1140*z**5 - 228*z**4 + 900*z**4 + 180*z**3 + 836*z**3 - 660*z**2\nCombining like terms, got -1140*z**5 + 672*z**4 + 1016*z**3 - 660*z**2\n#Step 6:\nCurrent expression: -1140*z**5 + 672*z**4 + 1016*z**3 - 660*z**2\nNo more calculations needed.\n-1140*z**5 + 672*z**4 + 1016*z**3 - 660*z**2", "generated_answer": "-1140*z**5 + 672*z**4 + 1016*z**3 - 660*z**2", "step_length": 6} {"cot_id": "9ca68cc768875b4e4487abcdc585c1b841822112660094f77691adbe31f19a81", "datapoint": {"question": "Calculate the following: -34*y**2*(50*y**3 - 58)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1700*y**5 + 1972*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 794, "polynomial_expr": "-34*y**2*(50*y**3 - 58)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -34*y**2*(50*y**3 - 58)\nExpanding the part (50*y**3 - 58) using the distributive property, and we got: -(-1)*1972*y**2 + (-34*y**2)*(50*y**3)\n#Step 2:\nCurrent expression: -(-1)*1972*y**2 + (-34*y**2)*(50*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -58*(-34*y**2) = 1972*y**2\n (50*y**3)*(-34*y**2) = -1700*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1700*y**5 + 1972*y**2\nNo more calculations needed.\n-1700*y**5 + 1972*y**2", "generated_answer": "-1700*y**5 + 1972*y**2", "step_length": 3} {"cot_id": "f1d0ae5852cbb919272cbc5a763986f2284989e87f1903f1e889551cb8e2e742", "datapoint": {"question": "Simplify this expression: (-40*z**3 + 8*z + 9)*(-38*z**3 + 42*z**2 - 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1520*z**6 - 1680*z**5 - 304*z**4 + 1434*z**3 + 378*z**2 - 288*z - 324", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 795, "polynomial_expr": "(-40*z**3 + 8*z + 9)*(-38*z**3 + 42*z**2 - 36)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-40*z**3 + 8*z + 9)*(-38*z**3 + 42*z**2 - 36)\nExpanding the part (-38*z**3 + 42*z**2 - 36) using the distributive property, and we got: (42*z**2)*(-40*z**3 + 8*z + 9) + (-38*z**3)*(-40*z**3 + 8*z + 9) - 36*(-40*z**3 + 8*z + 9)\n#Step 2:\nCurrent expression: (42*z**2)*(-40*z**3 + 8*z + 9) + (-38*z**3)*(-40*z**3 + 8*z + 9) - 36*(-40*z**3 + 8*z + 9)\nSimplifying the partial expression: -36*(-40*z**3 + 8*z + 9)\nExpanding the part (-40*z**3 + 8*z + 9) using the distributive property, and we got: (8*z)*(-36) - 40*z**3*(-36) + 9*(-36)\nReplacing -36*(-40*z**3 + 8*z + 9) with (8*z)*(-36) - 40*z**3*(-36) + 9*(-36) in the overall expression.\n#Step 3:\nCurrent expression: (8*z)*(-36) + (42*z**2)*(-40*z**3 + 8*z + 9) - 40*z**3*(-36) + (-38*z**3)*(-40*z**3 + 8*z + 9) - 324\nSimplifying the partial expression: (-38*z**3)*(-40*z**3 + 8*z + 9)\nExpanding the part (-40*z**3 + 8*z + 9) using the distributive property, and we got: 9*(-38*z**3) + (8*z)*(-38*z**3) + (-40*z**3)*(-38*z**3)\nReplacing (-38*z**3)*(-40*z**3 + 8*z + 9) with 9*(-38*z**3) + (8*z)*(-38*z**3) + (-40*z**3)*(-38*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 9*(-38)*z**3 + (8*z)*(-38*z**3) + (8*z)*(-36) + (42*z**2)*(-40*z**3 + 8*z + 9) + (-40*z**3)*(-38*z**3) - 40*z**3*(-36) - 324\nSimplifying the partial expression: (42*z**2)*(-40*z**3 + 8*z + 9)\nExpanding the part (-40*z**3 + 8*z + 9) using the distributive property, and we got: 9*(42*z**2) + (8*z)*(42*z**2) + (42*z**2)*(-40*z**3)\nReplacing (42*z**2)*(-40*z**3 + 8*z + 9) with 9*(42*z**2) + (8*z)*(42*z**2) + (42*z**2)*(-40*z**3) in the overall expression.\n#Step 5:\nCurrent expression: 9*(-38)*z**3 + 9*42*z**2 + (8*z)*(42*z**2) + (8*z)*(-38*z**3) + (8*z)*(-36) + (42*z**2)*(-40*z**3) + (-40*z**3)*(-38*z**3) - 40*z**3*(-36) - 324\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*z**3)*-36 = 1440*z**3\n (-40*z**3)*(-38*z**3) = 1520*z**6\n (-40*z**3)*(42*z**2) = -1680*z**5\n (8*z)*-36 = -288*z\n (8*z)*(-38*z**3) = -304*z**4\n (8*z)*(42*z**2) = 336*z**3\n 9*-38*z**3 = -342*z**3\n 9*42*z**2 = 378*z**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1520*z**6 - 1680*z**5 - 304*z**4 - 342*z**3 + 336*z**3 + 1440*z**3 + 378*z**2 - 288*z - 324\nCombining like terms, got 1520*z**6 - 1680*z**5 - 304*z**4 + 1434*z**3 + 378*z**2 - 288*z - 324\n#Step 7:\nCurrent expression: 1520*z**6 - 1680*z**5 - 304*z**4 + 1434*z**3 + 378*z**2 - 288*z - 324\nNo more calculations needed.\n1520*z**6 - 1680*z**5 - 304*z**4 + 1434*z**3 + 378*z**2 - 288*z - 324", "generated_answer": "1520*z**6 - 1680*z**5 - 304*z**4 + 1434*z**3 + 378*z**2 - 288*z - 324", "step_length": 7} {"cot_id": "7ff2b500647dc9a4f76ab1fe22e4f12eb7f0b0e691bd9d7fe6746222d4dcd3b4", "datapoint": {"question": "Simplify this expression: (33*z**2 + 46*z)*(-z**3 + z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-33*z**5 - 13*z**4 + 46*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 796, "polynomial_expr": "(33*z**2 + 46*z)*(-z**3 + z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (33*z**2 + 46*z)*(-z**3 + z**2)\nExpanding the part (-z**3 + z**2) using the distributive property, and we got: z**2*(33*z**2 + 46*z) + (-z**3)*(33*z**2 + 46*z)\n#Step 2:\nCurrent expression: z**2*(33*z**2 + 46*z) + (-z**3)*(33*z**2 + 46*z)\nSimplifying the partial expression: z**2*(33*z**2 + 46*z)\nExpanding the part (33*z**2 + 46*z) using the distributive property, and we got: (46*z)*z**2 + z**2*(33*z**2)\nReplacing z**2*(33*z**2 + 46*z) with (46*z)*z**2 + z**2*(33*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (46*z)*z**2 + z**2*(33*z**2) + (-z**3)*(33*z**2 + 46*z)\nSimplifying the partial expression: (-z**3)*(33*z**2 + 46*z)\nExpanding the part (33*z**2 + 46*z) using the distributive property, and we got: (46*z)*(-z**3) + (33*z**2)*(-z**3)\nReplacing (-z**3)*(33*z**2 + 46*z) with (46*z)*(-z**3) + (33*z**2)*(-z**3) in the overall expression.\n#Step 4:\nCurrent expression: (46*z)*z**2 + z**2*(33*z**2) + (46*z)*(-z**3) + (33*z**2)*(-z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (33*z**2)*z**2 = 33*z**4\n (33*z**2)*(-z**3) = -33*z**5\n (46*z)*z**2 = 46*z**3\n (46*z)*(-z**3) = -46*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -33*z**5 - 46*z**4 + 33*z**4 + 46*z**3\nCombining like terms, got -33*z**5 - 13*z**4 + 46*z**3\n#Step 6:\nCurrent expression: -33*z**5 - 13*z**4 + 46*z**3\nNo more calculations needed.\n-33*z**5 - 13*z**4 + 46*z**3", "generated_answer": "-33*z**5 - 13*z**4 + 46*z**3", "step_length": 6} {"cot_id": "b7657d470d403eb701d5504f33a8360283a0c207e3a3d7b65491ce8368f5b7dc", "datapoint": {"question": "Calculate the following: (20*z**2 - 15)*(-49*z**3 + 47*z**2 + 46*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-980*z**5 + 940*z**4 + 1655*z**3 - 705*z**2 - 690*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 797, "polynomial_expr": "(20*z**2 - 15)*(-49*z**3 + 47*z**2 + 46*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (20*z**2 - 15)*(-49*z**3 + 47*z**2 + 46*z)\nExpanding the part (20*z**2 - 15) using the distributive property, and we got: (20*z**2)*(-49*z**3 + 47*z**2 + 46*z) - 15*(-49*z**3 + 47*z**2 + 46*z)\n#Step 2:\nCurrent expression: (20*z**2)*(-49*z**3 + 47*z**2 + 46*z) - 15*(-49*z**3 + 47*z**2 + 46*z)\nSimplifying the partial expression: -15*(-49*z**3 + 47*z**2 + 46*z)\nExpanding the part (-49*z**3 + 47*z**2 + 46*z) using the distributive property, and we got: (46*z)*(-15) + (47*z**2)*(-15) - 49*z**3*(-15)\nReplacing -15*(-49*z**3 + 47*z**2 + 46*z) with (46*z)*(-15) + (47*z**2)*(-15) - 49*z**3*(-15) in the overall expression.\n#Step 3:\nCurrent expression: (46*z)*(-15) + (20*z**2)*(-49*z**3 + 47*z**2 + 46*z) + (47*z**2)*(-15) - 49*z**3*(-15)\nSimplifying the partial expression: (20*z**2)*(-49*z**3 + 47*z**2 + 46*z)\nExpanding the part (-49*z**3 + 47*z**2 + 46*z) using the distributive property, and we got: (46*z)*(20*z**2) + (20*z**2)*(47*z**2) + (20*z**2)*(-49*z**3)\nReplacing (20*z**2)*(-49*z**3 + 47*z**2 + 46*z) with (46*z)*(20*z**2) + (20*z**2)*(47*z**2) + (20*z**2)*(-49*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (46*z)*(20*z**2) + (46*z)*(-15) + (20*z**2)*(47*z**2) + (20*z**2)*(-49*z**3) + (47*z**2)*(-15) - 49*z**3*(-15)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*z**3)*-15 = 735*z**3\n (-49*z**3)*(20*z**2) = -980*z**5\n (46*z)*-15 = -690*z\n (46*z)*(20*z**2) = 920*z**3\n (47*z**2)*-15 = -705*z**2\n (47*z**2)*(20*z**2) = 940*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -980*z**5 + 940*z**4 + 735*z**3 + 920*z**3 - 705*z**2 - 690*z\nCombining like terms, got -980*z**5 + 940*z**4 + 1655*z**3 - 705*z**2 - 690*z\n#Step 6:\nCurrent expression: -980*z**5 + 940*z**4 + 1655*z**3 - 705*z**2 - 690*z\nNo more calculations needed.\n-980*z**5 + 940*z**4 + 1655*z**3 - 705*z**2 - 690*z", "generated_answer": "-980*z**5 + 940*z**4 + 1655*z**3 - 705*z**2 - 690*z", "step_length": 6} {"cot_id": "89c5fd4beb2bff112d7690f1332f15332621bc38aae13b190509f035ccac192f", "datapoint": {"question": "Calculate the following: (-69*x**3 + 15*x)*(-5*x**2 - 50*x + 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "345*x**5 + 3450*x**4 - 2007*x**3 - 750*x**2 + 420*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 798, "polynomial_expr": "(-69*x**3 + 15*x)*(-5*x**2 - 50*x + 28)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-69*x**3 + 15*x)*(-5*x**2 - 50*x + 28)\nExpanding the part (-69*x**3 + 15*x) using the distributive property, and we got: (15*x)*(-5*x**2 - 50*x + 28) + (-69*x**3)*(-5*x**2 - 50*x + 28)\n#Step 2:\nCurrent expression: (15*x)*(-5*x**2 - 50*x + 28) + (-69*x**3)*(-5*x**2 - 50*x + 28)\nSimplifying the partial expression: (-69*x**3)*(-5*x**2 - 50*x + 28)\nExpanding the part (-5*x**2 - 50*x + 28) using the distributive property, and we got: (-50*x)*(-69*x**3) + 28*(-69*x**3) + (-5*x**2)*(-69*x**3)\nReplacing (-69*x**3)*(-5*x**2 - 50*x + 28) with (-50*x)*(-69*x**3) + 28*(-69*x**3) + (-5*x**2)*(-69*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-50*x)*(-69*x**3) + 28*(-69)*x**3 + (15*x)*(-5*x**2 - 50*x + 28) + (-5*x**2)*(-69*x**3)\nSimplifying the partial expression: (15*x)*(-5*x**2 - 50*x + 28)\nExpanding the part (-5*x**2 - 50*x + 28) using the distributive property, and we got: (-50*x)*(15*x) + 28*(15*x) + (15*x)*(-5*x**2)\nReplacing (15*x)*(-5*x**2 - 50*x + 28) with (-50*x)*(15*x) + 28*(15*x) + (15*x)*(-5*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-50*x)*(15*x) + (-50*x)*(-69*x**3) + 28*(-69)*x**3 + 28*15*x + (15*x)*(-5*x**2) + (-5*x**2)*(-69*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-50*x)*(-69*x**3) = 3450*x**4\n (-50*x)*(15*x) = -750*x**2\n (-5*x**2)*(-69*x**3) = 345*x**5\n (-5*x**2)*(15*x) = -75*x**3\n 28*-69*x**3 = -1932*x**3\n 28*15*x = 420*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 345*x**5 + 3450*x**4 - 1932*x**3 - 75*x**3 - 750*x**2 + 420*x\nCombining like terms, got 345*x**5 + 3450*x**4 - 2007*x**3 - 750*x**2 + 420*x\n#Step 6:\nCurrent expression: 345*x**5 + 3450*x**4 - 2007*x**3 - 750*x**2 + 420*x\nNo more calculations needed.\n345*x**5 + 3450*x**4 - 2007*x**3 - 750*x**2 + 420*x", "generated_answer": "345*x**5 + 3450*x**4 - 2007*x**3 - 750*x**2 + 420*x", "step_length": 6} {"cot_id": "9c48860c8e98bfd7e19f8c0201bbc3872b225ea71ca8fae4eda367aa45151fbc", "datapoint": {"question": "Simplify this expression: (37 - 25*z**2)*(43*z**3 + 58*z + 27)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1075*z**5 + 141*z**3 - 675*z**2 + 2146*z + 999", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 799, "polynomial_expr": "(37 - 25*z**2)*(43*z**3 + 58*z + 27)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (37 - 25*z**2)*(43*z**3 + 58*z + 27)\nExpanding the part (37 - 25*z**2) using the distributive property, and we got: (-25*z**2)*(43*z**3 + 58*z + 27) + 37*(43*z**3 + 58*z + 27)\n#Step 2:\nCurrent expression: (-25*z**2)*(43*z**3 + 58*z + 27) + 37*(43*z**3 + 58*z + 27)\nSimplifying the partial expression: 37*(43*z**3 + 58*z + 27)\nExpanding the part (43*z**3 + 58*z + 27) using the distributive property, and we got: (58*z)*37 + (43*z**3)*37 + 27*37\nReplacing 37*(43*z**3 + 58*z + 27) with (58*z)*37 + (43*z**3)*37 + 27*37 in the overall expression.\n#Step 3:\nCurrent expression: (58*z)*37 + (-25*z**2)*(43*z**3 + 58*z + 27) + (43*z**3)*37 + 999\nSimplifying the partial expression: (-25*z**2)*(43*z**3 + 58*z + 27)\nExpanding the part (43*z**3 + 58*z + 27) using the distributive property, and we got: 27*(-25*z**2) + (58*z)*(-25*z**2) + (-25*z**2)*(43*z**3)\nReplacing (-25*z**2)*(43*z**3 + 58*z + 27) with 27*(-25*z**2) + (58*z)*(-25*z**2) + (-25*z**2)*(43*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 27*(-25)*z**2 + (58*z)*(-25*z**2) + (58*z)*37 + (-25*z**2)*(43*z**3) + (43*z**3)*37 + 999\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (43*z**3)*37 = 1591*z**3\n (43*z**3)*(-25*z**2) = -1075*z**5\n (58*z)*37 = 2146*z\n (58*z)*(-25*z**2) = -1450*z**3\n 27*-25*z**2 = -675*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1075*z**5 - 1450*z**3 + 1591*z**3 - 675*z**2 + 2146*z + 999\nCombining like terms, got -1075*z**5 + 141*z**3 - 675*z**2 + 2146*z + 999\n#Step 6:\nCurrent expression: -1075*z**5 + 141*z**3 - 675*z**2 + 2146*z + 999\nNo more calculations needed.\n-1075*z**5 + 141*z**3 - 675*z**2 + 2146*z + 999", "generated_answer": "-1075*z**5 + 141*z**3 - 675*z**2 + 2146*z + 999", "step_length": 6} {"cot_id": "0a22f47c7de03ab9e42c0e1e7f2f0e583e22f7c520dbb6474388042af1a359e3", "datapoint": {"question": "Calculate the following: -77*x*(7*x + 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-539*x**2 - 3388*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 800, "polynomial_expr": "-77*x*(7*x + 44)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -77*x*(7*x + 44)\nExpanding the part (7*x + 44) using the distributive property, and we got: (-77*x)*(7*x) + 44*(-77*x)\n#Step 2:\nCurrent expression: (-77*x)*(7*x) + 44*(-77*x)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 44*(-77*x) = -3388*x\n (7*x)*(-77*x) = -539*x**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -539*x**2 - 3388*x\nNo more calculations needed.\n-539*x**2 - 3388*x", "generated_answer": "-539*x**2 - 3388*x", "step_length": 3} {"cot_id": "4e7474761243d9feadb2c7be5efce9da2715e9fdbf001e290aac599dad6ddd30", "datapoint": {"question": "Calculate the following: (16*z**3 - 28*z**2)*(49*z**2 - 54*z - 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "784*z**5 - 2236*z**4 + 1352*z**3 + 280*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 801, "polynomial_expr": "(16*z**3 - 28*z**2)*(49*z**2 - 54*z - 10)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (16*z**3 - 28*z**2)*(49*z**2 - 54*z - 10)\nExpanding the part (16*z**3 - 28*z**2) using the distributive property, and we got: (-28*z**2)*(49*z**2 - 54*z - 10) + (16*z**3)*(49*z**2 - 54*z - 10)\n#Step 2:\nCurrent expression: (-28*z**2)*(49*z**2 - 54*z - 10) + (16*z**3)*(49*z**2 - 54*z - 10)\nSimplifying the partial expression: (-28*z**2)*(49*z**2 - 54*z - 10)\nExpanding the part (49*z**2 - 54*z - 10) using the distributive property, and we got: (-54*z)*(-28*z**2) - (-1)*280*z**2 + (-28*z**2)*(49*z**2)\nReplacing (-28*z**2)*(49*z**2 - 54*z - 10) with (-54*z)*(-28*z**2) - (-1)*280*z**2 + (-28*z**2)*(49*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-54*z)*(-28*z**2) - 10*(-28)*z**2 + (-28*z**2)*(49*z**2) + (16*z**3)*(49*z**2 - 54*z - 10)\nSimplifying the partial expression: (16*z**3)*(49*z**2 - 54*z - 10)\nExpanding the part (49*z**2 - 54*z - 10) using the distributive property, and we got: (-54*z)*(16*z**3) - 160*z**3 + (49*z**2)*(16*z**3)\nReplacing (16*z**3)*(49*z**2 - 54*z - 10) with (-54*z)*(16*z**3) - 160*z**3 + (49*z**2)*(16*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-54*z)*(-28*z**2) + (-54*z)*(16*z**3) - 10*16*z**3 - 10*(-28)*z**2 + (-28*z**2)*(49*z**2) + (49*z**2)*(16*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-54*z)*(-28*z**2) = 1512*z**3\n (-54*z)*(16*z**3) = -864*z**4\n (49*z**2)*(-28*z**2) = -1372*z**4\n (49*z**2)*(16*z**3) = 784*z**5\n -10*-28*z**2 = 280*z**2\n -10*16*z**3 = -160*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 784*z**5 - 1372*z**4 - 864*z**4 - 160*z**3 + 1512*z**3 + 280*z**2\nCombining like terms, got 784*z**5 - 2236*z**4 + 1352*z**3 + 280*z**2\n#Step 6:\nCurrent expression: 784*z**5 - 2236*z**4 + 1352*z**3 + 280*z**2\nNo more calculations needed.\n784*z**5 - 2236*z**4 + 1352*z**3 + 280*z**2", "generated_answer": "784*z**5 - 2236*z**4 + 1352*z**3 + 280*z**2", "step_length": 6} {"cot_id": "4c6c06934c3796f99edb30c64d817046b9f930458dec5ba9c7c73dc69dd2c734", "datapoint": {"question": "Calculate the following: 26*z*(10*z**3 - 41*z**2 - 51*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "260*z**4 - 1066*z**3 - 1326*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 802, "polynomial_expr": "26*z*(10*z**3 - 41*z**2 - 51*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 26*z*(10*z**3 - 41*z**2 - 51*z)\nExpanding the part (10*z**3 - 41*z**2 - 51*z) using the distributive property, and we got: (-51*z)*(26*z) + (26*z)*(-41*z**2) + (26*z)*(10*z**3)\n#Step 2:\nCurrent expression: (-51*z)*(26*z) + (26*z)*(-41*z**2) + (26*z)*(10*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-51*z)*(26*z) = -1326*z**2\n (-41*z**2)*(26*z) = -1066*z**3\n (10*z**3)*(26*z) = 260*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 260*z**4 - 1066*z**3 - 1326*z**2\nNo more calculations needed.\n260*z**4 - 1066*z**3 - 1326*z**2", "generated_answer": "260*z**4 - 1066*z**3 - 1326*z**2", "step_length": 3} {"cot_id": "b5808fd88ca49520251a7db28eae90db4c5d8cc9b2cccca14c09ce9fe9049eee", "datapoint": {"question": "Calculate the following: (38 - 44*x**2)*(-5*x**3 - 26*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "220*x**5 + 1144*x**4 - 190*x**3 - 988*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 803, "polynomial_expr": "(38 - 44*x**2)*(-5*x**3 - 26*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (38 - 44*x**2)*(-5*x**3 - 26*x**2)\nExpanding the part (38 - 44*x**2) using the distributive property, and we got: (-44*x**2)*(-5*x**3 - 26*x**2) + 38*(-5*x**3 - 26*x**2)\n#Step 2:\nCurrent expression: (-44*x**2)*(-5*x**3 - 26*x**2) + 38*(-5*x**3 - 26*x**2)\nSimplifying the partial expression: 38*(-5*x**3 - 26*x**2)\nExpanding the part (-5*x**3 - 26*x**2) using the distributive property, and we got: -26*x**2*38 - 5*x**3*38\nReplacing 38*(-5*x**3 - 26*x**2) with -26*x**2*38 - 5*x**3*38 in the overall expression.\n#Step 3:\nCurrent expression: (-44*x**2)*(-5*x**3 - 26*x**2) - 26*x**2*38 - 5*x**3*38\nSimplifying the partial expression: (-44*x**2)*(-5*x**3 - 26*x**2)\nExpanding the part (-5*x**3 - 26*x**2) using the distributive property, and we got: (-44*x**2)*(-26*x**2) + (-44*x**2)*(-5*x**3)\nReplacing (-44*x**2)*(-5*x**3 - 26*x**2) with (-44*x**2)*(-26*x**2) + (-44*x**2)*(-5*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-44*x**2)*(-26*x**2) + (-44*x**2)*(-5*x**3) - 26*x**2*38 - 5*x**3*38\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-26*x**2)*38 = -988*x**2\n (-26*x**2)*(-44*x**2) = 1144*x**4\n (-5*x**3)*38 = -190*x**3\n (-5*x**3)*(-44*x**2) = 220*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 220*x**5 + 1144*x**4 - 190*x**3 - 988*x**2\nNo more calculations needed.\n220*x**5 + 1144*x**4 - 190*x**3 - 988*x**2", "generated_answer": "220*x**5 + 1144*x**4 - 190*x**3 - 988*x**2", "step_length": 5} {"cot_id": "7bf77c858a1c93f7dc07d27ced453be41942f8fc27304bd14bc9eed542d4c411", "datapoint": {"question": "Calculate the following: (48*x - 1)*(-24*x**2 + 18*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1152*x**3 + 888*x**2 - 18*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 804, "polynomial_expr": "(48*x - 1)*(-24*x**2 + 18*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (48*x - 1)*(-24*x**2 + 18*x)\nExpanding the part (48*x - 1) using the distributive property, and we got: (48*x)*(-24*x**2 + 18*x) - (-24*x**2 + 18*x)\n#Step 2:\nCurrent expression: (48*x)*(-24*x**2 + 18*x) - (-24*x**2 + 18*x)\nSimplifying the partial expression: -(-24*x**2 + 18*x)\nExpanding the part (-24*x**2 + 18*x) using the distributive property, and we got: (18*x)*(-1) - 24*x**2*(-1)\nReplacing -(-24*x**2 + 18*x) with (18*x)*(-1) - 24*x**2*(-1) in the overall expression.\n#Step 3:\nCurrent expression: (18*x)*(-1) + (48*x)*(-24*x**2 + 18*x) - 24*x**2*(-1)\nSimplifying the partial expression: (48*x)*(-24*x**2 + 18*x)\nExpanding the part (-24*x**2 + 18*x) using the distributive property, and we got: (18*x)*(48*x) + (48*x)*(-24*x**2)\nReplacing (48*x)*(-24*x**2 + 18*x) with (18*x)*(48*x) + (48*x)*(-24*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (18*x)*(48*x) + (18*x)*(-1) + (48*x)*(-24*x**2) - 24*x**2*(-1)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-24*x**2)*-1 = 24*x**2\n (-24*x**2)*(48*x) = -1152*x**3\n (18*x)*-1 = -18*x\n (18*x)*(48*x) = 864*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1152*x**3 + 24*x**2 + 864*x**2 - 18*x\nCombining like terms, got -1152*x**3 + 888*x**2 - 18*x\n#Step 6:\nCurrent expression: -1152*x**3 + 888*x**2 - 18*x\nNo more calculations needed.\n-1152*x**3 + 888*x**2 - 18*x", "generated_answer": "-1152*x**3 + 888*x**2 - 18*x", "step_length": 6} {"cot_id": "2baaaefd952e77730e199a014ca7095317dd47193a0682c46185a4fa978425c7", "datapoint": {"question": "Calculate the following: -29*y*(46*y**3 - 14*y**2 - 42*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1334*y**4 + 406*y**3 + 1218*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 805, "polynomial_expr": "-29*y*(46*y**3 - 14*y**2 - 42*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -29*y*(46*y**3 - 14*y**2 - 42*y)\nExpanding the part (46*y**3 - 14*y**2 - 42*y) using the distributive property, and we got: (-42*y)*(-29*y) + (-29*y)*(-14*y**2) + (-29*y)*(46*y**3)\n#Step 2:\nCurrent expression: (-42*y)*(-29*y) + (-29*y)*(-14*y**2) + (-29*y)*(46*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*y)*(-29*y) = 1218*y**2\n (-14*y**2)*(-29*y) = 406*y**3\n (46*y**3)*(-29*y) = -1334*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1334*y**4 + 406*y**3 + 1218*y**2\nNo more calculations needed.\n-1334*y**4 + 406*y**3 + 1218*y**2", "generated_answer": "-1334*y**4 + 406*y**3 + 1218*y**2", "step_length": 3} {"cot_id": "8bc204249a55fc859f5fd61fed487ebee034d5ccc694342f02aaac6cfa70bba0", "datapoint": {"question": "Calculate the following: 4*y*(48*y**3 + 11*y - 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "192*y**4 + 44*y**2 - 124*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 806, "polynomial_expr": "4*y*(48*y**3 + 11*y - 31)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 4*y*(48*y**3 + 11*y - 31)\nExpanding the part (48*y**3 + 11*y - 31) using the distributive property, and we got: -124*y + (4*y)*(11*y) + (4*y)*(48*y**3)\n#Step 2:\nCurrent expression: -124*y + (4*y)*(11*y) + (4*y)*(48*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -31*(4*y) = -124*y\n (11*y)*(4*y) = 44*y**2\n (48*y**3)*(4*y) = 192*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 192*y**4 + 44*y**2 - 124*y\nNo more calculations needed.\n192*y**4 + 44*y**2 - 124*y", "generated_answer": "192*y**4 + 44*y**2 - 124*y", "step_length": 3} {"cot_id": "0c5458a3a28a71f5b0cc4956566aea90961e9f80f1f4c21baa7545225b5c14f3", "datapoint": {"question": "Calculate the following: 11*x**2*(-44*x**3 + 9*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-484*x**5 + 99*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 807, "polynomial_expr": "11*x**2*(-44*x**3 + 9*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 11*x**2*(-44*x**3 + 9*x)\nExpanding the part (-44*x**3 + 9*x) using the distributive property, and we got: (9*x)*(11*x**2) + (11*x**2)*(-44*x**3)\n#Step 2:\nCurrent expression: (9*x)*(11*x**2) + (11*x**2)*(-44*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-44*x**3)*(11*x**2) = -484*x**5\n (9*x)*(11*x**2) = 99*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -484*x**5 + 99*x**3\nNo more calculations needed.\n-484*x**5 + 99*x**3", "generated_answer": "-484*x**5 + 99*x**3", "step_length": 3} {"cot_id": "7fc9f3f2a59b3f48dd404ec9b067159ebcec1dd065f0290d13533192d29ff226", "datapoint": {"question": "Calculate the following: (36*y**2 + 17)*(-6*y**3 - 34*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-216*y**5 - 1224*y**4 - 102*y**3 - 578*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 808, "polynomial_expr": "(36*y**2 + 17)*(-6*y**3 - 34*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (36*y**2 + 17)*(-6*y**3 - 34*y**2)\nExpanding the part (36*y**2 + 17) using the distributive property, and we got: (36*y**2)*(-6*y**3 - 34*y**2) + 17*(-6*y**3 - 34*y**2)\n#Step 2:\nCurrent expression: (36*y**2)*(-6*y**3 - 34*y**2) + 17*(-6*y**3 - 34*y**2)\nSimplifying the partial expression: 17*(-6*y**3 - 34*y**2)\nExpanding the part (-6*y**3 - 34*y**2) using the distributive property, and we got: -34*y**2*17 - 6*y**3*17\nReplacing 17*(-6*y**3 - 34*y**2) with -34*y**2*17 - 6*y**3*17 in the overall expression.\n#Step 3:\nCurrent expression: -34*y**2*17 + (36*y**2)*(-6*y**3 - 34*y**2) - 6*y**3*17\nSimplifying the partial expression: (36*y**2)*(-6*y**3 - 34*y**2)\nExpanding the part (-6*y**3 - 34*y**2) using the distributive property, and we got: (-34*y**2)*(36*y**2) + (36*y**2)*(-6*y**3)\nReplacing (36*y**2)*(-6*y**3 - 34*y**2) with (-34*y**2)*(36*y**2) + (36*y**2)*(-6*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-34*y**2)*(36*y**2) - 34*y**2*17 + (36*y**2)*(-6*y**3) - 6*y**3*17\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*y**2)*17 = -578*y**2\n (-34*y**2)*(36*y**2) = -1224*y**4\n (-6*y**3)*17 = -102*y**3\n (-6*y**3)*(36*y**2) = -216*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -216*y**5 - 1224*y**4 - 102*y**3 - 578*y**2\nNo more calculations needed.\n-216*y**5 - 1224*y**4 - 102*y**3 - 578*y**2", "generated_answer": "-216*y**5 - 1224*y**4 - 102*y**3 - 578*y**2", "step_length": 5} {"cot_id": "678cbf3a462a67718d2d5fd03b1a5fdf48e13bcdb446027f4958d15fdb7ba224", "datapoint": {"question": "Calculate the following: 41*z**3*(11*z**3 + 20*z**2 - 30*z - 27)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "451*z**6 + 820*z**5 - 1230*z**4 - 1107*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 809, "polynomial_expr": "41*z**3*(11*z**3 + 20*z**2 - 30*z - 27)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 41*z**3*(11*z**3 + 20*z**2 - 30*z - 27)\nExpanding the part (11*z**3 + 20*z**2 - 30*z - 27) using the distributive property, and we got: (-30*z)*(41*z**3) - 1107*z**3 + (20*z**2)*(41*z**3) + (11*z**3)*(41*z**3)\n#Step 2:\nCurrent expression: (-30*z)*(41*z**3) - 1107*z**3 + (20*z**2)*(41*z**3) + (11*z**3)*(41*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -27*(41*z**3) = -1107*z**3\n (-30*z)*(41*z**3) = -1230*z**4\n (11*z**3)*(41*z**3) = 451*z**6\n (20*z**2)*(41*z**3) = 820*z**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 451*z**6 + 820*z**5 - 1230*z**4 - 1107*z**3\nNo more calculations needed.\n451*z**6 + 820*z**5 - 1230*z**4 - 1107*z**3", "generated_answer": "451*z**6 + 820*z**5 - 1230*z**4 - 1107*z**3", "step_length": 3} {"cot_id": "213f3f97d5bd80d6465fe1d6bb41381ce44b2e018a36a956a37c93fe68667218", "datapoint": {"question": "Simplify this expression: (23*z**3 - 31)*(-49*z**2 + 7*z - 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1127*z**5 + 161*z**4 - 1150*z**3 + 1519*z**2 - 217*z + 1550", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 810, "polynomial_expr": "(23*z**3 - 31)*(-49*z**2 + 7*z - 50)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (23*z**3 - 31)*(-49*z**2 + 7*z - 50)\nExpanding the part (23*z**3 - 31) using the distributive property, and we got: (23*z**3)*(-49*z**2 + 7*z - 50) - 31*(-49*z**2 + 7*z - 50)\n#Step 2:\nCurrent expression: (23*z**3)*(-49*z**2 + 7*z - 50) - 31*(-49*z**2 + 7*z - 50)\nSimplifying the partial expression: -31*(-49*z**2 + 7*z - 50)\nExpanding the part (-49*z**2 + 7*z - 50) using the distributive property, and we got: (7*z)*(-31) - 49*z**2*(-31) - 50*(-31)\nReplacing -31*(-49*z**2 + 7*z - 50) with (7*z)*(-31) - 49*z**2*(-31) - 50*(-31) in the overall expression.\n#Step 3:\nCurrent expression: (7*z)*(-31) - 49*z**2*(-31) + (23*z**3)*(-49*z**2 + 7*z - 50) + 1550\nSimplifying the partial expression: (23*z**3)*(-49*z**2 + 7*z - 50)\nExpanding the part (-49*z**2 + 7*z - 50) using the distributive property, and we got: -1150*z**3 + (7*z)*(23*z**3) + (-49*z**2)*(23*z**3)\nReplacing (23*z**3)*(-49*z**2 + 7*z - 50) with -1150*z**3 + (7*z)*(23*z**3) + (-49*z**2)*(23*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -50*23*z**3 + (7*z)*(23*z**3) + (7*z)*(-31) + (-49*z**2)*(23*z**3) - 49*z**2*(-31) + 1550\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*z**2)*-31 = 1519*z**2\n (-49*z**2)*(23*z**3) = -1127*z**5\n (7*z)*-31 = -217*z\n (7*z)*(23*z**3) = 161*z**4\n -50*23*z**3 = -1150*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1127*z**5 + 161*z**4 - 1150*z**3 + 1519*z**2 - 217*z + 1550\nNo more calculations needed.\n-1127*z**5 + 161*z**4 - 1150*z**3 + 1519*z**2 - 217*z + 1550", "generated_answer": "-1127*z**5 + 161*z**4 - 1150*z**3 + 1519*z**2 - 217*z + 1550", "step_length": 5} {"cot_id": "4d8744958ee13db6cd5f4b9a362a3eb3db6f742d35b22a89fc38dd549cf1a0ce", "datapoint": {"question": "Simplify this expression: (48*y**2 - 48*y + 7)*(46*y**3 + 24*y**2 - 43*y + 8)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2208*y**5 - 1056*y**4 - 2894*y**3 + 2616*y**2 - 685*y + 56", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 811, "polynomial_expr": "(48*y**2 - 48*y + 7)*(46*y**3 + 24*y**2 - 43*y + 8)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (48*y**2 - 48*y + 7)*(46*y**3 + 24*y**2 - 43*y + 8)\nExpanding the part (48*y**2 - 48*y + 7) using the distributive property, and we got: (-48*y)*(46*y**3 + 24*y**2 - 43*y + 8) + (48*y**2)*(46*y**3 + 24*y**2 - 43*y + 8) + 7*(46*y**3 + 24*y**2 - 43*y + 8)\n#Step 2:\nCurrent expression: (-48*y)*(46*y**3 + 24*y**2 - 43*y + 8) + (48*y**2)*(46*y**3 + 24*y**2 - 43*y + 8) + 7*(46*y**3 + 24*y**2 - 43*y + 8)\nSimplifying the partial expression: 7*(46*y**3 + 24*y**2 - 43*y + 8)\nExpanding the part (46*y**3 + 24*y**2 - 43*y + 8) using the distributive property, and we got: -43*y*7 + (24*y**2)*7 + (46*y**3)*7 + 8*7\nReplacing 7*(46*y**3 + 24*y**2 - 43*y + 8) with -43*y*7 + (24*y**2)*7 + (46*y**3)*7 + 8*7 in the overall expression.\n#Step 3:\nCurrent expression: (-48*y)*(46*y**3 + 24*y**2 - 43*y + 8) - 43*y*7 + (24*y**2)*7 + (48*y**2)*(46*y**3 + 24*y**2 - 43*y + 8) + (46*y**3)*7 + 56\nSimplifying the partial expression: (-48*y)*(46*y**3 + 24*y**2 - 43*y + 8)\nExpanding the part (46*y**3 + 24*y**2 - 43*y + 8) using the distributive property, and we got: (-48*y)*(-43*y) + (-48*y)*(24*y**2) + (-48*y)*(46*y**3) + 8*(-48*y)\nReplacing (-48*y)*(46*y**3 + 24*y**2 - 43*y + 8) with (-48*y)*(-43*y) + (-48*y)*(24*y**2) + (-48*y)*(46*y**3) + 8*(-48*y) in the overall expression.\n#Step 4:\nCurrent expression: (-48*y)*(-43*y) + (-48*y)*(24*y**2) + (-48*y)*(46*y**3) - 43*y*7 + 8*(-48)*y + (24*y**2)*7 + (48*y**2)*(46*y**3 + 24*y**2 - 43*y + 8) + (46*y**3)*7 + 56\nSimplifying the partial expression: (48*y**2)*(46*y**3 + 24*y**2 - 43*y + 8)\nExpanding the part (46*y**3 + 24*y**2 - 43*y + 8) using the distributive property, and we got: (-43*y)*(48*y**2) + 8*(48*y**2) + (24*y**2)*(48*y**2) + (48*y**2)*(46*y**3)\nReplacing (48*y**2)*(46*y**3 + 24*y**2 - 43*y + 8) with (-43*y)*(48*y**2) + 8*(48*y**2) + (24*y**2)*(48*y**2) + (48*y**2)*(46*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-48*y)*(-43*y) + (-48*y)*(24*y**2) + (-48*y)*(46*y**3) + (-43*y)*(48*y**2) - 43*y*7 + 8*48*y**2 + 8*(-48)*y + (24*y**2)*(48*y**2) + (24*y**2)*7 + (48*y**2)*(46*y**3) + (46*y**3)*7 + 56\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-43*y)*7 = -301*y\n (-43*y)*(-48*y) = 2064*y**2\n (-43*y)*(48*y**2) = -2064*y**3\n (24*y**2)*7 = 168*y**2\n (24*y**2)*(-48*y) = -1152*y**3\n (24*y**2)*(48*y**2) = 1152*y**4\n (46*y**3)*7 = 322*y**3\n (46*y**3)*(-48*y) = -2208*y**4\n (46*y**3)*(48*y**2) = 2208*y**5\n 8*-48*y = -384*y\n 8*48*y**2 = 384*y**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 2208*y**5 - 2208*y**4 + 1152*y**4 - 2064*y**3 - 1152*y**3 + 322*y**3 + 168*y**2 + 384*y**2 + 2064*y**2 - 384*y - 301*y + 56\nCombining like terms, got 2208*y**5 - 1056*y**4 - 2894*y**3 + 2616*y**2 - 685*y + 56\n#Step 7:\nCurrent expression: 2208*y**5 - 1056*y**4 - 2894*y**3 + 2616*y**2 - 685*y + 56\nNo more calculations needed.\n2208*y**5 - 1056*y**4 - 2894*y**3 + 2616*y**2 - 685*y + 56", "generated_answer": "2208*y**5 - 1056*y**4 - 2894*y**3 + 2616*y**2 - 685*y + 56", "step_length": 7} {"cot_id": "def181e51b56c152ed73c0a238f019bbe38f650bc256637143d2f94738fda68b", "datapoint": {"question": "Calculate the following: (-40*y**3 - 9*y**2)*(38*y**3 + 33*y**2 - 51*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1520*y**6 - 1662*y**5 + 1743*y**4 + 459*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 812, "polynomial_expr": "(-40*y**3 - 9*y**2)*(38*y**3 + 33*y**2 - 51*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-40*y**3 - 9*y**2)*(38*y**3 + 33*y**2 - 51*y)\nExpanding the part (-40*y**3 - 9*y**2) using the distributive property, and we got: (-9*y**2)*(38*y**3 + 33*y**2 - 51*y) + (-40*y**3)*(38*y**3 + 33*y**2 - 51*y)\n#Step 2:\nCurrent expression: (-9*y**2)*(38*y**3 + 33*y**2 - 51*y) + (-40*y**3)*(38*y**3 + 33*y**2 - 51*y)\nSimplifying the partial expression: (-40*y**3)*(38*y**3 + 33*y**2 - 51*y)\nExpanding the part (38*y**3 + 33*y**2 - 51*y) using the distributive property, and we got: (-51*y)*(-40*y**3) + (33*y**2)*(-40*y**3) + (-40*y**3)*(38*y**3)\nReplacing (-40*y**3)*(38*y**3 + 33*y**2 - 51*y) with (-51*y)*(-40*y**3) + (33*y**2)*(-40*y**3) + (-40*y**3)*(38*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-51*y)*(-40*y**3) + (-9*y**2)*(38*y**3 + 33*y**2 - 51*y) + (33*y**2)*(-40*y**3) + (-40*y**3)*(38*y**3)\nSimplifying the partial expression: (-9*y**2)*(38*y**3 + 33*y**2 - 51*y)\nExpanding the part (38*y**3 + 33*y**2 - 51*y) using the distributive property, and we got: (-51*y)*(-9*y**2) + (-9*y**2)*(33*y**2) + (-9*y**2)*(38*y**3)\nReplacing (-9*y**2)*(38*y**3 + 33*y**2 - 51*y) with (-51*y)*(-9*y**2) + (-9*y**2)*(33*y**2) + (-9*y**2)*(38*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-51*y)*(-9*y**2) + (-51*y)*(-40*y**3) + (-9*y**2)*(33*y**2) + (-9*y**2)*(38*y**3) + (33*y**2)*(-40*y**3) + (-40*y**3)*(38*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-51*y)*(-40*y**3) = 2040*y**4\n (-51*y)*(-9*y**2) = 459*y**3\n (33*y**2)*(-40*y**3) = -1320*y**5\n (33*y**2)*(-9*y**2) = -297*y**4\n (38*y**3)*(-40*y**3) = -1520*y**6\n (38*y**3)*(-9*y**2) = -342*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1520*y**6 - 1320*y**5 - 342*y**5 - 297*y**4 + 2040*y**4 + 459*y**3\nCombining like terms, got -1520*y**6 - 1662*y**5 + 1743*y**4 + 459*y**3\n#Step 6:\nCurrent expression: -1520*y**6 - 1662*y**5 + 1743*y**4 + 459*y**3\nNo more calculations needed.\n-1520*y**6 - 1662*y**5 + 1743*y**4 + 459*y**3", "generated_answer": "-1520*y**6 - 1662*y**5 + 1743*y**4 + 459*y**3", "step_length": 6} {"cot_id": "b7a576181849ba595925bc3678151fbbc8bf8517ea743a40dc3573aeafacdfa3", "datapoint": {"question": "Simplify this expression: (29*x**2 + 49)*(37*x**3 - 42*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1073*x**5 + 595*x**3 - 2058*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 813, "polynomial_expr": "(29*x**2 + 49)*(37*x**3 - 42*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29*x**2 + 49)*(37*x**3 - 42*x)\nExpanding the part (29*x**2 + 49) using the distributive property, and we got: (29*x**2)*(37*x**3 - 42*x) + 49*(37*x**3 - 42*x)\n#Step 2:\nCurrent expression: (29*x**2)*(37*x**3 - 42*x) + 49*(37*x**3 - 42*x)\nSimplifying the partial expression: 49*(37*x**3 - 42*x)\nExpanding the part (37*x**3 - 42*x) using the distributive property, and we got: -42*x*49 + (37*x**3)*49\nReplacing 49*(37*x**3 - 42*x) with -42*x*49 + (37*x**3)*49 in the overall expression.\n#Step 3:\nCurrent expression: -42*x*49 + (29*x**2)*(37*x**3 - 42*x) + (37*x**3)*49\nSimplifying the partial expression: (29*x**2)*(37*x**3 - 42*x)\nExpanding the part (37*x**3 - 42*x) using the distributive property, and we got: (-42*x)*(29*x**2) + (29*x**2)*(37*x**3)\nReplacing (29*x**2)*(37*x**3 - 42*x) with (-42*x)*(29*x**2) + (29*x**2)*(37*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-42*x)*(29*x**2) - 42*x*49 + (29*x**2)*(37*x**3) + (37*x**3)*49\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*x)*49 = -2058*x\n (-42*x)*(29*x**2) = -1218*x**3\n (37*x**3)*49 = 1813*x**3\n (37*x**3)*(29*x**2) = 1073*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1073*x**5 - 1218*x**3 + 1813*x**3 - 2058*x\nCombining like terms, got 1073*x**5 + 595*x**3 - 2058*x\n#Step 6:\nCurrent expression: 1073*x**5 + 595*x**3 - 2058*x\nNo more calculations needed.\n1073*x**5 + 595*x**3 - 2058*x", "generated_answer": "1073*x**5 + 595*x**3 - 2058*x", "step_length": 6} {"cot_id": "366b29a6415ec5e281c4afea9975bd81b34940c6a4a994f443a2fcdb6dd333c2", "datapoint": {"question": "Simplify this expression: (6*x**3 - 48*x)*(-32*x**3 + 17*x + 37)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-192*x**6 + 1638*x**4 + 222*x**3 - 816*x**2 - 1776*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 814, "polynomial_expr": "(6*x**3 - 48*x)*(-32*x**3 + 17*x + 37)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6*x**3 - 48*x)*(-32*x**3 + 17*x + 37)\nExpanding the part (6*x**3 - 48*x) using the distributive property, and we got: (-48*x)*(-32*x**3 + 17*x + 37) + (6*x**3)*(-32*x**3 + 17*x + 37)\n#Step 2:\nCurrent expression: (-48*x)*(-32*x**3 + 17*x + 37) + (6*x**3)*(-32*x**3 + 17*x + 37)\nSimplifying the partial expression: (-48*x)*(-32*x**3 + 17*x + 37)\nExpanding the part (-32*x**3 + 17*x + 37) using the distributive property, and we got: (-48*x)*(17*x) + (-48*x)*(-32*x**3) + 37*(-48*x)\nReplacing (-48*x)*(-32*x**3 + 17*x + 37) with (-48*x)*(17*x) + (-48*x)*(-32*x**3) + 37*(-48*x) in the overall expression.\n#Step 3:\nCurrent expression: (-48*x)*(17*x) + (-48*x)*(-32*x**3) + 37*(-48)*x + (6*x**3)*(-32*x**3 + 17*x + 37)\nSimplifying the partial expression: (6*x**3)*(-32*x**3 + 17*x + 37)\nExpanding the part (-32*x**3 + 17*x + 37) using the distributive property, and we got: 37*(6*x**3) + (17*x)*(6*x**3) + (-32*x**3)*(6*x**3)\nReplacing (6*x**3)*(-32*x**3 + 17*x + 37) with 37*(6*x**3) + (17*x)*(6*x**3) + (-32*x**3)*(6*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-48*x)*(17*x) + (-48*x)*(-32*x**3) + 37*6*x**3 + 37*(-48)*x + (17*x)*(6*x**3) + (-32*x**3)*(6*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*x**3)*(-48*x) = 1536*x**4\n (-32*x**3)*(6*x**3) = -192*x**6\n (17*x)*(-48*x) = -816*x**2\n (17*x)*(6*x**3) = 102*x**4\n 37*-48*x = -1776*x\n 37*6*x**3 = 222*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -192*x**6 + 102*x**4 + 1536*x**4 + 222*x**3 - 816*x**2 - 1776*x\nCombining like terms, got -192*x**6 + 1638*x**4 + 222*x**3 - 816*x**2 - 1776*x\n#Step 6:\nCurrent expression: -192*x**6 + 1638*x**4 + 222*x**3 - 816*x**2 - 1776*x\nNo more calculations needed.\n-192*x**6 + 1638*x**4 + 222*x**3 - 816*x**2 - 1776*x", "generated_answer": "-192*x**6 + 1638*x**4 + 222*x**3 - 816*x**2 - 1776*x", "step_length": 6} {"cot_id": "eb5501a878a7c5b18ada1ed6396449a9094547059237edfe0c9555d4fb735254", "datapoint": {"question": "Simplify this expression: (-14*y**2 + 46*y - 68)*(17*y**3 - 11*y**2 + 46*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-238*y**5 + 936*y**4 - 2306*y**3 + 2864*y**2 - 3128*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 815, "polynomial_expr": "(-14*y**2 + 46*y - 68)*(17*y**3 - 11*y**2 + 46*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-14*y**2 + 46*y - 68)*(17*y**3 - 11*y**2 + 46*y)\nExpanding the part (-14*y**2 + 46*y - 68) using the distributive property, and we got: (46*y)*(17*y**3 - 11*y**2 + 46*y) + (-14*y**2)*(17*y**3 - 11*y**2 + 46*y) - 68*(17*y**3 - 11*y**2 + 46*y)\n#Step 2:\nCurrent expression: (46*y)*(17*y**3 - 11*y**2 + 46*y) + (-14*y**2)*(17*y**3 - 11*y**2 + 46*y) - 68*(17*y**3 - 11*y**2 + 46*y)\nSimplifying the partial expression: -68*(17*y**3 - 11*y**2 + 46*y)\nExpanding the part (17*y**3 - 11*y**2 + 46*y) using the distributive property, and we got: (46*y)*(-68) - 11*y**2*(-68) + (17*y**3)*(-68)\nReplacing -68*(17*y**3 - 11*y**2 + 46*y) with (46*y)*(-68) - 11*y**2*(-68) + (17*y**3)*(-68) in the overall expression.\n#Step 3:\nCurrent expression: (46*y)*(17*y**3 - 11*y**2 + 46*y) + (46*y)*(-68) + (-14*y**2)*(17*y**3 - 11*y**2 + 46*y) - 11*y**2*(-68) + (17*y**3)*(-68)\nSimplifying the partial expression: (-14*y**2)*(17*y**3 - 11*y**2 + 46*y)\nExpanding the part (17*y**3 - 11*y**2 + 46*y) using the distributive property, and we got: (46*y)*(-14*y**2) + (-14*y**2)*(-11*y**2) + (-14*y**2)*(17*y**3)\nReplacing (-14*y**2)*(17*y**3 - 11*y**2 + 46*y) with (46*y)*(-14*y**2) + (-14*y**2)*(-11*y**2) + (-14*y**2)*(17*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (46*y)*(-14*y**2) + (46*y)*(17*y**3 - 11*y**2 + 46*y) + (46*y)*(-68) + (-14*y**2)*(-11*y**2) + (-14*y**2)*(17*y**3) - 11*y**2*(-68) + (17*y**3)*(-68)\nSimplifying the partial expression: (46*y)*(17*y**3 - 11*y**2 + 46*y)\nExpanding the part (17*y**3 - 11*y**2 + 46*y) using the distributive property, and we got: (46*y)*(-11*y**2) + (46*y)*(17*y**3) + (46*y)*(46*y)\nReplacing (46*y)*(17*y**3 - 11*y**2 + 46*y) with (46*y)*(-11*y**2) + (46*y)*(17*y**3) + (46*y)*(46*y) in the overall expression.\n#Step 5:\nCurrent expression: (46*y)*(-14*y**2) + (46*y)*(-11*y**2) + (46*y)*(17*y**3) + (46*y)*(-68) + (46*y)*(46*y) + (-14*y**2)*(-11*y**2) + (-14*y**2)*(17*y**3) - 11*y**2*(-68) + (17*y**3)*(-68)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*y**2)*-68 = 748*y**2\n (-11*y**2)*(-14*y**2) = 154*y**4\n (-11*y**2)*(46*y) = -506*y**3\n (17*y**3)*-68 = -1156*y**3\n (17*y**3)*(-14*y**2) = -238*y**5\n (17*y**3)*(46*y) = 782*y**4\n (46*y)*-68 = -3128*y\n (46*y)*(-14*y**2) = -644*y**3\n (46*y)*(46*y) = 2116*y**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -238*y**5 + 154*y**4 + 782*y**4 - 1156*y**3 - 644*y**3 - 506*y**3 + 748*y**2 + 2116*y**2 - 3128*y\nCombining like terms, got -238*y**5 + 936*y**4 - 2306*y**3 + 2864*y**2 - 3128*y\n#Step 7:\nCurrent expression: -238*y**5 + 936*y**4 - 2306*y**3 + 2864*y**2 - 3128*y\nNo more calculations needed.\n-238*y**5 + 936*y**4 - 2306*y**3 + 2864*y**2 - 3128*y", "generated_answer": "-238*y**5 + 936*y**4 - 2306*y**3 + 2864*y**2 - 3128*y", "step_length": 7} {"cot_id": "55c34a303a38c4eb163bdbca068bccef61062e749096db5fd811bb6aa94ccedb", "datapoint": {"question": "Calculate the following: 93*z**2\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "93*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 816, "polynomial_expr": "93*z**2", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 93*z**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 93*z**2\nNo more calculations needed.\n93*z**2", "generated_answer": "93*z**2", "step_length": 2} {"cot_id": "ee338abf894d62d3b57bf068251ba3fc17196bbced2be9dd71ae417868a95789", "datapoint": {"question": "Calculate the following: (14*z - 1)*(-6*z**3 + 9*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-84*z**4 + 132*z**3 - 9*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 817, "polynomial_expr": "(14*z - 1)*(-6*z**3 + 9*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14*z - 1)*(-6*z**3 + 9*z**2)\nExpanding the part (14*z - 1) using the distributive property, and we got: (14*z)*(-6*z**3 + 9*z**2) - (-6*z**3 + 9*z**2)\n#Step 2:\nCurrent expression: (14*z)*(-6*z**3 + 9*z**2) - (-6*z**3 + 9*z**2)\nSimplifying the partial expression: -(-6*z**3 + 9*z**2)\nExpanding the part (-6*z**3 + 9*z**2) using the distributive property, and we got: (9*z**2)*(-1) - 6*z**3*(-1)\nReplacing -(-6*z**3 + 9*z**2) with (9*z**2)*(-1) - 6*z**3*(-1) in the overall expression.\n#Step 3:\nCurrent expression: (14*z)*(-6*z**3 + 9*z**2) + (9*z**2)*(-1) - 6*z**3*(-1)\nSimplifying the partial expression: (14*z)*(-6*z**3 + 9*z**2)\nExpanding the part (-6*z**3 + 9*z**2) using the distributive property, and we got: (14*z)*(9*z**2) + (14*z)*(-6*z**3)\nReplacing (14*z)*(-6*z**3 + 9*z**2) with (14*z)*(9*z**2) + (14*z)*(-6*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (14*z)*(9*z**2) + (14*z)*(-6*z**3) + (9*z**2)*(-1) - 6*z**3*(-1)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-6*z**3)*-1 = 6*z**3\n (-6*z**3)*(14*z) = -84*z**4\n (9*z**2)*-1 = -9*z**2\n (9*z**2)*(14*z) = 126*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -84*z**4 + 6*z**3 + 126*z**3 - 9*z**2\nCombining like terms, got -84*z**4 + 132*z**3 - 9*z**2\n#Step 6:\nCurrent expression: -84*z**4 + 132*z**3 - 9*z**2\nNo more calculations needed.\n-84*z**4 + 132*z**3 - 9*z**2", "generated_answer": "-84*z**4 + 132*z**3 - 9*z**2", "step_length": 6} {"cot_id": "30cb3b72a27bc89a4335cefd9af1478b9360e066ec230b6d9ae2216d59ecb7a0", "datapoint": {"question": "Simplify this expression: (34*x + 25)*(-35*x**3 + 44*x**2 + 6*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1190*x**4 + 621*x**3 + 1304*x**2 + 150*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 818, "polynomial_expr": "(34*x + 25)*(-35*x**3 + 44*x**2 + 6*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (34*x + 25)*(-35*x**3 + 44*x**2 + 6*x)\nExpanding the part (34*x + 25) using the distributive property, and we got: (34*x)*(-35*x**3 + 44*x**2 + 6*x) + 25*(-35*x**3 + 44*x**2 + 6*x)\n#Step 2:\nCurrent expression: (34*x)*(-35*x**3 + 44*x**2 + 6*x) + 25*(-35*x**3 + 44*x**2 + 6*x)\nSimplifying the partial expression: 25*(-35*x**3 + 44*x**2 + 6*x)\nExpanding the part (-35*x**3 + 44*x**2 + 6*x) using the distributive property, and we got: (6*x)*25 + (44*x**2)*25 - 35*x**3*25\nReplacing 25*(-35*x**3 + 44*x**2 + 6*x) with (6*x)*25 + (44*x**2)*25 - 35*x**3*25 in the overall expression.\n#Step 3:\nCurrent expression: (6*x)*25 + (34*x)*(-35*x**3 + 44*x**2 + 6*x) + (44*x**2)*25 - 35*x**3*25\nSimplifying the partial expression: (34*x)*(-35*x**3 + 44*x**2 + 6*x)\nExpanding the part (-35*x**3 + 44*x**2 + 6*x) using the distributive property, and we got: (6*x)*(34*x) + (34*x)*(44*x**2) + (34*x)*(-35*x**3)\nReplacing (34*x)*(-35*x**3 + 44*x**2 + 6*x) with (6*x)*(34*x) + (34*x)*(44*x**2) + (34*x)*(-35*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (6*x)*(34*x) + (6*x)*25 + (34*x)*(44*x**2) + (34*x)*(-35*x**3) + (44*x**2)*25 - 35*x**3*25\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*x**3)*25 = -875*x**3\n (-35*x**3)*(34*x) = -1190*x**4\n (6*x)*25 = 150*x\n (6*x)*(34*x) = 204*x**2\n (44*x**2)*25 = 1100*x**2\n (44*x**2)*(34*x) = 1496*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1190*x**4 - 875*x**3 + 1496*x**3 + 204*x**2 + 1100*x**2 + 150*x\nCombining like terms, got -1190*x**4 + 621*x**3 + 1304*x**2 + 150*x\n#Step 6:\nCurrent expression: -1190*x**4 + 621*x**3 + 1304*x**2 + 150*x\nNo more calculations needed.\n-1190*x**4 + 621*x**3 + 1304*x**2 + 150*x", "generated_answer": "-1190*x**4 + 621*x**3 + 1304*x**2 + 150*x", "step_length": 6} {"cot_id": "ffb05a44b18a26c9110b400ea56c362f61804d96469949e5d31b01fdb16a9de0", "datapoint": {"question": "Simplify this expression: -29*y**2*(-43*y**3 + 50*y**2 - 19)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1247*y**5 - 1450*y**4 + 551*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 819, "polynomial_expr": "-29*y**2*(-43*y**3 + 50*y**2 - 19)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -29*y**2*(-43*y**3 + 50*y**2 - 19)\nExpanding the part (-43*y**3 + 50*y**2 - 19) using the distributive property, and we got: -(-1)*551*y**2 + (-29*y**2)*(50*y**2) + (-29*y**2)*(-43*y**3)\n#Step 2:\nCurrent expression: -(-1)*551*y**2 + (-29*y**2)*(50*y**2) + (-29*y**2)*(-43*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -19*(-29*y**2) = 551*y**2\n (-43*y**3)*(-29*y**2) = 1247*y**5\n (50*y**2)*(-29*y**2) = -1450*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1247*y**5 - 1450*y**4 + 551*y**2\nNo more calculations needed.\n1247*y**5 - 1450*y**4 + 551*y**2", "generated_answer": "1247*y**5 - 1450*y**4 + 551*y**2", "step_length": 3} {"cot_id": "1b07a81f6afc51bd58e8855a7bc411b5dab026951a972a5c9c29d9475f3d41e3", "datapoint": {"question": "Simplify this expression: (24*z**3 + 14*z**2)*(-22*z**2 - 9*z - 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-528*z**5 - 524*z**4 - 462*z**3 - 196*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 820, "polynomial_expr": "(24*z**3 + 14*z**2)*(-22*z**2 - 9*z - 14)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (24*z**3 + 14*z**2)*(-22*z**2 - 9*z - 14)\nExpanding the part (24*z**3 + 14*z**2) using the distributive property, and we got: (14*z**2)*(-22*z**2 - 9*z - 14) + (24*z**3)*(-22*z**2 - 9*z - 14)\n#Step 2:\nCurrent expression: (14*z**2)*(-22*z**2 - 9*z - 14) + (24*z**3)*(-22*z**2 - 9*z - 14)\nSimplifying the partial expression: (14*z**2)*(-22*z**2 - 9*z - 14)\nExpanding the part (-22*z**2 - 9*z - 14) using the distributive property, and we got: (-9*z)*(14*z**2) - 196*z**2 + (-22*z**2)*(14*z**2)\nReplacing (14*z**2)*(-22*z**2 - 9*z - 14) with (-9*z)*(14*z**2) - 196*z**2 + (-22*z**2)*(14*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-9*z)*(14*z**2) - 14*14*z**2 + (-22*z**2)*(14*z**2) + (24*z**3)*(-22*z**2 - 9*z - 14)\nSimplifying the partial expression: (24*z**3)*(-22*z**2 - 9*z - 14)\nExpanding the part (-22*z**2 - 9*z - 14) using the distributive property, and we got: (-9*z)*(24*z**3) - 336*z**3 + (-22*z**2)*(24*z**3)\nReplacing (24*z**3)*(-22*z**2 - 9*z - 14) with (-9*z)*(24*z**3) - 336*z**3 + (-22*z**2)*(24*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-9*z)*(14*z**2) + (-9*z)*(24*z**3) - 14*24*z**3 - 14*14*z**2 + (-22*z**2)*(14*z**2) + (-22*z**2)*(24*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*z**2)*(14*z**2) = -308*z**4\n (-22*z**2)*(24*z**3) = -528*z**5\n (-9*z)*(14*z**2) = -126*z**3\n (-9*z)*(24*z**3) = -216*z**4\n -14*14*z**2 = -196*z**2\n -14*24*z**3 = -336*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -528*z**5 - 308*z**4 - 216*z**4 - 336*z**3 - 126*z**3 - 196*z**2\nCombining like terms, got -528*z**5 - 524*z**4 - 462*z**3 - 196*z**2\n#Step 6:\nCurrent expression: -528*z**5 - 524*z**4 - 462*z**3 - 196*z**2\nNo more calculations needed.\n-528*z**5 - 524*z**4 - 462*z**3 - 196*z**2", "generated_answer": "-528*z**5 - 524*z**4 - 462*z**3 - 196*z**2", "step_length": 6} {"cot_id": "706a0deb7182ab679ed448488a24b6333ba76a54f9c998e6971129a976800e8d", "datapoint": {"question": "Simplify this expression: (-19*z**2 + 25*z - 21)*(2*z**3 + 47*z**2 + 42*z + 15)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-38*z**5 - 843*z**4 + 335*z**3 - 222*z**2 - 507*z - 315", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 821, "polynomial_expr": "(-19*z**2 + 25*z - 21)*(2*z**3 + 47*z**2 + 42*z + 15)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-19*z**2 + 25*z - 21)*(2*z**3 + 47*z**2 + 42*z + 15)\nExpanding the part (-19*z**2 + 25*z - 21) using the distributive property, and we got: (25*z)*(2*z**3 + 47*z**2 + 42*z + 15) + (-19*z**2)*(2*z**3 + 47*z**2 + 42*z + 15) - 21*(2*z**3 + 47*z**2 + 42*z + 15)\n#Step 2:\nCurrent expression: (25*z)*(2*z**3 + 47*z**2 + 42*z + 15) + (-19*z**2)*(2*z**3 + 47*z**2 + 42*z + 15) - 21*(2*z**3 + 47*z**2 + 42*z + 15)\nSimplifying the partial expression: -21*(2*z**3 + 47*z**2 + 42*z + 15)\nExpanding the part (2*z**3 + 47*z**2 + 42*z + 15) using the distributive property, and we got: (42*z)*(-21) + (47*z**2)*(-21) + (2*z**3)*(-21) + 15*(-21)\nReplacing -21*(2*z**3 + 47*z**2 + 42*z + 15) with (42*z)*(-21) + (47*z**2)*(-21) + (2*z**3)*(-21) + 15*(-21) in the overall expression.\n#Step 3:\nCurrent expression: (25*z)*(2*z**3 + 47*z**2 + 42*z + 15) + (42*z)*(-21) + (-19*z**2)*(2*z**3 + 47*z**2 + 42*z + 15) + (47*z**2)*(-21) + (2*z**3)*(-21) - 315\nSimplifying the partial expression: (-19*z**2)*(2*z**3 + 47*z**2 + 42*z + 15)\nExpanding the part (2*z**3 + 47*z**2 + 42*z + 15) using the distributive property, and we got: 15*(-19*z**2) + (42*z)*(-19*z**2) + (-19*z**2)*(47*z**2) + (-19*z**2)*(2*z**3)\nReplacing (-19*z**2)*(2*z**3 + 47*z**2 + 42*z + 15) with 15*(-19*z**2) + (42*z)*(-19*z**2) + (-19*z**2)*(47*z**2) + (-19*z**2)*(2*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 15*(-19)*z**2 + (25*z)*(2*z**3 + 47*z**2 + 42*z + 15) + (42*z)*(-19*z**2) + (42*z)*(-21) + (-19*z**2)*(47*z**2) + (-19*z**2)*(2*z**3) + (47*z**2)*(-21) + (2*z**3)*(-21) - 315\nSimplifying the partial expression: (25*z)*(2*z**3 + 47*z**2 + 42*z + 15)\nExpanding the part (2*z**3 + 47*z**2 + 42*z + 15) using the distributive property, and we got: 15*(25*z) + (25*z)*(42*z) + (25*z)*(47*z**2) + (25*z)*(2*z**3)\nReplacing (25*z)*(2*z**3 + 47*z**2 + 42*z + 15) with 15*(25*z) + (25*z)*(42*z) + (25*z)*(47*z**2) + (25*z)*(2*z**3) in the overall expression.\n#Step 5:\nCurrent expression: 15*(-19)*z**2 + 15*25*z + (25*z)*(42*z) + (25*z)*(47*z**2) + (25*z)*(2*z**3) + (42*z)*(-19*z**2) + (42*z)*(-21) + (-19*z**2)*(47*z**2) + (-19*z**2)*(2*z**3) + (47*z**2)*(-21) + (2*z**3)*(-21) - 315\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (2*z**3)*-21 = -42*z**3\n (2*z**3)*(-19*z**2) = -38*z**5\n (2*z**3)*(25*z) = 50*z**4\n (42*z)*-21 = -882*z\n (42*z)*(-19*z**2) = -798*z**3\n (42*z)*(25*z) = 1050*z**2\n (47*z**2)*-21 = -987*z**2\n (47*z**2)*(-19*z**2) = -893*z**4\n (47*z**2)*(25*z) = 1175*z**3\n 15*-19*z**2 = -285*z**2\n 15*25*z = 375*z\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -38*z**5 - 893*z**4 + 50*z**4 - 798*z**3 - 42*z**3 + 1175*z**3 - 987*z**2 - 285*z**2 + 1050*z**2 - 882*z + 375*z - 315\nCombining like terms, got -38*z**5 - 843*z**4 + 335*z**3 - 222*z**2 - 507*z - 315\n#Step 7:\nCurrent expression: -38*z**5 - 843*z**4 + 335*z**3 - 222*z**2 - 507*z - 315\nNo more calculations needed.\n-38*z**5 - 843*z**4 + 335*z**3 - 222*z**2 - 507*z - 315", "generated_answer": "-38*z**5 - 843*z**4 + 335*z**3 - 222*z**2 - 507*z - 315", "step_length": 7} {"cot_id": "a128ddcfa2189c1c4d1be181d484932cb9807dcb800ae75193c9c95fbdc053f6", "datapoint": {"question": "Simplify this expression: (-39*y - 18)*(-41*y**3 - 23)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1599*y**4 + 738*y**3 + 897*y + 414", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 822, "polynomial_expr": "(-39*y - 18)*(-41*y**3 - 23)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-39*y - 18)*(-41*y**3 - 23)\nExpanding the part (-41*y**3 - 23) using the distributive property, and we got: (-41*y**3)*(-39*y - 18) - 23*(-39*y - 18)\n#Step 2:\nCurrent expression: (-41*y**3)*(-39*y - 18) - 23*(-39*y - 18)\nSimplifying the partial expression: -23*(-39*y - 18)\nExpanding the part (-39*y - 18) using the distributive property, and we got: -39*y*(-23) - 18*(-23)\nReplacing -23*(-39*y - 18) with -39*y*(-23) - 18*(-23) in the overall expression.\n#Step 3:\nCurrent expression: -39*y*(-23) + (-41*y**3)*(-39*y - 18) + 414\nSimplifying the partial expression: (-41*y**3)*(-39*y - 18)\nExpanding the part (-39*y - 18) using the distributive property, and we got: (-39*y)*(-41*y**3) - (-1)*738*y**3\nReplacing (-41*y**3)*(-39*y - 18) with (-39*y)*(-41*y**3) - (-1)*738*y**3 in the overall expression.\n#Step 4:\nCurrent expression: (-39*y)*(-41*y**3) - 39*y*(-23) - 18*(-41)*y**3 + 414\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*y)*-23 = 897*y\n (-39*y)*(-41*y**3) = 1599*y**4\n -18*-41*y**3 = 738*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1599*y**4 + 738*y**3 + 897*y + 414\nNo more calculations needed.\n1599*y**4 + 738*y**3 + 897*y + 414", "generated_answer": "1599*y**4 + 738*y**3 + 897*y + 414", "step_length": 5} {"cot_id": "3c66b7ccfa6d3254146689db41de682b22deabaa02621a4bbe27e3bad183f4d8", "datapoint": {"question": "Simplify this expression: (27*y**2 + 22*y - 38)*(-42*y**3 + 48*y**2 - 42*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1134*y**5 + 372*y**4 + 1518*y**3 - 2748*y**2 + 1596*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 823, "polynomial_expr": "(27*y**2 + 22*y - 38)*(-42*y**3 + 48*y**2 - 42*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*y**2 + 22*y - 38)*(-42*y**3 + 48*y**2 - 42*y)\nExpanding the part (27*y**2 + 22*y - 38) using the distributive property, and we got: (22*y)*(-42*y**3 + 48*y**2 - 42*y) + (27*y**2)*(-42*y**3 + 48*y**2 - 42*y) - 38*(-42*y**3 + 48*y**2 - 42*y)\n#Step 2:\nCurrent expression: (22*y)*(-42*y**3 + 48*y**2 - 42*y) + (27*y**2)*(-42*y**3 + 48*y**2 - 42*y) - 38*(-42*y**3 + 48*y**2 - 42*y)\nSimplifying the partial expression: -38*(-42*y**3 + 48*y**2 - 42*y)\nExpanding the part (-42*y**3 + 48*y**2 - 42*y) using the distributive property, and we got: -42*y*(-38) + (48*y**2)*(-38) - 42*y**3*(-38)\nReplacing -38*(-42*y**3 + 48*y**2 - 42*y) with -42*y*(-38) + (48*y**2)*(-38) - 42*y**3*(-38) in the overall expression.\n#Step 3:\nCurrent expression: -42*y*(-38) + (22*y)*(-42*y**3 + 48*y**2 - 42*y) + (27*y**2)*(-42*y**3 + 48*y**2 - 42*y) + (48*y**2)*(-38) - 42*y**3*(-38)\nSimplifying the partial expression: (22*y)*(-42*y**3 + 48*y**2 - 42*y)\nExpanding the part (-42*y**3 + 48*y**2 - 42*y) using the distributive property, and we got: (-42*y)*(22*y) + (22*y)*(48*y**2) + (22*y)*(-42*y**3)\nReplacing (22*y)*(-42*y**3 + 48*y**2 - 42*y) with (-42*y)*(22*y) + (22*y)*(48*y**2) + (22*y)*(-42*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-42*y)*(22*y) - 42*y*(-38) + (22*y)*(48*y**2) + (22*y)*(-42*y**3) + (27*y**2)*(-42*y**3 + 48*y**2 - 42*y) + (48*y**2)*(-38) - 42*y**3*(-38)\nSimplifying the partial expression: (27*y**2)*(-42*y**3 + 48*y**2 - 42*y)\nExpanding the part (-42*y**3 + 48*y**2 - 42*y) using the distributive property, and we got: (-42*y)*(27*y**2) + (27*y**2)*(48*y**2) + (27*y**2)*(-42*y**3)\nReplacing (27*y**2)*(-42*y**3 + 48*y**2 - 42*y) with (-42*y)*(27*y**2) + (27*y**2)*(48*y**2) + (27*y**2)*(-42*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-42*y)*(22*y) + (-42*y)*(27*y**2) - 42*y*(-38) + (22*y)*(48*y**2) + (22*y)*(-42*y**3) + (27*y**2)*(48*y**2) + (27*y**2)*(-42*y**3) + (48*y**2)*(-38) - 42*y**3*(-38)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*y)*-38 = 1596*y\n (-42*y)*(22*y) = -924*y**2\n (-42*y)*(27*y**2) = -1134*y**3\n (-42*y**3)*-38 = 1596*y**3\n (-42*y**3)*(22*y) = -924*y**4\n (-42*y**3)*(27*y**2) = -1134*y**5\n (48*y**2)*-38 = -1824*y**2\n (48*y**2)*(22*y) = 1056*y**3\n (48*y**2)*(27*y**2) = 1296*y**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1134*y**5 - 924*y**4 + 1296*y**4 - 1134*y**3 + 1056*y**3 + 1596*y**3 - 1824*y**2 - 924*y**2 + 1596*y\nCombining like terms, got -1134*y**5 + 372*y**4 + 1518*y**3 - 2748*y**2 + 1596*y\n#Step 7:\nCurrent expression: -1134*y**5 + 372*y**4 + 1518*y**3 - 2748*y**2 + 1596*y\nNo more calculations needed.\n-1134*y**5 + 372*y**4 + 1518*y**3 - 2748*y**2 + 1596*y", "generated_answer": "-1134*y**5 + 372*y**4 + 1518*y**3 - 2748*y**2 + 1596*y", "step_length": 7} {"cot_id": "2de0ba781ecca653a26986eaa1a7d9e6f848010a1f3c69b22566c5854facdd60", "datapoint": {"question": "Calculate the following: (10*x**2 - 25*x)*(28*x**2 + 45)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "280*x**4 - 700*x**3 + 450*x**2 - 1125*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 824, "polynomial_expr": "(10*x**2 - 25*x)*(28*x**2 + 45)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (10*x**2 - 25*x)*(28*x**2 + 45)\nExpanding the part (28*x**2 + 45) using the distributive property, and we got: (28*x**2)*(10*x**2 - 25*x) + 45*(10*x**2 - 25*x)\n#Step 2:\nCurrent expression: (28*x**2)*(10*x**2 - 25*x) + 45*(10*x**2 - 25*x)\nSimplifying the partial expression: 45*(10*x**2 - 25*x)\nExpanding the part (10*x**2 - 25*x) using the distributive property, and we got: -25*x*45 + (10*x**2)*45\nReplacing 45*(10*x**2 - 25*x) with -25*x*45 + (10*x**2)*45 in the overall expression.\n#Step 3:\nCurrent expression: -25*x*45 + (10*x**2)*45 + (28*x**2)*(10*x**2 - 25*x)\nSimplifying the partial expression: (28*x**2)*(10*x**2 - 25*x)\nExpanding the part (10*x**2 - 25*x) using the distributive property, and we got: (-25*x)*(28*x**2) + (10*x**2)*(28*x**2)\nReplacing (28*x**2)*(10*x**2 - 25*x) with (-25*x)*(28*x**2) + (10*x**2)*(28*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-25*x)*(28*x**2) - 25*x*45 + (10*x**2)*(28*x**2) + (10*x**2)*45\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*x)*45 = -1125*x\n (-25*x)*(28*x**2) = -700*x**3\n (10*x**2)*45 = 450*x**2\n (10*x**2)*(28*x**2) = 280*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 280*x**4 - 700*x**3 + 450*x**2 - 1125*x\nNo more calculations needed.\n280*x**4 - 700*x**3 + 450*x**2 - 1125*x", "generated_answer": "280*x**4 - 700*x**3 + 450*x**2 - 1125*x", "step_length": 5} {"cot_id": "ee2a53070ae93163abc46d53a7db1a77d1c940c4c0e1be7465522c66c6071909", "datapoint": {"question": "Simplify this expression: (50 - 64*x**2)*(-25*x**3 - 33*x**2 + 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1600*x**5 + 2112*x**4 - 1250*x**3 - 2034*x**2 + 300", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 825, "polynomial_expr": "(50 - 64*x**2)*(-25*x**3 - 33*x**2 + 6)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (50 - 64*x**2)*(-25*x**3 - 33*x**2 + 6)\nExpanding the part (50 - 64*x**2) using the distributive property, and we got: (-64*x**2)*(-25*x**3 - 33*x**2 + 6) + 50*(-25*x**3 - 33*x**2 + 6)\n#Step 2:\nCurrent expression: (-64*x**2)*(-25*x**3 - 33*x**2 + 6) + 50*(-25*x**3 - 33*x**2 + 6)\nSimplifying the partial expression: 50*(-25*x**3 - 33*x**2 + 6)\nExpanding the part (-25*x**3 - 33*x**2 + 6) using the distributive property, and we got: -33*x**2*50 - 25*x**3*50 + 6*50\nReplacing 50*(-25*x**3 - 33*x**2 + 6) with -33*x**2*50 - 25*x**3*50 + 6*50 in the overall expression.\n#Step 3:\nCurrent expression: (-64*x**2)*(-25*x**3 - 33*x**2 + 6) - 33*x**2*50 - 25*x**3*50 + 300\nSimplifying the partial expression: (-64*x**2)*(-25*x**3 - 33*x**2 + 6)\nExpanding the part (-25*x**3 - 33*x**2 + 6) using the distributive property, and we got: 6*(-64*x**2) + (-64*x**2)*(-33*x**2) + (-64*x**2)*(-25*x**3)\nReplacing (-64*x**2)*(-25*x**3 - 33*x**2 + 6) with 6*(-64*x**2) + (-64*x**2)*(-33*x**2) + (-64*x**2)*(-25*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 6*(-64)*x**2 + (-64*x**2)*(-33*x**2) + (-64*x**2)*(-25*x**3) - 33*x**2*50 - 25*x**3*50 + 300\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*x**2)*50 = -1650*x**2\n (-33*x**2)*(-64*x**2) = 2112*x**4\n (-25*x**3)*50 = -1250*x**3\n (-25*x**3)*(-64*x**2) = 1600*x**5\n 6*-64*x**2 = -384*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1600*x**5 + 2112*x**4 - 1250*x**3 - 1650*x**2 - 384*x**2 + 300\nCombining like terms, got 1600*x**5 + 2112*x**4 - 1250*x**3 - 2034*x**2 + 300\n#Step 6:\nCurrent expression: 1600*x**5 + 2112*x**4 - 1250*x**3 - 2034*x**2 + 300\nNo more calculations needed.\n1600*x**5 + 2112*x**4 - 1250*x**3 - 2034*x**2 + 300", "generated_answer": "1600*x**5 + 2112*x**4 - 1250*x**3 - 2034*x**2 + 300", "step_length": 6} {"cot_id": "2f6850b33f1e66c6deecb9558e79ce38975a458c88bf70af0a83f9b9b1b160db", "datapoint": {"question": "Calculate the following: (39*y**2 + 17*y)*(-36*y**3 - 79)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1404*y**5 - 612*y**4 - 3081*y**2 - 1343*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 826, "polynomial_expr": "(39*y**2 + 17*y)*(-36*y**3 - 79)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (39*y**2 + 17*y)*(-36*y**3 - 79)\nExpanding the part (-36*y**3 - 79) using the distributive property, and we got: (-36*y**3)*(39*y**2 + 17*y) - 79*(39*y**2 + 17*y)\n#Step 2:\nCurrent expression: (-36*y**3)*(39*y**2 + 17*y) - 79*(39*y**2 + 17*y)\nSimplifying the partial expression: -79*(39*y**2 + 17*y)\nExpanding the part (39*y**2 + 17*y) using the distributive property, and we got: (17*y)*(-79) + (39*y**2)*(-79)\nReplacing -79*(39*y**2 + 17*y) with (17*y)*(-79) + (39*y**2)*(-79) in the overall expression.\n#Step 3:\nCurrent expression: (17*y)*(-79) + (39*y**2)*(-79) + (-36*y**3)*(39*y**2 + 17*y)\nSimplifying the partial expression: (-36*y**3)*(39*y**2 + 17*y)\nExpanding the part (39*y**2 + 17*y) using the distributive property, and we got: (17*y)*(-36*y**3) + (39*y**2)*(-36*y**3)\nReplacing (-36*y**3)*(39*y**2 + 17*y) with (17*y)*(-36*y**3) + (39*y**2)*(-36*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (17*y)*(-36*y**3) + (17*y)*(-79) + (39*y**2)*(-36*y**3) + (39*y**2)*(-79)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (17*y)*-79 = -1343*y\n (17*y)*(-36*y**3) = -612*y**4\n (39*y**2)*-79 = -3081*y**2\n (39*y**2)*(-36*y**3) = -1404*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1404*y**5 - 612*y**4 - 3081*y**2 - 1343*y\nNo more calculations needed.\n-1404*y**5 - 612*y**4 - 3081*y**2 - 1343*y", "generated_answer": "-1404*y**5 - 612*y**4 - 3081*y**2 - 1343*y", "step_length": 5} {"cot_id": "bad066b9fa6dc6277c9ff863bee39ee3548d7668509758e6541c120073cd7f1c", "datapoint": {"question": "Simplify this expression: (27*y - 31)*(-35*y**3 - 40)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-945*y**4 + 1085*y**3 - 1080*y + 1240", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 827, "polynomial_expr": "(27*y - 31)*(-35*y**3 - 40)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*y - 31)*(-35*y**3 - 40)\nExpanding the part (-35*y**3 - 40) using the distributive property, and we got: (-35*y**3)*(27*y - 31) - 40*(27*y - 31)\n#Step 2:\nCurrent expression: (-35*y**3)*(27*y - 31) - 40*(27*y - 31)\nSimplifying the partial expression: -40*(27*y - 31)\nExpanding the part (27*y - 31) using the distributive property, and we got: (27*y)*(-40) - 31*(-40)\nReplacing -40*(27*y - 31) with (27*y)*(-40) - 31*(-40) in the overall expression.\n#Step 3:\nCurrent expression: (27*y)*(-40) + (-35*y**3)*(27*y - 31) + 1240\nSimplifying the partial expression: (-35*y**3)*(27*y - 31)\nExpanding the part (27*y - 31) using the distributive property, and we got: -(-1)*1085*y**3 + (27*y)*(-35*y**3)\nReplacing (-35*y**3)*(27*y - 31) with -(-1)*1085*y**3 + (27*y)*(-35*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -31*(-35)*y**3 + (27*y)*(-35*y**3) + (27*y)*(-40) + 1240\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (27*y)*-40 = -1080*y\n (27*y)*(-35*y**3) = -945*y**4\n -31*-35*y**3 = 1085*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -945*y**4 + 1085*y**3 - 1080*y + 1240\nNo more calculations needed.\n-945*y**4 + 1085*y**3 - 1080*y + 1240", "generated_answer": "-945*y**4 + 1085*y**3 - 1080*y + 1240", "step_length": 5} {"cot_id": "8182140057b159b9b525b05427522a319d27ceba6998fc9e221627cf488281ca", "datapoint": {"question": "Calculate the following: (-73*x**3 + 47*x**2 - 14)*(-21*x**3 - 3*x**2 + 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1533*x**6 - 768*x**5 - 141*x**4 - 1896*x**3 + 1452*x**2 - 420", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 828, "polynomial_expr": "(-73*x**3 + 47*x**2 - 14)*(-21*x**3 - 3*x**2 + 30)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-73*x**3 + 47*x**2 - 14)*(-21*x**3 - 3*x**2 + 30)\nExpanding the part (-73*x**3 + 47*x**2 - 14) using the distributive property, and we got: (47*x**2)*(-21*x**3 - 3*x**2 + 30) + (-73*x**3)*(-21*x**3 - 3*x**2 + 30) - 14*(-21*x**3 - 3*x**2 + 30)\n#Step 2:\nCurrent expression: (47*x**2)*(-21*x**3 - 3*x**2 + 30) + (-73*x**3)*(-21*x**3 - 3*x**2 + 30) - 14*(-21*x**3 - 3*x**2 + 30)\nSimplifying the partial expression: -14*(-21*x**3 - 3*x**2 + 30)\nExpanding the part (-21*x**3 - 3*x**2 + 30) using the distributive property, and we got: -3*x**2*(-14) - 21*x**3*(-14) + 30*(-14)\nReplacing -14*(-21*x**3 - 3*x**2 + 30) with -3*x**2*(-14) - 21*x**3*(-14) + 30*(-14) in the overall expression.\n#Step 3:\nCurrent expression: -3*x**2*(-14) + (47*x**2)*(-21*x**3 - 3*x**2 + 30) + (-73*x**3)*(-21*x**3 - 3*x**2 + 30) - 21*x**3*(-14) - 420\nSimplifying the partial expression: (-73*x**3)*(-21*x**3 - 3*x**2 + 30)\nExpanding the part (-21*x**3 - 3*x**2 + 30) using the distributive property, and we got: 30*(-73*x**3) + (-3*x**2)*(-73*x**3) + (-73*x**3)*(-21*x**3)\nReplacing (-73*x**3)*(-21*x**3 - 3*x**2 + 30) with 30*(-73*x**3) + (-3*x**2)*(-73*x**3) + (-73*x**3)*(-21*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 30*(-73)*x**3 + (-3*x**2)*(-73*x**3) - 3*x**2*(-14) + (47*x**2)*(-21*x**3 - 3*x**2 + 30) + (-73*x**3)*(-21*x**3) - 21*x**3*(-14) - 420\nSimplifying the partial expression: (47*x**2)*(-21*x**3 - 3*x**2 + 30)\nExpanding the part (-21*x**3 - 3*x**2 + 30) using the distributive property, and we got: 30*(47*x**2) + (-3*x**2)*(47*x**2) + (47*x**2)*(-21*x**3)\nReplacing (47*x**2)*(-21*x**3 - 3*x**2 + 30) with 30*(47*x**2) + (-3*x**2)*(47*x**2) + (47*x**2)*(-21*x**3) in the overall expression.\n#Step 5:\nCurrent expression: 30*(-73)*x**3 + 30*47*x**2 + (-3*x**2)*(47*x**2) + (-3*x**2)*(-73*x**3) - 3*x**2*(-14) + (47*x**2)*(-21*x**3) + (-73*x**3)*(-21*x**3) - 21*x**3*(-14) - 420\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-21*x**3)*-14 = 294*x**3\n (-21*x**3)*(-73*x**3) = 1533*x**6\n (-21*x**3)*(47*x**2) = -987*x**5\n (-3*x**2)*-14 = 42*x**2\n (-3*x**2)*(-73*x**3) = 219*x**5\n (-3*x**2)*(47*x**2) = -141*x**4\n 30*-73*x**3 = -2190*x**3\n 30*47*x**2 = 1410*x**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1533*x**6 - 987*x**5 + 219*x**5 - 141*x**4 - 2190*x**3 + 294*x**3 + 42*x**2 + 1410*x**2 - 420\nCombining like terms, got 1533*x**6 - 768*x**5 - 141*x**4 - 1896*x**3 + 1452*x**2 - 420\n#Step 7:\nCurrent expression: 1533*x**6 - 768*x**5 - 141*x**4 - 1896*x**3 + 1452*x**2 - 420\nNo more calculations needed.\n1533*x**6 - 768*x**5 - 141*x**4 - 1896*x**3 + 1452*x**2 - 420", "generated_answer": "1533*x**6 - 768*x**5 - 141*x**4 - 1896*x**3 + 1452*x**2 - 420", "step_length": 7} {"cot_id": "da381f5f54a32008ddce0c10e258edc5ca24c2c1b7ef09b6ffb5dd10f8da0b4b", "datapoint": {"question": "Calculate the following: (-47*y**3 - 17*y - 48)*(57*y**3 + 30*y**2 + 3*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2679*y**6 - 1410*y**5 - 1110*y**4 - 3246*y**3 - 1491*y**2 - 144*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 829, "polynomial_expr": "(-47*y**3 - 17*y - 48)*(57*y**3 + 30*y**2 + 3*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-47*y**3 - 17*y - 48)*(57*y**3 + 30*y**2 + 3*y)\nExpanding the part (-47*y**3 - 17*y - 48) using the distributive property, and we got: (-17*y)*(57*y**3 + 30*y**2 + 3*y) + (-47*y**3)*(57*y**3 + 30*y**2 + 3*y) - 48*(57*y**3 + 30*y**2 + 3*y)\n#Step 2:\nCurrent expression: (-17*y)*(57*y**3 + 30*y**2 + 3*y) + (-47*y**3)*(57*y**3 + 30*y**2 + 3*y) - 48*(57*y**3 + 30*y**2 + 3*y)\nSimplifying the partial expression: -48*(57*y**3 + 30*y**2 + 3*y)\nExpanding the part (57*y**3 + 30*y**2 + 3*y) using the distributive property, and we got: (3*y)*(-48) + (30*y**2)*(-48) + (57*y**3)*(-48)\nReplacing -48*(57*y**3 + 30*y**2 + 3*y) with (3*y)*(-48) + (30*y**2)*(-48) + (57*y**3)*(-48) in the overall expression.\n#Step 3:\nCurrent expression: (-17*y)*(57*y**3 + 30*y**2 + 3*y) + (3*y)*(-48) + (30*y**2)*(-48) + (-47*y**3)*(57*y**3 + 30*y**2 + 3*y) + (57*y**3)*(-48)\nSimplifying the partial expression: (-47*y**3)*(57*y**3 + 30*y**2 + 3*y)\nExpanding the part (57*y**3 + 30*y**2 + 3*y) using the distributive property, and we got: (3*y)*(-47*y**3) + (30*y**2)*(-47*y**3) + (-47*y**3)*(57*y**3)\nReplacing (-47*y**3)*(57*y**3 + 30*y**2 + 3*y) with (3*y)*(-47*y**3) + (30*y**2)*(-47*y**3) + (-47*y**3)*(57*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-17*y)*(57*y**3 + 30*y**2 + 3*y) + (3*y)*(-47*y**3) + (3*y)*(-48) + (30*y**2)*(-47*y**3) + (30*y**2)*(-48) + (-47*y**3)*(57*y**3) + (57*y**3)*(-48)\nSimplifying the partial expression: (-17*y)*(57*y**3 + 30*y**2 + 3*y)\nExpanding the part (57*y**3 + 30*y**2 + 3*y) using the distributive property, and we got: (-17*y)*(3*y) + (-17*y)*(30*y**2) + (-17*y)*(57*y**3)\nReplacing (-17*y)*(57*y**3 + 30*y**2 + 3*y) with (-17*y)*(3*y) + (-17*y)*(30*y**2) + (-17*y)*(57*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-17*y)*(3*y) + (-17*y)*(30*y**2) + (-17*y)*(57*y**3) + (3*y)*(-47*y**3) + (3*y)*(-48) + (30*y**2)*(-47*y**3) + (30*y**2)*(-48) + (-47*y**3)*(57*y**3) + (57*y**3)*(-48)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (3*y)*-48 = -144*y\n (3*y)*(-47*y**3) = -141*y**4\n (3*y)*(-17*y) = -51*y**2\n (30*y**2)*-48 = -1440*y**2\n (30*y**2)*(-47*y**3) = -1410*y**5\n (30*y**2)*(-17*y) = -510*y**3\n (57*y**3)*-48 = -2736*y**3\n (57*y**3)*(-47*y**3) = -2679*y**6\n (57*y**3)*(-17*y) = -969*y**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -2679*y**6 - 1410*y**5 - 969*y**4 - 141*y**4 - 2736*y**3 - 510*y**3 - 1440*y**2 - 51*y**2 - 144*y\nCombining like terms, got -2679*y**6 - 1410*y**5 - 1110*y**4 - 3246*y**3 - 1491*y**2 - 144*y\n#Step 7:\nCurrent expression: -2679*y**6 - 1410*y**5 - 1110*y**4 - 3246*y**3 - 1491*y**2 - 144*y\nNo more calculations needed.\n-2679*y**6 - 1410*y**5 - 1110*y**4 - 3246*y**3 - 1491*y**2 - 144*y", "generated_answer": "-2679*y**6 - 1410*y**5 - 1110*y**4 - 3246*y**3 - 1491*y**2 - 144*y", "step_length": 7} {"cot_id": "300fc6dc9393b1a334b906557f1c052d11b51df81455c529c34380ef2058895d", "datapoint": {"question": "Calculate the following: (-25*z**2 - 38)*(32*z**2 - 43*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-800*z**4 + 1075*z**3 - 1216*z**2 + 1634*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 830, "polynomial_expr": "(-25*z**2 - 38)*(32*z**2 - 43*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-25*z**2 - 38)*(32*z**2 - 43*z)\nExpanding the part (-25*z**2 - 38) using the distributive property, and we got: (-25*z**2)*(32*z**2 - 43*z) - 38*(32*z**2 - 43*z)\n#Step 2:\nCurrent expression: (-25*z**2)*(32*z**2 - 43*z) - 38*(32*z**2 - 43*z)\nSimplifying the partial expression: -38*(32*z**2 - 43*z)\nExpanding the part (32*z**2 - 43*z) using the distributive property, and we got: -43*z*(-38) + (32*z**2)*(-38)\nReplacing -38*(32*z**2 - 43*z) with -43*z*(-38) + (32*z**2)*(-38) in the overall expression.\n#Step 3:\nCurrent expression: -43*z*(-38) + (-25*z**2)*(32*z**2 - 43*z) + (32*z**2)*(-38)\nSimplifying the partial expression: (-25*z**2)*(32*z**2 - 43*z)\nExpanding the part (32*z**2 - 43*z) using the distributive property, and we got: (-43*z)*(-25*z**2) + (-25*z**2)*(32*z**2)\nReplacing (-25*z**2)*(32*z**2 - 43*z) with (-43*z)*(-25*z**2) + (-25*z**2)*(32*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-43*z)*(-25*z**2) - 43*z*(-38) + (-25*z**2)*(32*z**2) + (32*z**2)*(-38)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-43*z)*-38 = 1634*z\n (-43*z)*(-25*z**2) = 1075*z**3\n (32*z**2)*-38 = -1216*z**2\n (32*z**2)*(-25*z**2) = -800*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -800*z**4 + 1075*z**3 - 1216*z**2 + 1634*z\nNo more calculations needed.\n-800*z**4 + 1075*z**3 - 1216*z**2 + 1634*z", "generated_answer": "-800*z**4 + 1075*z**3 - 1216*z**2 + 1634*z", "step_length": 5} {"cot_id": "ea9f16447b239eef388d76e33a62daae58652ef995e971428e842fc4cac810be", "datapoint": {"question": "Calculate the following: (-23*x**3 + 11*x**2)*(21*x**2 + 36*x - 45)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-483*x**5 - 597*x**4 + 1431*x**3 - 495*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 831, "polynomial_expr": "(-23*x**3 + 11*x**2)*(21*x**2 + 36*x - 45)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-23*x**3 + 11*x**2)*(21*x**2 + 36*x - 45)\nExpanding the part (-23*x**3 + 11*x**2) using the distributive property, and we got: (11*x**2)*(21*x**2 + 36*x - 45) + (-23*x**3)*(21*x**2 + 36*x - 45)\n#Step 2:\nCurrent expression: (11*x**2)*(21*x**2 + 36*x - 45) + (-23*x**3)*(21*x**2 + 36*x - 45)\nSimplifying the partial expression: (-23*x**3)*(21*x**2 + 36*x - 45)\nExpanding the part (21*x**2 + 36*x - 45) using the distributive property, and we got: -(-1)*1035*x**3 + (36*x)*(-23*x**3) + (21*x**2)*(-23*x**3)\nReplacing (-23*x**3)*(21*x**2 + 36*x - 45) with -(-1)*1035*x**3 + (36*x)*(-23*x**3) + (21*x**2)*(-23*x**3) in the overall expression.\n#Step 3:\nCurrent expression: -45*(-23)*x**3 + (36*x)*(-23*x**3) + (11*x**2)*(21*x**2 + 36*x - 45) + (21*x**2)*(-23*x**3)\nSimplifying the partial expression: (11*x**2)*(21*x**2 + 36*x - 45)\nExpanding the part (21*x**2 + 36*x - 45) using the distributive property, and we got: -495*x**2 + (36*x)*(11*x**2) + (11*x**2)*(21*x**2)\nReplacing (11*x**2)*(21*x**2 + 36*x - 45) with -495*x**2 + (36*x)*(11*x**2) + (11*x**2)*(21*x**2) in the overall expression.\n#Step 4:\nCurrent expression: -45*(-23)*x**3 - 45*11*x**2 + (36*x)*(11*x**2) + (36*x)*(-23*x**3) + (11*x**2)*(21*x**2) + (21*x**2)*(-23*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (21*x**2)*(-23*x**3) = -483*x**5\n (21*x**2)*(11*x**2) = 231*x**4\n (36*x)*(-23*x**3) = -828*x**4\n (36*x)*(11*x**2) = 396*x**3\n -45*-23*x**3 = 1035*x**3\n -45*11*x**2 = -495*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -483*x**5 - 828*x**4 + 231*x**4 + 396*x**3 + 1035*x**3 - 495*x**2\nCombining like terms, got -483*x**5 - 597*x**4 + 1431*x**3 - 495*x**2\n#Step 6:\nCurrent expression: -483*x**5 - 597*x**4 + 1431*x**3 - 495*x**2\nNo more calculations needed.\n-483*x**5 - 597*x**4 + 1431*x**3 - 495*x**2", "generated_answer": "-483*x**5 - 597*x**4 + 1431*x**3 - 495*x**2", "step_length": 6} {"cot_id": "814e16c1e8268b77ca24bbe182b26386f6b7ddeb7bcb6a4c35c512162eeb0eec", "datapoint": {"question": "Calculate the following: (40 - 41*z**3)*(15*z**3 + 30*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-615*z**6 - 1230*z**5 + 600*z**3 + 1200*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 833, "polynomial_expr": "(40 - 41*z**3)*(15*z**3 + 30*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (40 - 41*z**3)*(15*z**3 + 30*z**2)\nExpanding the part (40 - 41*z**3) using the distributive property, and we got: (-41*z**3)*(15*z**3 + 30*z**2) + 40*(15*z**3 + 30*z**2)\n#Step 2:\nCurrent expression: (-41*z**3)*(15*z**3 + 30*z**2) + 40*(15*z**3 + 30*z**2)\nSimplifying the partial expression: 40*(15*z**3 + 30*z**2)\nExpanding the part (15*z**3 + 30*z**2) using the distributive property, and we got: (30*z**2)*40 + (15*z**3)*40\nReplacing 40*(15*z**3 + 30*z**2) with (30*z**2)*40 + (15*z**3)*40 in the overall expression.\n#Step 3:\nCurrent expression: (30*z**2)*40 + (-41*z**3)*(15*z**3 + 30*z**2) + (15*z**3)*40\nSimplifying the partial expression: (-41*z**3)*(15*z**3 + 30*z**2)\nExpanding the part (15*z**3 + 30*z**2) using the distributive property, and we got: (30*z**2)*(-41*z**3) + (-41*z**3)*(15*z**3)\nReplacing (-41*z**3)*(15*z**3 + 30*z**2) with (30*z**2)*(-41*z**3) + (-41*z**3)*(15*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (30*z**2)*(-41*z**3) + (30*z**2)*40 + (-41*z**3)*(15*z**3) + (15*z**3)*40\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (15*z**3)*40 = 600*z**3\n (15*z**3)*(-41*z**3) = -615*z**6\n (30*z**2)*40 = 1200*z**2\n (30*z**2)*(-41*z**3) = -1230*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -615*z**6 - 1230*z**5 + 600*z**3 + 1200*z**2\nNo more calculations needed.\n-615*z**6 - 1230*z**5 + 600*z**3 + 1200*z**2", "generated_answer": "-615*z**6 - 1230*z**5 + 600*z**3 + 1200*z**2", "step_length": 5} {"cot_id": "3ce1f9b9b8f4bc5e397e9fda0bd5665564c627f4a29b17cc9581b66106f9dd2d", "datapoint": {"question": "Simplify this expression: (29 - 32*z)*(6*z**3 - 17*z**2 + 13*z + 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-192*z**4 + 718*z**3 - 909*z**2 - 647*z + 928", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 834, "polynomial_expr": "(29 - 32*z)*(6*z**3 - 17*z**2 + 13*z + 32)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29 - 32*z)*(6*z**3 - 17*z**2 + 13*z + 32)\nExpanding the part (29 - 32*z) using the distributive property, and we got: (-32*z)*(6*z**3 - 17*z**2 + 13*z + 32) + 29*(6*z**3 - 17*z**2 + 13*z + 32)\n#Step 2:\nCurrent expression: (-32*z)*(6*z**3 - 17*z**2 + 13*z + 32) + 29*(6*z**3 - 17*z**2 + 13*z + 32)\nSimplifying the partial expression: 29*(6*z**3 - 17*z**2 + 13*z + 32)\nExpanding the part (6*z**3 - 17*z**2 + 13*z + 32) using the distributive property, and we got: (13*z)*29 - 17*z**2*29 + (6*z**3)*29 + 32*29\nReplacing 29*(6*z**3 - 17*z**2 + 13*z + 32) with (13*z)*29 - 17*z**2*29 + (6*z**3)*29 + 32*29 in the overall expression.\n#Step 3:\nCurrent expression: (-32*z)*(6*z**3 - 17*z**2 + 13*z + 32) + (13*z)*29 - 17*z**2*29 + (6*z**3)*29 + 928\nSimplifying the partial expression: (-32*z)*(6*z**3 - 17*z**2 + 13*z + 32)\nExpanding the part (6*z**3 - 17*z**2 + 13*z + 32) using the distributive property, and we got: (-32*z)*(13*z) + (-32*z)*(-17*z**2) + (-32*z)*(6*z**3) + 32*(-32*z)\nReplacing (-32*z)*(6*z**3 - 17*z**2 + 13*z + 32) with (-32*z)*(13*z) + (-32*z)*(-17*z**2) + (-32*z)*(6*z**3) + 32*(-32*z) in the overall expression.\n#Step 4:\nCurrent expression: (-32*z)*(13*z) + (-32*z)*(-17*z**2) + (-32*z)*(6*z**3) + 32*(-32)*z + (13*z)*29 - 17*z**2*29 + (6*z**3)*29 + 928\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-17*z**2)*29 = -493*z**2\n (-17*z**2)*(-32*z) = 544*z**3\n (6*z**3)*29 = 174*z**3\n (6*z**3)*(-32*z) = -192*z**4\n (13*z)*29 = 377*z\n (13*z)*(-32*z) = -416*z**2\n 32*-32*z = -1024*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -192*z**4 + 174*z**3 + 544*z**3 - 493*z**2 - 416*z**2 - 1024*z + 377*z + 928\nCombining like terms, got -192*z**4 + 718*z**3 - 909*z**2 - 647*z + 928\n#Step 6:\nCurrent expression: -192*z**4 + 718*z**3 - 909*z**2 - 647*z + 928\nNo more calculations needed.\n-192*z**4 + 718*z**3 - 909*z**2 - 647*z + 928", "generated_answer": "-192*z**4 + 718*z**3 - 909*z**2 - 647*z + 928", "step_length": 6} {"cot_id": "b3a0fc86a36d2a2d7568f7d1083e44e798efe87e60ebe45392b5b4ff9c901be1", "datapoint": {"question": "Calculate the following: (23 - 48*x)*(31*x**2 - 39*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1488*x**3 + 2585*x**2 - 897*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 835, "polynomial_expr": "(23 - 48*x)*(31*x**2 - 39*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (23 - 48*x)*(31*x**2 - 39*x)\nExpanding the part (23 - 48*x) using the distributive property, and we got: (-48*x)*(31*x**2 - 39*x) + 23*(31*x**2 - 39*x)\n#Step 2:\nCurrent expression: (-48*x)*(31*x**2 - 39*x) + 23*(31*x**2 - 39*x)\nSimplifying the partial expression: 23*(31*x**2 - 39*x)\nExpanding the part (31*x**2 - 39*x) using the distributive property, and we got: -39*x*23 + (31*x**2)*23\nReplacing 23*(31*x**2 - 39*x) with -39*x*23 + (31*x**2)*23 in the overall expression.\n#Step 3:\nCurrent expression: (-48*x)*(31*x**2 - 39*x) - 39*x*23 + (31*x**2)*23\nSimplifying the partial expression: (-48*x)*(31*x**2 - 39*x)\nExpanding the part (31*x**2 - 39*x) using the distributive property, and we got: (-48*x)*(-39*x) + (-48*x)*(31*x**2)\nReplacing (-48*x)*(31*x**2 - 39*x) with (-48*x)*(-39*x) + (-48*x)*(31*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-48*x)*(-39*x) + (-48*x)*(31*x**2) - 39*x*23 + (31*x**2)*23\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*x)*23 = -897*x\n (-39*x)*(-48*x) = 1872*x**2\n (31*x**2)*23 = 713*x**2\n (31*x**2)*(-48*x) = -1488*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1488*x**3 + 713*x**2 + 1872*x**2 - 897*x\nCombining like terms, got -1488*x**3 + 2585*x**2 - 897*x\n#Step 6:\nCurrent expression: -1488*x**3 + 2585*x**2 - 897*x\nNo more calculations needed.\n-1488*x**3 + 2585*x**2 - 897*x", "generated_answer": "-1488*x**3 + 2585*x**2 - 897*x", "step_length": 6} {"cot_id": "6f0ee3207596280a79720948616d3a97f13c05ca4d08dcf64818fe702670b8cd", "datapoint": {"question": "Calculate the following: (-16*z**2 - 68)*(-26*z**2 - 43*z + 11)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "416*z**4 + 688*z**3 + 1592*z**2 + 2924*z - 748", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 836, "polynomial_expr": "(-16*z**2 - 68)*(-26*z**2 - 43*z + 11)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-16*z**2 - 68)*(-26*z**2 - 43*z + 11)\nExpanding the part (-16*z**2 - 68) using the distributive property, and we got: (-16*z**2)*(-26*z**2 - 43*z + 11) - 68*(-26*z**2 - 43*z + 11)\n#Step 2:\nCurrent expression: (-16*z**2)*(-26*z**2 - 43*z + 11) - 68*(-26*z**2 - 43*z + 11)\nSimplifying the partial expression: -68*(-26*z**2 - 43*z + 11)\nExpanding the part (-26*z**2 - 43*z + 11) using the distributive property, and we got: -43*z*(-68) - 26*z**2*(-68) + 11*(-68)\nReplacing -68*(-26*z**2 - 43*z + 11) with -43*z*(-68) - 26*z**2*(-68) + 11*(-68) in the overall expression.\n#Step 3:\nCurrent expression: -43*z*(-68) - 26*z**2*(-68) + (-16*z**2)*(-26*z**2 - 43*z + 11) - 748\nSimplifying the partial expression: (-16*z**2)*(-26*z**2 - 43*z + 11)\nExpanding the part (-26*z**2 - 43*z + 11) using the distributive property, and we got: (-43*z)*(-16*z**2) + 11*(-16*z**2) + (-26*z**2)*(-16*z**2)\nReplacing (-16*z**2)*(-26*z**2 - 43*z + 11) with (-43*z)*(-16*z**2) + 11*(-16*z**2) + (-26*z**2)*(-16*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-43*z)*(-16*z**2) - 43*z*(-68) + 11*(-16)*z**2 + (-26*z**2)*(-16*z**2) - 26*z**2*(-68) - 748\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-43*z)*-68 = 2924*z\n (-43*z)*(-16*z**2) = 688*z**3\n (-26*z**2)*-68 = 1768*z**2\n (-26*z**2)*(-16*z**2) = 416*z**4\n 11*-16*z**2 = -176*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 416*z**4 + 688*z**3 - 176*z**2 + 1768*z**2 + 2924*z - 748\nCombining like terms, got 416*z**4 + 688*z**3 + 1592*z**2 + 2924*z - 748\n#Step 6:\nCurrent expression: 416*z**4 + 688*z**3 + 1592*z**2 + 2924*z - 748\nNo more calculations needed.\n416*z**4 + 688*z**3 + 1592*z**2 + 2924*z - 748", "generated_answer": "416*z**4 + 688*z**3 + 1592*z**2 + 2924*z - 748", "step_length": 6} {"cot_id": "09b689179f74c71e268632ced7e9be87d89a9031a89be3f15d5782e1801903c4", "datapoint": {"question": "Simplify this expression: (8*x**2 - 1)*(-19*x**3 - 50*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-152*x**5 - 381*x**3 + 50*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 837, "polynomial_expr": "(8*x**2 - 1)*(-19*x**3 - 50*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (8*x**2 - 1)*(-19*x**3 - 50*x)\nExpanding the part (8*x**2 - 1) using the distributive property, and we got: (8*x**2)*(-19*x**3 - 50*x) - (-19*x**3 - 50*x)\n#Step 2:\nCurrent expression: (8*x**2)*(-19*x**3 - 50*x) - (-19*x**3 - 50*x)\nSimplifying the partial expression: -(-19*x**3 - 50*x)\nExpanding the part (-19*x**3 - 50*x) using the distributive property, and we got: -50*x*(-1) - 19*x**3*(-1)\nReplacing -(-19*x**3 - 50*x) with -50*x*(-1) - 19*x**3*(-1) in the overall expression.\n#Step 3:\nCurrent expression: -50*x*(-1) + (8*x**2)*(-19*x**3 - 50*x) - 19*x**3*(-1)\nSimplifying the partial expression: (8*x**2)*(-19*x**3 - 50*x)\nExpanding the part (-19*x**3 - 50*x) using the distributive property, and we got: (-50*x)*(8*x**2) + (8*x**2)*(-19*x**3)\nReplacing (8*x**2)*(-19*x**3 - 50*x) with (-50*x)*(8*x**2) + (8*x**2)*(-19*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-50*x)*(8*x**2) - 50*x*(-1) + (8*x**2)*(-19*x**3) - 19*x**3*(-1)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-50*x)*-1 = 50*x\n (-50*x)*(8*x**2) = -400*x**3\n (-19*x**3)*-1 = 19*x**3\n (-19*x**3)*(8*x**2) = -152*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -152*x**5 - 400*x**3 + 19*x**3 + 50*x\nCombining like terms, got -152*x**5 - 381*x**3 + 50*x\n#Step 6:\nCurrent expression: -152*x**5 - 381*x**3 + 50*x\nNo more calculations needed.\n-152*x**5 - 381*x**3 + 50*x", "generated_answer": "-152*x**5 - 381*x**3 + 50*x", "step_length": 6} {"cot_id": "9bd580a3910688e6b5bf34e2ce83452c92e3414c4f2a56e18b014bf4baf2e0fa", "datapoint": {"question": "Simplify this expression: (-41*x**2 - 26*x)*(-3*x**3 + 3*x + 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "123*x**5 + 78*x**4 - 123*x**3 - 775*x**2 - 442*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 838, "polynomial_expr": "(-41*x**2 - 26*x)*(-3*x**3 + 3*x + 17)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-41*x**2 - 26*x)*(-3*x**3 + 3*x + 17)\nExpanding the part (-41*x**2 - 26*x) using the distributive property, and we got: (-26*x)*(-3*x**3 + 3*x + 17) + (-41*x**2)*(-3*x**3 + 3*x + 17)\n#Step 2:\nCurrent expression: (-26*x)*(-3*x**3 + 3*x + 17) + (-41*x**2)*(-3*x**3 + 3*x + 17)\nSimplifying the partial expression: (-41*x**2)*(-3*x**3 + 3*x + 17)\nExpanding the part (-3*x**3 + 3*x + 17) using the distributive property, and we got: 17*(-41*x**2) + (3*x)*(-41*x**2) + (-41*x**2)*(-3*x**3)\nReplacing (-41*x**2)*(-3*x**3 + 3*x + 17) with 17*(-41*x**2) + (3*x)*(-41*x**2) + (-41*x**2)*(-3*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-26*x)*(-3*x**3 + 3*x + 17) + 17*(-41)*x**2 + (3*x)*(-41*x**2) + (-41*x**2)*(-3*x**3)\nSimplifying the partial expression: (-26*x)*(-3*x**3 + 3*x + 17)\nExpanding the part (-3*x**3 + 3*x + 17) using the distributive property, and we got: (-26*x)*(3*x) + (-26*x)*(-3*x**3) + 17*(-26*x)\nReplacing (-26*x)*(-3*x**3 + 3*x + 17) with (-26*x)*(3*x) + (-26*x)*(-3*x**3) + 17*(-26*x) in the overall expression.\n#Step 4:\nCurrent expression: (-26*x)*(3*x) + (-26*x)*(-3*x**3) + 17*(-41)*x**2 + 17*(-26)*x + (3*x)*(-41*x**2) + (-41*x**2)*(-3*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-3*x**3)*(-41*x**2) = 123*x**5\n (-3*x**3)*(-26*x) = 78*x**4\n (3*x)*(-41*x**2) = -123*x**3\n (3*x)*(-26*x) = -78*x**2\n 17*-41*x**2 = -697*x**2\n 17*-26*x = -442*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 123*x**5 + 78*x**4 - 123*x**3 - 697*x**2 - 78*x**2 - 442*x\nCombining like terms, got 123*x**5 + 78*x**4 - 123*x**3 - 775*x**2 - 442*x\n#Step 6:\nCurrent expression: 123*x**5 + 78*x**4 - 123*x**3 - 775*x**2 - 442*x\nNo more calculations needed.\n123*x**5 + 78*x**4 - 123*x**3 - 775*x**2 - 442*x", "generated_answer": "123*x**5 + 78*x**4 - 123*x**3 - 775*x**2 - 442*x", "step_length": 6} {"cot_id": "37a143609faced7404b28eb9e4a9178627baed69e43ee7db3dd82f4bb89a0dd3", "datapoint": {"question": "Simplify this expression: (29 - 26*z)*(40*z**3 + 8*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1040*z**4 + 1160*z**3 - 208*z**2 + 232*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 839, "polynomial_expr": "(29 - 26*z)*(40*z**3 + 8*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29 - 26*z)*(40*z**3 + 8*z)\nExpanding the part (29 - 26*z) using the distributive property, and we got: (-26*z)*(40*z**3 + 8*z) + 29*(40*z**3 + 8*z)\n#Step 2:\nCurrent expression: (-26*z)*(40*z**3 + 8*z) + 29*(40*z**3 + 8*z)\nSimplifying the partial expression: 29*(40*z**3 + 8*z)\nExpanding the part (40*z**3 + 8*z) using the distributive property, and we got: (8*z)*29 + (40*z**3)*29\nReplacing 29*(40*z**3 + 8*z) with (8*z)*29 + (40*z**3)*29 in the overall expression.\n#Step 3:\nCurrent expression: (-26*z)*(40*z**3 + 8*z) + (8*z)*29 + (40*z**3)*29\nSimplifying the partial expression: (-26*z)*(40*z**3 + 8*z)\nExpanding the part (40*z**3 + 8*z) using the distributive property, and we got: (-26*z)*(8*z) + (-26*z)*(40*z**3)\nReplacing (-26*z)*(40*z**3 + 8*z) with (-26*z)*(8*z) + (-26*z)*(40*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-26*z)*(8*z) + (-26*z)*(40*z**3) + (8*z)*29 + (40*z**3)*29\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (8*z)*29 = 232*z\n (8*z)*(-26*z) = -208*z**2\n (40*z**3)*29 = 1160*z**3\n (40*z**3)*(-26*z) = -1040*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1040*z**4 + 1160*z**3 - 208*z**2 + 232*z\nNo more calculations needed.\n-1040*z**4 + 1160*z**3 - 208*z**2 + 232*z", "generated_answer": "-1040*z**4 + 1160*z**3 - 208*z**2 + 232*z", "step_length": 5} {"cot_id": "ab0ab0ad6d894933fe2053ee58cdf755aaf5cc3d1e401fc3b1ca142f3c93c33d", "datapoint": {"question": "Simplify this expression: 13*x**3*(-13*x**3 + 33*x**2 - 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-169*x**6 + 429*x**5 - 494*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 840, "polynomial_expr": "13*x**3*(-13*x**3 + 33*x**2 - 38)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 13*x**3*(-13*x**3 + 33*x**2 - 38)\nExpanding the part (-13*x**3 + 33*x**2 - 38) using the distributive property, and we got: -494*x**3 + (33*x**2)*(13*x**3) + (-13*x**3)*(13*x**3)\n#Step 2:\nCurrent expression: -494*x**3 + (33*x**2)*(13*x**3) + (-13*x**3)*(13*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -38*(13*x**3) = -494*x**3\n (-13*x**3)*(13*x**3) = -169*x**6\n (33*x**2)*(13*x**3) = 429*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -169*x**6 + 429*x**5 - 494*x**3\nNo more calculations needed.\n-169*x**6 + 429*x**5 - 494*x**3", "generated_answer": "-169*x**6 + 429*x**5 - 494*x**3", "step_length": 3} {"cot_id": "2731abc733b1c751778c435860d5cc3f258e28675b8ab6bff009134d53996072", "datapoint": {"question": "Simplify this expression: (-22*z**3 + 36*z)*(66*z**3 - 34*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1452*z**6 + 3124*z**4 - 1224*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 841, "polynomial_expr": "(-22*z**3 + 36*z)*(66*z**3 - 34*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-22*z**3 + 36*z)*(66*z**3 - 34*z)\nExpanding the part (66*z**3 - 34*z) using the distributive property, and we got: (-34*z)*(-22*z**3 + 36*z) + (66*z**3)*(-22*z**3 + 36*z)\n#Step 2:\nCurrent expression: (-34*z)*(-22*z**3 + 36*z) + (66*z**3)*(-22*z**3 + 36*z)\nSimplifying the partial expression: (-34*z)*(-22*z**3 + 36*z)\nExpanding the part (-22*z**3 + 36*z) using the distributive property, and we got: (-34*z)*(36*z) + (-34*z)*(-22*z**3)\nReplacing (-34*z)*(-22*z**3 + 36*z) with (-34*z)*(36*z) + (-34*z)*(-22*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-34*z)*(36*z) + (-34*z)*(-22*z**3) + (66*z**3)*(-22*z**3 + 36*z)\nSimplifying the partial expression: (66*z**3)*(-22*z**3 + 36*z)\nExpanding the part (-22*z**3 + 36*z) using the distributive property, and we got: (36*z)*(66*z**3) + (-22*z**3)*(66*z**3)\nReplacing (66*z**3)*(-22*z**3 + 36*z) with (36*z)*(66*z**3) + (-22*z**3)*(66*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-34*z)*(36*z) + (-34*z)*(-22*z**3) + (36*z)*(66*z**3) + (-22*z**3)*(66*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*z**3)*(-34*z) = 748*z**4\n (-22*z**3)*(66*z**3) = -1452*z**6\n (36*z)*(-34*z) = -1224*z**2\n (36*z)*(66*z**3) = 2376*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1452*z**6 + 748*z**4 + 2376*z**4 - 1224*z**2\nCombining like terms, got -1452*z**6 + 3124*z**4 - 1224*z**2\n#Step 6:\nCurrent expression: -1452*z**6 + 3124*z**4 - 1224*z**2\nNo more calculations needed.\n-1452*z**6 + 3124*z**4 - 1224*z**2", "generated_answer": "-1452*z**6 + 3124*z**4 - 1224*z**2", "step_length": 6} {"cot_id": "6d79d6b21052fc22401630fec5793f4041accff9a4cd410b1691461adadff240", "datapoint": {"question": "Simplify this expression: (2*z**3 + 31)*(4*z**3 + 18*z + 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "8*z**6 + 36*z**4 + 188*z**3 + 558*z + 992", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 842, "polynomial_expr": "(2*z**3 + 31)*(4*z**3 + 18*z + 32)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2*z**3 + 31)*(4*z**3 + 18*z + 32)\nExpanding the part (2*z**3 + 31) using the distributive property, and we got: (2*z**3)*(4*z**3 + 18*z + 32) + 31*(4*z**3 + 18*z + 32)\n#Step 2:\nCurrent expression: (2*z**3)*(4*z**3 + 18*z + 32) + 31*(4*z**3 + 18*z + 32)\nSimplifying the partial expression: 31*(4*z**3 + 18*z + 32)\nExpanding the part (4*z**3 + 18*z + 32) using the distributive property, and we got: (18*z)*31 + (4*z**3)*31 + 32*31\nReplacing 31*(4*z**3 + 18*z + 32) with (18*z)*31 + (4*z**3)*31 + 32*31 in the overall expression.\n#Step 3:\nCurrent expression: (18*z)*31 + (2*z**3)*(4*z**3 + 18*z + 32) + (4*z**3)*31 + 992\nSimplifying the partial expression: (2*z**3)*(4*z**3 + 18*z + 32)\nExpanding the part (4*z**3 + 18*z + 32) using the distributive property, and we got: 32*(2*z**3) + (18*z)*(2*z**3) + (2*z**3)*(4*z**3)\nReplacing (2*z**3)*(4*z**3 + 18*z + 32) with 32*(2*z**3) + (18*z)*(2*z**3) + (2*z**3)*(4*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 32*2*z**3 + (18*z)*(2*z**3) + (18*z)*31 + (2*z**3)*(4*z**3) + (4*z**3)*31 + 992\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (4*z**3)*31 = 124*z**3\n (4*z**3)*(2*z**3) = 8*z**6\n (18*z)*31 = 558*z\n (18*z)*(2*z**3) = 36*z**4\n 32*2*z**3 = 64*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 8*z**6 + 36*z**4 + 64*z**3 + 124*z**3 + 558*z + 992\nCombining like terms, got 8*z**6 + 36*z**4 + 188*z**3 + 558*z + 992\n#Step 6:\nCurrent expression: 8*z**6 + 36*z**4 + 188*z**3 + 558*z + 992\nNo more calculations needed.\n8*z**6 + 36*z**4 + 188*z**3 + 558*z + 992", "generated_answer": "8*z**6 + 36*z**4 + 188*z**3 + 558*z + 992", "step_length": 6} {"cot_id": "fc5a882f69521d21d883e7b38c30d8bebf6990d94fadfce3a8961b772ae6fce2", "datapoint": {"question": "Calculate the following: (-19*y**2 - 5)*(93*y**3 - 3*y + 8)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1767*y**5 - 408*y**3 - 152*y**2 + 15*y - 40", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 843, "polynomial_expr": "(-19*y**2 - 5)*(93*y**3 - 3*y + 8)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-19*y**2 - 5)*(93*y**3 - 3*y + 8)\nExpanding the part (-19*y**2 - 5) using the distributive property, and we got: (-19*y**2)*(93*y**3 - 3*y + 8) - 5*(93*y**3 - 3*y + 8)\n#Step 2:\nCurrent expression: (-19*y**2)*(93*y**3 - 3*y + 8) - 5*(93*y**3 - 3*y + 8)\nSimplifying the partial expression: -5*(93*y**3 - 3*y + 8)\nExpanding the part (93*y**3 - 3*y + 8) using the distributive property, and we got: -3*y*(-5) + (93*y**3)*(-5) + 8*(-5)\nReplacing -5*(93*y**3 - 3*y + 8) with -3*y*(-5) + (93*y**3)*(-5) + 8*(-5) in the overall expression.\n#Step 3:\nCurrent expression: -3*y*(-5) + (-19*y**2)*(93*y**3 - 3*y + 8) + (93*y**3)*(-5) - 40\nSimplifying the partial expression: (-19*y**2)*(93*y**3 - 3*y + 8)\nExpanding the part (93*y**3 - 3*y + 8) using the distributive property, and we got: (-3*y)*(-19*y**2) + 8*(-19*y**2) + (-19*y**2)*(93*y**3)\nReplacing (-19*y**2)*(93*y**3 - 3*y + 8) with (-3*y)*(-19*y**2) + 8*(-19*y**2) + (-19*y**2)*(93*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-3*y)*(-19*y**2) - 3*y*(-5) + 8*(-19)*y**2 + (-19*y**2)*(93*y**3) + (93*y**3)*(-5) - 40\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-3*y)*-5 = 15*y\n (-3*y)*(-19*y**2) = 57*y**3\n (93*y**3)*-5 = -465*y**3\n (93*y**3)*(-19*y**2) = -1767*y**5\n 8*-19*y**2 = -152*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1767*y**5 - 465*y**3 + 57*y**3 - 152*y**2 + 15*y - 40\nCombining like terms, got -1767*y**5 - 408*y**3 - 152*y**2 + 15*y - 40\n#Step 6:\nCurrent expression: -1767*y**5 - 408*y**3 - 152*y**2 + 15*y - 40\nNo more calculations needed.\n-1767*y**5 - 408*y**3 - 152*y**2 + 15*y - 40", "generated_answer": "-1767*y**5 - 408*y**3 - 152*y**2 + 15*y - 40", "step_length": 6} {"cot_id": "ef5ef774d5fdd7559c7be5f06b4cbc1f7a7d1c1d93f052bb3108f6c3376e2c72", "datapoint": {"question": "Calculate the following: -36*x*(-11*x**3 + 16*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "396*x**4 - 576*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 844, "polynomial_expr": "-36*x*(-11*x**3 + 16*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -36*x*(-11*x**3 + 16*x**2)\nExpanding the part (-11*x**3 + 16*x**2) using the distributive property, and we got: (-36*x)*(16*x**2) + (-36*x)*(-11*x**3)\n#Step 2:\nCurrent expression: (-36*x)*(16*x**2) + (-36*x)*(-11*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*x**3)*(-36*x) = 396*x**4\n (16*x**2)*(-36*x) = -576*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 396*x**4 - 576*x**3\nNo more calculations needed.\n396*x**4 - 576*x**3", "generated_answer": "396*x**4 - 576*x**3", "step_length": 3} {"cot_id": "cd3ede80d54802e43e349a384a3378e623cca30e97e51b1a195b0fc054a08f39", "datapoint": {"question": "Calculate the following: (28*y**2 + 32*y - 11)*(-23*y**3 + 46*y + 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-644*y**5 - 736*y**4 + 1541*y**3 + 1836*y**2 - 90*y - 143", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 845, "polynomial_expr": "(28*y**2 + 32*y - 11)*(-23*y**3 + 46*y + 13)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28*y**2 + 32*y - 11)*(-23*y**3 + 46*y + 13)\nExpanding the part (28*y**2 + 32*y - 11) using the distributive property, and we got: (32*y)*(-23*y**3 + 46*y + 13) + (28*y**2)*(-23*y**3 + 46*y + 13) - 11*(-23*y**3 + 46*y + 13)\n#Step 2:\nCurrent expression: (32*y)*(-23*y**3 + 46*y + 13) + (28*y**2)*(-23*y**3 + 46*y + 13) - 11*(-23*y**3 + 46*y + 13)\nSimplifying the partial expression: -11*(-23*y**3 + 46*y + 13)\nExpanding the part (-23*y**3 + 46*y + 13) using the distributive property, and we got: (46*y)*(-11) - 23*y**3*(-11) + 13*(-11)\nReplacing -11*(-23*y**3 + 46*y + 13) with (46*y)*(-11) - 23*y**3*(-11) + 13*(-11) in the overall expression.\n#Step 3:\nCurrent expression: (32*y)*(-23*y**3 + 46*y + 13) + (46*y)*(-11) + (28*y**2)*(-23*y**3 + 46*y + 13) - 23*y**3*(-11) - 143\nSimplifying the partial expression: (28*y**2)*(-23*y**3 + 46*y + 13)\nExpanding the part (-23*y**3 + 46*y + 13) using the distributive property, and we got: 13*(28*y**2) + (46*y)*(28*y**2) + (28*y**2)*(-23*y**3)\nReplacing (28*y**2)*(-23*y**3 + 46*y + 13) with 13*(28*y**2) + (46*y)*(28*y**2) + (28*y**2)*(-23*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 13*28*y**2 + (32*y)*(-23*y**3 + 46*y + 13) + (46*y)*(28*y**2) + (46*y)*(-11) + (28*y**2)*(-23*y**3) - 23*y**3*(-11) - 143\nSimplifying the partial expression: (32*y)*(-23*y**3 + 46*y + 13)\nExpanding the part (-23*y**3 + 46*y + 13) using the distributive property, and we got: 13*(32*y) + (32*y)*(46*y) + (32*y)*(-23*y**3)\nReplacing (32*y)*(-23*y**3 + 46*y + 13) with 13*(32*y) + (32*y)*(46*y) + (32*y)*(-23*y**3) in the overall expression.\n#Step 5:\nCurrent expression: 13*28*y**2 + 13*32*y + (32*y)*(46*y) + (32*y)*(-23*y**3) + (46*y)*(28*y**2) + (46*y)*(-11) + (28*y**2)*(-23*y**3) - 23*y**3*(-11) - 143\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*y**3)*-11 = 253*y**3\n (-23*y**3)*(28*y**2) = -644*y**5\n (-23*y**3)*(32*y) = -736*y**4\n (46*y)*-11 = -506*y\n (46*y)*(28*y**2) = 1288*y**3\n (46*y)*(32*y) = 1472*y**2\n 13*28*y**2 = 364*y**2\n 13*32*y = 416*y\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -644*y**5 - 736*y**4 + 253*y**3 + 1288*y**3 + 364*y**2 + 1472*y**2 - 506*y + 416*y - 143\nCombining like terms, got -644*y**5 - 736*y**4 + 1541*y**3 + 1836*y**2 - 90*y - 143\n#Step 7:\nCurrent expression: -644*y**5 - 736*y**4 + 1541*y**3 + 1836*y**2 - 90*y - 143\nNo more calculations needed.\n-644*y**5 - 736*y**4 + 1541*y**3 + 1836*y**2 - 90*y - 143", "generated_answer": "-644*y**5 - 736*y**4 + 1541*y**3 + 1836*y**2 - 90*y - 143", "step_length": 7} {"cot_id": "a041bc28592d481e63e3ddbc9eedfb97c170b90ba75dc54e5f5952187668e7b0", "datapoint": {"question": "Calculate the following: -59*x**2*(-27*x**3 - 28*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1593*x**5 + 1652*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 846, "polynomial_expr": "-59*x**2*(-27*x**3 - 28*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -59*x**2*(-27*x**3 - 28*x**2)\nExpanding the part (-27*x**3 - 28*x**2) using the distributive property, and we got: (-59*x**2)*(-28*x**2) + (-59*x**2)*(-27*x**3)\n#Step 2:\nCurrent expression: (-59*x**2)*(-28*x**2) + (-59*x**2)*(-27*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*x**2)*(-59*x**2) = 1652*x**4\n (-27*x**3)*(-59*x**2) = 1593*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1593*x**5 + 1652*x**4\nNo more calculations needed.\n1593*x**5 + 1652*x**4", "generated_answer": "1593*x**5 + 1652*x**4", "step_length": 3} {"cot_id": "43c75dcc0bd673cbe515a0951c00bac4c252e46ad612e2f33b82b00dc4b11acc", "datapoint": {"question": "Calculate the following: (27 - 87*z**3)*(7*z - 22)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-609*z**4 + 1914*z**3 + 189*z - 594", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 847, "polynomial_expr": "(27 - 87*z**3)*(7*z - 22)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27 - 87*z**3)*(7*z - 22)\nExpanding the part (7*z - 22) using the distributive property, and we got: (7*z)*(27 - 87*z**3) - 22*(27 - 87*z**3)\n#Step 2:\nCurrent expression: (7*z)*(27 - 87*z**3) - 22*(27 - 87*z**3)\nSimplifying the partial expression: -22*(27 - 87*z**3)\nExpanding the part (27 - 87*z**3) using the distributive property, and we got: -87*z**3*(-22) + 27*(-22)\nReplacing -22*(27 - 87*z**3) with -87*z**3*(-22) + 27*(-22) in the overall expression.\n#Step 3:\nCurrent expression: (7*z)*(27 - 87*z**3) - 87*z**3*(-22) - 594\nSimplifying the partial expression: (7*z)*(27 - 87*z**3)\nExpanding the part (27 - 87*z**3) using the distributive property, and we got: 27*(7*z) + (7*z)*(-87*z**3)\nReplacing (7*z)*(27 - 87*z**3) with 27*(7*z) + (7*z)*(-87*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 27*7*z + (7*z)*(-87*z**3) - 87*z**3*(-22) - 594\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-87*z**3)*-22 = 1914*z**3\n (-87*z**3)*(7*z) = -609*z**4\n 27*7*z = 189*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -609*z**4 + 1914*z**3 + 189*z - 594\nNo more calculations needed.\n-609*z**4 + 1914*z**3 + 189*z - 594", "generated_answer": "-609*z**4 + 1914*z**3 + 189*z - 594", "step_length": 5} {"cot_id": "175a143d595a468ee5a31083f62562a83edfc09849596d25c177d5cfdb45c128", "datapoint": {"question": "Calculate the following: (21*x**2 + 14*x)*(-29*x**3 + 44*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-609*x**5 + 518*x**4 + 616*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 848, "polynomial_expr": "(21*x**2 + 14*x)*(-29*x**3 + 44*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21*x**2 + 14*x)*(-29*x**3 + 44*x**2)\nExpanding the part (-29*x**3 + 44*x**2) using the distributive property, and we got: (44*x**2)*(21*x**2 + 14*x) + (-29*x**3)*(21*x**2 + 14*x)\n#Step 2:\nCurrent expression: (44*x**2)*(21*x**2 + 14*x) + (-29*x**3)*(21*x**2 + 14*x)\nSimplifying the partial expression: (-29*x**3)*(21*x**2 + 14*x)\nExpanding the part (21*x**2 + 14*x) using the distributive property, and we got: (14*x)*(-29*x**3) + (21*x**2)*(-29*x**3)\nReplacing (-29*x**3)*(21*x**2 + 14*x) with (14*x)*(-29*x**3) + (21*x**2)*(-29*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (14*x)*(-29*x**3) + (21*x**2)*(-29*x**3) + (44*x**2)*(21*x**2 + 14*x)\nSimplifying the partial expression: (44*x**2)*(21*x**2 + 14*x)\nExpanding the part (21*x**2 + 14*x) using the distributive property, and we got: (14*x)*(44*x**2) + (21*x**2)*(44*x**2)\nReplacing (44*x**2)*(21*x**2 + 14*x) with (14*x)*(44*x**2) + (21*x**2)*(44*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (14*x)*(44*x**2) + (14*x)*(-29*x**3) + (21*x**2)*(44*x**2) + (21*x**2)*(-29*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (14*x)*(-29*x**3) = -406*x**4\n (14*x)*(44*x**2) = 616*x**3\n (21*x**2)*(-29*x**3) = -609*x**5\n (21*x**2)*(44*x**2) = 924*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -609*x**5 - 406*x**4 + 924*x**4 + 616*x**3\nCombining like terms, got -609*x**5 + 518*x**4 + 616*x**3\n#Step 6:\nCurrent expression: -609*x**5 + 518*x**4 + 616*x**3\nNo more calculations needed.\n-609*x**5 + 518*x**4 + 616*x**3", "generated_answer": "-609*x**5 + 518*x**4 + 616*x**3", "step_length": 6} {"cot_id": "26ec0413556b57d9e1b71bf22f69480462a034b11da2eebc01498b8bdee2e5b8", "datapoint": {"question": "Simplify this expression: (-12*z**2 + 37*z)*(-16*z**3 - 23*z**2 + 34)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "192*z**5 - 316*z**4 - 851*z**3 - 408*z**2 + 1258*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 849, "polynomial_expr": "(-12*z**2 + 37*z)*(-16*z**3 - 23*z**2 + 34)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-12*z**2 + 37*z)*(-16*z**3 - 23*z**2 + 34)\nExpanding the part (-12*z**2 + 37*z) using the distributive property, and we got: (37*z)*(-16*z**3 - 23*z**2 + 34) + (-12*z**2)*(-16*z**3 - 23*z**2 + 34)\n#Step 2:\nCurrent expression: (37*z)*(-16*z**3 - 23*z**2 + 34) + (-12*z**2)*(-16*z**3 - 23*z**2 + 34)\nSimplifying the partial expression: (-12*z**2)*(-16*z**3 - 23*z**2 + 34)\nExpanding the part (-16*z**3 - 23*z**2 + 34) using the distributive property, and we got: 34*(-12*z**2) + (-23*z**2)*(-12*z**2) + (-12*z**2)*(-16*z**3)\nReplacing (-12*z**2)*(-16*z**3 - 23*z**2 + 34) with 34*(-12*z**2) + (-23*z**2)*(-12*z**2) + (-12*z**2)*(-16*z**3) in the overall expression.\n#Step 3:\nCurrent expression: 34*(-12)*z**2 + (37*z)*(-16*z**3 - 23*z**2 + 34) + (-23*z**2)*(-12*z**2) + (-12*z**2)*(-16*z**3)\nSimplifying the partial expression: (37*z)*(-16*z**3 - 23*z**2 + 34)\nExpanding the part (-16*z**3 - 23*z**2 + 34) using the distributive property, and we got: 34*(37*z) + (37*z)*(-23*z**2) + (37*z)*(-16*z**3)\nReplacing (37*z)*(-16*z**3 - 23*z**2 + 34) with 34*(37*z) + (37*z)*(-23*z**2) + (37*z)*(-16*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 34*(-12)*z**2 + 34*37*z + (37*z)*(-23*z**2) + (37*z)*(-16*z**3) + (-23*z**2)*(-12*z**2) + (-12*z**2)*(-16*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*z**2)*(-12*z**2) = 276*z**4\n (-23*z**2)*(37*z) = -851*z**3\n (-16*z**3)*(-12*z**2) = 192*z**5\n (-16*z**3)*(37*z) = -592*z**4\n 34*-12*z**2 = -408*z**2\n 34*37*z = 1258*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 192*z**5 - 592*z**4 + 276*z**4 - 851*z**3 - 408*z**2 + 1258*z\nCombining like terms, got 192*z**5 - 316*z**4 - 851*z**3 - 408*z**2 + 1258*z\n#Step 6:\nCurrent expression: 192*z**5 - 316*z**4 - 851*z**3 - 408*z**2 + 1258*z\nNo more calculations needed.\n192*z**5 - 316*z**4 - 851*z**3 - 408*z**2 + 1258*z", "generated_answer": "192*z**5 - 316*z**4 - 851*z**3 - 408*z**2 + 1258*z", "step_length": 6} {"cot_id": "62f97215a668beadf46781ae789a123d8b1d4848a07c3f1fc42e87adba627536", "datapoint": {"question": "Simplify this expression: 85*x**3 + 221*x + 51\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "85*x**3 + 221*x + 51", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 850, "polynomial_expr": "85*x**3 + 221*x + 51", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 85*x**3 + 221*x + 51\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 85*x**3 + 221*x + 51\nNo more calculations needed.\n85*x**3 + 221*x + 51", "generated_answer": "85*x**3 + 221*x + 51", "step_length": 2} {"cot_id": "e928e3629b7bf165bfd1a376fe752ffb7dc2ccaa84a88c637a79c35087f12613", "datapoint": {"question": "Calculate the following: (42*z**3 - 43*z)*(-33*z**3 - 9*z**2 - 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1386*z**6 - 378*z**5 + 1419*z**4 - 33*z**3 + 430*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 851, "polynomial_expr": "(42*z**3 - 43*z)*(-33*z**3 - 9*z**2 - 10)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (42*z**3 - 43*z)*(-33*z**3 - 9*z**2 - 10)\nExpanding the part (42*z**3 - 43*z) using the distributive property, and we got: (-43*z)*(-33*z**3 - 9*z**2 - 10) + (42*z**3)*(-33*z**3 - 9*z**2 - 10)\n#Step 2:\nCurrent expression: (-43*z)*(-33*z**3 - 9*z**2 - 10) + (42*z**3)*(-33*z**3 - 9*z**2 - 10)\nSimplifying the partial expression: (-43*z)*(-33*z**3 - 9*z**2 - 10)\nExpanding the part (-33*z**3 - 9*z**2 - 10) using the distributive property, and we got: (-43*z)*(-9*z**2) + (-43*z)*(-33*z**3) - (-1)*430*z\nReplacing (-43*z)*(-33*z**3 - 9*z**2 - 10) with (-43*z)*(-9*z**2) + (-43*z)*(-33*z**3) - (-1)*430*z in the overall expression.\n#Step 3:\nCurrent expression: (-43*z)*(-9*z**2) + (-43*z)*(-33*z**3) - 10*(-43)*z + (42*z**3)*(-33*z**3 - 9*z**2 - 10)\nSimplifying the partial expression: (42*z**3)*(-33*z**3 - 9*z**2 - 10)\nExpanding the part (-33*z**3 - 9*z**2 - 10) using the distributive property, and we got: -420*z**3 + (-9*z**2)*(42*z**3) + (-33*z**3)*(42*z**3)\nReplacing (42*z**3)*(-33*z**3 - 9*z**2 - 10) with -420*z**3 + (-9*z**2)*(42*z**3) + (-33*z**3)*(42*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-43*z)*(-9*z**2) + (-43*z)*(-33*z**3) - 10*42*z**3 - 10*(-43)*z + (-9*z**2)*(42*z**3) + (-33*z**3)*(42*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*z**3)*(-43*z) = 1419*z**4\n (-33*z**3)*(42*z**3) = -1386*z**6\n (-9*z**2)*(-43*z) = 387*z**3\n (-9*z**2)*(42*z**3) = -378*z**5\n -10*-43*z = 430*z\n -10*42*z**3 = -420*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1386*z**6 - 378*z**5 + 1419*z**4 - 420*z**3 + 387*z**3 + 430*z\nCombining like terms, got -1386*z**6 - 378*z**5 + 1419*z**4 - 33*z**3 + 430*z\n#Step 6:\nCurrent expression: -1386*z**6 - 378*z**5 + 1419*z**4 - 33*z**3 + 430*z\nNo more calculations needed.\n-1386*z**6 - 378*z**5 + 1419*z**4 - 33*z**3 + 430*z", "generated_answer": "-1386*z**6 - 378*z**5 + 1419*z**4 - 33*z**3 + 430*z", "step_length": 6} {"cot_id": "e33bc2f533e3df0f04a515bed5562f3e4a113854ac8c82efe67c3ef23ad60b47", "datapoint": {"question": "Calculate the following: (44*y - 38)*(40*y**3 - 16*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1760*y**4 - 1520*y**3 - 704*y**2 + 608*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 852, "polynomial_expr": "(44*y - 38)*(40*y**3 - 16*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (44*y - 38)*(40*y**3 - 16*y)\nExpanding the part (44*y - 38) using the distributive property, and we got: (44*y)*(40*y**3 - 16*y) - 38*(40*y**3 - 16*y)\n#Step 2:\nCurrent expression: (44*y)*(40*y**3 - 16*y) - 38*(40*y**3 - 16*y)\nSimplifying the partial expression: -38*(40*y**3 - 16*y)\nExpanding the part (40*y**3 - 16*y) using the distributive property, and we got: -16*y*(-38) + (40*y**3)*(-38)\nReplacing -38*(40*y**3 - 16*y) with -16*y*(-38) + (40*y**3)*(-38) in the overall expression.\n#Step 3:\nCurrent expression: -16*y*(-38) + (44*y)*(40*y**3 - 16*y) + (40*y**3)*(-38)\nSimplifying the partial expression: (44*y)*(40*y**3 - 16*y)\nExpanding the part (40*y**3 - 16*y) using the distributive property, and we got: (-16*y)*(44*y) + (44*y)*(40*y**3)\nReplacing (44*y)*(40*y**3 - 16*y) with (-16*y)*(44*y) + (44*y)*(40*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-16*y)*(44*y) - 16*y*(-38) + (44*y)*(40*y**3) + (40*y**3)*(-38)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-16*y)*-38 = 608*y\n (-16*y)*(44*y) = -704*y**2\n (40*y**3)*-38 = -1520*y**3\n (40*y**3)*(44*y) = 1760*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1760*y**4 - 1520*y**3 - 704*y**2 + 608*y\nNo more calculations needed.\n1760*y**4 - 1520*y**3 - 704*y**2 + 608*y", "generated_answer": "1760*y**4 - 1520*y**3 - 704*y**2 + 608*y", "step_length": 5} {"cot_id": "e79895aa560c316a26ab66e95557899d92e706f1650882d8898b39d0ee90762c", "datapoint": {"question": "Simplify this expression: (64*z**2 - 15)*(-42*z**3 - 35*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2688*z**5 - 1610*z**3 + 525*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 853, "polynomial_expr": "(64*z**2 - 15)*(-42*z**3 - 35*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (64*z**2 - 15)*(-42*z**3 - 35*z)\nExpanding the part (64*z**2 - 15) using the distributive property, and we got: (64*z**2)*(-42*z**3 - 35*z) - 15*(-42*z**3 - 35*z)\n#Step 2:\nCurrent expression: (64*z**2)*(-42*z**3 - 35*z) - 15*(-42*z**3 - 35*z)\nSimplifying the partial expression: -15*(-42*z**3 - 35*z)\nExpanding the part (-42*z**3 - 35*z) using the distributive property, and we got: -35*z*(-15) - 42*z**3*(-15)\nReplacing -15*(-42*z**3 - 35*z) with -35*z*(-15) - 42*z**3*(-15) in the overall expression.\n#Step 3:\nCurrent expression: -35*z*(-15) + (64*z**2)*(-42*z**3 - 35*z) - 42*z**3*(-15)\nSimplifying the partial expression: (64*z**2)*(-42*z**3 - 35*z)\nExpanding the part (-42*z**3 - 35*z) using the distributive property, and we got: (-35*z)*(64*z**2) + (64*z**2)*(-42*z**3)\nReplacing (64*z**2)*(-42*z**3 - 35*z) with (-35*z)*(64*z**2) + (64*z**2)*(-42*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-35*z)*(64*z**2) - 35*z*(-15) + (64*z**2)*(-42*z**3) - 42*z**3*(-15)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*z**3)*-15 = 630*z**3\n (-42*z**3)*(64*z**2) = -2688*z**5\n (-35*z)*-15 = 525*z\n (-35*z)*(64*z**2) = -2240*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2688*z**5 - 2240*z**3 + 630*z**3 + 525*z\nCombining like terms, got -2688*z**5 - 1610*z**3 + 525*z\n#Step 6:\nCurrent expression: -2688*z**5 - 1610*z**3 + 525*z\nNo more calculations needed.\n-2688*z**5 - 1610*z**3 + 525*z", "generated_answer": "-2688*z**5 - 1610*z**3 + 525*z", "step_length": 6} {"cot_id": "4a5354294877c47603811a96509dbf3eaff8cce6bd4b94b660aece2f07f0c201", "datapoint": {"question": "Calculate the following: (-21*x**3 - 18*x**2)*(-12*x**2 - 9*x + 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "252*x**5 + 405*x**4 + 141*x**3 - 18*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 854, "polynomial_expr": "(-21*x**3 - 18*x**2)*(-12*x**2 - 9*x + 1)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-21*x**3 - 18*x**2)*(-12*x**2 - 9*x + 1)\nExpanding the part (-21*x**3 - 18*x**2) using the distributive property, and we got: (-18*x**2)*(-12*x**2 - 9*x + 1) + (-21*x**3)*(-12*x**2 - 9*x + 1)\n#Step 2:\nCurrent expression: (-18*x**2)*(-12*x**2 - 9*x + 1) + (-21*x**3)*(-12*x**2 - 9*x + 1)\nSimplifying the partial expression: (-21*x**3)*(-12*x**2 - 9*x + 1)\nExpanding the part (-12*x**2 - 9*x + 1) using the distributive property, and we got: (-9*x)*(-21*x**3) + 1*(-21*x**3) + (-12*x**2)*(-21*x**3)\nReplacing (-21*x**3)*(-12*x**2 - 9*x + 1) with (-9*x)*(-21*x**3) + 1*(-21*x**3) + (-12*x**2)*(-21*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-9*x)*(-21*x**3) - 21*x**3 + (-18*x**2)*(-12*x**2 - 9*x + 1) + (-12*x**2)*(-21*x**3)\nSimplifying the partial expression: (-18*x**2)*(-12*x**2 - 9*x + 1)\nExpanding the part (-12*x**2 - 9*x + 1) using the distributive property, and we got: (-9*x)*(-18*x**2) + 1*(-18*x**2) + (-18*x**2)*(-12*x**2)\nReplacing (-18*x**2)*(-12*x**2 - 9*x + 1) with (-9*x)*(-18*x**2) + 1*(-18*x**2) + (-18*x**2)*(-12*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-9*x)*(-18*x**2) + (-9*x)*(-21*x**3) - 21*x**3 - 18*x**2 + (-18*x**2)*(-12*x**2) + (-12*x**2)*(-21*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*x**2)*(-21*x**3) = 252*x**5\n (-12*x**2)*(-18*x**2) = 216*x**4\n (-9*x)*(-21*x**3) = 189*x**4\n (-9*x)*(-18*x**2) = 162*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 252*x**5 + 189*x**4 + 216*x**4 - 21*x**3 + 162*x**3 - 18*x**2\nCombining like terms, got 252*x**5 + 405*x**4 + 141*x**3 - 18*x**2\n#Step 6:\nCurrent expression: 252*x**5 + 405*x**4 + 141*x**3 - 18*x**2\nNo more calculations needed.\n252*x**5 + 405*x**4 + 141*x**3 - 18*x**2", "generated_answer": "252*x**5 + 405*x**4 + 141*x**3 - 18*x**2", "step_length": 6} {"cot_id": "78c645f458260a1893dea8a9ed72e63ef348500588e0704396ca324fc4c933ea", "datapoint": {"question": "Simplify this expression: -25*x**3*(68*x**2 - 25*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1700*x**5 + 625*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 855, "polynomial_expr": "-25*x**3*(68*x**2 - 25*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -25*x**3*(68*x**2 - 25*x)\nExpanding the part (68*x**2 - 25*x) using the distributive property, and we got: (-25*x)*(-25*x**3) + (68*x**2)*(-25*x**3)\n#Step 2:\nCurrent expression: (-25*x)*(-25*x**3) + (68*x**2)*(-25*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*x)*(-25*x**3) = 625*x**4\n (68*x**2)*(-25*x**3) = -1700*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1700*x**5 + 625*x**4\nNo more calculations needed.\n-1700*x**5 + 625*x**4", "generated_answer": "-1700*x**5 + 625*x**4", "step_length": 3} {"cot_id": "f25486d4a525193c9b9e98a2cec3487fa74f6bd176f6acf02e16c38f65119373", "datapoint": {"question": "Calculate the following: 6*y**3*(70*y**3 + 36*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "420*y**6 + 216*y**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 856, "polynomial_expr": "6*y**3*(70*y**3 + 36*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 6*y**3*(70*y**3 + 36*y)\nExpanding the part (70*y**3 + 36*y) using the distributive property, and we got: (36*y)*(6*y**3) + (6*y**3)*(70*y**3)\n#Step 2:\nCurrent expression: (36*y)*(6*y**3) + (6*y**3)*(70*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (36*y)*(6*y**3) = 216*y**4\n (70*y**3)*(6*y**3) = 420*y**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 420*y**6 + 216*y**4\nNo more calculations needed.\n420*y**6 + 216*y**4", "generated_answer": "420*y**6 + 216*y**4", "step_length": 3} {"cot_id": "55fe876f246ef5b0d441a63dba15bb9aa9300c914ce55fe0258e3f86397f462f", "datapoint": {"question": "Simplify this expression: (1 - 36*x**2)*(31*x**2 - 57*x - 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1116*x**4 + 2052*x**3 + 391*x**2 - 57*x - 10", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 857, "polynomial_expr": "(1 - 36*x**2)*(31*x**2 - 57*x - 10)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (1 - 36*x**2)*(31*x**2 - 57*x - 10)\nExpanding the part (1 - 36*x**2) using the distributive property, and we got: (-36*x**2)*(31*x**2 - 57*x - 10) + 1*(31*x**2 - 57*x - 10)\n#Step 2:\nCurrent expression: (-36*x**2)*(31*x**2 - 57*x - 10) + 1*(31*x**2 - 57*x - 10)\nSimplifying the partial expression: 1*(31*x**2 - 57*x - 10)\nExpanding the part (31*x**2 - 57*x - 10) using the distributive property, and we got: -57*x*1 + (31*x**2)*1 - 10*1\nReplacing 1*(31*x**2 - 57*x - 10) with -57*x*1 + (31*x**2)*1 - 10*1 in the overall expression.\n#Step 3:\nCurrent expression: -57*x*1 + (-36*x**2)*(31*x**2 - 57*x - 10) + (31*x**2)*1 - 10\nSimplifying the partial expression: (-36*x**2)*(31*x**2 - 57*x - 10)\nExpanding the part (31*x**2 - 57*x - 10) using the distributive property, and we got: (-57*x)*(-36*x**2) - (-1)*360*x**2 + (-36*x**2)*(31*x**2)\nReplacing (-36*x**2)*(31*x**2 - 57*x - 10) with (-57*x)*(-36*x**2) - (-1)*360*x**2 + (-36*x**2)*(31*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-57*x)*(-36*x**2) - 57*x*1 - 10*(-36)*x**2 + (-36*x**2)*(31*x**2) + (31*x**2)*1 - 10\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-57*x)*1 = -57*x\n (-57*x)*(-36*x**2) = 2052*x**3\n (31*x**2)*1 = 31*x**2\n (31*x**2)*(-36*x**2) = -1116*x**4\n -10*-36*x**2 = 360*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1116*x**4 + 2052*x**3 + 31*x**2 + 360*x**2 - 57*x - 10\nCombining like terms, got -1116*x**4 + 2052*x**3 + 391*x**2 - 57*x - 10\n#Step 6:\nCurrent expression: -1116*x**4 + 2052*x**3 + 391*x**2 - 57*x - 10\nNo more calculations needed.\n-1116*x**4 + 2052*x**3 + 391*x**2 - 57*x - 10", "generated_answer": "-1116*x**4 + 2052*x**3 + 391*x**2 - 57*x - 10", "step_length": 6} {"cot_id": "e3daa938d0b37dffa356407cc8706e50d47cebda882f7ab2fcb12750cd97f39b", "datapoint": {"question": "Calculate the following: (58*z + 42)*(49*z**3 + 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2842*z**4 + 2058*z**3 + 2378*z + 1722", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 858, "polynomial_expr": "(58*z + 42)*(49*z**3 + 41)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (58*z + 42)*(49*z**3 + 41)\nExpanding the part (49*z**3 + 41) using the distributive property, and we got: (49*z**3)*(58*z + 42) + 41*(58*z + 42)\n#Step 2:\nCurrent expression: (49*z**3)*(58*z + 42) + 41*(58*z + 42)\nSimplifying the partial expression: 41*(58*z + 42)\nExpanding the part (58*z + 42) using the distributive property, and we got: (58*z)*41 + 42*41\nReplacing 41*(58*z + 42) with (58*z)*41 + 42*41 in the overall expression.\n#Step 3:\nCurrent expression: (58*z)*41 + (49*z**3)*(58*z + 42) + 1722\nSimplifying the partial expression: (49*z**3)*(58*z + 42)\nExpanding the part (58*z + 42) using the distributive property, and we got: 42*(49*z**3) + (58*z)*(49*z**3)\nReplacing (49*z**3)*(58*z + 42) with 42*(49*z**3) + (58*z)*(49*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 42*49*z**3 + (58*z)*(49*z**3) + (58*z)*41 + 1722\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (58*z)*41 = 2378*z\n (58*z)*(49*z**3) = 2842*z**4\n 42*49*z**3 = 2058*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2842*z**4 + 2058*z**3 + 2378*z + 1722\nNo more calculations needed.\n2842*z**4 + 2058*z**3 + 2378*z + 1722", "generated_answer": "2842*z**4 + 2058*z**3 + 2378*z + 1722", "step_length": 5} {"cot_id": "dfc4251a4e335084160bb647cccca550d5c4077e4a493900a8454e2a75857b07", "datapoint": {"question": "Simplify this expression: (-49*y**2 - 38)*(30*y**3 + 32*y**2 + 36*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1470*y**5 - 1568*y**4 - 2904*y**3 - 1216*y**2 - 1368*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 859, "polynomial_expr": "(-49*y**2 - 38)*(30*y**3 + 32*y**2 + 36*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-49*y**2 - 38)*(30*y**3 + 32*y**2 + 36*y)\nExpanding the part (-49*y**2 - 38) using the distributive property, and we got: (-49*y**2)*(30*y**3 + 32*y**2 + 36*y) - 38*(30*y**3 + 32*y**2 + 36*y)\n#Step 2:\nCurrent expression: (-49*y**2)*(30*y**3 + 32*y**2 + 36*y) - 38*(30*y**3 + 32*y**2 + 36*y)\nSimplifying the partial expression: -38*(30*y**3 + 32*y**2 + 36*y)\nExpanding the part (30*y**3 + 32*y**2 + 36*y) using the distributive property, and we got: (36*y)*(-38) + (32*y**2)*(-38) + (30*y**3)*(-38)\nReplacing -38*(30*y**3 + 32*y**2 + 36*y) with (36*y)*(-38) + (32*y**2)*(-38) + (30*y**3)*(-38) in the overall expression.\n#Step 3:\nCurrent expression: (36*y)*(-38) + (-49*y**2)*(30*y**3 + 32*y**2 + 36*y) + (32*y**2)*(-38) + (30*y**3)*(-38)\nSimplifying the partial expression: (-49*y**2)*(30*y**3 + 32*y**2 + 36*y)\nExpanding the part (30*y**3 + 32*y**2 + 36*y) using the distributive property, and we got: (36*y)*(-49*y**2) + (-49*y**2)*(32*y**2) + (-49*y**2)*(30*y**3)\nReplacing (-49*y**2)*(30*y**3 + 32*y**2 + 36*y) with (36*y)*(-49*y**2) + (-49*y**2)*(32*y**2) + (-49*y**2)*(30*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (36*y)*(-49*y**2) + (36*y)*(-38) + (-49*y**2)*(32*y**2) + (-49*y**2)*(30*y**3) + (32*y**2)*(-38) + (30*y**3)*(-38)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (30*y**3)*-38 = -1140*y**3\n (30*y**3)*(-49*y**2) = -1470*y**5\n (32*y**2)*-38 = -1216*y**2\n (32*y**2)*(-49*y**2) = -1568*y**4\n (36*y)*-38 = -1368*y\n (36*y)*(-49*y**2) = -1764*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1470*y**5 - 1568*y**4 - 1764*y**3 - 1140*y**3 - 1216*y**2 - 1368*y\nCombining like terms, got -1470*y**5 - 1568*y**4 - 2904*y**3 - 1216*y**2 - 1368*y\n#Step 6:\nCurrent expression: -1470*y**5 - 1568*y**4 - 2904*y**3 - 1216*y**2 - 1368*y\nNo more calculations needed.\n-1470*y**5 - 1568*y**4 - 2904*y**3 - 1216*y**2 - 1368*y", "generated_answer": "-1470*y**5 - 1568*y**4 - 2904*y**3 - 1216*y**2 - 1368*y", "step_length": 6} {"cot_id": "c6785e6bb638c55fdadfa280e8cc9349bf5fec445fcc1fda614b846b7a1dbf96", "datapoint": {"question": "Simplify this expression: (10*y + 40)*(-45*y**2 - 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-450*y**3 - 1800*y**2 - 330*y - 1320", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 860, "polynomial_expr": "(10*y + 40)*(-45*y**2 - 33)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (10*y + 40)*(-45*y**2 - 33)\nExpanding the part (-45*y**2 - 33) using the distributive property, and we got: (-45*y**2)*(10*y + 40) - 33*(10*y + 40)\n#Step 2:\nCurrent expression: (-45*y**2)*(10*y + 40) - 33*(10*y + 40)\nSimplifying the partial expression: -33*(10*y + 40)\nExpanding the part (10*y + 40) using the distributive property, and we got: (10*y)*(-33) + 40*(-33)\nReplacing -33*(10*y + 40) with (10*y)*(-33) + 40*(-33) in the overall expression.\n#Step 3:\nCurrent expression: (10*y)*(-33) + (-45*y**2)*(10*y + 40) - 1320\nSimplifying the partial expression: (-45*y**2)*(10*y + 40)\nExpanding the part (10*y + 40) using the distributive property, and we got: 40*(-45*y**2) + (10*y)*(-45*y**2)\nReplacing (-45*y**2)*(10*y + 40) with 40*(-45*y**2) + (10*y)*(-45*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 40*(-45)*y**2 + (10*y)*(-45*y**2) + (10*y)*(-33) - 1320\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (10*y)*-33 = -330*y\n (10*y)*(-45*y**2) = -450*y**3\n 40*-45*y**2 = -1800*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -450*y**3 - 1800*y**2 - 330*y - 1320\nNo more calculations needed.\n-450*y**3 - 1800*y**2 - 330*y - 1320", "generated_answer": "-450*y**3 - 1800*y**2 - 330*y - 1320", "step_length": 5} {"cot_id": "c27fe4308e25e8eac2877c491131a3da2724c7a67f69a0bf3a4f96f0f6b31ef8", "datapoint": {"question": "Calculate the following: (67 - 13*x**3)*(-24*x**3 - 42*x**2 + 49*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "312*x**6 + 546*x**5 - 637*x**4 - 1608*x**3 - 2814*x**2 + 3283*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 861, "polynomial_expr": "(67 - 13*x**3)*(-24*x**3 - 42*x**2 + 49*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (67 - 13*x**3)*(-24*x**3 - 42*x**2 + 49*x)\nExpanding the part (67 - 13*x**3) using the distributive property, and we got: (-13*x**3)*(-24*x**3 - 42*x**2 + 49*x) + 67*(-24*x**3 - 42*x**2 + 49*x)\n#Step 2:\nCurrent expression: (-13*x**3)*(-24*x**3 - 42*x**2 + 49*x) + 67*(-24*x**3 - 42*x**2 + 49*x)\nSimplifying the partial expression: 67*(-24*x**3 - 42*x**2 + 49*x)\nExpanding the part (-24*x**3 - 42*x**2 + 49*x) using the distributive property, and we got: (49*x)*67 - 42*x**2*67 - 24*x**3*67\nReplacing 67*(-24*x**3 - 42*x**2 + 49*x) with (49*x)*67 - 42*x**2*67 - 24*x**3*67 in the overall expression.\n#Step 3:\nCurrent expression: (49*x)*67 - 42*x**2*67 - 24*x**3*67 + (-13*x**3)*(-24*x**3 - 42*x**2 + 49*x)\nSimplifying the partial expression: (-13*x**3)*(-24*x**3 - 42*x**2 + 49*x)\nExpanding the part (-24*x**3 - 42*x**2 + 49*x) using the distributive property, and we got: (49*x)*(-13*x**3) + (-42*x**2)*(-13*x**3) + (-24*x**3)*(-13*x**3)\nReplacing (-13*x**3)*(-24*x**3 - 42*x**2 + 49*x) with (49*x)*(-13*x**3) + (-42*x**2)*(-13*x**3) + (-24*x**3)*(-13*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (49*x)*(-13*x**3) + (49*x)*67 + (-42*x**2)*(-13*x**3) - 42*x**2*67 + (-24*x**3)*(-13*x**3) - 24*x**3*67\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*x**2)*67 = -2814*x**2\n (-42*x**2)*(-13*x**3) = 546*x**5\n (-24*x**3)*67 = -1608*x**3\n (-24*x**3)*(-13*x**3) = 312*x**6\n (49*x)*67 = 3283*x\n (49*x)*(-13*x**3) = -637*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 312*x**6 + 546*x**5 - 637*x**4 - 1608*x**3 - 2814*x**2 + 3283*x\nNo more calculations needed.\n312*x**6 + 546*x**5 - 637*x**4 - 1608*x**3 - 2814*x**2 + 3283*x", "generated_answer": "312*x**6 + 546*x**5 - 637*x**4 - 1608*x**3 - 2814*x**2 + 3283*x", "step_length": 5} {"cot_id": "d03b0ca3e458e730501c613dc59ca3510b9702e21cea6e2adab8707f3716ebe2", "datapoint": {"question": "Simplify this expression: (8 - 17*z**3)*(-101*z**3 + 21*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1717*z**6 - 357*z**5 - 808*z**3 + 168*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 862, "polynomial_expr": "(8 - 17*z**3)*(-101*z**3 + 21*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (8 - 17*z**3)*(-101*z**3 + 21*z**2)\nExpanding the part (8 - 17*z**3) using the distributive property, and we got: (-17*z**3)*(-101*z**3 + 21*z**2) + 8*(-101*z**3 + 21*z**2)\n#Step 2:\nCurrent expression: (-17*z**3)*(-101*z**3 + 21*z**2) + 8*(-101*z**3 + 21*z**2)\nSimplifying the partial expression: 8*(-101*z**3 + 21*z**2)\nExpanding the part (-101*z**3 + 21*z**2) using the distributive property, and we got: (21*z**2)*8 - 101*z**3*8\nReplacing 8*(-101*z**3 + 21*z**2) with (21*z**2)*8 - 101*z**3*8 in the overall expression.\n#Step 3:\nCurrent expression: (21*z**2)*8 - 101*z**3*8 + (-17*z**3)*(-101*z**3 + 21*z**2)\nSimplifying the partial expression: (-17*z**3)*(-101*z**3 + 21*z**2)\nExpanding the part (-101*z**3 + 21*z**2) using the distributive property, and we got: (21*z**2)*(-17*z**3) + (-101*z**3)*(-17*z**3)\nReplacing (-17*z**3)*(-101*z**3 + 21*z**2) with (21*z**2)*(-17*z**3) + (-101*z**3)*(-17*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (21*z**2)*(-17*z**3) + (21*z**2)*8 + (-101*z**3)*(-17*z**3) - 101*z**3*8\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-101*z**3)*8 = -808*z**3\n (-101*z**3)*(-17*z**3) = 1717*z**6\n (21*z**2)*8 = 168*z**2\n (21*z**2)*(-17*z**3) = -357*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1717*z**6 - 357*z**5 - 808*z**3 + 168*z**2\nNo more calculations needed.\n1717*z**6 - 357*z**5 - 808*z**3 + 168*z**2", "generated_answer": "1717*z**6 - 357*z**5 - 808*z**3 + 168*z**2", "step_length": 5} {"cot_id": "9198d076d2fed47b281f6bb7cc4ab8cce7820c317745945099b950aa27f42117", "datapoint": {"question": "Simplify this expression: (37*z**3 + 57*z**2)*(38*z**3 + 26*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1406*z**6 + 3128*z**5 + 1482*z**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 863, "polynomial_expr": "(37*z**3 + 57*z**2)*(38*z**3 + 26*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (37*z**3 + 57*z**2)*(38*z**3 + 26*z**2)\nExpanding the part (38*z**3 + 26*z**2) using the distributive property, and we got: (26*z**2)*(37*z**3 + 57*z**2) + (38*z**3)*(37*z**3 + 57*z**2)\n#Step 2:\nCurrent expression: (26*z**2)*(37*z**3 + 57*z**2) + (38*z**3)*(37*z**3 + 57*z**2)\nSimplifying the partial expression: (26*z**2)*(37*z**3 + 57*z**2)\nExpanding the part (37*z**3 + 57*z**2) using the distributive property, and we got: (26*z**2)*(57*z**2) + (26*z**2)*(37*z**3)\nReplacing (26*z**2)*(37*z**3 + 57*z**2) with (26*z**2)*(57*z**2) + (26*z**2)*(37*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (26*z**2)*(57*z**2) + (26*z**2)*(37*z**3) + (38*z**3)*(37*z**3 + 57*z**2)\nSimplifying the partial expression: (38*z**3)*(37*z**3 + 57*z**2)\nExpanding the part (37*z**3 + 57*z**2) using the distributive property, and we got: (57*z**2)*(38*z**3) + (37*z**3)*(38*z**3)\nReplacing (38*z**3)*(37*z**3 + 57*z**2) with (57*z**2)*(38*z**3) + (37*z**3)*(38*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (26*z**2)*(57*z**2) + (26*z**2)*(37*z**3) + (57*z**2)*(38*z**3) + (37*z**3)*(38*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (37*z**3)*(26*z**2) = 962*z**5\n (37*z**3)*(38*z**3) = 1406*z**6\n (57*z**2)*(26*z**2) = 1482*z**4\n (57*z**2)*(38*z**3) = 2166*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1406*z**6 + 962*z**5 + 2166*z**5 + 1482*z**4\nCombining like terms, got 1406*z**6 + 3128*z**5 + 1482*z**4\n#Step 6:\nCurrent expression: 1406*z**6 + 3128*z**5 + 1482*z**4\nNo more calculations needed.\n1406*z**6 + 3128*z**5 + 1482*z**4", "generated_answer": "1406*z**6 + 3128*z**5 + 1482*z**4", "step_length": 6} {"cot_id": "d15c0bbcff35d95b9492d94cfc800e7c32c53eb2685f82ffdfd8d6c6fbc4e9c0", "datapoint": {"question": "Calculate the following: (13*x**2 + 24*x - 27)*(-29*x**3 + 45*x**2 - 27*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-377*x**5 - 111*x**4 + 1512*x**3 - 1863*x**2 + 729*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 864, "polynomial_expr": "(13*x**2 + 24*x - 27)*(-29*x**3 + 45*x**2 - 27*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (13*x**2 + 24*x - 27)*(-29*x**3 + 45*x**2 - 27*x)\nExpanding the part (13*x**2 + 24*x - 27) using the distributive property, and we got: (24*x)*(-29*x**3 + 45*x**2 - 27*x) + (13*x**2)*(-29*x**3 + 45*x**2 - 27*x) - 27*(-29*x**3 + 45*x**2 - 27*x)\n#Step 2:\nCurrent expression: (24*x)*(-29*x**3 + 45*x**2 - 27*x) + (13*x**2)*(-29*x**3 + 45*x**2 - 27*x) - 27*(-29*x**3 + 45*x**2 - 27*x)\nSimplifying the partial expression: -27*(-29*x**3 + 45*x**2 - 27*x)\nExpanding the part (-29*x**3 + 45*x**2 - 27*x) using the distributive property, and we got: -27*x*(-27) + (45*x**2)*(-27) - 29*x**3*(-27)\nReplacing -27*(-29*x**3 + 45*x**2 - 27*x) with -27*x*(-27) + (45*x**2)*(-27) - 29*x**3*(-27) in the overall expression.\n#Step 3:\nCurrent expression: -27*x*(-27) + (24*x)*(-29*x**3 + 45*x**2 - 27*x) + (13*x**2)*(-29*x**3 + 45*x**2 - 27*x) + (45*x**2)*(-27) - 29*x**3*(-27)\nSimplifying the partial expression: (13*x**2)*(-29*x**3 + 45*x**2 - 27*x)\nExpanding the part (-29*x**3 + 45*x**2 - 27*x) using the distributive property, and we got: (-27*x)*(13*x**2) + (13*x**2)*(45*x**2) + (13*x**2)*(-29*x**3)\nReplacing (13*x**2)*(-29*x**3 + 45*x**2 - 27*x) with (-27*x)*(13*x**2) + (13*x**2)*(45*x**2) + (13*x**2)*(-29*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-27*x)*(13*x**2) - 27*x*(-27) + (24*x)*(-29*x**3 + 45*x**2 - 27*x) + (13*x**2)*(45*x**2) + (13*x**2)*(-29*x**3) + (45*x**2)*(-27) - 29*x**3*(-27)\nSimplifying the partial expression: (24*x)*(-29*x**3 + 45*x**2 - 27*x)\nExpanding the part (-29*x**3 + 45*x**2 - 27*x) using the distributive property, and we got: (-27*x)*(24*x) + (24*x)*(45*x**2) + (24*x)*(-29*x**3)\nReplacing (24*x)*(-29*x**3 + 45*x**2 - 27*x) with (-27*x)*(24*x) + (24*x)*(45*x**2) + (24*x)*(-29*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-27*x)*(24*x) + (-27*x)*(13*x**2) - 27*x*(-27) + (24*x)*(45*x**2) + (24*x)*(-29*x**3) + (13*x**2)*(45*x**2) + (13*x**2)*(-29*x**3) + (45*x**2)*(-27) - 29*x**3*(-27)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*x**3)*-27 = 783*x**3\n (-29*x**3)*(13*x**2) = -377*x**5\n (-29*x**3)*(24*x) = -696*x**4\n (-27*x)*-27 = 729*x\n (-27*x)*(13*x**2) = -351*x**3\n (-27*x)*(24*x) = -648*x**2\n (45*x**2)*-27 = -1215*x**2\n (45*x**2)*(13*x**2) = 585*x**4\n (45*x**2)*(24*x) = 1080*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -377*x**5 - 696*x**4 + 585*x**4 - 351*x**3 + 783*x**3 + 1080*x**3 - 1215*x**2 - 648*x**2 + 729*x\nCombining like terms, got -377*x**5 - 111*x**4 + 1512*x**3 - 1863*x**2 + 729*x\n#Step 7:\nCurrent expression: -377*x**5 - 111*x**4 + 1512*x**3 - 1863*x**2 + 729*x\nNo more calculations needed.\n-377*x**5 - 111*x**4 + 1512*x**3 - 1863*x**2 + 729*x", "generated_answer": "-377*x**5 - 111*x**4 + 1512*x**3 - 1863*x**2 + 729*x", "step_length": 7} {"cot_id": "3850f632c5d052e29572d2aa1398c9078996219e16bda9391916dd79e80f4511", "datapoint": {"question": "Calculate the following: (31 - 10*z)*(-13*z**2 - 46)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "130*z**3 - 403*z**2 + 460*z - 1426", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 865, "polynomial_expr": "(31 - 10*z)*(-13*z**2 - 46)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31 - 10*z)*(-13*z**2 - 46)\nExpanding the part (-13*z**2 - 46) using the distributive property, and we got: (-13*z**2)*(31 - 10*z) - 46*(31 - 10*z)\n#Step 2:\nCurrent expression: (-13*z**2)*(31 - 10*z) - 46*(31 - 10*z)\nSimplifying the partial expression: -46*(31 - 10*z)\nExpanding the part (31 - 10*z) using the distributive property, and we got: -10*z*(-46) + 31*(-46)\nReplacing -46*(31 - 10*z) with -10*z*(-46) + 31*(-46) in the overall expression.\n#Step 3:\nCurrent expression: -10*z*(-46) + (-13*z**2)*(31 - 10*z) - 1426\nSimplifying the partial expression: (-13*z**2)*(31 - 10*z)\nExpanding the part (31 - 10*z) using the distributive property, and we got: (-10*z)*(-13*z**2) + 31*(-13*z**2)\nReplacing (-13*z**2)*(31 - 10*z) with (-10*z)*(-13*z**2) + 31*(-13*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-10*z)*(-13*z**2) - 10*z*(-46) + 31*(-13)*z**2 - 1426\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*z)*-46 = 460*z\n (-10*z)*(-13*z**2) = 130*z**3\n 31*-13*z**2 = -403*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 130*z**3 - 403*z**2 + 460*z - 1426\nNo more calculations needed.\n130*z**3 - 403*z**2 + 460*z - 1426", "generated_answer": "130*z**3 - 403*z**2 + 460*z - 1426", "step_length": 5} {"cot_id": "01da5f77af8d2b0bc3e45b090e80343195a2d9b48f07866ec0c35fb430692525", "datapoint": {"question": "Calculate the following: (36*z + 9)*(-12*z**3 + 70*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-432*z**4 - 108*z**3 + 2520*z**2 + 630*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 866, "polynomial_expr": "(36*z + 9)*(-12*z**3 + 70*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (36*z + 9)*(-12*z**3 + 70*z)\nExpanding the part (36*z + 9) using the distributive property, and we got: (36*z)*(-12*z**3 + 70*z) + 9*(-12*z**3 + 70*z)\n#Step 2:\nCurrent expression: (36*z)*(-12*z**3 + 70*z) + 9*(-12*z**3 + 70*z)\nSimplifying the partial expression: 9*(-12*z**3 + 70*z)\nExpanding the part (-12*z**3 + 70*z) using the distributive property, and we got: (70*z)*9 - 12*z**3*9\nReplacing 9*(-12*z**3 + 70*z) with (70*z)*9 - 12*z**3*9 in the overall expression.\n#Step 3:\nCurrent expression: (36*z)*(-12*z**3 + 70*z) + (70*z)*9 - 12*z**3*9\nSimplifying the partial expression: (36*z)*(-12*z**3 + 70*z)\nExpanding the part (-12*z**3 + 70*z) using the distributive property, and we got: (36*z)*(70*z) + (36*z)*(-12*z**3)\nReplacing (36*z)*(-12*z**3 + 70*z) with (36*z)*(70*z) + (36*z)*(-12*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (36*z)*(70*z) + (36*z)*(-12*z**3) + (70*z)*9 - 12*z**3*9\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*z**3)*9 = -108*z**3\n (-12*z**3)*(36*z) = -432*z**4\n (70*z)*9 = 630*z\n (70*z)*(36*z) = 2520*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -432*z**4 - 108*z**3 + 2520*z**2 + 630*z\nNo more calculations needed.\n-432*z**4 - 108*z**3 + 2520*z**2 + 630*z", "generated_answer": "-432*z**4 - 108*z**3 + 2520*z**2 + 630*z", "step_length": 5} {"cot_id": "19fd2b7b9221d6d2d23bbd5de6fc4037d3ed4d0177e2d5d3181f2a85a75f9d75", "datapoint": {"question": "Calculate the following: (48*x**3 + 39*x + 9)*(60*x**3 + 40*x**2 - 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2880*x**6 + 1920*x**5 + 2340*x**4 + 1428*x**3 + 360*x**2 - 546*x - 126", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 867, "polynomial_expr": "(48*x**3 + 39*x + 9)*(60*x**3 + 40*x**2 - 14)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (48*x**3 + 39*x + 9)*(60*x**3 + 40*x**2 - 14)\nExpanding the part (60*x**3 + 40*x**2 - 14) using the distributive property, and we got: (40*x**2)*(48*x**3 + 39*x + 9) + (60*x**3)*(48*x**3 + 39*x + 9) - 14*(48*x**3 + 39*x + 9)\n#Step 2:\nCurrent expression: (40*x**2)*(48*x**3 + 39*x + 9) + (60*x**3)*(48*x**3 + 39*x + 9) - 14*(48*x**3 + 39*x + 9)\nSimplifying the partial expression: -14*(48*x**3 + 39*x + 9)\nExpanding the part (48*x**3 + 39*x + 9) using the distributive property, and we got: (39*x)*(-14) + (48*x**3)*(-14) + 9*(-14)\nReplacing -14*(48*x**3 + 39*x + 9) with (39*x)*(-14) + (48*x**3)*(-14) + 9*(-14) in the overall expression.\n#Step 3:\nCurrent expression: (39*x)*(-14) + (40*x**2)*(48*x**3 + 39*x + 9) + (48*x**3)*(-14) + (60*x**3)*(48*x**3 + 39*x + 9) - 126\nSimplifying the partial expression: (40*x**2)*(48*x**3 + 39*x + 9)\nExpanding the part (48*x**3 + 39*x + 9) using the distributive property, and we got: 9*(40*x**2) + (39*x)*(40*x**2) + (40*x**2)*(48*x**3)\nReplacing (40*x**2)*(48*x**3 + 39*x + 9) with 9*(40*x**2) + (39*x)*(40*x**2) + (40*x**2)*(48*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 9*40*x**2 + (39*x)*(40*x**2) + (39*x)*(-14) + (40*x**2)*(48*x**3) + (48*x**3)*(-14) + (60*x**3)*(48*x**3 + 39*x + 9) - 126\nSimplifying the partial expression: (60*x**3)*(48*x**3 + 39*x + 9)\nExpanding the part (48*x**3 + 39*x + 9) using the distributive property, and we got: 9*(60*x**3) + (39*x)*(60*x**3) + (48*x**3)*(60*x**3)\nReplacing (60*x**3)*(48*x**3 + 39*x + 9) with 9*(60*x**3) + (39*x)*(60*x**3) + (48*x**3)*(60*x**3) in the overall expression.\n#Step 5:\nCurrent expression: 9*60*x**3 + 9*40*x**2 + (39*x)*(40*x**2) + (39*x)*(60*x**3) + (39*x)*(-14) + (40*x**2)*(48*x**3) + (48*x**3)*(60*x**3) + (48*x**3)*(-14) - 126\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (39*x)*-14 = -546*x\n (39*x)*(40*x**2) = 1560*x**3\n (39*x)*(60*x**3) = 2340*x**4\n (48*x**3)*-14 = -672*x**3\n (48*x**3)*(40*x**2) = 1920*x**5\n (48*x**3)*(60*x**3) = 2880*x**6\n 9*40*x**2 = 360*x**2\n 9*60*x**3 = 540*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 2880*x**6 + 1920*x**5 + 2340*x**4 - 672*x**3 + 540*x**3 + 1560*x**3 + 360*x**2 - 546*x - 126\nCombining like terms, got 2880*x**6 + 1920*x**5 + 2340*x**4 + 1428*x**3 + 360*x**2 - 546*x - 126\n#Step 7:\nCurrent expression: 2880*x**6 + 1920*x**5 + 2340*x**4 + 1428*x**3 + 360*x**2 - 546*x - 126\nNo more calculations needed.\n2880*x**6 + 1920*x**5 + 2340*x**4 + 1428*x**3 + 360*x**2 - 546*x - 126", "generated_answer": "2880*x**6 + 1920*x**5 + 2340*x**4 + 1428*x**3 + 360*x**2 - 546*x - 126", "step_length": 7} {"cot_id": "b8287b4e325dee52bd9c0d36774a699e6a761d20b04de6f7f8ad21520e87fba2", "datapoint": {"question": "Calculate the following: (-20*z**3 - 8*z**2 - 28)*(43*z**3 - 44*z**2 - 6*z - 12)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-860*z**6 + 536*z**5 + 472*z**4 - 916*z**3 + 1328*z**2 + 168*z + 336", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 868, "polynomial_expr": "(-20*z**3 - 8*z**2 - 28)*(43*z**3 - 44*z**2 - 6*z - 12)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-20*z**3 - 8*z**2 - 28)*(43*z**3 - 44*z**2 - 6*z - 12)\nExpanding the part (-20*z**3 - 8*z**2 - 28) using the distributive property, and we got: (-8*z**2)*(43*z**3 - 44*z**2 - 6*z - 12) + (-20*z**3)*(43*z**3 - 44*z**2 - 6*z - 12) - 28*(43*z**3 - 44*z**2 - 6*z - 12)\n#Step 2:\nCurrent expression: (-8*z**2)*(43*z**3 - 44*z**2 - 6*z - 12) + (-20*z**3)*(43*z**3 - 44*z**2 - 6*z - 12) - 28*(43*z**3 - 44*z**2 - 6*z - 12)\nSimplifying the partial expression: -28*(43*z**3 - 44*z**2 - 6*z - 12)\nExpanding the part (43*z**3 - 44*z**2 - 6*z - 12) using the distributive property, and we got: -6*z*(-28) - 44*z**2*(-28) + (43*z**3)*(-28) - 12*(-28)\nReplacing -28*(43*z**3 - 44*z**2 - 6*z - 12) with -6*z*(-28) - 44*z**2*(-28) + (43*z**3)*(-28) - 12*(-28) in the overall expression.\n#Step 3:\nCurrent expression: -6*z*(-28) - 44*z**2*(-28) + (-8*z**2)*(43*z**3 - 44*z**2 - 6*z - 12) + (-20*z**3)*(43*z**3 - 44*z**2 - 6*z - 12) + (43*z**3)*(-28) + 336\nSimplifying the partial expression: (-20*z**3)*(43*z**3 - 44*z**2 - 6*z - 12)\nExpanding the part (43*z**3 - 44*z**2 - 6*z - 12) using the distributive property, and we got: (-6*z)*(-20*z**3) - (-1)*240*z**3 + (-44*z**2)*(-20*z**3) + (-20*z**3)*(43*z**3)\nReplacing (-20*z**3)*(43*z**3 - 44*z**2 - 6*z - 12) with (-6*z)*(-20*z**3) - (-1)*240*z**3 + (-44*z**2)*(-20*z**3) + (-20*z**3)*(43*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-6*z)*(-20*z**3) - 6*z*(-28) - 12*(-20)*z**3 + (-44*z**2)*(-20*z**3) - 44*z**2*(-28) + (-8*z**2)*(43*z**3 - 44*z**2 - 6*z - 12) + (-20*z**3)*(43*z**3) + (43*z**3)*(-28) + 336\nSimplifying the partial expression: (-8*z**2)*(43*z**3 - 44*z**2 - 6*z - 12)\nExpanding the part (43*z**3 - 44*z**2 - 6*z - 12) using the distributive property, and we got: (-6*z)*(-8*z**2) - (-1)*96*z**2 + (-44*z**2)*(-8*z**2) + (-8*z**2)*(43*z**3)\nReplacing (-8*z**2)*(43*z**3 - 44*z**2 - 6*z - 12) with (-6*z)*(-8*z**2) - (-1)*96*z**2 + (-44*z**2)*(-8*z**2) + (-8*z**2)*(43*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-6*z)*(-8*z**2) + (-6*z)*(-20*z**3) - 6*z*(-28) - 12*(-20)*z**3 - 12*(-8)*z**2 + (-44*z**2)*(-8*z**2) + (-44*z**2)*(-20*z**3) - 44*z**2*(-28) + (-8*z**2)*(43*z**3) + (-20*z**3)*(43*z**3) + (43*z**3)*(-28) + 336\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-44*z**2)*-28 = 1232*z**2\n (-44*z**2)*(-20*z**3) = 880*z**5\n (-44*z**2)*(-8*z**2) = 352*z**4\n (-6*z)*-28 = 168*z\n (-6*z)*(-20*z**3) = 120*z**4\n (-6*z)*(-8*z**2) = 48*z**3\n (43*z**3)*-28 = -1204*z**3\n (43*z**3)*(-20*z**3) = -860*z**6\n (43*z**3)*(-8*z**2) = -344*z**5\n -12*-20*z**3 = 240*z**3\n -12*-8*z**2 = 96*z**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -860*z**6 - 344*z**5 + 880*z**5 + 120*z**4 + 352*z**4 - 1204*z**3 + 48*z**3 + 240*z**3 + 96*z**2 + 1232*z**2 + 168*z + 336\nCombining like terms, got -860*z**6 + 536*z**5 + 472*z**4 - 916*z**3 + 1328*z**2 + 168*z + 336\n#Step 7:\nCurrent expression: -860*z**6 + 536*z**5 + 472*z**4 - 916*z**3 + 1328*z**2 + 168*z + 336\nNo more calculations needed.\n-860*z**6 + 536*z**5 + 472*z**4 - 916*z**3 + 1328*z**2 + 168*z + 336", "generated_answer": "-860*z**6 + 536*z**5 + 472*z**4 - 916*z**3 + 1328*z**2 + 168*z + 336", "step_length": 7} {"cot_id": "38d111b234a75a8bc87c6a9abf4e97844a0c68301132bb20d5a67a7fd9de1eea", "datapoint": {"question": "Calculate the following: (46 - 4*y)*(36*y**2 + 92)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-144*y**3 + 1656*y**2 - 368*y + 4232", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 869, "polynomial_expr": "(46 - 4*y)*(36*y**2 + 92)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (46 - 4*y)*(36*y**2 + 92)\nExpanding the part (46 - 4*y) using the distributive property, and we got: (-4*y)*(36*y**2 + 92) + 46*(36*y**2 + 92)\n#Step 2:\nCurrent expression: (-4*y)*(36*y**2 + 92) + 46*(36*y**2 + 92)\nSimplifying the partial expression: 46*(36*y**2 + 92)\nExpanding the part (36*y**2 + 92) using the distributive property, and we got: (36*y**2)*46 + 92*46\nReplacing 46*(36*y**2 + 92) with (36*y**2)*46 + 92*46 in the overall expression.\n#Step 3:\nCurrent expression: (-4*y)*(36*y**2 + 92) + (36*y**2)*46 + 4232\nSimplifying the partial expression: (-4*y)*(36*y**2 + 92)\nExpanding the part (36*y**2 + 92) using the distributive property, and we got: (-4*y)*(36*y**2) + 92*(-4*y)\nReplacing (-4*y)*(36*y**2 + 92) with (-4*y)*(36*y**2) + 92*(-4*y) in the overall expression.\n#Step 4:\nCurrent expression: (-4*y)*(36*y**2) + 92*(-4)*y + (36*y**2)*46 + 4232\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (36*y**2)*46 = 1656*y**2\n (36*y**2)*(-4*y) = -144*y**3\n 92*-4*y = -368*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -144*y**3 + 1656*y**2 - 368*y + 4232\nNo more calculations needed.\n-144*y**3 + 1656*y**2 - 368*y + 4232", "generated_answer": "-144*y**3 + 1656*y**2 - 368*y + 4232", "step_length": 5} {"cot_id": "ae8a433af15836524308d9dd2047fd41d792076cecde6707780ea6fb9b066368", "datapoint": {"question": "Simplify this expression: (41 - 35*z**2)*(36*z**2 - 35*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1260*z**4 + 1225*z**3 + 1476*z**2 - 1435*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 870, "polynomial_expr": "(41 - 35*z**2)*(36*z**2 - 35*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (41 - 35*z**2)*(36*z**2 - 35*z)\nExpanding the part (41 - 35*z**2) using the distributive property, and we got: (-35*z**2)*(36*z**2 - 35*z) + 41*(36*z**2 - 35*z)\n#Step 2:\nCurrent expression: (-35*z**2)*(36*z**2 - 35*z) + 41*(36*z**2 - 35*z)\nSimplifying the partial expression: 41*(36*z**2 - 35*z)\nExpanding the part (36*z**2 - 35*z) using the distributive property, and we got: -35*z*41 + (36*z**2)*41\nReplacing 41*(36*z**2 - 35*z) with -35*z*41 + (36*z**2)*41 in the overall expression.\n#Step 3:\nCurrent expression: -35*z*41 + (-35*z**2)*(36*z**2 - 35*z) + (36*z**2)*41\nSimplifying the partial expression: (-35*z**2)*(36*z**2 - 35*z)\nExpanding the part (36*z**2 - 35*z) using the distributive property, and we got: (-35*z)*(-35*z**2) + (-35*z**2)*(36*z**2)\nReplacing (-35*z**2)*(36*z**2 - 35*z) with (-35*z)*(-35*z**2) + (-35*z**2)*(36*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-35*z)*(-35*z**2) - 35*z*41 + (-35*z**2)*(36*z**2) + (36*z**2)*41\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*z)*41 = -1435*z\n (-35*z)*(-35*z**2) = 1225*z**3\n (36*z**2)*41 = 1476*z**2\n (36*z**2)*(-35*z**2) = -1260*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1260*z**4 + 1225*z**3 + 1476*z**2 - 1435*z\nNo more calculations needed.\n-1260*z**4 + 1225*z**3 + 1476*z**2 - 1435*z", "generated_answer": "-1260*z**4 + 1225*z**3 + 1476*z**2 - 1435*z", "step_length": 5} {"cot_id": "1a2182f53527ccc56a2110d7563a0cf11888fe6d42ca07e770900592c0dc2357", "datapoint": {"question": "Simplify this expression: (-32*x**3 - 33*x)*(-25*x**3 - 96*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "800*x**6 + 3072*x**5 + 825*x**4 + 3168*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 871, "polynomial_expr": "(-32*x**3 - 33*x)*(-25*x**3 - 96*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-32*x**3 - 33*x)*(-25*x**3 - 96*x**2)\nExpanding the part (-25*x**3 - 96*x**2) using the distributive property, and we got: (-96*x**2)*(-32*x**3 - 33*x) + (-25*x**3)*(-32*x**3 - 33*x)\n#Step 2:\nCurrent expression: (-96*x**2)*(-32*x**3 - 33*x) + (-25*x**3)*(-32*x**3 - 33*x)\nSimplifying the partial expression: (-96*x**2)*(-32*x**3 - 33*x)\nExpanding the part (-32*x**3 - 33*x) using the distributive property, and we got: (-33*x)*(-96*x**2) + (-96*x**2)*(-32*x**3)\nReplacing (-96*x**2)*(-32*x**3 - 33*x) with (-33*x)*(-96*x**2) + (-96*x**2)*(-32*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-33*x)*(-96*x**2) + (-96*x**2)*(-32*x**3) + (-25*x**3)*(-32*x**3 - 33*x)\nSimplifying the partial expression: (-25*x**3)*(-32*x**3 - 33*x)\nExpanding the part (-32*x**3 - 33*x) using the distributive property, and we got: (-33*x)*(-25*x**3) + (-32*x**3)*(-25*x**3)\nReplacing (-25*x**3)*(-32*x**3 - 33*x) with (-33*x)*(-25*x**3) + (-32*x**3)*(-25*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-33*x)*(-96*x**2) + (-33*x)*(-25*x**3) + (-96*x**2)*(-32*x**3) + (-32*x**3)*(-25*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*x)*(-96*x**2) = 3168*x**3\n (-33*x)*(-25*x**3) = 825*x**4\n (-32*x**3)*(-96*x**2) = 3072*x**5\n (-32*x**3)*(-25*x**3) = 800*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 800*x**6 + 3072*x**5 + 825*x**4 + 3168*x**3\nNo more calculations needed.\n800*x**6 + 3072*x**5 + 825*x**4 + 3168*x**3", "generated_answer": "800*x**6 + 3072*x**5 + 825*x**4 + 3168*x**3", "step_length": 5} {"cot_id": "1931440343860b910e0ec4286c39105fa1a619ef4a662b96d99d81ffc81f3bf0", "datapoint": {"question": "Calculate the following: (76*x**2 + 10*x + 5)*(-40*x**3 + 7*x**2 - 6*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-3040*x**5 + 132*x**4 - 586*x**3 - 25*x**2 - 30*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 872, "polynomial_expr": "(76*x**2 + 10*x + 5)*(-40*x**3 + 7*x**2 - 6*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (76*x**2 + 10*x + 5)*(-40*x**3 + 7*x**2 - 6*x)\nExpanding the part (76*x**2 + 10*x + 5) using the distributive property, and we got: (10*x)*(-40*x**3 + 7*x**2 - 6*x) + (76*x**2)*(-40*x**3 + 7*x**2 - 6*x) + 5*(-40*x**3 + 7*x**2 - 6*x)\n#Step 2:\nCurrent expression: (10*x)*(-40*x**3 + 7*x**2 - 6*x) + (76*x**2)*(-40*x**3 + 7*x**2 - 6*x) + 5*(-40*x**3 + 7*x**2 - 6*x)\nSimplifying the partial expression: 5*(-40*x**3 + 7*x**2 - 6*x)\nExpanding the part (-40*x**3 + 7*x**2 - 6*x) using the distributive property, and we got: -6*x*5 + (7*x**2)*5 - 40*x**3*5\nReplacing 5*(-40*x**3 + 7*x**2 - 6*x) with -6*x*5 + (7*x**2)*5 - 40*x**3*5 in the overall expression.\n#Step 3:\nCurrent expression: -6*x*5 + (10*x)*(-40*x**3 + 7*x**2 - 6*x) + (7*x**2)*5 + (76*x**2)*(-40*x**3 + 7*x**2 - 6*x) - 40*x**3*5\nSimplifying the partial expression: (10*x)*(-40*x**3 + 7*x**2 - 6*x)\nExpanding the part (-40*x**3 + 7*x**2 - 6*x) using the distributive property, and we got: (-6*x)*(10*x) + (10*x)*(7*x**2) + (10*x)*(-40*x**3)\nReplacing (10*x)*(-40*x**3 + 7*x**2 - 6*x) with (-6*x)*(10*x) + (10*x)*(7*x**2) + (10*x)*(-40*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-6*x)*(10*x) - 6*x*5 + (10*x)*(7*x**2) + (10*x)*(-40*x**3) + (7*x**2)*5 + (76*x**2)*(-40*x**3 + 7*x**2 - 6*x) - 40*x**3*5\nSimplifying the partial expression: (76*x**2)*(-40*x**3 + 7*x**2 - 6*x)\nExpanding the part (-40*x**3 + 7*x**2 - 6*x) using the distributive property, and we got: (-6*x)*(76*x**2) + (7*x**2)*(76*x**2) + (76*x**2)*(-40*x**3)\nReplacing (76*x**2)*(-40*x**3 + 7*x**2 - 6*x) with (-6*x)*(76*x**2) + (7*x**2)*(76*x**2) + (76*x**2)*(-40*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-6*x)*(10*x) + (-6*x)*(76*x**2) - 6*x*5 + (10*x)*(7*x**2) + (10*x)*(-40*x**3) + (7*x**2)*(76*x**2) + (7*x**2)*5 + (76*x**2)*(-40*x**3) - 40*x**3*5\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*x**3)*5 = -200*x**3\n (-40*x**3)*(10*x) = -400*x**4\n (-40*x**3)*(76*x**2) = -3040*x**5\n (-6*x)*5 = -30*x\n (-6*x)*(10*x) = -60*x**2\n (-6*x)*(76*x**2) = -456*x**3\n (7*x**2)*5 = 35*x**2\n (7*x**2)*(10*x) = 70*x**3\n (7*x**2)*(76*x**2) = 532*x**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -3040*x**5 - 400*x**4 + 532*x**4 - 456*x**3 - 200*x**3 + 70*x**3 - 60*x**2 + 35*x**2 - 30*x\nCombining like terms, got -3040*x**5 + 132*x**4 - 586*x**3 - 25*x**2 - 30*x\n#Step 7:\nCurrent expression: -3040*x**5 + 132*x**4 - 586*x**3 - 25*x**2 - 30*x\nNo more calculations needed.\n-3040*x**5 + 132*x**4 - 586*x**3 - 25*x**2 - 30*x", "generated_answer": "-3040*x**5 + 132*x**4 - 586*x**3 - 25*x**2 - 30*x", "step_length": 7} {"cot_id": "66482729e1756a4579a922a3bfcf584e9d3fe84f2e145212af9eadaad3bcf283", "datapoint": {"question": "Simplify this expression: (1 - 20*x)*(28*x**3 + 20*x**2 + 31*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-560*x**4 - 372*x**3 - 600*x**2 + 31*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 873, "polynomial_expr": "(1 - 20*x)*(28*x**3 + 20*x**2 + 31*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (1 - 20*x)*(28*x**3 + 20*x**2 + 31*x)\nExpanding the part (1 - 20*x) using the distributive property, and we got: (-20*x)*(28*x**3 + 20*x**2 + 31*x) + 1*(28*x**3 + 20*x**2 + 31*x)\n#Step 2:\nCurrent expression: (-20*x)*(28*x**3 + 20*x**2 + 31*x) + 1*(28*x**3 + 20*x**2 + 31*x)\nSimplifying the partial expression: 1*(28*x**3 + 20*x**2 + 31*x)\nExpanding the part (28*x**3 + 20*x**2 + 31*x) using the distributive property, and we got: (31*x)*1 + (20*x**2)*1 + (28*x**3)*1\nReplacing 1*(28*x**3 + 20*x**2 + 31*x) with (31*x)*1 + (20*x**2)*1 + (28*x**3)*1 in the overall expression.\n#Step 3:\nCurrent expression: (-20*x)*(28*x**3 + 20*x**2 + 31*x) + (31*x)*1 + (20*x**2)*1 + (28*x**3)*1\nSimplifying the partial expression: (-20*x)*(28*x**3 + 20*x**2 + 31*x)\nExpanding the part (28*x**3 + 20*x**2 + 31*x) using the distributive property, and we got: (-20*x)*(31*x) + (-20*x)*(20*x**2) + (-20*x)*(28*x**3)\nReplacing (-20*x)*(28*x**3 + 20*x**2 + 31*x) with (-20*x)*(31*x) + (-20*x)*(20*x**2) + (-20*x)*(28*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-20*x)*(31*x) + (-20*x)*(20*x**2) + (-20*x)*(28*x**3) + (31*x)*1 + (20*x**2)*1 + (28*x**3)*1\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (20*x**2)*1 = 20*x**2\n (20*x**2)*(-20*x) = -400*x**3\n (28*x**3)*1 = 28*x**3\n (28*x**3)*(-20*x) = -560*x**4\n (31*x)*1 = 31*x\n (31*x)*(-20*x) = -620*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -560*x**4 - 400*x**3 + 28*x**3 - 620*x**2 + 20*x**2 + 31*x\nCombining like terms, got -560*x**4 - 372*x**3 - 600*x**2 + 31*x\n#Step 6:\nCurrent expression: -560*x**4 - 372*x**3 - 600*x**2 + 31*x\nNo more calculations needed.\n-560*x**4 - 372*x**3 - 600*x**2 + 31*x", "generated_answer": "-560*x**4 - 372*x**3 - 600*x**2 + 31*x", "step_length": 6} {"cot_id": "d70b197f683d5b6a9f78f9b6e861e862dda5b7f9120d4a82606c865bab5bbcb8", "datapoint": {"question": "Simplify this expression: -330*z**2 + 880*z\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-330*z**2 + 880*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 874, "polynomial_expr": "-330*z**2 + 880*z", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -330*z**2 + 880*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -330*z**2 + 880*z\nNo more calculations needed.\n-330*z**2 + 880*z", "generated_answer": "-330*z**2 + 880*z", "step_length": 2} {"cot_id": "30c3bb772c60a5d7cab735ee701e3079a989b0445dbaf842378ceeea2ed9aaf7", "datapoint": {"question": "Calculate the following: (-25*z**2 + 26*z)*(-6*z**2 - 39*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "150*z**4 + 819*z**3 - 1014*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 875, "polynomial_expr": "(-25*z**2 + 26*z)*(-6*z**2 - 39*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-25*z**2 + 26*z)*(-6*z**2 - 39*z)\nExpanding the part (-6*z**2 - 39*z) using the distributive property, and we got: (-39*z)*(-25*z**2 + 26*z) + (-6*z**2)*(-25*z**2 + 26*z)\n#Step 2:\nCurrent expression: (-39*z)*(-25*z**2 + 26*z) + (-6*z**2)*(-25*z**2 + 26*z)\nSimplifying the partial expression: (-39*z)*(-25*z**2 + 26*z)\nExpanding the part (-25*z**2 + 26*z) using the distributive property, and we got: (-39*z)*(26*z) + (-39*z)*(-25*z**2)\nReplacing (-39*z)*(-25*z**2 + 26*z) with (-39*z)*(26*z) + (-39*z)*(-25*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-39*z)*(26*z) + (-39*z)*(-25*z**2) + (-6*z**2)*(-25*z**2 + 26*z)\nSimplifying the partial expression: (-6*z**2)*(-25*z**2 + 26*z)\nExpanding the part (-25*z**2 + 26*z) using the distributive property, and we got: (26*z)*(-6*z**2) + (-25*z**2)*(-6*z**2)\nReplacing (-6*z**2)*(-25*z**2 + 26*z) with (26*z)*(-6*z**2) + (-25*z**2)*(-6*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-39*z)*(26*z) + (-39*z)*(-25*z**2) + (26*z)*(-6*z**2) + (-25*z**2)*(-6*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*z**2)*(-39*z) = 975*z**3\n (-25*z**2)*(-6*z**2) = 150*z**4\n (26*z)*(-39*z) = -1014*z**2\n (26*z)*(-6*z**2) = -156*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 150*z**4 - 156*z**3 + 975*z**3 - 1014*z**2\nCombining like terms, got 150*z**4 + 819*z**3 - 1014*z**2\n#Step 6:\nCurrent expression: 150*z**4 + 819*z**3 - 1014*z**2\nNo more calculations needed.\n150*z**4 + 819*z**3 - 1014*z**2", "generated_answer": "150*z**4 + 819*z**3 - 1014*z**2", "step_length": 6} {"cot_id": "ef6b07120b95c63e3ba5df340b48e86b9d3683bd3ced26def819dbff7ee12664", "datapoint": {"question": "Simplify this expression: (-20*z**2 - 6)*(-42*z**2 - 2*z - 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "840*z**4 + 40*z**3 + 1072*z**2 + 12*z + 246", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 876, "polynomial_expr": "(-20*z**2 - 6)*(-42*z**2 - 2*z - 41)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-20*z**2 - 6)*(-42*z**2 - 2*z - 41)\nExpanding the part (-20*z**2 - 6) using the distributive property, and we got: (-20*z**2)*(-42*z**2 - 2*z - 41) - 6*(-42*z**2 - 2*z - 41)\n#Step 2:\nCurrent expression: (-20*z**2)*(-42*z**2 - 2*z - 41) - 6*(-42*z**2 - 2*z - 41)\nSimplifying the partial expression: -6*(-42*z**2 - 2*z - 41)\nExpanding the part (-42*z**2 - 2*z - 41) using the distributive property, and we got: -2*z*(-6) - 42*z**2*(-6) - 41*(-6)\nReplacing -6*(-42*z**2 - 2*z - 41) with -2*z*(-6) - 42*z**2*(-6) - 41*(-6) in the overall expression.\n#Step 3:\nCurrent expression: -2*z*(-6) - 42*z**2*(-6) + (-20*z**2)*(-42*z**2 - 2*z - 41) + 246\nSimplifying the partial expression: (-20*z**2)*(-42*z**2 - 2*z - 41)\nExpanding the part (-42*z**2 - 2*z - 41) using the distributive property, and we got: (-2*z)*(-20*z**2) - (-1)*820*z**2 + (-42*z**2)*(-20*z**2)\nReplacing (-20*z**2)*(-42*z**2 - 2*z - 41) with (-2*z)*(-20*z**2) - (-1)*820*z**2 + (-42*z**2)*(-20*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-2*z)*(-20*z**2) - 2*z*(-6) - 41*(-20)*z**2 + (-42*z**2)*(-20*z**2) - 42*z**2*(-6) + 246\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*z**2)*-6 = 252*z**2\n (-42*z**2)*(-20*z**2) = 840*z**4\n (-2*z)*-6 = 12*z\n (-2*z)*(-20*z**2) = 40*z**3\n -41*-20*z**2 = 820*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 840*z**4 + 40*z**3 + 252*z**2 + 820*z**2 + 12*z + 246\nCombining like terms, got 840*z**4 + 40*z**3 + 1072*z**2 + 12*z + 246\n#Step 6:\nCurrent expression: 840*z**4 + 40*z**3 + 1072*z**2 + 12*z + 246\nNo more calculations needed.\n840*z**4 + 40*z**3 + 1072*z**2 + 12*z + 246", "generated_answer": "840*z**4 + 40*z**3 + 1072*z**2 + 12*z + 246", "step_length": 6} {"cot_id": "da01f533f51cf083d77063ce212c5ffa99110c3e451628bd6225bae189eaf69c", "datapoint": {"question": "Simplify this expression: (4*z + 105)*(-8*z**2 - 51)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-32*z**3 - 840*z**2 - 204*z - 5355", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 877, "polynomial_expr": "(4*z + 105)*(-8*z**2 - 51)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (4*z + 105)*(-8*z**2 - 51)\nExpanding the part (-8*z**2 - 51) using the distributive property, and we got: (-8*z**2)*(4*z + 105) - 51*(4*z + 105)\n#Step 2:\nCurrent expression: (-8*z**2)*(4*z + 105) - 51*(4*z + 105)\nSimplifying the partial expression: -51*(4*z + 105)\nExpanding the part (4*z + 105) using the distributive property, and we got: (4*z)*(-51) + 105*(-51)\nReplacing -51*(4*z + 105) with (4*z)*(-51) + 105*(-51) in the overall expression.\n#Step 3:\nCurrent expression: (4*z)*(-51) + (-8*z**2)*(4*z + 105) - 5355\nSimplifying the partial expression: (-8*z**2)*(4*z + 105)\nExpanding the part (4*z + 105) using the distributive property, and we got: 105*(-8*z**2) + (4*z)*(-8*z**2)\nReplacing (-8*z**2)*(4*z + 105) with 105*(-8*z**2) + (4*z)*(-8*z**2) in the overall expression.\n#Step 4:\nCurrent expression: 105*(-8)*z**2 + (4*z)*(-8*z**2) + (4*z)*(-51) - 5355\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (4*z)*-51 = -204*z\n (4*z)*(-8*z**2) = -32*z**3\n 105*-8*z**2 = -840*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -32*z**3 - 840*z**2 - 204*z - 5355\nNo more calculations needed.\n-32*z**3 - 840*z**2 - 204*z - 5355", "generated_answer": "-32*z**3 - 840*z**2 - 204*z - 5355", "step_length": 5} {"cot_id": "349bf2b20a7f112dbee774ce862ca6f2ff4f8fc78fb06abc601ecf2c7292f48d", "datapoint": {"question": "Calculate the following: (31*z**3 - 44)*(-14*z**3 - 2*z**2 - 21*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-434*z**6 - 62*z**5 - 651*z**4 + 616*z**3 + 88*z**2 + 924*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 878, "polynomial_expr": "(31*z**3 - 44)*(-14*z**3 - 2*z**2 - 21*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31*z**3 - 44)*(-14*z**3 - 2*z**2 - 21*z)\nExpanding the part (31*z**3 - 44) using the distributive property, and we got: (31*z**3)*(-14*z**3 - 2*z**2 - 21*z) - 44*(-14*z**3 - 2*z**2 - 21*z)\n#Step 2:\nCurrent expression: (31*z**3)*(-14*z**3 - 2*z**2 - 21*z) - 44*(-14*z**3 - 2*z**2 - 21*z)\nSimplifying the partial expression: -44*(-14*z**3 - 2*z**2 - 21*z)\nExpanding the part (-14*z**3 - 2*z**2 - 21*z) using the distributive property, and we got: -21*z*(-44) - 2*z**2*(-44) - 14*z**3*(-44)\nReplacing -44*(-14*z**3 - 2*z**2 - 21*z) with -21*z*(-44) - 2*z**2*(-44) - 14*z**3*(-44) in the overall expression.\n#Step 3:\nCurrent expression: -21*z*(-44) - 2*z**2*(-44) - 14*z**3*(-44) + (31*z**3)*(-14*z**3 - 2*z**2 - 21*z)\nSimplifying the partial expression: (31*z**3)*(-14*z**3 - 2*z**2 - 21*z)\nExpanding the part (-14*z**3 - 2*z**2 - 21*z) using the distributive property, and we got: (-21*z)*(31*z**3) + (-2*z**2)*(31*z**3) + (-14*z**3)*(31*z**3)\nReplacing (31*z**3)*(-14*z**3 - 2*z**2 - 21*z) with (-21*z)*(31*z**3) + (-2*z**2)*(31*z**3) + (-14*z**3)*(31*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-21*z)*(31*z**3) - 21*z*(-44) + (-2*z**2)*(31*z**3) - 2*z**2*(-44) + (-14*z**3)*(31*z**3) - 14*z**3*(-44)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-21*z)*-44 = 924*z\n (-21*z)*(31*z**3) = -651*z**4\n (-14*z**3)*-44 = 616*z**3\n (-14*z**3)*(31*z**3) = -434*z**6\n (-2*z**2)*-44 = 88*z**2\n (-2*z**2)*(31*z**3) = -62*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -434*z**6 - 62*z**5 - 651*z**4 + 616*z**3 + 88*z**2 + 924*z\nNo more calculations needed.\n-434*z**6 - 62*z**5 - 651*z**4 + 616*z**3 + 88*z**2 + 924*z", "generated_answer": "-434*z**6 - 62*z**5 - 651*z**4 + 616*z**3 + 88*z**2 + 924*z", "step_length": 5} {"cot_id": "ab88f07e655a8d32260fb93516f117b1f84a36e209aae35e45a32e5d83516638", "datapoint": {"question": "Calculate the following: (37 - 3*y**2)*(-40*y**3 + 49*y**2 + 48*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "120*y**5 - 147*y**4 - 1624*y**3 + 1813*y**2 + 1776*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 879, "polynomial_expr": "(37 - 3*y**2)*(-40*y**3 + 49*y**2 + 48*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (37 - 3*y**2)*(-40*y**3 + 49*y**2 + 48*y)\nExpanding the part (37 - 3*y**2) using the distributive property, and we got: (-3*y**2)*(-40*y**3 + 49*y**2 + 48*y) + 37*(-40*y**3 + 49*y**2 + 48*y)\n#Step 2:\nCurrent expression: (-3*y**2)*(-40*y**3 + 49*y**2 + 48*y) + 37*(-40*y**3 + 49*y**2 + 48*y)\nSimplifying the partial expression: 37*(-40*y**3 + 49*y**2 + 48*y)\nExpanding the part (-40*y**3 + 49*y**2 + 48*y) using the distributive property, and we got: (48*y)*37 + (49*y**2)*37 - 40*y**3*37\nReplacing 37*(-40*y**3 + 49*y**2 + 48*y) with (48*y)*37 + (49*y**2)*37 - 40*y**3*37 in the overall expression.\n#Step 3:\nCurrent expression: (48*y)*37 + (-3*y**2)*(-40*y**3 + 49*y**2 + 48*y) + (49*y**2)*37 - 40*y**3*37\nSimplifying the partial expression: (-3*y**2)*(-40*y**3 + 49*y**2 + 48*y)\nExpanding the part (-40*y**3 + 49*y**2 + 48*y) using the distributive property, and we got: (48*y)*(-3*y**2) + (-3*y**2)*(49*y**2) + (-3*y**2)*(-40*y**3)\nReplacing (-3*y**2)*(-40*y**3 + 49*y**2 + 48*y) with (48*y)*(-3*y**2) + (-3*y**2)*(49*y**2) + (-3*y**2)*(-40*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (48*y)*(-3*y**2) + (48*y)*37 + (-3*y**2)*(49*y**2) + (-3*y**2)*(-40*y**3) + (49*y**2)*37 - 40*y**3*37\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*y**3)*37 = -1480*y**3\n (-40*y**3)*(-3*y**2) = 120*y**5\n (48*y)*37 = 1776*y\n (48*y)*(-3*y**2) = -144*y**3\n (49*y**2)*37 = 1813*y**2\n (49*y**2)*(-3*y**2) = -147*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 120*y**5 - 147*y**4 - 1480*y**3 - 144*y**3 + 1813*y**2 + 1776*y\nCombining like terms, got 120*y**5 - 147*y**4 - 1624*y**3 + 1813*y**2 + 1776*y\n#Step 6:\nCurrent expression: 120*y**5 - 147*y**4 - 1624*y**3 + 1813*y**2 + 1776*y\nNo more calculations needed.\n120*y**5 - 147*y**4 - 1624*y**3 + 1813*y**2 + 1776*y", "generated_answer": "120*y**5 - 147*y**4 - 1624*y**3 + 1813*y**2 + 1776*y", "step_length": 6} {"cot_id": "7a4b740314041c235f6162ebb34e88f1b4ddb6f616b500b9188d939d6f56cdff", "datapoint": {"question": "Simplify this expression: -67*x**2*(-19*x**2 + 14*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1273*x**4 - 938*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 880, "polynomial_expr": "-67*x**2*(-19*x**2 + 14*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -67*x**2*(-19*x**2 + 14*x)\nExpanding the part (-19*x**2 + 14*x) using the distributive property, and we got: (14*x)*(-67*x**2) + (-67*x**2)*(-19*x**2)\n#Step 2:\nCurrent expression: (14*x)*(-67*x**2) + (-67*x**2)*(-19*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*x**2)*(-67*x**2) = 1273*x**4\n (14*x)*(-67*x**2) = -938*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1273*x**4 - 938*x**3\nNo more calculations needed.\n1273*x**4 - 938*x**3", "generated_answer": "1273*x**4 - 938*x**3", "step_length": 3} {"cot_id": "2cb0dc557e13cd96c29ff9f5a43a89fcb9b653245d8ce88a9aeaef0f083efa82", "datapoint": {"question": "Simplify this expression: (-12*y**3 - 25*y**2)*(30*y**3 + 30*y**2 + 29)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-360*y**6 - 1110*y**5 - 750*y**4 - 348*y**3 - 725*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 881, "polynomial_expr": "(-12*y**3 - 25*y**2)*(30*y**3 + 30*y**2 + 29)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-12*y**3 - 25*y**2)*(30*y**3 + 30*y**2 + 29)\nExpanding the part (-12*y**3 - 25*y**2) using the distributive property, and we got: (-25*y**2)*(30*y**3 + 30*y**2 + 29) + (-12*y**3)*(30*y**3 + 30*y**2 + 29)\n#Step 2:\nCurrent expression: (-25*y**2)*(30*y**3 + 30*y**2 + 29) + (-12*y**3)*(30*y**3 + 30*y**2 + 29)\nSimplifying the partial expression: (-25*y**2)*(30*y**3 + 30*y**2 + 29)\nExpanding the part (30*y**3 + 30*y**2 + 29) using the distributive property, and we got: 29*(-25*y**2) + (-25*y**2)*(30*y**2) + (-25*y**2)*(30*y**3)\nReplacing (-25*y**2)*(30*y**3 + 30*y**2 + 29) with 29*(-25*y**2) + (-25*y**2)*(30*y**2) + (-25*y**2)*(30*y**3) in the overall expression.\n#Step 3:\nCurrent expression: 29*(-25)*y**2 + (-25*y**2)*(30*y**2) + (-25*y**2)*(30*y**3) + (-12*y**3)*(30*y**3 + 30*y**2 + 29)\nSimplifying the partial expression: (-12*y**3)*(30*y**3 + 30*y**2 + 29)\nExpanding the part (30*y**3 + 30*y**2 + 29) using the distributive property, and we got: 29*(-12*y**3) + (30*y**2)*(-12*y**3) + (-12*y**3)*(30*y**3)\nReplacing (-12*y**3)*(30*y**3 + 30*y**2 + 29) with 29*(-12*y**3) + (30*y**2)*(-12*y**3) + (-12*y**3)*(30*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 29*(-12)*y**3 + 29*(-25)*y**2 + (-25*y**2)*(30*y**2) + (-25*y**2)*(30*y**3) + (30*y**2)*(-12*y**3) + (-12*y**3)*(30*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (30*y**2)*(-25*y**2) = -750*y**4\n (30*y**2)*(-12*y**3) = -360*y**5\n (30*y**3)*(-25*y**2) = -750*y**5\n (30*y**3)*(-12*y**3) = -360*y**6\n 29*-25*y**2 = -725*y**2\n 29*-12*y**3 = -348*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -360*y**6 - 750*y**5 - 360*y**5 - 750*y**4 - 348*y**3 - 725*y**2\nCombining like terms, got -360*y**6 - 1110*y**5 - 750*y**4 - 348*y**3 - 725*y**2\n#Step 6:\nCurrent expression: -360*y**6 - 1110*y**5 - 750*y**4 - 348*y**3 - 725*y**2\nNo more calculations needed.\n-360*y**6 - 1110*y**5 - 750*y**4 - 348*y**3 - 725*y**2", "generated_answer": "-360*y**6 - 1110*y**5 - 750*y**4 - 348*y**3 - 725*y**2", "step_length": 6} {"cot_id": "a64de07129539e3f1892ec2bb5ca34bd41c846c4eb107171f1aea2962a55f3bc", "datapoint": {"question": "Simplify this expression: (-41*z**3 + 5*z**2 + 13*z)*(-18*z**3 - 36*z**2 - 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "738*z**6 + 1386*z**5 - 414*z**4 + 1008*z**3 - 180*z**2 - 468*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 882, "polynomial_expr": "(-41*z**3 + 5*z**2 + 13*z)*(-18*z**3 - 36*z**2 - 36)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-41*z**3 + 5*z**2 + 13*z)*(-18*z**3 - 36*z**2 - 36)\nExpanding the part (-18*z**3 - 36*z**2 - 36) using the distributive property, and we got: (-36*z**2)*(-41*z**3 + 5*z**2 + 13*z) + (-18*z**3)*(-41*z**3 + 5*z**2 + 13*z) - 36*(-41*z**3 + 5*z**2 + 13*z)\n#Step 2:\nCurrent expression: (-36*z**2)*(-41*z**3 + 5*z**2 + 13*z) + (-18*z**3)*(-41*z**3 + 5*z**2 + 13*z) - 36*(-41*z**3 + 5*z**2 + 13*z)\nSimplifying the partial expression: -36*(-41*z**3 + 5*z**2 + 13*z)\nExpanding the part (-41*z**3 + 5*z**2 + 13*z) using the distributive property, and we got: (13*z)*(-36) + (5*z**2)*(-36) - 41*z**3*(-36)\nReplacing -36*(-41*z**3 + 5*z**2 + 13*z) with (13*z)*(-36) + (5*z**2)*(-36) - 41*z**3*(-36) in the overall expression.\n#Step 3:\nCurrent expression: (13*z)*(-36) + (-36*z**2)*(-41*z**3 + 5*z**2 + 13*z) + (5*z**2)*(-36) - 41*z**3*(-36) + (-18*z**3)*(-41*z**3 + 5*z**2 + 13*z)\nSimplifying the partial expression: (-36*z**2)*(-41*z**3 + 5*z**2 + 13*z)\nExpanding the part (-41*z**3 + 5*z**2 + 13*z) using the distributive property, and we got: (13*z)*(-36*z**2) + (-36*z**2)*(5*z**2) + (-36*z**2)*(-41*z**3)\nReplacing (-36*z**2)*(-41*z**3 + 5*z**2 + 13*z) with (13*z)*(-36*z**2) + (-36*z**2)*(5*z**2) + (-36*z**2)*(-41*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (13*z)*(-36*z**2) + (13*z)*(-36) + (-36*z**2)*(5*z**2) + (-36*z**2)*(-41*z**3) + (5*z**2)*(-36) - 41*z**3*(-36) + (-18*z**3)*(-41*z**3 + 5*z**2 + 13*z)\nSimplifying the partial expression: (-18*z**3)*(-41*z**3 + 5*z**2 + 13*z)\nExpanding the part (-41*z**3 + 5*z**2 + 13*z) using the distributive property, and we got: (13*z)*(-18*z**3) + (5*z**2)*(-18*z**3) + (-41*z**3)*(-18*z**3)\nReplacing (-18*z**3)*(-41*z**3 + 5*z**2 + 13*z) with (13*z)*(-18*z**3) + (5*z**2)*(-18*z**3) + (-41*z**3)*(-18*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (13*z)*(-36*z**2) + (13*z)*(-18*z**3) + (13*z)*(-36) + (-36*z**2)*(5*z**2) + (-36*z**2)*(-41*z**3) + (5*z**2)*(-18*z**3) + (5*z**2)*(-36) + (-41*z**3)*(-18*z**3) - 41*z**3*(-36)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*z**3)*-36 = 1476*z**3\n (-41*z**3)*(-36*z**2) = 1476*z**5\n (-41*z**3)*(-18*z**3) = 738*z**6\n (5*z**2)*-36 = -180*z**2\n (5*z**2)*(-36*z**2) = -180*z**4\n (5*z**2)*(-18*z**3) = -90*z**5\n (13*z)*-36 = -468*z\n (13*z)*(-36*z**2) = -468*z**3\n (13*z)*(-18*z**3) = -234*z**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 738*z**6 - 90*z**5 + 1476*z**5 - 234*z**4 - 180*z**4 - 468*z**3 + 1476*z**3 - 180*z**2 - 468*z\nCombining like terms, got 738*z**6 + 1386*z**5 - 414*z**4 + 1008*z**3 - 180*z**2 - 468*z\n#Step 7:\nCurrent expression: 738*z**6 + 1386*z**5 - 414*z**4 + 1008*z**3 - 180*z**2 - 468*z\nNo more calculations needed.\n738*z**6 + 1386*z**5 - 414*z**4 + 1008*z**3 - 180*z**2 - 468*z", "generated_answer": "738*z**6 + 1386*z**5 - 414*z**4 + 1008*z**3 - 180*z**2 - 468*z", "step_length": 7} {"cot_id": "10a5147d69993b813e907414492c053ff9f169586c6a69ceb7cc8d389e3c2a7e", "datapoint": {"question": "Simplify this expression: (-18*x**3 - 50*x**2 - 19*x)*(-7*x**3 - 43*x**2 + 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "126*x**6 + 1124*x**5 + 2283*x**4 + 799*x**3 - 50*x**2 - 19*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 883, "polynomial_expr": "(-18*x**3 - 50*x**2 - 19*x)*(-7*x**3 - 43*x**2 + 1)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-18*x**3 - 50*x**2 - 19*x)*(-7*x**3 - 43*x**2 + 1)\nExpanding the part (-7*x**3 - 43*x**2 + 1) using the distributive property, and we got: (-43*x**2)*(-18*x**3 - 50*x**2 - 19*x) + (-7*x**3)*(-18*x**3 - 50*x**2 - 19*x) + 1*(-18*x**3 - 50*x**2 - 19*x)\n#Step 2:\nCurrent expression: (-43*x**2)*(-18*x**3 - 50*x**2 - 19*x) + (-7*x**3)*(-18*x**3 - 50*x**2 - 19*x) + 1*(-18*x**3 - 50*x**2 - 19*x)\nSimplifying the partial expression: 1*(-18*x**3 - 50*x**2 - 19*x)\nExpanding the part (-18*x**3 - 50*x**2 - 19*x) using the distributive property, and we got: -19*x*1 - 50*x**2*1 - 18*x**3*1\nReplacing 1*(-18*x**3 - 50*x**2 - 19*x) with -19*x*1 - 50*x**2*1 - 18*x**3*1 in the overall expression.\n#Step 3:\nCurrent expression: -19*x*1 - 50*x**2*1 + (-43*x**2)*(-18*x**3 - 50*x**2 - 19*x) - 18*x**3*1 + (-7*x**3)*(-18*x**3 - 50*x**2 - 19*x)\nSimplifying the partial expression: (-43*x**2)*(-18*x**3 - 50*x**2 - 19*x)\nExpanding the part (-18*x**3 - 50*x**2 - 19*x) using the distributive property, and we got: (-19*x)*(-43*x**2) + (-50*x**2)*(-43*x**2) + (-43*x**2)*(-18*x**3)\nReplacing (-43*x**2)*(-18*x**3 - 50*x**2 - 19*x) with (-19*x)*(-43*x**2) + (-50*x**2)*(-43*x**2) + (-43*x**2)*(-18*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-19*x)*(-43*x**2) - 19*x*1 + (-50*x**2)*(-43*x**2) - 50*x**2*1 + (-43*x**2)*(-18*x**3) - 18*x**3*1 + (-7*x**3)*(-18*x**3 - 50*x**2 - 19*x)\nSimplifying the partial expression: (-7*x**3)*(-18*x**3 - 50*x**2 - 19*x)\nExpanding the part (-18*x**3 - 50*x**2 - 19*x) using the distributive property, and we got: (-19*x)*(-7*x**3) + (-50*x**2)*(-7*x**3) + (-18*x**3)*(-7*x**3)\nReplacing (-7*x**3)*(-18*x**3 - 50*x**2 - 19*x) with (-19*x)*(-7*x**3) + (-50*x**2)*(-7*x**3) + (-18*x**3)*(-7*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-19*x)*(-43*x**2) + (-19*x)*(-7*x**3) - 19*x*1 + (-50*x**2)*(-43*x**2) + (-50*x**2)*(-7*x**3) - 50*x**2*1 + (-43*x**2)*(-18*x**3) + (-18*x**3)*(-7*x**3) - 18*x**3*1\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-50*x**2)*1 = -50*x**2\n (-50*x**2)*(-43*x**2) = 2150*x**4\n (-50*x**2)*(-7*x**3) = 350*x**5\n (-19*x)*1 = -19*x\n (-19*x)*(-43*x**2) = 817*x**3\n (-19*x)*(-7*x**3) = 133*x**4\n (-18*x**3)*1 = -18*x**3\n (-18*x**3)*(-43*x**2) = 774*x**5\n (-18*x**3)*(-7*x**3) = 126*x**6\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 126*x**6 + 350*x**5 + 774*x**5 + 133*x**4 + 2150*x**4 - 18*x**3 + 817*x**3 - 50*x**2 - 19*x\nCombining like terms, got 126*x**6 + 1124*x**5 + 2283*x**4 + 799*x**3 - 50*x**2 - 19*x\n#Step 7:\nCurrent expression: 126*x**6 + 1124*x**5 + 2283*x**4 + 799*x**3 - 50*x**2 - 19*x\nNo more calculations needed.\n126*x**6 + 1124*x**5 + 2283*x**4 + 799*x**3 - 50*x**2 - 19*x", "generated_answer": "126*x**6 + 1124*x**5 + 2283*x**4 + 799*x**3 - 50*x**2 - 19*x", "step_length": 7} {"cot_id": "45643b94c9042634ff6170c53141fffd8c1624c3251d781f3fce131ba3968b6e", "datapoint": {"question": "Calculate the following: (-39*z**2 - 11)*(12*z**3 + 40*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-468*z**5 - 1692*z**3 - 440*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 884, "polynomial_expr": "(-39*z**2 - 11)*(12*z**3 + 40*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-39*z**2 - 11)*(12*z**3 + 40*z)\nExpanding the part (-39*z**2 - 11) using the distributive property, and we got: (-39*z**2)*(12*z**3 + 40*z) - 11*(12*z**3 + 40*z)\n#Step 2:\nCurrent expression: (-39*z**2)*(12*z**3 + 40*z) - 11*(12*z**3 + 40*z)\nSimplifying the partial expression: -11*(12*z**3 + 40*z)\nExpanding the part (12*z**3 + 40*z) using the distributive property, and we got: (40*z)*(-11) + (12*z**3)*(-11)\nReplacing -11*(12*z**3 + 40*z) with (40*z)*(-11) + (12*z**3)*(-11) in the overall expression.\n#Step 3:\nCurrent expression: (40*z)*(-11) + (-39*z**2)*(12*z**3 + 40*z) + (12*z**3)*(-11)\nSimplifying the partial expression: (-39*z**2)*(12*z**3 + 40*z)\nExpanding the part (12*z**3 + 40*z) using the distributive property, and we got: (40*z)*(-39*z**2) + (-39*z**2)*(12*z**3)\nReplacing (-39*z**2)*(12*z**3 + 40*z) with (40*z)*(-39*z**2) + (-39*z**2)*(12*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (40*z)*(-39*z**2) + (40*z)*(-11) + (-39*z**2)*(12*z**3) + (12*z**3)*(-11)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (12*z**3)*-11 = -132*z**3\n (12*z**3)*(-39*z**2) = -468*z**5\n (40*z)*-11 = -440*z\n (40*z)*(-39*z**2) = -1560*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -468*z**5 - 1560*z**3 - 132*z**3 - 440*z\nCombining like terms, got -468*z**5 - 1692*z**3 - 440*z\n#Step 6:\nCurrent expression: -468*z**5 - 1692*z**3 - 440*z\nNo more calculations needed.\n-468*z**5 - 1692*z**3 - 440*z", "generated_answer": "-468*z**5 - 1692*z**3 - 440*z", "step_length": 6} {"cot_id": "6a33935f920ceb3d84fd9a3e907d01621f4932ef5941085650144acaef18f0ee", "datapoint": {"question": "Simplify this expression: (7 - 25*z**2)*(-15*z**2 - 43*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "375*z**4 + 1075*z**3 - 105*z**2 - 301*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 885, "polynomial_expr": "(7 - 25*z**2)*(-15*z**2 - 43*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7 - 25*z**2)*(-15*z**2 - 43*z)\nExpanding the part (7 - 25*z**2) using the distributive property, and we got: (-25*z**2)*(-15*z**2 - 43*z) + 7*(-15*z**2 - 43*z)\n#Step 2:\nCurrent expression: (-25*z**2)*(-15*z**2 - 43*z) + 7*(-15*z**2 - 43*z)\nSimplifying the partial expression: 7*(-15*z**2 - 43*z)\nExpanding the part (-15*z**2 - 43*z) using the distributive property, and we got: -43*z*7 - 15*z**2*7\nReplacing 7*(-15*z**2 - 43*z) with -43*z*7 - 15*z**2*7 in the overall expression.\n#Step 3:\nCurrent expression: -43*z*7 + (-25*z**2)*(-15*z**2 - 43*z) - 15*z**2*7\nSimplifying the partial expression: (-25*z**2)*(-15*z**2 - 43*z)\nExpanding the part (-15*z**2 - 43*z) using the distributive property, and we got: (-43*z)*(-25*z**2) + (-25*z**2)*(-15*z**2)\nReplacing (-25*z**2)*(-15*z**2 - 43*z) with (-43*z)*(-25*z**2) + (-25*z**2)*(-15*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-43*z)*(-25*z**2) - 43*z*7 + (-25*z**2)*(-15*z**2) - 15*z**2*7\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-43*z)*7 = -301*z\n (-43*z)*(-25*z**2) = 1075*z**3\n (-15*z**2)*7 = -105*z**2\n (-15*z**2)*(-25*z**2) = 375*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 375*z**4 + 1075*z**3 - 105*z**2 - 301*z\nNo more calculations needed.\n375*z**4 + 1075*z**3 - 105*z**2 - 301*z", "generated_answer": "375*z**4 + 1075*z**3 - 105*z**2 - 301*z", "step_length": 5} {"cot_id": "fd868d9000e054bd2bac207dff7208855708e9f29d4aa3f0ddf240564a7d6a26", "datapoint": {"question": "Simplify this expression: (2 - 18*y)*(47*y**3 - 39*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-846*y**4 + 796*y**3 - 78*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 886, "polynomial_expr": "(2 - 18*y)*(47*y**3 - 39*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2 - 18*y)*(47*y**3 - 39*y**2)\nExpanding the part (2 - 18*y) using the distributive property, and we got: (-18*y)*(47*y**3 - 39*y**2) + 2*(47*y**3 - 39*y**2)\n#Step 2:\nCurrent expression: (-18*y)*(47*y**3 - 39*y**2) + 2*(47*y**3 - 39*y**2)\nSimplifying the partial expression: 2*(47*y**3 - 39*y**2)\nExpanding the part (47*y**3 - 39*y**2) using the distributive property, and we got: -39*y**2*2 + (47*y**3)*2\nReplacing 2*(47*y**3 - 39*y**2) with -39*y**2*2 + (47*y**3)*2 in the overall expression.\n#Step 3:\nCurrent expression: (-18*y)*(47*y**3 - 39*y**2) - 39*y**2*2 + (47*y**3)*2\nSimplifying the partial expression: (-18*y)*(47*y**3 - 39*y**2)\nExpanding the part (47*y**3 - 39*y**2) using the distributive property, and we got: (-18*y)*(-39*y**2) + (-18*y)*(47*y**3)\nReplacing (-18*y)*(47*y**3 - 39*y**2) with (-18*y)*(-39*y**2) + (-18*y)*(47*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-18*y)*(-39*y**2) + (-18*y)*(47*y**3) - 39*y**2*2 + (47*y**3)*2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*y**2)*2 = -78*y**2\n (-39*y**2)*(-18*y) = 702*y**3\n (47*y**3)*2 = 94*y**3\n (47*y**3)*(-18*y) = -846*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -846*y**4 + 94*y**3 + 702*y**3 - 78*y**2\nCombining like terms, got -846*y**4 + 796*y**3 - 78*y**2\n#Step 6:\nCurrent expression: -846*y**4 + 796*y**3 - 78*y**2\nNo more calculations needed.\n-846*y**4 + 796*y**3 - 78*y**2", "generated_answer": "-846*y**4 + 796*y**3 - 78*y**2", "step_length": 6} {"cot_id": "260003babcea091c482b94f0af56a20acf8487bea5f55633416200ad7323f6af", "datapoint": {"question": "Simplify this expression: (26*x**2 - 33)*(5*x**3 - 44*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "130*x**5 - 1144*x**4 - 165*x**3 + 1452*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 887, "polynomial_expr": "(26*x**2 - 33)*(5*x**3 - 44*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (26*x**2 - 33)*(5*x**3 - 44*x**2)\nExpanding the part (26*x**2 - 33) using the distributive property, and we got: (26*x**2)*(5*x**3 - 44*x**2) - 33*(5*x**3 - 44*x**2)\n#Step 2:\nCurrent expression: (26*x**2)*(5*x**3 - 44*x**2) - 33*(5*x**3 - 44*x**2)\nSimplifying the partial expression: -33*(5*x**3 - 44*x**2)\nExpanding the part (5*x**3 - 44*x**2) using the distributive property, and we got: -44*x**2*(-33) + (5*x**3)*(-33)\nReplacing -33*(5*x**3 - 44*x**2) with -44*x**2*(-33) + (5*x**3)*(-33) in the overall expression.\n#Step 3:\nCurrent expression: -44*x**2*(-33) + (26*x**2)*(5*x**3 - 44*x**2) + (5*x**3)*(-33)\nSimplifying the partial expression: (26*x**2)*(5*x**3 - 44*x**2)\nExpanding the part (5*x**3 - 44*x**2) using the distributive property, and we got: (-44*x**2)*(26*x**2) + (26*x**2)*(5*x**3)\nReplacing (26*x**2)*(5*x**3 - 44*x**2) with (-44*x**2)*(26*x**2) + (26*x**2)*(5*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-44*x**2)*(26*x**2) - 44*x**2*(-33) + (26*x**2)*(5*x**3) + (5*x**3)*(-33)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-44*x**2)*-33 = 1452*x**2\n (-44*x**2)*(26*x**2) = -1144*x**4\n (5*x**3)*-33 = -165*x**3\n (5*x**3)*(26*x**2) = 130*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 130*x**5 - 1144*x**4 - 165*x**3 + 1452*x**2\nNo more calculations needed.\n130*x**5 - 1144*x**4 - 165*x**3 + 1452*x**2", "generated_answer": "130*x**5 - 1144*x**4 - 165*x**3 + 1452*x**2", "step_length": 5} {"cot_id": "e7aea65fb3783348704f893237a2ca4e4adeea0ecada1e75eda69c0958efd599", "datapoint": {"question": "Simplify this expression: (18*z - 2)*(-20*z**3 + 40*z**2 + 20*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-360*z**4 + 760*z**3 + 280*z**2 - 40*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 888, "polynomial_expr": "(18*z - 2)*(-20*z**3 + 40*z**2 + 20*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (18*z - 2)*(-20*z**3 + 40*z**2 + 20*z)\nExpanding the part (18*z - 2) using the distributive property, and we got: (18*z)*(-20*z**3 + 40*z**2 + 20*z) - 2*(-20*z**3 + 40*z**2 + 20*z)\n#Step 2:\nCurrent expression: (18*z)*(-20*z**3 + 40*z**2 + 20*z) - 2*(-20*z**3 + 40*z**2 + 20*z)\nSimplifying the partial expression: -2*(-20*z**3 + 40*z**2 + 20*z)\nExpanding the part (-20*z**3 + 40*z**2 + 20*z) using the distributive property, and we got: (20*z)*(-2) + (40*z**2)*(-2) - 20*z**3*(-2)\nReplacing -2*(-20*z**3 + 40*z**2 + 20*z) with (20*z)*(-2) + (40*z**2)*(-2) - 20*z**3*(-2) in the overall expression.\n#Step 3:\nCurrent expression: (18*z)*(-20*z**3 + 40*z**2 + 20*z) + (20*z)*(-2) + (40*z**2)*(-2) - 20*z**3*(-2)\nSimplifying the partial expression: (18*z)*(-20*z**3 + 40*z**2 + 20*z)\nExpanding the part (-20*z**3 + 40*z**2 + 20*z) using the distributive property, and we got: (18*z)*(20*z) + (18*z)*(40*z**2) + (18*z)*(-20*z**3)\nReplacing (18*z)*(-20*z**3 + 40*z**2 + 20*z) with (18*z)*(20*z) + (18*z)*(40*z**2) + (18*z)*(-20*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (18*z)*(20*z) + (18*z)*(40*z**2) + (18*z)*(-20*z**3) + (20*z)*(-2) + (40*z**2)*(-2) - 20*z**3*(-2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*z**3)*-2 = 40*z**3\n (-20*z**3)*(18*z) = -360*z**4\n (20*z)*-2 = -40*z\n (20*z)*(18*z) = 360*z**2\n (40*z**2)*-2 = -80*z**2\n (40*z**2)*(18*z) = 720*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -360*z**4 + 40*z**3 + 720*z**3 - 80*z**2 + 360*z**2 - 40*z\nCombining like terms, got -360*z**4 + 760*z**3 + 280*z**2 - 40*z\n#Step 6:\nCurrent expression: -360*z**4 + 760*z**3 + 280*z**2 - 40*z\nNo more calculations needed.\n-360*z**4 + 760*z**3 + 280*z**2 - 40*z", "generated_answer": "-360*z**4 + 760*z**3 + 280*z**2 - 40*z", "step_length": 6} {"cot_id": "8c5281ca6a98b8ccf4c71012ffc6cb7b806d14a3fe49b8a741821616b00fdf25", "datapoint": {"question": "Calculate the following: (59*y**2 - 48*y)*(67*y**3 + 41*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "3953*y**5 - 797*y**4 - 1968*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 889, "polynomial_expr": "(59*y**2 - 48*y)*(67*y**3 + 41*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (59*y**2 - 48*y)*(67*y**3 + 41*y**2)\nExpanding the part (59*y**2 - 48*y) using the distributive property, and we got: (-48*y)*(67*y**3 + 41*y**2) + (59*y**2)*(67*y**3 + 41*y**2)\n#Step 2:\nCurrent expression: (-48*y)*(67*y**3 + 41*y**2) + (59*y**2)*(67*y**3 + 41*y**2)\nSimplifying the partial expression: (-48*y)*(67*y**3 + 41*y**2)\nExpanding the part (67*y**3 + 41*y**2) using the distributive property, and we got: (-48*y)*(41*y**2) + (-48*y)*(67*y**3)\nReplacing (-48*y)*(67*y**3 + 41*y**2) with (-48*y)*(41*y**2) + (-48*y)*(67*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-48*y)*(41*y**2) + (-48*y)*(67*y**3) + (59*y**2)*(67*y**3 + 41*y**2)\nSimplifying the partial expression: (59*y**2)*(67*y**3 + 41*y**2)\nExpanding the part (67*y**3 + 41*y**2) using the distributive property, and we got: (41*y**2)*(59*y**2) + (59*y**2)*(67*y**3)\nReplacing (59*y**2)*(67*y**3 + 41*y**2) with (41*y**2)*(59*y**2) + (59*y**2)*(67*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-48*y)*(41*y**2) + (-48*y)*(67*y**3) + (41*y**2)*(59*y**2) + (59*y**2)*(67*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (41*y**2)*(-48*y) = -1968*y**3\n (41*y**2)*(59*y**2) = 2419*y**4\n (67*y**3)*(-48*y) = -3216*y**4\n (67*y**3)*(59*y**2) = 3953*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 3953*y**5 - 3216*y**4 + 2419*y**4 - 1968*y**3\nCombining like terms, got 3953*y**5 - 797*y**4 - 1968*y**3\n#Step 6:\nCurrent expression: 3953*y**5 - 797*y**4 - 1968*y**3\nNo more calculations needed.\n3953*y**5 - 797*y**4 - 1968*y**3", "generated_answer": "3953*y**5 - 797*y**4 - 1968*y**3", "step_length": 6} {"cot_id": "6fccf8be9eb5d41825de3c050aa09985bac75787d4c4b7b5a7c595b59949badf", "datapoint": {"question": "Calculate the following: (-30*z**3 + 30*z**2)*(9*z**3 - 33*z**2 + 49*z - 2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-270*z**6 + 1260*z**5 - 2460*z**4 + 1530*z**3 - 60*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 890, "polynomial_expr": "(-30*z**3 + 30*z**2)*(9*z**3 - 33*z**2 + 49*z - 2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-30*z**3 + 30*z**2)*(9*z**3 - 33*z**2 + 49*z - 2)\nExpanding the part (-30*z**3 + 30*z**2) using the distributive property, and we got: (30*z**2)*(9*z**3 - 33*z**2 + 49*z - 2) + (-30*z**3)*(9*z**3 - 33*z**2 + 49*z - 2)\n#Step 2:\nCurrent expression: (30*z**2)*(9*z**3 - 33*z**2 + 49*z - 2) + (-30*z**3)*(9*z**3 - 33*z**2 + 49*z - 2)\nSimplifying the partial expression: (-30*z**3)*(9*z**3 - 33*z**2 + 49*z - 2)\nExpanding the part (9*z**3 - 33*z**2 + 49*z - 2) using the distributive property, and we got: -(-1)*60*z**3 + (49*z)*(-30*z**3) + (-33*z**2)*(-30*z**3) + (-30*z**3)*(9*z**3)\nReplacing (-30*z**3)*(9*z**3 - 33*z**2 + 49*z - 2) with -(-1)*60*z**3 + (49*z)*(-30*z**3) + (-33*z**2)*(-30*z**3) + (-30*z**3)*(9*z**3) in the overall expression.\n#Step 3:\nCurrent expression: -2*(-30)*z**3 + (49*z)*(-30*z**3) + (-33*z**2)*(-30*z**3) + (30*z**2)*(9*z**3 - 33*z**2 + 49*z - 2) + (-30*z**3)*(9*z**3)\nSimplifying the partial expression: (30*z**2)*(9*z**3 - 33*z**2 + 49*z - 2)\nExpanding the part (9*z**3 - 33*z**2 + 49*z - 2) using the distributive property, and we got: -60*z**2 + (49*z)*(30*z**2) + (-33*z**2)*(30*z**2) + (30*z**2)*(9*z**3)\nReplacing (30*z**2)*(9*z**3 - 33*z**2 + 49*z - 2) with -60*z**2 + (49*z)*(30*z**2) + (-33*z**2)*(30*z**2) + (30*z**2)*(9*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -2*(-30)*z**3 - 2*30*z**2 + (49*z)*(30*z**2) + (49*z)*(-30*z**3) + (-33*z**2)*(30*z**2) + (-33*z**2)*(-30*z**3) + (30*z**2)*(9*z**3) + (-30*z**3)*(9*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*z**2)*(-30*z**3) = 990*z**5\n (-33*z**2)*(30*z**2) = -990*z**4\n (9*z**3)*(-30*z**3) = -270*z**6\n (9*z**3)*(30*z**2) = 270*z**5\n (49*z)*(-30*z**3) = -1470*z**4\n (49*z)*(30*z**2) = 1470*z**3\n -2*-30*z**3 = 60*z**3\n -2*30*z**2 = -60*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -270*z**6 + 270*z**5 + 990*z**5 - 1470*z**4 - 990*z**4 + 60*z**3 + 1470*z**3 - 60*z**2\nCombining like terms, got -270*z**6 + 1260*z**5 - 2460*z**4 + 1530*z**3 - 60*z**2\n#Step 6:\nCurrent expression: -270*z**6 + 1260*z**5 - 2460*z**4 + 1530*z**3 - 60*z**2\nNo more calculations needed.\n-270*z**6 + 1260*z**5 - 2460*z**4 + 1530*z**3 - 60*z**2", "generated_answer": "-270*z**6 + 1260*z**5 - 2460*z**4 + 1530*z**3 - 60*z**2", "step_length": 6} {"cot_id": "071079392578884015f823dad6858374e97aae61a239a935739023e4e67c679d", "datapoint": {"question": "Simplify this expression: (33*z**2 + 7)*(56*z**3 - 3*z**2 - 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1848*z**5 - 99*z**4 + 392*z**3 - 1308*z**2 - 273", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 891, "polynomial_expr": "(33*z**2 + 7)*(56*z**3 - 3*z**2 - 39)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (33*z**2 + 7)*(56*z**3 - 3*z**2 - 39)\nExpanding the part (33*z**2 + 7) using the distributive property, and we got: (33*z**2)*(56*z**3 - 3*z**2 - 39) + 7*(56*z**3 - 3*z**2 - 39)\n#Step 2:\nCurrent expression: (33*z**2)*(56*z**3 - 3*z**2 - 39) + 7*(56*z**3 - 3*z**2 - 39)\nSimplifying the partial expression: 7*(56*z**3 - 3*z**2 - 39)\nExpanding the part (56*z**3 - 3*z**2 - 39) using the distributive property, and we got: -3*z**2*7 + (56*z**3)*7 - 39*7\nReplacing 7*(56*z**3 - 3*z**2 - 39) with -3*z**2*7 + (56*z**3)*7 - 39*7 in the overall expression.\n#Step 3:\nCurrent expression: -3*z**2*7 + (33*z**2)*(56*z**3 - 3*z**2 - 39) + (56*z**3)*7 - 273\nSimplifying the partial expression: (33*z**2)*(56*z**3 - 3*z**2 - 39)\nExpanding the part (56*z**3 - 3*z**2 - 39) using the distributive property, and we got: -1287*z**2 + (-3*z**2)*(33*z**2) + (33*z**2)*(56*z**3)\nReplacing (33*z**2)*(56*z**3 - 3*z**2 - 39) with -1287*z**2 + (-3*z**2)*(33*z**2) + (33*z**2)*(56*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -39*33*z**2 + (-3*z**2)*(33*z**2) - 3*z**2*7 + (33*z**2)*(56*z**3) + (56*z**3)*7 - 273\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-3*z**2)*7 = -21*z**2\n (-3*z**2)*(33*z**2) = -99*z**4\n (56*z**3)*7 = 392*z**3\n (56*z**3)*(33*z**2) = 1848*z**5\n -39*33*z**2 = -1287*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1848*z**5 - 99*z**4 + 392*z**3 - 1287*z**2 - 21*z**2 - 273\nCombining like terms, got 1848*z**5 - 99*z**4 + 392*z**3 - 1308*z**2 - 273\n#Step 6:\nCurrent expression: 1848*z**5 - 99*z**4 + 392*z**3 - 1308*z**2 - 273\nNo more calculations needed.\n1848*z**5 - 99*z**4 + 392*z**3 - 1308*z**2 - 273", "generated_answer": "1848*z**5 - 99*z**4 + 392*z**3 - 1308*z**2 - 273", "step_length": 6} {"cot_id": "1de43c0a52253ce62e8b47ecb9a6294a33e9714085964f13d6293afd7b8ad996", "datapoint": {"question": "Calculate the following: (2*y**3 + 10*y)*(25*y**2 + 86*y + 23)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "50*y**5 + 172*y**4 + 296*y**3 + 860*y**2 + 230*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 892, "polynomial_expr": "(2*y**3 + 10*y)*(25*y**2 + 86*y + 23)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2*y**3 + 10*y)*(25*y**2 + 86*y + 23)\nExpanding the part (2*y**3 + 10*y) using the distributive property, and we got: (10*y)*(25*y**2 + 86*y + 23) + (2*y**3)*(25*y**2 + 86*y + 23)\n#Step 2:\nCurrent expression: (10*y)*(25*y**2 + 86*y + 23) + (2*y**3)*(25*y**2 + 86*y + 23)\nSimplifying the partial expression: (2*y**3)*(25*y**2 + 86*y + 23)\nExpanding the part (25*y**2 + 86*y + 23) using the distributive property, and we got: 23*(2*y**3) + (86*y)*(2*y**3) + (25*y**2)*(2*y**3)\nReplacing (2*y**3)*(25*y**2 + 86*y + 23) with 23*(2*y**3) + (86*y)*(2*y**3) + (25*y**2)*(2*y**3) in the overall expression.\n#Step 3:\nCurrent expression: 23*2*y**3 + (10*y)*(25*y**2 + 86*y + 23) + (86*y)*(2*y**3) + (25*y**2)*(2*y**3)\nSimplifying the partial expression: (10*y)*(25*y**2 + 86*y + 23)\nExpanding the part (25*y**2 + 86*y + 23) using the distributive property, and we got: 23*(10*y) + (10*y)*(86*y) + (10*y)*(25*y**2)\nReplacing (10*y)*(25*y**2 + 86*y + 23) with 23*(10*y) + (10*y)*(86*y) + (10*y)*(25*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 23*2*y**3 + 23*10*y + (10*y)*(86*y) + (10*y)*(25*y**2) + (86*y)*(2*y**3) + (25*y**2)*(2*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (25*y**2)*(2*y**3) = 50*y**5\n (25*y**2)*(10*y) = 250*y**3\n (86*y)*(2*y**3) = 172*y**4\n (86*y)*(10*y) = 860*y**2\n 23*2*y**3 = 46*y**3\n 23*10*y = 230*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 50*y**5 + 172*y**4 + 46*y**3 + 250*y**3 + 860*y**2 + 230*y\nCombining like terms, got 50*y**5 + 172*y**4 + 296*y**3 + 860*y**2 + 230*y\n#Step 6:\nCurrent expression: 50*y**5 + 172*y**4 + 296*y**3 + 860*y**2 + 230*y\nNo more calculations needed.\n50*y**5 + 172*y**4 + 296*y**3 + 860*y**2 + 230*y", "generated_answer": "50*y**5 + 172*y**4 + 296*y**3 + 860*y**2 + 230*y", "step_length": 6} {"cot_id": "a5d7db6b7f65e680736bf41796fef95878e6b1b70f906e0fa33b09a33aa8ca2b", "datapoint": {"question": "Calculate the following: (49*z**2 - 4*z)*(16*z**3 + 72)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "784*z**5 - 64*z**4 + 3528*z**2 - 288*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 893, "polynomial_expr": "(49*z**2 - 4*z)*(16*z**3 + 72)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (49*z**2 - 4*z)*(16*z**3 + 72)\nExpanding the part (16*z**3 + 72) using the distributive property, and we got: (16*z**3)*(49*z**2 - 4*z) + 72*(49*z**2 - 4*z)\n#Step 2:\nCurrent expression: (16*z**3)*(49*z**2 - 4*z) + 72*(49*z**2 - 4*z)\nSimplifying the partial expression: 72*(49*z**2 - 4*z)\nExpanding the part (49*z**2 - 4*z) using the distributive property, and we got: -4*z*72 + (49*z**2)*72\nReplacing 72*(49*z**2 - 4*z) with -4*z*72 + (49*z**2)*72 in the overall expression.\n#Step 3:\nCurrent expression: -4*z*72 + (49*z**2)*72 + (16*z**3)*(49*z**2 - 4*z)\nSimplifying the partial expression: (16*z**3)*(49*z**2 - 4*z)\nExpanding the part (49*z**2 - 4*z) using the distributive property, and we got: (-4*z)*(16*z**3) + (49*z**2)*(16*z**3)\nReplacing (16*z**3)*(49*z**2 - 4*z) with (-4*z)*(16*z**3) + (49*z**2)*(16*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-4*z)*(16*z**3) - 4*z*72 + (49*z**2)*(16*z**3) + (49*z**2)*72\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-4*z)*72 = -288*z\n (-4*z)*(16*z**3) = -64*z**4\n (49*z**2)*72 = 3528*z**2\n (49*z**2)*(16*z**3) = 784*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 784*z**5 - 64*z**4 + 3528*z**2 - 288*z\nNo more calculations needed.\n784*z**5 - 64*z**4 + 3528*z**2 - 288*z", "generated_answer": "784*z**5 - 64*z**4 + 3528*z**2 - 288*z", "step_length": 5} {"cot_id": "dcc5d7e48ff29301cff62807a2d81cf68fc168aaf546a2ef3524a654e9b5c0a2", "datapoint": {"question": "Simplify this expression: (32*z**3 + 12*z + 15)*(44*z**3 + 41*z**2 - 10*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1408*z**6 + 1312*z**5 + 208*z**4 + 1152*z**3 + 495*z**2 - 150*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 895, "polynomial_expr": "(32*z**3 + 12*z + 15)*(44*z**3 + 41*z**2 - 10*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (32*z**3 + 12*z + 15)*(44*z**3 + 41*z**2 - 10*z)\nExpanding the part (32*z**3 + 12*z + 15) using the distributive property, and we got: (12*z)*(44*z**3 + 41*z**2 - 10*z) + (32*z**3)*(44*z**3 + 41*z**2 - 10*z) + 15*(44*z**3 + 41*z**2 - 10*z)\n#Step 2:\nCurrent expression: (12*z)*(44*z**3 + 41*z**2 - 10*z) + (32*z**3)*(44*z**3 + 41*z**2 - 10*z) + 15*(44*z**3 + 41*z**2 - 10*z)\nSimplifying the partial expression: 15*(44*z**3 + 41*z**2 - 10*z)\nExpanding the part (44*z**3 + 41*z**2 - 10*z) using the distributive property, and we got: -10*z*15 + (41*z**2)*15 + (44*z**3)*15\nReplacing 15*(44*z**3 + 41*z**2 - 10*z) with -10*z*15 + (41*z**2)*15 + (44*z**3)*15 in the overall expression.\n#Step 3:\nCurrent expression: -10*z*15 + (12*z)*(44*z**3 + 41*z**2 - 10*z) + (41*z**2)*15 + (32*z**3)*(44*z**3 + 41*z**2 - 10*z) + (44*z**3)*15\nSimplifying the partial expression: (12*z)*(44*z**3 + 41*z**2 - 10*z)\nExpanding the part (44*z**3 + 41*z**2 - 10*z) using the distributive property, and we got: (-10*z)*(12*z) + (12*z)*(41*z**2) + (12*z)*(44*z**3)\nReplacing (12*z)*(44*z**3 + 41*z**2 - 10*z) with (-10*z)*(12*z) + (12*z)*(41*z**2) + (12*z)*(44*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-10*z)*(12*z) - 10*z*15 + (12*z)*(41*z**2) + (12*z)*(44*z**3) + (41*z**2)*15 + (32*z**3)*(44*z**3 + 41*z**2 - 10*z) + (44*z**3)*15\nSimplifying the partial expression: (32*z**3)*(44*z**3 + 41*z**2 - 10*z)\nExpanding the part (44*z**3 + 41*z**2 - 10*z) using the distributive property, and we got: (-10*z)*(32*z**3) + (41*z**2)*(32*z**3) + (32*z**3)*(44*z**3)\nReplacing (32*z**3)*(44*z**3 + 41*z**2 - 10*z) with (-10*z)*(32*z**3) + (41*z**2)*(32*z**3) + (32*z**3)*(44*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-10*z)*(12*z) + (-10*z)*(32*z**3) - 10*z*15 + (12*z)*(41*z**2) + (12*z)*(44*z**3) + (41*z**2)*(32*z**3) + (41*z**2)*15 + (32*z**3)*(44*z**3) + (44*z**3)*15\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*z)*15 = -150*z\n (-10*z)*(12*z) = -120*z**2\n (-10*z)*(32*z**3) = -320*z**4\n (41*z**2)*15 = 615*z**2\n (41*z**2)*(12*z) = 492*z**3\n (41*z**2)*(32*z**3) = 1312*z**5\n (44*z**3)*15 = 660*z**3\n (44*z**3)*(12*z) = 528*z**4\n (44*z**3)*(32*z**3) = 1408*z**6\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1408*z**6 + 1312*z**5 - 320*z**4 + 528*z**4 + 492*z**3 + 660*z**3 - 120*z**2 + 615*z**2 - 150*z\nCombining like terms, got 1408*z**6 + 1312*z**5 + 208*z**4 + 1152*z**3 + 495*z**2 - 150*z\n#Step 7:\nCurrent expression: 1408*z**6 + 1312*z**5 + 208*z**4 + 1152*z**3 + 495*z**2 - 150*z\nNo more calculations needed.\n1408*z**6 + 1312*z**5 + 208*z**4 + 1152*z**3 + 495*z**2 - 150*z", "generated_answer": "1408*z**6 + 1312*z**5 + 208*z**4 + 1152*z**3 + 495*z**2 - 150*z", "step_length": 7} {"cot_id": "7e6b3b9aaf8622eced2c1c408bd5765c5fbae8eca8c8dfa65da68b78f57ca8b8", "datapoint": {"question": "Simplify this expression: (-29*y**3 + 22*y + 44)*(21*y**3 - 30*y - 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-609*y**6 + 1332*y**4 + 2055*y**3 - 660*y**2 - 2178*y - 1716", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 896, "polynomial_expr": "(-29*y**3 + 22*y + 44)*(21*y**3 - 30*y - 39)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-29*y**3 + 22*y + 44)*(21*y**3 - 30*y - 39)\nExpanding the part (21*y**3 - 30*y - 39) using the distributive property, and we got: (-30*y)*(-29*y**3 + 22*y + 44) + (21*y**3)*(-29*y**3 + 22*y + 44) - 39*(-29*y**3 + 22*y + 44)\n#Step 2:\nCurrent expression: (-30*y)*(-29*y**3 + 22*y + 44) + (21*y**3)*(-29*y**3 + 22*y + 44) - 39*(-29*y**3 + 22*y + 44)\nSimplifying the partial expression: -39*(-29*y**3 + 22*y + 44)\nExpanding the part (-29*y**3 + 22*y + 44) using the distributive property, and we got: (22*y)*(-39) - 29*y**3*(-39) + 44*(-39)\nReplacing -39*(-29*y**3 + 22*y + 44) with (22*y)*(-39) - 29*y**3*(-39) + 44*(-39) in the overall expression.\n#Step 3:\nCurrent expression: (-30*y)*(-29*y**3 + 22*y + 44) + (22*y)*(-39) - 29*y**3*(-39) + (21*y**3)*(-29*y**3 + 22*y + 44) - 1716\nSimplifying the partial expression: (-30*y)*(-29*y**3 + 22*y + 44)\nExpanding the part (-29*y**3 + 22*y + 44) using the distributive property, and we got: (-30*y)*(22*y) + (-30*y)*(-29*y**3) + 44*(-30*y)\nReplacing (-30*y)*(-29*y**3 + 22*y + 44) with (-30*y)*(22*y) + (-30*y)*(-29*y**3) + 44*(-30*y) in the overall expression.\n#Step 4:\nCurrent expression: (-30*y)*(22*y) + (-30*y)*(-29*y**3) + 44*(-30)*y + (22*y)*(-39) - 29*y**3*(-39) + (21*y**3)*(-29*y**3 + 22*y + 44) - 1716\nSimplifying the partial expression: (21*y**3)*(-29*y**3 + 22*y + 44)\nExpanding the part (-29*y**3 + 22*y + 44) using the distributive property, and we got: 44*(21*y**3) + (22*y)*(21*y**3) + (-29*y**3)*(21*y**3)\nReplacing (21*y**3)*(-29*y**3 + 22*y + 44) with 44*(21*y**3) + (22*y)*(21*y**3) + (-29*y**3)*(21*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-30*y)*(22*y) + (-30*y)*(-29*y**3) + 44*21*y**3 + 44*(-30)*y + (22*y)*(21*y**3) + (22*y)*(-39) + (-29*y**3)*(21*y**3) - 29*y**3*(-39) - 1716\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*y**3)*-39 = 1131*y**3\n (-29*y**3)*(-30*y) = 870*y**4\n (-29*y**3)*(21*y**3) = -609*y**6\n (22*y)*-39 = -858*y\n (22*y)*(-30*y) = -660*y**2\n (22*y)*(21*y**3) = 462*y**4\n 44*-30*y = -1320*y\n 44*21*y**3 = 924*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -609*y**6 + 462*y**4 + 870*y**4 + 924*y**3 + 1131*y**3 - 660*y**2 - 1320*y - 858*y - 1716\nCombining like terms, got -609*y**6 + 1332*y**4 + 2055*y**3 - 660*y**2 - 2178*y - 1716\n#Step 7:\nCurrent expression: -609*y**6 + 1332*y**4 + 2055*y**3 - 660*y**2 - 2178*y - 1716\nNo more calculations needed.\n-609*y**6 + 1332*y**4 + 2055*y**3 - 660*y**2 - 2178*y - 1716", "generated_answer": "-609*y**6 + 1332*y**4 + 2055*y**3 - 660*y**2 - 2178*y - 1716", "step_length": 7} {"cot_id": "33e5ed83d7cbab7ec8c05bdf5244af81c50138a068c4c985b6dd22725ffb1345", "datapoint": {"question": "Simplify this expression: 28*x**2*(18*x**2 - 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "504*x**4 - 840*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 897, "polynomial_expr": "28*x**2*(18*x**2 - 30)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 28*x**2*(18*x**2 - 30)\nExpanding the part (18*x**2 - 30) using the distributive property, and we got: -840*x**2 + (18*x**2)*(28*x**2)\n#Step 2:\nCurrent expression: -840*x**2 + (18*x**2)*(28*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -30*(28*x**2) = -840*x**2\n (18*x**2)*(28*x**2) = 504*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 504*x**4 - 840*x**2\nNo more calculations needed.\n504*x**4 - 840*x**2", "generated_answer": "504*x**4 - 840*x**2", "step_length": 3} {"cot_id": "29051fcf694e5514dfc192a947ec180ce46ccd823fbd3a6df684745682222521", "datapoint": {"question": "Simplify this expression: (40*y**3 + 8*y)*(44*y**3 - 7*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1760*y**6 - 280*y**5 + 352*y**4 - 56*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 898, "polynomial_expr": "(40*y**3 + 8*y)*(44*y**3 - 7*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (40*y**3 + 8*y)*(44*y**3 - 7*y**2)\nExpanding the part (44*y**3 - 7*y**2) using the distributive property, and we got: (-7*y**2)*(40*y**3 + 8*y) + (44*y**3)*(40*y**3 + 8*y)\n#Step 2:\nCurrent expression: (-7*y**2)*(40*y**3 + 8*y) + (44*y**3)*(40*y**3 + 8*y)\nSimplifying the partial expression: (-7*y**2)*(40*y**3 + 8*y)\nExpanding the part (40*y**3 + 8*y) using the distributive property, and we got: (8*y)*(-7*y**2) + (-7*y**2)*(40*y**3)\nReplacing (-7*y**2)*(40*y**3 + 8*y) with (8*y)*(-7*y**2) + (-7*y**2)*(40*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (8*y)*(-7*y**2) + (-7*y**2)*(40*y**3) + (44*y**3)*(40*y**3 + 8*y)\nSimplifying the partial expression: (44*y**3)*(40*y**3 + 8*y)\nExpanding the part (40*y**3 + 8*y) using the distributive property, and we got: (8*y)*(44*y**3) + (40*y**3)*(44*y**3)\nReplacing (44*y**3)*(40*y**3 + 8*y) with (8*y)*(44*y**3) + (40*y**3)*(44*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (8*y)*(-7*y**2) + (8*y)*(44*y**3) + (-7*y**2)*(40*y**3) + (40*y**3)*(44*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (8*y)*(-7*y**2) = -56*y**3\n (8*y)*(44*y**3) = 352*y**4\n (40*y**3)*(-7*y**2) = -280*y**5\n (40*y**3)*(44*y**3) = 1760*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1760*y**6 - 280*y**5 + 352*y**4 - 56*y**3\nNo more calculations needed.\n1760*y**6 - 280*y**5 + 352*y**4 - 56*y**3", "generated_answer": "1760*y**6 - 280*y**5 + 352*y**4 - 56*y**3", "step_length": 5} {"cot_id": "d96a89480765f1ed7d3bc00f184f93d8f0068e820bc5be451f1571961d44fc4f", "datapoint": {"question": "Simplify this expression: (-13*y**3 + 39*y - 21)*(21*y**3 + 83*y**2 - 48*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-273*y**6 - 1079*y**5 + 1443*y**4 + 2796*y**3 - 3615*y**2 + 1008*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 899, "polynomial_expr": "(-13*y**3 + 39*y - 21)*(21*y**3 + 83*y**2 - 48*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-13*y**3 + 39*y - 21)*(21*y**3 + 83*y**2 - 48*y)\nExpanding the part (-13*y**3 + 39*y - 21) using the distributive property, and we got: (39*y)*(21*y**3 + 83*y**2 - 48*y) + (-13*y**3)*(21*y**3 + 83*y**2 - 48*y) - 21*(21*y**3 + 83*y**2 - 48*y)\n#Step 2:\nCurrent expression: (39*y)*(21*y**3 + 83*y**2 - 48*y) + (-13*y**3)*(21*y**3 + 83*y**2 - 48*y) - 21*(21*y**3 + 83*y**2 - 48*y)\nSimplifying the partial expression: -21*(21*y**3 + 83*y**2 - 48*y)\nExpanding the part (21*y**3 + 83*y**2 - 48*y) using the distributive property, and we got: -48*y*(-21) + (83*y**2)*(-21) + (21*y**3)*(-21)\nReplacing -21*(21*y**3 + 83*y**2 - 48*y) with -48*y*(-21) + (83*y**2)*(-21) + (21*y**3)*(-21) in the overall expression.\n#Step 3:\nCurrent expression: -48*y*(-21) + (39*y)*(21*y**3 + 83*y**2 - 48*y) + (83*y**2)*(-21) + (-13*y**3)*(21*y**3 + 83*y**2 - 48*y) + (21*y**3)*(-21)\nSimplifying the partial expression: (-13*y**3)*(21*y**3 + 83*y**2 - 48*y)\nExpanding the part (21*y**3 + 83*y**2 - 48*y) using the distributive property, and we got: (-48*y)*(-13*y**3) + (83*y**2)*(-13*y**3) + (-13*y**3)*(21*y**3)\nReplacing (-13*y**3)*(21*y**3 + 83*y**2 - 48*y) with (-48*y)*(-13*y**3) + (83*y**2)*(-13*y**3) + (-13*y**3)*(21*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-48*y)*(-13*y**3) - 48*y*(-21) + (39*y)*(21*y**3 + 83*y**2 - 48*y) + (83*y**2)*(-13*y**3) + (83*y**2)*(-21) + (-13*y**3)*(21*y**3) + (21*y**3)*(-21)\nSimplifying the partial expression: (39*y)*(21*y**3 + 83*y**2 - 48*y)\nExpanding the part (21*y**3 + 83*y**2 - 48*y) using the distributive property, and we got: (-48*y)*(39*y) + (39*y)*(83*y**2) + (39*y)*(21*y**3)\nReplacing (39*y)*(21*y**3 + 83*y**2 - 48*y) with (-48*y)*(39*y) + (39*y)*(83*y**2) + (39*y)*(21*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-48*y)*(39*y) + (-48*y)*(-13*y**3) - 48*y*(-21) + (39*y)*(83*y**2) + (39*y)*(21*y**3) + (83*y**2)*(-13*y**3) + (83*y**2)*(-21) + (-13*y**3)*(21*y**3) + (21*y**3)*(-21)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*y)*-21 = 1008*y\n (-48*y)*(-13*y**3) = 624*y**4\n (-48*y)*(39*y) = -1872*y**2\n (21*y**3)*-21 = -441*y**3\n (21*y**3)*(-13*y**3) = -273*y**6\n (21*y**3)*(39*y) = 819*y**4\n (83*y**2)*-21 = -1743*y**2\n (83*y**2)*(-13*y**3) = -1079*y**5\n (83*y**2)*(39*y) = 3237*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -273*y**6 - 1079*y**5 + 624*y**4 + 819*y**4 - 441*y**3 + 3237*y**3 - 1872*y**2 - 1743*y**2 + 1008*y\nCombining like terms, got -273*y**6 - 1079*y**5 + 1443*y**4 + 2796*y**3 - 3615*y**2 + 1008*y\n#Step 7:\nCurrent expression: -273*y**6 - 1079*y**5 + 1443*y**4 + 2796*y**3 - 3615*y**2 + 1008*y\nNo more calculations needed.\n-273*y**6 - 1079*y**5 + 1443*y**4 + 2796*y**3 - 3615*y**2 + 1008*y", "generated_answer": "-273*y**6 - 1079*y**5 + 1443*y**4 + 2796*y**3 - 3615*y**2 + 1008*y", "step_length": 7} {"cot_id": "63efc8d2c91d438c1c7470d981be832ff5e41c9be5b9e1815b5cbdc0b763c5ec", "datapoint": {"question": "Calculate the following: (58*y**2 + 31*y + 46)*(41*y**3 + 11*y**2 - 10*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2378*y**5 + 1909*y**4 + 1647*y**3 + 196*y**2 - 460*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 900, "polynomial_expr": "(58*y**2 + 31*y + 46)*(41*y**3 + 11*y**2 - 10*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (58*y**2 + 31*y + 46)*(41*y**3 + 11*y**2 - 10*y)\nExpanding the part (58*y**2 + 31*y + 46) using the distributive property, and we got: (31*y)*(41*y**3 + 11*y**2 - 10*y) + (58*y**2)*(41*y**3 + 11*y**2 - 10*y) + 46*(41*y**3 + 11*y**2 - 10*y)\n#Step 2:\nCurrent expression: (31*y)*(41*y**3 + 11*y**2 - 10*y) + (58*y**2)*(41*y**3 + 11*y**2 - 10*y) + 46*(41*y**3 + 11*y**2 - 10*y)\nSimplifying the partial expression: 46*(41*y**3 + 11*y**2 - 10*y)\nExpanding the part (41*y**3 + 11*y**2 - 10*y) using the distributive property, and we got: -10*y*46 + (11*y**2)*46 + (41*y**3)*46\nReplacing 46*(41*y**3 + 11*y**2 - 10*y) with -10*y*46 + (11*y**2)*46 + (41*y**3)*46 in the overall expression.\n#Step 3:\nCurrent expression: -10*y*46 + (31*y)*(41*y**3 + 11*y**2 - 10*y) + (11*y**2)*46 + (58*y**2)*(41*y**3 + 11*y**2 - 10*y) + (41*y**3)*46\nSimplifying the partial expression: (31*y)*(41*y**3 + 11*y**2 - 10*y)\nExpanding the part (41*y**3 + 11*y**2 - 10*y) using the distributive property, and we got: (-10*y)*(31*y) + (31*y)*(11*y**2) + (31*y)*(41*y**3)\nReplacing (31*y)*(41*y**3 + 11*y**2 - 10*y) with (-10*y)*(31*y) + (31*y)*(11*y**2) + (31*y)*(41*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-10*y)*(31*y) - 10*y*46 + (31*y)*(11*y**2) + (31*y)*(41*y**3) + (11*y**2)*46 + (58*y**2)*(41*y**3 + 11*y**2 - 10*y) + (41*y**3)*46\nSimplifying the partial expression: (58*y**2)*(41*y**3 + 11*y**2 - 10*y)\nExpanding the part (41*y**3 + 11*y**2 - 10*y) using the distributive property, and we got: (-10*y)*(58*y**2) + (11*y**2)*(58*y**2) + (58*y**2)*(41*y**3)\nReplacing (58*y**2)*(41*y**3 + 11*y**2 - 10*y) with (-10*y)*(58*y**2) + (11*y**2)*(58*y**2) + (58*y**2)*(41*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-10*y)*(31*y) + (-10*y)*(58*y**2) - 10*y*46 + (31*y)*(11*y**2) + (31*y)*(41*y**3) + (11*y**2)*(58*y**2) + (11*y**2)*46 + (58*y**2)*(41*y**3) + (41*y**3)*46\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*y)*46 = -460*y\n (-10*y)*(31*y) = -310*y**2\n (-10*y)*(58*y**2) = -580*y**3\n (11*y**2)*46 = 506*y**2\n (11*y**2)*(31*y) = 341*y**3\n (11*y**2)*(58*y**2) = 638*y**4\n (41*y**3)*46 = 1886*y**3\n (41*y**3)*(31*y) = 1271*y**4\n (41*y**3)*(58*y**2) = 2378*y**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 2378*y**5 + 638*y**4 + 1271*y**4 - 580*y**3 + 341*y**3 + 1886*y**3 - 310*y**2 + 506*y**2 - 460*y\nCombining like terms, got 2378*y**5 + 1909*y**4 + 1647*y**3 + 196*y**2 - 460*y\n#Step 7:\nCurrent expression: 2378*y**5 + 1909*y**4 + 1647*y**3 + 196*y**2 - 460*y\nNo more calculations needed.\n2378*y**5 + 1909*y**4 + 1647*y**3 + 196*y**2 - 460*y", "generated_answer": "2378*y**5 + 1909*y**4 + 1647*y**3 + 196*y**2 - 460*y", "step_length": 7} {"cot_id": "1deeac5fd165191b189979954c2cc1ba3d407808fb83b8c34dc412aa77f61e63", "datapoint": {"question": "Calculate the following: (-12*z**2 - 24*z + 45)*(-41*z**3 + 49*z**2 + 25*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "492*z**5 + 396*z**4 - 3321*z**3 + 1605*z**2 + 1125*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 901, "polynomial_expr": "(-12*z**2 - 24*z + 45)*(-41*z**3 + 49*z**2 + 25*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-12*z**2 - 24*z + 45)*(-41*z**3 + 49*z**2 + 25*z)\nExpanding the part (-12*z**2 - 24*z + 45) using the distributive property, and we got: (-24*z)*(-41*z**3 + 49*z**2 + 25*z) + (-12*z**2)*(-41*z**3 + 49*z**2 + 25*z) + 45*(-41*z**3 + 49*z**2 + 25*z)\n#Step 2:\nCurrent expression: (-24*z)*(-41*z**3 + 49*z**2 + 25*z) + (-12*z**2)*(-41*z**3 + 49*z**2 + 25*z) + 45*(-41*z**3 + 49*z**2 + 25*z)\nSimplifying the partial expression: 45*(-41*z**3 + 49*z**2 + 25*z)\nExpanding the part (-41*z**3 + 49*z**2 + 25*z) using the distributive property, and we got: (25*z)*45 + (49*z**2)*45 - 41*z**3*45\nReplacing 45*(-41*z**3 + 49*z**2 + 25*z) with (25*z)*45 + (49*z**2)*45 - 41*z**3*45 in the overall expression.\n#Step 3:\nCurrent expression: (-24*z)*(-41*z**3 + 49*z**2 + 25*z) + (25*z)*45 + (-12*z**2)*(-41*z**3 + 49*z**2 + 25*z) + (49*z**2)*45 - 41*z**3*45\nSimplifying the partial expression: (-24*z)*(-41*z**3 + 49*z**2 + 25*z)\nExpanding the part (-41*z**3 + 49*z**2 + 25*z) using the distributive property, and we got: (-24*z)*(25*z) + (-24*z)*(49*z**2) + (-24*z)*(-41*z**3)\nReplacing (-24*z)*(-41*z**3 + 49*z**2 + 25*z) with (-24*z)*(25*z) + (-24*z)*(49*z**2) + (-24*z)*(-41*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-24*z)*(25*z) + (-24*z)*(49*z**2) + (-24*z)*(-41*z**3) + (25*z)*45 + (-12*z**2)*(-41*z**3 + 49*z**2 + 25*z) + (49*z**2)*45 - 41*z**3*45\nSimplifying the partial expression: (-12*z**2)*(-41*z**3 + 49*z**2 + 25*z)\nExpanding the part (-41*z**3 + 49*z**2 + 25*z) using the distributive property, and we got: (25*z)*(-12*z**2) + (-12*z**2)*(49*z**2) + (-12*z**2)*(-41*z**3)\nReplacing (-12*z**2)*(-41*z**3 + 49*z**2 + 25*z) with (25*z)*(-12*z**2) + (-12*z**2)*(49*z**2) + (-12*z**2)*(-41*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-24*z)*(25*z) + (-24*z)*(49*z**2) + (-24*z)*(-41*z**3) + (25*z)*(-12*z**2) + (25*z)*45 + (-12*z**2)*(49*z**2) + (-12*z**2)*(-41*z**3) + (49*z**2)*45 - 41*z**3*45\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*z**3)*45 = -1845*z**3\n (-41*z**3)*(-24*z) = 984*z**4\n (-41*z**3)*(-12*z**2) = 492*z**5\n (25*z)*45 = 1125*z\n (25*z)*(-24*z) = -600*z**2\n (25*z)*(-12*z**2) = -300*z**3\n (49*z**2)*45 = 2205*z**2\n (49*z**2)*(-24*z) = -1176*z**3\n (49*z**2)*(-12*z**2) = -588*z**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 492*z**5 - 588*z**4 + 984*z**4 - 1845*z**3 - 1176*z**3 - 300*z**3 - 600*z**2 + 2205*z**2 + 1125*z\nCombining like terms, got 492*z**5 + 396*z**4 - 3321*z**3 + 1605*z**2 + 1125*z\n#Step 7:\nCurrent expression: 492*z**5 + 396*z**4 - 3321*z**3 + 1605*z**2 + 1125*z\nNo more calculations needed.\n492*z**5 + 396*z**4 - 3321*z**3 + 1605*z**2 + 1125*z", "generated_answer": "492*z**5 + 396*z**4 - 3321*z**3 + 1605*z**2 + 1125*z", "step_length": 7} {"cot_id": "b80c4d1cd045d1d490d0c1de41d6a7f6732172787687ecd367c3611a874eda8f", "datapoint": {"question": "Simplify this expression: (28*x - 1)*(44*x**3 - 35*x**2 + 38*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1232*x**4 - 1024*x**3 + 1099*x**2 - 38*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 902, "polynomial_expr": "(28*x - 1)*(44*x**3 - 35*x**2 + 38*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28*x - 1)*(44*x**3 - 35*x**2 + 38*x)\nExpanding the part (28*x - 1) using the distributive property, and we got: (28*x)*(44*x**3 - 35*x**2 + 38*x) - (44*x**3 - 35*x**2 + 38*x)\n#Step 2:\nCurrent expression: (28*x)*(44*x**3 - 35*x**2 + 38*x) - (44*x**3 - 35*x**2 + 38*x)\nSimplifying the partial expression: -(44*x**3 - 35*x**2 + 38*x)\nExpanding the part (44*x**3 - 35*x**2 + 38*x) using the distributive property, and we got: (38*x)*(-1) - 35*x**2*(-1) + (44*x**3)*(-1)\nReplacing -(44*x**3 - 35*x**2 + 38*x) with (38*x)*(-1) - 35*x**2*(-1) + (44*x**3)*(-1) in the overall expression.\n#Step 3:\nCurrent expression: (28*x)*(44*x**3 - 35*x**2 + 38*x) + (38*x)*(-1) - 35*x**2*(-1) + (44*x**3)*(-1)\nSimplifying the partial expression: (28*x)*(44*x**3 - 35*x**2 + 38*x)\nExpanding the part (44*x**3 - 35*x**2 + 38*x) using the distributive property, and we got: (28*x)*(38*x) + (28*x)*(-35*x**2) + (28*x)*(44*x**3)\nReplacing (28*x)*(44*x**3 - 35*x**2 + 38*x) with (28*x)*(38*x) + (28*x)*(-35*x**2) + (28*x)*(44*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (28*x)*(38*x) + (28*x)*(-35*x**2) + (28*x)*(44*x**3) + (38*x)*(-1) - 35*x**2*(-1) + (44*x**3)*(-1)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*x**2)*-1 = 35*x**2\n (-35*x**2)*(28*x) = -980*x**3\n (38*x)*-1 = -38*x\n (38*x)*(28*x) = 1064*x**2\n (44*x**3)*-1 = -44*x**3\n (44*x**3)*(28*x) = 1232*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1232*x**4 - 980*x**3 - 44*x**3 + 35*x**2 + 1064*x**2 - 38*x\nCombining like terms, got 1232*x**4 - 1024*x**3 + 1099*x**2 - 38*x\n#Step 6:\nCurrent expression: 1232*x**4 - 1024*x**3 + 1099*x**2 - 38*x\nNo more calculations needed.\n1232*x**4 - 1024*x**3 + 1099*x**2 - 38*x", "generated_answer": "1232*x**4 - 1024*x**3 + 1099*x**2 - 38*x", "step_length": 6} {"cot_id": "566513ffcaf909eb1a0b2f056ae49cfc43dce0eedf1c0f59a9e58cc6b1e5c534", "datapoint": {"question": "Calculate the following: (-35*y**2 - 43*y + 30)*(-19*y**3 + 31*y**2 + 57)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "665*y**5 - 268*y**4 - 1903*y**3 - 1065*y**2 - 2451*y + 1710", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 903, "polynomial_expr": "(-35*y**2 - 43*y + 30)*(-19*y**3 + 31*y**2 + 57)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-35*y**2 - 43*y + 30)*(-19*y**3 + 31*y**2 + 57)\nExpanding the part (-35*y**2 - 43*y + 30) using the distributive property, and we got: (-43*y)*(-19*y**3 + 31*y**2 + 57) + (-35*y**2)*(-19*y**3 + 31*y**2 + 57) + 30*(-19*y**3 + 31*y**2 + 57)\n#Step 2:\nCurrent expression: (-43*y)*(-19*y**3 + 31*y**2 + 57) + (-35*y**2)*(-19*y**3 + 31*y**2 + 57) + 30*(-19*y**3 + 31*y**2 + 57)\nSimplifying the partial expression: 30*(-19*y**3 + 31*y**2 + 57)\nExpanding the part (-19*y**3 + 31*y**2 + 57) using the distributive property, and we got: (31*y**2)*30 - 19*y**3*30 + 57*30\nReplacing 30*(-19*y**3 + 31*y**2 + 57) with (31*y**2)*30 - 19*y**3*30 + 57*30 in the overall expression.\n#Step 3:\nCurrent expression: (-43*y)*(-19*y**3 + 31*y**2 + 57) + (-35*y**2)*(-19*y**3 + 31*y**2 + 57) + (31*y**2)*30 - 19*y**3*30 + 1710\nSimplifying the partial expression: (-43*y)*(-19*y**3 + 31*y**2 + 57)\nExpanding the part (-19*y**3 + 31*y**2 + 57) using the distributive property, and we got: (-43*y)*(31*y**2) + (-43*y)*(-19*y**3) + 57*(-43*y)\nReplacing (-43*y)*(-19*y**3 + 31*y**2 + 57) with (-43*y)*(31*y**2) + (-43*y)*(-19*y**3) + 57*(-43*y) in the overall expression.\n#Step 4:\nCurrent expression: (-43*y)*(31*y**2) + (-43*y)*(-19*y**3) + 57*(-43)*y + (-35*y**2)*(-19*y**3 + 31*y**2 + 57) + (31*y**2)*30 - 19*y**3*30 + 1710\nSimplifying the partial expression: (-35*y**2)*(-19*y**3 + 31*y**2 + 57)\nExpanding the part (-19*y**3 + 31*y**2 + 57) using the distributive property, and we got: 57*(-35*y**2) + (-35*y**2)*(31*y**2) + (-35*y**2)*(-19*y**3)\nReplacing (-35*y**2)*(-19*y**3 + 31*y**2 + 57) with 57*(-35*y**2) + (-35*y**2)*(31*y**2) + (-35*y**2)*(-19*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-43*y)*(31*y**2) + (-43*y)*(-19*y**3) + 57*(-35)*y**2 + 57*(-43)*y + (-35*y**2)*(31*y**2) + (-35*y**2)*(-19*y**3) + (31*y**2)*30 - 19*y**3*30 + 1710\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*y**3)*30 = -570*y**3\n (-19*y**3)*(-43*y) = 817*y**4\n (-19*y**3)*(-35*y**2) = 665*y**5\n (31*y**2)*30 = 930*y**2\n (31*y**2)*(-43*y) = -1333*y**3\n (31*y**2)*(-35*y**2) = -1085*y**4\n 57*-43*y = -2451*y\n 57*-35*y**2 = -1995*y**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 665*y**5 - 1085*y**4 + 817*y**4 - 1333*y**3 - 570*y**3 - 1995*y**2 + 930*y**2 - 2451*y + 1710\nCombining like terms, got 665*y**5 - 268*y**4 - 1903*y**3 - 1065*y**2 - 2451*y + 1710\n#Step 7:\nCurrent expression: 665*y**5 - 268*y**4 - 1903*y**3 - 1065*y**2 - 2451*y + 1710\nNo more calculations needed.\n665*y**5 - 268*y**4 - 1903*y**3 - 1065*y**2 - 2451*y + 1710", "generated_answer": "665*y**5 - 268*y**4 - 1903*y**3 - 1065*y**2 - 2451*y + 1710", "step_length": 7} {"cot_id": "f99be5e9b3eb7f6f88787e934138e688a35ee43d28621ffaae3c33752dab7110", "datapoint": {"question": "Simplify this expression: (19 - x)*(44 - 19*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "19*x**3 - 361*x**2 - 44*x + 836", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 904, "polynomial_expr": "(19 - x)*(44 - 19*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (19 - x)*(44 - 19*x**2)\nExpanding the part (19 - x) using the distributive property, and we got: (-x)*(44 - 19*x**2) + 19*(44 - 19*x**2)\n#Step 2:\nCurrent expression: (-x)*(44 - 19*x**2) + 19*(44 - 19*x**2)\nSimplifying the partial expression: 19*(44 - 19*x**2)\nExpanding the part (44 - 19*x**2) using the distributive property, and we got: -19*x**2*19 + 44*19\nReplacing 19*(44 - 19*x**2) with -19*x**2*19 + 44*19 in the overall expression.\n#Step 3:\nCurrent expression: (-x)*(44 - 19*x**2) - 19*x**2*19 + 836\nSimplifying the partial expression: (-x)*(44 - 19*x**2)\nExpanding the part (44 - 19*x**2) using the distributive property, and we got: (-x)*(-19*x**2) + 44*(-x)\nReplacing (-x)*(44 - 19*x**2) with (-x)*(-19*x**2) + 44*(-x) in the overall expression.\n#Step 4:\nCurrent expression: (-x)*(-19*x**2) + 44*(-1)*x - 19*x**2*19 + 836\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*x**2)*19 = -361*x**2\n (-19*x**2)*(-x) = 19*x**3\n 44*-1*x = -44*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 19*x**3 - 361*x**2 - 44*x + 836\nNo more calculations needed.\n19*x**3 - 361*x**2 - 44*x + 836", "generated_answer": "19*x**3 - 361*x**2 - 44*x + 836", "step_length": 5} {"cot_id": "63a328699d841e7cd6f59c80764170374bc218437554098c6534373357308f78", "datapoint": {"question": "Simplify this expression: (-49*x**2 - 24)*(49*x**2 - 33*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2401*x**4 + 1617*x**3 - 1176*x**2 + 792*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 905, "polynomial_expr": "(-49*x**2 - 24)*(49*x**2 - 33*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-49*x**2 - 24)*(49*x**2 - 33*x)\nExpanding the part (-49*x**2 - 24) using the distributive property, and we got: (-49*x**2)*(49*x**2 - 33*x) - 24*(49*x**2 - 33*x)\n#Step 2:\nCurrent expression: (-49*x**2)*(49*x**2 - 33*x) - 24*(49*x**2 - 33*x)\nSimplifying the partial expression: -24*(49*x**2 - 33*x)\nExpanding the part (49*x**2 - 33*x) using the distributive property, and we got: -33*x*(-24) + (49*x**2)*(-24)\nReplacing -24*(49*x**2 - 33*x) with -33*x*(-24) + (49*x**2)*(-24) in the overall expression.\n#Step 3:\nCurrent expression: -33*x*(-24) + (-49*x**2)*(49*x**2 - 33*x) + (49*x**2)*(-24)\nSimplifying the partial expression: (-49*x**2)*(49*x**2 - 33*x)\nExpanding the part (49*x**2 - 33*x) using the distributive property, and we got: (-33*x)*(-49*x**2) + (-49*x**2)*(49*x**2)\nReplacing (-49*x**2)*(49*x**2 - 33*x) with (-33*x)*(-49*x**2) + (-49*x**2)*(49*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-33*x)*(-49*x**2) - 33*x*(-24) + (-49*x**2)*(49*x**2) + (49*x**2)*(-24)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*x)*-24 = 792*x\n (-33*x)*(-49*x**2) = 1617*x**3\n (49*x**2)*-24 = -1176*x**2\n (49*x**2)*(-49*x**2) = -2401*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2401*x**4 + 1617*x**3 - 1176*x**2 + 792*x\nNo more calculations needed.\n-2401*x**4 + 1617*x**3 - 1176*x**2 + 792*x", "generated_answer": "-2401*x**4 + 1617*x**3 - 1176*x**2 + 792*x", "step_length": 5} {"cot_id": "08d1d0ea7a5a4501c73d010abfe2850ff3ee4efe8275010c4dcf1cb53720c247", "datapoint": {"question": "Simplify this expression: -936*z**3 - 912*z**2\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-936*z**3 - 912*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 906, "polynomial_expr": "-936*z**3 - 912*z**2", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -936*z**3 - 912*z**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -936*z**3 - 912*z**2\nNo more calculations needed.\n-936*z**3 - 912*z**2", "generated_answer": "-936*z**3 - 912*z**2", "step_length": 2} {"cot_id": "fc74e21e1028425fc70e040e09aecbffd179e33bdd51f0e491c24a2e24a0f6fc", "datapoint": {"question": "Calculate the following: (41*y**2 - 25*y)*(-45*y**3 - 29*y - 8)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1845*y**5 + 1125*y**4 - 1189*y**3 + 397*y**2 + 200*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 907, "polynomial_expr": "(41*y**2 - 25*y)*(-45*y**3 - 29*y - 8)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (41*y**2 - 25*y)*(-45*y**3 - 29*y - 8)\nExpanding the part (41*y**2 - 25*y) using the distributive property, and we got: (-25*y)*(-45*y**3 - 29*y - 8) + (41*y**2)*(-45*y**3 - 29*y - 8)\n#Step 2:\nCurrent expression: (-25*y)*(-45*y**3 - 29*y - 8) + (41*y**2)*(-45*y**3 - 29*y - 8)\nSimplifying the partial expression: (-25*y)*(-45*y**3 - 29*y - 8)\nExpanding the part (-45*y**3 - 29*y - 8) using the distributive property, and we got: (-29*y)*(-25*y) + (-25*y)*(-45*y**3) - (-1)*200*y\nReplacing (-25*y)*(-45*y**3 - 29*y - 8) with (-29*y)*(-25*y) + (-25*y)*(-45*y**3) - (-1)*200*y in the overall expression.\n#Step 3:\nCurrent expression: (-29*y)*(-25*y) + (-25*y)*(-45*y**3) - 8*(-25)*y + (41*y**2)*(-45*y**3 - 29*y - 8)\nSimplifying the partial expression: (41*y**2)*(-45*y**3 - 29*y - 8)\nExpanding the part (-45*y**3 - 29*y - 8) using the distributive property, and we got: (-29*y)*(41*y**2) - 328*y**2 + (41*y**2)*(-45*y**3)\nReplacing (41*y**2)*(-45*y**3 - 29*y - 8) with (-29*y)*(41*y**2) - 328*y**2 + (41*y**2)*(-45*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-29*y)*(-25*y) + (-29*y)*(41*y**2) + (-25*y)*(-45*y**3) - 8*41*y**2 - 8*(-25)*y + (41*y**2)*(-45*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*y**3)*(-25*y) = 1125*y**4\n (-45*y**3)*(41*y**2) = -1845*y**5\n (-29*y)*(-25*y) = 725*y**2\n (-29*y)*(41*y**2) = -1189*y**3\n -8*-25*y = 200*y\n -8*41*y**2 = -328*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1845*y**5 + 1125*y**4 - 1189*y**3 - 328*y**2 + 725*y**2 + 200*y\nCombining like terms, got -1845*y**5 + 1125*y**4 - 1189*y**3 + 397*y**2 + 200*y\n#Step 6:\nCurrent expression: -1845*y**5 + 1125*y**4 - 1189*y**3 + 397*y**2 + 200*y\nNo more calculations needed.\n-1845*y**5 + 1125*y**4 - 1189*y**3 + 397*y**2 + 200*y", "generated_answer": "-1845*y**5 + 1125*y**4 - 1189*y**3 + 397*y**2 + 200*y", "step_length": 6} {"cot_id": "c9064079b0b5d040e4b4b700ee2fb6633e2dfc8b7f42fe25e7a63dc3e1654cc0", "datapoint": {"question": "Calculate the following: (-22*x**3 + 3*x)*(-19*x**3 - 23*x - 8)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "418*x**6 + 449*x**4 + 176*x**3 - 69*x**2 - 24*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 908, "polynomial_expr": "(-22*x**3 + 3*x)*(-19*x**3 - 23*x - 8)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-22*x**3 + 3*x)*(-19*x**3 - 23*x - 8)\nExpanding the part (-22*x**3 + 3*x) using the distributive property, and we got: (3*x)*(-19*x**3 - 23*x - 8) + (-22*x**3)*(-19*x**3 - 23*x - 8)\n#Step 2:\nCurrent expression: (3*x)*(-19*x**3 - 23*x - 8) + (-22*x**3)*(-19*x**3 - 23*x - 8)\nSimplifying the partial expression: (-22*x**3)*(-19*x**3 - 23*x - 8)\nExpanding the part (-19*x**3 - 23*x - 8) using the distributive property, and we got: (-23*x)*(-22*x**3) - (-1)*176*x**3 + (-22*x**3)*(-19*x**3)\nReplacing (-22*x**3)*(-19*x**3 - 23*x - 8) with (-23*x)*(-22*x**3) - (-1)*176*x**3 + (-22*x**3)*(-19*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-23*x)*(-22*x**3) - 8*(-22)*x**3 + (3*x)*(-19*x**3 - 23*x - 8) + (-22*x**3)*(-19*x**3)\nSimplifying the partial expression: (3*x)*(-19*x**3 - 23*x - 8)\nExpanding the part (-19*x**3 - 23*x - 8) using the distributive property, and we got: (-23*x)*(3*x) - 24*x + (3*x)*(-19*x**3)\nReplacing (3*x)*(-19*x**3 - 23*x - 8) with (-23*x)*(3*x) - 24*x + (3*x)*(-19*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-23*x)*(3*x) + (-23*x)*(-22*x**3) - 8*(-22)*x**3 - 8*3*x + (3*x)*(-19*x**3) + (-22*x**3)*(-19*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*x)*(-22*x**3) = 506*x**4\n (-23*x)*(3*x) = -69*x**2\n (-19*x**3)*(-22*x**3) = 418*x**6\n (-19*x**3)*(3*x) = -57*x**4\n -8*-22*x**3 = 176*x**3\n -8*3*x = -24*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 418*x**6 - 57*x**4 + 506*x**4 + 176*x**3 - 69*x**2 - 24*x\nCombining like terms, got 418*x**6 + 449*x**4 + 176*x**3 - 69*x**2 - 24*x\n#Step 6:\nCurrent expression: 418*x**6 + 449*x**4 + 176*x**3 - 69*x**2 - 24*x\nNo more calculations needed.\n418*x**6 + 449*x**4 + 176*x**3 - 69*x**2 - 24*x", "generated_answer": "418*x**6 + 449*x**4 + 176*x**3 - 69*x**2 - 24*x", "step_length": 6} {"cot_id": "8768785e3c90580b051882e193c4f002fb2768645cf41aceaf9354f5f6c952ca", "datapoint": {"question": "Simplify this expression: 18*x**2*(-x**3 + 9*x**2 - 20*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-18*x**5 + 162*x**4 - 360*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 909, "polynomial_expr": "18*x**2*(-x**3 + 9*x**2 - 20*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 18*x**2*(-x**3 + 9*x**2 - 20*x)\nExpanding the part (-x**3 + 9*x**2 - 20*x) using the distributive property, and we got: (-20*x)*(18*x**2) + (9*x**2)*(18*x**2) + (18*x**2)*(-x**3)\n#Step 2:\nCurrent expression: (-20*x)*(18*x**2) + (9*x**2)*(18*x**2) + (18*x**2)*(-x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-x**3)*(18*x**2) = -18*x**5\n (-20*x)*(18*x**2) = -360*x**3\n (9*x**2)*(18*x**2) = 162*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -18*x**5 + 162*x**4 - 360*x**3\nNo more calculations needed.\n-18*x**5 + 162*x**4 - 360*x**3", "generated_answer": "-18*x**5 + 162*x**4 - 360*x**3", "step_length": 3} {"cot_id": "99ee9178ed8e9caf9d0c948eae523ee9adf1e3587450577b050a7b3cf9716fb5", "datapoint": {"question": "Calculate the following: (-28*x**3 - 61*x)*(-3*x**3 - 18*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "84*x**6 + 687*x**4 + 1098*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 910, "polynomial_expr": "(-28*x**3 - 61*x)*(-3*x**3 - 18*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-28*x**3 - 61*x)*(-3*x**3 - 18*x)\nExpanding the part (-28*x**3 - 61*x) using the distributive property, and we got: (-61*x)*(-3*x**3 - 18*x) + (-28*x**3)*(-3*x**3 - 18*x)\n#Step 2:\nCurrent expression: (-61*x)*(-3*x**3 - 18*x) + (-28*x**3)*(-3*x**3 - 18*x)\nSimplifying the partial expression: (-61*x)*(-3*x**3 - 18*x)\nExpanding the part (-3*x**3 - 18*x) using the distributive property, and we got: (-61*x)*(-18*x) + (-61*x)*(-3*x**3)\nReplacing (-61*x)*(-3*x**3 - 18*x) with (-61*x)*(-18*x) + (-61*x)*(-3*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-61*x)*(-18*x) + (-61*x)*(-3*x**3) + (-28*x**3)*(-3*x**3 - 18*x)\nSimplifying the partial expression: (-28*x**3)*(-3*x**3 - 18*x)\nExpanding the part (-3*x**3 - 18*x) using the distributive property, and we got: (-18*x)*(-28*x**3) + (-28*x**3)*(-3*x**3)\nReplacing (-28*x**3)*(-3*x**3 - 18*x) with (-18*x)*(-28*x**3) + (-28*x**3)*(-3*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-61*x)*(-18*x) + (-61*x)*(-3*x**3) + (-18*x)*(-28*x**3) + (-28*x**3)*(-3*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-18*x)*(-61*x) = 1098*x**2\n (-18*x)*(-28*x**3) = 504*x**4\n (-3*x**3)*(-61*x) = 183*x**4\n (-3*x**3)*(-28*x**3) = 84*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 84*x**6 + 183*x**4 + 504*x**4 + 1098*x**2\nCombining like terms, got 84*x**6 + 687*x**4 + 1098*x**2\n#Step 6:\nCurrent expression: 84*x**6 + 687*x**4 + 1098*x**2\nNo more calculations needed.\n84*x**6 + 687*x**4 + 1098*x**2", "generated_answer": "84*x**6 + 687*x**4 + 1098*x**2", "step_length": 6} {"cot_id": "45885108c4f91464109a3beff843b337b8c822fddef58fa13fde78103689fc8e", "datapoint": {"question": "Calculate the following: (-15*x**2 - 20)*(40*x**3 + 45*x**2 - 16*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-600*x**5 - 675*x**4 - 560*x**3 - 900*x**2 + 320*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 911, "polynomial_expr": "(-15*x**2 - 20)*(40*x**3 + 45*x**2 - 16*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-15*x**2 - 20)*(40*x**3 + 45*x**2 - 16*x)\nExpanding the part (-15*x**2 - 20) using the distributive property, and we got: (-15*x**2)*(40*x**3 + 45*x**2 - 16*x) - 20*(40*x**3 + 45*x**2 - 16*x)\n#Step 2:\nCurrent expression: (-15*x**2)*(40*x**3 + 45*x**2 - 16*x) - 20*(40*x**3 + 45*x**2 - 16*x)\nSimplifying the partial expression: -20*(40*x**3 + 45*x**2 - 16*x)\nExpanding the part (40*x**3 + 45*x**2 - 16*x) using the distributive property, and we got: -16*x*(-20) + (45*x**2)*(-20) + (40*x**3)*(-20)\nReplacing -20*(40*x**3 + 45*x**2 - 16*x) with -16*x*(-20) + (45*x**2)*(-20) + (40*x**3)*(-20) in the overall expression.\n#Step 3:\nCurrent expression: -16*x*(-20) + (-15*x**2)*(40*x**3 + 45*x**2 - 16*x) + (45*x**2)*(-20) + (40*x**3)*(-20)\nSimplifying the partial expression: (-15*x**2)*(40*x**3 + 45*x**2 - 16*x)\nExpanding the part (40*x**3 + 45*x**2 - 16*x) using the distributive property, and we got: (-16*x)*(-15*x**2) + (-15*x**2)*(45*x**2) + (-15*x**2)*(40*x**3)\nReplacing (-15*x**2)*(40*x**3 + 45*x**2 - 16*x) with (-16*x)*(-15*x**2) + (-15*x**2)*(45*x**2) + (-15*x**2)*(40*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-16*x)*(-15*x**2) - 16*x*(-20) + (-15*x**2)*(45*x**2) + (-15*x**2)*(40*x**3) + (45*x**2)*(-20) + (40*x**3)*(-20)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-16*x)*-20 = 320*x\n (-16*x)*(-15*x**2) = 240*x**3\n (40*x**3)*-20 = -800*x**3\n (40*x**3)*(-15*x**2) = -600*x**5\n (45*x**2)*-20 = -900*x**2\n (45*x**2)*(-15*x**2) = -675*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -600*x**5 - 675*x**4 - 800*x**3 + 240*x**3 - 900*x**2 + 320*x\nCombining like terms, got -600*x**5 - 675*x**4 - 560*x**3 - 900*x**2 + 320*x\n#Step 6:\nCurrent expression: -600*x**5 - 675*x**4 - 560*x**3 - 900*x**2 + 320*x\nNo more calculations needed.\n-600*x**5 - 675*x**4 - 560*x**3 - 900*x**2 + 320*x", "generated_answer": "-600*x**5 - 675*x**4 - 560*x**3 - 900*x**2 + 320*x", "step_length": 6} {"cot_id": "86c84d1b8f74fa0a89f4990c1416bb0b0f8691aff9aa07b0da0713ebf9dcf364", "datapoint": {"question": "Simplify this expression: (-23*x**2 - 37*x)*(-46*x**2 - 27*x + 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1058*x**4 + 2323*x**3 - 13*x**2 - 1628*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 912, "polynomial_expr": "(-23*x**2 - 37*x)*(-46*x**2 - 27*x + 44)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-23*x**2 - 37*x)*(-46*x**2 - 27*x + 44)\nExpanding the part (-23*x**2 - 37*x) using the distributive property, and we got: (-37*x)*(-46*x**2 - 27*x + 44) + (-23*x**2)*(-46*x**2 - 27*x + 44)\n#Step 2:\nCurrent expression: (-37*x)*(-46*x**2 - 27*x + 44) + (-23*x**2)*(-46*x**2 - 27*x + 44)\nSimplifying the partial expression: (-37*x)*(-46*x**2 - 27*x + 44)\nExpanding the part (-46*x**2 - 27*x + 44) using the distributive property, and we got: (-37*x)*(-27*x) + (-37*x)*(-46*x**2) + 44*(-37*x)\nReplacing (-37*x)*(-46*x**2 - 27*x + 44) with (-37*x)*(-27*x) + (-37*x)*(-46*x**2) + 44*(-37*x) in the overall expression.\n#Step 3:\nCurrent expression: (-37*x)*(-27*x) + (-37*x)*(-46*x**2) + 44*(-37)*x + (-23*x**2)*(-46*x**2 - 27*x + 44)\nSimplifying the partial expression: (-23*x**2)*(-46*x**2 - 27*x + 44)\nExpanding the part (-46*x**2 - 27*x + 44) using the distributive property, and we got: (-27*x)*(-23*x**2) + 44*(-23*x**2) + (-46*x**2)*(-23*x**2)\nReplacing (-23*x**2)*(-46*x**2 - 27*x + 44) with (-27*x)*(-23*x**2) + 44*(-23*x**2) + (-46*x**2)*(-23*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-37*x)*(-27*x) + (-37*x)*(-46*x**2) + (-27*x)*(-23*x**2) + 44*(-23)*x**2 + 44*(-37)*x + (-46*x**2)*(-23*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*x**2)*(-37*x) = 1702*x**3\n (-46*x**2)*(-23*x**2) = 1058*x**4\n (-27*x)*(-37*x) = 999*x**2\n (-27*x)*(-23*x**2) = 621*x**3\n 44*-37*x = -1628*x\n 44*-23*x**2 = -1012*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1058*x**4 + 621*x**3 + 1702*x**3 - 1012*x**2 + 999*x**2 - 1628*x\nCombining like terms, got 1058*x**4 + 2323*x**3 - 13*x**2 - 1628*x\n#Step 6:\nCurrent expression: 1058*x**4 + 2323*x**3 - 13*x**2 - 1628*x\nNo more calculations needed.\n1058*x**4 + 2323*x**3 - 13*x**2 - 1628*x", "generated_answer": "1058*x**4 + 2323*x**3 - 13*x**2 - 1628*x", "step_length": 6} {"cot_id": "c7749c78c0ec1dd889d0245df849e3b91a4af94b21c9b303424ce8e9921d6624", "datapoint": {"question": "Calculate the following: -33*z*(15*z**2 - 32*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-495*z**3 + 1056*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 913, "polynomial_expr": "-33*z*(15*z**2 - 32*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -33*z*(15*z**2 - 32*z)\nExpanding the part (15*z**2 - 32*z) using the distributive property, and we got: (-33*z)*(-32*z) + (-33*z)*(15*z**2)\n#Step 2:\nCurrent expression: (-33*z)*(-32*z) + (-33*z)*(15*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*z)*(-33*z) = 1056*z**2\n (15*z**2)*(-33*z) = -495*z**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -495*z**3 + 1056*z**2\nNo more calculations needed.\n-495*z**3 + 1056*z**2", "generated_answer": "-495*z**3 + 1056*z**2", "step_length": 3} {"cot_id": "df203c6b2544472dc5022aba1d4abb5cf24e605892e1d31923365ad3f858a815", "datapoint": {"question": "Simplify this expression: (4*z + 8)*(43*z**3 + 28*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "172*z**4 + 456*z**3 + 224*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 914, "polynomial_expr": "(4*z + 8)*(43*z**3 + 28*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (4*z + 8)*(43*z**3 + 28*z**2)\nExpanding the part (4*z + 8) using the distributive property, and we got: (4*z)*(43*z**3 + 28*z**2) + 8*(43*z**3 + 28*z**2)\n#Step 2:\nCurrent expression: (4*z)*(43*z**3 + 28*z**2) + 8*(43*z**3 + 28*z**2)\nSimplifying the partial expression: 8*(43*z**3 + 28*z**2)\nExpanding the part (43*z**3 + 28*z**2) using the distributive property, and we got: (28*z**2)*8 + (43*z**3)*8\nReplacing 8*(43*z**3 + 28*z**2) with (28*z**2)*8 + (43*z**3)*8 in the overall expression.\n#Step 3:\nCurrent expression: (4*z)*(43*z**3 + 28*z**2) + (28*z**2)*8 + (43*z**3)*8\nSimplifying the partial expression: (4*z)*(43*z**3 + 28*z**2)\nExpanding the part (43*z**3 + 28*z**2) using the distributive property, and we got: (4*z)*(28*z**2) + (4*z)*(43*z**3)\nReplacing (4*z)*(43*z**3 + 28*z**2) with (4*z)*(28*z**2) + (4*z)*(43*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (4*z)*(28*z**2) + (4*z)*(43*z**3) + (28*z**2)*8 + (43*z**3)*8\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (28*z**2)*8 = 224*z**2\n (28*z**2)*(4*z) = 112*z**3\n (43*z**3)*8 = 344*z**3\n (43*z**3)*(4*z) = 172*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 172*z**4 + 112*z**3 + 344*z**3 + 224*z**2\nCombining like terms, got 172*z**4 + 456*z**3 + 224*z**2\n#Step 6:\nCurrent expression: 172*z**4 + 456*z**3 + 224*z**2\nNo more calculations needed.\n172*z**4 + 456*z**3 + 224*z**2", "generated_answer": "172*z**4 + 456*z**3 + 224*z**2", "step_length": 6} {"cot_id": "01d2b67c4ab7364c91425b80a92e79787d6ccd773d24a18a15faff0b8e30480d", "datapoint": {"question": "Calculate the following: -10*y**2*(33*y**3 - 18*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-330*y**5 + 180*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 915, "polynomial_expr": "-10*y**2*(33*y**3 - 18*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -10*y**2*(33*y**3 - 18*y)\nExpanding the part (33*y**3 - 18*y) using the distributive property, and we got: (-18*y)*(-10*y**2) + (-10*y**2)*(33*y**3)\n#Step 2:\nCurrent expression: (-18*y)*(-10*y**2) + (-10*y**2)*(33*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-18*y)*(-10*y**2) = 180*y**3\n (33*y**3)*(-10*y**2) = -330*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -330*y**5 + 180*y**3\nNo more calculations needed.\n-330*y**5 + 180*y**3", "generated_answer": "-330*y**5 + 180*y**3", "step_length": 3} {"cot_id": "121baef099072bf5950db2649d7f6f515051fe75f031ff264bbe3da015eba7b5", "datapoint": {"question": "Simplify this expression: (1 - 28*y**2)*(34*y**2 - 22*y + 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-952*y**4 + 616*y**3 - 1310*y**2 - 22*y + 48", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 916, "polynomial_expr": "(1 - 28*y**2)*(34*y**2 - 22*y + 48)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (1 - 28*y**2)*(34*y**2 - 22*y + 48)\nExpanding the part (1 - 28*y**2) using the distributive property, and we got: (-28*y**2)*(34*y**2 - 22*y + 48) + 1*(34*y**2 - 22*y + 48)\n#Step 2:\nCurrent expression: (-28*y**2)*(34*y**2 - 22*y + 48) + 1*(34*y**2 - 22*y + 48)\nSimplifying the partial expression: 1*(34*y**2 - 22*y + 48)\nExpanding the part (34*y**2 - 22*y + 48) using the distributive property, and we got: -22*y*1 + (34*y**2)*1 + 48*1\nReplacing 1*(34*y**2 - 22*y + 48) with -22*y*1 + (34*y**2)*1 + 48*1 in the overall expression.\n#Step 3:\nCurrent expression: -22*y*1 + (-28*y**2)*(34*y**2 - 22*y + 48) + (34*y**2)*1 + 48\nSimplifying the partial expression: (-28*y**2)*(34*y**2 - 22*y + 48)\nExpanding the part (34*y**2 - 22*y + 48) using the distributive property, and we got: (-22*y)*(-28*y**2) + 48*(-28*y**2) + (-28*y**2)*(34*y**2)\nReplacing (-28*y**2)*(34*y**2 - 22*y + 48) with (-22*y)*(-28*y**2) + 48*(-28*y**2) + (-28*y**2)*(34*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-22*y)*(-28*y**2) - 22*y*1 + 48*(-28)*y**2 + (-28*y**2)*(34*y**2) + (34*y**2)*1 + 48\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*y)*1 = -22*y\n (-22*y)*(-28*y**2) = 616*y**3\n (34*y**2)*1 = 34*y**2\n (34*y**2)*(-28*y**2) = -952*y**4\n 48*-28*y**2 = -1344*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -952*y**4 + 616*y**3 - 1344*y**2 + 34*y**2 - 22*y + 48\nCombining like terms, got -952*y**4 + 616*y**3 - 1310*y**2 - 22*y + 48\n#Step 6:\nCurrent expression: -952*y**4 + 616*y**3 - 1310*y**2 - 22*y + 48\nNo more calculations needed.\n-952*y**4 + 616*y**3 - 1310*y**2 - 22*y + 48", "generated_answer": "-952*y**4 + 616*y**3 - 1310*y**2 - 22*y + 48", "step_length": 6} {"cot_id": "5c4851fb16d16307518d18ce9b8d768ca38df38f7298538b878d69f916613606", "datapoint": {"question": "Calculate the following: (5*y**3 - 41*y**2)*(9*y**3 + 18*y**2 + 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "45*y**6 - 279*y**5 - 738*y**4 + 105*y**3 - 861*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 917, "polynomial_expr": "(5*y**3 - 41*y**2)*(9*y**3 + 18*y**2 + 21)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (5*y**3 - 41*y**2)*(9*y**3 + 18*y**2 + 21)\nExpanding the part (5*y**3 - 41*y**2) using the distributive property, and we got: (-41*y**2)*(9*y**3 + 18*y**2 + 21) + (5*y**3)*(9*y**3 + 18*y**2 + 21)\n#Step 2:\nCurrent expression: (-41*y**2)*(9*y**3 + 18*y**2 + 21) + (5*y**3)*(9*y**3 + 18*y**2 + 21)\nSimplifying the partial expression: (-41*y**2)*(9*y**3 + 18*y**2 + 21)\nExpanding the part (9*y**3 + 18*y**2 + 21) using the distributive property, and we got: 21*(-41*y**2) + (-41*y**2)*(18*y**2) + (-41*y**2)*(9*y**3)\nReplacing (-41*y**2)*(9*y**3 + 18*y**2 + 21) with 21*(-41*y**2) + (-41*y**2)*(18*y**2) + (-41*y**2)*(9*y**3) in the overall expression.\n#Step 3:\nCurrent expression: 21*(-41)*y**2 + (-41*y**2)*(18*y**2) + (-41*y**2)*(9*y**3) + (5*y**3)*(9*y**3 + 18*y**2 + 21)\nSimplifying the partial expression: (5*y**3)*(9*y**3 + 18*y**2 + 21)\nExpanding the part (9*y**3 + 18*y**2 + 21) using the distributive property, and we got: 21*(5*y**3) + (18*y**2)*(5*y**3) + (5*y**3)*(9*y**3)\nReplacing (5*y**3)*(9*y**3 + 18*y**2 + 21) with 21*(5*y**3) + (18*y**2)*(5*y**3) + (5*y**3)*(9*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 21*5*y**3 + 21*(-41)*y**2 + (-41*y**2)*(18*y**2) + (-41*y**2)*(9*y**3) + (18*y**2)*(5*y**3) + (5*y**3)*(9*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (9*y**3)*(-41*y**2) = -369*y**5\n (9*y**3)*(5*y**3) = 45*y**6\n (18*y**2)*(-41*y**2) = -738*y**4\n (18*y**2)*(5*y**3) = 90*y**5\n 21*-41*y**2 = -861*y**2\n 21*5*y**3 = 105*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 45*y**6 - 369*y**5 + 90*y**5 - 738*y**4 + 105*y**3 - 861*y**2\nCombining like terms, got 45*y**6 - 279*y**5 - 738*y**4 + 105*y**3 - 861*y**2\n#Step 6:\nCurrent expression: 45*y**6 - 279*y**5 - 738*y**4 + 105*y**3 - 861*y**2\nNo more calculations needed.\n45*y**6 - 279*y**5 - 738*y**4 + 105*y**3 - 861*y**2", "generated_answer": "45*y**6 - 279*y**5 - 738*y**4 + 105*y**3 - 861*y**2", "step_length": 6} {"cot_id": "f542690eea8ef4844adfd892244d56596e30fcc549662038aca7416820629146", "datapoint": {"question": "Simplify this expression: 50*y**2*(15*y + 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "750*y**3 + 700*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 918, "polynomial_expr": "50*y**2*(15*y + 14)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 50*y**2*(15*y + 14)\nExpanding the part (15*y + 14) using the distributive property, and we got: 14*(50*y**2) + (15*y)*(50*y**2)\n#Step 2:\nCurrent expression: 14*(50*y**2) + (15*y)*(50*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 14*(50*y**2) = 700*y**2\n (15*y)*(50*y**2) = 750*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 750*y**3 + 700*y**2\nNo more calculations needed.\n750*y**3 + 700*y**2", "generated_answer": "750*y**3 + 700*y**2", "step_length": 3} {"cot_id": "946e028eb395f6ae98c4d31ef6e088e0125878436e417dcc6ffd3dfa94307c74", "datapoint": {"question": "Calculate the following: (-23*z**2 + 27*z)*(-15*z**3 - 31*z**2 - 47*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "345*z**5 + 308*z**4 + 244*z**3 - 1269*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 919, "polynomial_expr": "(-23*z**2 + 27*z)*(-15*z**3 - 31*z**2 - 47*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-23*z**2 + 27*z)*(-15*z**3 - 31*z**2 - 47*z)\nExpanding the part (-23*z**2 + 27*z) using the distributive property, and we got: (27*z)*(-15*z**3 - 31*z**2 - 47*z) + (-23*z**2)*(-15*z**3 - 31*z**2 - 47*z)\n#Step 2:\nCurrent expression: (27*z)*(-15*z**3 - 31*z**2 - 47*z) + (-23*z**2)*(-15*z**3 - 31*z**2 - 47*z)\nSimplifying the partial expression: (-23*z**2)*(-15*z**3 - 31*z**2 - 47*z)\nExpanding the part (-15*z**3 - 31*z**2 - 47*z) using the distributive property, and we got: (-47*z)*(-23*z**2) + (-31*z**2)*(-23*z**2) + (-23*z**2)*(-15*z**3)\nReplacing (-23*z**2)*(-15*z**3 - 31*z**2 - 47*z) with (-47*z)*(-23*z**2) + (-31*z**2)*(-23*z**2) + (-23*z**2)*(-15*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-47*z)*(-23*z**2) + (27*z)*(-15*z**3 - 31*z**2 - 47*z) + (-31*z**2)*(-23*z**2) + (-23*z**2)*(-15*z**3)\nSimplifying the partial expression: (27*z)*(-15*z**3 - 31*z**2 - 47*z)\nExpanding the part (-15*z**3 - 31*z**2 - 47*z) using the distributive property, and we got: (-47*z)*(27*z) + (27*z)*(-31*z**2) + (27*z)*(-15*z**3)\nReplacing (27*z)*(-15*z**3 - 31*z**2 - 47*z) with (-47*z)*(27*z) + (27*z)*(-31*z**2) + (27*z)*(-15*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-47*z)*(27*z) + (-47*z)*(-23*z**2) + (27*z)*(-31*z**2) + (27*z)*(-15*z**3) + (-31*z**2)*(-23*z**2) + (-23*z**2)*(-15*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*z)*(-23*z**2) = 1081*z**3\n (-47*z)*(27*z) = -1269*z**2\n (-31*z**2)*(-23*z**2) = 713*z**4\n (-31*z**2)*(27*z) = -837*z**3\n (-15*z**3)*(-23*z**2) = 345*z**5\n (-15*z**3)*(27*z) = -405*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 345*z**5 - 405*z**4 + 713*z**4 - 837*z**3 + 1081*z**3 - 1269*z**2\nCombining like terms, got 345*z**5 + 308*z**4 + 244*z**3 - 1269*z**2\n#Step 6:\nCurrent expression: 345*z**5 + 308*z**4 + 244*z**3 - 1269*z**2\nNo more calculations needed.\n345*z**5 + 308*z**4 + 244*z**3 - 1269*z**2", "generated_answer": "345*z**5 + 308*z**4 + 244*z**3 - 1269*z**2", "step_length": 6} {"cot_id": "77477e2006ffffc50fa0d57a9ab711c938b87e62ffa7299f0dcdaea680ee186b", "datapoint": {"question": "Calculate the following: (-15*y**3 - 9*y**2 - 37*y)*(19*y**3 + 40*y - 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-285*y**6 - 171*y**5 - 1303*y**4 + 210*y**3 - 1138*y**2 + 1406*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 920, "polynomial_expr": "(-15*y**3 - 9*y**2 - 37*y)*(19*y**3 + 40*y - 38)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-15*y**3 - 9*y**2 - 37*y)*(19*y**3 + 40*y - 38)\nExpanding the part (19*y**3 + 40*y - 38) using the distributive property, and we got: (40*y)*(-15*y**3 - 9*y**2 - 37*y) + (19*y**3)*(-15*y**3 - 9*y**2 - 37*y) - 38*(-15*y**3 - 9*y**2 - 37*y)\n#Step 2:\nCurrent expression: (40*y)*(-15*y**3 - 9*y**2 - 37*y) + (19*y**3)*(-15*y**3 - 9*y**2 - 37*y) - 38*(-15*y**3 - 9*y**2 - 37*y)\nSimplifying the partial expression: -38*(-15*y**3 - 9*y**2 - 37*y)\nExpanding the part (-15*y**3 - 9*y**2 - 37*y) using the distributive property, and we got: -37*y*(-38) - 9*y**2*(-38) - 15*y**3*(-38)\nReplacing -38*(-15*y**3 - 9*y**2 - 37*y) with -37*y*(-38) - 9*y**2*(-38) - 15*y**3*(-38) in the overall expression.\n#Step 3:\nCurrent expression: -37*y*(-38) + (40*y)*(-15*y**3 - 9*y**2 - 37*y) - 9*y**2*(-38) - 15*y**3*(-38) + (19*y**3)*(-15*y**3 - 9*y**2 - 37*y)\nSimplifying the partial expression: (19*y**3)*(-15*y**3 - 9*y**2 - 37*y)\nExpanding the part (-15*y**3 - 9*y**2 - 37*y) using the distributive property, and we got: (-37*y)*(19*y**3) + (-9*y**2)*(19*y**3) + (-15*y**3)*(19*y**3)\nReplacing (19*y**3)*(-15*y**3 - 9*y**2 - 37*y) with (-37*y)*(19*y**3) + (-9*y**2)*(19*y**3) + (-15*y**3)*(19*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-37*y)*(19*y**3) - 37*y*(-38) + (40*y)*(-15*y**3 - 9*y**2 - 37*y) + (-9*y**2)*(19*y**3) - 9*y**2*(-38) + (-15*y**3)*(19*y**3) - 15*y**3*(-38)\nSimplifying the partial expression: (40*y)*(-15*y**3 - 9*y**2 - 37*y)\nExpanding the part (-15*y**3 - 9*y**2 - 37*y) using the distributive property, and we got: (-37*y)*(40*y) + (40*y)*(-9*y**2) + (40*y)*(-15*y**3)\nReplacing (40*y)*(-15*y**3 - 9*y**2 - 37*y) with (-37*y)*(40*y) + (40*y)*(-9*y**2) + (40*y)*(-15*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-37*y)*(40*y) + (-37*y)*(19*y**3) - 37*y*(-38) + (40*y)*(-9*y**2) + (40*y)*(-15*y**3) + (-9*y**2)*(19*y**3) - 9*y**2*(-38) + (-15*y**3)*(19*y**3) - 15*y**3*(-38)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*y)*-38 = 1406*y\n (-37*y)*(19*y**3) = -703*y**4\n (-37*y)*(40*y) = -1480*y**2\n (-15*y**3)*-38 = 570*y**3\n (-15*y**3)*(19*y**3) = -285*y**6\n (-15*y**3)*(40*y) = -600*y**4\n (-9*y**2)*-38 = 342*y**2\n (-9*y**2)*(19*y**3) = -171*y**5\n (-9*y**2)*(40*y) = -360*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -285*y**6 - 171*y**5 - 703*y**4 - 600*y**4 - 360*y**3 + 570*y**3 - 1480*y**2 + 342*y**2 + 1406*y\nCombining like terms, got -285*y**6 - 171*y**5 - 1303*y**4 + 210*y**3 - 1138*y**2 + 1406*y\n#Step 7:\nCurrent expression: -285*y**6 - 171*y**5 - 1303*y**4 + 210*y**3 - 1138*y**2 + 1406*y\nNo more calculations needed.\n-285*y**6 - 171*y**5 - 1303*y**4 + 210*y**3 - 1138*y**2 + 1406*y", "generated_answer": "-285*y**6 - 171*y**5 - 1303*y**4 + 210*y**3 - 1138*y**2 + 1406*y", "step_length": 7} {"cot_id": "d47a29edcd91ab51ca5bc62f3eb4a04a7711e22f517b47dfddbfc0a509015ea8", "datapoint": {"question": "Simplify this expression: (17 - 11*z**3)*(-7*z**3 + 44*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "77*z**6 - 484*z**4 - 119*z**3 + 748*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 921, "polynomial_expr": "(17 - 11*z**3)*(-7*z**3 + 44*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (17 - 11*z**3)*(-7*z**3 + 44*z)\nExpanding the part (17 - 11*z**3) using the distributive property, and we got: (-11*z**3)*(-7*z**3 + 44*z) + 17*(-7*z**3 + 44*z)\n#Step 2:\nCurrent expression: (-11*z**3)*(-7*z**3 + 44*z) + 17*(-7*z**3 + 44*z)\nSimplifying the partial expression: 17*(-7*z**3 + 44*z)\nExpanding the part (-7*z**3 + 44*z) using the distributive property, and we got: (44*z)*17 - 7*z**3*17\nReplacing 17*(-7*z**3 + 44*z) with (44*z)*17 - 7*z**3*17 in the overall expression.\n#Step 3:\nCurrent expression: (44*z)*17 + (-11*z**3)*(-7*z**3 + 44*z) - 7*z**3*17\nSimplifying the partial expression: (-11*z**3)*(-7*z**3 + 44*z)\nExpanding the part (-7*z**3 + 44*z) using the distributive property, and we got: (44*z)*(-11*z**3) + (-11*z**3)*(-7*z**3)\nReplacing (-11*z**3)*(-7*z**3 + 44*z) with (44*z)*(-11*z**3) + (-11*z**3)*(-7*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (44*z)*(-11*z**3) + (44*z)*17 + (-11*z**3)*(-7*z**3) - 7*z**3*17\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-7*z**3)*17 = -119*z**3\n (-7*z**3)*(-11*z**3) = 77*z**6\n (44*z)*17 = 748*z\n (44*z)*(-11*z**3) = -484*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 77*z**6 - 484*z**4 - 119*z**3 + 748*z\nNo more calculations needed.\n77*z**6 - 484*z**4 - 119*z**3 + 748*z", "generated_answer": "77*z**6 - 484*z**4 - 119*z**3 + 748*z", "step_length": 5} {"cot_id": "9f89d205fee4b17e772a2e6a6dc0428820362a2c712b15bf7ef84cb12c0c7529", "datapoint": {"question": "Calculate the following: (-36*z**2 + 37*z)*(3*z**3 - 14*z**2 + 8)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-108*z**5 + 615*z**4 - 518*z**3 - 288*z**2 + 296*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 922, "polynomial_expr": "(-36*z**2 + 37*z)*(3*z**3 - 14*z**2 + 8)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-36*z**2 + 37*z)*(3*z**3 - 14*z**2 + 8)\nExpanding the part (-36*z**2 + 37*z) using the distributive property, and we got: (37*z)*(3*z**3 - 14*z**2 + 8) + (-36*z**2)*(3*z**3 - 14*z**2 + 8)\n#Step 2:\nCurrent expression: (37*z)*(3*z**3 - 14*z**2 + 8) + (-36*z**2)*(3*z**3 - 14*z**2 + 8)\nSimplifying the partial expression: (-36*z**2)*(3*z**3 - 14*z**2 + 8)\nExpanding the part (3*z**3 - 14*z**2 + 8) using the distributive property, and we got: 8*(-36*z**2) + (-36*z**2)*(-14*z**2) + (-36*z**2)*(3*z**3)\nReplacing (-36*z**2)*(3*z**3 - 14*z**2 + 8) with 8*(-36*z**2) + (-36*z**2)*(-14*z**2) + (-36*z**2)*(3*z**3) in the overall expression.\n#Step 3:\nCurrent expression: 8*(-36)*z**2 + (37*z)*(3*z**3 - 14*z**2 + 8) + (-36*z**2)*(-14*z**2) + (-36*z**2)*(3*z**3)\nSimplifying the partial expression: (37*z)*(3*z**3 - 14*z**2 + 8)\nExpanding the part (3*z**3 - 14*z**2 + 8) using the distributive property, and we got: 8*(37*z) + (37*z)*(-14*z**2) + (37*z)*(3*z**3)\nReplacing (37*z)*(3*z**3 - 14*z**2 + 8) with 8*(37*z) + (37*z)*(-14*z**2) + (37*z)*(3*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 8*(-36)*z**2 + 8*37*z + (37*z)*(-14*z**2) + (37*z)*(3*z**3) + (-36*z**2)*(-14*z**2) + (-36*z**2)*(3*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-14*z**2)*(-36*z**2) = 504*z**4\n (-14*z**2)*(37*z) = -518*z**3\n (3*z**3)*(-36*z**2) = -108*z**5\n (3*z**3)*(37*z) = 111*z**4\n 8*-36*z**2 = -288*z**2\n 8*37*z = 296*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -108*z**5 + 111*z**4 + 504*z**4 - 518*z**3 - 288*z**2 + 296*z\nCombining like terms, got -108*z**5 + 615*z**4 - 518*z**3 - 288*z**2 + 296*z\n#Step 6:\nCurrent expression: -108*z**5 + 615*z**4 - 518*z**3 - 288*z**2 + 296*z\nNo more calculations needed.\n-108*z**5 + 615*z**4 - 518*z**3 - 288*z**2 + 296*z", "generated_answer": "-108*z**5 + 615*z**4 - 518*z**3 - 288*z**2 + 296*z", "step_length": 6} {"cot_id": "b59116ccbada5c5af0b7ad737531716e7af00881683e21853d30a5c114a1eab7", "datapoint": {"question": "Simplify this expression: (-26*x**3 + 29*x**2)*(45*x**3 - 32*x - 25)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1170*x**6 + 1305*x**5 + 832*x**4 - 278*x**3 - 725*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 923, "polynomial_expr": "(-26*x**3 + 29*x**2)*(45*x**3 - 32*x - 25)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-26*x**3 + 29*x**2)*(45*x**3 - 32*x - 25)\nExpanding the part (-26*x**3 + 29*x**2) using the distributive property, and we got: (29*x**2)*(45*x**3 - 32*x - 25) + (-26*x**3)*(45*x**3 - 32*x - 25)\n#Step 2:\nCurrent expression: (29*x**2)*(45*x**3 - 32*x - 25) + (-26*x**3)*(45*x**3 - 32*x - 25)\nSimplifying the partial expression: (-26*x**3)*(45*x**3 - 32*x - 25)\nExpanding the part (45*x**3 - 32*x - 25) using the distributive property, and we got: (-32*x)*(-26*x**3) - (-1)*650*x**3 + (-26*x**3)*(45*x**3)\nReplacing (-26*x**3)*(45*x**3 - 32*x - 25) with (-32*x)*(-26*x**3) - (-1)*650*x**3 + (-26*x**3)*(45*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-32*x)*(-26*x**3) - 25*(-26)*x**3 + (29*x**2)*(45*x**3 - 32*x - 25) + (-26*x**3)*(45*x**3)\nSimplifying the partial expression: (29*x**2)*(45*x**3 - 32*x - 25)\nExpanding the part (45*x**3 - 32*x - 25) using the distributive property, and we got: (-32*x)*(29*x**2) - 725*x**2 + (29*x**2)*(45*x**3)\nReplacing (29*x**2)*(45*x**3 - 32*x - 25) with (-32*x)*(29*x**2) - 725*x**2 + (29*x**2)*(45*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-32*x)*(29*x**2) + (-32*x)*(-26*x**3) - 25*(-26)*x**3 - 25*29*x**2 + (29*x**2)*(45*x**3) + (-26*x**3)*(45*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*x)*(-26*x**3) = 832*x**4\n (-32*x)*(29*x**2) = -928*x**3\n (45*x**3)*(-26*x**3) = -1170*x**6\n (45*x**3)*(29*x**2) = 1305*x**5\n -25*-26*x**3 = 650*x**3\n -25*29*x**2 = -725*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1170*x**6 + 1305*x**5 + 832*x**4 - 928*x**3 + 650*x**3 - 725*x**2\nCombining like terms, got -1170*x**6 + 1305*x**5 + 832*x**4 - 278*x**3 - 725*x**2\n#Step 6:\nCurrent expression: -1170*x**6 + 1305*x**5 + 832*x**4 - 278*x**3 - 725*x**2\nNo more calculations needed.\n-1170*x**6 + 1305*x**5 + 832*x**4 - 278*x**3 - 725*x**2", "generated_answer": "-1170*x**6 + 1305*x**5 + 832*x**4 - 278*x**3 - 725*x**2", "step_length": 6} {"cot_id": "2060462413551676ab63e13005c815cbbd7f79d7872852a2a8adddb9d0515eef", "datapoint": {"question": "Calculate the following: 1443*x**3 - 975*x**2 - 780*x + 741\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1443*x**3 - 975*x**2 - 780*x + 741", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 924, "polynomial_expr": "1443*x**3 - 975*x**2 - 780*x + 741", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 1443*x**3 - 975*x**2 - 780*x + 741\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 1443*x**3 - 975*x**2 - 780*x + 741\nNo more calculations needed.\n1443*x**3 - 975*x**2 - 780*x + 741", "generated_answer": "1443*x**3 - 975*x**2 - 780*x + 741", "step_length": 2} {"cot_id": "10646a7446d3bd897276bc95fb416b4af44f385bea14f614b18e639bf4d882b7", "datapoint": {"question": "Simplify this expression: (50*z**2 - 9*z)*(28*z**3 - 2*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1400*z**5 - 352*z**4 + 18*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 925, "polynomial_expr": "(50*z**2 - 9*z)*(28*z**3 - 2*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (50*z**2 - 9*z)*(28*z**3 - 2*z**2)\nExpanding the part (50*z**2 - 9*z) using the distributive property, and we got: (-9*z)*(28*z**3 - 2*z**2) + (50*z**2)*(28*z**3 - 2*z**2)\n#Step 2:\nCurrent expression: (-9*z)*(28*z**3 - 2*z**2) + (50*z**2)*(28*z**3 - 2*z**2)\nSimplifying the partial expression: (-9*z)*(28*z**3 - 2*z**2)\nExpanding the part (28*z**3 - 2*z**2) using the distributive property, and we got: (-9*z)*(-2*z**2) + (-9*z)*(28*z**3)\nReplacing (-9*z)*(28*z**3 - 2*z**2) with (-9*z)*(-2*z**2) + (-9*z)*(28*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-9*z)*(-2*z**2) + (-9*z)*(28*z**3) + (50*z**2)*(28*z**3 - 2*z**2)\nSimplifying the partial expression: (50*z**2)*(28*z**3 - 2*z**2)\nExpanding the part (28*z**3 - 2*z**2) using the distributive property, and we got: (-2*z**2)*(50*z**2) + (50*z**2)*(28*z**3)\nReplacing (50*z**2)*(28*z**3 - 2*z**2) with (-2*z**2)*(50*z**2) + (50*z**2)*(28*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-9*z)*(-2*z**2) + (-9*z)*(28*z**3) + (-2*z**2)*(50*z**2) + (50*z**2)*(28*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-2*z**2)*(-9*z) = 18*z**3\n (-2*z**2)*(50*z**2) = -100*z**4\n (28*z**3)*(-9*z) = -252*z**4\n (28*z**3)*(50*z**2) = 1400*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1400*z**5 - 252*z**4 - 100*z**4 + 18*z**3\nCombining like terms, got 1400*z**5 - 352*z**4 + 18*z**3\n#Step 6:\nCurrent expression: 1400*z**5 - 352*z**4 + 18*z**3\nNo more calculations needed.\n1400*z**5 - 352*z**4 + 18*z**3", "generated_answer": "1400*z**5 - 352*z**4 + 18*z**3", "step_length": 6} {"cot_id": "2ec2c445c0ac4e308edff081208bab31895c308c7feef708f98983bee6a1e790", "datapoint": {"question": "Simplify this expression: (-14*x**2 - 45*x - 14)*(-77*x**3 - 41*x - 37)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1078*x**5 + 3465*x**4 + 1652*x**3 + 2363*x**2 + 2239*x + 518", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 926, "polynomial_expr": "(-14*x**2 - 45*x - 14)*(-77*x**3 - 41*x - 37)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-14*x**2 - 45*x - 14)*(-77*x**3 - 41*x - 37)\nExpanding the part (-77*x**3 - 41*x - 37) using the distributive property, and we got: (-41*x)*(-14*x**2 - 45*x - 14) + (-77*x**3)*(-14*x**2 - 45*x - 14) - 37*(-14*x**2 - 45*x - 14)\n#Step 2:\nCurrent expression: (-41*x)*(-14*x**2 - 45*x - 14) + (-77*x**3)*(-14*x**2 - 45*x - 14) - 37*(-14*x**2 - 45*x - 14)\nSimplifying the partial expression: -37*(-14*x**2 - 45*x - 14)\nExpanding the part (-14*x**2 - 45*x - 14) using the distributive property, and we got: -45*x*(-37) - 14*x**2*(-37) - 14*(-37)\nReplacing -37*(-14*x**2 - 45*x - 14) with -45*x*(-37) - 14*x**2*(-37) - 14*(-37) in the overall expression.\n#Step 3:\nCurrent expression: -45*x*(-37) + (-41*x)*(-14*x**2 - 45*x - 14) - 14*x**2*(-37) + (-77*x**3)*(-14*x**2 - 45*x - 14) + 518\nSimplifying the partial expression: (-77*x**3)*(-14*x**2 - 45*x - 14)\nExpanding the part (-14*x**2 - 45*x - 14) using the distributive property, and we got: (-45*x)*(-77*x**3) - (-1)*1078*x**3 + (-14*x**2)*(-77*x**3)\nReplacing (-77*x**3)*(-14*x**2 - 45*x - 14) with (-45*x)*(-77*x**3) - (-1)*1078*x**3 + (-14*x**2)*(-77*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-45*x)*(-77*x**3) - 45*x*(-37) + (-41*x)*(-14*x**2 - 45*x - 14) - 14*(-77)*x**3 + (-14*x**2)*(-77*x**3) - 14*x**2*(-37) + 518\nSimplifying the partial expression: (-41*x)*(-14*x**2 - 45*x - 14)\nExpanding the part (-14*x**2 - 45*x - 14) using the distributive property, and we got: (-45*x)*(-41*x) + (-41*x)*(-14*x**2) - (-1)*574*x\nReplacing (-41*x)*(-14*x**2 - 45*x - 14) with (-45*x)*(-41*x) + (-41*x)*(-14*x**2) - (-1)*574*x in the overall expression.\n#Step 5:\nCurrent expression: (-45*x)*(-41*x) + (-45*x)*(-77*x**3) - 45*x*(-37) + (-41*x)*(-14*x**2) - 14*(-77)*x**3 - 14*(-41)*x + (-14*x**2)*(-77*x**3) - 14*x**2*(-37) + 518\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*x)*-37 = 1665*x\n (-45*x)*(-77*x**3) = 3465*x**4\n (-45*x)*(-41*x) = 1845*x**2\n (-14*x**2)*-37 = 518*x**2\n (-14*x**2)*(-77*x**3) = 1078*x**5\n (-14*x**2)*(-41*x) = 574*x**3\n -14*-77*x**3 = 1078*x**3\n -14*-41*x = 574*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1078*x**5 + 3465*x**4 + 574*x**3 + 1078*x**3 + 518*x**2 + 1845*x**2 + 574*x + 1665*x + 518\nCombining like terms, got 1078*x**5 + 3465*x**4 + 1652*x**3 + 2363*x**2 + 2239*x + 518\n#Step 7:\nCurrent expression: 1078*x**5 + 3465*x**4 + 1652*x**3 + 2363*x**2 + 2239*x + 518\nNo more calculations needed.\n1078*x**5 + 3465*x**4 + 1652*x**3 + 2363*x**2 + 2239*x + 518", "generated_answer": "1078*x**5 + 3465*x**4 + 1652*x**3 + 2363*x**2 + 2239*x + 518", "step_length": 7} {"cot_id": "5975ec60423d1177030afe304afad1d1db9ab745cf988065a7da2b72806d222f", "datapoint": {"question": "Simplify this expression: -7*y**2*(30*y**2 - 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-210*y**4 + 266*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 927, "polynomial_expr": "-7*y**2*(30*y**2 - 38)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -7*y**2*(30*y**2 - 38)\nExpanding the part (30*y**2 - 38) using the distributive property, and we got: -(-1)*266*y**2 + (-7*y**2)*(30*y**2)\n#Step 2:\nCurrent expression: -(-1)*266*y**2 + (-7*y**2)*(30*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -38*(-7*y**2) = 266*y**2\n (30*y**2)*(-7*y**2) = -210*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -210*y**4 + 266*y**2\nNo more calculations needed.\n-210*y**4 + 266*y**2", "generated_answer": "-210*y**4 + 266*y**2", "step_length": 3} {"cot_id": "2ba3ba1f7062ac053f4fbdf206ea10d4047d1b9752576389fd586a1c0a17f41f", "datapoint": {"question": "Simplify this expression: (21*y**3 - 45)*(2*y**3 + 17*y + 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "42*y**6 + 357*y**4 + 960*y**3 - 765*y - 2250", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 928, "polynomial_expr": "(21*y**3 - 45)*(2*y**3 + 17*y + 50)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21*y**3 - 45)*(2*y**3 + 17*y + 50)\nExpanding the part (21*y**3 - 45) using the distributive property, and we got: (21*y**3)*(2*y**3 + 17*y + 50) - 45*(2*y**3 + 17*y + 50)\n#Step 2:\nCurrent expression: (21*y**3)*(2*y**3 + 17*y + 50) - 45*(2*y**3 + 17*y + 50)\nSimplifying the partial expression: -45*(2*y**3 + 17*y + 50)\nExpanding the part (2*y**3 + 17*y + 50) using the distributive property, and we got: (17*y)*(-45) + (2*y**3)*(-45) + 50*(-45)\nReplacing -45*(2*y**3 + 17*y + 50) with (17*y)*(-45) + (2*y**3)*(-45) + 50*(-45) in the overall expression.\n#Step 3:\nCurrent expression: (17*y)*(-45) + (2*y**3)*(-45) + (21*y**3)*(2*y**3 + 17*y + 50) - 2250\nSimplifying the partial expression: (21*y**3)*(2*y**3 + 17*y + 50)\nExpanding the part (2*y**3 + 17*y + 50) using the distributive property, and we got: 50*(21*y**3) + (17*y)*(21*y**3) + (2*y**3)*(21*y**3)\nReplacing (21*y**3)*(2*y**3 + 17*y + 50) with 50*(21*y**3) + (17*y)*(21*y**3) + (2*y**3)*(21*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 50*21*y**3 + (17*y)*(21*y**3) + (17*y)*(-45) + (2*y**3)*(21*y**3) + (2*y**3)*(-45) - 2250\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (2*y**3)*-45 = -90*y**3\n (2*y**3)*(21*y**3) = 42*y**6\n (17*y)*-45 = -765*y\n (17*y)*(21*y**3) = 357*y**4\n 50*21*y**3 = 1050*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 42*y**6 + 357*y**4 - 90*y**3 + 1050*y**3 - 765*y - 2250\nCombining like terms, got 42*y**6 + 357*y**4 + 960*y**3 - 765*y - 2250\n#Step 6:\nCurrent expression: 42*y**6 + 357*y**4 + 960*y**3 - 765*y - 2250\nNo more calculations needed.\n42*y**6 + 357*y**4 + 960*y**3 - 765*y - 2250", "generated_answer": "42*y**6 + 357*y**4 + 960*y**3 - 765*y - 2250", "step_length": 6} {"cot_id": "6945f950208c3a2a265c3ae153efbfda4bc62e37b29424b669257610d5d2aff2", "datapoint": {"question": "Calculate the following: (-8*y**2 - 4*y)*(24*y**3 + 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-192*y**5 - 96*y**4 - 312*y**2 - 156*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 929, "polynomial_expr": "(-8*y**2 - 4*y)*(24*y**3 + 39)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-8*y**2 - 4*y)*(24*y**3 + 39)\nExpanding the part (24*y**3 + 39) using the distributive property, and we got: (24*y**3)*(-8*y**2 - 4*y) + 39*(-8*y**2 - 4*y)\n#Step 2:\nCurrent expression: (24*y**3)*(-8*y**2 - 4*y) + 39*(-8*y**2 - 4*y)\nSimplifying the partial expression: 39*(-8*y**2 - 4*y)\nExpanding the part (-8*y**2 - 4*y) using the distributive property, and we got: -4*y*39 - 8*y**2*39\nReplacing 39*(-8*y**2 - 4*y) with -4*y*39 - 8*y**2*39 in the overall expression.\n#Step 3:\nCurrent expression: -4*y*39 - 8*y**2*39 + (24*y**3)*(-8*y**2 - 4*y)\nSimplifying the partial expression: (24*y**3)*(-8*y**2 - 4*y)\nExpanding the part (-8*y**2 - 4*y) using the distributive property, and we got: (-4*y)*(24*y**3) + (-8*y**2)*(24*y**3)\nReplacing (24*y**3)*(-8*y**2 - 4*y) with (-4*y)*(24*y**3) + (-8*y**2)*(24*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-4*y)*(24*y**3) - 4*y*39 + (-8*y**2)*(24*y**3) - 8*y**2*39\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-8*y**2)*39 = -312*y**2\n (-8*y**2)*(24*y**3) = -192*y**5\n (-4*y)*39 = -156*y\n (-4*y)*(24*y**3) = -96*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -192*y**5 - 96*y**4 - 312*y**2 - 156*y\nNo more calculations needed.\n-192*y**5 - 96*y**4 - 312*y**2 - 156*y", "generated_answer": "-192*y**5 - 96*y**4 - 312*y**2 - 156*y", "step_length": 5} {"cot_id": "1f811ec35c2ba4219d80e0e264998222200c3cf60876007f01b5ebffbd122d6d", "datapoint": {"question": "Simplify this expression: (-38*z**2 + 33*z)*(-14*z**2 + 28*z - 27)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "532*z**4 - 1526*z**3 + 1950*z**2 - 891*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 930, "polynomial_expr": "(-38*z**2 + 33*z)*(-14*z**2 + 28*z - 27)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-38*z**2 + 33*z)*(-14*z**2 + 28*z - 27)\nExpanding the part (-38*z**2 + 33*z) using the distributive property, and we got: (33*z)*(-14*z**2 + 28*z - 27) + (-38*z**2)*(-14*z**2 + 28*z - 27)\n#Step 2:\nCurrent expression: (33*z)*(-14*z**2 + 28*z - 27) + (-38*z**2)*(-14*z**2 + 28*z - 27)\nSimplifying the partial expression: (-38*z**2)*(-14*z**2 + 28*z - 27)\nExpanding the part (-14*z**2 + 28*z - 27) using the distributive property, and we got: -(-1)*1026*z**2 + (28*z)*(-38*z**2) + (-38*z**2)*(-14*z**2)\nReplacing (-38*z**2)*(-14*z**2 + 28*z - 27) with -(-1)*1026*z**2 + (28*z)*(-38*z**2) + (-38*z**2)*(-14*z**2) in the overall expression.\n#Step 3:\nCurrent expression: -27*(-38)*z**2 + (28*z)*(-38*z**2) + (33*z)*(-14*z**2 + 28*z - 27) + (-38*z**2)*(-14*z**2)\nSimplifying the partial expression: (33*z)*(-14*z**2 + 28*z - 27)\nExpanding the part (-14*z**2 + 28*z - 27) using the distributive property, and we got: -891*z + (28*z)*(33*z) + (33*z)*(-14*z**2)\nReplacing (33*z)*(-14*z**2 + 28*z - 27) with -891*z + (28*z)*(33*z) + (33*z)*(-14*z**2) in the overall expression.\n#Step 4:\nCurrent expression: -27*(-38)*z**2 - 27*33*z + (28*z)*(33*z) + (28*z)*(-38*z**2) + (33*z)*(-14*z**2) + (-38*z**2)*(-14*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-14*z**2)*(-38*z**2) = 532*z**4\n (-14*z**2)*(33*z) = -462*z**3\n (28*z)*(-38*z**2) = -1064*z**3\n (28*z)*(33*z) = 924*z**2\n -27*-38*z**2 = 1026*z**2\n -27*33*z = -891*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 532*z**4 - 1064*z**3 - 462*z**3 + 924*z**2 + 1026*z**2 - 891*z\nCombining like terms, got 532*z**4 - 1526*z**3 + 1950*z**2 - 891*z\n#Step 6:\nCurrent expression: 532*z**4 - 1526*z**3 + 1950*z**2 - 891*z\nNo more calculations needed.\n532*z**4 - 1526*z**3 + 1950*z**2 - 891*z", "generated_answer": "532*z**4 - 1526*z**3 + 1950*z**2 - 891*z", "step_length": 6} {"cot_id": "121d4295029398535e86d91827cc598cbc351d240c790ebcb8048728ace8fe29", "datapoint": {"question": "Calculate the following: (46*x**2 - 23*x)*(6*x**3 + 60*x + 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "276*x**5 - 138*x**4 + 2760*x**3 + 276*x**2 - 828*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 931, "polynomial_expr": "(46*x**2 - 23*x)*(6*x**3 + 60*x + 36)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (46*x**2 - 23*x)*(6*x**3 + 60*x + 36)\nExpanding the part (46*x**2 - 23*x) using the distributive property, and we got: (-23*x)*(6*x**3 + 60*x + 36) + (46*x**2)*(6*x**3 + 60*x + 36)\n#Step 2:\nCurrent expression: (-23*x)*(6*x**3 + 60*x + 36) + (46*x**2)*(6*x**3 + 60*x + 36)\nSimplifying the partial expression: (-23*x)*(6*x**3 + 60*x + 36)\nExpanding the part (6*x**3 + 60*x + 36) using the distributive property, and we got: (-23*x)*(60*x) + (-23*x)*(6*x**3) + 36*(-23*x)\nReplacing (-23*x)*(6*x**3 + 60*x + 36) with (-23*x)*(60*x) + (-23*x)*(6*x**3) + 36*(-23*x) in the overall expression.\n#Step 3:\nCurrent expression: (-23*x)*(60*x) + (-23*x)*(6*x**3) + 36*(-23)*x + (46*x**2)*(6*x**3 + 60*x + 36)\nSimplifying the partial expression: (46*x**2)*(6*x**3 + 60*x + 36)\nExpanding the part (6*x**3 + 60*x + 36) using the distributive property, and we got: 36*(46*x**2) + (60*x)*(46*x**2) + (46*x**2)*(6*x**3)\nReplacing (46*x**2)*(6*x**3 + 60*x + 36) with 36*(46*x**2) + (60*x)*(46*x**2) + (46*x**2)*(6*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-23*x)*(60*x) + (-23*x)*(6*x**3) + 36*46*x**2 + 36*(-23)*x + (60*x)*(46*x**2) + (46*x**2)*(6*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (6*x**3)*(-23*x) = -138*x**4\n (6*x**3)*(46*x**2) = 276*x**5\n (60*x)*(-23*x) = -1380*x**2\n (60*x)*(46*x**2) = 2760*x**3\n 36*-23*x = -828*x\n 36*46*x**2 = 1656*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 276*x**5 - 138*x**4 + 2760*x**3 - 1380*x**2 + 1656*x**2 - 828*x\nCombining like terms, got 276*x**5 - 138*x**4 + 2760*x**3 + 276*x**2 - 828*x\n#Step 6:\nCurrent expression: 276*x**5 - 138*x**4 + 2760*x**3 + 276*x**2 - 828*x\nNo more calculations needed.\n276*x**5 - 138*x**4 + 2760*x**3 + 276*x**2 - 828*x", "generated_answer": "276*x**5 - 138*x**4 + 2760*x**3 + 276*x**2 - 828*x", "step_length": 6} {"cot_id": "2760d4a2acddb5232dcbac9f936a63c2dff559bb502d7a49ea4ae7c31409310d", "datapoint": {"question": "Calculate the following: (-31*y**2 - y)*(-18*y**3 - 30*y - 4)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "558*y**5 + 18*y**4 + 930*y**3 + 154*y**2 + 4*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 932, "polynomial_expr": "(-31*y**2 - y)*(-18*y**3 - 30*y - 4)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-31*y**2 - y)*(-18*y**3 - 30*y - 4)\nExpanding the part (-31*y**2 - y) using the distributive property, and we got: (-y)*(-18*y**3 - 30*y - 4) + (-31*y**2)*(-18*y**3 - 30*y - 4)\n#Step 2:\nCurrent expression: (-y)*(-18*y**3 - 30*y - 4) + (-31*y**2)*(-18*y**3 - 30*y - 4)\nSimplifying the partial expression: (-y)*(-18*y**3 - 30*y - 4)\nExpanding the part (-18*y**3 - 30*y - 4) using the distributive property, and we got: (-30*y)*(-y) + (-y)*(-18*y**3) - (-1)*4*y\nReplacing (-y)*(-18*y**3 - 30*y - 4) with (-30*y)*(-y) + (-y)*(-18*y**3) - (-1)*4*y in the overall expression.\n#Step 3:\nCurrent expression: (-30*y)*(-y) + (-y)*(-18*y**3) - 4*(-1)*y + (-31*y**2)*(-18*y**3 - 30*y - 4)\nSimplifying the partial expression: (-31*y**2)*(-18*y**3 - 30*y - 4)\nExpanding the part (-18*y**3 - 30*y - 4) using the distributive property, and we got: (-30*y)*(-31*y**2) - (-1)*124*y**2 + (-31*y**2)*(-18*y**3)\nReplacing (-31*y**2)*(-18*y**3 - 30*y - 4) with (-30*y)*(-31*y**2) - (-1)*124*y**2 + (-31*y**2)*(-18*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-30*y)*(-y) + (-30*y)*(-31*y**2) + (-y)*(-18*y**3) - 4*(-31)*y**2 - 4*(-1)*y + (-31*y**2)*(-18*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*y)*(-y) = 30*y**2\n (-30*y)*(-31*y**2) = 930*y**3\n (-18*y**3)*(-y) = 18*y**4\n (-18*y**3)*(-31*y**2) = 558*y**5\n -4*-1*y = 4*y\n -4*-31*y**2 = 124*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 558*y**5 + 18*y**4 + 930*y**3 + 30*y**2 + 124*y**2 + 4*y\nCombining like terms, got 558*y**5 + 18*y**4 + 930*y**3 + 154*y**2 + 4*y\n#Step 6:\nCurrent expression: 558*y**5 + 18*y**4 + 930*y**3 + 154*y**2 + 4*y\nNo more calculations needed.\n558*y**5 + 18*y**4 + 930*y**3 + 154*y**2 + 4*y", "generated_answer": "558*y**5 + 18*y**4 + 930*y**3 + 154*y**2 + 4*y", "step_length": 6} {"cot_id": "ba508e16e5eea67e950a1915accb0b8312720e75edbe08d37e5427993bc36e9e", "datapoint": {"question": "Calculate the following: (45*y**3 + 5*y)*(-50*y**2 + 34*y + 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2250*y**5 + 1530*y**4 + 695*y**3 + 170*y**2 + 105*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 933, "polynomial_expr": "(45*y**3 + 5*y)*(-50*y**2 + 34*y + 21)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (45*y**3 + 5*y)*(-50*y**2 + 34*y + 21)\nExpanding the part (45*y**3 + 5*y) using the distributive property, and we got: (5*y)*(-50*y**2 + 34*y + 21) + (45*y**3)*(-50*y**2 + 34*y + 21)\n#Step 2:\nCurrent expression: (5*y)*(-50*y**2 + 34*y + 21) + (45*y**3)*(-50*y**2 + 34*y + 21)\nSimplifying the partial expression: (5*y)*(-50*y**2 + 34*y + 21)\nExpanding the part (-50*y**2 + 34*y + 21) using the distributive property, and we got: 21*(5*y) + (5*y)*(34*y) + (5*y)*(-50*y**2)\nReplacing (5*y)*(-50*y**2 + 34*y + 21) with 21*(5*y) + (5*y)*(34*y) + (5*y)*(-50*y**2) in the overall expression.\n#Step 3:\nCurrent expression: 21*5*y + (5*y)*(34*y) + (5*y)*(-50*y**2) + (45*y**3)*(-50*y**2 + 34*y + 21)\nSimplifying the partial expression: (45*y**3)*(-50*y**2 + 34*y + 21)\nExpanding the part (-50*y**2 + 34*y + 21) using the distributive property, and we got: 21*(45*y**3) + (34*y)*(45*y**3) + (-50*y**2)*(45*y**3)\nReplacing (45*y**3)*(-50*y**2 + 34*y + 21) with 21*(45*y**3) + (34*y)*(45*y**3) + (-50*y**2)*(45*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 21*45*y**3 + 21*5*y + (5*y)*(34*y) + (5*y)*(-50*y**2) + (34*y)*(45*y**3) + (-50*y**2)*(45*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-50*y**2)*(5*y) = -250*y**3\n (-50*y**2)*(45*y**3) = -2250*y**5\n (34*y)*(5*y) = 170*y**2\n (34*y)*(45*y**3) = 1530*y**4\n 21*5*y = 105*y\n 21*45*y**3 = 945*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2250*y**5 + 1530*y**4 - 250*y**3 + 945*y**3 + 170*y**2 + 105*y\nCombining like terms, got -2250*y**5 + 1530*y**4 + 695*y**3 + 170*y**2 + 105*y\n#Step 6:\nCurrent expression: -2250*y**5 + 1530*y**4 + 695*y**3 + 170*y**2 + 105*y\nNo more calculations needed.\n-2250*y**5 + 1530*y**4 + 695*y**3 + 170*y**2 + 105*y", "generated_answer": "-2250*y**5 + 1530*y**4 + 695*y**3 + 170*y**2 + 105*y", "step_length": 6} {"cot_id": "b3475601b5c538eee4306de02f82506a4a07d871a1215a97784eed5f46c924ae", "datapoint": {"question": "Simplify this expression: (28*y**2 + y)*(-39*y**3 + 42*y**2 - 27*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1092*y**5 + 1137*y**4 - 714*y**3 - 27*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 934, "polynomial_expr": "(28*y**2 + y)*(-39*y**3 + 42*y**2 - 27*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28*y**2 + y)*(-39*y**3 + 42*y**2 - 27*y)\nExpanding the part (28*y**2 + y) using the distributive property, and we got: y*(-39*y**3 + 42*y**2 - 27*y) + (28*y**2)*(-39*y**3 + 42*y**2 - 27*y)\n#Step 2:\nCurrent expression: y*(-39*y**3 + 42*y**2 - 27*y) + (28*y**2)*(-39*y**3 + 42*y**2 - 27*y)\nSimplifying the partial expression: y*(-39*y**3 + 42*y**2 - 27*y)\nExpanding the part (-39*y**3 + 42*y**2 - 27*y) using the distributive property, and we got: (-27*y)*y + y*(42*y**2) + y*(-39*y**3)\nReplacing y*(-39*y**3 + 42*y**2 - 27*y) with (-27*y)*y + y*(42*y**2) + y*(-39*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-27*y)*y + y*(42*y**2) + y*(-39*y**3) + (28*y**2)*(-39*y**3 + 42*y**2 - 27*y)\nSimplifying the partial expression: (28*y**2)*(-39*y**3 + 42*y**2 - 27*y)\nExpanding the part (-39*y**3 + 42*y**2 - 27*y) using the distributive property, and we got: (-27*y)*(28*y**2) + (28*y**2)*(42*y**2) + (28*y**2)*(-39*y**3)\nReplacing (28*y**2)*(-39*y**3 + 42*y**2 - 27*y) with (-27*y)*(28*y**2) + (28*y**2)*(42*y**2) + (28*y**2)*(-39*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-27*y)*y + (-27*y)*(28*y**2) + y*(42*y**2) + y*(-39*y**3) + (28*y**2)*(42*y**2) + (28*y**2)*(-39*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*y**3)*y = -39*y**4\n (-39*y**3)*(28*y**2) = -1092*y**5\n (-27*y)*y = -27*y**2\n (-27*y)*(28*y**2) = -756*y**3\n (42*y**2)*y = 42*y**3\n (42*y**2)*(28*y**2) = 1176*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1092*y**5 - 39*y**4 + 1176*y**4 - 756*y**3 + 42*y**3 - 27*y**2\nCombining like terms, got -1092*y**5 + 1137*y**4 - 714*y**3 - 27*y**2\n#Step 6:\nCurrent expression: -1092*y**5 + 1137*y**4 - 714*y**3 - 27*y**2\nNo more calculations needed.\n-1092*y**5 + 1137*y**4 - 714*y**3 - 27*y**2", "generated_answer": "-1092*y**5 + 1137*y**4 - 714*y**3 - 27*y**2", "step_length": 6} {"cot_id": "a57366e52beeeae22fad1d088608798887e87d65db82b95cfdda99319e003853", "datapoint": {"question": "Calculate the following: (-17*z**3 + 14*z**2)*(38*z**3 + 13*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-646*z**6 + 532*z**5 - 221*z**4 + 182*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 935, "polynomial_expr": "(-17*z**3 + 14*z**2)*(38*z**3 + 13*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-17*z**3 + 14*z**2)*(38*z**3 + 13*z)\nExpanding the part (-17*z**3 + 14*z**2) using the distributive property, and we got: (14*z**2)*(38*z**3 + 13*z) + (-17*z**3)*(38*z**3 + 13*z)\n#Step 2:\nCurrent expression: (14*z**2)*(38*z**3 + 13*z) + (-17*z**3)*(38*z**3 + 13*z)\nSimplifying the partial expression: (-17*z**3)*(38*z**3 + 13*z)\nExpanding the part (38*z**3 + 13*z) using the distributive property, and we got: (13*z)*(-17*z**3) + (-17*z**3)*(38*z**3)\nReplacing (-17*z**3)*(38*z**3 + 13*z) with (13*z)*(-17*z**3) + (-17*z**3)*(38*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (13*z)*(-17*z**3) + (14*z**2)*(38*z**3 + 13*z) + (-17*z**3)*(38*z**3)\nSimplifying the partial expression: (14*z**2)*(38*z**3 + 13*z)\nExpanding the part (38*z**3 + 13*z) using the distributive property, and we got: (13*z)*(14*z**2) + (14*z**2)*(38*z**3)\nReplacing (14*z**2)*(38*z**3 + 13*z) with (13*z)*(14*z**2) + (14*z**2)*(38*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (13*z)*(14*z**2) + (13*z)*(-17*z**3) + (14*z**2)*(38*z**3) + (-17*z**3)*(38*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (13*z)*(-17*z**3) = -221*z**4\n (13*z)*(14*z**2) = 182*z**3\n (38*z**3)*(-17*z**3) = -646*z**6\n (38*z**3)*(14*z**2) = 532*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -646*z**6 + 532*z**5 - 221*z**4 + 182*z**3\nNo more calculations needed.\n-646*z**6 + 532*z**5 - 221*z**4 + 182*z**3", "generated_answer": "-646*z**6 + 532*z**5 - 221*z**4 + 182*z**3", "step_length": 5} {"cot_id": "5acd73c8b9bdf0f66cf90ba905e05aa1791858b72c9cf0bd4aa375fa63058030", "datapoint": {"question": "Calculate the following: 1566 - 1188*z\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1566 - 1188*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 936, "polynomial_expr": "1566 - 1188*z", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 1566 - 1188*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 1566 - 1188*z\nNo more calculations needed.\n1566 - 1188*z", "generated_answer": "1566 - 1188*z", "step_length": 2} {"cot_id": "181ba378a953395ba6eeeed8078338897b9877e3c95d61127464714dec46f7bc", "datapoint": {"question": "Simplify this expression: (-8*y**3 - 7*y)*(-3*y**3 + 16*y**2 - 8)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "24*y**6 - 128*y**5 + 21*y**4 - 48*y**3 + 56*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 937, "polynomial_expr": "(-8*y**3 - 7*y)*(-3*y**3 + 16*y**2 - 8)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-8*y**3 - 7*y)*(-3*y**3 + 16*y**2 - 8)\nExpanding the part (-8*y**3 - 7*y) using the distributive property, and we got: (-7*y)*(-3*y**3 + 16*y**2 - 8) + (-8*y**3)*(-3*y**3 + 16*y**2 - 8)\n#Step 2:\nCurrent expression: (-7*y)*(-3*y**3 + 16*y**2 - 8) + (-8*y**3)*(-3*y**3 + 16*y**2 - 8)\nSimplifying the partial expression: (-8*y**3)*(-3*y**3 + 16*y**2 - 8)\nExpanding the part (-3*y**3 + 16*y**2 - 8) using the distributive property, and we got: -(-1)*64*y**3 + (16*y**2)*(-8*y**3) + (-8*y**3)*(-3*y**3)\nReplacing (-8*y**3)*(-3*y**3 + 16*y**2 - 8) with -(-1)*64*y**3 + (16*y**2)*(-8*y**3) + (-8*y**3)*(-3*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-7*y)*(-3*y**3 + 16*y**2 - 8) - 8*(-8)*y**3 + (16*y**2)*(-8*y**3) + (-8*y**3)*(-3*y**3)\nSimplifying the partial expression: (-7*y)*(-3*y**3 + 16*y**2 - 8)\nExpanding the part (-3*y**3 + 16*y**2 - 8) using the distributive property, and we got: (-7*y)*(16*y**2) + (-7*y)*(-3*y**3) - (-1)*56*y\nReplacing (-7*y)*(-3*y**3 + 16*y**2 - 8) with (-7*y)*(16*y**2) + (-7*y)*(-3*y**3) - (-1)*56*y in the overall expression.\n#Step 4:\nCurrent expression: (-7*y)*(16*y**2) + (-7*y)*(-3*y**3) - 8*(-8)*y**3 - 8*(-7)*y + (16*y**2)*(-8*y**3) + (-8*y**3)*(-3*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-3*y**3)*(-8*y**3) = 24*y**6\n (-3*y**3)*(-7*y) = 21*y**4\n (16*y**2)*(-8*y**3) = -128*y**5\n (16*y**2)*(-7*y) = -112*y**3\n -8*-8*y**3 = 64*y**3\n -8*-7*y = 56*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 24*y**6 - 128*y**5 + 21*y**4 - 112*y**3 + 64*y**3 + 56*y\nCombining like terms, got 24*y**6 - 128*y**5 + 21*y**4 - 48*y**3 + 56*y\n#Step 6:\nCurrent expression: 24*y**6 - 128*y**5 + 21*y**4 - 48*y**3 + 56*y\nNo more calculations needed.\n24*y**6 - 128*y**5 + 21*y**4 - 48*y**3 + 56*y", "generated_answer": "24*y**6 - 128*y**5 + 21*y**4 - 48*y**3 + 56*y", "step_length": 6} {"cot_id": "1de8d3694c4dc996eaba7a47d08d69cc503df5580b8b72421851f1fc332de29b", "datapoint": {"question": "Simplify this expression: 13*y*(8*y**3 + 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "104*y**4 + 403*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 938, "polynomial_expr": "13*y*(8*y**3 + 31)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 13*y*(8*y**3 + 31)\nExpanding the part (8*y**3 + 31) using the distributive property, and we got: 31*(13*y) + (13*y)*(8*y**3)\n#Step 2:\nCurrent expression: 31*(13*y) + (13*y)*(8*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 31*(13*y) = 403*y\n (8*y**3)*(13*y) = 104*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 104*y**4 + 403*y\nNo more calculations needed.\n104*y**4 + 403*y", "generated_answer": "104*y**4 + 403*y", "step_length": 3} {"cot_id": "46d7028cf910d5858b7a25792a73f96c339f13c1519534d1a496255071d138fd", "datapoint": {"question": "Simplify this expression: 16*x**2*(-39*x**2 - 20*x - 15)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-624*x**4 - 320*x**3 - 240*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 939, "polynomial_expr": "16*x**2*(-39*x**2 - 20*x - 15)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 16*x**2*(-39*x**2 - 20*x - 15)\nExpanding the part (-39*x**2 - 20*x - 15) using the distributive property, and we got: (-20*x)*(16*x**2) - 240*x**2 + (-39*x**2)*(16*x**2)\n#Step 2:\nCurrent expression: (-20*x)*(16*x**2) - 240*x**2 + (-39*x**2)*(16*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -15*(16*x**2) = -240*x**2\n (-39*x**2)*(16*x**2) = -624*x**4\n (-20*x)*(16*x**2) = -320*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -624*x**4 - 320*x**3 - 240*x**2\nNo more calculations needed.\n-624*x**4 - 320*x**3 - 240*x**2", "generated_answer": "-624*x**4 - 320*x**3 - 240*x**2", "step_length": 3} {"cot_id": "882682381a56d664f96192b422d7a4f458d9c97b46de3aeba626b0c1734fb1e7", "datapoint": {"question": "Calculate the following: (6*z**2 - 35*z)*(-44*z**3 - 13*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-264*z**5 + 1462*z**4 + 455*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 940, "polynomial_expr": "(6*z**2 - 35*z)*(-44*z**3 - 13*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6*z**2 - 35*z)*(-44*z**3 - 13*z**2)\nExpanding the part (-44*z**3 - 13*z**2) using the distributive property, and we got: (-13*z**2)*(6*z**2 - 35*z) + (-44*z**3)*(6*z**2 - 35*z)\n#Step 2:\nCurrent expression: (-13*z**2)*(6*z**2 - 35*z) + (-44*z**3)*(6*z**2 - 35*z)\nSimplifying the partial expression: (-44*z**3)*(6*z**2 - 35*z)\nExpanding the part (6*z**2 - 35*z) using the distributive property, and we got: (-35*z)*(-44*z**3) + (6*z**2)*(-44*z**3)\nReplacing (-44*z**3)*(6*z**2 - 35*z) with (-35*z)*(-44*z**3) + (6*z**2)*(-44*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-35*z)*(-44*z**3) + (-13*z**2)*(6*z**2 - 35*z) + (6*z**2)*(-44*z**3)\nSimplifying the partial expression: (-13*z**2)*(6*z**2 - 35*z)\nExpanding the part (6*z**2 - 35*z) using the distributive property, and we got: (-35*z)*(-13*z**2) + (-13*z**2)*(6*z**2)\nReplacing (-13*z**2)*(6*z**2 - 35*z) with (-35*z)*(-13*z**2) + (-13*z**2)*(6*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-35*z)*(-13*z**2) + (-35*z)*(-44*z**3) + (-13*z**2)*(6*z**2) + (6*z**2)*(-44*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*z)*(-44*z**3) = 1540*z**4\n (-35*z)*(-13*z**2) = 455*z**3\n (6*z**2)*(-44*z**3) = -264*z**5\n (6*z**2)*(-13*z**2) = -78*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -264*z**5 - 78*z**4 + 1540*z**4 + 455*z**3\nCombining like terms, got -264*z**5 + 1462*z**4 + 455*z**3\n#Step 6:\nCurrent expression: -264*z**5 + 1462*z**4 + 455*z**3\nNo more calculations needed.\n-264*z**5 + 1462*z**4 + 455*z**3", "generated_answer": "-264*z**5 + 1462*z**4 + 455*z**3", "step_length": 6} {"cot_id": "925bc8d2a8dbe9075836b8f73ef3f218b07b0805d8f4d9eeee576558c737d10e", "datapoint": {"question": "Calculate the following: -675*z**3 - 570*z**2 - 390\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-675*z**3 - 570*z**2 - 390", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 941, "polynomial_expr": "-675*z**3 - 570*z**2 - 390", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -675*z**3 - 570*z**2 - 390\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -675*z**3 - 570*z**2 - 390\nNo more calculations needed.\n-675*z**3 - 570*z**2 - 390", "generated_answer": "-675*z**3 - 570*z**2 - 390", "step_length": 2} {"cot_id": "81f2b34d52533daa32ac821e9bf5b42d139a7aef663b532b8347695d1f4509f8", "datapoint": {"question": "Simplify this expression: (-49*z - 39)*(9*z**3 + 11*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-441*z**4 - 351*z**3 - 539*z**2 - 429*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 942, "polynomial_expr": "(-49*z - 39)*(9*z**3 + 11*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-49*z - 39)*(9*z**3 + 11*z)\nExpanding the part (-49*z - 39) using the distributive property, and we got: (-49*z)*(9*z**3 + 11*z) - 39*(9*z**3 + 11*z)\n#Step 2:\nCurrent expression: (-49*z)*(9*z**3 + 11*z) - 39*(9*z**3 + 11*z)\nSimplifying the partial expression: -39*(9*z**3 + 11*z)\nExpanding the part (9*z**3 + 11*z) using the distributive property, and we got: (11*z)*(-39) + (9*z**3)*(-39)\nReplacing -39*(9*z**3 + 11*z) with (11*z)*(-39) + (9*z**3)*(-39) in the overall expression.\n#Step 3:\nCurrent expression: (-49*z)*(9*z**3 + 11*z) + (11*z)*(-39) + (9*z**3)*(-39)\nSimplifying the partial expression: (-49*z)*(9*z**3 + 11*z)\nExpanding the part (9*z**3 + 11*z) using the distributive property, and we got: (-49*z)*(11*z) + (-49*z)*(9*z**3)\nReplacing (-49*z)*(9*z**3 + 11*z) with (-49*z)*(11*z) + (-49*z)*(9*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-49*z)*(11*z) + (-49*z)*(9*z**3) + (11*z)*(-39) + (9*z**3)*(-39)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (9*z**3)*-39 = -351*z**3\n (9*z**3)*(-49*z) = -441*z**4\n (11*z)*-39 = -429*z\n (11*z)*(-49*z) = -539*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -441*z**4 - 351*z**3 - 539*z**2 - 429*z\nNo more calculations needed.\n-441*z**4 - 351*z**3 - 539*z**2 - 429*z", "generated_answer": "-441*z**4 - 351*z**3 - 539*z**2 - 429*z", "step_length": 5} {"cot_id": "ac46e141ed65af93c781983520cde9b151d52e473b22d1504b53b67812c17eba", "datapoint": {"question": "Calculate the following: (31*y - 35)*(-2*y**2 - 29*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-62*y**3 - 829*y**2 + 1015*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 943, "polynomial_expr": "(31*y - 35)*(-2*y**2 - 29*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31*y - 35)*(-2*y**2 - 29*y)\nExpanding the part (31*y - 35) using the distributive property, and we got: (31*y)*(-2*y**2 - 29*y) - 35*(-2*y**2 - 29*y)\n#Step 2:\nCurrent expression: (31*y)*(-2*y**2 - 29*y) - 35*(-2*y**2 - 29*y)\nSimplifying the partial expression: -35*(-2*y**2 - 29*y)\nExpanding the part (-2*y**2 - 29*y) using the distributive property, and we got: -29*y*(-35) - 2*y**2*(-35)\nReplacing -35*(-2*y**2 - 29*y) with -29*y*(-35) - 2*y**2*(-35) in the overall expression.\n#Step 3:\nCurrent expression: -29*y*(-35) + (31*y)*(-2*y**2 - 29*y) - 2*y**2*(-35)\nSimplifying the partial expression: (31*y)*(-2*y**2 - 29*y)\nExpanding the part (-2*y**2 - 29*y) using the distributive property, and we got: (-29*y)*(31*y) + (31*y)*(-2*y**2)\nReplacing (31*y)*(-2*y**2 - 29*y) with (-29*y)*(31*y) + (31*y)*(-2*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-29*y)*(31*y) - 29*y*(-35) + (31*y)*(-2*y**2) - 2*y**2*(-35)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*y)*-35 = 1015*y\n (-29*y)*(31*y) = -899*y**2\n (-2*y**2)*-35 = 70*y**2\n (-2*y**2)*(31*y) = -62*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -62*y**3 - 899*y**2 + 70*y**2 + 1015*y\nCombining like terms, got -62*y**3 - 829*y**2 + 1015*y\n#Step 6:\nCurrent expression: -62*y**3 - 829*y**2 + 1015*y\nNo more calculations needed.\n-62*y**3 - 829*y**2 + 1015*y", "generated_answer": "-62*y**3 - 829*y**2 + 1015*y", "step_length": 6} {"cot_id": "36c87b9371c6ba588438b05501e1685c0a6753a801b89323624cfc34d8eb9e74", "datapoint": {"question": "Simplify this expression: (-17*x**3 + 12*x)*(-6*x**3 + 37*x**2 - 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "102*x**6 - 629*x**5 - 72*x**4 + 461*x**3 - 12*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 944, "polynomial_expr": "(-17*x**3 + 12*x)*(-6*x**3 + 37*x**2 - 1)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-17*x**3 + 12*x)*(-6*x**3 + 37*x**2 - 1)\nExpanding the part (-17*x**3 + 12*x) using the distributive property, and we got: (12*x)*(-6*x**3 + 37*x**2 - 1) + (-17*x**3)*(-6*x**3 + 37*x**2 - 1)\n#Step 2:\nCurrent expression: (12*x)*(-6*x**3 + 37*x**2 - 1) + (-17*x**3)*(-6*x**3 + 37*x**2 - 1)\nSimplifying the partial expression: (-17*x**3)*(-6*x**3 + 37*x**2 - 1)\nExpanding the part (-6*x**3 + 37*x**2 - 1) using the distributive property, and we got: -(-1)*17*x**3 + (37*x**2)*(-17*x**3) + (-17*x**3)*(-6*x**3)\nReplacing (-17*x**3)*(-6*x**3 + 37*x**2 - 1) with -(-1)*17*x**3 + (37*x**2)*(-17*x**3) + (-17*x**3)*(-6*x**3) in the overall expression.\n#Step 3:\nCurrent expression: -1*(-17)*x**3 + (12*x)*(-6*x**3 + 37*x**2 - 1) + (37*x**2)*(-17*x**3) + (-17*x**3)*(-6*x**3)\nSimplifying the partial expression: (12*x)*(-6*x**3 + 37*x**2 - 1)\nExpanding the part (-6*x**3 + 37*x**2 - 1) using the distributive property, and we got: -12*x + (12*x)*(37*x**2) + (12*x)*(-6*x**3)\nReplacing (12*x)*(-6*x**3 + 37*x**2 - 1) with -12*x + (12*x)*(37*x**2) + (12*x)*(-6*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -1*(-17)*x**3 - 1*12*x + (12*x)*(37*x**2) + (12*x)*(-6*x**3) + (37*x**2)*(-17*x**3) + (-17*x**3)*(-6*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-6*x**3)*(-17*x**3) = 102*x**6\n (-6*x**3)*(12*x) = -72*x**4\n (37*x**2)*(-17*x**3) = -629*x**5\n (37*x**2)*(12*x) = 444*x**3\n -1*-17*x**3 = 17*x**3\n -1*12*x = -12*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 102*x**6 - 629*x**5 - 72*x**4 + 17*x**3 + 444*x**3 - 12*x\nCombining like terms, got 102*x**6 - 629*x**5 - 72*x**4 + 461*x**3 - 12*x\n#Step 6:\nCurrent expression: 102*x**6 - 629*x**5 - 72*x**4 + 461*x**3 - 12*x\nNo more calculations needed.\n102*x**6 - 629*x**5 - 72*x**4 + 461*x**3 - 12*x", "generated_answer": "102*x**6 - 629*x**5 - 72*x**4 + 461*x**3 - 12*x", "step_length": 6} {"cot_id": "917609eb3d9b438b01d9a4a180745b9fb65ec155e19f0ad1f4170edc802d704f", "datapoint": {"question": "Simplify this expression: (-38*z**3 - 21)*(15*z**3 - 2*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-570*z**6 + 76*z**4 - 315*z**3 + 42*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 945, "polynomial_expr": "(-38*z**3 - 21)*(15*z**3 - 2*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-38*z**3 - 21)*(15*z**3 - 2*z)\nExpanding the part (-38*z**3 - 21) using the distributive property, and we got: (-38*z**3)*(15*z**3 - 2*z) - 21*(15*z**3 - 2*z)\n#Step 2:\nCurrent expression: (-38*z**3)*(15*z**3 - 2*z) - 21*(15*z**3 - 2*z)\nSimplifying the partial expression: -21*(15*z**3 - 2*z)\nExpanding the part (15*z**3 - 2*z) using the distributive property, and we got: -2*z*(-21) + (15*z**3)*(-21)\nReplacing -21*(15*z**3 - 2*z) with -2*z*(-21) + (15*z**3)*(-21) in the overall expression.\n#Step 3:\nCurrent expression: -2*z*(-21) + (-38*z**3)*(15*z**3 - 2*z) + (15*z**3)*(-21)\nSimplifying the partial expression: (-38*z**3)*(15*z**3 - 2*z)\nExpanding the part (15*z**3 - 2*z) using the distributive property, and we got: (-2*z)*(-38*z**3) + (-38*z**3)*(15*z**3)\nReplacing (-38*z**3)*(15*z**3 - 2*z) with (-2*z)*(-38*z**3) + (-38*z**3)*(15*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-2*z)*(-38*z**3) - 2*z*(-21) + (-38*z**3)*(15*z**3) + (15*z**3)*(-21)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-2*z)*-21 = 42*z\n (-2*z)*(-38*z**3) = 76*z**4\n (15*z**3)*-21 = -315*z**3\n (15*z**3)*(-38*z**3) = -570*z**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -570*z**6 + 76*z**4 - 315*z**3 + 42*z\nNo more calculations needed.\n-570*z**6 + 76*z**4 - 315*z**3 + 42*z", "generated_answer": "-570*z**6 + 76*z**4 - 315*z**3 + 42*z", "step_length": 5} {"cot_id": "394bb001e1a9df014b243089a2bfa178f13f61273f283c895fe2061bbacbe1b7", "datapoint": {"question": "Simplify this expression: (-11*y**3 - 30*y**2 + 74)*(-19*y**3 + 26*y**2 - 28*y - 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "209*y**6 + 284*y**5 - 472*y**4 - 489*y**3 + 2134*y**2 - 2072*y - 518", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 946, "polynomial_expr": "(-11*y**3 - 30*y**2 + 74)*(-19*y**3 + 26*y**2 - 28*y - 7)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-11*y**3 - 30*y**2 + 74)*(-19*y**3 + 26*y**2 - 28*y - 7)\nExpanding the part (-11*y**3 - 30*y**2 + 74) using the distributive property, and we got: (-30*y**2)*(-19*y**3 + 26*y**2 - 28*y - 7) + (-11*y**3)*(-19*y**3 + 26*y**2 - 28*y - 7) + 74*(-19*y**3 + 26*y**2 - 28*y - 7)\n#Step 2:\nCurrent expression: (-30*y**2)*(-19*y**3 + 26*y**2 - 28*y - 7) + (-11*y**3)*(-19*y**3 + 26*y**2 - 28*y - 7) + 74*(-19*y**3 + 26*y**2 - 28*y - 7)\nSimplifying the partial expression: 74*(-19*y**3 + 26*y**2 - 28*y - 7)\nExpanding the part (-19*y**3 + 26*y**2 - 28*y - 7) using the distributive property, and we got: -28*y*74 + (26*y**2)*74 - 19*y**3*74 - 7*74\nReplacing 74*(-19*y**3 + 26*y**2 - 28*y - 7) with -28*y*74 + (26*y**2)*74 - 19*y**3*74 - 7*74 in the overall expression.\n#Step 3:\nCurrent expression: -28*y*74 + (-30*y**2)*(-19*y**3 + 26*y**2 - 28*y - 7) + (26*y**2)*74 - 19*y**3*74 + (-11*y**3)*(-19*y**3 + 26*y**2 - 28*y - 7) - 518\nSimplifying the partial expression: (-30*y**2)*(-19*y**3 + 26*y**2 - 28*y - 7)\nExpanding the part (-19*y**3 + 26*y**2 - 28*y - 7) using the distributive property, and we got: (-28*y)*(-30*y**2) - (-1)*210*y**2 + (-30*y**2)*(26*y**2) + (-30*y**2)*(-19*y**3)\nReplacing (-30*y**2)*(-19*y**3 + 26*y**2 - 28*y - 7) with (-28*y)*(-30*y**2) - (-1)*210*y**2 + (-30*y**2)*(26*y**2) + (-30*y**2)*(-19*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-28*y)*(-30*y**2) - 28*y*74 - 7*(-30)*y**2 + (-30*y**2)*(26*y**2) + (-30*y**2)*(-19*y**3) + (26*y**2)*74 - 19*y**3*74 + (-11*y**3)*(-19*y**3 + 26*y**2 - 28*y - 7) - 518\nSimplifying the partial expression: (-11*y**3)*(-19*y**3 + 26*y**2 - 28*y - 7)\nExpanding the part (-19*y**3 + 26*y**2 - 28*y - 7) using the distributive property, and we got: (-28*y)*(-11*y**3) - (-1)*77*y**3 + (26*y**2)*(-11*y**3) + (-19*y**3)*(-11*y**3)\nReplacing (-11*y**3)*(-19*y**3 + 26*y**2 - 28*y - 7) with (-28*y)*(-11*y**3) - (-1)*77*y**3 + (26*y**2)*(-11*y**3) + (-19*y**3)*(-11*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-28*y)*(-30*y**2) + (-28*y)*(-11*y**3) - 28*y*74 - 7*(-11)*y**3 - 7*(-30)*y**2 + (-30*y**2)*(26*y**2) + (-30*y**2)*(-19*y**3) + (26*y**2)*(-11*y**3) + (26*y**2)*74 + (-19*y**3)*(-11*y**3) - 19*y**3*74 - 518\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*y)*74 = -2072*y\n (-28*y)*(-30*y**2) = 840*y**3\n (-28*y)*(-11*y**3) = 308*y**4\n (-19*y**3)*74 = -1406*y**3\n (-19*y**3)*(-30*y**2) = 570*y**5\n (-19*y**3)*(-11*y**3) = 209*y**6\n (26*y**2)*74 = 1924*y**2\n (26*y**2)*(-30*y**2) = -780*y**4\n (26*y**2)*(-11*y**3) = -286*y**5\n -7*-30*y**2 = 210*y**2\n -7*-11*y**3 = 77*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 209*y**6 - 286*y**5 + 570*y**5 - 780*y**4 + 308*y**4 - 1406*y**3 + 77*y**3 + 840*y**3 + 210*y**2 + 1924*y**2 - 2072*y - 518\nCombining like terms, got 209*y**6 + 284*y**5 - 472*y**4 - 489*y**3 + 2134*y**2 - 2072*y - 518\n#Step 7:\nCurrent expression: 209*y**6 + 284*y**5 - 472*y**4 - 489*y**3 + 2134*y**2 - 2072*y - 518\nNo more calculations needed.\n209*y**6 + 284*y**5 - 472*y**4 - 489*y**3 + 2134*y**2 - 2072*y - 518", "generated_answer": "209*y**6 + 284*y**5 - 472*y**4 - 489*y**3 + 2134*y**2 - 2072*y - 518", "step_length": 7} {"cot_id": "551ac82ca5fad645d0740c0ce39441358be606ab9c2919c50f7f524081f1da96", "datapoint": {"question": "Simplify this expression: (-45*x**2 + 43*x - 11)*(-27*x**3 - 21*x**2 + 45)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1215*x**5 - 216*x**4 - 606*x**3 - 1794*x**2 + 1935*x - 495", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 947, "polynomial_expr": "(-45*x**2 + 43*x - 11)*(-27*x**3 - 21*x**2 + 45)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-45*x**2 + 43*x - 11)*(-27*x**3 - 21*x**2 + 45)\nExpanding the part (-45*x**2 + 43*x - 11) using the distributive property, and we got: (43*x)*(-27*x**3 - 21*x**2 + 45) + (-45*x**2)*(-27*x**3 - 21*x**2 + 45) - 11*(-27*x**3 - 21*x**2 + 45)\n#Step 2:\nCurrent expression: (43*x)*(-27*x**3 - 21*x**2 + 45) + (-45*x**2)*(-27*x**3 - 21*x**2 + 45) - 11*(-27*x**3 - 21*x**2 + 45)\nSimplifying the partial expression: -11*(-27*x**3 - 21*x**2 + 45)\nExpanding the part (-27*x**3 - 21*x**2 + 45) using the distributive property, and we got: -21*x**2*(-11) - 27*x**3*(-11) + 45*(-11)\nReplacing -11*(-27*x**3 - 21*x**2 + 45) with -21*x**2*(-11) - 27*x**3*(-11) + 45*(-11) in the overall expression.\n#Step 3:\nCurrent expression: (43*x)*(-27*x**3 - 21*x**2 + 45) + (-45*x**2)*(-27*x**3 - 21*x**2 + 45) - 21*x**2*(-11) - 27*x**3*(-11) - 495\nSimplifying the partial expression: (-45*x**2)*(-27*x**3 - 21*x**2 + 45)\nExpanding the part (-27*x**3 - 21*x**2 + 45) using the distributive property, and we got: 45*(-45*x**2) + (-45*x**2)*(-21*x**2) + (-45*x**2)*(-27*x**3)\nReplacing (-45*x**2)*(-27*x**3 - 21*x**2 + 45) with 45*(-45*x**2) + (-45*x**2)*(-21*x**2) + (-45*x**2)*(-27*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 45*(-45)*x**2 + (43*x)*(-27*x**3 - 21*x**2 + 45) + (-45*x**2)*(-21*x**2) + (-45*x**2)*(-27*x**3) - 21*x**2*(-11) - 27*x**3*(-11) - 495\nSimplifying the partial expression: (43*x)*(-27*x**3 - 21*x**2 + 45)\nExpanding the part (-27*x**3 - 21*x**2 + 45) using the distributive property, and we got: 45*(43*x) + (43*x)*(-21*x**2) + (43*x)*(-27*x**3)\nReplacing (43*x)*(-27*x**3 - 21*x**2 + 45) with 45*(43*x) + (43*x)*(-21*x**2) + (43*x)*(-27*x**3) in the overall expression.\n#Step 5:\nCurrent expression: 45*(-45)*x**2 + 45*43*x + (43*x)*(-21*x**2) + (43*x)*(-27*x**3) + (-45*x**2)*(-21*x**2) + (-45*x**2)*(-27*x**3) - 21*x**2*(-11) - 27*x**3*(-11) - 495\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*x**3)*-11 = 297*x**3\n (-27*x**3)*(-45*x**2) = 1215*x**5\n (-27*x**3)*(43*x) = -1161*x**4\n (-21*x**2)*-11 = 231*x**2\n (-21*x**2)*(-45*x**2) = 945*x**4\n (-21*x**2)*(43*x) = -903*x**3\n 45*-45*x**2 = -2025*x**2\n 45*43*x = 1935*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1215*x**5 - 1161*x**4 + 945*x**4 - 903*x**3 + 297*x**3 - 2025*x**2 + 231*x**2 + 1935*x - 495\nCombining like terms, got 1215*x**5 - 216*x**4 - 606*x**3 - 1794*x**2 + 1935*x - 495\n#Step 7:\nCurrent expression: 1215*x**5 - 216*x**4 - 606*x**3 - 1794*x**2 + 1935*x - 495\nNo more calculations needed.\n1215*x**5 - 216*x**4 - 606*x**3 - 1794*x**2 + 1935*x - 495", "generated_answer": "1215*x**5 - 216*x**4 - 606*x**3 - 1794*x**2 + 1935*x - 495", "step_length": 7} {"cot_id": "e8b8980343f24417469c2e7d297761b80440599cd54bea269a4c38d9db3ab583", "datapoint": {"question": "Simplify this expression: (18*z**3 + 31*z**2 + 7*z)*(29*z**3 + 7*z**2 + 19)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "522*z**6 + 1025*z**5 + 420*z**4 + 391*z**3 + 589*z**2 + 133*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 948, "polynomial_expr": "(18*z**3 + 31*z**2 + 7*z)*(29*z**3 + 7*z**2 + 19)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (18*z**3 + 31*z**2 + 7*z)*(29*z**3 + 7*z**2 + 19)\nExpanding the part (29*z**3 + 7*z**2 + 19) using the distributive property, and we got: (7*z**2)*(18*z**3 + 31*z**2 + 7*z) + (29*z**3)*(18*z**3 + 31*z**2 + 7*z) + 19*(18*z**3 + 31*z**2 + 7*z)\n#Step 2:\nCurrent expression: (7*z**2)*(18*z**3 + 31*z**2 + 7*z) + (29*z**3)*(18*z**3 + 31*z**2 + 7*z) + 19*(18*z**3 + 31*z**2 + 7*z)\nSimplifying the partial expression: 19*(18*z**3 + 31*z**2 + 7*z)\nExpanding the part (18*z**3 + 31*z**2 + 7*z) using the distributive property, and we got: (7*z)*19 + (31*z**2)*19 + (18*z**3)*19\nReplacing 19*(18*z**3 + 31*z**2 + 7*z) with (7*z)*19 + (31*z**2)*19 + (18*z**3)*19 in the overall expression.\n#Step 3:\nCurrent expression: (7*z)*19 + (7*z**2)*(18*z**3 + 31*z**2 + 7*z) + (31*z**2)*19 + (18*z**3)*19 + (29*z**3)*(18*z**3 + 31*z**2 + 7*z)\nSimplifying the partial expression: (7*z**2)*(18*z**3 + 31*z**2 + 7*z)\nExpanding the part (18*z**3 + 31*z**2 + 7*z) using the distributive property, and we got: (7*z)*(7*z**2) + (7*z**2)*(31*z**2) + (7*z**2)*(18*z**3)\nReplacing (7*z**2)*(18*z**3 + 31*z**2 + 7*z) with (7*z)*(7*z**2) + (7*z**2)*(31*z**2) + (7*z**2)*(18*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (7*z)*(7*z**2) + (7*z)*19 + (7*z**2)*(31*z**2) + (7*z**2)*(18*z**3) + (31*z**2)*19 + (18*z**3)*19 + (29*z**3)*(18*z**3 + 31*z**2 + 7*z)\nSimplifying the partial expression: (29*z**3)*(18*z**3 + 31*z**2 + 7*z)\nExpanding the part (18*z**3 + 31*z**2 + 7*z) using the distributive property, and we got: (7*z)*(29*z**3) + (31*z**2)*(29*z**3) + (18*z**3)*(29*z**3)\nReplacing (29*z**3)*(18*z**3 + 31*z**2 + 7*z) with (7*z)*(29*z**3) + (31*z**2)*(29*z**3) + (18*z**3)*(29*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (7*z)*(7*z**2) + (7*z)*(29*z**3) + (7*z)*19 + (7*z**2)*(31*z**2) + (7*z**2)*(18*z**3) + (31*z**2)*(29*z**3) + (31*z**2)*19 + (18*z**3)*(29*z**3) + (18*z**3)*19\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (7*z)*19 = 133*z\n (7*z)*(7*z**2) = 49*z**3\n (7*z)*(29*z**3) = 203*z**4\n (18*z**3)*19 = 342*z**3\n (18*z**3)*(7*z**2) = 126*z**5\n (18*z**3)*(29*z**3) = 522*z**6\n (31*z**2)*19 = 589*z**2\n (31*z**2)*(7*z**2) = 217*z**4\n (31*z**2)*(29*z**3) = 899*z**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 522*z**6 + 126*z**5 + 899*z**5 + 203*z**4 + 217*z**4 + 49*z**3 + 342*z**3 + 589*z**2 + 133*z\nCombining like terms, got 522*z**6 + 1025*z**5 + 420*z**4 + 391*z**3 + 589*z**2 + 133*z\n#Step 7:\nCurrent expression: 522*z**6 + 1025*z**5 + 420*z**4 + 391*z**3 + 589*z**2 + 133*z\nNo more calculations needed.\n522*z**6 + 1025*z**5 + 420*z**4 + 391*z**3 + 589*z**2 + 133*z", "generated_answer": "522*z**6 + 1025*z**5 + 420*z**4 + 391*z**3 + 589*z**2 + 133*z", "step_length": 7} {"cot_id": "f027e06c204f99637af3574893b1ddbeabe428c2a66b9accafef5a5757cd6769", "datapoint": {"question": "Calculate the following: (-37*x**3 - 57*x**2)*(14*x**3 - 12*x**2 - 18)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-518*x**6 - 354*x**5 + 684*x**4 + 666*x**3 + 1026*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 949, "polynomial_expr": "(-37*x**3 - 57*x**2)*(14*x**3 - 12*x**2 - 18)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-37*x**3 - 57*x**2)*(14*x**3 - 12*x**2 - 18)\nExpanding the part (-37*x**3 - 57*x**2) using the distributive property, and we got: (-57*x**2)*(14*x**3 - 12*x**2 - 18) + (-37*x**3)*(14*x**3 - 12*x**2 - 18)\n#Step 2:\nCurrent expression: (-57*x**2)*(14*x**3 - 12*x**2 - 18) + (-37*x**3)*(14*x**3 - 12*x**2 - 18)\nSimplifying the partial expression: (-57*x**2)*(14*x**3 - 12*x**2 - 18)\nExpanding the part (14*x**3 - 12*x**2 - 18) using the distributive property, and we got: -(-1)*1026*x**2 + (-57*x**2)*(-12*x**2) + (-57*x**2)*(14*x**3)\nReplacing (-57*x**2)*(14*x**3 - 12*x**2 - 18) with -(-1)*1026*x**2 + (-57*x**2)*(-12*x**2) + (-57*x**2)*(14*x**3) in the overall expression.\n#Step 3:\nCurrent expression: -18*(-57)*x**2 + (-57*x**2)*(-12*x**2) + (-57*x**2)*(14*x**3) + (-37*x**3)*(14*x**3 - 12*x**2 - 18)\nSimplifying the partial expression: (-37*x**3)*(14*x**3 - 12*x**2 - 18)\nExpanding the part (14*x**3 - 12*x**2 - 18) using the distributive property, and we got: -(-1)*666*x**3 + (-12*x**2)*(-37*x**3) + (-37*x**3)*(14*x**3)\nReplacing (-37*x**3)*(14*x**3 - 12*x**2 - 18) with -(-1)*666*x**3 + (-12*x**2)*(-37*x**3) + (-37*x**3)*(14*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -18*(-37)*x**3 - 18*(-57)*x**2 + (-57*x**2)*(-12*x**2) + (-57*x**2)*(14*x**3) + (-12*x**2)*(-37*x**3) + (-37*x**3)*(14*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*x**2)*(-57*x**2) = 684*x**4\n (-12*x**2)*(-37*x**3) = 444*x**5\n (14*x**3)*(-57*x**2) = -798*x**5\n (14*x**3)*(-37*x**3) = -518*x**6\n -18*-57*x**2 = 1026*x**2\n -18*-37*x**3 = 666*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -518*x**6 - 798*x**5 + 444*x**5 + 684*x**4 + 666*x**3 + 1026*x**2\nCombining like terms, got -518*x**6 - 354*x**5 + 684*x**4 + 666*x**3 + 1026*x**2\n#Step 6:\nCurrent expression: -518*x**6 - 354*x**5 + 684*x**4 + 666*x**3 + 1026*x**2\nNo more calculations needed.\n-518*x**6 - 354*x**5 + 684*x**4 + 666*x**3 + 1026*x**2", "generated_answer": "-518*x**6 - 354*x**5 + 684*x**4 + 666*x**3 + 1026*x**2", "step_length": 6} {"cot_id": "cb503740205ff4ce98a9fb7c945a49a44ecdc1c12bbfe56893762653546f63cf", "datapoint": {"question": "Calculate the following: -152*x**5\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-152*x**5", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 950, "polynomial_expr": "-152*x**5", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -152*x**5\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -152*x**5\nNo more calculations needed.\n-152*x**5", "generated_answer": "-152*x**5", "step_length": 2} {"cot_id": "0d6e77f596aeb519708a9bdf09281297e43f568d46ab1ab3193529027ac599a8", "datapoint": {"question": "Simplify this expression: 50*x**2*(17*x**2 - 3*x - 27)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "850*x**4 - 150*x**3 - 1350*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 951, "polynomial_expr": "50*x**2*(17*x**2 - 3*x - 27)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 50*x**2*(17*x**2 - 3*x - 27)\nExpanding the part (17*x**2 - 3*x - 27) using the distributive property, and we got: (-3*x)*(50*x**2) - 1350*x**2 + (17*x**2)*(50*x**2)\n#Step 2:\nCurrent expression: (-3*x)*(50*x**2) - 1350*x**2 + (17*x**2)*(50*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -27*(50*x**2) = -1350*x**2\n (-3*x)*(50*x**2) = -150*x**3\n (17*x**2)*(50*x**2) = 850*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 850*x**4 - 150*x**3 - 1350*x**2\nNo more calculations needed.\n850*x**4 - 150*x**3 - 1350*x**2", "generated_answer": "850*x**4 - 150*x**3 - 1350*x**2", "step_length": 3} {"cot_id": "3afdd7acda147631c1538357bd435791a305d759fa8b7ac171f5fc6f896fc91b", "datapoint": {"question": "Calculate the following: (-17*x - 29)*(-x**3 + 7*x**2 + 5*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "17*x**4 - 90*x**3 - 288*x**2 - 145*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 952, "polynomial_expr": "(-17*x - 29)*(-x**3 + 7*x**2 + 5*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-17*x - 29)*(-x**3 + 7*x**2 + 5*x)\nExpanding the part (-17*x - 29) using the distributive property, and we got: (-17*x)*(-x**3 + 7*x**2 + 5*x) - 29*(-x**3 + 7*x**2 + 5*x)\n#Step 2:\nCurrent expression: (-17*x)*(-x**3 + 7*x**2 + 5*x) - 29*(-x**3 + 7*x**2 + 5*x)\nSimplifying the partial expression: -29*(-x**3 + 7*x**2 + 5*x)\nExpanding the part (-x**3 + 7*x**2 + 5*x) using the distributive property, and we got: (5*x)*(-29) + (7*x**2)*(-29) - x**3*(-29)\nReplacing -29*(-x**3 + 7*x**2 + 5*x) with (5*x)*(-29) + (7*x**2)*(-29) - x**3*(-29) in the overall expression.\n#Step 3:\nCurrent expression: (-17*x)*(-x**3 + 7*x**2 + 5*x) + (5*x)*(-29) + (7*x**2)*(-29) - x**3*(-29)\nSimplifying the partial expression: (-17*x)*(-x**3 + 7*x**2 + 5*x)\nExpanding the part (-x**3 + 7*x**2 + 5*x) using the distributive property, and we got: (-17*x)*(5*x) + (-17*x)*(7*x**2) + (-17*x)*(-x**3)\nReplacing (-17*x)*(-x**3 + 7*x**2 + 5*x) with (-17*x)*(5*x) + (-17*x)*(7*x**2) + (-17*x)*(-x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-17*x)*(5*x) + (-17*x)*(7*x**2) + (-17*x)*(-x**3) + (5*x)*(-29) + (7*x**2)*(-29) - x**3*(-29)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-x**3)*-29 = 29*x**3\n (-x**3)*(-17*x) = 17*x**4\n (5*x)*-29 = -145*x\n (5*x)*(-17*x) = -85*x**2\n (7*x**2)*-29 = -203*x**2\n (7*x**2)*(-17*x) = -119*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 17*x**4 - 119*x**3 + 29*x**3 - 203*x**2 - 85*x**2 - 145*x\nCombining like terms, got 17*x**4 - 90*x**3 - 288*x**2 - 145*x\n#Step 6:\nCurrent expression: 17*x**4 - 90*x**3 - 288*x**2 - 145*x\nNo more calculations needed.\n17*x**4 - 90*x**3 - 288*x**2 - 145*x", "generated_answer": "17*x**4 - 90*x**3 - 288*x**2 - 145*x", "step_length": 6} {"cot_id": "7e2d8f53923192cf1c7ba51dced9e292bb42eab02d4e6b0611f2cae54265d967", "datapoint": {"question": "Simplify this expression: (-3*x**3 + 14*x - 11)*(-x**3 - 42*x**2 + 43*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "3*x**6 + 126*x**5 - 143*x**4 - 577*x**3 + 1064*x**2 - 473*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 953, "polynomial_expr": "(-3*x**3 + 14*x - 11)*(-x**3 - 42*x**2 + 43*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-3*x**3 + 14*x - 11)*(-x**3 - 42*x**2 + 43*x)\nExpanding the part (-3*x**3 + 14*x - 11) using the distributive property, and we got: (14*x)*(-x**3 - 42*x**2 + 43*x) + (-3*x**3)*(-x**3 - 42*x**2 + 43*x) - 11*(-x**3 - 42*x**2 + 43*x)\n#Step 2:\nCurrent expression: (14*x)*(-x**3 - 42*x**2 + 43*x) + (-3*x**3)*(-x**3 - 42*x**2 + 43*x) - 11*(-x**3 - 42*x**2 + 43*x)\nSimplifying the partial expression: -11*(-x**3 - 42*x**2 + 43*x)\nExpanding the part (-x**3 - 42*x**2 + 43*x) using the distributive property, and we got: (43*x)*(-11) - 42*x**2*(-11) - x**3*(-11)\nReplacing -11*(-x**3 - 42*x**2 + 43*x) with (43*x)*(-11) - 42*x**2*(-11) - x**3*(-11) in the overall expression.\n#Step 3:\nCurrent expression: (14*x)*(-x**3 - 42*x**2 + 43*x) + (43*x)*(-11) - 42*x**2*(-11) + (-3*x**3)*(-x**3 - 42*x**2 + 43*x) - x**3*(-11)\nSimplifying the partial expression: (-3*x**3)*(-x**3 - 42*x**2 + 43*x)\nExpanding the part (-x**3 - 42*x**2 + 43*x) using the distributive property, and we got: (43*x)*(-3*x**3) + (-42*x**2)*(-3*x**3) + (-3*x**3)*(-x**3)\nReplacing (-3*x**3)*(-x**3 - 42*x**2 + 43*x) with (43*x)*(-3*x**3) + (-42*x**2)*(-3*x**3) + (-3*x**3)*(-x**3) in the overall expression.\n#Step 4:\nCurrent expression: (14*x)*(-x**3 - 42*x**2 + 43*x) + (43*x)*(-3*x**3) + (43*x)*(-11) + (-42*x**2)*(-3*x**3) - 42*x**2*(-11) + (-3*x**3)*(-x**3) - x**3*(-11)\nSimplifying the partial expression: (14*x)*(-x**3 - 42*x**2 + 43*x)\nExpanding the part (-x**3 - 42*x**2 + 43*x) using the distributive property, and we got: (14*x)*(43*x) + (14*x)*(-42*x**2) + (14*x)*(-x**3)\nReplacing (14*x)*(-x**3 - 42*x**2 + 43*x) with (14*x)*(43*x) + (14*x)*(-42*x**2) + (14*x)*(-x**3) in the overall expression.\n#Step 5:\nCurrent expression: (14*x)*(43*x) + (14*x)*(-42*x**2) + (14*x)*(-x**3) + (43*x)*(-3*x**3) + (43*x)*(-11) + (-42*x**2)*(-3*x**3) - 42*x**2*(-11) + (-3*x**3)*(-x**3) - x**3*(-11)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-x**3)*-11 = 11*x**3\n (-x**3)*(-3*x**3) = 3*x**6\n (-x**3)*(14*x) = -14*x**4\n (-42*x**2)*-11 = 462*x**2\n (-42*x**2)*(-3*x**3) = 126*x**5\n (-42*x**2)*(14*x) = -588*x**3\n (43*x)*-11 = -473*x\n (43*x)*(-3*x**3) = -129*x**4\n (43*x)*(14*x) = 602*x**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 3*x**6 + 126*x**5 - 129*x**4 - 14*x**4 - 588*x**3 + 11*x**3 + 462*x**2 + 602*x**2 - 473*x\nCombining like terms, got 3*x**6 + 126*x**5 - 143*x**4 - 577*x**3 + 1064*x**2 - 473*x\n#Step 7:\nCurrent expression: 3*x**6 + 126*x**5 - 143*x**4 - 577*x**3 + 1064*x**2 - 473*x\nNo more calculations needed.\n3*x**6 + 126*x**5 - 143*x**4 - 577*x**3 + 1064*x**2 - 473*x", "generated_answer": "3*x**6 + 126*x**5 - 143*x**4 - 577*x**3 + 1064*x**2 - 473*x", "step_length": 7} {"cot_id": "cc275b04a521990421973289f052c53f35e45ca89206331cf4a7198516083149", "datapoint": {"question": "Calculate the following: -17*y**3*(24*y + 101)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-408*y**4 - 1717*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 954, "polynomial_expr": "-17*y**3*(24*y + 101)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -17*y**3*(24*y + 101)\nExpanding the part (24*y + 101) using the distributive property, and we got: 101*(-17*y**3) + (24*y)*(-17*y**3)\n#Step 2:\nCurrent expression: 101*(-17*y**3) + (24*y)*(-17*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 101*(-17*y**3) = -1717*y**3\n (24*y)*(-17*y**3) = -408*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -408*y**4 - 1717*y**3\nNo more calculations needed.\n-408*y**4 - 1717*y**3", "generated_answer": "-408*y**4 - 1717*y**3", "step_length": 3} {"cot_id": "928e1ed4ce8b582525e85658b54073160ca16e8337591b8067490915b1731f78", "datapoint": {"question": "Simplify this expression: (34*y**3 - 31*y**2)*(46*y**3 - 13*y + 18)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1564*y**6 - 1426*y**5 - 442*y**4 + 1015*y**3 - 558*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 955, "polynomial_expr": "(34*y**3 - 31*y**2)*(46*y**3 - 13*y + 18)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (34*y**3 - 31*y**2)*(46*y**3 - 13*y + 18)\nExpanding the part (34*y**3 - 31*y**2) using the distributive property, and we got: (-31*y**2)*(46*y**3 - 13*y + 18) + (34*y**3)*(46*y**3 - 13*y + 18)\n#Step 2:\nCurrent expression: (-31*y**2)*(46*y**3 - 13*y + 18) + (34*y**3)*(46*y**3 - 13*y + 18)\nSimplifying the partial expression: (-31*y**2)*(46*y**3 - 13*y + 18)\nExpanding the part (46*y**3 - 13*y + 18) using the distributive property, and we got: (-13*y)*(-31*y**2) + 18*(-31*y**2) + (-31*y**2)*(46*y**3)\nReplacing (-31*y**2)*(46*y**3 - 13*y + 18) with (-13*y)*(-31*y**2) + 18*(-31*y**2) + (-31*y**2)*(46*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-13*y)*(-31*y**2) + 18*(-31)*y**2 + (-31*y**2)*(46*y**3) + (34*y**3)*(46*y**3 - 13*y + 18)\nSimplifying the partial expression: (34*y**3)*(46*y**3 - 13*y + 18)\nExpanding the part (46*y**3 - 13*y + 18) using the distributive property, and we got: (-13*y)*(34*y**3) + 18*(34*y**3) + (34*y**3)*(46*y**3)\nReplacing (34*y**3)*(46*y**3 - 13*y + 18) with (-13*y)*(34*y**3) + 18*(34*y**3) + (34*y**3)*(46*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-13*y)*(-31*y**2) + (-13*y)*(34*y**3) + 18*34*y**3 + 18*(-31)*y**2 + (-31*y**2)*(46*y**3) + (34*y**3)*(46*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*y)*(-31*y**2) = 403*y**3\n (-13*y)*(34*y**3) = -442*y**4\n (46*y**3)*(-31*y**2) = -1426*y**5\n (46*y**3)*(34*y**3) = 1564*y**6\n 18*-31*y**2 = -558*y**2\n 18*34*y**3 = 612*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1564*y**6 - 1426*y**5 - 442*y**4 + 403*y**3 + 612*y**3 - 558*y**2\nCombining like terms, got 1564*y**6 - 1426*y**5 - 442*y**4 + 1015*y**3 - 558*y**2\n#Step 6:\nCurrent expression: 1564*y**6 - 1426*y**5 - 442*y**4 + 1015*y**3 - 558*y**2\nNo more calculations needed.\n1564*y**6 - 1426*y**5 - 442*y**4 + 1015*y**3 - 558*y**2", "generated_answer": "1564*y**6 - 1426*y**5 - 442*y**4 + 1015*y**3 - 558*y**2", "step_length": 6} {"cot_id": "f446422fd4aafabdf5f42f09d532ee36edde1e58e36b9e8f1c78aa8e77bcd9d0", "datapoint": {"question": "Calculate the following: (-22*x**3 + 23*x**2 + 12*x)*(33*x**3 - x + 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-726*x**6 + 759*x**5 + 418*x**4 - 925*x**3 + 931*x**2 + 492*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 956, "polynomial_expr": "(-22*x**3 + 23*x**2 + 12*x)*(33*x**3 - x + 41)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-22*x**3 + 23*x**2 + 12*x)*(33*x**3 - x + 41)\nExpanding the part (33*x**3 - x + 41) using the distributive property, and we got: (-x)*(-22*x**3 + 23*x**2 + 12*x) + (33*x**3)*(-22*x**3 + 23*x**2 + 12*x) + 41*(-22*x**3 + 23*x**2 + 12*x)\n#Step 2:\nCurrent expression: (-x)*(-22*x**3 + 23*x**2 + 12*x) + (33*x**3)*(-22*x**3 + 23*x**2 + 12*x) + 41*(-22*x**3 + 23*x**2 + 12*x)\nSimplifying the partial expression: 41*(-22*x**3 + 23*x**2 + 12*x)\nExpanding the part (-22*x**3 + 23*x**2 + 12*x) using the distributive property, and we got: (12*x)*41 + (23*x**2)*41 - 22*x**3*41\nReplacing 41*(-22*x**3 + 23*x**2 + 12*x) with (12*x)*41 + (23*x**2)*41 - 22*x**3*41 in the overall expression.\n#Step 3:\nCurrent expression: (-x)*(-22*x**3 + 23*x**2 + 12*x) + (12*x)*41 + (23*x**2)*41 - 22*x**3*41 + (33*x**3)*(-22*x**3 + 23*x**2 + 12*x)\nSimplifying the partial expression: (-x)*(-22*x**3 + 23*x**2 + 12*x)\nExpanding the part (-22*x**3 + 23*x**2 + 12*x) using the distributive property, and we got: (-x)*(12*x) + (-x)*(23*x**2) + (-x)*(-22*x**3)\nReplacing (-x)*(-22*x**3 + 23*x**2 + 12*x) with (-x)*(12*x) + (-x)*(23*x**2) + (-x)*(-22*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-x)*(12*x) + (-x)*(23*x**2) + (-x)*(-22*x**3) + (12*x)*41 + (23*x**2)*41 - 22*x**3*41 + (33*x**3)*(-22*x**3 + 23*x**2 + 12*x)\nSimplifying the partial expression: (33*x**3)*(-22*x**3 + 23*x**2 + 12*x)\nExpanding the part (-22*x**3 + 23*x**2 + 12*x) using the distributive property, and we got: (12*x)*(33*x**3) + (23*x**2)*(33*x**3) + (-22*x**3)*(33*x**3)\nReplacing (33*x**3)*(-22*x**3 + 23*x**2 + 12*x) with (12*x)*(33*x**3) + (23*x**2)*(33*x**3) + (-22*x**3)*(33*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-x)*(12*x) + (-x)*(23*x**2) + (-x)*(-22*x**3) + (12*x)*(33*x**3) + (12*x)*41 + (23*x**2)*(33*x**3) + (23*x**2)*41 + (-22*x**3)*(33*x**3) - 22*x**3*41\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*x**3)*41 = -902*x**3\n (-22*x**3)*(-x) = 22*x**4\n (-22*x**3)*(33*x**3) = -726*x**6\n (12*x)*41 = 492*x\n (12*x)*(-x) = -12*x**2\n (12*x)*(33*x**3) = 396*x**4\n (23*x**2)*41 = 943*x**2\n (23*x**2)*(-x) = -23*x**3\n (23*x**2)*(33*x**3) = 759*x**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -726*x**6 + 759*x**5 + 22*x**4 + 396*x**4 - 902*x**3 - 23*x**3 - 12*x**2 + 943*x**2 + 492*x\nCombining like terms, got -726*x**6 + 759*x**5 + 418*x**4 - 925*x**3 + 931*x**2 + 492*x\n#Step 7:\nCurrent expression: -726*x**6 + 759*x**5 + 418*x**4 - 925*x**3 + 931*x**2 + 492*x\nNo more calculations needed.\n-726*x**6 + 759*x**5 + 418*x**4 - 925*x**3 + 931*x**2 + 492*x", "generated_answer": "-726*x**6 + 759*x**5 + 418*x**4 - 925*x**3 + 931*x**2 + 492*x", "step_length": 7} {"cot_id": "d6882782c4cd24649e9b55e2a288b1c4e699836d120abdecffb060df9d57e824", "datapoint": {"question": "Calculate the following: (-15*z**2 - 4*z - 31)*(42*z**3 - 37*z**2 + 42*z - 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-630*z**5 + 387*z**4 - 1784*z**3 + 1174*z**2 - 1250*z + 403", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 957, "polynomial_expr": "(-15*z**2 - 4*z - 31)*(42*z**3 - 37*z**2 + 42*z - 13)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-15*z**2 - 4*z - 31)*(42*z**3 - 37*z**2 + 42*z - 13)\nExpanding the part (-15*z**2 - 4*z - 31) using the distributive property, and we got: (-4*z)*(42*z**3 - 37*z**2 + 42*z - 13) + (-15*z**2)*(42*z**3 - 37*z**2 + 42*z - 13) - 31*(42*z**3 - 37*z**2 + 42*z - 13)\n#Step 2:\nCurrent expression: (-4*z)*(42*z**3 - 37*z**2 + 42*z - 13) + (-15*z**2)*(42*z**3 - 37*z**2 + 42*z - 13) - 31*(42*z**3 - 37*z**2 + 42*z - 13)\nSimplifying the partial expression: -31*(42*z**3 - 37*z**2 + 42*z - 13)\nExpanding the part (42*z**3 - 37*z**2 + 42*z - 13) using the distributive property, and we got: (42*z)*(-31) - 37*z**2*(-31) + (42*z**3)*(-31) - 13*(-31)\nReplacing -31*(42*z**3 - 37*z**2 + 42*z - 13) with (42*z)*(-31) - 37*z**2*(-31) + (42*z**3)*(-31) - 13*(-31) in the overall expression.\n#Step 3:\nCurrent expression: (-4*z)*(42*z**3 - 37*z**2 + 42*z - 13) + (42*z)*(-31) - 37*z**2*(-31) + (-15*z**2)*(42*z**3 - 37*z**2 + 42*z - 13) + (42*z**3)*(-31) + 403\nSimplifying the partial expression: (-15*z**2)*(42*z**3 - 37*z**2 + 42*z - 13)\nExpanding the part (42*z**3 - 37*z**2 + 42*z - 13) using the distributive property, and we got: -(-1)*195*z**2 + (42*z)*(-15*z**2) + (-37*z**2)*(-15*z**2) + (-15*z**2)*(42*z**3)\nReplacing (-15*z**2)*(42*z**3 - 37*z**2 + 42*z - 13) with -(-1)*195*z**2 + (42*z)*(-15*z**2) + (-37*z**2)*(-15*z**2) + (-15*z**2)*(42*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-4*z)*(42*z**3 - 37*z**2 + 42*z - 13) - 13*(-15)*z**2 + (42*z)*(-15*z**2) + (42*z)*(-31) + (-37*z**2)*(-15*z**2) - 37*z**2*(-31) + (-15*z**2)*(42*z**3) + (42*z**3)*(-31) + 403\nSimplifying the partial expression: (-4*z)*(42*z**3 - 37*z**2 + 42*z - 13)\nExpanding the part (42*z**3 - 37*z**2 + 42*z - 13) using the distributive property, and we got: (-4*z)*(42*z) + (-4*z)*(-37*z**2) + (-4*z)*(42*z**3) - (-1)*52*z\nReplacing (-4*z)*(42*z**3 - 37*z**2 + 42*z - 13) with (-4*z)*(42*z) + (-4*z)*(-37*z**2) + (-4*z)*(42*z**3) - (-1)*52*z in the overall expression.\n#Step 5:\nCurrent expression: (-4*z)*(42*z) + (-4*z)*(-37*z**2) + (-4*z)*(42*z**3) - 13*(-15)*z**2 - 13*(-4)*z + (42*z)*(-15*z**2) + (42*z)*(-31) + (-37*z**2)*(-15*z**2) - 37*z**2*(-31) + (-15*z**2)*(42*z**3) + (42*z**3)*(-31) + 403\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*z**2)*-31 = 1147*z**2\n (-37*z**2)*(-15*z**2) = 555*z**4\n (-37*z**2)*(-4*z) = 148*z**3\n (42*z)*-31 = -1302*z\n (42*z)*(-15*z**2) = -630*z**3\n (42*z)*(-4*z) = -168*z**2\n (42*z**3)*-31 = -1302*z**3\n (42*z**3)*(-15*z**2) = -630*z**5\n (42*z**3)*(-4*z) = -168*z**4\n -13*-15*z**2 = 195*z**2\n -13*-4*z = 52*z\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -630*z**5 - 168*z**4 + 555*z**4 - 1302*z**3 - 630*z**3 + 148*z**3 - 168*z**2 + 195*z**2 + 1147*z**2 - 1302*z + 52*z + 403\nCombining like terms, got -630*z**5 + 387*z**4 - 1784*z**3 + 1174*z**2 - 1250*z + 403\n#Step 7:\nCurrent expression: -630*z**5 + 387*z**4 - 1784*z**3 + 1174*z**2 - 1250*z + 403\nNo more calculations needed.\n-630*z**5 + 387*z**4 - 1784*z**3 + 1174*z**2 - 1250*z + 403", "generated_answer": "-630*z**5 + 387*z**4 - 1784*z**3 + 1174*z**2 - 1250*z + 403", "step_length": 7} {"cot_id": "b14adda7918bd4d835bfd24c4d1016926240f4b5ae894d45482e09abe4cab45f", "datapoint": {"question": "Calculate the following: (-48*y**2 - 13*y - 30)*(-23*y**3 - 35*y**2 - 43)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1104*y**5 + 1979*y**4 + 1145*y**3 + 3114*y**2 + 559*y + 1290", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 958, "polynomial_expr": "(-48*y**2 - 13*y - 30)*(-23*y**3 - 35*y**2 - 43)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-48*y**2 - 13*y - 30)*(-23*y**3 - 35*y**2 - 43)\nExpanding the part (-23*y**3 - 35*y**2 - 43) using the distributive property, and we got: (-35*y**2)*(-48*y**2 - 13*y - 30) + (-23*y**3)*(-48*y**2 - 13*y - 30) - 43*(-48*y**2 - 13*y - 30)\n#Step 2:\nCurrent expression: (-35*y**2)*(-48*y**2 - 13*y - 30) + (-23*y**3)*(-48*y**2 - 13*y - 30) - 43*(-48*y**2 - 13*y - 30)\nSimplifying the partial expression: -43*(-48*y**2 - 13*y - 30)\nExpanding the part (-48*y**2 - 13*y - 30) using the distributive property, and we got: -13*y*(-43) - 48*y**2*(-43) - 30*(-43)\nReplacing -43*(-48*y**2 - 13*y - 30) with -13*y*(-43) - 48*y**2*(-43) - 30*(-43) in the overall expression.\n#Step 3:\nCurrent expression: -13*y*(-43) - 48*y**2*(-43) + (-35*y**2)*(-48*y**2 - 13*y - 30) + (-23*y**3)*(-48*y**2 - 13*y - 30) + 1290\nSimplifying the partial expression: (-35*y**2)*(-48*y**2 - 13*y - 30)\nExpanding the part (-48*y**2 - 13*y - 30) using the distributive property, and we got: (-13*y)*(-35*y**2) - (-1)*1050*y**2 + (-48*y**2)*(-35*y**2)\nReplacing (-35*y**2)*(-48*y**2 - 13*y - 30) with (-13*y)*(-35*y**2) - (-1)*1050*y**2 + (-48*y**2)*(-35*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-13*y)*(-35*y**2) - 13*y*(-43) - 30*(-35)*y**2 + (-48*y**2)*(-35*y**2) - 48*y**2*(-43) + (-23*y**3)*(-48*y**2 - 13*y - 30) + 1290\nSimplifying the partial expression: (-23*y**3)*(-48*y**2 - 13*y - 30)\nExpanding the part (-48*y**2 - 13*y - 30) using the distributive property, and we got: (-13*y)*(-23*y**3) - (-1)*690*y**3 + (-48*y**2)*(-23*y**3)\nReplacing (-23*y**3)*(-48*y**2 - 13*y - 30) with (-13*y)*(-23*y**3) - (-1)*690*y**3 + (-48*y**2)*(-23*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-13*y)*(-35*y**2) + (-13*y)*(-23*y**3) - 13*y*(-43) - 30*(-23)*y**3 - 30*(-35)*y**2 + (-48*y**2)*(-35*y**2) + (-48*y**2)*(-23*y**3) - 48*y**2*(-43) + 1290\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*y**2)*-43 = 2064*y**2\n (-48*y**2)*(-35*y**2) = 1680*y**4\n (-48*y**2)*(-23*y**3) = 1104*y**5\n (-13*y)*-43 = 559*y\n (-13*y)*(-35*y**2) = 455*y**3\n (-13*y)*(-23*y**3) = 299*y**4\n -30*-35*y**2 = 1050*y**2\n -30*-23*y**3 = 690*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1104*y**5 + 299*y**4 + 1680*y**4 + 455*y**3 + 690*y**3 + 1050*y**2 + 2064*y**2 + 559*y + 1290\nCombining like terms, got 1104*y**5 + 1979*y**4 + 1145*y**3 + 3114*y**2 + 559*y + 1290\n#Step 7:\nCurrent expression: 1104*y**5 + 1979*y**4 + 1145*y**3 + 3114*y**2 + 559*y + 1290\nNo more calculations needed.\n1104*y**5 + 1979*y**4 + 1145*y**3 + 3114*y**2 + 559*y + 1290", "generated_answer": "1104*y**5 + 1979*y**4 + 1145*y**3 + 3114*y**2 + 559*y + 1290", "step_length": 7} {"cot_id": "ed8b6a80c657f200541f3ae61f2923ca488cccff5da4b69a77b0714505b62af7", "datapoint": {"question": "Simplify this expression: (36*x**3 + 27*x**2)*(46*x**3 + 4*x + 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1656*x**6 + 1242*x**5 + 144*x**4 + 1908*x**3 + 1350*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 959, "polynomial_expr": "(36*x**3 + 27*x**2)*(46*x**3 + 4*x + 50)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (36*x**3 + 27*x**2)*(46*x**3 + 4*x + 50)\nExpanding the part (36*x**3 + 27*x**2) using the distributive property, and we got: (27*x**2)*(46*x**3 + 4*x + 50) + (36*x**3)*(46*x**3 + 4*x + 50)\n#Step 2:\nCurrent expression: (27*x**2)*(46*x**3 + 4*x + 50) + (36*x**3)*(46*x**3 + 4*x + 50)\nSimplifying the partial expression: (27*x**2)*(46*x**3 + 4*x + 50)\nExpanding the part (46*x**3 + 4*x + 50) using the distributive property, and we got: 50*(27*x**2) + (4*x)*(27*x**2) + (27*x**2)*(46*x**3)\nReplacing (27*x**2)*(46*x**3 + 4*x + 50) with 50*(27*x**2) + (4*x)*(27*x**2) + (27*x**2)*(46*x**3) in the overall expression.\n#Step 3:\nCurrent expression: 50*27*x**2 + (4*x)*(27*x**2) + (27*x**2)*(46*x**3) + (36*x**3)*(46*x**3 + 4*x + 50)\nSimplifying the partial expression: (36*x**3)*(46*x**3 + 4*x + 50)\nExpanding the part (46*x**3 + 4*x + 50) using the distributive property, and we got: 50*(36*x**3) + (4*x)*(36*x**3) + (36*x**3)*(46*x**3)\nReplacing (36*x**3)*(46*x**3 + 4*x + 50) with 50*(36*x**3) + (4*x)*(36*x**3) + (36*x**3)*(46*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 50*36*x**3 + 50*27*x**2 + (4*x)*(27*x**2) + (4*x)*(36*x**3) + (27*x**2)*(46*x**3) + (36*x**3)*(46*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (4*x)*(27*x**2) = 108*x**3\n (4*x)*(36*x**3) = 144*x**4\n (46*x**3)*(27*x**2) = 1242*x**5\n (46*x**3)*(36*x**3) = 1656*x**6\n 50*27*x**2 = 1350*x**2\n 50*36*x**3 = 1800*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1656*x**6 + 1242*x**5 + 144*x**4 + 108*x**3 + 1800*x**3 + 1350*x**2\nCombining like terms, got 1656*x**6 + 1242*x**5 + 144*x**4 + 1908*x**3 + 1350*x**2\n#Step 6:\nCurrent expression: 1656*x**6 + 1242*x**5 + 144*x**4 + 1908*x**3 + 1350*x**2\nNo more calculations needed.\n1656*x**6 + 1242*x**5 + 144*x**4 + 1908*x**3 + 1350*x**2", "generated_answer": "1656*x**6 + 1242*x**5 + 144*x**4 + 1908*x**3 + 1350*x**2", "step_length": 6} {"cot_id": "79cb88afcf9407afc6e6684a087451a1d2e0ebd5bcee71bde878ba2c4b78d75b", "datapoint": {"question": "Simplify this expression: (9*z**3 - 10)*(-33*z**3 - 3*z**2 + 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-297*z**6 - 27*z**5 + 654*z**3 + 30*z**2 - 360", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 960, "polynomial_expr": "(9*z**3 - 10)*(-33*z**3 - 3*z**2 + 36)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9*z**3 - 10)*(-33*z**3 - 3*z**2 + 36)\nExpanding the part (9*z**3 - 10) using the distributive property, and we got: (9*z**3)*(-33*z**3 - 3*z**2 + 36) - 10*(-33*z**3 - 3*z**2 + 36)\n#Step 2:\nCurrent expression: (9*z**3)*(-33*z**3 - 3*z**2 + 36) - 10*(-33*z**3 - 3*z**2 + 36)\nSimplifying the partial expression: -10*(-33*z**3 - 3*z**2 + 36)\nExpanding the part (-33*z**3 - 3*z**2 + 36) using the distributive property, and we got: -3*z**2*(-10) - 33*z**3*(-10) + 36*(-10)\nReplacing -10*(-33*z**3 - 3*z**2 + 36) with -3*z**2*(-10) - 33*z**3*(-10) + 36*(-10) in the overall expression.\n#Step 3:\nCurrent expression: -3*z**2*(-10) - 33*z**3*(-10) + (9*z**3)*(-33*z**3 - 3*z**2 + 36) - 360\nSimplifying the partial expression: (9*z**3)*(-33*z**3 - 3*z**2 + 36)\nExpanding the part (-33*z**3 - 3*z**2 + 36) using the distributive property, and we got: 36*(9*z**3) + (-3*z**2)*(9*z**3) + (-33*z**3)*(9*z**3)\nReplacing (9*z**3)*(-33*z**3 - 3*z**2 + 36) with 36*(9*z**3) + (-3*z**2)*(9*z**3) + (-33*z**3)*(9*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 36*9*z**3 + (-3*z**2)*(9*z**3) - 3*z**2*(-10) + (-33*z**3)*(9*z**3) - 33*z**3*(-10) - 360\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*z**3)*-10 = 330*z**3\n (-33*z**3)*(9*z**3) = -297*z**6\n (-3*z**2)*-10 = 30*z**2\n (-3*z**2)*(9*z**3) = -27*z**5\n 36*9*z**3 = 324*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -297*z**6 - 27*z**5 + 324*z**3 + 330*z**3 + 30*z**2 - 360\nCombining like terms, got -297*z**6 - 27*z**5 + 654*z**3 + 30*z**2 - 360\n#Step 6:\nCurrent expression: -297*z**6 - 27*z**5 + 654*z**3 + 30*z**2 - 360\nNo more calculations needed.\n-297*z**6 - 27*z**5 + 654*z**3 + 30*z**2 - 360", "generated_answer": "-297*z**6 - 27*z**5 + 654*z**3 + 30*z**2 - 360", "step_length": 6} {"cot_id": "778513928ff20a3ad70a7f99879bd015523b9a194384b64cb01b07f312ce7d03", "datapoint": {"question": "Simplify this expression: -77*y**2*(55*y**3 + 5*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-4235*y**5 - 385*y**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 961, "polynomial_expr": "-77*y**2*(55*y**3 + 5*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -77*y**2*(55*y**3 + 5*y**2)\nExpanding the part (55*y**3 + 5*y**2) using the distributive property, and we got: (-77*y**2)*(5*y**2) + (-77*y**2)*(55*y**3)\n#Step 2:\nCurrent expression: (-77*y**2)*(5*y**2) + (-77*y**2)*(55*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (5*y**2)*(-77*y**2) = -385*y**4\n (55*y**3)*(-77*y**2) = -4235*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -4235*y**5 - 385*y**4\nNo more calculations needed.\n-4235*y**5 - 385*y**4", "generated_answer": "-4235*y**5 - 385*y**4", "step_length": 3} {"cot_id": "802480341d7fd8ad64153d49c6b8fc9488b24174d426aace8e11f3ac8598be0b", "datapoint": {"question": "Calculate the following: (24*y**3 - 6)*(-2*y**3 - 33*y - 8)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-48*y**6 - 792*y**4 - 180*y**3 + 198*y + 48", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 962, "polynomial_expr": "(24*y**3 - 6)*(-2*y**3 - 33*y - 8)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (24*y**3 - 6)*(-2*y**3 - 33*y - 8)\nExpanding the part (24*y**3 - 6) using the distributive property, and we got: (24*y**3)*(-2*y**3 - 33*y - 8) - 6*(-2*y**3 - 33*y - 8)\n#Step 2:\nCurrent expression: (24*y**3)*(-2*y**3 - 33*y - 8) - 6*(-2*y**3 - 33*y - 8)\nSimplifying the partial expression: -6*(-2*y**3 - 33*y - 8)\nExpanding the part (-2*y**3 - 33*y - 8) using the distributive property, and we got: -33*y*(-6) - 2*y**3*(-6) - 8*(-6)\nReplacing -6*(-2*y**3 - 33*y - 8) with -33*y*(-6) - 2*y**3*(-6) - 8*(-6) in the overall expression.\n#Step 3:\nCurrent expression: -33*y*(-6) - 2*y**3*(-6) + (24*y**3)*(-2*y**3 - 33*y - 8) + 48\nSimplifying the partial expression: (24*y**3)*(-2*y**3 - 33*y - 8)\nExpanding the part (-2*y**3 - 33*y - 8) using the distributive property, and we got: (-33*y)*(24*y**3) - 192*y**3 + (-2*y**3)*(24*y**3)\nReplacing (24*y**3)*(-2*y**3 - 33*y - 8) with (-33*y)*(24*y**3) - 192*y**3 + (-2*y**3)*(24*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-33*y)*(24*y**3) - 33*y*(-6) - 8*24*y**3 + (-2*y**3)*(24*y**3) - 2*y**3*(-6) + 48\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*y)*-6 = 198*y\n (-33*y)*(24*y**3) = -792*y**4\n (-2*y**3)*-6 = 12*y**3\n (-2*y**3)*(24*y**3) = -48*y**6\n -8*24*y**3 = -192*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -48*y**6 - 792*y**4 - 192*y**3 + 12*y**3 + 198*y + 48\nCombining like terms, got -48*y**6 - 792*y**4 - 180*y**3 + 198*y + 48\n#Step 6:\nCurrent expression: -48*y**6 - 792*y**4 - 180*y**3 + 198*y + 48\nNo more calculations needed.\n-48*y**6 - 792*y**4 - 180*y**3 + 198*y + 48", "generated_answer": "-48*y**6 - 792*y**4 - 180*y**3 + 198*y + 48", "step_length": 6} {"cot_id": "774b2b27426185a5de67923456da688377d39e19876e51057e86454093cc9545", "datapoint": {"question": "Calculate the following: (-15*y**3 - 30*y**2 + 3*y)*(14*y**3 - 64*y - 43)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-210*y**6 - 420*y**5 + 1002*y**4 + 2565*y**3 + 1098*y**2 - 129*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 963, "polynomial_expr": "(-15*y**3 - 30*y**2 + 3*y)*(14*y**3 - 64*y - 43)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-15*y**3 - 30*y**2 + 3*y)*(14*y**3 - 64*y - 43)\nExpanding the part (14*y**3 - 64*y - 43) using the distributive property, and we got: (-64*y)*(-15*y**3 - 30*y**2 + 3*y) + (14*y**3)*(-15*y**3 - 30*y**2 + 3*y) - 43*(-15*y**3 - 30*y**2 + 3*y)\n#Step 2:\nCurrent expression: (-64*y)*(-15*y**3 - 30*y**2 + 3*y) + (14*y**3)*(-15*y**3 - 30*y**2 + 3*y) - 43*(-15*y**3 - 30*y**2 + 3*y)\nSimplifying the partial expression: -43*(-15*y**3 - 30*y**2 + 3*y)\nExpanding the part (-15*y**3 - 30*y**2 + 3*y) using the distributive property, and we got: (3*y)*(-43) - 30*y**2*(-43) - 15*y**3*(-43)\nReplacing -43*(-15*y**3 - 30*y**2 + 3*y) with (3*y)*(-43) - 30*y**2*(-43) - 15*y**3*(-43) in the overall expression.\n#Step 3:\nCurrent expression: (-64*y)*(-15*y**3 - 30*y**2 + 3*y) + (3*y)*(-43) - 30*y**2*(-43) - 15*y**3*(-43) + (14*y**3)*(-15*y**3 - 30*y**2 + 3*y)\nSimplifying the partial expression: (-64*y)*(-15*y**3 - 30*y**2 + 3*y)\nExpanding the part (-15*y**3 - 30*y**2 + 3*y) using the distributive property, and we got: (-64*y)*(3*y) + (-64*y)*(-30*y**2) + (-64*y)*(-15*y**3)\nReplacing (-64*y)*(-15*y**3 - 30*y**2 + 3*y) with (-64*y)*(3*y) + (-64*y)*(-30*y**2) + (-64*y)*(-15*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-64*y)*(3*y) + (-64*y)*(-30*y**2) + (-64*y)*(-15*y**3) + (3*y)*(-43) - 30*y**2*(-43) - 15*y**3*(-43) + (14*y**3)*(-15*y**3 - 30*y**2 + 3*y)\nSimplifying the partial expression: (14*y**3)*(-15*y**3 - 30*y**2 + 3*y)\nExpanding the part (-15*y**3 - 30*y**2 + 3*y) using the distributive property, and we got: (3*y)*(14*y**3) + (-30*y**2)*(14*y**3) + (-15*y**3)*(14*y**3)\nReplacing (14*y**3)*(-15*y**3 - 30*y**2 + 3*y) with (3*y)*(14*y**3) + (-30*y**2)*(14*y**3) + (-15*y**3)*(14*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-64*y)*(3*y) + (-64*y)*(-30*y**2) + (-64*y)*(-15*y**3) + (3*y)*(14*y**3) + (3*y)*(-43) + (-30*y**2)*(14*y**3) - 30*y**2*(-43) + (-15*y**3)*(14*y**3) - 15*y**3*(-43)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*y**2)*-43 = 1290*y**2\n (-30*y**2)*(-64*y) = 1920*y**3\n (-30*y**2)*(14*y**3) = -420*y**5\n (-15*y**3)*-43 = 645*y**3\n (-15*y**3)*(-64*y) = 960*y**4\n (-15*y**3)*(14*y**3) = -210*y**6\n (3*y)*-43 = -129*y\n (3*y)*(-64*y) = -192*y**2\n (3*y)*(14*y**3) = 42*y**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -210*y**6 - 420*y**5 + 42*y**4 + 960*y**4 + 645*y**3 + 1920*y**3 - 192*y**2 + 1290*y**2 - 129*y\nCombining like terms, got -210*y**6 - 420*y**5 + 1002*y**4 + 2565*y**3 + 1098*y**2 - 129*y\n#Step 7:\nCurrent expression: -210*y**6 - 420*y**5 + 1002*y**4 + 2565*y**3 + 1098*y**2 - 129*y\nNo more calculations needed.\n-210*y**6 - 420*y**5 + 1002*y**4 + 2565*y**3 + 1098*y**2 - 129*y", "generated_answer": "-210*y**6 - 420*y**5 + 1002*y**4 + 2565*y**3 + 1098*y**2 - 129*y", "step_length": 7} {"cot_id": "c2d272c0668dab3283be63ad5d0aa40702638a3acd8e414ca7b8688b571dd272", "datapoint": {"question": "Simplify this expression: (-38*y**3 + 34*y)*(-29*y**3 + 37*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1102*y**6 - 2392*y**4 + 1258*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 964, "polynomial_expr": "(-38*y**3 + 34*y)*(-29*y**3 + 37*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-38*y**3 + 34*y)*(-29*y**3 + 37*y)\nExpanding the part (-38*y**3 + 34*y) using the distributive property, and we got: (34*y)*(-29*y**3 + 37*y) + (-38*y**3)*(-29*y**3 + 37*y)\n#Step 2:\nCurrent expression: (34*y)*(-29*y**3 + 37*y) + (-38*y**3)*(-29*y**3 + 37*y)\nSimplifying the partial expression: (-38*y**3)*(-29*y**3 + 37*y)\nExpanding the part (-29*y**3 + 37*y) using the distributive property, and we got: (37*y)*(-38*y**3) + (-38*y**3)*(-29*y**3)\nReplacing (-38*y**3)*(-29*y**3 + 37*y) with (37*y)*(-38*y**3) + (-38*y**3)*(-29*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (34*y)*(-29*y**3 + 37*y) + (37*y)*(-38*y**3) + (-38*y**3)*(-29*y**3)\nSimplifying the partial expression: (34*y)*(-29*y**3 + 37*y)\nExpanding the part (-29*y**3 + 37*y) using the distributive property, and we got: (34*y)*(37*y) + (34*y)*(-29*y**3)\nReplacing (34*y)*(-29*y**3 + 37*y) with (34*y)*(37*y) + (34*y)*(-29*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (34*y)*(37*y) + (34*y)*(-29*y**3) + (37*y)*(-38*y**3) + (-38*y**3)*(-29*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*y**3)*(-38*y**3) = 1102*y**6\n (-29*y**3)*(34*y) = -986*y**4\n (37*y)*(-38*y**3) = -1406*y**4\n (37*y)*(34*y) = 1258*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1102*y**6 - 1406*y**4 - 986*y**4 + 1258*y**2\nCombining like terms, got 1102*y**6 - 2392*y**4 + 1258*y**2\n#Step 6:\nCurrent expression: 1102*y**6 - 2392*y**4 + 1258*y**2\nNo more calculations needed.\n1102*y**6 - 2392*y**4 + 1258*y**2", "generated_answer": "1102*y**6 - 2392*y**4 + 1258*y**2", "step_length": 6} {"cot_id": "82fd59da06572b008e68dad5f2037a50c3a4418de8a83d4747274ae8d8e400e2", "datapoint": {"question": "Calculate the following: (43*x + 13)*(29*x**2 - 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1247*x**3 + 377*x**2 - 1892*x - 572", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 965, "polynomial_expr": "(43*x + 13)*(29*x**2 - 44)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (43*x + 13)*(29*x**2 - 44)\nExpanding the part (29*x**2 - 44) using the distributive property, and we got: (29*x**2)*(43*x + 13) - 44*(43*x + 13)\n#Step 2:\nCurrent expression: (29*x**2)*(43*x + 13) - 44*(43*x + 13)\nSimplifying the partial expression: -44*(43*x + 13)\nExpanding the part (43*x + 13) using the distributive property, and we got: (43*x)*(-44) + 13*(-44)\nReplacing -44*(43*x + 13) with (43*x)*(-44) + 13*(-44) in the overall expression.\n#Step 3:\nCurrent expression: (43*x)*(-44) + (29*x**2)*(43*x + 13) - 572\nSimplifying the partial expression: (29*x**2)*(43*x + 13)\nExpanding the part (43*x + 13) using the distributive property, and we got: 13*(29*x**2) + (43*x)*(29*x**2)\nReplacing (29*x**2)*(43*x + 13) with 13*(29*x**2) + (43*x)*(29*x**2) in the overall expression.\n#Step 4:\nCurrent expression: 13*29*x**2 + (43*x)*(29*x**2) + (43*x)*(-44) - 572\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (43*x)*-44 = -1892*x\n (43*x)*(29*x**2) = 1247*x**3\n 13*29*x**2 = 377*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1247*x**3 + 377*x**2 - 1892*x - 572\nNo more calculations needed.\n1247*x**3 + 377*x**2 - 1892*x - 572", "generated_answer": "1247*x**3 + 377*x**2 - 1892*x - 572", "step_length": 5} {"cot_id": "1355ae4a925df4f7476e52245821a49c7c305b1fb31c234974cccea2d6f707c8", "datapoint": {"question": "Simplify this expression: (32*z**3 + 43)*(-15*z**2 - z + 46)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-480*z**5 - 32*z**4 + 1472*z**3 - 645*z**2 - 43*z + 1978", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 966, "polynomial_expr": "(32*z**3 + 43)*(-15*z**2 - z + 46)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (32*z**3 + 43)*(-15*z**2 - z + 46)\nExpanding the part (32*z**3 + 43) using the distributive property, and we got: (32*z**3)*(-15*z**2 - z + 46) + 43*(-15*z**2 - z + 46)\n#Step 2:\nCurrent expression: (32*z**3)*(-15*z**2 - z + 46) + 43*(-15*z**2 - z + 46)\nSimplifying the partial expression: 43*(-15*z**2 - z + 46)\nExpanding the part (-15*z**2 - z + 46) using the distributive property, and we got: -z*43 - 15*z**2*43 + 46*43\nReplacing 43*(-15*z**2 - z + 46) with -z*43 - 15*z**2*43 + 46*43 in the overall expression.\n#Step 3:\nCurrent expression: -z*43 - 15*z**2*43 + (32*z**3)*(-15*z**2 - z + 46) + 1978\nSimplifying the partial expression: (32*z**3)*(-15*z**2 - z + 46)\nExpanding the part (-15*z**2 - z + 46) using the distributive property, and we got: (-z)*(32*z**3) + 46*(32*z**3) + (-15*z**2)*(32*z**3)\nReplacing (32*z**3)*(-15*z**2 - z + 46) with (-z)*(32*z**3) + 46*(32*z**3) + (-15*z**2)*(32*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-z)*(32*z**3) - z*43 + 46*32*z**3 + (-15*z**2)*(32*z**3) - 15*z**2*43 + 1978\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-z)*43 = -43*z\n (-z)*(32*z**3) = -32*z**4\n (-15*z**2)*43 = -645*z**2\n (-15*z**2)*(32*z**3) = -480*z**5\n 46*32*z**3 = 1472*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -480*z**5 - 32*z**4 + 1472*z**3 - 645*z**2 - 43*z + 1978\nNo more calculations needed.\n-480*z**5 - 32*z**4 + 1472*z**3 - 645*z**2 - 43*z + 1978", "generated_answer": "-480*z**5 - 32*z**4 + 1472*z**3 - 645*z**2 - 43*z + 1978", "step_length": 5} {"cot_id": "f3961083998a0b26dce540130af03bcd8dd517b6cc1a96a49f957aefa7d022a7", "datapoint": {"question": "Simplify this expression: (-5*x**3 + 9*x**2 + 78*x)*(5*x**3 - 6*x - 11)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-25*x**6 + 45*x**5 + 420*x**4 + x**3 - 567*x**2 - 858*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 967, "polynomial_expr": "(-5*x**3 + 9*x**2 + 78*x)*(5*x**3 - 6*x - 11)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-5*x**3 + 9*x**2 + 78*x)*(5*x**3 - 6*x - 11)\nExpanding the part (5*x**3 - 6*x - 11) using the distributive property, and we got: (-6*x)*(-5*x**3 + 9*x**2 + 78*x) + (5*x**3)*(-5*x**3 + 9*x**2 + 78*x) - 11*(-5*x**3 + 9*x**2 + 78*x)\n#Step 2:\nCurrent expression: (-6*x)*(-5*x**3 + 9*x**2 + 78*x) + (5*x**3)*(-5*x**3 + 9*x**2 + 78*x) - 11*(-5*x**3 + 9*x**2 + 78*x)\nSimplifying the partial expression: -11*(-5*x**3 + 9*x**2 + 78*x)\nExpanding the part (-5*x**3 + 9*x**2 + 78*x) using the distributive property, and we got: (78*x)*(-11) + (9*x**2)*(-11) - 5*x**3*(-11)\nReplacing -11*(-5*x**3 + 9*x**2 + 78*x) with (78*x)*(-11) + (9*x**2)*(-11) - 5*x**3*(-11) in the overall expression.\n#Step 3:\nCurrent expression: (-6*x)*(-5*x**3 + 9*x**2 + 78*x) + (78*x)*(-11) + (9*x**2)*(-11) - 5*x**3*(-11) + (5*x**3)*(-5*x**3 + 9*x**2 + 78*x)\nSimplifying the partial expression: (-6*x)*(-5*x**3 + 9*x**2 + 78*x)\nExpanding the part (-5*x**3 + 9*x**2 + 78*x) using the distributive property, and we got: (-6*x)*(78*x) + (-6*x)*(9*x**2) + (-6*x)*(-5*x**3)\nReplacing (-6*x)*(-5*x**3 + 9*x**2 + 78*x) with (-6*x)*(78*x) + (-6*x)*(9*x**2) + (-6*x)*(-5*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-6*x)*(78*x) + (-6*x)*(9*x**2) + (-6*x)*(-5*x**3) + (78*x)*(-11) + (9*x**2)*(-11) - 5*x**3*(-11) + (5*x**3)*(-5*x**3 + 9*x**2 + 78*x)\nSimplifying the partial expression: (5*x**3)*(-5*x**3 + 9*x**2 + 78*x)\nExpanding the part (-5*x**3 + 9*x**2 + 78*x) using the distributive property, and we got: (78*x)*(5*x**3) + (9*x**2)*(5*x**3) + (-5*x**3)*(5*x**3)\nReplacing (5*x**3)*(-5*x**3 + 9*x**2 + 78*x) with (78*x)*(5*x**3) + (9*x**2)*(5*x**3) + (-5*x**3)*(5*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-6*x)*(78*x) + (-6*x)*(9*x**2) + (-6*x)*(-5*x**3) + (78*x)*(5*x**3) + (78*x)*(-11) + (9*x**2)*(5*x**3) + (9*x**2)*(-11) + (-5*x**3)*(5*x**3) - 5*x**3*(-11)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-5*x**3)*-11 = 55*x**3\n (-5*x**3)*(-6*x) = 30*x**4\n (-5*x**3)*(5*x**3) = -25*x**6\n (9*x**2)*-11 = -99*x**2\n (9*x**2)*(-6*x) = -54*x**3\n (9*x**2)*(5*x**3) = 45*x**5\n (78*x)*-11 = -858*x\n (78*x)*(-6*x) = -468*x**2\n (78*x)*(5*x**3) = 390*x**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -25*x**6 + 45*x**5 + 30*x**4 + 390*x**4 - 54*x**3 + 55*x**3 - 468*x**2 - 99*x**2 - 858*x\nCombining like terms, got -25*x**6 + 45*x**5 + 420*x**4 + x**3 - 567*x**2 - 858*x\n#Step 7:\nCurrent expression: -25*x**6 + 45*x**5 + 420*x**4 + x**3 - 567*x**2 - 858*x\nNo more calculations needed.\n-25*x**6 + 45*x**5 + 420*x**4 + x**3 - 567*x**2 - 858*x", "generated_answer": "-25*x**6 + 45*x**5 + 420*x**4 + x**3 - 567*x**2 - 858*x", "step_length": 7} {"cot_id": "93718cb0c551760405ef0d38f786b7d627901331e922cc7c664b8693b489c180", "datapoint": {"question": "Simplify this expression: (40*z - 35)*(-6*z**2 + 47*z - 58)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-240*z**3 + 2090*z**2 - 3965*z + 2030", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 968, "polynomial_expr": "(40*z - 35)*(-6*z**2 + 47*z - 58)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (40*z - 35)*(-6*z**2 + 47*z - 58)\nExpanding the part (40*z - 35) using the distributive property, and we got: (40*z)*(-6*z**2 + 47*z - 58) - 35*(-6*z**2 + 47*z - 58)\n#Step 2:\nCurrent expression: (40*z)*(-6*z**2 + 47*z - 58) - 35*(-6*z**2 + 47*z - 58)\nSimplifying the partial expression: -35*(-6*z**2 + 47*z - 58)\nExpanding the part (-6*z**2 + 47*z - 58) using the distributive property, and we got: (47*z)*(-35) - 6*z**2*(-35) - 58*(-35)\nReplacing -35*(-6*z**2 + 47*z - 58) with (47*z)*(-35) - 6*z**2*(-35) - 58*(-35) in the overall expression.\n#Step 3:\nCurrent expression: (40*z)*(-6*z**2 + 47*z - 58) + (47*z)*(-35) - 6*z**2*(-35) + 2030\nSimplifying the partial expression: (40*z)*(-6*z**2 + 47*z - 58)\nExpanding the part (-6*z**2 + 47*z - 58) using the distributive property, and we got: -2320*z + (40*z)*(47*z) + (40*z)*(-6*z**2)\nReplacing (40*z)*(-6*z**2 + 47*z - 58) with -2320*z + (40*z)*(47*z) + (40*z)*(-6*z**2) in the overall expression.\n#Step 4:\nCurrent expression: -58*40*z + (40*z)*(47*z) + (40*z)*(-6*z**2) + (47*z)*(-35) - 6*z**2*(-35) + 2030\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-6*z**2)*-35 = 210*z**2\n (-6*z**2)*(40*z) = -240*z**3\n (47*z)*-35 = -1645*z\n (47*z)*(40*z) = 1880*z**2\n -58*40*z = -2320*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -240*z**3 + 210*z**2 + 1880*z**2 - 2320*z - 1645*z + 2030\nCombining like terms, got -240*z**3 + 2090*z**2 - 3965*z + 2030\n#Step 6:\nCurrent expression: -240*z**3 + 2090*z**2 - 3965*z + 2030\nNo more calculations needed.\n-240*z**3 + 2090*z**2 - 3965*z + 2030", "generated_answer": "-240*z**3 + 2090*z**2 - 3965*z + 2030", "step_length": 6} {"cot_id": "30ca84c30af24c9a6488ca9d337021ae68037060a4ee48b888ff1d6dd2ca6b1b", "datapoint": {"question": "Calculate the following: (26*y**2 + 27)*(-12*y**3 + 19*y**2 - 8*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-312*y**5 + 494*y**4 - 532*y**3 + 513*y**2 - 216*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 969, "polynomial_expr": "(26*y**2 + 27)*(-12*y**3 + 19*y**2 - 8*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (26*y**2 + 27)*(-12*y**3 + 19*y**2 - 8*y)\nExpanding the part (26*y**2 + 27) using the distributive property, and we got: (26*y**2)*(-12*y**3 + 19*y**2 - 8*y) + 27*(-12*y**3 + 19*y**2 - 8*y)\n#Step 2:\nCurrent expression: (26*y**2)*(-12*y**3 + 19*y**2 - 8*y) + 27*(-12*y**3 + 19*y**2 - 8*y)\nSimplifying the partial expression: 27*(-12*y**3 + 19*y**2 - 8*y)\nExpanding the part (-12*y**3 + 19*y**2 - 8*y) using the distributive property, and we got: -8*y*27 + (19*y**2)*27 - 12*y**3*27\nReplacing 27*(-12*y**3 + 19*y**2 - 8*y) with -8*y*27 + (19*y**2)*27 - 12*y**3*27 in the overall expression.\n#Step 3:\nCurrent expression: -8*y*27 + (19*y**2)*27 + (26*y**2)*(-12*y**3 + 19*y**2 - 8*y) - 12*y**3*27\nSimplifying the partial expression: (26*y**2)*(-12*y**3 + 19*y**2 - 8*y)\nExpanding the part (-12*y**3 + 19*y**2 - 8*y) using the distributive property, and we got: (-8*y)*(26*y**2) + (19*y**2)*(26*y**2) + (26*y**2)*(-12*y**3)\nReplacing (26*y**2)*(-12*y**3 + 19*y**2 - 8*y) with (-8*y)*(26*y**2) + (19*y**2)*(26*y**2) + (26*y**2)*(-12*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-8*y)*(26*y**2) - 8*y*27 + (19*y**2)*(26*y**2) + (19*y**2)*27 + (26*y**2)*(-12*y**3) - 12*y**3*27\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*y**3)*27 = -324*y**3\n (-12*y**3)*(26*y**2) = -312*y**5\n (-8*y)*27 = -216*y\n (-8*y)*(26*y**2) = -208*y**3\n (19*y**2)*27 = 513*y**2\n (19*y**2)*(26*y**2) = 494*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -312*y**5 + 494*y**4 - 324*y**3 - 208*y**3 + 513*y**2 - 216*y\nCombining like terms, got -312*y**5 + 494*y**4 - 532*y**3 + 513*y**2 - 216*y\n#Step 6:\nCurrent expression: -312*y**5 + 494*y**4 - 532*y**3 + 513*y**2 - 216*y\nNo more calculations needed.\n-312*y**5 + 494*y**4 - 532*y**3 + 513*y**2 - 216*y", "generated_answer": "-312*y**5 + 494*y**4 - 532*y**3 + 513*y**2 - 216*y", "step_length": 6} {"cot_id": "9b743fae28525ca80e05d9d88f4bb50bc2fa5b3f46a5a0a7fbd5300062667f77", "datapoint": {"question": "Simplify this expression: (23*y + 26)*(-30*y**3 - 29*y**2 + 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-690*y**4 - 1447*y**3 - 754*y**2 + 805*y + 910", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 970, "polynomial_expr": "(23*y + 26)*(-30*y**3 - 29*y**2 + 35)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (23*y + 26)*(-30*y**3 - 29*y**2 + 35)\nExpanding the part (23*y + 26) using the distributive property, and we got: (23*y)*(-30*y**3 - 29*y**2 + 35) + 26*(-30*y**3 - 29*y**2 + 35)\n#Step 2:\nCurrent expression: (23*y)*(-30*y**3 - 29*y**2 + 35) + 26*(-30*y**3 - 29*y**2 + 35)\nSimplifying the partial expression: 26*(-30*y**3 - 29*y**2 + 35)\nExpanding the part (-30*y**3 - 29*y**2 + 35) using the distributive property, and we got: -29*y**2*26 - 30*y**3*26 + 35*26\nReplacing 26*(-30*y**3 - 29*y**2 + 35) with -29*y**2*26 - 30*y**3*26 + 35*26 in the overall expression.\n#Step 3:\nCurrent expression: (23*y)*(-30*y**3 - 29*y**2 + 35) - 29*y**2*26 - 30*y**3*26 + 910\nSimplifying the partial expression: (23*y)*(-30*y**3 - 29*y**2 + 35)\nExpanding the part (-30*y**3 - 29*y**2 + 35) using the distributive property, and we got: 35*(23*y) + (23*y)*(-29*y**2) + (23*y)*(-30*y**3)\nReplacing (23*y)*(-30*y**3 - 29*y**2 + 35) with 35*(23*y) + (23*y)*(-29*y**2) + (23*y)*(-30*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 35*23*y + (23*y)*(-29*y**2) + (23*y)*(-30*y**3) - 29*y**2*26 - 30*y**3*26 + 910\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*y**3)*26 = -780*y**3\n (-30*y**3)*(23*y) = -690*y**4\n (-29*y**2)*26 = -754*y**2\n (-29*y**2)*(23*y) = -667*y**3\n 35*23*y = 805*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -690*y**4 - 780*y**3 - 667*y**3 - 754*y**2 + 805*y + 910\nCombining like terms, got -690*y**4 - 1447*y**3 - 754*y**2 + 805*y + 910\n#Step 6:\nCurrent expression: -690*y**4 - 1447*y**3 - 754*y**2 + 805*y + 910\nNo more calculations needed.\n-690*y**4 - 1447*y**3 - 754*y**2 + 805*y + 910", "generated_answer": "-690*y**4 - 1447*y**3 - 754*y**2 + 805*y + 910", "step_length": 6} {"cot_id": "1b0cd7ede47dc0305992f6855fa12590dd4dfd7a0d9ef2a89a03fdb3786954a2", "datapoint": {"question": "Simplify this expression: (39*y**2 - 5)*(17*y**3 - 2*y**2 + 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "663*y**5 - 78*y**4 - 85*y**3 + 1843*y**2 - 235", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 971, "polynomial_expr": "(39*y**2 - 5)*(17*y**3 - 2*y**2 + 47)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (39*y**2 - 5)*(17*y**3 - 2*y**2 + 47)\nExpanding the part (39*y**2 - 5) using the distributive property, and we got: (39*y**2)*(17*y**3 - 2*y**2 + 47) - 5*(17*y**3 - 2*y**2 + 47)\n#Step 2:\nCurrent expression: (39*y**2)*(17*y**3 - 2*y**2 + 47) - 5*(17*y**3 - 2*y**2 + 47)\nSimplifying the partial expression: -5*(17*y**3 - 2*y**2 + 47)\nExpanding the part (17*y**3 - 2*y**2 + 47) using the distributive property, and we got: -2*y**2*(-5) + (17*y**3)*(-5) + 47*(-5)\nReplacing -5*(17*y**3 - 2*y**2 + 47) with -2*y**2*(-5) + (17*y**3)*(-5) + 47*(-5) in the overall expression.\n#Step 3:\nCurrent expression: -2*y**2*(-5) + (39*y**2)*(17*y**3 - 2*y**2 + 47) + (17*y**3)*(-5) - 235\nSimplifying the partial expression: (39*y**2)*(17*y**3 - 2*y**2 + 47)\nExpanding the part (17*y**3 - 2*y**2 + 47) using the distributive property, and we got: 47*(39*y**2) + (-2*y**2)*(39*y**2) + (39*y**2)*(17*y**3)\nReplacing (39*y**2)*(17*y**3 - 2*y**2 + 47) with 47*(39*y**2) + (-2*y**2)*(39*y**2) + (39*y**2)*(17*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 47*39*y**2 + (-2*y**2)*(39*y**2) - 2*y**2*(-5) + (39*y**2)*(17*y**3) + (17*y**3)*(-5) - 235\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-2*y**2)*-5 = 10*y**2\n (-2*y**2)*(39*y**2) = -78*y**4\n (17*y**3)*-5 = -85*y**3\n (17*y**3)*(39*y**2) = 663*y**5\n 47*39*y**2 = 1833*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 663*y**5 - 78*y**4 - 85*y**3 + 10*y**2 + 1833*y**2 - 235\nCombining like terms, got 663*y**5 - 78*y**4 - 85*y**3 + 1843*y**2 - 235\n#Step 6:\nCurrent expression: 663*y**5 - 78*y**4 - 85*y**3 + 1843*y**2 - 235\nNo more calculations needed.\n663*y**5 - 78*y**4 - 85*y**3 + 1843*y**2 - 235", "generated_answer": "663*y**5 - 78*y**4 - 85*y**3 + 1843*y**2 - 235", "step_length": 6} {"cot_id": "f2b1a5a0d69d1ca6f58124840d1fe4ae4be5aaa47c1a76d542d88db38604bc60", "datapoint": {"question": "Simplify this expression: (-17*z**3 - 44)*(-27*z**2 + 42*z - 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "459*z**5 - 714*z**4 + 238*z**3 + 1188*z**2 - 1848*z + 616", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 972, "polynomial_expr": "(-17*z**3 - 44)*(-27*z**2 + 42*z - 14)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-17*z**3 - 44)*(-27*z**2 + 42*z - 14)\nExpanding the part (-17*z**3 - 44) using the distributive property, and we got: (-17*z**3)*(-27*z**2 + 42*z - 14) - 44*(-27*z**2 + 42*z - 14)\n#Step 2:\nCurrent expression: (-17*z**3)*(-27*z**2 + 42*z - 14) - 44*(-27*z**2 + 42*z - 14)\nSimplifying the partial expression: -44*(-27*z**2 + 42*z - 14)\nExpanding the part (-27*z**2 + 42*z - 14) using the distributive property, and we got: (42*z)*(-44) - 27*z**2*(-44) - 14*(-44)\nReplacing -44*(-27*z**2 + 42*z - 14) with (42*z)*(-44) - 27*z**2*(-44) - 14*(-44) in the overall expression.\n#Step 3:\nCurrent expression: (42*z)*(-44) - 27*z**2*(-44) + (-17*z**3)*(-27*z**2 + 42*z - 14) + 616\nSimplifying the partial expression: (-17*z**3)*(-27*z**2 + 42*z - 14)\nExpanding the part (-27*z**2 + 42*z - 14) using the distributive property, and we got: -(-1)*238*z**3 + (42*z)*(-17*z**3) + (-27*z**2)*(-17*z**3)\nReplacing (-17*z**3)*(-27*z**2 + 42*z - 14) with -(-1)*238*z**3 + (42*z)*(-17*z**3) + (-27*z**2)*(-17*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -14*(-17)*z**3 + (42*z)*(-17*z**3) + (42*z)*(-44) + (-27*z**2)*(-17*z**3) - 27*z**2*(-44) + 616\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*z**2)*-44 = 1188*z**2\n (-27*z**2)*(-17*z**3) = 459*z**5\n (42*z)*-44 = -1848*z\n (42*z)*(-17*z**3) = -714*z**4\n -14*-17*z**3 = 238*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 459*z**5 - 714*z**4 + 238*z**3 + 1188*z**2 - 1848*z + 616\nNo more calculations needed.\n459*z**5 - 714*z**4 + 238*z**3 + 1188*z**2 - 1848*z + 616", "generated_answer": "459*z**5 - 714*z**4 + 238*z**3 + 1188*z**2 - 1848*z + 616", "step_length": 5} {"cot_id": "dd87438273fec041c1bd11c71c81bb1f3a8c77bc04faa7ea200c10017aae5296", "datapoint": {"question": "Calculate the following: (-34*x**3 - 38*x**2 + 40*x)*(8*x**3 + 27*x**2 - 20*x + 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-272*x**6 - 1222*x**5 - 26*x**4 + 208*x**3 - 2624*x**2 + 1920*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 973, "polynomial_expr": "(-34*x**3 - 38*x**2 + 40*x)*(8*x**3 + 27*x**2 - 20*x + 48)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-34*x**3 - 38*x**2 + 40*x)*(8*x**3 + 27*x**2 - 20*x + 48)\nExpanding the part (-34*x**3 - 38*x**2 + 40*x) using the distributive property, and we got: (40*x)*(8*x**3 + 27*x**2 - 20*x + 48) + (-38*x**2)*(8*x**3 + 27*x**2 - 20*x + 48) + (-34*x**3)*(8*x**3 + 27*x**2 - 20*x + 48)\n#Step 2:\nCurrent expression: (40*x)*(8*x**3 + 27*x**2 - 20*x + 48) + (-38*x**2)*(8*x**3 + 27*x**2 - 20*x + 48) + (-34*x**3)*(8*x**3 + 27*x**2 - 20*x + 48)\nSimplifying the partial expression: (-38*x**2)*(8*x**3 + 27*x**2 - 20*x + 48)\nExpanding the part (8*x**3 + 27*x**2 - 20*x + 48) using the distributive property, and we got: (-20*x)*(-38*x**2) + 48*(-38*x**2) + (-38*x**2)*(27*x**2) + (-38*x**2)*(8*x**3)\nReplacing (-38*x**2)*(8*x**3 + 27*x**2 - 20*x + 48) with (-20*x)*(-38*x**2) + 48*(-38*x**2) + (-38*x**2)*(27*x**2) + (-38*x**2)*(8*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-20*x)*(-38*x**2) + 48*(-38)*x**2 + (40*x)*(8*x**3 + 27*x**2 - 20*x + 48) + (-38*x**2)*(27*x**2) + (-38*x**2)*(8*x**3) + (-34*x**3)*(8*x**3 + 27*x**2 - 20*x + 48)\nSimplifying the partial expression: (-34*x**3)*(8*x**3 + 27*x**2 - 20*x + 48)\nExpanding the part (8*x**3 + 27*x**2 - 20*x + 48) using the distributive property, and we got: (-20*x)*(-34*x**3) + 48*(-34*x**3) + (27*x**2)*(-34*x**3) + (-34*x**3)*(8*x**3)\nReplacing (-34*x**3)*(8*x**3 + 27*x**2 - 20*x + 48) with (-20*x)*(-34*x**3) + 48*(-34*x**3) + (27*x**2)*(-34*x**3) + (-34*x**3)*(8*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-20*x)*(-38*x**2) + (-20*x)*(-34*x**3) + 48*(-34)*x**3 + 48*(-38)*x**2 + (40*x)*(8*x**3 + 27*x**2 - 20*x + 48) + (-38*x**2)*(27*x**2) + (-38*x**2)*(8*x**3) + (27*x**2)*(-34*x**3) + (-34*x**3)*(8*x**3)\nSimplifying the partial expression: (40*x)*(8*x**3 + 27*x**2 - 20*x + 48)\nExpanding the part (8*x**3 + 27*x**2 - 20*x + 48) using the distributive property, and we got: (-20*x)*(40*x) + 48*(40*x) + (40*x)*(27*x**2) + (40*x)*(8*x**3)\nReplacing (40*x)*(8*x**3 + 27*x**2 - 20*x + 48) with (-20*x)*(40*x) + 48*(40*x) + (40*x)*(27*x**2) + (40*x)*(8*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-20*x)*(40*x) + (-20*x)*(-38*x**2) + (-20*x)*(-34*x**3) + 48*(-34)*x**3 + 48*(-38)*x**2 + 48*40*x + (40*x)*(27*x**2) + (40*x)*(8*x**3) + (-38*x**2)*(27*x**2) + (-38*x**2)*(8*x**3) + (27*x**2)*(-34*x**3) + (-34*x**3)*(8*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*x)*(-38*x**2) = 760*x**3\n (-20*x)*(-34*x**3) = 680*x**4\n (-20*x)*(40*x) = -800*x**2\n (8*x**3)*(-38*x**2) = -304*x**5\n (8*x**3)*(-34*x**3) = -272*x**6\n (8*x**3)*(40*x) = 320*x**4\n (27*x**2)*(-38*x**2) = -1026*x**4\n (27*x**2)*(-34*x**3) = -918*x**5\n (27*x**2)*(40*x) = 1080*x**3\n 48*-38*x**2 = -1824*x**2\n 48*-34*x**3 = -1632*x**3\n 48*40*x = 1920*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -272*x**6 - 918*x**5 - 304*x**5 - 1026*x**4 + 320*x**4 + 680*x**4 - 1632*x**3 + 760*x**3 + 1080*x**3 - 1824*x**2 - 800*x**2 + 1920*x\nCombining like terms, got -272*x**6 - 1222*x**5 - 26*x**4 + 208*x**3 - 2624*x**2 + 1920*x\n#Step 7:\nCurrent expression: -272*x**6 - 1222*x**5 - 26*x**4 + 208*x**3 - 2624*x**2 + 1920*x\nNo more calculations needed.\n-272*x**6 - 1222*x**5 - 26*x**4 + 208*x**3 - 2624*x**2 + 1920*x", "generated_answer": "-272*x**6 - 1222*x**5 - 26*x**4 + 208*x**3 - 2624*x**2 + 1920*x", "step_length": 7} {"cot_id": "0e27b66c0c1eb45795f60c1a10b06c9281b47d93df911df416567cf7b82d7129", "datapoint": {"question": "Calculate the following: (-74*y**3 + 49*y**2 + 23)*(12*y**3 - 21*y + 40)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-888*y**6 + 588*y**5 + 1554*y**4 - 3713*y**3 + 1960*y**2 - 483*y + 920", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 974, "polynomial_expr": "(-74*y**3 + 49*y**2 + 23)*(12*y**3 - 21*y + 40)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-74*y**3 + 49*y**2 + 23)*(12*y**3 - 21*y + 40)\nExpanding the part (-74*y**3 + 49*y**2 + 23) using the distributive property, and we got: (49*y**2)*(12*y**3 - 21*y + 40) + (-74*y**3)*(12*y**3 - 21*y + 40) + 23*(12*y**3 - 21*y + 40)\n#Step 2:\nCurrent expression: (49*y**2)*(12*y**3 - 21*y + 40) + (-74*y**3)*(12*y**3 - 21*y + 40) + 23*(12*y**3 - 21*y + 40)\nSimplifying the partial expression: 23*(12*y**3 - 21*y + 40)\nExpanding the part (12*y**3 - 21*y + 40) using the distributive property, and we got: -21*y*23 + (12*y**3)*23 + 40*23\nReplacing 23*(12*y**3 - 21*y + 40) with -21*y*23 + (12*y**3)*23 + 40*23 in the overall expression.\n#Step 3:\nCurrent expression: -21*y*23 + (49*y**2)*(12*y**3 - 21*y + 40) + (-74*y**3)*(12*y**3 - 21*y + 40) + (12*y**3)*23 + 920\nSimplifying the partial expression: (-74*y**3)*(12*y**3 - 21*y + 40)\nExpanding the part (12*y**3 - 21*y + 40) using the distributive property, and we got: (-21*y)*(-74*y**3) + 40*(-74*y**3) + (-74*y**3)*(12*y**3)\nReplacing (-74*y**3)*(12*y**3 - 21*y + 40) with (-21*y)*(-74*y**3) + 40*(-74*y**3) + (-74*y**3)*(12*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-21*y)*(-74*y**3) - 21*y*23 + 40*(-74)*y**3 + (49*y**2)*(12*y**3 - 21*y + 40) + (-74*y**3)*(12*y**3) + (12*y**3)*23 + 920\nSimplifying the partial expression: (49*y**2)*(12*y**3 - 21*y + 40)\nExpanding the part (12*y**3 - 21*y + 40) using the distributive property, and we got: (-21*y)*(49*y**2) + 40*(49*y**2) + (49*y**2)*(12*y**3)\nReplacing (49*y**2)*(12*y**3 - 21*y + 40) with (-21*y)*(49*y**2) + 40*(49*y**2) + (49*y**2)*(12*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-21*y)*(49*y**2) + (-21*y)*(-74*y**3) - 21*y*23 + 40*(-74)*y**3 + 40*49*y**2 + (49*y**2)*(12*y**3) + (-74*y**3)*(12*y**3) + (12*y**3)*23 + 920\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-21*y)*23 = -483*y\n (-21*y)*(-74*y**3) = 1554*y**4\n (-21*y)*(49*y**2) = -1029*y**3\n (12*y**3)*23 = 276*y**3\n (12*y**3)*(-74*y**3) = -888*y**6\n (12*y**3)*(49*y**2) = 588*y**5\n 40*-74*y**3 = -2960*y**3\n 40*49*y**2 = 1960*y**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -888*y**6 + 588*y**5 + 1554*y**4 - 2960*y**3 - 1029*y**3 + 276*y**3 + 1960*y**2 - 483*y + 920\nCombining like terms, got -888*y**6 + 588*y**5 + 1554*y**4 - 3713*y**3 + 1960*y**2 - 483*y + 920\n#Step 7:\nCurrent expression: -888*y**6 + 588*y**5 + 1554*y**4 - 3713*y**3 + 1960*y**2 - 483*y + 920\nNo more calculations needed.\n-888*y**6 + 588*y**5 + 1554*y**4 - 3713*y**3 + 1960*y**2 - 483*y + 920", "generated_answer": "-888*y**6 + 588*y**5 + 1554*y**4 - 3713*y**3 + 1960*y**2 - 483*y + 920", "step_length": 7} {"cot_id": "cc6cf1b97c8ef912a4f76fb4cfb624c9cd1001602373491b8e696ace2743e490", "datapoint": {"question": "Calculate the following: 12*y*(34*y**2 + 43*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "408*y**3 + 516*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 975, "polynomial_expr": "12*y*(34*y**2 + 43*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 12*y*(34*y**2 + 43*y)\nExpanding the part (34*y**2 + 43*y) using the distributive property, and we got: (12*y)*(43*y) + (12*y)*(34*y**2)\n#Step 2:\nCurrent expression: (12*y)*(43*y) + (12*y)*(34*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (34*y**2)*(12*y) = 408*y**3\n (43*y)*(12*y) = 516*y**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 408*y**3 + 516*y**2\nNo more calculations needed.\n408*y**3 + 516*y**2", "generated_answer": "408*y**3 + 516*y**2", "step_length": 3} {"cot_id": "9ed4f5817e70b201423c4e7daebbfd76d62e6c9e58ce8b9a8b827ce9e7891b78", "datapoint": {"question": "Simplify this expression: (25*y**3 + 25*y + 3)*(49*y**3 - 12*y**2 + 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1225*y**6 - 300*y**5 + 1225*y**4 + 547*y**3 - 36*y**2 + 700*y + 84", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 976, "polynomial_expr": "(25*y**3 + 25*y + 3)*(49*y**3 - 12*y**2 + 28)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (25*y**3 + 25*y + 3)*(49*y**3 - 12*y**2 + 28)\nExpanding the part (25*y**3 + 25*y + 3) using the distributive property, and we got: (25*y)*(49*y**3 - 12*y**2 + 28) + (25*y**3)*(49*y**3 - 12*y**2 + 28) + 3*(49*y**3 - 12*y**2 + 28)\n#Step 2:\nCurrent expression: (25*y)*(49*y**3 - 12*y**2 + 28) + (25*y**3)*(49*y**3 - 12*y**2 + 28) + 3*(49*y**3 - 12*y**2 + 28)\nSimplifying the partial expression: 3*(49*y**3 - 12*y**2 + 28)\nExpanding the part (49*y**3 - 12*y**2 + 28) using the distributive property, and we got: -12*y**2*3 + (49*y**3)*3 + 28*3\nReplacing 3*(49*y**3 - 12*y**2 + 28) with -12*y**2*3 + (49*y**3)*3 + 28*3 in the overall expression.\n#Step 3:\nCurrent expression: (25*y)*(49*y**3 - 12*y**2 + 28) - 12*y**2*3 + (25*y**3)*(49*y**3 - 12*y**2 + 28) + (49*y**3)*3 + 84\nSimplifying the partial expression: (25*y)*(49*y**3 - 12*y**2 + 28)\nExpanding the part (49*y**3 - 12*y**2 + 28) using the distributive property, and we got: 28*(25*y) + (25*y)*(-12*y**2) + (25*y)*(49*y**3)\nReplacing (25*y)*(49*y**3 - 12*y**2 + 28) with 28*(25*y) + (25*y)*(-12*y**2) + (25*y)*(49*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 28*25*y + (25*y)*(-12*y**2) + (25*y)*(49*y**3) - 12*y**2*3 + (25*y**3)*(49*y**3 - 12*y**2 + 28) + (49*y**3)*3 + 84\nSimplifying the partial expression: (25*y**3)*(49*y**3 - 12*y**2 + 28)\nExpanding the part (49*y**3 - 12*y**2 + 28) using the distributive property, and we got: 28*(25*y**3) + (-12*y**2)*(25*y**3) + (25*y**3)*(49*y**3)\nReplacing (25*y**3)*(49*y**3 - 12*y**2 + 28) with 28*(25*y**3) + (-12*y**2)*(25*y**3) + (25*y**3)*(49*y**3) in the overall expression.\n#Step 5:\nCurrent expression: 28*25*y**3 + 28*25*y + (25*y)*(-12*y**2) + (25*y)*(49*y**3) + (-12*y**2)*(25*y**3) - 12*y**2*3 + (25*y**3)*(49*y**3) + (49*y**3)*3 + 84\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*y**2)*3 = -36*y**2\n (-12*y**2)*(25*y) = -300*y**3\n (-12*y**2)*(25*y**3) = -300*y**5\n (49*y**3)*3 = 147*y**3\n (49*y**3)*(25*y) = 1225*y**4\n (49*y**3)*(25*y**3) = 1225*y**6\n 28*25*y = 700*y\n 28*25*y**3 = 700*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1225*y**6 - 300*y**5 + 1225*y**4 - 300*y**3 + 147*y**3 + 700*y**3 - 36*y**2 + 700*y + 84\nCombining like terms, got 1225*y**6 - 300*y**5 + 1225*y**4 + 547*y**3 - 36*y**2 + 700*y + 84\n#Step 7:\nCurrent expression: 1225*y**6 - 300*y**5 + 1225*y**4 + 547*y**3 - 36*y**2 + 700*y + 84\nNo more calculations needed.\n1225*y**6 - 300*y**5 + 1225*y**4 + 547*y**3 - 36*y**2 + 700*y + 84", "generated_answer": "1225*y**6 - 300*y**5 + 1225*y**4 + 547*y**3 - 36*y**2 + 700*y + 84", "step_length": 7} {"cot_id": "95258acbb755838dfb15bcbbbee869ef67bdc69d2926fc004945f4ec25c3b2a4", "datapoint": {"question": "Simplify this expression: -700*x**3 - 1596*x**2\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-700*x**3 - 1596*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 977, "polynomial_expr": "-700*x**3 - 1596*x**2", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -700*x**3 - 1596*x**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -700*x**3 - 1596*x**2\nNo more calculations needed.\n-700*x**3 - 1596*x**2", "generated_answer": "-700*x**3 - 1596*x**2", "step_length": 2} {"cot_id": "269276ed321656b1a42629288d3a2164eccbca49ea3a23dffe4f780efcd9a4eb", "datapoint": {"question": "Simplify this expression: (74*x**3 + 19)*(-20*x**3 + 9*x - 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1480*x**6 + 666*x**4 - 2748*x**3 + 171*x - 608", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 978, "polynomial_expr": "(74*x**3 + 19)*(-20*x**3 + 9*x - 32)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (74*x**3 + 19)*(-20*x**3 + 9*x - 32)\nExpanding the part (74*x**3 + 19) using the distributive property, and we got: (74*x**3)*(-20*x**3 + 9*x - 32) + 19*(-20*x**3 + 9*x - 32)\n#Step 2:\nCurrent expression: (74*x**3)*(-20*x**3 + 9*x - 32) + 19*(-20*x**3 + 9*x - 32)\nSimplifying the partial expression: 19*(-20*x**3 + 9*x - 32)\nExpanding the part (-20*x**3 + 9*x - 32) using the distributive property, and we got: (9*x)*19 - 20*x**3*19 - 32*19\nReplacing 19*(-20*x**3 + 9*x - 32) with (9*x)*19 - 20*x**3*19 - 32*19 in the overall expression.\n#Step 3:\nCurrent expression: (9*x)*19 - 20*x**3*19 + (74*x**3)*(-20*x**3 + 9*x - 32) - 608\nSimplifying the partial expression: (74*x**3)*(-20*x**3 + 9*x - 32)\nExpanding the part (-20*x**3 + 9*x - 32) using the distributive property, and we got: -2368*x**3 + (9*x)*(74*x**3) + (-20*x**3)*(74*x**3)\nReplacing (74*x**3)*(-20*x**3 + 9*x - 32) with -2368*x**3 + (9*x)*(74*x**3) + (-20*x**3)*(74*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -32*74*x**3 + (9*x)*(74*x**3) + (9*x)*19 + (-20*x**3)*(74*x**3) - 20*x**3*19 - 608\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*x**3)*19 = -380*x**3\n (-20*x**3)*(74*x**3) = -1480*x**6\n (9*x)*19 = 171*x\n (9*x)*(74*x**3) = 666*x**4\n -32*74*x**3 = -2368*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1480*x**6 + 666*x**4 - 2368*x**3 - 380*x**3 + 171*x - 608\nCombining like terms, got -1480*x**6 + 666*x**4 - 2748*x**3 + 171*x - 608\n#Step 6:\nCurrent expression: -1480*x**6 + 666*x**4 - 2748*x**3 + 171*x - 608\nNo more calculations needed.\n-1480*x**6 + 666*x**4 - 2748*x**3 + 171*x - 608", "generated_answer": "-1480*x**6 + 666*x**4 - 2748*x**3 + 171*x - 608", "step_length": 6} {"cot_id": "155d2e7564e9a0b39729cc155e14910da764439425667b3edfe8f15a17705c17", "datapoint": {"question": "Calculate the following: (-43*z**3 - 47*z + 1)*(-22*z**3 + 39*z**2 - 14*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "946*z**6 - 1677*z**5 + 1636*z**4 - 1855*z**3 + 697*z**2 - 14*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 979, "polynomial_expr": "(-43*z**3 - 47*z + 1)*(-22*z**3 + 39*z**2 - 14*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-43*z**3 - 47*z + 1)*(-22*z**3 + 39*z**2 - 14*z)\nExpanding the part (-43*z**3 - 47*z + 1) using the distributive property, and we got: (-47*z)*(-22*z**3 + 39*z**2 - 14*z) + (-43*z**3)*(-22*z**3 + 39*z**2 - 14*z) + 1*(-22*z**3 + 39*z**2 - 14*z)\n#Step 2:\nCurrent expression: (-47*z)*(-22*z**3 + 39*z**2 - 14*z) + (-43*z**3)*(-22*z**3 + 39*z**2 - 14*z) + 1*(-22*z**3 + 39*z**2 - 14*z)\nSimplifying the partial expression: 1*(-22*z**3 + 39*z**2 - 14*z)\nExpanding the part (-22*z**3 + 39*z**2 - 14*z) using the distributive property, and we got: -14*z*1 + (39*z**2)*1 - 22*z**3*1\nReplacing 1*(-22*z**3 + 39*z**2 - 14*z) with -14*z*1 + (39*z**2)*1 - 22*z**3*1 in the overall expression.\n#Step 3:\nCurrent expression: (-47*z)*(-22*z**3 + 39*z**2 - 14*z) - 14*z*1 + (39*z**2)*1 + (-43*z**3)*(-22*z**3 + 39*z**2 - 14*z) - 22*z**3*1\nSimplifying the partial expression: (-47*z)*(-22*z**3 + 39*z**2 - 14*z)\nExpanding the part (-22*z**3 + 39*z**2 - 14*z) using the distributive property, and we got: (-47*z)*(-14*z) + (-47*z)*(39*z**2) + (-47*z)*(-22*z**3)\nReplacing (-47*z)*(-22*z**3 + 39*z**2 - 14*z) with (-47*z)*(-14*z) + (-47*z)*(39*z**2) + (-47*z)*(-22*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-47*z)*(-14*z) + (-47*z)*(39*z**2) + (-47*z)*(-22*z**3) - 14*z*1 + (39*z**2)*1 + (-43*z**3)*(-22*z**3 + 39*z**2 - 14*z) - 22*z**3*1\nSimplifying the partial expression: (-43*z**3)*(-22*z**3 + 39*z**2 - 14*z)\nExpanding the part (-22*z**3 + 39*z**2 - 14*z) using the distributive property, and we got: (-14*z)*(-43*z**3) + (39*z**2)*(-43*z**3) + (-43*z**3)*(-22*z**3)\nReplacing (-43*z**3)*(-22*z**3 + 39*z**2 - 14*z) with (-14*z)*(-43*z**3) + (39*z**2)*(-43*z**3) + (-43*z**3)*(-22*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-47*z)*(-14*z) + (-47*z)*(39*z**2) + (-47*z)*(-22*z**3) + (-14*z)*(-43*z**3) - 14*z*1 + (39*z**2)*(-43*z**3) + (39*z**2)*1 + (-43*z**3)*(-22*z**3) - 22*z**3*1\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*z**3)*1 = -22*z**3\n (-22*z**3)*(-47*z) = 1034*z**4\n (-22*z**3)*(-43*z**3) = 946*z**6\n (-14*z)*1 = -14*z\n (-14*z)*(-47*z) = 658*z**2\n (-14*z)*(-43*z**3) = 602*z**4\n (39*z**2)*1 = 39*z**2\n (39*z**2)*(-47*z) = -1833*z**3\n (39*z**2)*(-43*z**3) = -1677*z**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 946*z**6 - 1677*z**5 + 602*z**4 + 1034*z**4 - 1833*z**3 - 22*z**3 + 39*z**2 + 658*z**2 - 14*z\nCombining like terms, got 946*z**6 - 1677*z**5 + 1636*z**4 - 1855*z**3 + 697*z**2 - 14*z\n#Step 7:\nCurrent expression: 946*z**6 - 1677*z**5 + 1636*z**4 - 1855*z**3 + 697*z**2 - 14*z\nNo more calculations needed.\n946*z**6 - 1677*z**5 + 1636*z**4 - 1855*z**3 + 697*z**2 - 14*z", "generated_answer": "946*z**6 - 1677*z**5 + 1636*z**4 - 1855*z**3 + 697*z**2 - 14*z", "step_length": 7} {"cot_id": "5080189173ed13d6b2ae6339b6ac1c63d66bad733eb5eaca7731f2d23106883e", "datapoint": {"question": "Simplify this expression: 6*x**3*(-49*x**2 + 59*x - 23)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-294*x**5 + 354*x**4 - 138*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 980, "polynomial_expr": "6*x**3*(-49*x**2 + 59*x - 23)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 6*x**3*(-49*x**2 + 59*x - 23)\nExpanding the part (-49*x**2 + 59*x - 23) using the distributive property, and we got: -138*x**3 + (59*x)*(6*x**3) + (-49*x**2)*(6*x**3)\n#Step 2:\nCurrent expression: -138*x**3 + (59*x)*(6*x**3) + (-49*x**2)*(6*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -23*(6*x**3) = -138*x**3\n (-49*x**2)*(6*x**3) = -294*x**5\n (59*x)*(6*x**3) = 354*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -294*x**5 + 354*x**4 - 138*x**3\nNo more calculations needed.\n-294*x**5 + 354*x**4 - 138*x**3", "generated_answer": "-294*x**5 + 354*x**4 - 138*x**3", "step_length": 3} {"cot_id": "f9bbc507fe07eedc5aa33f6a908455a458267c69769d71f07b250a9dbbee5321", "datapoint": {"question": "Calculate the following: (-5*y - 51)*(-51*y**2 - 24*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "255*y**3 + 2721*y**2 + 1224*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 981, "polynomial_expr": "(-5*y - 51)*(-51*y**2 - 24*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-5*y - 51)*(-51*y**2 - 24*y)\nExpanding the part (-5*y - 51) using the distributive property, and we got: (-5*y)*(-51*y**2 - 24*y) - 51*(-51*y**2 - 24*y)\n#Step 2:\nCurrent expression: (-5*y)*(-51*y**2 - 24*y) - 51*(-51*y**2 - 24*y)\nSimplifying the partial expression: -51*(-51*y**2 - 24*y)\nExpanding the part (-51*y**2 - 24*y) using the distributive property, and we got: -24*y*(-51) - 51*y**2*(-51)\nReplacing -51*(-51*y**2 - 24*y) with -24*y*(-51) - 51*y**2*(-51) in the overall expression.\n#Step 3:\nCurrent expression: -24*y*(-51) + (-5*y)*(-51*y**2 - 24*y) - 51*y**2*(-51)\nSimplifying the partial expression: (-5*y)*(-51*y**2 - 24*y)\nExpanding the part (-51*y**2 - 24*y) using the distributive property, and we got: (-24*y)*(-5*y) + (-5*y)*(-51*y**2)\nReplacing (-5*y)*(-51*y**2 - 24*y) with (-24*y)*(-5*y) + (-5*y)*(-51*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-24*y)*(-5*y) - 24*y*(-51) + (-5*y)*(-51*y**2) - 51*y**2*(-51)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-51*y**2)*-51 = 2601*y**2\n (-51*y**2)*(-5*y) = 255*y**3\n (-24*y)*-51 = 1224*y\n (-24*y)*(-5*y) = 120*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 255*y**3 + 120*y**2 + 2601*y**2 + 1224*y\nCombining like terms, got 255*y**3 + 2721*y**2 + 1224*y\n#Step 6:\nCurrent expression: 255*y**3 + 2721*y**2 + 1224*y\nNo more calculations needed.\n255*y**3 + 2721*y**2 + 1224*y", "generated_answer": "255*y**3 + 2721*y**2 + 1224*y", "step_length": 6} {"cot_id": "ce301da2547b40fe529347d1de906d79ca4d62e042524db90e91d7782eec4873", "datapoint": {"question": "Simplify this expression: (29*x**2 - 27)*(-24*x**2 - 21*x + 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-696*x**4 - 609*x**3 + 851*x**2 + 567*x - 189", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 982, "polynomial_expr": "(29*x**2 - 27)*(-24*x**2 - 21*x + 7)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29*x**2 - 27)*(-24*x**2 - 21*x + 7)\nExpanding the part (29*x**2 - 27) using the distributive property, and we got: (29*x**2)*(-24*x**2 - 21*x + 7) - 27*(-24*x**2 - 21*x + 7)\n#Step 2:\nCurrent expression: (29*x**2)*(-24*x**2 - 21*x + 7) - 27*(-24*x**2 - 21*x + 7)\nSimplifying the partial expression: -27*(-24*x**2 - 21*x + 7)\nExpanding the part (-24*x**2 - 21*x + 7) using the distributive property, and we got: -21*x*(-27) - 24*x**2*(-27) + 7*(-27)\nReplacing -27*(-24*x**2 - 21*x + 7) with -21*x*(-27) - 24*x**2*(-27) + 7*(-27) in the overall expression.\n#Step 3:\nCurrent expression: -21*x*(-27) - 24*x**2*(-27) + (29*x**2)*(-24*x**2 - 21*x + 7) - 189\nSimplifying the partial expression: (29*x**2)*(-24*x**2 - 21*x + 7)\nExpanding the part (-24*x**2 - 21*x + 7) using the distributive property, and we got: (-21*x)*(29*x**2) + 7*(29*x**2) + (-24*x**2)*(29*x**2)\nReplacing (29*x**2)*(-24*x**2 - 21*x + 7) with (-21*x)*(29*x**2) + 7*(29*x**2) + (-24*x**2)*(29*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-21*x)*(29*x**2) - 21*x*(-27) + 7*29*x**2 + (-24*x**2)*(29*x**2) - 24*x**2*(-27) - 189\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-24*x**2)*-27 = 648*x**2\n (-24*x**2)*(29*x**2) = -696*x**4\n (-21*x)*-27 = 567*x\n (-21*x)*(29*x**2) = -609*x**3\n 7*29*x**2 = 203*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -696*x**4 - 609*x**3 + 203*x**2 + 648*x**2 + 567*x - 189\nCombining like terms, got -696*x**4 - 609*x**3 + 851*x**2 + 567*x - 189\n#Step 6:\nCurrent expression: -696*x**4 - 609*x**3 + 851*x**2 + 567*x - 189\nNo more calculations needed.\n-696*x**4 - 609*x**3 + 851*x**2 + 567*x - 189", "generated_answer": "-696*x**4 - 609*x**3 + 851*x**2 + 567*x - 189", "step_length": 6} {"cot_id": "d3dc95f716df27830ed126bbefd729393c9b597c3275c162432dee56f3461ab2", "datapoint": {"question": "Calculate the following: (14*x**2 - 41)*(-31*x**2 + 19*x + 22)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-434*x**4 + 266*x**3 + 1579*x**2 - 779*x - 902", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 983, "polynomial_expr": "(14*x**2 - 41)*(-31*x**2 + 19*x + 22)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14*x**2 - 41)*(-31*x**2 + 19*x + 22)\nExpanding the part (14*x**2 - 41) using the distributive property, and we got: (14*x**2)*(-31*x**2 + 19*x + 22) - 41*(-31*x**2 + 19*x + 22)\n#Step 2:\nCurrent expression: (14*x**2)*(-31*x**2 + 19*x + 22) - 41*(-31*x**2 + 19*x + 22)\nSimplifying the partial expression: -41*(-31*x**2 + 19*x + 22)\nExpanding the part (-31*x**2 + 19*x + 22) using the distributive property, and we got: (19*x)*(-41) - 31*x**2*(-41) + 22*(-41)\nReplacing -41*(-31*x**2 + 19*x + 22) with (19*x)*(-41) - 31*x**2*(-41) + 22*(-41) in the overall expression.\n#Step 3:\nCurrent expression: (19*x)*(-41) - 31*x**2*(-41) + (14*x**2)*(-31*x**2 + 19*x + 22) - 902\nSimplifying the partial expression: (14*x**2)*(-31*x**2 + 19*x + 22)\nExpanding the part (-31*x**2 + 19*x + 22) using the distributive property, and we got: 22*(14*x**2) + (19*x)*(14*x**2) + (-31*x**2)*(14*x**2)\nReplacing (14*x**2)*(-31*x**2 + 19*x + 22) with 22*(14*x**2) + (19*x)*(14*x**2) + (-31*x**2)*(14*x**2) in the overall expression.\n#Step 4:\nCurrent expression: 22*14*x**2 + (19*x)*(14*x**2) + (19*x)*(-41) + (-31*x**2)*(14*x**2) - 31*x**2*(-41) - 902\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-31*x**2)*-41 = 1271*x**2\n (-31*x**2)*(14*x**2) = -434*x**4\n (19*x)*-41 = -779*x\n (19*x)*(14*x**2) = 266*x**3\n 22*14*x**2 = 308*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -434*x**4 + 266*x**3 + 308*x**2 + 1271*x**2 - 779*x - 902\nCombining like terms, got -434*x**4 + 266*x**3 + 1579*x**2 - 779*x - 902\n#Step 6:\nCurrent expression: -434*x**4 + 266*x**3 + 1579*x**2 - 779*x - 902\nNo more calculations needed.\n-434*x**4 + 266*x**3 + 1579*x**2 - 779*x - 902", "generated_answer": "-434*x**4 + 266*x**3 + 1579*x**2 - 779*x - 902", "step_length": 6} {"cot_id": "f6427982182b8eb6b2f54d62dd854d9cdbc3b73819678e93235bb11985cfdd88", "datapoint": {"question": "Simplify this expression: (-43*x**3 + 39*x**2 + 19*x)*(27*x**3 - 25*x**2 - 21*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1161*x**6 + 2128*x**5 + 441*x**4 - 1294*x**3 - 399*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 984, "polynomial_expr": "(-43*x**3 + 39*x**2 + 19*x)*(27*x**3 - 25*x**2 - 21*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-43*x**3 + 39*x**2 + 19*x)*(27*x**3 - 25*x**2 - 21*x)\nExpanding the part (-43*x**3 + 39*x**2 + 19*x) using the distributive property, and we got: (19*x)*(27*x**3 - 25*x**2 - 21*x) + (39*x**2)*(27*x**3 - 25*x**2 - 21*x) + (-43*x**3)*(27*x**3 - 25*x**2 - 21*x)\n#Step 2:\nCurrent expression: (19*x)*(27*x**3 - 25*x**2 - 21*x) + (39*x**2)*(27*x**3 - 25*x**2 - 21*x) + (-43*x**3)*(27*x**3 - 25*x**2 - 21*x)\nSimplifying the partial expression: (-43*x**3)*(27*x**3 - 25*x**2 - 21*x)\nExpanding the part (27*x**3 - 25*x**2 - 21*x) using the distributive property, and we got: (-21*x)*(-43*x**3) + (-25*x**2)*(-43*x**3) + (-43*x**3)*(27*x**3)\nReplacing (-43*x**3)*(27*x**3 - 25*x**2 - 21*x) with (-21*x)*(-43*x**3) + (-25*x**2)*(-43*x**3) + (-43*x**3)*(27*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-21*x)*(-43*x**3) + (19*x)*(27*x**3 - 25*x**2 - 21*x) + (-25*x**2)*(-43*x**3) + (39*x**2)*(27*x**3 - 25*x**2 - 21*x) + (-43*x**3)*(27*x**3)\nSimplifying the partial expression: (19*x)*(27*x**3 - 25*x**2 - 21*x)\nExpanding the part (27*x**3 - 25*x**2 - 21*x) using the distributive property, and we got: (-21*x)*(19*x) + (19*x)*(-25*x**2) + (19*x)*(27*x**3)\nReplacing (19*x)*(27*x**3 - 25*x**2 - 21*x) with (-21*x)*(19*x) + (19*x)*(-25*x**2) + (19*x)*(27*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-21*x)*(19*x) + (-21*x)*(-43*x**3) + (19*x)*(-25*x**2) + (19*x)*(27*x**3) + (-25*x**2)*(-43*x**3) + (39*x**2)*(27*x**3 - 25*x**2 - 21*x) + (-43*x**3)*(27*x**3)\nSimplifying the partial expression: (39*x**2)*(27*x**3 - 25*x**2 - 21*x)\nExpanding the part (27*x**3 - 25*x**2 - 21*x) using the distributive property, and we got: (-21*x)*(39*x**2) + (-25*x**2)*(39*x**2) + (39*x**2)*(27*x**3)\nReplacing (39*x**2)*(27*x**3 - 25*x**2 - 21*x) with (-21*x)*(39*x**2) + (-25*x**2)*(39*x**2) + (39*x**2)*(27*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-21*x)*(19*x) + (-21*x)*(39*x**2) + (-21*x)*(-43*x**3) + (19*x)*(-25*x**2) + (19*x)*(27*x**3) + (-25*x**2)*(39*x**2) + (-25*x**2)*(-43*x**3) + (39*x**2)*(27*x**3) + (-43*x**3)*(27*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*x**2)*(-43*x**3) = 1075*x**5\n (-25*x**2)*(19*x) = -475*x**3\n (-25*x**2)*(39*x**2) = -975*x**4\n (-21*x)*(-43*x**3) = 903*x**4\n (-21*x)*(19*x) = -399*x**2\n (-21*x)*(39*x**2) = -819*x**3\n (27*x**3)*(-43*x**3) = -1161*x**6\n (27*x**3)*(19*x) = 513*x**4\n (27*x**3)*(39*x**2) = 1053*x**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1161*x**6 + 1053*x**5 + 1075*x**5 - 975*x**4 + 513*x**4 + 903*x**4 - 819*x**3 - 475*x**3 - 399*x**2\nCombining like terms, got -1161*x**6 + 2128*x**5 + 441*x**4 - 1294*x**3 - 399*x**2\n#Step 7:\nCurrent expression: -1161*x**6 + 2128*x**5 + 441*x**4 - 1294*x**3 - 399*x**2\nNo more calculations needed.\n-1161*x**6 + 2128*x**5 + 441*x**4 - 1294*x**3 - 399*x**2", "generated_answer": "-1161*x**6 + 2128*x**5 + 441*x**4 - 1294*x**3 - 399*x**2", "step_length": 7} {"cot_id": "afe004f3b68e87ba5cb1dfe43b543b190551a4f8dea9188158096c13ef593307", "datapoint": {"question": "Calculate the following: 4*x**3*(18*x**3 - 38*x**2 + 83*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "72*x**6 - 152*x**5 + 332*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 985, "polynomial_expr": "4*x**3*(18*x**3 - 38*x**2 + 83*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 4*x**3*(18*x**3 - 38*x**2 + 83*x)\nExpanding the part (18*x**3 - 38*x**2 + 83*x) using the distributive property, and we got: (83*x)*(4*x**3) + (-38*x**2)*(4*x**3) + (4*x**3)*(18*x**3)\n#Step 2:\nCurrent expression: (83*x)*(4*x**3) + (-38*x**2)*(4*x**3) + (4*x**3)*(18*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*x**2)*(4*x**3) = -152*x**5\n (18*x**3)*(4*x**3) = 72*x**6\n (83*x)*(4*x**3) = 332*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 72*x**6 - 152*x**5 + 332*x**4\nNo more calculations needed.\n72*x**6 - 152*x**5 + 332*x**4", "generated_answer": "72*x**6 - 152*x**5 + 332*x**4", "step_length": 3} {"cot_id": "9410d52578db3803841828a800d484f7da2718c5469860fcc694cbb4ea3c6e3c", "datapoint": {"question": "Simplify this expression: (-37*y**3 + 7*y)*(48*y**3 + 35*y**2 - 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1776*y**6 - 1295*y**5 + 336*y**4 + 874*y**3 - 119*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 986, "polynomial_expr": "(-37*y**3 + 7*y)*(48*y**3 + 35*y**2 - 17)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-37*y**3 + 7*y)*(48*y**3 + 35*y**2 - 17)\nExpanding the part (-37*y**3 + 7*y) using the distributive property, and we got: (7*y)*(48*y**3 + 35*y**2 - 17) + (-37*y**3)*(48*y**3 + 35*y**2 - 17)\n#Step 2:\nCurrent expression: (7*y)*(48*y**3 + 35*y**2 - 17) + (-37*y**3)*(48*y**3 + 35*y**2 - 17)\nSimplifying the partial expression: (-37*y**3)*(48*y**3 + 35*y**2 - 17)\nExpanding the part (48*y**3 + 35*y**2 - 17) using the distributive property, and we got: -(-1)*629*y**3 + (35*y**2)*(-37*y**3) + (-37*y**3)*(48*y**3)\nReplacing (-37*y**3)*(48*y**3 + 35*y**2 - 17) with -(-1)*629*y**3 + (35*y**2)*(-37*y**3) + (-37*y**3)*(48*y**3) in the overall expression.\n#Step 3:\nCurrent expression: -17*(-37)*y**3 + (7*y)*(48*y**3 + 35*y**2 - 17) + (35*y**2)*(-37*y**3) + (-37*y**3)*(48*y**3)\nSimplifying the partial expression: (7*y)*(48*y**3 + 35*y**2 - 17)\nExpanding the part (48*y**3 + 35*y**2 - 17) using the distributive property, and we got: -119*y + (7*y)*(35*y**2) + (7*y)*(48*y**3)\nReplacing (7*y)*(48*y**3 + 35*y**2 - 17) with -119*y + (7*y)*(35*y**2) + (7*y)*(48*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -17*(-37)*y**3 - 17*7*y + (7*y)*(35*y**2) + (7*y)*(48*y**3) + (35*y**2)*(-37*y**3) + (-37*y**3)*(48*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (35*y**2)*(-37*y**3) = -1295*y**5\n (35*y**2)*(7*y) = 245*y**3\n (48*y**3)*(-37*y**3) = -1776*y**6\n (48*y**3)*(7*y) = 336*y**4\n -17*-37*y**3 = 629*y**3\n -17*7*y = -119*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1776*y**6 - 1295*y**5 + 336*y**4 + 245*y**3 + 629*y**3 - 119*y\nCombining like terms, got -1776*y**6 - 1295*y**5 + 336*y**4 + 874*y**3 - 119*y\n#Step 6:\nCurrent expression: -1776*y**6 - 1295*y**5 + 336*y**4 + 874*y**3 - 119*y\nNo more calculations needed.\n-1776*y**6 - 1295*y**5 + 336*y**4 + 874*y**3 - 119*y", "generated_answer": "-1776*y**6 - 1295*y**5 + 336*y**4 + 874*y**3 - 119*y", "step_length": 6} {"cot_id": "af9a24589bad0d8d963049e8d17dd7c412a7e5aea37b3eda0c2501f2a00d902b", "datapoint": {"question": "Simplify this expression: (42*z**3 - 43*z**2)*(19*z**2 - 7*z + 40)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "798*z**5 - 1111*z**4 + 1981*z**3 - 1720*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 987, "polynomial_expr": "(42*z**3 - 43*z**2)*(19*z**2 - 7*z + 40)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (42*z**3 - 43*z**2)*(19*z**2 - 7*z + 40)\nExpanding the part (42*z**3 - 43*z**2) using the distributive property, and we got: (-43*z**2)*(19*z**2 - 7*z + 40) + (42*z**3)*(19*z**2 - 7*z + 40)\n#Step 2:\nCurrent expression: (-43*z**2)*(19*z**2 - 7*z + 40) + (42*z**3)*(19*z**2 - 7*z + 40)\nSimplifying the partial expression: (-43*z**2)*(19*z**2 - 7*z + 40)\nExpanding the part (19*z**2 - 7*z + 40) using the distributive property, and we got: (-7*z)*(-43*z**2) + 40*(-43*z**2) + (-43*z**2)*(19*z**2)\nReplacing (-43*z**2)*(19*z**2 - 7*z + 40) with (-7*z)*(-43*z**2) + 40*(-43*z**2) + (-43*z**2)*(19*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-7*z)*(-43*z**2) + 40*(-43)*z**2 + (-43*z**2)*(19*z**2) + (42*z**3)*(19*z**2 - 7*z + 40)\nSimplifying the partial expression: (42*z**3)*(19*z**2 - 7*z + 40)\nExpanding the part (19*z**2 - 7*z + 40) using the distributive property, and we got: (-7*z)*(42*z**3) + 40*(42*z**3) + (19*z**2)*(42*z**3)\nReplacing (42*z**3)*(19*z**2 - 7*z + 40) with (-7*z)*(42*z**3) + 40*(42*z**3) + (19*z**2)*(42*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-7*z)*(-43*z**2) + (-7*z)*(42*z**3) + 40*42*z**3 + 40*(-43)*z**2 + (-43*z**2)*(19*z**2) + (19*z**2)*(42*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-7*z)*(-43*z**2) = 301*z**3\n (-7*z)*(42*z**3) = -294*z**4\n (19*z**2)*(-43*z**2) = -817*z**4\n (19*z**2)*(42*z**3) = 798*z**5\n 40*-43*z**2 = -1720*z**2\n 40*42*z**3 = 1680*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 798*z**5 - 817*z**4 - 294*z**4 + 301*z**3 + 1680*z**3 - 1720*z**2\nCombining like terms, got 798*z**5 - 1111*z**4 + 1981*z**3 - 1720*z**2\n#Step 6:\nCurrent expression: 798*z**5 - 1111*z**4 + 1981*z**3 - 1720*z**2\nNo more calculations needed.\n798*z**5 - 1111*z**4 + 1981*z**3 - 1720*z**2", "generated_answer": "798*z**5 - 1111*z**4 + 1981*z**3 - 1720*z**2", "step_length": 6} {"cot_id": "30d215132130ce97719591060ad1644b3098c498b84db5cd67ce7e5c6cfafcb8", "datapoint": {"question": "Simplify this expression: (5*x**3 - 49*x**2)*(29*x**3 + 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "145*x**6 - 1421*x**5 + 195*x**3 - 1911*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 988, "polynomial_expr": "(5*x**3 - 49*x**2)*(29*x**3 + 39)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (5*x**3 - 49*x**2)*(29*x**3 + 39)\nExpanding the part (29*x**3 + 39) using the distributive property, and we got: (29*x**3)*(5*x**3 - 49*x**2) + 39*(5*x**3 - 49*x**2)\n#Step 2:\nCurrent expression: (29*x**3)*(5*x**3 - 49*x**2) + 39*(5*x**3 - 49*x**2)\nSimplifying the partial expression: 39*(5*x**3 - 49*x**2)\nExpanding the part (5*x**3 - 49*x**2) using the distributive property, and we got: -49*x**2*39 + (5*x**3)*39\nReplacing 39*(5*x**3 - 49*x**2) with -49*x**2*39 + (5*x**3)*39 in the overall expression.\n#Step 3:\nCurrent expression: -49*x**2*39 + (5*x**3)*39 + (29*x**3)*(5*x**3 - 49*x**2)\nSimplifying the partial expression: (29*x**3)*(5*x**3 - 49*x**2)\nExpanding the part (5*x**3 - 49*x**2) using the distributive property, and we got: (-49*x**2)*(29*x**3) + (5*x**3)*(29*x**3)\nReplacing (29*x**3)*(5*x**3 - 49*x**2) with (-49*x**2)*(29*x**3) + (5*x**3)*(29*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-49*x**2)*(29*x**3) - 49*x**2*39 + (5*x**3)*(29*x**3) + (5*x**3)*39\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*x**2)*39 = -1911*x**2\n (-49*x**2)*(29*x**3) = -1421*x**5\n (5*x**3)*39 = 195*x**3\n (5*x**3)*(29*x**3) = 145*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 145*x**6 - 1421*x**5 + 195*x**3 - 1911*x**2\nNo more calculations needed.\n145*x**6 - 1421*x**5 + 195*x**3 - 1911*x**2", "generated_answer": "145*x**6 - 1421*x**5 + 195*x**3 - 1911*x**2", "step_length": 5} {"cot_id": "c7a6927f3fe12d1610fcb6d590a4a1fe905d1d7f90595cf46dfc384b0a908ee7", "datapoint": {"question": "Simplify this expression: -45*z*(12*z**3 + 4*z**2 + 30*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-540*z**4 - 180*z**3 - 1350*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 989, "polynomial_expr": "-45*z*(12*z**3 + 4*z**2 + 30*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -45*z*(12*z**3 + 4*z**2 + 30*z)\nExpanding the part (12*z**3 + 4*z**2 + 30*z) using the distributive property, and we got: (-45*z)*(30*z) + (-45*z)*(4*z**2) + (-45*z)*(12*z**3)\n#Step 2:\nCurrent expression: (-45*z)*(30*z) + (-45*z)*(4*z**2) + (-45*z)*(12*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (4*z**2)*(-45*z) = -180*z**3\n (12*z**3)*(-45*z) = -540*z**4\n (30*z)*(-45*z) = -1350*z**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -540*z**4 - 180*z**3 - 1350*z**2\nNo more calculations needed.\n-540*z**4 - 180*z**3 - 1350*z**2", "generated_answer": "-540*z**4 - 180*z**3 - 1350*z**2", "step_length": 3} {"cot_id": "93f8a72aa9400a202dfa90ece03f1ed02266f04a82363d275acd46bd6291c5fd", "datapoint": {"question": "Simplify this expression: -1156*y**3 - 1700\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1156*y**3 - 1700", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 990, "polynomial_expr": "-1156*y**3 - 1700", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -1156*y**3 - 1700\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -1156*y**3 - 1700\nNo more calculations needed.\n-1156*y**3 - 1700", "generated_answer": "-1156*y**3 - 1700", "step_length": 2} {"cot_id": "faf50fa0f74a1931e6a0e547b328f8ac8d033eff403cdb56522f7f32d2b28f21", "datapoint": {"question": "Simplify this expression: 15*z**3 + 54*z**2 - 54\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "15*z**3 + 54*z**2 - 54", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 991, "polynomial_expr": "15*z**3 + 54*z**2 - 54", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 15*z**3 + 54*z**2 - 54\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 15*z**3 + 54*z**2 - 54\nNo more calculations needed.\n15*z**3 + 54*z**2 - 54", "generated_answer": "15*z**3 + 54*z**2 - 54", "step_length": 2} {"cot_id": "84fb2dfe0e0c9dbde878edfab96e348dfa6251b9f8a5c8ce038e2c21b2c13a78", "datapoint": {"question": "Calculate the following: 42*x**3*(-12*x**2 - 11*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-504*x**5 - 462*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 992, "polynomial_expr": "42*x**3*(-12*x**2 - 11*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 42*x**3*(-12*x**2 - 11*x)\nExpanding the part (-12*x**2 - 11*x) using the distributive property, and we got: (-11*x)*(42*x**3) + (-12*x**2)*(42*x**3)\n#Step 2:\nCurrent expression: (-11*x)*(42*x**3) + (-12*x**2)*(42*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*x**2)*(42*x**3) = -504*x**5\n (-11*x)*(42*x**3) = -462*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -504*x**5 - 462*x**4\nNo more calculations needed.\n-504*x**5 - 462*x**4", "generated_answer": "-504*x**5 - 462*x**4", "step_length": 3} {"cot_id": "ddbee55c1d01f36870247bca9e5e26a94e055f27fc1db6004ca2d9763608b549", "datapoint": {"question": "Calculate the following: (26*z - 17)*(25*z**3 - 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "650*z**4 - 425*z**3 - 442*z + 289", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 993, "polynomial_expr": "(26*z - 17)*(25*z**3 - 17)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (26*z - 17)*(25*z**3 - 17)\nExpanding the part (25*z**3 - 17) using the distributive property, and we got: (25*z**3)*(26*z - 17) - 17*(26*z - 17)\n#Step 2:\nCurrent expression: (25*z**3)*(26*z - 17) - 17*(26*z - 17)\nSimplifying the partial expression: -17*(26*z - 17)\nExpanding the part (26*z - 17) using the distributive property, and we got: (26*z)*(-17) - 17*(-17)\nReplacing -17*(26*z - 17) with (26*z)*(-17) - 17*(-17) in the overall expression.\n#Step 3:\nCurrent expression: (26*z)*(-17) + (25*z**3)*(26*z - 17) + 289\nSimplifying the partial expression: (25*z**3)*(26*z - 17)\nExpanding the part (26*z - 17) using the distributive property, and we got: -425*z**3 + (26*z)*(25*z**3)\nReplacing (25*z**3)*(26*z - 17) with -425*z**3 + (26*z)*(25*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -17*25*z**3 + (26*z)*(25*z**3) + (26*z)*(-17) + 289\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (26*z)*-17 = -442*z\n (26*z)*(25*z**3) = 650*z**4\n -17*25*z**3 = -425*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 650*z**4 - 425*z**3 - 442*z + 289\nNo more calculations needed.\n650*z**4 - 425*z**3 - 442*z + 289", "generated_answer": "650*z**4 - 425*z**3 - 442*z + 289", "step_length": 5} {"cot_id": "e8e28a55b98ee5529dd98b5df1c07f8bdc03d5553e6b73163c97b773d0073795", "datapoint": {"question": "Calculate the following: 663*y**3 - 663*y**2 - 1170\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "663*y**3 - 663*y**2 - 1170", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 994, "polynomial_expr": "663*y**3 - 663*y**2 - 1170", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 663*y**3 - 663*y**2 - 1170\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 663*y**3 - 663*y**2 - 1170\nNo more calculations needed.\n663*y**3 - 663*y**2 - 1170", "generated_answer": "663*y**3 - 663*y**2 - 1170", "step_length": 2} {"cot_id": "44d72d5bc70d4661ac1c21f78ddf15be922cc1ad5ab00e17380df0e47334cbea", "datapoint": {"question": "Calculate the following: -10*x*(23*x**2 - 32*x + 42)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-230*x**3 + 320*x**2 - 420*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 995, "polynomial_expr": "-10*x*(23*x**2 - 32*x + 42)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -10*x*(23*x**2 - 32*x + 42)\nExpanding the part (23*x**2 - 32*x + 42) using the distributive property, and we got: (-32*x)*(-10*x) + (-10*x)*(23*x**2) + 42*(-10*x)\n#Step 2:\nCurrent expression: (-32*x)*(-10*x) + (-10*x)*(23*x**2) + 42*(-10*x)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 42*(-10*x) = -420*x\n (-32*x)*(-10*x) = 320*x**2\n (23*x**2)*(-10*x) = -230*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -230*x**3 + 320*x**2 - 420*x\nNo more calculations needed.\n-230*x**3 + 320*x**2 - 420*x", "generated_answer": "-230*x**3 + 320*x**2 - 420*x", "step_length": 3} {"cot_id": "2d661673c5840982a2dc4d04516a8e88efb0b84183d363c0ac201eabbbdf8de3", "datapoint": {"question": "Simplify this expression: (4*x**3 - 10*x - 49)*(68*x**3 + 19*x**2 - 36*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "272*x**6 + 76*x**5 - 824*x**4 - 3522*x**3 - 571*x**2 + 1764*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 996, "polynomial_expr": "(4*x**3 - 10*x - 49)*(68*x**3 + 19*x**2 - 36*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (4*x**3 - 10*x - 49)*(68*x**3 + 19*x**2 - 36*x)\nExpanding the part (4*x**3 - 10*x - 49) using the distributive property, and we got: (-10*x)*(68*x**3 + 19*x**2 - 36*x) + (4*x**3)*(68*x**3 + 19*x**2 - 36*x) - 49*(68*x**3 + 19*x**2 - 36*x)\n#Step 2:\nCurrent expression: (-10*x)*(68*x**3 + 19*x**2 - 36*x) + (4*x**3)*(68*x**3 + 19*x**2 - 36*x) - 49*(68*x**3 + 19*x**2 - 36*x)\nSimplifying the partial expression: -49*(68*x**3 + 19*x**2 - 36*x)\nExpanding the part (68*x**3 + 19*x**2 - 36*x) using the distributive property, and we got: -36*x*(-49) + (19*x**2)*(-49) + (68*x**3)*(-49)\nReplacing -49*(68*x**3 + 19*x**2 - 36*x) with -36*x*(-49) + (19*x**2)*(-49) + (68*x**3)*(-49) in the overall expression.\n#Step 3:\nCurrent expression: -36*x*(-49) + (-10*x)*(68*x**3 + 19*x**2 - 36*x) + (19*x**2)*(-49) + (4*x**3)*(68*x**3 + 19*x**2 - 36*x) + (68*x**3)*(-49)\nSimplifying the partial expression: (-10*x)*(68*x**3 + 19*x**2 - 36*x)\nExpanding the part (68*x**3 + 19*x**2 - 36*x) using the distributive property, and we got: (-36*x)*(-10*x) + (-10*x)*(19*x**2) + (-10*x)*(68*x**3)\nReplacing (-10*x)*(68*x**3 + 19*x**2 - 36*x) with (-36*x)*(-10*x) + (-10*x)*(19*x**2) + (-10*x)*(68*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-36*x)*(-10*x) - 36*x*(-49) + (-10*x)*(19*x**2) + (-10*x)*(68*x**3) + (19*x**2)*(-49) + (4*x**3)*(68*x**3 + 19*x**2 - 36*x) + (68*x**3)*(-49)\nSimplifying the partial expression: (4*x**3)*(68*x**3 + 19*x**2 - 36*x)\nExpanding the part (68*x**3 + 19*x**2 - 36*x) using the distributive property, and we got: (-36*x)*(4*x**3) + (19*x**2)*(4*x**3) + (4*x**3)*(68*x**3)\nReplacing (4*x**3)*(68*x**3 + 19*x**2 - 36*x) with (-36*x)*(4*x**3) + (19*x**2)*(4*x**3) + (4*x**3)*(68*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-36*x)*(-10*x) + (-36*x)*(4*x**3) - 36*x*(-49) + (-10*x)*(19*x**2) + (-10*x)*(68*x**3) + (19*x**2)*(4*x**3) + (19*x**2)*(-49) + (4*x**3)*(68*x**3) + (68*x**3)*(-49)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*x)*-49 = 1764*x\n (-36*x)*(-10*x) = 360*x**2\n (-36*x)*(4*x**3) = -144*x**4\n (19*x**2)*-49 = -931*x**2\n (19*x**2)*(-10*x) = -190*x**3\n (19*x**2)*(4*x**3) = 76*x**5\n (68*x**3)*-49 = -3332*x**3\n (68*x**3)*(-10*x) = -680*x**4\n (68*x**3)*(4*x**3) = 272*x**6\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 272*x**6 + 76*x**5 - 680*x**4 - 144*x**4 - 3332*x**3 - 190*x**3 - 931*x**2 + 360*x**2 + 1764*x\nCombining like terms, got 272*x**6 + 76*x**5 - 824*x**4 - 3522*x**3 - 571*x**2 + 1764*x\n#Step 7:\nCurrent expression: 272*x**6 + 76*x**5 - 824*x**4 - 3522*x**3 - 571*x**2 + 1764*x\nNo more calculations needed.\n272*x**6 + 76*x**5 - 824*x**4 - 3522*x**3 - 571*x**2 + 1764*x", "generated_answer": "272*x**6 + 76*x**5 - 824*x**4 - 3522*x**3 - 571*x**2 + 1764*x", "step_length": 7} {"cot_id": "beec38d318d9145143598994632f8a1e4ef927bc5dc268e24242229e09c5f6d9", "datapoint": {"question": "Calculate the following: -70*z**3*(24*z**3 - 2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1680*z**6 + 140*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 997, "polynomial_expr": "-70*z**3*(24*z**3 - 2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -70*z**3*(24*z**3 - 2)\nExpanding the part (24*z**3 - 2) using the distributive property, and we got: -(-1)*140*z**3 + (-70*z**3)*(24*z**3)\n#Step 2:\nCurrent expression: -(-1)*140*z**3 + (-70*z**3)*(24*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -2*(-70*z**3) = 140*z**3\n (24*z**3)*(-70*z**3) = -1680*z**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1680*z**6 + 140*z**3\nNo more calculations needed.\n-1680*z**6 + 140*z**3", "generated_answer": "-1680*z**6 + 140*z**3", "step_length": 3} {"cot_id": "4df66f18896a595f69e5ed826db1cb048b770dd3f63af76fd830ee563d569b7b", "datapoint": {"question": "Simplify this expression: (24*y**3 + 19*y)*(18*y**3 + 12*y**2 - 39*y + 46)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "432*y**6 + 288*y**5 - 594*y**4 + 1332*y**3 - 741*y**2 + 874*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 998, "polynomial_expr": "(24*y**3 + 19*y)*(18*y**3 + 12*y**2 - 39*y + 46)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (24*y**3 + 19*y)*(18*y**3 + 12*y**2 - 39*y + 46)\nExpanding the part (24*y**3 + 19*y) using the distributive property, and we got: (19*y)*(18*y**3 + 12*y**2 - 39*y + 46) + (24*y**3)*(18*y**3 + 12*y**2 - 39*y + 46)\n#Step 2:\nCurrent expression: (19*y)*(18*y**3 + 12*y**2 - 39*y + 46) + (24*y**3)*(18*y**3 + 12*y**2 - 39*y + 46)\nSimplifying the partial expression: (19*y)*(18*y**3 + 12*y**2 - 39*y + 46)\nExpanding the part (18*y**3 + 12*y**2 - 39*y + 46) using the distributive property, and we got: (-39*y)*(19*y) + 46*(19*y) + (19*y)*(12*y**2) + (19*y)*(18*y**3)\nReplacing (19*y)*(18*y**3 + 12*y**2 - 39*y + 46) with (-39*y)*(19*y) + 46*(19*y) + (19*y)*(12*y**2) + (19*y)*(18*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-39*y)*(19*y) + 46*19*y + (19*y)*(12*y**2) + (19*y)*(18*y**3) + (24*y**3)*(18*y**3 + 12*y**2 - 39*y + 46)\nSimplifying the partial expression: (24*y**3)*(18*y**3 + 12*y**2 - 39*y + 46)\nExpanding the part (18*y**3 + 12*y**2 - 39*y + 46) using the distributive property, and we got: (-39*y)*(24*y**3) + 46*(24*y**3) + (12*y**2)*(24*y**3) + (18*y**3)*(24*y**3)\nReplacing (24*y**3)*(18*y**3 + 12*y**2 - 39*y + 46) with (-39*y)*(24*y**3) + 46*(24*y**3) + (12*y**2)*(24*y**3) + (18*y**3)*(24*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-39*y)*(19*y) + (-39*y)*(24*y**3) + 46*24*y**3 + 46*19*y + (19*y)*(12*y**2) + (19*y)*(18*y**3) + (12*y**2)*(24*y**3) + (18*y**3)*(24*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*y)*(19*y) = -741*y**2\n (-39*y)*(24*y**3) = -936*y**4\n (12*y**2)*(19*y) = 228*y**3\n (12*y**2)*(24*y**3) = 288*y**5\n (18*y**3)*(19*y) = 342*y**4\n (18*y**3)*(24*y**3) = 432*y**6\n 46*19*y = 874*y\n 46*24*y**3 = 1104*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 432*y**6 + 288*y**5 - 936*y**4 + 342*y**4 + 228*y**3 + 1104*y**3 - 741*y**2 + 874*y\nCombining like terms, got 432*y**6 + 288*y**5 - 594*y**4 + 1332*y**3 - 741*y**2 + 874*y\n#Step 6:\nCurrent expression: 432*y**6 + 288*y**5 - 594*y**4 + 1332*y**3 - 741*y**2 + 874*y\nNo more calculations needed.\n432*y**6 + 288*y**5 - 594*y**4 + 1332*y**3 - 741*y**2 + 874*y", "generated_answer": "432*y**6 + 288*y**5 - 594*y**4 + 1332*y**3 - 741*y**2 + 874*y", "step_length": 6} {"cot_id": "4b8cc388903ea6b6d9198466cf4205596ef59722aa1a3de6b55042f05b6b912b", "datapoint": {"question": "Simplify this expression: (19 - 59*y**3)*(-25*y**3 + 48*y**2 + 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1475*y**6 - 2832*y**5 - 829*y**3 + 912*y**2 + 114", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 999, "polynomial_expr": "(19 - 59*y**3)*(-25*y**3 + 48*y**2 + 6)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (19 - 59*y**3)*(-25*y**3 + 48*y**2 + 6)\nExpanding the part (19 - 59*y**3) using the distributive property, and we got: (-59*y**3)*(-25*y**3 + 48*y**2 + 6) + 19*(-25*y**3 + 48*y**2 + 6)\n#Step 2:\nCurrent expression: (-59*y**3)*(-25*y**3 + 48*y**2 + 6) + 19*(-25*y**3 + 48*y**2 + 6)\nSimplifying the partial expression: 19*(-25*y**3 + 48*y**2 + 6)\nExpanding the part (-25*y**3 + 48*y**2 + 6) using the distributive property, and we got: (48*y**2)*19 - 25*y**3*19 + 6*19\nReplacing 19*(-25*y**3 + 48*y**2 + 6) with (48*y**2)*19 - 25*y**3*19 + 6*19 in the overall expression.\n#Step 3:\nCurrent expression: (48*y**2)*19 + (-59*y**3)*(-25*y**3 + 48*y**2 + 6) - 25*y**3*19 + 114\nSimplifying the partial expression: (-59*y**3)*(-25*y**3 + 48*y**2 + 6)\nExpanding the part (-25*y**3 + 48*y**2 + 6) using the distributive property, and we got: 6*(-59*y**3) + (48*y**2)*(-59*y**3) + (-59*y**3)*(-25*y**3)\nReplacing (-59*y**3)*(-25*y**3 + 48*y**2 + 6) with 6*(-59*y**3) + (48*y**2)*(-59*y**3) + (-59*y**3)*(-25*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 6*(-59)*y**3 + (48*y**2)*(-59*y**3) + (48*y**2)*19 + (-59*y**3)*(-25*y**3) - 25*y**3*19 + 114\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*y**3)*19 = -475*y**3\n (-25*y**3)*(-59*y**3) = 1475*y**6\n (48*y**2)*19 = 912*y**2\n (48*y**2)*(-59*y**3) = -2832*y**5\n 6*-59*y**3 = -354*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1475*y**6 - 2832*y**5 - 475*y**3 - 354*y**3 + 912*y**2 + 114\nCombining like terms, got 1475*y**6 - 2832*y**5 - 829*y**3 + 912*y**2 + 114\n#Step 6:\nCurrent expression: 1475*y**6 - 2832*y**5 - 829*y**3 + 912*y**2 + 114\nNo more calculations needed.\n1475*y**6 - 2832*y**5 - 829*y**3 + 912*y**2 + 114", "generated_answer": "1475*y**6 - 2832*y**5 - 829*y**3 + 912*y**2 + 114", "step_length": 6} {"cot_id": "e0e2cca9083788db2bc47ccc6791dad65b6a935fa2ac96b7959b482837b7166b", "datapoint": {"question": "Simplify this expression: (21 - 32*x**2)*(32*x**3 + 4*x**2 - 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1024*x**5 - 128*x**4 + 672*x**3 + 1652*x**2 - 1029", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1000, "polynomial_expr": "(21 - 32*x**2)*(32*x**3 + 4*x**2 - 49)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21 - 32*x**2)*(32*x**3 + 4*x**2 - 49)\nExpanding the part (21 - 32*x**2) using the distributive property, and we got: (-32*x**2)*(32*x**3 + 4*x**2 - 49) + 21*(32*x**3 + 4*x**2 - 49)\n#Step 2:\nCurrent expression: (-32*x**2)*(32*x**3 + 4*x**2 - 49) + 21*(32*x**3 + 4*x**2 - 49)\nSimplifying the partial expression: 21*(32*x**3 + 4*x**2 - 49)\nExpanding the part (32*x**3 + 4*x**2 - 49) using the distributive property, and we got: (4*x**2)*21 + (32*x**3)*21 - 49*21\nReplacing 21*(32*x**3 + 4*x**2 - 49) with (4*x**2)*21 + (32*x**3)*21 - 49*21 in the overall expression.\n#Step 3:\nCurrent expression: (-32*x**2)*(32*x**3 + 4*x**2 - 49) + (4*x**2)*21 + (32*x**3)*21 - 1029\nSimplifying the partial expression: (-32*x**2)*(32*x**3 + 4*x**2 - 49)\nExpanding the part (32*x**3 + 4*x**2 - 49) using the distributive property, and we got: -(-1)*1568*x**2 + (-32*x**2)*(4*x**2) + (-32*x**2)*(32*x**3)\nReplacing (-32*x**2)*(32*x**3 + 4*x**2 - 49) with -(-1)*1568*x**2 + (-32*x**2)*(4*x**2) + (-32*x**2)*(32*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -49*(-32)*x**2 + (-32*x**2)*(4*x**2) + (-32*x**2)*(32*x**3) + (4*x**2)*21 + (32*x**3)*21 - 1029\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (4*x**2)*21 = 84*x**2\n (4*x**2)*(-32*x**2) = -128*x**4\n (32*x**3)*21 = 672*x**3\n (32*x**3)*(-32*x**2) = -1024*x**5\n -49*-32*x**2 = 1568*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1024*x**5 - 128*x**4 + 672*x**3 + 84*x**2 + 1568*x**2 - 1029\nCombining like terms, got -1024*x**5 - 128*x**4 + 672*x**3 + 1652*x**2 - 1029\n#Step 6:\nCurrent expression: -1024*x**5 - 128*x**4 + 672*x**3 + 1652*x**2 - 1029\nNo more calculations needed.\n-1024*x**5 - 128*x**4 + 672*x**3 + 1652*x**2 - 1029", "generated_answer": "-1024*x**5 - 128*x**4 + 672*x**3 + 1652*x**2 - 1029", "step_length": 6} {"cot_id": "c751aa86d0dfa2a532a63ee03e0951528ebd0a488c34c8155e099d56ecd8cfc1", "datapoint": {"question": "Calculate the following: (3*z + 48)*(-6*z**2 - 30*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-18*z**3 - 378*z**2 - 1440*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1001, "polynomial_expr": "(3*z + 48)*(-6*z**2 - 30*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (3*z + 48)*(-6*z**2 - 30*z)\nExpanding the part (3*z + 48) using the distributive property, and we got: (3*z)*(-6*z**2 - 30*z) + 48*(-6*z**2 - 30*z)\n#Step 2:\nCurrent expression: (3*z)*(-6*z**2 - 30*z) + 48*(-6*z**2 - 30*z)\nSimplifying the partial expression: 48*(-6*z**2 - 30*z)\nExpanding the part (-6*z**2 - 30*z) using the distributive property, and we got: -30*z*48 - 6*z**2*48\nReplacing 48*(-6*z**2 - 30*z) with -30*z*48 - 6*z**2*48 in the overall expression.\n#Step 3:\nCurrent expression: -30*z*48 + (3*z)*(-6*z**2 - 30*z) - 6*z**2*48\nSimplifying the partial expression: (3*z)*(-6*z**2 - 30*z)\nExpanding the part (-6*z**2 - 30*z) using the distributive property, and we got: (-30*z)*(3*z) + (3*z)*(-6*z**2)\nReplacing (3*z)*(-6*z**2 - 30*z) with (-30*z)*(3*z) + (3*z)*(-6*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-30*z)*(3*z) - 30*z*48 + (3*z)*(-6*z**2) - 6*z**2*48\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*z)*48 = -1440*z\n (-30*z)*(3*z) = -90*z**2\n (-6*z**2)*48 = -288*z**2\n (-6*z**2)*(3*z) = -18*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -18*z**3 - 288*z**2 - 90*z**2 - 1440*z\nCombining like terms, got -18*z**3 - 378*z**2 - 1440*z\n#Step 6:\nCurrent expression: -18*z**3 - 378*z**2 - 1440*z\nNo more calculations needed.\n-18*z**3 - 378*z**2 - 1440*z", "generated_answer": "-18*z**3 - 378*z**2 - 1440*z", "step_length": 6} {"cot_id": "401452fa6460451c412132bf0a90d217dd38ce6a3fe7190b1ec3725a50d8ebeb", "datapoint": {"question": "Calculate the following: (14*x**3 - 41*x**2 - 34)*(49*x**3 + 39*x + 45)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "686*x**6 - 2009*x**5 + 546*x**4 - 2635*x**3 - 1845*x**2 - 1326*x - 1530", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1002, "polynomial_expr": "(14*x**3 - 41*x**2 - 34)*(49*x**3 + 39*x + 45)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14*x**3 - 41*x**2 - 34)*(49*x**3 + 39*x + 45)\nExpanding the part (14*x**3 - 41*x**2 - 34) using the distributive property, and we got: (-41*x**2)*(49*x**3 + 39*x + 45) + (14*x**3)*(49*x**3 + 39*x + 45) - 34*(49*x**3 + 39*x + 45)\n#Step 2:\nCurrent expression: (-41*x**2)*(49*x**3 + 39*x + 45) + (14*x**3)*(49*x**3 + 39*x + 45) - 34*(49*x**3 + 39*x + 45)\nSimplifying the partial expression: -34*(49*x**3 + 39*x + 45)\nExpanding the part (49*x**3 + 39*x + 45) using the distributive property, and we got: (39*x)*(-34) + (49*x**3)*(-34) + 45*(-34)\nReplacing -34*(49*x**3 + 39*x + 45) with (39*x)*(-34) + (49*x**3)*(-34) + 45*(-34) in the overall expression.\n#Step 3:\nCurrent expression: (39*x)*(-34) + (-41*x**2)*(49*x**3 + 39*x + 45) + (14*x**3)*(49*x**3 + 39*x + 45) + (49*x**3)*(-34) - 1530\nSimplifying the partial expression: (-41*x**2)*(49*x**3 + 39*x + 45)\nExpanding the part (49*x**3 + 39*x + 45) using the distributive property, and we got: 45*(-41*x**2) + (39*x)*(-41*x**2) + (-41*x**2)*(49*x**3)\nReplacing (-41*x**2)*(49*x**3 + 39*x + 45) with 45*(-41*x**2) + (39*x)*(-41*x**2) + (-41*x**2)*(49*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 45*(-41)*x**2 + (39*x)*(-41*x**2) + (39*x)*(-34) + (-41*x**2)*(49*x**3) + (14*x**3)*(49*x**3 + 39*x + 45) + (49*x**3)*(-34) - 1530\nSimplifying the partial expression: (14*x**3)*(49*x**3 + 39*x + 45)\nExpanding the part (49*x**3 + 39*x + 45) using the distributive property, and we got: 45*(14*x**3) + (39*x)*(14*x**3) + (14*x**3)*(49*x**3)\nReplacing (14*x**3)*(49*x**3 + 39*x + 45) with 45*(14*x**3) + (39*x)*(14*x**3) + (14*x**3)*(49*x**3) in the overall expression.\n#Step 5:\nCurrent expression: 45*14*x**3 + 45*(-41)*x**2 + (39*x)*(-41*x**2) + (39*x)*(14*x**3) + (39*x)*(-34) + (-41*x**2)*(49*x**3) + (14*x**3)*(49*x**3) + (49*x**3)*(-34) - 1530\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (39*x)*-34 = -1326*x\n (39*x)*(-41*x**2) = -1599*x**3\n (39*x)*(14*x**3) = 546*x**4\n (49*x**3)*-34 = -1666*x**3\n (49*x**3)*(-41*x**2) = -2009*x**5\n (49*x**3)*(14*x**3) = 686*x**6\n 45*-41*x**2 = -1845*x**2\n 45*14*x**3 = 630*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 686*x**6 - 2009*x**5 + 546*x**4 - 1666*x**3 - 1599*x**3 + 630*x**3 - 1845*x**2 - 1326*x - 1530\nCombining like terms, got 686*x**6 - 2009*x**5 + 546*x**4 - 2635*x**3 - 1845*x**2 - 1326*x - 1530\n#Step 7:\nCurrent expression: 686*x**6 - 2009*x**5 + 546*x**4 - 2635*x**3 - 1845*x**2 - 1326*x - 1530\nNo more calculations needed.\n686*x**6 - 2009*x**5 + 546*x**4 - 2635*x**3 - 1845*x**2 - 1326*x - 1530", "generated_answer": "686*x**6 - 2009*x**5 + 546*x**4 - 2635*x**3 - 1845*x**2 - 1326*x - 1530", "step_length": 7} {"cot_id": "2459003da065701b8adf63975ca9b69e7a17b06926dbf81e2db21cce54eaf743", "datapoint": {"question": "Calculate the following: (-49*z**3 - 22*z**2 + 44)*(-26*z**3 + 37*z + 23)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1274*z**6 + 572*z**5 - 1813*z**4 - 3085*z**3 - 506*z**2 + 1628*z + 1012", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1003, "polynomial_expr": "(-49*z**3 - 22*z**2 + 44)*(-26*z**3 + 37*z + 23)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-49*z**3 - 22*z**2 + 44)*(-26*z**3 + 37*z + 23)\nExpanding the part (-26*z**3 + 37*z + 23) using the distributive property, and we got: (37*z)*(-49*z**3 - 22*z**2 + 44) + (-26*z**3)*(-49*z**3 - 22*z**2 + 44) + 23*(-49*z**3 - 22*z**2 + 44)\n#Step 2:\nCurrent expression: (37*z)*(-49*z**3 - 22*z**2 + 44) + (-26*z**3)*(-49*z**3 - 22*z**2 + 44) + 23*(-49*z**3 - 22*z**2 + 44)\nSimplifying the partial expression: 23*(-49*z**3 - 22*z**2 + 44)\nExpanding the part (-49*z**3 - 22*z**2 + 44) using the distributive property, and we got: -22*z**2*23 - 49*z**3*23 + 44*23\nReplacing 23*(-49*z**3 - 22*z**2 + 44) with -22*z**2*23 - 49*z**3*23 + 44*23 in the overall expression.\n#Step 3:\nCurrent expression: (37*z)*(-49*z**3 - 22*z**2 + 44) - 22*z**2*23 - 49*z**3*23 + (-26*z**3)*(-49*z**3 - 22*z**2 + 44) + 1012\nSimplifying the partial expression: (-26*z**3)*(-49*z**3 - 22*z**2 + 44)\nExpanding the part (-49*z**3 - 22*z**2 + 44) using the distributive property, and we got: 44*(-26*z**3) + (-22*z**2)*(-26*z**3) + (-49*z**3)*(-26*z**3)\nReplacing (-26*z**3)*(-49*z**3 - 22*z**2 + 44) with 44*(-26*z**3) + (-22*z**2)*(-26*z**3) + (-49*z**3)*(-26*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 44*(-26)*z**3 + (37*z)*(-49*z**3 - 22*z**2 + 44) + (-22*z**2)*(-26*z**3) - 22*z**2*23 + (-49*z**3)*(-26*z**3) - 49*z**3*23 + 1012\nSimplifying the partial expression: (37*z)*(-49*z**3 - 22*z**2 + 44)\nExpanding the part (-49*z**3 - 22*z**2 + 44) using the distributive property, and we got: 44*(37*z) + (37*z)*(-22*z**2) + (37*z)*(-49*z**3)\nReplacing (37*z)*(-49*z**3 - 22*z**2 + 44) with 44*(37*z) + (37*z)*(-22*z**2) + (37*z)*(-49*z**3) in the overall expression.\n#Step 5:\nCurrent expression: 44*(-26)*z**3 + 44*37*z + (37*z)*(-22*z**2) + (37*z)*(-49*z**3) + (-22*z**2)*(-26*z**3) - 22*z**2*23 + (-49*z**3)*(-26*z**3) - 49*z**3*23 + 1012\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*z**3)*23 = -1127*z**3\n (-49*z**3)*(-26*z**3) = 1274*z**6\n (-49*z**3)*(37*z) = -1813*z**4\n (-22*z**2)*23 = -506*z**2\n (-22*z**2)*(-26*z**3) = 572*z**5\n (-22*z**2)*(37*z) = -814*z**3\n 44*-26*z**3 = -1144*z**3\n 44*37*z = 1628*z\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1274*z**6 + 572*z**5 - 1813*z**4 - 1144*z**3 - 1127*z**3 - 814*z**3 - 506*z**2 + 1628*z + 1012\nCombining like terms, got 1274*z**6 + 572*z**5 - 1813*z**4 - 3085*z**3 - 506*z**2 + 1628*z + 1012\n#Step 7:\nCurrent expression: 1274*z**6 + 572*z**5 - 1813*z**4 - 3085*z**3 - 506*z**2 + 1628*z + 1012\nNo more calculations needed.\n1274*z**6 + 572*z**5 - 1813*z**4 - 3085*z**3 - 506*z**2 + 1628*z + 1012", "generated_answer": "1274*z**6 + 572*z**5 - 1813*z**4 - 3085*z**3 - 506*z**2 + 1628*z + 1012", "step_length": 7} {"cot_id": "399d62b46911f4c5b28ebd116132bd237f2517fd76a874352bc3ded64f493ad7", "datapoint": {"question": "Simplify this expression: (10*y**3 + 24*y)*(-27*y**2 + 11*y + 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-270*y**5 + 110*y**4 - 148*y**3 + 264*y**2 + 1200*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1004, "polynomial_expr": "(10*y**3 + 24*y)*(-27*y**2 + 11*y + 50)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (10*y**3 + 24*y)*(-27*y**2 + 11*y + 50)\nExpanding the part (10*y**3 + 24*y) using the distributive property, and we got: (24*y)*(-27*y**2 + 11*y + 50) + (10*y**3)*(-27*y**2 + 11*y + 50)\n#Step 2:\nCurrent expression: (24*y)*(-27*y**2 + 11*y + 50) + (10*y**3)*(-27*y**2 + 11*y + 50)\nSimplifying the partial expression: (10*y**3)*(-27*y**2 + 11*y + 50)\nExpanding the part (-27*y**2 + 11*y + 50) using the distributive property, and we got: 50*(10*y**3) + (11*y)*(10*y**3) + (-27*y**2)*(10*y**3)\nReplacing (10*y**3)*(-27*y**2 + 11*y + 50) with 50*(10*y**3) + (11*y)*(10*y**3) + (-27*y**2)*(10*y**3) in the overall expression.\n#Step 3:\nCurrent expression: 50*10*y**3 + (11*y)*(10*y**3) + (24*y)*(-27*y**2 + 11*y + 50) + (-27*y**2)*(10*y**3)\nSimplifying the partial expression: (24*y)*(-27*y**2 + 11*y + 50)\nExpanding the part (-27*y**2 + 11*y + 50) using the distributive property, and we got: 50*(24*y) + (11*y)*(24*y) + (24*y)*(-27*y**2)\nReplacing (24*y)*(-27*y**2 + 11*y + 50) with 50*(24*y) + (11*y)*(24*y) + (24*y)*(-27*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 50*10*y**3 + 50*24*y + (11*y)*(24*y) + (11*y)*(10*y**3) + (24*y)*(-27*y**2) + (-27*y**2)*(10*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*y**2)*(10*y**3) = -270*y**5\n (-27*y**2)*(24*y) = -648*y**3\n (11*y)*(10*y**3) = 110*y**4\n (11*y)*(24*y) = 264*y**2\n 50*10*y**3 = 500*y**3\n 50*24*y = 1200*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -270*y**5 + 110*y**4 - 648*y**3 + 500*y**3 + 264*y**2 + 1200*y\nCombining like terms, got -270*y**5 + 110*y**4 - 148*y**3 + 264*y**2 + 1200*y\n#Step 6:\nCurrent expression: -270*y**5 + 110*y**4 - 148*y**3 + 264*y**2 + 1200*y\nNo more calculations needed.\n-270*y**5 + 110*y**4 - 148*y**3 + 264*y**2 + 1200*y", "generated_answer": "-270*y**5 + 110*y**4 - 148*y**3 + 264*y**2 + 1200*y", "step_length": 6} {"cot_id": "ed0a95df802c73af142c4a4291f285f0a39aa413aca8f2ad5f7541ece2cf6955", "datapoint": {"question": "Calculate the following: (-82*x**2 - 47*x)*(-17*x**3 + 12*x**2 - 10*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1394*x**5 - 185*x**4 + 256*x**3 + 470*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1005, "polynomial_expr": "(-82*x**2 - 47*x)*(-17*x**3 + 12*x**2 - 10*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-82*x**2 - 47*x)*(-17*x**3 + 12*x**2 - 10*x)\nExpanding the part (-82*x**2 - 47*x) using the distributive property, and we got: (-47*x)*(-17*x**3 + 12*x**2 - 10*x) + (-82*x**2)*(-17*x**3 + 12*x**2 - 10*x)\n#Step 2:\nCurrent expression: (-47*x)*(-17*x**3 + 12*x**2 - 10*x) + (-82*x**2)*(-17*x**3 + 12*x**2 - 10*x)\nSimplifying the partial expression: (-82*x**2)*(-17*x**3 + 12*x**2 - 10*x)\nExpanding the part (-17*x**3 + 12*x**2 - 10*x) using the distributive property, and we got: (-10*x)*(-82*x**2) + (-82*x**2)*(12*x**2) + (-82*x**2)*(-17*x**3)\nReplacing (-82*x**2)*(-17*x**3 + 12*x**2 - 10*x) with (-10*x)*(-82*x**2) + (-82*x**2)*(12*x**2) + (-82*x**2)*(-17*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-47*x)*(-17*x**3 + 12*x**2 - 10*x) + (-10*x)*(-82*x**2) + (-82*x**2)*(12*x**2) + (-82*x**2)*(-17*x**3)\nSimplifying the partial expression: (-47*x)*(-17*x**3 + 12*x**2 - 10*x)\nExpanding the part (-17*x**3 + 12*x**2 - 10*x) using the distributive property, and we got: (-47*x)*(-10*x) + (-47*x)*(12*x**2) + (-47*x)*(-17*x**3)\nReplacing (-47*x)*(-17*x**3 + 12*x**2 - 10*x) with (-47*x)*(-10*x) + (-47*x)*(12*x**2) + (-47*x)*(-17*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-47*x)*(-10*x) + (-47*x)*(12*x**2) + (-47*x)*(-17*x**3) + (-10*x)*(-82*x**2) + (-82*x**2)*(12*x**2) + (-82*x**2)*(-17*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-17*x**3)*(-82*x**2) = 1394*x**5\n (-17*x**3)*(-47*x) = 799*x**4\n (-10*x)*(-82*x**2) = 820*x**3\n (-10*x)*(-47*x) = 470*x**2\n (12*x**2)*(-82*x**2) = -984*x**4\n (12*x**2)*(-47*x) = -564*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1394*x**5 - 984*x**4 + 799*x**4 - 564*x**3 + 820*x**3 + 470*x**2\nCombining like terms, got 1394*x**5 - 185*x**4 + 256*x**3 + 470*x**2\n#Step 6:\nCurrent expression: 1394*x**5 - 185*x**4 + 256*x**3 + 470*x**2\nNo more calculations needed.\n1394*x**5 - 185*x**4 + 256*x**3 + 470*x**2", "generated_answer": "1394*x**5 - 185*x**4 + 256*x**3 + 470*x**2", "step_length": 6} {"cot_id": "b460cb0dffd04d6ca7678ace8d1efed575df657c076988296e2e00440aaad58b", "datapoint": {"question": "Simplify this expression: (-27*y**3 - 30*y**2)*(14*y**3 - 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-378*y**6 - 420*y**5 + 540*y**3 + 600*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1006, "polynomial_expr": "(-27*y**3 - 30*y**2)*(14*y**3 - 20)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-27*y**3 - 30*y**2)*(14*y**3 - 20)\nExpanding the part (14*y**3 - 20) using the distributive property, and we got: (14*y**3)*(-27*y**3 - 30*y**2) - 20*(-27*y**3 - 30*y**2)\n#Step 2:\nCurrent expression: (14*y**3)*(-27*y**3 - 30*y**2) - 20*(-27*y**3 - 30*y**2)\nSimplifying the partial expression: -20*(-27*y**3 - 30*y**2)\nExpanding the part (-27*y**3 - 30*y**2) using the distributive property, and we got: -30*y**2*(-20) - 27*y**3*(-20)\nReplacing -20*(-27*y**3 - 30*y**2) with -30*y**2*(-20) - 27*y**3*(-20) in the overall expression.\n#Step 3:\nCurrent expression: -30*y**2*(-20) - 27*y**3*(-20) + (14*y**3)*(-27*y**3 - 30*y**2)\nSimplifying the partial expression: (14*y**3)*(-27*y**3 - 30*y**2)\nExpanding the part (-27*y**3 - 30*y**2) using the distributive property, and we got: (-30*y**2)*(14*y**3) + (-27*y**3)*(14*y**3)\nReplacing (14*y**3)*(-27*y**3 - 30*y**2) with (-30*y**2)*(14*y**3) + (-27*y**3)*(14*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-30*y**2)*(14*y**3) - 30*y**2*(-20) + (-27*y**3)*(14*y**3) - 27*y**3*(-20)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*y**2)*-20 = 600*y**2\n (-30*y**2)*(14*y**3) = -420*y**5\n (-27*y**3)*-20 = 540*y**3\n (-27*y**3)*(14*y**3) = -378*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -378*y**6 - 420*y**5 + 540*y**3 + 600*y**2\nNo more calculations needed.\n-378*y**6 - 420*y**5 + 540*y**3 + 600*y**2", "generated_answer": "-378*y**6 - 420*y**5 + 540*y**3 + 600*y**2", "step_length": 5} {"cot_id": "bef3939c75750095c6adfeff15624b654067051c739a710ea92a1bfed8e4d7a1", "datapoint": {"question": "Simplify this expression: -21*z**3*(-16*z**2 + 36*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "336*z**5 - 756*z**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1007, "polynomial_expr": "-21*z**3*(-16*z**2 + 36*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -21*z**3*(-16*z**2 + 36*z)\nExpanding the part (-16*z**2 + 36*z) using the distributive property, and we got: (36*z)*(-21*z**3) + (-16*z**2)*(-21*z**3)\n#Step 2:\nCurrent expression: (36*z)*(-21*z**3) + (-16*z**2)*(-21*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-16*z**2)*(-21*z**3) = 336*z**5\n (36*z)*(-21*z**3) = -756*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 336*z**5 - 756*z**4\nNo more calculations needed.\n336*z**5 - 756*z**4", "generated_answer": "336*z**5 - 756*z**4", "step_length": 3} {"cot_id": "023dc7fb16ea561ae0cc536f4153af301a61a2eb689b7aeb16a7403949c617f5", "datapoint": {"question": "Calculate the following: (-46*y**2 + 27*y)*(23*y**3 + 39*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1058*y**5 - 1173*y**4 + 1053*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1008, "polynomial_expr": "(-46*y**2 + 27*y)*(23*y**3 + 39*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-46*y**2 + 27*y)*(23*y**3 + 39*y**2)\nExpanding the part (-46*y**2 + 27*y) using the distributive property, and we got: (27*y)*(23*y**3 + 39*y**2) + (-46*y**2)*(23*y**3 + 39*y**2)\n#Step 2:\nCurrent expression: (27*y)*(23*y**3 + 39*y**2) + (-46*y**2)*(23*y**3 + 39*y**2)\nSimplifying the partial expression: (-46*y**2)*(23*y**3 + 39*y**2)\nExpanding the part (23*y**3 + 39*y**2) using the distributive property, and we got: (-46*y**2)*(39*y**2) + (-46*y**2)*(23*y**3)\nReplacing (-46*y**2)*(23*y**3 + 39*y**2) with (-46*y**2)*(39*y**2) + (-46*y**2)*(23*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (27*y)*(23*y**3 + 39*y**2) + (-46*y**2)*(39*y**2) + (-46*y**2)*(23*y**3)\nSimplifying the partial expression: (27*y)*(23*y**3 + 39*y**2)\nExpanding the part (23*y**3 + 39*y**2) using the distributive property, and we got: (27*y)*(39*y**2) + (27*y)*(23*y**3)\nReplacing (27*y)*(23*y**3 + 39*y**2) with (27*y)*(39*y**2) + (27*y)*(23*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (27*y)*(39*y**2) + (27*y)*(23*y**3) + (-46*y**2)*(39*y**2) + (-46*y**2)*(23*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (23*y**3)*(-46*y**2) = -1058*y**5\n (23*y**3)*(27*y) = 621*y**4\n (39*y**2)*(-46*y**2) = -1794*y**4\n (39*y**2)*(27*y) = 1053*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1058*y**5 - 1794*y**4 + 621*y**4 + 1053*y**3\nCombining like terms, got -1058*y**5 - 1173*y**4 + 1053*y**3\n#Step 6:\nCurrent expression: -1058*y**5 - 1173*y**4 + 1053*y**3\nNo more calculations needed.\n-1058*y**5 - 1173*y**4 + 1053*y**3", "generated_answer": "-1058*y**5 - 1173*y**4 + 1053*y**3", "step_length": 6} {"cot_id": "2247d4fc809a1b3e93a4ffd2ef118ea972c061ff0abce1c19d149a83a4e4dde7", "datapoint": {"question": "Calculate the following: (-49*x**3 - 40)*(-49*x**3 - 29*x - 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2401*x**6 + 1421*x**4 + 3479*x**3 + 1160*x + 1240", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1009, "polynomial_expr": "(-49*x**3 - 40)*(-49*x**3 - 29*x - 31)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-49*x**3 - 40)*(-49*x**3 - 29*x - 31)\nExpanding the part (-49*x**3 - 40) using the distributive property, and we got: (-49*x**3)*(-49*x**3 - 29*x - 31) - 40*(-49*x**3 - 29*x - 31)\n#Step 2:\nCurrent expression: (-49*x**3)*(-49*x**3 - 29*x - 31) - 40*(-49*x**3 - 29*x - 31)\nSimplifying the partial expression: -40*(-49*x**3 - 29*x - 31)\nExpanding the part (-49*x**3 - 29*x - 31) using the distributive property, and we got: -29*x*(-40) - 49*x**3*(-40) - 31*(-40)\nReplacing -40*(-49*x**3 - 29*x - 31) with -29*x*(-40) - 49*x**3*(-40) - 31*(-40) in the overall expression.\n#Step 3:\nCurrent expression: -29*x*(-40) + (-49*x**3)*(-49*x**3 - 29*x - 31) - 49*x**3*(-40) + 1240\nSimplifying the partial expression: (-49*x**3)*(-49*x**3 - 29*x - 31)\nExpanding the part (-49*x**3 - 29*x - 31) using the distributive property, and we got: (-29*x)*(-49*x**3) - (-1)*1519*x**3 + (-49*x**3)*(-49*x**3)\nReplacing (-49*x**3)*(-49*x**3 - 29*x - 31) with (-29*x)*(-49*x**3) - (-1)*1519*x**3 + (-49*x**3)*(-49*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-29*x)*(-49*x**3) - 29*x*(-40) - 31*(-49)*x**3 - 49*x**3*(-40) + (-49*x**3)*(-49*x**3) + 1240\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*x**3)*-40 = 1960*x**3\n (-49*x**3)*(-49*x**3) = 2401*x**6\n (-29*x)*-40 = 1160*x\n (-29*x)*(-49*x**3) = 1421*x**4\n -31*-49*x**3 = 1519*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2401*x**6 + 1421*x**4 + 1519*x**3 + 1960*x**3 + 1160*x + 1240\nCombining like terms, got 2401*x**6 + 1421*x**4 + 3479*x**3 + 1160*x + 1240\n#Step 6:\nCurrent expression: 2401*x**6 + 1421*x**4 + 3479*x**3 + 1160*x + 1240\nNo more calculations needed.\n2401*x**6 + 1421*x**4 + 3479*x**3 + 1160*x + 1240", "generated_answer": "2401*x**6 + 1421*x**4 + 3479*x**3 + 1160*x + 1240", "step_length": 6} {"cot_id": "f272a8c0266b38d59476886e93ee3e92015a94b8e1540a83e391271ab4a64aa6", "datapoint": {"question": "Simplify this expression: (50 - 49*x**2)*(-9*x**3 + 30*x**2 - 17*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "441*x**5 - 1470*x**4 + 383*x**3 + 1500*x**2 - 850*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1010, "polynomial_expr": "(50 - 49*x**2)*(-9*x**3 + 30*x**2 - 17*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (50 - 49*x**2)*(-9*x**3 + 30*x**2 - 17*x)\nExpanding the part (50 - 49*x**2) using the distributive property, and we got: (-49*x**2)*(-9*x**3 + 30*x**2 - 17*x) + 50*(-9*x**3 + 30*x**2 - 17*x)\n#Step 2:\nCurrent expression: (-49*x**2)*(-9*x**3 + 30*x**2 - 17*x) + 50*(-9*x**3 + 30*x**2 - 17*x)\nSimplifying the partial expression: 50*(-9*x**3 + 30*x**2 - 17*x)\nExpanding the part (-9*x**3 + 30*x**2 - 17*x) using the distributive property, and we got: -17*x*50 + (30*x**2)*50 - 9*x**3*50\nReplacing 50*(-9*x**3 + 30*x**2 - 17*x) with -17*x*50 + (30*x**2)*50 - 9*x**3*50 in the overall expression.\n#Step 3:\nCurrent expression: -17*x*50 + (-49*x**2)*(-9*x**3 + 30*x**2 - 17*x) + (30*x**2)*50 - 9*x**3*50\nSimplifying the partial expression: (-49*x**2)*(-9*x**3 + 30*x**2 - 17*x)\nExpanding the part (-9*x**3 + 30*x**2 - 17*x) using the distributive property, and we got: (-17*x)*(-49*x**2) + (-49*x**2)*(30*x**2) + (-49*x**2)*(-9*x**3)\nReplacing (-49*x**2)*(-9*x**3 + 30*x**2 - 17*x) with (-17*x)*(-49*x**2) + (-49*x**2)*(30*x**2) + (-49*x**2)*(-9*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-17*x)*(-49*x**2) - 17*x*50 + (-49*x**2)*(30*x**2) + (-49*x**2)*(-9*x**3) + (30*x**2)*50 - 9*x**3*50\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-17*x)*50 = -850*x\n (-17*x)*(-49*x**2) = 833*x**3\n (-9*x**3)*50 = -450*x**3\n (-9*x**3)*(-49*x**2) = 441*x**5\n (30*x**2)*50 = 1500*x**2\n (30*x**2)*(-49*x**2) = -1470*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 441*x**5 - 1470*x**4 - 450*x**3 + 833*x**3 + 1500*x**2 - 850*x\nCombining like terms, got 441*x**5 - 1470*x**4 + 383*x**3 + 1500*x**2 - 850*x\n#Step 6:\nCurrent expression: 441*x**5 - 1470*x**4 + 383*x**3 + 1500*x**2 - 850*x\nNo more calculations needed.\n441*x**5 - 1470*x**4 + 383*x**3 + 1500*x**2 - 850*x", "generated_answer": "441*x**5 - 1470*x**4 + 383*x**3 + 1500*x**2 - 850*x", "step_length": 6} {"cot_id": "a78ff019684e5410a9f3227b06021fd881bf873a9d7469cabc427103b3be5124", "datapoint": {"question": "Simplify this expression: (97*y + 33)*(-42*y**2 - 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-4074*y**3 - 1386*y**2 - 1261*y - 429", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1011, "polynomial_expr": "(97*y + 33)*(-42*y**2 - 13)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (97*y + 33)*(-42*y**2 - 13)\nExpanding the part (-42*y**2 - 13) using the distributive property, and we got: (-42*y**2)*(97*y + 33) - 13*(97*y + 33)\n#Step 2:\nCurrent expression: (-42*y**2)*(97*y + 33) - 13*(97*y + 33)\nSimplifying the partial expression: -13*(97*y + 33)\nExpanding the part (97*y + 33) using the distributive property, and we got: (97*y)*(-13) + 33*(-13)\nReplacing -13*(97*y + 33) with (97*y)*(-13) + 33*(-13) in the overall expression.\n#Step 3:\nCurrent expression: (97*y)*(-13) + (-42*y**2)*(97*y + 33) - 429\nSimplifying the partial expression: (-42*y**2)*(97*y + 33)\nExpanding the part (97*y + 33) using the distributive property, and we got: 33*(-42*y**2) + (97*y)*(-42*y**2)\nReplacing (-42*y**2)*(97*y + 33) with 33*(-42*y**2) + (97*y)*(-42*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 33*(-42)*y**2 + (97*y)*(-42*y**2) + (97*y)*(-13) - 429\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (97*y)*-13 = -1261*y\n (97*y)*(-42*y**2) = -4074*y**3\n 33*-42*y**2 = -1386*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -4074*y**3 - 1386*y**2 - 1261*y - 429\nNo more calculations needed.\n-4074*y**3 - 1386*y**2 - 1261*y - 429", "generated_answer": "-4074*y**3 - 1386*y**2 - 1261*y - 429", "step_length": 5} {"cot_id": "aa3a4d4e590cf6ad7e5f2fdee454dcf4d7e2f53a28045f7fe840979991fabb8c", "datapoint": {"question": "Calculate the following: (29*x**2 + 5)*(43*x**3 - 10*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1247*x**5 - 290*x**4 + 215*x**3 - 50*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1012, "polynomial_expr": "(29*x**2 + 5)*(43*x**3 - 10*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29*x**2 + 5)*(43*x**3 - 10*x**2)\nExpanding the part (29*x**2 + 5) using the distributive property, and we got: (29*x**2)*(43*x**3 - 10*x**2) + 5*(43*x**3 - 10*x**2)\n#Step 2:\nCurrent expression: (29*x**2)*(43*x**3 - 10*x**2) + 5*(43*x**3 - 10*x**2)\nSimplifying the partial expression: 5*(43*x**3 - 10*x**2)\nExpanding the part (43*x**3 - 10*x**2) using the distributive property, and we got: -10*x**2*5 + (43*x**3)*5\nReplacing 5*(43*x**3 - 10*x**2) with -10*x**2*5 + (43*x**3)*5 in the overall expression.\n#Step 3:\nCurrent expression: -10*x**2*5 + (29*x**2)*(43*x**3 - 10*x**2) + (43*x**3)*5\nSimplifying the partial expression: (29*x**2)*(43*x**3 - 10*x**2)\nExpanding the part (43*x**3 - 10*x**2) using the distributive property, and we got: (-10*x**2)*(29*x**2) + (29*x**2)*(43*x**3)\nReplacing (29*x**2)*(43*x**3 - 10*x**2) with (-10*x**2)*(29*x**2) + (29*x**2)*(43*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-10*x**2)*(29*x**2) - 10*x**2*5 + (29*x**2)*(43*x**3) + (43*x**3)*5\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*x**2)*5 = -50*x**2\n (-10*x**2)*(29*x**2) = -290*x**4\n (43*x**3)*5 = 215*x**3\n (43*x**3)*(29*x**2) = 1247*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1247*x**5 - 290*x**4 + 215*x**3 - 50*x**2\nNo more calculations needed.\n1247*x**5 - 290*x**4 + 215*x**3 - 50*x**2", "generated_answer": "1247*x**5 - 290*x**4 + 215*x**3 - 50*x**2", "step_length": 5} {"cot_id": "7d9bbacd2756f397720f127da66a69123febcf5faf667d8fa4ff863abef49bce", "datapoint": {"question": "Calculate the following: (48*x**3 + 28*x - 37)*(59*x**3 + 9*x**2 + 18)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2832*x**6 + 432*x**5 + 1652*x**4 - 1067*x**3 - 333*x**2 + 504*x - 666", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1013, "polynomial_expr": "(48*x**3 + 28*x - 37)*(59*x**3 + 9*x**2 + 18)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (48*x**3 + 28*x - 37)*(59*x**3 + 9*x**2 + 18)\nExpanding the part (48*x**3 + 28*x - 37) using the distributive property, and we got: (28*x)*(59*x**3 + 9*x**2 + 18) + (48*x**3)*(59*x**3 + 9*x**2 + 18) - 37*(59*x**3 + 9*x**2 + 18)\n#Step 2:\nCurrent expression: (28*x)*(59*x**3 + 9*x**2 + 18) + (48*x**3)*(59*x**3 + 9*x**2 + 18) - 37*(59*x**3 + 9*x**2 + 18)\nSimplifying the partial expression: -37*(59*x**3 + 9*x**2 + 18)\nExpanding the part (59*x**3 + 9*x**2 + 18) using the distributive property, and we got: (9*x**2)*(-37) + (59*x**3)*(-37) + 18*(-37)\nReplacing -37*(59*x**3 + 9*x**2 + 18) with (9*x**2)*(-37) + (59*x**3)*(-37) + 18*(-37) in the overall expression.\n#Step 3:\nCurrent expression: (28*x)*(59*x**3 + 9*x**2 + 18) + (9*x**2)*(-37) + (48*x**3)*(59*x**3 + 9*x**2 + 18) + (59*x**3)*(-37) - 666\nSimplifying the partial expression: (28*x)*(59*x**3 + 9*x**2 + 18)\nExpanding the part (59*x**3 + 9*x**2 + 18) using the distributive property, and we got: 18*(28*x) + (28*x)*(9*x**2) + (28*x)*(59*x**3)\nReplacing (28*x)*(59*x**3 + 9*x**2 + 18) with 18*(28*x) + (28*x)*(9*x**2) + (28*x)*(59*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 18*28*x + (28*x)*(9*x**2) + (28*x)*(59*x**3) + (9*x**2)*(-37) + (48*x**3)*(59*x**3 + 9*x**2 + 18) + (59*x**3)*(-37) - 666\nSimplifying the partial expression: (48*x**3)*(59*x**3 + 9*x**2 + 18)\nExpanding the part (59*x**3 + 9*x**2 + 18) using the distributive property, and we got: 18*(48*x**3) + (9*x**2)*(48*x**3) + (48*x**3)*(59*x**3)\nReplacing (48*x**3)*(59*x**3 + 9*x**2 + 18) with 18*(48*x**3) + (9*x**2)*(48*x**3) + (48*x**3)*(59*x**3) in the overall expression.\n#Step 5:\nCurrent expression: 18*48*x**3 + 18*28*x + (28*x)*(9*x**2) + (28*x)*(59*x**3) + (9*x**2)*(48*x**3) + (9*x**2)*(-37) + (48*x**3)*(59*x**3) + (59*x**3)*(-37) - 666\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (9*x**2)*-37 = -333*x**2\n (9*x**2)*(28*x) = 252*x**3\n (9*x**2)*(48*x**3) = 432*x**5\n (59*x**3)*-37 = -2183*x**3\n (59*x**3)*(28*x) = 1652*x**4\n (59*x**3)*(48*x**3) = 2832*x**6\n 18*28*x = 504*x\n 18*48*x**3 = 864*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 2832*x**6 + 432*x**5 + 1652*x**4 - 2183*x**3 + 252*x**3 + 864*x**3 - 333*x**2 + 504*x - 666\nCombining like terms, got 2832*x**6 + 432*x**5 + 1652*x**4 - 1067*x**3 - 333*x**2 + 504*x - 666\n#Step 7:\nCurrent expression: 2832*x**6 + 432*x**5 + 1652*x**4 - 1067*x**3 - 333*x**2 + 504*x - 666\nNo more calculations needed.\n2832*x**6 + 432*x**5 + 1652*x**4 - 1067*x**3 - 333*x**2 + 504*x - 666", "generated_answer": "2832*x**6 + 432*x**5 + 1652*x**4 - 1067*x**3 - 333*x**2 + 504*x - 666", "step_length": 7} {"cot_id": "f7dac3119f5ef503ce5556841b49f0fbf30be0caf08f901a08a3403533e332fb", "datapoint": {"question": "Calculate the following: (-33*x**3 - 13*x**2 + 40)*(60*x**3 + 3*x**2 + 31*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1980*x**6 - 879*x**5 - 1062*x**4 + 1997*x**3 + 120*x**2 + 1240*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1014, "polynomial_expr": "(-33*x**3 - 13*x**2 + 40)*(60*x**3 + 3*x**2 + 31*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-33*x**3 - 13*x**2 + 40)*(60*x**3 + 3*x**2 + 31*x)\nExpanding the part (-33*x**3 - 13*x**2 + 40) using the distributive property, and we got: (-13*x**2)*(60*x**3 + 3*x**2 + 31*x) + (-33*x**3)*(60*x**3 + 3*x**2 + 31*x) + 40*(60*x**3 + 3*x**2 + 31*x)\n#Step 2:\nCurrent expression: (-13*x**2)*(60*x**3 + 3*x**2 + 31*x) + (-33*x**3)*(60*x**3 + 3*x**2 + 31*x) + 40*(60*x**3 + 3*x**2 + 31*x)\nSimplifying the partial expression: 40*(60*x**3 + 3*x**2 + 31*x)\nExpanding the part (60*x**3 + 3*x**2 + 31*x) using the distributive property, and we got: (31*x)*40 + (3*x**2)*40 + (60*x**3)*40\nReplacing 40*(60*x**3 + 3*x**2 + 31*x) with (31*x)*40 + (3*x**2)*40 + (60*x**3)*40 in the overall expression.\n#Step 3:\nCurrent expression: (31*x)*40 + (-13*x**2)*(60*x**3 + 3*x**2 + 31*x) + (3*x**2)*40 + (-33*x**3)*(60*x**3 + 3*x**2 + 31*x) + (60*x**3)*40\nSimplifying the partial expression: (-33*x**3)*(60*x**3 + 3*x**2 + 31*x)\nExpanding the part (60*x**3 + 3*x**2 + 31*x) using the distributive property, and we got: (31*x)*(-33*x**3) + (3*x**2)*(-33*x**3) + (-33*x**3)*(60*x**3)\nReplacing (-33*x**3)*(60*x**3 + 3*x**2 + 31*x) with (31*x)*(-33*x**3) + (3*x**2)*(-33*x**3) + (-33*x**3)*(60*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (31*x)*(-33*x**3) + (31*x)*40 + (-13*x**2)*(60*x**3 + 3*x**2 + 31*x) + (3*x**2)*(-33*x**3) + (3*x**2)*40 + (-33*x**3)*(60*x**3) + (60*x**3)*40\nSimplifying the partial expression: (-13*x**2)*(60*x**3 + 3*x**2 + 31*x)\nExpanding the part (60*x**3 + 3*x**2 + 31*x) using the distributive property, and we got: (31*x)*(-13*x**2) + (-13*x**2)*(3*x**2) + (-13*x**2)*(60*x**3)\nReplacing (-13*x**2)*(60*x**3 + 3*x**2 + 31*x) with (31*x)*(-13*x**2) + (-13*x**2)*(3*x**2) + (-13*x**2)*(60*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (31*x)*(-13*x**2) + (31*x)*(-33*x**3) + (31*x)*40 + (-13*x**2)*(3*x**2) + (-13*x**2)*(60*x**3) + (3*x**2)*(-33*x**3) + (3*x**2)*40 + (-33*x**3)*(60*x**3) + (60*x**3)*40\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (3*x**2)*40 = 120*x**2\n (3*x**2)*(-33*x**3) = -99*x**5\n (3*x**2)*(-13*x**2) = -39*x**4\n (31*x)*40 = 1240*x\n (31*x)*(-33*x**3) = -1023*x**4\n (31*x)*(-13*x**2) = -403*x**3\n (60*x**3)*40 = 2400*x**3\n (60*x**3)*(-33*x**3) = -1980*x**6\n (60*x**3)*(-13*x**2) = -780*x**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1980*x**6 - 780*x**5 - 99*x**5 - 1023*x**4 - 39*x**4 - 403*x**3 + 2400*x**3 + 120*x**2 + 1240*x\nCombining like terms, got -1980*x**6 - 879*x**5 - 1062*x**4 + 1997*x**3 + 120*x**2 + 1240*x\n#Step 7:\nCurrent expression: -1980*x**6 - 879*x**5 - 1062*x**4 + 1997*x**3 + 120*x**2 + 1240*x\nNo more calculations needed.\n-1980*x**6 - 879*x**5 - 1062*x**4 + 1997*x**3 + 120*x**2 + 1240*x", "generated_answer": "-1980*x**6 - 879*x**5 - 1062*x**4 + 1997*x**3 + 120*x**2 + 1240*x", "step_length": 7} {"cot_id": "823f712dc67507af77214dbe3549e8016e82dd923b5cbec10892142b2d981fbf", "datapoint": {"question": "Simplify this expression: (88*z**3 - 29*z)*(31*z**3 - 28*z - 23)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2728*z**6 - 3363*z**4 - 2024*z**3 + 812*z**2 + 667*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1015, "polynomial_expr": "(88*z**3 - 29*z)*(31*z**3 - 28*z - 23)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (88*z**3 - 29*z)*(31*z**3 - 28*z - 23)\nExpanding the part (88*z**3 - 29*z) using the distributive property, and we got: (-29*z)*(31*z**3 - 28*z - 23) + (88*z**3)*(31*z**3 - 28*z - 23)\n#Step 2:\nCurrent expression: (-29*z)*(31*z**3 - 28*z - 23) + (88*z**3)*(31*z**3 - 28*z - 23)\nSimplifying the partial expression: (-29*z)*(31*z**3 - 28*z - 23)\nExpanding the part (31*z**3 - 28*z - 23) using the distributive property, and we got: (-29*z)*(-28*z) + (-29*z)*(31*z**3) - (-1)*667*z\nReplacing (-29*z)*(31*z**3 - 28*z - 23) with (-29*z)*(-28*z) + (-29*z)*(31*z**3) - (-1)*667*z in the overall expression.\n#Step 3:\nCurrent expression: (-29*z)*(-28*z) + (-29*z)*(31*z**3) - 23*(-29)*z + (88*z**3)*(31*z**3 - 28*z - 23)\nSimplifying the partial expression: (88*z**3)*(31*z**3 - 28*z - 23)\nExpanding the part (31*z**3 - 28*z - 23) using the distributive property, and we got: (-28*z)*(88*z**3) - 2024*z**3 + (31*z**3)*(88*z**3)\nReplacing (88*z**3)*(31*z**3 - 28*z - 23) with (-28*z)*(88*z**3) - 2024*z**3 + (31*z**3)*(88*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-29*z)*(-28*z) + (-29*z)*(31*z**3) + (-28*z)*(88*z**3) - 23*88*z**3 - 23*(-29)*z + (31*z**3)*(88*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*z)*(-29*z) = 812*z**2\n (-28*z)*(88*z**3) = -2464*z**4\n (31*z**3)*(-29*z) = -899*z**4\n (31*z**3)*(88*z**3) = 2728*z**6\n -23*-29*z = 667*z\n -23*88*z**3 = -2024*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2728*z**6 - 2464*z**4 - 899*z**4 - 2024*z**3 + 812*z**2 + 667*z\nCombining like terms, got 2728*z**6 - 3363*z**4 - 2024*z**3 + 812*z**2 + 667*z\n#Step 6:\nCurrent expression: 2728*z**6 - 3363*z**4 - 2024*z**3 + 812*z**2 + 667*z\nNo more calculations needed.\n2728*z**6 - 3363*z**4 - 2024*z**3 + 812*z**2 + 667*z", "generated_answer": "2728*z**6 - 3363*z**4 - 2024*z**3 + 812*z**2 + 667*z", "step_length": 6} {"cot_id": "6e82a4896133f82491c4fd0f4462f460e01bb45dd6dc14e589552417a3341505", "datapoint": {"question": "Calculate the following: -40*y**3*(-3*y**3 - 7*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "120*y**6 + 280*y**5", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1016, "polynomial_expr": "-40*y**3*(-3*y**3 - 7*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -40*y**3*(-3*y**3 - 7*y**2)\nExpanding the part (-3*y**3 - 7*y**2) using the distributive property, and we got: (-7*y**2)*(-40*y**3) + (-40*y**3)*(-3*y**3)\n#Step 2:\nCurrent expression: (-7*y**2)*(-40*y**3) + (-40*y**3)*(-3*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-7*y**2)*(-40*y**3) = 280*y**5\n (-3*y**3)*(-40*y**3) = 120*y**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 120*y**6 + 280*y**5\nNo more calculations needed.\n120*y**6 + 280*y**5", "generated_answer": "120*y**6 + 280*y**5", "step_length": 3} {"cot_id": "2aa18f04fe1a54b17b63c3b8465037d1c15bc700dd7e0f15a60f3028bef80a45", "datapoint": {"question": "Simplify this expression: (-26*x**2 - 37)*(x**3 - 42*x**2 + 44*x + 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-26*x**5 + 1092*x**4 - 1181*x**3 + 1372*x**2 - 1628*x - 259", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1017, "polynomial_expr": "(-26*x**2 - 37)*(x**3 - 42*x**2 + 44*x + 7)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-26*x**2 - 37)*(x**3 - 42*x**2 + 44*x + 7)\nExpanding the part (-26*x**2 - 37) using the distributive property, and we got: (-26*x**2)*(x**3 - 42*x**2 + 44*x + 7) - 37*(x**3 - 42*x**2 + 44*x + 7)\n#Step 2:\nCurrent expression: (-26*x**2)*(x**3 - 42*x**2 + 44*x + 7) - 37*(x**3 - 42*x**2 + 44*x + 7)\nSimplifying the partial expression: -37*(x**3 - 42*x**2 + 44*x + 7)\nExpanding the part (x**3 - 42*x**2 + 44*x + 7) using the distributive property, and we got: x**3*(-37) + (44*x)*(-37) - 42*x**2*(-37) + 7*(-37)\nReplacing -37*(x**3 - 42*x**2 + 44*x + 7) with x**3*(-37) + (44*x)*(-37) - 42*x**2*(-37) + 7*(-37) in the overall expression.\n#Step 3:\nCurrent expression: x**3*(-37) + (44*x)*(-37) - 42*x**2*(-37) + (-26*x**2)*(x**3 - 42*x**2 + 44*x + 7) - 259\nSimplifying the partial expression: (-26*x**2)*(x**3 - 42*x**2 + 44*x + 7)\nExpanding the part (x**3 - 42*x**2 + 44*x + 7) using the distributive property, and we got: (-26*x**2)*x**3 + 7*(-26*x**2) + (44*x)*(-26*x**2) + (-42*x**2)*(-26*x**2)\nReplacing (-26*x**2)*(x**3 - 42*x**2 + 44*x + 7) with (-26*x**2)*x**3 + 7*(-26*x**2) + (44*x)*(-26*x**2) + (-42*x**2)*(-26*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-26*x**2)*x**3 + x**3*(-37) + 7*(-26)*x**2 + (44*x)*(-26*x**2) + (44*x)*(-37) + (-42*x**2)*(-26*x**2) - 42*x**2*(-37) - 259\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n x**3*-37 = -37*x**3\n x**3*(-26*x**2) = -26*x**5\n (-42*x**2)*-37 = 1554*x**2\n (-42*x**2)*(-26*x**2) = 1092*x**4\n (44*x)*-37 = -1628*x\n (44*x)*(-26*x**2) = -1144*x**3\n 7*-26*x**2 = -182*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -26*x**5 + 1092*x**4 - 1144*x**3 - 37*x**3 - 182*x**2 + 1554*x**2 - 1628*x - 259\nCombining like terms, got -26*x**5 + 1092*x**4 - 1181*x**3 + 1372*x**2 - 1628*x - 259\n#Step 6:\nCurrent expression: -26*x**5 + 1092*x**4 - 1181*x**3 + 1372*x**2 - 1628*x - 259\nNo more calculations needed.\n-26*x**5 + 1092*x**4 - 1181*x**3 + 1372*x**2 - 1628*x - 259", "generated_answer": "-26*x**5 + 1092*x**4 - 1181*x**3 + 1372*x**2 - 1628*x - 259", "step_length": 6} {"cot_id": "01723def4da698a5ae24308e12f31e8d83c180f679176f3f2018224631cd43fd", "datapoint": {"question": "Simplify this expression: 138 - 69*x\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "138 - 69*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1018, "polynomial_expr": "138 - 69*x", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 138 - 69*x\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 138 - 69*x\nNo more calculations needed.\n138 - 69*x", "generated_answer": "138 - 69*x", "step_length": 2} {"cot_id": "8e58c72b3e92a51a9f7fbb21c03d10c25d93f2a1495d54bb5dc0e50073206d41", "datapoint": {"question": "Simplify this expression: 99*z*(-7*z**3 - 9*z**2 - 9*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-693*z**4 - 891*z**3 - 891*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1019, "polynomial_expr": "99*z*(-7*z**3 - 9*z**2 - 9*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 99*z*(-7*z**3 - 9*z**2 - 9*z)\nExpanding the part (-7*z**3 - 9*z**2 - 9*z) using the distributive property, and we got: (-9*z)*(99*z) + (99*z)*(-9*z**2) + (99*z)*(-7*z**3)\n#Step 2:\nCurrent expression: (-9*z)*(99*z) + (99*z)*(-9*z**2) + (99*z)*(-7*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-9*z)*(99*z) = -891*z**2\n (-9*z**2)*(99*z) = -891*z**3\n (-7*z**3)*(99*z) = -693*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -693*z**4 - 891*z**3 - 891*z**2\nNo more calculations needed.\n-693*z**4 - 891*z**3 - 891*z**2", "generated_answer": "-693*z**4 - 891*z**3 - 891*z**2", "step_length": 3} {"cot_id": "8176e1969b39eb2a49d0b9b89280cf51f328ad2c42bc0c7d15fe2bc2349b12d2", "datapoint": {"question": "Calculate the following: (-59*x**2 + 44*x)*(3*x**3 + 37*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-177*x**5 + 132*x**4 - 2183*x**3 + 1628*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1020, "polynomial_expr": "(-59*x**2 + 44*x)*(3*x**3 + 37*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-59*x**2 + 44*x)*(3*x**3 + 37*x)\nExpanding the part (-59*x**2 + 44*x) using the distributive property, and we got: (44*x)*(3*x**3 + 37*x) + (-59*x**2)*(3*x**3 + 37*x)\n#Step 2:\nCurrent expression: (44*x)*(3*x**3 + 37*x) + (-59*x**2)*(3*x**3 + 37*x)\nSimplifying the partial expression: (-59*x**2)*(3*x**3 + 37*x)\nExpanding the part (3*x**3 + 37*x) using the distributive property, and we got: (37*x)*(-59*x**2) + (-59*x**2)*(3*x**3)\nReplacing (-59*x**2)*(3*x**3 + 37*x) with (37*x)*(-59*x**2) + (-59*x**2)*(3*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (37*x)*(-59*x**2) + (44*x)*(3*x**3 + 37*x) + (-59*x**2)*(3*x**3)\nSimplifying the partial expression: (44*x)*(3*x**3 + 37*x)\nExpanding the part (3*x**3 + 37*x) using the distributive property, and we got: (37*x)*(44*x) + (44*x)*(3*x**3)\nReplacing (44*x)*(3*x**3 + 37*x) with (37*x)*(44*x) + (44*x)*(3*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (37*x)*(44*x) + (37*x)*(-59*x**2) + (44*x)*(3*x**3) + (-59*x**2)*(3*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (3*x**3)*(-59*x**2) = -177*x**5\n (3*x**3)*(44*x) = 132*x**4\n (37*x)*(-59*x**2) = -2183*x**3\n (37*x)*(44*x) = 1628*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -177*x**5 + 132*x**4 - 2183*x**3 + 1628*x**2\nNo more calculations needed.\n-177*x**5 + 132*x**4 - 2183*x**3 + 1628*x**2", "generated_answer": "-177*x**5 + 132*x**4 - 2183*x**3 + 1628*x**2", "step_length": 5} {"cot_id": "4de5774180989dcf4ebb9e32221c4752babab92808050427c4ddc02d3fdc43a0", "datapoint": {"question": "Simplify this expression: (-3*x**3 + 26*x**2 + 40)*(13*x**3 + 20*x**2 + 34*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-39*x**6 + 278*x**5 + 418*x**4 + 1404*x**3 + 800*x**2 + 1360*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1021, "polynomial_expr": "(-3*x**3 + 26*x**2 + 40)*(13*x**3 + 20*x**2 + 34*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-3*x**3 + 26*x**2 + 40)*(13*x**3 + 20*x**2 + 34*x)\nExpanding the part (-3*x**3 + 26*x**2 + 40) using the distributive property, and we got: (26*x**2)*(13*x**3 + 20*x**2 + 34*x) + (-3*x**3)*(13*x**3 + 20*x**2 + 34*x) + 40*(13*x**3 + 20*x**2 + 34*x)\n#Step 2:\nCurrent expression: (26*x**2)*(13*x**3 + 20*x**2 + 34*x) + (-3*x**3)*(13*x**3 + 20*x**2 + 34*x) + 40*(13*x**3 + 20*x**2 + 34*x)\nSimplifying the partial expression: 40*(13*x**3 + 20*x**2 + 34*x)\nExpanding the part (13*x**3 + 20*x**2 + 34*x) using the distributive property, and we got: (34*x)*40 + (20*x**2)*40 + (13*x**3)*40\nReplacing 40*(13*x**3 + 20*x**2 + 34*x) with (34*x)*40 + (20*x**2)*40 + (13*x**3)*40 in the overall expression.\n#Step 3:\nCurrent expression: (34*x)*40 + (20*x**2)*40 + (26*x**2)*(13*x**3 + 20*x**2 + 34*x) + (-3*x**3)*(13*x**3 + 20*x**2 + 34*x) + (13*x**3)*40\nSimplifying the partial expression: (-3*x**3)*(13*x**3 + 20*x**2 + 34*x)\nExpanding the part (13*x**3 + 20*x**2 + 34*x) using the distributive property, and we got: (34*x)*(-3*x**3) + (20*x**2)*(-3*x**3) + (-3*x**3)*(13*x**3)\nReplacing (-3*x**3)*(13*x**3 + 20*x**2 + 34*x) with (34*x)*(-3*x**3) + (20*x**2)*(-3*x**3) + (-3*x**3)*(13*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (34*x)*(-3*x**3) + (34*x)*40 + (20*x**2)*(-3*x**3) + (20*x**2)*40 + (26*x**2)*(13*x**3 + 20*x**2 + 34*x) + (-3*x**3)*(13*x**3) + (13*x**3)*40\nSimplifying the partial expression: (26*x**2)*(13*x**3 + 20*x**2 + 34*x)\nExpanding the part (13*x**3 + 20*x**2 + 34*x) using the distributive property, and we got: (34*x)*(26*x**2) + (20*x**2)*(26*x**2) + (26*x**2)*(13*x**3)\nReplacing (26*x**2)*(13*x**3 + 20*x**2 + 34*x) with (34*x)*(26*x**2) + (20*x**2)*(26*x**2) + (26*x**2)*(13*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (34*x)*(26*x**2) + (34*x)*(-3*x**3) + (34*x)*40 + (20*x**2)*(26*x**2) + (20*x**2)*(-3*x**3) + (20*x**2)*40 + (26*x**2)*(13*x**3) + (-3*x**3)*(13*x**3) + (13*x**3)*40\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (13*x**3)*40 = 520*x**3\n (13*x**3)*(-3*x**3) = -39*x**6\n (13*x**3)*(26*x**2) = 338*x**5\n (20*x**2)*40 = 800*x**2\n (20*x**2)*(-3*x**3) = -60*x**5\n (20*x**2)*(26*x**2) = 520*x**4\n (34*x)*40 = 1360*x\n (34*x)*(-3*x**3) = -102*x**4\n (34*x)*(26*x**2) = 884*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -39*x**6 - 60*x**5 + 338*x**5 - 102*x**4 + 520*x**4 + 520*x**3 + 884*x**3 + 800*x**2 + 1360*x\nCombining like terms, got -39*x**6 + 278*x**5 + 418*x**4 + 1404*x**3 + 800*x**2 + 1360*x\n#Step 7:\nCurrent expression: -39*x**6 + 278*x**5 + 418*x**4 + 1404*x**3 + 800*x**2 + 1360*x\nNo more calculations needed.\n-39*x**6 + 278*x**5 + 418*x**4 + 1404*x**3 + 800*x**2 + 1360*x", "generated_answer": "-39*x**6 + 278*x**5 + 418*x**4 + 1404*x**3 + 800*x**2 + 1360*x", "step_length": 7} {"cot_id": "1e77ad2187894527d21a4144a40f39d3b5eae1f6a6f6ad11336ca24148e65b7c", "datapoint": {"question": "Calculate the following: (-25*x - 48)*(-19*x**2 - 45)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "475*x**3 + 912*x**2 + 1125*x + 2160", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1022, "polynomial_expr": "(-25*x - 48)*(-19*x**2 - 45)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-25*x - 48)*(-19*x**2 - 45)\nExpanding the part (-25*x - 48) using the distributive property, and we got: (-25*x)*(-19*x**2 - 45) - 48*(-19*x**2 - 45)\n#Step 2:\nCurrent expression: (-25*x)*(-19*x**2 - 45) - 48*(-19*x**2 - 45)\nSimplifying the partial expression: -48*(-19*x**2 - 45)\nExpanding the part (-19*x**2 - 45) using the distributive property, and we got: -19*x**2*(-48) - 45*(-48)\nReplacing -48*(-19*x**2 - 45) with -19*x**2*(-48) - 45*(-48) in the overall expression.\n#Step 3:\nCurrent expression: (-25*x)*(-19*x**2 - 45) - 19*x**2*(-48) + 2160\nSimplifying the partial expression: (-25*x)*(-19*x**2 - 45)\nExpanding the part (-19*x**2 - 45) using the distributive property, and we got: (-25*x)*(-19*x**2) - (-1)*1125*x\nReplacing (-25*x)*(-19*x**2 - 45) with (-25*x)*(-19*x**2) - (-1)*1125*x in the overall expression.\n#Step 4:\nCurrent expression: (-25*x)*(-19*x**2) - 45*(-25)*x - 19*x**2*(-48) + 2160\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*x**2)*-48 = 912*x**2\n (-19*x**2)*(-25*x) = 475*x**3\n -45*-25*x = 1125*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 475*x**3 + 912*x**2 + 1125*x + 2160\nNo more calculations needed.\n475*x**3 + 912*x**2 + 1125*x + 2160", "generated_answer": "475*x**3 + 912*x**2 + 1125*x + 2160", "step_length": 5} {"cot_id": "2aa890df42eb8d0e2493e00d8ef44c7e10c3415ba42b40a7d93189cd351bacc8", "datapoint": {"question": "Simplify this expression: (10*z - 29)*(-13*z**3 + 12*z - 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-130*z**4 + 377*z**3 + 120*z**2 - 668*z + 928", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1023, "polynomial_expr": "(10*z - 29)*(-13*z**3 + 12*z - 32)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (10*z - 29)*(-13*z**3 + 12*z - 32)\nExpanding the part (10*z - 29) using the distributive property, and we got: (10*z)*(-13*z**3 + 12*z - 32) - 29*(-13*z**3 + 12*z - 32)\n#Step 2:\nCurrent expression: (10*z)*(-13*z**3 + 12*z - 32) - 29*(-13*z**3 + 12*z - 32)\nSimplifying the partial expression: -29*(-13*z**3 + 12*z - 32)\nExpanding the part (-13*z**3 + 12*z - 32) using the distributive property, and we got: (12*z)*(-29) - 13*z**3*(-29) - 32*(-29)\nReplacing -29*(-13*z**3 + 12*z - 32) with (12*z)*(-29) - 13*z**3*(-29) - 32*(-29) in the overall expression.\n#Step 3:\nCurrent expression: (10*z)*(-13*z**3 + 12*z - 32) + (12*z)*(-29) - 13*z**3*(-29) + 928\nSimplifying the partial expression: (10*z)*(-13*z**3 + 12*z - 32)\nExpanding the part (-13*z**3 + 12*z - 32) using the distributive property, and we got: -320*z + (10*z)*(12*z) + (10*z)*(-13*z**3)\nReplacing (10*z)*(-13*z**3 + 12*z - 32) with -320*z + (10*z)*(12*z) + (10*z)*(-13*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -32*10*z + (10*z)*(12*z) + (10*z)*(-13*z**3) + (12*z)*(-29) - 13*z**3*(-29) + 928\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*z**3)*-29 = 377*z**3\n (-13*z**3)*(10*z) = -130*z**4\n (12*z)*-29 = -348*z\n (12*z)*(10*z) = 120*z**2\n -32*10*z = -320*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -130*z**4 + 377*z**3 + 120*z**2 - 348*z - 320*z + 928\nCombining like terms, got -130*z**4 + 377*z**3 + 120*z**2 - 668*z + 928\n#Step 6:\nCurrent expression: -130*z**4 + 377*z**3 + 120*z**2 - 668*z + 928\nNo more calculations needed.\n-130*z**4 + 377*z**3 + 120*z**2 - 668*z + 928", "generated_answer": "-130*z**4 + 377*z**3 + 120*z**2 - 668*z + 928", "step_length": 6} {"cot_id": "15852c2f31e9614da6a6bfd8323c0acac0671d38f5223a462c906ebec28b0072", "datapoint": {"question": "Simplify this expression: (47*y**3 + 4)*(-20*y**2 + 26*y - 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-940*y**5 + 1222*y**4 - 1692*y**3 - 80*y**2 + 104*y - 144", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1024, "polynomial_expr": "(47*y**3 + 4)*(-20*y**2 + 26*y - 36)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (47*y**3 + 4)*(-20*y**2 + 26*y - 36)\nExpanding the part (47*y**3 + 4) using the distributive property, and we got: (47*y**3)*(-20*y**2 + 26*y - 36) + 4*(-20*y**2 + 26*y - 36)\n#Step 2:\nCurrent expression: (47*y**3)*(-20*y**2 + 26*y - 36) + 4*(-20*y**2 + 26*y - 36)\nSimplifying the partial expression: 4*(-20*y**2 + 26*y - 36)\nExpanding the part (-20*y**2 + 26*y - 36) using the distributive property, and we got: (26*y)*4 - 20*y**2*4 - 36*4\nReplacing 4*(-20*y**2 + 26*y - 36) with (26*y)*4 - 20*y**2*4 - 36*4 in the overall expression.\n#Step 3:\nCurrent expression: (26*y)*4 - 20*y**2*4 + (47*y**3)*(-20*y**2 + 26*y - 36) - 144\nSimplifying the partial expression: (47*y**3)*(-20*y**2 + 26*y - 36)\nExpanding the part (-20*y**2 + 26*y - 36) using the distributive property, and we got: -1692*y**3 + (26*y)*(47*y**3) + (-20*y**2)*(47*y**3)\nReplacing (47*y**3)*(-20*y**2 + 26*y - 36) with -1692*y**3 + (26*y)*(47*y**3) + (-20*y**2)*(47*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -36*47*y**3 + (26*y)*(47*y**3) + (26*y)*4 + (-20*y**2)*(47*y**3) - 20*y**2*4 - 144\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*y**2)*4 = -80*y**2\n (-20*y**2)*(47*y**3) = -940*y**5\n (26*y)*4 = 104*y\n (26*y)*(47*y**3) = 1222*y**4\n -36*47*y**3 = -1692*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -940*y**5 + 1222*y**4 - 1692*y**3 - 80*y**2 + 104*y - 144\nNo more calculations needed.\n-940*y**5 + 1222*y**4 - 1692*y**3 - 80*y**2 + 104*y - 144", "generated_answer": "-940*y**5 + 1222*y**4 - 1692*y**3 - 80*y**2 + 104*y - 144", "step_length": 5} {"cot_id": "cc7f1b12bb0819bd5b76a54ce505fe9ee8a6ee8a3f8b2ddd71646f348407b7f1", "datapoint": {"question": "Simplify this expression: (29*x**2 + 6*x)*(-21*x**3 + 3*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-609*x**5 - 39*x**4 + 18*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1025, "polynomial_expr": "(29*x**2 + 6*x)*(-21*x**3 + 3*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29*x**2 + 6*x)*(-21*x**3 + 3*x**2)\nExpanding the part (-21*x**3 + 3*x**2) using the distributive property, and we got: (3*x**2)*(29*x**2 + 6*x) + (-21*x**3)*(29*x**2 + 6*x)\n#Step 2:\nCurrent expression: (3*x**2)*(29*x**2 + 6*x) + (-21*x**3)*(29*x**2 + 6*x)\nSimplifying the partial expression: (-21*x**3)*(29*x**2 + 6*x)\nExpanding the part (29*x**2 + 6*x) using the distributive property, and we got: (6*x)*(-21*x**3) + (29*x**2)*(-21*x**3)\nReplacing (-21*x**3)*(29*x**2 + 6*x) with (6*x)*(-21*x**3) + (29*x**2)*(-21*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (6*x)*(-21*x**3) + (3*x**2)*(29*x**2 + 6*x) + (29*x**2)*(-21*x**3)\nSimplifying the partial expression: (3*x**2)*(29*x**2 + 6*x)\nExpanding the part (29*x**2 + 6*x) using the distributive property, and we got: (6*x)*(3*x**2) + (3*x**2)*(29*x**2)\nReplacing (3*x**2)*(29*x**2 + 6*x) with (6*x)*(3*x**2) + (3*x**2)*(29*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (6*x)*(3*x**2) + (6*x)*(-21*x**3) + (3*x**2)*(29*x**2) + (29*x**2)*(-21*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (6*x)*(-21*x**3) = -126*x**4\n (6*x)*(3*x**2) = 18*x**3\n (29*x**2)*(-21*x**3) = -609*x**5\n (29*x**2)*(3*x**2) = 87*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -609*x**5 - 126*x**4 + 87*x**4 + 18*x**3\nCombining like terms, got -609*x**5 - 39*x**4 + 18*x**3\n#Step 6:\nCurrent expression: -609*x**5 - 39*x**4 + 18*x**3\nNo more calculations needed.\n-609*x**5 - 39*x**4 + 18*x**3", "generated_answer": "-609*x**5 - 39*x**4 + 18*x**3", "step_length": 6} {"cot_id": "14c0f13b6e497f08312ff3327ee07174cfac8e648b8354f60e507bc18685d0f0", "datapoint": {"question": "Calculate the following: (-36*y**3 - 28*y)*(41*y**3 - 28*y + 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1476*y**6 - 140*y**4 - 864*y**3 + 784*y**2 - 672*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1026, "polynomial_expr": "(-36*y**3 - 28*y)*(41*y**3 - 28*y + 24)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-36*y**3 - 28*y)*(41*y**3 - 28*y + 24)\nExpanding the part (-36*y**3 - 28*y) using the distributive property, and we got: (-28*y)*(41*y**3 - 28*y + 24) + (-36*y**3)*(41*y**3 - 28*y + 24)\n#Step 2:\nCurrent expression: (-28*y)*(41*y**3 - 28*y + 24) + (-36*y**3)*(41*y**3 - 28*y + 24)\nSimplifying the partial expression: (-36*y**3)*(41*y**3 - 28*y + 24)\nExpanding the part (41*y**3 - 28*y + 24) using the distributive property, and we got: (-28*y)*(-36*y**3) + 24*(-36*y**3) + (-36*y**3)*(41*y**3)\nReplacing (-36*y**3)*(41*y**3 - 28*y + 24) with (-28*y)*(-36*y**3) + 24*(-36*y**3) + (-36*y**3)*(41*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-28*y)*(-36*y**3) + (-28*y)*(41*y**3 - 28*y + 24) + 24*(-36)*y**3 + (-36*y**3)*(41*y**3)\nSimplifying the partial expression: (-28*y)*(41*y**3 - 28*y + 24)\nExpanding the part (41*y**3 - 28*y + 24) using the distributive property, and we got: (-28*y)*(41*y**3) + (-28*y)*(-28*y) + 24*(-28*y)\nReplacing (-28*y)*(41*y**3 - 28*y + 24) with (-28*y)*(41*y**3) + (-28*y)*(-28*y) + 24*(-28*y) in the overall expression.\n#Step 4:\nCurrent expression: (-28*y)*(-36*y**3) + (-28*y)*(41*y**3) + (-28*y)*(-28*y) + 24*(-36)*y**3 + 24*(-28)*y + (-36*y**3)*(41*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*y)*(-36*y**3) = 1008*y**4\n (-28*y)*(-28*y) = 784*y**2\n (41*y**3)*(-36*y**3) = -1476*y**6\n (41*y**3)*(-28*y) = -1148*y**4\n 24*-36*y**3 = -864*y**3\n 24*-28*y = -672*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1476*y**6 - 1148*y**4 + 1008*y**4 - 864*y**3 + 784*y**2 - 672*y\nCombining like terms, got -1476*y**6 - 140*y**4 - 864*y**3 + 784*y**2 - 672*y\n#Step 6:\nCurrent expression: -1476*y**6 - 140*y**4 - 864*y**3 + 784*y**2 - 672*y\nNo more calculations needed.\n-1476*y**6 - 140*y**4 - 864*y**3 + 784*y**2 - 672*y", "generated_answer": "-1476*y**6 - 140*y**4 - 864*y**3 + 784*y**2 - 672*y", "step_length": 6} {"cot_id": "b4edf7698731953cd5a4569ea814f2fef02acc5e036038d6f4c48c623c2bf603", "datapoint": {"question": "Simplify this expression: (-2*y**2 - 24)*(26*y**3 + 33*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-52*y**5 - 66*y**4 - 624*y**3 - 792*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1027, "polynomial_expr": "(-2*y**2 - 24)*(26*y**3 + 33*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-2*y**2 - 24)*(26*y**3 + 33*y**2)\nExpanding the part (-2*y**2 - 24) using the distributive property, and we got: (-2*y**2)*(26*y**3 + 33*y**2) - 24*(26*y**3 + 33*y**2)\n#Step 2:\nCurrent expression: (-2*y**2)*(26*y**3 + 33*y**2) - 24*(26*y**3 + 33*y**2)\nSimplifying the partial expression: -24*(26*y**3 + 33*y**2)\nExpanding the part (26*y**3 + 33*y**2) using the distributive property, and we got: (33*y**2)*(-24) + (26*y**3)*(-24)\nReplacing -24*(26*y**3 + 33*y**2) with (33*y**2)*(-24) + (26*y**3)*(-24) in the overall expression.\n#Step 3:\nCurrent expression: (-2*y**2)*(26*y**3 + 33*y**2) + (33*y**2)*(-24) + (26*y**3)*(-24)\nSimplifying the partial expression: (-2*y**2)*(26*y**3 + 33*y**2)\nExpanding the part (26*y**3 + 33*y**2) using the distributive property, and we got: (-2*y**2)*(33*y**2) + (-2*y**2)*(26*y**3)\nReplacing (-2*y**2)*(26*y**3 + 33*y**2) with (-2*y**2)*(33*y**2) + (-2*y**2)*(26*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-2*y**2)*(33*y**2) + (-2*y**2)*(26*y**3) + (33*y**2)*(-24) + (26*y**3)*(-24)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (26*y**3)*-24 = -624*y**3\n (26*y**3)*(-2*y**2) = -52*y**5\n (33*y**2)*-24 = -792*y**2\n (33*y**2)*(-2*y**2) = -66*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -52*y**5 - 66*y**4 - 624*y**3 - 792*y**2\nNo more calculations needed.\n-52*y**5 - 66*y**4 - 624*y**3 - 792*y**2", "generated_answer": "-52*y**5 - 66*y**4 - 624*y**3 - 792*y**2", "step_length": 5} {"cot_id": "f086cf6ddd9729b54fd65456b28ba073e75a670d664a0c24906e2c3a18443881", "datapoint": {"question": "Simplify this expression: (38 - 10*y**3)*(-15*y**2 + y - 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "150*y**5 - 10*y**4 + 100*y**3 - 570*y**2 + 38*y - 380", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1028, "polynomial_expr": "(38 - 10*y**3)*(-15*y**2 + y - 10)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (38 - 10*y**3)*(-15*y**2 + y - 10)\nExpanding the part (38 - 10*y**3) using the distributive property, and we got: (-10*y**3)*(-15*y**2 + y - 10) + 38*(-15*y**2 + y - 10)\n#Step 2:\nCurrent expression: (-10*y**3)*(-15*y**2 + y - 10) + 38*(-15*y**2 + y - 10)\nSimplifying the partial expression: 38*(-15*y**2 + y - 10)\nExpanding the part (-15*y**2 + y - 10) using the distributive property, and we got: y*38 - 15*y**2*38 - 10*38\nReplacing 38*(-15*y**2 + y - 10) with y*38 - 15*y**2*38 - 10*38 in the overall expression.\n#Step 3:\nCurrent expression: y*38 - 15*y**2*38 + (-10*y**3)*(-15*y**2 + y - 10) - 380\nSimplifying the partial expression: (-10*y**3)*(-15*y**2 + y - 10)\nExpanding the part (-15*y**2 + y - 10) using the distributive property, and we got: -(-1)*100*y**3 + y*(-10*y**3) + (-15*y**2)*(-10*y**3)\nReplacing (-10*y**3)*(-15*y**2 + y - 10) with -(-1)*100*y**3 + y*(-10*y**3) + (-15*y**2)*(-10*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -10*(-10)*y**3 + y*(-10*y**3) + y*38 + (-15*y**2)*(-10*y**3) - 15*y**2*38 - 380\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n y*38 = 38*y\n y*(-10*y**3) = -10*y**4\n (-15*y**2)*38 = -570*y**2\n (-15*y**2)*(-10*y**3) = 150*y**5\n -10*-10*y**3 = 100*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 150*y**5 - 10*y**4 + 100*y**3 - 570*y**2 + 38*y - 380\nNo more calculations needed.\n150*y**5 - 10*y**4 + 100*y**3 - 570*y**2 + 38*y - 380", "generated_answer": "150*y**5 - 10*y**4 + 100*y**3 - 570*y**2 + 38*y - 380", "step_length": 5} {"cot_id": "37a6dc613797d7fb88e5a6aab15881edbdb3e8c052f0331cce50752d4a791343", "datapoint": {"question": "Simplify this expression: (-47*x**2 - 35*x)*(-4*x**3 - 23*x**2 + 34*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "188*x**5 + 1221*x**4 - 793*x**3 - 1190*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1029, "polynomial_expr": "(-47*x**2 - 35*x)*(-4*x**3 - 23*x**2 + 34*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-47*x**2 - 35*x)*(-4*x**3 - 23*x**2 + 34*x)\nExpanding the part (-47*x**2 - 35*x) using the distributive property, and we got: (-35*x)*(-4*x**3 - 23*x**2 + 34*x) + (-47*x**2)*(-4*x**3 - 23*x**2 + 34*x)\n#Step 2:\nCurrent expression: (-35*x)*(-4*x**3 - 23*x**2 + 34*x) + (-47*x**2)*(-4*x**3 - 23*x**2 + 34*x)\nSimplifying the partial expression: (-47*x**2)*(-4*x**3 - 23*x**2 + 34*x)\nExpanding the part (-4*x**3 - 23*x**2 + 34*x) using the distributive property, and we got: (34*x)*(-47*x**2) + (-47*x**2)*(-23*x**2) + (-47*x**2)*(-4*x**3)\nReplacing (-47*x**2)*(-4*x**3 - 23*x**2 + 34*x) with (34*x)*(-47*x**2) + (-47*x**2)*(-23*x**2) + (-47*x**2)*(-4*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-35*x)*(-4*x**3 - 23*x**2 + 34*x) + (34*x)*(-47*x**2) + (-47*x**2)*(-23*x**2) + (-47*x**2)*(-4*x**3)\nSimplifying the partial expression: (-35*x)*(-4*x**3 - 23*x**2 + 34*x)\nExpanding the part (-4*x**3 - 23*x**2 + 34*x) using the distributive property, and we got: (-35*x)*(34*x) + (-35*x)*(-23*x**2) + (-35*x)*(-4*x**3)\nReplacing (-35*x)*(-4*x**3 - 23*x**2 + 34*x) with (-35*x)*(34*x) + (-35*x)*(-23*x**2) + (-35*x)*(-4*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-35*x)*(34*x) + (-35*x)*(-23*x**2) + (-35*x)*(-4*x**3) + (34*x)*(-47*x**2) + (-47*x**2)*(-23*x**2) + (-47*x**2)*(-4*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*x**2)*(-47*x**2) = 1081*x**4\n (-23*x**2)*(-35*x) = 805*x**3\n (-4*x**3)*(-47*x**2) = 188*x**5\n (-4*x**3)*(-35*x) = 140*x**4\n (34*x)*(-47*x**2) = -1598*x**3\n (34*x)*(-35*x) = -1190*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 188*x**5 + 140*x**4 + 1081*x**4 - 1598*x**3 + 805*x**3 - 1190*x**2\nCombining like terms, got 188*x**5 + 1221*x**4 - 793*x**3 - 1190*x**2\n#Step 6:\nCurrent expression: 188*x**5 + 1221*x**4 - 793*x**3 - 1190*x**2\nNo more calculations needed.\n188*x**5 + 1221*x**4 - 793*x**3 - 1190*x**2", "generated_answer": "188*x**5 + 1221*x**4 - 793*x**3 - 1190*x**2", "step_length": 6} {"cot_id": "86b149dd9550bcd4d63f36d7770904820569369e15b8ba009533a00a909c232d", "datapoint": {"question": "Calculate the following: (28*y**2 - 48)*(-49*y**3 - 39*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1372*y**5 - 1092*y**4 + 2352*y**3 + 1872*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1030, "polynomial_expr": "(28*y**2 - 48)*(-49*y**3 - 39*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28*y**2 - 48)*(-49*y**3 - 39*y**2)\nExpanding the part (28*y**2 - 48) using the distributive property, and we got: (28*y**2)*(-49*y**3 - 39*y**2) - 48*(-49*y**3 - 39*y**2)\n#Step 2:\nCurrent expression: (28*y**2)*(-49*y**3 - 39*y**2) - 48*(-49*y**3 - 39*y**2)\nSimplifying the partial expression: -48*(-49*y**3 - 39*y**2)\nExpanding the part (-49*y**3 - 39*y**2) using the distributive property, and we got: -39*y**2*(-48) - 49*y**3*(-48)\nReplacing -48*(-49*y**3 - 39*y**2) with -39*y**2*(-48) - 49*y**3*(-48) in the overall expression.\n#Step 3:\nCurrent expression: -39*y**2*(-48) + (28*y**2)*(-49*y**3 - 39*y**2) - 49*y**3*(-48)\nSimplifying the partial expression: (28*y**2)*(-49*y**3 - 39*y**2)\nExpanding the part (-49*y**3 - 39*y**2) using the distributive property, and we got: (-39*y**2)*(28*y**2) + (28*y**2)*(-49*y**3)\nReplacing (28*y**2)*(-49*y**3 - 39*y**2) with (-39*y**2)*(28*y**2) + (28*y**2)*(-49*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-39*y**2)*(28*y**2) - 39*y**2*(-48) + (28*y**2)*(-49*y**3) - 49*y**3*(-48)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*y**3)*-48 = 2352*y**3\n (-49*y**3)*(28*y**2) = -1372*y**5\n (-39*y**2)*-48 = 1872*y**2\n (-39*y**2)*(28*y**2) = -1092*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1372*y**5 - 1092*y**4 + 2352*y**3 + 1872*y**2\nNo more calculations needed.\n-1372*y**5 - 1092*y**4 + 2352*y**3 + 1872*y**2", "generated_answer": "-1372*y**5 - 1092*y**4 + 2352*y**3 + 1872*y**2", "step_length": 5} {"cot_id": "9190ff64f2468a0bc7e42d7ec80efb962edced5b1323563becbfec71d60caa19", "datapoint": {"question": "Simplify this expression: -6*y**3*(38*y**3 - 3*y**2 + 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-228*y**6 + 18*y**5 - 84*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1031, "polynomial_expr": "-6*y**3*(38*y**3 - 3*y**2 + 14)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -6*y**3*(38*y**3 - 3*y**2 + 14)\nExpanding the part (38*y**3 - 3*y**2 + 14) using the distributive property, and we got: 14*(-6*y**3) + (-3*y**2)*(-6*y**3) + (-6*y**3)*(38*y**3)\n#Step 2:\nCurrent expression: 14*(-6*y**3) + (-3*y**2)*(-6*y**3) + (-6*y**3)*(38*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 14*(-6*y**3) = -84*y**3\n (-3*y**2)*(-6*y**3) = 18*y**5\n (38*y**3)*(-6*y**3) = -228*y**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -228*y**6 + 18*y**5 - 84*y**3\nNo more calculations needed.\n-228*y**6 + 18*y**5 - 84*y**3", "generated_answer": "-228*y**6 + 18*y**5 - 84*y**3", "step_length": 3} {"cot_id": "37a331014fec7926374cd688ecf307629d555da813ab3a652becf70e726434df", "datapoint": {"question": "Calculate the following: 56*z**2*(-29*z**3 - 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1624*z**5 - 2632*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1032, "polynomial_expr": "56*z**2*(-29*z**3 - 47)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 56*z**2*(-29*z**3 - 47)\nExpanding the part (-29*z**3 - 47) using the distributive property, and we got: -2632*z**2 + (56*z**2)*(-29*z**3)\n#Step 2:\nCurrent expression: -2632*z**2 + (56*z**2)*(-29*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -47*(56*z**2) = -2632*z**2\n (-29*z**3)*(56*z**2) = -1624*z**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1624*z**5 - 2632*z**2\nNo more calculations needed.\n-1624*z**5 - 2632*z**2", "generated_answer": "-1624*z**5 - 2632*z**2", "step_length": 3} {"cot_id": "08175e7b4bdb5314a12e8d3dc04c113b7855b09771b002c80a5819e7344d1784", "datapoint": {"question": "Simplify this expression: -16*y**2*(3*y - 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-48*y**3 + 608*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1033, "polynomial_expr": "-16*y**2*(3*y - 38)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -16*y**2*(3*y - 38)\nExpanding the part (3*y - 38) using the distributive property, and we got: -(-1)*608*y**2 + (3*y)*(-16*y**2)\n#Step 2:\nCurrent expression: -(-1)*608*y**2 + (3*y)*(-16*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -38*(-16*y**2) = 608*y**2\n (3*y)*(-16*y**2) = -48*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -48*y**3 + 608*y**2\nNo more calculations needed.\n-48*y**3 + 608*y**2", "generated_answer": "-48*y**3 + 608*y**2", "step_length": 3} {"cot_id": "2e99bd1137bea31ec73213a9d6dc5d77668d9971203a00e21ca10c7b575ee940", "datapoint": {"question": "Simplify this expression: (29 - 32*y)*(-23*y**3 - 11*y - 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "736*y**4 - 667*y**3 + 352*y**2 + 897*y - 1102", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1034, "polynomial_expr": "(29 - 32*y)*(-23*y**3 - 11*y - 38)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29 - 32*y)*(-23*y**3 - 11*y - 38)\nExpanding the part (29 - 32*y) using the distributive property, and we got: (-32*y)*(-23*y**3 - 11*y - 38) + 29*(-23*y**3 - 11*y - 38)\n#Step 2:\nCurrent expression: (-32*y)*(-23*y**3 - 11*y - 38) + 29*(-23*y**3 - 11*y - 38)\nSimplifying the partial expression: 29*(-23*y**3 - 11*y - 38)\nExpanding the part (-23*y**3 - 11*y - 38) using the distributive property, and we got: -11*y*29 - 23*y**3*29 - 38*29\nReplacing 29*(-23*y**3 - 11*y - 38) with -11*y*29 - 23*y**3*29 - 38*29 in the overall expression.\n#Step 3:\nCurrent expression: (-32*y)*(-23*y**3 - 11*y - 38) - 11*y*29 - 23*y**3*29 - 1102\nSimplifying the partial expression: (-32*y)*(-23*y**3 - 11*y - 38)\nExpanding the part (-23*y**3 - 11*y - 38) using the distributive property, and we got: (-32*y)*(-11*y) + (-32*y)*(-23*y**3) - (-1)*1216*y\nReplacing (-32*y)*(-23*y**3 - 11*y - 38) with (-32*y)*(-11*y) + (-32*y)*(-23*y**3) - (-1)*1216*y in the overall expression.\n#Step 4:\nCurrent expression: (-32*y)*(-11*y) + (-32*y)*(-23*y**3) - 11*y*29 - 38*(-32)*y - 23*y**3*29 - 1102\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*y**3)*29 = -667*y**3\n (-23*y**3)*(-32*y) = 736*y**4\n (-11*y)*29 = -319*y\n (-11*y)*(-32*y) = 352*y**2\n -38*-32*y = 1216*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 736*y**4 - 667*y**3 + 352*y**2 - 319*y + 1216*y - 1102\nCombining like terms, got 736*y**4 - 667*y**3 + 352*y**2 + 897*y - 1102\n#Step 6:\nCurrent expression: 736*y**4 - 667*y**3 + 352*y**2 + 897*y - 1102\nNo more calculations needed.\n736*y**4 - 667*y**3 + 352*y**2 + 897*y - 1102", "generated_answer": "736*y**4 - 667*y**3 + 352*y**2 + 897*y - 1102", "step_length": 6} {"cot_id": "593d2c404be40ec7c0847d15d5214fe62fc14b1534e40a22a77f21e7e6cc6e47", "datapoint": {"question": "Calculate the following: (22*z - 29)*(25*z**3 - 2*z - 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "550*z**4 - 725*z**3 - 44*z**2 - 646*z + 928", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1035, "polynomial_expr": "(22*z - 29)*(25*z**3 - 2*z - 32)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (22*z - 29)*(25*z**3 - 2*z - 32)\nExpanding the part (22*z - 29) using the distributive property, and we got: (22*z)*(25*z**3 - 2*z - 32) - 29*(25*z**3 - 2*z - 32)\n#Step 2:\nCurrent expression: (22*z)*(25*z**3 - 2*z - 32) - 29*(25*z**3 - 2*z - 32)\nSimplifying the partial expression: -29*(25*z**3 - 2*z - 32)\nExpanding the part (25*z**3 - 2*z - 32) using the distributive property, and we got: -2*z*(-29) + (25*z**3)*(-29) - 32*(-29)\nReplacing -29*(25*z**3 - 2*z - 32) with -2*z*(-29) + (25*z**3)*(-29) - 32*(-29) in the overall expression.\n#Step 3:\nCurrent expression: -2*z*(-29) + (22*z)*(25*z**3 - 2*z - 32) + (25*z**3)*(-29) + 928\nSimplifying the partial expression: (22*z)*(25*z**3 - 2*z - 32)\nExpanding the part (25*z**3 - 2*z - 32) using the distributive property, and we got: (-2*z)*(22*z) - 704*z + (22*z)*(25*z**3)\nReplacing (22*z)*(25*z**3 - 2*z - 32) with (-2*z)*(22*z) - 704*z + (22*z)*(25*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-2*z)*(22*z) - 2*z*(-29) - 32*22*z + (22*z)*(25*z**3) + (25*z**3)*(-29) + 928\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-2*z)*-29 = 58*z\n (-2*z)*(22*z) = -44*z**2\n (25*z**3)*-29 = -725*z**3\n (25*z**3)*(22*z) = 550*z**4\n -32*22*z = -704*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 550*z**4 - 725*z**3 - 44*z**2 - 704*z + 58*z + 928\nCombining like terms, got 550*z**4 - 725*z**3 - 44*z**2 - 646*z + 928\n#Step 6:\nCurrent expression: 550*z**4 - 725*z**3 - 44*z**2 - 646*z + 928\nNo more calculations needed.\n550*z**4 - 725*z**3 - 44*z**2 - 646*z + 928", "generated_answer": "550*z**4 - 725*z**3 - 44*z**2 - 646*z + 928", "step_length": 6} {"cot_id": "d4dd6b2927631f4dc426163e9b70971b4475a2239355d9314378b38c6ceab3b0", "datapoint": {"question": "Simplify this expression: -120*x**2*(-68*x**2 - 32*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "8160*x**4 + 3840*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1036, "polynomial_expr": "-120*x**2*(-68*x**2 - 32*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -120*x**2*(-68*x**2 - 32*x)\nExpanding the part (-68*x**2 - 32*x) using the distributive property, and we got: (-32*x)*(-120*x**2) + (-120*x**2)*(-68*x**2)\n#Step 2:\nCurrent expression: (-32*x)*(-120*x**2) + (-120*x**2)*(-68*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-68*x**2)*(-120*x**2) = 8160*x**4\n (-32*x)*(-120*x**2) = 3840*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 8160*x**4 + 3840*x**3\nNo more calculations needed.\n8160*x**4 + 3840*x**3", "generated_answer": "8160*x**4 + 3840*x**3", "step_length": 3} {"cot_id": "e51548e011500d744ad4f59c9e1cf2b079b45c76a709703cfb56a8f75726a340", "datapoint": {"question": "Simplify this expression: 1275*z**3 + 2465*z**2 + 2380*z - 3145\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1275*z**3 + 2465*z**2 + 2380*z - 3145", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1037, "polynomial_expr": "1275*z**3 + 2465*z**2 + 2380*z - 3145", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 1275*z**3 + 2465*z**2 + 2380*z - 3145\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 1275*z**3 + 2465*z**2 + 2380*z - 3145\nNo more calculations needed.\n1275*z**3 + 2465*z**2 + 2380*z - 3145", "generated_answer": "1275*z**3 + 2465*z**2 + 2380*z - 3145", "step_length": 2} {"cot_id": "47381779f1482afb00c4dac979bff43cbde988f30aca7042524fb2be7beb3c66", "datapoint": {"question": "Calculate the following: -51*y*(-9*y**2 - 21*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "459*y**3 + 1071*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1038, "polynomial_expr": "-51*y*(-9*y**2 - 21*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -51*y*(-9*y**2 - 21*y)\nExpanding the part (-9*y**2 - 21*y) using the distributive property, and we got: (-51*y)*(-21*y) + (-51*y)*(-9*y**2)\n#Step 2:\nCurrent expression: (-51*y)*(-21*y) + (-51*y)*(-9*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-21*y)*(-51*y) = 1071*y**2\n (-9*y**2)*(-51*y) = 459*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 459*y**3 + 1071*y**2\nNo more calculations needed.\n459*y**3 + 1071*y**2", "generated_answer": "459*y**3 + 1071*y**2", "step_length": 3} {"cot_id": "90ee390bb3e4021edd69852e17cf70f8e209f6ffebc9b783848b6fc567d4d4db", "datapoint": {"question": "Calculate the following: (-41*y - 25)*(39*y**3 + 3*y**2 - 32*y - 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1599*y**4 - 1098*y**3 + 1237*y**2 + 1456*y + 400", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1039, "polynomial_expr": "(-41*y - 25)*(39*y**3 + 3*y**2 - 32*y - 16)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-41*y - 25)*(39*y**3 + 3*y**2 - 32*y - 16)\nExpanding the part (-41*y - 25) using the distributive property, and we got: (-41*y)*(39*y**3 + 3*y**2 - 32*y - 16) - 25*(39*y**3 + 3*y**2 - 32*y - 16)\n#Step 2:\nCurrent expression: (-41*y)*(39*y**3 + 3*y**2 - 32*y - 16) - 25*(39*y**3 + 3*y**2 - 32*y - 16)\nSimplifying the partial expression: -25*(39*y**3 + 3*y**2 - 32*y - 16)\nExpanding the part (39*y**3 + 3*y**2 - 32*y - 16) using the distributive property, and we got: -32*y*(-25) + (3*y**2)*(-25) + (39*y**3)*(-25) - 16*(-25)\nReplacing -25*(39*y**3 + 3*y**2 - 32*y - 16) with -32*y*(-25) + (3*y**2)*(-25) + (39*y**3)*(-25) - 16*(-25) in the overall expression.\n#Step 3:\nCurrent expression: (-41*y)*(39*y**3 + 3*y**2 - 32*y - 16) - 32*y*(-25) + (3*y**2)*(-25) + (39*y**3)*(-25) + 400\nSimplifying the partial expression: (-41*y)*(39*y**3 + 3*y**2 - 32*y - 16)\nExpanding the part (39*y**3 + 3*y**2 - 32*y - 16) using the distributive property, and we got: (-41*y)*(-32*y) + (-41*y)*(3*y**2) + (-41*y)*(39*y**3) - (-1)*656*y\nReplacing (-41*y)*(39*y**3 + 3*y**2 - 32*y - 16) with (-41*y)*(-32*y) + (-41*y)*(3*y**2) + (-41*y)*(39*y**3) - (-1)*656*y in the overall expression.\n#Step 4:\nCurrent expression: (-41*y)*(-32*y) + (-41*y)*(3*y**2) + (-41*y)*(39*y**3) - 32*y*(-25) - 16*(-41)*y + (3*y**2)*(-25) + (39*y**3)*(-25) + 400\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*y)*-25 = 800*y\n (-32*y)*(-41*y) = 1312*y**2\n (3*y**2)*-25 = -75*y**2\n (3*y**2)*(-41*y) = -123*y**3\n (39*y**3)*-25 = -975*y**3\n (39*y**3)*(-41*y) = -1599*y**4\n -16*-41*y = 656*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1599*y**4 - 975*y**3 - 123*y**3 - 75*y**2 + 1312*y**2 + 656*y + 800*y + 400\nCombining like terms, got -1599*y**4 - 1098*y**3 + 1237*y**2 + 1456*y + 400\n#Step 6:\nCurrent expression: -1599*y**4 - 1098*y**3 + 1237*y**2 + 1456*y + 400\nNo more calculations needed.\n-1599*y**4 - 1098*y**3 + 1237*y**2 + 1456*y + 400", "generated_answer": "-1599*y**4 - 1098*y**3 + 1237*y**2 + 1456*y + 400", "step_length": 6} {"cot_id": "eeb883d3898e22aa40d07db31057ea33c3ade9b17b3a4ec766f8cd05238dae6a", "datapoint": {"question": "Calculate the following: (-44*x**3 + 6*x)*(11*x**3 + 30*x**2 + 4*x + 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-484*x**6 - 1320*x**5 - 110*x**4 - 1140*x**3 + 24*x**2 + 180*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1040, "polynomial_expr": "(-44*x**3 + 6*x)*(11*x**3 + 30*x**2 + 4*x + 30)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-44*x**3 + 6*x)*(11*x**3 + 30*x**2 + 4*x + 30)\nExpanding the part (-44*x**3 + 6*x) using the distributive property, and we got: (6*x)*(11*x**3 + 30*x**2 + 4*x + 30) + (-44*x**3)*(11*x**3 + 30*x**2 + 4*x + 30)\n#Step 2:\nCurrent expression: (6*x)*(11*x**3 + 30*x**2 + 4*x + 30) + (-44*x**3)*(11*x**3 + 30*x**2 + 4*x + 30)\nSimplifying the partial expression: (-44*x**3)*(11*x**3 + 30*x**2 + 4*x + 30)\nExpanding the part (11*x**3 + 30*x**2 + 4*x + 30) using the distributive property, and we got: 30*(-44*x**3) + (4*x)*(-44*x**3) + (30*x**2)*(-44*x**3) + (-44*x**3)*(11*x**3)\nReplacing (-44*x**3)*(11*x**3 + 30*x**2 + 4*x + 30) with 30*(-44*x**3) + (4*x)*(-44*x**3) + (30*x**2)*(-44*x**3) + (-44*x**3)*(11*x**3) in the overall expression.\n#Step 3:\nCurrent expression: 30*(-44)*x**3 + (4*x)*(-44*x**3) + (6*x)*(11*x**3 + 30*x**2 + 4*x + 30) + (30*x**2)*(-44*x**3) + (-44*x**3)*(11*x**3)\nSimplifying the partial expression: (6*x)*(11*x**3 + 30*x**2 + 4*x + 30)\nExpanding the part (11*x**3 + 30*x**2 + 4*x + 30) using the distributive property, and we got: 30*(6*x) + (4*x)*(6*x) + (6*x)*(30*x**2) + (6*x)*(11*x**3)\nReplacing (6*x)*(11*x**3 + 30*x**2 + 4*x + 30) with 30*(6*x) + (4*x)*(6*x) + (6*x)*(30*x**2) + (6*x)*(11*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 30*(-44)*x**3 + 30*6*x + (4*x)*(6*x) + (4*x)*(-44*x**3) + (6*x)*(30*x**2) + (6*x)*(11*x**3) + (30*x**2)*(-44*x**3) + (-44*x**3)*(11*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (4*x)*(-44*x**3) = -176*x**4\n (4*x)*(6*x) = 24*x**2\n (11*x**3)*(-44*x**3) = -484*x**6\n (11*x**3)*(6*x) = 66*x**4\n (30*x**2)*(-44*x**3) = -1320*x**5\n (30*x**2)*(6*x) = 180*x**3\n 30*-44*x**3 = -1320*x**3\n 30*6*x = 180*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -484*x**6 - 1320*x**5 - 176*x**4 + 66*x**4 - 1320*x**3 + 180*x**3 + 24*x**2 + 180*x\nCombining like terms, got -484*x**6 - 1320*x**5 - 110*x**4 - 1140*x**3 + 24*x**2 + 180*x\n#Step 6:\nCurrent expression: -484*x**6 - 1320*x**5 - 110*x**4 - 1140*x**3 + 24*x**2 + 180*x\nNo more calculations needed.\n-484*x**6 - 1320*x**5 - 110*x**4 - 1140*x**3 + 24*x**2 + 180*x", "generated_answer": "-484*x**6 - 1320*x**5 - 110*x**4 - 1140*x**3 + 24*x**2 + 180*x", "step_length": 6} {"cot_id": "d3a97d129739a6c4f4a58864cfda7a215cd7dd3d85753cb1745401a9592ff414", "datapoint": {"question": "Simplify this expression: (14*x**3 - 23*x**2 + 20*x)*(32*x**3 - 6*x**2 - 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "448*x**6 - 820*x**5 + 778*x**4 - 820*x**3 + 1150*x**2 - 1000*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1041, "polynomial_expr": "(14*x**3 - 23*x**2 + 20*x)*(32*x**3 - 6*x**2 - 50)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14*x**3 - 23*x**2 + 20*x)*(32*x**3 - 6*x**2 - 50)\nExpanding the part (32*x**3 - 6*x**2 - 50) using the distributive property, and we got: (-6*x**2)*(14*x**3 - 23*x**2 + 20*x) + (32*x**3)*(14*x**3 - 23*x**2 + 20*x) - 50*(14*x**3 - 23*x**2 + 20*x)\n#Step 2:\nCurrent expression: (-6*x**2)*(14*x**3 - 23*x**2 + 20*x) + (32*x**3)*(14*x**3 - 23*x**2 + 20*x) - 50*(14*x**3 - 23*x**2 + 20*x)\nSimplifying the partial expression: -50*(14*x**3 - 23*x**2 + 20*x)\nExpanding the part (14*x**3 - 23*x**2 + 20*x) using the distributive property, and we got: (20*x)*(-50) - 23*x**2*(-50) + (14*x**3)*(-50)\nReplacing -50*(14*x**3 - 23*x**2 + 20*x) with (20*x)*(-50) - 23*x**2*(-50) + (14*x**3)*(-50) in the overall expression.\n#Step 3:\nCurrent expression: (20*x)*(-50) - 23*x**2*(-50) + (-6*x**2)*(14*x**3 - 23*x**2 + 20*x) + (14*x**3)*(-50) + (32*x**3)*(14*x**3 - 23*x**2 + 20*x)\nSimplifying the partial expression: (-6*x**2)*(14*x**3 - 23*x**2 + 20*x)\nExpanding the part (14*x**3 - 23*x**2 + 20*x) using the distributive property, and we got: (20*x)*(-6*x**2) + (-23*x**2)*(-6*x**2) + (-6*x**2)*(14*x**3)\nReplacing (-6*x**2)*(14*x**3 - 23*x**2 + 20*x) with (20*x)*(-6*x**2) + (-23*x**2)*(-6*x**2) + (-6*x**2)*(14*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (20*x)*(-6*x**2) + (20*x)*(-50) + (-23*x**2)*(-6*x**2) - 23*x**2*(-50) + (-6*x**2)*(14*x**3) + (14*x**3)*(-50) + (32*x**3)*(14*x**3 - 23*x**2 + 20*x)\nSimplifying the partial expression: (32*x**3)*(14*x**3 - 23*x**2 + 20*x)\nExpanding the part (14*x**3 - 23*x**2 + 20*x) using the distributive property, and we got: (20*x)*(32*x**3) + (-23*x**2)*(32*x**3) + (14*x**3)*(32*x**3)\nReplacing (32*x**3)*(14*x**3 - 23*x**2 + 20*x) with (20*x)*(32*x**3) + (-23*x**2)*(32*x**3) + (14*x**3)*(32*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (20*x)*(-6*x**2) + (20*x)*(32*x**3) + (20*x)*(-50) + (-23*x**2)*(-6*x**2) + (-23*x**2)*(32*x**3) - 23*x**2*(-50) + (-6*x**2)*(14*x**3) + (14*x**3)*(32*x**3) + (14*x**3)*(-50)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*x**2)*-50 = 1150*x**2\n (-23*x**2)*(-6*x**2) = 138*x**4\n (-23*x**2)*(32*x**3) = -736*x**5\n (14*x**3)*-50 = -700*x**3\n (14*x**3)*(-6*x**2) = -84*x**5\n (14*x**3)*(32*x**3) = 448*x**6\n (20*x)*-50 = -1000*x\n (20*x)*(-6*x**2) = -120*x**3\n (20*x)*(32*x**3) = 640*x**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 448*x**6 - 736*x**5 - 84*x**5 + 138*x**4 + 640*x**4 - 700*x**3 - 120*x**3 + 1150*x**2 - 1000*x\nCombining like terms, got 448*x**6 - 820*x**5 + 778*x**4 - 820*x**3 + 1150*x**2 - 1000*x\n#Step 7:\nCurrent expression: 448*x**6 - 820*x**5 + 778*x**4 - 820*x**3 + 1150*x**2 - 1000*x\nNo more calculations needed.\n448*x**6 - 820*x**5 + 778*x**4 - 820*x**3 + 1150*x**2 - 1000*x", "generated_answer": "448*x**6 - 820*x**5 + 778*x**4 - 820*x**3 + 1150*x**2 - 1000*x", "step_length": 7} {"cot_id": "8bf3ee8ce4bb1196bb3ceaf32f7ce470a2a964dd326aa4f8b7d11bbd07fba89d", "datapoint": {"question": "Simplify this expression: (9*z - 3)*(-56*z**2 - 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-504*z**3 + 168*z**2 - 144*z + 48", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1042, "polynomial_expr": "(9*z - 3)*(-56*z**2 - 16)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9*z - 3)*(-56*z**2 - 16)\nExpanding the part (-56*z**2 - 16) using the distributive property, and we got: (-56*z**2)*(9*z - 3) - 16*(9*z - 3)\n#Step 2:\nCurrent expression: (-56*z**2)*(9*z - 3) - 16*(9*z - 3)\nSimplifying the partial expression: -16*(9*z - 3)\nExpanding the part (9*z - 3) using the distributive property, and we got: (9*z)*(-16) - 3*(-16)\nReplacing -16*(9*z - 3) with (9*z)*(-16) - 3*(-16) in the overall expression.\n#Step 3:\nCurrent expression: (9*z)*(-16) + (-56*z**2)*(9*z - 3) + 48\nSimplifying the partial expression: (-56*z**2)*(9*z - 3)\nExpanding the part (9*z - 3) using the distributive property, and we got: -(-1)*168*z**2 + (9*z)*(-56*z**2)\nReplacing (-56*z**2)*(9*z - 3) with -(-1)*168*z**2 + (9*z)*(-56*z**2) in the overall expression.\n#Step 4:\nCurrent expression: -3*(-56)*z**2 + (9*z)*(-56*z**2) + (9*z)*(-16) + 48\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (9*z)*-16 = -144*z\n (9*z)*(-56*z**2) = -504*z**3\n -3*-56*z**2 = 168*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -504*z**3 + 168*z**2 - 144*z + 48\nNo more calculations needed.\n-504*z**3 + 168*z**2 - 144*z + 48", "generated_answer": "-504*z**3 + 168*z**2 - 144*z + 48", "step_length": 5} {"cot_id": "d4dcf7173cc039f691c5286e2e9ab51be020f7397d6acb47e391ab5701b5b4c7", "datapoint": {"question": "Simplify this expression: (-13*z**3 - 22*z**2 - 44)*(-11*z**3 + 50*z + 34)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "143*z**6 + 242*z**5 - 650*z**4 - 1058*z**3 - 748*z**2 - 2200*z - 1496", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1043, "polynomial_expr": "(-13*z**3 - 22*z**2 - 44)*(-11*z**3 + 50*z + 34)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-13*z**3 - 22*z**2 - 44)*(-11*z**3 + 50*z + 34)\nExpanding the part (-13*z**3 - 22*z**2 - 44) using the distributive property, and we got: (-22*z**2)*(-11*z**3 + 50*z + 34) + (-13*z**3)*(-11*z**3 + 50*z + 34) - 44*(-11*z**3 + 50*z + 34)\n#Step 2:\nCurrent expression: (-22*z**2)*(-11*z**3 + 50*z + 34) + (-13*z**3)*(-11*z**3 + 50*z + 34) - 44*(-11*z**3 + 50*z + 34)\nSimplifying the partial expression: -44*(-11*z**3 + 50*z + 34)\nExpanding the part (-11*z**3 + 50*z + 34) using the distributive property, and we got: (50*z)*(-44) - 11*z**3*(-44) + 34*(-44)\nReplacing -44*(-11*z**3 + 50*z + 34) with (50*z)*(-44) - 11*z**3*(-44) + 34*(-44) in the overall expression.\n#Step 3:\nCurrent expression: (50*z)*(-44) + (-22*z**2)*(-11*z**3 + 50*z + 34) + (-13*z**3)*(-11*z**3 + 50*z + 34) - 11*z**3*(-44) - 1496\nSimplifying the partial expression: (-22*z**2)*(-11*z**3 + 50*z + 34)\nExpanding the part (-11*z**3 + 50*z + 34) using the distributive property, and we got: 34*(-22*z**2) + (50*z)*(-22*z**2) + (-22*z**2)*(-11*z**3)\nReplacing (-22*z**2)*(-11*z**3 + 50*z + 34) with 34*(-22*z**2) + (50*z)*(-22*z**2) + (-22*z**2)*(-11*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 34*(-22)*z**2 + (50*z)*(-22*z**2) + (50*z)*(-44) + (-22*z**2)*(-11*z**3) + (-13*z**3)*(-11*z**3 + 50*z + 34) - 11*z**3*(-44) - 1496\nSimplifying the partial expression: (-13*z**3)*(-11*z**3 + 50*z + 34)\nExpanding the part (-11*z**3 + 50*z + 34) using the distributive property, and we got: 34*(-13*z**3) + (50*z)*(-13*z**3) + (-13*z**3)*(-11*z**3)\nReplacing (-13*z**3)*(-11*z**3 + 50*z + 34) with 34*(-13*z**3) + (50*z)*(-13*z**3) + (-13*z**3)*(-11*z**3) in the overall expression.\n#Step 5:\nCurrent expression: 34*(-13)*z**3 + 34*(-22)*z**2 + (50*z)*(-22*z**2) + (50*z)*(-13*z**3) + (50*z)*(-44) + (-22*z**2)*(-11*z**3) + (-13*z**3)*(-11*z**3) - 11*z**3*(-44) - 1496\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*z**3)*-44 = 484*z**3\n (-11*z**3)*(-22*z**2) = 242*z**5\n (-11*z**3)*(-13*z**3) = 143*z**6\n (50*z)*-44 = -2200*z\n (50*z)*(-22*z**2) = -1100*z**3\n (50*z)*(-13*z**3) = -650*z**4\n 34*-22*z**2 = -748*z**2\n 34*-13*z**3 = -442*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 143*z**6 + 242*z**5 - 650*z**4 - 1100*z**3 - 442*z**3 + 484*z**3 - 748*z**2 - 2200*z - 1496\nCombining like terms, got 143*z**6 + 242*z**5 - 650*z**4 - 1058*z**3 - 748*z**2 - 2200*z - 1496\n#Step 7:\nCurrent expression: 143*z**6 + 242*z**5 - 650*z**4 - 1058*z**3 - 748*z**2 - 2200*z - 1496\nNo more calculations needed.\n143*z**6 + 242*z**5 - 650*z**4 - 1058*z**3 - 748*z**2 - 2200*z - 1496", "generated_answer": "143*z**6 + 242*z**5 - 650*z**4 - 1058*z**3 - 748*z**2 - 2200*z - 1496", "step_length": 7} {"cot_id": "35b01d39d84f575286d6c36858800193c2a66c8f46575c9cfdf06c2d973840c4", "datapoint": {"question": "Calculate the following: (67*z**2 + 23)*(-7*z**3 - 35*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-469*z**5 - 2345*z**4 - 161*z**3 - 805*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1044, "polynomial_expr": "(67*z**2 + 23)*(-7*z**3 - 35*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (67*z**2 + 23)*(-7*z**3 - 35*z**2)\nExpanding the part (67*z**2 + 23) using the distributive property, and we got: (67*z**2)*(-7*z**3 - 35*z**2) + 23*(-7*z**3 - 35*z**2)\n#Step 2:\nCurrent expression: (67*z**2)*(-7*z**3 - 35*z**2) + 23*(-7*z**3 - 35*z**2)\nSimplifying the partial expression: 23*(-7*z**3 - 35*z**2)\nExpanding the part (-7*z**3 - 35*z**2) using the distributive property, and we got: -35*z**2*23 - 7*z**3*23\nReplacing 23*(-7*z**3 - 35*z**2) with -35*z**2*23 - 7*z**3*23 in the overall expression.\n#Step 3:\nCurrent expression: -35*z**2*23 + (67*z**2)*(-7*z**3 - 35*z**2) - 7*z**3*23\nSimplifying the partial expression: (67*z**2)*(-7*z**3 - 35*z**2)\nExpanding the part (-7*z**3 - 35*z**2) using the distributive property, and we got: (-35*z**2)*(67*z**2) + (67*z**2)*(-7*z**3)\nReplacing (67*z**2)*(-7*z**3 - 35*z**2) with (-35*z**2)*(67*z**2) + (67*z**2)*(-7*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-35*z**2)*(67*z**2) - 35*z**2*23 + (67*z**2)*(-7*z**3) - 7*z**3*23\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*z**2)*23 = -805*z**2\n (-35*z**2)*(67*z**2) = -2345*z**4\n (-7*z**3)*23 = -161*z**3\n (-7*z**3)*(67*z**2) = -469*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -469*z**5 - 2345*z**4 - 161*z**3 - 805*z**2\nNo more calculations needed.\n-469*z**5 - 2345*z**4 - 161*z**3 - 805*z**2", "generated_answer": "-469*z**5 - 2345*z**4 - 161*z**3 - 805*z**2", "step_length": 5} {"cot_id": "f41cda70e9871df1cd7c7a23b04c036e44c6ffd155c2b6b38f20ac9f70127628", "datapoint": {"question": "Calculate the following: (4 - 39*x**2)*(-56*x**3 - 11)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2184*x**5 - 224*x**3 + 429*x**2 - 44", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1045, "polynomial_expr": "(4 - 39*x**2)*(-56*x**3 - 11)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (4 - 39*x**2)*(-56*x**3 - 11)\nExpanding the part (-56*x**3 - 11) using the distributive property, and we got: (-56*x**3)*(4 - 39*x**2) - 11*(4 - 39*x**2)\n#Step 2:\nCurrent expression: (-56*x**3)*(4 - 39*x**2) - 11*(4 - 39*x**2)\nSimplifying the partial expression: -11*(4 - 39*x**2)\nExpanding the part (4 - 39*x**2) using the distributive property, and we got: -39*x**2*(-11) + 4*(-11)\nReplacing -11*(4 - 39*x**2) with -39*x**2*(-11) + 4*(-11) in the overall expression.\n#Step 3:\nCurrent expression: -39*x**2*(-11) + (-56*x**3)*(4 - 39*x**2) - 44\nSimplifying the partial expression: (-56*x**3)*(4 - 39*x**2)\nExpanding the part (4 - 39*x**2) using the distributive property, and we got: 4*(-56*x**3) + (-39*x**2)*(-56*x**3)\nReplacing (-56*x**3)*(4 - 39*x**2) with 4*(-56*x**3) + (-39*x**2)*(-56*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 4*(-56)*x**3 + (-39*x**2)*(-56*x**3) - 39*x**2*(-11) - 44\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*x**2)*-11 = 429*x**2\n (-39*x**2)*(-56*x**3) = 2184*x**5\n 4*-56*x**3 = -224*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2184*x**5 - 224*x**3 + 429*x**2 - 44\nNo more calculations needed.\n2184*x**5 - 224*x**3 + 429*x**2 - 44", "generated_answer": "2184*x**5 - 224*x**3 + 429*x**2 - 44", "step_length": 5} {"cot_id": "364284e22700225cf308bbee0d07d37c9c0850d4b91deea6d42480e5e058714e", "datapoint": {"question": "Calculate the following: (-17*z**3 - 43*z - 27)*(22*z**3 - 24*z**2 - 25)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-374*z**6 + 408*z**5 - 946*z**4 + 863*z**3 + 648*z**2 + 1075*z + 675", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1046, "polynomial_expr": "(-17*z**3 - 43*z - 27)*(22*z**3 - 24*z**2 - 25)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-17*z**3 - 43*z - 27)*(22*z**3 - 24*z**2 - 25)\nExpanding the part (-17*z**3 - 43*z - 27) using the distributive property, and we got: (-43*z)*(22*z**3 - 24*z**2 - 25) + (-17*z**3)*(22*z**3 - 24*z**2 - 25) - 27*(22*z**3 - 24*z**2 - 25)\n#Step 2:\nCurrent expression: (-43*z)*(22*z**3 - 24*z**2 - 25) + (-17*z**3)*(22*z**3 - 24*z**2 - 25) - 27*(22*z**3 - 24*z**2 - 25)\nSimplifying the partial expression: -27*(22*z**3 - 24*z**2 - 25)\nExpanding the part (22*z**3 - 24*z**2 - 25) using the distributive property, and we got: -24*z**2*(-27) + (22*z**3)*(-27) - 25*(-27)\nReplacing -27*(22*z**3 - 24*z**2 - 25) with -24*z**2*(-27) + (22*z**3)*(-27) - 25*(-27) in the overall expression.\n#Step 3:\nCurrent expression: (-43*z)*(22*z**3 - 24*z**2 - 25) - 24*z**2*(-27) + (-17*z**3)*(22*z**3 - 24*z**2 - 25) + (22*z**3)*(-27) + 675\nSimplifying the partial expression: (-43*z)*(22*z**3 - 24*z**2 - 25)\nExpanding the part (22*z**3 - 24*z**2 - 25) using the distributive property, and we got: (-43*z)*(-24*z**2) + (-43*z)*(22*z**3) - (-1)*1075*z\nReplacing (-43*z)*(22*z**3 - 24*z**2 - 25) with (-43*z)*(-24*z**2) + (-43*z)*(22*z**3) - (-1)*1075*z in the overall expression.\n#Step 4:\nCurrent expression: (-43*z)*(-24*z**2) + (-43*z)*(22*z**3) - 25*(-43)*z - 24*z**2*(-27) + (-17*z**3)*(22*z**3 - 24*z**2 - 25) + (22*z**3)*(-27) + 675\nSimplifying the partial expression: (-17*z**3)*(22*z**3 - 24*z**2 - 25)\nExpanding the part (22*z**3 - 24*z**2 - 25) using the distributive property, and we got: -(-1)*425*z**3 + (-24*z**2)*(-17*z**3) + (-17*z**3)*(22*z**3)\nReplacing (-17*z**3)*(22*z**3 - 24*z**2 - 25) with -(-1)*425*z**3 + (-24*z**2)*(-17*z**3) + (-17*z**3)*(22*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-43*z)*(-24*z**2) + (-43*z)*(22*z**3) - 25*(-17)*z**3 - 25*(-43)*z + (-24*z**2)*(-17*z**3) - 24*z**2*(-27) + (-17*z**3)*(22*z**3) + (22*z**3)*(-27) + 675\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-24*z**2)*-27 = 648*z**2\n (-24*z**2)*(-43*z) = 1032*z**3\n (-24*z**2)*(-17*z**3) = 408*z**5\n (22*z**3)*-27 = -594*z**3\n (22*z**3)*(-43*z) = -946*z**4\n (22*z**3)*(-17*z**3) = -374*z**6\n -25*-43*z = 1075*z\n -25*-17*z**3 = 425*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -374*z**6 + 408*z**5 - 946*z**4 - 594*z**3 + 425*z**3 + 1032*z**3 + 648*z**2 + 1075*z + 675\nCombining like terms, got -374*z**6 + 408*z**5 - 946*z**4 + 863*z**3 + 648*z**2 + 1075*z + 675\n#Step 7:\nCurrent expression: -374*z**6 + 408*z**5 - 946*z**4 + 863*z**3 + 648*z**2 + 1075*z + 675\nNo more calculations needed.\n-374*z**6 + 408*z**5 - 946*z**4 + 863*z**3 + 648*z**2 + 1075*z + 675", "generated_answer": "-374*z**6 + 408*z**5 - 946*z**4 + 863*z**3 + 648*z**2 + 1075*z + 675", "step_length": 7} {"cot_id": "b12fdac8ba156b072cbc383f434f39e08cc46ff8c3ceacfabb6e38c1db4f9b80", "datapoint": {"question": "Simplify this expression: (9*y**3 + 50)*(10*y**3 + 39*y**2 - 22)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "90*y**6 + 351*y**5 + 302*y**3 + 1950*y**2 - 1100", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1047, "polynomial_expr": "(9*y**3 + 50)*(10*y**3 + 39*y**2 - 22)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9*y**3 + 50)*(10*y**3 + 39*y**2 - 22)\nExpanding the part (9*y**3 + 50) using the distributive property, and we got: (9*y**3)*(10*y**3 + 39*y**2 - 22) + 50*(10*y**3 + 39*y**2 - 22)\n#Step 2:\nCurrent expression: (9*y**3)*(10*y**3 + 39*y**2 - 22) + 50*(10*y**3 + 39*y**2 - 22)\nSimplifying the partial expression: 50*(10*y**3 + 39*y**2 - 22)\nExpanding the part (10*y**3 + 39*y**2 - 22) using the distributive property, and we got: (39*y**2)*50 + (10*y**3)*50 - 22*50\nReplacing 50*(10*y**3 + 39*y**2 - 22) with (39*y**2)*50 + (10*y**3)*50 - 22*50 in the overall expression.\n#Step 3:\nCurrent expression: (39*y**2)*50 + (9*y**3)*(10*y**3 + 39*y**2 - 22) + (10*y**3)*50 - 1100\nSimplifying the partial expression: (9*y**3)*(10*y**3 + 39*y**2 - 22)\nExpanding the part (10*y**3 + 39*y**2 - 22) using the distributive property, and we got: -198*y**3 + (39*y**2)*(9*y**3) + (9*y**3)*(10*y**3)\nReplacing (9*y**3)*(10*y**3 + 39*y**2 - 22) with -198*y**3 + (39*y**2)*(9*y**3) + (9*y**3)*(10*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -22*9*y**3 + (39*y**2)*(9*y**3) + (39*y**2)*50 + (9*y**3)*(10*y**3) + (10*y**3)*50 - 1100\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (10*y**3)*50 = 500*y**3\n (10*y**3)*(9*y**3) = 90*y**6\n (39*y**2)*50 = 1950*y**2\n (39*y**2)*(9*y**3) = 351*y**5\n -22*9*y**3 = -198*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 90*y**6 + 351*y**5 - 198*y**3 + 500*y**3 + 1950*y**2 - 1100\nCombining like terms, got 90*y**6 + 351*y**5 + 302*y**3 + 1950*y**2 - 1100\n#Step 6:\nCurrent expression: 90*y**6 + 351*y**5 + 302*y**3 + 1950*y**2 - 1100\nNo more calculations needed.\n90*y**6 + 351*y**5 + 302*y**3 + 1950*y**2 - 1100", "generated_answer": "90*y**6 + 351*y**5 + 302*y**3 + 1950*y**2 - 1100", "step_length": 6} {"cot_id": "dc7c12e460557324404e7b75d1f4227b4fcc5661f41032c7534379bdcf118281", "datapoint": {"question": "Simplify this expression: (45*y**3 - 4*y)*(-47*y**3 - 39*y + 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2115*y**6 - 1567*y**4 + 1080*y**3 + 156*y**2 - 96*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1048, "polynomial_expr": "(45*y**3 - 4*y)*(-47*y**3 - 39*y + 24)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (45*y**3 - 4*y)*(-47*y**3 - 39*y + 24)\nExpanding the part (45*y**3 - 4*y) using the distributive property, and we got: (-4*y)*(-47*y**3 - 39*y + 24) + (45*y**3)*(-47*y**3 - 39*y + 24)\n#Step 2:\nCurrent expression: (-4*y)*(-47*y**3 - 39*y + 24) + (45*y**3)*(-47*y**3 - 39*y + 24)\nSimplifying the partial expression: (-4*y)*(-47*y**3 - 39*y + 24)\nExpanding the part (-47*y**3 - 39*y + 24) using the distributive property, and we got: (-39*y)*(-4*y) + (-4*y)*(-47*y**3) + 24*(-4*y)\nReplacing (-4*y)*(-47*y**3 - 39*y + 24) with (-39*y)*(-4*y) + (-4*y)*(-47*y**3) + 24*(-4*y) in the overall expression.\n#Step 3:\nCurrent expression: (-39*y)*(-4*y) + (-4*y)*(-47*y**3) + 24*(-4)*y + (45*y**3)*(-47*y**3 - 39*y + 24)\nSimplifying the partial expression: (45*y**3)*(-47*y**3 - 39*y + 24)\nExpanding the part (-47*y**3 - 39*y + 24) using the distributive property, and we got: (-39*y)*(45*y**3) + 24*(45*y**3) + (-47*y**3)*(45*y**3)\nReplacing (45*y**3)*(-47*y**3 - 39*y + 24) with (-39*y)*(45*y**3) + 24*(45*y**3) + (-47*y**3)*(45*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-39*y)*(-4*y) + (-39*y)*(45*y**3) + (-4*y)*(-47*y**3) + 24*45*y**3 + 24*(-4)*y + (-47*y**3)*(45*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*y**3)*(-4*y) = 188*y**4\n (-47*y**3)*(45*y**3) = -2115*y**6\n (-39*y)*(-4*y) = 156*y**2\n (-39*y)*(45*y**3) = -1755*y**4\n 24*-4*y = -96*y\n 24*45*y**3 = 1080*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2115*y**6 - 1755*y**4 + 188*y**4 + 1080*y**3 + 156*y**2 - 96*y\nCombining like terms, got -2115*y**6 - 1567*y**4 + 1080*y**3 + 156*y**2 - 96*y\n#Step 6:\nCurrent expression: -2115*y**6 - 1567*y**4 + 1080*y**3 + 156*y**2 - 96*y\nNo more calculations needed.\n-2115*y**6 - 1567*y**4 + 1080*y**3 + 156*y**2 - 96*y", "generated_answer": "-2115*y**6 - 1567*y**4 + 1080*y**3 + 156*y**2 - 96*y", "step_length": 6} {"cot_id": "00e2f04b7c14f615aa6949c5c1654d23df38d662ecfe609fcc17be86811320b8", "datapoint": {"question": "Calculate the following: (-18*y**3 - 33*y - 1)*(-9*y**3 + 7*y + 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "162*y**6 + 171*y**4 - 675*y**3 - 231*y**2 - 1261*y - 38", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1049, "polynomial_expr": "(-18*y**3 - 33*y - 1)*(-9*y**3 + 7*y + 38)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-18*y**3 - 33*y - 1)*(-9*y**3 + 7*y + 38)\nExpanding the part (-18*y**3 - 33*y - 1) using the distributive property, and we got: (-33*y)*(-9*y**3 + 7*y + 38) + (-18*y**3)*(-9*y**3 + 7*y + 38) - (-9*y**3 + 7*y + 38)\n#Step 2:\nCurrent expression: (-33*y)*(-9*y**3 + 7*y + 38) + (-18*y**3)*(-9*y**3 + 7*y + 38) - (-9*y**3 + 7*y + 38)\nSimplifying the partial expression: -(-9*y**3 + 7*y + 38)\nExpanding the part (-9*y**3 + 7*y + 38) using the distributive property, and we got: (7*y)*(-1) - 9*y**3*(-1) + 38*(-1)\nReplacing -(-9*y**3 + 7*y + 38) with (7*y)*(-1) - 9*y**3*(-1) + 38*(-1) in the overall expression.\n#Step 3:\nCurrent expression: (-33*y)*(-9*y**3 + 7*y + 38) + (7*y)*(-1) + (-18*y**3)*(-9*y**3 + 7*y + 38) - 9*y**3*(-1) - 38\nSimplifying the partial expression: (-33*y)*(-9*y**3 + 7*y + 38)\nExpanding the part (-9*y**3 + 7*y + 38) using the distributive property, and we got: (-33*y)*(7*y) + (-33*y)*(-9*y**3) + 38*(-33*y)\nReplacing (-33*y)*(-9*y**3 + 7*y + 38) with (-33*y)*(7*y) + (-33*y)*(-9*y**3) + 38*(-33*y) in the overall expression.\n#Step 4:\nCurrent expression: (-33*y)*(7*y) + (-33*y)*(-9*y**3) + 38*(-33)*y + (7*y)*(-1) + (-18*y**3)*(-9*y**3 + 7*y + 38) - 9*y**3*(-1) - 38\nSimplifying the partial expression: (-18*y**3)*(-9*y**3 + 7*y + 38)\nExpanding the part (-9*y**3 + 7*y + 38) using the distributive property, and we got: 38*(-18*y**3) + (7*y)*(-18*y**3) + (-18*y**3)*(-9*y**3)\nReplacing (-18*y**3)*(-9*y**3 + 7*y + 38) with 38*(-18*y**3) + (7*y)*(-18*y**3) + (-18*y**3)*(-9*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-33*y)*(7*y) + (-33*y)*(-9*y**3) + 38*(-18)*y**3 + 38*(-33)*y + (7*y)*(-18*y**3) + (7*y)*(-1) + (-18*y**3)*(-9*y**3) - 9*y**3*(-1) - 38\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-9*y**3)*-1 = 9*y**3\n (-9*y**3)*(-33*y) = 297*y**4\n (-9*y**3)*(-18*y**3) = 162*y**6\n (7*y)*-1 = -7*y\n (7*y)*(-33*y) = -231*y**2\n (7*y)*(-18*y**3) = -126*y**4\n 38*-33*y = -1254*y\n 38*-18*y**3 = -684*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 162*y**6 - 126*y**4 + 297*y**4 - 684*y**3 + 9*y**3 - 231*y**2 - 1254*y - 7*y - 38\nCombining like terms, got 162*y**6 + 171*y**4 - 675*y**3 - 231*y**2 - 1261*y - 38\n#Step 7:\nCurrent expression: 162*y**6 + 171*y**4 - 675*y**3 - 231*y**2 - 1261*y - 38\nNo more calculations needed.\n162*y**6 + 171*y**4 - 675*y**3 - 231*y**2 - 1261*y - 38", "generated_answer": "162*y**6 + 171*y**4 - 675*y**3 - 231*y**2 - 1261*y - 38", "step_length": 7} {"cot_id": "c8e31ebe9a2a924c9996668822c2f97d7f05884a6cb4001dd4277b23638da1d9", "datapoint": {"question": "Calculate the following: (-35*z**3 + 17*z**2)*(5*z**2 + 38*z - 15)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-175*z**5 - 1245*z**4 + 1171*z**3 - 255*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1050, "polynomial_expr": "(-35*z**3 + 17*z**2)*(5*z**2 + 38*z - 15)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-35*z**3 + 17*z**2)*(5*z**2 + 38*z - 15)\nExpanding the part (-35*z**3 + 17*z**2) using the distributive property, and we got: (17*z**2)*(5*z**2 + 38*z - 15) + (-35*z**3)*(5*z**2 + 38*z - 15)\n#Step 2:\nCurrent expression: (17*z**2)*(5*z**2 + 38*z - 15) + (-35*z**3)*(5*z**2 + 38*z - 15)\nSimplifying the partial expression: (-35*z**3)*(5*z**2 + 38*z - 15)\nExpanding the part (5*z**2 + 38*z - 15) using the distributive property, and we got: -(-1)*525*z**3 + (38*z)*(-35*z**3) + (5*z**2)*(-35*z**3)\nReplacing (-35*z**3)*(5*z**2 + 38*z - 15) with -(-1)*525*z**3 + (38*z)*(-35*z**3) + (5*z**2)*(-35*z**3) in the overall expression.\n#Step 3:\nCurrent expression: -15*(-35)*z**3 + (38*z)*(-35*z**3) + (5*z**2)*(-35*z**3) + (17*z**2)*(5*z**2 + 38*z - 15)\nSimplifying the partial expression: (17*z**2)*(5*z**2 + 38*z - 15)\nExpanding the part (5*z**2 + 38*z - 15) using the distributive property, and we got: -255*z**2 + (38*z)*(17*z**2) + (5*z**2)*(17*z**2)\nReplacing (17*z**2)*(5*z**2 + 38*z - 15) with -255*z**2 + (38*z)*(17*z**2) + (5*z**2)*(17*z**2) in the overall expression.\n#Step 4:\nCurrent expression: -15*(-35)*z**3 - 15*17*z**2 + (38*z)*(17*z**2) + (38*z)*(-35*z**3) + (5*z**2)*(17*z**2) + (5*z**2)*(-35*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (5*z**2)*(-35*z**3) = -175*z**5\n (5*z**2)*(17*z**2) = 85*z**4\n (38*z)*(-35*z**3) = -1330*z**4\n (38*z)*(17*z**2) = 646*z**3\n -15*-35*z**3 = 525*z**3\n -15*17*z**2 = -255*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -175*z**5 - 1330*z**4 + 85*z**4 + 525*z**3 + 646*z**3 - 255*z**2\nCombining like terms, got -175*z**5 - 1245*z**4 + 1171*z**3 - 255*z**2\n#Step 6:\nCurrent expression: -175*z**5 - 1245*z**4 + 1171*z**3 - 255*z**2\nNo more calculations needed.\n-175*z**5 - 1245*z**4 + 1171*z**3 - 255*z**2", "generated_answer": "-175*z**5 - 1245*z**4 + 1171*z**3 - 255*z**2", "step_length": 6} {"cot_id": "0a6e23f282523a33cb835538b338af9010d263f189fe4a281f1ba680f42f5b65", "datapoint": {"question": "Calculate the following: (16*y + 27)*(y**2 - 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "16*y**3 + 27*y**2 - 528*y - 891", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1051, "polynomial_expr": "(16*y + 27)*(y**2 - 33)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (16*y + 27)*(y**2 - 33)\nExpanding the part (y**2 - 33) using the distributive property, and we got: y**2*(16*y + 27) - 33*(16*y + 27)\n#Step 2:\nCurrent expression: y**2*(16*y + 27) - 33*(16*y + 27)\nSimplifying the partial expression: -33*(16*y + 27)\nExpanding the part (16*y + 27) using the distributive property, and we got: (16*y)*(-33) + 27*(-33)\nReplacing -33*(16*y + 27) with (16*y)*(-33) + 27*(-33) in the overall expression.\n#Step 3:\nCurrent expression: y**2*(16*y + 27) + (16*y)*(-33) - 891\nSimplifying the partial expression: y**2*(16*y + 27)\nExpanding the part (16*y + 27) using the distributive property, and we got: (16*y)*y**2 + 27*y**2\nReplacing y**2*(16*y + 27) with (16*y)*y**2 + 27*y**2 in the overall expression.\n#Step 4:\nCurrent expression: (16*y)*y**2 + 27*y**2 + (16*y)*(-33) - 891\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (16*y)*-33 = -528*y\n (16*y)*y**2 = 16*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 16*y**3 + 27*y**2 - 528*y - 891\nNo more calculations needed.\n16*y**3 + 27*y**2 - 528*y - 891", "generated_answer": "16*y**3 + 27*y**2 - 528*y - 891", "step_length": 5} {"cot_id": "57aeaad275f2027772630df2fee19585a0e2568814700e46d103ef28ed03033e", "datapoint": {"question": "Simplify this expression: (31*z**3 - 46*z**2)*(44*z**3 - 33*z + 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1364*z**6 - 2024*z**5 - 1023*z**4 + 3006*z**3 - 2208*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1052, "polynomial_expr": "(31*z**3 - 46*z**2)*(44*z**3 - 33*z + 48)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31*z**3 - 46*z**2)*(44*z**3 - 33*z + 48)\nExpanding the part (31*z**3 - 46*z**2) using the distributive property, and we got: (-46*z**2)*(44*z**3 - 33*z + 48) + (31*z**3)*(44*z**3 - 33*z + 48)\n#Step 2:\nCurrent expression: (-46*z**2)*(44*z**3 - 33*z + 48) + (31*z**3)*(44*z**3 - 33*z + 48)\nSimplifying the partial expression: (-46*z**2)*(44*z**3 - 33*z + 48)\nExpanding the part (44*z**3 - 33*z + 48) using the distributive property, and we got: (-33*z)*(-46*z**2) + 48*(-46*z**2) + (-46*z**2)*(44*z**3)\nReplacing (-46*z**2)*(44*z**3 - 33*z + 48) with (-33*z)*(-46*z**2) + 48*(-46*z**2) + (-46*z**2)*(44*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-33*z)*(-46*z**2) + 48*(-46)*z**2 + (-46*z**2)*(44*z**3) + (31*z**3)*(44*z**3 - 33*z + 48)\nSimplifying the partial expression: (31*z**3)*(44*z**3 - 33*z + 48)\nExpanding the part (44*z**3 - 33*z + 48) using the distributive property, and we got: (-33*z)*(31*z**3) + 48*(31*z**3) + (31*z**3)*(44*z**3)\nReplacing (31*z**3)*(44*z**3 - 33*z + 48) with (-33*z)*(31*z**3) + 48*(31*z**3) + (31*z**3)*(44*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-33*z)*(-46*z**2) + (-33*z)*(31*z**3) + 48*31*z**3 + 48*(-46)*z**2 + (-46*z**2)*(44*z**3) + (31*z**3)*(44*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*z)*(-46*z**2) = 1518*z**3\n (-33*z)*(31*z**3) = -1023*z**4\n (44*z**3)*(-46*z**2) = -2024*z**5\n (44*z**3)*(31*z**3) = 1364*z**6\n 48*-46*z**2 = -2208*z**2\n 48*31*z**3 = 1488*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1364*z**6 - 2024*z**5 - 1023*z**4 + 1488*z**3 + 1518*z**3 - 2208*z**2\nCombining like terms, got 1364*z**6 - 2024*z**5 - 1023*z**4 + 3006*z**3 - 2208*z**2\n#Step 6:\nCurrent expression: 1364*z**6 - 2024*z**5 - 1023*z**4 + 3006*z**3 - 2208*z**2\nNo more calculations needed.\n1364*z**6 - 2024*z**5 - 1023*z**4 + 3006*z**3 - 2208*z**2", "generated_answer": "1364*z**6 - 2024*z**5 - 1023*z**4 + 3006*z**3 - 2208*z**2", "step_length": 6} {"cot_id": "2a6cca7be395bb4dae5426ee602afa516aaca11c1e7077c644eaeafc71b0277b", "datapoint": {"question": "Simplify this expression: 49*x**3*(33 - 17*x**3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-833*x**6 + 1617*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1053, "polynomial_expr": "49*x**3*(33 - 17*x**3)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 49*x**3*(33 - 17*x**3)\nExpanding the part (33 - 17*x**3) using the distributive property, and we got: 33*(49*x**3) + (-17*x**3)*(49*x**3)\n#Step 2:\nCurrent expression: 33*(49*x**3) + (-17*x**3)*(49*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 33*(49*x**3) = 1617*x**3\n (-17*x**3)*(49*x**3) = -833*x**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -833*x**6 + 1617*x**3\nNo more calculations needed.\n-833*x**6 + 1617*x**3", "generated_answer": "-833*x**6 + 1617*x**3", "step_length": 3} {"cot_id": "e7233cacffc10d508d43566a8a6cc49fd39de7598fd2ce789b9c6bd762c05680", "datapoint": {"question": "Simplify this expression: (27*z**2 - 20*z)*(4*z**3 - 3*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "108*z**5 - 161*z**4 + 60*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1054, "polynomial_expr": "(27*z**2 - 20*z)*(4*z**3 - 3*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*z**2 - 20*z)*(4*z**3 - 3*z**2)\nExpanding the part (27*z**2 - 20*z) using the distributive property, and we got: (-20*z)*(4*z**3 - 3*z**2) + (27*z**2)*(4*z**3 - 3*z**2)\n#Step 2:\nCurrent expression: (-20*z)*(4*z**3 - 3*z**2) + (27*z**2)*(4*z**3 - 3*z**2)\nSimplifying the partial expression: (-20*z)*(4*z**3 - 3*z**2)\nExpanding the part (4*z**3 - 3*z**2) using the distributive property, and we got: (-20*z)*(-3*z**2) + (-20*z)*(4*z**3)\nReplacing (-20*z)*(4*z**3 - 3*z**2) with (-20*z)*(-3*z**2) + (-20*z)*(4*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-20*z)*(-3*z**2) + (-20*z)*(4*z**3) + (27*z**2)*(4*z**3 - 3*z**2)\nSimplifying the partial expression: (27*z**2)*(4*z**3 - 3*z**2)\nExpanding the part (4*z**3 - 3*z**2) using the distributive property, and we got: (-3*z**2)*(27*z**2) + (27*z**2)*(4*z**3)\nReplacing (27*z**2)*(4*z**3 - 3*z**2) with (-3*z**2)*(27*z**2) + (27*z**2)*(4*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-20*z)*(-3*z**2) + (-20*z)*(4*z**3) + (-3*z**2)*(27*z**2) + (27*z**2)*(4*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-3*z**2)*(-20*z) = 60*z**3\n (-3*z**2)*(27*z**2) = -81*z**4\n (4*z**3)*(-20*z) = -80*z**4\n (4*z**3)*(27*z**2) = 108*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 108*z**5 - 81*z**4 - 80*z**4 + 60*z**3\nCombining like terms, got 108*z**5 - 161*z**4 + 60*z**3\n#Step 6:\nCurrent expression: 108*z**5 - 161*z**4 + 60*z**3\nNo more calculations needed.\n108*z**5 - 161*z**4 + 60*z**3", "generated_answer": "108*z**5 - 161*z**4 + 60*z**3", "step_length": 6} {"cot_id": "86d79b5f7bef14653c49e0613b903d8f2f1aaab4e5bee70728305d21e3cf26fa", "datapoint": {"question": "Simplify this expression: (37 - 44*z)*(28*z**2 + 38*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1232*z**3 - 636*z**2 + 1406*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1055, "polynomial_expr": "(37 - 44*z)*(28*z**2 + 38*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (37 - 44*z)*(28*z**2 + 38*z)\nExpanding the part (37 - 44*z) using the distributive property, and we got: (-44*z)*(28*z**2 + 38*z) + 37*(28*z**2 + 38*z)\n#Step 2:\nCurrent expression: (-44*z)*(28*z**2 + 38*z) + 37*(28*z**2 + 38*z)\nSimplifying the partial expression: 37*(28*z**2 + 38*z)\nExpanding the part (28*z**2 + 38*z) using the distributive property, and we got: (38*z)*37 + (28*z**2)*37\nReplacing 37*(28*z**2 + 38*z) with (38*z)*37 + (28*z**2)*37 in the overall expression.\n#Step 3:\nCurrent expression: (-44*z)*(28*z**2 + 38*z) + (38*z)*37 + (28*z**2)*37\nSimplifying the partial expression: (-44*z)*(28*z**2 + 38*z)\nExpanding the part (28*z**2 + 38*z) using the distributive property, and we got: (-44*z)*(38*z) + (-44*z)*(28*z**2)\nReplacing (-44*z)*(28*z**2 + 38*z) with (-44*z)*(38*z) + (-44*z)*(28*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-44*z)*(38*z) + (-44*z)*(28*z**2) + (38*z)*37 + (28*z**2)*37\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (28*z**2)*37 = 1036*z**2\n (28*z**2)*(-44*z) = -1232*z**3\n (38*z)*37 = 1406*z\n (38*z)*(-44*z) = -1672*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1232*z**3 - 1672*z**2 + 1036*z**2 + 1406*z\nCombining like terms, got -1232*z**3 - 636*z**2 + 1406*z\n#Step 6:\nCurrent expression: -1232*z**3 - 636*z**2 + 1406*z\nNo more calculations needed.\n-1232*z**3 - 636*z**2 + 1406*z", "generated_answer": "-1232*z**3 - 636*z**2 + 1406*z", "step_length": 6} {"cot_id": "1301f1d7ccd787f50b03a6d556fb6b0074616192cd36878db615c84421b7d5ac", "datapoint": {"question": "Calculate the following: (-21*x - 41)*(-35*x**3 + 57*x**2 + 49*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "735*x**4 + 238*x**3 - 3366*x**2 - 2009*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1056, "polynomial_expr": "(-21*x - 41)*(-35*x**3 + 57*x**2 + 49*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-21*x - 41)*(-35*x**3 + 57*x**2 + 49*x)\nExpanding the part (-21*x - 41) using the distributive property, and we got: (-21*x)*(-35*x**3 + 57*x**2 + 49*x) - 41*(-35*x**3 + 57*x**2 + 49*x)\n#Step 2:\nCurrent expression: (-21*x)*(-35*x**3 + 57*x**2 + 49*x) - 41*(-35*x**3 + 57*x**2 + 49*x)\nSimplifying the partial expression: -41*(-35*x**3 + 57*x**2 + 49*x)\nExpanding the part (-35*x**3 + 57*x**2 + 49*x) using the distributive property, and we got: (49*x)*(-41) + (57*x**2)*(-41) - 35*x**3*(-41)\nReplacing -41*(-35*x**3 + 57*x**2 + 49*x) with (49*x)*(-41) + (57*x**2)*(-41) - 35*x**3*(-41) in the overall expression.\n#Step 3:\nCurrent expression: (-21*x)*(-35*x**3 + 57*x**2 + 49*x) + (49*x)*(-41) + (57*x**2)*(-41) - 35*x**3*(-41)\nSimplifying the partial expression: (-21*x)*(-35*x**3 + 57*x**2 + 49*x)\nExpanding the part (-35*x**3 + 57*x**2 + 49*x) using the distributive property, and we got: (-21*x)*(49*x) + (-21*x)*(57*x**2) + (-21*x)*(-35*x**3)\nReplacing (-21*x)*(-35*x**3 + 57*x**2 + 49*x) with (-21*x)*(49*x) + (-21*x)*(57*x**2) + (-21*x)*(-35*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-21*x)*(49*x) + (-21*x)*(57*x**2) + (-21*x)*(-35*x**3) + (49*x)*(-41) + (57*x**2)*(-41) - 35*x**3*(-41)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*x**3)*-41 = 1435*x**3\n (-35*x**3)*(-21*x) = 735*x**4\n (49*x)*-41 = -2009*x\n (49*x)*(-21*x) = -1029*x**2\n (57*x**2)*-41 = -2337*x**2\n (57*x**2)*(-21*x) = -1197*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 735*x**4 - 1197*x**3 + 1435*x**3 - 2337*x**2 - 1029*x**2 - 2009*x\nCombining like terms, got 735*x**4 + 238*x**3 - 3366*x**2 - 2009*x\n#Step 6:\nCurrent expression: 735*x**4 + 238*x**3 - 3366*x**2 - 2009*x\nNo more calculations needed.\n735*x**4 + 238*x**3 - 3366*x**2 - 2009*x", "generated_answer": "735*x**4 + 238*x**3 - 3366*x**2 - 2009*x", "step_length": 6} {"cot_id": "9c059e3aae6514059964839d9d2f8b45c7f3d0ba1c80470b09475573d58c28b5", "datapoint": {"question": "Simplify this expression: (8*y**3 - 43)*(-47*y**3 - 28*y**2 - 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-376*y**6 - 224*y**5 + 1965*y**3 + 1204*y**2 + 301", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1057, "polynomial_expr": "(8*y**3 - 43)*(-47*y**3 - 28*y**2 - 7)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (8*y**3 - 43)*(-47*y**3 - 28*y**2 - 7)\nExpanding the part (8*y**3 - 43) using the distributive property, and we got: (8*y**3)*(-47*y**3 - 28*y**2 - 7) - 43*(-47*y**3 - 28*y**2 - 7)\n#Step 2:\nCurrent expression: (8*y**3)*(-47*y**3 - 28*y**2 - 7) - 43*(-47*y**3 - 28*y**2 - 7)\nSimplifying the partial expression: -43*(-47*y**3 - 28*y**2 - 7)\nExpanding the part (-47*y**3 - 28*y**2 - 7) using the distributive property, and we got: -28*y**2*(-43) - 47*y**3*(-43) - 7*(-43)\nReplacing -43*(-47*y**3 - 28*y**2 - 7) with -28*y**2*(-43) - 47*y**3*(-43) - 7*(-43) in the overall expression.\n#Step 3:\nCurrent expression: -28*y**2*(-43) - 47*y**3*(-43) + (8*y**3)*(-47*y**3 - 28*y**2 - 7) + 301\nSimplifying the partial expression: (8*y**3)*(-47*y**3 - 28*y**2 - 7)\nExpanding the part (-47*y**3 - 28*y**2 - 7) using the distributive property, and we got: -56*y**3 + (-28*y**2)*(8*y**3) + (-47*y**3)*(8*y**3)\nReplacing (8*y**3)*(-47*y**3 - 28*y**2 - 7) with -56*y**3 + (-28*y**2)*(8*y**3) + (-47*y**3)*(8*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -7*8*y**3 + (-28*y**2)*(8*y**3) - 28*y**2*(-43) + (-47*y**3)*(8*y**3) - 47*y**3*(-43) + 301\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*y**3)*-43 = 2021*y**3\n (-47*y**3)*(8*y**3) = -376*y**6\n (-28*y**2)*-43 = 1204*y**2\n (-28*y**2)*(8*y**3) = -224*y**5\n -7*8*y**3 = -56*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -376*y**6 - 224*y**5 - 56*y**3 + 2021*y**3 + 1204*y**2 + 301\nCombining like terms, got -376*y**6 - 224*y**5 + 1965*y**3 + 1204*y**2 + 301\n#Step 6:\nCurrent expression: -376*y**6 - 224*y**5 + 1965*y**3 + 1204*y**2 + 301\nNo more calculations needed.\n-376*y**6 - 224*y**5 + 1965*y**3 + 1204*y**2 + 301", "generated_answer": "-376*y**6 - 224*y**5 + 1965*y**3 + 1204*y**2 + 301", "step_length": 6} {"cot_id": "fedf14395f4931ed72676c9d3ab97a65a46d8647943bb310f4457996455ed749", "datapoint": {"question": "Calculate the following: (-45*x**3 + 13*x - 22)*(9*x**3 + 26*x**2 - 16*x - 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-405*x**6 - 1170*x**5 + 837*x**4 + 1580*x**3 - 780*x**2 - 64*x + 704", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1058, "polynomial_expr": "(-45*x**3 + 13*x - 22)*(9*x**3 + 26*x**2 - 16*x - 32)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-45*x**3 + 13*x - 22)*(9*x**3 + 26*x**2 - 16*x - 32)\nExpanding the part (-45*x**3 + 13*x - 22) using the distributive property, and we got: (13*x)*(9*x**3 + 26*x**2 - 16*x - 32) + (-45*x**3)*(9*x**3 + 26*x**2 - 16*x - 32) - 22*(9*x**3 + 26*x**2 - 16*x - 32)\n#Step 2:\nCurrent expression: (13*x)*(9*x**3 + 26*x**2 - 16*x - 32) + (-45*x**3)*(9*x**3 + 26*x**2 - 16*x - 32) - 22*(9*x**3 + 26*x**2 - 16*x - 32)\nSimplifying the partial expression: -22*(9*x**3 + 26*x**2 - 16*x - 32)\nExpanding the part (9*x**3 + 26*x**2 - 16*x - 32) using the distributive property, and we got: -16*x*(-22) + (26*x**2)*(-22) + (9*x**3)*(-22) - 32*(-22)\nReplacing -22*(9*x**3 + 26*x**2 - 16*x - 32) with -16*x*(-22) + (26*x**2)*(-22) + (9*x**3)*(-22) - 32*(-22) in the overall expression.\n#Step 3:\nCurrent expression: -16*x*(-22) + (13*x)*(9*x**3 + 26*x**2 - 16*x - 32) + (26*x**2)*(-22) + (-45*x**3)*(9*x**3 + 26*x**2 - 16*x - 32) + (9*x**3)*(-22) + 704\nSimplifying the partial expression: (-45*x**3)*(9*x**3 + 26*x**2 - 16*x - 32)\nExpanding the part (9*x**3 + 26*x**2 - 16*x - 32) using the distributive property, and we got: (-16*x)*(-45*x**3) - (-1)*1440*x**3 + (26*x**2)*(-45*x**3) + (-45*x**3)*(9*x**3)\nReplacing (-45*x**3)*(9*x**3 + 26*x**2 - 16*x - 32) with (-16*x)*(-45*x**3) - (-1)*1440*x**3 + (26*x**2)*(-45*x**3) + (-45*x**3)*(9*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-16*x)*(-45*x**3) - 16*x*(-22) - 32*(-45)*x**3 + (13*x)*(9*x**3 + 26*x**2 - 16*x - 32) + (26*x**2)*(-45*x**3) + (26*x**2)*(-22) + (-45*x**3)*(9*x**3) + (9*x**3)*(-22) + 704\nSimplifying the partial expression: (13*x)*(9*x**3 + 26*x**2 - 16*x - 32)\nExpanding the part (9*x**3 + 26*x**2 - 16*x - 32) using the distributive property, and we got: (-16*x)*(13*x) - 416*x + (13*x)*(26*x**2) + (13*x)*(9*x**3)\nReplacing (13*x)*(9*x**3 + 26*x**2 - 16*x - 32) with (-16*x)*(13*x) - 416*x + (13*x)*(26*x**2) + (13*x)*(9*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-16*x)*(13*x) + (-16*x)*(-45*x**3) - 16*x*(-22) - 32*(-45)*x**3 - 32*13*x + (13*x)*(26*x**2) + (13*x)*(9*x**3) + (26*x**2)*(-45*x**3) + (26*x**2)*(-22) + (-45*x**3)*(9*x**3) + (9*x**3)*(-22) + 704\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-16*x)*-22 = 352*x\n (-16*x)*(-45*x**3) = 720*x**4\n (-16*x)*(13*x) = -208*x**2\n (9*x**3)*-22 = -198*x**3\n (9*x**3)*(-45*x**3) = -405*x**6\n (9*x**3)*(13*x) = 117*x**4\n (26*x**2)*-22 = -572*x**2\n (26*x**2)*(-45*x**3) = -1170*x**5\n (26*x**2)*(13*x) = 338*x**3\n -32*-45*x**3 = 1440*x**3\n -32*13*x = -416*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -405*x**6 - 1170*x**5 + 117*x**4 + 720*x**4 - 198*x**3 + 338*x**3 + 1440*x**3 - 572*x**2 - 208*x**2 - 416*x + 352*x + 704\nCombining like terms, got -405*x**6 - 1170*x**5 + 837*x**4 + 1580*x**3 - 780*x**2 - 64*x + 704\n#Step 7:\nCurrent expression: -405*x**6 - 1170*x**5 + 837*x**4 + 1580*x**3 - 780*x**2 - 64*x + 704\nNo more calculations needed.\n-405*x**6 - 1170*x**5 + 837*x**4 + 1580*x**3 - 780*x**2 - 64*x + 704", "generated_answer": "-405*x**6 - 1170*x**5 + 837*x**4 + 1580*x**3 - 780*x**2 - 64*x + 704", "step_length": 7} {"cot_id": "57dd01bb15fda0984926332d1a21f9f8c9709edd1d7b66ba72a3c44661d8ce5d", "datapoint": {"question": "Simplify this expression: (39*y**2 - 4)*(-19*y**3 + 34*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-741*y**5 + 1402*y**3 - 136*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1059, "polynomial_expr": "(39*y**2 - 4)*(-19*y**3 + 34*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (39*y**2 - 4)*(-19*y**3 + 34*y)\nExpanding the part (39*y**2 - 4) using the distributive property, and we got: (39*y**2)*(-19*y**3 + 34*y) - 4*(-19*y**3 + 34*y)\n#Step 2:\nCurrent expression: (39*y**2)*(-19*y**3 + 34*y) - 4*(-19*y**3 + 34*y)\nSimplifying the partial expression: -4*(-19*y**3 + 34*y)\nExpanding the part (-19*y**3 + 34*y) using the distributive property, and we got: (34*y)*(-4) - 19*y**3*(-4)\nReplacing -4*(-19*y**3 + 34*y) with (34*y)*(-4) - 19*y**3*(-4) in the overall expression.\n#Step 3:\nCurrent expression: (34*y)*(-4) + (39*y**2)*(-19*y**3 + 34*y) - 19*y**3*(-4)\nSimplifying the partial expression: (39*y**2)*(-19*y**3 + 34*y)\nExpanding the part (-19*y**3 + 34*y) using the distributive property, and we got: (34*y)*(39*y**2) + (39*y**2)*(-19*y**3)\nReplacing (39*y**2)*(-19*y**3 + 34*y) with (34*y)*(39*y**2) + (39*y**2)*(-19*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (34*y)*(39*y**2) + (34*y)*(-4) + (39*y**2)*(-19*y**3) - 19*y**3*(-4)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*y**3)*-4 = 76*y**3\n (-19*y**3)*(39*y**2) = -741*y**5\n (34*y)*-4 = -136*y\n (34*y)*(39*y**2) = 1326*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -741*y**5 + 76*y**3 + 1326*y**3 - 136*y\nCombining like terms, got -741*y**5 + 1402*y**3 - 136*y\n#Step 6:\nCurrent expression: -741*y**5 + 1402*y**3 - 136*y\nNo more calculations needed.\n-741*y**5 + 1402*y**3 - 136*y", "generated_answer": "-741*y**5 + 1402*y**3 - 136*y", "step_length": 6} {"cot_id": "fb25d9719d7da883f48a816db0adaf826120b4b7f27dd3243bb1723f41426529", "datapoint": {"question": "Calculate the following: (-42*z**2 + 13*z)*(32*z**3 + 17*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1344*z**5 - 298*z**4 + 221*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1060, "polynomial_expr": "(-42*z**2 + 13*z)*(32*z**3 + 17*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-42*z**2 + 13*z)*(32*z**3 + 17*z**2)\nExpanding the part (-42*z**2 + 13*z) using the distributive property, and we got: (13*z)*(32*z**3 + 17*z**2) + (-42*z**2)*(32*z**3 + 17*z**2)\n#Step 2:\nCurrent expression: (13*z)*(32*z**3 + 17*z**2) + (-42*z**2)*(32*z**3 + 17*z**2)\nSimplifying the partial expression: (-42*z**2)*(32*z**3 + 17*z**2)\nExpanding the part (32*z**3 + 17*z**2) using the distributive property, and we got: (-42*z**2)*(17*z**2) + (-42*z**2)*(32*z**3)\nReplacing (-42*z**2)*(32*z**3 + 17*z**2) with (-42*z**2)*(17*z**2) + (-42*z**2)*(32*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (13*z)*(32*z**3 + 17*z**2) + (-42*z**2)*(17*z**2) + (-42*z**2)*(32*z**3)\nSimplifying the partial expression: (13*z)*(32*z**3 + 17*z**2)\nExpanding the part (32*z**3 + 17*z**2) using the distributive property, and we got: (13*z)*(17*z**2) + (13*z)*(32*z**3)\nReplacing (13*z)*(32*z**3 + 17*z**2) with (13*z)*(17*z**2) + (13*z)*(32*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (13*z)*(17*z**2) + (13*z)*(32*z**3) + (-42*z**2)*(17*z**2) + (-42*z**2)*(32*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (17*z**2)*(-42*z**2) = -714*z**4\n (17*z**2)*(13*z) = 221*z**3\n (32*z**3)*(-42*z**2) = -1344*z**5\n (32*z**3)*(13*z) = 416*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1344*z**5 - 714*z**4 + 416*z**4 + 221*z**3\nCombining like terms, got -1344*z**5 - 298*z**4 + 221*z**3\n#Step 6:\nCurrent expression: -1344*z**5 - 298*z**4 + 221*z**3\nNo more calculations needed.\n-1344*z**5 - 298*z**4 + 221*z**3", "generated_answer": "-1344*z**5 - 298*z**4 + 221*z**3", "step_length": 6} {"cot_id": "b82a89b3ed378b80d3f9ad8f70eb88e98640ccb34c439bb8aeb0beab42b0cb55", "datapoint": {"question": "Calculate the following: (17*y**3 - 29)*(13*y**3 + 43*y**2 + 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "221*y**6 + 731*y**5 + 133*y**3 - 1247*y**2 - 870", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1061, "polynomial_expr": "(17*y**3 - 29)*(13*y**3 + 43*y**2 + 30)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (17*y**3 - 29)*(13*y**3 + 43*y**2 + 30)\nExpanding the part (17*y**3 - 29) using the distributive property, and we got: (17*y**3)*(13*y**3 + 43*y**2 + 30) - 29*(13*y**3 + 43*y**2 + 30)\n#Step 2:\nCurrent expression: (17*y**3)*(13*y**3 + 43*y**2 + 30) - 29*(13*y**3 + 43*y**2 + 30)\nSimplifying the partial expression: -29*(13*y**3 + 43*y**2 + 30)\nExpanding the part (13*y**3 + 43*y**2 + 30) using the distributive property, and we got: (43*y**2)*(-29) + (13*y**3)*(-29) + 30*(-29)\nReplacing -29*(13*y**3 + 43*y**2 + 30) with (43*y**2)*(-29) + (13*y**3)*(-29) + 30*(-29) in the overall expression.\n#Step 3:\nCurrent expression: (43*y**2)*(-29) + (13*y**3)*(-29) + (17*y**3)*(13*y**3 + 43*y**2 + 30) - 870\nSimplifying the partial expression: (17*y**3)*(13*y**3 + 43*y**2 + 30)\nExpanding the part (13*y**3 + 43*y**2 + 30) using the distributive property, and we got: 30*(17*y**3) + (43*y**2)*(17*y**3) + (13*y**3)*(17*y**3)\nReplacing (17*y**3)*(13*y**3 + 43*y**2 + 30) with 30*(17*y**3) + (43*y**2)*(17*y**3) + (13*y**3)*(17*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 30*17*y**3 + (43*y**2)*(17*y**3) + (43*y**2)*(-29) + (13*y**3)*(17*y**3) + (13*y**3)*(-29) - 870\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (13*y**3)*-29 = -377*y**3\n (13*y**3)*(17*y**3) = 221*y**6\n (43*y**2)*-29 = -1247*y**2\n (43*y**2)*(17*y**3) = 731*y**5\n 30*17*y**3 = 510*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 221*y**6 + 731*y**5 - 377*y**3 + 510*y**3 - 1247*y**2 - 870\nCombining like terms, got 221*y**6 + 731*y**5 + 133*y**3 - 1247*y**2 - 870\n#Step 6:\nCurrent expression: 221*y**6 + 731*y**5 + 133*y**3 - 1247*y**2 - 870\nNo more calculations needed.\n221*y**6 + 731*y**5 + 133*y**3 - 1247*y**2 - 870", "generated_answer": "221*y**6 + 731*y**5 + 133*y**3 - 1247*y**2 - 870", "step_length": 6} {"cot_id": "be52348e317a296fd760f9df9b92986a5142f79fb4bba8b74a81ab0aad0398ec", "datapoint": {"question": "Calculate the following: (-21*y**3 - 31*y)*(-7*y**3 - 25*y**2 - 4*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "147*y**6 + 525*y**5 + 301*y**4 + 775*y**3 + 124*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1062, "polynomial_expr": "(-21*y**3 - 31*y)*(-7*y**3 - 25*y**2 - 4*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-21*y**3 - 31*y)*(-7*y**3 - 25*y**2 - 4*y)\nExpanding the part (-21*y**3 - 31*y) using the distributive property, and we got: (-31*y)*(-7*y**3 - 25*y**2 - 4*y) + (-21*y**3)*(-7*y**3 - 25*y**2 - 4*y)\n#Step 2:\nCurrent expression: (-31*y)*(-7*y**3 - 25*y**2 - 4*y) + (-21*y**3)*(-7*y**3 - 25*y**2 - 4*y)\nSimplifying the partial expression: (-31*y)*(-7*y**3 - 25*y**2 - 4*y)\nExpanding the part (-7*y**3 - 25*y**2 - 4*y) using the distributive property, and we got: (-31*y)*(-4*y) + (-31*y)*(-25*y**2) + (-31*y)*(-7*y**3)\nReplacing (-31*y)*(-7*y**3 - 25*y**2 - 4*y) with (-31*y)*(-4*y) + (-31*y)*(-25*y**2) + (-31*y)*(-7*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-31*y)*(-4*y) + (-31*y)*(-25*y**2) + (-31*y)*(-7*y**3) + (-21*y**3)*(-7*y**3 - 25*y**2 - 4*y)\nSimplifying the partial expression: (-21*y**3)*(-7*y**3 - 25*y**2 - 4*y)\nExpanding the part (-7*y**3 - 25*y**2 - 4*y) using the distributive property, and we got: (-4*y)*(-21*y**3) + (-25*y**2)*(-21*y**3) + (-21*y**3)*(-7*y**3)\nReplacing (-21*y**3)*(-7*y**3 - 25*y**2 - 4*y) with (-4*y)*(-21*y**3) + (-25*y**2)*(-21*y**3) + (-21*y**3)*(-7*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-31*y)*(-4*y) + (-31*y)*(-25*y**2) + (-31*y)*(-7*y**3) + (-4*y)*(-21*y**3) + (-25*y**2)*(-21*y**3) + (-21*y**3)*(-7*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*y**2)*(-31*y) = 775*y**3\n (-25*y**2)*(-21*y**3) = 525*y**5\n (-7*y**3)*(-31*y) = 217*y**4\n (-7*y**3)*(-21*y**3) = 147*y**6\n (-4*y)*(-31*y) = 124*y**2\n (-4*y)*(-21*y**3) = 84*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 147*y**6 + 525*y**5 + 84*y**4 + 217*y**4 + 775*y**3 + 124*y**2\nCombining like terms, got 147*y**6 + 525*y**5 + 301*y**4 + 775*y**3 + 124*y**2\n#Step 6:\nCurrent expression: 147*y**6 + 525*y**5 + 301*y**4 + 775*y**3 + 124*y**2\nNo more calculations needed.\n147*y**6 + 525*y**5 + 301*y**4 + 775*y**3 + 124*y**2", "generated_answer": "147*y**6 + 525*y**5 + 301*y**4 + 775*y**3 + 124*y**2", "step_length": 6} {"cot_id": "232c1d66886ad8d69ab1cd64df438b83a7a37b771584d30fca62f03e408177fc", "datapoint": {"question": "Simplify this expression: (-34*x**3 - 10*x)*(33*x**3 - 34*x + 42)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1122*x**6 + 826*x**4 - 1428*x**3 + 340*x**2 - 420*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1063, "polynomial_expr": "(-34*x**3 - 10*x)*(33*x**3 - 34*x + 42)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-34*x**3 - 10*x)*(33*x**3 - 34*x + 42)\nExpanding the part (-34*x**3 - 10*x) using the distributive property, and we got: (-10*x)*(33*x**3 - 34*x + 42) + (-34*x**3)*(33*x**3 - 34*x + 42)\n#Step 2:\nCurrent expression: (-10*x)*(33*x**3 - 34*x + 42) + (-34*x**3)*(33*x**3 - 34*x + 42)\nSimplifying the partial expression: (-34*x**3)*(33*x**3 - 34*x + 42)\nExpanding the part (33*x**3 - 34*x + 42) using the distributive property, and we got: (-34*x)*(-34*x**3) + 42*(-34*x**3) + (-34*x**3)*(33*x**3)\nReplacing (-34*x**3)*(33*x**3 - 34*x + 42) with (-34*x)*(-34*x**3) + 42*(-34*x**3) + (-34*x**3)*(33*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-34*x)*(-34*x**3) + (-10*x)*(33*x**3 - 34*x + 42) + 42*(-34)*x**3 + (-34*x**3)*(33*x**3)\nSimplifying the partial expression: (-10*x)*(33*x**3 - 34*x + 42)\nExpanding the part (33*x**3 - 34*x + 42) using the distributive property, and we got: (-34*x)*(-10*x) + (-10*x)*(33*x**3) + 42*(-10*x)\nReplacing (-10*x)*(33*x**3 - 34*x + 42) with (-34*x)*(-10*x) + (-10*x)*(33*x**3) + 42*(-10*x) in the overall expression.\n#Step 4:\nCurrent expression: (-34*x)*(-10*x) + (-34*x)*(-34*x**3) + (-10*x)*(33*x**3) + 42*(-34)*x**3 + 42*(-10)*x + (-34*x**3)*(33*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*x)*(-34*x**3) = 1156*x**4\n (-34*x)*(-10*x) = 340*x**2\n (33*x**3)*(-34*x**3) = -1122*x**6\n (33*x**3)*(-10*x) = -330*x**4\n 42*-34*x**3 = -1428*x**3\n 42*-10*x = -420*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1122*x**6 - 330*x**4 + 1156*x**4 - 1428*x**3 + 340*x**2 - 420*x\nCombining like terms, got -1122*x**6 + 826*x**4 - 1428*x**3 + 340*x**2 - 420*x\n#Step 6:\nCurrent expression: -1122*x**6 + 826*x**4 - 1428*x**3 + 340*x**2 - 420*x\nNo more calculations needed.\n-1122*x**6 + 826*x**4 - 1428*x**3 + 340*x**2 - 420*x", "generated_answer": "-1122*x**6 + 826*x**4 - 1428*x**3 + 340*x**2 - 420*x", "step_length": 6} {"cot_id": "efd6726e939c3df6631b49ef97a39c5d0056adc00d7bb41261ed664d5f83828f", "datapoint": {"question": "Simplify this expression: (-4*y**2 - 7)*(-26*y**3 - 16*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "104*y**5 + 64*y**4 + 182*y**3 + 112*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1064, "polynomial_expr": "(-4*y**2 - 7)*(-26*y**3 - 16*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-4*y**2 - 7)*(-26*y**3 - 16*y**2)\nExpanding the part (-4*y**2 - 7) using the distributive property, and we got: (-4*y**2)*(-26*y**3 - 16*y**2) - 7*(-26*y**3 - 16*y**2)\n#Step 2:\nCurrent expression: (-4*y**2)*(-26*y**3 - 16*y**2) - 7*(-26*y**3 - 16*y**2)\nSimplifying the partial expression: -7*(-26*y**3 - 16*y**2)\nExpanding the part (-26*y**3 - 16*y**2) using the distributive property, and we got: -16*y**2*(-7) - 26*y**3*(-7)\nReplacing -7*(-26*y**3 - 16*y**2) with -16*y**2*(-7) - 26*y**3*(-7) in the overall expression.\n#Step 3:\nCurrent expression: -16*y**2*(-7) + (-4*y**2)*(-26*y**3 - 16*y**2) - 26*y**3*(-7)\nSimplifying the partial expression: (-4*y**2)*(-26*y**3 - 16*y**2)\nExpanding the part (-26*y**3 - 16*y**2) using the distributive property, and we got: (-16*y**2)*(-4*y**2) + (-4*y**2)*(-26*y**3)\nReplacing (-4*y**2)*(-26*y**3 - 16*y**2) with (-16*y**2)*(-4*y**2) + (-4*y**2)*(-26*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-16*y**2)*(-4*y**2) - 16*y**2*(-7) + (-4*y**2)*(-26*y**3) - 26*y**3*(-7)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-26*y**3)*-7 = 182*y**3\n (-26*y**3)*(-4*y**2) = 104*y**5\n (-16*y**2)*-7 = 112*y**2\n (-16*y**2)*(-4*y**2) = 64*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 104*y**5 + 64*y**4 + 182*y**3 + 112*y**2\nNo more calculations needed.\n104*y**5 + 64*y**4 + 182*y**3 + 112*y**2", "generated_answer": "104*y**5 + 64*y**4 + 182*y**3 + 112*y**2", "step_length": 5} {"cot_id": "56be16275f90c135f2c389ea9239a319c6954e76400e77021e574960da93afc4", "datapoint": {"question": "Simplify this expression: (-11*z**3 + 10*z**2 + 41)*(5*z**3 + 23*z + 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-55*z**6 + 50*z**5 - 253*z**4 + 204*z**3 + 210*z**2 + 943*z + 861", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1065, "polynomial_expr": "(-11*z**3 + 10*z**2 + 41)*(5*z**3 + 23*z + 21)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-11*z**3 + 10*z**2 + 41)*(5*z**3 + 23*z + 21)\nExpanding the part (5*z**3 + 23*z + 21) using the distributive property, and we got: (23*z)*(-11*z**3 + 10*z**2 + 41) + (5*z**3)*(-11*z**3 + 10*z**2 + 41) + 21*(-11*z**3 + 10*z**2 + 41)\n#Step 2:\nCurrent expression: (23*z)*(-11*z**3 + 10*z**2 + 41) + (5*z**3)*(-11*z**3 + 10*z**2 + 41) + 21*(-11*z**3 + 10*z**2 + 41)\nSimplifying the partial expression: 21*(-11*z**3 + 10*z**2 + 41)\nExpanding the part (-11*z**3 + 10*z**2 + 41) using the distributive property, and we got: (10*z**2)*21 - 11*z**3*21 + 41*21\nReplacing 21*(-11*z**3 + 10*z**2 + 41) with (10*z**2)*21 - 11*z**3*21 + 41*21 in the overall expression.\n#Step 3:\nCurrent expression: (23*z)*(-11*z**3 + 10*z**2 + 41) + (10*z**2)*21 - 11*z**3*21 + (5*z**3)*(-11*z**3 + 10*z**2 + 41) + 861\nSimplifying the partial expression: (5*z**3)*(-11*z**3 + 10*z**2 + 41)\nExpanding the part (-11*z**3 + 10*z**2 + 41) using the distributive property, and we got: 41*(5*z**3) + (10*z**2)*(5*z**3) + (-11*z**3)*(5*z**3)\nReplacing (5*z**3)*(-11*z**3 + 10*z**2 + 41) with 41*(5*z**3) + (10*z**2)*(5*z**3) + (-11*z**3)*(5*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 41*5*z**3 + (23*z)*(-11*z**3 + 10*z**2 + 41) + (10*z**2)*(5*z**3) + (10*z**2)*21 + (-11*z**3)*(5*z**3) - 11*z**3*21 + 861\nSimplifying the partial expression: (23*z)*(-11*z**3 + 10*z**2 + 41)\nExpanding the part (-11*z**3 + 10*z**2 + 41) using the distributive property, and we got: 41*(23*z) + (23*z)*(10*z**2) + (23*z)*(-11*z**3)\nReplacing (23*z)*(-11*z**3 + 10*z**2 + 41) with 41*(23*z) + (23*z)*(10*z**2) + (23*z)*(-11*z**3) in the overall expression.\n#Step 5:\nCurrent expression: 41*5*z**3 + 41*23*z + (23*z)*(10*z**2) + (23*z)*(-11*z**3) + (10*z**2)*(5*z**3) + (10*z**2)*21 + (-11*z**3)*(5*z**3) - 11*z**3*21 + 861\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*z**3)*21 = -231*z**3\n (-11*z**3)*(5*z**3) = -55*z**6\n (-11*z**3)*(23*z) = -253*z**4\n (10*z**2)*21 = 210*z**2\n (10*z**2)*(5*z**3) = 50*z**5\n (10*z**2)*(23*z) = 230*z**3\n 41*5*z**3 = 205*z**3\n 41*23*z = 943*z\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -55*z**6 + 50*z**5 - 253*z**4 - 231*z**3 + 205*z**3 + 230*z**3 + 210*z**2 + 943*z + 861\nCombining like terms, got -55*z**6 + 50*z**5 - 253*z**4 + 204*z**3 + 210*z**2 + 943*z + 861\n#Step 7:\nCurrent expression: -55*z**6 + 50*z**5 - 253*z**4 + 204*z**3 + 210*z**2 + 943*z + 861\nNo more calculations needed.\n-55*z**6 + 50*z**5 - 253*z**4 + 204*z**3 + 210*z**2 + 943*z + 861", "generated_answer": "-55*z**6 + 50*z**5 - 253*z**4 + 204*z**3 + 210*z**2 + 943*z + 861", "step_length": 7} {"cot_id": "6a0057fd3fc78d0ddd17caac3e32b38825044831744d05936881ced5a86d9f56", "datapoint": {"question": "Calculate the following: 2444*x**3 + 4420*x**2 + 468*x\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2444*x**3 + 4420*x**2 + 468*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1066, "polynomial_expr": "2444*x**3 + 4420*x**2 + 468*x", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 2444*x**3 + 4420*x**2 + 468*x\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 2444*x**3 + 4420*x**2 + 468*x\nNo more calculations needed.\n2444*x**3 + 4420*x**2 + 468*x", "generated_answer": "2444*x**3 + 4420*x**2 + 468*x", "step_length": 2} {"cot_id": "e938951a4d6c891bc1ac2663c0eb3f13f4fe23e2f137c21eccf65240de60abdd", "datapoint": {"question": "Simplify this expression: (-27*y**2 + 14*y)*(39*y**3 - 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1053*y**5 + 546*y**4 + 648*y**2 - 336*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1067, "polynomial_expr": "(-27*y**2 + 14*y)*(39*y**3 - 24)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-27*y**2 + 14*y)*(39*y**3 - 24)\nExpanding the part (39*y**3 - 24) using the distributive property, and we got: (39*y**3)*(-27*y**2 + 14*y) - 24*(-27*y**2 + 14*y)\n#Step 2:\nCurrent expression: (39*y**3)*(-27*y**2 + 14*y) - 24*(-27*y**2 + 14*y)\nSimplifying the partial expression: -24*(-27*y**2 + 14*y)\nExpanding the part (-27*y**2 + 14*y) using the distributive property, and we got: (14*y)*(-24) - 27*y**2*(-24)\nReplacing -24*(-27*y**2 + 14*y) with (14*y)*(-24) - 27*y**2*(-24) in the overall expression.\n#Step 3:\nCurrent expression: (14*y)*(-24) - 27*y**2*(-24) + (39*y**3)*(-27*y**2 + 14*y)\nSimplifying the partial expression: (39*y**3)*(-27*y**2 + 14*y)\nExpanding the part (-27*y**2 + 14*y) using the distributive property, and we got: (14*y)*(39*y**3) + (-27*y**2)*(39*y**3)\nReplacing (39*y**3)*(-27*y**2 + 14*y) with (14*y)*(39*y**3) + (-27*y**2)*(39*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (14*y)*(39*y**3) + (14*y)*(-24) + (-27*y**2)*(39*y**3) - 27*y**2*(-24)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*y**2)*-24 = 648*y**2\n (-27*y**2)*(39*y**3) = -1053*y**5\n (14*y)*-24 = -336*y\n (14*y)*(39*y**3) = 546*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1053*y**5 + 546*y**4 + 648*y**2 - 336*y\nNo more calculations needed.\n-1053*y**5 + 546*y**4 + 648*y**2 - 336*y", "generated_answer": "-1053*y**5 + 546*y**4 + 648*y**2 - 336*y", "step_length": 5} {"cot_id": "ab6cc2567ef74936211a500b3606a9085034561ea2ffb22b0b003f25d1abca0d", "datapoint": {"question": "Calculate the following: (-20*y**3 + 25*y**2)*(-12*y**3 + 17*y**2 + 26*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "240*y**6 - 640*y**5 - 95*y**4 + 650*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1068, "polynomial_expr": "(-20*y**3 + 25*y**2)*(-12*y**3 + 17*y**2 + 26*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-20*y**3 + 25*y**2)*(-12*y**3 + 17*y**2 + 26*y)\nExpanding the part (-20*y**3 + 25*y**2) using the distributive property, and we got: (25*y**2)*(-12*y**3 + 17*y**2 + 26*y) + (-20*y**3)*(-12*y**3 + 17*y**2 + 26*y)\n#Step 2:\nCurrent expression: (25*y**2)*(-12*y**3 + 17*y**2 + 26*y) + (-20*y**3)*(-12*y**3 + 17*y**2 + 26*y)\nSimplifying the partial expression: (-20*y**3)*(-12*y**3 + 17*y**2 + 26*y)\nExpanding the part (-12*y**3 + 17*y**2 + 26*y) using the distributive property, and we got: (26*y)*(-20*y**3) + (17*y**2)*(-20*y**3) + (-20*y**3)*(-12*y**3)\nReplacing (-20*y**3)*(-12*y**3 + 17*y**2 + 26*y) with (26*y)*(-20*y**3) + (17*y**2)*(-20*y**3) + (-20*y**3)*(-12*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (26*y)*(-20*y**3) + (17*y**2)*(-20*y**3) + (25*y**2)*(-12*y**3 + 17*y**2 + 26*y) + (-20*y**3)*(-12*y**3)\nSimplifying the partial expression: (25*y**2)*(-12*y**3 + 17*y**2 + 26*y)\nExpanding the part (-12*y**3 + 17*y**2 + 26*y) using the distributive property, and we got: (26*y)*(25*y**2) + (17*y**2)*(25*y**2) + (25*y**2)*(-12*y**3)\nReplacing (25*y**2)*(-12*y**3 + 17*y**2 + 26*y) with (26*y)*(25*y**2) + (17*y**2)*(25*y**2) + (25*y**2)*(-12*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (26*y)*(25*y**2) + (26*y)*(-20*y**3) + (17*y**2)*(25*y**2) + (17*y**2)*(-20*y**3) + (25*y**2)*(-12*y**3) + (-20*y**3)*(-12*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*y**3)*(-20*y**3) = 240*y**6\n (-12*y**3)*(25*y**2) = -300*y**5\n (17*y**2)*(-20*y**3) = -340*y**5\n (17*y**2)*(25*y**2) = 425*y**4\n (26*y)*(-20*y**3) = -520*y**4\n (26*y)*(25*y**2) = 650*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 240*y**6 - 340*y**5 - 300*y**5 - 520*y**4 + 425*y**4 + 650*y**3\nCombining like terms, got 240*y**6 - 640*y**5 - 95*y**4 + 650*y**3\n#Step 6:\nCurrent expression: 240*y**6 - 640*y**5 - 95*y**4 + 650*y**3\nNo more calculations needed.\n240*y**6 - 640*y**5 - 95*y**4 + 650*y**3", "generated_answer": "240*y**6 - 640*y**5 - 95*y**4 + 650*y**3", "step_length": 6} {"cot_id": "7d31e91391b1814ac9bb0578bc1c389e777cd2a2b80c2fc6285d1e199b1ec93d", "datapoint": {"question": "Simplify this expression: 2574*x**2 - 3630\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2574*x**2 - 3630", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1069, "polynomial_expr": "2574*x**2 - 3630", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 2574*x**2 - 3630\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 2574*x**2 - 3630\nNo more calculations needed.\n2574*x**2 - 3630", "generated_answer": "2574*x**2 - 3630", "step_length": 2} {"cot_id": "9f917b31a8f7da03d3c8179fe9f0b6e5be426c06e86b4d48622b1faa707a6830", "datapoint": {"question": "Calculate the following: (-49*y**3 + 16*y)*(-44*y**3 + 29*y - 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2156*y**6 - 2125*y**4 + 980*y**3 + 464*y**2 - 320*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1070, "polynomial_expr": "(-49*y**3 + 16*y)*(-44*y**3 + 29*y - 20)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-49*y**3 + 16*y)*(-44*y**3 + 29*y - 20)\nExpanding the part (-49*y**3 + 16*y) using the distributive property, and we got: (16*y)*(-44*y**3 + 29*y - 20) + (-49*y**3)*(-44*y**3 + 29*y - 20)\n#Step 2:\nCurrent expression: (16*y)*(-44*y**3 + 29*y - 20) + (-49*y**3)*(-44*y**3 + 29*y - 20)\nSimplifying the partial expression: (-49*y**3)*(-44*y**3 + 29*y - 20)\nExpanding the part (-44*y**3 + 29*y - 20) using the distributive property, and we got: -(-1)*980*y**3 + (29*y)*(-49*y**3) + (-49*y**3)*(-44*y**3)\nReplacing (-49*y**3)*(-44*y**3 + 29*y - 20) with -(-1)*980*y**3 + (29*y)*(-49*y**3) + (-49*y**3)*(-44*y**3) in the overall expression.\n#Step 3:\nCurrent expression: -20*(-49)*y**3 + (16*y)*(-44*y**3 + 29*y - 20) + (29*y)*(-49*y**3) + (-49*y**3)*(-44*y**3)\nSimplifying the partial expression: (16*y)*(-44*y**3 + 29*y - 20)\nExpanding the part (-44*y**3 + 29*y - 20) using the distributive property, and we got: -320*y + (16*y)*(29*y) + (16*y)*(-44*y**3)\nReplacing (16*y)*(-44*y**3 + 29*y - 20) with -320*y + (16*y)*(29*y) + (16*y)*(-44*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -20*(-49)*y**3 - 20*16*y + (16*y)*(29*y) + (16*y)*(-44*y**3) + (29*y)*(-49*y**3) + (-49*y**3)*(-44*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-44*y**3)*(-49*y**3) = 2156*y**6\n (-44*y**3)*(16*y) = -704*y**4\n (29*y)*(-49*y**3) = -1421*y**4\n (29*y)*(16*y) = 464*y**2\n -20*-49*y**3 = 980*y**3\n -20*16*y = -320*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2156*y**6 - 1421*y**4 - 704*y**4 + 980*y**3 + 464*y**2 - 320*y\nCombining like terms, got 2156*y**6 - 2125*y**4 + 980*y**3 + 464*y**2 - 320*y\n#Step 6:\nCurrent expression: 2156*y**6 - 2125*y**4 + 980*y**3 + 464*y**2 - 320*y\nNo more calculations needed.\n2156*y**6 - 2125*y**4 + 980*y**3 + 464*y**2 - 320*y", "generated_answer": "2156*y**6 - 2125*y**4 + 980*y**3 + 464*y**2 - 320*y", "step_length": 6} {"cot_id": "16d963c64f057d553f5174624a17607c2ba5e0dfe5bd003d6e0109f11ce53cfd", "datapoint": {"question": "Calculate the following: 304*x**2\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "304*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1071, "polynomial_expr": "304*x**2", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 304*x**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 304*x**2\nNo more calculations needed.\n304*x**2", "generated_answer": "304*x**2", "step_length": 2} {"cot_id": "1555da0dddf40ad7a9f225fd414766978ce042ecd81be706c86978b74812407f", "datapoint": {"question": "Calculate the following: 44*z**2*(-28*z**2 - 11*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1232*z**4 - 484*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1072, "polynomial_expr": "44*z**2*(-28*z**2 - 11*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 44*z**2*(-28*z**2 - 11*z)\nExpanding the part (-28*z**2 - 11*z) using the distributive property, and we got: (-11*z)*(44*z**2) + (-28*z**2)*(44*z**2)\n#Step 2:\nCurrent expression: (-11*z)*(44*z**2) + (-28*z**2)*(44*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*z**2)*(44*z**2) = -1232*z**4\n (-11*z)*(44*z**2) = -484*z**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1232*z**4 - 484*z**3\nNo more calculations needed.\n-1232*z**4 - 484*z**3", "generated_answer": "-1232*z**4 - 484*z**3", "step_length": 3} {"cot_id": "d36bbc20e0e8114f34045fd86ad19ed13a2ff16099ccf018e9f62dff438b8137", "datapoint": {"question": "Calculate the following: (26*y + 3)*(64*y**3 + 37)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1664*y**4 + 192*y**3 + 962*y + 111", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1073, "polynomial_expr": "(26*y + 3)*(64*y**3 + 37)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (26*y + 3)*(64*y**3 + 37)\nExpanding the part (26*y + 3) using the distributive property, and we got: (26*y)*(64*y**3 + 37) + 3*(64*y**3 + 37)\n#Step 2:\nCurrent expression: (26*y)*(64*y**3 + 37) + 3*(64*y**3 + 37)\nSimplifying the partial expression: 3*(64*y**3 + 37)\nExpanding the part (64*y**3 + 37) using the distributive property, and we got: (64*y**3)*3 + 37*3\nReplacing 3*(64*y**3 + 37) with (64*y**3)*3 + 37*3 in the overall expression.\n#Step 3:\nCurrent expression: (26*y)*(64*y**3 + 37) + (64*y**3)*3 + 111\nSimplifying the partial expression: (26*y)*(64*y**3 + 37)\nExpanding the part (64*y**3 + 37) using the distributive property, and we got: 37*(26*y) + (26*y)*(64*y**3)\nReplacing (26*y)*(64*y**3 + 37) with 37*(26*y) + (26*y)*(64*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 37*26*y + (26*y)*(64*y**3) + (64*y**3)*3 + 111\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (64*y**3)*3 = 192*y**3\n (64*y**3)*(26*y) = 1664*y**4\n 37*26*y = 962*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1664*y**4 + 192*y**3 + 962*y + 111\nNo more calculations needed.\n1664*y**4 + 192*y**3 + 962*y + 111", "generated_answer": "1664*y**4 + 192*y**3 + 962*y + 111", "step_length": 5} {"cot_id": "bf543b20e0562a9613139e9a86869a5cfb0b285b352b6a316c69d294ad91ad2f", "datapoint": {"question": "Calculate the following: (35 - 37*z**3)*(82*z**3 - 7*z**2 - 39*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-3034*z**6 + 259*z**5 + 1443*z**4 + 2870*z**3 - 245*z**2 - 1365*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1074, "polynomial_expr": "(35 - 37*z**3)*(82*z**3 - 7*z**2 - 39*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (35 - 37*z**3)*(82*z**3 - 7*z**2 - 39*z)\nExpanding the part (35 - 37*z**3) using the distributive property, and we got: (-37*z**3)*(82*z**3 - 7*z**2 - 39*z) + 35*(82*z**3 - 7*z**2 - 39*z)\n#Step 2:\nCurrent expression: (-37*z**3)*(82*z**3 - 7*z**2 - 39*z) + 35*(82*z**3 - 7*z**2 - 39*z)\nSimplifying the partial expression: 35*(82*z**3 - 7*z**2 - 39*z)\nExpanding the part (82*z**3 - 7*z**2 - 39*z) using the distributive property, and we got: -39*z*35 - 7*z**2*35 + (82*z**3)*35\nReplacing 35*(82*z**3 - 7*z**2 - 39*z) with -39*z*35 - 7*z**2*35 + (82*z**3)*35 in the overall expression.\n#Step 3:\nCurrent expression: -39*z*35 - 7*z**2*35 + (-37*z**3)*(82*z**3 - 7*z**2 - 39*z) + (82*z**3)*35\nSimplifying the partial expression: (-37*z**3)*(82*z**3 - 7*z**2 - 39*z)\nExpanding the part (82*z**3 - 7*z**2 - 39*z) using the distributive property, and we got: (-39*z)*(-37*z**3) + (-7*z**2)*(-37*z**3) + (-37*z**3)*(82*z**3)\nReplacing (-37*z**3)*(82*z**3 - 7*z**2 - 39*z) with (-39*z)*(-37*z**3) + (-7*z**2)*(-37*z**3) + (-37*z**3)*(82*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-39*z)*(-37*z**3) - 39*z*35 + (-7*z**2)*(-37*z**3) - 7*z**2*35 + (-37*z**3)*(82*z**3) + (82*z**3)*35\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*z)*35 = -1365*z\n (-39*z)*(-37*z**3) = 1443*z**4\n (-7*z**2)*35 = -245*z**2\n (-7*z**2)*(-37*z**3) = 259*z**5\n (82*z**3)*35 = 2870*z**3\n (82*z**3)*(-37*z**3) = -3034*z**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -3034*z**6 + 259*z**5 + 1443*z**4 + 2870*z**3 - 245*z**2 - 1365*z\nNo more calculations needed.\n-3034*z**6 + 259*z**5 + 1443*z**4 + 2870*z**3 - 245*z**2 - 1365*z", "generated_answer": "-3034*z**6 + 259*z**5 + 1443*z**4 + 2870*z**3 - 245*z**2 - 1365*z", "step_length": 5} {"cot_id": "ba6934082600d8e332cc2d2647ffe6f7bfbcf31af8b409a6d850aea48ae8037a", "datapoint": {"question": "Simplify this expression: 85*y**3*(-24*y**2 + 48*y - 40)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2040*y**5 + 4080*y**4 - 3400*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1075, "polynomial_expr": "85*y**3*(-24*y**2 + 48*y - 40)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 85*y**3*(-24*y**2 + 48*y - 40)\nExpanding the part (-24*y**2 + 48*y - 40) using the distributive property, and we got: -3400*y**3 + (48*y)*(85*y**3) + (-24*y**2)*(85*y**3)\n#Step 2:\nCurrent expression: -3400*y**3 + (48*y)*(85*y**3) + (-24*y**2)*(85*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -40*(85*y**3) = -3400*y**3\n (-24*y**2)*(85*y**3) = -2040*y**5\n (48*y)*(85*y**3) = 4080*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -2040*y**5 + 4080*y**4 - 3400*y**3\nNo more calculations needed.\n-2040*y**5 + 4080*y**4 - 3400*y**3", "generated_answer": "-2040*y**5 + 4080*y**4 - 3400*y**3", "step_length": 3} {"cot_id": "3162b984eed9493ebfa638fbbc865ed83df1ec48634212b3569047b28384c4d2", "datapoint": {"question": "Simplify this expression: -20*x**2*(34*x - 40)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-680*x**3 + 800*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1076, "polynomial_expr": "-20*x**2*(34*x - 40)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -20*x**2*(34*x - 40)\nExpanding the part (34*x - 40) using the distributive property, and we got: -(-1)*800*x**2 + (34*x)*(-20*x**2)\n#Step 2:\nCurrent expression: -(-1)*800*x**2 + (34*x)*(-20*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -40*(-20*x**2) = 800*x**2\n (34*x)*(-20*x**2) = -680*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -680*x**3 + 800*x**2\nNo more calculations needed.\n-680*x**3 + 800*x**2", "generated_answer": "-680*x**3 + 800*x**2", "step_length": 3} {"cot_id": "16407af25cd32f1e0f1bb7338d17999211974f9cf9fad0335132262b323afa83", "datapoint": {"question": "Calculate the following: 33*x*(28*x**2 + 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "924*x**3 + 1551*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1077, "polynomial_expr": "33*x*(28*x**2 + 47)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 33*x*(28*x**2 + 47)\nExpanding the part (28*x**2 + 47) using the distributive property, and we got: 47*(33*x) + (33*x)*(28*x**2)\n#Step 2:\nCurrent expression: 47*(33*x) + (33*x)*(28*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 47*(33*x) = 1551*x\n (28*x**2)*(33*x) = 924*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 924*x**3 + 1551*x\nNo more calculations needed.\n924*x**3 + 1551*x", "generated_answer": "924*x**3 + 1551*x", "step_length": 3} {"cot_id": "55882d2c0fa402b5020345b17e6d9c29ef89105237465c3085ea7f3bde04f048", "datapoint": {"question": "Simplify this expression: (42*z + 39)*(-2*z**3 - 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-84*z**4 - 78*z**3 - 2016*z - 1872", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1078, "polynomial_expr": "(42*z + 39)*(-2*z**3 - 48)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (42*z + 39)*(-2*z**3 - 48)\nExpanding the part (-2*z**3 - 48) using the distributive property, and we got: (-2*z**3)*(42*z + 39) - 48*(42*z + 39)\n#Step 2:\nCurrent expression: (-2*z**3)*(42*z + 39) - 48*(42*z + 39)\nSimplifying the partial expression: -48*(42*z + 39)\nExpanding the part (42*z + 39) using the distributive property, and we got: (42*z)*(-48) + 39*(-48)\nReplacing -48*(42*z + 39) with (42*z)*(-48) + 39*(-48) in the overall expression.\n#Step 3:\nCurrent expression: (42*z)*(-48) + (-2*z**3)*(42*z + 39) - 1872\nSimplifying the partial expression: (-2*z**3)*(42*z + 39)\nExpanding the part (42*z + 39) using the distributive property, and we got: 39*(-2*z**3) + (42*z)*(-2*z**3)\nReplacing (-2*z**3)*(42*z + 39) with 39*(-2*z**3) + (42*z)*(-2*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 39*(-2)*z**3 + (42*z)*(-2*z**3) + (42*z)*(-48) - 1872\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (42*z)*-48 = -2016*z\n (42*z)*(-2*z**3) = -84*z**4\n 39*-2*z**3 = -78*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -84*z**4 - 78*z**3 - 2016*z - 1872\nNo more calculations needed.\n-84*z**4 - 78*z**3 - 2016*z - 1872", "generated_answer": "-84*z**4 - 78*z**3 - 2016*z - 1872", "step_length": 5} {"cot_id": "dac11ee2b315b9b552787bdd38d91f09b354fc40461fc6d9bd701beda165d840", "datapoint": {"question": "Calculate the following: (-28*z**3 + 24*z)*(-47*z**3 + 3*z**2 + 3*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1316*z**6 - 84*z**5 - 1212*z**4 + 72*z**3 + 72*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1079, "polynomial_expr": "(-28*z**3 + 24*z)*(-47*z**3 + 3*z**2 + 3*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-28*z**3 + 24*z)*(-47*z**3 + 3*z**2 + 3*z)\nExpanding the part (-28*z**3 + 24*z) using the distributive property, and we got: (24*z)*(-47*z**3 + 3*z**2 + 3*z) + (-28*z**3)*(-47*z**3 + 3*z**2 + 3*z)\n#Step 2:\nCurrent expression: (24*z)*(-47*z**3 + 3*z**2 + 3*z) + (-28*z**3)*(-47*z**3 + 3*z**2 + 3*z)\nSimplifying the partial expression: (-28*z**3)*(-47*z**3 + 3*z**2 + 3*z)\nExpanding the part (-47*z**3 + 3*z**2 + 3*z) using the distributive property, and we got: (3*z)*(-28*z**3) + (3*z**2)*(-28*z**3) + (-47*z**3)*(-28*z**3)\nReplacing (-28*z**3)*(-47*z**3 + 3*z**2 + 3*z) with (3*z)*(-28*z**3) + (3*z**2)*(-28*z**3) + (-47*z**3)*(-28*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (3*z)*(-28*z**3) + (24*z)*(-47*z**3 + 3*z**2 + 3*z) + (3*z**2)*(-28*z**3) + (-47*z**3)*(-28*z**3)\nSimplifying the partial expression: (24*z)*(-47*z**3 + 3*z**2 + 3*z)\nExpanding the part (-47*z**3 + 3*z**2 + 3*z) using the distributive property, and we got: (3*z)*(24*z) + (24*z)*(3*z**2) + (24*z)*(-47*z**3)\nReplacing (24*z)*(-47*z**3 + 3*z**2 + 3*z) with (3*z)*(24*z) + (24*z)*(3*z**2) + (24*z)*(-47*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (3*z)*(24*z) + (3*z)*(-28*z**3) + (24*z)*(3*z**2) + (24*z)*(-47*z**3) + (3*z**2)*(-28*z**3) + (-47*z**3)*(-28*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*z**3)*(-28*z**3) = 1316*z**6\n (-47*z**3)*(24*z) = -1128*z**4\n (3*z)*(-28*z**3) = -84*z**4\n (3*z)*(24*z) = 72*z**2\n (3*z**2)*(-28*z**3) = -84*z**5\n (3*z**2)*(24*z) = 72*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1316*z**6 - 84*z**5 - 1128*z**4 - 84*z**4 + 72*z**3 + 72*z**2\nCombining like terms, got 1316*z**6 - 84*z**5 - 1212*z**4 + 72*z**3 + 72*z**2\n#Step 6:\nCurrent expression: 1316*z**6 - 84*z**5 - 1212*z**4 + 72*z**3 + 72*z**2\nNo more calculations needed.\n1316*z**6 - 84*z**5 - 1212*z**4 + 72*z**3 + 72*z**2", "generated_answer": "1316*z**6 - 84*z**5 - 1212*z**4 + 72*z**3 + 72*z**2", "step_length": 6} {"cot_id": "9534a0b25af0ffe4e22bf53ce478fb5612b0b2d479ea1e85171bdd152a403a4e", "datapoint": {"question": "Calculate the following: (17*y - 37)*(13*y**2 + 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "221*y**3 - 481*y**2 + 850*y - 1850", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1080, "polynomial_expr": "(17*y - 37)*(13*y**2 + 50)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (17*y - 37)*(13*y**2 + 50)\nExpanding the part (17*y - 37) using the distributive property, and we got: (17*y)*(13*y**2 + 50) - 37*(13*y**2 + 50)\n#Step 2:\nCurrent expression: (17*y)*(13*y**2 + 50) - 37*(13*y**2 + 50)\nSimplifying the partial expression: -37*(13*y**2 + 50)\nExpanding the part (13*y**2 + 50) using the distributive property, and we got: (13*y**2)*(-37) + 50*(-37)\nReplacing -37*(13*y**2 + 50) with (13*y**2)*(-37) + 50*(-37) in the overall expression.\n#Step 3:\nCurrent expression: (17*y)*(13*y**2 + 50) + (13*y**2)*(-37) - 1850\nSimplifying the partial expression: (17*y)*(13*y**2 + 50)\nExpanding the part (13*y**2 + 50) using the distributive property, and we got: 50*(17*y) + (17*y)*(13*y**2)\nReplacing (17*y)*(13*y**2 + 50) with 50*(17*y) + (17*y)*(13*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 50*17*y + (17*y)*(13*y**2) + (13*y**2)*(-37) - 1850\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (13*y**2)*-37 = -481*y**2\n (13*y**2)*(17*y) = 221*y**3\n 50*17*y = 850*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 221*y**3 - 481*y**2 + 850*y - 1850\nNo more calculations needed.\n221*y**3 - 481*y**2 + 850*y - 1850", "generated_answer": "221*y**3 - 481*y**2 + 850*y - 1850", "step_length": 5} {"cot_id": "a8742b29df56c962d55aa07c127530489b9f28129e6d7bc7ce6611dcaa072126", "datapoint": {"question": "Simplify this expression: (-59*y**2 + 45*y)*(29*y**3 + 3*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1711*y**5 + 1128*y**4 + 135*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1081, "polynomial_expr": "(-59*y**2 + 45*y)*(29*y**3 + 3*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-59*y**2 + 45*y)*(29*y**3 + 3*y**2)\nExpanding the part (-59*y**2 + 45*y) using the distributive property, and we got: (45*y)*(29*y**3 + 3*y**2) + (-59*y**2)*(29*y**3 + 3*y**2)\n#Step 2:\nCurrent expression: (45*y)*(29*y**3 + 3*y**2) + (-59*y**2)*(29*y**3 + 3*y**2)\nSimplifying the partial expression: (-59*y**2)*(29*y**3 + 3*y**2)\nExpanding the part (29*y**3 + 3*y**2) using the distributive property, and we got: (-59*y**2)*(3*y**2) + (-59*y**2)*(29*y**3)\nReplacing (-59*y**2)*(29*y**3 + 3*y**2) with (-59*y**2)*(3*y**2) + (-59*y**2)*(29*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (45*y)*(29*y**3 + 3*y**2) + (-59*y**2)*(3*y**2) + (-59*y**2)*(29*y**3)\nSimplifying the partial expression: (45*y)*(29*y**3 + 3*y**2)\nExpanding the part (29*y**3 + 3*y**2) using the distributive property, and we got: (45*y)*(3*y**2) + (45*y)*(29*y**3)\nReplacing (45*y)*(29*y**3 + 3*y**2) with (45*y)*(3*y**2) + (45*y)*(29*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (45*y)*(3*y**2) + (45*y)*(29*y**3) + (-59*y**2)*(3*y**2) + (-59*y**2)*(29*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (3*y**2)*(-59*y**2) = -177*y**4\n (3*y**2)*(45*y) = 135*y**3\n (29*y**3)*(-59*y**2) = -1711*y**5\n (29*y**3)*(45*y) = 1305*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1711*y**5 - 177*y**4 + 1305*y**4 + 135*y**3\nCombining like terms, got -1711*y**5 + 1128*y**4 + 135*y**3\n#Step 6:\nCurrent expression: -1711*y**5 + 1128*y**4 + 135*y**3\nNo more calculations needed.\n-1711*y**5 + 1128*y**4 + 135*y**3", "generated_answer": "-1711*y**5 + 1128*y**4 + 135*y**3", "step_length": 6} {"cot_id": "e8be15e6007c1b85d084805baa51a088d86f9bc4a9bb890efe9d209064291bae", "datapoint": {"question": "Calculate the following: (11 - 36*x**3)*(-33*x**3 - 45*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1188*x**6 + 1620*x**5 - 363*x**3 - 495*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1082, "polynomial_expr": "(11 - 36*x**3)*(-33*x**3 - 45*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11 - 36*x**3)*(-33*x**3 - 45*x**2)\nExpanding the part (11 - 36*x**3) using the distributive property, and we got: (-36*x**3)*(-33*x**3 - 45*x**2) + 11*(-33*x**3 - 45*x**2)\n#Step 2:\nCurrent expression: (-36*x**3)*(-33*x**3 - 45*x**2) + 11*(-33*x**3 - 45*x**2)\nSimplifying the partial expression: 11*(-33*x**3 - 45*x**2)\nExpanding the part (-33*x**3 - 45*x**2) using the distributive property, and we got: -45*x**2*11 - 33*x**3*11\nReplacing 11*(-33*x**3 - 45*x**2) with -45*x**2*11 - 33*x**3*11 in the overall expression.\n#Step 3:\nCurrent expression: -45*x**2*11 + (-36*x**3)*(-33*x**3 - 45*x**2) - 33*x**3*11\nSimplifying the partial expression: (-36*x**3)*(-33*x**3 - 45*x**2)\nExpanding the part (-33*x**3 - 45*x**2) using the distributive property, and we got: (-45*x**2)*(-36*x**3) + (-36*x**3)*(-33*x**3)\nReplacing (-36*x**3)*(-33*x**3 - 45*x**2) with (-45*x**2)*(-36*x**3) + (-36*x**3)*(-33*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-45*x**2)*(-36*x**3) - 45*x**2*11 + (-36*x**3)*(-33*x**3) - 33*x**3*11\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*x**2)*11 = -495*x**2\n (-45*x**2)*(-36*x**3) = 1620*x**5\n (-33*x**3)*11 = -363*x**3\n (-33*x**3)*(-36*x**3) = 1188*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1188*x**6 + 1620*x**5 - 363*x**3 - 495*x**2\nNo more calculations needed.\n1188*x**6 + 1620*x**5 - 363*x**3 - 495*x**2", "generated_answer": "1188*x**6 + 1620*x**5 - 363*x**3 - 495*x**2", "step_length": 5} {"cot_id": "75bf4e7df5f4d1a0bf3979cd49603b4201aaa05a0b77319d27956e1f0f6f2435", "datapoint": {"question": "Calculate the following: (29*x**2 + 20)*(-9*x**3 + 37*x + 43)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-261*x**5 + 893*x**3 + 1247*x**2 + 740*x + 860", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1083, "polynomial_expr": "(29*x**2 + 20)*(-9*x**3 + 37*x + 43)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29*x**2 + 20)*(-9*x**3 + 37*x + 43)\nExpanding the part (29*x**2 + 20) using the distributive property, and we got: (29*x**2)*(-9*x**3 + 37*x + 43) + 20*(-9*x**3 + 37*x + 43)\n#Step 2:\nCurrent expression: (29*x**2)*(-9*x**3 + 37*x + 43) + 20*(-9*x**3 + 37*x + 43)\nSimplifying the partial expression: 20*(-9*x**3 + 37*x + 43)\nExpanding the part (-9*x**3 + 37*x + 43) using the distributive property, and we got: (37*x)*20 - 9*x**3*20 + 43*20\nReplacing 20*(-9*x**3 + 37*x + 43) with (37*x)*20 - 9*x**3*20 + 43*20 in the overall expression.\n#Step 3:\nCurrent expression: (37*x)*20 + (29*x**2)*(-9*x**3 + 37*x + 43) - 9*x**3*20 + 860\nSimplifying the partial expression: (29*x**2)*(-9*x**3 + 37*x + 43)\nExpanding the part (-9*x**3 + 37*x + 43) using the distributive property, and we got: 43*(29*x**2) + (37*x)*(29*x**2) + (29*x**2)*(-9*x**3)\nReplacing (29*x**2)*(-9*x**3 + 37*x + 43) with 43*(29*x**2) + (37*x)*(29*x**2) + (29*x**2)*(-9*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 43*29*x**2 + (37*x)*(29*x**2) + (37*x)*20 + (29*x**2)*(-9*x**3) - 9*x**3*20 + 860\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-9*x**3)*20 = -180*x**3\n (-9*x**3)*(29*x**2) = -261*x**5\n (37*x)*20 = 740*x\n (37*x)*(29*x**2) = 1073*x**3\n 43*29*x**2 = 1247*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -261*x**5 - 180*x**3 + 1073*x**3 + 1247*x**2 + 740*x + 860\nCombining like terms, got -261*x**5 + 893*x**3 + 1247*x**2 + 740*x + 860\n#Step 6:\nCurrent expression: -261*x**5 + 893*x**3 + 1247*x**2 + 740*x + 860\nNo more calculations needed.\n-261*x**5 + 893*x**3 + 1247*x**2 + 740*x + 860", "generated_answer": "-261*x**5 + 893*x**3 + 1247*x**2 + 740*x + 860", "step_length": 6} {"cot_id": "1c917da3ac35ff28805a10b59f563aaee630b883bcbfd830853912927b5121ff", "datapoint": {"question": "Simplify this expression: (-49*y**2 - 41)*(29*y**3 - 2*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1421*y**5 - 1091*y**3 + 82*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1084, "polynomial_expr": "(-49*y**2 - 41)*(29*y**3 - 2*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-49*y**2 - 41)*(29*y**3 - 2*y)\nExpanding the part (-49*y**2 - 41) using the distributive property, and we got: (-49*y**2)*(29*y**3 - 2*y) - 41*(29*y**3 - 2*y)\n#Step 2:\nCurrent expression: (-49*y**2)*(29*y**3 - 2*y) - 41*(29*y**3 - 2*y)\nSimplifying the partial expression: -41*(29*y**3 - 2*y)\nExpanding the part (29*y**3 - 2*y) using the distributive property, and we got: -2*y*(-41) + (29*y**3)*(-41)\nReplacing -41*(29*y**3 - 2*y) with -2*y*(-41) + (29*y**3)*(-41) in the overall expression.\n#Step 3:\nCurrent expression: -2*y*(-41) + (-49*y**2)*(29*y**3 - 2*y) + (29*y**3)*(-41)\nSimplifying the partial expression: (-49*y**2)*(29*y**3 - 2*y)\nExpanding the part (29*y**3 - 2*y) using the distributive property, and we got: (-2*y)*(-49*y**2) + (-49*y**2)*(29*y**3)\nReplacing (-49*y**2)*(29*y**3 - 2*y) with (-2*y)*(-49*y**2) + (-49*y**2)*(29*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-2*y)*(-49*y**2) - 2*y*(-41) + (-49*y**2)*(29*y**3) + (29*y**3)*(-41)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-2*y)*-41 = 82*y\n (-2*y)*(-49*y**2) = 98*y**3\n (29*y**3)*-41 = -1189*y**3\n (29*y**3)*(-49*y**2) = -1421*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1421*y**5 - 1189*y**3 + 98*y**3 + 82*y\nCombining like terms, got -1421*y**5 - 1091*y**3 + 82*y\n#Step 6:\nCurrent expression: -1421*y**5 - 1091*y**3 + 82*y\nNo more calculations needed.\n-1421*y**5 - 1091*y**3 + 82*y", "generated_answer": "-1421*y**5 - 1091*y**3 + 82*y", "step_length": 6} {"cot_id": "5df73f4e85c147b84e081a2a8144a2e3fcc31424075f07e695d330122652453c", "datapoint": {"question": "Simplify this expression: (y**2 + 30)*(-32*y**3 - 11*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-32*y**5 - 971*y**3 - 330*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1085, "polynomial_expr": "(y**2 + 30)*(-32*y**3 - 11*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (y**2 + 30)*(-32*y**3 - 11*y)\nExpanding the part (y**2 + 30) using the distributive property, and we got: y**2*(-32*y**3 - 11*y) + 30*(-32*y**3 - 11*y)\n#Step 2:\nCurrent expression: y**2*(-32*y**3 - 11*y) + 30*(-32*y**3 - 11*y)\nSimplifying the partial expression: 30*(-32*y**3 - 11*y)\nExpanding the part (-32*y**3 - 11*y) using the distributive property, and we got: -11*y*30 - 32*y**3*30\nReplacing 30*(-32*y**3 - 11*y) with -11*y*30 - 32*y**3*30 in the overall expression.\n#Step 3:\nCurrent expression: -11*y*30 + y**2*(-32*y**3 - 11*y) - 32*y**3*30\nSimplifying the partial expression: y**2*(-32*y**3 - 11*y)\nExpanding the part (-32*y**3 - 11*y) using the distributive property, and we got: (-11*y)*y**2 + y**2*(-32*y**3)\nReplacing y**2*(-32*y**3 - 11*y) with (-11*y)*y**2 + y**2*(-32*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-11*y)*y**2 - 11*y*30 + y**2*(-32*y**3) - 32*y**3*30\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*y**3)*30 = -960*y**3\n (-32*y**3)*y**2 = -32*y**5\n (-11*y)*30 = -330*y\n (-11*y)*y**2 = -11*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -32*y**5 - 960*y**3 - 11*y**3 - 330*y\nCombining like terms, got -32*y**5 - 971*y**3 - 330*y\n#Step 6:\nCurrent expression: -32*y**5 - 971*y**3 - 330*y\nNo more calculations needed.\n-32*y**5 - 971*y**3 - 330*y", "generated_answer": "-32*y**5 - 971*y**3 - 330*y", "step_length": 6} {"cot_id": "79329c5dd32714dd089740140084c184ec396a50ea42e4eedb3357a90daec0bc", "datapoint": {"question": "Calculate the following: (-3*x**2 - 25*x)*(-31*x**3 + 25*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "93*x**5 + 700*x**4 - 625*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1086, "polynomial_expr": "(-3*x**2 - 25*x)*(-31*x**3 + 25*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-3*x**2 - 25*x)*(-31*x**3 + 25*x**2)\nExpanding the part (-31*x**3 + 25*x**2) using the distributive property, and we got: (25*x**2)*(-3*x**2 - 25*x) + (-31*x**3)*(-3*x**2 - 25*x)\n#Step 2:\nCurrent expression: (25*x**2)*(-3*x**2 - 25*x) + (-31*x**3)*(-3*x**2 - 25*x)\nSimplifying the partial expression: (-31*x**3)*(-3*x**2 - 25*x)\nExpanding the part (-3*x**2 - 25*x) using the distributive property, and we got: (-25*x)*(-31*x**3) + (-3*x**2)*(-31*x**3)\nReplacing (-31*x**3)*(-3*x**2 - 25*x) with (-25*x)*(-31*x**3) + (-3*x**2)*(-31*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-25*x)*(-31*x**3) + (-3*x**2)*(-31*x**3) + (25*x**2)*(-3*x**2 - 25*x)\nSimplifying the partial expression: (25*x**2)*(-3*x**2 - 25*x)\nExpanding the part (-3*x**2 - 25*x) using the distributive property, and we got: (-25*x)*(25*x**2) + (-3*x**2)*(25*x**2)\nReplacing (25*x**2)*(-3*x**2 - 25*x) with (-25*x)*(25*x**2) + (-3*x**2)*(25*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-25*x)*(25*x**2) + (-25*x)*(-31*x**3) + (-3*x**2)*(25*x**2) + (-3*x**2)*(-31*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*x)*(-31*x**3) = 775*x**4\n (-25*x)*(25*x**2) = -625*x**3\n (-3*x**2)*(-31*x**3) = 93*x**5\n (-3*x**2)*(25*x**2) = -75*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 93*x**5 - 75*x**4 + 775*x**4 - 625*x**3\nCombining like terms, got 93*x**5 + 700*x**4 - 625*x**3\n#Step 6:\nCurrent expression: 93*x**5 + 700*x**4 - 625*x**3\nNo more calculations needed.\n93*x**5 + 700*x**4 - 625*x**3", "generated_answer": "93*x**5 + 700*x**4 - 625*x**3", "step_length": 6} {"cot_id": "2a56f1bf6cf10a95d8e2a455b8fd1c8142b44f6390ed9fa1422cae5e1c2bdb47", "datapoint": {"question": "Simplify this expression: (74 - 13*z**3)*(5*z**2 + 14*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-65*z**5 - 182*z**4 + 370*z**2 + 1036*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1087, "polynomial_expr": "(74 - 13*z**3)*(5*z**2 + 14*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (74 - 13*z**3)*(5*z**2 + 14*z)\nExpanding the part (74 - 13*z**3) using the distributive property, and we got: (-13*z**3)*(5*z**2 + 14*z) + 74*(5*z**2 + 14*z)\n#Step 2:\nCurrent expression: (-13*z**3)*(5*z**2 + 14*z) + 74*(5*z**2 + 14*z)\nSimplifying the partial expression: 74*(5*z**2 + 14*z)\nExpanding the part (5*z**2 + 14*z) using the distributive property, and we got: (14*z)*74 + (5*z**2)*74\nReplacing 74*(5*z**2 + 14*z) with (14*z)*74 + (5*z**2)*74 in the overall expression.\n#Step 3:\nCurrent expression: (14*z)*74 + (5*z**2)*74 + (-13*z**3)*(5*z**2 + 14*z)\nSimplifying the partial expression: (-13*z**3)*(5*z**2 + 14*z)\nExpanding the part (5*z**2 + 14*z) using the distributive property, and we got: (14*z)*(-13*z**3) + (5*z**2)*(-13*z**3)\nReplacing (-13*z**3)*(5*z**2 + 14*z) with (14*z)*(-13*z**3) + (5*z**2)*(-13*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (14*z)*(-13*z**3) + (14*z)*74 + (5*z**2)*(-13*z**3) + (5*z**2)*74\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (5*z**2)*74 = 370*z**2\n (5*z**2)*(-13*z**3) = -65*z**5\n (14*z)*74 = 1036*z\n (14*z)*(-13*z**3) = -182*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -65*z**5 - 182*z**4 + 370*z**2 + 1036*z\nNo more calculations needed.\n-65*z**5 - 182*z**4 + 370*z**2 + 1036*z", "generated_answer": "-65*z**5 - 182*z**4 + 370*z**2 + 1036*z", "step_length": 5} {"cot_id": "859cee4231763f872f1c11f60f4f39de884b99dfe89bb09fc99248b48e61937a", "datapoint": {"question": "Simplify this expression: (15 - 42*z**2)*(-30*z**3 + 40*z**2 - 27)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1260*z**5 - 1680*z**4 - 450*z**3 + 1734*z**2 - 405", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1088, "polynomial_expr": "(15 - 42*z**2)*(-30*z**3 + 40*z**2 - 27)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (15 - 42*z**2)*(-30*z**3 + 40*z**2 - 27)\nExpanding the part (15 - 42*z**2) using the distributive property, and we got: (-42*z**2)*(-30*z**3 + 40*z**2 - 27) + 15*(-30*z**3 + 40*z**2 - 27)\n#Step 2:\nCurrent expression: (-42*z**2)*(-30*z**3 + 40*z**2 - 27) + 15*(-30*z**3 + 40*z**2 - 27)\nSimplifying the partial expression: 15*(-30*z**3 + 40*z**2 - 27)\nExpanding the part (-30*z**3 + 40*z**2 - 27) using the distributive property, and we got: (40*z**2)*15 - 30*z**3*15 - 27*15\nReplacing 15*(-30*z**3 + 40*z**2 - 27) with (40*z**2)*15 - 30*z**3*15 - 27*15 in the overall expression.\n#Step 3:\nCurrent expression: (-42*z**2)*(-30*z**3 + 40*z**2 - 27) + (40*z**2)*15 - 30*z**3*15 - 405\nSimplifying the partial expression: (-42*z**2)*(-30*z**3 + 40*z**2 - 27)\nExpanding the part (-30*z**3 + 40*z**2 - 27) using the distributive property, and we got: -(-1)*1134*z**2 + (-42*z**2)*(40*z**2) + (-42*z**2)*(-30*z**3)\nReplacing (-42*z**2)*(-30*z**3 + 40*z**2 - 27) with -(-1)*1134*z**2 + (-42*z**2)*(40*z**2) + (-42*z**2)*(-30*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -27*(-42)*z**2 + (-42*z**2)*(40*z**2) + (-42*z**2)*(-30*z**3) + (40*z**2)*15 - 30*z**3*15 - 405\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*z**3)*15 = -450*z**3\n (-30*z**3)*(-42*z**2) = 1260*z**5\n (40*z**2)*15 = 600*z**2\n (40*z**2)*(-42*z**2) = -1680*z**4\n -27*-42*z**2 = 1134*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1260*z**5 - 1680*z**4 - 450*z**3 + 600*z**2 + 1134*z**2 - 405\nCombining like terms, got 1260*z**5 - 1680*z**4 - 450*z**3 + 1734*z**2 - 405\n#Step 6:\nCurrent expression: 1260*z**5 - 1680*z**4 - 450*z**3 + 1734*z**2 - 405\nNo more calculations needed.\n1260*z**5 - 1680*z**4 - 450*z**3 + 1734*z**2 - 405", "generated_answer": "1260*z**5 - 1680*z**4 - 450*z**3 + 1734*z**2 - 405", "step_length": 6} {"cot_id": "dc3d9f2d4bf2b876f2fba3d27ca26ae0a2eb3f884c0978dd7ac7749fc19ed146", "datapoint": {"question": "Simplify this expression: (-40*x**3 - 32)*(15*x**3 - 20*x**2 + 26*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-600*x**6 + 800*x**5 - 1040*x**4 - 480*x**3 + 640*x**2 - 832*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1089, "polynomial_expr": "(-40*x**3 - 32)*(15*x**3 - 20*x**2 + 26*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-40*x**3 - 32)*(15*x**3 - 20*x**2 + 26*x)\nExpanding the part (-40*x**3 - 32) using the distributive property, and we got: (-40*x**3)*(15*x**3 - 20*x**2 + 26*x) - 32*(15*x**3 - 20*x**2 + 26*x)\n#Step 2:\nCurrent expression: (-40*x**3)*(15*x**3 - 20*x**2 + 26*x) - 32*(15*x**3 - 20*x**2 + 26*x)\nSimplifying the partial expression: -32*(15*x**3 - 20*x**2 + 26*x)\nExpanding the part (15*x**3 - 20*x**2 + 26*x) using the distributive property, and we got: (26*x)*(-32) - 20*x**2*(-32) + (15*x**3)*(-32)\nReplacing -32*(15*x**3 - 20*x**2 + 26*x) with (26*x)*(-32) - 20*x**2*(-32) + (15*x**3)*(-32) in the overall expression.\n#Step 3:\nCurrent expression: (26*x)*(-32) - 20*x**2*(-32) + (-40*x**3)*(15*x**3 - 20*x**2 + 26*x) + (15*x**3)*(-32)\nSimplifying the partial expression: (-40*x**3)*(15*x**3 - 20*x**2 + 26*x)\nExpanding the part (15*x**3 - 20*x**2 + 26*x) using the distributive property, and we got: (26*x)*(-40*x**3) + (-20*x**2)*(-40*x**3) + (-40*x**3)*(15*x**3)\nReplacing (-40*x**3)*(15*x**3 - 20*x**2 + 26*x) with (26*x)*(-40*x**3) + (-20*x**2)*(-40*x**3) + (-40*x**3)*(15*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (26*x)*(-40*x**3) + (26*x)*(-32) + (-20*x**2)*(-40*x**3) - 20*x**2*(-32) + (-40*x**3)*(15*x**3) + (15*x**3)*(-32)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*x**2)*-32 = 640*x**2\n (-20*x**2)*(-40*x**3) = 800*x**5\n (15*x**3)*-32 = -480*x**3\n (15*x**3)*(-40*x**3) = -600*x**6\n (26*x)*-32 = -832*x\n (26*x)*(-40*x**3) = -1040*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -600*x**6 + 800*x**5 - 1040*x**4 - 480*x**3 + 640*x**2 - 832*x\nNo more calculations needed.\n-600*x**6 + 800*x**5 - 1040*x**4 - 480*x**3 + 640*x**2 - 832*x", "generated_answer": "-600*x**6 + 800*x**5 - 1040*x**4 - 480*x**3 + 640*x**2 - 832*x", "step_length": 5} {"cot_id": "c8bf77b5e1fa35dabd5a2ca7eba5b072f36fdb80ead707e546676df456891457", "datapoint": {"question": "Simplify this expression: -73*z**3*(22*z + 27)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1606*z**4 - 1971*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1090, "polynomial_expr": "-73*z**3*(22*z + 27)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -73*z**3*(22*z + 27)\nExpanding the part (22*z + 27) using the distributive property, and we got: 27*(-73*z**3) + (22*z)*(-73*z**3)\n#Step 2:\nCurrent expression: 27*(-73*z**3) + (22*z)*(-73*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 27*(-73*z**3) = -1971*z**3\n (22*z)*(-73*z**3) = -1606*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1606*z**4 - 1971*z**3\nNo more calculations needed.\n-1606*z**4 - 1971*z**3", "generated_answer": "-1606*z**4 - 1971*z**3", "step_length": 3} {"cot_id": "cf989b07eaa07e04b08bc3efa937ec049ca9d04d1c0f0e52febdfc833c4b192f", "datapoint": {"question": "Simplify this expression: (46*y**2 + 45)*(-25*y**3 + 12*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1150*y**5 + 552*y**4 - 1125*y**3 + 540*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1091, "polynomial_expr": "(46*y**2 + 45)*(-25*y**3 + 12*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (46*y**2 + 45)*(-25*y**3 + 12*y**2)\nExpanding the part (46*y**2 + 45) using the distributive property, and we got: (46*y**2)*(-25*y**3 + 12*y**2) + 45*(-25*y**3 + 12*y**2)\n#Step 2:\nCurrent expression: (46*y**2)*(-25*y**3 + 12*y**2) + 45*(-25*y**3 + 12*y**2)\nSimplifying the partial expression: 45*(-25*y**3 + 12*y**2)\nExpanding the part (-25*y**3 + 12*y**2) using the distributive property, and we got: (12*y**2)*45 - 25*y**3*45\nReplacing 45*(-25*y**3 + 12*y**2) with (12*y**2)*45 - 25*y**3*45 in the overall expression.\n#Step 3:\nCurrent expression: (12*y**2)*45 + (46*y**2)*(-25*y**3 + 12*y**2) - 25*y**3*45\nSimplifying the partial expression: (46*y**2)*(-25*y**3 + 12*y**2)\nExpanding the part (-25*y**3 + 12*y**2) using the distributive property, and we got: (12*y**2)*(46*y**2) + (46*y**2)*(-25*y**3)\nReplacing (46*y**2)*(-25*y**3 + 12*y**2) with (12*y**2)*(46*y**2) + (46*y**2)*(-25*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (12*y**2)*(46*y**2) + (12*y**2)*45 + (46*y**2)*(-25*y**3) - 25*y**3*45\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*y**3)*45 = -1125*y**3\n (-25*y**3)*(46*y**2) = -1150*y**5\n (12*y**2)*45 = 540*y**2\n (12*y**2)*(46*y**2) = 552*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1150*y**5 + 552*y**4 - 1125*y**3 + 540*y**2\nNo more calculations needed.\n-1150*y**5 + 552*y**4 - 1125*y**3 + 540*y**2", "generated_answer": "-1150*y**5 + 552*y**4 - 1125*y**3 + 540*y**2", "step_length": 5} {"cot_id": "f7736c965c00f995e9c8ed2325b4706ad124eedc5c4f3dd05e8c3bc0686d1eca", "datapoint": {"question": "Simplify this expression: (35 - 43*x**3)*(-37*x**3 - 38*x**2 - 37)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1591*x**6 + 1634*x**5 + 296*x**3 - 1330*x**2 - 1295", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1092, "polynomial_expr": "(35 - 43*x**3)*(-37*x**3 - 38*x**2 - 37)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (35 - 43*x**3)*(-37*x**3 - 38*x**2 - 37)\nExpanding the part (35 - 43*x**3) using the distributive property, and we got: (-43*x**3)*(-37*x**3 - 38*x**2 - 37) + 35*(-37*x**3 - 38*x**2 - 37)\n#Step 2:\nCurrent expression: (-43*x**3)*(-37*x**3 - 38*x**2 - 37) + 35*(-37*x**3 - 38*x**2 - 37)\nSimplifying the partial expression: 35*(-37*x**3 - 38*x**2 - 37)\nExpanding the part (-37*x**3 - 38*x**2 - 37) using the distributive property, and we got: -38*x**2*35 - 37*x**3*35 - 37*35\nReplacing 35*(-37*x**3 - 38*x**2 - 37) with -38*x**2*35 - 37*x**3*35 - 37*35 in the overall expression.\n#Step 3:\nCurrent expression: -38*x**2*35 + (-43*x**3)*(-37*x**3 - 38*x**2 - 37) - 37*x**3*35 - 1295\nSimplifying the partial expression: (-43*x**3)*(-37*x**3 - 38*x**2 - 37)\nExpanding the part (-37*x**3 - 38*x**2 - 37) using the distributive property, and we got: -(-1)*1591*x**3 + (-38*x**2)*(-43*x**3) + (-43*x**3)*(-37*x**3)\nReplacing (-43*x**3)*(-37*x**3 - 38*x**2 - 37) with -(-1)*1591*x**3 + (-38*x**2)*(-43*x**3) + (-43*x**3)*(-37*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -37*(-43)*x**3 + (-38*x**2)*(-43*x**3) - 38*x**2*35 + (-43*x**3)*(-37*x**3) - 37*x**3*35 - 1295\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*x**2)*35 = -1330*x**2\n (-38*x**2)*(-43*x**3) = 1634*x**5\n (-37*x**3)*35 = -1295*x**3\n (-37*x**3)*(-43*x**3) = 1591*x**6\n -37*-43*x**3 = 1591*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1591*x**6 + 1634*x**5 - 1295*x**3 + 1591*x**3 - 1330*x**2 - 1295\nCombining like terms, got 1591*x**6 + 1634*x**5 + 296*x**3 - 1330*x**2 - 1295\n#Step 6:\nCurrent expression: 1591*x**6 + 1634*x**5 + 296*x**3 - 1330*x**2 - 1295\nNo more calculations needed.\n1591*x**6 + 1634*x**5 + 296*x**3 - 1330*x**2 - 1295", "generated_answer": "1591*x**6 + 1634*x**5 + 296*x**3 - 1330*x**2 - 1295", "step_length": 6} {"cot_id": "844b42ff09686da7920a6c912f8db113d9b5565a1182c77dc0c40ce0fdcdf78a", "datapoint": {"question": "Calculate the following: (-21*z**3 - 13)*(41*z**3 + 36*z**2 + 21*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-861*z**6 - 756*z**5 - 441*z**4 - 533*z**3 - 468*z**2 - 273*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1093, "polynomial_expr": "(-21*z**3 - 13)*(41*z**3 + 36*z**2 + 21*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-21*z**3 - 13)*(41*z**3 + 36*z**2 + 21*z)\nExpanding the part (-21*z**3 - 13) using the distributive property, and we got: (-21*z**3)*(41*z**3 + 36*z**2 + 21*z) - 13*(41*z**3 + 36*z**2 + 21*z)\n#Step 2:\nCurrent expression: (-21*z**3)*(41*z**3 + 36*z**2 + 21*z) - 13*(41*z**3 + 36*z**2 + 21*z)\nSimplifying the partial expression: -13*(41*z**3 + 36*z**2 + 21*z)\nExpanding the part (41*z**3 + 36*z**2 + 21*z) using the distributive property, and we got: (21*z)*(-13) + (36*z**2)*(-13) + (41*z**3)*(-13)\nReplacing -13*(41*z**3 + 36*z**2 + 21*z) with (21*z)*(-13) + (36*z**2)*(-13) + (41*z**3)*(-13) in the overall expression.\n#Step 3:\nCurrent expression: (21*z)*(-13) + (36*z**2)*(-13) + (-21*z**3)*(41*z**3 + 36*z**2 + 21*z) + (41*z**3)*(-13)\nSimplifying the partial expression: (-21*z**3)*(41*z**3 + 36*z**2 + 21*z)\nExpanding the part (41*z**3 + 36*z**2 + 21*z) using the distributive property, and we got: (21*z)*(-21*z**3) + (36*z**2)*(-21*z**3) + (-21*z**3)*(41*z**3)\nReplacing (-21*z**3)*(41*z**3 + 36*z**2 + 21*z) with (21*z)*(-21*z**3) + (36*z**2)*(-21*z**3) + (-21*z**3)*(41*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (21*z)*(-21*z**3) + (21*z)*(-13) + (36*z**2)*(-21*z**3) + (36*z**2)*(-13) + (-21*z**3)*(41*z**3) + (41*z**3)*(-13)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (21*z)*-13 = -273*z\n (21*z)*(-21*z**3) = -441*z**4\n (36*z**2)*-13 = -468*z**2\n (36*z**2)*(-21*z**3) = -756*z**5\n (41*z**3)*-13 = -533*z**3\n (41*z**3)*(-21*z**3) = -861*z**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -861*z**6 - 756*z**5 - 441*z**4 - 533*z**3 - 468*z**2 - 273*z\nNo more calculations needed.\n-861*z**6 - 756*z**5 - 441*z**4 - 533*z**3 - 468*z**2 - 273*z", "generated_answer": "-861*z**6 - 756*z**5 - 441*z**4 - 533*z**3 - 468*z**2 - 273*z", "step_length": 5} {"cot_id": "7a8ab635362adb417a72bf326174c4aa86502d5e3af0fe51d73a911ff06d90cf", "datapoint": {"question": "Calculate the following: (22*x**3 + 15*x**2 - 48*x)*(49*x**3 - 23*x**2 + 7*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1078*x**6 + 229*x**5 - 2543*x**4 + 1209*x**3 - 336*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1094, "polynomial_expr": "(22*x**3 + 15*x**2 - 48*x)*(49*x**3 - 23*x**2 + 7*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (22*x**3 + 15*x**2 - 48*x)*(49*x**3 - 23*x**2 + 7*x)\nExpanding the part (22*x**3 + 15*x**2 - 48*x) using the distributive property, and we got: (-48*x)*(49*x**3 - 23*x**2 + 7*x) + (15*x**2)*(49*x**3 - 23*x**2 + 7*x) + (22*x**3)*(49*x**3 - 23*x**2 + 7*x)\n#Step 2:\nCurrent expression: (-48*x)*(49*x**3 - 23*x**2 + 7*x) + (15*x**2)*(49*x**3 - 23*x**2 + 7*x) + (22*x**3)*(49*x**3 - 23*x**2 + 7*x)\nSimplifying the partial expression: (-48*x)*(49*x**3 - 23*x**2 + 7*x)\nExpanding the part (49*x**3 - 23*x**2 + 7*x) using the distributive property, and we got: (-48*x)*(7*x) + (-48*x)*(-23*x**2) + (-48*x)*(49*x**3)\nReplacing (-48*x)*(49*x**3 - 23*x**2 + 7*x) with (-48*x)*(7*x) + (-48*x)*(-23*x**2) + (-48*x)*(49*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-48*x)*(7*x) + (-48*x)*(-23*x**2) + (-48*x)*(49*x**3) + (15*x**2)*(49*x**3 - 23*x**2 + 7*x) + (22*x**3)*(49*x**3 - 23*x**2 + 7*x)\nSimplifying the partial expression: (15*x**2)*(49*x**3 - 23*x**2 + 7*x)\nExpanding the part (49*x**3 - 23*x**2 + 7*x) using the distributive property, and we got: (7*x)*(15*x**2) + (-23*x**2)*(15*x**2) + (15*x**2)*(49*x**3)\nReplacing (15*x**2)*(49*x**3 - 23*x**2 + 7*x) with (7*x)*(15*x**2) + (-23*x**2)*(15*x**2) + (15*x**2)*(49*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-48*x)*(7*x) + (-48*x)*(-23*x**2) + (-48*x)*(49*x**3) + (7*x)*(15*x**2) + (-23*x**2)*(15*x**2) + (15*x**2)*(49*x**3) + (22*x**3)*(49*x**3 - 23*x**2 + 7*x)\nSimplifying the partial expression: (22*x**3)*(49*x**3 - 23*x**2 + 7*x)\nExpanding the part (49*x**3 - 23*x**2 + 7*x) using the distributive property, and we got: (7*x)*(22*x**3) + (-23*x**2)*(22*x**3) + (22*x**3)*(49*x**3)\nReplacing (22*x**3)*(49*x**3 - 23*x**2 + 7*x) with (7*x)*(22*x**3) + (-23*x**2)*(22*x**3) + (22*x**3)*(49*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-48*x)*(7*x) + (-48*x)*(-23*x**2) + (-48*x)*(49*x**3) + (7*x)*(15*x**2) + (7*x)*(22*x**3) + (-23*x**2)*(15*x**2) + (-23*x**2)*(22*x**3) + (15*x**2)*(49*x**3) + (22*x**3)*(49*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*x**2)*(-48*x) = 1104*x**3\n (-23*x**2)*(15*x**2) = -345*x**4\n (-23*x**2)*(22*x**3) = -506*x**5\n (7*x)*(-48*x) = -336*x**2\n (7*x)*(15*x**2) = 105*x**3\n (7*x)*(22*x**3) = 154*x**4\n (49*x**3)*(-48*x) = -2352*x**4\n (49*x**3)*(15*x**2) = 735*x**5\n (49*x**3)*(22*x**3) = 1078*x**6\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1078*x**6 - 506*x**5 + 735*x**5 - 2352*x**4 - 345*x**4 + 154*x**4 + 105*x**3 + 1104*x**3 - 336*x**2\nCombining like terms, got 1078*x**6 + 229*x**5 - 2543*x**4 + 1209*x**3 - 336*x**2\n#Step 7:\nCurrent expression: 1078*x**6 + 229*x**5 - 2543*x**4 + 1209*x**3 - 336*x**2\nNo more calculations needed.\n1078*x**6 + 229*x**5 - 2543*x**4 + 1209*x**3 - 336*x**2", "generated_answer": "1078*x**6 + 229*x**5 - 2543*x**4 + 1209*x**3 - 336*x**2", "step_length": 7} {"cot_id": "cd9f299ae11e5b1776bc0fb87136ead48d574cff499e87cdec218188f0c3f0f7", "datapoint": {"question": "Calculate the following: (-14*y - 37)*(20*y**3 - 44*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-280*y**4 - 124*y**3 + 1628*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1095, "polynomial_expr": "(-14*y - 37)*(20*y**3 - 44*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-14*y - 37)*(20*y**3 - 44*y**2)\nExpanding the part (-14*y - 37) using the distributive property, and we got: (-14*y)*(20*y**3 - 44*y**2) - 37*(20*y**3 - 44*y**2)\n#Step 2:\nCurrent expression: (-14*y)*(20*y**3 - 44*y**2) - 37*(20*y**3 - 44*y**2)\nSimplifying the partial expression: -37*(20*y**3 - 44*y**2)\nExpanding the part (20*y**3 - 44*y**2) using the distributive property, and we got: -44*y**2*(-37) + (20*y**3)*(-37)\nReplacing -37*(20*y**3 - 44*y**2) with -44*y**2*(-37) + (20*y**3)*(-37) in the overall expression.\n#Step 3:\nCurrent expression: (-14*y)*(20*y**3 - 44*y**2) - 44*y**2*(-37) + (20*y**3)*(-37)\nSimplifying the partial expression: (-14*y)*(20*y**3 - 44*y**2)\nExpanding the part (20*y**3 - 44*y**2) using the distributive property, and we got: (-14*y)*(-44*y**2) + (-14*y)*(20*y**3)\nReplacing (-14*y)*(20*y**3 - 44*y**2) with (-14*y)*(-44*y**2) + (-14*y)*(20*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-14*y)*(-44*y**2) + (-14*y)*(20*y**3) - 44*y**2*(-37) + (20*y**3)*(-37)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-44*y**2)*-37 = 1628*y**2\n (-44*y**2)*(-14*y) = 616*y**3\n (20*y**3)*-37 = -740*y**3\n (20*y**3)*(-14*y) = -280*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -280*y**4 - 740*y**3 + 616*y**3 + 1628*y**2\nCombining like terms, got -280*y**4 - 124*y**3 + 1628*y**2\n#Step 6:\nCurrent expression: -280*y**4 - 124*y**3 + 1628*y**2\nNo more calculations needed.\n-280*y**4 - 124*y**3 + 1628*y**2", "generated_answer": "-280*y**4 - 124*y**3 + 1628*y**2", "step_length": 6} {"cot_id": "c45c552aee24521b6047232243335b6cce8e0ce57f804d40f342298d662e5c61", "datapoint": {"question": "Simplify this expression: -15*y**3*(9*y**2 + 24*y - 29)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-135*y**5 - 360*y**4 + 435*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1096, "polynomial_expr": "-15*y**3*(9*y**2 + 24*y - 29)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -15*y**3*(9*y**2 + 24*y - 29)\nExpanding the part (9*y**2 + 24*y - 29) using the distributive property, and we got: -(-1)*435*y**3 + (24*y)*(-15*y**3) + (9*y**2)*(-15*y**3)\n#Step 2:\nCurrent expression: -(-1)*435*y**3 + (24*y)*(-15*y**3) + (9*y**2)*(-15*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -29*(-15*y**3) = 435*y**3\n (9*y**2)*(-15*y**3) = -135*y**5\n (24*y)*(-15*y**3) = -360*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -135*y**5 - 360*y**4 + 435*y**3\nNo more calculations needed.\n-135*y**5 - 360*y**4 + 435*y**3", "generated_answer": "-135*y**5 - 360*y**4 + 435*y**3", "step_length": 3} {"cot_id": "ff53e3133099cdd4eb6b5f2b22774017bbafab21e270ffca82d6bf19ab726496", "datapoint": {"question": "Calculate the following: (8 - 15*x)*(41*x**3 + 32*x**2 + 18*x + 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-615*x**4 - 152*x**3 - 14*x**2 - 396*x + 288", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1097, "polynomial_expr": "(8 - 15*x)*(41*x**3 + 32*x**2 + 18*x + 36)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (8 - 15*x)*(41*x**3 + 32*x**2 + 18*x + 36)\nExpanding the part (8 - 15*x) using the distributive property, and we got: (-15*x)*(41*x**3 + 32*x**2 + 18*x + 36) + 8*(41*x**3 + 32*x**2 + 18*x + 36)\n#Step 2:\nCurrent expression: (-15*x)*(41*x**3 + 32*x**2 + 18*x + 36) + 8*(41*x**3 + 32*x**2 + 18*x + 36)\nSimplifying the partial expression: 8*(41*x**3 + 32*x**2 + 18*x + 36)\nExpanding the part (41*x**3 + 32*x**2 + 18*x + 36) using the distributive property, and we got: (18*x)*8 + (32*x**2)*8 + (41*x**3)*8 + 36*8\nReplacing 8*(41*x**3 + 32*x**2 + 18*x + 36) with (18*x)*8 + (32*x**2)*8 + (41*x**3)*8 + 36*8 in the overall expression.\n#Step 3:\nCurrent expression: (-15*x)*(41*x**3 + 32*x**2 + 18*x + 36) + (18*x)*8 + (32*x**2)*8 + (41*x**3)*8 + 288\nSimplifying the partial expression: (-15*x)*(41*x**3 + 32*x**2 + 18*x + 36)\nExpanding the part (41*x**3 + 32*x**2 + 18*x + 36) using the distributive property, and we got: (-15*x)*(18*x) + (-15*x)*(32*x**2) + (-15*x)*(41*x**3) + 36*(-15*x)\nReplacing (-15*x)*(41*x**3 + 32*x**2 + 18*x + 36) with (-15*x)*(18*x) + (-15*x)*(32*x**2) + (-15*x)*(41*x**3) + 36*(-15*x) in the overall expression.\n#Step 4:\nCurrent expression: (-15*x)*(18*x) + (-15*x)*(32*x**2) + (-15*x)*(41*x**3) + 36*(-15)*x + (18*x)*8 + (32*x**2)*8 + (41*x**3)*8 + 288\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (18*x)*8 = 144*x\n (18*x)*(-15*x) = -270*x**2\n (32*x**2)*8 = 256*x**2\n (32*x**2)*(-15*x) = -480*x**3\n (41*x**3)*8 = 328*x**3\n (41*x**3)*(-15*x) = -615*x**4\n 36*-15*x = -540*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -615*x**4 - 480*x**3 + 328*x**3 - 270*x**2 + 256*x**2 - 540*x + 144*x + 288\nCombining like terms, got -615*x**4 - 152*x**3 - 14*x**2 - 396*x + 288\n#Step 6:\nCurrent expression: -615*x**4 - 152*x**3 - 14*x**2 - 396*x + 288\nNo more calculations needed.\n-615*x**4 - 152*x**3 - 14*x**2 - 396*x + 288", "generated_answer": "-615*x**4 - 152*x**3 - 14*x**2 - 396*x + 288", "step_length": 6} {"cot_id": "cce02b35236116a23f0ac9ac6a84ff2841e23d58a0eb2a0b94cfa276118b03f4", "datapoint": {"question": "Simplify this expression: (-47*y**2 - 50)*(-68*y**2 + 33*y + 19)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "3196*y**4 - 1551*y**3 + 2507*y**2 - 1650*y - 950", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1098, "polynomial_expr": "(-47*y**2 - 50)*(-68*y**2 + 33*y + 19)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-47*y**2 - 50)*(-68*y**2 + 33*y + 19)\nExpanding the part (-47*y**2 - 50) using the distributive property, and we got: (-47*y**2)*(-68*y**2 + 33*y + 19) - 50*(-68*y**2 + 33*y + 19)\n#Step 2:\nCurrent expression: (-47*y**2)*(-68*y**2 + 33*y + 19) - 50*(-68*y**2 + 33*y + 19)\nSimplifying the partial expression: -50*(-68*y**2 + 33*y + 19)\nExpanding the part (-68*y**2 + 33*y + 19) using the distributive property, and we got: (33*y)*(-50) - 68*y**2*(-50) + 19*(-50)\nReplacing -50*(-68*y**2 + 33*y + 19) with (33*y)*(-50) - 68*y**2*(-50) + 19*(-50) in the overall expression.\n#Step 3:\nCurrent expression: (33*y)*(-50) - 68*y**2*(-50) + (-47*y**2)*(-68*y**2 + 33*y + 19) - 950\nSimplifying the partial expression: (-47*y**2)*(-68*y**2 + 33*y + 19)\nExpanding the part (-68*y**2 + 33*y + 19) using the distributive property, and we got: 19*(-47*y**2) + (33*y)*(-47*y**2) + (-68*y**2)*(-47*y**2)\nReplacing (-47*y**2)*(-68*y**2 + 33*y + 19) with 19*(-47*y**2) + (33*y)*(-47*y**2) + (-68*y**2)*(-47*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 19*(-47)*y**2 + (33*y)*(-47*y**2) + (33*y)*(-50) + (-68*y**2)*(-47*y**2) - 68*y**2*(-50) - 950\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-68*y**2)*-50 = 3400*y**2\n (-68*y**2)*(-47*y**2) = 3196*y**4\n (33*y)*-50 = -1650*y\n (33*y)*(-47*y**2) = -1551*y**3\n 19*-47*y**2 = -893*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 3196*y**4 - 1551*y**3 - 893*y**2 + 3400*y**2 - 1650*y - 950\nCombining like terms, got 3196*y**4 - 1551*y**3 + 2507*y**2 - 1650*y - 950\n#Step 6:\nCurrent expression: 3196*y**4 - 1551*y**3 + 2507*y**2 - 1650*y - 950\nNo more calculations needed.\n3196*y**4 - 1551*y**3 + 2507*y**2 - 1650*y - 950", "generated_answer": "3196*y**4 - 1551*y**3 + 2507*y**2 - 1650*y - 950", "step_length": 6} {"cot_id": "048ce8c52cdb8a368c35fd87fa4c1f8a8c1c8316dae4f3cfabd673c2beeeea96", "datapoint": {"question": "Calculate the following: (-44*y**2 + 40*y)*(-29*y**3 + 48*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1276*y**5 - 3272*y**4 + 1920*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1099, "polynomial_expr": "(-44*y**2 + 40*y)*(-29*y**3 + 48*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-44*y**2 + 40*y)*(-29*y**3 + 48*y**2)\nExpanding the part (-44*y**2 + 40*y) using the distributive property, and we got: (40*y)*(-29*y**3 + 48*y**2) + (-44*y**2)*(-29*y**3 + 48*y**2)\n#Step 2:\nCurrent expression: (40*y)*(-29*y**3 + 48*y**2) + (-44*y**2)*(-29*y**3 + 48*y**2)\nSimplifying the partial expression: (-44*y**2)*(-29*y**3 + 48*y**2)\nExpanding the part (-29*y**3 + 48*y**2) using the distributive property, and we got: (-44*y**2)*(48*y**2) + (-44*y**2)*(-29*y**3)\nReplacing (-44*y**2)*(-29*y**3 + 48*y**2) with (-44*y**2)*(48*y**2) + (-44*y**2)*(-29*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (40*y)*(-29*y**3 + 48*y**2) + (-44*y**2)*(48*y**2) + (-44*y**2)*(-29*y**3)\nSimplifying the partial expression: (40*y)*(-29*y**3 + 48*y**2)\nExpanding the part (-29*y**3 + 48*y**2) using the distributive property, and we got: (40*y)*(48*y**2) + (40*y)*(-29*y**3)\nReplacing (40*y)*(-29*y**3 + 48*y**2) with (40*y)*(48*y**2) + (40*y)*(-29*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (40*y)*(48*y**2) + (40*y)*(-29*y**3) + (-44*y**2)*(48*y**2) + (-44*y**2)*(-29*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*y**3)*(-44*y**2) = 1276*y**5\n (-29*y**3)*(40*y) = -1160*y**4\n (48*y**2)*(-44*y**2) = -2112*y**4\n (48*y**2)*(40*y) = 1920*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1276*y**5 - 2112*y**4 - 1160*y**4 + 1920*y**3\nCombining like terms, got 1276*y**5 - 3272*y**4 + 1920*y**3\n#Step 6:\nCurrent expression: 1276*y**5 - 3272*y**4 + 1920*y**3\nNo more calculations needed.\n1276*y**5 - 3272*y**4 + 1920*y**3", "generated_answer": "1276*y**5 - 3272*y**4 + 1920*y**3", "step_length": 6} {"cot_id": "9394d66873f4fe3c2901a69de4bf99cc16928052daffe46df776e911dec90beb", "datapoint": {"question": "Calculate the following: 30*x**3*(73 - 20*x**3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-600*x**6 + 2190*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1100, "polynomial_expr": "30*x**3*(73 - 20*x**3)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 30*x**3*(73 - 20*x**3)\nExpanding the part (73 - 20*x**3) using the distributive property, and we got: 73*(30*x**3) + (-20*x**3)*(30*x**3)\n#Step 2:\nCurrent expression: 73*(30*x**3) + (-20*x**3)*(30*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 73*(30*x**3) = 2190*x**3\n (-20*x**3)*(30*x**3) = -600*x**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -600*x**6 + 2190*x**3\nNo more calculations needed.\n-600*x**6 + 2190*x**3", "generated_answer": "-600*x**6 + 2190*x**3", "step_length": 3} {"cot_id": "6c755751efa84b16854fd557f492f5e7d6b3c58e28a306ba15eb30f07838d2a9", "datapoint": {"question": "Simplify this expression: 16*z**2*(-48*z**2 - 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-768*z**4 - 784*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1101, "polynomial_expr": "16*z**2*(-48*z**2 - 49)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 16*z**2*(-48*z**2 - 49)\nExpanding the part (-48*z**2 - 49) using the distributive property, and we got: -784*z**2 + (-48*z**2)*(16*z**2)\n#Step 2:\nCurrent expression: -784*z**2 + (-48*z**2)*(16*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -49*(16*z**2) = -784*z**2\n (-48*z**2)*(16*z**2) = -768*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -768*z**4 - 784*z**2\nNo more calculations needed.\n-768*z**4 - 784*z**2", "generated_answer": "-768*z**4 - 784*z**2", "step_length": 3} {"cot_id": "4401fc720d163b8523c999045c76ffcaedf7a1ae22a544dbd7d914c830254775", "datapoint": {"question": "Calculate the following: (-3*z**3 - z + 32)*(26*z**3 + 43*z**2 + 5*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-78*z**6 - 129*z**5 - 41*z**4 + 789*z**3 + 1371*z**2 + 160*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1102, "polynomial_expr": "(-3*z**3 - z + 32)*(26*z**3 + 43*z**2 + 5*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-3*z**3 - z + 32)*(26*z**3 + 43*z**2 + 5*z)\nExpanding the part (-3*z**3 - z + 32) using the distributive property, and we got: (-z)*(26*z**3 + 43*z**2 + 5*z) + (-3*z**3)*(26*z**3 + 43*z**2 + 5*z) + 32*(26*z**3 + 43*z**2 + 5*z)\n#Step 2:\nCurrent expression: (-z)*(26*z**3 + 43*z**2 + 5*z) + (-3*z**3)*(26*z**3 + 43*z**2 + 5*z) + 32*(26*z**3 + 43*z**2 + 5*z)\nSimplifying the partial expression: 32*(26*z**3 + 43*z**2 + 5*z)\nExpanding the part (26*z**3 + 43*z**2 + 5*z) using the distributive property, and we got: (5*z)*32 + (43*z**2)*32 + (26*z**3)*32\nReplacing 32*(26*z**3 + 43*z**2 + 5*z) with (5*z)*32 + (43*z**2)*32 + (26*z**3)*32 in the overall expression.\n#Step 3:\nCurrent expression: (-z)*(26*z**3 + 43*z**2 + 5*z) + (5*z)*32 + (43*z**2)*32 + (-3*z**3)*(26*z**3 + 43*z**2 + 5*z) + (26*z**3)*32\nSimplifying the partial expression: (-z)*(26*z**3 + 43*z**2 + 5*z)\nExpanding the part (26*z**3 + 43*z**2 + 5*z) using the distributive property, and we got: (-z)*(5*z) + (-z)*(43*z**2) + (-z)*(26*z**3)\nReplacing (-z)*(26*z**3 + 43*z**2 + 5*z) with (-z)*(5*z) + (-z)*(43*z**2) + (-z)*(26*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-z)*(5*z) + (-z)*(43*z**2) + (-z)*(26*z**3) + (5*z)*32 + (43*z**2)*32 + (-3*z**3)*(26*z**3 + 43*z**2 + 5*z) + (26*z**3)*32\nSimplifying the partial expression: (-3*z**3)*(26*z**3 + 43*z**2 + 5*z)\nExpanding the part (26*z**3 + 43*z**2 + 5*z) using the distributive property, and we got: (5*z)*(-3*z**3) + (43*z**2)*(-3*z**3) + (-3*z**3)*(26*z**3)\nReplacing (-3*z**3)*(26*z**3 + 43*z**2 + 5*z) with (5*z)*(-3*z**3) + (43*z**2)*(-3*z**3) + (-3*z**3)*(26*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-z)*(5*z) + (-z)*(43*z**2) + (-z)*(26*z**3) + (5*z)*(-3*z**3) + (5*z)*32 + (43*z**2)*(-3*z**3) + (43*z**2)*32 + (-3*z**3)*(26*z**3) + (26*z**3)*32\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (5*z)*32 = 160*z\n (5*z)*(-z) = -5*z**2\n (5*z)*(-3*z**3) = -15*z**4\n (26*z**3)*32 = 832*z**3\n (26*z**3)*(-z) = -26*z**4\n (26*z**3)*(-3*z**3) = -78*z**6\n (43*z**2)*32 = 1376*z**2\n (43*z**2)*(-z) = -43*z**3\n (43*z**2)*(-3*z**3) = -129*z**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -78*z**6 - 129*z**5 - 26*z**4 - 15*z**4 - 43*z**3 + 832*z**3 - 5*z**2 + 1376*z**2 + 160*z\nCombining like terms, got -78*z**6 - 129*z**5 - 41*z**4 + 789*z**3 + 1371*z**2 + 160*z\n#Step 7:\nCurrent expression: -78*z**6 - 129*z**5 - 41*z**4 + 789*z**3 + 1371*z**2 + 160*z\nNo more calculations needed.\n-78*z**6 - 129*z**5 - 41*z**4 + 789*z**3 + 1371*z**2 + 160*z", "generated_answer": "-78*z**6 - 129*z**5 - 41*z**4 + 789*z**3 + 1371*z**2 + 160*z", "step_length": 7} {"cot_id": "086faa243bfc1ab71c0a7d264a23195c85a72c43bad14506ded3dd0d07af305f", "datapoint": {"question": "Calculate the following: (30 - 36*x)*(37*x**2 - 35*x + 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1332*x**3 + 2370*x**2 - 2526*x + 1230", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1103, "polynomial_expr": "(30 - 36*x)*(37*x**2 - 35*x + 41)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (30 - 36*x)*(37*x**2 - 35*x + 41)\nExpanding the part (30 - 36*x) using the distributive property, and we got: (-36*x)*(37*x**2 - 35*x + 41) + 30*(37*x**2 - 35*x + 41)\n#Step 2:\nCurrent expression: (-36*x)*(37*x**2 - 35*x + 41) + 30*(37*x**2 - 35*x + 41)\nSimplifying the partial expression: 30*(37*x**2 - 35*x + 41)\nExpanding the part (37*x**2 - 35*x + 41) using the distributive property, and we got: -35*x*30 + (37*x**2)*30 + 41*30\nReplacing 30*(37*x**2 - 35*x + 41) with -35*x*30 + (37*x**2)*30 + 41*30 in the overall expression.\n#Step 3:\nCurrent expression: (-36*x)*(37*x**2 - 35*x + 41) - 35*x*30 + (37*x**2)*30 + 1230\nSimplifying the partial expression: (-36*x)*(37*x**2 - 35*x + 41)\nExpanding the part (37*x**2 - 35*x + 41) using the distributive property, and we got: (-36*x)*(-35*x) + (-36*x)*(37*x**2) + 41*(-36*x)\nReplacing (-36*x)*(37*x**2 - 35*x + 41) with (-36*x)*(-35*x) + (-36*x)*(37*x**2) + 41*(-36*x) in the overall expression.\n#Step 4:\nCurrent expression: (-36*x)*(-35*x) + (-36*x)*(37*x**2) - 35*x*30 + 41*(-36)*x + (37*x**2)*30 + 1230\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*x)*30 = -1050*x\n (-35*x)*(-36*x) = 1260*x**2\n (37*x**2)*30 = 1110*x**2\n (37*x**2)*(-36*x) = -1332*x**3\n 41*-36*x = -1476*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1332*x**3 + 1110*x**2 + 1260*x**2 - 1476*x - 1050*x + 1230\nCombining like terms, got -1332*x**3 + 2370*x**2 - 2526*x + 1230\n#Step 6:\nCurrent expression: -1332*x**3 + 2370*x**2 - 2526*x + 1230\nNo more calculations needed.\n-1332*x**3 + 2370*x**2 - 2526*x + 1230", "generated_answer": "-1332*x**3 + 2370*x**2 - 2526*x + 1230", "step_length": 6} {"cot_id": "e114d11130147ae2a464a8922cdbcc1681eb29b779e2dda468c1ab94f163f330", "datapoint": {"question": "Calculate the following: 2*z**3*(8*z**3 + 42*z - 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "16*z**6 + 84*z**4 - 100*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1104, "polynomial_expr": "2*z**3*(8*z**3 + 42*z - 50)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 2*z**3*(8*z**3 + 42*z - 50)\nExpanding the part (8*z**3 + 42*z - 50) using the distributive property, and we got: -100*z**3 + (42*z)*(2*z**3) + (2*z**3)*(8*z**3)\n#Step 2:\nCurrent expression: -100*z**3 + (42*z)*(2*z**3) + (2*z**3)*(8*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -50*(2*z**3) = -100*z**3\n (8*z**3)*(2*z**3) = 16*z**6\n (42*z)*(2*z**3) = 84*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 16*z**6 + 84*z**4 - 100*z**3\nNo more calculations needed.\n16*z**6 + 84*z**4 - 100*z**3", "generated_answer": "16*z**6 + 84*z**4 - 100*z**3", "step_length": 3} {"cot_id": "e4afdf99e3edfc353c42c60139fb02b5a7ebcd0fba57e8fbb9e9a97bb6c8a252", "datapoint": {"question": "Simplify this expression: (12 - 41*x)*(-46*x**3 - 33*x**2 - 34*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1886*x**4 + 801*x**3 + 998*x**2 - 408*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1105, "polynomial_expr": "(12 - 41*x)*(-46*x**3 - 33*x**2 - 34*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (12 - 41*x)*(-46*x**3 - 33*x**2 - 34*x)\nExpanding the part (12 - 41*x) using the distributive property, and we got: (-41*x)*(-46*x**3 - 33*x**2 - 34*x) + 12*(-46*x**3 - 33*x**2 - 34*x)\n#Step 2:\nCurrent expression: (-41*x)*(-46*x**3 - 33*x**2 - 34*x) + 12*(-46*x**3 - 33*x**2 - 34*x)\nSimplifying the partial expression: 12*(-46*x**3 - 33*x**2 - 34*x)\nExpanding the part (-46*x**3 - 33*x**2 - 34*x) using the distributive property, and we got: -34*x*12 - 33*x**2*12 - 46*x**3*12\nReplacing 12*(-46*x**3 - 33*x**2 - 34*x) with -34*x*12 - 33*x**2*12 - 46*x**3*12 in the overall expression.\n#Step 3:\nCurrent expression: (-41*x)*(-46*x**3 - 33*x**2 - 34*x) - 34*x*12 - 33*x**2*12 - 46*x**3*12\nSimplifying the partial expression: (-41*x)*(-46*x**3 - 33*x**2 - 34*x)\nExpanding the part (-46*x**3 - 33*x**2 - 34*x) using the distributive property, and we got: (-41*x)*(-34*x) + (-41*x)*(-33*x**2) + (-41*x)*(-46*x**3)\nReplacing (-41*x)*(-46*x**3 - 33*x**2 - 34*x) with (-41*x)*(-34*x) + (-41*x)*(-33*x**2) + (-41*x)*(-46*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-41*x)*(-34*x) + (-41*x)*(-33*x**2) + (-41*x)*(-46*x**3) - 34*x*12 - 33*x**2*12 - 46*x**3*12\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*x**3)*12 = -552*x**3\n (-46*x**3)*(-41*x) = 1886*x**4\n (-34*x)*12 = -408*x\n (-34*x)*(-41*x) = 1394*x**2\n (-33*x**2)*12 = -396*x**2\n (-33*x**2)*(-41*x) = 1353*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1886*x**4 - 552*x**3 + 1353*x**3 - 396*x**2 + 1394*x**2 - 408*x\nCombining like terms, got 1886*x**4 + 801*x**3 + 998*x**2 - 408*x\n#Step 6:\nCurrent expression: 1886*x**4 + 801*x**3 + 998*x**2 - 408*x\nNo more calculations needed.\n1886*x**4 + 801*x**3 + 998*x**2 - 408*x", "generated_answer": "1886*x**4 + 801*x**3 + 998*x**2 - 408*x", "step_length": 6} {"cot_id": "ce838958d711c8ae923414b56d82555b4228e4d90488fc6cb2a3468d5011584d", "datapoint": {"question": "Calculate the following: (22*y - 68)*(-4*y**2 + 50*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-88*y**3 + 1372*y**2 - 3400*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1106, "polynomial_expr": "(22*y - 68)*(-4*y**2 + 50*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (22*y - 68)*(-4*y**2 + 50*y)\nExpanding the part (22*y - 68) using the distributive property, and we got: (22*y)*(-4*y**2 + 50*y) - 68*(-4*y**2 + 50*y)\n#Step 2:\nCurrent expression: (22*y)*(-4*y**2 + 50*y) - 68*(-4*y**2 + 50*y)\nSimplifying the partial expression: -68*(-4*y**2 + 50*y)\nExpanding the part (-4*y**2 + 50*y) using the distributive property, and we got: (50*y)*(-68) - 4*y**2*(-68)\nReplacing -68*(-4*y**2 + 50*y) with (50*y)*(-68) - 4*y**2*(-68) in the overall expression.\n#Step 3:\nCurrent expression: (22*y)*(-4*y**2 + 50*y) + (50*y)*(-68) - 4*y**2*(-68)\nSimplifying the partial expression: (22*y)*(-4*y**2 + 50*y)\nExpanding the part (-4*y**2 + 50*y) using the distributive property, and we got: (22*y)*(50*y) + (22*y)*(-4*y**2)\nReplacing (22*y)*(-4*y**2 + 50*y) with (22*y)*(50*y) + (22*y)*(-4*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (22*y)*(50*y) + (22*y)*(-4*y**2) + (50*y)*(-68) - 4*y**2*(-68)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-4*y**2)*-68 = 272*y**2\n (-4*y**2)*(22*y) = -88*y**3\n (50*y)*-68 = -3400*y\n (50*y)*(22*y) = 1100*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -88*y**3 + 272*y**2 + 1100*y**2 - 3400*y\nCombining like terms, got -88*y**3 + 1372*y**2 - 3400*y\n#Step 6:\nCurrent expression: -88*y**3 + 1372*y**2 - 3400*y\nNo more calculations needed.\n-88*y**3 + 1372*y**2 - 3400*y", "generated_answer": "-88*y**3 + 1372*y**2 - 3400*y", "step_length": 6} {"cot_id": "4af3e52c99ddc977f0934efcbb7f76b913622590dbbebbfde2c7dc3597a0318b", "datapoint": {"question": "Simplify this expression: (9 - 63*z**2)*(-27*z**2 + 2*z - 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1701*z**4 - 126*z**3 + 135*z**2 + 18*z - 54", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1107, "polynomial_expr": "(9 - 63*z**2)*(-27*z**2 + 2*z - 6)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9 - 63*z**2)*(-27*z**2 + 2*z - 6)\nExpanding the part (9 - 63*z**2) using the distributive property, and we got: (-63*z**2)*(-27*z**2 + 2*z - 6) + 9*(-27*z**2 + 2*z - 6)\n#Step 2:\nCurrent expression: (-63*z**2)*(-27*z**2 + 2*z - 6) + 9*(-27*z**2 + 2*z - 6)\nSimplifying the partial expression: 9*(-27*z**2 + 2*z - 6)\nExpanding the part (-27*z**2 + 2*z - 6) using the distributive property, and we got: (2*z)*9 - 27*z**2*9 - 6*9\nReplacing 9*(-27*z**2 + 2*z - 6) with (2*z)*9 - 27*z**2*9 - 6*9 in the overall expression.\n#Step 3:\nCurrent expression: (2*z)*9 + (-63*z**2)*(-27*z**2 + 2*z - 6) - 27*z**2*9 - 54\nSimplifying the partial expression: (-63*z**2)*(-27*z**2 + 2*z - 6)\nExpanding the part (-27*z**2 + 2*z - 6) using the distributive property, and we got: -(-1)*378*z**2 + (2*z)*(-63*z**2) + (-63*z**2)*(-27*z**2)\nReplacing (-63*z**2)*(-27*z**2 + 2*z - 6) with -(-1)*378*z**2 + (2*z)*(-63*z**2) + (-63*z**2)*(-27*z**2) in the overall expression.\n#Step 4:\nCurrent expression: -6*(-63)*z**2 + (2*z)*(-63*z**2) + (2*z)*9 + (-63*z**2)*(-27*z**2) - 27*z**2*9 - 54\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*z**2)*9 = -243*z**2\n (-27*z**2)*(-63*z**2) = 1701*z**4\n (2*z)*9 = 18*z\n (2*z)*(-63*z**2) = -126*z**3\n -6*-63*z**2 = 378*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1701*z**4 - 126*z**3 - 243*z**2 + 378*z**2 + 18*z - 54\nCombining like terms, got 1701*z**4 - 126*z**3 + 135*z**2 + 18*z - 54\n#Step 6:\nCurrent expression: 1701*z**4 - 126*z**3 + 135*z**2 + 18*z - 54\nNo more calculations needed.\n1701*z**4 - 126*z**3 + 135*z**2 + 18*z - 54", "generated_answer": "1701*z**4 - 126*z**3 + 135*z**2 + 18*z - 54", "step_length": 6} {"cot_id": "fad9b2aaff650eb62994fa41ba57064d2ea055559ac5d5d5ff2503befe7148de", "datapoint": {"question": "Simplify this expression: (13 - 25*x**3)*(-37*x**2 - x - 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "925*x**5 + 25*x**4 + 175*x**3 - 481*x**2 - 13*x - 91", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1108, "polynomial_expr": "(13 - 25*x**3)*(-37*x**2 - x - 7)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (13 - 25*x**3)*(-37*x**2 - x - 7)\nExpanding the part (13 - 25*x**3) using the distributive property, and we got: (-25*x**3)*(-37*x**2 - x - 7) + 13*(-37*x**2 - x - 7)\n#Step 2:\nCurrent expression: (-25*x**3)*(-37*x**2 - x - 7) + 13*(-37*x**2 - x - 7)\nSimplifying the partial expression: 13*(-37*x**2 - x - 7)\nExpanding the part (-37*x**2 - x - 7) using the distributive property, and we got: -x*13 - 37*x**2*13 - 7*13\nReplacing 13*(-37*x**2 - x - 7) with -x*13 - 37*x**2*13 - 7*13 in the overall expression.\n#Step 3:\nCurrent expression: -x*13 - 37*x**2*13 + (-25*x**3)*(-37*x**2 - x - 7) - 91\nSimplifying the partial expression: (-25*x**3)*(-37*x**2 - x - 7)\nExpanding the part (-37*x**2 - x - 7) using the distributive property, and we got: (-x)*(-25*x**3) - (-1)*175*x**3 + (-37*x**2)*(-25*x**3)\nReplacing (-25*x**3)*(-37*x**2 - x - 7) with (-x)*(-25*x**3) - (-1)*175*x**3 + (-37*x**2)*(-25*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-x)*(-25*x**3) - x*13 - 7*(-25)*x**3 + (-37*x**2)*(-25*x**3) - 37*x**2*13 - 91\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-x)*13 = -13*x\n (-x)*(-25*x**3) = 25*x**4\n (-37*x**2)*13 = -481*x**2\n (-37*x**2)*(-25*x**3) = 925*x**5\n -7*-25*x**3 = 175*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 925*x**5 + 25*x**4 + 175*x**3 - 481*x**2 - 13*x - 91\nNo more calculations needed.\n925*x**5 + 25*x**4 + 175*x**3 - 481*x**2 - 13*x - 91", "generated_answer": "925*x**5 + 25*x**4 + 175*x**3 - 481*x**2 - 13*x - 91", "step_length": 5} {"cot_id": "a1e3f8757ed0d16c2a909c9373752be0e24bad984a476bae75cd2c3f369268c0", "datapoint": {"question": "Calculate the following: (-20*x**2 + 19*x)*(27*x**3 + 17*x**2 - 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-540*x**5 + 173*x**4 + 323*x**3 + 560*x**2 - 532*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1109, "polynomial_expr": "(-20*x**2 + 19*x)*(27*x**3 + 17*x**2 - 28)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-20*x**2 + 19*x)*(27*x**3 + 17*x**2 - 28)\nExpanding the part (-20*x**2 + 19*x) using the distributive property, and we got: (19*x)*(27*x**3 + 17*x**2 - 28) + (-20*x**2)*(27*x**3 + 17*x**2 - 28)\n#Step 2:\nCurrent expression: (19*x)*(27*x**3 + 17*x**2 - 28) + (-20*x**2)*(27*x**3 + 17*x**2 - 28)\nSimplifying the partial expression: (-20*x**2)*(27*x**3 + 17*x**2 - 28)\nExpanding the part (27*x**3 + 17*x**2 - 28) using the distributive property, and we got: -(-1)*560*x**2 + (-20*x**2)*(17*x**2) + (-20*x**2)*(27*x**3)\nReplacing (-20*x**2)*(27*x**3 + 17*x**2 - 28) with -(-1)*560*x**2 + (-20*x**2)*(17*x**2) + (-20*x**2)*(27*x**3) in the overall expression.\n#Step 3:\nCurrent expression: -28*(-20)*x**2 + (19*x)*(27*x**3 + 17*x**2 - 28) + (-20*x**2)*(17*x**2) + (-20*x**2)*(27*x**3)\nSimplifying the partial expression: (19*x)*(27*x**3 + 17*x**2 - 28)\nExpanding the part (27*x**3 + 17*x**2 - 28) using the distributive property, and we got: -532*x + (19*x)*(17*x**2) + (19*x)*(27*x**3)\nReplacing (19*x)*(27*x**3 + 17*x**2 - 28) with -532*x + (19*x)*(17*x**2) + (19*x)*(27*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -28*(-20)*x**2 - 28*19*x + (19*x)*(17*x**2) + (19*x)*(27*x**3) + (-20*x**2)*(17*x**2) + (-20*x**2)*(27*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (17*x**2)*(-20*x**2) = -340*x**4\n (17*x**2)*(19*x) = 323*x**3\n (27*x**3)*(-20*x**2) = -540*x**5\n (27*x**3)*(19*x) = 513*x**4\n -28*-20*x**2 = 560*x**2\n -28*19*x = -532*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -540*x**5 - 340*x**4 + 513*x**4 + 323*x**3 + 560*x**2 - 532*x\nCombining like terms, got -540*x**5 + 173*x**4 + 323*x**3 + 560*x**2 - 532*x\n#Step 6:\nCurrent expression: -540*x**5 + 173*x**4 + 323*x**3 + 560*x**2 - 532*x\nNo more calculations needed.\n-540*x**5 + 173*x**4 + 323*x**3 + 560*x**2 - 532*x", "generated_answer": "-540*x**5 + 173*x**4 + 323*x**3 + 560*x**2 - 532*x", "step_length": 6} {"cot_id": "b493290ce8995ed451a119b0fac5b2e8ca3b77946a39cf531ce6a91662ae1b8f", "datapoint": {"question": "Calculate the following: (-72*z**3 + 50*z**2)*(32*z**3 - 66*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2304*z**6 + 6352*z**5 - 3300*z**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1110, "polynomial_expr": "(-72*z**3 + 50*z**2)*(32*z**3 - 66*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-72*z**3 + 50*z**2)*(32*z**3 - 66*z**2)\nExpanding the part (-72*z**3 + 50*z**2) using the distributive property, and we got: (50*z**2)*(32*z**3 - 66*z**2) + (-72*z**3)*(32*z**3 - 66*z**2)\n#Step 2:\nCurrent expression: (50*z**2)*(32*z**3 - 66*z**2) + (-72*z**3)*(32*z**3 - 66*z**2)\nSimplifying the partial expression: (-72*z**3)*(32*z**3 - 66*z**2)\nExpanding the part (32*z**3 - 66*z**2) using the distributive property, and we got: (-66*z**2)*(-72*z**3) + (-72*z**3)*(32*z**3)\nReplacing (-72*z**3)*(32*z**3 - 66*z**2) with (-66*z**2)*(-72*z**3) + (-72*z**3)*(32*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-66*z**2)*(-72*z**3) + (50*z**2)*(32*z**3 - 66*z**2) + (-72*z**3)*(32*z**3)\nSimplifying the partial expression: (50*z**2)*(32*z**3 - 66*z**2)\nExpanding the part (32*z**3 - 66*z**2) using the distributive property, and we got: (-66*z**2)*(50*z**2) + (50*z**2)*(32*z**3)\nReplacing (50*z**2)*(32*z**3 - 66*z**2) with (-66*z**2)*(50*z**2) + (50*z**2)*(32*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-66*z**2)*(50*z**2) + (-66*z**2)*(-72*z**3) + (50*z**2)*(32*z**3) + (-72*z**3)*(32*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-66*z**2)*(-72*z**3) = 4752*z**5\n (-66*z**2)*(50*z**2) = -3300*z**4\n (32*z**3)*(-72*z**3) = -2304*z**6\n (32*z**3)*(50*z**2) = 1600*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2304*z**6 + 1600*z**5 + 4752*z**5 - 3300*z**4\nCombining like terms, got -2304*z**6 + 6352*z**5 - 3300*z**4\n#Step 6:\nCurrent expression: -2304*z**6 + 6352*z**5 - 3300*z**4\nNo more calculations needed.\n-2304*z**6 + 6352*z**5 - 3300*z**4", "generated_answer": "-2304*z**6 + 6352*z**5 - 3300*z**4", "step_length": 6} {"cot_id": "f0e630b4234d60f241aa642eb8cd2dc44daa612c6ef95d11427a4c4f8387c811", "datapoint": {"question": "Calculate the following: (47*x**2 - 50*x - 13)*(55*x**3 + 14*x**2 - 40*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2585*x**5 - 2092*x**4 - 3295*x**3 + 1818*x**2 + 520*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1111, "polynomial_expr": "(47*x**2 - 50*x - 13)*(55*x**3 + 14*x**2 - 40*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (47*x**2 - 50*x - 13)*(55*x**3 + 14*x**2 - 40*x)\nExpanding the part (47*x**2 - 50*x - 13) using the distributive property, and we got: (-50*x)*(55*x**3 + 14*x**2 - 40*x) + (47*x**2)*(55*x**3 + 14*x**2 - 40*x) - 13*(55*x**3 + 14*x**2 - 40*x)\n#Step 2:\nCurrent expression: (-50*x)*(55*x**3 + 14*x**2 - 40*x) + (47*x**2)*(55*x**3 + 14*x**2 - 40*x) - 13*(55*x**3 + 14*x**2 - 40*x)\nSimplifying the partial expression: -13*(55*x**3 + 14*x**2 - 40*x)\nExpanding the part (55*x**3 + 14*x**2 - 40*x) using the distributive property, and we got: -40*x*(-13) + (14*x**2)*(-13) + (55*x**3)*(-13)\nReplacing -13*(55*x**3 + 14*x**2 - 40*x) with -40*x*(-13) + (14*x**2)*(-13) + (55*x**3)*(-13) in the overall expression.\n#Step 3:\nCurrent expression: (-50*x)*(55*x**3 + 14*x**2 - 40*x) - 40*x*(-13) + (14*x**2)*(-13) + (47*x**2)*(55*x**3 + 14*x**2 - 40*x) + (55*x**3)*(-13)\nSimplifying the partial expression: (-50*x)*(55*x**3 + 14*x**2 - 40*x)\nExpanding the part (55*x**3 + 14*x**2 - 40*x) using the distributive property, and we got: (-50*x)*(-40*x) + (-50*x)*(14*x**2) + (-50*x)*(55*x**3)\nReplacing (-50*x)*(55*x**3 + 14*x**2 - 40*x) with (-50*x)*(-40*x) + (-50*x)*(14*x**2) + (-50*x)*(55*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-50*x)*(-40*x) + (-50*x)*(14*x**2) + (-50*x)*(55*x**3) - 40*x*(-13) + (14*x**2)*(-13) + (47*x**2)*(55*x**3 + 14*x**2 - 40*x) + (55*x**3)*(-13)\nSimplifying the partial expression: (47*x**2)*(55*x**3 + 14*x**2 - 40*x)\nExpanding the part (55*x**3 + 14*x**2 - 40*x) using the distributive property, and we got: (-40*x)*(47*x**2) + (14*x**2)*(47*x**2) + (47*x**2)*(55*x**3)\nReplacing (47*x**2)*(55*x**3 + 14*x**2 - 40*x) with (-40*x)*(47*x**2) + (14*x**2)*(47*x**2) + (47*x**2)*(55*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-50*x)*(-40*x) + (-50*x)*(14*x**2) + (-50*x)*(55*x**3) + (-40*x)*(47*x**2) - 40*x*(-13) + (14*x**2)*(47*x**2) + (14*x**2)*(-13) + (47*x**2)*(55*x**3) + (55*x**3)*(-13)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*x)*-13 = 520*x\n (-40*x)*(-50*x) = 2000*x**2\n (-40*x)*(47*x**2) = -1880*x**3\n (14*x**2)*-13 = -182*x**2\n (14*x**2)*(-50*x) = -700*x**3\n (14*x**2)*(47*x**2) = 658*x**4\n (55*x**3)*-13 = -715*x**3\n (55*x**3)*(-50*x) = -2750*x**4\n (55*x**3)*(47*x**2) = 2585*x**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 2585*x**5 - 2750*x**4 + 658*x**4 - 1880*x**3 - 715*x**3 - 700*x**3 - 182*x**2 + 2000*x**2 + 520*x\nCombining like terms, got 2585*x**5 - 2092*x**4 - 3295*x**3 + 1818*x**2 + 520*x\n#Step 7:\nCurrent expression: 2585*x**5 - 2092*x**4 - 3295*x**3 + 1818*x**2 + 520*x\nNo more calculations needed.\n2585*x**5 - 2092*x**4 - 3295*x**3 + 1818*x**2 + 520*x", "generated_answer": "2585*x**5 - 2092*x**4 - 3295*x**3 + 1818*x**2 + 520*x", "step_length": 7} {"cot_id": "8b006426e8df373825ee92ce259d8df09dee44ab46dadcdac21efda5c7616b02", "datapoint": {"question": "Simplify this expression: (42*z**3 + 42*z**2)*(41*z**3 - 17*z**2 - 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1722*z**6 + 1008*z**5 - 714*z**4 - 1176*z**3 - 1176*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1112, "polynomial_expr": "(42*z**3 + 42*z**2)*(41*z**3 - 17*z**2 - 28)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (42*z**3 + 42*z**2)*(41*z**3 - 17*z**2 - 28)\nExpanding the part (42*z**3 + 42*z**2) using the distributive property, and we got: (42*z**2)*(41*z**3 - 17*z**2 - 28) + (42*z**3)*(41*z**3 - 17*z**2 - 28)\n#Step 2:\nCurrent expression: (42*z**2)*(41*z**3 - 17*z**2 - 28) + (42*z**3)*(41*z**3 - 17*z**2 - 28)\nSimplifying the partial expression: (42*z**2)*(41*z**3 - 17*z**2 - 28)\nExpanding the part (41*z**3 - 17*z**2 - 28) using the distributive property, and we got: -1176*z**2 + (-17*z**2)*(42*z**2) + (42*z**2)*(41*z**3)\nReplacing (42*z**2)*(41*z**3 - 17*z**2 - 28) with -1176*z**2 + (-17*z**2)*(42*z**2) + (42*z**2)*(41*z**3) in the overall expression.\n#Step 3:\nCurrent expression: -28*42*z**2 + (-17*z**2)*(42*z**2) + (42*z**2)*(41*z**3) + (42*z**3)*(41*z**3 - 17*z**2 - 28)\nSimplifying the partial expression: (42*z**3)*(41*z**3 - 17*z**2 - 28)\nExpanding the part (41*z**3 - 17*z**2 - 28) using the distributive property, and we got: -1176*z**3 + (-17*z**2)*(42*z**3) + (41*z**3)*(42*z**3)\nReplacing (42*z**3)*(41*z**3 - 17*z**2 - 28) with -1176*z**3 + (-17*z**2)*(42*z**3) + (41*z**3)*(42*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -28*42*z**3 - 28*42*z**2 + (-17*z**2)*(42*z**2) + (-17*z**2)*(42*z**3) + (42*z**2)*(41*z**3) + (41*z**3)*(42*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-17*z**2)*(42*z**2) = -714*z**4\n (-17*z**2)*(42*z**3) = -714*z**5\n (41*z**3)*(42*z**2) = 1722*z**5\n (41*z**3)*(42*z**3) = 1722*z**6\n -28*42*z**2 = -1176*z**2\n -28*42*z**3 = -1176*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1722*z**6 - 714*z**5 + 1722*z**5 - 714*z**4 - 1176*z**3 - 1176*z**2\nCombining like terms, got 1722*z**6 + 1008*z**5 - 714*z**4 - 1176*z**3 - 1176*z**2\n#Step 6:\nCurrent expression: 1722*z**6 + 1008*z**5 - 714*z**4 - 1176*z**3 - 1176*z**2\nNo more calculations needed.\n1722*z**6 + 1008*z**5 - 714*z**4 - 1176*z**3 - 1176*z**2", "generated_answer": "1722*z**6 + 1008*z**5 - 714*z**4 - 1176*z**3 - 1176*z**2", "step_length": 6} {"cot_id": "09c2b7a5acf17aeb983dc2c314c4ef2fd76ab9259f9ba8d6a829ce9cf1281f26", "datapoint": {"question": "Simplify this expression: (46 - 16*x)*(12*x**2 + 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-192*x**3 + 552*x**2 - 784*x + 2254", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1113, "polynomial_expr": "(46 - 16*x)*(12*x**2 + 49)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (46 - 16*x)*(12*x**2 + 49)\nExpanding the part (46 - 16*x) using the distributive property, and we got: (-16*x)*(12*x**2 + 49) + 46*(12*x**2 + 49)\n#Step 2:\nCurrent expression: (-16*x)*(12*x**2 + 49) + 46*(12*x**2 + 49)\nSimplifying the partial expression: 46*(12*x**2 + 49)\nExpanding the part (12*x**2 + 49) using the distributive property, and we got: (12*x**2)*46 + 49*46\nReplacing 46*(12*x**2 + 49) with (12*x**2)*46 + 49*46 in the overall expression.\n#Step 3:\nCurrent expression: (-16*x)*(12*x**2 + 49) + (12*x**2)*46 + 2254\nSimplifying the partial expression: (-16*x)*(12*x**2 + 49)\nExpanding the part (12*x**2 + 49) using the distributive property, and we got: (-16*x)*(12*x**2) + 49*(-16*x)\nReplacing (-16*x)*(12*x**2 + 49) with (-16*x)*(12*x**2) + 49*(-16*x) in the overall expression.\n#Step 4:\nCurrent expression: (-16*x)*(12*x**2) + 49*(-16)*x + (12*x**2)*46 + 2254\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (12*x**2)*46 = 552*x**2\n (12*x**2)*(-16*x) = -192*x**3\n 49*-16*x = -784*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -192*x**3 + 552*x**2 - 784*x + 2254\nNo more calculations needed.\n-192*x**3 + 552*x**2 - 784*x + 2254", "generated_answer": "-192*x**3 + 552*x**2 - 784*x + 2254", "step_length": 5} {"cot_id": "4deb38fe05f1cf2afb9bf4d802192a335e582ff1c15b75d3fb4662671d3381ea", "datapoint": {"question": "Simplify this expression: (35 - 17*z**2)*(-31*z - 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "527*z**3 + 510*z**2 - 1085*z - 1050", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1114, "polynomial_expr": "(35 - 17*z**2)*(-31*z - 30)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (35 - 17*z**2)*(-31*z - 30)\nExpanding the part (-31*z - 30) using the distributive property, and we got: (-31*z)*(35 - 17*z**2) - 30*(35 - 17*z**2)\n#Step 2:\nCurrent expression: (-31*z)*(35 - 17*z**2) - 30*(35 - 17*z**2)\nSimplifying the partial expression: -30*(35 - 17*z**2)\nExpanding the part (35 - 17*z**2) using the distributive property, and we got: -17*z**2*(-30) + 35*(-30)\nReplacing -30*(35 - 17*z**2) with -17*z**2*(-30) + 35*(-30) in the overall expression.\n#Step 3:\nCurrent expression: (-31*z)*(35 - 17*z**2) - 17*z**2*(-30) - 1050\nSimplifying the partial expression: (-31*z)*(35 - 17*z**2)\nExpanding the part (35 - 17*z**2) using the distributive property, and we got: (-31*z)*(-17*z**2) + 35*(-31*z)\nReplacing (-31*z)*(35 - 17*z**2) with (-31*z)*(-17*z**2) + 35*(-31*z) in the overall expression.\n#Step 4:\nCurrent expression: (-31*z)*(-17*z**2) + 35*(-31)*z - 17*z**2*(-30) - 1050\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-17*z**2)*-30 = 510*z**2\n (-17*z**2)*(-31*z) = 527*z**3\n 35*-31*z = -1085*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 527*z**3 + 510*z**2 - 1085*z - 1050\nNo more calculations needed.\n527*z**3 + 510*z**2 - 1085*z - 1050", "generated_answer": "527*z**3 + 510*z**2 - 1085*z - 1050", "step_length": 5} {"cot_id": "f0a627bc7cd9bdb56dfdaffba6079f70903c3596a2383dde17db0a6455690fa9", "datapoint": {"question": "Calculate the following: (-32*z**3 - 18)*(42*z**3 - 25)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1344*z**6 + 44*z**3 + 450", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1115, "polynomial_expr": "(-32*z**3 - 18)*(42*z**3 - 25)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-32*z**3 - 18)*(42*z**3 - 25)\nExpanding the part (42*z**3 - 25) using the distributive property, and we got: (42*z**3)*(-32*z**3 - 18) - 25*(-32*z**3 - 18)\n#Step 2:\nCurrent expression: (42*z**3)*(-32*z**3 - 18) - 25*(-32*z**3 - 18)\nSimplifying the partial expression: -25*(-32*z**3 - 18)\nExpanding the part (-32*z**3 - 18) using the distributive property, and we got: -32*z**3*(-25) - 18*(-25)\nReplacing -25*(-32*z**3 - 18) with -32*z**3*(-25) - 18*(-25) in the overall expression.\n#Step 3:\nCurrent expression: -32*z**3*(-25) + (42*z**3)*(-32*z**3 - 18) + 450\nSimplifying the partial expression: (42*z**3)*(-32*z**3 - 18)\nExpanding the part (-32*z**3 - 18) using the distributive property, and we got: -756*z**3 + (-32*z**3)*(42*z**3)\nReplacing (42*z**3)*(-32*z**3 - 18) with -756*z**3 + (-32*z**3)*(42*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -18*42*z**3 + (-32*z**3)*(42*z**3) - 32*z**3*(-25) + 450\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*z**3)*-25 = 800*z**3\n (-32*z**3)*(42*z**3) = -1344*z**6\n -18*42*z**3 = -756*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1344*z**6 - 756*z**3 + 800*z**3 + 450\nCombining like terms, got -1344*z**6 + 44*z**3 + 450\n#Step 6:\nCurrent expression: -1344*z**6 + 44*z**3 + 450\nNo more calculations needed.\n-1344*z**6 + 44*z**3 + 450", "generated_answer": "-1344*z**6 + 44*z**3 + 450", "step_length": 6} {"cot_id": "57f11b9f23ce13bcbf5577a0f2d3eee7a0e3725687cba0c3f87b5cdd962977e8", "datapoint": {"question": "Simplify this expression: (13*y**2 - 27*y)*(-5*y**2 - 14*y - 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-65*y**4 - 47*y**3 + 14*y**2 + 756*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1116, "polynomial_expr": "(13*y**2 - 27*y)*(-5*y**2 - 14*y - 28)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (13*y**2 - 27*y)*(-5*y**2 - 14*y - 28)\nExpanding the part (13*y**2 - 27*y) using the distributive property, and we got: (-27*y)*(-5*y**2 - 14*y - 28) + (13*y**2)*(-5*y**2 - 14*y - 28)\n#Step 2:\nCurrent expression: (-27*y)*(-5*y**2 - 14*y - 28) + (13*y**2)*(-5*y**2 - 14*y - 28)\nSimplifying the partial expression: (-27*y)*(-5*y**2 - 14*y - 28)\nExpanding the part (-5*y**2 - 14*y - 28) using the distributive property, and we got: (-27*y)*(-14*y) + (-27*y)*(-5*y**2) - (-1)*756*y\nReplacing (-27*y)*(-5*y**2 - 14*y - 28) with (-27*y)*(-14*y) + (-27*y)*(-5*y**2) - (-1)*756*y in the overall expression.\n#Step 3:\nCurrent expression: (-27*y)*(-14*y) + (-27*y)*(-5*y**2) - 28*(-27)*y + (13*y**2)*(-5*y**2 - 14*y - 28)\nSimplifying the partial expression: (13*y**2)*(-5*y**2 - 14*y - 28)\nExpanding the part (-5*y**2 - 14*y - 28) using the distributive property, and we got: (-14*y)*(13*y**2) - 364*y**2 + (-5*y**2)*(13*y**2)\nReplacing (13*y**2)*(-5*y**2 - 14*y - 28) with (-14*y)*(13*y**2) - 364*y**2 + (-5*y**2)*(13*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-27*y)*(-14*y) + (-27*y)*(-5*y**2) + (-14*y)*(13*y**2) - 28*13*y**2 - 28*(-27)*y + (-5*y**2)*(13*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-14*y)*(-27*y) = 378*y**2\n (-14*y)*(13*y**2) = -182*y**3\n (-5*y**2)*(-27*y) = 135*y**3\n (-5*y**2)*(13*y**2) = -65*y**4\n -28*-27*y = 756*y\n -28*13*y**2 = -364*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -65*y**4 - 182*y**3 + 135*y**3 - 364*y**2 + 378*y**2 + 756*y\nCombining like terms, got -65*y**4 - 47*y**3 + 14*y**2 + 756*y\n#Step 6:\nCurrent expression: -65*y**4 - 47*y**3 + 14*y**2 + 756*y\nNo more calculations needed.\n-65*y**4 - 47*y**3 + 14*y**2 + 756*y", "generated_answer": "-65*y**4 - 47*y**3 + 14*y**2 + 756*y", "step_length": 6} {"cot_id": "01d298b2954fe452bc21ae5bfe91b24cb75df7f13fcaa82d0ee1d7aa8c3852e9", "datapoint": {"question": "Simplify this expression: (31*x + 28)*(-42*x**2 - 54*x + 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1302*x**3 - 2850*x**2 - 551*x + 868", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1117, "polynomial_expr": "(31*x + 28)*(-42*x**2 - 54*x + 31)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31*x + 28)*(-42*x**2 - 54*x + 31)\nExpanding the part (31*x + 28) using the distributive property, and we got: (31*x)*(-42*x**2 - 54*x + 31) + 28*(-42*x**2 - 54*x + 31)\n#Step 2:\nCurrent expression: (31*x)*(-42*x**2 - 54*x + 31) + 28*(-42*x**2 - 54*x + 31)\nSimplifying the partial expression: 28*(-42*x**2 - 54*x + 31)\nExpanding the part (-42*x**2 - 54*x + 31) using the distributive property, and we got: -54*x*28 - 42*x**2*28 + 31*28\nReplacing 28*(-42*x**2 - 54*x + 31) with -54*x*28 - 42*x**2*28 + 31*28 in the overall expression.\n#Step 3:\nCurrent expression: -54*x*28 + (31*x)*(-42*x**2 - 54*x + 31) - 42*x**2*28 + 868\nSimplifying the partial expression: (31*x)*(-42*x**2 - 54*x + 31)\nExpanding the part (-42*x**2 - 54*x + 31) using the distributive property, and we got: (-54*x)*(31*x) + 31*(31*x) + (31*x)*(-42*x**2)\nReplacing (31*x)*(-42*x**2 - 54*x + 31) with (-54*x)*(31*x) + 31*(31*x) + (31*x)*(-42*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-54*x)*(31*x) - 54*x*28 + 31*31*x + (31*x)*(-42*x**2) - 42*x**2*28 + 868\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-54*x)*28 = -1512*x\n (-54*x)*(31*x) = -1674*x**2\n (-42*x**2)*28 = -1176*x**2\n (-42*x**2)*(31*x) = -1302*x**3\n 31*31*x = 961*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1302*x**3 - 1674*x**2 - 1176*x**2 - 1512*x + 961*x + 868\nCombining like terms, got -1302*x**3 - 2850*x**2 - 551*x + 868\n#Step 6:\nCurrent expression: -1302*x**3 - 2850*x**2 - 551*x + 868\nNo more calculations needed.\n-1302*x**3 - 2850*x**2 - 551*x + 868", "generated_answer": "-1302*x**3 - 2850*x**2 - 551*x + 868", "step_length": 6} {"cot_id": "d1d3e96abf8942fbea791d4dc6d20001847e473b09a19528f9175954ae1a69e7", "datapoint": {"question": "Calculate the following: (74*y**3 - 19)*(26*y**2 + 37*y - 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1924*y**5 + 2738*y**4 - 74*y**3 - 494*y**2 - 703*y + 19", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1118, "polynomial_expr": "(74*y**3 - 19)*(26*y**2 + 37*y - 1)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (74*y**3 - 19)*(26*y**2 + 37*y - 1)\nExpanding the part (74*y**3 - 19) using the distributive property, and we got: (74*y**3)*(26*y**2 + 37*y - 1) - 19*(26*y**2 + 37*y - 1)\n#Step 2:\nCurrent expression: (74*y**3)*(26*y**2 + 37*y - 1) - 19*(26*y**2 + 37*y - 1)\nSimplifying the partial expression: -19*(26*y**2 + 37*y - 1)\nExpanding the part (26*y**2 + 37*y - 1) using the distributive property, and we got: (37*y)*(-19) + (26*y**2)*(-19) - 1*(-19)\nReplacing -19*(26*y**2 + 37*y - 1) with (37*y)*(-19) + (26*y**2)*(-19) - 1*(-19) in the overall expression.\n#Step 3:\nCurrent expression: (37*y)*(-19) + (26*y**2)*(-19) + (74*y**3)*(26*y**2 + 37*y - 1) + 19\nSimplifying the partial expression: (74*y**3)*(26*y**2 + 37*y - 1)\nExpanding the part (26*y**2 + 37*y - 1) using the distributive property, and we got: -74*y**3 + (37*y)*(74*y**3) + (26*y**2)*(74*y**3)\nReplacing (74*y**3)*(26*y**2 + 37*y - 1) with -74*y**3 + (37*y)*(74*y**3) + (26*y**2)*(74*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -1*74*y**3 + (37*y)*(74*y**3) + (37*y)*(-19) + (26*y**2)*(74*y**3) + (26*y**2)*(-19) + 19\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (26*y**2)*-19 = -494*y**2\n (26*y**2)*(74*y**3) = 1924*y**5\n (37*y)*-19 = -703*y\n (37*y)*(74*y**3) = 2738*y**4\n -1*74*y**3 = -74*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1924*y**5 + 2738*y**4 - 74*y**3 - 494*y**2 - 703*y + 19\nNo more calculations needed.\n1924*y**5 + 2738*y**4 - 74*y**3 - 494*y**2 - 703*y + 19", "generated_answer": "1924*y**5 + 2738*y**4 - 74*y**3 - 494*y**2 - 703*y + 19", "step_length": 5} {"cot_id": "00ebdefc3a94e10b36aabc12cc4dae65a616b79966081e65e3cd31054801ff30", "datapoint": {"question": "Simplify this expression: (21*z**3 - 6*z**2 - 3)*(30*z**3 - 10*z**2 + 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "630*z**6 - 390*z**5 + 60*z**4 + 603*z**3 - 168*z**2 - 99", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1119, "polynomial_expr": "(21*z**3 - 6*z**2 - 3)*(30*z**3 - 10*z**2 + 33)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21*z**3 - 6*z**2 - 3)*(30*z**3 - 10*z**2 + 33)\nExpanding the part (21*z**3 - 6*z**2 - 3) using the distributive property, and we got: (-6*z**2)*(30*z**3 - 10*z**2 + 33) + (21*z**3)*(30*z**3 - 10*z**2 + 33) - 3*(30*z**3 - 10*z**2 + 33)\n#Step 2:\nCurrent expression: (-6*z**2)*(30*z**3 - 10*z**2 + 33) + (21*z**3)*(30*z**3 - 10*z**2 + 33) - 3*(30*z**3 - 10*z**2 + 33)\nSimplifying the partial expression: -3*(30*z**3 - 10*z**2 + 33)\nExpanding the part (30*z**3 - 10*z**2 + 33) using the distributive property, and we got: -10*z**2*(-3) + (30*z**3)*(-3) + 33*(-3)\nReplacing -3*(30*z**3 - 10*z**2 + 33) with -10*z**2*(-3) + (30*z**3)*(-3) + 33*(-3) in the overall expression.\n#Step 3:\nCurrent expression: -10*z**2*(-3) + (-6*z**2)*(30*z**3 - 10*z**2 + 33) + (21*z**3)*(30*z**3 - 10*z**2 + 33) + (30*z**3)*(-3) - 99\nSimplifying the partial expression: (-6*z**2)*(30*z**3 - 10*z**2 + 33)\nExpanding the part (30*z**3 - 10*z**2 + 33) using the distributive property, and we got: 33*(-6*z**2) + (-10*z**2)*(-6*z**2) + (-6*z**2)*(30*z**3)\nReplacing (-6*z**2)*(30*z**3 - 10*z**2 + 33) with 33*(-6*z**2) + (-10*z**2)*(-6*z**2) + (-6*z**2)*(30*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 33*(-6)*z**2 + (-10*z**2)*(-6*z**2) - 10*z**2*(-3) + (-6*z**2)*(30*z**3) + (21*z**3)*(30*z**3 - 10*z**2 + 33) + (30*z**3)*(-3) - 99\nSimplifying the partial expression: (21*z**3)*(30*z**3 - 10*z**2 + 33)\nExpanding the part (30*z**3 - 10*z**2 + 33) using the distributive property, and we got: 33*(21*z**3) + (-10*z**2)*(21*z**3) + (21*z**3)*(30*z**3)\nReplacing (21*z**3)*(30*z**3 - 10*z**2 + 33) with 33*(21*z**3) + (-10*z**2)*(21*z**3) + (21*z**3)*(30*z**3) in the overall expression.\n#Step 5:\nCurrent expression: 33*21*z**3 + 33*(-6)*z**2 + (-10*z**2)*(-6*z**2) + (-10*z**2)*(21*z**3) - 10*z**2*(-3) + (-6*z**2)*(30*z**3) + (21*z**3)*(30*z**3) + (30*z**3)*(-3) - 99\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*z**2)*-3 = 30*z**2\n (-10*z**2)*(-6*z**2) = 60*z**4\n (-10*z**2)*(21*z**3) = -210*z**5\n (30*z**3)*-3 = -90*z**3\n (30*z**3)*(-6*z**2) = -180*z**5\n (30*z**3)*(21*z**3) = 630*z**6\n 33*-6*z**2 = -198*z**2\n 33*21*z**3 = 693*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 630*z**6 - 210*z**5 - 180*z**5 + 60*z**4 - 90*z**3 + 693*z**3 - 198*z**2 + 30*z**2 - 99\nCombining like terms, got 630*z**6 - 390*z**5 + 60*z**4 + 603*z**3 - 168*z**2 - 99\n#Step 7:\nCurrent expression: 630*z**6 - 390*z**5 + 60*z**4 + 603*z**3 - 168*z**2 - 99\nNo more calculations needed.\n630*z**6 - 390*z**5 + 60*z**4 + 603*z**3 - 168*z**2 - 99", "generated_answer": "630*z**6 - 390*z**5 + 60*z**4 + 603*z**3 - 168*z**2 - 99", "step_length": 7} {"cot_id": "ddaa316f923b383828eb16a8f6f3932cf1a5219da26f8491de6c1d316cbfc248", "datapoint": {"question": "Calculate the following: (19 - 19*y**3)*(-14*y**3 - 45*y**2 + 11*y - 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "266*y**6 + 855*y**5 - 209*y**4 - 19*y**3 - 855*y**2 + 209*y - 247", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1120, "polynomial_expr": "(19 - 19*y**3)*(-14*y**3 - 45*y**2 + 11*y - 13)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (19 - 19*y**3)*(-14*y**3 - 45*y**2 + 11*y - 13)\nExpanding the part (19 - 19*y**3) using the distributive property, and we got: (-19*y**3)*(-14*y**3 - 45*y**2 + 11*y - 13) + 19*(-14*y**3 - 45*y**2 + 11*y - 13)\n#Step 2:\nCurrent expression: (-19*y**3)*(-14*y**3 - 45*y**2 + 11*y - 13) + 19*(-14*y**3 - 45*y**2 + 11*y - 13)\nSimplifying the partial expression: 19*(-14*y**3 - 45*y**2 + 11*y - 13)\nExpanding the part (-14*y**3 - 45*y**2 + 11*y - 13) using the distributive property, and we got: (11*y)*19 - 45*y**2*19 - 14*y**3*19 - 13*19\nReplacing 19*(-14*y**3 - 45*y**2 + 11*y - 13) with (11*y)*19 - 45*y**2*19 - 14*y**3*19 - 13*19 in the overall expression.\n#Step 3:\nCurrent expression: (11*y)*19 - 45*y**2*19 + (-19*y**3)*(-14*y**3 - 45*y**2 + 11*y - 13) - 14*y**3*19 - 247\nSimplifying the partial expression: (-19*y**3)*(-14*y**3 - 45*y**2 + 11*y - 13)\nExpanding the part (-14*y**3 - 45*y**2 + 11*y - 13) using the distributive property, and we got: -(-1)*247*y**3 + (11*y)*(-19*y**3) + (-45*y**2)*(-19*y**3) + (-19*y**3)*(-14*y**3)\nReplacing (-19*y**3)*(-14*y**3 - 45*y**2 + 11*y - 13) with -(-1)*247*y**3 + (11*y)*(-19*y**3) + (-45*y**2)*(-19*y**3) + (-19*y**3)*(-14*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -13*(-19)*y**3 + (11*y)*(-19*y**3) + (11*y)*19 + (-45*y**2)*(-19*y**3) - 45*y**2*19 + (-19*y**3)*(-14*y**3) - 14*y**3*19 - 247\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*y**2)*19 = -855*y**2\n (-45*y**2)*(-19*y**3) = 855*y**5\n (-14*y**3)*19 = -266*y**3\n (-14*y**3)*(-19*y**3) = 266*y**6\n (11*y)*19 = 209*y\n (11*y)*(-19*y**3) = -209*y**4\n -13*-19*y**3 = 247*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 266*y**6 + 855*y**5 - 209*y**4 - 266*y**3 + 247*y**3 - 855*y**2 + 209*y - 247\nCombining like terms, got 266*y**6 + 855*y**5 - 209*y**4 - 19*y**3 - 855*y**2 + 209*y - 247\n#Step 6:\nCurrent expression: 266*y**6 + 855*y**5 - 209*y**4 - 19*y**3 - 855*y**2 + 209*y - 247\nNo more calculations needed.\n266*y**6 + 855*y**5 - 209*y**4 - 19*y**3 - 855*y**2 + 209*y - 247", "generated_answer": "266*y**6 + 855*y**5 - 209*y**4 - 19*y**3 - 855*y**2 + 209*y - 247", "step_length": 6} {"cot_id": "9fd3907fa189588501a44c81464fcca3ec2f0f0a0d6f4d7333ab69a393330011", "datapoint": {"question": "Calculate the following: -4*x*(18*x**2 + 46*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-72*x**3 - 184*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1121, "polynomial_expr": "-4*x*(18*x**2 + 46*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -4*x*(18*x**2 + 46*x)\nExpanding the part (18*x**2 + 46*x) using the distributive property, and we got: (-4*x)*(46*x) + (-4*x)*(18*x**2)\n#Step 2:\nCurrent expression: (-4*x)*(46*x) + (-4*x)*(18*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (18*x**2)*(-4*x) = -72*x**3\n (46*x)*(-4*x) = -184*x**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -72*x**3 - 184*x**2\nNo more calculations needed.\n-72*x**3 - 184*x**2", "generated_answer": "-72*x**3 - 184*x**2", "step_length": 3} {"cot_id": "0d0bf93e7c1e2d9b28d1fd26b3b6e175397d8ea80df34d3b3fb9e567843b401a", "datapoint": {"question": "Simplify this expression: (-13*x**3 - 49*x)*(-8*x**3 + 3*x**2 - 17*x + 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "104*x**6 - 39*x**5 + 613*x**4 - 511*x**3 + 833*x**2 - 1372*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1122, "polynomial_expr": "(-13*x**3 - 49*x)*(-8*x**3 + 3*x**2 - 17*x + 28)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-13*x**3 - 49*x)*(-8*x**3 + 3*x**2 - 17*x + 28)\nExpanding the part (-13*x**3 - 49*x) using the distributive property, and we got: (-49*x)*(-8*x**3 + 3*x**2 - 17*x + 28) + (-13*x**3)*(-8*x**3 + 3*x**2 - 17*x + 28)\n#Step 2:\nCurrent expression: (-49*x)*(-8*x**3 + 3*x**2 - 17*x + 28) + (-13*x**3)*(-8*x**3 + 3*x**2 - 17*x + 28)\nSimplifying the partial expression: (-49*x)*(-8*x**3 + 3*x**2 - 17*x + 28)\nExpanding the part (-8*x**3 + 3*x**2 - 17*x + 28) using the distributive property, and we got: (-49*x)*(-17*x) + (-49*x)*(3*x**2) + (-49*x)*(-8*x**3) + 28*(-49*x)\nReplacing (-49*x)*(-8*x**3 + 3*x**2 - 17*x + 28) with (-49*x)*(-17*x) + (-49*x)*(3*x**2) + (-49*x)*(-8*x**3) + 28*(-49*x) in the overall expression.\n#Step 3:\nCurrent expression: (-49*x)*(-17*x) + (-49*x)*(3*x**2) + (-49*x)*(-8*x**3) + 28*(-49)*x + (-13*x**3)*(-8*x**3 + 3*x**2 - 17*x + 28)\nSimplifying the partial expression: (-13*x**3)*(-8*x**3 + 3*x**2 - 17*x + 28)\nExpanding the part (-8*x**3 + 3*x**2 - 17*x + 28) using the distributive property, and we got: (-17*x)*(-13*x**3) + 28*(-13*x**3) + (3*x**2)*(-13*x**3) + (-13*x**3)*(-8*x**3)\nReplacing (-13*x**3)*(-8*x**3 + 3*x**2 - 17*x + 28) with (-17*x)*(-13*x**3) + 28*(-13*x**3) + (3*x**2)*(-13*x**3) + (-13*x**3)*(-8*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-49*x)*(-17*x) + (-49*x)*(3*x**2) + (-49*x)*(-8*x**3) + (-17*x)*(-13*x**3) + 28*(-13)*x**3 + 28*(-49)*x + (3*x**2)*(-13*x**3) + (-13*x**3)*(-8*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-17*x)*(-49*x) = 833*x**2\n (-17*x)*(-13*x**3) = 221*x**4\n (-8*x**3)*(-49*x) = 392*x**4\n (-8*x**3)*(-13*x**3) = 104*x**6\n (3*x**2)*(-49*x) = -147*x**3\n (3*x**2)*(-13*x**3) = -39*x**5\n 28*-49*x = -1372*x\n 28*-13*x**3 = -364*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 104*x**6 - 39*x**5 + 221*x**4 + 392*x**4 - 364*x**3 - 147*x**3 + 833*x**2 - 1372*x\nCombining like terms, got 104*x**6 - 39*x**5 + 613*x**4 - 511*x**3 + 833*x**2 - 1372*x\n#Step 6:\nCurrent expression: 104*x**6 - 39*x**5 + 613*x**4 - 511*x**3 + 833*x**2 - 1372*x\nNo more calculations needed.\n104*x**6 - 39*x**5 + 613*x**4 - 511*x**3 + 833*x**2 - 1372*x", "generated_answer": "104*x**6 - 39*x**5 + 613*x**4 - 511*x**3 + 833*x**2 - 1372*x", "step_length": 6} {"cot_id": "23a2ed17a58617a6d991b5e15709344746adbdda9f74a04b31ab472e6a7671fa", "datapoint": {"question": "Calculate the following: (1 - 43*x**2)*(-16*x**2 + 7*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "688*x**4 - 301*x**3 - 16*x**2 + 7*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1123, "polynomial_expr": "(1 - 43*x**2)*(-16*x**2 + 7*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (1 - 43*x**2)*(-16*x**2 + 7*x)\nExpanding the part (1 - 43*x**2) using the distributive property, and we got: (-43*x**2)*(-16*x**2 + 7*x) + 1*(-16*x**2 + 7*x)\n#Step 2:\nCurrent expression: (-43*x**2)*(-16*x**2 + 7*x) + 1*(-16*x**2 + 7*x)\nSimplifying the partial expression: 1*(-16*x**2 + 7*x)\nExpanding the part (-16*x**2 + 7*x) using the distributive property, and we got: (7*x)*1 - 16*x**2*1\nReplacing 1*(-16*x**2 + 7*x) with (7*x)*1 - 16*x**2*1 in the overall expression.\n#Step 3:\nCurrent expression: (7*x)*1 + (-43*x**2)*(-16*x**2 + 7*x) - 16*x**2*1\nSimplifying the partial expression: (-43*x**2)*(-16*x**2 + 7*x)\nExpanding the part (-16*x**2 + 7*x) using the distributive property, and we got: (7*x)*(-43*x**2) + (-43*x**2)*(-16*x**2)\nReplacing (-43*x**2)*(-16*x**2 + 7*x) with (7*x)*(-43*x**2) + (-43*x**2)*(-16*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (7*x)*(-43*x**2) + (7*x)*1 + (-43*x**2)*(-16*x**2) - 16*x**2*1\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-16*x**2)*1 = -16*x**2\n (-16*x**2)*(-43*x**2) = 688*x**4\n (7*x)*1 = 7*x\n (7*x)*(-43*x**2) = -301*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 688*x**4 - 301*x**3 - 16*x**2 + 7*x\nNo more calculations needed.\n688*x**4 - 301*x**3 - 16*x**2 + 7*x", "generated_answer": "688*x**4 - 301*x**3 - 16*x**2 + 7*x", "step_length": 5} {"cot_id": "d6dcc80d69f08c06a9627c92060106f17b49b640a6468fa90fa8f19328d80aea", "datapoint": {"question": "Simplify this expression: -108*z**3 - 282*z + 12\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-108*z**3 - 282*z + 12", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1124, "polynomial_expr": "-108*z**3 - 282*z + 12", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -108*z**3 - 282*z + 12\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -108*z**3 - 282*z + 12\nNo more calculations needed.\n-108*z**3 - 282*z + 12", "generated_answer": "-108*z**3 - 282*z + 12", "step_length": 2} {"cot_id": "5f896a8c9ed19b19f140e163c34f9f087de8a06eed744e8252136949ef591617", "datapoint": {"question": "Simplify this expression: (-44*z**3 + 36*z - 5)*(16*z**3 + 34*z**2 - 38*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-704*z**6 - 1496*z**5 + 2248*z**4 + 1144*z**3 - 1538*z**2 + 190*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1125, "polynomial_expr": "(-44*z**3 + 36*z - 5)*(16*z**3 + 34*z**2 - 38*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-44*z**3 + 36*z - 5)*(16*z**3 + 34*z**2 - 38*z)\nExpanding the part (-44*z**3 + 36*z - 5) using the distributive property, and we got: (36*z)*(16*z**3 + 34*z**2 - 38*z) + (-44*z**3)*(16*z**3 + 34*z**2 - 38*z) - 5*(16*z**3 + 34*z**2 - 38*z)\n#Step 2:\nCurrent expression: (36*z)*(16*z**3 + 34*z**2 - 38*z) + (-44*z**3)*(16*z**3 + 34*z**2 - 38*z) - 5*(16*z**3 + 34*z**2 - 38*z)\nSimplifying the partial expression: -5*(16*z**3 + 34*z**2 - 38*z)\nExpanding the part (16*z**3 + 34*z**2 - 38*z) using the distributive property, and we got: -38*z*(-5) + (34*z**2)*(-5) + (16*z**3)*(-5)\nReplacing -5*(16*z**3 + 34*z**2 - 38*z) with -38*z*(-5) + (34*z**2)*(-5) + (16*z**3)*(-5) in the overall expression.\n#Step 3:\nCurrent expression: -38*z*(-5) + (36*z)*(16*z**3 + 34*z**2 - 38*z) + (34*z**2)*(-5) + (-44*z**3)*(16*z**3 + 34*z**2 - 38*z) + (16*z**3)*(-5)\nSimplifying the partial expression: (-44*z**3)*(16*z**3 + 34*z**2 - 38*z)\nExpanding the part (16*z**3 + 34*z**2 - 38*z) using the distributive property, and we got: (-38*z)*(-44*z**3) + (34*z**2)*(-44*z**3) + (-44*z**3)*(16*z**3)\nReplacing (-44*z**3)*(16*z**3 + 34*z**2 - 38*z) with (-38*z)*(-44*z**3) + (34*z**2)*(-44*z**3) + (-44*z**3)*(16*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-38*z)*(-44*z**3) - 38*z*(-5) + (36*z)*(16*z**3 + 34*z**2 - 38*z) + (34*z**2)*(-44*z**3) + (34*z**2)*(-5) + (-44*z**3)*(16*z**3) + (16*z**3)*(-5)\nSimplifying the partial expression: (36*z)*(16*z**3 + 34*z**2 - 38*z)\nExpanding the part (16*z**3 + 34*z**2 - 38*z) using the distributive property, and we got: (-38*z)*(36*z) + (36*z)*(34*z**2) + (36*z)*(16*z**3)\nReplacing (36*z)*(16*z**3 + 34*z**2 - 38*z) with (-38*z)*(36*z) + (36*z)*(34*z**2) + (36*z)*(16*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-38*z)*(36*z) + (-38*z)*(-44*z**3) - 38*z*(-5) + (36*z)*(34*z**2) + (36*z)*(16*z**3) + (34*z**2)*(-44*z**3) + (34*z**2)*(-5) + (-44*z**3)*(16*z**3) + (16*z**3)*(-5)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*z)*-5 = 190*z\n (-38*z)*(-44*z**3) = 1672*z**4\n (-38*z)*(36*z) = -1368*z**2\n (16*z**3)*-5 = -80*z**3\n (16*z**3)*(-44*z**3) = -704*z**6\n (16*z**3)*(36*z) = 576*z**4\n (34*z**2)*-5 = -170*z**2\n (34*z**2)*(-44*z**3) = -1496*z**5\n (34*z**2)*(36*z) = 1224*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -704*z**6 - 1496*z**5 + 576*z**4 + 1672*z**4 - 80*z**3 + 1224*z**3 - 1368*z**2 - 170*z**2 + 190*z\nCombining like terms, got -704*z**6 - 1496*z**5 + 2248*z**4 + 1144*z**3 - 1538*z**2 + 190*z\n#Step 7:\nCurrent expression: -704*z**6 - 1496*z**5 + 2248*z**4 + 1144*z**3 - 1538*z**2 + 190*z\nNo more calculations needed.\n-704*z**6 - 1496*z**5 + 2248*z**4 + 1144*z**3 - 1538*z**2 + 190*z", "generated_answer": "-704*z**6 - 1496*z**5 + 2248*z**4 + 1144*z**3 - 1538*z**2 + 190*z", "step_length": 7} {"cot_id": "557a1211801197948553da6f3378985d7b35bff045e157a1547e6d490e622253", "datapoint": {"question": "Simplify this expression: (-9*z**3 - 29)*(z**3 + 34*z + 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-9*z**6 - 306*z**4 - 452*z**3 - 986*z - 1363", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1126, "polynomial_expr": "(-9*z**3 - 29)*(z**3 + 34*z + 47)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-9*z**3 - 29)*(z**3 + 34*z + 47)\nExpanding the part (-9*z**3 - 29) using the distributive property, and we got: (-9*z**3)*(z**3 + 34*z + 47) - 29*(z**3 + 34*z + 47)\n#Step 2:\nCurrent expression: (-9*z**3)*(z**3 + 34*z + 47) - 29*(z**3 + 34*z + 47)\nSimplifying the partial expression: -29*(z**3 + 34*z + 47)\nExpanding the part (z**3 + 34*z + 47) using the distributive property, and we got: z**3*(-29) + (34*z)*(-29) + 47*(-29)\nReplacing -29*(z**3 + 34*z + 47) with z**3*(-29) + (34*z)*(-29) + 47*(-29) in the overall expression.\n#Step 3:\nCurrent expression: z**3*(-29) + (34*z)*(-29) + (-9*z**3)*(z**3 + 34*z + 47) - 1363\nSimplifying the partial expression: (-9*z**3)*(z**3 + 34*z + 47)\nExpanding the part (z**3 + 34*z + 47) using the distributive property, and we got: (-9*z**3)*z**3 + 47*(-9*z**3) + (34*z)*(-9*z**3)\nReplacing (-9*z**3)*(z**3 + 34*z + 47) with (-9*z**3)*z**3 + 47*(-9*z**3) + (34*z)*(-9*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-9*z**3)*z**3 + 47*(-9)*z**3 + z**3*(-29) + (34*z)*(-9*z**3) + (34*z)*(-29) - 1363\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n z**3*-29 = -29*z**3\n z**3*(-9*z**3) = -9*z**6\n (34*z)*-29 = -986*z\n (34*z)*(-9*z**3) = -306*z**4\n 47*-9*z**3 = -423*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -9*z**6 - 306*z**4 - 423*z**3 - 29*z**3 - 986*z - 1363\nCombining like terms, got -9*z**6 - 306*z**4 - 452*z**3 - 986*z - 1363\n#Step 6:\nCurrent expression: -9*z**6 - 306*z**4 - 452*z**3 - 986*z - 1363\nNo more calculations needed.\n-9*z**6 - 306*z**4 - 452*z**3 - 986*z - 1363", "generated_answer": "-9*z**6 - 306*z**4 - 452*z**3 - 986*z - 1363", "step_length": 6} {"cot_id": "3e95c2cf2f549d6f4534b2773866babc88b5ff05da72ac69137f89223a34d39b", "datapoint": {"question": "Calculate the following: (-31*x**2 - 9*x)*(30*x**2 + 45)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-930*x**4 - 270*x**3 - 1395*x**2 - 405*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1127, "polynomial_expr": "(-31*x**2 - 9*x)*(30*x**2 + 45)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-31*x**2 - 9*x)*(30*x**2 + 45)\nExpanding the part (30*x**2 + 45) using the distributive property, and we got: (30*x**2)*(-31*x**2 - 9*x) + 45*(-31*x**2 - 9*x)\n#Step 2:\nCurrent expression: (30*x**2)*(-31*x**2 - 9*x) + 45*(-31*x**2 - 9*x)\nSimplifying the partial expression: 45*(-31*x**2 - 9*x)\nExpanding the part (-31*x**2 - 9*x) using the distributive property, and we got: -9*x*45 - 31*x**2*45\nReplacing 45*(-31*x**2 - 9*x) with -9*x*45 - 31*x**2*45 in the overall expression.\n#Step 3:\nCurrent expression: -9*x*45 - 31*x**2*45 + (30*x**2)*(-31*x**2 - 9*x)\nSimplifying the partial expression: (30*x**2)*(-31*x**2 - 9*x)\nExpanding the part (-31*x**2 - 9*x) using the distributive property, and we got: (-9*x)*(30*x**2) + (-31*x**2)*(30*x**2)\nReplacing (30*x**2)*(-31*x**2 - 9*x) with (-9*x)*(30*x**2) + (-31*x**2)*(30*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-9*x)*(30*x**2) - 9*x*45 + (-31*x**2)*(30*x**2) - 31*x**2*45\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-31*x**2)*45 = -1395*x**2\n (-31*x**2)*(30*x**2) = -930*x**4\n (-9*x)*45 = -405*x\n (-9*x)*(30*x**2) = -270*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -930*x**4 - 270*x**3 - 1395*x**2 - 405*x\nNo more calculations needed.\n-930*x**4 - 270*x**3 - 1395*x**2 - 405*x", "generated_answer": "-930*x**4 - 270*x**3 - 1395*x**2 - 405*x", "step_length": 5} {"cot_id": "ba532d4e50ff83d2b14c351a4afe9919fae9db1e08237b61a4bbafd69264934e", "datapoint": {"question": "Calculate the following: 27*x**3*(41*x**3 - 38*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1107*x**6 - 1026*x**5", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1128, "polynomial_expr": "27*x**3*(41*x**3 - 38*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 27*x**3*(41*x**3 - 38*x**2)\nExpanding the part (41*x**3 - 38*x**2) using the distributive property, and we got: (-38*x**2)*(27*x**3) + (27*x**3)*(41*x**3)\n#Step 2:\nCurrent expression: (-38*x**2)*(27*x**3) + (27*x**3)*(41*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*x**2)*(27*x**3) = -1026*x**5\n (41*x**3)*(27*x**3) = 1107*x**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1107*x**6 - 1026*x**5\nNo more calculations needed.\n1107*x**6 - 1026*x**5", "generated_answer": "1107*x**6 - 1026*x**5", "step_length": 3} {"cot_id": "d7a64ac951cb43e67c588fd91dc4c4c6de2ce2234cd014cd4f978de3e8ec60c8", "datapoint": {"question": "Calculate the following: (4 - 4*z)*(9*z**3 - 13*z**2 + 36*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-36*z**4 + 88*z**3 - 196*z**2 + 144*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1129, "polynomial_expr": "(4 - 4*z)*(9*z**3 - 13*z**2 + 36*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (4 - 4*z)*(9*z**3 - 13*z**2 + 36*z)\nExpanding the part (4 - 4*z) using the distributive property, and we got: (-4*z)*(9*z**3 - 13*z**2 + 36*z) + 4*(9*z**3 - 13*z**2 + 36*z)\n#Step 2:\nCurrent expression: (-4*z)*(9*z**3 - 13*z**2 + 36*z) + 4*(9*z**3 - 13*z**2 + 36*z)\nSimplifying the partial expression: 4*(9*z**3 - 13*z**2 + 36*z)\nExpanding the part (9*z**3 - 13*z**2 + 36*z) using the distributive property, and we got: (36*z)*4 - 13*z**2*4 + (9*z**3)*4\nReplacing 4*(9*z**3 - 13*z**2 + 36*z) with (36*z)*4 - 13*z**2*4 + (9*z**3)*4 in the overall expression.\n#Step 3:\nCurrent expression: (-4*z)*(9*z**3 - 13*z**2 + 36*z) + (36*z)*4 - 13*z**2*4 + (9*z**3)*4\nSimplifying the partial expression: (-4*z)*(9*z**3 - 13*z**2 + 36*z)\nExpanding the part (9*z**3 - 13*z**2 + 36*z) using the distributive property, and we got: (-4*z)*(36*z) + (-4*z)*(-13*z**2) + (-4*z)*(9*z**3)\nReplacing (-4*z)*(9*z**3 - 13*z**2 + 36*z) with (-4*z)*(36*z) + (-4*z)*(-13*z**2) + (-4*z)*(9*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-4*z)*(36*z) + (-4*z)*(-13*z**2) + (-4*z)*(9*z**3) + (36*z)*4 - 13*z**2*4 + (9*z**3)*4\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*z**2)*4 = -52*z**2\n (-13*z**2)*(-4*z) = 52*z**3\n (9*z**3)*4 = 36*z**3\n (9*z**3)*(-4*z) = -36*z**4\n (36*z)*4 = 144*z\n (36*z)*(-4*z) = -144*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -36*z**4 + 36*z**3 + 52*z**3 - 144*z**2 - 52*z**2 + 144*z\nCombining like terms, got -36*z**4 + 88*z**3 - 196*z**2 + 144*z\n#Step 6:\nCurrent expression: -36*z**4 + 88*z**3 - 196*z**2 + 144*z\nNo more calculations needed.\n-36*z**4 + 88*z**3 - 196*z**2 + 144*z", "generated_answer": "-36*z**4 + 88*z**3 - 196*z**2 + 144*z", "step_length": 6} {"cot_id": "62a68191b4d473d521275fef8ae12af1bfde0a56856de5f1baa42a45d1fa6b45", "datapoint": {"question": "Simplify this expression: (23 - 57*z**3)*(26*z**3 - 5*z**2 + 15)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1482*z**6 + 285*z**5 - 257*z**3 - 115*z**2 + 345", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1130, "polynomial_expr": "(23 - 57*z**3)*(26*z**3 - 5*z**2 + 15)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (23 - 57*z**3)*(26*z**3 - 5*z**2 + 15)\nExpanding the part (23 - 57*z**3) using the distributive property, and we got: (-57*z**3)*(26*z**3 - 5*z**2 + 15) + 23*(26*z**3 - 5*z**2 + 15)\n#Step 2:\nCurrent expression: (-57*z**3)*(26*z**3 - 5*z**2 + 15) + 23*(26*z**3 - 5*z**2 + 15)\nSimplifying the partial expression: 23*(26*z**3 - 5*z**2 + 15)\nExpanding the part (26*z**3 - 5*z**2 + 15) using the distributive property, and we got: -5*z**2*23 + (26*z**3)*23 + 15*23\nReplacing 23*(26*z**3 - 5*z**2 + 15) with -5*z**2*23 + (26*z**3)*23 + 15*23 in the overall expression.\n#Step 3:\nCurrent expression: -5*z**2*23 + (-57*z**3)*(26*z**3 - 5*z**2 + 15) + (26*z**3)*23 + 345\nSimplifying the partial expression: (-57*z**3)*(26*z**3 - 5*z**2 + 15)\nExpanding the part (26*z**3 - 5*z**2 + 15) using the distributive property, and we got: 15*(-57*z**3) + (-5*z**2)*(-57*z**3) + (-57*z**3)*(26*z**3)\nReplacing (-57*z**3)*(26*z**3 - 5*z**2 + 15) with 15*(-57*z**3) + (-5*z**2)*(-57*z**3) + (-57*z**3)*(26*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 15*(-57)*z**3 + (-5*z**2)*(-57*z**3) - 5*z**2*23 + (-57*z**3)*(26*z**3) + (26*z**3)*23 + 345\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-5*z**2)*23 = -115*z**2\n (-5*z**2)*(-57*z**3) = 285*z**5\n (26*z**3)*23 = 598*z**3\n (26*z**3)*(-57*z**3) = -1482*z**6\n 15*-57*z**3 = -855*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1482*z**6 + 285*z**5 - 855*z**3 + 598*z**3 - 115*z**2 + 345\nCombining like terms, got -1482*z**6 + 285*z**5 - 257*z**3 - 115*z**2 + 345\n#Step 6:\nCurrent expression: -1482*z**6 + 285*z**5 - 257*z**3 - 115*z**2 + 345\nNo more calculations needed.\n-1482*z**6 + 285*z**5 - 257*z**3 - 115*z**2 + 345", "generated_answer": "-1482*z**6 + 285*z**5 - 257*z**3 - 115*z**2 + 345", "step_length": 6} {"cot_id": "1de76e9e5598b04c0df63c604bf7e3e6a2862e18063d2cc6007aeac2bfa2949e", "datapoint": {"question": "Calculate the following: (27*y**3 - y - 25)*(37*y**3 + 7*y + 18)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "999*y**6 + 152*y**4 - 439*y**3 - 7*y**2 - 193*y - 450", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1131, "polynomial_expr": "(27*y**3 - y - 25)*(37*y**3 + 7*y + 18)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*y**3 - y - 25)*(37*y**3 + 7*y + 18)\nExpanding the part (27*y**3 - y - 25) using the distributive property, and we got: (-y)*(37*y**3 + 7*y + 18) + (27*y**3)*(37*y**3 + 7*y + 18) - 25*(37*y**3 + 7*y + 18)\n#Step 2:\nCurrent expression: (-y)*(37*y**3 + 7*y + 18) + (27*y**3)*(37*y**3 + 7*y + 18) - 25*(37*y**3 + 7*y + 18)\nSimplifying the partial expression: -25*(37*y**3 + 7*y + 18)\nExpanding the part (37*y**3 + 7*y + 18) using the distributive property, and we got: (7*y)*(-25) + (37*y**3)*(-25) + 18*(-25)\nReplacing -25*(37*y**3 + 7*y + 18) with (7*y)*(-25) + (37*y**3)*(-25) + 18*(-25) in the overall expression.\n#Step 3:\nCurrent expression: (-y)*(37*y**3 + 7*y + 18) + (7*y)*(-25) + (27*y**3)*(37*y**3 + 7*y + 18) + (37*y**3)*(-25) - 450\nSimplifying the partial expression: (-y)*(37*y**3 + 7*y + 18)\nExpanding the part (37*y**3 + 7*y + 18) using the distributive property, and we got: (-y)*(7*y) + (-y)*(37*y**3) + 18*(-y)\nReplacing (-y)*(37*y**3 + 7*y + 18) with (-y)*(7*y) + (-y)*(37*y**3) + 18*(-y) in the overall expression.\n#Step 4:\nCurrent expression: (-y)*(7*y) + (-y)*(37*y**3) + 18*(-1)*y + (7*y)*(-25) + (27*y**3)*(37*y**3 + 7*y + 18) + (37*y**3)*(-25) - 450\nSimplifying the partial expression: (27*y**3)*(37*y**3 + 7*y + 18)\nExpanding the part (37*y**3 + 7*y + 18) using the distributive property, and we got: 18*(27*y**3) + (7*y)*(27*y**3) + (27*y**3)*(37*y**3)\nReplacing (27*y**3)*(37*y**3 + 7*y + 18) with 18*(27*y**3) + (7*y)*(27*y**3) + (27*y**3)*(37*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-y)*(7*y) + (-y)*(37*y**3) + 18*27*y**3 + 18*(-1)*y + (7*y)*(27*y**3) + (7*y)*(-25) + (27*y**3)*(37*y**3) + (37*y**3)*(-25) - 450\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (7*y)*-25 = -175*y\n (7*y)*(-y) = -7*y**2\n (7*y)*(27*y**3) = 189*y**4\n (37*y**3)*-25 = -925*y**3\n (37*y**3)*(-y) = -37*y**4\n (37*y**3)*(27*y**3) = 999*y**6\n 18*-1*y = -18*y\n 18*27*y**3 = 486*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 999*y**6 - 37*y**4 + 189*y**4 - 925*y**3 + 486*y**3 - 7*y**2 - 175*y - 18*y - 450\nCombining like terms, got 999*y**6 + 152*y**4 - 439*y**3 - 7*y**2 - 193*y - 450\n#Step 7:\nCurrent expression: 999*y**6 + 152*y**4 - 439*y**3 - 7*y**2 - 193*y - 450\nNo more calculations needed.\n999*y**6 + 152*y**4 - 439*y**3 - 7*y**2 - 193*y - 450", "generated_answer": "999*y**6 + 152*y**4 - 439*y**3 - 7*y**2 - 193*y - 450", "step_length": 7} {"cot_id": "22c867eb7739407daea8a89a93c0e352ac868e8b501af5ccdefe29aee1df56a3", "datapoint": {"question": "Calculate the following: (16 - 13*x**2)*(-36*x**3 - 48*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "468*x**5 + 624*x**4 - 576*x**3 - 768*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1132, "polynomial_expr": "(16 - 13*x**2)*(-36*x**3 - 48*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (16 - 13*x**2)*(-36*x**3 - 48*x**2)\nExpanding the part (16 - 13*x**2) using the distributive property, and we got: (-13*x**2)*(-36*x**3 - 48*x**2) + 16*(-36*x**3 - 48*x**2)\n#Step 2:\nCurrent expression: (-13*x**2)*(-36*x**3 - 48*x**2) + 16*(-36*x**3 - 48*x**2)\nSimplifying the partial expression: 16*(-36*x**3 - 48*x**2)\nExpanding the part (-36*x**3 - 48*x**2) using the distributive property, and we got: -48*x**2*16 - 36*x**3*16\nReplacing 16*(-36*x**3 - 48*x**2) with -48*x**2*16 - 36*x**3*16 in the overall expression.\n#Step 3:\nCurrent expression: -48*x**2*16 + (-13*x**2)*(-36*x**3 - 48*x**2) - 36*x**3*16\nSimplifying the partial expression: (-13*x**2)*(-36*x**3 - 48*x**2)\nExpanding the part (-36*x**3 - 48*x**2) using the distributive property, and we got: (-48*x**2)*(-13*x**2) + (-13*x**2)*(-36*x**3)\nReplacing (-13*x**2)*(-36*x**3 - 48*x**2) with (-48*x**2)*(-13*x**2) + (-13*x**2)*(-36*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-48*x**2)*(-13*x**2) - 48*x**2*16 + (-13*x**2)*(-36*x**3) - 36*x**3*16\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*x**2)*16 = -768*x**2\n (-48*x**2)*(-13*x**2) = 624*x**4\n (-36*x**3)*16 = -576*x**3\n (-36*x**3)*(-13*x**2) = 468*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 468*x**5 + 624*x**4 - 576*x**3 - 768*x**2\nNo more calculations needed.\n468*x**5 + 624*x**4 - 576*x**3 - 768*x**2", "generated_answer": "468*x**5 + 624*x**4 - 576*x**3 - 768*x**2", "step_length": 5} {"cot_id": "501d5dfba31841e1582ce8cc7729ec4296671a65006948c91c965a6e698ef6c0", "datapoint": {"question": "Calculate the following: (10*y**3 - 22*y)*(23*y**3 + 12*y - 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "230*y**6 - 386*y**4 - 480*y**3 - 264*y**2 + 1056*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1133, "polynomial_expr": "(10*y**3 - 22*y)*(23*y**3 + 12*y - 48)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (10*y**3 - 22*y)*(23*y**3 + 12*y - 48)\nExpanding the part (10*y**3 - 22*y) using the distributive property, and we got: (-22*y)*(23*y**3 + 12*y - 48) + (10*y**3)*(23*y**3 + 12*y - 48)\n#Step 2:\nCurrent expression: (-22*y)*(23*y**3 + 12*y - 48) + (10*y**3)*(23*y**3 + 12*y - 48)\nSimplifying the partial expression: (-22*y)*(23*y**3 + 12*y - 48)\nExpanding the part (23*y**3 + 12*y - 48) using the distributive property, and we got: (-22*y)*(12*y) + (-22*y)*(23*y**3) - (-1)*1056*y\nReplacing (-22*y)*(23*y**3 + 12*y - 48) with (-22*y)*(12*y) + (-22*y)*(23*y**3) - (-1)*1056*y in the overall expression.\n#Step 3:\nCurrent expression: (-22*y)*(12*y) + (-22*y)*(23*y**3) - 48*(-22)*y + (10*y**3)*(23*y**3 + 12*y - 48)\nSimplifying the partial expression: (10*y**3)*(23*y**3 + 12*y - 48)\nExpanding the part (23*y**3 + 12*y - 48) using the distributive property, and we got: -480*y**3 + (12*y)*(10*y**3) + (10*y**3)*(23*y**3)\nReplacing (10*y**3)*(23*y**3 + 12*y - 48) with -480*y**3 + (12*y)*(10*y**3) + (10*y**3)*(23*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-22*y)*(12*y) + (-22*y)*(23*y**3) - 48*10*y**3 - 48*(-22)*y + (12*y)*(10*y**3) + (10*y**3)*(23*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (12*y)*(-22*y) = -264*y**2\n (12*y)*(10*y**3) = 120*y**4\n (23*y**3)*(-22*y) = -506*y**4\n (23*y**3)*(10*y**3) = 230*y**6\n -48*-22*y = 1056*y\n -48*10*y**3 = -480*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 230*y**6 - 506*y**4 + 120*y**4 - 480*y**3 - 264*y**2 + 1056*y\nCombining like terms, got 230*y**6 - 386*y**4 - 480*y**3 - 264*y**2 + 1056*y\n#Step 6:\nCurrent expression: 230*y**6 - 386*y**4 - 480*y**3 - 264*y**2 + 1056*y\nNo more calculations needed.\n230*y**6 - 386*y**4 - 480*y**3 - 264*y**2 + 1056*y", "generated_answer": "230*y**6 - 386*y**4 - 480*y**3 - 264*y**2 + 1056*y", "step_length": 6} {"cot_id": "0b0e12bce868052990e960b9548130892a7655a23cf8565293bf1c32dfc31d00", "datapoint": {"question": "Calculate the following: (-42*z**3 - 10*z)*(44*z**3 - 12*z**2 + 27*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1848*z**6 + 504*z**5 - 1574*z**4 + 120*z**3 - 270*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1134, "polynomial_expr": "(-42*z**3 - 10*z)*(44*z**3 - 12*z**2 + 27*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-42*z**3 - 10*z)*(44*z**3 - 12*z**2 + 27*z)\nExpanding the part (-42*z**3 - 10*z) using the distributive property, and we got: (-10*z)*(44*z**3 - 12*z**2 + 27*z) + (-42*z**3)*(44*z**3 - 12*z**2 + 27*z)\n#Step 2:\nCurrent expression: (-10*z)*(44*z**3 - 12*z**2 + 27*z) + (-42*z**3)*(44*z**3 - 12*z**2 + 27*z)\nSimplifying the partial expression: (-42*z**3)*(44*z**3 - 12*z**2 + 27*z)\nExpanding the part (44*z**3 - 12*z**2 + 27*z) using the distributive property, and we got: (27*z)*(-42*z**3) + (-12*z**2)*(-42*z**3) + (-42*z**3)*(44*z**3)\nReplacing (-42*z**3)*(44*z**3 - 12*z**2 + 27*z) with (27*z)*(-42*z**3) + (-12*z**2)*(-42*z**3) + (-42*z**3)*(44*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-10*z)*(44*z**3 - 12*z**2 + 27*z) + (27*z)*(-42*z**3) + (-12*z**2)*(-42*z**3) + (-42*z**3)*(44*z**3)\nSimplifying the partial expression: (-10*z)*(44*z**3 - 12*z**2 + 27*z)\nExpanding the part (44*z**3 - 12*z**2 + 27*z) using the distributive property, and we got: (-10*z)*(27*z) + (-10*z)*(-12*z**2) + (-10*z)*(44*z**3)\nReplacing (-10*z)*(44*z**3 - 12*z**2 + 27*z) with (-10*z)*(27*z) + (-10*z)*(-12*z**2) + (-10*z)*(44*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-10*z)*(27*z) + (-10*z)*(-12*z**2) + (-10*z)*(44*z**3) + (27*z)*(-42*z**3) + (-12*z**2)*(-42*z**3) + (-42*z**3)*(44*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*z**2)*(-42*z**3) = 504*z**5\n (-12*z**2)*(-10*z) = 120*z**3\n (27*z)*(-42*z**3) = -1134*z**4\n (27*z)*(-10*z) = -270*z**2\n (44*z**3)*(-42*z**3) = -1848*z**6\n (44*z**3)*(-10*z) = -440*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1848*z**6 + 504*z**5 - 1134*z**4 - 440*z**4 + 120*z**3 - 270*z**2\nCombining like terms, got -1848*z**6 + 504*z**5 - 1574*z**4 + 120*z**3 - 270*z**2\n#Step 6:\nCurrent expression: -1848*z**6 + 504*z**5 - 1574*z**4 + 120*z**3 - 270*z**2\nNo more calculations needed.\n-1848*z**6 + 504*z**5 - 1574*z**4 + 120*z**3 - 270*z**2", "generated_answer": "-1848*z**6 + 504*z**5 - 1574*z**4 + 120*z**3 - 270*z**2", "step_length": 6} {"cot_id": "ed5dbf7ef800f02be346bca42da69f542723c8ae86bcdea6bf74b1d1f31b0e51", "datapoint": {"question": "Simplify this expression: (-30*y**3 - 30*y**2 - 12)*(21*y**3 + 44*y**2 - 33*y - 25)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-630*y**6 - 1950*y**5 - 330*y**4 + 1488*y**3 + 222*y**2 + 396*y + 300", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1135, "polynomial_expr": "(-30*y**3 - 30*y**2 - 12)*(21*y**3 + 44*y**2 - 33*y - 25)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-30*y**3 - 30*y**2 - 12)*(21*y**3 + 44*y**2 - 33*y - 25)\nExpanding the part (-30*y**3 - 30*y**2 - 12) using the distributive property, and we got: (-30*y**2)*(21*y**3 + 44*y**2 - 33*y - 25) + (-30*y**3)*(21*y**3 + 44*y**2 - 33*y - 25) - 12*(21*y**3 + 44*y**2 - 33*y - 25)\n#Step 2:\nCurrent expression: (-30*y**2)*(21*y**3 + 44*y**2 - 33*y - 25) + (-30*y**3)*(21*y**3 + 44*y**2 - 33*y - 25) - 12*(21*y**3 + 44*y**2 - 33*y - 25)\nSimplifying the partial expression: -12*(21*y**3 + 44*y**2 - 33*y - 25)\nExpanding the part (21*y**3 + 44*y**2 - 33*y - 25) using the distributive property, and we got: -33*y*(-12) + (44*y**2)*(-12) + (21*y**3)*(-12) - 25*(-12)\nReplacing -12*(21*y**3 + 44*y**2 - 33*y - 25) with -33*y*(-12) + (44*y**2)*(-12) + (21*y**3)*(-12) - 25*(-12) in the overall expression.\n#Step 3:\nCurrent expression: -33*y*(-12) + (-30*y**2)*(21*y**3 + 44*y**2 - 33*y - 25) + (44*y**2)*(-12) + (-30*y**3)*(21*y**3 + 44*y**2 - 33*y - 25) + (21*y**3)*(-12) + 300\nSimplifying the partial expression: (-30*y**2)*(21*y**3 + 44*y**2 - 33*y - 25)\nExpanding the part (21*y**3 + 44*y**2 - 33*y - 25) using the distributive property, and we got: (-33*y)*(-30*y**2) - (-1)*750*y**2 + (-30*y**2)*(44*y**2) + (-30*y**2)*(21*y**3)\nReplacing (-30*y**2)*(21*y**3 + 44*y**2 - 33*y - 25) with (-33*y)*(-30*y**2) - (-1)*750*y**2 + (-30*y**2)*(44*y**2) + (-30*y**2)*(21*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-33*y)*(-30*y**2) - 33*y*(-12) - 25*(-30)*y**2 + (-30*y**2)*(44*y**2) + (-30*y**2)*(21*y**3) + (44*y**2)*(-12) + (-30*y**3)*(21*y**3 + 44*y**2 - 33*y - 25) + (21*y**3)*(-12) + 300\nSimplifying the partial expression: (-30*y**3)*(21*y**3 + 44*y**2 - 33*y - 25)\nExpanding the part (21*y**3 + 44*y**2 - 33*y - 25) using the distributive property, and we got: (-33*y)*(-30*y**3) - (-1)*750*y**3 + (44*y**2)*(-30*y**3) + (-30*y**3)*(21*y**3)\nReplacing (-30*y**3)*(21*y**3 + 44*y**2 - 33*y - 25) with (-33*y)*(-30*y**3) - (-1)*750*y**3 + (44*y**2)*(-30*y**3) + (-30*y**3)*(21*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-33*y)*(-30*y**2) + (-33*y)*(-30*y**3) - 33*y*(-12) - 25*(-30)*y**3 - 25*(-30)*y**2 + (-30*y**2)*(44*y**2) + (-30*y**2)*(21*y**3) + (44*y**2)*(-30*y**3) + (44*y**2)*(-12) + (-30*y**3)*(21*y**3) + (21*y**3)*(-12) + 300\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*y)*-12 = 396*y\n (-33*y)*(-30*y**2) = 990*y**3\n (-33*y)*(-30*y**3) = 990*y**4\n (21*y**3)*-12 = -252*y**3\n (21*y**3)*(-30*y**2) = -630*y**5\n (21*y**3)*(-30*y**3) = -630*y**6\n (44*y**2)*-12 = -528*y**2\n (44*y**2)*(-30*y**2) = -1320*y**4\n (44*y**2)*(-30*y**3) = -1320*y**5\n -25*-30*y**2 = 750*y**2\n -25*-30*y**3 = 750*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -630*y**6 - 1320*y**5 - 630*y**5 - 1320*y**4 + 990*y**4 - 252*y**3 + 750*y**3 + 990*y**3 - 528*y**2 + 750*y**2 + 396*y + 300\nCombining like terms, got -630*y**6 - 1950*y**5 - 330*y**4 + 1488*y**3 + 222*y**2 + 396*y + 300\n#Step 7:\nCurrent expression: -630*y**6 - 1950*y**5 - 330*y**4 + 1488*y**3 + 222*y**2 + 396*y + 300\nNo more calculations needed.\n-630*y**6 - 1950*y**5 - 330*y**4 + 1488*y**3 + 222*y**2 + 396*y + 300", "generated_answer": "-630*y**6 - 1950*y**5 - 330*y**4 + 1488*y**3 + 222*y**2 + 396*y + 300", "step_length": 7} {"cot_id": "64d7693f13352c7a0bf49eda030cf89f204be1f0de0abc183e9faf7a77a9cada", "datapoint": {"question": "Simplify this expression: (6*z**3 + 17*z**2)*(-9*z**2 - 50*z + 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-54*z**5 - 453*z**4 - 586*z**3 + 748*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1136, "polynomial_expr": "(6*z**3 + 17*z**2)*(-9*z**2 - 50*z + 44)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6*z**3 + 17*z**2)*(-9*z**2 - 50*z + 44)\nExpanding the part (6*z**3 + 17*z**2) using the distributive property, and we got: (17*z**2)*(-9*z**2 - 50*z + 44) + (6*z**3)*(-9*z**2 - 50*z + 44)\n#Step 2:\nCurrent expression: (17*z**2)*(-9*z**2 - 50*z + 44) + (6*z**3)*(-9*z**2 - 50*z + 44)\nSimplifying the partial expression: (6*z**3)*(-9*z**2 - 50*z + 44)\nExpanding the part (-9*z**2 - 50*z + 44) using the distributive property, and we got: (-50*z)*(6*z**3) + 44*(6*z**3) + (-9*z**2)*(6*z**3)\nReplacing (6*z**3)*(-9*z**2 - 50*z + 44) with (-50*z)*(6*z**3) + 44*(6*z**3) + (-9*z**2)*(6*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-50*z)*(6*z**3) + 44*6*z**3 + (-9*z**2)*(6*z**3) + (17*z**2)*(-9*z**2 - 50*z + 44)\nSimplifying the partial expression: (17*z**2)*(-9*z**2 - 50*z + 44)\nExpanding the part (-9*z**2 - 50*z + 44) using the distributive property, and we got: (-50*z)*(17*z**2) + 44*(17*z**2) + (-9*z**2)*(17*z**2)\nReplacing (17*z**2)*(-9*z**2 - 50*z + 44) with (-50*z)*(17*z**2) + 44*(17*z**2) + (-9*z**2)*(17*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-50*z)*(17*z**2) + (-50*z)*(6*z**3) + 44*6*z**3 + 44*17*z**2 + (-9*z**2)*(17*z**2) + (-9*z**2)*(6*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-50*z)*(6*z**3) = -300*z**4\n (-50*z)*(17*z**2) = -850*z**3\n (-9*z**2)*(6*z**3) = -54*z**5\n (-9*z**2)*(17*z**2) = -153*z**4\n 44*6*z**3 = 264*z**3\n 44*17*z**2 = 748*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -54*z**5 - 300*z**4 - 153*z**4 - 850*z**3 + 264*z**3 + 748*z**2\nCombining like terms, got -54*z**5 - 453*z**4 - 586*z**3 + 748*z**2\n#Step 6:\nCurrent expression: -54*z**5 - 453*z**4 - 586*z**3 + 748*z**2\nNo more calculations needed.\n-54*z**5 - 453*z**4 - 586*z**3 + 748*z**2", "generated_answer": "-54*z**5 - 453*z**4 - 586*z**3 + 748*z**2", "step_length": 6} {"cot_id": "c2932d53fadad08a7eac4e7c706fb6dbca00143d1354f7561433f644eeaf5f15", "datapoint": {"question": "Simplify this expression: 420*z**3 - 238*z\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "420*z**3 - 238*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1137, "polynomial_expr": "420*z**3 - 238*z", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 420*z**3 - 238*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 420*z**3 - 238*z\nNo more calculations needed.\n420*z**3 - 238*z", "generated_answer": "420*z**3 - 238*z", "step_length": 2} {"cot_id": "9493572d7bb3d5d8b99ee11b98417d0981dfdfb4e77d246dd3e1cea4d530c251", "datapoint": {"question": "Simplify this expression: (-6*y**3 + 3*y)*(43*y**3 - 18*y + 34)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-258*y**6 + 237*y**4 - 204*y**3 - 54*y**2 + 102*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1138, "polynomial_expr": "(-6*y**3 + 3*y)*(43*y**3 - 18*y + 34)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-6*y**3 + 3*y)*(43*y**3 - 18*y + 34)\nExpanding the part (-6*y**3 + 3*y) using the distributive property, and we got: (3*y)*(43*y**3 - 18*y + 34) + (-6*y**3)*(43*y**3 - 18*y + 34)\n#Step 2:\nCurrent expression: (3*y)*(43*y**3 - 18*y + 34) + (-6*y**3)*(43*y**3 - 18*y + 34)\nSimplifying the partial expression: (-6*y**3)*(43*y**3 - 18*y + 34)\nExpanding the part (43*y**3 - 18*y + 34) using the distributive property, and we got: (-18*y)*(-6*y**3) + 34*(-6*y**3) + (-6*y**3)*(43*y**3)\nReplacing (-6*y**3)*(43*y**3 - 18*y + 34) with (-18*y)*(-6*y**3) + 34*(-6*y**3) + (-6*y**3)*(43*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-18*y)*(-6*y**3) + 34*(-6)*y**3 + (3*y)*(43*y**3 - 18*y + 34) + (-6*y**3)*(43*y**3)\nSimplifying the partial expression: (3*y)*(43*y**3 - 18*y + 34)\nExpanding the part (43*y**3 - 18*y + 34) using the distributive property, and we got: (-18*y)*(3*y) + 34*(3*y) + (3*y)*(43*y**3)\nReplacing (3*y)*(43*y**3 - 18*y + 34) with (-18*y)*(3*y) + 34*(3*y) + (3*y)*(43*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-18*y)*(3*y) + (-18*y)*(-6*y**3) + 34*(-6)*y**3 + 34*3*y + (3*y)*(43*y**3) + (-6*y**3)*(43*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-18*y)*(-6*y**3) = 108*y**4\n (-18*y)*(3*y) = -54*y**2\n (43*y**3)*(-6*y**3) = -258*y**6\n (43*y**3)*(3*y) = 129*y**4\n 34*-6*y**3 = -204*y**3\n 34*3*y = 102*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -258*y**6 + 108*y**4 + 129*y**4 - 204*y**3 - 54*y**2 + 102*y\nCombining like terms, got -258*y**6 + 237*y**4 - 204*y**3 - 54*y**2 + 102*y\n#Step 6:\nCurrent expression: -258*y**6 + 237*y**4 - 204*y**3 - 54*y**2 + 102*y\nNo more calculations needed.\n-258*y**6 + 237*y**4 - 204*y**3 - 54*y**2 + 102*y", "generated_answer": "-258*y**6 + 237*y**4 - 204*y**3 - 54*y**2 + 102*y", "step_length": 6} {"cot_id": "cb238a25251a958f8b6bafc0afc473aeebc4b5b477bb29345d24b4aeef5f6446", "datapoint": {"question": "Calculate the following: (-10*y**3 + 15*y)*(-11*y**2 - 20*y - 3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "110*y**5 + 200*y**4 - 135*y**3 - 300*y**2 - 45*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1139, "polynomial_expr": "(-10*y**3 + 15*y)*(-11*y**2 - 20*y - 3)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-10*y**3 + 15*y)*(-11*y**2 - 20*y - 3)\nExpanding the part (-10*y**3 + 15*y) using the distributive property, and we got: (15*y)*(-11*y**2 - 20*y - 3) + (-10*y**3)*(-11*y**2 - 20*y - 3)\n#Step 2:\nCurrent expression: (15*y)*(-11*y**2 - 20*y - 3) + (-10*y**3)*(-11*y**2 - 20*y - 3)\nSimplifying the partial expression: (-10*y**3)*(-11*y**2 - 20*y - 3)\nExpanding the part (-11*y**2 - 20*y - 3) using the distributive property, and we got: (-20*y)*(-10*y**3) - (-1)*30*y**3 + (-11*y**2)*(-10*y**3)\nReplacing (-10*y**3)*(-11*y**2 - 20*y - 3) with (-20*y)*(-10*y**3) - (-1)*30*y**3 + (-11*y**2)*(-10*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-20*y)*(-10*y**3) - 3*(-10)*y**3 + (15*y)*(-11*y**2 - 20*y - 3) + (-11*y**2)*(-10*y**3)\nSimplifying the partial expression: (15*y)*(-11*y**2 - 20*y - 3)\nExpanding the part (-11*y**2 - 20*y - 3) using the distributive property, and we got: (-20*y)*(15*y) - 45*y + (15*y)*(-11*y**2)\nReplacing (15*y)*(-11*y**2 - 20*y - 3) with (-20*y)*(15*y) - 45*y + (15*y)*(-11*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-20*y)*(15*y) + (-20*y)*(-10*y**3) - 3*(-10)*y**3 - 3*15*y + (15*y)*(-11*y**2) + (-11*y**2)*(-10*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*y)*(-10*y**3) = 200*y**4\n (-20*y)*(15*y) = -300*y**2\n (-11*y**2)*(-10*y**3) = 110*y**5\n (-11*y**2)*(15*y) = -165*y**3\n -3*-10*y**3 = 30*y**3\n -3*15*y = -45*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 110*y**5 + 200*y**4 - 165*y**3 + 30*y**3 - 300*y**2 - 45*y\nCombining like terms, got 110*y**5 + 200*y**4 - 135*y**3 - 300*y**2 - 45*y\n#Step 6:\nCurrent expression: 110*y**5 + 200*y**4 - 135*y**3 - 300*y**2 - 45*y\nNo more calculations needed.\n110*y**5 + 200*y**4 - 135*y**3 - 300*y**2 - 45*y", "generated_answer": "110*y**5 + 200*y**4 - 135*y**3 - 300*y**2 - 45*y", "step_length": 6} {"cot_id": "e353aaea254421c7e362caf36eed66b5caeb0d49f3e29c856654627a02e3f477", "datapoint": {"question": "Calculate the following: (36 - 22*z**3)*(14*z**3 - 39*z**2 - 36*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-308*z**6 + 858*z**5 + 792*z**4 + 504*z**3 - 1404*z**2 - 1296*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1140, "polynomial_expr": "(36 - 22*z**3)*(14*z**3 - 39*z**2 - 36*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (36 - 22*z**3)*(14*z**3 - 39*z**2 - 36*z)\nExpanding the part (36 - 22*z**3) using the distributive property, and we got: (-22*z**3)*(14*z**3 - 39*z**2 - 36*z) + 36*(14*z**3 - 39*z**2 - 36*z)\n#Step 2:\nCurrent expression: (-22*z**3)*(14*z**3 - 39*z**2 - 36*z) + 36*(14*z**3 - 39*z**2 - 36*z)\nSimplifying the partial expression: 36*(14*z**3 - 39*z**2 - 36*z)\nExpanding the part (14*z**3 - 39*z**2 - 36*z) using the distributive property, and we got: -36*z*36 - 39*z**2*36 + (14*z**3)*36\nReplacing 36*(14*z**3 - 39*z**2 - 36*z) with -36*z*36 - 39*z**2*36 + (14*z**3)*36 in the overall expression.\n#Step 3:\nCurrent expression: -36*z*36 - 39*z**2*36 + (-22*z**3)*(14*z**3 - 39*z**2 - 36*z) + (14*z**3)*36\nSimplifying the partial expression: (-22*z**3)*(14*z**3 - 39*z**2 - 36*z)\nExpanding the part (14*z**3 - 39*z**2 - 36*z) using the distributive property, and we got: (-36*z)*(-22*z**3) + (-39*z**2)*(-22*z**3) + (-22*z**3)*(14*z**3)\nReplacing (-22*z**3)*(14*z**3 - 39*z**2 - 36*z) with (-36*z)*(-22*z**3) + (-39*z**2)*(-22*z**3) + (-22*z**3)*(14*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-36*z)*(-22*z**3) - 36*z*36 + (-39*z**2)*(-22*z**3) - 39*z**2*36 + (-22*z**3)*(14*z**3) + (14*z**3)*36\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*z**2)*36 = -1404*z**2\n (-39*z**2)*(-22*z**3) = 858*z**5\n (-36*z)*36 = -1296*z\n (-36*z)*(-22*z**3) = 792*z**4\n (14*z**3)*36 = 504*z**3\n (14*z**3)*(-22*z**3) = -308*z**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -308*z**6 + 858*z**5 + 792*z**4 + 504*z**3 - 1404*z**2 - 1296*z\nNo more calculations needed.\n-308*z**6 + 858*z**5 + 792*z**4 + 504*z**3 - 1404*z**2 - 1296*z", "generated_answer": "-308*z**6 + 858*z**5 + 792*z**4 + 504*z**3 - 1404*z**2 - 1296*z", "step_length": 5} {"cot_id": "795b833968cdd2fbae6f10f8bb4f0d110cec1807bf63256cf965d89efea9f2ee", "datapoint": {"question": "Simplify this expression: -5*y**2*(33*y**3 + 69*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-165*y**5 - 345*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1141, "polynomial_expr": "-5*y**2*(33*y**3 + 69*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -5*y**2*(33*y**3 + 69*y)\nExpanding the part (33*y**3 + 69*y) using the distributive property, and we got: (69*y)*(-5*y**2) + (-5*y**2)*(33*y**3)\n#Step 2:\nCurrent expression: (69*y)*(-5*y**2) + (-5*y**2)*(33*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (33*y**3)*(-5*y**2) = -165*y**5\n (69*y)*(-5*y**2) = -345*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -165*y**5 - 345*y**3\nNo more calculations needed.\n-165*y**5 - 345*y**3", "generated_answer": "-165*y**5 - 345*y**3", "step_length": 3} {"cot_id": "e55f5bdad5272b730eb725c45fb45e56b373c8c17d0fd55a03a27fcb3f5c6987", "datapoint": {"question": "Calculate the following: 21*z**2*(-37*z**3 - 48*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-777*z**5 - 1008*z**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1142, "polynomial_expr": "21*z**2*(-37*z**3 - 48*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 21*z**2*(-37*z**3 - 48*z**2)\nExpanding the part (-37*z**3 - 48*z**2) using the distributive property, and we got: (-48*z**2)*(21*z**2) + (21*z**2)*(-37*z**3)\n#Step 2:\nCurrent expression: (-48*z**2)*(21*z**2) + (21*z**2)*(-37*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*z**2)*(21*z**2) = -1008*z**4\n (-37*z**3)*(21*z**2) = -777*z**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -777*z**5 - 1008*z**4\nNo more calculations needed.\n-777*z**5 - 1008*z**4", "generated_answer": "-777*z**5 - 1008*z**4", "step_length": 3} {"cot_id": "903fcba79a73bbd076b8b6b06bb1760ebac2abba9a854e468a88afa6283995f1", "datapoint": {"question": "Calculate the following: (49 - 49*y**2)*(50*y**2 - 19)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2450*y**4 + 3381*y**2 - 931", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1143, "polynomial_expr": "(49 - 49*y**2)*(50*y**2 - 19)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (49 - 49*y**2)*(50*y**2 - 19)\nExpanding the part (50*y**2 - 19) using the distributive property, and we got: (50*y**2)*(49 - 49*y**2) - 19*(49 - 49*y**2)\n#Step 2:\nCurrent expression: (50*y**2)*(49 - 49*y**2) - 19*(49 - 49*y**2)\nSimplifying the partial expression: -19*(49 - 49*y**2)\nExpanding the part (49 - 49*y**2) using the distributive property, and we got: -49*y**2*(-19) + 49*(-19)\nReplacing -19*(49 - 49*y**2) with -49*y**2*(-19) + 49*(-19) in the overall expression.\n#Step 3:\nCurrent expression: -49*y**2*(-19) + (50*y**2)*(49 - 49*y**2) - 931\nSimplifying the partial expression: (50*y**2)*(49 - 49*y**2)\nExpanding the part (49 - 49*y**2) using the distributive property, and we got: 49*(50*y**2) + (-49*y**2)*(50*y**2)\nReplacing (50*y**2)*(49 - 49*y**2) with 49*(50*y**2) + (-49*y**2)*(50*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 49*50*y**2 + (-49*y**2)*(50*y**2) - 49*y**2*(-19) - 931\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*y**2)*-19 = 931*y**2\n (-49*y**2)*(50*y**2) = -2450*y**4\n 49*50*y**2 = 2450*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2450*y**4 + 931*y**2 + 2450*y**2 - 931\nCombining like terms, got -2450*y**4 + 3381*y**2 - 931\n#Step 6:\nCurrent expression: -2450*y**4 + 3381*y**2 - 931\nNo more calculations needed.\n-2450*y**4 + 3381*y**2 - 931", "generated_answer": "-2450*y**4 + 3381*y**2 - 931", "step_length": 6} {"cot_id": "8d6a58feb9df10f7278be46949fbc3065ca4d76c5693ca38984ecbdc6f2ceb6e", "datapoint": {"question": "Simplify this expression: (2*y**3 - 19*y - 31)*(52*y**3 - 30*y**2 + 11)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "104*y**6 - 60*y**5 - 988*y**4 - 1020*y**3 + 930*y**2 - 209*y - 341", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1144, "polynomial_expr": "(2*y**3 - 19*y - 31)*(52*y**3 - 30*y**2 + 11)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2*y**3 - 19*y - 31)*(52*y**3 - 30*y**2 + 11)\nExpanding the part (2*y**3 - 19*y - 31) using the distributive property, and we got: (-19*y)*(52*y**3 - 30*y**2 + 11) + (2*y**3)*(52*y**3 - 30*y**2 + 11) - 31*(52*y**3 - 30*y**2 + 11)\n#Step 2:\nCurrent expression: (-19*y)*(52*y**3 - 30*y**2 + 11) + (2*y**3)*(52*y**3 - 30*y**2 + 11) - 31*(52*y**3 - 30*y**2 + 11)\nSimplifying the partial expression: -31*(52*y**3 - 30*y**2 + 11)\nExpanding the part (52*y**3 - 30*y**2 + 11) using the distributive property, and we got: -30*y**2*(-31) + (52*y**3)*(-31) + 11*(-31)\nReplacing -31*(52*y**3 - 30*y**2 + 11) with -30*y**2*(-31) + (52*y**3)*(-31) + 11*(-31) in the overall expression.\n#Step 3:\nCurrent expression: (-19*y)*(52*y**3 - 30*y**2 + 11) - 30*y**2*(-31) + (2*y**3)*(52*y**3 - 30*y**2 + 11) + (52*y**3)*(-31) - 341\nSimplifying the partial expression: (-19*y)*(52*y**3 - 30*y**2 + 11)\nExpanding the part (52*y**3 - 30*y**2 + 11) using the distributive property, and we got: (-19*y)*(-30*y**2) + (-19*y)*(52*y**3) + 11*(-19*y)\nReplacing (-19*y)*(52*y**3 - 30*y**2 + 11) with (-19*y)*(-30*y**2) + (-19*y)*(52*y**3) + 11*(-19*y) in the overall expression.\n#Step 4:\nCurrent expression: (-19*y)*(-30*y**2) + (-19*y)*(52*y**3) + 11*(-19)*y - 30*y**2*(-31) + (2*y**3)*(52*y**3 - 30*y**2 + 11) + (52*y**3)*(-31) - 341\nSimplifying the partial expression: (2*y**3)*(52*y**3 - 30*y**2 + 11)\nExpanding the part (52*y**3 - 30*y**2 + 11) using the distributive property, and we got: 11*(2*y**3) + (-30*y**2)*(2*y**3) + (2*y**3)*(52*y**3)\nReplacing (2*y**3)*(52*y**3 - 30*y**2 + 11) with 11*(2*y**3) + (-30*y**2)*(2*y**3) + (2*y**3)*(52*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-19*y)*(-30*y**2) + (-19*y)*(52*y**3) + 11*2*y**3 + 11*(-19)*y + (-30*y**2)*(2*y**3) - 30*y**2*(-31) + (2*y**3)*(52*y**3) + (52*y**3)*(-31) - 341\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*y**2)*-31 = 930*y**2\n (-30*y**2)*(-19*y) = 570*y**3\n (-30*y**2)*(2*y**3) = -60*y**5\n (52*y**3)*-31 = -1612*y**3\n (52*y**3)*(-19*y) = -988*y**4\n (52*y**3)*(2*y**3) = 104*y**6\n 11*-19*y = -209*y\n 11*2*y**3 = 22*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 104*y**6 - 60*y**5 - 988*y**4 - 1612*y**3 + 22*y**3 + 570*y**3 + 930*y**2 - 209*y - 341\nCombining like terms, got 104*y**6 - 60*y**5 - 988*y**4 - 1020*y**3 + 930*y**2 - 209*y - 341\n#Step 7:\nCurrent expression: 104*y**6 - 60*y**5 - 988*y**4 - 1020*y**3 + 930*y**2 - 209*y - 341\nNo more calculations needed.\n104*y**6 - 60*y**5 - 988*y**4 - 1020*y**3 + 930*y**2 - 209*y - 341", "generated_answer": "104*y**6 - 60*y**5 - 988*y**4 - 1020*y**3 + 930*y**2 - 209*y - 341", "step_length": 7} {"cot_id": "11e8ba63efe4c0653e5bdc6b832d62f06dca59479cf589d54968d204fc67a0e4", "datapoint": {"question": "Simplify this expression: -12*z*(14*z**3 - 22*z - 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-168*z**4 + 264*z**2 + 372*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1145, "polynomial_expr": "-12*z*(14*z**3 - 22*z - 31)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -12*z*(14*z**3 - 22*z - 31)\nExpanding the part (14*z**3 - 22*z - 31) using the distributive property, and we got: (-22*z)*(-12*z) + (-12*z)*(14*z**3) - (-1)*372*z\n#Step 2:\nCurrent expression: (-22*z)*(-12*z) + (-12*z)*(14*z**3) - (-1)*372*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -31*(-12*z) = 372*z\n (-22*z)*(-12*z) = 264*z**2\n (14*z**3)*(-12*z) = -168*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -168*z**4 + 264*z**2 + 372*z\nNo more calculations needed.\n-168*z**4 + 264*z**2 + 372*z", "generated_answer": "-168*z**4 + 264*z**2 + 372*z", "step_length": 3} {"cot_id": "74d0c06c5cf1b6756690b47555830c1d7dd050922baca3863e7fc529ccdf1974", "datapoint": {"question": "Calculate the following: (-61*z**2 - 27)*(27*z**2 - 10*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1647*z**4 + 610*z**3 - 729*z**2 + 270*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1146, "polynomial_expr": "(-61*z**2 - 27)*(27*z**2 - 10*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-61*z**2 - 27)*(27*z**2 - 10*z)\nExpanding the part (-61*z**2 - 27) using the distributive property, and we got: (-61*z**2)*(27*z**2 - 10*z) - 27*(27*z**2 - 10*z)\n#Step 2:\nCurrent expression: (-61*z**2)*(27*z**2 - 10*z) - 27*(27*z**2 - 10*z)\nSimplifying the partial expression: -27*(27*z**2 - 10*z)\nExpanding the part (27*z**2 - 10*z) using the distributive property, and we got: -10*z*(-27) + (27*z**2)*(-27)\nReplacing -27*(27*z**2 - 10*z) with -10*z*(-27) + (27*z**2)*(-27) in the overall expression.\n#Step 3:\nCurrent expression: -10*z*(-27) + (-61*z**2)*(27*z**2 - 10*z) + (27*z**2)*(-27)\nSimplifying the partial expression: (-61*z**2)*(27*z**2 - 10*z)\nExpanding the part (27*z**2 - 10*z) using the distributive property, and we got: (-10*z)*(-61*z**2) + (-61*z**2)*(27*z**2)\nReplacing (-61*z**2)*(27*z**2 - 10*z) with (-10*z)*(-61*z**2) + (-61*z**2)*(27*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-10*z)*(-61*z**2) - 10*z*(-27) + (-61*z**2)*(27*z**2) + (27*z**2)*(-27)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*z)*-27 = 270*z\n (-10*z)*(-61*z**2) = 610*z**3\n (27*z**2)*-27 = -729*z**2\n (27*z**2)*(-61*z**2) = -1647*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1647*z**4 + 610*z**3 - 729*z**2 + 270*z\nNo more calculations needed.\n-1647*z**4 + 610*z**3 - 729*z**2 + 270*z", "generated_answer": "-1647*z**4 + 610*z**3 - 729*z**2 + 270*z", "step_length": 5} {"cot_id": "36baeb9343424fa135792b6a728dfeebde47044d21f6214ecd57169fd5cbedb3", "datapoint": {"question": "Calculate the following: (46*z + 30)*(16*z**2 - 58*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "736*z**3 - 2188*z**2 - 1740*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1147, "polynomial_expr": "(46*z + 30)*(16*z**2 - 58*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (46*z + 30)*(16*z**2 - 58*z)\nExpanding the part (46*z + 30) using the distributive property, and we got: (46*z)*(16*z**2 - 58*z) + 30*(16*z**2 - 58*z)\n#Step 2:\nCurrent expression: (46*z)*(16*z**2 - 58*z) + 30*(16*z**2 - 58*z)\nSimplifying the partial expression: 30*(16*z**2 - 58*z)\nExpanding the part (16*z**2 - 58*z) using the distributive property, and we got: -58*z*30 + (16*z**2)*30\nReplacing 30*(16*z**2 - 58*z) with -58*z*30 + (16*z**2)*30 in the overall expression.\n#Step 3:\nCurrent expression: -58*z*30 + (46*z)*(16*z**2 - 58*z) + (16*z**2)*30\nSimplifying the partial expression: (46*z)*(16*z**2 - 58*z)\nExpanding the part (16*z**2 - 58*z) using the distributive property, and we got: (-58*z)*(46*z) + (46*z)*(16*z**2)\nReplacing (46*z)*(16*z**2 - 58*z) with (-58*z)*(46*z) + (46*z)*(16*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-58*z)*(46*z) - 58*z*30 + (46*z)*(16*z**2) + (16*z**2)*30\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-58*z)*30 = -1740*z\n (-58*z)*(46*z) = -2668*z**2\n (16*z**2)*30 = 480*z**2\n (16*z**2)*(46*z) = 736*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 736*z**3 - 2668*z**2 + 480*z**2 - 1740*z\nCombining like terms, got 736*z**3 - 2188*z**2 - 1740*z\n#Step 6:\nCurrent expression: 736*z**3 - 2188*z**2 - 1740*z\nNo more calculations needed.\n736*z**3 - 2188*z**2 - 1740*z", "generated_answer": "736*z**3 - 2188*z**2 - 1740*z", "step_length": 6} {"cot_id": "80c1a9bea1167af6e2f548e66ac67af951ad10671d0a7cd74bd73bdd9d53b769", "datapoint": {"question": "Simplify this expression: (-29*y**3 - 45)*(14*y**3 + 22*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-406*y**6 - 638*y**4 - 630*y**3 - 990*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1148, "polynomial_expr": "(-29*y**3 - 45)*(14*y**3 + 22*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-29*y**3 - 45)*(14*y**3 + 22*y)\nExpanding the part (-29*y**3 - 45) using the distributive property, and we got: (-29*y**3)*(14*y**3 + 22*y) - 45*(14*y**3 + 22*y)\n#Step 2:\nCurrent expression: (-29*y**3)*(14*y**3 + 22*y) - 45*(14*y**3 + 22*y)\nSimplifying the partial expression: -45*(14*y**3 + 22*y)\nExpanding the part (14*y**3 + 22*y) using the distributive property, and we got: (22*y)*(-45) + (14*y**3)*(-45)\nReplacing -45*(14*y**3 + 22*y) with (22*y)*(-45) + (14*y**3)*(-45) in the overall expression.\n#Step 3:\nCurrent expression: (22*y)*(-45) + (-29*y**3)*(14*y**3 + 22*y) + (14*y**3)*(-45)\nSimplifying the partial expression: (-29*y**3)*(14*y**3 + 22*y)\nExpanding the part (14*y**3 + 22*y) using the distributive property, and we got: (22*y)*(-29*y**3) + (-29*y**3)*(14*y**3)\nReplacing (-29*y**3)*(14*y**3 + 22*y) with (22*y)*(-29*y**3) + (-29*y**3)*(14*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (22*y)*(-29*y**3) + (22*y)*(-45) + (-29*y**3)*(14*y**3) + (14*y**3)*(-45)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (14*y**3)*-45 = -630*y**3\n (14*y**3)*(-29*y**3) = -406*y**6\n (22*y)*-45 = -990*y\n (22*y)*(-29*y**3) = -638*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -406*y**6 - 638*y**4 - 630*y**3 - 990*y\nNo more calculations needed.\n-406*y**6 - 638*y**4 - 630*y**3 - 990*y", "generated_answer": "-406*y**6 - 638*y**4 - 630*y**3 - 990*y", "step_length": 5} {"cot_id": "cba688bfd4d8730c83dc1343c59d16012323eca8831bd68ea5d702220f625ef2", "datapoint": {"question": "Simplify this expression: (-35*y**2 - 38*y + 24)*(-45*y**3 + 32*y - 42)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1575*y**5 + 1710*y**4 - 2200*y**3 + 254*y**2 + 2364*y - 1008", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1149, "polynomial_expr": "(-35*y**2 - 38*y + 24)*(-45*y**3 + 32*y - 42)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-35*y**2 - 38*y + 24)*(-45*y**3 + 32*y - 42)\nExpanding the part (-45*y**3 + 32*y - 42) using the distributive property, and we got: (32*y)*(-35*y**2 - 38*y + 24) + (-45*y**3)*(-35*y**2 - 38*y + 24) - 42*(-35*y**2 - 38*y + 24)\n#Step 2:\nCurrent expression: (32*y)*(-35*y**2 - 38*y + 24) + (-45*y**3)*(-35*y**2 - 38*y + 24) - 42*(-35*y**2 - 38*y + 24)\nSimplifying the partial expression: -42*(-35*y**2 - 38*y + 24)\nExpanding the part (-35*y**2 - 38*y + 24) using the distributive property, and we got: -38*y*(-42) - 35*y**2*(-42) + 24*(-42)\nReplacing -42*(-35*y**2 - 38*y + 24) with -38*y*(-42) - 35*y**2*(-42) + 24*(-42) in the overall expression.\n#Step 3:\nCurrent expression: -38*y*(-42) + (32*y)*(-35*y**2 - 38*y + 24) - 35*y**2*(-42) + (-45*y**3)*(-35*y**2 - 38*y + 24) - 1008\nSimplifying the partial expression: (-45*y**3)*(-35*y**2 - 38*y + 24)\nExpanding the part (-35*y**2 - 38*y + 24) using the distributive property, and we got: (-38*y)*(-45*y**3) + 24*(-45*y**3) + (-35*y**2)*(-45*y**3)\nReplacing (-45*y**3)*(-35*y**2 - 38*y + 24) with (-38*y)*(-45*y**3) + 24*(-45*y**3) + (-35*y**2)*(-45*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-38*y)*(-45*y**3) - 38*y*(-42) + 24*(-45)*y**3 + (32*y)*(-35*y**2 - 38*y + 24) + (-35*y**2)*(-45*y**3) - 35*y**2*(-42) - 1008\nSimplifying the partial expression: (32*y)*(-35*y**2 - 38*y + 24)\nExpanding the part (-35*y**2 - 38*y + 24) using the distributive property, and we got: (-38*y)*(32*y) + 24*(32*y) + (32*y)*(-35*y**2)\nReplacing (32*y)*(-35*y**2 - 38*y + 24) with (-38*y)*(32*y) + 24*(32*y) + (32*y)*(-35*y**2) in the overall expression.\n#Step 5:\nCurrent expression: (-38*y)*(32*y) + (-38*y)*(-45*y**3) - 38*y*(-42) + 24*(-45)*y**3 + 24*32*y + (32*y)*(-35*y**2) + (-35*y**2)*(-45*y**3) - 35*y**2*(-42) - 1008\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*y)*-42 = 1596*y\n (-38*y)*(-45*y**3) = 1710*y**4\n (-38*y)*(32*y) = -1216*y**2\n (-35*y**2)*-42 = 1470*y**2\n (-35*y**2)*(-45*y**3) = 1575*y**5\n (-35*y**2)*(32*y) = -1120*y**3\n 24*-45*y**3 = -1080*y**3\n 24*32*y = 768*y\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1575*y**5 + 1710*y**4 - 1120*y**3 - 1080*y**3 - 1216*y**2 + 1470*y**2 + 768*y + 1596*y - 1008\nCombining like terms, got 1575*y**5 + 1710*y**4 - 2200*y**3 + 254*y**2 + 2364*y - 1008\n#Step 7:\nCurrent expression: 1575*y**5 + 1710*y**4 - 2200*y**3 + 254*y**2 + 2364*y - 1008\nNo more calculations needed.\n1575*y**5 + 1710*y**4 - 2200*y**3 + 254*y**2 + 2364*y - 1008", "generated_answer": "1575*y**5 + 1710*y**4 - 2200*y**3 + 254*y**2 + 2364*y - 1008", "step_length": 7} {"cot_id": "8dc5a898cce6bb41dce7227b38ec834839322c3f7bb0a3b80fa3cf500cf2496e", "datapoint": {"question": "Calculate the following: (11 - 47*z)*(-7*z**2 - 86)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "329*z**3 - 77*z**2 + 4042*z - 946", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1150, "polynomial_expr": "(11 - 47*z)*(-7*z**2 - 86)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11 - 47*z)*(-7*z**2 - 86)\nExpanding the part (-7*z**2 - 86) using the distributive property, and we got: (-7*z**2)*(11 - 47*z) - 86*(11 - 47*z)\n#Step 2:\nCurrent expression: (-7*z**2)*(11 - 47*z) - 86*(11 - 47*z)\nSimplifying the partial expression: -86*(11 - 47*z)\nExpanding the part (11 - 47*z) using the distributive property, and we got: -47*z*(-86) + 11*(-86)\nReplacing -86*(11 - 47*z) with -47*z*(-86) + 11*(-86) in the overall expression.\n#Step 3:\nCurrent expression: -47*z*(-86) + (-7*z**2)*(11 - 47*z) - 946\nSimplifying the partial expression: (-7*z**2)*(11 - 47*z)\nExpanding the part (11 - 47*z) using the distributive property, and we got: (-47*z)*(-7*z**2) + 11*(-7*z**2)\nReplacing (-7*z**2)*(11 - 47*z) with (-47*z)*(-7*z**2) + 11*(-7*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-47*z)*(-7*z**2) - 47*z*(-86) + 11*(-7)*z**2 - 946\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*z)*-86 = 4042*z\n (-47*z)*(-7*z**2) = 329*z**3\n 11*-7*z**2 = -77*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 329*z**3 - 77*z**2 + 4042*z - 946\nNo more calculations needed.\n329*z**3 - 77*z**2 + 4042*z - 946", "generated_answer": "329*z**3 - 77*z**2 + 4042*z - 946", "step_length": 5} {"cot_id": "80ccf429de7e76a79782961195c3334ba3b815dfcfbf5362be5e4581712dfe1b", "datapoint": {"question": "Calculate the following: (-44*y**2 - 65*y)*(9*y**2 - 16*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-396*y**4 + 119*y**3 + 1040*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1151, "polynomial_expr": "(-44*y**2 - 65*y)*(9*y**2 - 16*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-44*y**2 - 65*y)*(9*y**2 - 16*y)\nExpanding the part (-44*y**2 - 65*y) using the distributive property, and we got: (-65*y)*(9*y**2 - 16*y) + (-44*y**2)*(9*y**2 - 16*y)\n#Step 2:\nCurrent expression: (-65*y)*(9*y**2 - 16*y) + (-44*y**2)*(9*y**2 - 16*y)\nSimplifying the partial expression: (-65*y)*(9*y**2 - 16*y)\nExpanding the part (9*y**2 - 16*y) using the distributive property, and we got: (-65*y)*(-16*y) + (-65*y)*(9*y**2)\nReplacing (-65*y)*(9*y**2 - 16*y) with (-65*y)*(-16*y) + (-65*y)*(9*y**2) in the overall expression.\n#Step 3:\nCurrent expression: (-65*y)*(-16*y) + (-65*y)*(9*y**2) + (-44*y**2)*(9*y**2 - 16*y)\nSimplifying the partial expression: (-44*y**2)*(9*y**2 - 16*y)\nExpanding the part (9*y**2 - 16*y) using the distributive property, and we got: (-16*y)*(-44*y**2) + (-44*y**2)*(9*y**2)\nReplacing (-44*y**2)*(9*y**2 - 16*y) with (-16*y)*(-44*y**2) + (-44*y**2)*(9*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-65*y)*(-16*y) + (-65*y)*(9*y**2) + (-16*y)*(-44*y**2) + (-44*y**2)*(9*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-16*y)*(-65*y) = 1040*y**2\n (-16*y)*(-44*y**2) = 704*y**3\n (9*y**2)*(-65*y) = -585*y**3\n (9*y**2)*(-44*y**2) = -396*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -396*y**4 - 585*y**3 + 704*y**3 + 1040*y**2\nCombining like terms, got -396*y**4 + 119*y**3 + 1040*y**2\n#Step 6:\nCurrent expression: -396*y**4 + 119*y**3 + 1040*y**2\nNo more calculations needed.\n-396*y**4 + 119*y**3 + 1040*y**2", "generated_answer": "-396*y**4 + 119*y**3 + 1040*y**2", "step_length": 6} {"cot_id": "b95bcbec0cae98d28aec3217e4c3284164380838b6efd34d526561908a5994bb", "datapoint": {"question": "Calculate the following: (11*z**2 + 12)*(-26*z**3 - 8*z + 2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-286*z**5 - 400*z**3 + 22*z**2 - 96*z + 24", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1152, "polynomial_expr": "(11*z**2 + 12)*(-26*z**3 - 8*z + 2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11*z**2 + 12)*(-26*z**3 - 8*z + 2)\nExpanding the part (11*z**2 + 12) using the distributive property, and we got: (11*z**2)*(-26*z**3 - 8*z + 2) + 12*(-26*z**3 - 8*z + 2)\n#Step 2:\nCurrent expression: (11*z**2)*(-26*z**3 - 8*z + 2) + 12*(-26*z**3 - 8*z + 2)\nSimplifying the partial expression: 12*(-26*z**3 - 8*z + 2)\nExpanding the part (-26*z**3 - 8*z + 2) using the distributive property, and we got: -8*z*12 - 26*z**3*12 + 2*12\nReplacing 12*(-26*z**3 - 8*z + 2) with -8*z*12 - 26*z**3*12 + 2*12 in the overall expression.\n#Step 3:\nCurrent expression: -8*z*12 + (11*z**2)*(-26*z**3 - 8*z + 2) - 26*z**3*12 + 24\nSimplifying the partial expression: (11*z**2)*(-26*z**3 - 8*z + 2)\nExpanding the part (-26*z**3 - 8*z + 2) using the distributive property, and we got: (-8*z)*(11*z**2) + 2*(11*z**2) + (11*z**2)*(-26*z**3)\nReplacing (11*z**2)*(-26*z**3 - 8*z + 2) with (-8*z)*(11*z**2) + 2*(11*z**2) + (11*z**2)*(-26*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-8*z)*(11*z**2) - 8*z*12 + 2*11*z**2 + (11*z**2)*(-26*z**3) - 26*z**3*12 + 24\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-26*z**3)*12 = -312*z**3\n (-26*z**3)*(11*z**2) = -286*z**5\n (-8*z)*12 = -96*z\n (-8*z)*(11*z**2) = -88*z**3\n 2*11*z**2 = 22*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -286*z**5 - 312*z**3 - 88*z**3 + 22*z**2 - 96*z + 24\nCombining like terms, got -286*z**5 - 400*z**3 + 22*z**2 - 96*z + 24\n#Step 6:\nCurrent expression: -286*z**5 - 400*z**3 + 22*z**2 - 96*z + 24\nNo more calculations needed.\n-286*z**5 - 400*z**3 + 22*z**2 - 96*z + 24", "generated_answer": "-286*z**5 - 400*z**3 + 22*z**2 - 96*z + 24", "step_length": 6} {"cot_id": "33c6cefee1039f2bec01ceeaab0eb10562496dca6b1d8ca2d40f4abeba265f2d", "datapoint": {"question": "Calculate the following: (-9*y**3 + 32*y**2 + 11)*(34*y**3 - 21*y**2 + 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-306*y**6 + 1277*y**5 - 672*y**4 - 49*y**3 + 1273*y**2 + 517", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1153, "polynomial_expr": "(-9*y**3 + 32*y**2 + 11)*(34*y**3 - 21*y**2 + 47)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-9*y**3 + 32*y**2 + 11)*(34*y**3 - 21*y**2 + 47)\nExpanding the part (-9*y**3 + 32*y**2 + 11) using the distributive property, and we got: (32*y**2)*(34*y**3 - 21*y**2 + 47) + (-9*y**3)*(34*y**3 - 21*y**2 + 47) + 11*(34*y**3 - 21*y**2 + 47)\n#Step 2:\nCurrent expression: (32*y**2)*(34*y**3 - 21*y**2 + 47) + (-9*y**3)*(34*y**3 - 21*y**2 + 47) + 11*(34*y**3 - 21*y**2 + 47)\nSimplifying the partial expression: 11*(34*y**3 - 21*y**2 + 47)\nExpanding the part (34*y**3 - 21*y**2 + 47) using the distributive property, and we got: -21*y**2*11 + (34*y**3)*11 + 47*11\nReplacing 11*(34*y**3 - 21*y**2 + 47) with -21*y**2*11 + (34*y**3)*11 + 47*11 in the overall expression.\n#Step 3:\nCurrent expression: -21*y**2*11 + (32*y**2)*(34*y**3 - 21*y**2 + 47) + (-9*y**3)*(34*y**3 - 21*y**2 + 47) + (34*y**3)*11 + 517\nSimplifying the partial expression: (-9*y**3)*(34*y**3 - 21*y**2 + 47)\nExpanding the part (34*y**3 - 21*y**2 + 47) using the distributive property, and we got: 47*(-9*y**3) + (-21*y**2)*(-9*y**3) + (-9*y**3)*(34*y**3)\nReplacing (-9*y**3)*(34*y**3 - 21*y**2 + 47) with 47*(-9*y**3) + (-21*y**2)*(-9*y**3) + (-9*y**3)*(34*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 47*(-9)*y**3 + (-21*y**2)*(-9*y**3) - 21*y**2*11 + (32*y**2)*(34*y**3 - 21*y**2 + 47) + (-9*y**3)*(34*y**3) + (34*y**3)*11 + 517\nSimplifying the partial expression: (32*y**2)*(34*y**3 - 21*y**2 + 47)\nExpanding the part (34*y**3 - 21*y**2 + 47) using the distributive property, and we got: 47*(32*y**2) + (-21*y**2)*(32*y**2) + (32*y**2)*(34*y**3)\nReplacing (32*y**2)*(34*y**3 - 21*y**2 + 47) with 47*(32*y**2) + (-21*y**2)*(32*y**2) + (32*y**2)*(34*y**3) in the overall expression.\n#Step 5:\nCurrent expression: 47*(-9)*y**3 + 47*32*y**2 + (-21*y**2)*(32*y**2) + (-21*y**2)*(-9*y**3) - 21*y**2*11 + (32*y**2)*(34*y**3) + (-9*y**3)*(34*y**3) + (34*y**3)*11 + 517\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-21*y**2)*11 = -231*y**2\n (-21*y**2)*(-9*y**3) = 189*y**5\n (-21*y**2)*(32*y**2) = -672*y**4\n (34*y**3)*11 = 374*y**3\n (34*y**3)*(-9*y**3) = -306*y**6\n (34*y**3)*(32*y**2) = 1088*y**5\n 47*-9*y**3 = -423*y**3\n 47*32*y**2 = 1504*y**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -306*y**6 + 189*y**5 + 1088*y**5 - 672*y**4 - 423*y**3 + 374*y**3 - 231*y**2 + 1504*y**2 + 517\nCombining like terms, got -306*y**6 + 1277*y**5 - 672*y**4 - 49*y**3 + 1273*y**2 + 517\n#Step 7:\nCurrent expression: -306*y**6 + 1277*y**5 - 672*y**4 - 49*y**3 + 1273*y**2 + 517\nNo more calculations needed.\n-306*y**6 + 1277*y**5 - 672*y**4 - 49*y**3 + 1273*y**2 + 517", "generated_answer": "-306*y**6 + 1277*y**5 - 672*y**4 - 49*y**3 + 1273*y**2 + 517", "step_length": 7} {"cot_id": "ae00b2c65189962f65a783dcd357b50d702953e2c7f93f03ce4424b59d1344fa", "datapoint": {"question": "Simplify this expression: 6360*x**2\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "6360*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1154, "polynomial_expr": "6360*x**2", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 6360*x**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 6360*x**2\nNo more calculations needed.\n6360*x**2", "generated_answer": "6360*x**2", "step_length": 2} {"cot_id": "9e859729a51f5d6c4f0feadf021440addf5e9e37236c598e2a8164c97259e069", "datapoint": {"question": "Calculate the following: (16*z**3 - 14*z)*(-75*z**3 - 24*z**2 - 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1200*z**6 - 384*z**5 + 1050*z**4 + 112*z**3 + 196*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1155, "polynomial_expr": "(16*z**3 - 14*z)*(-75*z**3 - 24*z**2 - 14)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (16*z**3 - 14*z)*(-75*z**3 - 24*z**2 - 14)\nExpanding the part (16*z**3 - 14*z) using the distributive property, and we got: (-14*z)*(-75*z**3 - 24*z**2 - 14) + (16*z**3)*(-75*z**3 - 24*z**2 - 14)\n#Step 2:\nCurrent expression: (-14*z)*(-75*z**3 - 24*z**2 - 14) + (16*z**3)*(-75*z**3 - 24*z**2 - 14)\nSimplifying the partial expression: (-14*z)*(-75*z**3 - 24*z**2 - 14)\nExpanding the part (-75*z**3 - 24*z**2 - 14) using the distributive property, and we got: (-14*z)*(-24*z**2) + (-14*z)*(-75*z**3) - (-1)*196*z\nReplacing (-14*z)*(-75*z**3 - 24*z**2 - 14) with (-14*z)*(-24*z**2) + (-14*z)*(-75*z**3) - (-1)*196*z in the overall expression.\n#Step 3:\nCurrent expression: (-14*z)*(-24*z**2) + (-14*z)*(-75*z**3) - 14*(-14)*z + (16*z**3)*(-75*z**3 - 24*z**2 - 14)\nSimplifying the partial expression: (16*z**3)*(-75*z**3 - 24*z**2 - 14)\nExpanding the part (-75*z**3 - 24*z**2 - 14) using the distributive property, and we got: -224*z**3 + (-24*z**2)*(16*z**3) + (-75*z**3)*(16*z**3)\nReplacing (16*z**3)*(-75*z**3 - 24*z**2 - 14) with -224*z**3 + (-24*z**2)*(16*z**3) + (-75*z**3)*(16*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-14*z)*(-24*z**2) + (-14*z)*(-75*z**3) - 14*16*z**3 - 14*(-14)*z + (-24*z**2)*(16*z**3) + (-75*z**3)*(16*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-75*z**3)*(-14*z) = 1050*z**4\n (-75*z**3)*(16*z**3) = -1200*z**6\n (-24*z**2)*(-14*z) = 336*z**3\n (-24*z**2)*(16*z**3) = -384*z**5\n -14*-14*z = 196*z\n -14*16*z**3 = -224*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1200*z**6 - 384*z**5 + 1050*z**4 - 224*z**3 + 336*z**3 + 196*z\nCombining like terms, got -1200*z**6 - 384*z**5 + 1050*z**4 + 112*z**3 + 196*z\n#Step 6:\nCurrent expression: -1200*z**6 - 384*z**5 + 1050*z**4 + 112*z**3 + 196*z\nNo more calculations needed.\n-1200*z**6 - 384*z**5 + 1050*z**4 + 112*z**3 + 196*z", "generated_answer": "-1200*z**6 - 384*z**5 + 1050*z**4 + 112*z**3 + 196*z", "step_length": 6} {"cot_id": "76dfa020f5d617e172f0f0bfac24e59dc164540dff58237361b698592f285f86", "datapoint": {"question": "Simplify this expression: (27*y - 70)*(-36*y**2 - 31*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-972*y**3 + 1683*y**2 + 2170*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1156, "polynomial_expr": "(27*y - 70)*(-36*y**2 - 31*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*y - 70)*(-36*y**2 - 31*y)\nExpanding the part (27*y - 70) using the distributive property, and we got: (27*y)*(-36*y**2 - 31*y) - 70*(-36*y**2 - 31*y)\n#Step 2:\nCurrent expression: (27*y)*(-36*y**2 - 31*y) - 70*(-36*y**2 - 31*y)\nSimplifying the partial expression: -70*(-36*y**2 - 31*y)\nExpanding the part (-36*y**2 - 31*y) using the distributive property, and we got: -31*y*(-70) - 36*y**2*(-70)\nReplacing -70*(-36*y**2 - 31*y) with -31*y*(-70) - 36*y**2*(-70) in the overall expression.\n#Step 3:\nCurrent expression: -31*y*(-70) + (27*y)*(-36*y**2 - 31*y) - 36*y**2*(-70)\nSimplifying the partial expression: (27*y)*(-36*y**2 - 31*y)\nExpanding the part (-36*y**2 - 31*y) using the distributive property, and we got: (-31*y)*(27*y) + (27*y)*(-36*y**2)\nReplacing (27*y)*(-36*y**2 - 31*y) with (-31*y)*(27*y) + (27*y)*(-36*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-31*y)*(27*y) - 31*y*(-70) + (27*y)*(-36*y**2) - 36*y**2*(-70)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*y**2)*-70 = 2520*y**2\n (-36*y**2)*(27*y) = -972*y**3\n (-31*y)*-70 = 2170*y\n (-31*y)*(27*y) = -837*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -972*y**3 - 837*y**2 + 2520*y**2 + 2170*y\nCombining like terms, got -972*y**3 + 1683*y**2 + 2170*y\n#Step 6:\nCurrent expression: -972*y**3 + 1683*y**2 + 2170*y\nNo more calculations needed.\n-972*y**3 + 1683*y**2 + 2170*y", "generated_answer": "-972*y**3 + 1683*y**2 + 2170*y", "step_length": 6} {"cot_id": "7dff8e4d36500a50f91846d81174d8d6064b445d8c3d9ca52cce8997c4bab8e0", "datapoint": {"question": "Calculate the following: (-39*z**3 - 26*z - 44)*(41*z**3 + 47*z**2 - 20*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1599*z**6 - 1833*z**5 - 286*z**4 - 3026*z**3 - 1548*z**2 + 880*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1157, "polynomial_expr": "(-39*z**3 - 26*z - 44)*(41*z**3 + 47*z**2 - 20*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-39*z**3 - 26*z - 44)*(41*z**3 + 47*z**2 - 20*z)\nExpanding the part (-39*z**3 - 26*z - 44) using the distributive property, and we got: (-26*z)*(41*z**3 + 47*z**2 - 20*z) + (-39*z**3)*(41*z**3 + 47*z**2 - 20*z) - 44*(41*z**3 + 47*z**2 - 20*z)\n#Step 2:\nCurrent expression: (-26*z)*(41*z**3 + 47*z**2 - 20*z) + (-39*z**3)*(41*z**3 + 47*z**2 - 20*z) - 44*(41*z**3 + 47*z**2 - 20*z)\nSimplifying the partial expression: -44*(41*z**3 + 47*z**2 - 20*z)\nExpanding the part (41*z**3 + 47*z**2 - 20*z) using the distributive property, and we got: -20*z*(-44) + (47*z**2)*(-44) + (41*z**3)*(-44)\nReplacing -44*(41*z**3 + 47*z**2 - 20*z) with -20*z*(-44) + (47*z**2)*(-44) + (41*z**3)*(-44) in the overall expression.\n#Step 3:\nCurrent expression: (-26*z)*(41*z**3 + 47*z**2 - 20*z) - 20*z*(-44) + (47*z**2)*(-44) + (-39*z**3)*(41*z**3 + 47*z**2 - 20*z) + (41*z**3)*(-44)\nSimplifying the partial expression: (-39*z**3)*(41*z**3 + 47*z**2 - 20*z)\nExpanding the part (41*z**3 + 47*z**2 - 20*z) using the distributive property, and we got: (-20*z)*(-39*z**3) + (47*z**2)*(-39*z**3) + (-39*z**3)*(41*z**3)\nReplacing (-39*z**3)*(41*z**3 + 47*z**2 - 20*z) with (-20*z)*(-39*z**3) + (47*z**2)*(-39*z**3) + (-39*z**3)*(41*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-26*z)*(41*z**3 + 47*z**2 - 20*z) + (-20*z)*(-39*z**3) - 20*z*(-44) + (47*z**2)*(-39*z**3) + (47*z**2)*(-44) + (-39*z**3)*(41*z**3) + (41*z**3)*(-44)\nSimplifying the partial expression: (-26*z)*(41*z**3 + 47*z**2 - 20*z)\nExpanding the part (41*z**3 + 47*z**2 - 20*z) using the distributive property, and we got: (-26*z)*(-20*z) + (-26*z)*(47*z**2) + (-26*z)*(41*z**3)\nReplacing (-26*z)*(41*z**3 + 47*z**2 - 20*z) with (-26*z)*(-20*z) + (-26*z)*(47*z**2) + (-26*z)*(41*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-26*z)*(-20*z) + (-26*z)*(47*z**2) + (-26*z)*(41*z**3) + (-20*z)*(-39*z**3) - 20*z*(-44) + (47*z**2)*(-39*z**3) + (47*z**2)*(-44) + (-39*z**3)*(41*z**3) + (41*z**3)*(-44)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*z)*-44 = 880*z\n (-20*z)*(-39*z**3) = 780*z**4\n (-20*z)*(-26*z) = 520*z**2\n (41*z**3)*-44 = -1804*z**3\n (41*z**3)*(-39*z**3) = -1599*z**6\n (41*z**3)*(-26*z) = -1066*z**4\n (47*z**2)*-44 = -2068*z**2\n (47*z**2)*(-39*z**3) = -1833*z**5\n (47*z**2)*(-26*z) = -1222*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1599*z**6 - 1833*z**5 - 1066*z**4 + 780*z**4 - 1804*z**3 - 1222*z**3 - 2068*z**2 + 520*z**2 + 880*z\nCombining like terms, got -1599*z**6 - 1833*z**5 - 286*z**4 - 3026*z**3 - 1548*z**2 + 880*z\n#Step 7:\nCurrent expression: -1599*z**6 - 1833*z**5 - 286*z**4 - 3026*z**3 - 1548*z**2 + 880*z\nNo more calculations needed.\n-1599*z**6 - 1833*z**5 - 286*z**4 - 3026*z**3 - 1548*z**2 + 880*z", "generated_answer": "-1599*z**6 - 1833*z**5 - 286*z**4 - 3026*z**3 - 1548*z**2 + 880*z", "step_length": 7} {"cot_id": "e8b3bf7160f91338f323da705df3922e64bb4491272c6f1bdd9f797e65478b7b", "datapoint": {"question": "Simplify this expression: -32*y**3*(17*y**2 - 11)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-544*y**5 + 352*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1158, "polynomial_expr": "-32*y**3*(17*y**2 - 11)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -32*y**3*(17*y**2 - 11)\nExpanding the part (17*y**2 - 11) using the distributive property, and we got: -(-1)*352*y**3 + (17*y**2)*(-32*y**3)\n#Step 2:\nCurrent expression: -(-1)*352*y**3 + (17*y**2)*(-32*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -11*(-32*y**3) = 352*y**3\n (17*y**2)*(-32*y**3) = -544*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -544*y**5 + 352*y**3\nNo more calculations needed.\n-544*y**5 + 352*y**3", "generated_answer": "-544*y**5 + 352*y**3", "step_length": 3} {"cot_id": "59e61afb804bd755a5e89abc08f2b56290ba39f11280ebfaadc90298fde805b9", "datapoint": {"question": "Simplify this expression: (-9*x**3 - 27*x - 28)*(25*x**3 - 11*x**2 + 46)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-225*x**6 + 99*x**5 - 675*x**4 - 817*x**3 + 308*x**2 - 1242*x - 1288", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1159, "polynomial_expr": "(-9*x**3 - 27*x - 28)*(25*x**3 - 11*x**2 + 46)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-9*x**3 - 27*x - 28)*(25*x**3 - 11*x**2 + 46)\nExpanding the part (-9*x**3 - 27*x - 28) using the distributive property, and we got: (-27*x)*(25*x**3 - 11*x**2 + 46) + (-9*x**3)*(25*x**3 - 11*x**2 + 46) - 28*(25*x**3 - 11*x**2 + 46)\n#Step 2:\nCurrent expression: (-27*x)*(25*x**3 - 11*x**2 + 46) + (-9*x**3)*(25*x**3 - 11*x**2 + 46) - 28*(25*x**3 - 11*x**2 + 46)\nSimplifying the partial expression: -28*(25*x**3 - 11*x**2 + 46)\nExpanding the part (25*x**3 - 11*x**2 + 46) using the distributive property, and we got: -11*x**2*(-28) + (25*x**3)*(-28) + 46*(-28)\nReplacing -28*(25*x**3 - 11*x**2 + 46) with -11*x**2*(-28) + (25*x**3)*(-28) + 46*(-28) in the overall expression.\n#Step 3:\nCurrent expression: (-27*x)*(25*x**3 - 11*x**2 + 46) - 11*x**2*(-28) + (-9*x**3)*(25*x**3 - 11*x**2 + 46) + (25*x**3)*(-28) - 1288\nSimplifying the partial expression: (-27*x)*(25*x**3 - 11*x**2 + 46)\nExpanding the part (25*x**3 - 11*x**2 + 46) using the distributive property, and we got: (-27*x)*(-11*x**2) + (-27*x)*(25*x**3) + 46*(-27*x)\nReplacing (-27*x)*(25*x**3 - 11*x**2 + 46) with (-27*x)*(-11*x**2) + (-27*x)*(25*x**3) + 46*(-27*x) in the overall expression.\n#Step 4:\nCurrent expression: (-27*x)*(-11*x**2) + (-27*x)*(25*x**3) + 46*(-27)*x - 11*x**2*(-28) + (-9*x**3)*(25*x**3 - 11*x**2 + 46) + (25*x**3)*(-28) - 1288\nSimplifying the partial expression: (-9*x**3)*(25*x**3 - 11*x**2 + 46)\nExpanding the part (25*x**3 - 11*x**2 + 46) using the distributive property, and we got: 46*(-9*x**3) + (-11*x**2)*(-9*x**3) + (-9*x**3)*(25*x**3)\nReplacing (-9*x**3)*(25*x**3 - 11*x**2 + 46) with 46*(-9*x**3) + (-11*x**2)*(-9*x**3) + (-9*x**3)*(25*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-27*x)*(-11*x**2) + (-27*x)*(25*x**3) + 46*(-9)*x**3 + 46*(-27)*x + (-11*x**2)*(-9*x**3) - 11*x**2*(-28) + (-9*x**3)*(25*x**3) + (25*x**3)*(-28) - 1288\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*x**2)*-28 = 308*x**2\n (-11*x**2)*(-27*x) = 297*x**3\n (-11*x**2)*(-9*x**3) = 99*x**5\n (25*x**3)*-28 = -700*x**3\n (25*x**3)*(-27*x) = -675*x**4\n (25*x**3)*(-9*x**3) = -225*x**6\n 46*-27*x = -1242*x\n 46*-9*x**3 = -414*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -225*x**6 + 99*x**5 - 675*x**4 - 700*x**3 - 414*x**3 + 297*x**3 + 308*x**2 - 1242*x - 1288\nCombining like terms, got -225*x**6 + 99*x**5 - 675*x**4 - 817*x**3 + 308*x**2 - 1242*x - 1288\n#Step 7:\nCurrent expression: -225*x**6 + 99*x**5 - 675*x**4 - 817*x**3 + 308*x**2 - 1242*x - 1288\nNo more calculations needed.\n-225*x**6 + 99*x**5 - 675*x**4 - 817*x**3 + 308*x**2 - 1242*x - 1288", "generated_answer": "-225*x**6 + 99*x**5 - 675*x**4 - 817*x**3 + 308*x**2 - 1242*x - 1288", "step_length": 7} {"cot_id": "9385deb4525976d0f4682084f88b8f66d966439f33c9c72daf4bb38b471eade5", "datapoint": {"question": "Calculate the following: -41*y**2*(23*y**3 - 4*y**2 + 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-943*y**5 + 164*y**4 - 1804*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1160, "polynomial_expr": "-41*y**2*(23*y**3 - 4*y**2 + 44)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -41*y**2*(23*y**3 - 4*y**2 + 44)\nExpanding the part (23*y**3 - 4*y**2 + 44) using the distributive property, and we got: 44*(-41*y**2) + (-41*y**2)*(-4*y**2) + (-41*y**2)*(23*y**3)\n#Step 2:\nCurrent expression: 44*(-41*y**2) + (-41*y**2)*(-4*y**2) + (-41*y**2)*(23*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 44*(-41*y**2) = -1804*y**2\n (-4*y**2)*(-41*y**2) = 164*y**4\n (23*y**3)*(-41*y**2) = -943*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -943*y**5 + 164*y**4 - 1804*y**2\nNo more calculations needed.\n-943*y**5 + 164*y**4 - 1804*y**2", "generated_answer": "-943*y**5 + 164*y**4 - 1804*y**2", "step_length": 3} {"cot_id": "21c2cdca26ed348b486a098c875caecf8ce1c00d71c3098af0f953963c8909cc", "datapoint": {"question": "Simplify this expression: (-x**3 - 9)*(49*x**3 - 45*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-49*x**6 + 45*x**5 - 441*x**3 + 405*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1161, "polynomial_expr": "(-x**3 - 9)*(49*x**3 - 45*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-x**3 - 9)*(49*x**3 - 45*x**2)\nExpanding the part (-x**3 - 9) using the distributive property, and we got: (-x**3)*(49*x**3 - 45*x**2) - 9*(49*x**3 - 45*x**2)\n#Step 2:\nCurrent expression: (-x**3)*(49*x**3 - 45*x**2) - 9*(49*x**3 - 45*x**2)\nSimplifying the partial expression: -9*(49*x**3 - 45*x**2)\nExpanding the part (49*x**3 - 45*x**2) using the distributive property, and we got: -45*x**2*(-9) + (49*x**3)*(-9)\nReplacing -9*(49*x**3 - 45*x**2) with -45*x**2*(-9) + (49*x**3)*(-9) in the overall expression.\n#Step 3:\nCurrent expression: -45*x**2*(-9) + (-x**3)*(49*x**3 - 45*x**2) + (49*x**3)*(-9)\nSimplifying the partial expression: (-x**3)*(49*x**3 - 45*x**2)\nExpanding the part (49*x**3 - 45*x**2) using the distributive property, and we got: (-45*x**2)*(-x**3) + (-x**3)*(49*x**3)\nReplacing (-x**3)*(49*x**3 - 45*x**2) with (-45*x**2)*(-x**3) + (-x**3)*(49*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-45*x**2)*(-x**3) - 45*x**2*(-9) + (-x**3)*(49*x**3) + (49*x**3)*(-9)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*x**2)*-9 = 405*x**2\n (-45*x**2)*(-x**3) = 45*x**5\n (49*x**3)*-9 = -441*x**3\n (49*x**3)*(-x**3) = -49*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -49*x**6 + 45*x**5 - 441*x**3 + 405*x**2\nNo more calculations needed.\n-49*x**6 + 45*x**5 - 441*x**3 + 405*x**2", "generated_answer": "-49*x**6 + 45*x**5 - 441*x**3 + 405*x**2", "step_length": 5} {"cot_id": "56fb22dcb2b2fb60d25cf79d3e158e105a72342fee68081c00d24eeba49730ca", "datapoint": {"question": "Simplify this expression: (37*y**2 - 56)*(-16*y**3 - 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-592*y**5 + 896*y**3 - 1295*y**2 + 1960", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1162, "polynomial_expr": "(37*y**2 - 56)*(-16*y**3 - 35)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (37*y**2 - 56)*(-16*y**3 - 35)\nExpanding the part (37*y**2 - 56) using the distributive property, and we got: (37*y**2)*(-16*y**3 - 35) - 56*(-16*y**3 - 35)\n#Step 2:\nCurrent expression: (37*y**2)*(-16*y**3 - 35) - 56*(-16*y**3 - 35)\nSimplifying the partial expression: -56*(-16*y**3 - 35)\nExpanding the part (-16*y**3 - 35) using the distributive property, and we got: -16*y**3*(-56) - 35*(-56)\nReplacing -56*(-16*y**3 - 35) with -16*y**3*(-56) - 35*(-56) in the overall expression.\n#Step 3:\nCurrent expression: (37*y**2)*(-16*y**3 - 35) - 16*y**3*(-56) + 1960\nSimplifying the partial expression: (37*y**2)*(-16*y**3 - 35)\nExpanding the part (-16*y**3 - 35) using the distributive property, and we got: -1295*y**2 + (37*y**2)*(-16*y**3)\nReplacing (37*y**2)*(-16*y**3 - 35) with -1295*y**2 + (37*y**2)*(-16*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -35*37*y**2 + (37*y**2)*(-16*y**3) - 16*y**3*(-56) + 1960\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-16*y**3)*-56 = 896*y**3\n (-16*y**3)*(37*y**2) = -592*y**5\n -35*37*y**2 = -1295*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -592*y**5 + 896*y**3 - 1295*y**2 + 1960\nNo more calculations needed.\n-592*y**5 + 896*y**3 - 1295*y**2 + 1960", "generated_answer": "-592*y**5 + 896*y**3 - 1295*y**2 + 1960", "step_length": 5} {"cot_id": "c63eb16352ad26728550ee3f75b0a5d3613ee1e47d7f669ea4cef71a0b4d874f", "datapoint": {"question": "Calculate the following: (20*z**3 + 3*z**2)*(-13*z**3 + 8*z**2 + 37*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-260*z**6 + 121*z**5 + 764*z**4 + 111*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1163, "polynomial_expr": "(20*z**3 + 3*z**2)*(-13*z**3 + 8*z**2 + 37*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (20*z**3 + 3*z**2)*(-13*z**3 + 8*z**2 + 37*z)\nExpanding the part (20*z**3 + 3*z**2) using the distributive property, and we got: (3*z**2)*(-13*z**3 + 8*z**2 + 37*z) + (20*z**3)*(-13*z**3 + 8*z**2 + 37*z)\n#Step 2:\nCurrent expression: (3*z**2)*(-13*z**3 + 8*z**2 + 37*z) + (20*z**3)*(-13*z**3 + 8*z**2 + 37*z)\nSimplifying the partial expression: (3*z**2)*(-13*z**3 + 8*z**2 + 37*z)\nExpanding the part (-13*z**3 + 8*z**2 + 37*z) using the distributive property, and we got: (37*z)*(3*z**2) + (3*z**2)*(8*z**2) + (3*z**2)*(-13*z**3)\nReplacing (3*z**2)*(-13*z**3 + 8*z**2 + 37*z) with (37*z)*(3*z**2) + (3*z**2)*(8*z**2) + (3*z**2)*(-13*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (37*z)*(3*z**2) + (3*z**2)*(8*z**2) + (3*z**2)*(-13*z**3) + (20*z**3)*(-13*z**3 + 8*z**2 + 37*z)\nSimplifying the partial expression: (20*z**3)*(-13*z**3 + 8*z**2 + 37*z)\nExpanding the part (-13*z**3 + 8*z**2 + 37*z) using the distributive property, and we got: (37*z)*(20*z**3) + (8*z**2)*(20*z**3) + (-13*z**3)*(20*z**3)\nReplacing (20*z**3)*(-13*z**3 + 8*z**2 + 37*z) with (37*z)*(20*z**3) + (8*z**2)*(20*z**3) + (-13*z**3)*(20*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (37*z)*(3*z**2) + (37*z)*(20*z**3) + (3*z**2)*(8*z**2) + (3*z**2)*(-13*z**3) + (8*z**2)*(20*z**3) + (-13*z**3)*(20*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*z**3)*(3*z**2) = -39*z**5\n (-13*z**3)*(20*z**3) = -260*z**6\n (8*z**2)*(3*z**2) = 24*z**4\n (8*z**2)*(20*z**3) = 160*z**5\n (37*z)*(3*z**2) = 111*z**3\n (37*z)*(20*z**3) = 740*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -260*z**6 - 39*z**5 + 160*z**5 + 24*z**4 + 740*z**4 + 111*z**3\nCombining like terms, got -260*z**6 + 121*z**5 + 764*z**4 + 111*z**3\n#Step 6:\nCurrent expression: -260*z**6 + 121*z**5 + 764*z**4 + 111*z**3\nNo more calculations needed.\n-260*z**6 + 121*z**5 + 764*z**4 + 111*z**3", "generated_answer": "-260*z**6 + 121*z**5 + 764*z**4 + 111*z**3", "step_length": 6} {"cot_id": "41e657be5e0b37fab601c80a9bf98d765de5d1af6a30fc593c953501f0652b0a", "datapoint": {"question": "Calculate the following: (-28*y**3 - 50*y)*(19*y**3 - 12*y + 2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-532*y**6 - 614*y**4 - 56*y**3 + 600*y**2 - 100*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1164, "polynomial_expr": "(-28*y**3 - 50*y)*(19*y**3 - 12*y + 2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-28*y**3 - 50*y)*(19*y**3 - 12*y + 2)\nExpanding the part (-28*y**3 - 50*y) using the distributive property, and we got: (-50*y)*(19*y**3 - 12*y + 2) + (-28*y**3)*(19*y**3 - 12*y + 2)\n#Step 2:\nCurrent expression: (-50*y)*(19*y**3 - 12*y + 2) + (-28*y**3)*(19*y**3 - 12*y + 2)\nSimplifying the partial expression: (-50*y)*(19*y**3 - 12*y + 2)\nExpanding the part (19*y**3 - 12*y + 2) using the distributive property, and we got: (-50*y)*(-12*y) + (-50*y)*(19*y**3) + 2*(-50*y)\nReplacing (-50*y)*(19*y**3 - 12*y + 2) with (-50*y)*(-12*y) + (-50*y)*(19*y**3) + 2*(-50*y) in the overall expression.\n#Step 3:\nCurrent expression: (-50*y)*(-12*y) + (-50*y)*(19*y**3) + 2*(-50)*y + (-28*y**3)*(19*y**3 - 12*y + 2)\nSimplifying the partial expression: (-28*y**3)*(19*y**3 - 12*y + 2)\nExpanding the part (19*y**3 - 12*y + 2) using the distributive property, and we got: (-12*y)*(-28*y**3) + 2*(-28*y**3) + (-28*y**3)*(19*y**3)\nReplacing (-28*y**3)*(19*y**3 - 12*y + 2) with (-12*y)*(-28*y**3) + 2*(-28*y**3) + (-28*y**3)*(19*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-50*y)*(-12*y) + (-50*y)*(19*y**3) + (-12*y)*(-28*y**3) + 2*(-28)*y**3 + 2*(-50)*y + (-28*y**3)*(19*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*y)*(-50*y) = 600*y**2\n (-12*y)*(-28*y**3) = 336*y**4\n (19*y**3)*(-50*y) = -950*y**4\n (19*y**3)*(-28*y**3) = -532*y**6\n 2*-50*y = -100*y\n 2*-28*y**3 = -56*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -532*y**6 - 950*y**4 + 336*y**4 - 56*y**3 + 600*y**2 - 100*y\nCombining like terms, got -532*y**6 - 614*y**4 - 56*y**3 + 600*y**2 - 100*y\n#Step 6:\nCurrent expression: -532*y**6 - 614*y**4 - 56*y**3 + 600*y**2 - 100*y\nNo more calculations needed.\n-532*y**6 - 614*y**4 - 56*y**3 + 600*y**2 - 100*y", "generated_answer": "-532*y**6 - 614*y**4 - 56*y**3 + 600*y**2 - 100*y", "step_length": 6} {"cot_id": "38a982d179461bee2b19bac362908e0bdb054e06498618e06af3b0f6dcbaa89a", "datapoint": {"question": "Simplify this expression: (-37*z**2 - 19)*(z**3 - 5)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-37*z**5 - 19*z**3 + 185*z**2 + 95", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1165, "polynomial_expr": "(-37*z**2 - 19)*(z**3 - 5)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-37*z**2 - 19)*(z**3 - 5)\nExpanding the part (-37*z**2 - 19) using the distributive property, and we got: (-37*z**2)*(z**3 - 5) - 19*(z**3 - 5)\n#Step 2:\nCurrent expression: (-37*z**2)*(z**3 - 5) - 19*(z**3 - 5)\nSimplifying the partial expression: -19*(z**3 - 5)\nExpanding the part (z**3 - 5) using the distributive property, and we got: z**3*(-19) - 5*(-19)\nReplacing -19*(z**3 - 5) with z**3*(-19) - 5*(-19) in the overall expression.\n#Step 3:\nCurrent expression: z**3*(-19) + (-37*z**2)*(z**3 - 5) + 95\nSimplifying the partial expression: (-37*z**2)*(z**3 - 5)\nExpanding the part (z**3 - 5) using the distributive property, and we got: (-37*z**2)*z**3 - (-1)*185*z**2\nReplacing (-37*z**2)*(z**3 - 5) with (-37*z**2)*z**3 - (-1)*185*z**2 in the overall expression.\n#Step 4:\nCurrent expression: (-37*z**2)*z**3 + z**3*(-19) - 5*(-37)*z**2 + 95\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n z**3*-19 = -19*z**3\n z**3*(-37*z**2) = -37*z**5\n -5*-37*z**2 = 185*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -37*z**5 - 19*z**3 + 185*z**2 + 95\nNo more calculations needed.\n-37*z**5 - 19*z**3 + 185*z**2 + 95", "generated_answer": "-37*z**5 - 19*z**3 + 185*z**2 + 95", "step_length": 5} {"cot_id": "338e74bea610957e8d9afff8c1508a9614957bef9b1c483f8cf2487ef55ccf46", "datapoint": {"question": "Simplify this expression: (-54*x**3 - 21*x)*(-14*x**3 - 36*x**2 + 17*x + 27)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "756*x**6 + 1944*x**5 - 624*x**4 - 702*x**3 - 357*x**2 - 567*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1166, "polynomial_expr": "(-54*x**3 - 21*x)*(-14*x**3 - 36*x**2 + 17*x + 27)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-54*x**3 - 21*x)*(-14*x**3 - 36*x**2 + 17*x + 27)\nExpanding the part (-54*x**3 - 21*x) using the distributive property, and we got: (-21*x)*(-14*x**3 - 36*x**2 + 17*x + 27) + (-54*x**3)*(-14*x**3 - 36*x**2 + 17*x + 27)\n#Step 2:\nCurrent expression: (-21*x)*(-14*x**3 - 36*x**2 + 17*x + 27) + (-54*x**3)*(-14*x**3 - 36*x**2 + 17*x + 27)\nSimplifying the partial expression: (-54*x**3)*(-14*x**3 - 36*x**2 + 17*x + 27)\nExpanding the part (-14*x**3 - 36*x**2 + 17*x + 27) using the distributive property, and we got: 27*(-54*x**3) + (17*x)*(-54*x**3) + (-36*x**2)*(-54*x**3) + (-54*x**3)*(-14*x**3)\nReplacing (-54*x**3)*(-14*x**3 - 36*x**2 + 17*x + 27) with 27*(-54*x**3) + (17*x)*(-54*x**3) + (-36*x**2)*(-54*x**3) + (-54*x**3)*(-14*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-21*x)*(-14*x**3 - 36*x**2 + 17*x + 27) + 27*(-54)*x**3 + (17*x)*(-54*x**3) + (-36*x**2)*(-54*x**3) + (-54*x**3)*(-14*x**3)\nSimplifying the partial expression: (-21*x)*(-14*x**3 - 36*x**2 + 17*x + 27)\nExpanding the part (-14*x**3 - 36*x**2 + 17*x + 27) using the distributive property, and we got: (-21*x)*(17*x) + (-21*x)*(-36*x**2) + (-21*x)*(-14*x**3) + 27*(-21*x)\nReplacing (-21*x)*(-14*x**3 - 36*x**2 + 17*x + 27) with (-21*x)*(17*x) + (-21*x)*(-36*x**2) + (-21*x)*(-14*x**3) + 27*(-21*x) in the overall expression.\n#Step 4:\nCurrent expression: (-21*x)*(17*x) + (-21*x)*(-36*x**2) + (-21*x)*(-14*x**3) + 27*(-54)*x**3 + 27*(-21)*x + (17*x)*(-54*x**3) + (-36*x**2)*(-54*x**3) + (-54*x**3)*(-14*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*x**2)*(-54*x**3) = 1944*x**5\n (-36*x**2)*(-21*x) = 756*x**3\n (-14*x**3)*(-54*x**3) = 756*x**6\n (-14*x**3)*(-21*x) = 294*x**4\n (17*x)*(-54*x**3) = -918*x**4\n (17*x)*(-21*x) = -357*x**2\n 27*-54*x**3 = -1458*x**3\n 27*-21*x = -567*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 756*x**6 + 1944*x**5 - 918*x**4 + 294*x**4 - 1458*x**3 + 756*x**3 - 357*x**2 - 567*x\nCombining like terms, got 756*x**6 + 1944*x**5 - 624*x**4 - 702*x**3 - 357*x**2 - 567*x\n#Step 6:\nCurrent expression: 756*x**6 + 1944*x**5 - 624*x**4 - 702*x**3 - 357*x**2 - 567*x\nNo more calculations needed.\n756*x**6 + 1944*x**5 - 624*x**4 - 702*x**3 - 357*x**2 - 567*x", "generated_answer": "756*x**6 + 1944*x**5 - 624*x**4 - 702*x**3 - 357*x**2 - 567*x", "step_length": 6} {"cot_id": "744edde6d6fa77e9937c4a40ee65b8be358ba3ab3edf73aaa1c4ab1d4f5f2c48", "datapoint": {"question": "Simplify this expression: (-33*z**3 - 22*z**2 + 24)*(38*z**3 + 10*z**2 + 65*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1254*z**6 - 1166*z**5 - 2365*z**4 - 518*z**3 + 240*z**2 + 1560*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1167, "polynomial_expr": "(-33*z**3 - 22*z**2 + 24)*(38*z**3 + 10*z**2 + 65*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-33*z**3 - 22*z**2 + 24)*(38*z**3 + 10*z**2 + 65*z)\nExpanding the part (-33*z**3 - 22*z**2 + 24) using the distributive property, and we got: (-22*z**2)*(38*z**3 + 10*z**2 + 65*z) + (-33*z**3)*(38*z**3 + 10*z**2 + 65*z) + 24*(38*z**3 + 10*z**2 + 65*z)\n#Step 2:\nCurrent expression: (-22*z**2)*(38*z**3 + 10*z**2 + 65*z) + (-33*z**3)*(38*z**3 + 10*z**2 + 65*z) + 24*(38*z**3 + 10*z**2 + 65*z)\nSimplifying the partial expression: 24*(38*z**3 + 10*z**2 + 65*z)\nExpanding the part (38*z**3 + 10*z**2 + 65*z) using the distributive property, and we got: (65*z)*24 + (10*z**2)*24 + (38*z**3)*24\nReplacing 24*(38*z**3 + 10*z**2 + 65*z) with (65*z)*24 + (10*z**2)*24 + (38*z**3)*24 in the overall expression.\n#Step 3:\nCurrent expression: (65*z)*24 + (-22*z**2)*(38*z**3 + 10*z**2 + 65*z) + (10*z**2)*24 + (-33*z**3)*(38*z**3 + 10*z**2 + 65*z) + (38*z**3)*24\nSimplifying the partial expression: (-33*z**3)*(38*z**3 + 10*z**2 + 65*z)\nExpanding the part (38*z**3 + 10*z**2 + 65*z) using the distributive property, and we got: (65*z)*(-33*z**3) + (10*z**2)*(-33*z**3) + (-33*z**3)*(38*z**3)\nReplacing (-33*z**3)*(38*z**3 + 10*z**2 + 65*z) with (65*z)*(-33*z**3) + (10*z**2)*(-33*z**3) + (-33*z**3)*(38*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (65*z)*(-33*z**3) + (65*z)*24 + (-22*z**2)*(38*z**3 + 10*z**2 + 65*z) + (10*z**2)*(-33*z**3) + (10*z**2)*24 + (-33*z**3)*(38*z**3) + (38*z**3)*24\nSimplifying the partial expression: (-22*z**2)*(38*z**3 + 10*z**2 + 65*z)\nExpanding the part (38*z**3 + 10*z**2 + 65*z) using the distributive property, and we got: (65*z)*(-22*z**2) + (-22*z**2)*(10*z**2) + (-22*z**2)*(38*z**3)\nReplacing (-22*z**2)*(38*z**3 + 10*z**2 + 65*z) with (65*z)*(-22*z**2) + (-22*z**2)*(10*z**2) + (-22*z**2)*(38*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (65*z)*(-22*z**2) + (65*z)*(-33*z**3) + (65*z)*24 + (-22*z**2)*(10*z**2) + (-22*z**2)*(38*z**3) + (10*z**2)*(-33*z**3) + (10*z**2)*24 + (-33*z**3)*(38*z**3) + (38*z**3)*24\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (10*z**2)*24 = 240*z**2\n (10*z**2)*(-33*z**3) = -330*z**5\n (10*z**2)*(-22*z**2) = -220*z**4\n (38*z**3)*24 = 912*z**3\n (38*z**3)*(-33*z**3) = -1254*z**6\n (38*z**3)*(-22*z**2) = -836*z**5\n (65*z)*24 = 1560*z\n (65*z)*(-33*z**3) = -2145*z**4\n (65*z)*(-22*z**2) = -1430*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1254*z**6 - 836*z**5 - 330*z**5 - 2145*z**4 - 220*z**4 - 1430*z**3 + 912*z**3 + 240*z**2 + 1560*z\nCombining like terms, got -1254*z**6 - 1166*z**5 - 2365*z**4 - 518*z**3 + 240*z**2 + 1560*z\n#Step 7:\nCurrent expression: -1254*z**6 - 1166*z**5 - 2365*z**4 - 518*z**3 + 240*z**2 + 1560*z\nNo more calculations needed.\n-1254*z**6 - 1166*z**5 - 2365*z**4 - 518*z**3 + 240*z**2 + 1560*z", "generated_answer": "-1254*z**6 - 1166*z**5 - 2365*z**4 - 518*z**3 + 240*z**2 + 1560*z", "step_length": 7} {"cot_id": "ddc254499e3f97f7395a8b9dd3102edcc494b80a05b5d3f7e8bca4fc1d0cccfc", "datapoint": {"question": "Calculate the following: (2*x + 15)*(-20*x**2 - 9*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-40*x**3 - 318*x**2 - 135*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1168, "polynomial_expr": "(2*x + 15)*(-20*x**2 - 9*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2*x + 15)*(-20*x**2 - 9*x)\nExpanding the part (2*x + 15) using the distributive property, and we got: (2*x)*(-20*x**2 - 9*x) + 15*(-20*x**2 - 9*x)\n#Step 2:\nCurrent expression: (2*x)*(-20*x**2 - 9*x) + 15*(-20*x**2 - 9*x)\nSimplifying the partial expression: 15*(-20*x**2 - 9*x)\nExpanding the part (-20*x**2 - 9*x) using the distributive property, and we got: -9*x*15 - 20*x**2*15\nReplacing 15*(-20*x**2 - 9*x) with -9*x*15 - 20*x**2*15 in the overall expression.\n#Step 3:\nCurrent expression: -9*x*15 + (2*x)*(-20*x**2 - 9*x) - 20*x**2*15\nSimplifying the partial expression: (2*x)*(-20*x**2 - 9*x)\nExpanding the part (-20*x**2 - 9*x) using the distributive property, and we got: (-9*x)*(2*x) + (2*x)*(-20*x**2)\nReplacing (2*x)*(-20*x**2 - 9*x) with (-9*x)*(2*x) + (2*x)*(-20*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-9*x)*(2*x) - 9*x*15 + (2*x)*(-20*x**2) - 20*x**2*15\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*x**2)*15 = -300*x**2\n (-20*x**2)*(2*x) = -40*x**3\n (-9*x)*15 = -135*x\n (-9*x)*(2*x) = -18*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -40*x**3 - 300*x**2 - 18*x**2 - 135*x\nCombining like terms, got -40*x**3 - 318*x**2 - 135*x\n#Step 6:\nCurrent expression: -40*x**3 - 318*x**2 - 135*x\nNo more calculations needed.\n-40*x**3 - 318*x**2 - 135*x", "generated_answer": "-40*x**3 - 318*x**2 - 135*x", "step_length": 6} {"cot_id": "ecc3a77ff9221597e90679533e7c751d1d641b4e9117d5a055aac170b9688c19", "datapoint": {"question": "Simplify this expression: (-49*y - 5)*(-67*y**3 - 38*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "3283*y**4 + 335*y**3 + 1862*y**2 + 190*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1169, "polynomial_expr": "(-49*y - 5)*(-67*y**3 - 38*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-49*y - 5)*(-67*y**3 - 38*y)\nExpanding the part (-49*y - 5) using the distributive property, and we got: (-49*y)*(-67*y**3 - 38*y) - 5*(-67*y**3 - 38*y)\n#Step 2:\nCurrent expression: (-49*y)*(-67*y**3 - 38*y) - 5*(-67*y**3 - 38*y)\nSimplifying the partial expression: -5*(-67*y**3 - 38*y)\nExpanding the part (-67*y**3 - 38*y) using the distributive property, and we got: -38*y*(-5) - 67*y**3*(-5)\nReplacing -5*(-67*y**3 - 38*y) with -38*y*(-5) - 67*y**3*(-5) in the overall expression.\n#Step 3:\nCurrent expression: (-49*y)*(-67*y**3 - 38*y) - 38*y*(-5) - 67*y**3*(-5)\nSimplifying the partial expression: (-49*y)*(-67*y**3 - 38*y)\nExpanding the part (-67*y**3 - 38*y) using the distributive property, and we got: (-49*y)*(-38*y) + (-49*y)*(-67*y**3)\nReplacing (-49*y)*(-67*y**3 - 38*y) with (-49*y)*(-38*y) + (-49*y)*(-67*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-49*y)*(-38*y) + (-49*y)*(-67*y**3) - 38*y*(-5) - 67*y**3*(-5)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-67*y**3)*-5 = 335*y**3\n (-67*y**3)*(-49*y) = 3283*y**4\n (-38*y)*-5 = 190*y\n (-38*y)*(-49*y) = 1862*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 3283*y**4 + 335*y**3 + 1862*y**2 + 190*y\nNo more calculations needed.\n3283*y**4 + 335*y**3 + 1862*y**2 + 190*y", "generated_answer": "3283*y**4 + 335*y**3 + 1862*y**2 + 190*y", "step_length": 5} {"cot_id": "a5e446c22e77913ced71effbe24aa04b3615dab4288d840436d615800a8d6962", "datapoint": {"question": "Simplify this expression: (-y**3 - y**2)*(-4*y**3 + 28*y - 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "4*y**6 + 4*y**5 - 28*y**4 - 21*y**3 + 7*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1170, "polynomial_expr": "(-y**3 - y**2)*(-4*y**3 + 28*y - 7)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-y**3 - y**2)*(-4*y**3 + 28*y - 7)\nExpanding the part (-y**3 - y**2) using the distributive property, and we got: (-y**2)*(-4*y**3 + 28*y - 7) + (-y**3)*(-4*y**3 + 28*y - 7)\n#Step 2:\nCurrent expression: (-y**2)*(-4*y**3 + 28*y - 7) + (-y**3)*(-4*y**3 + 28*y - 7)\nSimplifying the partial expression: (-y**2)*(-4*y**3 + 28*y - 7)\nExpanding the part (-4*y**3 + 28*y - 7) using the distributive property, and we got: -(-1)*7*y**2 + (28*y)*(-y**2) + (-y**2)*(-4*y**3)\nReplacing (-y**2)*(-4*y**3 + 28*y - 7) with -(-1)*7*y**2 + (28*y)*(-y**2) + (-y**2)*(-4*y**3) in the overall expression.\n#Step 3:\nCurrent expression: -7*(-1)*y**2 + (28*y)*(-y**2) + (-y**2)*(-4*y**3) + (-y**3)*(-4*y**3 + 28*y - 7)\nSimplifying the partial expression: (-y**3)*(-4*y**3 + 28*y - 7)\nExpanding the part (-4*y**3 + 28*y - 7) using the distributive property, and we got: -(-1)*7*y**3 + (28*y)*(-y**3) + (-4*y**3)*(-y**3)\nReplacing (-y**3)*(-4*y**3 + 28*y - 7) with -(-1)*7*y**3 + (28*y)*(-y**3) + (-4*y**3)*(-y**3) in the overall expression.\n#Step 4:\nCurrent expression: -7*(-1)*y**3 - 7*(-1)*y**2 + (28*y)*(-y**2) + (28*y)*(-y**3) + (-y**2)*(-4*y**3) + (-4*y**3)*(-y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-4*y**3)*(-y**2) = 4*y**5\n (-4*y**3)*(-y**3) = 4*y**6\n (28*y)*(-y**2) = -28*y**3\n (28*y)*(-y**3) = -28*y**4\n -7*-1*y**2 = 7*y**2\n -7*-1*y**3 = 7*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 4*y**6 + 4*y**5 - 28*y**4 - 28*y**3 + 7*y**3 + 7*y**2\nCombining like terms, got 4*y**6 + 4*y**5 - 28*y**4 - 21*y**3 + 7*y**2\n#Step 6:\nCurrent expression: 4*y**6 + 4*y**5 - 28*y**4 - 21*y**3 + 7*y**2\nNo more calculations needed.\n4*y**6 + 4*y**5 - 28*y**4 - 21*y**3 + 7*y**2", "generated_answer": "4*y**6 + 4*y**5 - 28*y**4 - 21*y**3 + 7*y**2", "step_length": 6} {"cot_id": "7a8341b655bb98c7920b653f8fdb3f69e4959284084dc40a0c914b8796669377", "datapoint": {"question": "Calculate the following: (22*z**2 - 21)*(-35*z**2 - 8*z + 26)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-770*z**4 - 176*z**3 + 1307*z**2 + 168*z - 546", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1171, "polynomial_expr": "(22*z**2 - 21)*(-35*z**2 - 8*z + 26)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (22*z**2 - 21)*(-35*z**2 - 8*z + 26)\nExpanding the part (22*z**2 - 21) using the distributive property, and we got: (22*z**2)*(-35*z**2 - 8*z + 26) - 21*(-35*z**2 - 8*z + 26)\n#Step 2:\nCurrent expression: (22*z**2)*(-35*z**2 - 8*z + 26) - 21*(-35*z**2 - 8*z + 26)\nSimplifying the partial expression: -21*(-35*z**2 - 8*z + 26)\nExpanding the part (-35*z**2 - 8*z + 26) using the distributive property, and we got: -8*z*(-21) - 35*z**2*(-21) + 26*(-21)\nReplacing -21*(-35*z**2 - 8*z + 26) with -8*z*(-21) - 35*z**2*(-21) + 26*(-21) in the overall expression.\n#Step 3:\nCurrent expression: -8*z*(-21) - 35*z**2*(-21) + (22*z**2)*(-35*z**2 - 8*z + 26) - 546\nSimplifying the partial expression: (22*z**2)*(-35*z**2 - 8*z + 26)\nExpanding the part (-35*z**2 - 8*z + 26) using the distributive property, and we got: (-8*z)*(22*z**2) + 26*(22*z**2) + (-35*z**2)*(22*z**2)\nReplacing (22*z**2)*(-35*z**2 - 8*z + 26) with (-8*z)*(22*z**2) + 26*(22*z**2) + (-35*z**2)*(22*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-8*z)*(22*z**2) - 8*z*(-21) + 26*22*z**2 + (-35*z**2)*(22*z**2) - 35*z**2*(-21) - 546\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*z**2)*-21 = 735*z**2\n (-35*z**2)*(22*z**2) = -770*z**4\n (-8*z)*-21 = 168*z\n (-8*z)*(22*z**2) = -176*z**3\n 26*22*z**2 = 572*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -770*z**4 - 176*z**3 + 572*z**2 + 735*z**2 + 168*z - 546\nCombining like terms, got -770*z**4 - 176*z**3 + 1307*z**2 + 168*z - 546\n#Step 6:\nCurrent expression: -770*z**4 - 176*z**3 + 1307*z**2 + 168*z - 546\nNo more calculations needed.\n-770*z**4 - 176*z**3 + 1307*z**2 + 168*z - 546", "generated_answer": "-770*z**4 - 176*z**3 + 1307*z**2 + 168*z - 546", "step_length": 6} {"cot_id": "a803ee303fa3ff4a7f165370be6e0a18248cbeb64941ab9524339196c483f8d1", "datapoint": {"question": "Simplify this expression: -67*y**2*(-33*y**3 - 2*y**2 + 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2211*y**5 + 134*y**4 - 2546*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1172, "polynomial_expr": "-67*y**2*(-33*y**3 - 2*y**2 + 38)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -67*y**2*(-33*y**3 - 2*y**2 + 38)\nExpanding the part (-33*y**3 - 2*y**2 + 38) using the distributive property, and we got: 38*(-67*y**2) + (-67*y**2)*(-2*y**2) + (-67*y**2)*(-33*y**3)\n#Step 2:\nCurrent expression: 38*(-67*y**2) + (-67*y**2)*(-2*y**2) + (-67*y**2)*(-33*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 38*(-67*y**2) = -2546*y**2\n (-33*y**3)*(-67*y**2) = 2211*y**5\n (-2*y**2)*(-67*y**2) = 134*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 2211*y**5 + 134*y**4 - 2546*y**2\nNo more calculations needed.\n2211*y**5 + 134*y**4 - 2546*y**2", "generated_answer": "2211*y**5 + 134*y**4 - 2546*y**2", "step_length": 3} {"cot_id": "f5cfd3cccfac8b12346418f741f59d2eba2a712693d1ad9fbd94611cea0f33e6", "datapoint": {"question": "Simplify this expression: (21*y**3 - 28*y)*(26*y**3 + 12*y + 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "546*y**6 - 476*y**4 + 1008*y**3 - 336*y**2 - 1344*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1173, "polynomial_expr": "(21*y**3 - 28*y)*(26*y**3 + 12*y + 48)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21*y**3 - 28*y)*(26*y**3 + 12*y + 48)\nExpanding the part (21*y**3 - 28*y) using the distributive property, and we got: (-28*y)*(26*y**3 + 12*y + 48) + (21*y**3)*(26*y**3 + 12*y + 48)\n#Step 2:\nCurrent expression: (-28*y)*(26*y**3 + 12*y + 48) + (21*y**3)*(26*y**3 + 12*y + 48)\nSimplifying the partial expression: (-28*y)*(26*y**3 + 12*y + 48)\nExpanding the part (26*y**3 + 12*y + 48) using the distributive property, and we got: (-28*y)*(12*y) + (-28*y)*(26*y**3) + 48*(-28*y)\nReplacing (-28*y)*(26*y**3 + 12*y + 48) with (-28*y)*(12*y) + (-28*y)*(26*y**3) + 48*(-28*y) in the overall expression.\n#Step 3:\nCurrent expression: (-28*y)*(12*y) + (-28*y)*(26*y**3) + 48*(-28)*y + (21*y**3)*(26*y**3 + 12*y + 48)\nSimplifying the partial expression: (21*y**3)*(26*y**3 + 12*y + 48)\nExpanding the part (26*y**3 + 12*y + 48) using the distributive property, and we got: 48*(21*y**3) + (12*y)*(21*y**3) + (21*y**3)*(26*y**3)\nReplacing (21*y**3)*(26*y**3 + 12*y + 48) with 48*(21*y**3) + (12*y)*(21*y**3) + (21*y**3)*(26*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-28*y)*(12*y) + (-28*y)*(26*y**3) + 48*21*y**3 + 48*(-28)*y + (12*y)*(21*y**3) + (21*y**3)*(26*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (12*y)*(-28*y) = -336*y**2\n (12*y)*(21*y**3) = 252*y**4\n (26*y**3)*(-28*y) = -728*y**4\n (26*y**3)*(21*y**3) = 546*y**6\n 48*-28*y = -1344*y\n 48*21*y**3 = 1008*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 546*y**6 - 728*y**4 + 252*y**4 + 1008*y**3 - 336*y**2 - 1344*y\nCombining like terms, got 546*y**6 - 476*y**4 + 1008*y**3 - 336*y**2 - 1344*y\n#Step 6:\nCurrent expression: 546*y**6 - 476*y**4 + 1008*y**3 - 336*y**2 - 1344*y\nNo more calculations needed.\n546*y**6 - 476*y**4 + 1008*y**3 - 336*y**2 - 1344*y", "generated_answer": "546*y**6 - 476*y**4 + 1008*y**3 - 336*y**2 - 1344*y", "step_length": 6} {"cot_id": "2a7f8eac4b66462efa99b21c88b788d9148358528eb1550068b4f2abbc4253fa", "datapoint": {"question": "Simplify this expression: -174*z**5\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-174*z**5", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1174, "polynomial_expr": "-174*z**5", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -174*z**5\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -174*z**5\nNo more calculations needed.\n-174*z**5", "generated_answer": "-174*z**5", "step_length": 2} {"cot_id": "6ec6813c18cf269d40de069bcf8c2040268b2e085871ebc5c49aae293d9b47ab", "datapoint": {"question": "Calculate the following: (40*x**3 + 22*x + 5)*(56*x**3 - 11*x**2 + 5*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2240*x**6 - 440*x**5 + 1432*x**4 + 38*x**3 + 55*x**2 + 25*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1175, "polynomial_expr": "(40*x**3 + 22*x + 5)*(56*x**3 - 11*x**2 + 5*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (40*x**3 + 22*x + 5)*(56*x**3 - 11*x**2 + 5*x)\nExpanding the part (40*x**3 + 22*x + 5) using the distributive property, and we got: (22*x)*(56*x**3 - 11*x**2 + 5*x) + (40*x**3)*(56*x**3 - 11*x**2 + 5*x) + 5*(56*x**3 - 11*x**2 + 5*x)\n#Step 2:\nCurrent expression: (22*x)*(56*x**3 - 11*x**2 + 5*x) + (40*x**3)*(56*x**3 - 11*x**2 + 5*x) + 5*(56*x**3 - 11*x**2 + 5*x)\nSimplifying the partial expression: 5*(56*x**3 - 11*x**2 + 5*x)\nExpanding the part (56*x**3 - 11*x**2 + 5*x) using the distributive property, and we got: (5*x)*5 - 11*x**2*5 + (56*x**3)*5\nReplacing 5*(56*x**3 - 11*x**2 + 5*x) with (5*x)*5 - 11*x**2*5 + (56*x**3)*5 in the overall expression.\n#Step 3:\nCurrent expression: (5*x)*5 + (22*x)*(56*x**3 - 11*x**2 + 5*x) - 11*x**2*5 + (40*x**3)*(56*x**3 - 11*x**2 + 5*x) + (56*x**3)*5\nSimplifying the partial expression: (22*x)*(56*x**3 - 11*x**2 + 5*x)\nExpanding the part (56*x**3 - 11*x**2 + 5*x) using the distributive property, and we got: (5*x)*(22*x) + (22*x)*(-11*x**2) + (22*x)*(56*x**3)\nReplacing (22*x)*(56*x**3 - 11*x**2 + 5*x) with (5*x)*(22*x) + (22*x)*(-11*x**2) + (22*x)*(56*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (5*x)*(22*x) + (5*x)*5 + (22*x)*(-11*x**2) + (22*x)*(56*x**3) - 11*x**2*5 + (40*x**3)*(56*x**3 - 11*x**2 + 5*x) + (56*x**3)*5\nSimplifying the partial expression: (40*x**3)*(56*x**3 - 11*x**2 + 5*x)\nExpanding the part (56*x**3 - 11*x**2 + 5*x) using the distributive property, and we got: (5*x)*(40*x**3) + (-11*x**2)*(40*x**3) + (40*x**3)*(56*x**3)\nReplacing (40*x**3)*(56*x**3 - 11*x**2 + 5*x) with (5*x)*(40*x**3) + (-11*x**2)*(40*x**3) + (40*x**3)*(56*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (5*x)*(22*x) + (5*x)*(40*x**3) + (5*x)*5 + (22*x)*(-11*x**2) + (22*x)*(56*x**3) + (-11*x**2)*(40*x**3) - 11*x**2*5 + (40*x**3)*(56*x**3) + (56*x**3)*5\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*x**2)*5 = -55*x**2\n (-11*x**2)*(22*x) = -242*x**3\n (-11*x**2)*(40*x**3) = -440*x**5\n (5*x)*5 = 25*x\n (5*x)*(22*x) = 110*x**2\n (5*x)*(40*x**3) = 200*x**4\n (56*x**3)*5 = 280*x**3\n (56*x**3)*(22*x) = 1232*x**4\n (56*x**3)*(40*x**3) = 2240*x**6\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 2240*x**6 - 440*x**5 + 200*x**4 + 1232*x**4 - 242*x**3 + 280*x**3 - 55*x**2 + 110*x**2 + 25*x\nCombining like terms, got 2240*x**6 - 440*x**5 + 1432*x**4 + 38*x**3 + 55*x**2 + 25*x\n#Step 7:\nCurrent expression: 2240*x**6 - 440*x**5 + 1432*x**4 + 38*x**3 + 55*x**2 + 25*x\nNo more calculations needed.\n2240*x**6 - 440*x**5 + 1432*x**4 + 38*x**3 + 55*x**2 + 25*x", "generated_answer": "2240*x**6 - 440*x**5 + 1432*x**4 + 38*x**3 + 55*x**2 + 25*x", "step_length": 7} {"cot_id": "c67a7d58c74335331b2e4101e958d2165df6e0131eef4ccd9f55a2edcd215a49", "datapoint": {"question": "Simplify this expression: -66*z**3*(-12*z**3 + 80*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "792*z**6 - 5280*z**5", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1176, "polynomial_expr": "-66*z**3*(-12*z**3 + 80*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -66*z**3*(-12*z**3 + 80*z**2)\nExpanding the part (-12*z**3 + 80*z**2) using the distributive property, and we got: (80*z**2)*(-66*z**3) + (-66*z**3)*(-12*z**3)\n#Step 2:\nCurrent expression: (80*z**2)*(-66*z**3) + (-66*z**3)*(-12*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*z**3)*(-66*z**3) = 792*z**6\n (80*z**2)*(-66*z**3) = -5280*z**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 792*z**6 - 5280*z**5\nNo more calculations needed.\n792*z**6 - 5280*z**5", "generated_answer": "792*z**6 - 5280*z**5", "step_length": 3} {"cot_id": "596833995619631cbdbf59ae38caa6ff24f7e010f01efaeed869bc48cc78afc2", "datapoint": {"question": "Calculate the following: 15*z**3*(4*z - 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "60*z**4 - 195*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1177, "polynomial_expr": "15*z**3*(4*z - 13)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 15*z**3*(4*z - 13)\nExpanding the part (4*z - 13) using the distributive property, and we got: -195*z**3 + (4*z)*(15*z**3)\n#Step 2:\nCurrent expression: -195*z**3 + (4*z)*(15*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -13*(15*z**3) = -195*z**3\n (4*z)*(15*z**3) = 60*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 60*z**4 - 195*z**3\nNo more calculations needed.\n60*z**4 - 195*z**3", "generated_answer": "60*z**4 - 195*z**3", "step_length": 3} {"cot_id": "fd0399101df58e783bf66c2282d9a88ffeca00611974aed5fe9b0c33a83bd142", "datapoint": {"question": "Calculate the following: (20 - 17*y**2)*(23*y**2 - 50*y + 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-391*y**4 + 850*y**3 - 67*y**2 - 1000*y + 620", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1178, "polynomial_expr": "(20 - 17*y**2)*(23*y**2 - 50*y + 31)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (20 - 17*y**2)*(23*y**2 - 50*y + 31)\nExpanding the part (20 - 17*y**2) using the distributive property, and we got: (-17*y**2)*(23*y**2 - 50*y + 31) + 20*(23*y**2 - 50*y + 31)\n#Step 2:\nCurrent expression: (-17*y**2)*(23*y**2 - 50*y + 31) + 20*(23*y**2 - 50*y + 31)\nSimplifying the partial expression: 20*(23*y**2 - 50*y + 31)\nExpanding the part (23*y**2 - 50*y + 31) using the distributive property, and we got: -50*y*20 + (23*y**2)*20 + 31*20\nReplacing 20*(23*y**2 - 50*y + 31) with -50*y*20 + (23*y**2)*20 + 31*20 in the overall expression.\n#Step 3:\nCurrent expression: -50*y*20 + (-17*y**2)*(23*y**2 - 50*y + 31) + (23*y**2)*20 + 620\nSimplifying the partial expression: (-17*y**2)*(23*y**2 - 50*y + 31)\nExpanding the part (23*y**2 - 50*y + 31) using the distributive property, and we got: (-50*y)*(-17*y**2) + 31*(-17*y**2) + (-17*y**2)*(23*y**2)\nReplacing (-17*y**2)*(23*y**2 - 50*y + 31) with (-50*y)*(-17*y**2) + 31*(-17*y**2) + (-17*y**2)*(23*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-50*y)*(-17*y**2) - 50*y*20 + 31*(-17)*y**2 + (-17*y**2)*(23*y**2) + (23*y**2)*20 + 620\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-50*y)*20 = -1000*y\n (-50*y)*(-17*y**2) = 850*y**3\n (23*y**2)*20 = 460*y**2\n (23*y**2)*(-17*y**2) = -391*y**4\n 31*-17*y**2 = -527*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -391*y**4 + 850*y**3 - 527*y**2 + 460*y**2 - 1000*y + 620\nCombining like terms, got -391*y**4 + 850*y**3 - 67*y**2 - 1000*y + 620\n#Step 6:\nCurrent expression: -391*y**4 + 850*y**3 - 67*y**2 - 1000*y + 620\nNo more calculations needed.\n-391*y**4 + 850*y**3 - 67*y**2 - 1000*y + 620", "generated_answer": "-391*y**4 + 850*y**3 - 67*y**2 - 1000*y + 620", "step_length": 6} {"cot_id": "2167285c95f3e8dccb9c8be0c9d2d6b4c6a0f088e3a6511033e95663b3d7cc72", "datapoint": {"question": "Simplify this expression: (38*x**3 + 39*x + 22)*(15*x**3 + 14*x**2 + 45*x - 22)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "570*x**6 + 532*x**5 + 2295*x**4 + 40*x**3 + 2063*x**2 + 132*x - 484", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1179, "polynomial_expr": "(38*x**3 + 39*x + 22)*(15*x**3 + 14*x**2 + 45*x - 22)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (38*x**3 + 39*x + 22)*(15*x**3 + 14*x**2 + 45*x - 22)\nExpanding the part (38*x**3 + 39*x + 22) using the distributive property, and we got: (39*x)*(15*x**3 + 14*x**2 + 45*x - 22) + (38*x**3)*(15*x**3 + 14*x**2 + 45*x - 22) + 22*(15*x**3 + 14*x**2 + 45*x - 22)\n#Step 2:\nCurrent expression: (39*x)*(15*x**3 + 14*x**2 + 45*x - 22) + (38*x**3)*(15*x**3 + 14*x**2 + 45*x - 22) + 22*(15*x**3 + 14*x**2 + 45*x - 22)\nSimplifying the partial expression: 22*(15*x**3 + 14*x**2 + 45*x - 22)\nExpanding the part (15*x**3 + 14*x**2 + 45*x - 22) using the distributive property, and we got: (45*x)*22 + (14*x**2)*22 + (15*x**3)*22 - 22*22\nReplacing 22*(15*x**3 + 14*x**2 + 45*x - 22) with (45*x)*22 + (14*x**2)*22 + (15*x**3)*22 - 22*22 in the overall expression.\n#Step 3:\nCurrent expression: (39*x)*(15*x**3 + 14*x**2 + 45*x - 22) + (45*x)*22 + (14*x**2)*22 + (15*x**3)*22 + (38*x**3)*(15*x**3 + 14*x**2 + 45*x - 22) - 484\nSimplifying the partial expression: (38*x**3)*(15*x**3 + 14*x**2 + 45*x - 22)\nExpanding the part (15*x**3 + 14*x**2 + 45*x - 22) using the distributive property, and we got: -836*x**3 + (45*x)*(38*x**3) + (14*x**2)*(38*x**3) + (15*x**3)*(38*x**3)\nReplacing (38*x**3)*(15*x**3 + 14*x**2 + 45*x - 22) with -836*x**3 + (45*x)*(38*x**3) + (14*x**2)*(38*x**3) + (15*x**3)*(38*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -22*38*x**3 + (39*x)*(15*x**3 + 14*x**2 + 45*x - 22) + (45*x)*(38*x**3) + (45*x)*22 + (14*x**2)*(38*x**3) + (14*x**2)*22 + (15*x**3)*(38*x**3) + (15*x**3)*22 - 484\nSimplifying the partial expression: (39*x)*(15*x**3 + 14*x**2 + 45*x - 22)\nExpanding the part (15*x**3 + 14*x**2 + 45*x - 22) using the distributive property, and we got: -858*x + (39*x)*(45*x) + (39*x)*(14*x**2) + (39*x)*(15*x**3)\nReplacing (39*x)*(15*x**3 + 14*x**2 + 45*x - 22) with -858*x + (39*x)*(45*x) + (39*x)*(14*x**2) + (39*x)*(15*x**3) in the overall expression.\n#Step 5:\nCurrent expression: -22*38*x**3 - 22*39*x + (39*x)*(45*x) + (39*x)*(14*x**2) + (39*x)*(15*x**3) + (45*x)*(38*x**3) + (45*x)*22 + (14*x**2)*(38*x**3) + (14*x**2)*22 + (15*x**3)*(38*x**3) + (15*x**3)*22 - 484\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (14*x**2)*22 = 308*x**2\n (14*x**2)*(38*x**3) = 532*x**5\n (14*x**2)*(39*x) = 546*x**3\n (15*x**3)*22 = 330*x**3\n (15*x**3)*(38*x**3) = 570*x**6\n (15*x**3)*(39*x) = 585*x**4\n (45*x)*22 = 990*x\n (45*x)*(38*x**3) = 1710*x**4\n (45*x)*(39*x) = 1755*x**2\n -22*38*x**3 = -836*x**3\n -22*39*x = -858*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 570*x**6 + 532*x**5 + 585*x**4 + 1710*x**4 - 836*x**3 + 330*x**3 + 546*x**3 + 308*x**2 + 1755*x**2 - 858*x + 990*x - 484\nCombining like terms, got 570*x**6 + 532*x**5 + 2295*x**4 + 40*x**3 + 2063*x**2 + 132*x - 484\n#Step 7:\nCurrent expression: 570*x**6 + 532*x**5 + 2295*x**4 + 40*x**3 + 2063*x**2 + 132*x - 484\nNo more calculations needed.\n570*x**6 + 532*x**5 + 2295*x**4 + 40*x**3 + 2063*x**2 + 132*x - 484", "generated_answer": "570*x**6 + 532*x**5 + 2295*x**4 + 40*x**3 + 2063*x**2 + 132*x - 484", "step_length": 7} {"cot_id": "49365d7374984fab97208bd4977f9c5f4f324aa68813d25d6b35c10ef6814f18", "datapoint": {"question": "Simplify this expression: (13*z**3 + 3*z)*(-42*z**3 + 37*z**2 - 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-546*z**6 + 481*z**5 - 126*z**4 - 344*z**3 - 105*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1180, "polynomial_expr": "(13*z**3 + 3*z)*(-42*z**3 + 37*z**2 - 35)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (13*z**3 + 3*z)*(-42*z**3 + 37*z**2 - 35)\nExpanding the part (13*z**3 + 3*z) using the distributive property, and we got: (3*z)*(-42*z**3 + 37*z**2 - 35) + (13*z**3)*(-42*z**3 + 37*z**2 - 35)\n#Step 2:\nCurrent expression: (3*z)*(-42*z**3 + 37*z**2 - 35) + (13*z**3)*(-42*z**3 + 37*z**2 - 35)\nSimplifying the partial expression: (3*z)*(-42*z**3 + 37*z**2 - 35)\nExpanding the part (-42*z**3 + 37*z**2 - 35) using the distributive property, and we got: -105*z + (3*z)*(37*z**2) + (3*z)*(-42*z**3)\nReplacing (3*z)*(-42*z**3 + 37*z**2 - 35) with -105*z + (3*z)*(37*z**2) + (3*z)*(-42*z**3) in the overall expression.\n#Step 3:\nCurrent expression: -35*3*z + (3*z)*(37*z**2) + (3*z)*(-42*z**3) + (13*z**3)*(-42*z**3 + 37*z**2 - 35)\nSimplifying the partial expression: (13*z**3)*(-42*z**3 + 37*z**2 - 35)\nExpanding the part (-42*z**3 + 37*z**2 - 35) using the distributive property, and we got: -455*z**3 + (37*z**2)*(13*z**3) + (-42*z**3)*(13*z**3)\nReplacing (13*z**3)*(-42*z**3 + 37*z**2 - 35) with -455*z**3 + (37*z**2)*(13*z**3) + (-42*z**3)*(13*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -35*13*z**3 - 35*3*z + (3*z)*(37*z**2) + (3*z)*(-42*z**3) + (37*z**2)*(13*z**3) + (-42*z**3)*(13*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*z**3)*(3*z) = -126*z**4\n (-42*z**3)*(13*z**3) = -546*z**6\n (37*z**2)*(3*z) = 111*z**3\n (37*z**2)*(13*z**3) = 481*z**5\n -35*3*z = -105*z\n -35*13*z**3 = -455*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -546*z**6 + 481*z**5 - 126*z**4 - 455*z**3 + 111*z**3 - 105*z\nCombining like terms, got -546*z**6 + 481*z**5 - 126*z**4 - 344*z**3 - 105*z\n#Step 6:\nCurrent expression: -546*z**6 + 481*z**5 - 126*z**4 - 344*z**3 - 105*z\nNo more calculations needed.\n-546*z**6 + 481*z**5 - 126*z**4 - 344*z**3 - 105*z", "generated_answer": "-546*z**6 + 481*z**5 - 126*z**4 - 344*z**3 - 105*z", "step_length": 6} {"cot_id": "08bbe512820fcaca6797fb79e5f3226a85a94a5a1ab84bf28cd5cb384f9064f6", "datapoint": {"question": "Simplify this expression: (23 - 54*z**2)*(61*z**3 - 15)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-3294*z**5 + 1403*z**3 + 810*z**2 - 345", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1181, "polynomial_expr": "(23 - 54*z**2)*(61*z**3 - 15)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (23 - 54*z**2)*(61*z**3 - 15)\nExpanding the part (61*z**3 - 15) using the distributive property, and we got: (61*z**3)*(23 - 54*z**2) - 15*(23 - 54*z**2)\n#Step 2:\nCurrent expression: (61*z**3)*(23 - 54*z**2) - 15*(23 - 54*z**2)\nSimplifying the partial expression: -15*(23 - 54*z**2)\nExpanding the part (23 - 54*z**2) using the distributive property, and we got: -54*z**2*(-15) + 23*(-15)\nReplacing -15*(23 - 54*z**2) with -54*z**2*(-15) + 23*(-15) in the overall expression.\n#Step 3:\nCurrent expression: -54*z**2*(-15) + (61*z**3)*(23 - 54*z**2) - 345\nSimplifying the partial expression: (61*z**3)*(23 - 54*z**2)\nExpanding the part (23 - 54*z**2) using the distributive property, and we got: 23*(61*z**3) + (-54*z**2)*(61*z**3)\nReplacing (61*z**3)*(23 - 54*z**2) with 23*(61*z**3) + (-54*z**2)*(61*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 23*61*z**3 + (-54*z**2)*(61*z**3) - 54*z**2*(-15) - 345\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-54*z**2)*-15 = 810*z**2\n (-54*z**2)*(61*z**3) = -3294*z**5\n 23*61*z**3 = 1403*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -3294*z**5 + 1403*z**3 + 810*z**2 - 345\nNo more calculations needed.\n-3294*z**5 + 1403*z**3 + 810*z**2 - 345", "generated_answer": "-3294*z**5 + 1403*z**3 + 810*z**2 - 345", "step_length": 5} {"cot_id": "def82c7a87051e8f9d15ab46136648770b6089a55b7627433a7fed272aeab361", "datapoint": {"question": "Calculate the following: (-68*x**3 - 40*x)*(-19*x**3 - 3*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1292*x**6 + 964*x**4 + 120*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1182, "polynomial_expr": "(-68*x**3 - 40*x)*(-19*x**3 - 3*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-68*x**3 - 40*x)*(-19*x**3 - 3*x)\nExpanding the part (-68*x**3 - 40*x) using the distributive property, and we got: (-40*x)*(-19*x**3 - 3*x) + (-68*x**3)*(-19*x**3 - 3*x)\n#Step 2:\nCurrent expression: (-40*x)*(-19*x**3 - 3*x) + (-68*x**3)*(-19*x**3 - 3*x)\nSimplifying the partial expression: (-68*x**3)*(-19*x**3 - 3*x)\nExpanding the part (-19*x**3 - 3*x) using the distributive property, and we got: (-3*x)*(-68*x**3) + (-68*x**3)*(-19*x**3)\nReplacing (-68*x**3)*(-19*x**3 - 3*x) with (-3*x)*(-68*x**3) + (-68*x**3)*(-19*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-40*x)*(-19*x**3 - 3*x) + (-3*x)*(-68*x**3) + (-68*x**3)*(-19*x**3)\nSimplifying the partial expression: (-40*x)*(-19*x**3 - 3*x)\nExpanding the part (-19*x**3 - 3*x) using the distributive property, and we got: (-40*x)*(-3*x) + (-40*x)*(-19*x**3)\nReplacing (-40*x)*(-19*x**3 - 3*x) with (-40*x)*(-3*x) + (-40*x)*(-19*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-40*x)*(-3*x) + (-40*x)*(-19*x**3) + (-3*x)*(-68*x**3) + (-68*x**3)*(-19*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*x**3)*(-68*x**3) = 1292*x**6\n (-19*x**3)*(-40*x) = 760*x**4\n (-3*x)*(-68*x**3) = 204*x**4\n (-3*x)*(-40*x) = 120*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1292*x**6 + 204*x**4 + 760*x**4 + 120*x**2\nCombining like terms, got 1292*x**6 + 964*x**4 + 120*x**2\n#Step 6:\nCurrent expression: 1292*x**6 + 964*x**4 + 120*x**2\nNo more calculations needed.\n1292*x**6 + 964*x**4 + 120*x**2", "generated_answer": "1292*x**6 + 964*x**4 + 120*x**2", "step_length": 6} {"cot_id": "64fc787d00398ffdff26c6978c9192b57ce907ab2596aa1a1f60758909dc559b", "datapoint": {"question": "Simplify this expression: (-92*y**2 - 1)*(-50*y**3 + 71*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "4600*y**5 - 6482*y**3 - 71*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1183, "polynomial_expr": "(-92*y**2 - 1)*(-50*y**3 + 71*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-92*y**2 - 1)*(-50*y**3 + 71*y)\nExpanding the part (-92*y**2 - 1) using the distributive property, and we got: (-92*y**2)*(-50*y**3 + 71*y) - (-50*y**3 + 71*y)\n#Step 2:\nCurrent expression: (-92*y**2)*(-50*y**3 + 71*y) - (-50*y**3 + 71*y)\nSimplifying the partial expression: -(-50*y**3 + 71*y)\nExpanding the part (-50*y**3 + 71*y) using the distributive property, and we got: (71*y)*(-1) - 50*y**3*(-1)\nReplacing -(-50*y**3 + 71*y) with (71*y)*(-1) - 50*y**3*(-1) in the overall expression.\n#Step 3:\nCurrent expression: (71*y)*(-1) + (-92*y**2)*(-50*y**3 + 71*y) - 50*y**3*(-1)\nSimplifying the partial expression: (-92*y**2)*(-50*y**3 + 71*y)\nExpanding the part (-50*y**3 + 71*y) using the distributive property, and we got: (71*y)*(-92*y**2) + (-92*y**2)*(-50*y**3)\nReplacing (-92*y**2)*(-50*y**3 + 71*y) with (71*y)*(-92*y**2) + (-92*y**2)*(-50*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (71*y)*(-92*y**2) + (71*y)*(-1) + (-92*y**2)*(-50*y**3) - 50*y**3*(-1)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-50*y**3)*-1 = 50*y**3\n (-50*y**3)*(-92*y**2) = 4600*y**5\n (71*y)*-1 = -71*y\n (71*y)*(-92*y**2) = -6532*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 4600*y**5 - 6532*y**3 + 50*y**3 - 71*y\nCombining like terms, got 4600*y**5 - 6482*y**3 - 71*y\n#Step 6:\nCurrent expression: 4600*y**5 - 6482*y**3 - 71*y\nNo more calculations needed.\n4600*y**5 - 6482*y**3 - 71*y", "generated_answer": "4600*y**5 - 6482*y**3 - 71*y", "step_length": 6} {"cot_id": "8e4bb49170d857f362781fcad4c0dc815e082fbfa75660f91fc57bf4acd316ea", "datapoint": {"question": "Calculate the following: (19*y**2 + 42*y)*(14*y**3 + 48*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "266*y**5 + 588*y**4 + 912*y**3 + 2016*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1184, "polynomial_expr": "(19*y**2 + 42*y)*(14*y**3 + 48*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (19*y**2 + 42*y)*(14*y**3 + 48*y)\nExpanding the part (14*y**3 + 48*y) using the distributive property, and we got: (48*y)*(19*y**2 + 42*y) + (14*y**3)*(19*y**2 + 42*y)\n#Step 2:\nCurrent expression: (48*y)*(19*y**2 + 42*y) + (14*y**3)*(19*y**2 + 42*y)\nSimplifying the partial expression: (14*y**3)*(19*y**2 + 42*y)\nExpanding the part (19*y**2 + 42*y) using the distributive property, and we got: (42*y)*(14*y**3) + (19*y**2)*(14*y**3)\nReplacing (14*y**3)*(19*y**2 + 42*y) with (42*y)*(14*y**3) + (19*y**2)*(14*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (42*y)*(14*y**3) + (48*y)*(19*y**2 + 42*y) + (19*y**2)*(14*y**3)\nSimplifying the partial expression: (48*y)*(19*y**2 + 42*y)\nExpanding the part (19*y**2 + 42*y) using the distributive property, and we got: (42*y)*(48*y) + (48*y)*(19*y**2)\nReplacing (48*y)*(19*y**2 + 42*y) with (42*y)*(48*y) + (48*y)*(19*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (42*y)*(48*y) + (42*y)*(14*y**3) + (48*y)*(19*y**2) + (19*y**2)*(14*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (19*y**2)*(14*y**3) = 266*y**5\n (19*y**2)*(48*y) = 912*y**3\n (42*y)*(14*y**3) = 588*y**4\n (42*y)*(48*y) = 2016*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 266*y**5 + 588*y**4 + 912*y**3 + 2016*y**2\nNo more calculations needed.\n266*y**5 + 588*y**4 + 912*y**3 + 2016*y**2", "generated_answer": "266*y**5 + 588*y**4 + 912*y**3 + 2016*y**2", "step_length": 5} {"cot_id": "74e1d1f4797d0ee092a658049054187243cb18de6290efc16fdd3f4a61f27832", "datapoint": {"question": "Calculate the following: (21*z - 45)*(-17*z**2 + 28*z - 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-357*z**3 + 1353*z**2 - 2268*z + 2160", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1185, "polynomial_expr": "(21*z - 45)*(-17*z**2 + 28*z - 48)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21*z - 45)*(-17*z**2 + 28*z - 48)\nExpanding the part (21*z - 45) using the distributive property, and we got: (21*z)*(-17*z**2 + 28*z - 48) - 45*(-17*z**2 + 28*z - 48)\n#Step 2:\nCurrent expression: (21*z)*(-17*z**2 + 28*z - 48) - 45*(-17*z**2 + 28*z - 48)\nSimplifying the partial expression: -45*(-17*z**2 + 28*z - 48)\nExpanding the part (-17*z**2 + 28*z - 48) using the distributive property, and we got: (28*z)*(-45) - 17*z**2*(-45) - 48*(-45)\nReplacing -45*(-17*z**2 + 28*z - 48) with (28*z)*(-45) - 17*z**2*(-45) - 48*(-45) in the overall expression.\n#Step 3:\nCurrent expression: (21*z)*(-17*z**2 + 28*z - 48) + (28*z)*(-45) - 17*z**2*(-45) + 2160\nSimplifying the partial expression: (21*z)*(-17*z**2 + 28*z - 48)\nExpanding the part (-17*z**2 + 28*z - 48) using the distributive property, and we got: -1008*z + (21*z)*(28*z) + (21*z)*(-17*z**2)\nReplacing (21*z)*(-17*z**2 + 28*z - 48) with -1008*z + (21*z)*(28*z) + (21*z)*(-17*z**2) in the overall expression.\n#Step 4:\nCurrent expression: -48*21*z + (21*z)*(28*z) + (21*z)*(-17*z**2) + (28*z)*(-45) - 17*z**2*(-45) + 2160\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-17*z**2)*-45 = 765*z**2\n (-17*z**2)*(21*z) = -357*z**3\n (28*z)*-45 = -1260*z\n (28*z)*(21*z) = 588*z**2\n -48*21*z = -1008*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -357*z**3 + 588*z**2 + 765*z**2 - 1260*z - 1008*z + 2160\nCombining like terms, got -357*z**3 + 1353*z**2 - 2268*z + 2160\n#Step 6:\nCurrent expression: -357*z**3 + 1353*z**2 - 2268*z + 2160\nNo more calculations needed.\n-357*z**3 + 1353*z**2 - 2268*z + 2160", "generated_answer": "-357*z**3 + 1353*z**2 - 2268*z + 2160", "step_length": 6} {"cot_id": "ca39faaab1b52f1bfc833444bca1d1108df95812dd7d1724340169bafba22b5a", "datapoint": {"question": "Calculate the following: x**3*(-20*x**2 - 35*x + 11)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-20*x**5 - 35*x**4 + 11*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1186, "polynomial_expr": "x**3*(-20*x**2 - 35*x + 11)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: x**3*(-20*x**2 - 35*x + 11)\nExpanding the part (-20*x**2 - 35*x + 11) using the distributive property, and we got: (-35*x)*x**3 + (-20*x**2)*x**3 + 11*x**3\n#Step 2:\nCurrent expression: (-35*x)*x**3 + (-20*x**2)*x**3 + 11*x**3\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*x)*x**3 = -35*x**4\n (-20*x**2)*x**3 = -20*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -20*x**5 - 35*x**4 + 11*x**3\nNo more calculations needed.\n-20*x**5 - 35*x**4 + 11*x**3", "generated_answer": "-20*x**5 - 35*x**4 + 11*x**3", "step_length": 3} {"cot_id": "4ddca81375143f4ecbb42ede5f6cfccc8b36d6205e8d406c9159a6b563670b0f", "datapoint": {"question": "Calculate the following: -2*x**3*(-23*x**3 + 9*x**2 - 46*x - 11)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "46*x**6 - 18*x**5 + 92*x**4 + 22*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1187, "polynomial_expr": "-2*x**3*(-23*x**3 + 9*x**2 - 46*x - 11)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -2*x**3*(-23*x**3 + 9*x**2 - 46*x - 11)\nExpanding the part (-23*x**3 + 9*x**2 - 46*x - 11) using the distributive property, and we got: (-46*x)*(-2*x**3) - (-1)*22*x**3 + (9*x**2)*(-2*x**3) + (-23*x**3)*(-2*x**3)\n#Step 2:\nCurrent expression: (-46*x)*(-2*x**3) - (-1)*22*x**3 + (9*x**2)*(-2*x**3) + (-23*x**3)*(-2*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -11*(-2*x**3) = 22*x**3\n (-46*x)*(-2*x**3) = 92*x**4\n (-23*x**3)*(-2*x**3) = 46*x**6\n (9*x**2)*(-2*x**3) = -18*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 46*x**6 - 18*x**5 + 92*x**4 + 22*x**3\nNo more calculations needed.\n46*x**6 - 18*x**5 + 92*x**4 + 22*x**3", "generated_answer": "46*x**6 - 18*x**5 + 92*x**4 + 22*x**3", "step_length": 3} {"cot_id": "3f28d3c334b2a2c78c61e329f97ff008fb194f3e57e51f8f34021775872b461b", "datapoint": {"question": "Simplify this expression: (34 - 43*z)*(-25*z**3 + 18*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1075*z**4 - 1624*z**3 + 612*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1188, "polynomial_expr": "(34 - 43*z)*(-25*z**3 + 18*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (34 - 43*z)*(-25*z**3 + 18*z**2)\nExpanding the part (34 - 43*z) using the distributive property, and we got: (-43*z)*(-25*z**3 + 18*z**2) + 34*(-25*z**3 + 18*z**2)\n#Step 2:\nCurrent expression: (-43*z)*(-25*z**3 + 18*z**2) + 34*(-25*z**3 + 18*z**2)\nSimplifying the partial expression: 34*(-25*z**3 + 18*z**2)\nExpanding the part (-25*z**3 + 18*z**2) using the distributive property, and we got: (18*z**2)*34 - 25*z**3*34\nReplacing 34*(-25*z**3 + 18*z**2) with (18*z**2)*34 - 25*z**3*34 in the overall expression.\n#Step 3:\nCurrent expression: (-43*z)*(-25*z**3 + 18*z**2) + (18*z**2)*34 - 25*z**3*34\nSimplifying the partial expression: (-43*z)*(-25*z**3 + 18*z**2)\nExpanding the part (-25*z**3 + 18*z**2) using the distributive property, and we got: (-43*z)*(18*z**2) + (-43*z)*(-25*z**3)\nReplacing (-43*z)*(-25*z**3 + 18*z**2) with (-43*z)*(18*z**2) + (-43*z)*(-25*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-43*z)*(18*z**2) + (-43*z)*(-25*z**3) + (18*z**2)*34 - 25*z**3*34\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*z**3)*34 = -850*z**3\n (-25*z**3)*(-43*z) = 1075*z**4\n (18*z**2)*34 = 612*z**2\n (18*z**2)*(-43*z) = -774*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1075*z**4 - 850*z**3 - 774*z**3 + 612*z**2\nCombining like terms, got 1075*z**4 - 1624*z**3 + 612*z**2\n#Step 6:\nCurrent expression: 1075*z**4 - 1624*z**3 + 612*z**2\nNo more calculations needed.\n1075*z**4 - 1624*z**3 + 612*z**2", "generated_answer": "1075*z**4 - 1624*z**3 + 612*z**2", "step_length": 6} {"cot_id": "f878df94c236752ee778a290ef0a460c5817ef594746b7557d77f818b1f4ae65", "datapoint": {"question": "Calculate the following: 3*y*(-27*y**2 - 12*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-81*y**3 - 36*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1189, "polynomial_expr": "3*y*(-27*y**2 - 12*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 3*y*(-27*y**2 - 12*y)\nExpanding the part (-27*y**2 - 12*y) using the distributive property, and we got: (-12*y)*(3*y) + (3*y)*(-27*y**2)\n#Step 2:\nCurrent expression: (-12*y)*(3*y) + (3*y)*(-27*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*y**2)*(3*y) = -81*y**3\n (-12*y)*(3*y) = -36*y**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -81*y**3 - 36*y**2\nNo more calculations needed.\n-81*y**3 - 36*y**2", "generated_answer": "-81*y**3 - 36*y**2", "step_length": 3} {"cot_id": "ed86e134216846bb04cc809ed0369f54366d026b14c91a279996a3a3b4712b34", "datapoint": {"question": "Simplify this expression: (-19*z**2 - 53*z + 9)*(52*z**3 - 19*z**2 + 3*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-988*z**5 - 2395*z**4 + 1418*z**3 - 330*z**2 + 27*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1190, "polynomial_expr": "(-19*z**2 - 53*z + 9)*(52*z**3 - 19*z**2 + 3*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-19*z**2 - 53*z + 9)*(52*z**3 - 19*z**2 + 3*z)\nExpanding the part (-19*z**2 - 53*z + 9) using the distributive property, and we got: (-53*z)*(52*z**3 - 19*z**2 + 3*z) + (-19*z**2)*(52*z**3 - 19*z**2 + 3*z) + 9*(52*z**3 - 19*z**2 + 3*z)\n#Step 2:\nCurrent expression: (-53*z)*(52*z**3 - 19*z**2 + 3*z) + (-19*z**2)*(52*z**3 - 19*z**2 + 3*z) + 9*(52*z**3 - 19*z**2 + 3*z)\nSimplifying the partial expression: 9*(52*z**3 - 19*z**2 + 3*z)\nExpanding the part (52*z**3 - 19*z**2 + 3*z) using the distributive property, and we got: (3*z)*9 - 19*z**2*9 + (52*z**3)*9\nReplacing 9*(52*z**3 - 19*z**2 + 3*z) with (3*z)*9 - 19*z**2*9 + (52*z**3)*9 in the overall expression.\n#Step 3:\nCurrent expression: (-53*z)*(52*z**3 - 19*z**2 + 3*z) + (3*z)*9 + (-19*z**2)*(52*z**3 - 19*z**2 + 3*z) - 19*z**2*9 + (52*z**3)*9\nSimplifying the partial expression: (-53*z)*(52*z**3 - 19*z**2 + 3*z)\nExpanding the part (52*z**3 - 19*z**2 + 3*z) using the distributive property, and we got: (-53*z)*(3*z) + (-53*z)*(-19*z**2) + (-53*z)*(52*z**3)\nReplacing (-53*z)*(52*z**3 - 19*z**2 + 3*z) with (-53*z)*(3*z) + (-53*z)*(-19*z**2) + (-53*z)*(52*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-53*z)*(3*z) + (-53*z)*(-19*z**2) + (-53*z)*(52*z**3) + (3*z)*9 + (-19*z**2)*(52*z**3 - 19*z**2 + 3*z) - 19*z**2*9 + (52*z**3)*9\nSimplifying the partial expression: (-19*z**2)*(52*z**3 - 19*z**2 + 3*z)\nExpanding the part (52*z**3 - 19*z**2 + 3*z) using the distributive property, and we got: (3*z)*(-19*z**2) + (-19*z**2)*(52*z**3) + (-19*z**2)*(-19*z**2)\nReplacing (-19*z**2)*(52*z**3 - 19*z**2 + 3*z) with (3*z)*(-19*z**2) + (-19*z**2)*(52*z**3) + (-19*z**2)*(-19*z**2) in the overall expression.\n#Step 5:\nCurrent expression: (-53*z)*(3*z) + (-53*z)*(-19*z**2) + (-53*z)*(52*z**3) + (3*z)*(-19*z**2) + (3*z)*9 + (-19*z**2)*(52*z**3) + (-19*z**2)*(-19*z**2) - 19*z**2*9 + (52*z**3)*9\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*z**2)*9 = -171*z**2\n (-19*z**2)*(-53*z) = 1007*z**3\n (-19*z**2)*(-19*z**2) = 361*z**4\n (3*z)*9 = 27*z\n (3*z)*(-53*z) = -159*z**2\n (3*z)*(-19*z**2) = -57*z**3\n (52*z**3)*9 = 468*z**3\n (52*z**3)*(-53*z) = -2756*z**4\n (52*z**3)*(-19*z**2) = -988*z**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -988*z**5 - 2756*z**4 + 361*z**4 - 57*z**3 + 468*z**3 + 1007*z**3 - 171*z**2 - 159*z**2 + 27*z\nCombining like terms, got -988*z**5 - 2395*z**4 + 1418*z**3 - 330*z**2 + 27*z\n#Step 7:\nCurrent expression: -988*z**5 - 2395*z**4 + 1418*z**3 - 330*z**2 + 27*z\nNo more calculations needed.\n-988*z**5 - 2395*z**4 + 1418*z**3 - 330*z**2 + 27*z", "generated_answer": "-988*z**5 - 2395*z**4 + 1418*z**3 - 330*z**2 + 27*z", "step_length": 7} {"cot_id": "1839f0b00cd904fd90d0d2de1aa8259d4f54ac249b6985880d12f98e4f493f7f", "datapoint": {"question": "Calculate the following: (8*y**2 - 18)*(43*y**3 - 42*y**2 - 8*y + 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "344*y**5 - 336*y**4 - 838*y**3 + 916*y**2 + 144*y - 360", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1191, "polynomial_expr": "(8*y**2 - 18)*(43*y**3 - 42*y**2 - 8*y + 20)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (8*y**2 - 18)*(43*y**3 - 42*y**2 - 8*y + 20)\nExpanding the part (8*y**2 - 18) using the distributive property, and we got: (8*y**2)*(43*y**3 - 42*y**2 - 8*y + 20) - 18*(43*y**3 - 42*y**2 - 8*y + 20)\n#Step 2:\nCurrent expression: (8*y**2)*(43*y**3 - 42*y**2 - 8*y + 20) - 18*(43*y**3 - 42*y**2 - 8*y + 20)\nSimplifying the partial expression: -18*(43*y**3 - 42*y**2 - 8*y + 20)\nExpanding the part (43*y**3 - 42*y**2 - 8*y + 20) using the distributive property, and we got: -8*y*(-18) - 42*y**2*(-18) + (43*y**3)*(-18) + 20*(-18)\nReplacing -18*(43*y**3 - 42*y**2 - 8*y + 20) with -8*y*(-18) - 42*y**2*(-18) + (43*y**3)*(-18) + 20*(-18) in the overall expression.\n#Step 3:\nCurrent expression: -8*y*(-18) - 42*y**2*(-18) + (8*y**2)*(43*y**3 - 42*y**2 - 8*y + 20) + (43*y**3)*(-18) - 360\nSimplifying the partial expression: (8*y**2)*(43*y**3 - 42*y**2 - 8*y + 20)\nExpanding the part (43*y**3 - 42*y**2 - 8*y + 20) using the distributive property, and we got: (-8*y)*(8*y**2) + 20*(8*y**2) + (-42*y**2)*(8*y**2) + (8*y**2)*(43*y**3)\nReplacing (8*y**2)*(43*y**3 - 42*y**2 - 8*y + 20) with (-8*y)*(8*y**2) + 20*(8*y**2) + (-42*y**2)*(8*y**2) + (8*y**2)*(43*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-8*y)*(8*y**2) - 8*y*(-18) + 20*8*y**2 + (-42*y**2)*(8*y**2) - 42*y**2*(-18) + (8*y**2)*(43*y**3) + (43*y**3)*(-18) - 360\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*y**2)*-18 = 756*y**2\n (-42*y**2)*(8*y**2) = -336*y**4\n (-8*y)*-18 = 144*y\n (-8*y)*(8*y**2) = -64*y**3\n (43*y**3)*-18 = -774*y**3\n (43*y**3)*(8*y**2) = 344*y**5\n 20*8*y**2 = 160*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 344*y**5 - 336*y**4 - 774*y**3 - 64*y**3 + 160*y**2 + 756*y**2 + 144*y - 360\nCombining like terms, got 344*y**5 - 336*y**4 - 838*y**3 + 916*y**2 + 144*y - 360\n#Step 6:\nCurrent expression: 344*y**5 - 336*y**4 - 838*y**3 + 916*y**2 + 144*y - 360\nNo more calculations needed.\n344*y**5 - 336*y**4 - 838*y**3 + 916*y**2 + 144*y - 360", "generated_answer": "344*y**5 - 336*y**4 - 838*y**3 + 916*y**2 + 144*y - 360", "step_length": 6} {"cot_id": "1969ac8de012c0863b9ec76e887d04ec0946fc31fa6f27f3174de84c5adef712", "datapoint": {"question": "Calculate the following: 12*y**3*(2*y**3 + 2*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "24*y**6 + 24*y**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1192, "polynomial_expr": "12*y**3*(2*y**3 + 2*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 12*y**3*(2*y**3 + 2*y)\nExpanding the part (2*y**3 + 2*y) using the distributive property, and we got: (2*y)*(12*y**3) + (2*y**3)*(12*y**3)\n#Step 2:\nCurrent expression: (2*y)*(12*y**3) + (2*y**3)*(12*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (2*y)*(12*y**3) = 24*y**4\n (2*y**3)*(12*y**3) = 24*y**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 24*y**6 + 24*y**4\nNo more calculations needed.\n24*y**6 + 24*y**4", "generated_answer": "24*y**6 + 24*y**4", "step_length": 3} {"cot_id": "b622f5b73f298f1d3e71aaacce7c8a314df766918f168478bb32172a683ea232", "datapoint": {"question": "Calculate the following: (-38*z**2 + 19*z + 28)*(-2*z**3 + 45*z**2 + 30*z + 22)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "76*z**5 - 1748*z**4 - 341*z**3 + 994*z**2 + 1258*z + 616", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1193, "polynomial_expr": "(-38*z**2 + 19*z + 28)*(-2*z**3 + 45*z**2 + 30*z + 22)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-38*z**2 + 19*z + 28)*(-2*z**3 + 45*z**2 + 30*z + 22)\nExpanding the part (-38*z**2 + 19*z + 28) using the distributive property, and we got: (19*z)*(-2*z**3 + 45*z**2 + 30*z + 22) + (-38*z**2)*(-2*z**3 + 45*z**2 + 30*z + 22) + 28*(-2*z**3 + 45*z**2 + 30*z + 22)\n#Step 2:\nCurrent expression: (19*z)*(-2*z**3 + 45*z**2 + 30*z + 22) + (-38*z**2)*(-2*z**3 + 45*z**2 + 30*z + 22) + 28*(-2*z**3 + 45*z**2 + 30*z + 22)\nSimplifying the partial expression: 28*(-2*z**3 + 45*z**2 + 30*z + 22)\nExpanding the part (-2*z**3 + 45*z**2 + 30*z + 22) using the distributive property, and we got: (30*z)*28 + (45*z**2)*28 - 2*z**3*28 + 22*28\nReplacing 28*(-2*z**3 + 45*z**2 + 30*z + 22) with (30*z)*28 + (45*z**2)*28 - 2*z**3*28 + 22*28 in the overall expression.\n#Step 3:\nCurrent expression: (19*z)*(-2*z**3 + 45*z**2 + 30*z + 22) + (30*z)*28 + (-38*z**2)*(-2*z**3 + 45*z**2 + 30*z + 22) + (45*z**2)*28 - 2*z**3*28 + 616\nSimplifying the partial expression: (-38*z**2)*(-2*z**3 + 45*z**2 + 30*z + 22)\nExpanding the part (-2*z**3 + 45*z**2 + 30*z + 22) using the distributive property, and we got: 22*(-38*z**2) + (30*z)*(-38*z**2) + (-38*z**2)*(45*z**2) + (-38*z**2)*(-2*z**3)\nReplacing (-38*z**2)*(-2*z**3 + 45*z**2 + 30*z + 22) with 22*(-38*z**2) + (30*z)*(-38*z**2) + (-38*z**2)*(45*z**2) + (-38*z**2)*(-2*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 22*(-38)*z**2 + (19*z)*(-2*z**3 + 45*z**2 + 30*z + 22) + (30*z)*(-38*z**2) + (30*z)*28 + (-38*z**2)*(45*z**2) + (-38*z**2)*(-2*z**3) + (45*z**2)*28 - 2*z**3*28 + 616\nSimplifying the partial expression: (19*z)*(-2*z**3 + 45*z**2 + 30*z + 22)\nExpanding the part (-2*z**3 + 45*z**2 + 30*z + 22) using the distributive property, and we got: 22*(19*z) + (19*z)*(30*z) + (19*z)*(45*z**2) + (19*z)*(-2*z**3)\nReplacing (19*z)*(-2*z**3 + 45*z**2 + 30*z + 22) with 22*(19*z) + (19*z)*(30*z) + (19*z)*(45*z**2) + (19*z)*(-2*z**3) in the overall expression.\n#Step 5:\nCurrent expression: 22*(-38)*z**2 + 22*19*z + (19*z)*(30*z) + (19*z)*(45*z**2) + (19*z)*(-2*z**3) + (30*z)*(-38*z**2) + (30*z)*28 + (-38*z**2)*(45*z**2) + (-38*z**2)*(-2*z**3) + (45*z**2)*28 - 2*z**3*28 + 616\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-2*z**3)*28 = -56*z**3\n (-2*z**3)*(-38*z**2) = 76*z**5\n (-2*z**3)*(19*z) = -38*z**4\n (30*z)*28 = 840*z\n (30*z)*(-38*z**2) = -1140*z**3\n (30*z)*(19*z) = 570*z**2\n (45*z**2)*28 = 1260*z**2\n (45*z**2)*(-38*z**2) = -1710*z**4\n (45*z**2)*(19*z) = 855*z**3\n 22*-38*z**2 = -836*z**2\n 22*19*z = 418*z\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 76*z**5 - 1710*z**4 - 38*z**4 - 1140*z**3 - 56*z**3 + 855*z**3 - 836*z**2 + 570*z**2 + 1260*z**2 + 418*z + 840*z + 616\nCombining like terms, got 76*z**5 - 1748*z**4 - 341*z**3 + 994*z**2 + 1258*z + 616\n#Step 7:\nCurrent expression: 76*z**5 - 1748*z**4 - 341*z**3 + 994*z**2 + 1258*z + 616\nNo more calculations needed.\n76*z**5 - 1748*z**4 - 341*z**3 + 994*z**2 + 1258*z + 616", "generated_answer": "76*z**5 - 1748*z**4 - 341*z**3 + 994*z**2 + 1258*z + 616", "step_length": 7} {"cot_id": "d0570d5ff8487b115e428d04cbb82695dadd47cf912eb953578561dc2947d4d3", "datapoint": {"question": "Simplify this expression: (31 - 49*z**3)*(22*z**3 - 40*z**2 - 26*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1078*z**6 + 1960*z**5 + 1274*z**4 + 682*z**3 - 1240*z**2 - 806*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1194, "polynomial_expr": "(31 - 49*z**3)*(22*z**3 - 40*z**2 - 26*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31 - 49*z**3)*(22*z**3 - 40*z**2 - 26*z)\nExpanding the part (31 - 49*z**3) using the distributive property, and we got: (-49*z**3)*(22*z**3 - 40*z**2 - 26*z) + 31*(22*z**3 - 40*z**2 - 26*z)\n#Step 2:\nCurrent expression: (-49*z**3)*(22*z**3 - 40*z**2 - 26*z) + 31*(22*z**3 - 40*z**2 - 26*z)\nSimplifying the partial expression: 31*(22*z**3 - 40*z**2 - 26*z)\nExpanding the part (22*z**3 - 40*z**2 - 26*z) using the distributive property, and we got: -26*z*31 - 40*z**2*31 + (22*z**3)*31\nReplacing 31*(22*z**3 - 40*z**2 - 26*z) with -26*z*31 - 40*z**2*31 + (22*z**3)*31 in the overall expression.\n#Step 3:\nCurrent expression: -26*z*31 - 40*z**2*31 + (-49*z**3)*(22*z**3 - 40*z**2 - 26*z) + (22*z**3)*31\nSimplifying the partial expression: (-49*z**3)*(22*z**3 - 40*z**2 - 26*z)\nExpanding the part (22*z**3 - 40*z**2 - 26*z) using the distributive property, and we got: (-26*z)*(-49*z**3) + (-40*z**2)*(-49*z**3) + (-49*z**3)*(22*z**3)\nReplacing (-49*z**3)*(22*z**3 - 40*z**2 - 26*z) with (-26*z)*(-49*z**3) + (-40*z**2)*(-49*z**3) + (-49*z**3)*(22*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-26*z)*(-49*z**3) - 26*z*31 + (-40*z**2)*(-49*z**3) - 40*z**2*31 + (-49*z**3)*(22*z**3) + (22*z**3)*31\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*z**2)*31 = -1240*z**2\n (-40*z**2)*(-49*z**3) = 1960*z**5\n (-26*z)*31 = -806*z\n (-26*z)*(-49*z**3) = 1274*z**4\n (22*z**3)*31 = 682*z**3\n (22*z**3)*(-49*z**3) = -1078*z**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1078*z**6 + 1960*z**5 + 1274*z**4 + 682*z**3 - 1240*z**2 - 806*z\nNo more calculations needed.\n-1078*z**6 + 1960*z**5 + 1274*z**4 + 682*z**3 - 1240*z**2 - 806*z", "generated_answer": "-1078*z**6 + 1960*z**5 + 1274*z**4 + 682*z**3 - 1240*z**2 - 806*z", "step_length": 5} {"cot_id": "5aa27535c02d955e84376e42e7b769838ee5e27d622e18c5bf60a3ef9c8b7292", "datapoint": {"question": "Simplify this expression: (40*x**2 + 11)*(-35*x**3 + 17*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1400*x**5 + 680*x**4 - 385*x**3 + 187*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1195, "polynomial_expr": "(40*x**2 + 11)*(-35*x**3 + 17*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (40*x**2 + 11)*(-35*x**3 + 17*x**2)\nExpanding the part (40*x**2 + 11) using the distributive property, and we got: (40*x**2)*(-35*x**3 + 17*x**2) + 11*(-35*x**3 + 17*x**2)\n#Step 2:\nCurrent expression: (40*x**2)*(-35*x**3 + 17*x**2) + 11*(-35*x**3 + 17*x**2)\nSimplifying the partial expression: 11*(-35*x**3 + 17*x**2)\nExpanding the part (-35*x**3 + 17*x**2) using the distributive property, and we got: (17*x**2)*11 - 35*x**3*11\nReplacing 11*(-35*x**3 + 17*x**2) with (17*x**2)*11 - 35*x**3*11 in the overall expression.\n#Step 3:\nCurrent expression: (17*x**2)*11 + (40*x**2)*(-35*x**3 + 17*x**2) - 35*x**3*11\nSimplifying the partial expression: (40*x**2)*(-35*x**3 + 17*x**2)\nExpanding the part (-35*x**3 + 17*x**2) using the distributive property, and we got: (17*x**2)*(40*x**2) + (40*x**2)*(-35*x**3)\nReplacing (40*x**2)*(-35*x**3 + 17*x**2) with (17*x**2)*(40*x**2) + (40*x**2)*(-35*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (17*x**2)*(40*x**2) + (17*x**2)*11 + (40*x**2)*(-35*x**3) - 35*x**3*11\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*x**3)*11 = -385*x**3\n (-35*x**3)*(40*x**2) = -1400*x**5\n (17*x**2)*11 = 187*x**2\n (17*x**2)*(40*x**2) = 680*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1400*x**5 + 680*x**4 - 385*x**3 + 187*x**2\nNo more calculations needed.\n-1400*x**5 + 680*x**4 - 385*x**3 + 187*x**2", "generated_answer": "-1400*x**5 + 680*x**4 - 385*x**3 + 187*x**2", "step_length": 5} {"cot_id": "e48bbca454f08e2a51aa85bc783c53cc7b8025c6647cfd83a163abcf80e2ddf7", "datapoint": {"question": "Calculate the following: -63*x**2*(21*x**3 - 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1323*x**5 + 2079*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1196, "polynomial_expr": "-63*x**2*(21*x**3 - 33)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -63*x**2*(21*x**3 - 33)\nExpanding the part (21*x**3 - 33) using the distributive property, and we got: -(-1)*2079*x**2 + (-63*x**2)*(21*x**3)\n#Step 2:\nCurrent expression: -(-1)*2079*x**2 + (-63*x**2)*(21*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -33*(-63*x**2) = 2079*x**2\n (21*x**3)*(-63*x**2) = -1323*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1323*x**5 + 2079*x**2\nNo more calculations needed.\n-1323*x**5 + 2079*x**2", "generated_answer": "-1323*x**5 + 2079*x**2", "step_length": 3} {"cot_id": "865f839cd15d251883ddb56070e6f3cba5386bc24ab4a724da6c95d1bf63322e", "datapoint": {"question": "Simplify this expression: (-15*x**2 - 2*x - 31)*(27*x**3 - 48*x**2 - 21*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-405*x**5 + 666*x**4 - 426*x**3 + 1530*x**2 + 651*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1197, "polynomial_expr": "(-15*x**2 - 2*x - 31)*(27*x**3 - 48*x**2 - 21*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-15*x**2 - 2*x - 31)*(27*x**3 - 48*x**2 - 21*x)\nExpanding the part (-15*x**2 - 2*x - 31) using the distributive property, and we got: (-2*x)*(27*x**3 - 48*x**2 - 21*x) + (-15*x**2)*(27*x**3 - 48*x**2 - 21*x) - 31*(27*x**3 - 48*x**2 - 21*x)\n#Step 2:\nCurrent expression: (-2*x)*(27*x**3 - 48*x**2 - 21*x) + (-15*x**2)*(27*x**3 - 48*x**2 - 21*x) - 31*(27*x**3 - 48*x**2 - 21*x)\nSimplifying the partial expression: -31*(27*x**3 - 48*x**2 - 21*x)\nExpanding the part (27*x**3 - 48*x**2 - 21*x) using the distributive property, and we got: -21*x*(-31) - 48*x**2*(-31) + (27*x**3)*(-31)\nReplacing -31*(27*x**3 - 48*x**2 - 21*x) with -21*x*(-31) - 48*x**2*(-31) + (27*x**3)*(-31) in the overall expression.\n#Step 3:\nCurrent expression: -21*x*(-31) + (-2*x)*(27*x**3 - 48*x**2 - 21*x) - 48*x**2*(-31) + (-15*x**2)*(27*x**3 - 48*x**2 - 21*x) + (27*x**3)*(-31)\nSimplifying the partial expression: (-15*x**2)*(27*x**3 - 48*x**2 - 21*x)\nExpanding the part (27*x**3 - 48*x**2 - 21*x) using the distributive property, and we got: (-21*x)*(-15*x**2) + (-48*x**2)*(-15*x**2) + (-15*x**2)*(27*x**3)\nReplacing (-15*x**2)*(27*x**3 - 48*x**2 - 21*x) with (-21*x)*(-15*x**2) + (-48*x**2)*(-15*x**2) + (-15*x**2)*(27*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-21*x)*(-15*x**2) - 21*x*(-31) + (-2*x)*(27*x**3 - 48*x**2 - 21*x) + (-48*x**2)*(-15*x**2) - 48*x**2*(-31) + (-15*x**2)*(27*x**3) + (27*x**3)*(-31)\nSimplifying the partial expression: (-2*x)*(27*x**3 - 48*x**2 - 21*x)\nExpanding the part (27*x**3 - 48*x**2 - 21*x) using the distributive property, and we got: (-21*x)*(-2*x) + (-2*x)*(-48*x**2) + (-2*x)*(27*x**3)\nReplacing (-2*x)*(27*x**3 - 48*x**2 - 21*x) with (-21*x)*(-2*x) + (-2*x)*(-48*x**2) + (-2*x)*(27*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-21*x)*(-2*x) + (-21*x)*(-15*x**2) - 21*x*(-31) + (-2*x)*(-48*x**2) + (-2*x)*(27*x**3) + (-48*x**2)*(-15*x**2) - 48*x**2*(-31) + (-15*x**2)*(27*x**3) + (27*x**3)*(-31)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*x**2)*-31 = 1488*x**2\n (-48*x**2)*(-15*x**2) = 720*x**4\n (-48*x**2)*(-2*x) = 96*x**3\n (-21*x)*-31 = 651*x\n (-21*x)*(-15*x**2) = 315*x**3\n (-21*x)*(-2*x) = 42*x**2\n (27*x**3)*-31 = -837*x**3\n (27*x**3)*(-15*x**2) = -405*x**5\n (27*x**3)*(-2*x) = -54*x**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -405*x**5 - 54*x**4 + 720*x**4 - 837*x**3 + 96*x**3 + 315*x**3 + 42*x**2 + 1488*x**2 + 651*x\nCombining like terms, got -405*x**5 + 666*x**4 - 426*x**3 + 1530*x**2 + 651*x\n#Step 7:\nCurrent expression: -405*x**5 + 666*x**4 - 426*x**3 + 1530*x**2 + 651*x\nNo more calculations needed.\n-405*x**5 + 666*x**4 - 426*x**3 + 1530*x**2 + 651*x", "generated_answer": "-405*x**5 + 666*x**4 - 426*x**3 + 1530*x**2 + 651*x", "step_length": 7} {"cot_id": "df5a0621a80fe4adab6aa3976fe48f45b477ed4179a44c23d3070d6e47ae6a74", "datapoint": {"question": "Calculate the following: (-38*z**3 + 20*z**2)*(-6*z**3 - 39*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "228*z**6 - 120*z**5 + 1482*z**4 - 780*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1198, "polynomial_expr": "(-38*z**3 + 20*z**2)*(-6*z**3 - 39*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-38*z**3 + 20*z**2)*(-6*z**3 - 39*z)\nExpanding the part (-6*z**3 - 39*z) using the distributive property, and we got: (-39*z)*(-38*z**3 + 20*z**2) + (-6*z**3)*(-38*z**3 + 20*z**2)\n#Step 2:\nCurrent expression: (-39*z)*(-38*z**3 + 20*z**2) + (-6*z**3)*(-38*z**3 + 20*z**2)\nSimplifying the partial expression: (-39*z)*(-38*z**3 + 20*z**2)\nExpanding the part (-38*z**3 + 20*z**2) using the distributive property, and we got: (-39*z)*(20*z**2) + (-39*z)*(-38*z**3)\nReplacing (-39*z)*(-38*z**3 + 20*z**2) with (-39*z)*(20*z**2) + (-39*z)*(-38*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-39*z)*(20*z**2) + (-39*z)*(-38*z**3) + (-6*z**3)*(-38*z**3 + 20*z**2)\nSimplifying the partial expression: (-6*z**3)*(-38*z**3 + 20*z**2)\nExpanding the part (-38*z**3 + 20*z**2) using the distributive property, and we got: (20*z**2)*(-6*z**3) + (-38*z**3)*(-6*z**3)\nReplacing (-6*z**3)*(-38*z**3 + 20*z**2) with (20*z**2)*(-6*z**3) + (-38*z**3)*(-6*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-39*z)*(20*z**2) + (-39*z)*(-38*z**3) + (20*z**2)*(-6*z**3) + (-38*z**3)*(-6*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*z**3)*(-39*z) = 1482*z**4\n (-38*z**3)*(-6*z**3) = 228*z**6\n (20*z**2)*(-39*z) = -780*z**3\n (20*z**2)*(-6*z**3) = -120*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 228*z**6 - 120*z**5 + 1482*z**4 - 780*z**3\nNo more calculations needed.\n228*z**6 - 120*z**5 + 1482*z**4 - 780*z**3", "generated_answer": "228*z**6 - 120*z**5 + 1482*z**4 - 780*z**3", "step_length": 5} {"cot_id": "822833d929adfb291a6eecdfc326988715c90c177c6dd1513a0bd2c3cf0bb4f8", "datapoint": {"question": "Calculate the following: (30*z**2 - 34*z)*(46*z**2 + 19*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1380*z**4 - 994*z**3 - 646*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1199, "polynomial_expr": "(30*z**2 - 34*z)*(46*z**2 + 19*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (30*z**2 - 34*z)*(46*z**2 + 19*z)\nExpanding the part (30*z**2 - 34*z) using the distributive property, and we got: (-34*z)*(46*z**2 + 19*z) + (30*z**2)*(46*z**2 + 19*z)\n#Step 2:\nCurrent expression: (-34*z)*(46*z**2 + 19*z) + (30*z**2)*(46*z**2 + 19*z)\nSimplifying the partial expression: (-34*z)*(46*z**2 + 19*z)\nExpanding the part (46*z**2 + 19*z) using the distributive property, and we got: (-34*z)*(19*z) + (-34*z)*(46*z**2)\nReplacing (-34*z)*(46*z**2 + 19*z) with (-34*z)*(19*z) + (-34*z)*(46*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-34*z)*(19*z) + (-34*z)*(46*z**2) + (30*z**2)*(46*z**2 + 19*z)\nSimplifying the partial expression: (30*z**2)*(46*z**2 + 19*z)\nExpanding the part (46*z**2 + 19*z) using the distributive property, and we got: (19*z)*(30*z**2) + (30*z**2)*(46*z**2)\nReplacing (30*z**2)*(46*z**2 + 19*z) with (19*z)*(30*z**2) + (30*z**2)*(46*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-34*z)*(19*z) + (-34*z)*(46*z**2) + (19*z)*(30*z**2) + (30*z**2)*(46*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (19*z)*(-34*z) = -646*z**2\n (19*z)*(30*z**2) = 570*z**3\n (46*z**2)*(-34*z) = -1564*z**3\n (46*z**2)*(30*z**2) = 1380*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1380*z**4 - 1564*z**3 + 570*z**3 - 646*z**2\nCombining like terms, got 1380*z**4 - 994*z**3 - 646*z**2\n#Step 6:\nCurrent expression: 1380*z**4 - 994*z**3 - 646*z**2\nNo more calculations needed.\n1380*z**4 - 994*z**3 - 646*z**2", "generated_answer": "1380*z**4 - 994*z**3 - 646*z**2", "step_length": 6} {"cot_id": "48e4e55116fc9e89d7332ba1013ef8887f0d400528abe133ec8aa7ad87b5e975", "datapoint": {"question": "Calculate the following: (-45*x**3 + 11*x**2)*(-61*x**3 - 33*x**2 - 46)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2745*x**6 + 814*x**5 - 363*x**4 + 2070*x**3 - 506*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1200, "polynomial_expr": "(-45*x**3 + 11*x**2)*(-61*x**3 - 33*x**2 - 46)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-45*x**3 + 11*x**2)*(-61*x**3 - 33*x**2 - 46)\nExpanding the part (-45*x**3 + 11*x**2) using the distributive property, and we got: (11*x**2)*(-61*x**3 - 33*x**2 - 46) + (-45*x**3)*(-61*x**3 - 33*x**2 - 46)\n#Step 2:\nCurrent expression: (11*x**2)*(-61*x**3 - 33*x**2 - 46) + (-45*x**3)*(-61*x**3 - 33*x**2 - 46)\nSimplifying the partial expression: (-45*x**3)*(-61*x**3 - 33*x**2 - 46)\nExpanding the part (-61*x**3 - 33*x**2 - 46) using the distributive property, and we got: -(-1)*2070*x**3 + (-33*x**2)*(-45*x**3) + (-61*x**3)*(-45*x**3)\nReplacing (-45*x**3)*(-61*x**3 - 33*x**2 - 46) with -(-1)*2070*x**3 + (-33*x**2)*(-45*x**3) + (-61*x**3)*(-45*x**3) in the overall expression.\n#Step 3:\nCurrent expression: -46*(-45)*x**3 + (-33*x**2)*(-45*x**3) + (11*x**2)*(-61*x**3 - 33*x**2 - 46) + (-61*x**3)*(-45*x**3)\nSimplifying the partial expression: (11*x**2)*(-61*x**3 - 33*x**2 - 46)\nExpanding the part (-61*x**3 - 33*x**2 - 46) using the distributive property, and we got: -506*x**2 + (-33*x**2)*(11*x**2) + (11*x**2)*(-61*x**3)\nReplacing (11*x**2)*(-61*x**3 - 33*x**2 - 46) with -506*x**2 + (-33*x**2)*(11*x**2) + (11*x**2)*(-61*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -46*(-45)*x**3 - 46*11*x**2 + (-33*x**2)*(11*x**2) + (-33*x**2)*(-45*x**3) + (11*x**2)*(-61*x**3) + (-61*x**3)*(-45*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-61*x**3)*(-45*x**3) = 2745*x**6\n (-61*x**3)*(11*x**2) = -671*x**5\n (-33*x**2)*(-45*x**3) = 1485*x**5\n (-33*x**2)*(11*x**2) = -363*x**4\n -46*-45*x**3 = 2070*x**3\n -46*11*x**2 = -506*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2745*x**6 - 671*x**5 + 1485*x**5 - 363*x**4 + 2070*x**3 - 506*x**2\nCombining like terms, got 2745*x**6 + 814*x**5 - 363*x**4 + 2070*x**3 - 506*x**2\n#Step 6:\nCurrent expression: 2745*x**6 + 814*x**5 - 363*x**4 + 2070*x**3 - 506*x**2\nNo more calculations needed.\n2745*x**6 + 814*x**5 - 363*x**4 + 2070*x**3 - 506*x**2", "generated_answer": "2745*x**6 + 814*x**5 - 363*x**4 + 2070*x**3 - 506*x**2", "step_length": 6} {"cot_id": "d9498044f993182ca460f362225ec987ce6ad67d3dd0f696e6accf566eb870bd", "datapoint": {"question": "Calculate the following: (19*z**2 - 35)*(-47*z**3 + 2*z**2 + 13*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-893*z**5 + 38*z**4 + 1892*z**3 - 70*z**2 - 455*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1201, "polynomial_expr": "(19*z**2 - 35)*(-47*z**3 + 2*z**2 + 13*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (19*z**2 - 35)*(-47*z**3 + 2*z**2 + 13*z)\nExpanding the part (19*z**2 - 35) using the distributive property, and we got: (19*z**2)*(-47*z**3 + 2*z**2 + 13*z) - 35*(-47*z**3 + 2*z**2 + 13*z)\n#Step 2:\nCurrent expression: (19*z**2)*(-47*z**3 + 2*z**2 + 13*z) - 35*(-47*z**3 + 2*z**2 + 13*z)\nSimplifying the partial expression: -35*(-47*z**3 + 2*z**2 + 13*z)\nExpanding the part (-47*z**3 + 2*z**2 + 13*z) using the distributive property, and we got: (13*z)*(-35) + (2*z**2)*(-35) - 47*z**3*(-35)\nReplacing -35*(-47*z**3 + 2*z**2 + 13*z) with (13*z)*(-35) + (2*z**2)*(-35) - 47*z**3*(-35) in the overall expression.\n#Step 3:\nCurrent expression: (13*z)*(-35) + (2*z**2)*(-35) + (19*z**2)*(-47*z**3 + 2*z**2 + 13*z) - 47*z**3*(-35)\nSimplifying the partial expression: (19*z**2)*(-47*z**3 + 2*z**2 + 13*z)\nExpanding the part (-47*z**3 + 2*z**2 + 13*z) using the distributive property, and we got: (13*z)*(19*z**2) + (2*z**2)*(19*z**2) + (19*z**2)*(-47*z**3)\nReplacing (19*z**2)*(-47*z**3 + 2*z**2 + 13*z) with (13*z)*(19*z**2) + (2*z**2)*(19*z**2) + (19*z**2)*(-47*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (13*z)*(19*z**2) + (13*z)*(-35) + (2*z**2)*(19*z**2) + (2*z**2)*(-35) + (19*z**2)*(-47*z**3) - 47*z**3*(-35)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*z**3)*-35 = 1645*z**3\n (-47*z**3)*(19*z**2) = -893*z**5\n (2*z**2)*-35 = -70*z**2\n (2*z**2)*(19*z**2) = 38*z**4\n (13*z)*-35 = -455*z\n (13*z)*(19*z**2) = 247*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -893*z**5 + 38*z**4 + 247*z**3 + 1645*z**3 - 70*z**2 - 455*z\nCombining like terms, got -893*z**5 + 38*z**4 + 1892*z**3 - 70*z**2 - 455*z\n#Step 6:\nCurrent expression: -893*z**5 + 38*z**4 + 1892*z**3 - 70*z**2 - 455*z\nNo more calculations needed.\n-893*z**5 + 38*z**4 + 1892*z**3 - 70*z**2 - 455*z", "generated_answer": "-893*z**5 + 38*z**4 + 1892*z**3 - 70*z**2 - 455*z", "step_length": 6} {"cot_id": "c31d17f51cf6ad38f019ac4c35229dbac4722ab1a0c8ccbe9a816e23b8339bda", "datapoint": {"question": "Calculate the following: (-54*y**2 - 23)*(35*y**2 + 50*y - 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1890*y**4 - 2700*y**3 + 1247*y**2 - 1150*y + 874", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1202, "polynomial_expr": "(-54*y**2 - 23)*(35*y**2 + 50*y - 38)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-54*y**2 - 23)*(35*y**2 + 50*y - 38)\nExpanding the part (-54*y**2 - 23) using the distributive property, and we got: (-54*y**2)*(35*y**2 + 50*y - 38) - 23*(35*y**2 + 50*y - 38)\n#Step 2:\nCurrent expression: (-54*y**2)*(35*y**2 + 50*y - 38) - 23*(35*y**2 + 50*y - 38)\nSimplifying the partial expression: -23*(35*y**2 + 50*y - 38)\nExpanding the part (35*y**2 + 50*y - 38) using the distributive property, and we got: (50*y)*(-23) + (35*y**2)*(-23) - 38*(-23)\nReplacing -23*(35*y**2 + 50*y - 38) with (50*y)*(-23) + (35*y**2)*(-23) - 38*(-23) in the overall expression.\n#Step 3:\nCurrent expression: (50*y)*(-23) + (-54*y**2)*(35*y**2 + 50*y - 38) + (35*y**2)*(-23) + 874\nSimplifying the partial expression: (-54*y**2)*(35*y**2 + 50*y - 38)\nExpanding the part (35*y**2 + 50*y - 38) using the distributive property, and we got: -(-1)*2052*y**2 + (50*y)*(-54*y**2) + (-54*y**2)*(35*y**2)\nReplacing (-54*y**2)*(35*y**2 + 50*y - 38) with -(-1)*2052*y**2 + (50*y)*(-54*y**2) + (-54*y**2)*(35*y**2) in the overall expression.\n#Step 4:\nCurrent expression: -38*(-54)*y**2 + (50*y)*(-54*y**2) + (50*y)*(-23) + (-54*y**2)*(35*y**2) + (35*y**2)*(-23) + 874\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (35*y**2)*-23 = -805*y**2\n (35*y**2)*(-54*y**2) = -1890*y**4\n (50*y)*-23 = -1150*y\n (50*y)*(-54*y**2) = -2700*y**3\n -38*-54*y**2 = 2052*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1890*y**4 - 2700*y**3 - 805*y**2 + 2052*y**2 - 1150*y + 874\nCombining like terms, got -1890*y**4 - 2700*y**3 + 1247*y**2 - 1150*y + 874\n#Step 6:\nCurrent expression: -1890*y**4 - 2700*y**3 + 1247*y**2 - 1150*y + 874\nNo more calculations needed.\n-1890*y**4 - 2700*y**3 + 1247*y**2 - 1150*y + 874", "generated_answer": "-1890*y**4 - 2700*y**3 + 1247*y**2 - 1150*y + 874", "step_length": 6} {"cot_id": "32f63d6f6188738956780f9a7f1a1e332870c585a44128073a25c8d278c7f354", "datapoint": {"question": "Calculate the following: (-41*z**2 - 40)*(48*z**2 + 48*z + 9)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1968*z**4 - 1968*z**3 - 2289*z**2 - 1920*z - 360", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1203, "polynomial_expr": "(-41*z**2 - 40)*(48*z**2 + 48*z + 9)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-41*z**2 - 40)*(48*z**2 + 48*z + 9)\nExpanding the part (-41*z**2 - 40) using the distributive property, and we got: (-41*z**2)*(48*z**2 + 48*z + 9) - 40*(48*z**2 + 48*z + 9)\n#Step 2:\nCurrent expression: (-41*z**2)*(48*z**2 + 48*z + 9) - 40*(48*z**2 + 48*z + 9)\nSimplifying the partial expression: -40*(48*z**2 + 48*z + 9)\nExpanding the part (48*z**2 + 48*z + 9) using the distributive property, and we got: (48*z)*(-40) + (48*z**2)*(-40) + 9*(-40)\nReplacing -40*(48*z**2 + 48*z + 9) with (48*z)*(-40) + (48*z**2)*(-40) + 9*(-40) in the overall expression.\n#Step 3:\nCurrent expression: (48*z)*(-40) + (-41*z**2)*(48*z**2 + 48*z + 9) + (48*z**2)*(-40) - 360\nSimplifying the partial expression: (-41*z**2)*(48*z**2 + 48*z + 9)\nExpanding the part (48*z**2 + 48*z + 9) using the distributive property, and we got: 9*(-41*z**2) + (48*z)*(-41*z**2) + (-41*z**2)*(48*z**2)\nReplacing (-41*z**2)*(48*z**2 + 48*z + 9) with 9*(-41*z**2) + (48*z)*(-41*z**2) + (-41*z**2)*(48*z**2) in the overall expression.\n#Step 4:\nCurrent expression: 9*(-41)*z**2 + (48*z)*(-41*z**2) + (48*z)*(-40) + (-41*z**2)*(48*z**2) + (48*z**2)*(-40) - 360\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (48*z)*-40 = -1920*z\n (48*z)*(-41*z**2) = -1968*z**3\n (48*z**2)*-40 = -1920*z**2\n (48*z**2)*(-41*z**2) = -1968*z**4\n 9*-41*z**2 = -369*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1968*z**4 - 1968*z**3 - 1920*z**2 - 369*z**2 - 1920*z - 360\nCombining like terms, got -1968*z**4 - 1968*z**3 - 2289*z**2 - 1920*z - 360\n#Step 6:\nCurrent expression: -1968*z**4 - 1968*z**3 - 2289*z**2 - 1920*z - 360\nNo more calculations needed.\n-1968*z**4 - 1968*z**3 - 2289*z**2 - 1920*z - 360", "generated_answer": "-1968*z**4 - 1968*z**3 - 2289*z**2 - 1920*z - 360", "step_length": 6} {"cot_id": "5371975e79031159db47e0d623095de036e8b5890e36b717d038676b4cc7ef51", "datapoint": {"question": "Calculate the following: (21*x**2 - 46)*(-7*x**3 - 9*x**2 + 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-147*x**5 - 189*x**4 + 322*x**3 + 750*x**2 - 736", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1204, "polynomial_expr": "(21*x**2 - 46)*(-7*x**3 - 9*x**2 + 16)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21*x**2 - 46)*(-7*x**3 - 9*x**2 + 16)\nExpanding the part (21*x**2 - 46) using the distributive property, and we got: (21*x**2)*(-7*x**3 - 9*x**2 + 16) - 46*(-7*x**3 - 9*x**2 + 16)\n#Step 2:\nCurrent expression: (21*x**2)*(-7*x**3 - 9*x**2 + 16) - 46*(-7*x**3 - 9*x**2 + 16)\nSimplifying the partial expression: -46*(-7*x**3 - 9*x**2 + 16)\nExpanding the part (-7*x**3 - 9*x**2 + 16) using the distributive property, and we got: -9*x**2*(-46) - 7*x**3*(-46) + 16*(-46)\nReplacing -46*(-7*x**3 - 9*x**2 + 16) with -9*x**2*(-46) - 7*x**3*(-46) + 16*(-46) in the overall expression.\n#Step 3:\nCurrent expression: -9*x**2*(-46) + (21*x**2)*(-7*x**3 - 9*x**2 + 16) - 7*x**3*(-46) - 736\nSimplifying the partial expression: (21*x**2)*(-7*x**3 - 9*x**2 + 16)\nExpanding the part (-7*x**3 - 9*x**2 + 16) using the distributive property, and we got: 16*(21*x**2) + (-9*x**2)*(21*x**2) + (21*x**2)*(-7*x**3)\nReplacing (21*x**2)*(-7*x**3 - 9*x**2 + 16) with 16*(21*x**2) + (-9*x**2)*(21*x**2) + (21*x**2)*(-7*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 16*21*x**2 + (-9*x**2)*(21*x**2) - 9*x**2*(-46) + (21*x**2)*(-7*x**3) - 7*x**3*(-46) - 736\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-9*x**2)*-46 = 414*x**2\n (-9*x**2)*(21*x**2) = -189*x**4\n (-7*x**3)*-46 = 322*x**3\n (-7*x**3)*(21*x**2) = -147*x**5\n 16*21*x**2 = 336*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -147*x**5 - 189*x**4 + 322*x**3 + 336*x**2 + 414*x**2 - 736\nCombining like terms, got -147*x**5 - 189*x**4 + 322*x**3 + 750*x**2 - 736\n#Step 6:\nCurrent expression: -147*x**5 - 189*x**4 + 322*x**3 + 750*x**2 - 736\nNo more calculations needed.\n-147*x**5 - 189*x**4 + 322*x**3 + 750*x**2 - 736", "generated_answer": "-147*x**5 - 189*x**4 + 322*x**3 + 750*x**2 - 736", "step_length": 6} {"cot_id": "ed6f380958e4cc8de6a570e94989380902b19b3b47f284e1e5e45617a6ae10f5", "datapoint": {"question": "Calculate the following: (60*x**2 + 46*x)*(9*x**3 + 15*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "540*x**5 + 1314*x**4 + 690*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1205, "polynomial_expr": "(60*x**2 + 46*x)*(9*x**3 + 15*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (60*x**2 + 46*x)*(9*x**3 + 15*x**2)\nExpanding the part (9*x**3 + 15*x**2) using the distributive property, and we got: (15*x**2)*(60*x**2 + 46*x) + (9*x**3)*(60*x**2 + 46*x)\n#Step 2:\nCurrent expression: (15*x**2)*(60*x**2 + 46*x) + (9*x**3)*(60*x**2 + 46*x)\nSimplifying the partial expression: (9*x**3)*(60*x**2 + 46*x)\nExpanding the part (60*x**2 + 46*x) using the distributive property, and we got: (46*x)*(9*x**3) + (60*x**2)*(9*x**3)\nReplacing (9*x**3)*(60*x**2 + 46*x) with (46*x)*(9*x**3) + (60*x**2)*(9*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (46*x)*(9*x**3) + (15*x**2)*(60*x**2 + 46*x) + (60*x**2)*(9*x**3)\nSimplifying the partial expression: (15*x**2)*(60*x**2 + 46*x)\nExpanding the part (60*x**2 + 46*x) using the distributive property, and we got: (46*x)*(15*x**2) + (15*x**2)*(60*x**2)\nReplacing (15*x**2)*(60*x**2 + 46*x) with (46*x)*(15*x**2) + (15*x**2)*(60*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (46*x)*(15*x**2) + (46*x)*(9*x**3) + (15*x**2)*(60*x**2) + (60*x**2)*(9*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (46*x)*(9*x**3) = 414*x**4\n (46*x)*(15*x**2) = 690*x**3\n (60*x**2)*(9*x**3) = 540*x**5\n (60*x**2)*(15*x**2) = 900*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 540*x**5 + 414*x**4 + 900*x**4 + 690*x**3\nCombining like terms, got 540*x**5 + 1314*x**4 + 690*x**3\n#Step 6:\nCurrent expression: 540*x**5 + 1314*x**4 + 690*x**3\nNo more calculations needed.\n540*x**5 + 1314*x**4 + 690*x**3", "generated_answer": "540*x**5 + 1314*x**4 + 690*x**3", "step_length": 6} {"cot_id": "ebbf95a4f5b95bd3b2404f7395a41e7ba6c06ab8b612f869aad8830dfc9b28e5", "datapoint": {"question": "Calculate the following: (-48*z**2 + 43*z)*(-23*z**3 + 50*z**2 + 20*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1104*z**5 - 3389*z**4 + 1190*z**3 + 860*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1206, "polynomial_expr": "(-48*z**2 + 43*z)*(-23*z**3 + 50*z**2 + 20*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-48*z**2 + 43*z)*(-23*z**3 + 50*z**2 + 20*z)\nExpanding the part (-48*z**2 + 43*z) using the distributive property, and we got: (43*z)*(-23*z**3 + 50*z**2 + 20*z) + (-48*z**2)*(-23*z**3 + 50*z**2 + 20*z)\n#Step 2:\nCurrent expression: (43*z)*(-23*z**3 + 50*z**2 + 20*z) + (-48*z**2)*(-23*z**3 + 50*z**2 + 20*z)\nSimplifying the partial expression: (-48*z**2)*(-23*z**3 + 50*z**2 + 20*z)\nExpanding the part (-23*z**3 + 50*z**2 + 20*z) using the distributive property, and we got: (20*z)*(-48*z**2) + (-48*z**2)*(50*z**2) + (-48*z**2)*(-23*z**3)\nReplacing (-48*z**2)*(-23*z**3 + 50*z**2 + 20*z) with (20*z)*(-48*z**2) + (-48*z**2)*(50*z**2) + (-48*z**2)*(-23*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (20*z)*(-48*z**2) + (43*z)*(-23*z**3 + 50*z**2 + 20*z) + (-48*z**2)*(50*z**2) + (-48*z**2)*(-23*z**3)\nSimplifying the partial expression: (43*z)*(-23*z**3 + 50*z**2 + 20*z)\nExpanding the part (-23*z**3 + 50*z**2 + 20*z) using the distributive property, and we got: (20*z)*(43*z) + (43*z)*(50*z**2) + (43*z)*(-23*z**3)\nReplacing (43*z)*(-23*z**3 + 50*z**2 + 20*z) with (20*z)*(43*z) + (43*z)*(50*z**2) + (43*z)*(-23*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (20*z)*(43*z) + (20*z)*(-48*z**2) + (43*z)*(50*z**2) + (43*z)*(-23*z**3) + (-48*z**2)*(50*z**2) + (-48*z**2)*(-23*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*z**3)*(-48*z**2) = 1104*z**5\n (-23*z**3)*(43*z) = -989*z**4\n (20*z)*(-48*z**2) = -960*z**3\n (20*z)*(43*z) = 860*z**2\n (50*z**2)*(-48*z**2) = -2400*z**4\n (50*z**2)*(43*z) = 2150*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1104*z**5 - 2400*z**4 - 989*z**4 - 960*z**3 + 2150*z**3 + 860*z**2\nCombining like terms, got 1104*z**5 - 3389*z**4 + 1190*z**3 + 860*z**2\n#Step 6:\nCurrent expression: 1104*z**5 - 3389*z**4 + 1190*z**3 + 860*z**2\nNo more calculations needed.\n1104*z**5 - 3389*z**4 + 1190*z**3 + 860*z**2", "generated_answer": "1104*z**5 - 3389*z**4 + 1190*z**3 + 860*z**2", "step_length": 6} {"cot_id": "33b1ac83bcf83599db9eda974287a7f2e4bb5b588094e48a96b12ae9ae455fc1", "datapoint": {"question": "Simplify this expression: (49 - 2*z)*(51 - 39*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "78*z**2 - 2013*z + 2499", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1207, "polynomial_expr": "(49 - 2*z)*(51 - 39*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (49 - 2*z)*(51 - 39*z)\nExpanding the part (49 - 2*z) using the distributive property, and we got: (-2*z)*(51 - 39*z) + 49*(51 - 39*z)\n#Step 2:\nCurrent expression: (-2*z)*(51 - 39*z) + 49*(51 - 39*z)\nSimplifying the partial expression: 49*(51 - 39*z)\nExpanding the part (51 - 39*z) using the distributive property, and we got: -39*z*49 + 51*49\nReplacing 49*(51 - 39*z) with -39*z*49 + 51*49 in the overall expression.\n#Step 3:\nCurrent expression: -39*z*49 + (-2*z)*(51 - 39*z) + 2499\nSimplifying the partial expression: (-2*z)*(51 - 39*z)\nExpanding the part (51 - 39*z) using the distributive property, and we got: (-39*z)*(-2*z) + 51*(-2*z)\nReplacing (-2*z)*(51 - 39*z) with (-39*z)*(-2*z) + 51*(-2*z) in the overall expression.\n#Step 4:\nCurrent expression: (-39*z)*(-2*z) - 39*z*49 + 51*(-2)*z + 2499\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*z)*49 = -1911*z\n (-39*z)*(-2*z) = 78*z**2\n 51*-2*z = -102*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 78*z**2 - 1911*z - 102*z + 2499\nCombining like terms, got 78*z**2 - 2013*z + 2499\n#Step 6:\nCurrent expression: 78*z**2 - 2013*z + 2499\nNo more calculations needed.\n78*z**2 - 2013*z + 2499", "generated_answer": "78*z**2 - 2013*z + 2499", "step_length": 6} {"cot_id": "c0595f8e6cebcd05c4dfc6e2b2dd28fa199246e4db3f0b39e24182e10136e0d0", "datapoint": {"question": "Simplify this expression: (31*x**2 + 40*x)*(48*x**3 - 21*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1488*x**5 + 1920*x**4 - 651*x**3 - 840*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1208, "polynomial_expr": "(31*x**2 + 40*x)*(48*x**3 - 21*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31*x**2 + 40*x)*(48*x**3 - 21*x)\nExpanding the part (48*x**3 - 21*x) using the distributive property, and we got: (-21*x)*(31*x**2 + 40*x) + (48*x**3)*(31*x**2 + 40*x)\n#Step 2:\nCurrent expression: (-21*x)*(31*x**2 + 40*x) + (48*x**3)*(31*x**2 + 40*x)\nSimplifying the partial expression: (-21*x)*(31*x**2 + 40*x)\nExpanding the part (31*x**2 + 40*x) using the distributive property, and we got: (-21*x)*(40*x) + (-21*x)*(31*x**2)\nReplacing (-21*x)*(31*x**2 + 40*x) with (-21*x)*(40*x) + (-21*x)*(31*x**2) in the overall expression.\n#Step 3:\nCurrent expression: (-21*x)*(40*x) + (-21*x)*(31*x**2) + (48*x**3)*(31*x**2 + 40*x)\nSimplifying the partial expression: (48*x**3)*(31*x**2 + 40*x)\nExpanding the part (31*x**2 + 40*x) using the distributive property, and we got: (40*x)*(48*x**3) + (31*x**2)*(48*x**3)\nReplacing (48*x**3)*(31*x**2 + 40*x) with (40*x)*(48*x**3) + (31*x**2)*(48*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-21*x)*(40*x) + (-21*x)*(31*x**2) + (40*x)*(48*x**3) + (31*x**2)*(48*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (31*x**2)*(-21*x) = -651*x**3\n (31*x**2)*(48*x**3) = 1488*x**5\n (40*x)*(-21*x) = -840*x**2\n (40*x)*(48*x**3) = 1920*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1488*x**5 + 1920*x**4 - 651*x**3 - 840*x**2\nNo more calculations needed.\n1488*x**5 + 1920*x**4 - 651*x**3 - 840*x**2", "generated_answer": "1488*x**5 + 1920*x**4 - 651*x**3 - 840*x**2", "step_length": 5} {"cot_id": "ed0af4f2323b1489f6b6d5cf70ba6419039cc0441d254ccc2a290d46f6f3515c", "datapoint": {"question": "Calculate the following: (-48*z**2 - 30*z - 24)*(-34*z**2 + 32*z + 26)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1632*z**4 - 516*z**3 - 1392*z**2 - 1548*z - 624", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1209, "polynomial_expr": "(-48*z**2 - 30*z - 24)*(-34*z**2 + 32*z + 26)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-48*z**2 - 30*z - 24)*(-34*z**2 + 32*z + 26)\nExpanding the part (-48*z**2 - 30*z - 24) using the distributive property, and we got: (-30*z)*(-34*z**2 + 32*z + 26) + (-48*z**2)*(-34*z**2 + 32*z + 26) - 24*(-34*z**2 + 32*z + 26)\n#Step 2:\nCurrent expression: (-30*z)*(-34*z**2 + 32*z + 26) + (-48*z**2)*(-34*z**2 + 32*z + 26) - 24*(-34*z**2 + 32*z + 26)\nSimplifying the partial expression: -24*(-34*z**2 + 32*z + 26)\nExpanding the part (-34*z**2 + 32*z + 26) using the distributive property, and we got: (32*z)*(-24) - 34*z**2*(-24) + 26*(-24)\nReplacing -24*(-34*z**2 + 32*z + 26) with (32*z)*(-24) - 34*z**2*(-24) + 26*(-24) in the overall expression.\n#Step 3:\nCurrent expression: (-30*z)*(-34*z**2 + 32*z + 26) + (32*z)*(-24) + (-48*z**2)*(-34*z**2 + 32*z + 26) - 34*z**2*(-24) - 624\nSimplifying the partial expression: (-48*z**2)*(-34*z**2 + 32*z + 26)\nExpanding the part (-34*z**2 + 32*z + 26) using the distributive property, and we got: 26*(-48*z**2) + (32*z)*(-48*z**2) + (-48*z**2)*(-34*z**2)\nReplacing (-48*z**2)*(-34*z**2 + 32*z + 26) with 26*(-48*z**2) + (32*z)*(-48*z**2) + (-48*z**2)*(-34*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-30*z)*(-34*z**2 + 32*z + 26) + 26*(-48)*z**2 + (32*z)*(-48*z**2) + (32*z)*(-24) + (-48*z**2)*(-34*z**2) - 34*z**2*(-24) - 624\nSimplifying the partial expression: (-30*z)*(-34*z**2 + 32*z + 26)\nExpanding the part (-34*z**2 + 32*z + 26) using the distributive property, and we got: (-30*z)*(32*z) + (-30*z)*(-34*z**2) + 26*(-30*z)\nReplacing (-30*z)*(-34*z**2 + 32*z + 26) with (-30*z)*(32*z) + (-30*z)*(-34*z**2) + 26*(-30*z) in the overall expression.\n#Step 5:\nCurrent expression: (-30*z)*(32*z) + (-30*z)*(-34*z**2) + 26*(-48)*z**2 + 26*(-30)*z + (32*z)*(-48*z**2) + (32*z)*(-24) + (-48*z**2)*(-34*z**2) - 34*z**2*(-24) - 624\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*z**2)*-24 = 816*z**2\n (-34*z**2)*(-48*z**2) = 1632*z**4\n (-34*z**2)*(-30*z) = 1020*z**3\n (32*z)*-24 = -768*z\n (32*z)*(-48*z**2) = -1536*z**3\n (32*z)*(-30*z) = -960*z**2\n 26*-48*z**2 = -1248*z**2\n 26*-30*z = -780*z\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1632*z**4 - 1536*z**3 + 1020*z**3 - 1248*z**2 - 960*z**2 + 816*z**2 - 780*z - 768*z - 624\nCombining like terms, got 1632*z**4 - 516*z**3 - 1392*z**2 - 1548*z - 624\n#Step 7:\nCurrent expression: 1632*z**4 - 516*z**3 - 1392*z**2 - 1548*z - 624\nNo more calculations needed.\n1632*z**4 - 516*z**3 - 1392*z**2 - 1548*z - 624", "generated_answer": "1632*z**4 - 516*z**3 - 1392*z**2 - 1548*z - 624", "step_length": 7} {"cot_id": "d14dfc105cda32828a00c856426b90d62ca572b6cbef44d3d1cc168587c4abf3", "datapoint": {"question": "Calculate the following: (5*y**2 + 46*y)*(34*y**2 - 39*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "170*y**4 + 1369*y**3 - 1794*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1210, "polynomial_expr": "(5*y**2 + 46*y)*(34*y**2 - 39*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (5*y**2 + 46*y)*(34*y**2 - 39*y)\nExpanding the part (34*y**2 - 39*y) using the distributive property, and we got: (-39*y)*(5*y**2 + 46*y) + (34*y**2)*(5*y**2 + 46*y)\n#Step 2:\nCurrent expression: (-39*y)*(5*y**2 + 46*y) + (34*y**2)*(5*y**2 + 46*y)\nSimplifying the partial expression: (-39*y)*(5*y**2 + 46*y)\nExpanding the part (5*y**2 + 46*y) using the distributive property, and we got: (-39*y)*(46*y) + (-39*y)*(5*y**2)\nReplacing (-39*y)*(5*y**2 + 46*y) with (-39*y)*(46*y) + (-39*y)*(5*y**2) in the overall expression.\n#Step 3:\nCurrent expression: (-39*y)*(46*y) + (-39*y)*(5*y**2) + (34*y**2)*(5*y**2 + 46*y)\nSimplifying the partial expression: (34*y**2)*(5*y**2 + 46*y)\nExpanding the part (5*y**2 + 46*y) using the distributive property, and we got: (46*y)*(34*y**2) + (5*y**2)*(34*y**2)\nReplacing (34*y**2)*(5*y**2 + 46*y) with (46*y)*(34*y**2) + (5*y**2)*(34*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-39*y)*(46*y) + (-39*y)*(5*y**2) + (46*y)*(34*y**2) + (5*y**2)*(34*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (5*y**2)*(-39*y) = -195*y**3\n (5*y**2)*(34*y**2) = 170*y**4\n (46*y)*(-39*y) = -1794*y**2\n (46*y)*(34*y**2) = 1564*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 170*y**4 - 195*y**3 + 1564*y**3 - 1794*y**2\nCombining like terms, got 170*y**4 + 1369*y**3 - 1794*y**2\n#Step 6:\nCurrent expression: 170*y**4 + 1369*y**3 - 1794*y**2\nNo more calculations needed.\n170*y**4 + 1369*y**3 - 1794*y**2", "generated_answer": "170*y**4 + 1369*y**3 - 1794*y**2", "step_length": 6} {"cot_id": "a2c879619d280d0b475a8d605a15e8876010a02048c4831840c1830eb81e9e5c", "datapoint": {"question": "Calculate the following: (-20*z**3 - 22*z)*(47*z**3 - 40*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-940*z**6 + 800*z**5 - 1034*z**4 + 880*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1211, "polynomial_expr": "(-20*z**3 - 22*z)*(47*z**3 - 40*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-20*z**3 - 22*z)*(47*z**3 - 40*z**2)\nExpanding the part (47*z**3 - 40*z**2) using the distributive property, and we got: (-40*z**2)*(-20*z**3 - 22*z) + (47*z**3)*(-20*z**3 - 22*z)\n#Step 2:\nCurrent expression: (-40*z**2)*(-20*z**3 - 22*z) + (47*z**3)*(-20*z**3 - 22*z)\nSimplifying the partial expression: (-40*z**2)*(-20*z**3 - 22*z)\nExpanding the part (-20*z**3 - 22*z) using the distributive property, and we got: (-22*z)*(-40*z**2) + (-40*z**2)*(-20*z**3)\nReplacing (-40*z**2)*(-20*z**3 - 22*z) with (-22*z)*(-40*z**2) + (-40*z**2)*(-20*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-22*z)*(-40*z**2) + (-40*z**2)*(-20*z**3) + (47*z**3)*(-20*z**3 - 22*z)\nSimplifying the partial expression: (47*z**3)*(-20*z**3 - 22*z)\nExpanding the part (-20*z**3 - 22*z) using the distributive property, and we got: (-22*z)*(47*z**3) + (-20*z**3)*(47*z**3)\nReplacing (47*z**3)*(-20*z**3 - 22*z) with (-22*z)*(47*z**3) + (-20*z**3)*(47*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-22*z)*(-40*z**2) + (-22*z)*(47*z**3) + (-40*z**2)*(-20*z**3) + (-20*z**3)*(47*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*z)*(-40*z**2) = 880*z**3\n (-22*z)*(47*z**3) = -1034*z**4\n (-20*z**3)*(-40*z**2) = 800*z**5\n (-20*z**3)*(47*z**3) = -940*z**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -940*z**6 + 800*z**5 - 1034*z**4 + 880*z**3\nNo more calculations needed.\n-940*z**6 + 800*z**5 - 1034*z**4 + 880*z**3", "generated_answer": "-940*z**6 + 800*z**5 - 1034*z**4 + 880*z**3", "step_length": 5} {"cot_id": "b55ab33168c8aa2841dc97cf452d4c888283ecca86ec589f81507b2794a46a8b", "datapoint": {"question": "Calculate the following: (4*y**2 + 30)*(-38*y**3 + 75*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-152*y**5 - 840*y**3 + 2250*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1212, "polynomial_expr": "(4*y**2 + 30)*(-38*y**3 + 75*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (4*y**2 + 30)*(-38*y**3 + 75*y)\nExpanding the part (4*y**2 + 30) using the distributive property, and we got: (4*y**2)*(-38*y**3 + 75*y) + 30*(-38*y**3 + 75*y)\n#Step 2:\nCurrent expression: (4*y**2)*(-38*y**3 + 75*y) + 30*(-38*y**3 + 75*y)\nSimplifying the partial expression: 30*(-38*y**3 + 75*y)\nExpanding the part (-38*y**3 + 75*y) using the distributive property, and we got: (75*y)*30 - 38*y**3*30\nReplacing 30*(-38*y**3 + 75*y) with (75*y)*30 - 38*y**3*30 in the overall expression.\n#Step 3:\nCurrent expression: (75*y)*30 + (4*y**2)*(-38*y**3 + 75*y) - 38*y**3*30\nSimplifying the partial expression: (4*y**2)*(-38*y**3 + 75*y)\nExpanding the part (-38*y**3 + 75*y) using the distributive property, and we got: (75*y)*(4*y**2) + (4*y**2)*(-38*y**3)\nReplacing (4*y**2)*(-38*y**3 + 75*y) with (75*y)*(4*y**2) + (4*y**2)*(-38*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (75*y)*(4*y**2) + (75*y)*30 + (4*y**2)*(-38*y**3) - 38*y**3*30\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*y**3)*30 = -1140*y**3\n (-38*y**3)*(4*y**2) = -152*y**5\n (75*y)*30 = 2250*y\n (75*y)*(4*y**2) = 300*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -152*y**5 - 1140*y**3 + 300*y**3 + 2250*y\nCombining like terms, got -152*y**5 - 840*y**3 + 2250*y\n#Step 6:\nCurrent expression: -152*y**5 - 840*y**3 + 2250*y\nNo more calculations needed.\n-152*y**5 - 840*y**3 + 2250*y", "generated_answer": "-152*y**5 - 840*y**3 + 2250*y", "step_length": 6} {"cot_id": "9872d79e6b584b2748ce4fa9faec6ccb77d5203f68f514ce64c59e22d065abba", "datapoint": {"question": "Simplify this expression: (-8*y**2 - 29*y)*(25*y**3 + 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-200*y**5 - 725*y**4 - 224*y**2 - 812*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1213, "polynomial_expr": "(-8*y**2 - 29*y)*(25*y**3 + 28)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-8*y**2 - 29*y)*(25*y**3 + 28)\nExpanding the part (25*y**3 + 28) using the distributive property, and we got: (25*y**3)*(-8*y**2 - 29*y) + 28*(-8*y**2 - 29*y)\n#Step 2:\nCurrent expression: (25*y**3)*(-8*y**2 - 29*y) + 28*(-8*y**2 - 29*y)\nSimplifying the partial expression: 28*(-8*y**2 - 29*y)\nExpanding the part (-8*y**2 - 29*y) using the distributive property, and we got: -29*y*28 - 8*y**2*28\nReplacing 28*(-8*y**2 - 29*y) with -29*y*28 - 8*y**2*28 in the overall expression.\n#Step 3:\nCurrent expression: -29*y*28 - 8*y**2*28 + (25*y**3)*(-8*y**2 - 29*y)\nSimplifying the partial expression: (25*y**3)*(-8*y**2 - 29*y)\nExpanding the part (-8*y**2 - 29*y) using the distributive property, and we got: (-29*y)*(25*y**3) + (-8*y**2)*(25*y**3)\nReplacing (25*y**3)*(-8*y**2 - 29*y) with (-29*y)*(25*y**3) + (-8*y**2)*(25*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-29*y)*(25*y**3) - 29*y*28 + (-8*y**2)*(25*y**3) - 8*y**2*28\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*y)*28 = -812*y\n (-29*y)*(25*y**3) = -725*y**4\n (-8*y**2)*28 = -224*y**2\n (-8*y**2)*(25*y**3) = -200*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -200*y**5 - 725*y**4 - 224*y**2 - 812*y\nNo more calculations needed.\n-200*y**5 - 725*y**4 - 224*y**2 - 812*y", "generated_answer": "-200*y**5 - 725*y**4 - 224*y**2 - 812*y", "step_length": 5} {"cot_id": "73e44485191311e27b40ee27e87a5a1d743d7525bcfc5955a6a707d8d02a20fa", "datapoint": {"question": "Calculate the following: (35*z**2 + 28*z)*(65*z**3 - 39*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2275*z**5 + 1820*z**4 - 1365*z**3 - 1092*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1214, "polynomial_expr": "(35*z**2 + 28*z)*(65*z**3 - 39*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (35*z**2 + 28*z)*(65*z**3 - 39*z)\nExpanding the part (65*z**3 - 39*z) using the distributive property, and we got: (-39*z)*(35*z**2 + 28*z) + (65*z**3)*(35*z**2 + 28*z)\n#Step 2:\nCurrent expression: (-39*z)*(35*z**2 + 28*z) + (65*z**3)*(35*z**2 + 28*z)\nSimplifying the partial expression: (-39*z)*(35*z**2 + 28*z)\nExpanding the part (35*z**2 + 28*z) using the distributive property, and we got: (-39*z)*(28*z) + (-39*z)*(35*z**2)\nReplacing (-39*z)*(35*z**2 + 28*z) with (-39*z)*(28*z) + (-39*z)*(35*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-39*z)*(28*z) + (-39*z)*(35*z**2) + (65*z**3)*(35*z**2 + 28*z)\nSimplifying the partial expression: (65*z**3)*(35*z**2 + 28*z)\nExpanding the part (35*z**2 + 28*z) using the distributive property, and we got: (28*z)*(65*z**3) + (35*z**2)*(65*z**3)\nReplacing (65*z**3)*(35*z**2 + 28*z) with (28*z)*(65*z**3) + (35*z**2)*(65*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-39*z)*(28*z) + (-39*z)*(35*z**2) + (28*z)*(65*z**3) + (35*z**2)*(65*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (28*z)*(-39*z) = -1092*z**2\n (28*z)*(65*z**3) = 1820*z**4\n (35*z**2)*(-39*z) = -1365*z**3\n (35*z**2)*(65*z**3) = 2275*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2275*z**5 + 1820*z**4 - 1365*z**3 - 1092*z**2\nNo more calculations needed.\n2275*z**5 + 1820*z**4 - 1365*z**3 - 1092*z**2", "generated_answer": "2275*z**5 + 1820*z**4 - 1365*z**3 - 1092*z**2", "step_length": 5} {"cot_id": "56b7d687d286c9b89ce485e350af058dfcbe427f3a3f29153a1dbff011847fc8", "datapoint": {"question": "Simplify this expression: (40*z - 23)*(31*z**3 + 30*z**2 - 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1240*z**4 + 487*z**3 - 690*z**2 - 520*z + 299", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1215, "polynomial_expr": "(40*z - 23)*(31*z**3 + 30*z**2 - 13)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (40*z - 23)*(31*z**3 + 30*z**2 - 13)\nExpanding the part (40*z - 23) using the distributive property, and we got: (40*z)*(31*z**3 + 30*z**2 - 13) - 23*(31*z**3 + 30*z**2 - 13)\n#Step 2:\nCurrent expression: (40*z)*(31*z**3 + 30*z**2 - 13) - 23*(31*z**3 + 30*z**2 - 13)\nSimplifying the partial expression: -23*(31*z**3 + 30*z**2 - 13)\nExpanding the part (31*z**3 + 30*z**2 - 13) using the distributive property, and we got: (30*z**2)*(-23) + (31*z**3)*(-23) - 13*(-23)\nReplacing -23*(31*z**3 + 30*z**2 - 13) with (30*z**2)*(-23) + (31*z**3)*(-23) - 13*(-23) in the overall expression.\n#Step 3:\nCurrent expression: (40*z)*(31*z**3 + 30*z**2 - 13) + (30*z**2)*(-23) + (31*z**3)*(-23) + 299\nSimplifying the partial expression: (40*z)*(31*z**3 + 30*z**2 - 13)\nExpanding the part (31*z**3 + 30*z**2 - 13) using the distributive property, and we got: -520*z + (40*z)*(30*z**2) + (40*z)*(31*z**3)\nReplacing (40*z)*(31*z**3 + 30*z**2 - 13) with -520*z + (40*z)*(30*z**2) + (40*z)*(31*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -13*40*z + (40*z)*(30*z**2) + (40*z)*(31*z**3) + (30*z**2)*(-23) + (31*z**3)*(-23) + 299\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (30*z**2)*-23 = -690*z**2\n (30*z**2)*(40*z) = 1200*z**3\n (31*z**3)*-23 = -713*z**3\n (31*z**3)*(40*z) = 1240*z**4\n -13*40*z = -520*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1240*z**4 - 713*z**3 + 1200*z**3 - 690*z**2 - 520*z + 299\nCombining like terms, got 1240*z**4 + 487*z**3 - 690*z**2 - 520*z + 299\n#Step 6:\nCurrent expression: 1240*z**4 + 487*z**3 - 690*z**2 - 520*z + 299\nNo more calculations needed.\n1240*z**4 + 487*z**3 - 690*z**2 - 520*z + 299", "generated_answer": "1240*z**4 + 487*z**3 - 690*z**2 - 520*z + 299", "step_length": 6} {"cot_id": "160502f5acf69a3e54c0c02adf8fa3310fb2bdf2e837343a7e3e86a3a045bf25", "datapoint": {"question": "Calculate the following: (2*x**3 + 20*x)*(-34*x**2 - 33*x + 22)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-68*x**5 - 66*x**4 - 636*x**3 - 660*x**2 + 440*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1216, "polynomial_expr": "(2*x**3 + 20*x)*(-34*x**2 - 33*x + 22)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2*x**3 + 20*x)*(-34*x**2 - 33*x + 22)\nExpanding the part (2*x**3 + 20*x) using the distributive property, and we got: (20*x)*(-34*x**2 - 33*x + 22) + (2*x**3)*(-34*x**2 - 33*x + 22)\n#Step 2:\nCurrent expression: (20*x)*(-34*x**2 - 33*x + 22) + (2*x**3)*(-34*x**2 - 33*x + 22)\nSimplifying the partial expression: (2*x**3)*(-34*x**2 - 33*x + 22)\nExpanding the part (-34*x**2 - 33*x + 22) using the distributive property, and we got: (-33*x)*(2*x**3) + 22*(2*x**3) + (-34*x**2)*(2*x**3)\nReplacing (2*x**3)*(-34*x**2 - 33*x + 22) with (-33*x)*(2*x**3) + 22*(2*x**3) + (-34*x**2)*(2*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-33*x)*(2*x**3) + 22*2*x**3 + (20*x)*(-34*x**2 - 33*x + 22) + (-34*x**2)*(2*x**3)\nSimplifying the partial expression: (20*x)*(-34*x**2 - 33*x + 22)\nExpanding the part (-34*x**2 - 33*x + 22) using the distributive property, and we got: (-33*x)*(20*x) + 22*(20*x) + (20*x)*(-34*x**2)\nReplacing (20*x)*(-34*x**2 - 33*x + 22) with (-33*x)*(20*x) + 22*(20*x) + (20*x)*(-34*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-33*x)*(20*x) + (-33*x)*(2*x**3) + 22*2*x**3 + 22*20*x + (20*x)*(-34*x**2) + (-34*x**2)*(2*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*x**2)*(2*x**3) = -68*x**5\n (-34*x**2)*(20*x) = -680*x**3\n (-33*x)*(2*x**3) = -66*x**4\n (-33*x)*(20*x) = -660*x**2\n 22*2*x**3 = 44*x**3\n 22*20*x = 440*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -68*x**5 - 66*x**4 - 680*x**3 + 44*x**3 - 660*x**2 + 440*x\nCombining like terms, got -68*x**5 - 66*x**4 - 636*x**3 - 660*x**2 + 440*x\n#Step 6:\nCurrent expression: -68*x**5 - 66*x**4 - 636*x**3 - 660*x**2 + 440*x\nNo more calculations needed.\n-68*x**5 - 66*x**4 - 636*x**3 - 660*x**2 + 440*x", "generated_answer": "-68*x**5 - 66*x**4 - 636*x**3 - 660*x**2 + 440*x", "step_length": 6} {"cot_id": "a4c23f2bfcd31a4633ef3fe303312d31d95e5881b632f8f43977b5edd3fa2cf9", "datapoint": {"question": "Simplify this expression: (-31*y - 37)*(3*y**2 + 25*y - 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-93*y**3 - 886*y**2 + 5*y + 1110", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1217, "polynomial_expr": "(-31*y - 37)*(3*y**2 + 25*y - 30)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-31*y - 37)*(3*y**2 + 25*y - 30)\nExpanding the part (-31*y - 37) using the distributive property, and we got: (-31*y)*(3*y**2 + 25*y - 30) - 37*(3*y**2 + 25*y - 30)\n#Step 2:\nCurrent expression: (-31*y)*(3*y**2 + 25*y - 30) - 37*(3*y**2 + 25*y - 30)\nSimplifying the partial expression: -37*(3*y**2 + 25*y - 30)\nExpanding the part (3*y**2 + 25*y - 30) using the distributive property, and we got: (25*y)*(-37) + (3*y**2)*(-37) - 30*(-37)\nReplacing -37*(3*y**2 + 25*y - 30) with (25*y)*(-37) + (3*y**2)*(-37) - 30*(-37) in the overall expression.\n#Step 3:\nCurrent expression: (-31*y)*(3*y**2 + 25*y - 30) + (25*y)*(-37) + (3*y**2)*(-37) + 1110\nSimplifying the partial expression: (-31*y)*(3*y**2 + 25*y - 30)\nExpanding the part (3*y**2 + 25*y - 30) using the distributive property, and we got: (-31*y)*(25*y) + (-31*y)*(3*y**2) - (-1)*930*y\nReplacing (-31*y)*(3*y**2 + 25*y - 30) with (-31*y)*(25*y) + (-31*y)*(3*y**2) - (-1)*930*y in the overall expression.\n#Step 4:\nCurrent expression: (-31*y)*(25*y) + (-31*y)*(3*y**2) - 30*(-31)*y + (25*y)*(-37) + (3*y**2)*(-37) + 1110\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (3*y**2)*-37 = -111*y**2\n (3*y**2)*(-31*y) = -93*y**3\n (25*y)*-37 = -925*y\n (25*y)*(-31*y) = -775*y**2\n -30*-31*y = 930*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -93*y**3 - 775*y**2 - 111*y**2 - 925*y + 930*y + 1110\nCombining like terms, got -93*y**3 - 886*y**2 + 5*y + 1110\n#Step 6:\nCurrent expression: -93*y**3 - 886*y**2 + 5*y + 1110\nNo more calculations needed.\n-93*y**3 - 886*y**2 + 5*y + 1110", "generated_answer": "-93*y**3 - 886*y**2 + 5*y + 1110", "step_length": 6} {"cot_id": "3ef8cb3a5aa6f114625cea0a1157527280430f13daa87440c48a2d3341af0fbe", "datapoint": {"question": "Calculate the following: (12*x**2 - 29*x + 38)*(-28*x**3 + 13*x**2 - 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-336*x**5 + 968*x**4 - 1441*x**3 - 70*x**2 + 1363*x - 1786", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1218, "polynomial_expr": "(12*x**2 - 29*x + 38)*(-28*x**3 + 13*x**2 - 47)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (12*x**2 - 29*x + 38)*(-28*x**3 + 13*x**2 - 47)\nExpanding the part (-28*x**3 + 13*x**2 - 47) using the distributive property, and we got: (13*x**2)*(12*x**2 - 29*x + 38) + (-28*x**3)*(12*x**2 - 29*x + 38) - 47*(12*x**2 - 29*x + 38)\n#Step 2:\nCurrent expression: (13*x**2)*(12*x**2 - 29*x + 38) + (-28*x**3)*(12*x**2 - 29*x + 38) - 47*(12*x**2 - 29*x + 38)\nSimplifying the partial expression: -47*(12*x**2 - 29*x + 38)\nExpanding the part (12*x**2 - 29*x + 38) using the distributive property, and we got: -29*x*(-47) + (12*x**2)*(-47) + 38*(-47)\nReplacing -47*(12*x**2 - 29*x + 38) with -29*x*(-47) + (12*x**2)*(-47) + 38*(-47) in the overall expression.\n#Step 3:\nCurrent expression: -29*x*(-47) + (12*x**2)*(-47) + (13*x**2)*(12*x**2 - 29*x + 38) + (-28*x**3)*(12*x**2 - 29*x + 38) - 1786\nSimplifying the partial expression: (-28*x**3)*(12*x**2 - 29*x + 38)\nExpanding the part (12*x**2 - 29*x + 38) using the distributive property, and we got: (-29*x)*(-28*x**3) + 38*(-28*x**3) + (12*x**2)*(-28*x**3)\nReplacing (-28*x**3)*(12*x**2 - 29*x + 38) with (-29*x)*(-28*x**3) + 38*(-28*x**3) + (12*x**2)*(-28*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-29*x)*(-28*x**3) - 29*x*(-47) + 38*(-28)*x**3 + (12*x**2)*(-28*x**3) + (12*x**2)*(-47) + (13*x**2)*(12*x**2 - 29*x + 38) - 1786\nSimplifying the partial expression: (13*x**2)*(12*x**2 - 29*x + 38)\nExpanding the part (12*x**2 - 29*x + 38) using the distributive property, and we got: (-29*x)*(13*x**2) + 38*(13*x**2) + (12*x**2)*(13*x**2)\nReplacing (13*x**2)*(12*x**2 - 29*x + 38) with (-29*x)*(13*x**2) + 38*(13*x**2) + (12*x**2)*(13*x**2) in the overall expression.\n#Step 5:\nCurrent expression: (-29*x)*(13*x**2) + (-29*x)*(-28*x**3) - 29*x*(-47) + 38*(-28)*x**3 + 38*13*x**2 + (12*x**2)*(13*x**2) + (12*x**2)*(-28*x**3) + (12*x**2)*(-47) - 1786\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*x)*-47 = 1363*x\n (-29*x)*(-28*x**3) = 812*x**4\n (-29*x)*(13*x**2) = -377*x**3\n (12*x**2)*-47 = -564*x**2\n (12*x**2)*(-28*x**3) = -336*x**5\n (12*x**2)*(13*x**2) = 156*x**4\n 38*-28*x**3 = -1064*x**3\n 38*13*x**2 = 494*x**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -336*x**5 + 156*x**4 + 812*x**4 - 1064*x**3 - 377*x**3 - 564*x**2 + 494*x**2 + 1363*x - 1786\nCombining like terms, got -336*x**5 + 968*x**4 - 1441*x**3 - 70*x**2 + 1363*x - 1786\n#Step 7:\nCurrent expression: -336*x**5 + 968*x**4 - 1441*x**3 - 70*x**2 + 1363*x - 1786\nNo more calculations needed.\n-336*x**5 + 968*x**4 - 1441*x**3 - 70*x**2 + 1363*x - 1786", "generated_answer": "-336*x**5 + 968*x**4 - 1441*x**3 - 70*x**2 + 1363*x - 1786", "step_length": 7} {"cot_id": "4b1477a15ac8eb5048264465947e53a61531a16341d59d83cdbb50e2aa15142d", "datapoint": {"question": "Simplify this expression: (49 - 28*x**2)*(4*x - 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-112*x**3 + 364*x**2 + 196*x - 637", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1219, "polynomial_expr": "(49 - 28*x**2)*(4*x - 13)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (49 - 28*x**2)*(4*x - 13)\nExpanding the part (4*x - 13) using the distributive property, and we got: (4*x)*(49 - 28*x**2) - 13*(49 - 28*x**2)\n#Step 2:\nCurrent expression: (4*x)*(49 - 28*x**2) - 13*(49 - 28*x**2)\nSimplifying the partial expression: -13*(49 - 28*x**2)\nExpanding the part (49 - 28*x**2) using the distributive property, and we got: -28*x**2*(-13) + 49*(-13)\nReplacing -13*(49 - 28*x**2) with -28*x**2*(-13) + 49*(-13) in the overall expression.\n#Step 3:\nCurrent expression: (4*x)*(49 - 28*x**2) - 28*x**2*(-13) - 637\nSimplifying the partial expression: (4*x)*(49 - 28*x**2)\nExpanding the part (49 - 28*x**2) using the distributive property, and we got: 49*(4*x) + (4*x)*(-28*x**2)\nReplacing (4*x)*(49 - 28*x**2) with 49*(4*x) + (4*x)*(-28*x**2) in the overall expression.\n#Step 4:\nCurrent expression: 49*4*x + (4*x)*(-28*x**2) - 28*x**2*(-13) - 637\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*x**2)*-13 = 364*x**2\n (-28*x**2)*(4*x) = -112*x**3\n 49*4*x = 196*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -112*x**3 + 364*x**2 + 196*x - 637\nNo more calculations needed.\n-112*x**3 + 364*x**2 + 196*x - 637", "generated_answer": "-112*x**3 + 364*x**2 + 196*x - 637", "step_length": 5} {"cot_id": "30b21edc63778f1babd66cee27e10a39d41e482b79721676d63348c6231b8b59", "datapoint": {"question": "Calculate the following: (-25*x - 13)*(33*x**3 - 10*x**2 + 28*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-825*x**4 - 179*x**3 - 570*x**2 - 364*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1220, "polynomial_expr": "(-25*x - 13)*(33*x**3 - 10*x**2 + 28*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-25*x - 13)*(33*x**3 - 10*x**2 + 28*x)\nExpanding the part (-25*x - 13) using the distributive property, and we got: (-25*x)*(33*x**3 - 10*x**2 + 28*x) - 13*(33*x**3 - 10*x**2 + 28*x)\n#Step 2:\nCurrent expression: (-25*x)*(33*x**3 - 10*x**2 + 28*x) - 13*(33*x**3 - 10*x**2 + 28*x)\nSimplifying the partial expression: -13*(33*x**3 - 10*x**2 + 28*x)\nExpanding the part (33*x**3 - 10*x**2 + 28*x) using the distributive property, and we got: (28*x)*(-13) - 10*x**2*(-13) + (33*x**3)*(-13)\nReplacing -13*(33*x**3 - 10*x**2 + 28*x) with (28*x)*(-13) - 10*x**2*(-13) + (33*x**3)*(-13) in the overall expression.\n#Step 3:\nCurrent expression: (-25*x)*(33*x**3 - 10*x**2 + 28*x) + (28*x)*(-13) - 10*x**2*(-13) + (33*x**3)*(-13)\nSimplifying the partial expression: (-25*x)*(33*x**3 - 10*x**2 + 28*x)\nExpanding the part (33*x**3 - 10*x**2 + 28*x) using the distributive property, and we got: (-25*x)*(28*x) + (-25*x)*(-10*x**2) + (-25*x)*(33*x**3)\nReplacing (-25*x)*(33*x**3 - 10*x**2 + 28*x) with (-25*x)*(28*x) + (-25*x)*(-10*x**2) + (-25*x)*(33*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-25*x)*(28*x) + (-25*x)*(-10*x**2) + (-25*x)*(33*x**3) + (28*x)*(-13) - 10*x**2*(-13) + (33*x**3)*(-13)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*x**2)*-13 = 130*x**2\n (-10*x**2)*(-25*x) = 250*x**3\n (28*x)*-13 = -364*x\n (28*x)*(-25*x) = -700*x**2\n (33*x**3)*-13 = -429*x**3\n (33*x**3)*(-25*x) = -825*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -825*x**4 - 429*x**3 + 250*x**3 - 700*x**2 + 130*x**2 - 364*x\nCombining like terms, got -825*x**4 - 179*x**3 - 570*x**2 - 364*x\n#Step 6:\nCurrent expression: -825*x**4 - 179*x**3 - 570*x**2 - 364*x\nNo more calculations needed.\n-825*x**4 - 179*x**3 - 570*x**2 - 364*x", "generated_answer": "-825*x**4 - 179*x**3 - 570*x**2 - 364*x", "step_length": 6} {"cot_id": "c6785a282ea02b7a218e1820abf992780d08a1050bf74ab56ec691081a294f7e", "datapoint": {"question": "Calculate the following: (34*x**3 + 51*x)*(14*x**2 - 43*x + 65)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "476*x**5 - 1462*x**4 + 2924*x**3 - 2193*x**2 + 3315*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1221, "polynomial_expr": "(34*x**3 + 51*x)*(14*x**2 - 43*x + 65)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (34*x**3 + 51*x)*(14*x**2 - 43*x + 65)\nExpanding the part (34*x**3 + 51*x) using the distributive property, and we got: (51*x)*(14*x**2 - 43*x + 65) + (34*x**3)*(14*x**2 - 43*x + 65)\n#Step 2:\nCurrent expression: (51*x)*(14*x**2 - 43*x + 65) + (34*x**3)*(14*x**2 - 43*x + 65)\nSimplifying the partial expression: (34*x**3)*(14*x**2 - 43*x + 65)\nExpanding the part (14*x**2 - 43*x + 65) using the distributive property, and we got: (-43*x)*(34*x**3) + 65*(34*x**3) + (14*x**2)*(34*x**3)\nReplacing (34*x**3)*(14*x**2 - 43*x + 65) with (-43*x)*(34*x**3) + 65*(34*x**3) + (14*x**2)*(34*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-43*x)*(34*x**3) + 65*34*x**3 + (51*x)*(14*x**2 - 43*x + 65) + (14*x**2)*(34*x**3)\nSimplifying the partial expression: (51*x)*(14*x**2 - 43*x + 65)\nExpanding the part (14*x**2 - 43*x + 65) using the distributive property, and we got: (-43*x)*(51*x) + 65*(51*x) + (51*x)*(14*x**2)\nReplacing (51*x)*(14*x**2 - 43*x + 65) with (-43*x)*(51*x) + 65*(51*x) + (51*x)*(14*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-43*x)*(51*x) + (-43*x)*(34*x**3) + 65*34*x**3 + 65*51*x + (51*x)*(14*x**2) + (14*x**2)*(34*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-43*x)*(34*x**3) = -1462*x**4\n (-43*x)*(51*x) = -2193*x**2\n (14*x**2)*(34*x**3) = 476*x**5\n (14*x**2)*(51*x) = 714*x**3\n 65*34*x**3 = 2210*x**3\n 65*51*x = 3315*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 476*x**5 - 1462*x**4 + 714*x**3 + 2210*x**3 - 2193*x**2 + 3315*x\nCombining like terms, got 476*x**5 - 1462*x**4 + 2924*x**3 - 2193*x**2 + 3315*x\n#Step 6:\nCurrent expression: 476*x**5 - 1462*x**4 + 2924*x**3 - 2193*x**2 + 3315*x\nNo more calculations needed.\n476*x**5 - 1462*x**4 + 2924*x**3 - 2193*x**2 + 3315*x", "generated_answer": "476*x**5 - 1462*x**4 + 2924*x**3 - 2193*x**2 + 3315*x", "step_length": 6} {"cot_id": "5216515f7e47a894cafd52637fccfc82e23824b0d6839501835cb86aee113aa1", "datapoint": {"question": "Calculate the following: (39*x**3 - 31*x**2)*(-32*x**3 + 4*x**2 - 20*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1248*x**6 + 1148*x**5 - 904*x**4 + 620*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1222, "polynomial_expr": "(39*x**3 - 31*x**2)*(-32*x**3 + 4*x**2 - 20*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (39*x**3 - 31*x**2)*(-32*x**3 + 4*x**2 - 20*x)\nExpanding the part (39*x**3 - 31*x**2) using the distributive property, and we got: (-31*x**2)*(-32*x**3 + 4*x**2 - 20*x) + (39*x**3)*(-32*x**3 + 4*x**2 - 20*x)\n#Step 2:\nCurrent expression: (-31*x**2)*(-32*x**3 + 4*x**2 - 20*x) + (39*x**3)*(-32*x**3 + 4*x**2 - 20*x)\nSimplifying the partial expression: (-31*x**2)*(-32*x**3 + 4*x**2 - 20*x)\nExpanding the part (-32*x**3 + 4*x**2 - 20*x) using the distributive property, and we got: (-20*x)*(-31*x**2) + (-31*x**2)*(4*x**2) + (-31*x**2)*(-32*x**3)\nReplacing (-31*x**2)*(-32*x**3 + 4*x**2 - 20*x) with (-20*x)*(-31*x**2) + (-31*x**2)*(4*x**2) + (-31*x**2)*(-32*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-20*x)*(-31*x**2) + (-31*x**2)*(4*x**2) + (-31*x**2)*(-32*x**3) + (39*x**3)*(-32*x**3 + 4*x**2 - 20*x)\nSimplifying the partial expression: (39*x**3)*(-32*x**3 + 4*x**2 - 20*x)\nExpanding the part (-32*x**3 + 4*x**2 - 20*x) using the distributive property, and we got: (-20*x)*(39*x**3) + (4*x**2)*(39*x**3) + (-32*x**3)*(39*x**3)\nReplacing (39*x**3)*(-32*x**3 + 4*x**2 - 20*x) with (-20*x)*(39*x**3) + (4*x**2)*(39*x**3) + (-32*x**3)*(39*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-20*x)*(-31*x**2) + (-20*x)*(39*x**3) + (-31*x**2)*(4*x**2) + (-31*x**2)*(-32*x**3) + (4*x**2)*(39*x**3) + (-32*x**3)*(39*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*x**3)*(-31*x**2) = 992*x**5\n (-32*x**3)*(39*x**3) = -1248*x**6\n (-20*x)*(-31*x**2) = 620*x**3\n (-20*x)*(39*x**3) = -780*x**4\n (4*x**2)*(-31*x**2) = -124*x**4\n (4*x**2)*(39*x**3) = 156*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1248*x**6 + 156*x**5 + 992*x**5 - 780*x**4 - 124*x**4 + 620*x**3\nCombining like terms, got -1248*x**6 + 1148*x**5 - 904*x**4 + 620*x**3\n#Step 6:\nCurrent expression: -1248*x**6 + 1148*x**5 - 904*x**4 + 620*x**3\nNo more calculations needed.\n-1248*x**6 + 1148*x**5 - 904*x**4 + 620*x**3", "generated_answer": "-1248*x**6 + 1148*x**5 - 904*x**4 + 620*x**3", "step_length": 6} {"cot_id": "7d18ed12d681817175a5d660276fac9a2039552cce60118d1f7f3f795be36fcd", "datapoint": {"question": "Calculate the following: (-2*x**2 + 35*x - 27)*(6*x**3 + 45*x**2 + 28*x + 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-12*x**5 + 120*x**4 + 1357*x**3 - 313*x**2 + 609*x - 1053", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1223, "polynomial_expr": "(-2*x**2 + 35*x - 27)*(6*x**3 + 45*x**2 + 28*x + 39)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-2*x**2 + 35*x - 27)*(6*x**3 + 45*x**2 + 28*x + 39)\nExpanding the part (-2*x**2 + 35*x - 27) using the distributive property, and we got: (35*x)*(6*x**3 + 45*x**2 + 28*x + 39) + (-2*x**2)*(6*x**3 + 45*x**2 + 28*x + 39) - 27*(6*x**3 + 45*x**2 + 28*x + 39)\n#Step 2:\nCurrent expression: (35*x)*(6*x**3 + 45*x**2 + 28*x + 39) + (-2*x**2)*(6*x**3 + 45*x**2 + 28*x + 39) - 27*(6*x**3 + 45*x**2 + 28*x + 39)\nSimplifying the partial expression: -27*(6*x**3 + 45*x**2 + 28*x + 39)\nExpanding the part (6*x**3 + 45*x**2 + 28*x + 39) using the distributive property, and we got: (28*x)*(-27) + (45*x**2)*(-27) + (6*x**3)*(-27) + 39*(-27)\nReplacing -27*(6*x**3 + 45*x**2 + 28*x + 39) with (28*x)*(-27) + (45*x**2)*(-27) + (6*x**3)*(-27) + 39*(-27) in the overall expression.\n#Step 3:\nCurrent expression: (28*x)*(-27) + (35*x)*(6*x**3 + 45*x**2 + 28*x + 39) + (-2*x**2)*(6*x**3 + 45*x**2 + 28*x + 39) + (45*x**2)*(-27) + (6*x**3)*(-27) - 1053\nSimplifying the partial expression: (-2*x**2)*(6*x**3 + 45*x**2 + 28*x + 39)\nExpanding the part (6*x**3 + 45*x**2 + 28*x + 39) using the distributive property, and we got: 39*(-2*x**2) + (28*x)*(-2*x**2) + (-2*x**2)*(45*x**2) + (-2*x**2)*(6*x**3)\nReplacing (-2*x**2)*(6*x**3 + 45*x**2 + 28*x + 39) with 39*(-2*x**2) + (28*x)*(-2*x**2) + (-2*x**2)*(45*x**2) + (-2*x**2)*(6*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 39*(-2)*x**2 + (28*x)*(-2*x**2) + (28*x)*(-27) + (35*x)*(6*x**3 + 45*x**2 + 28*x + 39) + (-2*x**2)*(45*x**2) + (-2*x**2)*(6*x**3) + (45*x**2)*(-27) + (6*x**3)*(-27) - 1053\nSimplifying the partial expression: (35*x)*(6*x**3 + 45*x**2 + 28*x + 39)\nExpanding the part (6*x**3 + 45*x**2 + 28*x + 39) using the distributive property, and we got: 39*(35*x) + (28*x)*(35*x) + (35*x)*(45*x**2) + (35*x)*(6*x**3)\nReplacing (35*x)*(6*x**3 + 45*x**2 + 28*x + 39) with 39*(35*x) + (28*x)*(35*x) + (35*x)*(45*x**2) + (35*x)*(6*x**3) in the overall expression.\n#Step 5:\nCurrent expression: 39*(-2)*x**2 + 39*35*x + (28*x)*(35*x) + (28*x)*(-2*x**2) + (28*x)*(-27) + (35*x)*(45*x**2) + (35*x)*(6*x**3) + (-2*x**2)*(45*x**2) + (-2*x**2)*(6*x**3) + (45*x**2)*(-27) + (6*x**3)*(-27) - 1053\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (6*x**3)*-27 = -162*x**3\n (6*x**3)*(-2*x**2) = -12*x**5\n (6*x**3)*(35*x) = 210*x**4\n (28*x)*-27 = -756*x\n (28*x)*(-2*x**2) = -56*x**3\n (28*x)*(35*x) = 980*x**2\n (45*x**2)*-27 = -1215*x**2\n (45*x**2)*(-2*x**2) = -90*x**4\n (45*x**2)*(35*x) = 1575*x**3\n 39*-2*x**2 = -78*x**2\n 39*35*x = 1365*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -12*x**5 - 90*x**4 + 210*x**4 - 162*x**3 - 56*x**3 + 1575*x**3 - 1215*x**2 - 78*x**2 + 980*x**2 - 756*x + 1365*x - 1053\nCombining like terms, got -12*x**5 + 120*x**4 + 1357*x**3 - 313*x**2 + 609*x - 1053\n#Step 7:\nCurrent expression: -12*x**5 + 120*x**4 + 1357*x**3 - 313*x**2 + 609*x - 1053\nNo more calculations needed.\n-12*x**5 + 120*x**4 + 1357*x**3 - 313*x**2 + 609*x - 1053", "generated_answer": "-12*x**5 + 120*x**4 + 1357*x**3 - 313*x**2 + 609*x - 1053", "step_length": 7} {"cot_id": "bc4220689187efb782d66d9583ec9ae84ff9fecc1418b0dd9d9250c629b5c498", "datapoint": {"question": "Calculate the following: (-5*z**3 - 50*z**2)*(66*z**3 + 30*z**2 + 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-330*z**6 - 3450*z**5 - 1500*z**4 - 100*z**3 - 1000*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1224, "polynomial_expr": "(-5*z**3 - 50*z**2)*(66*z**3 + 30*z**2 + 20)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-5*z**3 - 50*z**2)*(66*z**3 + 30*z**2 + 20)\nExpanding the part (-5*z**3 - 50*z**2) using the distributive property, and we got: (-50*z**2)*(66*z**3 + 30*z**2 + 20) + (-5*z**3)*(66*z**3 + 30*z**2 + 20)\n#Step 2:\nCurrent expression: (-50*z**2)*(66*z**3 + 30*z**2 + 20) + (-5*z**3)*(66*z**3 + 30*z**2 + 20)\nSimplifying the partial expression: (-50*z**2)*(66*z**3 + 30*z**2 + 20)\nExpanding the part (66*z**3 + 30*z**2 + 20) using the distributive property, and we got: 20*(-50*z**2) + (-50*z**2)*(30*z**2) + (-50*z**2)*(66*z**3)\nReplacing (-50*z**2)*(66*z**3 + 30*z**2 + 20) with 20*(-50*z**2) + (-50*z**2)*(30*z**2) + (-50*z**2)*(66*z**3) in the overall expression.\n#Step 3:\nCurrent expression: 20*(-50)*z**2 + (-50*z**2)*(30*z**2) + (-50*z**2)*(66*z**3) + (-5*z**3)*(66*z**3 + 30*z**2 + 20)\nSimplifying the partial expression: (-5*z**3)*(66*z**3 + 30*z**2 + 20)\nExpanding the part (66*z**3 + 30*z**2 + 20) using the distributive property, and we got: 20*(-5*z**3) + (30*z**2)*(-5*z**3) + (-5*z**3)*(66*z**3)\nReplacing (-5*z**3)*(66*z**3 + 30*z**2 + 20) with 20*(-5*z**3) + (30*z**2)*(-5*z**3) + (-5*z**3)*(66*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 20*(-5)*z**3 + 20*(-50)*z**2 + (-50*z**2)*(30*z**2) + (-50*z**2)*(66*z**3) + (30*z**2)*(-5*z**3) + (-5*z**3)*(66*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (30*z**2)*(-50*z**2) = -1500*z**4\n (30*z**2)*(-5*z**3) = -150*z**5\n (66*z**3)*(-50*z**2) = -3300*z**5\n (66*z**3)*(-5*z**3) = -330*z**6\n 20*-50*z**2 = -1000*z**2\n 20*-5*z**3 = -100*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -330*z**6 - 3300*z**5 - 150*z**5 - 1500*z**4 - 100*z**3 - 1000*z**2\nCombining like terms, got -330*z**6 - 3450*z**5 - 1500*z**4 - 100*z**3 - 1000*z**2\n#Step 6:\nCurrent expression: -330*z**6 - 3450*z**5 - 1500*z**4 - 100*z**3 - 1000*z**2\nNo more calculations needed.\n-330*z**6 - 3450*z**5 - 1500*z**4 - 100*z**3 - 1000*z**2", "generated_answer": "-330*z**6 - 3450*z**5 - 1500*z**4 - 100*z**3 - 1000*z**2", "step_length": 6} {"cot_id": "aca97ce619d22ae0d0ae9d733872557a9b0f137559b37c537420446fa3023215", "datapoint": {"question": "Simplify this expression: (27*x**2 - 36)*(13*x**3 + x**2 + 4*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "351*x**5 + 27*x**4 - 360*x**3 - 36*x**2 - 144*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1225, "polynomial_expr": "(27*x**2 - 36)*(13*x**3 + x**2 + 4*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*x**2 - 36)*(13*x**3 + x**2 + 4*x)\nExpanding the part (27*x**2 - 36) using the distributive property, and we got: (27*x**2)*(13*x**3 + x**2 + 4*x) - 36*(13*x**3 + x**2 + 4*x)\n#Step 2:\nCurrent expression: (27*x**2)*(13*x**3 + x**2 + 4*x) - 36*(13*x**3 + x**2 + 4*x)\nSimplifying the partial expression: -36*(13*x**3 + x**2 + 4*x)\nExpanding the part (13*x**3 + x**2 + 4*x) using the distributive property, and we got: x**2*(-36) + (4*x)*(-36) + (13*x**3)*(-36)\nReplacing -36*(13*x**3 + x**2 + 4*x) with x**2*(-36) + (4*x)*(-36) + (13*x**3)*(-36) in the overall expression.\n#Step 3:\nCurrent expression: x**2*(-36) + (4*x)*(-36) + (27*x**2)*(13*x**3 + x**2 + 4*x) + (13*x**3)*(-36)\nSimplifying the partial expression: (27*x**2)*(13*x**3 + x**2 + 4*x)\nExpanding the part (13*x**3 + x**2 + 4*x) using the distributive property, and we got: x**2*(27*x**2) + (4*x)*(27*x**2) + (27*x**2)*(13*x**3)\nReplacing (27*x**2)*(13*x**3 + x**2 + 4*x) with x**2*(27*x**2) + (4*x)*(27*x**2) + (27*x**2)*(13*x**3) in the overall expression.\n#Step 4:\nCurrent expression: x**2*(27*x**2) + x**2*(-36) + (4*x)*(27*x**2) + (4*x)*(-36) + (27*x**2)*(13*x**3) + (13*x**3)*(-36)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n x**2*-36 = -36*x**2\n x**2*(27*x**2) = 27*x**4\n (4*x)*-36 = -144*x\n (4*x)*(27*x**2) = 108*x**3\n (13*x**3)*-36 = -468*x**3\n (13*x**3)*(27*x**2) = 351*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 351*x**5 + 27*x**4 - 468*x**3 + 108*x**3 - 36*x**2 - 144*x\nCombining like terms, got 351*x**5 + 27*x**4 - 360*x**3 - 36*x**2 - 144*x\n#Step 6:\nCurrent expression: 351*x**5 + 27*x**4 - 360*x**3 - 36*x**2 - 144*x\nNo more calculations needed.\n351*x**5 + 27*x**4 - 360*x**3 - 36*x**2 - 144*x", "generated_answer": "351*x**5 + 27*x**4 - 360*x**3 - 36*x**2 - 144*x", "step_length": 6} {"cot_id": "e7e8047bd51fe0716414068971c91be3eff5fa3fa52ab753647c5d1ce2fe5884", "datapoint": {"question": "Simplify this expression: (25 - 24*x)*(39 - 39*x**3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "936*x**4 - 975*x**3 - 936*x + 975", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1226, "polynomial_expr": "(25 - 24*x)*(39 - 39*x**3)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (25 - 24*x)*(39 - 39*x**3)\nExpanding the part (25 - 24*x) using the distributive property, and we got: (-24*x)*(39 - 39*x**3) + 25*(39 - 39*x**3)\n#Step 2:\nCurrent expression: (-24*x)*(39 - 39*x**3) + 25*(39 - 39*x**3)\nSimplifying the partial expression: 25*(39 - 39*x**3)\nExpanding the part (39 - 39*x**3) using the distributive property, and we got: -39*x**3*25 + 39*25\nReplacing 25*(39 - 39*x**3) with -39*x**3*25 + 39*25 in the overall expression.\n#Step 3:\nCurrent expression: (-24*x)*(39 - 39*x**3) - 39*x**3*25 + 975\nSimplifying the partial expression: (-24*x)*(39 - 39*x**3)\nExpanding the part (39 - 39*x**3) using the distributive property, and we got: (-24*x)*(-39*x**3) + 39*(-24*x)\nReplacing (-24*x)*(39 - 39*x**3) with (-24*x)*(-39*x**3) + 39*(-24*x) in the overall expression.\n#Step 4:\nCurrent expression: (-24*x)*(-39*x**3) + 39*(-24)*x - 39*x**3*25 + 975\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*x**3)*25 = -975*x**3\n (-39*x**3)*(-24*x) = 936*x**4\n 39*-24*x = -936*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 936*x**4 - 975*x**3 - 936*x + 975\nNo more calculations needed.\n936*x**4 - 975*x**3 - 936*x + 975", "generated_answer": "936*x**4 - 975*x**3 - 936*x + 975", "step_length": 5} {"cot_id": "6676b07297106016440b0f2da4225e497e0ae836d9453422107b533dbbd4837e", "datapoint": {"question": "Calculate the following: (-54*z**3 + 20*z)*(-54*z**2 + 42*z - 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2916*z**5 - 2268*z**4 - 216*z**3 + 840*z**2 - 320*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1227, "polynomial_expr": "(-54*z**3 + 20*z)*(-54*z**2 + 42*z - 16)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-54*z**3 + 20*z)*(-54*z**2 + 42*z - 16)\nExpanding the part (-54*z**3 + 20*z) using the distributive property, and we got: (20*z)*(-54*z**2 + 42*z - 16) + (-54*z**3)*(-54*z**2 + 42*z - 16)\n#Step 2:\nCurrent expression: (20*z)*(-54*z**2 + 42*z - 16) + (-54*z**3)*(-54*z**2 + 42*z - 16)\nSimplifying the partial expression: (-54*z**3)*(-54*z**2 + 42*z - 16)\nExpanding the part (-54*z**2 + 42*z - 16) using the distributive property, and we got: -(-1)*864*z**3 + (42*z)*(-54*z**3) + (-54*z**2)*(-54*z**3)\nReplacing (-54*z**3)*(-54*z**2 + 42*z - 16) with -(-1)*864*z**3 + (42*z)*(-54*z**3) + (-54*z**2)*(-54*z**3) in the overall expression.\n#Step 3:\nCurrent expression: -16*(-54)*z**3 + (20*z)*(-54*z**2 + 42*z - 16) + (42*z)*(-54*z**3) + (-54*z**2)*(-54*z**3)\nSimplifying the partial expression: (20*z)*(-54*z**2 + 42*z - 16)\nExpanding the part (-54*z**2 + 42*z - 16) using the distributive property, and we got: -320*z + (20*z)*(42*z) + (20*z)*(-54*z**2)\nReplacing (20*z)*(-54*z**2 + 42*z - 16) with -320*z + (20*z)*(42*z) + (20*z)*(-54*z**2) in the overall expression.\n#Step 4:\nCurrent expression: -16*(-54)*z**3 - 16*20*z + (20*z)*(42*z) + (20*z)*(-54*z**2) + (42*z)*(-54*z**3) + (-54*z**2)*(-54*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-54*z**2)*(-54*z**3) = 2916*z**5\n (-54*z**2)*(20*z) = -1080*z**3\n (42*z)*(-54*z**3) = -2268*z**4\n (42*z)*(20*z) = 840*z**2\n -16*-54*z**3 = 864*z**3\n -16*20*z = -320*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2916*z**5 - 2268*z**4 - 1080*z**3 + 864*z**3 + 840*z**2 - 320*z\nCombining like terms, got 2916*z**5 - 2268*z**4 - 216*z**3 + 840*z**2 - 320*z\n#Step 6:\nCurrent expression: 2916*z**5 - 2268*z**4 - 216*z**3 + 840*z**2 - 320*z\nNo more calculations needed.\n2916*z**5 - 2268*z**4 - 216*z**3 + 840*z**2 - 320*z", "generated_answer": "2916*z**5 - 2268*z**4 - 216*z**3 + 840*z**2 - 320*z", "step_length": 6} {"cot_id": "54dee2489852dd2d414ce2ac6aa68ecc0ffe97be3541d63df7231df4039c6977", "datapoint": {"question": "Simplify this expression: (-10*z**2 - 8*z)*(32*z**3 + 2*z - 34)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-320*z**5 - 256*z**4 - 20*z**3 + 324*z**2 + 272*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1228, "polynomial_expr": "(-10*z**2 - 8*z)*(32*z**3 + 2*z - 34)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-10*z**2 - 8*z)*(32*z**3 + 2*z - 34)\nExpanding the part (-10*z**2 - 8*z) using the distributive property, and we got: (-8*z)*(32*z**3 + 2*z - 34) + (-10*z**2)*(32*z**3 + 2*z - 34)\n#Step 2:\nCurrent expression: (-8*z)*(32*z**3 + 2*z - 34) + (-10*z**2)*(32*z**3 + 2*z - 34)\nSimplifying the partial expression: (-10*z**2)*(32*z**3 + 2*z - 34)\nExpanding the part (32*z**3 + 2*z - 34) using the distributive property, and we got: -(-1)*340*z**2 + (2*z)*(-10*z**2) + (-10*z**2)*(32*z**3)\nReplacing (-10*z**2)*(32*z**3 + 2*z - 34) with -(-1)*340*z**2 + (2*z)*(-10*z**2) + (-10*z**2)*(32*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-8*z)*(32*z**3 + 2*z - 34) - 34*(-10)*z**2 + (2*z)*(-10*z**2) + (-10*z**2)*(32*z**3)\nSimplifying the partial expression: (-8*z)*(32*z**3 + 2*z - 34)\nExpanding the part (32*z**3 + 2*z - 34) using the distributive property, and we got: (-8*z)*(2*z) + (-8*z)*(32*z**3) - (-1)*272*z\nReplacing (-8*z)*(32*z**3 + 2*z - 34) with (-8*z)*(2*z) + (-8*z)*(32*z**3) - (-1)*272*z in the overall expression.\n#Step 4:\nCurrent expression: (-8*z)*(2*z) + (-8*z)*(32*z**3) - 34*(-10)*z**2 - 34*(-8)*z + (2*z)*(-10*z**2) + (-10*z**2)*(32*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (2*z)*(-10*z**2) = -20*z**3\n (2*z)*(-8*z) = -16*z**2\n (32*z**3)*(-10*z**2) = -320*z**5\n (32*z**3)*(-8*z) = -256*z**4\n -34*-10*z**2 = 340*z**2\n -34*-8*z = 272*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -320*z**5 - 256*z**4 - 20*z**3 - 16*z**2 + 340*z**2 + 272*z\nCombining like terms, got -320*z**5 - 256*z**4 - 20*z**3 + 324*z**2 + 272*z\n#Step 6:\nCurrent expression: -320*z**5 - 256*z**4 - 20*z**3 + 324*z**2 + 272*z\nNo more calculations needed.\n-320*z**5 - 256*z**4 - 20*z**3 + 324*z**2 + 272*z", "generated_answer": "-320*z**5 - 256*z**4 - 20*z**3 + 324*z**2 + 272*z", "step_length": 6} {"cot_id": "975d2ab83158eb80e03794fb0e08875ebd693e77a4950885036962d4811957a1", "datapoint": {"question": "Calculate the following: -37*y**3*(-3*y**3 + 30*y - 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "111*y**6 - 1110*y**4 + 37*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1229, "polynomial_expr": "-37*y**3*(-3*y**3 + 30*y - 1)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -37*y**3*(-3*y**3 + 30*y - 1)\nExpanding the part (-3*y**3 + 30*y - 1) using the distributive property, and we got: -(-1)*37*y**3 + (30*y)*(-37*y**3) + (-37*y**3)*(-3*y**3)\n#Step 2:\nCurrent expression: -(-1)*37*y**3 + (30*y)*(-37*y**3) + (-37*y**3)*(-3*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -1*(-37*y**3) = 37*y**3\n (-3*y**3)*(-37*y**3) = 111*y**6\n (30*y)*(-37*y**3) = -1110*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 111*y**6 - 1110*y**4 + 37*y**3\nNo more calculations needed.\n111*y**6 - 1110*y**4 + 37*y**3", "generated_answer": "111*y**6 - 1110*y**4 + 37*y**3", "step_length": 3} {"cot_id": "ed5069623357e65315e6d5691805e9c6a05e54a96a54356efc949c787297c790", "datapoint": {"question": "Simplify this expression: (10 - 23*x**3)*(-38*x**3 + 28*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "874*x**6 - 644*x**4 - 380*x**3 + 280*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1230, "polynomial_expr": "(10 - 23*x**3)*(-38*x**3 + 28*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (10 - 23*x**3)*(-38*x**3 + 28*x)\nExpanding the part (10 - 23*x**3) using the distributive property, and we got: (-23*x**3)*(-38*x**3 + 28*x) + 10*(-38*x**3 + 28*x)\n#Step 2:\nCurrent expression: (-23*x**3)*(-38*x**3 + 28*x) + 10*(-38*x**3 + 28*x)\nSimplifying the partial expression: 10*(-38*x**3 + 28*x)\nExpanding the part (-38*x**3 + 28*x) using the distributive property, and we got: (28*x)*10 - 38*x**3*10\nReplacing 10*(-38*x**3 + 28*x) with (28*x)*10 - 38*x**3*10 in the overall expression.\n#Step 3:\nCurrent expression: (28*x)*10 - 38*x**3*10 + (-23*x**3)*(-38*x**3 + 28*x)\nSimplifying the partial expression: (-23*x**3)*(-38*x**3 + 28*x)\nExpanding the part (-38*x**3 + 28*x) using the distributive property, and we got: (28*x)*(-23*x**3) + (-38*x**3)*(-23*x**3)\nReplacing (-23*x**3)*(-38*x**3 + 28*x) with (28*x)*(-23*x**3) + (-38*x**3)*(-23*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (28*x)*(-23*x**3) + (28*x)*10 + (-38*x**3)*(-23*x**3) - 38*x**3*10\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*x**3)*10 = -380*x**3\n (-38*x**3)*(-23*x**3) = 874*x**6\n (28*x)*10 = 280*x\n (28*x)*(-23*x**3) = -644*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 874*x**6 - 644*x**4 - 380*x**3 + 280*x\nNo more calculations needed.\n874*x**6 - 644*x**4 - 380*x**3 + 280*x", "generated_answer": "874*x**6 - 644*x**4 - 380*x**3 + 280*x", "step_length": 5} {"cot_id": "722df646efcc67c9ef712387e7268962b69be0273c5618dcecfe30fc9c358f35", "datapoint": {"question": "Calculate the following: (18 - 2*z**3)*(-22*z**3 - 78*z**2 + 9)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "44*z**6 + 156*z**5 - 414*z**3 - 1404*z**2 + 162", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1231, "polynomial_expr": "(18 - 2*z**3)*(-22*z**3 - 78*z**2 + 9)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (18 - 2*z**3)*(-22*z**3 - 78*z**2 + 9)\nExpanding the part (18 - 2*z**3) using the distributive property, and we got: (-2*z**3)*(-22*z**3 - 78*z**2 + 9) + 18*(-22*z**3 - 78*z**2 + 9)\n#Step 2:\nCurrent expression: (-2*z**3)*(-22*z**3 - 78*z**2 + 9) + 18*(-22*z**3 - 78*z**2 + 9)\nSimplifying the partial expression: 18*(-22*z**3 - 78*z**2 + 9)\nExpanding the part (-22*z**3 - 78*z**2 + 9) using the distributive property, and we got: -78*z**2*18 - 22*z**3*18 + 9*18\nReplacing 18*(-22*z**3 - 78*z**2 + 9) with -78*z**2*18 - 22*z**3*18 + 9*18 in the overall expression.\n#Step 3:\nCurrent expression: -78*z**2*18 - 22*z**3*18 + (-2*z**3)*(-22*z**3 - 78*z**2 + 9) + 162\nSimplifying the partial expression: (-2*z**3)*(-22*z**3 - 78*z**2 + 9)\nExpanding the part (-22*z**3 - 78*z**2 + 9) using the distributive property, and we got: 9*(-2*z**3) + (-78*z**2)*(-2*z**3) + (-22*z**3)*(-2*z**3)\nReplacing (-2*z**3)*(-22*z**3 - 78*z**2 + 9) with 9*(-2*z**3) + (-78*z**2)*(-2*z**3) + (-22*z**3)*(-2*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 9*(-2)*z**3 + (-78*z**2)*(-2*z**3) - 78*z**2*18 + (-22*z**3)*(-2*z**3) - 22*z**3*18 + 162\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-78*z**2)*18 = -1404*z**2\n (-78*z**2)*(-2*z**3) = 156*z**5\n (-22*z**3)*18 = -396*z**3\n (-22*z**3)*(-2*z**3) = 44*z**6\n 9*-2*z**3 = -18*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 44*z**6 + 156*z**5 - 396*z**3 - 18*z**3 - 1404*z**2 + 162\nCombining like terms, got 44*z**6 + 156*z**5 - 414*z**3 - 1404*z**2 + 162\n#Step 6:\nCurrent expression: 44*z**6 + 156*z**5 - 414*z**3 - 1404*z**2 + 162\nNo more calculations needed.\n44*z**6 + 156*z**5 - 414*z**3 - 1404*z**2 + 162", "generated_answer": "44*z**6 + 156*z**5 - 414*z**3 - 1404*z**2 + 162", "step_length": 6} {"cot_id": "1196b7ebfd0cc3ab4929d41fd682ceb6962a31dad3982c46bd0cf3a00aa69964", "datapoint": {"question": "Calculate the following: (12*x**2 + 42)*(3*x**3 + 35*x - 27)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "36*x**5 + 546*x**3 - 324*x**2 + 1470*x - 1134", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1232, "polynomial_expr": "(12*x**2 + 42)*(3*x**3 + 35*x - 27)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (12*x**2 + 42)*(3*x**3 + 35*x - 27)\nExpanding the part (12*x**2 + 42) using the distributive property, and we got: (12*x**2)*(3*x**3 + 35*x - 27) + 42*(3*x**3 + 35*x - 27)\n#Step 2:\nCurrent expression: (12*x**2)*(3*x**3 + 35*x - 27) + 42*(3*x**3 + 35*x - 27)\nSimplifying the partial expression: 42*(3*x**3 + 35*x - 27)\nExpanding the part (3*x**3 + 35*x - 27) using the distributive property, and we got: (35*x)*42 + (3*x**3)*42 - 27*42\nReplacing 42*(3*x**3 + 35*x - 27) with (35*x)*42 + (3*x**3)*42 - 27*42 in the overall expression.\n#Step 3:\nCurrent expression: (35*x)*42 + (12*x**2)*(3*x**3 + 35*x - 27) + (3*x**3)*42 - 1134\nSimplifying the partial expression: (12*x**2)*(3*x**3 + 35*x - 27)\nExpanding the part (3*x**3 + 35*x - 27) using the distributive property, and we got: -324*x**2 + (35*x)*(12*x**2) + (12*x**2)*(3*x**3)\nReplacing (12*x**2)*(3*x**3 + 35*x - 27) with -324*x**2 + (35*x)*(12*x**2) + (12*x**2)*(3*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -27*12*x**2 + (35*x)*(12*x**2) + (35*x)*42 + (12*x**2)*(3*x**3) + (3*x**3)*42 - 1134\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (3*x**3)*42 = 126*x**3\n (3*x**3)*(12*x**2) = 36*x**5\n (35*x)*42 = 1470*x\n (35*x)*(12*x**2) = 420*x**3\n -27*12*x**2 = -324*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 36*x**5 + 126*x**3 + 420*x**3 - 324*x**2 + 1470*x - 1134\nCombining like terms, got 36*x**5 + 546*x**3 - 324*x**2 + 1470*x - 1134\n#Step 6:\nCurrent expression: 36*x**5 + 546*x**3 - 324*x**2 + 1470*x - 1134\nNo more calculations needed.\n36*x**5 + 546*x**3 - 324*x**2 + 1470*x - 1134", "generated_answer": "36*x**5 + 546*x**3 - 324*x**2 + 1470*x - 1134", "step_length": 6} {"cot_id": "5e16b3f476efc8b20a04bc8b3b0da936c6b57ce3c1aa3839902f5cdc38f23ffa", "datapoint": {"question": "Simplify this expression: (-28*z - 42)*(-27*z**3 + 34*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "756*z**4 + 1134*z**3 - 952*z**2 - 1428*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1233, "polynomial_expr": "(-28*z - 42)*(-27*z**3 + 34*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-28*z - 42)*(-27*z**3 + 34*z)\nExpanding the part (-28*z - 42) using the distributive property, and we got: (-28*z)*(-27*z**3 + 34*z) - 42*(-27*z**3 + 34*z)\n#Step 2:\nCurrent expression: (-28*z)*(-27*z**3 + 34*z) - 42*(-27*z**3 + 34*z)\nSimplifying the partial expression: -42*(-27*z**3 + 34*z)\nExpanding the part (-27*z**3 + 34*z) using the distributive property, and we got: (34*z)*(-42) - 27*z**3*(-42)\nReplacing -42*(-27*z**3 + 34*z) with (34*z)*(-42) - 27*z**3*(-42) in the overall expression.\n#Step 3:\nCurrent expression: (-28*z)*(-27*z**3 + 34*z) + (34*z)*(-42) - 27*z**3*(-42)\nSimplifying the partial expression: (-28*z)*(-27*z**3 + 34*z)\nExpanding the part (-27*z**3 + 34*z) using the distributive property, and we got: (-28*z)*(34*z) + (-28*z)*(-27*z**3)\nReplacing (-28*z)*(-27*z**3 + 34*z) with (-28*z)*(34*z) + (-28*z)*(-27*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-28*z)*(34*z) + (-28*z)*(-27*z**3) + (34*z)*(-42) - 27*z**3*(-42)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*z**3)*-42 = 1134*z**3\n (-27*z**3)*(-28*z) = 756*z**4\n (34*z)*-42 = -1428*z\n (34*z)*(-28*z) = -952*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 756*z**4 + 1134*z**3 - 952*z**2 - 1428*z\nNo more calculations needed.\n756*z**4 + 1134*z**3 - 952*z**2 - 1428*z", "generated_answer": "756*z**4 + 1134*z**3 - 952*z**2 - 1428*z", "step_length": 5} {"cot_id": "284a6fc80242a463a491956e035f3fcbcd4f7c1927bce37dff7b6d7c277026fa", "datapoint": {"question": "Calculate the following: (16*x**2 + 38)*(-5*x**3 + 41*x**2 - 39*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-80*x**5 + 656*x**4 - 814*x**3 + 1558*x**2 - 1482*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1234, "polynomial_expr": "(16*x**2 + 38)*(-5*x**3 + 41*x**2 - 39*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (16*x**2 + 38)*(-5*x**3 + 41*x**2 - 39*x)\nExpanding the part (16*x**2 + 38) using the distributive property, and we got: (16*x**2)*(-5*x**3 + 41*x**2 - 39*x) + 38*(-5*x**3 + 41*x**2 - 39*x)\n#Step 2:\nCurrent expression: (16*x**2)*(-5*x**3 + 41*x**2 - 39*x) + 38*(-5*x**3 + 41*x**2 - 39*x)\nSimplifying the partial expression: 38*(-5*x**3 + 41*x**2 - 39*x)\nExpanding the part (-5*x**3 + 41*x**2 - 39*x) using the distributive property, and we got: -39*x*38 + (41*x**2)*38 - 5*x**3*38\nReplacing 38*(-5*x**3 + 41*x**2 - 39*x) with -39*x*38 + (41*x**2)*38 - 5*x**3*38 in the overall expression.\n#Step 3:\nCurrent expression: -39*x*38 + (16*x**2)*(-5*x**3 + 41*x**2 - 39*x) + (41*x**2)*38 - 5*x**3*38\nSimplifying the partial expression: (16*x**2)*(-5*x**3 + 41*x**2 - 39*x)\nExpanding the part (-5*x**3 + 41*x**2 - 39*x) using the distributive property, and we got: (-39*x)*(16*x**2) + (16*x**2)*(41*x**2) + (16*x**2)*(-5*x**3)\nReplacing (16*x**2)*(-5*x**3 + 41*x**2 - 39*x) with (-39*x)*(16*x**2) + (16*x**2)*(41*x**2) + (16*x**2)*(-5*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-39*x)*(16*x**2) - 39*x*38 + (16*x**2)*(41*x**2) + (16*x**2)*(-5*x**3) + (41*x**2)*38 - 5*x**3*38\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*x)*38 = -1482*x\n (-39*x)*(16*x**2) = -624*x**3\n (-5*x**3)*38 = -190*x**3\n (-5*x**3)*(16*x**2) = -80*x**5\n (41*x**2)*38 = 1558*x**2\n (41*x**2)*(16*x**2) = 656*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -80*x**5 + 656*x**4 - 624*x**3 - 190*x**3 + 1558*x**2 - 1482*x\nCombining like terms, got -80*x**5 + 656*x**4 - 814*x**3 + 1558*x**2 - 1482*x\n#Step 6:\nCurrent expression: -80*x**5 + 656*x**4 - 814*x**3 + 1558*x**2 - 1482*x\nNo more calculations needed.\n-80*x**5 + 656*x**4 - 814*x**3 + 1558*x**2 - 1482*x", "generated_answer": "-80*x**5 + 656*x**4 - 814*x**3 + 1558*x**2 - 1482*x", "step_length": 6} {"cot_id": "136c56ed41b66652fbe9eddae2168f0741219169683a34940dca020bd65e5707", "datapoint": {"question": "Simplify this expression: (x**2 + 44*x)*(32*x**3 - 13*x**2 - 20*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "32*x**5 + 1395*x**4 - 592*x**3 - 880*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1235, "polynomial_expr": "(x**2 + 44*x)*(32*x**3 - 13*x**2 - 20*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (x**2 + 44*x)*(32*x**3 - 13*x**2 - 20*x)\nExpanding the part (x**2 + 44*x) using the distributive property, and we got: x**2*(32*x**3 - 13*x**2 - 20*x) + (44*x)*(32*x**3 - 13*x**2 - 20*x)\n#Step 2:\nCurrent expression: x**2*(32*x**3 - 13*x**2 - 20*x) + (44*x)*(32*x**3 - 13*x**2 - 20*x)\nSimplifying the partial expression: x**2*(32*x**3 - 13*x**2 - 20*x)\nExpanding the part (32*x**3 - 13*x**2 - 20*x) using the distributive property, and we got: (-20*x)*x**2 + (-13*x**2)*x**2 + x**2*(32*x**3)\nReplacing x**2*(32*x**3 - 13*x**2 - 20*x) with (-20*x)*x**2 + (-13*x**2)*x**2 + x**2*(32*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-20*x)*x**2 + (-13*x**2)*x**2 + x**2*(32*x**3) + (44*x)*(32*x**3 - 13*x**2 - 20*x)\nSimplifying the partial expression: (44*x)*(32*x**3 - 13*x**2 - 20*x)\nExpanding the part (32*x**3 - 13*x**2 - 20*x) using the distributive property, and we got: (-20*x)*(44*x) + (44*x)*(-13*x**2) + (44*x)*(32*x**3)\nReplacing (44*x)*(32*x**3 - 13*x**2 - 20*x) with (-20*x)*(44*x) + (44*x)*(-13*x**2) + (44*x)*(32*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-20*x)*x**2 + (-20*x)*(44*x) + (-13*x**2)*x**2 + x**2*(32*x**3) + (44*x)*(-13*x**2) + (44*x)*(32*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*x)*x**2 = -20*x**3\n (-20*x)*(44*x) = -880*x**2\n (-13*x**2)*x**2 = -13*x**4\n (-13*x**2)*(44*x) = -572*x**3\n (32*x**3)*x**2 = 32*x**5\n (32*x**3)*(44*x) = 1408*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 32*x**5 - 13*x**4 + 1408*x**4 - 572*x**3 - 20*x**3 - 880*x**2\nCombining like terms, got 32*x**5 + 1395*x**4 - 592*x**3 - 880*x**2\n#Step 6:\nCurrent expression: 32*x**5 + 1395*x**4 - 592*x**3 - 880*x**2\nNo more calculations needed.\n32*x**5 + 1395*x**4 - 592*x**3 - 880*x**2", "generated_answer": "32*x**5 + 1395*x**4 - 592*x**3 - 880*x**2", "step_length": 6} {"cot_id": "746199243eeea37665bd0c6df7e5d877aac9a141ae4edd78f71d6d548d2580a9", "datapoint": {"question": "Simplify this expression: (36*x**3 + 37*x)*(-43*x**3 + 23*x**2 - 23)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1548*x**6 + 828*x**5 - 1591*x**4 + 23*x**3 - 851*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1236, "polynomial_expr": "(36*x**3 + 37*x)*(-43*x**3 + 23*x**2 - 23)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (36*x**3 + 37*x)*(-43*x**3 + 23*x**2 - 23)\nExpanding the part (36*x**3 + 37*x) using the distributive property, and we got: (37*x)*(-43*x**3 + 23*x**2 - 23) + (36*x**3)*(-43*x**3 + 23*x**2 - 23)\n#Step 2:\nCurrent expression: (37*x)*(-43*x**3 + 23*x**2 - 23) + (36*x**3)*(-43*x**3 + 23*x**2 - 23)\nSimplifying the partial expression: (36*x**3)*(-43*x**3 + 23*x**2 - 23)\nExpanding the part (-43*x**3 + 23*x**2 - 23) using the distributive property, and we got: -828*x**3 + (23*x**2)*(36*x**3) + (-43*x**3)*(36*x**3)\nReplacing (36*x**3)*(-43*x**3 + 23*x**2 - 23) with -828*x**3 + (23*x**2)*(36*x**3) + (-43*x**3)*(36*x**3) in the overall expression.\n#Step 3:\nCurrent expression: -23*36*x**3 + (37*x)*(-43*x**3 + 23*x**2 - 23) + (23*x**2)*(36*x**3) + (-43*x**3)*(36*x**3)\nSimplifying the partial expression: (37*x)*(-43*x**3 + 23*x**2 - 23)\nExpanding the part (-43*x**3 + 23*x**2 - 23) using the distributive property, and we got: -851*x + (37*x)*(23*x**2) + (37*x)*(-43*x**3)\nReplacing (37*x)*(-43*x**3 + 23*x**2 - 23) with -851*x + (37*x)*(23*x**2) + (37*x)*(-43*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -23*36*x**3 - 23*37*x + (37*x)*(23*x**2) + (37*x)*(-43*x**3) + (23*x**2)*(36*x**3) + (-43*x**3)*(36*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-43*x**3)*(36*x**3) = -1548*x**6\n (-43*x**3)*(37*x) = -1591*x**4\n (23*x**2)*(36*x**3) = 828*x**5\n (23*x**2)*(37*x) = 851*x**3\n -23*36*x**3 = -828*x**3\n -23*37*x = -851*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1548*x**6 + 828*x**5 - 1591*x**4 - 828*x**3 + 851*x**3 - 851*x\nCombining like terms, got -1548*x**6 + 828*x**5 - 1591*x**4 + 23*x**3 - 851*x\n#Step 6:\nCurrent expression: -1548*x**6 + 828*x**5 - 1591*x**4 + 23*x**3 - 851*x\nNo more calculations needed.\n-1548*x**6 + 828*x**5 - 1591*x**4 + 23*x**3 - 851*x", "generated_answer": "-1548*x**6 + 828*x**5 - 1591*x**4 + 23*x**3 - 851*x", "step_length": 6} {"cot_id": "ac79b8985b1614ba42f0abe50b440ce9f9bc69c7f920aae947856494170d330b", "datapoint": {"question": "Simplify this expression: -9*z**2*(43*z**3 + 2*z - 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-387*z**5 - 18*z**3 + 297*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1237, "polynomial_expr": "-9*z**2*(43*z**3 + 2*z - 33)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -9*z**2*(43*z**3 + 2*z - 33)\nExpanding the part (43*z**3 + 2*z - 33) using the distributive property, and we got: -(-1)*297*z**2 + (2*z)*(-9*z**2) + (-9*z**2)*(43*z**3)\n#Step 2:\nCurrent expression: -(-1)*297*z**2 + (2*z)*(-9*z**2) + (-9*z**2)*(43*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -33*(-9*z**2) = 297*z**2\n (2*z)*(-9*z**2) = -18*z**3\n (43*z**3)*(-9*z**2) = -387*z**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -387*z**5 - 18*z**3 + 297*z**2\nNo more calculations needed.\n-387*z**5 - 18*z**3 + 297*z**2", "generated_answer": "-387*z**5 - 18*z**3 + 297*z**2", "step_length": 3} {"cot_id": "1c5aac0f3b8fc8efba7f62363394b5d485813a8bd34398641d8549e5d0036dd9", "datapoint": {"question": "Calculate the following: (-59*z**3 - 37*z)*(-49*z**3 - 39*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2891*z**6 + 2301*z**5 + 1813*z**4 + 1443*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1238, "polynomial_expr": "(-59*z**3 - 37*z)*(-49*z**3 - 39*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-59*z**3 - 37*z)*(-49*z**3 - 39*z**2)\nExpanding the part (-59*z**3 - 37*z) using the distributive property, and we got: (-37*z)*(-49*z**3 - 39*z**2) + (-59*z**3)*(-49*z**3 - 39*z**2)\n#Step 2:\nCurrent expression: (-37*z)*(-49*z**3 - 39*z**2) + (-59*z**3)*(-49*z**3 - 39*z**2)\nSimplifying the partial expression: (-59*z**3)*(-49*z**3 - 39*z**2)\nExpanding the part (-49*z**3 - 39*z**2) using the distributive property, and we got: (-39*z**2)*(-59*z**3) + (-59*z**3)*(-49*z**3)\nReplacing (-59*z**3)*(-49*z**3 - 39*z**2) with (-39*z**2)*(-59*z**3) + (-59*z**3)*(-49*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-37*z)*(-49*z**3 - 39*z**2) + (-39*z**2)*(-59*z**3) + (-59*z**3)*(-49*z**3)\nSimplifying the partial expression: (-37*z)*(-49*z**3 - 39*z**2)\nExpanding the part (-49*z**3 - 39*z**2) using the distributive property, and we got: (-37*z)*(-39*z**2) + (-37*z)*(-49*z**3)\nReplacing (-37*z)*(-49*z**3 - 39*z**2) with (-37*z)*(-39*z**2) + (-37*z)*(-49*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-37*z)*(-39*z**2) + (-37*z)*(-49*z**3) + (-39*z**2)*(-59*z**3) + (-59*z**3)*(-49*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*z**3)*(-59*z**3) = 2891*z**6\n (-49*z**3)*(-37*z) = 1813*z**4\n (-39*z**2)*(-59*z**3) = 2301*z**5\n (-39*z**2)*(-37*z) = 1443*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2891*z**6 + 2301*z**5 + 1813*z**4 + 1443*z**3\nNo more calculations needed.\n2891*z**6 + 2301*z**5 + 1813*z**4 + 1443*z**3", "generated_answer": "2891*z**6 + 2301*z**5 + 1813*z**4 + 1443*z**3", "step_length": 5} {"cot_id": "bb3829d11caaa8f3aa9117b7e94217c81d2d79752b5cc68c06ca0ff202e5a6f2", "datapoint": {"question": "Simplify this expression: -6*x**2*(20*x**2 + 22*x - 54)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-120*x**4 - 132*x**3 + 324*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1239, "polynomial_expr": "-6*x**2*(20*x**2 + 22*x - 54)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -6*x**2*(20*x**2 + 22*x - 54)\nExpanding the part (20*x**2 + 22*x - 54) using the distributive property, and we got: -(-1)*324*x**2 + (22*x)*(-6*x**2) + (-6*x**2)*(20*x**2)\n#Step 2:\nCurrent expression: -(-1)*324*x**2 + (22*x)*(-6*x**2) + (-6*x**2)*(20*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -54*(-6*x**2) = 324*x**2\n (20*x**2)*(-6*x**2) = -120*x**4\n (22*x)*(-6*x**2) = -132*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -120*x**4 - 132*x**3 + 324*x**2\nNo more calculations needed.\n-120*x**4 - 132*x**3 + 324*x**2", "generated_answer": "-120*x**4 - 132*x**3 + 324*x**2", "step_length": 3} {"cot_id": "19178d524e7fc5d6b1d81445af7facfae5ff7a0152d66bb3e4e3dc019e4437c5", "datapoint": {"question": "Simplify this expression: (-32*x**3 + 24*x)*(-14*x**3 - x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "448*x**6 + 32*x**5 - 336*x**4 - 24*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1240, "polynomial_expr": "(-32*x**3 + 24*x)*(-14*x**3 - x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-32*x**3 + 24*x)*(-14*x**3 - x**2)\nExpanding the part (-14*x**3 - x**2) using the distributive property, and we got: (-x**2)*(-32*x**3 + 24*x) + (-14*x**3)*(-32*x**3 + 24*x)\n#Step 2:\nCurrent expression: (-x**2)*(-32*x**3 + 24*x) + (-14*x**3)*(-32*x**3 + 24*x)\nSimplifying the partial expression: (-x**2)*(-32*x**3 + 24*x)\nExpanding the part (-32*x**3 + 24*x) using the distributive property, and we got: (24*x)*(-x**2) + (-x**2)*(-32*x**3)\nReplacing (-x**2)*(-32*x**3 + 24*x) with (24*x)*(-x**2) + (-x**2)*(-32*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (24*x)*(-x**2) + (-x**2)*(-32*x**3) + (-14*x**3)*(-32*x**3 + 24*x)\nSimplifying the partial expression: (-14*x**3)*(-32*x**3 + 24*x)\nExpanding the part (-32*x**3 + 24*x) using the distributive property, and we got: (24*x)*(-14*x**3) + (-32*x**3)*(-14*x**3)\nReplacing (-14*x**3)*(-32*x**3 + 24*x) with (24*x)*(-14*x**3) + (-32*x**3)*(-14*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (24*x)*(-x**2) + (24*x)*(-14*x**3) + (-x**2)*(-32*x**3) + (-32*x**3)*(-14*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*x**3)*(-x**2) = 32*x**5\n (-32*x**3)*(-14*x**3) = 448*x**6\n (24*x)*(-x**2) = -24*x**3\n (24*x)*(-14*x**3) = -336*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 448*x**6 + 32*x**5 - 336*x**4 - 24*x**3\nNo more calculations needed.\n448*x**6 + 32*x**5 - 336*x**4 - 24*x**3", "generated_answer": "448*x**6 + 32*x**5 - 336*x**4 - 24*x**3", "step_length": 5} {"cot_id": "ca6331deedc4d49efb378043ea699c316e93c1a0616178a74c61a7d1ad0eee16", "datapoint": {"question": "Calculate the following: (8*y**3 + 34*y**2 - 48)*(22*y**3 - 27*y**2 - 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "176*y**6 + 532*y**5 - 918*y**4 - 1216*y**3 + 616*y**2 + 960", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1241, "polynomial_expr": "(8*y**3 + 34*y**2 - 48)*(22*y**3 - 27*y**2 - 20)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (8*y**3 + 34*y**2 - 48)*(22*y**3 - 27*y**2 - 20)\nExpanding the part (8*y**3 + 34*y**2 - 48) using the distributive property, and we got: (34*y**2)*(22*y**3 - 27*y**2 - 20) + (8*y**3)*(22*y**3 - 27*y**2 - 20) - 48*(22*y**3 - 27*y**2 - 20)\n#Step 2:\nCurrent expression: (34*y**2)*(22*y**3 - 27*y**2 - 20) + (8*y**3)*(22*y**3 - 27*y**2 - 20) - 48*(22*y**3 - 27*y**2 - 20)\nSimplifying the partial expression: -48*(22*y**3 - 27*y**2 - 20)\nExpanding the part (22*y**3 - 27*y**2 - 20) using the distributive property, and we got: -27*y**2*(-48) + (22*y**3)*(-48) - 20*(-48)\nReplacing -48*(22*y**3 - 27*y**2 - 20) with -27*y**2*(-48) + (22*y**3)*(-48) - 20*(-48) in the overall expression.\n#Step 3:\nCurrent expression: -27*y**2*(-48) + (34*y**2)*(22*y**3 - 27*y**2 - 20) + (8*y**3)*(22*y**3 - 27*y**2 - 20) + (22*y**3)*(-48) + 960\nSimplifying the partial expression: (8*y**3)*(22*y**3 - 27*y**2 - 20)\nExpanding the part (22*y**3 - 27*y**2 - 20) using the distributive property, and we got: -160*y**3 + (-27*y**2)*(8*y**3) + (8*y**3)*(22*y**3)\nReplacing (8*y**3)*(22*y**3 - 27*y**2 - 20) with -160*y**3 + (-27*y**2)*(8*y**3) + (8*y**3)*(22*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -20*8*y**3 + (-27*y**2)*(8*y**3) - 27*y**2*(-48) + (34*y**2)*(22*y**3 - 27*y**2 - 20) + (8*y**3)*(22*y**3) + (22*y**3)*(-48) + 960\nSimplifying the partial expression: (34*y**2)*(22*y**3 - 27*y**2 - 20)\nExpanding the part (22*y**3 - 27*y**2 - 20) using the distributive property, and we got: -680*y**2 + (-27*y**2)*(34*y**2) + (34*y**2)*(22*y**3)\nReplacing (34*y**2)*(22*y**3 - 27*y**2 - 20) with -680*y**2 + (-27*y**2)*(34*y**2) + (34*y**2)*(22*y**3) in the overall expression.\n#Step 5:\nCurrent expression: -20*8*y**3 - 20*34*y**2 + (-27*y**2)*(34*y**2) + (-27*y**2)*(8*y**3) - 27*y**2*(-48) + (34*y**2)*(22*y**3) + (8*y**3)*(22*y**3) + (22*y**3)*(-48) + 960\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*y**2)*-48 = 1296*y**2\n (-27*y**2)*(8*y**3) = -216*y**5\n (-27*y**2)*(34*y**2) = -918*y**4\n (22*y**3)*-48 = -1056*y**3\n (22*y**3)*(8*y**3) = 176*y**6\n (22*y**3)*(34*y**2) = 748*y**5\n -20*8*y**3 = -160*y**3\n -20*34*y**2 = -680*y**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 176*y**6 - 216*y**5 + 748*y**5 - 918*y**4 - 1056*y**3 - 160*y**3 - 680*y**2 + 1296*y**2 + 960\nCombining like terms, got 176*y**6 + 532*y**5 - 918*y**4 - 1216*y**3 + 616*y**2 + 960\n#Step 7:\nCurrent expression: 176*y**6 + 532*y**5 - 918*y**4 - 1216*y**3 + 616*y**2 + 960\nNo more calculations needed.\n176*y**6 + 532*y**5 - 918*y**4 - 1216*y**3 + 616*y**2 + 960", "generated_answer": "176*y**6 + 532*y**5 - 918*y**4 - 1216*y**3 + 616*y**2 + 960", "step_length": 7} {"cot_id": "332c4f4b3dc8a12f84fea131cc97cffac4d56637602e59fa1d61020c8abdd34c", "datapoint": {"question": "Simplify this expression: -7*y**3*(-26*y**3 - 6*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "182*y**6 + 42*y**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1242, "polynomial_expr": "-7*y**3*(-26*y**3 - 6*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -7*y**3*(-26*y**3 - 6*y)\nExpanding the part (-26*y**3 - 6*y) using the distributive property, and we got: (-6*y)*(-7*y**3) + (-26*y**3)*(-7*y**3)\n#Step 2:\nCurrent expression: (-6*y)*(-7*y**3) + (-26*y**3)*(-7*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-26*y**3)*(-7*y**3) = 182*y**6\n (-6*y)*(-7*y**3) = 42*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 182*y**6 + 42*y**4\nNo more calculations needed.\n182*y**6 + 42*y**4", "generated_answer": "182*y**6 + 42*y**4", "step_length": 3} {"cot_id": "681b46e6a9e43860fa73830a615ab5ca1ba83beb37bec0cab36be6e17b5caa60", "datapoint": {"question": "Simplify this expression: 160*y - 60\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "160*y - 60", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1243, "polynomial_expr": "160*y - 60", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 160*y - 60\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 160*y - 60\nNo more calculations needed.\n160*y - 60", "generated_answer": "160*y - 60", "step_length": 2} {"cot_id": "4a1214e251fca4cf0af798f29e9d5fe990119421a76053140ef904b0bbfae6cd", "datapoint": {"question": "Calculate the following: (35 - 18*y**2)*(20*y**2 + 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-360*y**4 - 38*y**2 + 1435", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1244, "polynomial_expr": "(35 - 18*y**2)*(20*y**2 + 41)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (35 - 18*y**2)*(20*y**2 + 41)\nExpanding the part (35 - 18*y**2) using the distributive property, and we got: (-18*y**2)*(20*y**2 + 41) + 35*(20*y**2 + 41)\n#Step 2:\nCurrent expression: (-18*y**2)*(20*y**2 + 41) + 35*(20*y**2 + 41)\nSimplifying the partial expression: 35*(20*y**2 + 41)\nExpanding the part (20*y**2 + 41) using the distributive property, and we got: (20*y**2)*35 + 41*35\nReplacing 35*(20*y**2 + 41) with (20*y**2)*35 + 41*35 in the overall expression.\n#Step 3:\nCurrent expression: (-18*y**2)*(20*y**2 + 41) + (20*y**2)*35 + 1435\nSimplifying the partial expression: (-18*y**2)*(20*y**2 + 41)\nExpanding the part (20*y**2 + 41) using the distributive property, and we got: 41*(-18*y**2) + (-18*y**2)*(20*y**2)\nReplacing (-18*y**2)*(20*y**2 + 41) with 41*(-18*y**2) + (-18*y**2)*(20*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 41*(-18)*y**2 + (-18*y**2)*(20*y**2) + (20*y**2)*35 + 1435\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (20*y**2)*35 = 700*y**2\n (20*y**2)*(-18*y**2) = -360*y**4\n 41*-18*y**2 = -738*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -360*y**4 - 738*y**2 + 700*y**2 + 1435\nCombining like terms, got -360*y**4 - 38*y**2 + 1435\n#Step 6:\nCurrent expression: -360*y**4 - 38*y**2 + 1435\nNo more calculations needed.\n-360*y**4 - 38*y**2 + 1435", "generated_answer": "-360*y**4 - 38*y**2 + 1435", "step_length": 6} {"cot_id": "e44f9a3b85005fc4af7b0a2e12be32cb427935bd5ba744de76bd00c60f2de157", "datapoint": {"question": "Simplify this expression: -92*y**2 - 1702\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-92*y**2 - 1702", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1245, "polynomial_expr": "-92*y**2 - 1702", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -92*y**2 - 1702\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -92*y**2 - 1702\nNo more calculations needed.\n-92*y**2 - 1702", "generated_answer": "-92*y**2 - 1702", "step_length": 2} {"cot_id": "9fe092f57df1cb35ea9170946e2c7958362c6316a6618e4f722e3099b9cf6f92", "datapoint": {"question": "Simplify this expression: (z**2 - 3*z)*(-8*z**3 + 49*z**2 - 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-8*z**5 + 73*z**4 - 147*z**3 - 24*z**2 + 72*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1246, "polynomial_expr": "(z**2 - 3*z)*(-8*z**3 + 49*z**2 - 24)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (z**2 - 3*z)*(-8*z**3 + 49*z**2 - 24)\nExpanding the part (z**2 - 3*z) using the distributive property, and we got: (-3*z)*(-8*z**3 + 49*z**2 - 24) + z**2*(-8*z**3 + 49*z**2 - 24)\n#Step 2:\nCurrent expression: (-3*z)*(-8*z**3 + 49*z**2 - 24) + z**2*(-8*z**3 + 49*z**2 - 24)\nSimplifying the partial expression: z**2*(-8*z**3 + 49*z**2 - 24)\nExpanding the part (-8*z**3 + 49*z**2 - 24) using the distributive property, and we got: z**2*(49*z**2) + z**2*(-8*z**3) - 24*z**2\nReplacing z**2*(-8*z**3 + 49*z**2 - 24) with z**2*(49*z**2) + z**2*(-8*z**3) - 24*z**2 in the overall expression.\n#Step 3:\nCurrent expression: (-3*z)*(-8*z**3 + 49*z**2 - 24) + z**2*(49*z**2) + z**2*(-8*z**3) - 24*z**2\nSimplifying the partial expression: (-3*z)*(-8*z**3 + 49*z**2 - 24)\nExpanding the part (-8*z**3 + 49*z**2 - 24) using the distributive property, and we got: (-3*z)*(49*z**2) + (-3*z)*(-8*z**3) - (-1)*72*z\nReplacing (-3*z)*(-8*z**3 + 49*z**2 - 24) with (-3*z)*(49*z**2) + (-3*z)*(-8*z**3) - (-1)*72*z in the overall expression.\n#Step 4:\nCurrent expression: (-3*z)*(49*z**2) + (-3*z)*(-8*z**3) + z**2*(49*z**2) + z**2*(-8*z**3) - 24*z**2 - 24*(-3)*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-8*z**3)*z**2 = -8*z**5\n (-8*z**3)*(-3*z) = 24*z**4\n (49*z**2)*z**2 = 49*z**4\n (49*z**2)*(-3*z) = -147*z**3\n -24*-3*z = 72*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -8*z**5 + 24*z**4 + 49*z**4 - 147*z**3 - 24*z**2 + 72*z\nCombining like terms, got -8*z**5 + 73*z**4 - 147*z**3 - 24*z**2 + 72*z\n#Step 6:\nCurrent expression: -8*z**5 + 73*z**4 - 147*z**3 - 24*z**2 + 72*z\nNo more calculations needed.\n-8*z**5 + 73*z**4 - 147*z**3 - 24*z**2 + 72*z", "generated_answer": "-8*z**5 + 73*z**4 - 147*z**3 - 24*z**2 + 72*z", "step_length": 6} {"cot_id": "4aee3e74f47827884dbbd28cb9f05e22bdb8dec2c14976009c98d78448a247b8", "datapoint": {"question": "Simplify this expression: 33*z**2*(9*z**2 - 45*z + 34)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "297*z**4 - 1485*z**3 + 1122*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1247, "polynomial_expr": "33*z**2*(9*z**2 - 45*z + 34)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 33*z**2*(9*z**2 - 45*z + 34)\nExpanding the part (9*z**2 - 45*z + 34) using the distributive property, and we got: (-45*z)*(33*z**2) + 34*(33*z**2) + (9*z**2)*(33*z**2)\n#Step 2:\nCurrent expression: (-45*z)*(33*z**2) + 34*(33*z**2) + (9*z**2)*(33*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 34*(33*z**2) = 1122*z**2\n (-45*z)*(33*z**2) = -1485*z**3\n (9*z**2)*(33*z**2) = 297*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 297*z**4 - 1485*z**3 + 1122*z**2\nNo more calculations needed.\n297*z**4 - 1485*z**3 + 1122*z**2", "generated_answer": "297*z**4 - 1485*z**3 + 1122*z**2", "step_length": 3} {"cot_id": "2d0b279539400b2e55f111ef377baf95615109f2127689de8b5417f770977eff", "datapoint": {"question": "Simplify this expression: 924*y - 957\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "924*y - 957", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1248, "polynomial_expr": "924*y - 957", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 924*y - 957\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 924*y - 957\nNo more calculations needed.\n924*y - 957", "generated_answer": "924*y - 957", "step_length": 2} {"cot_id": "86e2c3c13c22450e8a812efbed09992b5df344bdb1f6124abf01b10f8d0ca6a6", "datapoint": {"question": "Calculate the following: 1440*z**3 + 1440*z\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1440*z**3 + 1440*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1249, "polynomial_expr": "1440*z**3 + 1440*z", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 1440*z**3 + 1440*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 1440*z**3 + 1440*z\nNo more calculations needed.\n1440*z**3 + 1440*z", "generated_answer": "1440*z**3 + 1440*z", "step_length": 2} {"cot_id": "f8bd4c43a60ade8a4b846c97ffb52055875c5f22654fae96e9d2758c08bb0175", "datapoint": {"question": "Simplify this expression: (-29*y**3 + 27*y**2 + 20)*(35*y**3 + 33*y**2 - 20*y + 2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1015*y**6 - 12*y**5 + 1471*y**4 + 102*y**3 + 714*y**2 - 400*y + 40", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1250, "polynomial_expr": "(-29*y**3 + 27*y**2 + 20)*(35*y**3 + 33*y**2 - 20*y + 2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-29*y**3 + 27*y**2 + 20)*(35*y**3 + 33*y**2 - 20*y + 2)\nExpanding the part (-29*y**3 + 27*y**2 + 20) using the distributive property, and we got: (27*y**2)*(35*y**3 + 33*y**2 - 20*y + 2) + (-29*y**3)*(35*y**3 + 33*y**2 - 20*y + 2) + 20*(35*y**3 + 33*y**2 - 20*y + 2)\n#Step 2:\nCurrent expression: (27*y**2)*(35*y**3 + 33*y**2 - 20*y + 2) + (-29*y**3)*(35*y**3 + 33*y**2 - 20*y + 2) + 20*(35*y**3 + 33*y**2 - 20*y + 2)\nSimplifying the partial expression: 20*(35*y**3 + 33*y**2 - 20*y + 2)\nExpanding the part (35*y**3 + 33*y**2 - 20*y + 2) using the distributive property, and we got: -20*y*20 + (33*y**2)*20 + (35*y**3)*20 + 2*20\nReplacing 20*(35*y**3 + 33*y**2 - 20*y + 2) with -20*y*20 + (33*y**2)*20 + (35*y**3)*20 + 2*20 in the overall expression.\n#Step 3:\nCurrent expression: -20*y*20 + (27*y**2)*(35*y**3 + 33*y**2 - 20*y + 2) + (33*y**2)*20 + (-29*y**3)*(35*y**3 + 33*y**2 - 20*y + 2) + (35*y**3)*20 + 40\nSimplifying the partial expression: (-29*y**3)*(35*y**3 + 33*y**2 - 20*y + 2)\nExpanding the part (35*y**3 + 33*y**2 - 20*y + 2) using the distributive property, and we got: (-20*y)*(-29*y**3) + 2*(-29*y**3) + (33*y**2)*(-29*y**3) + (-29*y**3)*(35*y**3)\nReplacing (-29*y**3)*(35*y**3 + 33*y**2 - 20*y + 2) with (-20*y)*(-29*y**3) + 2*(-29*y**3) + (33*y**2)*(-29*y**3) + (-29*y**3)*(35*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-20*y)*(-29*y**3) - 20*y*20 + 2*(-29)*y**3 + (27*y**2)*(35*y**3 + 33*y**2 - 20*y + 2) + (33*y**2)*(-29*y**3) + (33*y**2)*20 + (-29*y**3)*(35*y**3) + (35*y**3)*20 + 40\nSimplifying the partial expression: (27*y**2)*(35*y**3 + 33*y**2 - 20*y + 2)\nExpanding the part (35*y**3 + 33*y**2 - 20*y + 2) using the distributive property, and we got: (-20*y)*(27*y**2) + 2*(27*y**2) + (27*y**2)*(33*y**2) + (27*y**2)*(35*y**3)\nReplacing (27*y**2)*(35*y**3 + 33*y**2 - 20*y + 2) with (-20*y)*(27*y**2) + 2*(27*y**2) + (27*y**2)*(33*y**2) + (27*y**2)*(35*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-20*y)*(27*y**2) + (-20*y)*(-29*y**3) - 20*y*20 + 2*(-29)*y**3 + 2*27*y**2 + (27*y**2)*(33*y**2) + (27*y**2)*(35*y**3) + (33*y**2)*(-29*y**3) + (33*y**2)*20 + (-29*y**3)*(35*y**3) + (35*y**3)*20 + 40\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*y)*20 = -400*y\n (-20*y)*(-29*y**3) = 580*y**4\n (-20*y)*(27*y**2) = -540*y**3\n (33*y**2)*20 = 660*y**2\n (33*y**2)*(-29*y**3) = -957*y**5\n (33*y**2)*(27*y**2) = 891*y**4\n (35*y**3)*20 = 700*y**3\n (35*y**3)*(-29*y**3) = -1015*y**6\n (35*y**3)*(27*y**2) = 945*y**5\n 2*-29*y**3 = -58*y**3\n 2*27*y**2 = 54*y**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1015*y**6 - 957*y**5 + 945*y**5 + 580*y**4 + 891*y**4 - 540*y**3 - 58*y**3 + 700*y**3 + 54*y**2 + 660*y**2 - 400*y + 40\nCombining like terms, got -1015*y**6 - 12*y**5 + 1471*y**4 + 102*y**3 + 714*y**2 - 400*y + 40\n#Step 7:\nCurrent expression: -1015*y**6 - 12*y**5 + 1471*y**4 + 102*y**3 + 714*y**2 - 400*y + 40\nNo more calculations needed.\n-1015*y**6 - 12*y**5 + 1471*y**4 + 102*y**3 + 714*y**2 - 400*y + 40", "generated_answer": "-1015*y**6 - 12*y**5 + 1471*y**4 + 102*y**3 + 714*y**2 - 400*y + 40", "step_length": 7} {"cot_id": "578d963933730320ac71aa05d39d90793eef8e718e4c1f3190869557f757416d", "datapoint": {"question": "Simplify this expression: (-87*y**3 - 36*y**2)*(-33*y**3 - 49*y**2 + 38*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2871*y**6 + 5451*y**5 - 1542*y**4 - 1368*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1251, "polynomial_expr": "(-87*y**3 - 36*y**2)*(-33*y**3 - 49*y**2 + 38*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-87*y**3 - 36*y**2)*(-33*y**3 - 49*y**2 + 38*y)\nExpanding the part (-87*y**3 - 36*y**2) using the distributive property, and we got: (-36*y**2)*(-33*y**3 - 49*y**2 + 38*y) + (-87*y**3)*(-33*y**3 - 49*y**2 + 38*y)\n#Step 2:\nCurrent expression: (-36*y**2)*(-33*y**3 - 49*y**2 + 38*y) + (-87*y**3)*(-33*y**3 - 49*y**2 + 38*y)\nSimplifying the partial expression: (-87*y**3)*(-33*y**3 - 49*y**2 + 38*y)\nExpanding the part (-33*y**3 - 49*y**2 + 38*y) using the distributive property, and we got: (38*y)*(-87*y**3) + (-49*y**2)*(-87*y**3) + (-87*y**3)*(-33*y**3)\nReplacing (-87*y**3)*(-33*y**3 - 49*y**2 + 38*y) with (38*y)*(-87*y**3) + (-49*y**2)*(-87*y**3) + (-87*y**3)*(-33*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (38*y)*(-87*y**3) + (-49*y**2)*(-87*y**3) + (-36*y**2)*(-33*y**3 - 49*y**2 + 38*y) + (-87*y**3)*(-33*y**3)\nSimplifying the partial expression: (-36*y**2)*(-33*y**3 - 49*y**2 + 38*y)\nExpanding the part (-33*y**3 - 49*y**2 + 38*y) using the distributive property, and we got: (38*y)*(-36*y**2) + (-49*y**2)*(-36*y**2) + (-36*y**2)*(-33*y**3)\nReplacing (-36*y**2)*(-33*y**3 - 49*y**2 + 38*y) with (38*y)*(-36*y**2) + (-49*y**2)*(-36*y**2) + (-36*y**2)*(-33*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (38*y)*(-36*y**2) + (38*y)*(-87*y**3) + (-49*y**2)*(-36*y**2) + (-49*y**2)*(-87*y**3) + (-36*y**2)*(-33*y**3) + (-87*y**3)*(-33*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*y**2)*(-87*y**3) = 4263*y**5\n (-49*y**2)*(-36*y**2) = 1764*y**4\n (-33*y**3)*(-87*y**3) = 2871*y**6\n (-33*y**3)*(-36*y**2) = 1188*y**5\n (38*y)*(-87*y**3) = -3306*y**4\n (38*y)*(-36*y**2) = -1368*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2871*y**6 + 1188*y**5 + 4263*y**5 - 3306*y**4 + 1764*y**4 - 1368*y**3\nCombining like terms, got 2871*y**6 + 5451*y**5 - 1542*y**4 - 1368*y**3\n#Step 6:\nCurrent expression: 2871*y**6 + 5451*y**5 - 1542*y**4 - 1368*y**3\nNo more calculations needed.\n2871*y**6 + 5451*y**5 - 1542*y**4 - 1368*y**3", "generated_answer": "2871*y**6 + 5451*y**5 - 1542*y**4 - 1368*y**3", "step_length": 6} {"cot_id": "63783921ebac5e5065bdacd9e911b18435d36f089850e4e6f217f8b604b18dd1", "datapoint": {"question": "Simplify this expression: (-15*y**3 - 46)*(13*y**3 - 3*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-195*y**6 + 45*y**5 - 598*y**3 + 138*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1252, "polynomial_expr": "(-15*y**3 - 46)*(13*y**3 - 3*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-15*y**3 - 46)*(13*y**3 - 3*y**2)\nExpanding the part (-15*y**3 - 46) using the distributive property, and we got: (-15*y**3)*(13*y**3 - 3*y**2) - 46*(13*y**3 - 3*y**2)\n#Step 2:\nCurrent expression: (-15*y**3)*(13*y**3 - 3*y**2) - 46*(13*y**3 - 3*y**2)\nSimplifying the partial expression: -46*(13*y**3 - 3*y**2)\nExpanding the part (13*y**3 - 3*y**2) using the distributive property, and we got: -3*y**2*(-46) + (13*y**3)*(-46)\nReplacing -46*(13*y**3 - 3*y**2) with -3*y**2*(-46) + (13*y**3)*(-46) in the overall expression.\n#Step 3:\nCurrent expression: -3*y**2*(-46) + (-15*y**3)*(13*y**3 - 3*y**2) + (13*y**3)*(-46)\nSimplifying the partial expression: (-15*y**3)*(13*y**3 - 3*y**2)\nExpanding the part (13*y**3 - 3*y**2) using the distributive property, and we got: (-3*y**2)*(-15*y**3) + (-15*y**3)*(13*y**3)\nReplacing (-15*y**3)*(13*y**3 - 3*y**2) with (-3*y**2)*(-15*y**3) + (-15*y**3)*(13*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-3*y**2)*(-15*y**3) - 3*y**2*(-46) + (-15*y**3)*(13*y**3) + (13*y**3)*(-46)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-3*y**2)*-46 = 138*y**2\n (-3*y**2)*(-15*y**3) = 45*y**5\n (13*y**3)*-46 = -598*y**3\n (13*y**3)*(-15*y**3) = -195*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -195*y**6 + 45*y**5 - 598*y**3 + 138*y**2\nNo more calculations needed.\n-195*y**6 + 45*y**5 - 598*y**3 + 138*y**2", "generated_answer": "-195*y**6 + 45*y**5 - 598*y**3 + 138*y**2", "step_length": 5} {"cot_id": "2ef2c5e5ea4493e7098cd4f07ef02913fa25af1207854c9fb0bcf19e076476fe", "datapoint": {"question": "Calculate the following: (-29*x**3 - 24*x**2)*(28*x**3 + 25)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-812*x**6 - 672*x**5 - 725*x**3 - 600*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1253, "polynomial_expr": "(-29*x**3 - 24*x**2)*(28*x**3 + 25)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-29*x**3 - 24*x**2)*(28*x**3 + 25)\nExpanding the part (28*x**3 + 25) using the distributive property, and we got: (28*x**3)*(-29*x**3 - 24*x**2) + 25*(-29*x**3 - 24*x**2)\n#Step 2:\nCurrent expression: (28*x**3)*(-29*x**3 - 24*x**2) + 25*(-29*x**3 - 24*x**2)\nSimplifying the partial expression: 25*(-29*x**3 - 24*x**2)\nExpanding the part (-29*x**3 - 24*x**2) using the distributive property, and we got: -24*x**2*25 - 29*x**3*25\nReplacing 25*(-29*x**3 - 24*x**2) with -24*x**2*25 - 29*x**3*25 in the overall expression.\n#Step 3:\nCurrent expression: -24*x**2*25 - 29*x**3*25 + (28*x**3)*(-29*x**3 - 24*x**2)\nSimplifying the partial expression: (28*x**3)*(-29*x**3 - 24*x**2)\nExpanding the part (-29*x**3 - 24*x**2) using the distributive property, and we got: (-24*x**2)*(28*x**3) + (-29*x**3)*(28*x**3)\nReplacing (28*x**3)*(-29*x**3 - 24*x**2) with (-24*x**2)*(28*x**3) + (-29*x**3)*(28*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-24*x**2)*(28*x**3) - 24*x**2*25 + (-29*x**3)*(28*x**3) - 29*x**3*25\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*x**3)*25 = -725*x**3\n (-29*x**3)*(28*x**3) = -812*x**6\n (-24*x**2)*25 = -600*x**2\n (-24*x**2)*(28*x**3) = -672*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -812*x**6 - 672*x**5 - 725*x**3 - 600*x**2\nNo more calculations needed.\n-812*x**6 - 672*x**5 - 725*x**3 - 600*x**2", "generated_answer": "-812*x**6 - 672*x**5 - 725*x**3 - 600*x**2", "step_length": 5} {"cot_id": "fa0464e8f62b18623f008588099402e3857884cf16c36e77204188e33098a969", "datapoint": {"question": "Simplify this expression: (-24*y**3 - 50)*(50*y**3 + 3*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1200*y**6 - 72*y**5 - 2500*y**3 - 150*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1254, "polynomial_expr": "(-24*y**3 - 50)*(50*y**3 + 3*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-24*y**3 - 50)*(50*y**3 + 3*y**2)\nExpanding the part (-24*y**3 - 50) using the distributive property, and we got: (-24*y**3)*(50*y**3 + 3*y**2) - 50*(50*y**3 + 3*y**2)\n#Step 2:\nCurrent expression: (-24*y**3)*(50*y**3 + 3*y**2) - 50*(50*y**3 + 3*y**2)\nSimplifying the partial expression: -50*(50*y**3 + 3*y**2)\nExpanding the part (50*y**3 + 3*y**2) using the distributive property, and we got: (3*y**2)*(-50) + (50*y**3)*(-50)\nReplacing -50*(50*y**3 + 3*y**2) with (3*y**2)*(-50) + (50*y**3)*(-50) in the overall expression.\n#Step 3:\nCurrent expression: (3*y**2)*(-50) + (-24*y**3)*(50*y**3 + 3*y**2) + (50*y**3)*(-50)\nSimplifying the partial expression: (-24*y**3)*(50*y**3 + 3*y**2)\nExpanding the part (50*y**3 + 3*y**2) using the distributive property, and we got: (3*y**2)*(-24*y**3) + (-24*y**3)*(50*y**3)\nReplacing (-24*y**3)*(50*y**3 + 3*y**2) with (3*y**2)*(-24*y**3) + (-24*y**3)*(50*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (3*y**2)*(-24*y**3) + (3*y**2)*(-50) + (-24*y**3)*(50*y**3) + (50*y**3)*(-50)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (3*y**2)*-50 = -150*y**2\n (3*y**2)*(-24*y**3) = -72*y**5\n (50*y**3)*-50 = -2500*y**3\n (50*y**3)*(-24*y**3) = -1200*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1200*y**6 - 72*y**5 - 2500*y**3 - 150*y**2\nNo more calculations needed.\n-1200*y**6 - 72*y**5 - 2500*y**3 - 150*y**2", "generated_answer": "-1200*y**6 - 72*y**5 - 2500*y**3 - 150*y**2", "step_length": 5} {"cot_id": "b8ef5b36907067223b4ea3592ed880fdb8b1099da505043df9969841f07931e0", "datapoint": {"question": "Simplify this expression: (20*y**2 + 53)*(30*y**3 + 25*y**2 + 42*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "600*y**5 + 500*y**4 + 2430*y**3 + 1325*y**2 + 2226*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1255, "polynomial_expr": "(20*y**2 + 53)*(30*y**3 + 25*y**2 + 42*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (20*y**2 + 53)*(30*y**3 + 25*y**2 + 42*y)\nExpanding the part (20*y**2 + 53) using the distributive property, and we got: (20*y**2)*(30*y**3 + 25*y**2 + 42*y) + 53*(30*y**3 + 25*y**2 + 42*y)\n#Step 2:\nCurrent expression: (20*y**2)*(30*y**3 + 25*y**2 + 42*y) + 53*(30*y**3 + 25*y**2 + 42*y)\nSimplifying the partial expression: 53*(30*y**3 + 25*y**2 + 42*y)\nExpanding the part (30*y**3 + 25*y**2 + 42*y) using the distributive property, and we got: (42*y)*53 + (25*y**2)*53 + (30*y**3)*53\nReplacing 53*(30*y**3 + 25*y**2 + 42*y) with (42*y)*53 + (25*y**2)*53 + (30*y**3)*53 in the overall expression.\n#Step 3:\nCurrent expression: (42*y)*53 + (20*y**2)*(30*y**3 + 25*y**2 + 42*y) + (25*y**2)*53 + (30*y**3)*53\nSimplifying the partial expression: (20*y**2)*(30*y**3 + 25*y**2 + 42*y)\nExpanding the part (30*y**3 + 25*y**2 + 42*y) using the distributive property, and we got: (42*y)*(20*y**2) + (20*y**2)*(25*y**2) + (20*y**2)*(30*y**3)\nReplacing (20*y**2)*(30*y**3 + 25*y**2 + 42*y) with (42*y)*(20*y**2) + (20*y**2)*(25*y**2) + (20*y**2)*(30*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (42*y)*(20*y**2) + (42*y)*53 + (20*y**2)*(25*y**2) + (20*y**2)*(30*y**3) + (25*y**2)*53 + (30*y**3)*53\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (25*y**2)*53 = 1325*y**2\n (25*y**2)*(20*y**2) = 500*y**4\n (30*y**3)*53 = 1590*y**3\n (30*y**3)*(20*y**2) = 600*y**5\n (42*y)*53 = 2226*y\n (42*y)*(20*y**2) = 840*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 600*y**5 + 500*y**4 + 840*y**3 + 1590*y**3 + 1325*y**2 + 2226*y\nCombining like terms, got 600*y**5 + 500*y**4 + 2430*y**3 + 1325*y**2 + 2226*y\n#Step 6:\nCurrent expression: 600*y**5 + 500*y**4 + 2430*y**3 + 1325*y**2 + 2226*y\nNo more calculations needed.\n600*y**5 + 500*y**4 + 2430*y**3 + 1325*y**2 + 2226*y", "generated_answer": "600*y**5 + 500*y**4 + 2430*y**3 + 1325*y**2 + 2226*y", "step_length": 6} {"cot_id": "8a064205ad3a4b13f21b1f61ab0fe51ae1a4bdcf62c3e631ffe4b5bf1cbb30ec", "datapoint": {"question": "Calculate the following: (-11*x - 1)*(23*x**3 + 15*x**2 + 4)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-253*x**4 - 188*x**3 - 15*x**2 - 44*x - 4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1256, "polynomial_expr": "(-11*x - 1)*(23*x**3 + 15*x**2 + 4)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-11*x - 1)*(23*x**3 + 15*x**2 + 4)\nExpanding the part (-11*x - 1) using the distributive property, and we got: (-11*x)*(23*x**3 + 15*x**2 + 4) - (23*x**3 + 15*x**2 + 4)\n#Step 2:\nCurrent expression: (-11*x)*(23*x**3 + 15*x**2 + 4) - (23*x**3 + 15*x**2 + 4)\nSimplifying the partial expression: -(23*x**3 + 15*x**2 + 4)\nExpanding the part (23*x**3 + 15*x**2 + 4) using the distributive property, and we got: (15*x**2)*(-1) + (23*x**3)*(-1) + 4*(-1)\nReplacing -(23*x**3 + 15*x**2 + 4) with (15*x**2)*(-1) + (23*x**3)*(-1) + 4*(-1) in the overall expression.\n#Step 3:\nCurrent expression: (-11*x)*(23*x**3 + 15*x**2 + 4) + (15*x**2)*(-1) + (23*x**3)*(-1) - 4\nSimplifying the partial expression: (-11*x)*(23*x**3 + 15*x**2 + 4)\nExpanding the part (23*x**3 + 15*x**2 + 4) using the distributive property, and we got: (-11*x)*(15*x**2) + (-11*x)*(23*x**3) + 4*(-11*x)\nReplacing (-11*x)*(23*x**3 + 15*x**2 + 4) with (-11*x)*(15*x**2) + (-11*x)*(23*x**3) + 4*(-11*x) in the overall expression.\n#Step 4:\nCurrent expression: (-11*x)*(15*x**2) + (-11*x)*(23*x**3) + 4*(-11)*x + (15*x**2)*(-1) + (23*x**3)*(-1) - 4\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (15*x**2)*-1 = -15*x**2\n (15*x**2)*(-11*x) = -165*x**3\n (23*x**3)*-1 = -23*x**3\n (23*x**3)*(-11*x) = -253*x**4\n 4*-11*x = -44*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -253*x**4 - 165*x**3 - 23*x**3 - 15*x**2 - 44*x - 4\nCombining like terms, got -253*x**4 - 188*x**3 - 15*x**2 - 44*x - 4\n#Step 6:\nCurrent expression: -253*x**4 - 188*x**3 - 15*x**2 - 44*x - 4\nNo more calculations needed.\n-253*x**4 - 188*x**3 - 15*x**2 - 44*x - 4", "generated_answer": "-253*x**4 - 188*x**3 - 15*x**2 - 44*x - 4", "step_length": 6} {"cot_id": "caa175723d603f5c474db6a1182498c55759332b62a972890d79d1583e6ab4cc", "datapoint": {"question": "Simplify this expression: (-9*y - 9)*(43*y**3 + 44*y**2 - 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-387*y**4 - 783*y**3 - 396*y**2 + 288*y + 288", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1257, "polynomial_expr": "(-9*y - 9)*(43*y**3 + 44*y**2 - 32)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-9*y - 9)*(43*y**3 + 44*y**2 - 32)\nExpanding the part (-9*y - 9) using the distributive property, and we got: (-9*y)*(43*y**3 + 44*y**2 - 32) - 9*(43*y**3 + 44*y**2 - 32)\n#Step 2:\nCurrent expression: (-9*y)*(43*y**3 + 44*y**2 - 32) - 9*(43*y**3 + 44*y**2 - 32)\nSimplifying the partial expression: -9*(43*y**3 + 44*y**2 - 32)\nExpanding the part (43*y**3 + 44*y**2 - 32) using the distributive property, and we got: (44*y**2)*(-9) + (43*y**3)*(-9) - 32*(-9)\nReplacing -9*(43*y**3 + 44*y**2 - 32) with (44*y**2)*(-9) + (43*y**3)*(-9) - 32*(-9) in the overall expression.\n#Step 3:\nCurrent expression: (-9*y)*(43*y**3 + 44*y**2 - 32) + (44*y**2)*(-9) + (43*y**3)*(-9) + 288\nSimplifying the partial expression: (-9*y)*(43*y**3 + 44*y**2 - 32)\nExpanding the part (43*y**3 + 44*y**2 - 32) using the distributive property, and we got: (-9*y)*(44*y**2) + (-9*y)*(43*y**3) - (-1)*288*y\nReplacing (-9*y)*(43*y**3 + 44*y**2 - 32) with (-9*y)*(44*y**2) + (-9*y)*(43*y**3) - (-1)*288*y in the overall expression.\n#Step 4:\nCurrent expression: (-9*y)*(44*y**2) + (-9*y)*(43*y**3) - 32*(-9)*y + (44*y**2)*(-9) + (43*y**3)*(-9) + 288\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (43*y**3)*-9 = -387*y**3\n (43*y**3)*(-9*y) = -387*y**4\n (44*y**2)*-9 = -396*y**2\n (44*y**2)*(-9*y) = -396*y**3\n -32*-9*y = 288*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -387*y**4 - 396*y**3 - 387*y**3 - 396*y**2 + 288*y + 288\nCombining like terms, got -387*y**4 - 783*y**3 - 396*y**2 + 288*y + 288\n#Step 6:\nCurrent expression: -387*y**4 - 783*y**3 - 396*y**2 + 288*y + 288\nNo more calculations needed.\n-387*y**4 - 783*y**3 - 396*y**2 + 288*y + 288", "generated_answer": "-387*y**4 - 783*y**3 - 396*y**2 + 288*y + 288", "step_length": 6} {"cot_id": "7ec3d51c8cf48bf0badaac478e020812447ee9439b70fb7a15edba625af55b32", "datapoint": {"question": "Simplify this expression: (25*y**2 + 5*y)*(27*y**3 - 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "675*y**5 + 135*y**4 - 600*y**2 - 120*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1258, "polynomial_expr": "(25*y**2 + 5*y)*(27*y**3 - 24)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (25*y**2 + 5*y)*(27*y**3 - 24)\nExpanding the part (27*y**3 - 24) using the distributive property, and we got: (27*y**3)*(25*y**2 + 5*y) - 24*(25*y**2 + 5*y)\n#Step 2:\nCurrent expression: (27*y**3)*(25*y**2 + 5*y) - 24*(25*y**2 + 5*y)\nSimplifying the partial expression: -24*(25*y**2 + 5*y)\nExpanding the part (25*y**2 + 5*y) using the distributive property, and we got: (5*y)*(-24) + (25*y**2)*(-24)\nReplacing -24*(25*y**2 + 5*y) with (5*y)*(-24) + (25*y**2)*(-24) in the overall expression.\n#Step 3:\nCurrent expression: (5*y)*(-24) + (25*y**2)*(-24) + (27*y**3)*(25*y**2 + 5*y)\nSimplifying the partial expression: (27*y**3)*(25*y**2 + 5*y)\nExpanding the part (25*y**2 + 5*y) using the distributive property, and we got: (5*y)*(27*y**3) + (25*y**2)*(27*y**3)\nReplacing (27*y**3)*(25*y**2 + 5*y) with (5*y)*(27*y**3) + (25*y**2)*(27*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (5*y)*(27*y**3) + (5*y)*(-24) + (25*y**2)*(27*y**3) + (25*y**2)*(-24)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (5*y)*-24 = -120*y\n (5*y)*(27*y**3) = 135*y**4\n (25*y**2)*-24 = -600*y**2\n (25*y**2)*(27*y**3) = 675*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 675*y**5 + 135*y**4 - 600*y**2 - 120*y\nNo more calculations needed.\n675*y**5 + 135*y**4 - 600*y**2 - 120*y", "generated_answer": "675*y**5 + 135*y**4 - 600*y**2 - 120*y", "step_length": 5} {"cot_id": "2fe7aee07a9095a95c199952dfed311894a9a3dad27ed22115e3edcc18d51f6d", "datapoint": {"question": "Simplify this expression: (-29*y**2 - 36)*(48*y**3 - 8*y**2 + 2*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1392*y**5 + 232*y**4 - 1786*y**3 + 288*y**2 - 72*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1259, "polynomial_expr": "(-29*y**2 - 36)*(48*y**3 - 8*y**2 + 2*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-29*y**2 - 36)*(48*y**3 - 8*y**2 + 2*y)\nExpanding the part (-29*y**2 - 36) using the distributive property, and we got: (-29*y**2)*(48*y**3 - 8*y**2 + 2*y) - 36*(48*y**3 - 8*y**2 + 2*y)\n#Step 2:\nCurrent expression: (-29*y**2)*(48*y**3 - 8*y**2 + 2*y) - 36*(48*y**3 - 8*y**2 + 2*y)\nSimplifying the partial expression: -36*(48*y**3 - 8*y**2 + 2*y)\nExpanding the part (48*y**3 - 8*y**2 + 2*y) using the distributive property, and we got: (2*y)*(-36) - 8*y**2*(-36) + (48*y**3)*(-36)\nReplacing -36*(48*y**3 - 8*y**2 + 2*y) with (2*y)*(-36) - 8*y**2*(-36) + (48*y**3)*(-36) in the overall expression.\n#Step 3:\nCurrent expression: (2*y)*(-36) + (-29*y**2)*(48*y**3 - 8*y**2 + 2*y) - 8*y**2*(-36) + (48*y**3)*(-36)\nSimplifying the partial expression: (-29*y**2)*(48*y**3 - 8*y**2 + 2*y)\nExpanding the part (48*y**3 - 8*y**2 + 2*y) using the distributive property, and we got: (2*y)*(-29*y**2) + (-29*y**2)*(-8*y**2) + (-29*y**2)*(48*y**3)\nReplacing (-29*y**2)*(48*y**3 - 8*y**2 + 2*y) with (2*y)*(-29*y**2) + (-29*y**2)*(-8*y**2) + (-29*y**2)*(48*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (2*y)*(-29*y**2) + (2*y)*(-36) + (-29*y**2)*(-8*y**2) + (-29*y**2)*(48*y**3) - 8*y**2*(-36) + (48*y**3)*(-36)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-8*y**2)*-36 = 288*y**2\n (-8*y**2)*(-29*y**2) = 232*y**4\n (2*y)*-36 = -72*y\n (2*y)*(-29*y**2) = -58*y**3\n (48*y**3)*-36 = -1728*y**3\n (48*y**3)*(-29*y**2) = -1392*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1392*y**5 + 232*y**4 - 1728*y**3 - 58*y**3 + 288*y**2 - 72*y\nCombining like terms, got -1392*y**5 + 232*y**4 - 1786*y**3 + 288*y**2 - 72*y\n#Step 6:\nCurrent expression: -1392*y**5 + 232*y**4 - 1786*y**3 + 288*y**2 - 72*y\nNo more calculations needed.\n-1392*y**5 + 232*y**4 - 1786*y**3 + 288*y**2 - 72*y", "generated_answer": "-1392*y**5 + 232*y**4 - 1786*y**3 + 288*y**2 - 72*y", "step_length": 6} {"cot_id": "29bebc0aaf125d0249cfe602a57305a8270fc64d84fc2429e8bf447cd5009c22", "datapoint": {"question": "Simplify this expression: (26 - 48*y)*(80*y**3 - 33*y**2 + 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-3840*y**4 + 3664*y**3 - 858*y**2 - 1680*y + 910", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1260, "polynomial_expr": "(26 - 48*y)*(80*y**3 - 33*y**2 + 35)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (26 - 48*y)*(80*y**3 - 33*y**2 + 35)\nExpanding the part (26 - 48*y) using the distributive property, and we got: (-48*y)*(80*y**3 - 33*y**2 + 35) + 26*(80*y**3 - 33*y**2 + 35)\n#Step 2:\nCurrent expression: (-48*y)*(80*y**3 - 33*y**2 + 35) + 26*(80*y**3 - 33*y**2 + 35)\nSimplifying the partial expression: 26*(80*y**3 - 33*y**2 + 35)\nExpanding the part (80*y**3 - 33*y**2 + 35) using the distributive property, and we got: -33*y**2*26 + (80*y**3)*26 + 35*26\nReplacing 26*(80*y**3 - 33*y**2 + 35) with -33*y**2*26 + (80*y**3)*26 + 35*26 in the overall expression.\n#Step 3:\nCurrent expression: (-48*y)*(80*y**3 - 33*y**2 + 35) - 33*y**2*26 + (80*y**3)*26 + 910\nSimplifying the partial expression: (-48*y)*(80*y**3 - 33*y**2 + 35)\nExpanding the part (80*y**3 - 33*y**2 + 35) using the distributive property, and we got: (-48*y)*(-33*y**2) + (-48*y)*(80*y**3) + 35*(-48*y)\nReplacing (-48*y)*(80*y**3 - 33*y**2 + 35) with (-48*y)*(-33*y**2) + (-48*y)*(80*y**3) + 35*(-48*y) in the overall expression.\n#Step 4:\nCurrent expression: (-48*y)*(-33*y**2) + (-48*y)*(80*y**3) + 35*(-48)*y - 33*y**2*26 + (80*y**3)*26 + 910\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*y**2)*26 = -858*y**2\n (-33*y**2)*(-48*y) = 1584*y**3\n (80*y**3)*26 = 2080*y**3\n (80*y**3)*(-48*y) = -3840*y**4\n 35*-48*y = -1680*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -3840*y**4 + 1584*y**3 + 2080*y**3 - 858*y**2 - 1680*y + 910\nCombining like terms, got -3840*y**4 + 3664*y**3 - 858*y**2 - 1680*y + 910\n#Step 6:\nCurrent expression: -3840*y**4 + 3664*y**3 - 858*y**2 - 1680*y + 910\nNo more calculations needed.\n-3840*y**4 + 3664*y**3 - 858*y**2 - 1680*y + 910", "generated_answer": "-3840*y**4 + 3664*y**3 - 858*y**2 - 1680*y + 910", "step_length": 6} {"cot_id": "e5c3f2ac37c65aaf4bc95364328f6dc596d2293e92ab623f5ffe7bc83fe0133b", "datapoint": {"question": "Calculate the following: 48*y*(2*y**3 + 39*y + 45)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "96*y**4 + 1872*y**2 + 2160*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1261, "polynomial_expr": "48*y*(2*y**3 + 39*y + 45)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 48*y*(2*y**3 + 39*y + 45)\nExpanding the part (2*y**3 + 39*y + 45) using the distributive property, and we got: 45*(48*y) + (39*y)*(48*y) + (48*y)*(2*y**3)\n#Step 2:\nCurrent expression: 45*(48*y) + (39*y)*(48*y) + (48*y)*(2*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 45*(48*y) = 2160*y\n (2*y**3)*(48*y) = 96*y**4\n (39*y)*(48*y) = 1872*y**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 96*y**4 + 1872*y**2 + 2160*y\nNo more calculations needed.\n96*y**4 + 1872*y**2 + 2160*y", "generated_answer": "96*y**4 + 1872*y**2 + 2160*y", "step_length": 3} {"cot_id": "5bcb7494b9ee3ca795f588922112563b929a95bce9e1250bc6da8528fc3c273e", "datapoint": {"question": "Calculate the following: (47*y**2 - 26*y)*(-49*y**3 + 50*y**2 - 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2303*y**5 + 3624*y**4 - 1300*y**3 - 1645*y**2 + 910*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1262, "polynomial_expr": "(47*y**2 - 26*y)*(-49*y**3 + 50*y**2 - 35)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (47*y**2 - 26*y)*(-49*y**3 + 50*y**2 - 35)\nExpanding the part (47*y**2 - 26*y) using the distributive property, and we got: (-26*y)*(-49*y**3 + 50*y**2 - 35) + (47*y**2)*(-49*y**3 + 50*y**2 - 35)\n#Step 2:\nCurrent expression: (-26*y)*(-49*y**3 + 50*y**2 - 35) + (47*y**2)*(-49*y**3 + 50*y**2 - 35)\nSimplifying the partial expression: (-26*y)*(-49*y**3 + 50*y**2 - 35)\nExpanding the part (-49*y**3 + 50*y**2 - 35) using the distributive property, and we got: (-26*y)*(50*y**2) + (-26*y)*(-49*y**3) - (-1)*910*y\nReplacing (-26*y)*(-49*y**3 + 50*y**2 - 35) with (-26*y)*(50*y**2) + (-26*y)*(-49*y**3) - (-1)*910*y in the overall expression.\n#Step 3:\nCurrent expression: (-26*y)*(50*y**2) + (-26*y)*(-49*y**3) - 35*(-26)*y + (47*y**2)*(-49*y**3 + 50*y**2 - 35)\nSimplifying the partial expression: (47*y**2)*(-49*y**3 + 50*y**2 - 35)\nExpanding the part (-49*y**3 + 50*y**2 - 35) using the distributive property, and we got: -1645*y**2 + (47*y**2)*(50*y**2) + (47*y**2)*(-49*y**3)\nReplacing (47*y**2)*(-49*y**3 + 50*y**2 - 35) with -1645*y**2 + (47*y**2)*(50*y**2) + (47*y**2)*(-49*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-26*y)*(50*y**2) + (-26*y)*(-49*y**3) - 35*47*y**2 - 35*(-26)*y + (47*y**2)*(50*y**2) + (47*y**2)*(-49*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*y**3)*(-26*y) = 1274*y**4\n (-49*y**3)*(47*y**2) = -2303*y**5\n (50*y**2)*(-26*y) = -1300*y**3\n (50*y**2)*(47*y**2) = 2350*y**4\n -35*-26*y = 910*y\n -35*47*y**2 = -1645*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2303*y**5 + 1274*y**4 + 2350*y**4 - 1300*y**3 - 1645*y**2 + 910*y\nCombining like terms, got -2303*y**5 + 3624*y**4 - 1300*y**3 - 1645*y**2 + 910*y\n#Step 6:\nCurrent expression: -2303*y**5 + 3624*y**4 - 1300*y**3 - 1645*y**2 + 910*y\nNo more calculations needed.\n-2303*y**5 + 3624*y**4 - 1300*y**3 - 1645*y**2 + 910*y", "generated_answer": "-2303*y**5 + 3624*y**4 - 1300*y**3 - 1645*y**2 + 910*y", "step_length": 6} {"cot_id": "83190de6adabadfdf8c28b0e44b90d55f3d48c88c662e859aea7007af63e0b62", "datapoint": {"question": "Calculate the following: (29*x**2 + 9*x)*(-66*x**3 - 7*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1914*x**5 - 594*x**4 - 203*x**3 - 63*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1263, "polynomial_expr": "(29*x**2 + 9*x)*(-66*x**3 - 7*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29*x**2 + 9*x)*(-66*x**3 - 7*x)\nExpanding the part (-66*x**3 - 7*x) using the distributive property, and we got: (-7*x)*(29*x**2 + 9*x) + (-66*x**3)*(29*x**2 + 9*x)\n#Step 2:\nCurrent expression: (-7*x)*(29*x**2 + 9*x) + (-66*x**3)*(29*x**2 + 9*x)\nSimplifying the partial expression: (-66*x**3)*(29*x**2 + 9*x)\nExpanding the part (29*x**2 + 9*x) using the distributive property, and we got: (9*x)*(-66*x**3) + (29*x**2)*(-66*x**3)\nReplacing (-66*x**3)*(29*x**2 + 9*x) with (9*x)*(-66*x**3) + (29*x**2)*(-66*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-7*x)*(29*x**2 + 9*x) + (9*x)*(-66*x**3) + (29*x**2)*(-66*x**3)\nSimplifying the partial expression: (-7*x)*(29*x**2 + 9*x)\nExpanding the part (29*x**2 + 9*x) using the distributive property, and we got: (-7*x)*(9*x) + (-7*x)*(29*x**2)\nReplacing (-7*x)*(29*x**2 + 9*x) with (-7*x)*(9*x) + (-7*x)*(29*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-7*x)*(9*x) + (-7*x)*(29*x**2) + (9*x)*(-66*x**3) + (29*x**2)*(-66*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (9*x)*(-66*x**3) = -594*x**4\n (9*x)*(-7*x) = -63*x**2\n (29*x**2)*(-66*x**3) = -1914*x**5\n (29*x**2)*(-7*x) = -203*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1914*x**5 - 594*x**4 - 203*x**3 - 63*x**2\nNo more calculations needed.\n-1914*x**5 - 594*x**4 - 203*x**3 - 63*x**2", "generated_answer": "-1914*x**5 - 594*x**4 - 203*x**3 - 63*x**2", "step_length": 5} {"cot_id": "fe22112c05f378eb8acfd42b04af0ef759d5ecde6983bded42ad99edde04f935", "datapoint": {"question": "Simplify this expression: (20*y**2 - 21*y)*(-22*y**3 - 20*y**2 - 16*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-440*y**5 + 62*y**4 + 100*y**3 + 336*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1264, "polynomial_expr": "(20*y**2 - 21*y)*(-22*y**3 - 20*y**2 - 16*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (20*y**2 - 21*y)*(-22*y**3 - 20*y**2 - 16*y)\nExpanding the part (20*y**2 - 21*y) using the distributive property, and we got: (-21*y)*(-22*y**3 - 20*y**2 - 16*y) + (20*y**2)*(-22*y**3 - 20*y**2 - 16*y)\n#Step 2:\nCurrent expression: (-21*y)*(-22*y**3 - 20*y**2 - 16*y) + (20*y**2)*(-22*y**3 - 20*y**2 - 16*y)\nSimplifying the partial expression: (-21*y)*(-22*y**3 - 20*y**2 - 16*y)\nExpanding the part (-22*y**3 - 20*y**2 - 16*y) using the distributive property, and we got: (-21*y)*(-16*y) + (-21*y)*(-20*y**2) + (-21*y)*(-22*y**3)\nReplacing (-21*y)*(-22*y**3 - 20*y**2 - 16*y) with (-21*y)*(-16*y) + (-21*y)*(-20*y**2) + (-21*y)*(-22*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-21*y)*(-16*y) + (-21*y)*(-20*y**2) + (-21*y)*(-22*y**3) + (20*y**2)*(-22*y**3 - 20*y**2 - 16*y)\nSimplifying the partial expression: (20*y**2)*(-22*y**3 - 20*y**2 - 16*y)\nExpanding the part (-22*y**3 - 20*y**2 - 16*y) using the distributive property, and we got: (-16*y)*(20*y**2) + (-20*y**2)*(20*y**2) + (20*y**2)*(-22*y**3)\nReplacing (20*y**2)*(-22*y**3 - 20*y**2 - 16*y) with (-16*y)*(20*y**2) + (-20*y**2)*(20*y**2) + (20*y**2)*(-22*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-21*y)*(-16*y) + (-21*y)*(-20*y**2) + (-21*y)*(-22*y**3) + (-16*y)*(20*y**2) + (-20*y**2)*(20*y**2) + (20*y**2)*(-22*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*y**3)*(-21*y) = 462*y**4\n (-22*y**3)*(20*y**2) = -440*y**5\n (-20*y**2)*(-21*y) = 420*y**3\n (-20*y**2)*(20*y**2) = -400*y**4\n (-16*y)*(-21*y) = 336*y**2\n (-16*y)*(20*y**2) = -320*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -440*y**5 - 400*y**4 + 462*y**4 - 320*y**3 + 420*y**3 + 336*y**2\nCombining like terms, got -440*y**5 + 62*y**4 + 100*y**3 + 336*y**2\n#Step 6:\nCurrent expression: -440*y**5 + 62*y**4 + 100*y**3 + 336*y**2\nNo more calculations needed.\n-440*y**5 + 62*y**4 + 100*y**3 + 336*y**2", "generated_answer": "-440*y**5 + 62*y**4 + 100*y**3 + 336*y**2", "step_length": 6} {"cot_id": "7a9d32a6c138221c178852f518c761233eeaecc83f6d0aa79c9bb6f4c19cdd71", "datapoint": {"question": "Simplify this expression: (-53*z**2 + 4*z)*(-3*z**3 - 73*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "159*z**5 - 12*z**4 + 3869*z**3 - 292*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1265, "polynomial_expr": "(-53*z**2 + 4*z)*(-3*z**3 - 73*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-53*z**2 + 4*z)*(-3*z**3 - 73*z)\nExpanding the part (-3*z**3 - 73*z) using the distributive property, and we got: (-73*z)*(-53*z**2 + 4*z) + (-3*z**3)*(-53*z**2 + 4*z)\n#Step 2:\nCurrent expression: (-73*z)*(-53*z**2 + 4*z) + (-3*z**3)*(-53*z**2 + 4*z)\nSimplifying the partial expression: (-73*z)*(-53*z**2 + 4*z)\nExpanding the part (-53*z**2 + 4*z) using the distributive property, and we got: (-73*z)*(4*z) + (-73*z)*(-53*z**2)\nReplacing (-73*z)*(-53*z**2 + 4*z) with (-73*z)*(4*z) + (-73*z)*(-53*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-73*z)*(4*z) + (-73*z)*(-53*z**2) + (-3*z**3)*(-53*z**2 + 4*z)\nSimplifying the partial expression: (-3*z**3)*(-53*z**2 + 4*z)\nExpanding the part (-53*z**2 + 4*z) using the distributive property, and we got: (4*z)*(-3*z**3) + (-53*z**2)*(-3*z**3)\nReplacing (-3*z**3)*(-53*z**2 + 4*z) with (4*z)*(-3*z**3) + (-53*z**2)*(-3*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-73*z)*(4*z) + (-73*z)*(-53*z**2) + (4*z)*(-3*z**3) + (-53*z**2)*(-3*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-53*z**2)*(-73*z) = 3869*z**3\n (-53*z**2)*(-3*z**3) = 159*z**5\n (4*z)*(-73*z) = -292*z**2\n (4*z)*(-3*z**3) = -12*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 159*z**5 - 12*z**4 + 3869*z**3 - 292*z**2\nNo more calculations needed.\n159*z**5 - 12*z**4 + 3869*z**3 - 292*z**2", "generated_answer": "159*z**5 - 12*z**4 + 3869*z**3 - 292*z**2", "step_length": 5} {"cot_id": "f023efc5bd2cee4021938425fcbd96f6658cc6f4ceea61c6012b89fcd4e63866", "datapoint": {"question": "Calculate the following: (9 - 11*y**2)*(13 - 44*y**3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "484*y**5 - 396*y**3 - 143*y**2 + 117", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1266, "polynomial_expr": "(9 - 11*y**2)*(13 - 44*y**3)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9 - 11*y**2)*(13 - 44*y**3)\nExpanding the part (9 - 11*y**2) using the distributive property, and we got: (-11*y**2)*(13 - 44*y**3) + 9*(13 - 44*y**3)\n#Step 2:\nCurrent expression: (-11*y**2)*(13 - 44*y**3) + 9*(13 - 44*y**3)\nSimplifying the partial expression: 9*(13 - 44*y**3)\nExpanding the part (13 - 44*y**3) using the distributive property, and we got: -44*y**3*9 + 13*9\nReplacing 9*(13 - 44*y**3) with -44*y**3*9 + 13*9 in the overall expression.\n#Step 3:\nCurrent expression: (-11*y**2)*(13 - 44*y**3) - 44*y**3*9 + 117\nSimplifying the partial expression: (-11*y**2)*(13 - 44*y**3)\nExpanding the part (13 - 44*y**3) using the distributive property, and we got: 13*(-11*y**2) + (-11*y**2)*(-44*y**3)\nReplacing (-11*y**2)*(13 - 44*y**3) with 13*(-11*y**2) + (-11*y**2)*(-44*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 13*(-11)*y**2 + (-11*y**2)*(-44*y**3) - 44*y**3*9 + 117\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-44*y**3)*9 = -396*y**3\n (-44*y**3)*(-11*y**2) = 484*y**5\n 13*-11*y**2 = -143*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 484*y**5 - 396*y**3 - 143*y**2 + 117\nNo more calculations needed.\n484*y**5 - 396*y**3 - 143*y**2 + 117", "generated_answer": "484*y**5 - 396*y**3 - 143*y**2 + 117", "step_length": 5} {"cot_id": "12d4d8396797bc147370c919d31a96ead6e9c17fbe9efa30b60becc124144ab8", "datapoint": {"question": "Calculate the following: (-19*y**2 + 37*y + 22)*(50*y**2 + 46*y + 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-950*y**4 + 976*y**3 + 2403*y**2 + 1789*y + 462", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1267, "polynomial_expr": "(-19*y**2 + 37*y + 22)*(50*y**2 + 46*y + 21)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-19*y**2 + 37*y + 22)*(50*y**2 + 46*y + 21)\nExpanding the part (50*y**2 + 46*y + 21) using the distributive property, and we got: (46*y)*(-19*y**2 + 37*y + 22) + (50*y**2)*(-19*y**2 + 37*y + 22) + 21*(-19*y**2 + 37*y + 22)\n#Step 2:\nCurrent expression: (46*y)*(-19*y**2 + 37*y + 22) + (50*y**2)*(-19*y**2 + 37*y + 22) + 21*(-19*y**2 + 37*y + 22)\nSimplifying the partial expression: 21*(-19*y**2 + 37*y + 22)\nExpanding the part (-19*y**2 + 37*y + 22) using the distributive property, and we got: (37*y)*21 - 19*y**2*21 + 22*21\nReplacing 21*(-19*y**2 + 37*y + 22) with (37*y)*21 - 19*y**2*21 + 22*21 in the overall expression.\n#Step 3:\nCurrent expression: (37*y)*21 + (46*y)*(-19*y**2 + 37*y + 22) - 19*y**2*21 + (50*y**2)*(-19*y**2 + 37*y + 22) + 462\nSimplifying the partial expression: (46*y)*(-19*y**2 + 37*y + 22)\nExpanding the part (-19*y**2 + 37*y + 22) using the distributive property, and we got: 22*(46*y) + (37*y)*(46*y) + (46*y)*(-19*y**2)\nReplacing (46*y)*(-19*y**2 + 37*y + 22) with 22*(46*y) + (37*y)*(46*y) + (46*y)*(-19*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 22*46*y + (37*y)*(46*y) + (37*y)*21 + (46*y)*(-19*y**2) - 19*y**2*21 + (50*y**2)*(-19*y**2 + 37*y + 22) + 462\nSimplifying the partial expression: (50*y**2)*(-19*y**2 + 37*y + 22)\nExpanding the part (-19*y**2 + 37*y + 22) using the distributive property, and we got: 22*(50*y**2) + (37*y)*(50*y**2) + (-19*y**2)*(50*y**2)\nReplacing (50*y**2)*(-19*y**2 + 37*y + 22) with 22*(50*y**2) + (37*y)*(50*y**2) + (-19*y**2)*(50*y**2) in the overall expression.\n#Step 5:\nCurrent expression: 22*50*y**2 + 22*46*y + (37*y)*(46*y) + (37*y)*(50*y**2) + (37*y)*21 + (46*y)*(-19*y**2) + (-19*y**2)*(50*y**2) - 19*y**2*21 + 462\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*y**2)*21 = -399*y**2\n (-19*y**2)*(46*y) = -874*y**3\n (-19*y**2)*(50*y**2) = -950*y**4\n (37*y)*21 = 777*y\n (37*y)*(46*y) = 1702*y**2\n (37*y)*(50*y**2) = 1850*y**3\n 22*46*y = 1012*y\n 22*50*y**2 = 1100*y**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -950*y**4 - 874*y**3 + 1850*y**3 - 399*y**2 + 1100*y**2 + 1702*y**2 + 777*y + 1012*y + 462\nCombining like terms, got -950*y**4 + 976*y**3 + 2403*y**2 + 1789*y + 462\n#Step 7:\nCurrent expression: -950*y**4 + 976*y**3 + 2403*y**2 + 1789*y + 462\nNo more calculations needed.\n-950*y**4 + 976*y**3 + 2403*y**2 + 1789*y + 462", "generated_answer": "-950*y**4 + 976*y**3 + 2403*y**2 + 1789*y + 462", "step_length": 7} {"cot_id": "fac76d8711e6b376295a01799080bb568cd6e96f644c570d7af89711c54ccc37", "datapoint": {"question": "Simplify this expression: -38*x**2*(-35*x**3 - 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1330*x**5 + 1254*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1268, "polynomial_expr": "-38*x**2*(-35*x**3 - 33)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -38*x**2*(-35*x**3 - 33)\nExpanding the part (-35*x**3 - 33) using the distributive property, and we got: -(-1)*1254*x**2 + (-38*x**2)*(-35*x**3)\n#Step 2:\nCurrent expression: -(-1)*1254*x**2 + (-38*x**2)*(-35*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -33*(-38*x**2) = 1254*x**2\n (-35*x**3)*(-38*x**2) = 1330*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1330*x**5 + 1254*x**2\nNo more calculations needed.\n1330*x**5 + 1254*x**2", "generated_answer": "1330*x**5 + 1254*x**2", "step_length": 3} {"cot_id": "53eb259b34fef291c6852a756880bddcaedab9d9611698838100718eb08013e1", "datapoint": {"question": "Calculate the following: 84*x**3*(6*x**3 + 43)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "504*x**6 + 3612*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1269, "polynomial_expr": "84*x**3*(6*x**3 + 43)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 84*x**3*(6*x**3 + 43)\nExpanding the part (6*x**3 + 43) using the distributive property, and we got: 43*(84*x**3) + (6*x**3)*(84*x**3)\n#Step 2:\nCurrent expression: 43*(84*x**3) + (6*x**3)*(84*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 43*(84*x**3) = 3612*x**3\n (6*x**3)*(84*x**3) = 504*x**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 504*x**6 + 3612*x**3\nNo more calculations needed.\n504*x**6 + 3612*x**3", "generated_answer": "504*x**6 + 3612*x**3", "step_length": 3} {"cot_id": "003b97b7d5cdfcac1d0a49e9fa8b52fe8e99b015528084efe322db9ed4af8529", "datapoint": {"question": "Calculate the following: (2 - 12*z**3)*(42*z**2 + 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-504*z**5 - 396*z**3 + 84*z**2 + 66", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1270, "polynomial_expr": "(2 - 12*z**3)*(42*z**2 + 33)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2 - 12*z**3)*(42*z**2 + 33)\nExpanding the part (2 - 12*z**3) using the distributive property, and we got: (-12*z**3)*(42*z**2 + 33) + 2*(42*z**2 + 33)\n#Step 2:\nCurrent expression: (-12*z**3)*(42*z**2 + 33) + 2*(42*z**2 + 33)\nSimplifying the partial expression: 2*(42*z**2 + 33)\nExpanding the part (42*z**2 + 33) using the distributive property, and we got: (42*z**2)*2 + 33*2\nReplacing 2*(42*z**2 + 33) with (42*z**2)*2 + 33*2 in the overall expression.\n#Step 3:\nCurrent expression: (42*z**2)*2 + (-12*z**3)*(42*z**2 + 33) + 66\nSimplifying the partial expression: (-12*z**3)*(42*z**2 + 33)\nExpanding the part (42*z**2 + 33) using the distributive property, and we got: 33*(-12*z**3) + (42*z**2)*(-12*z**3)\nReplacing (-12*z**3)*(42*z**2 + 33) with 33*(-12*z**3) + (42*z**2)*(-12*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 33*(-12)*z**3 + (42*z**2)*(-12*z**3) + (42*z**2)*2 + 66\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (42*z**2)*2 = 84*z**2\n (42*z**2)*(-12*z**3) = -504*z**5\n 33*-12*z**3 = -396*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -504*z**5 - 396*z**3 + 84*z**2 + 66\nNo more calculations needed.\n-504*z**5 - 396*z**3 + 84*z**2 + 66", "generated_answer": "-504*z**5 - 396*z**3 + 84*z**2 + 66", "step_length": 5} {"cot_id": "274b512675d9527a94a7c4958f01d1c3d021b0840f325d433b88c2c008de72df", "datapoint": {"question": "Calculate the following: -24*z*(-11*z**2 - 6*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "264*z**3 + 144*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1271, "polynomial_expr": "-24*z*(-11*z**2 - 6*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -24*z*(-11*z**2 - 6*z)\nExpanding the part (-11*z**2 - 6*z) using the distributive property, and we got: (-24*z)*(-6*z) + (-24*z)*(-11*z**2)\n#Step 2:\nCurrent expression: (-24*z)*(-6*z) + (-24*z)*(-11*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*z**2)*(-24*z) = 264*z**3\n (-6*z)*(-24*z) = 144*z**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 264*z**3 + 144*z**2\nNo more calculations needed.\n264*z**3 + 144*z**2", "generated_answer": "264*z**3 + 144*z**2", "step_length": 3} {"cot_id": "c7b50193ea46946b38e15cc840be4b73751a9084cd697938b5fd110fc5c18a66", "datapoint": {"question": "Calculate the following: (6 - 31*y**2)*(55*y**3 - 13*y**2 - 2*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1705*y**5 + 403*y**4 + 392*y**3 - 78*y**2 - 12*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1272, "polynomial_expr": "(6 - 31*y**2)*(55*y**3 - 13*y**2 - 2*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6 - 31*y**2)*(55*y**3 - 13*y**2 - 2*y)\nExpanding the part (6 - 31*y**2) using the distributive property, and we got: (-31*y**2)*(55*y**3 - 13*y**2 - 2*y) + 6*(55*y**3 - 13*y**2 - 2*y)\n#Step 2:\nCurrent expression: (-31*y**2)*(55*y**3 - 13*y**2 - 2*y) + 6*(55*y**3 - 13*y**2 - 2*y)\nSimplifying the partial expression: 6*(55*y**3 - 13*y**2 - 2*y)\nExpanding the part (55*y**3 - 13*y**2 - 2*y) using the distributive property, and we got: -2*y*6 - 13*y**2*6 + (55*y**3)*6\nReplacing 6*(55*y**3 - 13*y**2 - 2*y) with -2*y*6 - 13*y**2*6 + (55*y**3)*6 in the overall expression.\n#Step 3:\nCurrent expression: -2*y*6 + (-31*y**2)*(55*y**3 - 13*y**2 - 2*y) - 13*y**2*6 + (55*y**3)*6\nSimplifying the partial expression: (-31*y**2)*(55*y**3 - 13*y**2 - 2*y)\nExpanding the part (55*y**3 - 13*y**2 - 2*y) using the distributive property, and we got: (-2*y)*(-31*y**2) + (-31*y**2)*(-13*y**2) + (-31*y**2)*(55*y**3)\nReplacing (-31*y**2)*(55*y**3 - 13*y**2 - 2*y) with (-2*y)*(-31*y**2) + (-31*y**2)*(-13*y**2) + (-31*y**2)*(55*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-2*y)*(-31*y**2) - 2*y*6 + (-31*y**2)*(-13*y**2) + (-31*y**2)*(55*y**3) - 13*y**2*6 + (55*y**3)*6\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*y**2)*6 = -78*y**2\n (-13*y**2)*(-31*y**2) = 403*y**4\n (-2*y)*6 = -12*y\n (-2*y)*(-31*y**2) = 62*y**3\n (55*y**3)*6 = 330*y**3\n (55*y**3)*(-31*y**2) = -1705*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1705*y**5 + 403*y**4 + 62*y**3 + 330*y**3 - 78*y**2 - 12*y\nCombining like terms, got -1705*y**5 + 403*y**4 + 392*y**3 - 78*y**2 - 12*y\n#Step 6:\nCurrent expression: -1705*y**5 + 403*y**4 + 392*y**3 - 78*y**2 - 12*y\nNo more calculations needed.\n-1705*y**5 + 403*y**4 + 392*y**3 - 78*y**2 - 12*y", "generated_answer": "-1705*y**5 + 403*y**4 + 392*y**3 - 78*y**2 - 12*y", "step_length": 6} {"cot_id": "1832777fc22f7e8c32f74fbe280498d18b04e7c2075cedc47b2b445b7799d83a", "datapoint": {"question": "Calculate the following: (21*y**3 - 41*y**2)*(60*y**3 - 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1260*y**6 - 2460*y**5 - 1008*y**3 + 1968*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1273, "polynomial_expr": "(21*y**3 - 41*y**2)*(60*y**3 - 48)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21*y**3 - 41*y**2)*(60*y**3 - 48)\nExpanding the part (60*y**3 - 48) using the distributive property, and we got: (60*y**3)*(21*y**3 - 41*y**2) - 48*(21*y**3 - 41*y**2)\n#Step 2:\nCurrent expression: (60*y**3)*(21*y**3 - 41*y**2) - 48*(21*y**3 - 41*y**2)\nSimplifying the partial expression: -48*(21*y**3 - 41*y**2)\nExpanding the part (21*y**3 - 41*y**2) using the distributive property, and we got: -41*y**2*(-48) + (21*y**3)*(-48)\nReplacing -48*(21*y**3 - 41*y**2) with -41*y**2*(-48) + (21*y**3)*(-48) in the overall expression.\n#Step 3:\nCurrent expression: -41*y**2*(-48) + (21*y**3)*(-48) + (60*y**3)*(21*y**3 - 41*y**2)\nSimplifying the partial expression: (60*y**3)*(21*y**3 - 41*y**2)\nExpanding the part (21*y**3 - 41*y**2) using the distributive property, and we got: (-41*y**2)*(60*y**3) + (21*y**3)*(60*y**3)\nReplacing (60*y**3)*(21*y**3 - 41*y**2) with (-41*y**2)*(60*y**3) + (21*y**3)*(60*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-41*y**2)*(60*y**3) - 41*y**2*(-48) + (21*y**3)*(60*y**3) + (21*y**3)*(-48)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*y**2)*-48 = 1968*y**2\n (-41*y**2)*(60*y**3) = -2460*y**5\n (21*y**3)*-48 = -1008*y**3\n (21*y**3)*(60*y**3) = 1260*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1260*y**6 - 2460*y**5 - 1008*y**3 + 1968*y**2\nNo more calculations needed.\n1260*y**6 - 2460*y**5 - 1008*y**3 + 1968*y**2", "generated_answer": "1260*y**6 - 2460*y**5 - 1008*y**3 + 1968*y**2", "step_length": 5} {"cot_id": "12cf09abf19552edb175de966f6dd6ad98cb7c4874fcf098b51caf633613f20a", "datapoint": {"question": "Calculate the following: (15*x**2 + 24)*(-x**2 + 29*x + 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-15*x**4 + 435*x**3 + 711*x**2 + 696*x + 1176", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1274, "polynomial_expr": "(15*x**2 + 24)*(-x**2 + 29*x + 49)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (15*x**2 + 24)*(-x**2 + 29*x + 49)\nExpanding the part (15*x**2 + 24) using the distributive property, and we got: (15*x**2)*(-x**2 + 29*x + 49) + 24*(-x**2 + 29*x + 49)\n#Step 2:\nCurrent expression: (15*x**2)*(-x**2 + 29*x + 49) + 24*(-x**2 + 29*x + 49)\nSimplifying the partial expression: 24*(-x**2 + 29*x + 49)\nExpanding the part (-x**2 + 29*x + 49) using the distributive property, and we got: (29*x)*24 - x**2*24 + 49*24\nReplacing 24*(-x**2 + 29*x + 49) with (29*x)*24 - x**2*24 + 49*24 in the overall expression.\n#Step 3:\nCurrent expression: (29*x)*24 - x**2*24 + (15*x**2)*(-x**2 + 29*x + 49) + 1176\nSimplifying the partial expression: (15*x**2)*(-x**2 + 29*x + 49)\nExpanding the part (-x**2 + 29*x + 49) using the distributive property, and we got: 49*(15*x**2) + (29*x)*(15*x**2) + (-x**2)*(15*x**2)\nReplacing (15*x**2)*(-x**2 + 29*x + 49) with 49*(15*x**2) + (29*x)*(15*x**2) + (-x**2)*(15*x**2) in the overall expression.\n#Step 4:\nCurrent expression: 49*15*x**2 + (29*x)*(15*x**2) + (29*x)*24 + (-x**2)*(15*x**2) - x**2*24 + 1176\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-x**2)*24 = -24*x**2\n (-x**2)*(15*x**2) = -15*x**4\n (29*x)*24 = 696*x\n (29*x)*(15*x**2) = 435*x**3\n 49*15*x**2 = 735*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -15*x**4 + 435*x**3 - 24*x**2 + 735*x**2 + 696*x + 1176\nCombining like terms, got -15*x**4 + 435*x**3 + 711*x**2 + 696*x + 1176\n#Step 6:\nCurrent expression: -15*x**4 + 435*x**3 + 711*x**2 + 696*x + 1176\nNo more calculations needed.\n-15*x**4 + 435*x**3 + 711*x**2 + 696*x + 1176", "generated_answer": "-15*x**4 + 435*x**3 + 711*x**2 + 696*x + 1176", "step_length": 6} {"cot_id": "08184c0f630175ff130b60271319ba83569acb0cd077c920ed4b3e0ebccbf77b", "datapoint": {"question": "Simplify this expression: (-21*z**3 - 40)*(32*z**3 - 3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-672*z**6 - 1217*z**3 + 120", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1275, "polynomial_expr": "(-21*z**3 - 40)*(32*z**3 - 3)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-21*z**3 - 40)*(32*z**3 - 3)\nExpanding the part (-21*z**3 - 40) using the distributive property, and we got: (-21*z**3)*(32*z**3 - 3) - 40*(32*z**3 - 3)\n#Step 2:\nCurrent expression: (-21*z**3)*(32*z**3 - 3) - 40*(32*z**3 - 3)\nSimplifying the partial expression: -40*(32*z**3 - 3)\nExpanding the part (32*z**3 - 3) using the distributive property, and we got: (32*z**3)*(-40) - 3*(-40)\nReplacing -40*(32*z**3 - 3) with (32*z**3)*(-40) - 3*(-40) in the overall expression.\n#Step 3:\nCurrent expression: (-21*z**3)*(32*z**3 - 3) + (32*z**3)*(-40) + 120\nSimplifying the partial expression: (-21*z**3)*(32*z**3 - 3)\nExpanding the part (32*z**3 - 3) using the distributive property, and we got: -(-1)*63*z**3 + (-21*z**3)*(32*z**3)\nReplacing (-21*z**3)*(32*z**3 - 3) with -(-1)*63*z**3 + (-21*z**3)*(32*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -3*(-21)*z**3 + (-21*z**3)*(32*z**3) + (32*z**3)*(-40) + 120\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (32*z**3)*-40 = -1280*z**3\n (32*z**3)*(-21*z**3) = -672*z**6\n -3*-21*z**3 = 63*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -672*z**6 - 1280*z**3 + 63*z**3 + 120\nCombining like terms, got -672*z**6 - 1217*z**3 + 120\n#Step 6:\nCurrent expression: -672*z**6 - 1217*z**3 + 120\nNo more calculations needed.\n-672*z**6 - 1217*z**3 + 120", "generated_answer": "-672*z**6 - 1217*z**3 + 120", "step_length": 6} {"cot_id": "c66699e924dd8ac2582687ca09674db32e237fd6ad12d4085969bc328049c586", "datapoint": {"question": "Simplify this expression: (6 - 14*z)*(88*z + 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1232*z**2 - 158*z + 294", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1276, "polynomial_expr": "(6 - 14*z)*(88*z + 49)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6 - 14*z)*(88*z + 49)\nExpanding the part (6 - 14*z) using the distributive property, and we got: (-14*z)*(88*z + 49) + 6*(88*z + 49)\n#Step 2:\nCurrent expression: (-14*z)*(88*z + 49) + 6*(88*z + 49)\nSimplifying the partial expression: 6*(88*z + 49)\nExpanding the part (88*z + 49) using the distributive property, and we got: (88*z)*6 + 49*6\nReplacing 6*(88*z + 49) with (88*z)*6 + 49*6 in the overall expression.\n#Step 3:\nCurrent expression: (-14*z)*(88*z + 49) + (88*z)*6 + 294\nSimplifying the partial expression: (-14*z)*(88*z + 49)\nExpanding the part (88*z + 49) using the distributive property, and we got: (-14*z)*(88*z) + 49*(-14*z)\nReplacing (-14*z)*(88*z + 49) with (-14*z)*(88*z) + 49*(-14*z) in the overall expression.\n#Step 4:\nCurrent expression: (-14*z)*(88*z) + 49*(-14)*z + (88*z)*6 + 294\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (88*z)*6 = 528*z\n (88*z)*(-14*z) = -1232*z**2\n 49*-14*z = -686*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1232*z**2 - 686*z + 528*z + 294\nCombining like terms, got -1232*z**2 - 158*z + 294\n#Step 6:\nCurrent expression: -1232*z**2 - 158*z + 294\nNo more calculations needed.\n-1232*z**2 - 158*z + 294", "generated_answer": "-1232*z**2 - 158*z + 294", "step_length": 6} {"cot_id": "4ae7984d1e23cd06cbb5da93dbfe5fa08031ab8892752c0e4ed579cc23ea68c0", "datapoint": {"question": "Simplify this expression: (-5*y**2 - 17*y + 26)*(6*y**3 - 23*y**2 + 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-30*y**5 + 13*y**4 + 547*y**3 - 788*y**2 - 646*y + 988", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1277, "polynomial_expr": "(-5*y**2 - 17*y + 26)*(6*y**3 - 23*y**2 + 38)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-5*y**2 - 17*y + 26)*(6*y**3 - 23*y**2 + 38)\nExpanding the part (-5*y**2 - 17*y + 26) using the distributive property, and we got: (-17*y)*(6*y**3 - 23*y**2 + 38) + (-5*y**2)*(6*y**3 - 23*y**2 + 38) + 26*(6*y**3 - 23*y**2 + 38)\n#Step 2:\nCurrent expression: (-17*y)*(6*y**3 - 23*y**2 + 38) + (-5*y**2)*(6*y**3 - 23*y**2 + 38) + 26*(6*y**3 - 23*y**2 + 38)\nSimplifying the partial expression: 26*(6*y**3 - 23*y**2 + 38)\nExpanding the part (6*y**3 - 23*y**2 + 38) using the distributive property, and we got: -23*y**2*26 + (6*y**3)*26 + 38*26\nReplacing 26*(6*y**3 - 23*y**2 + 38) with -23*y**2*26 + (6*y**3)*26 + 38*26 in the overall expression.\n#Step 3:\nCurrent expression: (-17*y)*(6*y**3 - 23*y**2 + 38) - 23*y**2*26 + (-5*y**2)*(6*y**3 - 23*y**2 + 38) + (6*y**3)*26 + 988\nSimplifying the partial expression: (-17*y)*(6*y**3 - 23*y**2 + 38)\nExpanding the part (6*y**3 - 23*y**2 + 38) using the distributive property, and we got: (-17*y)*(-23*y**2) + (-17*y)*(6*y**3) + 38*(-17*y)\nReplacing (-17*y)*(6*y**3 - 23*y**2 + 38) with (-17*y)*(-23*y**2) + (-17*y)*(6*y**3) + 38*(-17*y) in the overall expression.\n#Step 4:\nCurrent expression: (-17*y)*(-23*y**2) + (-17*y)*(6*y**3) + 38*(-17)*y - 23*y**2*26 + (-5*y**2)*(6*y**3 - 23*y**2 + 38) + (6*y**3)*26 + 988\nSimplifying the partial expression: (-5*y**2)*(6*y**3 - 23*y**2 + 38)\nExpanding the part (6*y**3 - 23*y**2 + 38) using the distributive property, and we got: 38*(-5*y**2) + (-23*y**2)*(-5*y**2) + (-5*y**2)*(6*y**3)\nReplacing (-5*y**2)*(6*y**3 - 23*y**2 + 38) with 38*(-5*y**2) + (-23*y**2)*(-5*y**2) + (-5*y**2)*(6*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-17*y)*(-23*y**2) + (-17*y)*(6*y**3) + 38*(-5)*y**2 + 38*(-17)*y + (-23*y**2)*(-5*y**2) - 23*y**2*26 + (-5*y**2)*(6*y**3) + (6*y**3)*26 + 988\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*y**2)*26 = -598*y**2\n (-23*y**2)*(-17*y) = 391*y**3\n (-23*y**2)*(-5*y**2) = 115*y**4\n (6*y**3)*26 = 156*y**3\n (6*y**3)*(-17*y) = -102*y**4\n (6*y**3)*(-5*y**2) = -30*y**5\n 38*-17*y = -646*y\n 38*-5*y**2 = -190*y**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -30*y**5 - 102*y**4 + 115*y**4 + 156*y**3 + 391*y**3 - 598*y**2 - 190*y**2 - 646*y + 988\nCombining like terms, got -30*y**5 + 13*y**4 + 547*y**3 - 788*y**2 - 646*y + 988\n#Step 7:\nCurrent expression: -30*y**5 + 13*y**4 + 547*y**3 - 788*y**2 - 646*y + 988\nNo more calculations needed.\n-30*y**5 + 13*y**4 + 547*y**3 - 788*y**2 - 646*y + 988", "generated_answer": "-30*y**5 + 13*y**4 + 547*y**3 - 788*y**2 - 646*y + 988", "step_length": 7} {"cot_id": "990628eafaa8bfc3df62552ab27158e12e1fd795df6db83877eaf578bc820977", "datapoint": {"question": "Calculate the following: (42*x**3 + 13*x)*(48*x**3 - 12*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2016*x**6 + 120*x**4 - 156*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1278, "polynomial_expr": "(42*x**3 + 13*x)*(48*x**3 - 12*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (42*x**3 + 13*x)*(48*x**3 - 12*x)\nExpanding the part (48*x**3 - 12*x) using the distributive property, and we got: (-12*x)*(42*x**3 + 13*x) + (48*x**3)*(42*x**3 + 13*x)\n#Step 2:\nCurrent expression: (-12*x)*(42*x**3 + 13*x) + (48*x**3)*(42*x**3 + 13*x)\nSimplifying the partial expression: (-12*x)*(42*x**3 + 13*x)\nExpanding the part (42*x**3 + 13*x) using the distributive property, and we got: (-12*x)*(13*x) + (-12*x)*(42*x**3)\nReplacing (-12*x)*(42*x**3 + 13*x) with (-12*x)*(13*x) + (-12*x)*(42*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-12*x)*(13*x) + (-12*x)*(42*x**3) + (48*x**3)*(42*x**3 + 13*x)\nSimplifying the partial expression: (48*x**3)*(42*x**3 + 13*x)\nExpanding the part (42*x**3 + 13*x) using the distributive property, and we got: (13*x)*(48*x**3) + (42*x**3)*(48*x**3)\nReplacing (48*x**3)*(42*x**3 + 13*x) with (13*x)*(48*x**3) + (42*x**3)*(48*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-12*x)*(13*x) + (-12*x)*(42*x**3) + (13*x)*(48*x**3) + (42*x**3)*(48*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (13*x)*(-12*x) = -156*x**2\n (13*x)*(48*x**3) = 624*x**4\n (42*x**3)*(-12*x) = -504*x**4\n (42*x**3)*(48*x**3) = 2016*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2016*x**6 - 504*x**4 + 624*x**4 - 156*x**2\nCombining like terms, got 2016*x**6 + 120*x**4 - 156*x**2\n#Step 6:\nCurrent expression: 2016*x**6 + 120*x**4 - 156*x**2\nNo more calculations needed.\n2016*x**6 + 120*x**4 - 156*x**2", "generated_answer": "2016*x**6 + 120*x**4 - 156*x**2", "step_length": 6} {"cot_id": "dddf6c9e95c5a6bbe2c3ffe92e404e834d365c153ae2f3e327ffda3086a4a19c", "datapoint": {"question": "Calculate the following: (-15*z - 28)*(-35*z**3 - 77*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "525*z**4 + 980*z**3 + 1155*z**2 + 2156*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1279, "polynomial_expr": "(-15*z - 28)*(-35*z**3 - 77*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-15*z - 28)*(-35*z**3 - 77*z)\nExpanding the part (-15*z - 28) using the distributive property, and we got: (-15*z)*(-35*z**3 - 77*z) - 28*(-35*z**3 - 77*z)\n#Step 2:\nCurrent expression: (-15*z)*(-35*z**3 - 77*z) - 28*(-35*z**3 - 77*z)\nSimplifying the partial expression: -28*(-35*z**3 - 77*z)\nExpanding the part (-35*z**3 - 77*z) using the distributive property, and we got: -77*z*(-28) - 35*z**3*(-28)\nReplacing -28*(-35*z**3 - 77*z) with -77*z*(-28) - 35*z**3*(-28) in the overall expression.\n#Step 3:\nCurrent expression: -77*z*(-28) + (-15*z)*(-35*z**3 - 77*z) - 35*z**3*(-28)\nSimplifying the partial expression: (-15*z)*(-35*z**3 - 77*z)\nExpanding the part (-35*z**3 - 77*z) using the distributive property, and we got: (-77*z)*(-15*z) + (-15*z)*(-35*z**3)\nReplacing (-15*z)*(-35*z**3 - 77*z) with (-77*z)*(-15*z) + (-15*z)*(-35*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-77*z)*(-15*z) - 77*z*(-28) + (-15*z)*(-35*z**3) - 35*z**3*(-28)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-77*z)*-28 = 2156*z\n (-77*z)*(-15*z) = 1155*z**2\n (-35*z**3)*-28 = 980*z**3\n (-35*z**3)*(-15*z) = 525*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 525*z**4 + 980*z**3 + 1155*z**2 + 2156*z\nNo more calculations needed.\n525*z**4 + 980*z**3 + 1155*z**2 + 2156*z", "generated_answer": "525*z**4 + 980*z**3 + 1155*z**2 + 2156*z", "step_length": 5} {"cot_id": "9365e2d6c14b570e97cf23cbd8889ef01265852fc643651a19d9675043deee58", "datapoint": {"question": "Simplify this expression: -39*y**3*(-28*y**3 + 10*y + 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1092*y**6 - 390*y**4 - 1404*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1280, "polynomial_expr": "-39*y**3*(-28*y**3 + 10*y + 36)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -39*y**3*(-28*y**3 + 10*y + 36)\nExpanding the part (-28*y**3 + 10*y + 36) using the distributive property, and we got: 36*(-39*y**3) + (10*y)*(-39*y**3) + (-39*y**3)*(-28*y**3)\n#Step 2:\nCurrent expression: 36*(-39*y**3) + (10*y)*(-39*y**3) + (-39*y**3)*(-28*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 36*(-39*y**3) = -1404*y**3\n (-28*y**3)*(-39*y**3) = 1092*y**6\n (10*y)*(-39*y**3) = -390*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1092*y**6 - 390*y**4 - 1404*y**3\nNo more calculations needed.\n1092*y**6 - 390*y**4 - 1404*y**3", "generated_answer": "1092*y**6 - 390*y**4 - 1404*y**3", "step_length": 3} {"cot_id": "c464e2423ff92fbdfb180a31441b41d660731c0db928f902798f6a51a6748264", "datapoint": {"question": "Calculate the following: (-16*y**3 + 32*y)*(3*y**2 - 50*y - 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-48*y**5 + 800*y**4 + 672*y**3 - 1600*y**2 - 1152*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1281, "polynomial_expr": "(-16*y**3 + 32*y)*(3*y**2 - 50*y - 36)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-16*y**3 + 32*y)*(3*y**2 - 50*y - 36)\nExpanding the part (-16*y**3 + 32*y) using the distributive property, and we got: (32*y)*(3*y**2 - 50*y - 36) + (-16*y**3)*(3*y**2 - 50*y - 36)\n#Step 2:\nCurrent expression: (32*y)*(3*y**2 - 50*y - 36) + (-16*y**3)*(3*y**2 - 50*y - 36)\nSimplifying the partial expression: (-16*y**3)*(3*y**2 - 50*y - 36)\nExpanding the part (3*y**2 - 50*y - 36) using the distributive property, and we got: (-50*y)*(-16*y**3) - (-1)*576*y**3 + (3*y**2)*(-16*y**3)\nReplacing (-16*y**3)*(3*y**2 - 50*y - 36) with (-50*y)*(-16*y**3) - (-1)*576*y**3 + (3*y**2)*(-16*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-50*y)*(-16*y**3) - 36*(-16)*y**3 + (32*y)*(3*y**2 - 50*y - 36) + (3*y**2)*(-16*y**3)\nSimplifying the partial expression: (32*y)*(3*y**2 - 50*y - 36)\nExpanding the part (3*y**2 - 50*y - 36) using the distributive property, and we got: (-50*y)*(32*y) - 1152*y + (32*y)*(3*y**2)\nReplacing (32*y)*(3*y**2 - 50*y - 36) with (-50*y)*(32*y) - 1152*y + (32*y)*(3*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-50*y)*(32*y) + (-50*y)*(-16*y**3) - 36*(-16)*y**3 - 36*32*y + (32*y)*(3*y**2) + (3*y**2)*(-16*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-50*y)*(-16*y**3) = 800*y**4\n (-50*y)*(32*y) = -1600*y**2\n (3*y**2)*(-16*y**3) = -48*y**5\n (3*y**2)*(32*y) = 96*y**3\n -36*-16*y**3 = 576*y**3\n -36*32*y = -1152*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -48*y**5 + 800*y**4 + 96*y**3 + 576*y**3 - 1600*y**2 - 1152*y\nCombining like terms, got -48*y**5 + 800*y**4 + 672*y**3 - 1600*y**2 - 1152*y\n#Step 6:\nCurrent expression: -48*y**5 + 800*y**4 + 672*y**3 - 1600*y**2 - 1152*y\nNo more calculations needed.\n-48*y**5 + 800*y**4 + 672*y**3 - 1600*y**2 - 1152*y", "generated_answer": "-48*y**5 + 800*y**4 + 672*y**3 - 1600*y**2 - 1152*y", "step_length": 6} {"cot_id": "41d0fa194a1d4e5500133445a984a71c4413ba54f7e697a2f346890d7c00459a", "datapoint": {"question": "Calculate the following: 14*y**3 - 672*y**2 - 420*y - 434\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "14*y**3 - 672*y**2 - 420*y - 434", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1282, "polynomial_expr": "14*y**3 - 672*y**2 - 420*y - 434", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 14*y**3 - 672*y**2 - 420*y - 434\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 14*y**3 - 672*y**2 - 420*y - 434\nNo more calculations needed.\n14*y**3 - 672*y**2 - 420*y - 434", "generated_answer": "14*y**3 - 672*y**2 - 420*y - 434", "step_length": 2} {"cot_id": "9e73ca4a2bb5089135004d3135c087fe89fa0d22c4dc0f2cdd2f8592ff7e4011", "datapoint": {"question": "Calculate the following: (48*z**2 + 26)*(19*z**3 + 16*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "912*z**5 + 768*z**4 + 494*z**3 + 416*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1283, "polynomial_expr": "(48*z**2 + 26)*(19*z**3 + 16*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (48*z**2 + 26)*(19*z**3 + 16*z**2)\nExpanding the part (48*z**2 + 26) using the distributive property, and we got: (48*z**2)*(19*z**3 + 16*z**2) + 26*(19*z**3 + 16*z**2)\n#Step 2:\nCurrent expression: (48*z**2)*(19*z**3 + 16*z**2) + 26*(19*z**3 + 16*z**2)\nSimplifying the partial expression: 26*(19*z**3 + 16*z**2)\nExpanding the part (19*z**3 + 16*z**2) using the distributive property, and we got: (16*z**2)*26 + (19*z**3)*26\nReplacing 26*(19*z**3 + 16*z**2) with (16*z**2)*26 + (19*z**3)*26 in the overall expression.\n#Step 3:\nCurrent expression: (16*z**2)*26 + (48*z**2)*(19*z**3 + 16*z**2) + (19*z**3)*26\nSimplifying the partial expression: (48*z**2)*(19*z**3 + 16*z**2)\nExpanding the part (19*z**3 + 16*z**2) using the distributive property, and we got: (16*z**2)*(48*z**2) + (48*z**2)*(19*z**3)\nReplacing (48*z**2)*(19*z**3 + 16*z**2) with (16*z**2)*(48*z**2) + (48*z**2)*(19*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (16*z**2)*(48*z**2) + (16*z**2)*26 + (48*z**2)*(19*z**3) + (19*z**3)*26\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (16*z**2)*26 = 416*z**2\n (16*z**2)*(48*z**2) = 768*z**4\n (19*z**3)*26 = 494*z**3\n (19*z**3)*(48*z**2) = 912*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 912*z**5 + 768*z**4 + 494*z**3 + 416*z**2\nNo more calculations needed.\n912*z**5 + 768*z**4 + 494*z**3 + 416*z**2", "generated_answer": "912*z**5 + 768*z**4 + 494*z**3 + 416*z**2", "step_length": 5} {"cot_id": "36843a9feba28f421ec98af5420276f9f54ff1f52323902b9a1886fdcc0849e2", "datapoint": {"question": "Simplify this expression: -1870*y**3 - 2720*y\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1870*y**3 - 2720*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1284, "polynomial_expr": "-1870*y**3 - 2720*y", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -1870*y**3 - 2720*y\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -1870*y**3 - 2720*y\nNo more calculations needed.\n-1870*y**3 - 2720*y", "generated_answer": "-1870*y**3 - 2720*y", "step_length": 2} {"cot_id": "ce729fb3720c28d9f8e51f35c0dca17185f652ab9a196de05a740618df960ee5", "datapoint": {"question": "Calculate the following: (31 - 25*x**3)*(-35*x**2 - 39*x - 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "875*x**5 + 975*x**4 + 150*x**3 - 1085*x**2 - 1209*x - 186", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1285, "polynomial_expr": "(31 - 25*x**3)*(-35*x**2 - 39*x - 6)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31 - 25*x**3)*(-35*x**2 - 39*x - 6)\nExpanding the part (31 - 25*x**3) using the distributive property, and we got: (-25*x**3)*(-35*x**2 - 39*x - 6) + 31*(-35*x**2 - 39*x - 6)\n#Step 2:\nCurrent expression: (-25*x**3)*(-35*x**2 - 39*x - 6) + 31*(-35*x**2 - 39*x - 6)\nSimplifying the partial expression: 31*(-35*x**2 - 39*x - 6)\nExpanding the part (-35*x**2 - 39*x - 6) using the distributive property, and we got: -39*x*31 - 35*x**2*31 - 6*31\nReplacing 31*(-35*x**2 - 39*x - 6) with -39*x*31 - 35*x**2*31 - 6*31 in the overall expression.\n#Step 3:\nCurrent expression: -39*x*31 - 35*x**2*31 + (-25*x**3)*(-35*x**2 - 39*x - 6) - 186\nSimplifying the partial expression: (-25*x**3)*(-35*x**2 - 39*x - 6)\nExpanding the part (-35*x**2 - 39*x - 6) using the distributive property, and we got: (-39*x)*(-25*x**3) - (-1)*150*x**3 + (-35*x**2)*(-25*x**3)\nReplacing (-25*x**3)*(-35*x**2 - 39*x - 6) with (-39*x)*(-25*x**3) - (-1)*150*x**3 + (-35*x**2)*(-25*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-39*x)*(-25*x**3) - 39*x*31 - 6*(-25)*x**3 + (-35*x**2)*(-25*x**3) - 35*x**2*31 - 186\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*x)*31 = -1209*x\n (-39*x)*(-25*x**3) = 975*x**4\n (-35*x**2)*31 = -1085*x**2\n (-35*x**2)*(-25*x**3) = 875*x**5\n -6*-25*x**3 = 150*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 875*x**5 + 975*x**4 + 150*x**3 - 1085*x**2 - 1209*x - 186\nNo more calculations needed.\n875*x**5 + 975*x**4 + 150*x**3 - 1085*x**2 - 1209*x - 186", "generated_answer": "875*x**5 + 975*x**4 + 150*x**3 - 1085*x**2 - 1209*x - 186", "step_length": 5} {"cot_id": "24528e6aaf785d61f8dc500f5c1719cce2171df1719b8a136081ce031f550f24", "datapoint": {"question": "Calculate the following: (46*x**3 - 5*x**2)*(-47*x**3 - 30*x**2 + 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2162*x**6 - 1145*x**5 + 150*x**4 + 736*x**3 - 80*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1286, "polynomial_expr": "(46*x**3 - 5*x**2)*(-47*x**3 - 30*x**2 + 16)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (46*x**3 - 5*x**2)*(-47*x**3 - 30*x**2 + 16)\nExpanding the part (46*x**3 - 5*x**2) using the distributive property, and we got: (-5*x**2)*(-47*x**3 - 30*x**2 + 16) + (46*x**3)*(-47*x**3 - 30*x**2 + 16)\n#Step 2:\nCurrent expression: (-5*x**2)*(-47*x**3 - 30*x**2 + 16) + (46*x**3)*(-47*x**3 - 30*x**2 + 16)\nSimplifying the partial expression: (-5*x**2)*(-47*x**3 - 30*x**2 + 16)\nExpanding the part (-47*x**3 - 30*x**2 + 16) using the distributive property, and we got: 16*(-5*x**2) + (-30*x**2)*(-5*x**2) + (-5*x**2)*(-47*x**3)\nReplacing (-5*x**2)*(-47*x**3 - 30*x**2 + 16) with 16*(-5*x**2) + (-30*x**2)*(-5*x**2) + (-5*x**2)*(-47*x**3) in the overall expression.\n#Step 3:\nCurrent expression: 16*(-5)*x**2 + (-30*x**2)*(-5*x**2) + (-5*x**2)*(-47*x**3) + (46*x**3)*(-47*x**3 - 30*x**2 + 16)\nSimplifying the partial expression: (46*x**3)*(-47*x**3 - 30*x**2 + 16)\nExpanding the part (-47*x**3 - 30*x**2 + 16) using the distributive property, and we got: 16*(46*x**3) + (-30*x**2)*(46*x**3) + (-47*x**3)*(46*x**3)\nReplacing (46*x**3)*(-47*x**3 - 30*x**2 + 16) with 16*(46*x**3) + (-30*x**2)*(46*x**3) + (-47*x**3)*(46*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 16*46*x**3 + 16*(-5)*x**2 + (-30*x**2)*(-5*x**2) + (-30*x**2)*(46*x**3) + (-5*x**2)*(-47*x**3) + (-47*x**3)*(46*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*x**3)*(-5*x**2) = 235*x**5\n (-47*x**3)*(46*x**3) = -2162*x**6\n (-30*x**2)*(-5*x**2) = 150*x**4\n (-30*x**2)*(46*x**3) = -1380*x**5\n 16*-5*x**2 = -80*x**2\n 16*46*x**3 = 736*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2162*x**6 - 1380*x**5 + 235*x**5 + 150*x**4 + 736*x**3 - 80*x**2\nCombining like terms, got -2162*x**6 - 1145*x**5 + 150*x**4 + 736*x**3 - 80*x**2\n#Step 6:\nCurrent expression: -2162*x**6 - 1145*x**5 + 150*x**4 + 736*x**3 - 80*x**2\nNo more calculations needed.\n-2162*x**6 - 1145*x**5 + 150*x**4 + 736*x**3 - 80*x**2", "generated_answer": "-2162*x**6 - 1145*x**5 + 150*x**4 + 736*x**3 - 80*x**2", "step_length": 6} {"cot_id": "d79d2de587466e713af69c3791cca6f898444791a885c70f3ae88c7d8b5ccca5", "datapoint": {"question": "Simplify this expression: (50*y**3 + 39*y**2)*(-21*y**3 - 4*y**2 + 2*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1050*y**6 - 1019*y**5 - 56*y**4 + 78*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1287, "polynomial_expr": "(50*y**3 + 39*y**2)*(-21*y**3 - 4*y**2 + 2*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (50*y**3 + 39*y**2)*(-21*y**3 - 4*y**2 + 2*y)\nExpanding the part (50*y**3 + 39*y**2) using the distributive property, and we got: (39*y**2)*(-21*y**3 - 4*y**2 + 2*y) + (50*y**3)*(-21*y**3 - 4*y**2 + 2*y)\n#Step 2:\nCurrent expression: (39*y**2)*(-21*y**3 - 4*y**2 + 2*y) + (50*y**3)*(-21*y**3 - 4*y**2 + 2*y)\nSimplifying the partial expression: (39*y**2)*(-21*y**3 - 4*y**2 + 2*y)\nExpanding the part (-21*y**3 - 4*y**2 + 2*y) using the distributive property, and we got: (2*y)*(39*y**2) + (-4*y**2)*(39*y**2) + (39*y**2)*(-21*y**3)\nReplacing (39*y**2)*(-21*y**3 - 4*y**2 + 2*y) with (2*y)*(39*y**2) + (-4*y**2)*(39*y**2) + (39*y**2)*(-21*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (2*y)*(39*y**2) + (-4*y**2)*(39*y**2) + (39*y**2)*(-21*y**3) + (50*y**3)*(-21*y**3 - 4*y**2 + 2*y)\nSimplifying the partial expression: (50*y**3)*(-21*y**3 - 4*y**2 + 2*y)\nExpanding the part (-21*y**3 - 4*y**2 + 2*y) using the distributive property, and we got: (2*y)*(50*y**3) + (-4*y**2)*(50*y**3) + (-21*y**3)*(50*y**3)\nReplacing (50*y**3)*(-21*y**3 - 4*y**2 + 2*y) with (2*y)*(50*y**3) + (-4*y**2)*(50*y**3) + (-21*y**3)*(50*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (2*y)*(39*y**2) + (2*y)*(50*y**3) + (-4*y**2)*(39*y**2) + (-4*y**2)*(50*y**3) + (39*y**2)*(-21*y**3) + (-21*y**3)*(50*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-21*y**3)*(39*y**2) = -819*y**5\n (-21*y**3)*(50*y**3) = -1050*y**6\n (-4*y**2)*(39*y**2) = -156*y**4\n (-4*y**2)*(50*y**3) = -200*y**5\n (2*y)*(39*y**2) = 78*y**3\n (2*y)*(50*y**3) = 100*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1050*y**6 - 819*y**5 - 200*y**5 - 156*y**4 + 100*y**4 + 78*y**3\nCombining like terms, got -1050*y**6 - 1019*y**5 - 56*y**4 + 78*y**3\n#Step 6:\nCurrent expression: -1050*y**6 - 1019*y**5 - 56*y**4 + 78*y**3\nNo more calculations needed.\n-1050*y**6 - 1019*y**5 - 56*y**4 + 78*y**3", "generated_answer": "-1050*y**6 - 1019*y**5 - 56*y**4 + 78*y**3", "step_length": 6} {"cot_id": "234c576e0a1aacdb8ab5713343b20c173e3e304517079e6580b46e77754ee8a3", "datapoint": {"question": "Calculate the following: (-8*y**2 - 27)*(49*y**3 - 5*y**2 + 33*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-392*y**5 + 40*y**4 - 1587*y**3 + 135*y**2 - 891*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1288, "polynomial_expr": "(-8*y**2 - 27)*(49*y**3 - 5*y**2 + 33*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-8*y**2 - 27)*(49*y**3 - 5*y**2 + 33*y)\nExpanding the part (-8*y**2 - 27) using the distributive property, and we got: (-8*y**2)*(49*y**3 - 5*y**2 + 33*y) - 27*(49*y**3 - 5*y**2 + 33*y)\n#Step 2:\nCurrent expression: (-8*y**2)*(49*y**3 - 5*y**2 + 33*y) - 27*(49*y**3 - 5*y**2 + 33*y)\nSimplifying the partial expression: -27*(49*y**3 - 5*y**2 + 33*y)\nExpanding the part (49*y**3 - 5*y**2 + 33*y) using the distributive property, and we got: (33*y)*(-27) - 5*y**2*(-27) + (49*y**3)*(-27)\nReplacing -27*(49*y**3 - 5*y**2 + 33*y) with (33*y)*(-27) - 5*y**2*(-27) + (49*y**3)*(-27) in the overall expression.\n#Step 3:\nCurrent expression: (33*y)*(-27) + (-8*y**2)*(49*y**3 - 5*y**2 + 33*y) - 5*y**2*(-27) + (49*y**3)*(-27)\nSimplifying the partial expression: (-8*y**2)*(49*y**3 - 5*y**2 + 33*y)\nExpanding the part (49*y**3 - 5*y**2 + 33*y) using the distributive property, and we got: (33*y)*(-8*y**2) + (-8*y**2)*(-5*y**2) + (-8*y**2)*(49*y**3)\nReplacing (-8*y**2)*(49*y**3 - 5*y**2 + 33*y) with (33*y)*(-8*y**2) + (-8*y**2)*(-5*y**2) + (-8*y**2)*(49*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (33*y)*(-8*y**2) + (33*y)*(-27) + (-8*y**2)*(-5*y**2) + (-8*y**2)*(49*y**3) - 5*y**2*(-27) + (49*y**3)*(-27)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-5*y**2)*-27 = 135*y**2\n (-5*y**2)*(-8*y**2) = 40*y**4\n (33*y)*-27 = -891*y\n (33*y)*(-8*y**2) = -264*y**3\n (49*y**3)*-27 = -1323*y**3\n (49*y**3)*(-8*y**2) = -392*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -392*y**5 + 40*y**4 - 1323*y**3 - 264*y**3 + 135*y**2 - 891*y\nCombining like terms, got -392*y**5 + 40*y**4 - 1587*y**3 + 135*y**2 - 891*y\n#Step 6:\nCurrent expression: -392*y**5 + 40*y**4 - 1587*y**3 + 135*y**2 - 891*y\nNo more calculations needed.\n-392*y**5 + 40*y**4 - 1587*y**3 + 135*y**2 - 891*y", "generated_answer": "-392*y**5 + 40*y**4 - 1587*y**3 + 135*y**2 - 891*y", "step_length": 6} {"cot_id": "b6858bc4da5246a396d99ec641a6aef6b6be525f15a3f09a06439853fd5ae946", "datapoint": {"question": "Simplify this expression: (-67*z**3 - 11*z)*(42*z**3 - 23*z**2 - 15*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2814*z**6 + 1541*z**5 + 543*z**4 + 253*z**3 + 165*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1289, "polynomial_expr": "(-67*z**3 - 11*z)*(42*z**3 - 23*z**2 - 15*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-67*z**3 - 11*z)*(42*z**3 - 23*z**2 - 15*z)\nExpanding the part (-67*z**3 - 11*z) using the distributive property, and we got: (-11*z)*(42*z**3 - 23*z**2 - 15*z) + (-67*z**3)*(42*z**3 - 23*z**2 - 15*z)\n#Step 2:\nCurrent expression: (-11*z)*(42*z**3 - 23*z**2 - 15*z) + (-67*z**3)*(42*z**3 - 23*z**2 - 15*z)\nSimplifying the partial expression: (-67*z**3)*(42*z**3 - 23*z**2 - 15*z)\nExpanding the part (42*z**3 - 23*z**2 - 15*z) using the distributive property, and we got: (-15*z)*(-67*z**3) + (-23*z**2)*(-67*z**3) + (-67*z**3)*(42*z**3)\nReplacing (-67*z**3)*(42*z**3 - 23*z**2 - 15*z) with (-15*z)*(-67*z**3) + (-23*z**2)*(-67*z**3) + (-67*z**3)*(42*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-15*z)*(-67*z**3) + (-11*z)*(42*z**3 - 23*z**2 - 15*z) + (-23*z**2)*(-67*z**3) + (-67*z**3)*(42*z**3)\nSimplifying the partial expression: (-11*z)*(42*z**3 - 23*z**2 - 15*z)\nExpanding the part (42*z**3 - 23*z**2 - 15*z) using the distributive property, and we got: (-15*z)*(-11*z) + (-11*z)*(-23*z**2) + (-11*z)*(42*z**3)\nReplacing (-11*z)*(42*z**3 - 23*z**2 - 15*z) with (-15*z)*(-11*z) + (-11*z)*(-23*z**2) + (-11*z)*(42*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-15*z)*(-11*z) + (-15*z)*(-67*z**3) + (-11*z)*(-23*z**2) + (-11*z)*(42*z**3) + (-23*z**2)*(-67*z**3) + (-67*z**3)*(42*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*z**2)*(-67*z**3) = 1541*z**5\n (-23*z**2)*(-11*z) = 253*z**3\n (-15*z)*(-67*z**3) = 1005*z**4\n (-15*z)*(-11*z) = 165*z**2\n (42*z**3)*(-67*z**3) = -2814*z**6\n (42*z**3)*(-11*z) = -462*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2814*z**6 + 1541*z**5 - 462*z**4 + 1005*z**4 + 253*z**3 + 165*z**2\nCombining like terms, got -2814*z**6 + 1541*z**5 + 543*z**4 + 253*z**3 + 165*z**2\n#Step 6:\nCurrent expression: -2814*z**6 + 1541*z**5 + 543*z**4 + 253*z**3 + 165*z**2\nNo more calculations needed.\n-2814*z**6 + 1541*z**5 + 543*z**4 + 253*z**3 + 165*z**2", "generated_answer": "-2814*z**6 + 1541*z**5 + 543*z**4 + 253*z**3 + 165*z**2", "step_length": 6} {"cot_id": "0aa1061a37c4ac44ae19bc15959b9879d36b5118f5837ea18562c46412a76e9f", "datapoint": {"question": "Calculate the following: 943*x**2 - 1722\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "943*x**2 - 1722", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1290, "polynomial_expr": "943*x**2 - 1722", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 943*x**2 - 1722\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 943*x**2 - 1722\nNo more calculations needed.\n943*x**2 - 1722", "generated_answer": "943*x**2 - 1722", "step_length": 2} {"cot_id": "f7acb10fae4a1afb20f33aa0fe45fd71961b449ce4e318a38ada55339340283f", "datapoint": {"question": "Calculate the following: (y**3 + 92*y**2 - 14*y)*(43*y**3 + 43*y - 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "43*y**6 + 3956*y**5 - 559*y**4 + 3926*y**3 - 3362*y**2 + 420*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1291, "polynomial_expr": "(y**3 + 92*y**2 - 14*y)*(43*y**3 + 43*y - 30)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (y**3 + 92*y**2 - 14*y)*(43*y**3 + 43*y - 30)\nExpanding the part (43*y**3 + 43*y - 30) using the distributive property, and we got: (43*y)*(y**3 + 92*y**2 - 14*y) + (43*y**3)*(y**3 + 92*y**2 - 14*y) - 30*(y**3 + 92*y**2 - 14*y)\n#Step 2:\nCurrent expression: (43*y)*(y**3 + 92*y**2 - 14*y) + (43*y**3)*(y**3 + 92*y**2 - 14*y) - 30*(y**3 + 92*y**2 - 14*y)\nSimplifying the partial expression: -30*(y**3 + 92*y**2 - 14*y)\nExpanding the part (y**3 + 92*y**2 - 14*y) using the distributive property, and we got: -14*y*(-30) + y**3*(-30) + (92*y**2)*(-30)\nReplacing -30*(y**3 + 92*y**2 - 14*y) with -14*y*(-30) + y**3*(-30) + (92*y**2)*(-30) in the overall expression.\n#Step 3:\nCurrent expression: -14*y*(-30) + y**3*(-30) + (43*y)*(y**3 + 92*y**2 - 14*y) + (92*y**2)*(-30) + (43*y**3)*(y**3 + 92*y**2 - 14*y)\nSimplifying the partial expression: (43*y)*(y**3 + 92*y**2 - 14*y)\nExpanding the part (y**3 + 92*y**2 - 14*y) using the distributive property, and we got: (-14*y)*(43*y) + (43*y)*y**3 + (43*y)*(92*y**2)\nReplacing (43*y)*(y**3 + 92*y**2 - 14*y) with (-14*y)*(43*y) + (43*y)*y**3 + (43*y)*(92*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-14*y)*(43*y) - 14*y*(-30) + (43*y)*y**3 + y**3*(-30) + (43*y)*(92*y**2) + (92*y**2)*(-30) + (43*y**3)*(y**3 + 92*y**2 - 14*y)\nSimplifying the partial expression: (43*y**3)*(y**3 + 92*y**2 - 14*y)\nExpanding the part (y**3 + 92*y**2 - 14*y) using the distributive property, and we got: (-14*y)*(43*y**3) + y**3*(43*y**3) + (92*y**2)*(43*y**3)\nReplacing (43*y**3)*(y**3 + 92*y**2 - 14*y) with (-14*y)*(43*y**3) + y**3*(43*y**3) + (92*y**2)*(43*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-14*y)*(43*y) + (-14*y)*(43*y**3) - 14*y*(-30) + (43*y)*y**3 + y**3*(43*y**3) + y**3*(-30) + (43*y)*(92*y**2) + (92*y**2)*(43*y**3) + (92*y**2)*(-30)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n y**3*-30 = -30*y**3\n y**3*(43*y) = 43*y**4\n y**3*(43*y**3) = 43*y**6\n (-14*y)*-30 = 420*y\n (-14*y)*(43*y) = -602*y**2\n (-14*y)*(43*y**3) = -602*y**4\n (92*y**2)*-30 = -2760*y**2\n (92*y**2)*(43*y) = 3956*y**3\n (92*y**2)*(43*y**3) = 3956*y**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 43*y**6 + 3956*y**5 - 602*y**4 + 43*y**4 - 30*y**3 + 3956*y**3 - 2760*y**2 - 602*y**2 + 420*y\nCombining like terms, got 43*y**6 + 3956*y**5 - 559*y**4 + 3926*y**3 - 3362*y**2 + 420*y\n#Step 7:\nCurrent expression: 43*y**6 + 3956*y**5 - 559*y**4 + 3926*y**3 - 3362*y**2 + 420*y\nNo more calculations needed.\n43*y**6 + 3956*y**5 - 559*y**4 + 3926*y**3 - 3362*y**2 + 420*y", "generated_answer": "43*y**6 + 3956*y**5 - 559*y**4 + 3926*y**3 - 3362*y**2 + 420*y", "step_length": 7} {"cot_id": "f30e60a7338ca3a536d2cf16fea14fce0c85f46a0e361a6579aff67760016581", "datapoint": {"question": "Calculate the following: -10*z**2*(-91*z**2 - 7*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "910*z**4 + 70*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1292, "polynomial_expr": "-10*z**2*(-91*z**2 - 7*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -10*z**2*(-91*z**2 - 7*z)\nExpanding the part (-91*z**2 - 7*z) using the distributive property, and we got: (-7*z)*(-10*z**2) + (-91*z**2)*(-10*z**2)\n#Step 2:\nCurrent expression: (-7*z)*(-10*z**2) + (-91*z**2)*(-10*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-91*z**2)*(-10*z**2) = 910*z**4\n (-7*z)*(-10*z**2) = 70*z**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 910*z**4 + 70*z**3\nNo more calculations needed.\n910*z**4 + 70*z**3", "generated_answer": "910*z**4 + 70*z**3", "step_length": 3} {"cot_id": "afc3b561e6f7b2166e646f32fe121f1e1187896758b54f5dd831817ea2dcd770", "datapoint": {"question": "Simplify this expression: 73*z*(8*z**2 + 66)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "584*z**3 + 4818*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1293, "polynomial_expr": "73*z*(8*z**2 + 66)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 73*z*(8*z**2 + 66)\nExpanding the part (8*z**2 + 66) using the distributive property, and we got: 66*(73*z) + (73*z)*(8*z**2)\n#Step 2:\nCurrent expression: 66*(73*z) + (73*z)*(8*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 66*(73*z) = 4818*z\n (8*z**2)*(73*z) = 584*z**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 584*z**3 + 4818*z\nNo more calculations needed.\n584*z**3 + 4818*z", "generated_answer": "584*z**3 + 4818*z", "step_length": 3} {"cot_id": "d62c02a5039eccf239519d6d0b3081cd877f8c77b3302935096a286149d9b64a", "datapoint": {"question": "Simplify this expression: (56 - 8*z**3)*(-43*z**3 + 11*z**2 - 30*z - 37)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "344*z**6 - 88*z**5 + 240*z**4 - 2112*z**3 + 616*z**2 - 1680*z - 2072", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1294, "polynomial_expr": "(56 - 8*z**3)*(-43*z**3 + 11*z**2 - 30*z - 37)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (56 - 8*z**3)*(-43*z**3 + 11*z**2 - 30*z - 37)\nExpanding the part (56 - 8*z**3) using the distributive property, and we got: (-8*z**3)*(-43*z**3 + 11*z**2 - 30*z - 37) + 56*(-43*z**3 + 11*z**2 - 30*z - 37)\n#Step 2:\nCurrent expression: (-8*z**3)*(-43*z**3 + 11*z**2 - 30*z - 37) + 56*(-43*z**3 + 11*z**2 - 30*z - 37)\nSimplifying the partial expression: 56*(-43*z**3 + 11*z**2 - 30*z - 37)\nExpanding the part (-43*z**3 + 11*z**2 - 30*z - 37) using the distributive property, and we got: -30*z*56 + (11*z**2)*56 - 43*z**3*56 - 37*56\nReplacing 56*(-43*z**3 + 11*z**2 - 30*z - 37) with -30*z*56 + (11*z**2)*56 - 43*z**3*56 - 37*56 in the overall expression.\n#Step 3:\nCurrent expression: -30*z*56 + (11*z**2)*56 - 43*z**3*56 + (-8*z**3)*(-43*z**3 + 11*z**2 - 30*z - 37) - 2072\nSimplifying the partial expression: (-8*z**3)*(-43*z**3 + 11*z**2 - 30*z - 37)\nExpanding the part (-43*z**3 + 11*z**2 - 30*z - 37) using the distributive property, and we got: (-30*z)*(-8*z**3) - (-1)*296*z**3 + (11*z**2)*(-8*z**3) + (-43*z**3)*(-8*z**3)\nReplacing (-8*z**3)*(-43*z**3 + 11*z**2 - 30*z - 37) with (-30*z)*(-8*z**3) - (-1)*296*z**3 + (11*z**2)*(-8*z**3) + (-43*z**3)*(-8*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-30*z)*(-8*z**3) - 30*z*56 - 37*(-8)*z**3 + (11*z**2)*(-8*z**3) + (11*z**2)*56 + (-43*z**3)*(-8*z**3) - 43*z**3*56 - 2072\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-43*z**3)*56 = -2408*z**3\n (-43*z**3)*(-8*z**3) = 344*z**6\n (-30*z)*56 = -1680*z\n (-30*z)*(-8*z**3) = 240*z**4\n (11*z**2)*56 = 616*z**2\n (11*z**2)*(-8*z**3) = -88*z**5\n -37*-8*z**3 = 296*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 344*z**6 - 88*z**5 + 240*z**4 - 2408*z**3 + 296*z**3 + 616*z**2 - 1680*z - 2072\nCombining like terms, got 344*z**6 - 88*z**5 + 240*z**4 - 2112*z**3 + 616*z**2 - 1680*z - 2072\n#Step 6:\nCurrent expression: 344*z**6 - 88*z**5 + 240*z**4 - 2112*z**3 + 616*z**2 - 1680*z - 2072\nNo more calculations needed.\n344*z**6 - 88*z**5 + 240*z**4 - 2112*z**3 + 616*z**2 - 1680*z - 2072", "generated_answer": "344*z**6 - 88*z**5 + 240*z**4 - 2112*z**3 + 616*z**2 - 1680*z - 2072", "step_length": 6} {"cot_id": "d7d0163a6899920ea730b7a87276b0489ea93d618da3fcca370de7bf6607834b", "datapoint": {"question": "Calculate the following: (22*z**2 - 24*z + 83)*(26*z**3 + 7*z**2 + 43*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "572*z**5 - 470*z**4 + 2936*z**3 - 451*z**2 + 3569*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1295, "polynomial_expr": "(22*z**2 - 24*z + 83)*(26*z**3 + 7*z**2 + 43*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (22*z**2 - 24*z + 83)*(26*z**3 + 7*z**2 + 43*z)\nExpanding the part (22*z**2 - 24*z + 83) using the distributive property, and we got: (-24*z)*(26*z**3 + 7*z**2 + 43*z) + (22*z**2)*(26*z**3 + 7*z**2 + 43*z) + 83*(26*z**3 + 7*z**2 + 43*z)\n#Step 2:\nCurrent expression: (-24*z)*(26*z**3 + 7*z**2 + 43*z) + (22*z**2)*(26*z**3 + 7*z**2 + 43*z) + 83*(26*z**3 + 7*z**2 + 43*z)\nSimplifying the partial expression: 83*(26*z**3 + 7*z**2 + 43*z)\nExpanding the part (26*z**3 + 7*z**2 + 43*z) using the distributive property, and we got: (43*z)*83 + (7*z**2)*83 + (26*z**3)*83\nReplacing 83*(26*z**3 + 7*z**2 + 43*z) with (43*z)*83 + (7*z**2)*83 + (26*z**3)*83 in the overall expression.\n#Step 3:\nCurrent expression: (-24*z)*(26*z**3 + 7*z**2 + 43*z) + (43*z)*83 + (7*z**2)*83 + (22*z**2)*(26*z**3 + 7*z**2 + 43*z) + (26*z**3)*83\nSimplifying the partial expression: (-24*z)*(26*z**3 + 7*z**2 + 43*z)\nExpanding the part (26*z**3 + 7*z**2 + 43*z) using the distributive property, and we got: (-24*z)*(43*z) + (-24*z)*(7*z**2) + (-24*z)*(26*z**3)\nReplacing (-24*z)*(26*z**3 + 7*z**2 + 43*z) with (-24*z)*(43*z) + (-24*z)*(7*z**2) + (-24*z)*(26*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-24*z)*(43*z) + (-24*z)*(7*z**2) + (-24*z)*(26*z**3) + (43*z)*83 + (7*z**2)*83 + (22*z**2)*(26*z**3 + 7*z**2 + 43*z) + (26*z**3)*83\nSimplifying the partial expression: (22*z**2)*(26*z**3 + 7*z**2 + 43*z)\nExpanding the part (26*z**3 + 7*z**2 + 43*z) using the distributive property, and we got: (43*z)*(22*z**2) + (7*z**2)*(22*z**2) + (22*z**2)*(26*z**3)\nReplacing (22*z**2)*(26*z**3 + 7*z**2 + 43*z) with (43*z)*(22*z**2) + (7*z**2)*(22*z**2) + (22*z**2)*(26*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-24*z)*(43*z) + (-24*z)*(7*z**2) + (-24*z)*(26*z**3) + (43*z)*(22*z**2) + (43*z)*83 + (7*z**2)*(22*z**2) + (7*z**2)*83 + (22*z**2)*(26*z**3) + (26*z**3)*83\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (7*z**2)*83 = 581*z**2\n (7*z**2)*(-24*z) = -168*z**3\n (7*z**2)*(22*z**2) = 154*z**4\n (26*z**3)*83 = 2158*z**3\n (26*z**3)*(-24*z) = -624*z**4\n (26*z**3)*(22*z**2) = 572*z**5\n (43*z)*83 = 3569*z\n (43*z)*(-24*z) = -1032*z**2\n (43*z)*(22*z**2) = 946*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 572*z**5 - 624*z**4 + 154*z**4 - 168*z**3 + 946*z**3 + 2158*z**3 - 1032*z**2 + 581*z**2 + 3569*z\nCombining like terms, got 572*z**5 - 470*z**4 + 2936*z**3 - 451*z**2 + 3569*z\n#Step 7:\nCurrent expression: 572*z**5 - 470*z**4 + 2936*z**3 - 451*z**2 + 3569*z\nNo more calculations needed.\n572*z**5 - 470*z**4 + 2936*z**3 - 451*z**2 + 3569*z", "generated_answer": "572*z**5 - 470*z**4 + 2936*z**3 - 451*z**2 + 3569*z", "step_length": 7} {"cot_id": "fc9e1222c09ff8fb2731bfb0def2df2caab5bb5a8f10222acb1705c2096db224", "datapoint": {"question": "Calculate the following: -637*z**3 + 559*z**2 - 455*z\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-637*z**3 + 559*z**2 - 455*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1296, "polynomial_expr": "-637*z**3 + 559*z**2 - 455*z", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -637*z**3 + 559*z**2 - 455*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -637*z**3 + 559*z**2 - 455*z\nNo more calculations needed.\n-637*z**3 + 559*z**2 - 455*z", "generated_answer": "-637*z**3 + 559*z**2 - 455*z", "step_length": 2} {"cot_id": "b090d1b0b6fe10a92f3626301da33539c1d042effc22fb8828c375afdefc8bab", "datapoint": {"question": "Simplify this expression: (39*z**3 - 69*z**2)*(3*z**3 - 43*z + 27)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "117*z**6 - 207*z**5 - 1677*z**4 + 4020*z**3 - 1863*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1297, "polynomial_expr": "(39*z**3 - 69*z**2)*(3*z**3 - 43*z + 27)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (39*z**3 - 69*z**2)*(3*z**3 - 43*z + 27)\nExpanding the part (39*z**3 - 69*z**2) using the distributive property, and we got: (-69*z**2)*(3*z**3 - 43*z + 27) + (39*z**3)*(3*z**3 - 43*z + 27)\n#Step 2:\nCurrent expression: (-69*z**2)*(3*z**3 - 43*z + 27) + (39*z**3)*(3*z**3 - 43*z + 27)\nSimplifying the partial expression: (-69*z**2)*(3*z**3 - 43*z + 27)\nExpanding the part (3*z**3 - 43*z + 27) using the distributive property, and we got: (-43*z)*(-69*z**2) + 27*(-69*z**2) + (-69*z**2)*(3*z**3)\nReplacing (-69*z**2)*(3*z**3 - 43*z + 27) with (-43*z)*(-69*z**2) + 27*(-69*z**2) + (-69*z**2)*(3*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-43*z)*(-69*z**2) + 27*(-69)*z**2 + (-69*z**2)*(3*z**3) + (39*z**3)*(3*z**3 - 43*z + 27)\nSimplifying the partial expression: (39*z**3)*(3*z**3 - 43*z + 27)\nExpanding the part (3*z**3 - 43*z + 27) using the distributive property, and we got: (-43*z)*(39*z**3) + 27*(39*z**3) + (3*z**3)*(39*z**3)\nReplacing (39*z**3)*(3*z**3 - 43*z + 27) with (-43*z)*(39*z**3) + 27*(39*z**3) + (3*z**3)*(39*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-43*z)*(-69*z**2) + (-43*z)*(39*z**3) + 27*39*z**3 + 27*(-69)*z**2 + (-69*z**2)*(3*z**3) + (3*z**3)*(39*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-43*z)*(-69*z**2) = 2967*z**3\n (-43*z)*(39*z**3) = -1677*z**4\n (3*z**3)*(-69*z**2) = -207*z**5\n (3*z**3)*(39*z**3) = 117*z**6\n 27*-69*z**2 = -1863*z**2\n 27*39*z**3 = 1053*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 117*z**6 - 207*z**5 - 1677*z**4 + 1053*z**3 + 2967*z**3 - 1863*z**2\nCombining like terms, got 117*z**6 - 207*z**5 - 1677*z**4 + 4020*z**3 - 1863*z**2\n#Step 6:\nCurrent expression: 117*z**6 - 207*z**5 - 1677*z**4 + 4020*z**3 - 1863*z**2\nNo more calculations needed.\n117*z**6 - 207*z**5 - 1677*z**4 + 4020*z**3 - 1863*z**2", "generated_answer": "117*z**6 - 207*z**5 - 1677*z**4 + 4020*z**3 - 1863*z**2", "step_length": 6} {"cot_id": "a2a23aaf0150d0018dafc40f286dd606dbcb60616087308e03669d377ec2ec85", "datapoint": {"question": "Calculate the following: (11*y**2 + 2)*(y**3 - 35*y**2 + 7*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "11*y**5 - 385*y**4 + 79*y**3 - 70*y**2 + 14*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1298, "polynomial_expr": "(11*y**2 + 2)*(y**3 - 35*y**2 + 7*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11*y**2 + 2)*(y**3 - 35*y**2 + 7*y)\nExpanding the part (11*y**2 + 2) using the distributive property, and we got: (11*y**2)*(y**3 - 35*y**2 + 7*y) + 2*(y**3 - 35*y**2 + 7*y)\n#Step 2:\nCurrent expression: (11*y**2)*(y**3 - 35*y**2 + 7*y) + 2*(y**3 - 35*y**2 + 7*y)\nSimplifying the partial expression: 2*(y**3 - 35*y**2 + 7*y)\nExpanding the part (y**3 - 35*y**2 + 7*y) using the distributive property, and we got: y**3*2 + (7*y)*2 - 35*y**2*2\nReplacing 2*(y**3 - 35*y**2 + 7*y) with y**3*2 + (7*y)*2 - 35*y**2*2 in the overall expression.\n#Step 3:\nCurrent expression: y**3*2 + (7*y)*2 - 35*y**2*2 + (11*y**2)*(y**3 - 35*y**2 + 7*y)\nSimplifying the partial expression: (11*y**2)*(y**3 - 35*y**2 + 7*y)\nExpanding the part (y**3 - 35*y**2 + 7*y) using the distributive property, and we got: (11*y**2)*y**3 + (7*y)*(11*y**2) + (-35*y**2)*(11*y**2)\nReplacing (11*y**2)*(y**3 - 35*y**2 + 7*y) with (11*y**2)*y**3 + (7*y)*(11*y**2) + (-35*y**2)*(11*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (11*y**2)*y**3 + y**3*2 + (7*y)*(11*y**2) + (7*y)*2 + (-35*y**2)*(11*y**2) - 35*y**2*2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n y**3*2 = 2*y**3\n y**3*(11*y**2) = 11*y**5\n (-35*y**2)*2 = -70*y**2\n (-35*y**2)*(11*y**2) = -385*y**4\n (7*y)*2 = 14*y\n (7*y)*(11*y**2) = 77*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 11*y**5 - 385*y**4 + 2*y**3 + 77*y**3 - 70*y**2 + 14*y\nCombining like terms, got 11*y**5 - 385*y**4 + 79*y**3 - 70*y**2 + 14*y\n#Step 6:\nCurrent expression: 11*y**5 - 385*y**4 + 79*y**3 - 70*y**2 + 14*y\nNo more calculations needed.\n11*y**5 - 385*y**4 + 79*y**3 - 70*y**2 + 14*y", "generated_answer": "11*y**5 - 385*y**4 + 79*y**3 - 70*y**2 + 14*y", "step_length": 6} {"cot_id": "6c0a093a90d2eaeb7b2db0703f8345bde227696ad6f3260f2860900f72d3208b", "datapoint": {"question": "Simplify this expression: (11 - 23*y**2)*(-12*y**3 + 19*y**2 - 11*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "276*y**5 - 437*y**4 + 121*y**3 + 209*y**2 - 121*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1299, "polynomial_expr": "(11 - 23*y**2)*(-12*y**3 + 19*y**2 - 11*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11 - 23*y**2)*(-12*y**3 + 19*y**2 - 11*y)\nExpanding the part (11 - 23*y**2) using the distributive property, and we got: (-23*y**2)*(-12*y**3 + 19*y**2 - 11*y) + 11*(-12*y**3 + 19*y**2 - 11*y)\n#Step 2:\nCurrent expression: (-23*y**2)*(-12*y**3 + 19*y**2 - 11*y) + 11*(-12*y**3 + 19*y**2 - 11*y)\nSimplifying the partial expression: 11*(-12*y**3 + 19*y**2 - 11*y)\nExpanding the part (-12*y**3 + 19*y**2 - 11*y) using the distributive property, and we got: -11*y*11 + (19*y**2)*11 - 12*y**3*11\nReplacing 11*(-12*y**3 + 19*y**2 - 11*y) with -11*y*11 + (19*y**2)*11 - 12*y**3*11 in the overall expression.\n#Step 3:\nCurrent expression: -11*y*11 + (-23*y**2)*(-12*y**3 + 19*y**2 - 11*y) + (19*y**2)*11 - 12*y**3*11\nSimplifying the partial expression: (-23*y**2)*(-12*y**3 + 19*y**2 - 11*y)\nExpanding the part (-12*y**3 + 19*y**2 - 11*y) using the distributive property, and we got: (-11*y)*(-23*y**2) + (-23*y**2)*(19*y**2) + (-23*y**2)*(-12*y**3)\nReplacing (-23*y**2)*(-12*y**3 + 19*y**2 - 11*y) with (-11*y)*(-23*y**2) + (-23*y**2)*(19*y**2) + (-23*y**2)*(-12*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-11*y)*(-23*y**2) - 11*y*11 + (-23*y**2)*(19*y**2) + (-23*y**2)*(-12*y**3) + (19*y**2)*11 - 12*y**3*11\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*y**3)*11 = -132*y**3\n (-12*y**3)*(-23*y**2) = 276*y**5\n (-11*y)*11 = -121*y\n (-11*y)*(-23*y**2) = 253*y**3\n (19*y**2)*11 = 209*y**2\n (19*y**2)*(-23*y**2) = -437*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 276*y**5 - 437*y**4 - 132*y**3 + 253*y**3 + 209*y**2 - 121*y\nCombining like terms, got 276*y**5 - 437*y**4 + 121*y**3 + 209*y**2 - 121*y\n#Step 6:\nCurrent expression: 276*y**5 - 437*y**4 + 121*y**3 + 209*y**2 - 121*y\nNo more calculations needed.\n276*y**5 - 437*y**4 + 121*y**3 + 209*y**2 - 121*y", "generated_answer": "276*y**5 - 437*y**4 + 121*y**3 + 209*y**2 - 121*y", "step_length": 6} {"cot_id": "b1b8f148579c51c1d241a2b890c8412765c90af32fcd76e4eefe4e56fdf180fc", "datapoint": {"question": "Calculate the following: (3*x - 68)*(15*x**3 - 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "45*x**4 - 1020*x**3 - 39*x + 884", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1300, "polynomial_expr": "(3*x - 68)*(15*x**3 - 13)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (3*x - 68)*(15*x**3 - 13)\nExpanding the part (3*x - 68) using the distributive property, and we got: (3*x)*(15*x**3 - 13) - 68*(15*x**3 - 13)\n#Step 2:\nCurrent expression: (3*x)*(15*x**3 - 13) - 68*(15*x**3 - 13)\nSimplifying the partial expression: -68*(15*x**3 - 13)\nExpanding the part (15*x**3 - 13) using the distributive property, and we got: (15*x**3)*(-68) - 13*(-68)\nReplacing -68*(15*x**3 - 13) with (15*x**3)*(-68) - 13*(-68) in the overall expression.\n#Step 3:\nCurrent expression: (3*x)*(15*x**3 - 13) + (15*x**3)*(-68) + 884\nSimplifying the partial expression: (3*x)*(15*x**3 - 13)\nExpanding the part (15*x**3 - 13) using the distributive property, and we got: -39*x + (3*x)*(15*x**3)\nReplacing (3*x)*(15*x**3 - 13) with -39*x + (3*x)*(15*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -13*3*x + (3*x)*(15*x**3) + (15*x**3)*(-68) + 884\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (15*x**3)*-68 = -1020*x**3\n (15*x**3)*(3*x) = 45*x**4\n -13*3*x = -39*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 45*x**4 - 1020*x**3 - 39*x + 884\nNo more calculations needed.\n45*x**4 - 1020*x**3 - 39*x + 884", "generated_answer": "45*x**4 - 1020*x**3 - 39*x + 884", "step_length": 5} {"cot_id": "a0f9f8e693d0e4351f3fe3854bd9bb8b2ab44a3b6686b0f26b8d63c33e92b849", "datapoint": {"question": "Calculate the following: (40*y - 44)*(22*y**3 - 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "880*y**4 - 968*y**3 - 640*y + 704", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1301, "polynomial_expr": "(40*y - 44)*(22*y**3 - 16)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (40*y - 44)*(22*y**3 - 16)\nExpanding the part (40*y - 44) using the distributive property, and we got: (40*y)*(22*y**3 - 16) - 44*(22*y**3 - 16)\n#Step 2:\nCurrent expression: (40*y)*(22*y**3 - 16) - 44*(22*y**3 - 16)\nSimplifying the partial expression: -44*(22*y**3 - 16)\nExpanding the part (22*y**3 - 16) using the distributive property, and we got: (22*y**3)*(-44) - 16*(-44)\nReplacing -44*(22*y**3 - 16) with (22*y**3)*(-44) - 16*(-44) in the overall expression.\n#Step 3:\nCurrent expression: (40*y)*(22*y**3 - 16) + (22*y**3)*(-44) + 704\nSimplifying the partial expression: (40*y)*(22*y**3 - 16)\nExpanding the part (22*y**3 - 16) using the distributive property, and we got: -640*y + (40*y)*(22*y**3)\nReplacing (40*y)*(22*y**3 - 16) with -640*y + (40*y)*(22*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -16*40*y + (40*y)*(22*y**3) + (22*y**3)*(-44) + 704\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (22*y**3)*-44 = -968*y**3\n (22*y**3)*(40*y) = 880*y**4\n -16*40*y = -640*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 880*y**4 - 968*y**3 - 640*y + 704\nNo more calculations needed.\n880*y**4 - 968*y**3 - 640*y + 704", "generated_answer": "880*y**4 - 968*y**3 - 640*y + 704", "step_length": 5} {"cot_id": "886d6b5805c05438cc573fcdda9f00cbc6fe77bdc038ddee0461f5dc38bf00df", "datapoint": {"question": "Simplify this expression: (-10*y**2 - 31)*(-48*y**2 + 21*y + 29)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "480*y**4 - 210*y**3 + 1198*y**2 - 651*y - 899", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1302, "polynomial_expr": "(-10*y**2 - 31)*(-48*y**2 + 21*y + 29)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-10*y**2 - 31)*(-48*y**2 + 21*y + 29)\nExpanding the part (-10*y**2 - 31) using the distributive property, and we got: (-10*y**2)*(-48*y**2 + 21*y + 29) - 31*(-48*y**2 + 21*y + 29)\n#Step 2:\nCurrent expression: (-10*y**2)*(-48*y**2 + 21*y + 29) - 31*(-48*y**2 + 21*y + 29)\nSimplifying the partial expression: -31*(-48*y**2 + 21*y + 29)\nExpanding the part (-48*y**2 + 21*y + 29) using the distributive property, and we got: (21*y)*(-31) - 48*y**2*(-31) + 29*(-31)\nReplacing -31*(-48*y**2 + 21*y + 29) with (21*y)*(-31) - 48*y**2*(-31) + 29*(-31) in the overall expression.\n#Step 3:\nCurrent expression: (21*y)*(-31) - 48*y**2*(-31) + (-10*y**2)*(-48*y**2 + 21*y + 29) - 899\nSimplifying the partial expression: (-10*y**2)*(-48*y**2 + 21*y + 29)\nExpanding the part (-48*y**2 + 21*y + 29) using the distributive property, and we got: 29*(-10*y**2) + (21*y)*(-10*y**2) + (-48*y**2)*(-10*y**2)\nReplacing (-10*y**2)*(-48*y**2 + 21*y + 29) with 29*(-10*y**2) + (21*y)*(-10*y**2) + (-48*y**2)*(-10*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 29*(-10)*y**2 + (21*y)*(-10*y**2) + (21*y)*(-31) + (-48*y**2)*(-10*y**2) - 48*y**2*(-31) - 899\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*y**2)*-31 = 1488*y**2\n (-48*y**2)*(-10*y**2) = 480*y**4\n (21*y)*-31 = -651*y\n (21*y)*(-10*y**2) = -210*y**3\n 29*-10*y**2 = -290*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 480*y**4 - 210*y**3 - 290*y**2 + 1488*y**2 - 651*y - 899\nCombining like terms, got 480*y**4 - 210*y**3 + 1198*y**2 - 651*y - 899\n#Step 6:\nCurrent expression: 480*y**4 - 210*y**3 + 1198*y**2 - 651*y - 899\nNo more calculations needed.\n480*y**4 - 210*y**3 + 1198*y**2 - 651*y - 899", "generated_answer": "480*y**4 - 210*y**3 + 1198*y**2 - 651*y - 899", "step_length": 6} {"cot_id": "cd7c7eb5b4d5e5fb263897c34f03b31b0aa53ed5f186f9ef92c40cc9c1642bd4", "datapoint": {"question": "Simplify this expression: (44*x**2 + 47)*(46*x**3 + 32*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2024*x**5 + 1408*x**4 + 2162*x**3 + 1504*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1303, "polynomial_expr": "(44*x**2 + 47)*(46*x**3 + 32*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (44*x**2 + 47)*(46*x**3 + 32*x**2)\nExpanding the part (44*x**2 + 47) using the distributive property, and we got: (44*x**2)*(46*x**3 + 32*x**2) + 47*(46*x**3 + 32*x**2)\n#Step 2:\nCurrent expression: (44*x**2)*(46*x**3 + 32*x**2) + 47*(46*x**3 + 32*x**2)\nSimplifying the partial expression: 47*(46*x**3 + 32*x**2)\nExpanding the part (46*x**3 + 32*x**2) using the distributive property, and we got: (32*x**2)*47 + (46*x**3)*47\nReplacing 47*(46*x**3 + 32*x**2) with (32*x**2)*47 + (46*x**3)*47 in the overall expression.\n#Step 3:\nCurrent expression: (32*x**2)*47 + (44*x**2)*(46*x**3 + 32*x**2) + (46*x**3)*47\nSimplifying the partial expression: (44*x**2)*(46*x**3 + 32*x**2)\nExpanding the part (46*x**3 + 32*x**2) using the distributive property, and we got: (32*x**2)*(44*x**2) + (44*x**2)*(46*x**3)\nReplacing (44*x**2)*(46*x**3 + 32*x**2) with (32*x**2)*(44*x**2) + (44*x**2)*(46*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (32*x**2)*(44*x**2) + (32*x**2)*47 + (44*x**2)*(46*x**3) + (46*x**3)*47\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (32*x**2)*47 = 1504*x**2\n (32*x**2)*(44*x**2) = 1408*x**4\n (46*x**3)*47 = 2162*x**3\n (46*x**3)*(44*x**2) = 2024*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2024*x**5 + 1408*x**4 + 2162*x**3 + 1504*x**2\nNo more calculations needed.\n2024*x**5 + 1408*x**4 + 2162*x**3 + 1504*x**2", "generated_answer": "2024*x**5 + 1408*x**4 + 2162*x**3 + 1504*x**2", "step_length": 5} {"cot_id": "15cc151ccced3c53795915a0d1bffb5684068f6da3001aabf6ac347e0c64fa92", "datapoint": {"question": "Calculate the following: (-39*y**3 - 42*y + 6)*(-5*y**3 + 34*y**2 - 26*y + 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "195*y**6 - 1326*y**5 + 1224*y**4 - 3330*y**3 + 1296*y**2 - 2172*y + 288", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1304, "polynomial_expr": "(-39*y**3 - 42*y + 6)*(-5*y**3 + 34*y**2 - 26*y + 48)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-39*y**3 - 42*y + 6)*(-5*y**3 + 34*y**2 - 26*y + 48)\nExpanding the part (-39*y**3 - 42*y + 6) using the distributive property, and we got: (-42*y)*(-5*y**3 + 34*y**2 - 26*y + 48) + (-39*y**3)*(-5*y**3 + 34*y**2 - 26*y + 48) + 6*(-5*y**3 + 34*y**2 - 26*y + 48)\n#Step 2:\nCurrent expression: (-42*y)*(-5*y**3 + 34*y**2 - 26*y + 48) + (-39*y**3)*(-5*y**3 + 34*y**2 - 26*y + 48) + 6*(-5*y**3 + 34*y**2 - 26*y + 48)\nSimplifying the partial expression: 6*(-5*y**3 + 34*y**2 - 26*y + 48)\nExpanding the part (-5*y**3 + 34*y**2 - 26*y + 48) using the distributive property, and we got: -26*y*6 + (34*y**2)*6 - 5*y**3*6 + 48*6\nReplacing 6*(-5*y**3 + 34*y**2 - 26*y + 48) with -26*y*6 + (34*y**2)*6 - 5*y**3*6 + 48*6 in the overall expression.\n#Step 3:\nCurrent expression: (-42*y)*(-5*y**3 + 34*y**2 - 26*y + 48) - 26*y*6 + (34*y**2)*6 + (-39*y**3)*(-5*y**3 + 34*y**2 - 26*y + 48) - 5*y**3*6 + 288\nSimplifying the partial expression: (-42*y)*(-5*y**3 + 34*y**2 - 26*y + 48)\nExpanding the part (-5*y**3 + 34*y**2 - 26*y + 48) using the distributive property, and we got: (-42*y)*(-26*y) + (-42*y)*(34*y**2) + (-42*y)*(-5*y**3) + 48*(-42*y)\nReplacing (-42*y)*(-5*y**3 + 34*y**2 - 26*y + 48) with (-42*y)*(-26*y) + (-42*y)*(34*y**2) + (-42*y)*(-5*y**3) + 48*(-42*y) in the overall expression.\n#Step 4:\nCurrent expression: (-42*y)*(-26*y) + (-42*y)*(34*y**2) + (-42*y)*(-5*y**3) - 26*y*6 + 48*(-42)*y + (34*y**2)*6 + (-39*y**3)*(-5*y**3 + 34*y**2 - 26*y + 48) - 5*y**3*6 + 288\nSimplifying the partial expression: (-39*y**3)*(-5*y**3 + 34*y**2 - 26*y + 48)\nExpanding the part (-5*y**3 + 34*y**2 - 26*y + 48) using the distributive property, and we got: (-26*y)*(-39*y**3) + 48*(-39*y**3) + (34*y**2)*(-39*y**3) + (-39*y**3)*(-5*y**3)\nReplacing (-39*y**3)*(-5*y**3 + 34*y**2 - 26*y + 48) with (-26*y)*(-39*y**3) + 48*(-39*y**3) + (34*y**2)*(-39*y**3) + (-39*y**3)*(-5*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-42*y)*(-26*y) + (-42*y)*(34*y**2) + (-42*y)*(-5*y**3) + (-26*y)*(-39*y**3) - 26*y*6 + 48*(-39)*y**3 + 48*(-42)*y + (34*y**2)*(-39*y**3) + (34*y**2)*6 + (-39*y**3)*(-5*y**3) - 5*y**3*6 + 288\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-26*y)*6 = -156*y\n (-26*y)*(-42*y) = 1092*y**2\n (-26*y)*(-39*y**3) = 1014*y**4\n (-5*y**3)*6 = -30*y**3\n (-5*y**3)*(-42*y) = 210*y**4\n (-5*y**3)*(-39*y**3) = 195*y**6\n (34*y**2)*6 = 204*y**2\n (34*y**2)*(-42*y) = -1428*y**3\n (34*y**2)*(-39*y**3) = -1326*y**5\n 48*-42*y = -2016*y\n 48*-39*y**3 = -1872*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 195*y**6 - 1326*y**5 + 210*y**4 + 1014*y**4 - 1872*y**3 - 1428*y**3 - 30*y**3 + 204*y**2 + 1092*y**2 - 2016*y - 156*y + 288\nCombining like terms, got 195*y**6 - 1326*y**5 + 1224*y**4 - 3330*y**3 + 1296*y**2 - 2172*y + 288\n#Step 7:\nCurrent expression: 195*y**6 - 1326*y**5 + 1224*y**4 - 3330*y**3 + 1296*y**2 - 2172*y + 288\nNo more calculations needed.\n195*y**6 - 1326*y**5 + 1224*y**4 - 3330*y**3 + 1296*y**2 - 2172*y + 288", "generated_answer": "195*y**6 - 1326*y**5 + 1224*y**4 - 3330*y**3 + 1296*y**2 - 2172*y + 288", "step_length": 7} {"cot_id": "d0e08c77f3ca518d6fb3bc672da5156df77e22fd34a8a3d4308615ccfbb25347", "datapoint": {"question": "Calculate the following: -1368*y**2 + 1800*y - 792\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1368*y**2 + 1800*y - 792", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1305, "polynomial_expr": "-1368*y**2 + 1800*y - 792", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -1368*y**2 + 1800*y - 792\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -1368*y**2 + 1800*y - 792\nNo more calculations needed.\n-1368*y**2 + 1800*y - 792", "generated_answer": "-1368*y**2 + 1800*y - 792", "step_length": 2} {"cot_id": "d26102344415667681282abb15162b7eeb3c00afc5de3292428d51b223ce919b", "datapoint": {"question": "Simplify this expression: (-39*y**3 - 30)*(16*y**3 - 37*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-624*y**6 + 1443*y**4 - 480*y**3 + 1110*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1306, "polynomial_expr": "(-39*y**3 - 30)*(16*y**3 - 37*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-39*y**3 - 30)*(16*y**3 - 37*y)\nExpanding the part (-39*y**3 - 30) using the distributive property, and we got: (-39*y**3)*(16*y**3 - 37*y) - 30*(16*y**3 - 37*y)\n#Step 2:\nCurrent expression: (-39*y**3)*(16*y**3 - 37*y) - 30*(16*y**3 - 37*y)\nSimplifying the partial expression: -30*(16*y**3 - 37*y)\nExpanding the part (16*y**3 - 37*y) using the distributive property, and we got: -37*y*(-30) + (16*y**3)*(-30)\nReplacing -30*(16*y**3 - 37*y) with -37*y*(-30) + (16*y**3)*(-30) in the overall expression.\n#Step 3:\nCurrent expression: -37*y*(-30) + (-39*y**3)*(16*y**3 - 37*y) + (16*y**3)*(-30)\nSimplifying the partial expression: (-39*y**3)*(16*y**3 - 37*y)\nExpanding the part (16*y**3 - 37*y) using the distributive property, and we got: (-37*y)*(-39*y**3) + (-39*y**3)*(16*y**3)\nReplacing (-39*y**3)*(16*y**3 - 37*y) with (-37*y)*(-39*y**3) + (-39*y**3)*(16*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-37*y)*(-39*y**3) - 37*y*(-30) + (-39*y**3)*(16*y**3) + (16*y**3)*(-30)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*y)*-30 = 1110*y\n (-37*y)*(-39*y**3) = 1443*y**4\n (16*y**3)*-30 = -480*y**3\n (16*y**3)*(-39*y**3) = -624*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -624*y**6 + 1443*y**4 - 480*y**3 + 1110*y\nNo more calculations needed.\n-624*y**6 + 1443*y**4 - 480*y**3 + 1110*y", "generated_answer": "-624*y**6 + 1443*y**4 - 480*y**3 + 1110*y", "step_length": 5} {"cot_id": "cfa2ab7fd6471dc34cd946ea5f7d8f4f6fe96c833ca501028b28dc1dbc5e26a7", "datapoint": {"question": "Simplify this expression: (11*x**3 - 14*x + 17)*(-39*x**3 - 24*x**2 - 45*x - 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-429*x**6 - 264*x**5 + 51*x**4 - 690*x**3 + 222*x**2 - 303*x - 561", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1307, "polynomial_expr": "(11*x**3 - 14*x + 17)*(-39*x**3 - 24*x**2 - 45*x - 33)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11*x**3 - 14*x + 17)*(-39*x**3 - 24*x**2 - 45*x - 33)\nExpanding the part (11*x**3 - 14*x + 17) using the distributive property, and we got: (-14*x)*(-39*x**3 - 24*x**2 - 45*x - 33) + (11*x**3)*(-39*x**3 - 24*x**2 - 45*x - 33) + 17*(-39*x**3 - 24*x**2 - 45*x - 33)\n#Step 2:\nCurrent expression: (-14*x)*(-39*x**3 - 24*x**2 - 45*x - 33) + (11*x**3)*(-39*x**3 - 24*x**2 - 45*x - 33) + 17*(-39*x**3 - 24*x**2 - 45*x - 33)\nSimplifying the partial expression: 17*(-39*x**3 - 24*x**2 - 45*x - 33)\nExpanding the part (-39*x**3 - 24*x**2 - 45*x - 33) using the distributive property, and we got: -45*x*17 - 24*x**2*17 - 39*x**3*17 - 33*17\nReplacing 17*(-39*x**3 - 24*x**2 - 45*x - 33) with -45*x*17 - 24*x**2*17 - 39*x**3*17 - 33*17 in the overall expression.\n#Step 3:\nCurrent expression: -45*x*17 + (-14*x)*(-39*x**3 - 24*x**2 - 45*x - 33) - 24*x**2*17 - 39*x**3*17 + (11*x**3)*(-39*x**3 - 24*x**2 - 45*x - 33) - 561\nSimplifying the partial expression: (-14*x)*(-39*x**3 - 24*x**2 - 45*x - 33)\nExpanding the part (-39*x**3 - 24*x**2 - 45*x - 33) using the distributive property, and we got: (-45*x)*(-14*x) + (-14*x)*(-24*x**2) + (-14*x)*(-39*x**3) - (-1)*462*x\nReplacing (-14*x)*(-39*x**3 - 24*x**2 - 45*x - 33) with (-45*x)*(-14*x) + (-14*x)*(-24*x**2) + (-14*x)*(-39*x**3) - (-1)*462*x in the overall expression.\n#Step 4:\nCurrent expression: (-45*x)*(-14*x) - 45*x*17 + (-14*x)*(-24*x**2) + (-14*x)*(-39*x**3) - 33*(-14)*x - 24*x**2*17 - 39*x**3*17 + (11*x**3)*(-39*x**3 - 24*x**2 - 45*x - 33) - 561\nSimplifying the partial expression: (11*x**3)*(-39*x**3 - 24*x**2 - 45*x - 33)\nExpanding the part (-39*x**3 - 24*x**2 - 45*x - 33) using the distributive property, and we got: (-45*x)*(11*x**3) - 363*x**3 + (-24*x**2)*(11*x**3) + (-39*x**3)*(11*x**3)\nReplacing (11*x**3)*(-39*x**3 - 24*x**2 - 45*x - 33) with (-45*x)*(11*x**3) - 363*x**3 + (-24*x**2)*(11*x**3) + (-39*x**3)*(11*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-45*x)*(-14*x) + (-45*x)*(11*x**3) - 45*x*17 + (-14*x)*(-24*x**2) + (-14*x)*(-39*x**3) - 33*11*x**3 - 33*(-14)*x + (-24*x**2)*(11*x**3) - 24*x**2*17 + (-39*x**3)*(11*x**3) - 39*x**3*17 - 561\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*x)*17 = -765*x\n (-45*x)*(-14*x) = 630*x**2\n (-45*x)*(11*x**3) = -495*x**4\n (-39*x**3)*17 = -663*x**3\n (-39*x**3)*(-14*x) = 546*x**4\n (-39*x**3)*(11*x**3) = -429*x**6\n (-24*x**2)*17 = -408*x**2\n (-24*x**2)*(-14*x) = 336*x**3\n (-24*x**2)*(11*x**3) = -264*x**5\n -33*-14*x = 462*x\n -33*11*x**3 = -363*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -429*x**6 - 264*x**5 - 495*x**4 + 546*x**4 - 663*x**3 - 363*x**3 + 336*x**3 - 408*x**2 + 630*x**2 - 765*x + 462*x - 561\nCombining like terms, got -429*x**6 - 264*x**5 + 51*x**4 - 690*x**3 + 222*x**2 - 303*x - 561\n#Step 7:\nCurrent expression: -429*x**6 - 264*x**5 + 51*x**4 - 690*x**3 + 222*x**2 - 303*x - 561\nNo more calculations needed.\n-429*x**6 - 264*x**5 + 51*x**4 - 690*x**3 + 222*x**2 - 303*x - 561", "generated_answer": "-429*x**6 - 264*x**5 + 51*x**4 - 690*x**3 + 222*x**2 - 303*x - 561", "step_length": 7} {"cot_id": "382c2fc8903645330b0ae336931e4da55755f264ebcb17db548a8a6a2056357f", "datapoint": {"question": "Simplify this expression: (38*y**3 - 34)*(49*y**3 - 33*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1862*y**6 - 1254*y**4 - 1666*y**3 + 1122*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1308, "polynomial_expr": "(38*y**3 - 34)*(49*y**3 - 33*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (38*y**3 - 34)*(49*y**3 - 33*y)\nExpanding the part (38*y**3 - 34) using the distributive property, and we got: (38*y**3)*(49*y**3 - 33*y) - 34*(49*y**3 - 33*y)\n#Step 2:\nCurrent expression: (38*y**3)*(49*y**3 - 33*y) - 34*(49*y**3 - 33*y)\nSimplifying the partial expression: -34*(49*y**3 - 33*y)\nExpanding the part (49*y**3 - 33*y) using the distributive property, and we got: -33*y*(-34) + (49*y**3)*(-34)\nReplacing -34*(49*y**3 - 33*y) with -33*y*(-34) + (49*y**3)*(-34) in the overall expression.\n#Step 3:\nCurrent expression: -33*y*(-34) + (38*y**3)*(49*y**3 - 33*y) + (49*y**3)*(-34)\nSimplifying the partial expression: (38*y**3)*(49*y**3 - 33*y)\nExpanding the part (49*y**3 - 33*y) using the distributive property, and we got: (-33*y)*(38*y**3) + (38*y**3)*(49*y**3)\nReplacing (38*y**3)*(49*y**3 - 33*y) with (-33*y)*(38*y**3) + (38*y**3)*(49*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-33*y)*(38*y**3) - 33*y*(-34) + (38*y**3)*(49*y**3) + (49*y**3)*(-34)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*y)*-34 = 1122*y\n (-33*y)*(38*y**3) = -1254*y**4\n (49*y**3)*-34 = -1666*y**3\n (49*y**3)*(38*y**3) = 1862*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1862*y**6 - 1254*y**4 - 1666*y**3 + 1122*y\nNo more calculations needed.\n1862*y**6 - 1254*y**4 - 1666*y**3 + 1122*y", "generated_answer": "1862*y**6 - 1254*y**4 - 1666*y**3 + 1122*y", "step_length": 5} {"cot_id": "d0c4d56687da73d1b041dbf8afaeffac6b27685663181b1bcd4f3af84eb5da23", "datapoint": {"question": "Simplify this expression: (37*x**3 + 17)*(43*x**3 + 47*x - 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1591*x**6 + 1739*x**4 - 675*x**3 + 799*x - 646", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1309, "polynomial_expr": "(37*x**3 + 17)*(43*x**3 + 47*x - 38)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (37*x**3 + 17)*(43*x**3 + 47*x - 38)\nExpanding the part (37*x**3 + 17) using the distributive property, and we got: (37*x**3)*(43*x**3 + 47*x - 38) + 17*(43*x**3 + 47*x - 38)\n#Step 2:\nCurrent expression: (37*x**3)*(43*x**3 + 47*x - 38) + 17*(43*x**3 + 47*x - 38)\nSimplifying the partial expression: 17*(43*x**3 + 47*x - 38)\nExpanding the part (43*x**3 + 47*x - 38) using the distributive property, and we got: (47*x)*17 + (43*x**3)*17 - 38*17\nReplacing 17*(43*x**3 + 47*x - 38) with (47*x)*17 + (43*x**3)*17 - 38*17 in the overall expression.\n#Step 3:\nCurrent expression: (47*x)*17 + (37*x**3)*(43*x**3 + 47*x - 38) + (43*x**3)*17 - 646\nSimplifying the partial expression: (37*x**3)*(43*x**3 + 47*x - 38)\nExpanding the part (43*x**3 + 47*x - 38) using the distributive property, and we got: -1406*x**3 + (47*x)*(37*x**3) + (37*x**3)*(43*x**3)\nReplacing (37*x**3)*(43*x**3 + 47*x - 38) with -1406*x**3 + (47*x)*(37*x**3) + (37*x**3)*(43*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -38*37*x**3 + (47*x)*(37*x**3) + (47*x)*17 + (37*x**3)*(43*x**3) + (43*x**3)*17 - 646\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (43*x**3)*17 = 731*x**3\n (43*x**3)*(37*x**3) = 1591*x**6\n (47*x)*17 = 799*x\n (47*x)*(37*x**3) = 1739*x**4\n -38*37*x**3 = -1406*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1591*x**6 + 1739*x**4 - 1406*x**3 + 731*x**3 + 799*x - 646\nCombining like terms, got 1591*x**6 + 1739*x**4 - 675*x**3 + 799*x - 646\n#Step 6:\nCurrent expression: 1591*x**6 + 1739*x**4 - 675*x**3 + 799*x - 646\nNo more calculations needed.\n1591*x**6 + 1739*x**4 - 675*x**3 + 799*x - 646", "generated_answer": "1591*x**6 + 1739*x**4 - 675*x**3 + 799*x - 646", "step_length": 6} {"cot_id": "dcece272648b5fbd5252112da64b123d8f4c49ad0329db56dd38c5a1d034d322", "datapoint": {"question": "Calculate the following: (35*y**3 + 3)*(-26*y**3 + 31*y**2 - 9*y + 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-910*y**6 + 1085*y**5 - 315*y**4 + 1287*y**3 + 93*y**2 - 27*y + 117", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1310, "polynomial_expr": "(35*y**3 + 3)*(-26*y**3 + 31*y**2 - 9*y + 39)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (35*y**3 + 3)*(-26*y**3 + 31*y**2 - 9*y + 39)\nExpanding the part (35*y**3 + 3) using the distributive property, and we got: (35*y**3)*(-26*y**3 + 31*y**2 - 9*y + 39) + 3*(-26*y**3 + 31*y**2 - 9*y + 39)\n#Step 2:\nCurrent expression: (35*y**3)*(-26*y**3 + 31*y**2 - 9*y + 39) + 3*(-26*y**3 + 31*y**2 - 9*y + 39)\nSimplifying the partial expression: 3*(-26*y**3 + 31*y**2 - 9*y + 39)\nExpanding the part (-26*y**3 + 31*y**2 - 9*y + 39) using the distributive property, and we got: -9*y*3 + (31*y**2)*3 - 26*y**3*3 + 39*3\nReplacing 3*(-26*y**3 + 31*y**2 - 9*y + 39) with -9*y*3 + (31*y**2)*3 - 26*y**3*3 + 39*3 in the overall expression.\n#Step 3:\nCurrent expression: -9*y*3 + (31*y**2)*3 - 26*y**3*3 + (35*y**3)*(-26*y**3 + 31*y**2 - 9*y + 39) + 117\nSimplifying the partial expression: (35*y**3)*(-26*y**3 + 31*y**2 - 9*y + 39)\nExpanding the part (-26*y**3 + 31*y**2 - 9*y + 39) using the distributive property, and we got: (-9*y)*(35*y**3) + 39*(35*y**3) + (31*y**2)*(35*y**3) + (-26*y**3)*(35*y**3)\nReplacing (35*y**3)*(-26*y**3 + 31*y**2 - 9*y + 39) with (-9*y)*(35*y**3) + 39*(35*y**3) + (31*y**2)*(35*y**3) + (-26*y**3)*(35*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-9*y)*(35*y**3) - 9*y*3 + 39*35*y**3 + (31*y**2)*(35*y**3) + (31*y**2)*3 + (-26*y**3)*(35*y**3) - 26*y**3*3 + 117\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-26*y**3)*3 = -78*y**3\n (-26*y**3)*(35*y**3) = -910*y**6\n (-9*y)*3 = -27*y\n (-9*y)*(35*y**3) = -315*y**4\n (31*y**2)*3 = 93*y**2\n (31*y**2)*(35*y**3) = 1085*y**5\n 39*35*y**3 = 1365*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -910*y**6 + 1085*y**5 - 315*y**4 - 78*y**3 + 1365*y**3 + 93*y**2 - 27*y + 117\nCombining like terms, got -910*y**6 + 1085*y**5 - 315*y**4 + 1287*y**3 + 93*y**2 - 27*y + 117\n#Step 6:\nCurrent expression: -910*y**6 + 1085*y**5 - 315*y**4 + 1287*y**3 + 93*y**2 - 27*y + 117\nNo more calculations needed.\n-910*y**6 + 1085*y**5 - 315*y**4 + 1287*y**3 + 93*y**2 - 27*y + 117", "generated_answer": "-910*y**6 + 1085*y**5 - 315*y**4 + 1287*y**3 + 93*y**2 - 27*y + 117", "step_length": 6} {"cot_id": "96c8ceedcf0e4b63a51f96b3bde5822128f0eb8155895788e0786516c1519245", "datapoint": {"question": "Simplify this expression: (-38*x**2 + 10*x + 22)*(-14*x**3 + 5*x**2 + 63)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "532*x**5 - 330*x**4 - 258*x**3 - 2284*x**2 + 630*x + 1386", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1311, "polynomial_expr": "(-38*x**2 + 10*x + 22)*(-14*x**3 + 5*x**2 + 63)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-38*x**2 + 10*x + 22)*(-14*x**3 + 5*x**2 + 63)\nExpanding the part (-38*x**2 + 10*x + 22) using the distributive property, and we got: (10*x)*(-14*x**3 + 5*x**2 + 63) + (-38*x**2)*(-14*x**3 + 5*x**2 + 63) + 22*(-14*x**3 + 5*x**2 + 63)\n#Step 2:\nCurrent expression: (10*x)*(-14*x**3 + 5*x**2 + 63) + (-38*x**2)*(-14*x**3 + 5*x**2 + 63) + 22*(-14*x**3 + 5*x**2 + 63)\nSimplifying the partial expression: 22*(-14*x**3 + 5*x**2 + 63)\nExpanding the part (-14*x**3 + 5*x**2 + 63) using the distributive property, and we got: (5*x**2)*22 - 14*x**3*22 + 63*22\nReplacing 22*(-14*x**3 + 5*x**2 + 63) with (5*x**2)*22 - 14*x**3*22 + 63*22 in the overall expression.\n#Step 3:\nCurrent expression: (10*x)*(-14*x**3 + 5*x**2 + 63) + (-38*x**2)*(-14*x**3 + 5*x**2 + 63) + (5*x**2)*22 - 14*x**3*22 + 1386\nSimplifying the partial expression: (-38*x**2)*(-14*x**3 + 5*x**2 + 63)\nExpanding the part (-14*x**3 + 5*x**2 + 63) using the distributive property, and we got: 63*(-38*x**2) + (-38*x**2)*(5*x**2) + (-38*x**2)*(-14*x**3)\nReplacing (-38*x**2)*(-14*x**3 + 5*x**2 + 63) with 63*(-38*x**2) + (-38*x**2)*(5*x**2) + (-38*x**2)*(-14*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 63*(-38)*x**2 + (10*x)*(-14*x**3 + 5*x**2 + 63) + (-38*x**2)*(5*x**2) + (-38*x**2)*(-14*x**3) + (5*x**2)*22 - 14*x**3*22 + 1386\nSimplifying the partial expression: (10*x)*(-14*x**3 + 5*x**2 + 63)\nExpanding the part (-14*x**3 + 5*x**2 + 63) using the distributive property, and we got: 63*(10*x) + (10*x)*(5*x**2) + (10*x)*(-14*x**3)\nReplacing (10*x)*(-14*x**3 + 5*x**2 + 63) with 63*(10*x) + (10*x)*(5*x**2) + (10*x)*(-14*x**3) in the overall expression.\n#Step 5:\nCurrent expression: 63*(-38)*x**2 + 63*10*x + (10*x)*(5*x**2) + (10*x)*(-14*x**3) + (-38*x**2)*(5*x**2) + (-38*x**2)*(-14*x**3) + (5*x**2)*22 - 14*x**3*22 + 1386\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-14*x**3)*22 = -308*x**3\n (-14*x**3)*(-38*x**2) = 532*x**5\n (-14*x**3)*(10*x) = -140*x**4\n (5*x**2)*22 = 110*x**2\n (5*x**2)*(-38*x**2) = -190*x**4\n (5*x**2)*(10*x) = 50*x**3\n 63*-38*x**2 = -2394*x**2\n 63*10*x = 630*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 532*x**5 - 190*x**4 - 140*x**4 - 308*x**3 + 50*x**3 - 2394*x**2 + 110*x**2 + 630*x + 1386\nCombining like terms, got 532*x**5 - 330*x**4 - 258*x**3 - 2284*x**2 + 630*x + 1386\n#Step 7:\nCurrent expression: 532*x**5 - 330*x**4 - 258*x**3 - 2284*x**2 + 630*x + 1386\nNo more calculations needed.\n532*x**5 - 330*x**4 - 258*x**3 - 2284*x**2 + 630*x + 1386", "generated_answer": "532*x**5 - 330*x**4 - 258*x**3 - 2284*x**2 + 630*x + 1386", "step_length": 7} {"cot_id": "a1f102a90a3fc1ca9a5ffbdc4f749fd84e21e123e7b29cf5f12b587f11ff7aa7", "datapoint": {"question": "Calculate the following: -50*z**2*(31*z**2 - 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1550*z**4 + 700*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1312, "polynomial_expr": "-50*z**2*(31*z**2 - 14)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -50*z**2*(31*z**2 - 14)\nExpanding the part (31*z**2 - 14) using the distributive property, and we got: -(-1)*700*z**2 + (-50*z**2)*(31*z**2)\n#Step 2:\nCurrent expression: -(-1)*700*z**2 + (-50*z**2)*(31*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -14*(-50*z**2) = 700*z**2\n (31*z**2)*(-50*z**2) = -1550*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1550*z**4 + 700*z**2\nNo more calculations needed.\n-1550*z**4 + 700*z**2", "generated_answer": "-1550*z**4 + 700*z**2", "step_length": 3} {"cot_id": "788a658dced2df0a13c574718172b7c4cb95fd718d03171317378c25cd2b595a", "datapoint": {"question": "Simplify this expression: (15*z**3 - z)*(-9*z**3 + 3*z**2 - 29)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-135*z**6 + 45*z**5 + 9*z**4 - 438*z**3 + 29*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1313, "polynomial_expr": "(15*z**3 - z)*(-9*z**3 + 3*z**2 - 29)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (15*z**3 - z)*(-9*z**3 + 3*z**2 - 29)\nExpanding the part (15*z**3 - z) using the distributive property, and we got: (-z)*(-9*z**3 + 3*z**2 - 29) + (15*z**3)*(-9*z**3 + 3*z**2 - 29)\n#Step 2:\nCurrent expression: (-z)*(-9*z**3 + 3*z**2 - 29) + (15*z**3)*(-9*z**3 + 3*z**2 - 29)\nSimplifying the partial expression: (-z)*(-9*z**3 + 3*z**2 - 29)\nExpanding the part (-9*z**3 + 3*z**2 - 29) using the distributive property, and we got: (-z)*(3*z**2) + (-z)*(-9*z**3) - (-1)*29*z\nReplacing (-z)*(-9*z**3 + 3*z**2 - 29) with (-z)*(3*z**2) + (-z)*(-9*z**3) - (-1)*29*z in the overall expression.\n#Step 3:\nCurrent expression: (-z)*(3*z**2) + (-z)*(-9*z**3) - 29*(-1)*z + (15*z**3)*(-9*z**3 + 3*z**2 - 29)\nSimplifying the partial expression: (15*z**3)*(-9*z**3 + 3*z**2 - 29)\nExpanding the part (-9*z**3 + 3*z**2 - 29) using the distributive property, and we got: -435*z**3 + (3*z**2)*(15*z**3) + (-9*z**3)*(15*z**3)\nReplacing (15*z**3)*(-9*z**3 + 3*z**2 - 29) with -435*z**3 + (3*z**2)*(15*z**3) + (-9*z**3)*(15*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-z)*(3*z**2) + (-z)*(-9*z**3) - 29*15*z**3 - 29*(-1)*z + (3*z**2)*(15*z**3) + (-9*z**3)*(15*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-9*z**3)*(-z) = 9*z**4\n (-9*z**3)*(15*z**3) = -135*z**6\n (3*z**2)*(-z) = -3*z**3\n (3*z**2)*(15*z**3) = 45*z**5\n -29*-1*z = 29*z\n -29*15*z**3 = -435*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -135*z**6 + 45*z**5 + 9*z**4 - 435*z**3 - 3*z**3 + 29*z\nCombining like terms, got -135*z**6 + 45*z**5 + 9*z**4 - 438*z**3 + 29*z\n#Step 6:\nCurrent expression: -135*z**6 + 45*z**5 + 9*z**4 - 438*z**3 + 29*z\nNo more calculations needed.\n-135*z**6 + 45*z**5 + 9*z**4 - 438*z**3 + 29*z", "generated_answer": "-135*z**6 + 45*z**5 + 9*z**4 - 438*z**3 + 29*z", "step_length": 6} {"cot_id": "5f32e6aa1518144ea0b3df8b642e315358175e3bd8bc1525e58cb531d0e1617e", "datapoint": {"question": "Calculate the following: (-7*x**2 - 34*x)*(-41*x**2 + 40*x + 9)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "287*x**4 + 1114*x**3 - 1423*x**2 - 306*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1314, "polynomial_expr": "(-7*x**2 - 34*x)*(-41*x**2 + 40*x + 9)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-7*x**2 - 34*x)*(-41*x**2 + 40*x + 9)\nExpanding the part (-7*x**2 - 34*x) using the distributive property, and we got: (-34*x)*(-41*x**2 + 40*x + 9) + (-7*x**2)*(-41*x**2 + 40*x + 9)\n#Step 2:\nCurrent expression: (-34*x)*(-41*x**2 + 40*x + 9) + (-7*x**2)*(-41*x**2 + 40*x + 9)\nSimplifying the partial expression: (-34*x)*(-41*x**2 + 40*x + 9)\nExpanding the part (-41*x**2 + 40*x + 9) using the distributive property, and we got: (-34*x)*(40*x) + (-34*x)*(-41*x**2) + 9*(-34*x)\nReplacing (-34*x)*(-41*x**2 + 40*x + 9) with (-34*x)*(40*x) + (-34*x)*(-41*x**2) + 9*(-34*x) in the overall expression.\n#Step 3:\nCurrent expression: (-34*x)*(40*x) + (-34*x)*(-41*x**2) + 9*(-34)*x + (-7*x**2)*(-41*x**2 + 40*x + 9)\nSimplifying the partial expression: (-7*x**2)*(-41*x**2 + 40*x + 9)\nExpanding the part (-41*x**2 + 40*x + 9) using the distributive property, and we got: 9*(-7*x**2) + (40*x)*(-7*x**2) + (-41*x**2)*(-7*x**2)\nReplacing (-7*x**2)*(-41*x**2 + 40*x + 9) with 9*(-7*x**2) + (40*x)*(-7*x**2) + (-41*x**2)*(-7*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-34*x)*(40*x) + (-34*x)*(-41*x**2) + 9*(-7)*x**2 + 9*(-34)*x + (40*x)*(-7*x**2) + (-41*x**2)*(-7*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*x**2)*(-34*x) = 1394*x**3\n (-41*x**2)*(-7*x**2) = 287*x**4\n (40*x)*(-34*x) = -1360*x**2\n (40*x)*(-7*x**2) = -280*x**3\n 9*-34*x = -306*x\n 9*-7*x**2 = -63*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 287*x**4 - 280*x**3 + 1394*x**3 - 1360*x**2 - 63*x**2 - 306*x\nCombining like terms, got 287*x**4 + 1114*x**3 - 1423*x**2 - 306*x\n#Step 6:\nCurrent expression: 287*x**4 + 1114*x**3 - 1423*x**2 - 306*x\nNo more calculations needed.\n287*x**4 + 1114*x**3 - 1423*x**2 - 306*x", "generated_answer": "287*x**4 + 1114*x**3 - 1423*x**2 - 306*x", "step_length": 6} {"cot_id": "8a9c54c970cc92bc2a0c86b1cbf1aaf8300330184d28bb73b691a80f2babd706", "datapoint": {"question": "Simplify this expression: (43 - 31*z**2)*(14*z**3 - 33*z + 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-434*z**5 + 1625*z**3 - 310*z**2 - 1419*z + 430", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1315, "polynomial_expr": "(43 - 31*z**2)*(14*z**3 - 33*z + 10)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (43 - 31*z**2)*(14*z**3 - 33*z + 10)\nExpanding the part (43 - 31*z**2) using the distributive property, and we got: (-31*z**2)*(14*z**3 - 33*z + 10) + 43*(14*z**3 - 33*z + 10)\n#Step 2:\nCurrent expression: (-31*z**2)*(14*z**3 - 33*z + 10) + 43*(14*z**3 - 33*z + 10)\nSimplifying the partial expression: 43*(14*z**3 - 33*z + 10)\nExpanding the part (14*z**3 - 33*z + 10) using the distributive property, and we got: -33*z*43 + (14*z**3)*43 + 10*43\nReplacing 43*(14*z**3 - 33*z + 10) with -33*z*43 + (14*z**3)*43 + 10*43 in the overall expression.\n#Step 3:\nCurrent expression: -33*z*43 + (-31*z**2)*(14*z**3 - 33*z + 10) + (14*z**3)*43 + 430\nSimplifying the partial expression: (-31*z**2)*(14*z**3 - 33*z + 10)\nExpanding the part (14*z**3 - 33*z + 10) using the distributive property, and we got: (-33*z)*(-31*z**2) + 10*(-31*z**2) + (-31*z**2)*(14*z**3)\nReplacing (-31*z**2)*(14*z**3 - 33*z + 10) with (-33*z)*(-31*z**2) + 10*(-31*z**2) + (-31*z**2)*(14*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-33*z)*(-31*z**2) - 33*z*43 + 10*(-31)*z**2 + (-31*z**2)*(14*z**3) + (14*z**3)*43 + 430\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*z)*43 = -1419*z\n (-33*z)*(-31*z**2) = 1023*z**3\n (14*z**3)*43 = 602*z**3\n (14*z**3)*(-31*z**2) = -434*z**5\n 10*-31*z**2 = -310*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -434*z**5 + 602*z**3 + 1023*z**3 - 310*z**2 - 1419*z + 430\nCombining like terms, got -434*z**5 + 1625*z**3 - 310*z**2 - 1419*z + 430\n#Step 6:\nCurrent expression: -434*z**5 + 1625*z**3 - 310*z**2 - 1419*z + 430\nNo more calculations needed.\n-434*z**5 + 1625*z**3 - 310*z**2 - 1419*z + 430", "generated_answer": "-434*z**5 + 1625*z**3 - 310*z**2 - 1419*z + 430", "step_length": 6} {"cot_id": "d098f9947d548c75b0d016510fbc0bc0f691cecdc4757ae7840763c82d6c8335", "datapoint": {"question": "Simplify this expression: (36*x + 66)*(32*x**2 + 29*x - 26)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1152*x**3 + 3156*x**2 + 978*x - 1716", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1316, "polynomial_expr": "(36*x + 66)*(32*x**2 + 29*x - 26)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (36*x + 66)*(32*x**2 + 29*x - 26)\nExpanding the part (36*x + 66) using the distributive property, and we got: (36*x)*(32*x**2 + 29*x - 26) + 66*(32*x**2 + 29*x - 26)\n#Step 2:\nCurrent expression: (36*x)*(32*x**2 + 29*x - 26) + 66*(32*x**2 + 29*x - 26)\nSimplifying the partial expression: 66*(32*x**2 + 29*x - 26)\nExpanding the part (32*x**2 + 29*x - 26) using the distributive property, and we got: (29*x)*66 + (32*x**2)*66 - 26*66\nReplacing 66*(32*x**2 + 29*x - 26) with (29*x)*66 + (32*x**2)*66 - 26*66 in the overall expression.\n#Step 3:\nCurrent expression: (29*x)*66 + (36*x)*(32*x**2 + 29*x - 26) + (32*x**2)*66 - 1716\nSimplifying the partial expression: (36*x)*(32*x**2 + 29*x - 26)\nExpanding the part (32*x**2 + 29*x - 26) using the distributive property, and we got: -936*x + (29*x)*(36*x) + (36*x)*(32*x**2)\nReplacing (36*x)*(32*x**2 + 29*x - 26) with -936*x + (29*x)*(36*x) + (36*x)*(32*x**2) in the overall expression.\n#Step 4:\nCurrent expression: -26*36*x + (29*x)*(36*x) + (29*x)*66 + (36*x)*(32*x**2) + (32*x**2)*66 - 1716\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (29*x)*66 = 1914*x\n (29*x)*(36*x) = 1044*x**2\n (32*x**2)*66 = 2112*x**2\n (32*x**2)*(36*x) = 1152*x**3\n -26*36*x = -936*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1152*x**3 + 1044*x**2 + 2112*x**2 - 936*x + 1914*x - 1716\nCombining like terms, got 1152*x**3 + 3156*x**2 + 978*x - 1716\n#Step 6:\nCurrent expression: 1152*x**3 + 3156*x**2 + 978*x - 1716\nNo more calculations needed.\n1152*x**3 + 3156*x**2 + 978*x - 1716", "generated_answer": "1152*x**3 + 3156*x**2 + 978*x - 1716", "step_length": 6} {"cot_id": "3fe60ef3ae06d7fd8d4c7c65c247ca684bd9fcd091443d8c98048d0991f9030f", "datapoint": {"question": "Calculate the following: (-8*y**3 + 31*y)*(-15*y**3 + 12*y**2 + 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "120*y**6 - 96*y**5 - 465*y**4 + 124*y**3 + 961*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1317, "polynomial_expr": "(-8*y**3 + 31*y)*(-15*y**3 + 12*y**2 + 31)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-8*y**3 + 31*y)*(-15*y**3 + 12*y**2 + 31)\nExpanding the part (-8*y**3 + 31*y) using the distributive property, and we got: (31*y)*(-15*y**3 + 12*y**2 + 31) + (-8*y**3)*(-15*y**3 + 12*y**2 + 31)\n#Step 2:\nCurrent expression: (31*y)*(-15*y**3 + 12*y**2 + 31) + (-8*y**3)*(-15*y**3 + 12*y**2 + 31)\nSimplifying the partial expression: (-8*y**3)*(-15*y**3 + 12*y**2 + 31)\nExpanding the part (-15*y**3 + 12*y**2 + 31) using the distributive property, and we got: 31*(-8*y**3) + (12*y**2)*(-8*y**3) + (-15*y**3)*(-8*y**3)\nReplacing (-8*y**3)*(-15*y**3 + 12*y**2 + 31) with 31*(-8*y**3) + (12*y**2)*(-8*y**3) + (-15*y**3)*(-8*y**3) in the overall expression.\n#Step 3:\nCurrent expression: 31*(-8)*y**3 + (31*y)*(-15*y**3 + 12*y**2 + 31) + (12*y**2)*(-8*y**3) + (-15*y**3)*(-8*y**3)\nSimplifying the partial expression: (31*y)*(-15*y**3 + 12*y**2 + 31)\nExpanding the part (-15*y**3 + 12*y**2 + 31) using the distributive property, and we got: 31*(31*y) + (31*y)*(12*y**2) + (31*y)*(-15*y**3)\nReplacing (31*y)*(-15*y**3 + 12*y**2 + 31) with 31*(31*y) + (31*y)*(12*y**2) + (31*y)*(-15*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 31*(-8)*y**3 + 31*31*y + (31*y)*(12*y**2) + (31*y)*(-15*y**3) + (12*y**2)*(-8*y**3) + (-15*y**3)*(-8*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-15*y**3)*(-8*y**3) = 120*y**6\n (-15*y**3)*(31*y) = -465*y**4\n (12*y**2)*(-8*y**3) = -96*y**5\n (12*y**2)*(31*y) = 372*y**3\n 31*-8*y**3 = -248*y**3\n 31*31*y = 961*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 120*y**6 - 96*y**5 - 465*y**4 - 248*y**3 + 372*y**3 + 961*y\nCombining like terms, got 120*y**6 - 96*y**5 - 465*y**4 + 124*y**3 + 961*y\n#Step 6:\nCurrent expression: 120*y**6 - 96*y**5 - 465*y**4 + 124*y**3 + 961*y\nNo more calculations needed.\n120*y**6 - 96*y**5 - 465*y**4 + 124*y**3 + 961*y", "generated_answer": "120*y**6 - 96*y**5 - 465*y**4 + 124*y**3 + 961*y", "step_length": 6} {"cot_id": "56cbf082f1c7523b39d22c97456c23fd4048c3d87a82f438da9d8ff408e0c75e", "datapoint": {"question": "Simplify this expression: (-4*z**3 + 24*z - 44)*(46*z**3 + 32*z - 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-184*z**6 + 976*z**4 - 1968*z**3 + 768*z**2 - 1744*z + 616", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1318, "polynomial_expr": "(-4*z**3 + 24*z - 44)*(46*z**3 + 32*z - 14)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-4*z**3 + 24*z - 44)*(46*z**3 + 32*z - 14)\nExpanding the part (-4*z**3 + 24*z - 44) using the distributive property, and we got: (24*z)*(46*z**3 + 32*z - 14) + (-4*z**3)*(46*z**3 + 32*z - 14) - 44*(46*z**3 + 32*z - 14)\n#Step 2:\nCurrent expression: (24*z)*(46*z**3 + 32*z - 14) + (-4*z**3)*(46*z**3 + 32*z - 14) - 44*(46*z**3 + 32*z - 14)\nSimplifying the partial expression: -44*(46*z**3 + 32*z - 14)\nExpanding the part (46*z**3 + 32*z - 14) using the distributive property, and we got: (32*z)*(-44) + (46*z**3)*(-44) - 14*(-44)\nReplacing -44*(46*z**3 + 32*z - 14) with (32*z)*(-44) + (46*z**3)*(-44) - 14*(-44) in the overall expression.\n#Step 3:\nCurrent expression: (24*z)*(46*z**3 + 32*z - 14) + (32*z)*(-44) + (-4*z**3)*(46*z**3 + 32*z - 14) + (46*z**3)*(-44) + 616\nSimplifying the partial expression: (-4*z**3)*(46*z**3 + 32*z - 14)\nExpanding the part (46*z**3 + 32*z - 14) using the distributive property, and we got: -(-1)*56*z**3 + (32*z)*(-4*z**3) + (-4*z**3)*(46*z**3)\nReplacing (-4*z**3)*(46*z**3 + 32*z - 14) with -(-1)*56*z**3 + (32*z)*(-4*z**3) + (-4*z**3)*(46*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -14*(-4)*z**3 + (24*z)*(46*z**3 + 32*z - 14) + (32*z)*(-4*z**3) + (32*z)*(-44) + (-4*z**3)*(46*z**3) + (46*z**3)*(-44) + 616\nSimplifying the partial expression: (24*z)*(46*z**3 + 32*z - 14)\nExpanding the part (46*z**3 + 32*z - 14) using the distributive property, and we got: -336*z + (24*z)*(32*z) + (24*z)*(46*z**3)\nReplacing (24*z)*(46*z**3 + 32*z - 14) with -336*z + (24*z)*(32*z) + (24*z)*(46*z**3) in the overall expression.\n#Step 5:\nCurrent expression: -14*(-4)*z**3 - 14*24*z + (24*z)*(32*z) + (24*z)*(46*z**3) + (32*z)*(-4*z**3) + (32*z)*(-44) + (-4*z**3)*(46*z**3) + (46*z**3)*(-44) + 616\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (32*z)*-44 = -1408*z\n (32*z)*(-4*z**3) = -128*z**4\n (32*z)*(24*z) = 768*z**2\n (46*z**3)*-44 = -2024*z**3\n (46*z**3)*(-4*z**3) = -184*z**6\n (46*z**3)*(24*z) = 1104*z**4\n -14*-4*z**3 = 56*z**3\n -14*24*z = -336*z\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -184*z**6 - 128*z**4 + 1104*z**4 - 2024*z**3 + 56*z**3 + 768*z**2 - 1408*z - 336*z + 616\nCombining like terms, got -184*z**6 + 976*z**4 - 1968*z**3 + 768*z**2 - 1744*z + 616\n#Step 7:\nCurrent expression: -184*z**6 + 976*z**4 - 1968*z**3 + 768*z**2 - 1744*z + 616\nNo more calculations needed.\n-184*z**6 + 976*z**4 - 1968*z**3 + 768*z**2 - 1744*z + 616", "generated_answer": "-184*z**6 + 976*z**4 - 1968*z**3 + 768*z**2 - 1744*z + 616", "step_length": 7} {"cot_id": "e6b49999edc2f7717ad03328fb5177d31059f91310dede703321b2d75258c85a", "datapoint": {"question": "Calculate the following: 28*x*(3*x**3 + 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "84*x**4 + 1008*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1319, "polynomial_expr": "28*x*(3*x**3 + 36)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 28*x*(3*x**3 + 36)\nExpanding the part (3*x**3 + 36) using the distributive property, and we got: 36*(28*x) + (28*x)*(3*x**3)\n#Step 2:\nCurrent expression: 36*(28*x) + (28*x)*(3*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 36*(28*x) = 1008*x\n (3*x**3)*(28*x) = 84*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 84*x**4 + 1008*x\nNo more calculations needed.\n84*x**4 + 1008*x", "generated_answer": "84*x**4 + 1008*x", "step_length": 3} {"cot_id": "8b5a3d85f364c3faa884c3590bdcb785d2eb2b6e77d0d9f2a48fe517823260c1", "datapoint": {"question": "Calculate the following: 57*x*(-20*x**3 + 17*x**2 - 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1140*x**4 + 969*x**3 - 1995*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1320, "polynomial_expr": "57*x*(-20*x**3 + 17*x**2 - 35)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 57*x*(-20*x**3 + 17*x**2 - 35)\nExpanding the part (-20*x**3 + 17*x**2 - 35) using the distributive property, and we got: -1995*x + (57*x)*(17*x**2) + (57*x)*(-20*x**3)\n#Step 2:\nCurrent expression: -1995*x + (57*x)*(17*x**2) + (57*x)*(-20*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -35*(57*x) = -1995*x\n (-20*x**3)*(57*x) = -1140*x**4\n (17*x**2)*(57*x) = 969*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1140*x**4 + 969*x**3 - 1995*x\nNo more calculations needed.\n-1140*x**4 + 969*x**3 - 1995*x", "generated_answer": "-1140*x**4 + 969*x**3 - 1995*x", "step_length": 3} {"cot_id": "18c420ec94c9a22799cadf0a2642d3b8b9d2fa8f0c0c35912acd15f46ffc37ee", "datapoint": {"question": "Simplify this expression: (-5*x**2 + 8*x + 29)*(32*x**3 - 49*x**2 - 20*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-160*x**5 + 501*x**4 + 636*x**3 - 1581*x**2 - 580*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1321, "polynomial_expr": "(-5*x**2 + 8*x + 29)*(32*x**3 - 49*x**2 - 20*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-5*x**2 + 8*x + 29)*(32*x**3 - 49*x**2 - 20*x)\nExpanding the part (-5*x**2 + 8*x + 29) using the distributive property, and we got: (8*x)*(32*x**3 - 49*x**2 - 20*x) + (-5*x**2)*(32*x**3 - 49*x**2 - 20*x) + 29*(32*x**3 - 49*x**2 - 20*x)\n#Step 2:\nCurrent expression: (8*x)*(32*x**3 - 49*x**2 - 20*x) + (-5*x**2)*(32*x**3 - 49*x**2 - 20*x) + 29*(32*x**3 - 49*x**2 - 20*x)\nSimplifying the partial expression: 29*(32*x**3 - 49*x**2 - 20*x)\nExpanding the part (32*x**3 - 49*x**2 - 20*x) using the distributive property, and we got: -20*x*29 - 49*x**2*29 + (32*x**3)*29\nReplacing 29*(32*x**3 - 49*x**2 - 20*x) with -20*x*29 - 49*x**2*29 + (32*x**3)*29 in the overall expression.\n#Step 3:\nCurrent expression: -20*x*29 + (8*x)*(32*x**3 - 49*x**2 - 20*x) - 49*x**2*29 + (-5*x**2)*(32*x**3 - 49*x**2 - 20*x) + (32*x**3)*29\nSimplifying the partial expression: (-5*x**2)*(32*x**3 - 49*x**2 - 20*x)\nExpanding the part (32*x**3 - 49*x**2 - 20*x) using the distributive property, and we got: (-20*x)*(-5*x**2) + (-49*x**2)*(-5*x**2) + (-5*x**2)*(32*x**3)\nReplacing (-5*x**2)*(32*x**3 - 49*x**2 - 20*x) with (-20*x)*(-5*x**2) + (-49*x**2)*(-5*x**2) + (-5*x**2)*(32*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-20*x)*(-5*x**2) - 20*x*29 + (8*x)*(32*x**3 - 49*x**2 - 20*x) + (-49*x**2)*(-5*x**2) - 49*x**2*29 + (-5*x**2)*(32*x**3) + (32*x**3)*29\nSimplifying the partial expression: (8*x)*(32*x**3 - 49*x**2 - 20*x)\nExpanding the part (32*x**3 - 49*x**2 - 20*x) using the distributive property, and we got: (-20*x)*(8*x) + (8*x)*(-49*x**2) + (8*x)*(32*x**3)\nReplacing (8*x)*(32*x**3 - 49*x**2 - 20*x) with (-20*x)*(8*x) + (8*x)*(-49*x**2) + (8*x)*(32*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-20*x)*(8*x) + (-20*x)*(-5*x**2) - 20*x*29 + (8*x)*(-49*x**2) + (8*x)*(32*x**3) + (-49*x**2)*(-5*x**2) - 49*x**2*29 + (-5*x**2)*(32*x**3) + (32*x**3)*29\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*x**2)*29 = -1421*x**2\n (-49*x**2)*(-5*x**2) = 245*x**4\n (-49*x**2)*(8*x) = -392*x**3\n (-20*x)*29 = -580*x\n (-20*x)*(-5*x**2) = 100*x**3\n (-20*x)*(8*x) = -160*x**2\n (32*x**3)*29 = 928*x**3\n (32*x**3)*(-5*x**2) = -160*x**5\n (32*x**3)*(8*x) = 256*x**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -160*x**5 + 245*x**4 + 256*x**4 - 392*x**3 + 100*x**3 + 928*x**3 - 1421*x**2 - 160*x**2 - 580*x\nCombining like terms, got -160*x**5 + 501*x**4 + 636*x**3 - 1581*x**2 - 580*x\n#Step 7:\nCurrent expression: -160*x**5 + 501*x**4 + 636*x**3 - 1581*x**2 - 580*x\nNo more calculations needed.\n-160*x**5 + 501*x**4 + 636*x**3 - 1581*x**2 - 580*x", "generated_answer": "-160*x**5 + 501*x**4 + 636*x**3 - 1581*x**2 - 580*x", "step_length": 7} {"cot_id": "dbea4dd1832b69b9141258b90baa4c33c746aa062a0e32fa06890d19d3b50cb2", "datapoint": {"question": "Calculate the following: (-11*x**3 - 11*x)*(37*x**3 + 57*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-407*x**6 - 627*x**5 - 407*x**4 - 627*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1322, "polynomial_expr": "(-11*x**3 - 11*x)*(37*x**3 + 57*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-11*x**3 - 11*x)*(37*x**3 + 57*x**2)\nExpanding the part (-11*x**3 - 11*x) using the distributive property, and we got: (-11*x)*(37*x**3 + 57*x**2) + (-11*x**3)*(37*x**3 + 57*x**2)\n#Step 2:\nCurrent expression: (-11*x)*(37*x**3 + 57*x**2) + (-11*x**3)*(37*x**3 + 57*x**2)\nSimplifying the partial expression: (-11*x)*(37*x**3 + 57*x**2)\nExpanding the part (37*x**3 + 57*x**2) using the distributive property, and we got: (-11*x)*(57*x**2) + (-11*x)*(37*x**3)\nReplacing (-11*x)*(37*x**3 + 57*x**2) with (-11*x)*(57*x**2) + (-11*x)*(37*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-11*x)*(57*x**2) + (-11*x)*(37*x**3) + (-11*x**3)*(37*x**3 + 57*x**2)\nSimplifying the partial expression: (-11*x**3)*(37*x**3 + 57*x**2)\nExpanding the part (37*x**3 + 57*x**2) using the distributive property, and we got: (57*x**2)*(-11*x**3) + (-11*x**3)*(37*x**3)\nReplacing (-11*x**3)*(37*x**3 + 57*x**2) with (57*x**2)*(-11*x**3) + (-11*x**3)*(37*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-11*x)*(57*x**2) + (-11*x)*(37*x**3) + (57*x**2)*(-11*x**3) + (-11*x**3)*(37*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (37*x**3)*(-11*x) = -407*x**4\n (37*x**3)*(-11*x**3) = -407*x**6\n (57*x**2)*(-11*x) = -627*x**3\n (57*x**2)*(-11*x**3) = -627*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -407*x**6 - 627*x**5 - 407*x**4 - 627*x**3\nNo more calculations needed.\n-407*x**6 - 627*x**5 - 407*x**4 - 627*x**3", "generated_answer": "-407*x**6 - 627*x**5 - 407*x**4 - 627*x**3", "step_length": 5} {"cot_id": "9685413f30252b04b4d5cbf3a8e90be476e023c25ebc552f5db6efb30701a5f8", "datapoint": {"question": "Simplify this expression: (36 - 27*y**2)*(-16*y**3 - 33*y + 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "432*y**5 + 315*y**3 - 891*y**2 - 1188*y + 1188", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1323, "polynomial_expr": "(36 - 27*y**2)*(-16*y**3 - 33*y + 33)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (36 - 27*y**2)*(-16*y**3 - 33*y + 33)\nExpanding the part (36 - 27*y**2) using the distributive property, and we got: (-27*y**2)*(-16*y**3 - 33*y + 33) + 36*(-16*y**3 - 33*y + 33)\n#Step 2:\nCurrent expression: (-27*y**2)*(-16*y**3 - 33*y + 33) + 36*(-16*y**3 - 33*y + 33)\nSimplifying the partial expression: 36*(-16*y**3 - 33*y + 33)\nExpanding the part (-16*y**3 - 33*y + 33) using the distributive property, and we got: -33*y*36 - 16*y**3*36 + 33*36\nReplacing 36*(-16*y**3 - 33*y + 33) with -33*y*36 - 16*y**3*36 + 33*36 in the overall expression.\n#Step 3:\nCurrent expression: -33*y*36 + (-27*y**2)*(-16*y**3 - 33*y + 33) - 16*y**3*36 + 1188\nSimplifying the partial expression: (-27*y**2)*(-16*y**3 - 33*y + 33)\nExpanding the part (-16*y**3 - 33*y + 33) using the distributive property, and we got: (-33*y)*(-27*y**2) + 33*(-27*y**2) + (-27*y**2)*(-16*y**3)\nReplacing (-27*y**2)*(-16*y**3 - 33*y + 33) with (-33*y)*(-27*y**2) + 33*(-27*y**2) + (-27*y**2)*(-16*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-33*y)*(-27*y**2) - 33*y*36 + 33*(-27)*y**2 + (-27*y**2)*(-16*y**3) - 16*y**3*36 + 1188\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*y)*36 = -1188*y\n (-33*y)*(-27*y**2) = 891*y**3\n (-16*y**3)*36 = -576*y**3\n (-16*y**3)*(-27*y**2) = 432*y**5\n 33*-27*y**2 = -891*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 432*y**5 - 576*y**3 + 891*y**3 - 891*y**2 - 1188*y + 1188\nCombining like terms, got 432*y**5 + 315*y**3 - 891*y**2 - 1188*y + 1188\n#Step 6:\nCurrent expression: 432*y**5 + 315*y**3 - 891*y**2 - 1188*y + 1188\nNo more calculations needed.\n432*y**5 + 315*y**3 - 891*y**2 - 1188*y + 1188", "generated_answer": "432*y**5 + 315*y**3 - 891*y**2 - 1188*y + 1188", "step_length": 6} {"cot_id": "29714b5a1790ac49f6383e75fea268832ae1945a7c3b991ad39f186a578e29e0", "datapoint": {"question": "Simplify this expression: -65*z*(30*z**3 - 3*z**2 - 27*z - 34)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1950*z**4 + 195*z**3 + 1755*z**2 + 2210*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1324, "polynomial_expr": "-65*z*(30*z**3 - 3*z**2 - 27*z - 34)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -65*z*(30*z**3 - 3*z**2 - 27*z - 34)\nExpanding the part (30*z**3 - 3*z**2 - 27*z - 34) using the distributive property, and we got: (-65*z)*(-27*z) + (-65*z)*(-3*z**2) + (-65*z)*(30*z**3) - (-1)*2210*z\n#Step 2:\nCurrent expression: (-65*z)*(-27*z) + (-65*z)*(-3*z**2) + (-65*z)*(30*z**3) - (-1)*2210*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -34*(-65*z) = 2210*z\n (-27*z)*(-65*z) = 1755*z**2\n (-3*z**2)*(-65*z) = 195*z**3\n (30*z**3)*(-65*z) = -1950*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1950*z**4 + 195*z**3 + 1755*z**2 + 2210*z\nNo more calculations needed.\n-1950*z**4 + 195*z**3 + 1755*z**2 + 2210*z", "generated_answer": "-1950*z**4 + 195*z**3 + 1755*z**2 + 2210*z", "step_length": 3} {"cot_id": "8061aaae83b476de6be376281372502198fa856f6545c0ab20d92bdfdd4bcb3c", "datapoint": {"question": "Calculate the following: -412*y**3\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-412*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1325, "polynomial_expr": "-412*y**3", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -412*y**3\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -412*y**3\nNo more calculations needed.\n-412*y**3", "generated_answer": "-412*y**3", "step_length": 2} {"cot_id": "bd91cda0ecdbc9f12933daf2e0d56f5a15fd5140befa2e045356577385d7dd4f", "datapoint": {"question": "Calculate the following: (6*x**2 - 33*x - 40)*(35*x**3 - 46*x**2 - 17*x + 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "210*x**5 - 1431*x**4 + 16*x**3 + 2497*x**2 + 152*x - 640", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1326, "polynomial_expr": "(6*x**2 - 33*x - 40)*(35*x**3 - 46*x**2 - 17*x + 16)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6*x**2 - 33*x - 40)*(35*x**3 - 46*x**2 - 17*x + 16)\nExpanding the part (6*x**2 - 33*x - 40) using the distributive property, and we got: (-33*x)*(35*x**3 - 46*x**2 - 17*x + 16) + (6*x**2)*(35*x**3 - 46*x**2 - 17*x + 16) - 40*(35*x**3 - 46*x**2 - 17*x + 16)\n#Step 2:\nCurrent expression: (-33*x)*(35*x**3 - 46*x**2 - 17*x + 16) + (6*x**2)*(35*x**3 - 46*x**2 - 17*x + 16) - 40*(35*x**3 - 46*x**2 - 17*x + 16)\nSimplifying the partial expression: -40*(35*x**3 - 46*x**2 - 17*x + 16)\nExpanding the part (35*x**3 - 46*x**2 - 17*x + 16) using the distributive property, and we got: -17*x*(-40) - 46*x**2*(-40) + (35*x**3)*(-40) + 16*(-40)\nReplacing -40*(35*x**3 - 46*x**2 - 17*x + 16) with -17*x*(-40) - 46*x**2*(-40) + (35*x**3)*(-40) + 16*(-40) in the overall expression.\n#Step 3:\nCurrent expression: (-33*x)*(35*x**3 - 46*x**2 - 17*x + 16) - 17*x*(-40) - 46*x**2*(-40) + (6*x**2)*(35*x**3 - 46*x**2 - 17*x + 16) + (35*x**3)*(-40) - 640\nSimplifying the partial expression: (-33*x)*(35*x**3 - 46*x**2 - 17*x + 16)\nExpanding the part (35*x**3 - 46*x**2 - 17*x + 16) using the distributive property, and we got: (-33*x)*(-17*x) + (-33*x)*(-46*x**2) + (-33*x)*(35*x**3) + 16*(-33*x)\nReplacing (-33*x)*(35*x**3 - 46*x**2 - 17*x + 16) with (-33*x)*(-17*x) + (-33*x)*(-46*x**2) + (-33*x)*(35*x**3) + 16*(-33*x) in the overall expression.\n#Step 4:\nCurrent expression: (-33*x)*(-17*x) + (-33*x)*(-46*x**2) + (-33*x)*(35*x**3) - 17*x*(-40) + 16*(-33)*x - 46*x**2*(-40) + (6*x**2)*(35*x**3 - 46*x**2 - 17*x + 16) + (35*x**3)*(-40) - 640\nSimplifying the partial expression: (6*x**2)*(35*x**3 - 46*x**2 - 17*x + 16)\nExpanding the part (35*x**3 - 46*x**2 - 17*x + 16) using the distributive property, and we got: (-17*x)*(6*x**2) + 16*(6*x**2) + (-46*x**2)*(6*x**2) + (6*x**2)*(35*x**3)\nReplacing (6*x**2)*(35*x**3 - 46*x**2 - 17*x + 16) with (-17*x)*(6*x**2) + 16*(6*x**2) + (-46*x**2)*(6*x**2) + (6*x**2)*(35*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-33*x)*(-17*x) + (-33*x)*(-46*x**2) + (-33*x)*(35*x**3) + (-17*x)*(6*x**2) - 17*x*(-40) + 16*6*x**2 + 16*(-33)*x + (-46*x**2)*(6*x**2) - 46*x**2*(-40) + (6*x**2)*(35*x**3) + (35*x**3)*(-40) - 640\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*x**2)*-40 = 1840*x**2\n (-46*x**2)*(-33*x) = 1518*x**3\n (-46*x**2)*(6*x**2) = -276*x**4\n (-17*x)*-40 = 680*x\n (-17*x)*(-33*x) = 561*x**2\n (-17*x)*(6*x**2) = -102*x**3\n (35*x**3)*-40 = -1400*x**3\n (35*x**3)*(-33*x) = -1155*x**4\n (35*x**3)*(6*x**2) = 210*x**5\n 16*-33*x = -528*x\n 16*6*x**2 = 96*x**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 210*x**5 - 1155*x**4 - 276*x**4 - 1400*x**3 - 102*x**3 + 1518*x**3 + 96*x**2 + 561*x**2 + 1840*x**2 - 528*x + 680*x - 640\nCombining like terms, got 210*x**5 - 1431*x**4 + 16*x**3 + 2497*x**2 + 152*x - 640\n#Step 7:\nCurrent expression: 210*x**5 - 1431*x**4 + 16*x**3 + 2497*x**2 + 152*x - 640\nNo more calculations needed.\n210*x**5 - 1431*x**4 + 16*x**3 + 2497*x**2 + 152*x - 640", "generated_answer": "210*x**5 - 1431*x**4 + 16*x**3 + 2497*x**2 + 152*x - 640", "step_length": 7} {"cot_id": "771170c032eec227350c8e970e589ac8cdd4c00570f8e168079f10a3af29f1c4", "datapoint": {"question": "Calculate the following: (-21*z**3 - 43*z)*(-69*z**3 + 46*z**2 - 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1449*z**6 - 966*z**5 + 2967*z**4 - 1831*z**3 + 301*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1327, "polynomial_expr": "(-21*z**3 - 43*z)*(-69*z**3 + 46*z**2 - 7)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-21*z**3 - 43*z)*(-69*z**3 + 46*z**2 - 7)\nExpanding the part (-21*z**3 - 43*z) using the distributive property, and we got: (-43*z)*(-69*z**3 + 46*z**2 - 7) + (-21*z**3)*(-69*z**3 + 46*z**2 - 7)\n#Step 2:\nCurrent expression: (-43*z)*(-69*z**3 + 46*z**2 - 7) + (-21*z**3)*(-69*z**3 + 46*z**2 - 7)\nSimplifying the partial expression: (-43*z)*(-69*z**3 + 46*z**2 - 7)\nExpanding the part (-69*z**3 + 46*z**2 - 7) using the distributive property, and we got: (-43*z)*(46*z**2) + (-43*z)*(-69*z**3) - (-1)*301*z\nReplacing (-43*z)*(-69*z**3 + 46*z**2 - 7) with (-43*z)*(46*z**2) + (-43*z)*(-69*z**3) - (-1)*301*z in the overall expression.\n#Step 3:\nCurrent expression: (-43*z)*(46*z**2) + (-43*z)*(-69*z**3) - 7*(-43)*z + (-21*z**3)*(-69*z**3 + 46*z**2 - 7)\nSimplifying the partial expression: (-21*z**3)*(-69*z**3 + 46*z**2 - 7)\nExpanding the part (-69*z**3 + 46*z**2 - 7) using the distributive property, and we got: -(-1)*147*z**3 + (46*z**2)*(-21*z**3) + (-69*z**3)*(-21*z**3)\nReplacing (-21*z**3)*(-69*z**3 + 46*z**2 - 7) with -(-1)*147*z**3 + (46*z**2)*(-21*z**3) + (-69*z**3)*(-21*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-43*z)*(46*z**2) + (-43*z)*(-69*z**3) - 7*(-21)*z**3 - 7*(-43)*z + (46*z**2)*(-21*z**3) + (-69*z**3)*(-21*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-69*z**3)*(-43*z) = 2967*z**4\n (-69*z**3)*(-21*z**3) = 1449*z**6\n (46*z**2)*(-43*z) = -1978*z**3\n (46*z**2)*(-21*z**3) = -966*z**5\n -7*-43*z = 301*z\n -7*-21*z**3 = 147*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1449*z**6 - 966*z**5 + 2967*z**4 - 1978*z**3 + 147*z**3 + 301*z\nCombining like terms, got 1449*z**6 - 966*z**5 + 2967*z**4 - 1831*z**3 + 301*z\n#Step 6:\nCurrent expression: 1449*z**6 - 966*z**5 + 2967*z**4 - 1831*z**3 + 301*z\nNo more calculations needed.\n1449*z**6 - 966*z**5 + 2967*z**4 - 1831*z**3 + 301*z", "generated_answer": "1449*z**6 - 966*z**5 + 2967*z**4 - 1831*z**3 + 301*z", "step_length": 6} {"cot_id": "c5d246f5a83c335d79a2a11107605f459e607b93da43d97047f5dc626ae59820", "datapoint": {"question": "Simplify this expression: (-49*z**2 + 25*z)*(-40*z**3 + 31*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1960*z**5 - 2519*z**4 + 775*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1328, "polynomial_expr": "(-49*z**2 + 25*z)*(-40*z**3 + 31*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-49*z**2 + 25*z)*(-40*z**3 + 31*z**2)\nExpanding the part (-49*z**2 + 25*z) using the distributive property, and we got: (25*z)*(-40*z**3 + 31*z**2) + (-49*z**2)*(-40*z**3 + 31*z**2)\n#Step 2:\nCurrent expression: (25*z)*(-40*z**3 + 31*z**2) + (-49*z**2)*(-40*z**3 + 31*z**2)\nSimplifying the partial expression: (-49*z**2)*(-40*z**3 + 31*z**2)\nExpanding the part (-40*z**3 + 31*z**2) using the distributive property, and we got: (-49*z**2)*(31*z**2) + (-49*z**2)*(-40*z**3)\nReplacing (-49*z**2)*(-40*z**3 + 31*z**2) with (-49*z**2)*(31*z**2) + (-49*z**2)*(-40*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (25*z)*(-40*z**3 + 31*z**2) + (-49*z**2)*(31*z**2) + (-49*z**2)*(-40*z**3)\nSimplifying the partial expression: (25*z)*(-40*z**3 + 31*z**2)\nExpanding the part (-40*z**3 + 31*z**2) using the distributive property, and we got: (25*z)*(31*z**2) + (25*z)*(-40*z**3)\nReplacing (25*z)*(-40*z**3 + 31*z**2) with (25*z)*(31*z**2) + (25*z)*(-40*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (25*z)*(31*z**2) + (25*z)*(-40*z**3) + (-49*z**2)*(31*z**2) + (-49*z**2)*(-40*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*z**3)*(-49*z**2) = 1960*z**5\n (-40*z**3)*(25*z) = -1000*z**4\n (31*z**2)*(-49*z**2) = -1519*z**4\n (31*z**2)*(25*z) = 775*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1960*z**5 - 1519*z**4 - 1000*z**4 + 775*z**3\nCombining like terms, got 1960*z**5 - 2519*z**4 + 775*z**3\n#Step 6:\nCurrent expression: 1960*z**5 - 2519*z**4 + 775*z**3\nNo more calculations needed.\n1960*z**5 - 2519*z**4 + 775*z**3", "generated_answer": "1960*z**5 - 2519*z**4 + 775*z**3", "step_length": 6} {"cot_id": "7cdd802c36325f03f52fc565a1adc2884ac65be2cb39c501fb0d6377db1091ff", "datapoint": {"question": "Simplify this expression: (35*z**3 - 35*z)*(52*z**3 - 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1820*z**6 - 1820*z**4 - 245*z**3 + 245*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1329, "polynomial_expr": "(35*z**3 - 35*z)*(52*z**3 - 7)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (35*z**3 - 35*z)*(52*z**3 - 7)\nExpanding the part (52*z**3 - 7) using the distributive property, and we got: (52*z**3)*(35*z**3 - 35*z) - 7*(35*z**3 - 35*z)\n#Step 2:\nCurrent expression: (52*z**3)*(35*z**3 - 35*z) - 7*(35*z**3 - 35*z)\nSimplifying the partial expression: -7*(35*z**3 - 35*z)\nExpanding the part (35*z**3 - 35*z) using the distributive property, and we got: -35*z*(-7) + (35*z**3)*(-7)\nReplacing -7*(35*z**3 - 35*z) with -35*z*(-7) + (35*z**3)*(-7) in the overall expression.\n#Step 3:\nCurrent expression: -35*z*(-7) + (35*z**3)*(-7) + (52*z**3)*(35*z**3 - 35*z)\nSimplifying the partial expression: (52*z**3)*(35*z**3 - 35*z)\nExpanding the part (35*z**3 - 35*z) using the distributive property, and we got: (-35*z)*(52*z**3) + (35*z**3)*(52*z**3)\nReplacing (52*z**3)*(35*z**3 - 35*z) with (-35*z)*(52*z**3) + (35*z**3)*(52*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-35*z)*(52*z**3) - 35*z*(-7) + (35*z**3)*(52*z**3) + (35*z**3)*(-7)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*z)*-7 = 245*z\n (-35*z)*(52*z**3) = -1820*z**4\n (35*z**3)*-7 = -245*z**3\n (35*z**3)*(52*z**3) = 1820*z**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1820*z**6 - 1820*z**4 - 245*z**3 + 245*z\nNo more calculations needed.\n1820*z**6 - 1820*z**4 - 245*z**3 + 245*z", "generated_answer": "1820*z**6 - 1820*z**4 - 245*z**3 + 245*z", "step_length": 5} {"cot_id": "1ac8bee0406c700fb5bae2a01c33b594ac20c920078b7f5201cc96d2b38c1a0b", "datapoint": {"question": "Simplify this expression: (17*z**2 + 100*z)*(53*z**2 - 48*z + 37)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "901*z**4 + 4484*z**3 - 4171*z**2 + 3700*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1330, "polynomial_expr": "(17*z**2 + 100*z)*(53*z**2 - 48*z + 37)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (17*z**2 + 100*z)*(53*z**2 - 48*z + 37)\nExpanding the part (17*z**2 + 100*z) using the distributive property, and we got: (100*z)*(53*z**2 - 48*z + 37) + (17*z**2)*(53*z**2 - 48*z + 37)\n#Step 2:\nCurrent expression: (100*z)*(53*z**2 - 48*z + 37) + (17*z**2)*(53*z**2 - 48*z + 37)\nSimplifying the partial expression: (17*z**2)*(53*z**2 - 48*z + 37)\nExpanding the part (53*z**2 - 48*z + 37) using the distributive property, and we got: (-48*z)*(17*z**2) + 37*(17*z**2) + (17*z**2)*(53*z**2)\nReplacing (17*z**2)*(53*z**2 - 48*z + 37) with (-48*z)*(17*z**2) + 37*(17*z**2) + (17*z**2)*(53*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-48*z)*(17*z**2) + 37*17*z**2 + (100*z)*(53*z**2 - 48*z + 37) + (17*z**2)*(53*z**2)\nSimplifying the partial expression: (100*z)*(53*z**2 - 48*z + 37)\nExpanding the part (53*z**2 - 48*z + 37) using the distributive property, and we got: (-48*z)*(100*z) + 37*(100*z) + (100*z)*(53*z**2)\nReplacing (100*z)*(53*z**2 - 48*z + 37) with (-48*z)*(100*z) + 37*(100*z) + (100*z)*(53*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-48*z)*(100*z) + (-48*z)*(17*z**2) + 37*17*z**2 + 37*100*z + (100*z)*(53*z**2) + (17*z**2)*(53*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*z)*(17*z**2) = -816*z**3\n (-48*z)*(100*z) = -4800*z**2\n (53*z**2)*(17*z**2) = 901*z**4\n (53*z**2)*(100*z) = 5300*z**3\n 37*17*z**2 = 629*z**2\n 37*100*z = 3700*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 901*z**4 - 816*z**3 + 5300*z**3 - 4800*z**2 + 629*z**2 + 3700*z\nCombining like terms, got 901*z**4 + 4484*z**3 - 4171*z**2 + 3700*z\n#Step 6:\nCurrent expression: 901*z**4 + 4484*z**3 - 4171*z**2 + 3700*z\nNo more calculations needed.\n901*z**4 + 4484*z**3 - 4171*z**2 + 3700*z", "generated_answer": "901*z**4 + 4484*z**3 - 4171*z**2 + 3700*z", "step_length": 6} {"cot_id": "639f9d1e5789544e111117fede7b531f303436d3c389a79a8630e4cdadc28a14", "datapoint": {"question": "Calculate the following: 512 - 576*x\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "512 - 576*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1331, "polynomial_expr": "512 - 576*x", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 512 - 576*x\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 512 - 576*x\nNo more calculations needed.\n512 - 576*x", "generated_answer": "512 - 576*x", "step_length": 2} {"cot_id": "d71ba43c542552171dc14a3be737a2cba5c6aa1c8c87491dfd2a7d7a0988b288", "datapoint": {"question": "Calculate the following: -21*x*(30*x**3 + 93*x + 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-630*x**4 - 1953*x**2 - 861*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1332, "polynomial_expr": "-21*x*(30*x**3 + 93*x + 41)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -21*x*(30*x**3 + 93*x + 41)\nExpanding the part (30*x**3 + 93*x + 41) using the distributive property, and we got: (-21*x)*(93*x) + (-21*x)*(30*x**3) + 41*(-21*x)\n#Step 2:\nCurrent expression: (-21*x)*(93*x) + (-21*x)*(30*x**3) + 41*(-21*x)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 41*(-21*x) = -861*x\n (30*x**3)*(-21*x) = -630*x**4\n (93*x)*(-21*x) = -1953*x**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -630*x**4 - 1953*x**2 - 861*x\nNo more calculations needed.\n-630*x**4 - 1953*x**2 - 861*x", "generated_answer": "-630*x**4 - 1953*x**2 - 861*x", "step_length": 3} {"cot_id": "9650631525c52ebd490ce64b325f2cc6a00e39d458cce4cce052f9fb896f269e", "datapoint": {"question": "Calculate the following: (-38*x**3 - 29*x**2)*(19*x**3 - 7*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-722*x**6 - 551*x**5 + 266*x**4 + 203*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1333, "polynomial_expr": "(-38*x**3 - 29*x**2)*(19*x**3 - 7*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-38*x**3 - 29*x**2)*(19*x**3 - 7*x)\nExpanding the part (-38*x**3 - 29*x**2) using the distributive property, and we got: (-29*x**2)*(19*x**3 - 7*x) + (-38*x**3)*(19*x**3 - 7*x)\n#Step 2:\nCurrent expression: (-29*x**2)*(19*x**3 - 7*x) + (-38*x**3)*(19*x**3 - 7*x)\nSimplifying the partial expression: (-38*x**3)*(19*x**3 - 7*x)\nExpanding the part (19*x**3 - 7*x) using the distributive property, and we got: (-7*x)*(-38*x**3) + (-38*x**3)*(19*x**3)\nReplacing (-38*x**3)*(19*x**3 - 7*x) with (-7*x)*(-38*x**3) + (-38*x**3)*(19*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-7*x)*(-38*x**3) + (-29*x**2)*(19*x**3 - 7*x) + (-38*x**3)*(19*x**3)\nSimplifying the partial expression: (-29*x**2)*(19*x**3 - 7*x)\nExpanding the part (19*x**3 - 7*x) using the distributive property, and we got: (-7*x)*(-29*x**2) + (-29*x**2)*(19*x**3)\nReplacing (-29*x**2)*(19*x**3 - 7*x) with (-7*x)*(-29*x**2) + (-29*x**2)*(19*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-7*x)*(-29*x**2) + (-7*x)*(-38*x**3) + (-29*x**2)*(19*x**3) + (-38*x**3)*(19*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-7*x)*(-38*x**3) = 266*x**4\n (-7*x)*(-29*x**2) = 203*x**3\n (19*x**3)*(-38*x**3) = -722*x**6\n (19*x**3)*(-29*x**2) = -551*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -722*x**6 - 551*x**5 + 266*x**4 + 203*x**3\nNo more calculations needed.\n-722*x**6 - 551*x**5 + 266*x**4 + 203*x**3", "generated_answer": "-722*x**6 - 551*x**5 + 266*x**4 + 203*x**3", "step_length": 5} {"cot_id": "327f297369dbc90f0c719bd833107f7ca5153e8e9d85d9c8515b846e10a8b35c", "datapoint": {"question": "Calculate the following: (-14*y - 32)*(-47*y**3 - 9*y**2 + 34*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "658*y**4 + 1630*y**3 - 188*y**2 - 1088*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1334, "polynomial_expr": "(-14*y - 32)*(-47*y**3 - 9*y**2 + 34*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-14*y - 32)*(-47*y**3 - 9*y**2 + 34*y)\nExpanding the part (-14*y - 32) using the distributive property, and we got: (-14*y)*(-47*y**3 - 9*y**2 + 34*y) - 32*(-47*y**3 - 9*y**2 + 34*y)\n#Step 2:\nCurrent expression: (-14*y)*(-47*y**3 - 9*y**2 + 34*y) - 32*(-47*y**3 - 9*y**2 + 34*y)\nSimplifying the partial expression: -32*(-47*y**3 - 9*y**2 + 34*y)\nExpanding the part (-47*y**3 - 9*y**2 + 34*y) using the distributive property, and we got: (34*y)*(-32) - 9*y**2*(-32) - 47*y**3*(-32)\nReplacing -32*(-47*y**3 - 9*y**2 + 34*y) with (34*y)*(-32) - 9*y**2*(-32) - 47*y**3*(-32) in the overall expression.\n#Step 3:\nCurrent expression: (-14*y)*(-47*y**3 - 9*y**2 + 34*y) + (34*y)*(-32) - 9*y**2*(-32) - 47*y**3*(-32)\nSimplifying the partial expression: (-14*y)*(-47*y**3 - 9*y**2 + 34*y)\nExpanding the part (-47*y**3 - 9*y**2 + 34*y) using the distributive property, and we got: (-14*y)*(34*y) + (-14*y)*(-9*y**2) + (-14*y)*(-47*y**3)\nReplacing (-14*y)*(-47*y**3 - 9*y**2 + 34*y) with (-14*y)*(34*y) + (-14*y)*(-9*y**2) + (-14*y)*(-47*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-14*y)*(34*y) + (-14*y)*(-9*y**2) + (-14*y)*(-47*y**3) + (34*y)*(-32) - 9*y**2*(-32) - 47*y**3*(-32)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*y**3)*-32 = 1504*y**3\n (-47*y**3)*(-14*y) = 658*y**4\n (-9*y**2)*-32 = 288*y**2\n (-9*y**2)*(-14*y) = 126*y**3\n (34*y)*-32 = -1088*y\n (34*y)*(-14*y) = -476*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 658*y**4 + 126*y**3 + 1504*y**3 - 476*y**2 + 288*y**2 - 1088*y\nCombining like terms, got 658*y**4 + 1630*y**3 - 188*y**2 - 1088*y\n#Step 6:\nCurrent expression: 658*y**4 + 1630*y**3 - 188*y**2 - 1088*y\nNo more calculations needed.\n658*y**4 + 1630*y**3 - 188*y**2 - 1088*y", "generated_answer": "658*y**4 + 1630*y**3 - 188*y**2 - 1088*y", "step_length": 6} {"cot_id": "56ccbc10d90379ba5e8a1a4f0d5838d1567bee2d9b76d30a5f4a4bcb111694a0", "datapoint": {"question": "Simplify this expression: 75*x**3*(14*x**3 - 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1050*x**6 - 1050*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1335, "polynomial_expr": "75*x**3*(14*x**3 - 14)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 75*x**3*(14*x**3 - 14)\nExpanding the part (14*x**3 - 14) using the distributive property, and we got: -1050*x**3 + (14*x**3)*(75*x**3)\n#Step 2:\nCurrent expression: -1050*x**3 + (14*x**3)*(75*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -14*(75*x**3) = -1050*x**3\n (14*x**3)*(75*x**3) = 1050*x**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1050*x**6 - 1050*x**3\nNo more calculations needed.\n1050*x**6 - 1050*x**3", "generated_answer": "1050*x**6 - 1050*x**3", "step_length": 3} {"cot_id": "020c8cc68d80c3fe342dbfcd0b25073e7eefe5e04bb277a0c77b911ec7ab578d", "datapoint": {"question": "Simplify this expression: (15 - 20*x**3)*(-36*x**2 - 26)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "720*x**5 + 520*x**3 - 540*x**2 - 390", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1336, "polynomial_expr": "(15 - 20*x**3)*(-36*x**2 - 26)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (15 - 20*x**3)*(-36*x**2 - 26)\nExpanding the part (-36*x**2 - 26) using the distributive property, and we got: (-36*x**2)*(15 - 20*x**3) - 26*(15 - 20*x**3)\n#Step 2:\nCurrent expression: (-36*x**2)*(15 - 20*x**3) - 26*(15 - 20*x**3)\nSimplifying the partial expression: -26*(15 - 20*x**3)\nExpanding the part (15 - 20*x**3) using the distributive property, and we got: -20*x**3*(-26) + 15*(-26)\nReplacing -26*(15 - 20*x**3) with -20*x**3*(-26) + 15*(-26) in the overall expression.\n#Step 3:\nCurrent expression: (-36*x**2)*(15 - 20*x**3) - 20*x**3*(-26) - 390\nSimplifying the partial expression: (-36*x**2)*(15 - 20*x**3)\nExpanding the part (15 - 20*x**3) using the distributive property, and we got: 15*(-36*x**2) + (-36*x**2)*(-20*x**3)\nReplacing (-36*x**2)*(15 - 20*x**3) with 15*(-36*x**2) + (-36*x**2)*(-20*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 15*(-36)*x**2 + (-36*x**2)*(-20*x**3) - 20*x**3*(-26) - 390\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*x**3)*-26 = 520*x**3\n (-20*x**3)*(-36*x**2) = 720*x**5\n 15*-36*x**2 = -540*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 720*x**5 + 520*x**3 - 540*x**2 - 390\nNo more calculations needed.\n720*x**5 + 520*x**3 - 540*x**2 - 390", "generated_answer": "720*x**5 + 520*x**3 - 540*x**2 - 390", "step_length": 5} {"cot_id": "780dfbdf4cbf9848e5a1f984c4d098192bd83bf79c62377c9f7fa16044ae9234", "datapoint": {"question": "Simplify this expression: (46*z**2 + 22*z)*(3*z**3 + 45*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "138*z**5 + 2136*z**4 + 990*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1337, "polynomial_expr": "(46*z**2 + 22*z)*(3*z**3 + 45*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (46*z**2 + 22*z)*(3*z**3 + 45*z**2)\nExpanding the part (3*z**3 + 45*z**2) using the distributive property, and we got: (45*z**2)*(46*z**2 + 22*z) + (3*z**3)*(46*z**2 + 22*z)\n#Step 2:\nCurrent expression: (45*z**2)*(46*z**2 + 22*z) + (3*z**3)*(46*z**2 + 22*z)\nSimplifying the partial expression: (3*z**3)*(46*z**2 + 22*z)\nExpanding the part (46*z**2 + 22*z) using the distributive property, and we got: (22*z)*(3*z**3) + (46*z**2)*(3*z**3)\nReplacing (3*z**3)*(46*z**2 + 22*z) with (22*z)*(3*z**3) + (46*z**2)*(3*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (22*z)*(3*z**3) + (45*z**2)*(46*z**2 + 22*z) + (46*z**2)*(3*z**3)\nSimplifying the partial expression: (45*z**2)*(46*z**2 + 22*z)\nExpanding the part (46*z**2 + 22*z) using the distributive property, and we got: (22*z)*(45*z**2) + (45*z**2)*(46*z**2)\nReplacing (45*z**2)*(46*z**2 + 22*z) with (22*z)*(45*z**2) + (45*z**2)*(46*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (22*z)*(45*z**2) + (22*z)*(3*z**3) + (45*z**2)*(46*z**2) + (46*z**2)*(3*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (22*z)*(3*z**3) = 66*z**4\n (22*z)*(45*z**2) = 990*z**3\n (46*z**2)*(3*z**3) = 138*z**5\n (46*z**2)*(45*z**2) = 2070*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 138*z**5 + 66*z**4 + 2070*z**4 + 990*z**3\nCombining like terms, got 138*z**5 + 2136*z**4 + 990*z**3\n#Step 6:\nCurrent expression: 138*z**5 + 2136*z**4 + 990*z**3\nNo more calculations needed.\n138*z**5 + 2136*z**4 + 990*z**3", "generated_answer": "138*z**5 + 2136*z**4 + 990*z**3", "step_length": 6} {"cot_id": "4908d96625f6d1aa1d0aa7e137c4edc937a2065f5cc42b20023f76e18497f08f", "datapoint": {"question": "Calculate the following: -115*z**2 + 90*z\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-115*z**2 + 90*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1338, "polynomial_expr": "-115*z**2 + 90*z", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -115*z**2 + 90*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -115*z**2 + 90*z\nNo more calculations needed.\n-115*z**2 + 90*z", "generated_answer": "-115*z**2 + 90*z", "step_length": 2} {"cot_id": "f6c9012fb9069d79fcadee7523f00b90e00115685440073aecd6af4a2f20fb22", "datapoint": {"question": "Calculate the following: (18*z**3 + 30*z**2)*(-48*z**3 + 16*z**2 - 4*z - 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-864*z**6 - 1152*z**5 + 408*z**4 - 624*z**3 - 840*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1339, "polynomial_expr": "(18*z**3 + 30*z**2)*(-48*z**3 + 16*z**2 - 4*z - 28)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (18*z**3 + 30*z**2)*(-48*z**3 + 16*z**2 - 4*z - 28)\nExpanding the part (18*z**3 + 30*z**2) using the distributive property, and we got: (30*z**2)*(-48*z**3 + 16*z**2 - 4*z - 28) + (18*z**3)*(-48*z**3 + 16*z**2 - 4*z - 28)\n#Step 2:\nCurrent expression: (30*z**2)*(-48*z**3 + 16*z**2 - 4*z - 28) + (18*z**3)*(-48*z**3 + 16*z**2 - 4*z - 28)\nSimplifying the partial expression: (18*z**3)*(-48*z**3 + 16*z**2 - 4*z - 28)\nExpanding the part (-48*z**3 + 16*z**2 - 4*z - 28) using the distributive property, and we got: (-4*z)*(18*z**3) - 504*z**3 + (16*z**2)*(18*z**3) + (-48*z**3)*(18*z**3)\nReplacing (18*z**3)*(-48*z**3 + 16*z**2 - 4*z - 28) with (-4*z)*(18*z**3) - 504*z**3 + (16*z**2)*(18*z**3) + (-48*z**3)*(18*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-4*z)*(18*z**3) - 28*18*z**3 + (16*z**2)*(18*z**3) + (30*z**2)*(-48*z**3 + 16*z**2 - 4*z - 28) + (-48*z**3)*(18*z**3)\nSimplifying the partial expression: (30*z**2)*(-48*z**3 + 16*z**2 - 4*z - 28)\nExpanding the part (-48*z**3 + 16*z**2 - 4*z - 28) using the distributive property, and we got: (-4*z)*(30*z**2) - 840*z**2 + (16*z**2)*(30*z**2) + (30*z**2)*(-48*z**3)\nReplacing (30*z**2)*(-48*z**3 + 16*z**2 - 4*z - 28) with (-4*z)*(30*z**2) - 840*z**2 + (16*z**2)*(30*z**2) + (30*z**2)*(-48*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-4*z)*(30*z**2) + (-4*z)*(18*z**3) - 28*18*z**3 - 28*30*z**2 + (16*z**2)*(30*z**2) + (16*z**2)*(18*z**3) + (30*z**2)*(-48*z**3) + (-48*z**3)*(18*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*z**3)*(18*z**3) = -864*z**6\n (-48*z**3)*(30*z**2) = -1440*z**5\n (-4*z)*(18*z**3) = -72*z**4\n (-4*z)*(30*z**2) = -120*z**3\n (16*z**2)*(18*z**3) = 288*z**5\n (16*z**2)*(30*z**2) = 480*z**4\n -28*18*z**3 = -504*z**3\n -28*30*z**2 = -840*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -864*z**6 - 1440*z**5 + 288*z**5 - 72*z**4 + 480*z**4 - 504*z**3 - 120*z**3 - 840*z**2\nCombining like terms, got -864*z**6 - 1152*z**5 + 408*z**4 - 624*z**3 - 840*z**2\n#Step 6:\nCurrent expression: -864*z**6 - 1152*z**5 + 408*z**4 - 624*z**3 - 840*z**2\nNo more calculations needed.\n-864*z**6 - 1152*z**5 + 408*z**4 - 624*z**3 - 840*z**2", "generated_answer": "-864*z**6 - 1152*z**5 + 408*z**4 - 624*z**3 - 840*z**2", "step_length": 6} {"cot_id": "dd625e151620dc9078a30acbd9a65cf3ab5e87cc57fd5c24b1265d7d0a3ddfe4", "datapoint": {"question": "Simplify this expression: (9*z**3 + 16*z)*(22*z**3 - 38*z**2 + 30*z - 27)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "198*z**6 - 342*z**5 + 622*z**4 - 851*z**3 + 480*z**2 - 432*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1340, "polynomial_expr": "(9*z**3 + 16*z)*(22*z**3 - 38*z**2 + 30*z - 27)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9*z**3 + 16*z)*(22*z**3 - 38*z**2 + 30*z - 27)\nExpanding the part (9*z**3 + 16*z) using the distributive property, and we got: (16*z)*(22*z**3 - 38*z**2 + 30*z - 27) + (9*z**3)*(22*z**3 - 38*z**2 + 30*z - 27)\n#Step 2:\nCurrent expression: (16*z)*(22*z**3 - 38*z**2 + 30*z - 27) + (9*z**3)*(22*z**3 - 38*z**2 + 30*z - 27)\nSimplifying the partial expression: (9*z**3)*(22*z**3 - 38*z**2 + 30*z - 27)\nExpanding the part (22*z**3 - 38*z**2 + 30*z - 27) using the distributive property, and we got: -243*z**3 + (30*z)*(9*z**3) + (-38*z**2)*(9*z**3) + (9*z**3)*(22*z**3)\nReplacing (9*z**3)*(22*z**3 - 38*z**2 + 30*z - 27) with -243*z**3 + (30*z)*(9*z**3) + (-38*z**2)*(9*z**3) + (9*z**3)*(22*z**3) in the overall expression.\n#Step 3:\nCurrent expression: -27*9*z**3 + (16*z)*(22*z**3 - 38*z**2 + 30*z - 27) + (30*z)*(9*z**3) + (-38*z**2)*(9*z**3) + (9*z**3)*(22*z**3)\nSimplifying the partial expression: (16*z)*(22*z**3 - 38*z**2 + 30*z - 27)\nExpanding the part (22*z**3 - 38*z**2 + 30*z - 27) using the distributive property, and we got: -432*z + (16*z)*(30*z) + (16*z)*(-38*z**2) + (16*z)*(22*z**3)\nReplacing (16*z)*(22*z**3 - 38*z**2 + 30*z - 27) with -432*z + (16*z)*(30*z) + (16*z)*(-38*z**2) + (16*z)*(22*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -27*9*z**3 - 27*16*z + (16*z)*(30*z) + (16*z)*(-38*z**2) + (16*z)*(22*z**3) + (30*z)*(9*z**3) + (-38*z**2)*(9*z**3) + (9*z**3)*(22*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*z**2)*(9*z**3) = -342*z**5\n (-38*z**2)*(16*z) = -608*z**3\n (22*z**3)*(9*z**3) = 198*z**6\n (22*z**3)*(16*z) = 352*z**4\n (30*z)*(9*z**3) = 270*z**4\n (30*z)*(16*z) = 480*z**2\n -27*9*z**3 = -243*z**3\n -27*16*z = -432*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 198*z**6 - 342*z**5 + 270*z**4 + 352*z**4 - 608*z**3 - 243*z**3 + 480*z**2 - 432*z\nCombining like terms, got 198*z**6 - 342*z**5 + 622*z**4 - 851*z**3 + 480*z**2 - 432*z\n#Step 6:\nCurrent expression: 198*z**6 - 342*z**5 + 622*z**4 - 851*z**3 + 480*z**2 - 432*z\nNo more calculations needed.\n198*z**6 - 342*z**5 + 622*z**4 - 851*z**3 + 480*z**2 - 432*z", "generated_answer": "198*z**6 - 342*z**5 + 622*z**4 - 851*z**3 + 480*z**2 - 432*z", "step_length": 6} {"cot_id": "0de3f63c64253e33426d913f741e048ab3ca5e81ad38acdd8c6a329ca5dea15c", "datapoint": {"question": "Simplify this expression: (23*x**3 + 36*x - 50)*(23*x**3 - 61*x**2 - 26)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "529*x**6 - 1403*x**5 + 828*x**4 - 3944*x**3 + 3050*x**2 - 936*x + 1300", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1341, "polynomial_expr": "(23*x**3 + 36*x - 50)*(23*x**3 - 61*x**2 - 26)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (23*x**3 + 36*x - 50)*(23*x**3 - 61*x**2 - 26)\nExpanding the part (23*x**3 + 36*x - 50) using the distributive property, and we got: (36*x)*(23*x**3 - 61*x**2 - 26) + (23*x**3)*(23*x**3 - 61*x**2 - 26) - 50*(23*x**3 - 61*x**2 - 26)\n#Step 2:\nCurrent expression: (36*x)*(23*x**3 - 61*x**2 - 26) + (23*x**3)*(23*x**3 - 61*x**2 - 26) - 50*(23*x**3 - 61*x**2 - 26)\nSimplifying the partial expression: -50*(23*x**3 - 61*x**2 - 26)\nExpanding the part (23*x**3 - 61*x**2 - 26) using the distributive property, and we got: -61*x**2*(-50) + (23*x**3)*(-50) - 26*(-50)\nReplacing -50*(23*x**3 - 61*x**2 - 26) with -61*x**2*(-50) + (23*x**3)*(-50) - 26*(-50) in the overall expression.\n#Step 3:\nCurrent expression: (36*x)*(23*x**3 - 61*x**2 - 26) - 61*x**2*(-50) + (23*x**3)*(23*x**3 - 61*x**2 - 26) + (23*x**3)*(-50) + 1300\nSimplifying the partial expression: (23*x**3)*(23*x**3 - 61*x**2 - 26)\nExpanding the part (23*x**3 - 61*x**2 - 26) using the distributive property, and we got: -598*x**3 + (-61*x**2)*(23*x**3) + (23*x**3)*(23*x**3)\nReplacing (23*x**3)*(23*x**3 - 61*x**2 - 26) with -598*x**3 + (-61*x**2)*(23*x**3) + (23*x**3)*(23*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -26*23*x**3 + (36*x)*(23*x**3 - 61*x**2 - 26) + (-61*x**2)*(23*x**3) - 61*x**2*(-50) + (23*x**3)*(-50) + (23*x**3)*(23*x**3) + 1300\nSimplifying the partial expression: (36*x)*(23*x**3 - 61*x**2 - 26)\nExpanding the part (23*x**3 - 61*x**2 - 26) using the distributive property, and we got: -936*x + (36*x)*(-61*x**2) + (36*x)*(23*x**3)\nReplacing (36*x)*(23*x**3 - 61*x**2 - 26) with -936*x + (36*x)*(-61*x**2) + (36*x)*(23*x**3) in the overall expression.\n#Step 5:\nCurrent expression: -26*23*x**3 - 26*36*x + (36*x)*(-61*x**2) + (36*x)*(23*x**3) + (-61*x**2)*(23*x**3) - 61*x**2*(-50) + (23*x**3)*(-50) + (23*x**3)*(23*x**3) + 1300\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-61*x**2)*-50 = 3050*x**2\n (-61*x**2)*(23*x**3) = -1403*x**5\n (-61*x**2)*(36*x) = -2196*x**3\n (23*x**3)*-50 = -1150*x**3\n (23*x**3)*(23*x**3) = 529*x**6\n (23*x**3)*(36*x) = 828*x**4\n -26*23*x**3 = -598*x**3\n -26*36*x = -936*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 529*x**6 - 1403*x**5 + 828*x**4 - 2196*x**3 - 1150*x**3 - 598*x**3 + 3050*x**2 - 936*x + 1300\nCombining like terms, got 529*x**6 - 1403*x**5 + 828*x**4 - 3944*x**3 + 3050*x**2 - 936*x + 1300\n#Step 7:\nCurrent expression: 529*x**6 - 1403*x**5 + 828*x**4 - 3944*x**3 + 3050*x**2 - 936*x + 1300\nNo more calculations needed.\n529*x**6 - 1403*x**5 + 828*x**4 - 3944*x**3 + 3050*x**2 - 936*x + 1300", "generated_answer": "529*x**6 - 1403*x**5 + 828*x**4 - 3944*x**3 + 3050*x**2 - 936*x + 1300", "step_length": 7} {"cot_id": "9f0642b1611713bf8d6d72abb261d6fde6360c2adc9eeca39416ff13041d8e2e", "datapoint": {"question": "Calculate the following: (11 - y**2)*(-32*y**3 + 70*y + 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "32*y**5 - 422*y**3 - 49*y**2 + 770*y + 539", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1342, "polynomial_expr": "(11 - y**2)*(-32*y**3 + 70*y + 49)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11 - y**2)*(-32*y**3 + 70*y + 49)\nExpanding the part (11 - y**2) using the distributive property, and we got: (-y**2)*(-32*y**3 + 70*y + 49) + 11*(-32*y**3 + 70*y + 49)\n#Step 2:\nCurrent expression: (-y**2)*(-32*y**3 + 70*y + 49) + 11*(-32*y**3 + 70*y + 49)\nSimplifying the partial expression: 11*(-32*y**3 + 70*y + 49)\nExpanding the part (-32*y**3 + 70*y + 49) using the distributive property, and we got: (70*y)*11 - 32*y**3*11 + 49*11\nReplacing 11*(-32*y**3 + 70*y + 49) with (70*y)*11 - 32*y**3*11 + 49*11 in the overall expression.\n#Step 3:\nCurrent expression: (70*y)*11 + (-y**2)*(-32*y**3 + 70*y + 49) - 32*y**3*11 + 539\nSimplifying the partial expression: (-y**2)*(-32*y**3 + 70*y + 49)\nExpanding the part (-32*y**3 + 70*y + 49) using the distributive property, and we got: 49*(-y**2) + (70*y)*(-y**2) + (-y**2)*(-32*y**3)\nReplacing (-y**2)*(-32*y**3 + 70*y + 49) with 49*(-y**2) + (70*y)*(-y**2) + (-y**2)*(-32*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 49*(-1)*y**2 + (70*y)*(-y**2) + (70*y)*11 + (-y**2)*(-32*y**3) - 32*y**3*11 + 539\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*y**3)*11 = -352*y**3\n (-32*y**3)*(-y**2) = 32*y**5\n (70*y)*11 = 770*y\n (70*y)*(-y**2) = -70*y**3\n 49*-1*y**2 = -49*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 32*y**5 - 352*y**3 - 70*y**3 - 49*y**2 + 770*y + 539\nCombining like terms, got 32*y**5 - 422*y**3 - 49*y**2 + 770*y + 539\n#Step 6:\nCurrent expression: 32*y**5 - 422*y**3 - 49*y**2 + 770*y + 539\nNo more calculations needed.\n32*y**5 - 422*y**3 - 49*y**2 + 770*y + 539", "generated_answer": "32*y**5 - 422*y**3 - 49*y**2 + 770*y + 539", "step_length": 6} {"cot_id": "ce5ecba3f7a6f362813806f084b58bda1e24eff6d869cb12c6f7d60b202efcee", "datapoint": {"question": "Calculate the following: (5 - 11*x**3)*(31*x**2 + 3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-341*x**5 - 33*x**3 + 155*x**2 + 15", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1343, "polynomial_expr": "(5 - 11*x**3)*(31*x**2 + 3)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (5 - 11*x**3)*(31*x**2 + 3)\nExpanding the part (31*x**2 + 3) using the distributive property, and we got: (31*x**2)*(5 - 11*x**3) + 3*(5 - 11*x**3)\n#Step 2:\nCurrent expression: (31*x**2)*(5 - 11*x**3) + 3*(5 - 11*x**3)\nSimplifying the partial expression: 3*(5 - 11*x**3)\nExpanding the part (5 - 11*x**3) using the distributive property, and we got: -11*x**3*3 + 5*3\nReplacing 3*(5 - 11*x**3) with -11*x**3*3 + 5*3 in the overall expression.\n#Step 3:\nCurrent expression: (31*x**2)*(5 - 11*x**3) - 11*x**3*3 + 15\nSimplifying the partial expression: (31*x**2)*(5 - 11*x**3)\nExpanding the part (5 - 11*x**3) using the distributive property, and we got: 5*(31*x**2) + (31*x**2)*(-11*x**3)\nReplacing (31*x**2)*(5 - 11*x**3) with 5*(31*x**2) + (31*x**2)*(-11*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 5*31*x**2 + (31*x**2)*(-11*x**3) - 11*x**3*3 + 15\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*x**3)*3 = -33*x**3\n (-11*x**3)*(31*x**2) = -341*x**5\n 5*31*x**2 = 155*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -341*x**5 - 33*x**3 + 155*x**2 + 15\nNo more calculations needed.\n-341*x**5 - 33*x**3 + 155*x**2 + 15", "generated_answer": "-341*x**5 - 33*x**3 + 155*x**2 + 15", "step_length": 5} {"cot_id": "84cb982ae9b578c0b61579147a5109933b16ff6bad94987b93b8316304bea917", "datapoint": {"question": "Calculate the following: (-81*z**3 - 46)*(-22*z**3 - 10*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1782*z**6 + 810*z**4 + 1012*z**3 + 460*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1344, "polynomial_expr": "(-81*z**3 - 46)*(-22*z**3 - 10*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-81*z**3 - 46)*(-22*z**3 - 10*z)\nExpanding the part (-81*z**3 - 46) using the distributive property, and we got: (-81*z**3)*(-22*z**3 - 10*z) - 46*(-22*z**3 - 10*z)\n#Step 2:\nCurrent expression: (-81*z**3)*(-22*z**3 - 10*z) - 46*(-22*z**3 - 10*z)\nSimplifying the partial expression: -46*(-22*z**3 - 10*z)\nExpanding the part (-22*z**3 - 10*z) using the distributive property, and we got: -10*z*(-46) - 22*z**3*(-46)\nReplacing -46*(-22*z**3 - 10*z) with -10*z*(-46) - 22*z**3*(-46) in the overall expression.\n#Step 3:\nCurrent expression: -10*z*(-46) + (-81*z**3)*(-22*z**3 - 10*z) - 22*z**3*(-46)\nSimplifying the partial expression: (-81*z**3)*(-22*z**3 - 10*z)\nExpanding the part (-22*z**3 - 10*z) using the distributive property, and we got: (-10*z)*(-81*z**3) + (-81*z**3)*(-22*z**3)\nReplacing (-81*z**3)*(-22*z**3 - 10*z) with (-10*z)*(-81*z**3) + (-81*z**3)*(-22*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-10*z)*(-81*z**3) - 10*z*(-46) + (-81*z**3)*(-22*z**3) - 22*z**3*(-46)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*z**3)*-46 = 1012*z**3\n (-22*z**3)*(-81*z**3) = 1782*z**6\n (-10*z)*-46 = 460*z\n (-10*z)*(-81*z**3) = 810*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1782*z**6 + 810*z**4 + 1012*z**3 + 460*z\nNo more calculations needed.\n1782*z**6 + 810*z**4 + 1012*z**3 + 460*z", "generated_answer": "1782*z**6 + 810*z**4 + 1012*z**3 + 460*z", "step_length": 5} {"cot_id": "74df5cfd4336a53579df46a99df1b57ccd94843b6028ea476b4655aecfddd511", "datapoint": {"question": "Simplify this expression: (-59*x**3 + 11*x**2)*(42*x**3 - 30*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2478*x**6 + 2232*x**5 - 330*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1345, "polynomial_expr": "(-59*x**3 + 11*x**2)*(42*x**3 - 30*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-59*x**3 + 11*x**2)*(42*x**3 - 30*x**2)\nExpanding the part (-59*x**3 + 11*x**2) using the distributive property, and we got: (11*x**2)*(42*x**3 - 30*x**2) + (-59*x**3)*(42*x**3 - 30*x**2)\n#Step 2:\nCurrent expression: (11*x**2)*(42*x**3 - 30*x**2) + (-59*x**3)*(42*x**3 - 30*x**2)\nSimplifying the partial expression: (-59*x**3)*(42*x**3 - 30*x**2)\nExpanding the part (42*x**3 - 30*x**2) using the distributive property, and we got: (-30*x**2)*(-59*x**3) + (-59*x**3)*(42*x**3)\nReplacing (-59*x**3)*(42*x**3 - 30*x**2) with (-30*x**2)*(-59*x**3) + (-59*x**3)*(42*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-30*x**2)*(-59*x**3) + (11*x**2)*(42*x**3 - 30*x**2) + (-59*x**3)*(42*x**3)\nSimplifying the partial expression: (11*x**2)*(42*x**3 - 30*x**2)\nExpanding the part (42*x**3 - 30*x**2) using the distributive property, and we got: (-30*x**2)*(11*x**2) + (11*x**2)*(42*x**3)\nReplacing (11*x**2)*(42*x**3 - 30*x**2) with (-30*x**2)*(11*x**2) + (11*x**2)*(42*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-30*x**2)*(11*x**2) + (-30*x**2)*(-59*x**3) + (11*x**2)*(42*x**3) + (-59*x**3)*(42*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*x**2)*(-59*x**3) = 1770*x**5\n (-30*x**2)*(11*x**2) = -330*x**4\n (42*x**3)*(-59*x**3) = -2478*x**6\n (42*x**3)*(11*x**2) = 462*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2478*x**6 + 462*x**5 + 1770*x**5 - 330*x**4\nCombining like terms, got -2478*x**6 + 2232*x**5 - 330*x**4\n#Step 6:\nCurrent expression: -2478*x**6 + 2232*x**5 - 330*x**4\nNo more calculations needed.\n-2478*x**6 + 2232*x**5 - 330*x**4", "generated_answer": "-2478*x**6 + 2232*x**5 - 330*x**4", "step_length": 6} {"cot_id": "4d4408b4a118d4e52f48a132b55ad9c546c35a0703a178e2f56ac913c7ee4cb0", "datapoint": {"question": "Calculate the following: (-22*z**3 + 28*z**2)*(-2*z**3 - 13*z**2 - 8)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "44*z**6 + 230*z**5 - 364*z**4 + 176*z**3 - 224*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1346, "polynomial_expr": "(-22*z**3 + 28*z**2)*(-2*z**3 - 13*z**2 - 8)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-22*z**3 + 28*z**2)*(-2*z**3 - 13*z**2 - 8)\nExpanding the part (-22*z**3 + 28*z**2) using the distributive property, and we got: (28*z**2)*(-2*z**3 - 13*z**2 - 8) + (-22*z**3)*(-2*z**3 - 13*z**2 - 8)\n#Step 2:\nCurrent expression: (28*z**2)*(-2*z**3 - 13*z**2 - 8) + (-22*z**3)*(-2*z**3 - 13*z**2 - 8)\nSimplifying the partial expression: (-22*z**3)*(-2*z**3 - 13*z**2 - 8)\nExpanding the part (-2*z**3 - 13*z**2 - 8) using the distributive property, and we got: -(-1)*176*z**3 + (-13*z**2)*(-22*z**3) + (-22*z**3)*(-2*z**3)\nReplacing (-22*z**3)*(-2*z**3 - 13*z**2 - 8) with -(-1)*176*z**3 + (-13*z**2)*(-22*z**3) + (-22*z**3)*(-2*z**3) in the overall expression.\n#Step 3:\nCurrent expression: -8*(-22)*z**3 + (-13*z**2)*(-22*z**3) + (28*z**2)*(-2*z**3 - 13*z**2 - 8) + (-22*z**3)*(-2*z**3)\nSimplifying the partial expression: (28*z**2)*(-2*z**3 - 13*z**2 - 8)\nExpanding the part (-2*z**3 - 13*z**2 - 8) using the distributive property, and we got: -224*z**2 + (-13*z**2)*(28*z**2) + (28*z**2)*(-2*z**3)\nReplacing (28*z**2)*(-2*z**3 - 13*z**2 - 8) with -224*z**2 + (-13*z**2)*(28*z**2) + (28*z**2)*(-2*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -8*(-22)*z**3 - 8*28*z**2 + (-13*z**2)*(28*z**2) + (-13*z**2)*(-22*z**3) + (28*z**2)*(-2*z**3) + (-22*z**3)*(-2*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*z**2)*(-22*z**3) = 286*z**5\n (-13*z**2)*(28*z**2) = -364*z**4\n (-2*z**3)*(-22*z**3) = 44*z**6\n (-2*z**3)*(28*z**2) = -56*z**5\n -8*-22*z**3 = 176*z**3\n -8*28*z**2 = -224*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 44*z**6 - 56*z**5 + 286*z**5 - 364*z**4 + 176*z**3 - 224*z**2\nCombining like terms, got 44*z**6 + 230*z**5 - 364*z**4 + 176*z**3 - 224*z**2\n#Step 6:\nCurrent expression: 44*z**6 + 230*z**5 - 364*z**4 + 176*z**3 - 224*z**2\nNo more calculations needed.\n44*z**6 + 230*z**5 - 364*z**4 + 176*z**3 - 224*z**2", "generated_answer": "44*z**6 + 230*z**5 - 364*z**4 + 176*z**3 - 224*z**2", "step_length": 6} {"cot_id": "20b46138ef315800c2f2c53edbff65a7cf276d8b556ceb4c7906fc6985117310", "datapoint": {"question": "Simplify this expression: 6*x**4\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "6*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1347, "polynomial_expr": "6*x**4", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 6*x**4\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 6*x**4\nNo more calculations needed.\n6*x**4", "generated_answer": "6*x**4", "step_length": 2} {"cot_id": "ab5699b479930bbae1793e31ec234171102b4e7ed44571ed3fa05ccf62236cea", "datapoint": {"question": "Calculate the following: (-6*x**3 - 38*x**2)*(-16*x**3 - 28*x**2 - 32*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "96*x**6 + 776*x**5 + 1256*x**4 + 1216*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1348, "polynomial_expr": "(-6*x**3 - 38*x**2)*(-16*x**3 - 28*x**2 - 32*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-6*x**3 - 38*x**2)*(-16*x**3 - 28*x**2 - 32*x)\nExpanding the part (-6*x**3 - 38*x**2) using the distributive property, and we got: (-38*x**2)*(-16*x**3 - 28*x**2 - 32*x) + (-6*x**3)*(-16*x**3 - 28*x**2 - 32*x)\n#Step 2:\nCurrent expression: (-38*x**2)*(-16*x**3 - 28*x**2 - 32*x) + (-6*x**3)*(-16*x**3 - 28*x**2 - 32*x)\nSimplifying the partial expression: (-38*x**2)*(-16*x**3 - 28*x**2 - 32*x)\nExpanding the part (-16*x**3 - 28*x**2 - 32*x) using the distributive property, and we got: (-32*x)*(-38*x**2) + (-38*x**2)*(-28*x**2) + (-38*x**2)*(-16*x**3)\nReplacing (-38*x**2)*(-16*x**3 - 28*x**2 - 32*x) with (-32*x)*(-38*x**2) + (-38*x**2)*(-28*x**2) + (-38*x**2)*(-16*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-32*x)*(-38*x**2) + (-38*x**2)*(-28*x**2) + (-38*x**2)*(-16*x**3) + (-6*x**3)*(-16*x**3 - 28*x**2 - 32*x)\nSimplifying the partial expression: (-6*x**3)*(-16*x**3 - 28*x**2 - 32*x)\nExpanding the part (-16*x**3 - 28*x**2 - 32*x) using the distributive property, and we got: (-32*x)*(-6*x**3) + (-28*x**2)*(-6*x**3) + (-16*x**3)*(-6*x**3)\nReplacing (-6*x**3)*(-16*x**3 - 28*x**2 - 32*x) with (-32*x)*(-6*x**3) + (-28*x**2)*(-6*x**3) + (-16*x**3)*(-6*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-32*x)*(-38*x**2) + (-32*x)*(-6*x**3) + (-38*x**2)*(-28*x**2) + (-38*x**2)*(-16*x**3) + (-28*x**2)*(-6*x**3) + (-16*x**3)*(-6*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*x)*(-38*x**2) = 1216*x**3\n (-32*x)*(-6*x**3) = 192*x**4\n (-28*x**2)*(-38*x**2) = 1064*x**4\n (-28*x**2)*(-6*x**3) = 168*x**5\n (-16*x**3)*(-38*x**2) = 608*x**5\n (-16*x**3)*(-6*x**3) = 96*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 96*x**6 + 168*x**5 + 608*x**5 + 192*x**4 + 1064*x**4 + 1216*x**3\nCombining like terms, got 96*x**6 + 776*x**5 + 1256*x**4 + 1216*x**3\n#Step 6:\nCurrent expression: 96*x**6 + 776*x**5 + 1256*x**4 + 1216*x**3\nNo more calculations needed.\n96*x**6 + 776*x**5 + 1256*x**4 + 1216*x**3", "generated_answer": "96*x**6 + 776*x**5 + 1256*x**4 + 1216*x**3", "step_length": 6} {"cot_id": "78aefa358c4837833424ae1caad82a2a7bf474e361938ba87336f5c027f8bb97", "datapoint": {"question": "Calculate the following: (22*x**2 - 18*x)*(-11*x**3 + 14*x**2 - 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-242*x**5 + 506*x**4 - 252*x**3 - 22*x**2 + 18*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1349, "polynomial_expr": "(22*x**2 - 18*x)*(-11*x**3 + 14*x**2 - 1)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (22*x**2 - 18*x)*(-11*x**3 + 14*x**2 - 1)\nExpanding the part (22*x**2 - 18*x) using the distributive property, and we got: (-18*x)*(-11*x**3 + 14*x**2 - 1) + (22*x**2)*(-11*x**3 + 14*x**2 - 1)\n#Step 2:\nCurrent expression: (-18*x)*(-11*x**3 + 14*x**2 - 1) + (22*x**2)*(-11*x**3 + 14*x**2 - 1)\nSimplifying the partial expression: (-18*x)*(-11*x**3 + 14*x**2 - 1)\nExpanding the part (-11*x**3 + 14*x**2 - 1) using the distributive property, and we got: (-18*x)*(14*x**2) + (-18*x)*(-11*x**3) - (-1)*18*x\nReplacing (-18*x)*(-11*x**3 + 14*x**2 - 1) with (-18*x)*(14*x**2) + (-18*x)*(-11*x**3) - (-1)*18*x in the overall expression.\n#Step 3:\nCurrent expression: (-18*x)*(14*x**2) + (-18*x)*(-11*x**3) - 1*(-18)*x + (22*x**2)*(-11*x**3 + 14*x**2 - 1)\nSimplifying the partial expression: (22*x**2)*(-11*x**3 + 14*x**2 - 1)\nExpanding the part (-11*x**3 + 14*x**2 - 1) using the distributive property, and we got: -22*x**2 + (14*x**2)*(22*x**2) + (22*x**2)*(-11*x**3)\nReplacing (22*x**2)*(-11*x**3 + 14*x**2 - 1) with -22*x**2 + (14*x**2)*(22*x**2) + (22*x**2)*(-11*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-18*x)*(14*x**2) + (-18*x)*(-11*x**3) - 1*22*x**2 - 1*(-18)*x + (14*x**2)*(22*x**2) + (22*x**2)*(-11*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*x**3)*(-18*x) = 198*x**4\n (-11*x**3)*(22*x**2) = -242*x**5\n (14*x**2)*(-18*x) = -252*x**3\n (14*x**2)*(22*x**2) = 308*x**4\n -1*-18*x = 18*x\n -1*22*x**2 = -22*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -242*x**5 + 198*x**4 + 308*x**4 - 252*x**3 - 22*x**2 + 18*x\nCombining like terms, got -242*x**5 + 506*x**4 - 252*x**3 - 22*x**2 + 18*x\n#Step 6:\nCurrent expression: -242*x**5 + 506*x**4 - 252*x**3 - 22*x**2 + 18*x\nNo more calculations needed.\n-242*x**5 + 506*x**4 - 252*x**3 - 22*x**2 + 18*x", "generated_answer": "-242*x**5 + 506*x**4 - 252*x**3 - 22*x**2 + 18*x", "step_length": 6} {"cot_id": "f41c4362db7d893353839d13e9a9adeaa692858cc77077d92ea5994813570cc2", "datapoint": {"question": "Calculate the following: (-2*y - 30)*(27*y**2 - 76)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-54*y**3 - 810*y**2 + 152*y + 2280", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1350, "polynomial_expr": "(-2*y - 30)*(27*y**2 - 76)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-2*y - 30)*(27*y**2 - 76)\nExpanding the part (27*y**2 - 76) using the distributive property, and we got: (27*y**2)*(-2*y - 30) - 76*(-2*y - 30)\n#Step 2:\nCurrent expression: (27*y**2)*(-2*y - 30) - 76*(-2*y - 30)\nSimplifying the partial expression: -76*(-2*y - 30)\nExpanding the part (-2*y - 30) using the distributive property, and we got: -2*y*(-76) - 30*(-76)\nReplacing -76*(-2*y - 30) with -2*y*(-76) - 30*(-76) in the overall expression.\n#Step 3:\nCurrent expression: -2*y*(-76) + (27*y**2)*(-2*y - 30) + 2280\nSimplifying the partial expression: (27*y**2)*(-2*y - 30)\nExpanding the part (-2*y - 30) using the distributive property, and we got: (-2*y)*(27*y**2) - 810*y**2\nReplacing (27*y**2)*(-2*y - 30) with (-2*y)*(27*y**2) - 810*y**2 in the overall expression.\n#Step 4:\nCurrent expression: (-2*y)*(27*y**2) - 2*y*(-76) - 30*27*y**2 + 2280\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-2*y)*-76 = 152*y\n (-2*y)*(27*y**2) = -54*y**3\n -30*27*y**2 = -810*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -54*y**3 - 810*y**2 + 152*y + 2280\nNo more calculations needed.\n-54*y**3 - 810*y**2 + 152*y + 2280", "generated_answer": "-54*y**3 - 810*y**2 + 152*y + 2280", "step_length": 5} {"cot_id": "1edeaff322f0e5242dc2a2e4aa31c48e1b9d0b4b069a60d4fd784ffb509a3a81", "datapoint": {"question": "Simplify this expression: (24*y + 31)*(-48*y**3 + 33*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1152*y**4 - 1488*y**3 + 792*y**2 + 1023*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1352, "polynomial_expr": "(24*y + 31)*(-48*y**3 + 33*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (24*y + 31)*(-48*y**3 + 33*y)\nExpanding the part (24*y + 31) using the distributive property, and we got: (24*y)*(-48*y**3 + 33*y) + 31*(-48*y**3 + 33*y)\n#Step 2:\nCurrent expression: (24*y)*(-48*y**3 + 33*y) + 31*(-48*y**3 + 33*y)\nSimplifying the partial expression: 31*(-48*y**3 + 33*y)\nExpanding the part (-48*y**3 + 33*y) using the distributive property, and we got: (33*y)*31 - 48*y**3*31\nReplacing 31*(-48*y**3 + 33*y) with (33*y)*31 - 48*y**3*31 in the overall expression.\n#Step 3:\nCurrent expression: (24*y)*(-48*y**3 + 33*y) + (33*y)*31 - 48*y**3*31\nSimplifying the partial expression: (24*y)*(-48*y**3 + 33*y)\nExpanding the part (-48*y**3 + 33*y) using the distributive property, and we got: (24*y)*(33*y) + (24*y)*(-48*y**3)\nReplacing (24*y)*(-48*y**3 + 33*y) with (24*y)*(33*y) + (24*y)*(-48*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (24*y)*(33*y) + (24*y)*(-48*y**3) + (33*y)*31 - 48*y**3*31\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*y**3)*31 = -1488*y**3\n (-48*y**3)*(24*y) = -1152*y**4\n (33*y)*31 = 1023*y\n (33*y)*(24*y) = 792*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1152*y**4 - 1488*y**3 + 792*y**2 + 1023*y\nNo more calculations needed.\n-1152*y**4 - 1488*y**3 + 792*y**2 + 1023*y", "generated_answer": "-1152*y**4 - 1488*y**3 + 792*y**2 + 1023*y", "step_length": 5} {"cot_id": "dfdba9346c4d8515db7b3f2619e5038d2b404e8780ef53732470b911f7aebe0d", "datapoint": {"question": "Calculate the following: (26*z**3 + 14*z**2)*(-38*z**3 - 37*z - 37)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-988*z**6 - 532*z**5 - 962*z**4 - 1480*z**3 - 518*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1353, "polynomial_expr": "(26*z**3 + 14*z**2)*(-38*z**3 - 37*z - 37)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (26*z**3 + 14*z**2)*(-38*z**3 - 37*z - 37)\nExpanding the part (26*z**3 + 14*z**2) using the distributive property, and we got: (14*z**2)*(-38*z**3 - 37*z - 37) + (26*z**3)*(-38*z**3 - 37*z - 37)\n#Step 2:\nCurrent expression: (14*z**2)*(-38*z**3 - 37*z - 37) + (26*z**3)*(-38*z**3 - 37*z - 37)\nSimplifying the partial expression: (14*z**2)*(-38*z**3 - 37*z - 37)\nExpanding the part (-38*z**3 - 37*z - 37) using the distributive property, and we got: (-37*z)*(14*z**2) - 518*z**2 + (14*z**2)*(-38*z**3)\nReplacing (14*z**2)*(-38*z**3 - 37*z - 37) with (-37*z)*(14*z**2) - 518*z**2 + (14*z**2)*(-38*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-37*z)*(14*z**2) - 37*14*z**2 + (14*z**2)*(-38*z**3) + (26*z**3)*(-38*z**3 - 37*z - 37)\nSimplifying the partial expression: (26*z**3)*(-38*z**3 - 37*z - 37)\nExpanding the part (-38*z**3 - 37*z - 37) using the distributive property, and we got: (-37*z)*(26*z**3) - 962*z**3 + (-38*z**3)*(26*z**3)\nReplacing (26*z**3)*(-38*z**3 - 37*z - 37) with (-37*z)*(26*z**3) - 962*z**3 + (-38*z**3)*(26*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-37*z)*(14*z**2) + (-37*z)*(26*z**3) - 37*26*z**3 - 37*14*z**2 + (14*z**2)*(-38*z**3) + (-38*z**3)*(26*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*z**3)*(14*z**2) = -532*z**5\n (-38*z**3)*(26*z**3) = -988*z**6\n (-37*z)*(14*z**2) = -518*z**3\n (-37*z)*(26*z**3) = -962*z**4\n -37*14*z**2 = -518*z**2\n -37*26*z**3 = -962*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -988*z**6 - 532*z**5 - 962*z**4 - 962*z**3 - 518*z**3 - 518*z**2\nCombining like terms, got -988*z**6 - 532*z**5 - 962*z**4 - 1480*z**3 - 518*z**2\n#Step 6:\nCurrent expression: -988*z**6 - 532*z**5 - 962*z**4 - 1480*z**3 - 518*z**2\nNo more calculations needed.\n-988*z**6 - 532*z**5 - 962*z**4 - 1480*z**3 - 518*z**2", "generated_answer": "-988*z**6 - 532*z**5 - 962*z**4 - 1480*z**3 - 518*z**2", "step_length": 6} {"cot_id": "362ec9a66e14b3ce66ff09b29e1f2f6279b8b25202ac6ad17ddf1e665585a003", "datapoint": {"question": "Calculate the following: (-33*x**2 - 20*x + 9)*(18*x**3 - 16*x**2 + 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-594*x**5 + 168*x**4 + 482*x**3 - 837*x**2 - 420*x + 189", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1354, "polynomial_expr": "(-33*x**2 - 20*x + 9)*(18*x**3 - 16*x**2 + 21)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-33*x**2 - 20*x + 9)*(18*x**3 - 16*x**2 + 21)\nExpanding the part (-33*x**2 - 20*x + 9) using the distributive property, and we got: (-20*x)*(18*x**3 - 16*x**2 + 21) + (-33*x**2)*(18*x**3 - 16*x**2 + 21) + 9*(18*x**3 - 16*x**2 + 21)\n#Step 2:\nCurrent expression: (-20*x)*(18*x**3 - 16*x**2 + 21) + (-33*x**2)*(18*x**3 - 16*x**2 + 21) + 9*(18*x**3 - 16*x**2 + 21)\nSimplifying the partial expression: 9*(18*x**3 - 16*x**2 + 21)\nExpanding the part (18*x**3 - 16*x**2 + 21) using the distributive property, and we got: -16*x**2*9 + (18*x**3)*9 + 21*9\nReplacing 9*(18*x**3 - 16*x**2 + 21) with -16*x**2*9 + (18*x**3)*9 + 21*9 in the overall expression.\n#Step 3:\nCurrent expression: (-20*x)*(18*x**3 - 16*x**2 + 21) + (-33*x**2)*(18*x**3 - 16*x**2 + 21) - 16*x**2*9 + (18*x**3)*9 + 189\nSimplifying the partial expression: (-33*x**2)*(18*x**3 - 16*x**2 + 21)\nExpanding the part (18*x**3 - 16*x**2 + 21) using the distributive property, and we got: 21*(-33*x**2) + (-33*x**2)*(-16*x**2) + (-33*x**2)*(18*x**3)\nReplacing (-33*x**2)*(18*x**3 - 16*x**2 + 21) with 21*(-33*x**2) + (-33*x**2)*(-16*x**2) + (-33*x**2)*(18*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-20*x)*(18*x**3 - 16*x**2 + 21) + 21*(-33)*x**2 + (-33*x**2)*(-16*x**2) + (-33*x**2)*(18*x**3) - 16*x**2*9 + (18*x**3)*9 + 189\nSimplifying the partial expression: (-20*x)*(18*x**3 - 16*x**2 + 21)\nExpanding the part (18*x**3 - 16*x**2 + 21) using the distributive property, and we got: (-20*x)*(-16*x**2) + (-20*x)*(18*x**3) + 21*(-20*x)\nReplacing (-20*x)*(18*x**3 - 16*x**2 + 21) with (-20*x)*(-16*x**2) + (-20*x)*(18*x**3) + 21*(-20*x) in the overall expression.\n#Step 5:\nCurrent expression: (-20*x)*(-16*x**2) + (-20*x)*(18*x**3) + 21*(-33)*x**2 + 21*(-20)*x + (-33*x**2)*(-16*x**2) + (-33*x**2)*(18*x**3) - 16*x**2*9 + (18*x**3)*9 + 189\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-16*x**2)*9 = -144*x**2\n (-16*x**2)*(-33*x**2) = 528*x**4\n (-16*x**2)*(-20*x) = 320*x**3\n (18*x**3)*9 = 162*x**3\n (18*x**3)*(-33*x**2) = -594*x**5\n (18*x**3)*(-20*x) = -360*x**4\n 21*-33*x**2 = -693*x**2\n 21*-20*x = -420*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -594*x**5 - 360*x**4 + 528*x**4 + 162*x**3 + 320*x**3 - 693*x**2 - 144*x**2 - 420*x + 189\nCombining like terms, got -594*x**5 + 168*x**4 + 482*x**3 - 837*x**2 - 420*x + 189\n#Step 7:\nCurrent expression: -594*x**5 + 168*x**4 + 482*x**3 - 837*x**2 - 420*x + 189\nNo more calculations needed.\n-594*x**5 + 168*x**4 + 482*x**3 - 837*x**2 - 420*x + 189", "generated_answer": "-594*x**5 + 168*x**4 + 482*x**3 - 837*x**2 - 420*x + 189", "step_length": 7} {"cot_id": "1a308de9950113c639993ad0ce2a298de53e0c6bf5d64abeac9da143827fc07d", "datapoint": {"question": "Simplify this expression: -62*x**3*(24*x - 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1488*x**4 + 3100*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1355, "polynomial_expr": "-62*x**3*(24*x - 50)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -62*x**3*(24*x - 50)\nExpanding the part (24*x - 50) using the distributive property, and we got: -(-1)*3100*x**3 + (24*x)*(-62*x**3)\n#Step 2:\nCurrent expression: -(-1)*3100*x**3 + (24*x)*(-62*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -50*(-62*x**3) = 3100*x**3\n (24*x)*(-62*x**3) = -1488*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1488*x**4 + 3100*x**3\nNo more calculations needed.\n-1488*x**4 + 3100*x**3", "generated_answer": "-1488*x**4 + 3100*x**3", "step_length": 3} {"cot_id": "f7de22ab81902f26162df3085d95ab85f2757d9b77bc3f94a2a37dcaa46131bb", "datapoint": {"question": "Simplify this expression: (24 - 4*y)*(33*y**3 - 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-132*y**4 + 792*y**3 + 140*y - 840", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1356, "polynomial_expr": "(24 - 4*y)*(33*y**3 - 35)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (24 - 4*y)*(33*y**3 - 35)\nExpanding the part (33*y**3 - 35) using the distributive property, and we got: (33*y**3)*(24 - 4*y) - 35*(24 - 4*y)\n#Step 2:\nCurrent expression: (33*y**3)*(24 - 4*y) - 35*(24 - 4*y)\nSimplifying the partial expression: -35*(24 - 4*y)\nExpanding the part (24 - 4*y) using the distributive property, and we got: -4*y*(-35) + 24*(-35)\nReplacing -35*(24 - 4*y) with -4*y*(-35) + 24*(-35) in the overall expression.\n#Step 3:\nCurrent expression: -4*y*(-35) + (33*y**3)*(24 - 4*y) - 840\nSimplifying the partial expression: (33*y**3)*(24 - 4*y)\nExpanding the part (24 - 4*y) using the distributive property, and we got: (-4*y)*(33*y**3) + 24*(33*y**3)\nReplacing (33*y**3)*(24 - 4*y) with (-4*y)*(33*y**3) + 24*(33*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-4*y)*(33*y**3) - 4*y*(-35) + 24*33*y**3 - 840\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-4*y)*-35 = 140*y\n (-4*y)*(33*y**3) = -132*y**4\n 24*33*y**3 = 792*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -132*y**4 + 792*y**3 + 140*y - 840\nNo more calculations needed.\n-132*y**4 + 792*y**3 + 140*y - 840", "generated_answer": "-132*y**4 + 792*y**3 + 140*y - 840", "step_length": 5} {"cot_id": "8eb634ee04dd826fe43551bef764492ac2fa2fb20a7035906647b3ff29808fe7", "datapoint": {"question": "Simplify this expression: (-30*z**2 - 69*z - 12)*(-40*z**3 + 32*z + 2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1200*z**5 + 2760*z**4 - 480*z**3 - 2268*z**2 - 522*z - 24", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1357, "polynomial_expr": "(-30*z**2 - 69*z - 12)*(-40*z**3 + 32*z + 2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-30*z**2 - 69*z - 12)*(-40*z**3 + 32*z + 2)\nExpanding the part (-30*z**2 - 69*z - 12) using the distributive property, and we got: (-69*z)*(-40*z**3 + 32*z + 2) + (-30*z**2)*(-40*z**3 + 32*z + 2) - 12*(-40*z**3 + 32*z + 2)\n#Step 2:\nCurrent expression: (-69*z)*(-40*z**3 + 32*z + 2) + (-30*z**2)*(-40*z**3 + 32*z + 2) - 12*(-40*z**3 + 32*z + 2)\nSimplifying the partial expression: -12*(-40*z**3 + 32*z + 2)\nExpanding the part (-40*z**3 + 32*z + 2) using the distributive property, and we got: (32*z)*(-12) - 40*z**3*(-12) + 2*(-12)\nReplacing -12*(-40*z**3 + 32*z + 2) with (32*z)*(-12) - 40*z**3*(-12) + 2*(-12) in the overall expression.\n#Step 3:\nCurrent expression: (-69*z)*(-40*z**3 + 32*z + 2) + (32*z)*(-12) + (-30*z**2)*(-40*z**3 + 32*z + 2) - 40*z**3*(-12) - 24\nSimplifying the partial expression: (-69*z)*(-40*z**3 + 32*z + 2)\nExpanding the part (-40*z**3 + 32*z + 2) using the distributive property, and we got: (-69*z)*(32*z) + (-69*z)*(-40*z**3) + 2*(-69*z)\nReplacing (-69*z)*(-40*z**3 + 32*z + 2) with (-69*z)*(32*z) + (-69*z)*(-40*z**3) + 2*(-69*z) in the overall expression.\n#Step 4:\nCurrent expression: (-69*z)*(32*z) + (-69*z)*(-40*z**3) + 2*(-69)*z + (32*z)*(-12) + (-30*z**2)*(-40*z**3 + 32*z + 2) - 40*z**3*(-12) - 24\nSimplifying the partial expression: (-30*z**2)*(-40*z**3 + 32*z + 2)\nExpanding the part (-40*z**3 + 32*z + 2) using the distributive property, and we got: 2*(-30*z**2) + (32*z)*(-30*z**2) + (-30*z**2)*(-40*z**3)\nReplacing (-30*z**2)*(-40*z**3 + 32*z + 2) with 2*(-30*z**2) + (32*z)*(-30*z**2) + (-30*z**2)*(-40*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-69*z)*(32*z) + (-69*z)*(-40*z**3) + 2*(-30)*z**2 + 2*(-69)*z + (32*z)*(-30*z**2) + (32*z)*(-12) + (-30*z**2)*(-40*z**3) - 40*z**3*(-12) - 24\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*z**3)*-12 = 480*z**3\n (-40*z**3)*(-69*z) = 2760*z**4\n (-40*z**3)*(-30*z**2) = 1200*z**5\n (32*z)*-12 = -384*z\n (32*z)*(-69*z) = -2208*z**2\n (32*z)*(-30*z**2) = -960*z**3\n 2*-69*z = -138*z\n 2*-30*z**2 = -60*z**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1200*z**5 + 2760*z**4 - 960*z**3 + 480*z**3 - 2208*z**2 - 60*z**2 - 384*z - 138*z - 24\nCombining like terms, got 1200*z**5 + 2760*z**4 - 480*z**3 - 2268*z**2 - 522*z - 24\n#Step 7:\nCurrent expression: 1200*z**5 + 2760*z**4 - 480*z**3 - 2268*z**2 - 522*z - 24\nNo more calculations needed.\n1200*z**5 + 2760*z**4 - 480*z**3 - 2268*z**2 - 522*z - 24", "generated_answer": "1200*z**5 + 2760*z**4 - 480*z**3 - 2268*z**2 - 522*z - 24", "step_length": 7} {"cot_id": "36aa45f0ce1a3fb657f198c1e8bf07004f5b83ef2d3951410571942b10c86d89", "datapoint": {"question": "Simplify this expression: 496*x**3 + 1581*x\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "496*x**3 + 1581*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1358, "polynomial_expr": "496*x**3 + 1581*x", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 496*x**3 + 1581*x\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 496*x**3 + 1581*x\nNo more calculations needed.\n496*x**3 + 1581*x", "generated_answer": "496*x**3 + 1581*x", "step_length": 2} {"cot_id": "fde82885dafd3ea57d2ec1920618a00bbf9eae7a579a9846881c725f20ecdbe5", "datapoint": {"question": "Calculate the following: 420*z**3 - 270*z**2 - 300*z\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "420*z**3 - 270*z**2 - 300*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1359, "polynomial_expr": "420*z**3 - 270*z**2 - 300*z", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 420*z**3 - 270*z**2 - 300*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 420*z**3 - 270*z**2 - 300*z\nNo more calculations needed.\n420*z**3 - 270*z**2 - 300*z", "generated_answer": "420*z**3 - 270*z**2 - 300*z", "step_length": 2} {"cot_id": "566c4919d861947f5edaa6d67c34ea0702b2960093408166de913face47498ad", "datapoint": {"question": "Simplify this expression: (2 - 14*z**2)*(-82*z**3 + 3*z + 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1148*z**5 - 206*z**3 - 238*z**2 + 6*z + 34", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1360, "polynomial_expr": "(2 - 14*z**2)*(-82*z**3 + 3*z + 17)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2 - 14*z**2)*(-82*z**3 + 3*z + 17)\nExpanding the part (2 - 14*z**2) using the distributive property, and we got: (-14*z**2)*(-82*z**3 + 3*z + 17) + 2*(-82*z**3 + 3*z + 17)\n#Step 2:\nCurrent expression: (-14*z**2)*(-82*z**3 + 3*z + 17) + 2*(-82*z**3 + 3*z + 17)\nSimplifying the partial expression: 2*(-82*z**3 + 3*z + 17)\nExpanding the part (-82*z**3 + 3*z + 17) using the distributive property, and we got: (3*z)*2 - 82*z**3*2 + 17*2\nReplacing 2*(-82*z**3 + 3*z + 17) with (3*z)*2 - 82*z**3*2 + 17*2 in the overall expression.\n#Step 3:\nCurrent expression: (3*z)*2 + (-14*z**2)*(-82*z**3 + 3*z + 17) - 82*z**3*2 + 34\nSimplifying the partial expression: (-14*z**2)*(-82*z**3 + 3*z + 17)\nExpanding the part (-82*z**3 + 3*z + 17) using the distributive property, and we got: 17*(-14*z**2) + (3*z)*(-14*z**2) + (-14*z**2)*(-82*z**3)\nReplacing (-14*z**2)*(-82*z**3 + 3*z + 17) with 17*(-14*z**2) + (3*z)*(-14*z**2) + (-14*z**2)*(-82*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 17*(-14)*z**2 + (3*z)*(-14*z**2) + (3*z)*2 + (-14*z**2)*(-82*z**3) - 82*z**3*2 + 34\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-82*z**3)*2 = -164*z**3\n (-82*z**3)*(-14*z**2) = 1148*z**5\n (3*z)*2 = 6*z\n (3*z)*(-14*z**2) = -42*z**3\n 17*-14*z**2 = -238*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1148*z**5 - 164*z**3 - 42*z**3 - 238*z**2 + 6*z + 34\nCombining like terms, got 1148*z**5 - 206*z**3 - 238*z**2 + 6*z + 34\n#Step 6:\nCurrent expression: 1148*z**5 - 206*z**3 - 238*z**2 + 6*z + 34\nNo more calculations needed.\n1148*z**5 - 206*z**3 - 238*z**2 + 6*z + 34", "generated_answer": "1148*z**5 - 206*z**3 - 238*z**2 + 6*z + 34", "step_length": 6} {"cot_id": "922a665ca14aa1a11e2e4d6e43f011e3d252c95190b1c6465e721da579470e46", "datapoint": {"question": "Simplify this expression: (-20*y - 38)*(34*y**3 - 25*y**2 + 21*y + 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-680*y**4 - 792*y**3 + 530*y**2 - 1618*y - 1558", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1361, "polynomial_expr": "(-20*y - 38)*(34*y**3 - 25*y**2 + 21*y + 41)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-20*y - 38)*(34*y**3 - 25*y**2 + 21*y + 41)\nExpanding the part (-20*y - 38) using the distributive property, and we got: (-20*y)*(34*y**3 - 25*y**2 + 21*y + 41) - 38*(34*y**3 - 25*y**2 + 21*y + 41)\n#Step 2:\nCurrent expression: (-20*y)*(34*y**3 - 25*y**2 + 21*y + 41) - 38*(34*y**3 - 25*y**2 + 21*y + 41)\nSimplifying the partial expression: -38*(34*y**3 - 25*y**2 + 21*y + 41)\nExpanding the part (34*y**3 - 25*y**2 + 21*y + 41) using the distributive property, and we got: (21*y)*(-38) - 25*y**2*(-38) + (34*y**3)*(-38) + 41*(-38)\nReplacing -38*(34*y**3 - 25*y**2 + 21*y + 41) with (21*y)*(-38) - 25*y**2*(-38) + (34*y**3)*(-38) + 41*(-38) in the overall expression.\n#Step 3:\nCurrent expression: (-20*y)*(34*y**3 - 25*y**2 + 21*y + 41) + (21*y)*(-38) - 25*y**2*(-38) + (34*y**3)*(-38) - 1558\nSimplifying the partial expression: (-20*y)*(34*y**3 - 25*y**2 + 21*y + 41)\nExpanding the part (34*y**3 - 25*y**2 + 21*y + 41) using the distributive property, and we got: (-20*y)*(21*y) + (-20*y)*(-25*y**2) + (-20*y)*(34*y**3) + 41*(-20*y)\nReplacing (-20*y)*(34*y**3 - 25*y**2 + 21*y + 41) with (-20*y)*(21*y) + (-20*y)*(-25*y**2) + (-20*y)*(34*y**3) + 41*(-20*y) in the overall expression.\n#Step 4:\nCurrent expression: (-20*y)*(21*y) + (-20*y)*(-25*y**2) + (-20*y)*(34*y**3) + 41*(-20)*y + (21*y)*(-38) - 25*y**2*(-38) + (34*y**3)*(-38) - 1558\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*y**2)*-38 = 950*y**2\n (-25*y**2)*(-20*y) = 500*y**3\n (21*y)*-38 = -798*y\n (21*y)*(-20*y) = -420*y**2\n (34*y**3)*-38 = -1292*y**3\n (34*y**3)*(-20*y) = -680*y**4\n 41*-20*y = -820*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -680*y**4 - 1292*y**3 + 500*y**3 - 420*y**2 + 950*y**2 - 820*y - 798*y - 1558\nCombining like terms, got -680*y**4 - 792*y**3 + 530*y**2 - 1618*y - 1558\n#Step 6:\nCurrent expression: -680*y**4 - 792*y**3 + 530*y**2 - 1618*y - 1558\nNo more calculations needed.\n-680*y**4 - 792*y**3 + 530*y**2 - 1618*y - 1558", "generated_answer": "-680*y**4 - 792*y**3 + 530*y**2 - 1618*y - 1558", "step_length": 6} {"cot_id": "82f3db8a5180851a7bb16031b928adb916860b328d9b2e2d258faa33af82db2a", "datapoint": {"question": "Calculate the following: (-48*x**3 - 19*x**2)*(18*x**3 - 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-864*x**6 - 342*x**5 + 480*x**3 + 190*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1362, "polynomial_expr": "(-48*x**3 - 19*x**2)*(18*x**3 - 10)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-48*x**3 - 19*x**2)*(18*x**3 - 10)\nExpanding the part (18*x**3 - 10) using the distributive property, and we got: (18*x**3)*(-48*x**3 - 19*x**2) - 10*(-48*x**3 - 19*x**2)\n#Step 2:\nCurrent expression: (18*x**3)*(-48*x**3 - 19*x**2) - 10*(-48*x**3 - 19*x**2)\nSimplifying the partial expression: -10*(-48*x**3 - 19*x**2)\nExpanding the part (-48*x**3 - 19*x**2) using the distributive property, and we got: -19*x**2*(-10) - 48*x**3*(-10)\nReplacing -10*(-48*x**3 - 19*x**2) with -19*x**2*(-10) - 48*x**3*(-10) in the overall expression.\n#Step 3:\nCurrent expression: -19*x**2*(-10) - 48*x**3*(-10) + (18*x**3)*(-48*x**3 - 19*x**2)\nSimplifying the partial expression: (18*x**3)*(-48*x**3 - 19*x**2)\nExpanding the part (-48*x**3 - 19*x**2) using the distributive property, and we got: (-19*x**2)*(18*x**3) + (-48*x**3)*(18*x**3)\nReplacing (18*x**3)*(-48*x**3 - 19*x**2) with (-19*x**2)*(18*x**3) + (-48*x**3)*(18*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-19*x**2)*(18*x**3) - 19*x**2*(-10) + (-48*x**3)*(18*x**3) - 48*x**3*(-10)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*x**3)*-10 = 480*x**3\n (-48*x**3)*(18*x**3) = -864*x**6\n (-19*x**2)*-10 = 190*x**2\n (-19*x**2)*(18*x**3) = -342*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -864*x**6 - 342*x**5 + 480*x**3 + 190*x**2\nNo more calculations needed.\n-864*x**6 - 342*x**5 + 480*x**3 + 190*x**2", "generated_answer": "-864*x**6 - 342*x**5 + 480*x**3 + 190*x**2", "step_length": 5} {"cot_id": "5f7aa549c6159581dfb8a88de5a33aef26d5db382b22984fcd79d00ce0e1a1f6", "datapoint": {"question": "Simplify this expression: -56*y**3*(-18*y**3 - 28*y + 3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1008*y**6 + 1568*y**4 - 168*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1363, "polynomial_expr": "-56*y**3*(-18*y**3 - 28*y + 3)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -56*y**3*(-18*y**3 - 28*y + 3)\nExpanding the part (-18*y**3 - 28*y + 3) using the distributive property, and we got: (-28*y)*(-56*y**3) + 3*(-56*y**3) + (-56*y**3)*(-18*y**3)\n#Step 2:\nCurrent expression: (-28*y)*(-56*y**3) + 3*(-56*y**3) + (-56*y**3)*(-18*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 3*(-56*y**3) = -168*y**3\n (-28*y)*(-56*y**3) = 1568*y**4\n (-18*y**3)*(-56*y**3) = 1008*y**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1008*y**6 + 1568*y**4 - 168*y**3\nNo more calculations needed.\n1008*y**6 + 1568*y**4 - 168*y**3", "generated_answer": "1008*y**6 + 1568*y**4 - 168*y**3", "step_length": 3} {"cot_id": "a86048000c05ebfafab00795b86600979de8698ff53f9accc2c2cde23140b8ba", "datapoint": {"question": "Calculate the following: (48*x**3 - 73*x)*(7*x**3 + 26*x**2 + 30*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "336*x**6 + 1248*x**5 + 929*x**4 - 1898*x**3 - 2190*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1364, "polynomial_expr": "(48*x**3 - 73*x)*(7*x**3 + 26*x**2 + 30*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (48*x**3 - 73*x)*(7*x**3 + 26*x**2 + 30*x)\nExpanding the part (48*x**3 - 73*x) using the distributive property, and we got: (-73*x)*(7*x**3 + 26*x**2 + 30*x) + (48*x**3)*(7*x**3 + 26*x**2 + 30*x)\n#Step 2:\nCurrent expression: (-73*x)*(7*x**3 + 26*x**2 + 30*x) + (48*x**3)*(7*x**3 + 26*x**2 + 30*x)\nSimplifying the partial expression: (-73*x)*(7*x**3 + 26*x**2 + 30*x)\nExpanding the part (7*x**3 + 26*x**2 + 30*x) using the distributive property, and we got: (-73*x)*(30*x) + (-73*x)*(26*x**2) + (-73*x)*(7*x**3)\nReplacing (-73*x)*(7*x**3 + 26*x**2 + 30*x) with (-73*x)*(30*x) + (-73*x)*(26*x**2) + (-73*x)*(7*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-73*x)*(30*x) + (-73*x)*(26*x**2) + (-73*x)*(7*x**3) + (48*x**3)*(7*x**3 + 26*x**2 + 30*x)\nSimplifying the partial expression: (48*x**3)*(7*x**3 + 26*x**2 + 30*x)\nExpanding the part (7*x**3 + 26*x**2 + 30*x) using the distributive property, and we got: (30*x)*(48*x**3) + (26*x**2)*(48*x**3) + (7*x**3)*(48*x**3)\nReplacing (48*x**3)*(7*x**3 + 26*x**2 + 30*x) with (30*x)*(48*x**3) + (26*x**2)*(48*x**3) + (7*x**3)*(48*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-73*x)*(30*x) + (-73*x)*(26*x**2) + (-73*x)*(7*x**3) + (30*x)*(48*x**3) + (26*x**2)*(48*x**3) + (7*x**3)*(48*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (7*x**3)*(-73*x) = -511*x**4\n (7*x**3)*(48*x**3) = 336*x**6\n (26*x**2)*(-73*x) = -1898*x**3\n (26*x**2)*(48*x**3) = 1248*x**5\n (30*x)*(-73*x) = -2190*x**2\n (30*x)*(48*x**3) = 1440*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 336*x**6 + 1248*x**5 - 511*x**4 + 1440*x**4 - 1898*x**3 - 2190*x**2\nCombining like terms, got 336*x**6 + 1248*x**5 + 929*x**4 - 1898*x**3 - 2190*x**2\n#Step 6:\nCurrent expression: 336*x**6 + 1248*x**5 + 929*x**4 - 1898*x**3 - 2190*x**2\nNo more calculations needed.\n336*x**6 + 1248*x**5 + 929*x**4 - 1898*x**3 - 2190*x**2", "generated_answer": "336*x**6 + 1248*x**5 + 929*x**4 - 1898*x**3 - 2190*x**2", "step_length": 6} {"cot_id": "11eb3d1242c7d9251a64f4f3023ba2696a48e931608ef54ff5e6cfc79a525454", "datapoint": {"question": "Calculate the following: -2205*x - 2772\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2205*x - 2772", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1365, "polynomial_expr": "-2205*x - 2772", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -2205*x - 2772\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -2205*x - 2772\nNo more calculations needed.\n-2205*x - 2772", "generated_answer": "-2205*x - 2772", "step_length": 2} {"cot_id": "ebd8e0966978acee05849710d369810059cccdf26df9cc16668b857c372fbbde", "datapoint": {"question": "Simplify this expression: (8*y - 22)*(15*y**3 + 2*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "120*y**4 - 330*y**3 + 16*y**2 - 44*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1366, "polynomial_expr": "(8*y - 22)*(15*y**3 + 2*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (8*y - 22)*(15*y**3 + 2*y)\nExpanding the part (8*y - 22) using the distributive property, and we got: (8*y)*(15*y**3 + 2*y) - 22*(15*y**3 + 2*y)\n#Step 2:\nCurrent expression: (8*y)*(15*y**3 + 2*y) - 22*(15*y**3 + 2*y)\nSimplifying the partial expression: -22*(15*y**3 + 2*y)\nExpanding the part (15*y**3 + 2*y) using the distributive property, and we got: (2*y)*(-22) + (15*y**3)*(-22)\nReplacing -22*(15*y**3 + 2*y) with (2*y)*(-22) + (15*y**3)*(-22) in the overall expression.\n#Step 3:\nCurrent expression: (2*y)*(-22) + (8*y)*(15*y**3 + 2*y) + (15*y**3)*(-22)\nSimplifying the partial expression: (8*y)*(15*y**3 + 2*y)\nExpanding the part (15*y**3 + 2*y) using the distributive property, and we got: (2*y)*(8*y) + (8*y)*(15*y**3)\nReplacing (8*y)*(15*y**3 + 2*y) with (2*y)*(8*y) + (8*y)*(15*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (2*y)*(8*y) + (2*y)*(-22) + (8*y)*(15*y**3) + (15*y**3)*(-22)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (2*y)*-22 = -44*y\n (2*y)*(8*y) = 16*y**2\n (15*y**3)*-22 = -330*y**3\n (15*y**3)*(8*y) = 120*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 120*y**4 - 330*y**3 + 16*y**2 - 44*y\nNo more calculations needed.\n120*y**4 - 330*y**3 + 16*y**2 - 44*y", "generated_answer": "120*y**4 - 330*y**3 + 16*y**2 - 44*y", "step_length": 5} {"cot_id": "ca1469ee0f5f4327a4aef4775471b0aae2c0a2739c9933e66c3582d3f018353c", "datapoint": {"question": "Calculate the following: 52*x**3*(47*x**3 - 23*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2444*x**6 - 1196*x**5", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1367, "polynomial_expr": "52*x**3*(47*x**3 - 23*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 52*x**3*(47*x**3 - 23*x**2)\nExpanding the part (47*x**3 - 23*x**2) using the distributive property, and we got: (-23*x**2)*(52*x**3) + (47*x**3)*(52*x**3)\n#Step 2:\nCurrent expression: (-23*x**2)*(52*x**3) + (47*x**3)*(52*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*x**2)*(52*x**3) = -1196*x**5\n (47*x**3)*(52*x**3) = 2444*x**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 2444*x**6 - 1196*x**5\nNo more calculations needed.\n2444*x**6 - 1196*x**5", "generated_answer": "2444*x**6 - 1196*x**5", "step_length": 3} {"cot_id": "9fac598c9eb4303b8a63b31fd16703185b85f644490bda8236a089b5709f5fd3", "datapoint": {"question": "Calculate the following: (41*y**2 + 13*y + 50)*(-7*y**3 + 9*y**2 + 40*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-287*y**5 + 278*y**4 + 1407*y**3 + 970*y**2 + 2000*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1368, "polynomial_expr": "(41*y**2 + 13*y + 50)*(-7*y**3 + 9*y**2 + 40*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (41*y**2 + 13*y + 50)*(-7*y**3 + 9*y**2 + 40*y)\nExpanding the part (41*y**2 + 13*y + 50) using the distributive property, and we got: (13*y)*(-7*y**3 + 9*y**2 + 40*y) + (41*y**2)*(-7*y**3 + 9*y**2 + 40*y) + 50*(-7*y**3 + 9*y**2 + 40*y)\n#Step 2:\nCurrent expression: (13*y)*(-7*y**3 + 9*y**2 + 40*y) + (41*y**2)*(-7*y**3 + 9*y**2 + 40*y) + 50*(-7*y**3 + 9*y**2 + 40*y)\nSimplifying the partial expression: 50*(-7*y**3 + 9*y**2 + 40*y)\nExpanding the part (-7*y**3 + 9*y**2 + 40*y) using the distributive property, and we got: (40*y)*50 + (9*y**2)*50 - 7*y**3*50\nReplacing 50*(-7*y**3 + 9*y**2 + 40*y) with (40*y)*50 + (9*y**2)*50 - 7*y**3*50 in the overall expression.\n#Step 3:\nCurrent expression: (13*y)*(-7*y**3 + 9*y**2 + 40*y) + (40*y)*50 + (9*y**2)*50 + (41*y**2)*(-7*y**3 + 9*y**2 + 40*y) - 7*y**3*50\nSimplifying the partial expression: (13*y)*(-7*y**3 + 9*y**2 + 40*y)\nExpanding the part (-7*y**3 + 9*y**2 + 40*y) using the distributive property, and we got: (13*y)*(40*y) + (13*y)*(9*y**2) + (13*y)*(-7*y**3)\nReplacing (13*y)*(-7*y**3 + 9*y**2 + 40*y) with (13*y)*(40*y) + (13*y)*(9*y**2) + (13*y)*(-7*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (13*y)*(40*y) + (13*y)*(9*y**2) + (13*y)*(-7*y**3) + (40*y)*50 + (9*y**2)*50 + (41*y**2)*(-7*y**3 + 9*y**2 + 40*y) - 7*y**3*50\nSimplifying the partial expression: (41*y**2)*(-7*y**3 + 9*y**2 + 40*y)\nExpanding the part (-7*y**3 + 9*y**2 + 40*y) using the distributive property, and we got: (40*y)*(41*y**2) + (9*y**2)*(41*y**2) + (41*y**2)*(-7*y**3)\nReplacing (41*y**2)*(-7*y**3 + 9*y**2 + 40*y) with (40*y)*(41*y**2) + (9*y**2)*(41*y**2) + (41*y**2)*(-7*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (13*y)*(40*y) + (13*y)*(9*y**2) + (13*y)*(-7*y**3) + (40*y)*(41*y**2) + (40*y)*50 + (9*y**2)*(41*y**2) + (9*y**2)*50 + (41*y**2)*(-7*y**3) - 7*y**3*50\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-7*y**3)*50 = -350*y**3\n (-7*y**3)*(13*y) = -91*y**4\n (-7*y**3)*(41*y**2) = -287*y**5\n (9*y**2)*50 = 450*y**2\n (9*y**2)*(13*y) = 117*y**3\n (9*y**2)*(41*y**2) = 369*y**4\n (40*y)*50 = 2000*y\n (40*y)*(13*y) = 520*y**2\n (40*y)*(41*y**2) = 1640*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -287*y**5 - 91*y**4 + 369*y**4 - 350*y**3 + 117*y**3 + 1640*y**3 + 450*y**2 + 520*y**2 + 2000*y\nCombining like terms, got -287*y**5 + 278*y**4 + 1407*y**3 + 970*y**2 + 2000*y\n#Step 7:\nCurrent expression: -287*y**5 + 278*y**4 + 1407*y**3 + 970*y**2 + 2000*y\nNo more calculations needed.\n-287*y**5 + 278*y**4 + 1407*y**3 + 970*y**2 + 2000*y", "generated_answer": "-287*y**5 + 278*y**4 + 1407*y**3 + 970*y**2 + 2000*y", "step_length": 7} {"cot_id": "66f8d36cd3cd30071b15aa5230fbe6a42a9089fa6dcb9a98bbaa8546902a861a", "datapoint": {"question": "Simplify this expression: 22*x*(45*x - 4)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "990*x**2 - 88*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1369, "polynomial_expr": "22*x*(45*x - 4)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 22*x*(45*x - 4)\nExpanding the part (45*x - 4) using the distributive property, and we got: -88*x + (22*x)*(45*x)\n#Step 2:\nCurrent expression: -88*x + (22*x)*(45*x)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -4*(22*x) = -88*x\n (45*x)*(22*x) = 990*x**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 990*x**2 - 88*x\nNo more calculations needed.\n990*x**2 - 88*x", "generated_answer": "990*x**2 - 88*x", "step_length": 3} {"cot_id": "a6565440cf69d760a92ddc8867f63bfe6759e3e4e38d067aa4b1b515078decbf", "datapoint": {"question": "Simplify this expression: (8*y + 13)*(-38*y**2 + 39*y - 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-304*y**3 - 182*y**2 + 155*y - 572", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1370, "polynomial_expr": "(8*y + 13)*(-38*y**2 + 39*y - 44)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (8*y + 13)*(-38*y**2 + 39*y - 44)\nExpanding the part (8*y + 13) using the distributive property, and we got: (8*y)*(-38*y**2 + 39*y - 44) + 13*(-38*y**2 + 39*y - 44)\n#Step 2:\nCurrent expression: (8*y)*(-38*y**2 + 39*y - 44) + 13*(-38*y**2 + 39*y - 44)\nSimplifying the partial expression: 13*(-38*y**2 + 39*y - 44)\nExpanding the part (-38*y**2 + 39*y - 44) using the distributive property, and we got: (39*y)*13 - 38*y**2*13 - 44*13\nReplacing 13*(-38*y**2 + 39*y - 44) with (39*y)*13 - 38*y**2*13 - 44*13 in the overall expression.\n#Step 3:\nCurrent expression: (8*y)*(-38*y**2 + 39*y - 44) + (39*y)*13 - 38*y**2*13 - 572\nSimplifying the partial expression: (8*y)*(-38*y**2 + 39*y - 44)\nExpanding the part (-38*y**2 + 39*y - 44) using the distributive property, and we got: -352*y + (8*y)*(39*y) + (8*y)*(-38*y**2)\nReplacing (8*y)*(-38*y**2 + 39*y - 44) with -352*y + (8*y)*(39*y) + (8*y)*(-38*y**2) in the overall expression.\n#Step 4:\nCurrent expression: -44*8*y + (8*y)*(39*y) + (8*y)*(-38*y**2) + (39*y)*13 - 38*y**2*13 - 572\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*y**2)*13 = -494*y**2\n (-38*y**2)*(8*y) = -304*y**3\n (39*y)*13 = 507*y\n (39*y)*(8*y) = 312*y**2\n -44*8*y = -352*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -304*y**3 - 494*y**2 + 312*y**2 - 352*y + 507*y - 572\nCombining like terms, got -304*y**3 - 182*y**2 + 155*y - 572\n#Step 6:\nCurrent expression: -304*y**3 - 182*y**2 + 155*y - 572\nNo more calculations needed.\n-304*y**3 - 182*y**2 + 155*y - 572", "generated_answer": "-304*y**3 - 182*y**2 + 155*y - 572", "step_length": 6} {"cot_id": "39d4dd4184b279982bcccd512e970ec82e408767cfc82d37f2637cf35a88a263", "datapoint": {"question": "Calculate the following: (-42*y**2 - 10*y)*(57*y**3 + 55*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2394*y**5 - 570*y**4 - 2310*y**3 - 550*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1371, "polynomial_expr": "(-42*y**2 - 10*y)*(57*y**3 + 55*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-42*y**2 - 10*y)*(57*y**3 + 55*y)\nExpanding the part (-42*y**2 - 10*y) using the distributive property, and we got: (-10*y)*(57*y**3 + 55*y) + (-42*y**2)*(57*y**3 + 55*y)\n#Step 2:\nCurrent expression: (-10*y)*(57*y**3 + 55*y) + (-42*y**2)*(57*y**3 + 55*y)\nSimplifying the partial expression: (-42*y**2)*(57*y**3 + 55*y)\nExpanding the part (57*y**3 + 55*y) using the distributive property, and we got: (55*y)*(-42*y**2) + (-42*y**2)*(57*y**3)\nReplacing (-42*y**2)*(57*y**3 + 55*y) with (55*y)*(-42*y**2) + (-42*y**2)*(57*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-10*y)*(57*y**3 + 55*y) + (55*y)*(-42*y**2) + (-42*y**2)*(57*y**3)\nSimplifying the partial expression: (-10*y)*(57*y**3 + 55*y)\nExpanding the part (57*y**3 + 55*y) using the distributive property, and we got: (-10*y)*(55*y) + (-10*y)*(57*y**3)\nReplacing (-10*y)*(57*y**3 + 55*y) with (-10*y)*(55*y) + (-10*y)*(57*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-10*y)*(55*y) + (-10*y)*(57*y**3) + (55*y)*(-42*y**2) + (-42*y**2)*(57*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (55*y)*(-42*y**2) = -2310*y**3\n (55*y)*(-10*y) = -550*y**2\n (57*y**3)*(-42*y**2) = -2394*y**5\n (57*y**3)*(-10*y) = -570*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2394*y**5 - 570*y**4 - 2310*y**3 - 550*y**2\nNo more calculations needed.\n-2394*y**5 - 570*y**4 - 2310*y**3 - 550*y**2", "generated_answer": "-2394*y**5 - 570*y**4 - 2310*y**3 - 550*y**2", "step_length": 5} {"cot_id": "5a8f4800dd7340e66bd2ca7783e76675235843cbaef47de5cc52492b3ce0c61e", "datapoint": {"question": "Calculate the following: (15*x**3 + 31*x)*(-23*x**3 - 44*x**2 + 24*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-345*x**6 - 660*x**5 - 353*x**4 - 1364*x**3 + 744*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1372, "polynomial_expr": "(15*x**3 + 31*x)*(-23*x**3 - 44*x**2 + 24*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (15*x**3 + 31*x)*(-23*x**3 - 44*x**2 + 24*x)\nExpanding the part (15*x**3 + 31*x) using the distributive property, and we got: (31*x)*(-23*x**3 - 44*x**2 + 24*x) + (15*x**3)*(-23*x**3 - 44*x**2 + 24*x)\n#Step 2:\nCurrent expression: (31*x)*(-23*x**3 - 44*x**2 + 24*x) + (15*x**3)*(-23*x**3 - 44*x**2 + 24*x)\nSimplifying the partial expression: (15*x**3)*(-23*x**3 - 44*x**2 + 24*x)\nExpanding the part (-23*x**3 - 44*x**2 + 24*x) using the distributive property, and we got: (24*x)*(15*x**3) + (-44*x**2)*(15*x**3) + (-23*x**3)*(15*x**3)\nReplacing (15*x**3)*(-23*x**3 - 44*x**2 + 24*x) with (24*x)*(15*x**3) + (-44*x**2)*(15*x**3) + (-23*x**3)*(15*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (24*x)*(15*x**3) + (31*x)*(-23*x**3 - 44*x**2 + 24*x) + (-44*x**2)*(15*x**3) + (-23*x**3)*(15*x**3)\nSimplifying the partial expression: (31*x)*(-23*x**3 - 44*x**2 + 24*x)\nExpanding the part (-23*x**3 - 44*x**2 + 24*x) using the distributive property, and we got: (24*x)*(31*x) + (31*x)*(-44*x**2) + (31*x)*(-23*x**3)\nReplacing (31*x)*(-23*x**3 - 44*x**2 + 24*x) with (24*x)*(31*x) + (31*x)*(-44*x**2) + (31*x)*(-23*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (24*x)*(31*x) + (24*x)*(15*x**3) + (31*x)*(-44*x**2) + (31*x)*(-23*x**3) + (-44*x**2)*(15*x**3) + (-23*x**3)*(15*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-44*x**2)*(15*x**3) = -660*x**5\n (-44*x**2)*(31*x) = -1364*x**3\n (-23*x**3)*(15*x**3) = -345*x**6\n (-23*x**3)*(31*x) = -713*x**4\n (24*x)*(15*x**3) = 360*x**4\n (24*x)*(31*x) = 744*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -345*x**6 - 660*x**5 - 713*x**4 + 360*x**4 - 1364*x**3 + 744*x**2\nCombining like terms, got -345*x**6 - 660*x**5 - 353*x**4 - 1364*x**3 + 744*x**2\n#Step 6:\nCurrent expression: -345*x**6 - 660*x**5 - 353*x**4 - 1364*x**3 + 744*x**2\nNo more calculations needed.\n-345*x**6 - 660*x**5 - 353*x**4 - 1364*x**3 + 744*x**2", "generated_answer": "-345*x**6 - 660*x**5 - 353*x**4 - 1364*x**3 + 744*x**2", "step_length": 6} {"cot_id": "5e481670e8fe5c58380b7faa05ee573ee6bb38f2e747e3130d6f195eb7133c22", "datapoint": {"question": "Simplify this expression: 3567 - 2001*z\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "3567 - 2001*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1373, "polynomial_expr": "3567 - 2001*z", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 3567 - 2001*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 3567 - 2001*z\nNo more calculations needed.\n3567 - 2001*z", "generated_answer": "3567 - 2001*z", "step_length": 2} {"cot_id": "766c0d39e46710cd4940850ad8f6123aefec79c3e2b11ae37e3f73a0d12de001", "datapoint": {"question": "Simplify this expression: (-39*x**3 + 39*x)*(4*x**3 + 41*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-156*x**6 - 1443*x**4 + 1599*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1374, "polynomial_expr": "(-39*x**3 + 39*x)*(4*x**3 + 41*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-39*x**3 + 39*x)*(4*x**3 + 41*x)\nExpanding the part (-39*x**3 + 39*x) using the distributive property, and we got: (39*x)*(4*x**3 + 41*x) + (-39*x**3)*(4*x**3 + 41*x)\n#Step 2:\nCurrent expression: (39*x)*(4*x**3 + 41*x) + (-39*x**3)*(4*x**3 + 41*x)\nSimplifying the partial expression: (-39*x**3)*(4*x**3 + 41*x)\nExpanding the part (4*x**3 + 41*x) using the distributive property, and we got: (41*x)*(-39*x**3) + (-39*x**3)*(4*x**3)\nReplacing (-39*x**3)*(4*x**3 + 41*x) with (41*x)*(-39*x**3) + (-39*x**3)*(4*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (39*x)*(4*x**3 + 41*x) + (41*x)*(-39*x**3) + (-39*x**3)*(4*x**3)\nSimplifying the partial expression: (39*x)*(4*x**3 + 41*x)\nExpanding the part (4*x**3 + 41*x) using the distributive property, and we got: (39*x)*(41*x) + (39*x)*(4*x**3)\nReplacing (39*x)*(4*x**3 + 41*x) with (39*x)*(41*x) + (39*x)*(4*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (39*x)*(41*x) + (39*x)*(4*x**3) + (41*x)*(-39*x**3) + (-39*x**3)*(4*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (4*x**3)*(-39*x**3) = -156*x**6\n (4*x**3)*(39*x) = 156*x**4\n (41*x)*(-39*x**3) = -1599*x**4\n (41*x)*(39*x) = 1599*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -156*x**6 - 1599*x**4 + 156*x**4 + 1599*x**2\nCombining like terms, got -156*x**6 - 1443*x**4 + 1599*x**2\n#Step 6:\nCurrent expression: -156*x**6 - 1443*x**4 + 1599*x**2\nNo more calculations needed.\n-156*x**6 - 1443*x**4 + 1599*x**2", "generated_answer": "-156*x**6 - 1443*x**4 + 1599*x**2", "step_length": 6} {"cot_id": "79a1b242804e98ac4d4498b4a22c51e50d7a6144c664926a7b86cdc16c1bd082", "datapoint": {"question": "Calculate the following: (28*y**2 - 47*y + 47)*(4*y**3 - 2*y**2 + 75*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "112*y**5 - 244*y**4 + 2382*y**3 - 3619*y**2 + 3525*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1375, "polynomial_expr": "(28*y**2 - 47*y + 47)*(4*y**3 - 2*y**2 + 75*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28*y**2 - 47*y + 47)*(4*y**3 - 2*y**2 + 75*y)\nExpanding the part (28*y**2 - 47*y + 47) using the distributive property, and we got: (-47*y)*(4*y**3 - 2*y**2 + 75*y) + (28*y**2)*(4*y**3 - 2*y**2 + 75*y) + 47*(4*y**3 - 2*y**2 + 75*y)\n#Step 2:\nCurrent expression: (-47*y)*(4*y**3 - 2*y**2 + 75*y) + (28*y**2)*(4*y**3 - 2*y**2 + 75*y) + 47*(4*y**3 - 2*y**2 + 75*y)\nSimplifying the partial expression: 47*(4*y**3 - 2*y**2 + 75*y)\nExpanding the part (4*y**3 - 2*y**2 + 75*y) using the distributive property, and we got: (75*y)*47 - 2*y**2*47 + (4*y**3)*47\nReplacing 47*(4*y**3 - 2*y**2 + 75*y) with (75*y)*47 - 2*y**2*47 + (4*y**3)*47 in the overall expression.\n#Step 3:\nCurrent expression: (-47*y)*(4*y**3 - 2*y**2 + 75*y) + (75*y)*47 - 2*y**2*47 + (28*y**2)*(4*y**3 - 2*y**2 + 75*y) + (4*y**3)*47\nSimplifying the partial expression: (-47*y)*(4*y**3 - 2*y**2 + 75*y)\nExpanding the part (4*y**3 - 2*y**2 + 75*y) using the distributive property, and we got: (-47*y)*(75*y) + (-47*y)*(-2*y**2) + (-47*y)*(4*y**3)\nReplacing (-47*y)*(4*y**3 - 2*y**2 + 75*y) with (-47*y)*(75*y) + (-47*y)*(-2*y**2) + (-47*y)*(4*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-47*y)*(75*y) + (-47*y)*(-2*y**2) + (-47*y)*(4*y**3) + (75*y)*47 - 2*y**2*47 + (28*y**2)*(4*y**3 - 2*y**2 + 75*y) + (4*y**3)*47\nSimplifying the partial expression: (28*y**2)*(4*y**3 - 2*y**2 + 75*y)\nExpanding the part (4*y**3 - 2*y**2 + 75*y) using the distributive property, and we got: (75*y)*(28*y**2) + (-2*y**2)*(28*y**2) + (28*y**2)*(4*y**3)\nReplacing (28*y**2)*(4*y**3 - 2*y**2 + 75*y) with (75*y)*(28*y**2) + (-2*y**2)*(28*y**2) + (28*y**2)*(4*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-47*y)*(75*y) + (-47*y)*(-2*y**2) + (-47*y)*(4*y**3) + (75*y)*(28*y**2) + (75*y)*47 + (-2*y**2)*(28*y**2) - 2*y**2*47 + (28*y**2)*(4*y**3) + (4*y**3)*47\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-2*y**2)*47 = -94*y**2\n (-2*y**2)*(-47*y) = 94*y**3\n (-2*y**2)*(28*y**2) = -56*y**4\n (4*y**3)*47 = 188*y**3\n (4*y**3)*(-47*y) = -188*y**4\n (4*y**3)*(28*y**2) = 112*y**5\n (75*y)*47 = 3525*y\n (75*y)*(-47*y) = -3525*y**2\n (75*y)*(28*y**2) = 2100*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 112*y**5 - 188*y**4 - 56*y**4 + 94*y**3 + 188*y**3 + 2100*y**3 - 3525*y**2 - 94*y**2 + 3525*y\nCombining like terms, got 112*y**5 - 244*y**4 + 2382*y**3 - 3619*y**2 + 3525*y\n#Step 7:\nCurrent expression: 112*y**5 - 244*y**4 + 2382*y**3 - 3619*y**2 + 3525*y\nNo more calculations needed.\n112*y**5 - 244*y**4 + 2382*y**3 - 3619*y**2 + 3525*y", "generated_answer": "112*y**5 - 244*y**4 + 2382*y**3 - 3619*y**2 + 3525*y", "step_length": 7} {"cot_id": "cdbb0206b0ca1db0be947107131d89aeea0ab478096af03fc2dad02944154502", "datapoint": {"question": "Simplify this expression: (34*x**2 + 47)*(95*x**3 - 23*x**2 - 27*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "3230*x**5 - 782*x**4 + 3547*x**3 - 1081*x**2 - 1269*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1376, "polynomial_expr": "(34*x**2 + 47)*(95*x**3 - 23*x**2 - 27*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (34*x**2 + 47)*(95*x**3 - 23*x**2 - 27*x)\nExpanding the part (34*x**2 + 47) using the distributive property, and we got: (34*x**2)*(95*x**3 - 23*x**2 - 27*x) + 47*(95*x**3 - 23*x**2 - 27*x)\n#Step 2:\nCurrent expression: (34*x**2)*(95*x**3 - 23*x**2 - 27*x) + 47*(95*x**3 - 23*x**2 - 27*x)\nSimplifying the partial expression: 47*(95*x**3 - 23*x**2 - 27*x)\nExpanding the part (95*x**3 - 23*x**2 - 27*x) using the distributive property, and we got: -27*x*47 - 23*x**2*47 + (95*x**3)*47\nReplacing 47*(95*x**3 - 23*x**2 - 27*x) with -27*x*47 - 23*x**2*47 + (95*x**3)*47 in the overall expression.\n#Step 3:\nCurrent expression: -27*x*47 - 23*x**2*47 + (34*x**2)*(95*x**3 - 23*x**2 - 27*x) + (95*x**3)*47\nSimplifying the partial expression: (34*x**2)*(95*x**3 - 23*x**2 - 27*x)\nExpanding the part (95*x**3 - 23*x**2 - 27*x) using the distributive property, and we got: (-27*x)*(34*x**2) + (-23*x**2)*(34*x**2) + (34*x**2)*(95*x**3)\nReplacing (34*x**2)*(95*x**3 - 23*x**2 - 27*x) with (-27*x)*(34*x**2) + (-23*x**2)*(34*x**2) + (34*x**2)*(95*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-27*x)*(34*x**2) - 27*x*47 + (-23*x**2)*(34*x**2) - 23*x**2*47 + (34*x**2)*(95*x**3) + (95*x**3)*47\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*x)*47 = -1269*x\n (-27*x)*(34*x**2) = -918*x**3\n (-23*x**2)*47 = -1081*x**2\n (-23*x**2)*(34*x**2) = -782*x**4\n (95*x**3)*47 = 4465*x**3\n (95*x**3)*(34*x**2) = 3230*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 3230*x**5 - 782*x**4 - 918*x**3 + 4465*x**3 - 1081*x**2 - 1269*x\nCombining like terms, got 3230*x**5 - 782*x**4 + 3547*x**3 - 1081*x**2 - 1269*x\n#Step 6:\nCurrent expression: 3230*x**5 - 782*x**4 + 3547*x**3 - 1081*x**2 - 1269*x\nNo more calculations needed.\n3230*x**5 - 782*x**4 + 3547*x**3 - 1081*x**2 - 1269*x", "generated_answer": "3230*x**5 - 782*x**4 + 3547*x**3 - 1081*x**2 - 1269*x", "step_length": 6} {"cot_id": "23b08451afc180b0f9cd9601dcea15b05b9679adbb0456a3b37b52e7be7b8f70", "datapoint": {"question": "Simplify this expression: (-31*z**3 - 11)*(-45*z**2 - 18*z + 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1395*z**5 + 558*z**4 - 310*z**3 + 495*z**2 + 198*z - 110", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1377, "polynomial_expr": "(-31*z**3 - 11)*(-45*z**2 - 18*z + 10)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-31*z**3 - 11)*(-45*z**2 - 18*z + 10)\nExpanding the part (-31*z**3 - 11) using the distributive property, and we got: (-31*z**3)*(-45*z**2 - 18*z + 10) - 11*(-45*z**2 - 18*z + 10)\n#Step 2:\nCurrent expression: (-31*z**3)*(-45*z**2 - 18*z + 10) - 11*(-45*z**2 - 18*z + 10)\nSimplifying the partial expression: -11*(-45*z**2 - 18*z + 10)\nExpanding the part (-45*z**2 - 18*z + 10) using the distributive property, and we got: -18*z*(-11) - 45*z**2*(-11) + 10*(-11)\nReplacing -11*(-45*z**2 - 18*z + 10) with -18*z*(-11) - 45*z**2*(-11) + 10*(-11) in the overall expression.\n#Step 3:\nCurrent expression: -18*z*(-11) - 45*z**2*(-11) + (-31*z**3)*(-45*z**2 - 18*z + 10) - 110\nSimplifying the partial expression: (-31*z**3)*(-45*z**2 - 18*z + 10)\nExpanding the part (-45*z**2 - 18*z + 10) using the distributive property, and we got: (-18*z)*(-31*z**3) + 10*(-31*z**3) + (-45*z**2)*(-31*z**3)\nReplacing (-31*z**3)*(-45*z**2 - 18*z + 10) with (-18*z)*(-31*z**3) + 10*(-31*z**3) + (-45*z**2)*(-31*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-18*z)*(-31*z**3) - 18*z*(-11) + 10*(-31)*z**3 + (-45*z**2)*(-31*z**3) - 45*z**2*(-11) - 110\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*z**2)*-11 = 495*z**2\n (-45*z**2)*(-31*z**3) = 1395*z**5\n (-18*z)*-11 = 198*z\n (-18*z)*(-31*z**3) = 558*z**4\n 10*-31*z**3 = -310*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1395*z**5 + 558*z**4 - 310*z**3 + 495*z**2 + 198*z - 110\nNo more calculations needed.\n1395*z**5 + 558*z**4 - 310*z**3 + 495*z**2 + 198*z - 110", "generated_answer": "1395*z**5 + 558*z**4 - 310*z**3 + 495*z**2 + 198*z - 110", "step_length": 5} {"cot_id": "4224e9f0d49984173fc98854c91a6d487abbc6703858445874c6365d0681bdc8", "datapoint": {"question": "Simplify this expression: (37*z**2 - 10*z - 32)*(-2*z**3 - 9*z**2 + 19)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-74*z**5 - 313*z**4 + 154*z**3 + 991*z**2 - 190*z - 608", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1378, "polynomial_expr": "(37*z**2 - 10*z - 32)*(-2*z**3 - 9*z**2 + 19)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (37*z**2 - 10*z - 32)*(-2*z**3 - 9*z**2 + 19)\nExpanding the part (37*z**2 - 10*z - 32) using the distributive property, and we got: (-10*z)*(-2*z**3 - 9*z**2 + 19) + (37*z**2)*(-2*z**3 - 9*z**2 + 19) - 32*(-2*z**3 - 9*z**2 + 19)\n#Step 2:\nCurrent expression: (-10*z)*(-2*z**3 - 9*z**2 + 19) + (37*z**2)*(-2*z**3 - 9*z**2 + 19) - 32*(-2*z**3 - 9*z**2 + 19)\nSimplifying the partial expression: -32*(-2*z**3 - 9*z**2 + 19)\nExpanding the part (-2*z**3 - 9*z**2 + 19) using the distributive property, and we got: -9*z**2*(-32) - 2*z**3*(-32) + 19*(-32)\nReplacing -32*(-2*z**3 - 9*z**2 + 19) with -9*z**2*(-32) - 2*z**3*(-32) + 19*(-32) in the overall expression.\n#Step 3:\nCurrent expression: (-10*z)*(-2*z**3 - 9*z**2 + 19) - 9*z**2*(-32) + (37*z**2)*(-2*z**3 - 9*z**2 + 19) - 2*z**3*(-32) - 608\nSimplifying the partial expression: (-10*z)*(-2*z**3 - 9*z**2 + 19)\nExpanding the part (-2*z**3 - 9*z**2 + 19) using the distributive property, and we got: (-10*z)*(-9*z**2) + (-10*z)*(-2*z**3) + 19*(-10*z)\nReplacing (-10*z)*(-2*z**3 - 9*z**2 + 19) with (-10*z)*(-9*z**2) + (-10*z)*(-2*z**3) + 19*(-10*z) in the overall expression.\n#Step 4:\nCurrent expression: (-10*z)*(-9*z**2) + (-10*z)*(-2*z**3) + 19*(-10)*z - 9*z**2*(-32) + (37*z**2)*(-2*z**3 - 9*z**2 + 19) - 2*z**3*(-32) - 608\nSimplifying the partial expression: (37*z**2)*(-2*z**3 - 9*z**2 + 19)\nExpanding the part (-2*z**3 - 9*z**2 + 19) using the distributive property, and we got: 19*(37*z**2) + (-9*z**2)*(37*z**2) + (37*z**2)*(-2*z**3)\nReplacing (37*z**2)*(-2*z**3 - 9*z**2 + 19) with 19*(37*z**2) + (-9*z**2)*(37*z**2) + (37*z**2)*(-2*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-10*z)*(-9*z**2) + (-10*z)*(-2*z**3) + 19*37*z**2 + 19*(-10)*z + (-9*z**2)*(37*z**2) - 9*z**2*(-32) + (37*z**2)*(-2*z**3) - 2*z**3*(-32) - 608\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-9*z**2)*-32 = 288*z**2\n (-9*z**2)*(-10*z) = 90*z**3\n (-9*z**2)*(37*z**2) = -333*z**4\n (-2*z**3)*-32 = 64*z**3\n (-2*z**3)*(-10*z) = 20*z**4\n (-2*z**3)*(37*z**2) = -74*z**5\n 19*-10*z = -190*z\n 19*37*z**2 = 703*z**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -74*z**5 - 333*z**4 + 20*z**4 + 64*z**3 + 90*z**3 + 288*z**2 + 703*z**2 - 190*z - 608\nCombining like terms, got -74*z**5 - 313*z**4 + 154*z**3 + 991*z**2 - 190*z - 608\n#Step 7:\nCurrent expression: -74*z**5 - 313*z**4 + 154*z**3 + 991*z**2 - 190*z - 608\nNo more calculations needed.\n-74*z**5 - 313*z**4 + 154*z**3 + 991*z**2 - 190*z - 608", "generated_answer": "-74*z**5 - 313*z**4 + 154*z**3 + 991*z**2 - 190*z - 608", "step_length": 7} {"cot_id": "87de6831428955c468bb08248af218cc2e1a7954f5786f291af67dcaaa042e56", "datapoint": {"question": "Calculate the following: (26*x - 22)*(39*x**2 - 18)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1014*x**3 - 858*x**2 - 468*x + 396", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1379, "polynomial_expr": "(26*x - 22)*(39*x**2 - 18)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (26*x - 22)*(39*x**2 - 18)\nExpanding the part (26*x - 22) using the distributive property, and we got: (26*x)*(39*x**2 - 18) - 22*(39*x**2 - 18)\n#Step 2:\nCurrent expression: (26*x)*(39*x**2 - 18) - 22*(39*x**2 - 18)\nSimplifying the partial expression: -22*(39*x**2 - 18)\nExpanding the part (39*x**2 - 18) using the distributive property, and we got: (39*x**2)*(-22) - 18*(-22)\nReplacing -22*(39*x**2 - 18) with (39*x**2)*(-22) - 18*(-22) in the overall expression.\n#Step 3:\nCurrent expression: (26*x)*(39*x**2 - 18) + (39*x**2)*(-22) + 396\nSimplifying the partial expression: (26*x)*(39*x**2 - 18)\nExpanding the part (39*x**2 - 18) using the distributive property, and we got: -468*x + (26*x)*(39*x**2)\nReplacing (26*x)*(39*x**2 - 18) with -468*x + (26*x)*(39*x**2) in the overall expression.\n#Step 4:\nCurrent expression: -18*26*x + (26*x)*(39*x**2) + (39*x**2)*(-22) + 396\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (39*x**2)*-22 = -858*x**2\n (39*x**2)*(26*x) = 1014*x**3\n -18*26*x = -468*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1014*x**3 - 858*x**2 - 468*x + 396\nNo more calculations needed.\n1014*x**3 - 858*x**2 - 468*x + 396", "generated_answer": "1014*x**3 - 858*x**2 - 468*x + 396", "step_length": 5} {"cot_id": "c2a35502e2035d114422aecd1cb3595304670a84ff627148e98a1a40bd47b45b", "datapoint": {"question": "Calculate the following: (21 - 36*x**3)*(9*x**2 + 20*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-324*x**5 - 720*x**4 + 189*x**2 + 420*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1380, "polynomial_expr": "(21 - 36*x**3)*(9*x**2 + 20*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21 - 36*x**3)*(9*x**2 + 20*x)\nExpanding the part (21 - 36*x**3) using the distributive property, and we got: (-36*x**3)*(9*x**2 + 20*x) + 21*(9*x**2 + 20*x)\n#Step 2:\nCurrent expression: (-36*x**3)*(9*x**2 + 20*x) + 21*(9*x**2 + 20*x)\nSimplifying the partial expression: 21*(9*x**2 + 20*x)\nExpanding the part (9*x**2 + 20*x) using the distributive property, and we got: (20*x)*21 + (9*x**2)*21\nReplacing 21*(9*x**2 + 20*x) with (20*x)*21 + (9*x**2)*21 in the overall expression.\n#Step 3:\nCurrent expression: (20*x)*21 + (9*x**2)*21 + (-36*x**3)*(9*x**2 + 20*x)\nSimplifying the partial expression: (-36*x**3)*(9*x**2 + 20*x)\nExpanding the part (9*x**2 + 20*x) using the distributive property, and we got: (20*x)*(-36*x**3) + (9*x**2)*(-36*x**3)\nReplacing (-36*x**3)*(9*x**2 + 20*x) with (20*x)*(-36*x**3) + (9*x**2)*(-36*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (20*x)*(-36*x**3) + (20*x)*21 + (9*x**2)*(-36*x**3) + (9*x**2)*21\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (9*x**2)*21 = 189*x**2\n (9*x**2)*(-36*x**3) = -324*x**5\n (20*x)*21 = 420*x\n (20*x)*(-36*x**3) = -720*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -324*x**5 - 720*x**4 + 189*x**2 + 420*x\nNo more calculations needed.\n-324*x**5 - 720*x**4 + 189*x**2 + 420*x", "generated_answer": "-324*x**5 - 720*x**4 + 189*x**2 + 420*x", "step_length": 5} {"cot_id": "e9ef22ba7880cfb73522c564216e6366d3ef4f0564108a7dbeca9a1f458ed070", "datapoint": {"question": "Simplify this expression: (35 - 24*y**2)*(-12*y**3 + 39*y**2 - 47*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "288*y**5 - 936*y**4 + 708*y**3 + 1365*y**2 - 1645*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1381, "polynomial_expr": "(35 - 24*y**2)*(-12*y**3 + 39*y**2 - 47*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (35 - 24*y**2)*(-12*y**3 + 39*y**2 - 47*y)\nExpanding the part (35 - 24*y**2) using the distributive property, and we got: (-24*y**2)*(-12*y**3 + 39*y**2 - 47*y) + 35*(-12*y**3 + 39*y**2 - 47*y)\n#Step 2:\nCurrent expression: (-24*y**2)*(-12*y**3 + 39*y**2 - 47*y) + 35*(-12*y**3 + 39*y**2 - 47*y)\nSimplifying the partial expression: 35*(-12*y**3 + 39*y**2 - 47*y)\nExpanding the part (-12*y**3 + 39*y**2 - 47*y) using the distributive property, and we got: -47*y*35 + (39*y**2)*35 - 12*y**3*35\nReplacing 35*(-12*y**3 + 39*y**2 - 47*y) with -47*y*35 + (39*y**2)*35 - 12*y**3*35 in the overall expression.\n#Step 3:\nCurrent expression: -47*y*35 + (-24*y**2)*(-12*y**3 + 39*y**2 - 47*y) + (39*y**2)*35 - 12*y**3*35\nSimplifying the partial expression: (-24*y**2)*(-12*y**3 + 39*y**2 - 47*y)\nExpanding the part (-12*y**3 + 39*y**2 - 47*y) using the distributive property, and we got: (-47*y)*(-24*y**2) + (-24*y**2)*(39*y**2) + (-24*y**2)*(-12*y**3)\nReplacing (-24*y**2)*(-12*y**3 + 39*y**2 - 47*y) with (-47*y)*(-24*y**2) + (-24*y**2)*(39*y**2) + (-24*y**2)*(-12*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-47*y)*(-24*y**2) - 47*y*35 + (-24*y**2)*(39*y**2) + (-24*y**2)*(-12*y**3) + (39*y**2)*35 - 12*y**3*35\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*y)*35 = -1645*y\n (-47*y)*(-24*y**2) = 1128*y**3\n (-12*y**3)*35 = -420*y**3\n (-12*y**3)*(-24*y**2) = 288*y**5\n (39*y**2)*35 = 1365*y**2\n (39*y**2)*(-24*y**2) = -936*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 288*y**5 - 936*y**4 - 420*y**3 + 1128*y**3 + 1365*y**2 - 1645*y\nCombining like terms, got 288*y**5 - 936*y**4 + 708*y**3 + 1365*y**2 - 1645*y\n#Step 6:\nCurrent expression: 288*y**5 - 936*y**4 + 708*y**3 + 1365*y**2 - 1645*y\nNo more calculations needed.\n288*y**5 - 936*y**4 + 708*y**3 + 1365*y**2 - 1645*y", "generated_answer": "288*y**5 - 936*y**4 + 708*y**3 + 1365*y**2 - 1645*y", "step_length": 6} {"cot_id": "ac61211ca4b03bb272ca23c8b2345b36450845e2ce466586483cad8da784439f", "datapoint": {"question": "Calculate the following: (-32*x**3 + 35*x**2)*(18*x**3 + 23*x**2 - 31*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-576*x**6 - 106*x**5 + 1797*x**4 - 1085*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1382, "polynomial_expr": "(-32*x**3 + 35*x**2)*(18*x**3 + 23*x**2 - 31*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-32*x**3 + 35*x**2)*(18*x**3 + 23*x**2 - 31*x)\nExpanding the part (-32*x**3 + 35*x**2) using the distributive property, and we got: (35*x**2)*(18*x**3 + 23*x**2 - 31*x) + (-32*x**3)*(18*x**3 + 23*x**2 - 31*x)\n#Step 2:\nCurrent expression: (35*x**2)*(18*x**3 + 23*x**2 - 31*x) + (-32*x**3)*(18*x**3 + 23*x**2 - 31*x)\nSimplifying the partial expression: (-32*x**3)*(18*x**3 + 23*x**2 - 31*x)\nExpanding the part (18*x**3 + 23*x**2 - 31*x) using the distributive property, and we got: (-31*x)*(-32*x**3) + (23*x**2)*(-32*x**3) + (-32*x**3)*(18*x**3)\nReplacing (-32*x**3)*(18*x**3 + 23*x**2 - 31*x) with (-31*x)*(-32*x**3) + (23*x**2)*(-32*x**3) + (-32*x**3)*(18*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-31*x)*(-32*x**3) + (23*x**2)*(-32*x**3) + (35*x**2)*(18*x**3 + 23*x**2 - 31*x) + (-32*x**3)*(18*x**3)\nSimplifying the partial expression: (35*x**2)*(18*x**3 + 23*x**2 - 31*x)\nExpanding the part (18*x**3 + 23*x**2 - 31*x) using the distributive property, and we got: (-31*x)*(35*x**2) + (23*x**2)*(35*x**2) + (35*x**2)*(18*x**3)\nReplacing (35*x**2)*(18*x**3 + 23*x**2 - 31*x) with (-31*x)*(35*x**2) + (23*x**2)*(35*x**2) + (35*x**2)*(18*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-31*x)*(35*x**2) + (-31*x)*(-32*x**3) + (23*x**2)*(35*x**2) + (23*x**2)*(-32*x**3) + (35*x**2)*(18*x**3) + (-32*x**3)*(18*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-31*x)*(-32*x**3) = 992*x**4\n (-31*x)*(35*x**2) = -1085*x**3\n (18*x**3)*(-32*x**3) = -576*x**6\n (18*x**3)*(35*x**2) = 630*x**5\n (23*x**2)*(-32*x**3) = -736*x**5\n (23*x**2)*(35*x**2) = 805*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -576*x**6 - 736*x**5 + 630*x**5 + 805*x**4 + 992*x**4 - 1085*x**3\nCombining like terms, got -576*x**6 - 106*x**5 + 1797*x**4 - 1085*x**3\n#Step 6:\nCurrent expression: -576*x**6 - 106*x**5 + 1797*x**4 - 1085*x**3\nNo more calculations needed.\n-576*x**6 - 106*x**5 + 1797*x**4 - 1085*x**3", "generated_answer": "-576*x**6 - 106*x**5 + 1797*x**4 - 1085*x**3", "step_length": 6} {"cot_id": "1cf35c5ef228cd2f5bcb8ee139069247ce07101a0494d460073d66e0f9b9dce5", "datapoint": {"question": "Simplify this expression: (-40*y**2 - 12*y - 30)*(-12*y**3 - 43*y**2 + 2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "480*y**5 + 1864*y**4 + 876*y**3 + 1210*y**2 - 24*y - 60", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1383, "polynomial_expr": "(-40*y**2 - 12*y - 30)*(-12*y**3 - 43*y**2 + 2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-40*y**2 - 12*y - 30)*(-12*y**3 - 43*y**2 + 2)\nExpanding the part (-40*y**2 - 12*y - 30) using the distributive property, and we got: (-12*y)*(-12*y**3 - 43*y**2 + 2) + (-40*y**2)*(-12*y**3 - 43*y**2 + 2) - 30*(-12*y**3 - 43*y**2 + 2)\n#Step 2:\nCurrent expression: (-12*y)*(-12*y**3 - 43*y**2 + 2) + (-40*y**2)*(-12*y**3 - 43*y**2 + 2) - 30*(-12*y**3 - 43*y**2 + 2)\nSimplifying the partial expression: -30*(-12*y**3 - 43*y**2 + 2)\nExpanding the part (-12*y**3 - 43*y**2 + 2) using the distributive property, and we got: -43*y**2*(-30) - 12*y**3*(-30) + 2*(-30)\nReplacing -30*(-12*y**3 - 43*y**2 + 2) with -43*y**2*(-30) - 12*y**3*(-30) + 2*(-30) in the overall expression.\n#Step 3:\nCurrent expression: (-12*y)*(-12*y**3 - 43*y**2 + 2) - 43*y**2*(-30) + (-40*y**2)*(-12*y**3 - 43*y**2 + 2) - 12*y**3*(-30) - 60\nSimplifying the partial expression: (-40*y**2)*(-12*y**3 - 43*y**2 + 2)\nExpanding the part (-12*y**3 - 43*y**2 + 2) using the distributive property, and we got: 2*(-40*y**2) + (-43*y**2)*(-40*y**2) + (-40*y**2)*(-12*y**3)\nReplacing (-40*y**2)*(-12*y**3 - 43*y**2 + 2) with 2*(-40*y**2) + (-43*y**2)*(-40*y**2) + (-40*y**2)*(-12*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-12*y)*(-12*y**3 - 43*y**2 + 2) + 2*(-40)*y**2 + (-43*y**2)*(-40*y**2) - 43*y**2*(-30) + (-40*y**2)*(-12*y**3) - 12*y**3*(-30) - 60\nSimplifying the partial expression: (-12*y)*(-12*y**3 - 43*y**2 + 2)\nExpanding the part (-12*y**3 - 43*y**2 + 2) using the distributive property, and we got: (-12*y)*(-43*y**2) + (-12*y)*(-12*y**3) + 2*(-12*y)\nReplacing (-12*y)*(-12*y**3 - 43*y**2 + 2) with (-12*y)*(-43*y**2) + (-12*y)*(-12*y**3) + 2*(-12*y) in the overall expression.\n#Step 5:\nCurrent expression: (-12*y)*(-43*y**2) + (-12*y)*(-12*y**3) + 2*(-40)*y**2 + 2*(-12)*y + (-43*y**2)*(-40*y**2) - 43*y**2*(-30) + (-40*y**2)*(-12*y**3) - 12*y**3*(-30) - 60\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-43*y**2)*-30 = 1290*y**2\n (-43*y**2)*(-40*y**2) = 1720*y**4\n (-43*y**2)*(-12*y) = 516*y**3\n (-12*y**3)*-30 = 360*y**3\n (-12*y**3)*(-40*y**2) = 480*y**5\n (-12*y**3)*(-12*y) = 144*y**4\n 2*-40*y**2 = -80*y**2\n 2*-12*y = -24*y\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 480*y**5 + 144*y**4 + 1720*y**4 + 360*y**3 + 516*y**3 - 80*y**2 + 1290*y**2 - 24*y - 60\nCombining like terms, got 480*y**5 + 1864*y**4 + 876*y**3 + 1210*y**2 - 24*y - 60\n#Step 7:\nCurrent expression: 480*y**5 + 1864*y**4 + 876*y**3 + 1210*y**2 - 24*y - 60\nNo more calculations needed.\n480*y**5 + 1864*y**4 + 876*y**3 + 1210*y**2 - 24*y - 60", "generated_answer": "480*y**5 + 1864*y**4 + 876*y**3 + 1210*y**2 - 24*y - 60", "step_length": 7} {"cot_id": "35ab731ea3dff4513dae582e3ccbce6fca71a472dfd3154f5f94dcee3cbc8452", "datapoint": {"question": "Calculate the following: 17*x**2*(-60*x**3 - 18*x**2 - 4*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1020*x**5 - 306*x**4 - 68*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1384, "polynomial_expr": "17*x**2*(-60*x**3 - 18*x**2 - 4*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 17*x**2*(-60*x**3 - 18*x**2 - 4*x)\nExpanding the part (-60*x**3 - 18*x**2 - 4*x) using the distributive property, and we got: (-4*x)*(17*x**2) + (-18*x**2)*(17*x**2) + (17*x**2)*(-60*x**3)\n#Step 2:\nCurrent expression: (-4*x)*(17*x**2) + (-18*x**2)*(17*x**2) + (17*x**2)*(-60*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-60*x**3)*(17*x**2) = -1020*x**5\n (-18*x**2)*(17*x**2) = -306*x**4\n (-4*x)*(17*x**2) = -68*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1020*x**5 - 306*x**4 - 68*x**3\nNo more calculations needed.\n-1020*x**5 - 306*x**4 - 68*x**3", "generated_answer": "-1020*x**5 - 306*x**4 - 68*x**3", "step_length": 3} {"cot_id": "04a84b19c7a01e84e619a391689cc3e307dc2c0cfb4f20c149fe3bee50bce975", "datapoint": {"question": "Simplify this expression: (-50*x**3 - 18*x)*(44*x**3 + 5*x**2 + 9)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2200*x**6 - 250*x**5 - 792*x**4 - 540*x**3 - 162*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1385, "polynomial_expr": "(-50*x**3 - 18*x)*(44*x**3 + 5*x**2 + 9)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-50*x**3 - 18*x)*(44*x**3 + 5*x**2 + 9)\nExpanding the part (-50*x**3 - 18*x) using the distributive property, and we got: (-18*x)*(44*x**3 + 5*x**2 + 9) + (-50*x**3)*(44*x**3 + 5*x**2 + 9)\n#Step 2:\nCurrent expression: (-18*x)*(44*x**3 + 5*x**2 + 9) + (-50*x**3)*(44*x**3 + 5*x**2 + 9)\nSimplifying the partial expression: (-50*x**3)*(44*x**3 + 5*x**2 + 9)\nExpanding the part (44*x**3 + 5*x**2 + 9) using the distributive property, and we got: 9*(-50*x**3) + (5*x**2)*(-50*x**3) + (-50*x**3)*(44*x**3)\nReplacing (-50*x**3)*(44*x**3 + 5*x**2 + 9) with 9*(-50*x**3) + (5*x**2)*(-50*x**3) + (-50*x**3)*(44*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-18*x)*(44*x**3 + 5*x**2 + 9) + 9*(-50)*x**3 + (5*x**2)*(-50*x**3) + (-50*x**3)*(44*x**3)\nSimplifying the partial expression: (-18*x)*(44*x**3 + 5*x**2 + 9)\nExpanding the part (44*x**3 + 5*x**2 + 9) using the distributive property, and we got: (-18*x)*(5*x**2) + (-18*x)*(44*x**3) + 9*(-18*x)\nReplacing (-18*x)*(44*x**3 + 5*x**2 + 9) with (-18*x)*(5*x**2) + (-18*x)*(44*x**3) + 9*(-18*x) in the overall expression.\n#Step 4:\nCurrent expression: (-18*x)*(5*x**2) + (-18*x)*(44*x**3) + 9*(-50)*x**3 + 9*(-18)*x + (5*x**2)*(-50*x**3) + (-50*x**3)*(44*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (5*x**2)*(-50*x**3) = -250*x**5\n (5*x**2)*(-18*x) = -90*x**3\n (44*x**3)*(-50*x**3) = -2200*x**6\n (44*x**3)*(-18*x) = -792*x**4\n 9*-50*x**3 = -450*x**3\n 9*-18*x = -162*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2200*x**6 - 250*x**5 - 792*x**4 - 450*x**3 - 90*x**3 - 162*x\nCombining like terms, got -2200*x**6 - 250*x**5 - 792*x**4 - 540*x**3 - 162*x\n#Step 6:\nCurrent expression: -2200*x**6 - 250*x**5 - 792*x**4 - 540*x**3 - 162*x\nNo more calculations needed.\n-2200*x**6 - 250*x**5 - 792*x**4 - 540*x**3 - 162*x", "generated_answer": "-2200*x**6 - 250*x**5 - 792*x**4 - 540*x**3 - 162*x", "step_length": 6} {"cot_id": "54a2e091eb13ad38329465c3f0f15c08d50f04f8ddf94da1a348287a78a44e5a", "datapoint": {"question": "Simplify this expression: 24*z**2*(49*z**2 - 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1176*z**4 - 1128*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1386, "polynomial_expr": "24*z**2*(49*z**2 - 47)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 24*z**2*(49*z**2 - 47)\nExpanding the part (49*z**2 - 47) using the distributive property, and we got: -1128*z**2 + (24*z**2)*(49*z**2)\n#Step 2:\nCurrent expression: -1128*z**2 + (24*z**2)*(49*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -47*(24*z**2) = -1128*z**2\n (49*z**2)*(24*z**2) = 1176*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1176*z**4 - 1128*z**2\nNo more calculations needed.\n1176*z**4 - 1128*z**2", "generated_answer": "1176*z**4 - 1128*z**2", "step_length": 3} {"cot_id": "99313d7db55b87799b82eb5e43c644a3625ded07812a5c152fddee26b0788353", "datapoint": {"question": "Calculate the following: (2*x**3 + 20*x**2)*(26*x**3 + 7*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "52*x**6 + 534*x**5 + 140*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1387, "polynomial_expr": "(2*x**3 + 20*x**2)*(26*x**3 + 7*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2*x**3 + 20*x**2)*(26*x**3 + 7*x**2)\nExpanding the part (2*x**3 + 20*x**2) using the distributive property, and we got: (20*x**2)*(26*x**3 + 7*x**2) + (2*x**3)*(26*x**3 + 7*x**2)\n#Step 2:\nCurrent expression: (20*x**2)*(26*x**3 + 7*x**2) + (2*x**3)*(26*x**3 + 7*x**2)\nSimplifying the partial expression: (2*x**3)*(26*x**3 + 7*x**2)\nExpanding the part (26*x**3 + 7*x**2) using the distributive property, and we got: (7*x**2)*(2*x**3) + (2*x**3)*(26*x**3)\nReplacing (2*x**3)*(26*x**3 + 7*x**2) with (7*x**2)*(2*x**3) + (2*x**3)*(26*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (7*x**2)*(2*x**3) + (20*x**2)*(26*x**3 + 7*x**2) + (2*x**3)*(26*x**3)\nSimplifying the partial expression: (20*x**2)*(26*x**3 + 7*x**2)\nExpanding the part (26*x**3 + 7*x**2) using the distributive property, and we got: (7*x**2)*(20*x**2) + (20*x**2)*(26*x**3)\nReplacing (20*x**2)*(26*x**3 + 7*x**2) with (7*x**2)*(20*x**2) + (20*x**2)*(26*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (7*x**2)*(20*x**2) + (7*x**2)*(2*x**3) + (20*x**2)*(26*x**3) + (2*x**3)*(26*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (7*x**2)*(2*x**3) = 14*x**5\n (7*x**2)*(20*x**2) = 140*x**4\n (26*x**3)*(2*x**3) = 52*x**6\n (26*x**3)*(20*x**2) = 520*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 52*x**6 + 14*x**5 + 520*x**5 + 140*x**4\nCombining like terms, got 52*x**6 + 534*x**5 + 140*x**4\n#Step 6:\nCurrent expression: 52*x**6 + 534*x**5 + 140*x**4\nNo more calculations needed.\n52*x**6 + 534*x**5 + 140*x**4", "generated_answer": "52*x**6 + 534*x**5 + 140*x**4", "step_length": 6} {"cot_id": "575f3b0c3834a9d14f0dc7e86d89c74791ad860b260a42c9fdf861c3e9cb36af", "datapoint": {"question": "Calculate the following: -58*y**2*(33*y**2 - 11*y + 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1914*y**4 + 638*y**3 - 58*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1388, "polynomial_expr": "-58*y**2*(33*y**2 - 11*y + 1)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -58*y**2*(33*y**2 - 11*y + 1)\nExpanding the part (33*y**2 - 11*y + 1) using the distributive property, and we got: (-11*y)*(-58*y**2) + 1*(-58*y**2) + (-58*y**2)*(33*y**2)\n#Step 2:\nCurrent expression: (-11*y)*(-58*y**2) + 1*(-58*y**2) + (-58*y**2)*(33*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 1*(-58*y**2) = -58*y**2\n (-11*y)*(-58*y**2) = 638*y**3\n (33*y**2)*(-58*y**2) = -1914*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1914*y**4 + 638*y**3 - 58*y**2\nNo more calculations needed.\n-1914*y**4 + 638*y**3 - 58*y**2", "generated_answer": "-1914*y**4 + 638*y**3 - 58*y**2", "step_length": 3} {"cot_id": "96f31ca074a15d55aa317f386b855abff13c1bf49cad8859592fae451b406e5b", "datapoint": {"question": "Calculate the following: -96*z**2\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-96*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1389, "polynomial_expr": "-96*z**2", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -96*z**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -96*z**2\nNo more calculations needed.\n-96*z**2", "generated_answer": "-96*z**2", "step_length": 2} {"cot_id": "0b0915fc39d3b68b11717b288b506fbbcb55d0765d5a6329d4f854fa94646042", "datapoint": {"question": "Simplify this expression: 16*y**3*(3*y**2 - 10*y + 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "48*y**5 - 160*y**4 + 160*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1390, "polynomial_expr": "16*y**3*(3*y**2 - 10*y + 10)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 16*y**3*(3*y**2 - 10*y + 10)\nExpanding the part (3*y**2 - 10*y + 10) using the distributive property, and we got: (-10*y)*(16*y**3) + 10*(16*y**3) + (3*y**2)*(16*y**3)\n#Step 2:\nCurrent expression: (-10*y)*(16*y**3) + 10*(16*y**3) + (3*y**2)*(16*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 10*(16*y**3) = 160*y**3\n (-10*y)*(16*y**3) = -160*y**4\n (3*y**2)*(16*y**3) = 48*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 48*y**5 - 160*y**4 + 160*y**3\nNo more calculations needed.\n48*y**5 - 160*y**4 + 160*y**3", "generated_answer": "48*y**5 - 160*y**4 + 160*y**3", "step_length": 3} {"cot_id": "1d64e228c0980a44b0b56e7f86df223f37328a40d8558267b1361f77f43407f1", "datapoint": {"question": "Simplify this expression: (-45*z**3 + 9*z**2)*(-50*z**3 - 39*z**2 - 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2250*z**6 + 1305*z**5 - 351*z**4 + 45*z**3 - 9*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1391, "polynomial_expr": "(-45*z**3 + 9*z**2)*(-50*z**3 - 39*z**2 - 1)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-45*z**3 + 9*z**2)*(-50*z**3 - 39*z**2 - 1)\nExpanding the part (-45*z**3 + 9*z**2) using the distributive property, and we got: (9*z**2)*(-50*z**3 - 39*z**2 - 1) + (-45*z**3)*(-50*z**3 - 39*z**2 - 1)\n#Step 2:\nCurrent expression: (9*z**2)*(-50*z**3 - 39*z**2 - 1) + (-45*z**3)*(-50*z**3 - 39*z**2 - 1)\nSimplifying the partial expression: (-45*z**3)*(-50*z**3 - 39*z**2 - 1)\nExpanding the part (-50*z**3 - 39*z**2 - 1) using the distributive property, and we got: -(-1)*45*z**3 + (-39*z**2)*(-45*z**3) + (-50*z**3)*(-45*z**3)\nReplacing (-45*z**3)*(-50*z**3 - 39*z**2 - 1) with -(-1)*45*z**3 + (-39*z**2)*(-45*z**3) + (-50*z**3)*(-45*z**3) in the overall expression.\n#Step 3:\nCurrent expression: -1*(-45)*z**3 + (-39*z**2)*(-45*z**3) + (9*z**2)*(-50*z**3 - 39*z**2 - 1) + (-50*z**3)*(-45*z**3)\nSimplifying the partial expression: (9*z**2)*(-50*z**3 - 39*z**2 - 1)\nExpanding the part (-50*z**3 - 39*z**2 - 1) using the distributive property, and we got: -9*z**2 + (-39*z**2)*(9*z**2) + (9*z**2)*(-50*z**3)\nReplacing (9*z**2)*(-50*z**3 - 39*z**2 - 1) with -9*z**2 + (-39*z**2)*(9*z**2) + (9*z**2)*(-50*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -1*(-45)*z**3 - 1*9*z**2 + (-39*z**2)*(9*z**2) + (-39*z**2)*(-45*z**3) + (9*z**2)*(-50*z**3) + (-50*z**3)*(-45*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-50*z**3)*(-45*z**3) = 2250*z**6\n (-50*z**3)*(9*z**2) = -450*z**5\n (-39*z**2)*(-45*z**3) = 1755*z**5\n (-39*z**2)*(9*z**2) = -351*z**4\n -1*-45*z**3 = 45*z**3\n -1*9*z**2 = -9*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2250*z**6 - 450*z**5 + 1755*z**5 - 351*z**4 + 45*z**3 - 9*z**2\nCombining like terms, got 2250*z**6 + 1305*z**5 - 351*z**4 + 45*z**3 - 9*z**2\n#Step 6:\nCurrent expression: 2250*z**6 + 1305*z**5 - 351*z**4 + 45*z**3 - 9*z**2\nNo more calculations needed.\n2250*z**6 + 1305*z**5 - 351*z**4 + 45*z**3 - 9*z**2", "generated_answer": "2250*z**6 + 1305*z**5 - 351*z**4 + 45*z**3 - 9*z**2", "step_length": 6} {"cot_id": "772c4d2a4f07bdaa0e4b271d342ad09f1dd675de954ef6f61651bdf1effe2a50", "datapoint": {"question": "Simplify this expression: (36*x**3 + 11*x)*(-12*x**3 - 17*x - 26)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-432*x**6 - 744*x**4 - 936*x**3 - 187*x**2 - 286*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1392, "polynomial_expr": "(36*x**3 + 11*x)*(-12*x**3 - 17*x - 26)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (36*x**3 + 11*x)*(-12*x**3 - 17*x - 26)\nExpanding the part (36*x**3 + 11*x) using the distributive property, and we got: (11*x)*(-12*x**3 - 17*x - 26) + (36*x**3)*(-12*x**3 - 17*x - 26)\n#Step 2:\nCurrent expression: (11*x)*(-12*x**3 - 17*x - 26) + (36*x**3)*(-12*x**3 - 17*x - 26)\nSimplifying the partial expression: (11*x)*(-12*x**3 - 17*x - 26)\nExpanding the part (-12*x**3 - 17*x - 26) using the distributive property, and we got: (-17*x)*(11*x) - 286*x + (11*x)*(-12*x**3)\nReplacing (11*x)*(-12*x**3 - 17*x - 26) with (-17*x)*(11*x) - 286*x + (11*x)*(-12*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-17*x)*(11*x) - 26*11*x + (11*x)*(-12*x**3) + (36*x**3)*(-12*x**3 - 17*x - 26)\nSimplifying the partial expression: (36*x**3)*(-12*x**3 - 17*x - 26)\nExpanding the part (-12*x**3 - 17*x - 26) using the distributive property, and we got: (-17*x)*(36*x**3) - 936*x**3 + (-12*x**3)*(36*x**3)\nReplacing (36*x**3)*(-12*x**3 - 17*x - 26) with (-17*x)*(36*x**3) - 936*x**3 + (-12*x**3)*(36*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-17*x)*(11*x) + (-17*x)*(36*x**3) - 26*36*x**3 - 26*11*x + (11*x)*(-12*x**3) + (-12*x**3)*(36*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-17*x)*(11*x) = -187*x**2\n (-17*x)*(36*x**3) = -612*x**4\n (-12*x**3)*(11*x) = -132*x**4\n (-12*x**3)*(36*x**3) = -432*x**6\n -26*11*x = -286*x\n -26*36*x**3 = -936*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -432*x**6 - 612*x**4 - 132*x**4 - 936*x**3 - 187*x**2 - 286*x\nCombining like terms, got -432*x**6 - 744*x**4 - 936*x**3 - 187*x**2 - 286*x\n#Step 6:\nCurrent expression: -432*x**6 - 744*x**4 - 936*x**3 - 187*x**2 - 286*x\nNo more calculations needed.\n-432*x**6 - 744*x**4 - 936*x**3 - 187*x**2 - 286*x", "generated_answer": "-432*x**6 - 744*x**4 - 936*x**3 - 187*x**2 - 286*x", "step_length": 6} {"cot_id": "2fb66f2467166f3bcc1c802d040c2091a860f92cd85ccf6e62f9e6a9bb837719", "datapoint": {"question": "Calculate the following: -924*y**3 - 1302*y\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-924*y**3 - 1302*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1393, "polynomial_expr": "-924*y**3 - 1302*y", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -924*y**3 - 1302*y\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -924*y**3 - 1302*y\nNo more calculations needed.\n-924*y**3 - 1302*y", "generated_answer": "-924*y**3 - 1302*y", "step_length": 2} {"cot_id": "1992a7443b572cd3042aae4ca2a91ea3ea402c8f38150df09ada0f3c3170a8ad", "datapoint": {"question": "Simplify this expression: (-16*y**2 - 38)*(48*y**3 + 7*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-768*y**5 - 112*y**4 - 1824*y**3 - 266*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1394, "polynomial_expr": "(-16*y**2 - 38)*(48*y**3 + 7*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-16*y**2 - 38)*(48*y**3 + 7*y**2)\nExpanding the part (-16*y**2 - 38) using the distributive property, and we got: (-16*y**2)*(48*y**3 + 7*y**2) - 38*(48*y**3 + 7*y**2)\n#Step 2:\nCurrent expression: (-16*y**2)*(48*y**3 + 7*y**2) - 38*(48*y**3 + 7*y**2)\nSimplifying the partial expression: -38*(48*y**3 + 7*y**2)\nExpanding the part (48*y**3 + 7*y**2) using the distributive property, and we got: (7*y**2)*(-38) + (48*y**3)*(-38)\nReplacing -38*(48*y**3 + 7*y**2) with (7*y**2)*(-38) + (48*y**3)*(-38) in the overall expression.\n#Step 3:\nCurrent expression: (-16*y**2)*(48*y**3 + 7*y**2) + (7*y**2)*(-38) + (48*y**3)*(-38)\nSimplifying the partial expression: (-16*y**2)*(48*y**3 + 7*y**2)\nExpanding the part (48*y**3 + 7*y**2) using the distributive property, and we got: (-16*y**2)*(7*y**2) + (-16*y**2)*(48*y**3)\nReplacing (-16*y**2)*(48*y**3 + 7*y**2) with (-16*y**2)*(7*y**2) + (-16*y**2)*(48*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-16*y**2)*(7*y**2) + (-16*y**2)*(48*y**3) + (7*y**2)*(-38) + (48*y**3)*(-38)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (7*y**2)*-38 = -266*y**2\n (7*y**2)*(-16*y**2) = -112*y**4\n (48*y**3)*-38 = -1824*y**3\n (48*y**3)*(-16*y**2) = -768*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -768*y**5 - 112*y**4 - 1824*y**3 - 266*y**2\nNo more calculations needed.\n-768*y**5 - 112*y**4 - 1824*y**3 - 266*y**2", "generated_answer": "-768*y**5 - 112*y**4 - 1824*y**3 - 266*y**2", "step_length": 5} {"cot_id": "29bb9c5471d946f584ade4c7711819ca60d5f3c1bbbef2773e2372690c05da99", "datapoint": {"question": "Calculate the following: (47*x + 11)*(35*x**3 - 23*x**2 - 32*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1645*x**4 - 696*x**3 - 1757*x**2 - 352*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1395, "polynomial_expr": "(47*x + 11)*(35*x**3 - 23*x**2 - 32*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (47*x + 11)*(35*x**3 - 23*x**2 - 32*x)\nExpanding the part (47*x + 11) using the distributive property, and we got: (47*x)*(35*x**3 - 23*x**2 - 32*x) + 11*(35*x**3 - 23*x**2 - 32*x)\n#Step 2:\nCurrent expression: (47*x)*(35*x**3 - 23*x**2 - 32*x) + 11*(35*x**3 - 23*x**2 - 32*x)\nSimplifying the partial expression: 11*(35*x**3 - 23*x**2 - 32*x)\nExpanding the part (35*x**3 - 23*x**2 - 32*x) using the distributive property, and we got: -32*x*11 - 23*x**2*11 + (35*x**3)*11\nReplacing 11*(35*x**3 - 23*x**2 - 32*x) with -32*x*11 - 23*x**2*11 + (35*x**3)*11 in the overall expression.\n#Step 3:\nCurrent expression: -32*x*11 + (47*x)*(35*x**3 - 23*x**2 - 32*x) - 23*x**2*11 + (35*x**3)*11\nSimplifying the partial expression: (47*x)*(35*x**3 - 23*x**2 - 32*x)\nExpanding the part (35*x**3 - 23*x**2 - 32*x) using the distributive property, and we got: (-32*x)*(47*x) + (47*x)*(-23*x**2) + (47*x)*(35*x**3)\nReplacing (47*x)*(35*x**3 - 23*x**2 - 32*x) with (-32*x)*(47*x) + (47*x)*(-23*x**2) + (47*x)*(35*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-32*x)*(47*x) - 32*x*11 + (47*x)*(-23*x**2) + (47*x)*(35*x**3) - 23*x**2*11 + (35*x**3)*11\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*x)*11 = -352*x\n (-32*x)*(47*x) = -1504*x**2\n (-23*x**2)*11 = -253*x**2\n (-23*x**2)*(47*x) = -1081*x**3\n (35*x**3)*11 = 385*x**3\n (35*x**3)*(47*x) = 1645*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1645*x**4 - 1081*x**3 + 385*x**3 - 1504*x**2 - 253*x**2 - 352*x\nCombining like terms, got 1645*x**4 - 696*x**3 - 1757*x**2 - 352*x\n#Step 6:\nCurrent expression: 1645*x**4 - 696*x**3 - 1757*x**2 - 352*x\nNo more calculations needed.\n1645*x**4 - 696*x**3 - 1757*x**2 - 352*x", "generated_answer": "1645*x**4 - 696*x**3 - 1757*x**2 - 352*x", "step_length": 6} {"cot_id": "65e41f7c974204db444f4d1837de547faf7aaf21b7f92f2f9214565877913f56", "datapoint": {"question": "Calculate the following: (38*y**2 + 1)*(-10*y**3 + 34*y**2 + 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-380*y**5 + 1292*y**4 - 10*y**3 + 1896*y**2 + 49", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1396, "polynomial_expr": "(38*y**2 + 1)*(-10*y**3 + 34*y**2 + 49)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (38*y**2 + 1)*(-10*y**3 + 34*y**2 + 49)\nExpanding the part (38*y**2 + 1) using the distributive property, and we got: (38*y**2)*(-10*y**3 + 34*y**2 + 49) + 1*(-10*y**3 + 34*y**2 + 49)\n#Step 2:\nCurrent expression: (38*y**2)*(-10*y**3 + 34*y**2 + 49) + 1*(-10*y**3 + 34*y**2 + 49)\nSimplifying the partial expression: 1*(-10*y**3 + 34*y**2 + 49)\nExpanding the part (-10*y**3 + 34*y**2 + 49) using the distributive property, and we got: (34*y**2)*1 - 10*y**3*1 + 49*1\nReplacing 1*(-10*y**3 + 34*y**2 + 49) with (34*y**2)*1 - 10*y**3*1 + 49*1 in the overall expression.\n#Step 3:\nCurrent expression: (34*y**2)*1 + (38*y**2)*(-10*y**3 + 34*y**2 + 49) - 10*y**3*1 + 49\nSimplifying the partial expression: (38*y**2)*(-10*y**3 + 34*y**2 + 49)\nExpanding the part (-10*y**3 + 34*y**2 + 49) using the distributive property, and we got: 49*(38*y**2) + (34*y**2)*(38*y**2) + (38*y**2)*(-10*y**3)\nReplacing (38*y**2)*(-10*y**3 + 34*y**2 + 49) with 49*(38*y**2) + (34*y**2)*(38*y**2) + (38*y**2)*(-10*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 49*38*y**2 + (34*y**2)*(38*y**2) + (34*y**2)*1 + (38*y**2)*(-10*y**3) - 10*y**3*1 + 49\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*y**3)*1 = -10*y**3\n (-10*y**3)*(38*y**2) = -380*y**5\n (34*y**2)*1 = 34*y**2\n (34*y**2)*(38*y**2) = 1292*y**4\n 49*38*y**2 = 1862*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -380*y**5 + 1292*y**4 - 10*y**3 + 34*y**2 + 1862*y**2 + 49\nCombining like terms, got -380*y**5 + 1292*y**4 - 10*y**3 + 1896*y**2 + 49\n#Step 6:\nCurrent expression: -380*y**5 + 1292*y**4 - 10*y**3 + 1896*y**2 + 49\nNo more calculations needed.\n-380*y**5 + 1292*y**4 - 10*y**3 + 1896*y**2 + 49", "generated_answer": "-380*y**5 + 1292*y**4 - 10*y**3 + 1896*y**2 + 49", "step_length": 6} {"cot_id": "2751ee3716f7407b32108338dce2918cab2d52144cf1eda507a65e99db5d77e9", "datapoint": {"question": "Calculate the following: (-7*z**3 + 44*z)*(5*z**3 + 34*z**2 + 48*z + 43)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-35*z**6 - 238*z**5 - 116*z**4 + 1195*z**3 + 2112*z**2 + 1892*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1397, "polynomial_expr": "(-7*z**3 + 44*z)*(5*z**3 + 34*z**2 + 48*z + 43)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-7*z**3 + 44*z)*(5*z**3 + 34*z**2 + 48*z + 43)\nExpanding the part (-7*z**3 + 44*z) using the distributive property, and we got: (44*z)*(5*z**3 + 34*z**2 + 48*z + 43) + (-7*z**3)*(5*z**3 + 34*z**2 + 48*z + 43)\n#Step 2:\nCurrent expression: (44*z)*(5*z**3 + 34*z**2 + 48*z + 43) + (-7*z**3)*(5*z**3 + 34*z**2 + 48*z + 43)\nSimplifying the partial expression: (-7*z**3)*(5*z**3 + 34*z**2 + 48*z + 43)\nExpanding the part (5*z**3 + 34*z**2 + 48*z + 43) using the distributive property, and we got: 43*(-7*z**3) + (48*z)*(-7*z**3) + (34*z**2)*(-7*z**3) + (-7*z**3)*(5*z**3)\nReplacing (-7*z**3)*(5*z**3 + 34*z**2 + 48*z + 43) with 43*(-7*z**3) + (48*z)*(-7*z**3) + (34*z**2)*(-7*z**3) + (-7*z**3)*(5*z**3) in the overall expression.\n#Step 3:\nCurrent expression: 43*(-7)*z**3 + (44*z)*(5*z**3 + 34*z**2 + 48*z + 43) + (48*z)*(-7*z**3) + (34*z**2)*(-7*z**3) + (-7*z**3)*(5*z**3)\nSimplifying the partial expression: (44*z)*(5*z**3 + 34*z**2 + 48*z + 43)\nExpanding the part (5*z**3 + 34*z**2 + 48*z + 43) using the distributive property, and we got: 43*(44*z) + (44*z)*(48*z) + (44*z)*(34*z**2) + (44*z)*(5*z**3)\nReplacing (44*z)*(5*z**3 + 34*z**2 + 48*z + 43) with 43*(44*z) + (44*z)*(48*z) + (44*z)*(34*z**2) + (44*z)*(5*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 43*(-7)*z**3 + 43*44*z + (44*z)*(48*z) + (44*z)*(34*z**2) + (44*z)*(5*z**3) + (48*z)*(-7*z**3) + (34*z**2)*(-7*z**3) + (-7*z**3)*(5*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (5*z**3)*(-7*z**3) = -35*z**6\n (5*z**3)*(44*z) = 220*z**4\n (34*z**2)*(-7*z**3) = -238*z**5\n (34*z**2)*(44*z) = 1496*z**3\n (48*z)*(-7*z**3) = -336*z**4\n (48*z)*(44*z) = 2112*z**2\n 43*-7*z**3 = -301*z**3\n 43*44*z = 1892*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -35*z**6 - 238*z**5 - 336*z**4 + 220*z**4 - 301*z**3 + 1496*z**3 + 2112*z**2 + 1892*z\nCombining like terms, got -35*z**6 - 238*z**5 - 116*z**4 + 1195*z**3 + 2112*z**2 + 1892*z\n#Step 6:\nCurrent expression: -35*z**6 - 238*z**5 - 116*z**4 + 1195*z**3 + 2112*z**2 + 1892*z\nNo more calculations needed.\n-35*z**6 - 238*z**5 - 116*z**4 + 1195*z**3 + 2112*z**2 + 1892*z", "generated_answer": "-35*z**6 - 238*z**5 - 116*z**4 + 1195*z**3 + 2112*z**2 + 1892*z", "step_length": 6} {"cot_id": "877b9d0b179113c6ed08a5cd985b18837203751fe0958126acbd0c7bda83e9a7", "datapoint": {"question": "Calculate the following: (35 - 3*x**2)*(-18*x**3 - 30*x**2 - 49*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "54*x**5 + 90*x**4 - 483*x**3 - 1050*x**2 - 1715*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1398, "polynomial_expr": "(35 - 3*x**2)*(-18*x**3 - 30*x**2 - 49*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (35 - 3*x**2)*(-18*x**3 - 30*x**2 - 49*x)\nExpanding the part (35 - 3*x**2) using the distributive property, and we got: (-3*x**2)*(-18*x**3 - 30*x**2 - 49*x) + 35*(-18*x**3 - 30*x**2 - 49*x)\n#Step 2:\nCurrent expression: (-3*x**2)*(-18*x**3 - 30*x**2 - 49*x) + 35*(-18*x**3 - 30*x**2 - 49*x)\nSimplifying the partial expression: 35*(-18*x**3 - 30*x**2 - 49*x)\nExpanding the part (-18*x**3 - 30*x**2 - 49*x) using the distributive property, and we got: -49*x*35 - 30*x**2*35 - 18*x**3*35\nReplacing 35*(-18*x**3 - 30*x**2 - 49*x) with -49*x*35 - 30*x**2*35 - 18*x**3*35 in the overall expression.\n#Step 3:\nCurrent expression: -49*x*35 - 30*x**2*35 + (-3*x**2)*(-18*x**3 - 30*x**2 - 49*x) - 18*x**3*35\nSimplifying the partial expression: (-3*x**2)*(-18*x**3 - 30*x**2 - 49*x)\nExpanding the part (-18*x**3 - 30*x**2 - 49*x) using the distributive property, and we got: (-49*x)*(-3*x**2) + (-30*x**2)*(-3*x**2) + (-3*x**2)*(-18*x**3)\nReplacing (-3*x**2)*(-18*x**3 - 30*x**2 - 49*x) with (-49*x)*(-3*x**2) + (-30*x**2)*(-3*x**2) + (-3*x**2)*(-18*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-49*x)*(-3*x**2) - 49*x*35 + (-30*x**2)*(-3*x**2) - 30*x**2*35 + (-3*x**2)*(-18*x**3) - 18*x**3*35\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*x)*35 = -1715*x\n (-49*x)*(-3*x**2) = 147*x**3\n (-30*x**2)*35 = -1050*x**2\n (-30*x**2)*(-3*x**2) = 90*x**4\n (-18*x**3)*35 = -630*x**3\n (-18*x**3)*(-3*x**2) = 54*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 54*x**5 + 90*x**4 - 630*x**3 + 147*x**3 - 1050*x**2 - 1715*x\nCombining like terms, got 54*x**5 + 90*x**4 - 483*x**3 - 1050*x**2 - 1715*x\n#Step 6:\nCurrent expression: 54*x**5 + 90*x**4 - 483*x**3 - 1050*x**2 - 1715*x\nNo more calculations needed.\n54*x**5 + 90*x**4 - 483*x**3 - 1050*x**2 - 1715*x", "generated_answer": "54*x**5 + 90*x**4 - 483*x**3 - 1050*x**2 - 1715*x", "step_length": 6} {"cot_id": "ede8452c96b0bf1cb2e5e76d185179acb921990b4f4285827a3d08a1e1d00078", "datapoint": {"question": "Simplify this expression: (-33*z**2 - 20*z - 7)*(7*z**3 + 7*z - 65)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-231*z**5 - 140*z**4 - 280*z**3 + 2005*z**2 + 1251*z + 455", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1399, "polynomial_expr": "(-33*z**2 - 20*z - 7)*(7*z**3 + 7*z - 65)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-33*z**2 - 20*z - 7)*(7*z**3 + 7*z - 65)\nExpanding the part (7*z**3 + 7*z - 65) using the distributive property, and we got: (7*z)*(-33*z**2 - 20*z - 7) + (7*z**3)*(-33*z**2 - 20*z - 7) - 65*(-33*z**2 - 20*z - 7)\n#Step 2:\nCurrent expression: (7*z)*(-33*z**2 - 20*z - 7) + (7*z**3)*(-33*z**2 - 20*z - 7) - 65*(-33*z**2 - 20*z - 7)\nSimplifying the partial expression: -65*(-33*z**2 - 20*z - 7)\nExpanding the part (-33*z**2 - 20*z - 7) using the distributive property, and we got: -20*z*(-65) - 33*z**2*(-65) - 7*(-65)\nReplacing -65*(-33*z**2 - 20*z - 7) with -20*z*(-65) - 33*z**2*(-65) - 7*(-65) in the overall expression.\n#Step 3:\nCurrent expression: -20*z*(-65) + (7*z)*(-33*z**2 - 20*z - 7) - 33*z**2*(-65) + (7*z**3)*(-33*z**2 - 20*z - 7) + 455\nSimplifying the partial expression: (7*z)*(-33*z**2 - 20*z - 7)\nExpanding the part (-33*z**2 - 20*z - 7) using the distributive property, and we got: (-20*z)*(7*z) - 49*z + (7*z)*(-33*z**2)\nReplacing (7*z)*(-33*z**2 - 20*z - 7) with (-20*z)*(7*z) - 49*z + (7*z)*(-33*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-20*z)*(7*z) - 20*z*(-65) - 7*7*z + (7*z)*(-33*z**2) - 33*z**2*(-65) + (7*z**3)*(-33*z**2 - 20*z - 7) + 455\nSimplifying the partial expression: (7*z**3)*(-33*z**2 - 20*z - 7)\nExpanding the part (-33*z**2 - 20*z - 7) using the distributive property, and we got: (-20*z)*(7*z**3) - 49*z**3 + (-33*z**2)*(7*z**3)\nReplacing (7*z**3)*(-33*z**2 - 20*z - 7) with (-20*z)*(7*z**3) - 49*z**3 + (-33*z**2)*(7*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-20*z)*(7*z) + (-20*z)*(7*z**3) - 20*z*(-65) - 7*7*z**3 - 7*7*z + (7*z)*(-33*z**2) + (-33*z**2)*(7*z**3) - 33*z**2*(-65) + 455\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*z**2)*-65 = 2145*z**2\n (-33*z**2)*(7*z) = -231*z**3\n (-33*z**2)*(7*z**3) = -231*z**5\n (-20*z)*-65 = 1300*z\n (-20*z)*(7*z) = -140*z**2\n (-20*z)*(7*z**3) = -140*z**4\n -7*7*z = -49*z\n -7*7*z**3 = -49*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -231*z**5 - 140*z**4 - 231*z**3 - 49*z**3 - 140*z**2 + 2145*z**2 - 49*z + 1300*z + 455\nCombining like terms, got -231*z**5 - 140*z**4 - 280*z**3 + 2005*z**2 + 1251*z + 455\n#Step 7:\nCurrent expression: -231*z**5 - 140*z**4 - 280*z**3 + 2005*z**2 + 1251*z + 455\nNo more calculations needed.\n-231*z**5 - 140*z**4 - 280*z**3 + 2005*z**2 + 1251*z + 455", "generated_answer": "-231*z**5 - 140*z**4 - 280*z**3 + 2005*z**2 + 1251*z + 455", "step_length": 7} {"cot_id": "9088d072dc8ecbfead11957c1be5a60b1f7924ac20a873910cb70d5c8b3c229f", "datapoint": {"question": "Calculate the following: (-37*z**3 + 20*z + 13)*(38*z**3 + 15*z**2 - 42*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1406*z**6 - 555*z**5 + 2314*z**4 + 794*z**3 - 645*z**2 - 546*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1400, "polynomial_expr": "(-37*z**3 + 20*z + 13)*(38*z**3 + 15*z**2 - 42*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-37*z**3 + 20*z + 13)*(38*z**3 + 15*z**2 - 42*z)\nExpanding the part (-37*z**3 + 20*z + 13) using the distributive property, and we got: (20*z)*(38*z**3 + 15*z**2 - 42*z) + (-37*z**3)*(38*z**3 + 15*z**2 - 42*z) + 13*(38*z**3 + 15*z**2 - 42*z)\n#Step 2:\nCurrent expression: (20*z)*(38*z**3 + 15*z**2 - 42*z) + (-37*z**3)*(38*z**3 + 15*z**2 - 42*z) + 13*(38*z**3 + 15*z**2 - 42*z)\nSimplifying the partial expression: 13*(38*z**3 + 15*z**2 - 42*z)\nExpanding the part (38*z**3 + 15*z**2 - 42*z) using the distributive property, and we got: -42*z*13 + (15*z**2)*13 + (38*z**3)*13\nReplacing 13*(38*z**3 + 15*z**2 - 42*z) with -42*z*13 + (15*z**2)*13 + (38*z**3)*13 in the overall expression.\n#Step 3:\nCurrent expression: -42*z*13 + (20*z)*(38*z**3 + 15*z**2 - 42*z) + (15*z**2)*13 + (-37*z**3)*(38*z**3 + 15*z**2 - 42*z) + (38*z**3)*13\nSimplifying the partial expression: (-37*z**3)*(38*z**3 + 15*z**2 - 42*z)\nExpanding the part (38*z**3 + 15*z**2 - 42*z) using the distributive property, and we got: (-42*z)*(-37*z**3) + (15*z**2)*(-37*z**3) + (-37*z**3)*(38*z**3)\nReplacing (-37*z**3)*(38*z**3 + 15*z**2 - 42*z) with (-42*z)*(-37*z**3) + (15*z**2)*(-37*z**3) + (-37*z**3)*(38*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-42*z)*(-37*z**3) - 42*z*13 + (20*z)*(38*z**3 + 15*z**2 - 42*z) + (15*z**2)*(-37*z**3) + (15*z**2)*13 + (-37*z**3)*(38*z**3) + (38*z**3)*13\nSimplifying the partial expression: (20*z)*(38*z**3 + 15*z**2 - 42*z)\nExpanding the part (38*z**3 + 15*z**2 - 42*z) using the distributive property, and we got: (-42*z)*(20*z) + (20*z)*(15*z**2) + (20*z)*(38*z**3)\nReplacing (20*z)*(38*z**3 + 15*z**2 - 42*z) with (-42*z)*(20*z) + (20*z)*(15*z**2) + (20*z)*(38*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-42*z)*(20*z) + (-42*z)*(-37*z**3) - 42*z*13 + (20*z)*(15*z**2) + (20*z)*(38*z**3) + (15*z**2)*(-37*z**3) + (15*z**2)*13 + (-37*z**3)*(38*z**3) + (38*z**3)*13\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*z)*13 = -546*z\n (-42*z)*(-37*z**3) = 1554*z**4\n (-42*z)*(20*z) = -840*z**2\n (15*z**2)*13 = 195*z**2\n (15*z**2)*(-37*z**3) = -555*z**5\n (15*z**2)*(20*z) = 300*z**3\n (38*z**3)*13 = 494*z**3\n (38*z**3)*(-37*z**3) = -1406*z**6\n (38*z**3)*(20*z) = 760*z**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1406*z**6 - 555*z**5 + 760*z**4 + 1554*z**4 + 300*z**3 + 494*z**3 - 840*z**2 + 195*z**2 - 546*z\nCombining like terms, got -1406*z**6 - 555*z**5 + 2314*z**4 + 794*z**3 - 645*z**2 - 546*z\n#Step 7:\nCurrent expression: -1406*z**6 - 555*z**5 + 2314*z**4 + 794*z**3 - 645*z**2 - 546*z\nNo more calculations needed.\n-1406*z**6 - 555*z**5 + 2314*z**4 + 794*z**3 - 645*z**2 - 546*z", "generated_answer": "-1406*z**6 - 555*z**5 + 2314*z**4 + 794*z**3 - 645*z**2 - 546*z", "step_length": 7} {"cot_id": "4b2075964c2e6de6d177a13d8df9c6b02b1df223240092b638a8fa9587c2eecc", "datapoint": {"question": "Calculate the following: (3*x - 5)*(46*x**3 - 16*x**2 - 46*x + 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "138*x**4 - 278*x**3 - 58*x**2 + 380*x - 250", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1401, "polynomial_expr": "(3*x - 5)*(46*x**3 - 16*x**2 - 46*x + 50)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (3*x - 5)*(46*x**3 - 16*x**2 - 46*x + 50)\nExpanding the part (3*x - 5) using the distributive property, and we got: (3*x)*(46*x**3 - 16*x**2 - 46*x + 50) - 5*(46*x**3 - 16*x**2 - 46*x + 50)\n#Step 2:\nCurrent expression: (3*x)*(46*x**3 - 16*x**2 - 46*x + 50) - 5*(46*x**3 - 16*x**2 - 46*x + 50)\nSimplifying the partial expression: -5*(46*x**3 - 16*x**2 - 46*x + 50)\nExpanding the part (46*x**3 - 16*x**2 - 46*x + 50) using the distributive property, and we got: -46*x*(-5) - 16*x**2*(-5) + (46*x**3)*(-5) + 50*(-5)\nReplacing -5*(46*x**3 - 16*x**2 - 46*x + 50) with -46*x*(-5) - 16*x**2*(-5) + (46*x**3)*(-5) + 50*(-5) in the overall expression.\n#Step 3:\nCurrent expression: -46*x*(-5) + (3*x)*(46*x**3 - 16*x**2 - 46*x + 50) - 16*x**2*(-5) + (46*x**3)*(-5) - 250\nSimplifying the partial expression: (3*x)*(46*x**3 - 16*x**2 - 46*x + 50)\nExpanding the part (46*x**3 - 16*x**2 - 46*x + 50) using the distributive property, and we got: (-46*x)*(3*x) + 50*(3*x) + (3*x)*(-16*x**2) + (3*x)*(46*x**3)\nReplacing (3*x)*(46*x**3 - 16*x**2 - 46*x + 50) with (-46*x)*(3*x) + 50*(3*x) + (3*x)*(-16*x**2) + (3*x)*(46*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-46*x)*(3*x) - 46*x*(-5) + 50*3*x + (3*x)*(-16*x**2) + (3*x)*(46*x**3) - 16*x**2*(-5) + (46*x**3)*(-5) - 250\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*x)*-5 = 230*x\n (-46*x)*(3*x) = -138*x**2\n (-16*x**2)*-5 = 80*x**2\n (-16*x**2)*(3*x) = -48*x**3\n (46*x**3)*-5 = -230*x**3\n (46*x**3)*(3*x) = 138*x**4\n 50*3*x = 150*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 138*x**4 - 230*x**3 - 48*x**3 - 138*x**2 + 80*x**2 + 150*x + 230*x - 250\nCombining like terms, got 138*x**4 - 278*x**3 - 58*x**2 + 380*x - 250\n#Step 6:\nCurrent expression: 138*x**4 - 278*x**3 - 58*x**2 + 380*x - 250\nNo more calculations needed.\n138*x**4 - 278*x**3 - 58*x**2 + 380*x - 250", "generated_answer": "138*x**4 - 278*x**3 - 58*x**2 + 380*x - 250", "step_length": 6} {"cot_id": "720de51c671a649129dd26b090c0408941cf069b3f508a23adaef36bfb72d2f6", "datapoint": {"question": "Simplify this expression: (-64*z**2 + 24*z)*(89*z**2 + 47*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-5696*z**4 - 872*z**3 + 1128*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1402, "polynomial_expr": "(-64*z**2 + 24*z)*(89*z**2 + 47*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-64*z**2 + 24*z)*(89*z**2 + 47*z)\nExpanding the part (-64*z**2 + 24*z) using the distributive property, and we got: (24*z)*(89*z**2 + 47*z) + (-64*z**2)*(89*z**2 + 47*z)\n#Step 2:\nCurrent expression: (24*z)*(89*z**2 + 47*z) + (-64*z**2)*(89*z**2 + 47*z)\nSimplifying the partial expression: (-64*z**2)*(89*z**2 + 47*z)\nExpanding the part (89*z**2 + 47*z) using the distributive property, and we got: (47*z)*(-64*z**2) + (-64*z**2)*(89*z**2)\nReplacing (-64*z**2)*(89*z**2 + 47*z) with (47*z)*(-64*z**2) + (-64*z**2)*(89*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (24*z)*(89*z**2 + 47*z) + (47*z)*(-64*z**2) + (-64*z**2)*(89*z**2)\nSimplifying the partial expression: (24*z)*(89*z**2 + 47*z)\nExpanding the part (89*z**2 + 47*z) using the distributive property, and we got: (24*z)*(47*z) + (24*z)*(89*z**2)\nReplacing (24*z)*(89*z**2 + 47*z) with (24*z)*(47*z) + (24*z)*(89*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (24*z)*(47*z) + (24*z)*(89*z**2) + (47*z)*(-64*z**2) + (-64*z**2)*(89*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (47*z)*(-64*z**2) = -3008*z**3\n (47*z)*(24*z) = 1128*z**2\n (89*z**2)*(-64*z**2) = -5696*z**4\n (89*z**2)*(24*z) = 2136*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -5696*z**4 - 3008*z**3 + 2136*z**3 + 1128*z**2\nCombining like terms, got -5696*z**4 - 872*z**3 + 1128*z**2\n#Step 6:\nCurrent expression: -5696*z**4 - 872*z**3 + 1128*z**2\nNo more calculations needed.\n-5696*z**4 - 872*z**3 + 1128*z**2", "generated_answer": "-5696*z**4 - 872*z**3 + 1128*z**2", "step_length": 6} {"cot_id": "3001467c6ae2d6c35967fed1b2bc5da5290023f405e9fc6b7b9c34269deba3ff", "datapoint": {"question": "Simplify this expression: (-45*x**3 + 2*x**2 - 45*x)*(35*x**3 + 50*x**2 - 7*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1575*x**6 - 2180*x**5 - 1160*x**4 - 2264*x**3 + 315*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1403, "polynomial_expr": "(-45*x**3 + 2*x**2 - 45*x)*(35*x**3 + 50*x**2 - 7*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-45*x**3 + 2*x**2 - 45*x)*(35*x**3 + 50*x**2 - 7*x)\nExpanding the part (-45*x**3 + 2*x**2 - 45*x) using the distributive property, and we got: (-45*x)*(35*x**3 + 50*x**2 - 7*x) + (2*x**2)*(35*x**3 + 50*x**2 - 7*x) + (-45*x**3)*(35*x**3 + 50*x**2 - 7*x)\n#Step 2:\nCurrent expression: (-45*x)*(35*x**3 + 50*x**2 - 7*x) + (2*x**2)*(35*x**3 + 50*x**2 - 7*x) + (-45*x**3)*(35*x**3 + 50*x**2 - 7*x)\nSimplifying the partial expression: (-45*x)*(35*x**3 + 50*x**2 - 7*x)\nExpanding the part (35*x**3 + 50*x**2 - 7*x) using the distributive property, and we got: (-45*x)*(-7*x) + (-45*x)*(50*x**2) + (-45*x)*(35*x**3)\nReplacing (-45*x)*(35*x**3 + 50*x**2 - 7*x) with (-45*x)*(-7*x) + (-45*x)*(50*x**2) + (-45*x)*(35*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-45*x)*(-7*x) + (-45*x)*(50*x**2) + (-45*x)*(35*x**3) + (2*x**2)*(35*x**3 + 50*x**2 - 7*x) + (-45*x**3)*(35*x**3 + 50*x**2 - 7*x)\nSimplifying the partial expression: (-45*x**3)*(35*x**3 + 50*x**2 - 7*x)\nExpanding the part (35*x**3 + 50*x**2 - 7*x) using the distributive property, and we got: (-7*x)*(-45*x**3) + (50*x**2)*(-45*x**3) + (-45*x**3)*(35*x**3)\nReplacing (-45*x**3)*(35*x**3 + 50*x**2 - 7*x) with (-7*x)*(-45*x**3) + (50*x**2)*(-45*x**3) + (-45*x**3)*(35*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-45*x)*(-7*x) + (-45*x)*(50*x**2) + (-45*x)*(35*x**3) + (-7*x)*(-45*x**3) + (2*x**2)*(35*x**3 + 50*x**2 - 7*x) + (50*x**2)*(-45*x**3) + (-45*x**3)*(35*x**3)\nSimplifying the partial expression: (2*x**2)*(35*x**3 + 50*x**2 - 7*x)\nExpanding the part (35*x**3 + 50*x**2 - 7*x) using the distributive property, and we got: (-7*x)*(2*x**2) + (2*x**2)*(50*x**2) + (2*x**2)*(35*x**3)\nReplacing (2*x**2)*(35*x**3 + 50*x**2 - 7*x) with (-7*x)*(2*x**2) + (2*x**2)*(50*x**2) + (2*x**2)*(35*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-45*x)*(-7*x) + (-45*x)*(50*x**2) + (-45*x)*(35*x**3) + (-7*x)*(2*x**2) + (-7*x)*(-45*x**3) + (2*x**2)*(50*x**2) + (2*x**2)*(35*x**3) + (50*x**2)*(-45*x**3) + (-45*x**3)*(35*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-7*x)*(-45*x) = 315*x**2\n (-7*x)*(-45*x**3) = 315*x**4\n (-7*x)*(2*x**2) = -14*x**3\n (35*x**3)*(-45*x) = -1575*x**4\n (35*x**3)*(-45*x**3) = -1575*x**6\n (35*x**3)*(2*x**2) = 70*x**5\n (50*x**2)*(-45*x) = -2250*x**3\n (50*x**2)*(-45*x**3) = -2250*x**5\n (50*x**2)*(2*x**2) = 100*x**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1575*x**6 - 2250*x**5 + 70*x**5 - 1575*x**4 + 100*x**4 + 315*x**4 - 2250*x**3 - 14*x**3 + 315*x**2\nCombining like terms, got -1575*x**6 - 2180*x**5 - 1160*x**4 - 2264*x**3 + 315*x**2\n#Step 7:\nCurrent expression: -1575*x**6 - 2180*x**5 - 1160*x**4 - 2264*x**3 + 315*x**2\nNo more calculations needed.\n-1575*x**6 - 2180*x**5 - 1160*x**4 - 2264*x**3 + 315*x**2", "generated_answer": "-1575*x**6 - 2180*x**5 - 1160*x**4 - 2264*x**3 + 315*x**2", "step_length": 7} {"cot_id": "f2a4785745bc3851223ddb726eca2d62c486ae3d9068b2779938ed923bda8916", "datapoint": {"question": "Simplify this expression: -3*y*(-46*y - 72)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "138*y**2 + 216*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1404, "polynomial_expr": "-3*y*(-46*y - 72)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -3*y*(-46*y - 72)\nExpanding the part (-46*y - 72) using the distributive property, and we got: (-46*y)*(-3*y) - (-1)*216*y\n#Step 2:\nCurrent expression: (-46*y)*(-3*y) - (-1)*216*y\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -72*(-3*y) = 216*y\n (-46*y)*(-3*y) = 138*y**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 138*y**2 + 216*y\nNo more calculations needed.\n138*y**2 + 216*y", "generated_answer": "138*y**2 + 216*y", "step_length": 3} {"cot_id": "fbe45f5b3b9238cf28d1aabedff6060382b4169eab75760a9fa4c73aaa5336bd", "datapoint": {"question": "Simplify this expression: -22*x**2*(-70*x**3 + 5*x + 4)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1540*x**5 - 110*x**3 - 88*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1405, "polynomial_expr": "-22*x**2*(-70*x**3 + 5*x + 4)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -22*x**2*(-70*x**3 + 5*x + 4)\nExpanding the part (-70*x**3 + 5*x + 4) using the distributive property, and we got: 4*(-22*x**2) + (5*x)*(-22*x**2) + (-22*x**2)*(-70*x**3)\n#Step 2:\nCurrent expression: 4*(-22*x**2) + (5*x)*(-22*x**2) + (-22*x**2)*(-70*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 4*(-22*x**2) = -88*x**2\n (-70*x**3)*(-22*x**2) = 1540*x**5\n (5*x)*(-22*x**2) = -110*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1540*x**5 - 110*x**3 - 88*x**2\nNo more calculations needed.\n1540*x**5 - 110*x**3 - 88*x**2", "generated_answer": "1540*x**5 - 110*x**3 - 88*x**2", "step_length": 3} {"cot_id": "4fe48ea3723162b5e9e01e4e0f53a98e1a10cedc08790dfe1894d25312d211db", "datapoint": {"question": "Calculate the following: (3 - 23*y**2)*(25*y**3 - 50*y**2 + 3*y + 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-575*y**5 + 1150*y**4 + 6*y**3 - 472*y**2 + 9*y + 42", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1406, "polynomial_expr": "(3 - 23*y**2)*(25*y**3 - 50*y**2 + 3*y + 14)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (3 - 23*y**2)*(25*y**3 - 50*y**2 + 3*y + 14)\nExpanding the part (3 - 23*y**2) using the distributive property, and we got: (-23*y**2)*(25*y**3 - 50*y**2 + 3*y + 14) + 3*(25*y**3 - 50*y**2 + 3*y + 14)\n#Step 2:\nCurrent expression: (-23*y**2)*(25*y**3 - 50*y**2 + 3*y + 14) + 3*(25*y**3 - 50*y**2 + 3*y + 14)\nSimplifying the partial expression: 3*(25*y**3 - 50*y**2 + 3*y + 14)\nExpanding the part (25*y**3 - 50*y**2 + 3*y + 14) using the distributive property, and we got: (3*y)*3 - 50*y**2*3 + (25*y**3)*3 + 14*3\nReplacing 3*(25*y**3 - 50*y**2 + 3*y + 14) with (3*y)*3 - 50*y**2*3 + (25*y**3)*3 + 14*3 in the overall expression.\n#Step 3:\nCurrent expression: (3*y)*3 - 50*y**2*3 + (-23*y**2)*(25*y**3 - 50*y**2 + 3*y + 14) + (25*y**3)*3 + 42\nSimplifying the partial expression: (-23*y**2)*(25*y**3 - 50*y**2 + 3*y + 14)\nExpanding the part (25*y**3 - 50*y**2 + 3*y + 14) using the distributive property, and we got: 14*(-23*y**2) + (3*y)*(-23*y**2) + (-50*y**2)*(-23*y**2) + (-23*y**2)*(25*y**3)\nReplacing (-23*y**2)*(25*y**3 - 50*y**2 + 3*y + 14) with 14*(-23*y**2) + (3*y)*(-23*y**2) + (-50*y**2)*(-23*y**2) + (-23*y**2)*(25*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 14*(-23)*y**2 + (3*y)*(-23*y**2) + (3*y)*3 + (-50*y**2)*(-23*y**2) - 50*y**2*3 + (-23*y**2)*(25*y**3) + (25*y**3)*3 + 42\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-50*y**2)*3 = -150*y**2\n (-50*y**2)*(-23*y**2) = 1150*y**4\n (3*y)*3 = 9*y\n (3*y)*(-23*y**2) = -69*y**3\n (25*y**3)*3 = 75*y**3\n (25*y**3)*(-23*y**2) = -575*y**5\n 14*-23*y**2 = -322*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -575*y**5 + 1150*y**4 - 69*y**3 + 75*y**3 - 322*y**2 - 150*y**2 + 9*y + 42\nCombining like terms, got -575*y**5 + 1150*y**4 + 6*y**3 - 472*y**2 + 9*y + 42\n#Step 6:\nCurrent expression: -575*y**5 + 1150*y**4 + 6*y**3 - 472*y**2 + 9*y + 42\nNo more calculations needed.\n-575*y**5 + 1150*y**4 + 6*y**3 - 472*y**2 + 9*y + 42", "generated_answer": "-575*y**5 + 1150*y**4 + 6*y**3 - 472*y**2 + 9*y + 42", "step_length": 6} {"cot_id": "86d15a20b97e2995060c1837f7a26deac2120d7a19de0f3b2e088b8c66112d28", "datapoint": {"question": "Calculate the following: 8*x**2*(43*x**3 + 38*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "344*x**5 + 304*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1407, "polynomial_expr": "8*x**2*(43*x**3 + 38*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 8*x**2*(43*x**3 + 38*x)\nExpanding the part (43*x**3 + 38*x) using the distributive property, and we got: (38*x)*(8*x**2) + (8*x**2)*(43*x**3)\n#Step 2:\nCurrent expression: (38*x)*(8*x**2) + (8*x**2)*(43*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (38*x)*(8*x**2) = 304*x**3\n (43*x**3)*(8*x**2) = 344*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 344*x**5 + 304*x**3\nNo more calculations needed.\n344*x**5 + 304*x**3", "generated_answer": "344*x**5 + 304*x**3", "step_length": 3} {"cot_id": "34ea7f2155e1faf24baa4e5c282a73640af9996a7f82d156b86c53e4989eabf3", "datapoint": {"question": "Simplify this expression: (-15*z**2 + 30*z)*(-38*z**2 - 35*z + 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "570*z**4 - 615*z**3 - 1500*z**2 + 900*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1408, "polynomial_expr": "(-15*z**2 + 30*z)*(-38*z**2 - 35*z + 30)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-15*z**2 + 30*z)*(-38*z**2 - 35*z + 30)\nExpanding the part (-15*z**2 + 30*z) using the distributive property, and we got: (30*z)*(-38*z**2 - 35*z + 30) + (-15*z**2)*(-38*z**2 - 35*z + 30)\n#Step 2:\nCurrent expression: (30*z)*(-38*z**2 - 35*z + 30) + (-15*z**2)*(-38*z**2 - 35*z + 30)\nSimplifying the partial expression: (-15*z**2)*(-38*z**2 - 35*z + 30)\nExpanding the part (-38*z**2 - 35*z + 30) using the distributive property, and we got: (-35*z)*(-15*z**2) + 30*(-15*z**2) + (-38*z**2)*(-15*z**2)\nReplacing (-15*z**2)*(-38*z**2 - 35*z + 30) with (-35*z)*(-15*z**2) + 30*(-15*z**2) + (-38*z**2)*(-15*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-35*z)*(-15*z**2) + 30*(-15)*z**2 + (30*z)*(-38*z**2 - 35*z + 30) + (-38*z**2)*(-15*z**2)\nSimplifying the partial expression: (30*z)*(-38*z**2 - 35*z + 30)\nExpanding the part (-38*z**2 - 35*z + 30) using the distributive property, and we got: (-35*z)*(30*z) + 30*(30*z) + (30*z)*(-38*z**2)\nReplacing (30*z)*(-38*z**2 - 35*z + 30) with (-35*z)*(30*z) + 30*(30*z) + (30*z)*(-38*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-35*z)*(30*z) + (-35*z)*(-15*z**2) + 30*(-15)*z**2 + 30*30*z + (30*z)*(-38*z**2) + (-38*z**2)*(-15*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*z**2)*(-15*z**2) = 570*z**4\n (-38*z**2)*(30*z) = -1140*z**3\n (-35*z)*(-15*z**2) = 525*z**3\n (-35*z)*(30*z) = -1050*z**2\n 30*-15*z**2 = -450*z**2\n 30*30*z = 900*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 570*z**4 - 1140*z**3 + 525*z**3 - 1050*z**2 - 450*z**2 + 900*z\nCombining like terms, got 570*z**4 - 615*z**3 - 1500*z**2 + 900*z\n#Step 6:\nCurrent expression: 570*z**4 - 615*z**3 - 1500*z**2 + 900*z\nNo more calculations needed.\n570*z**4 - 615*z**3 - 1500*z**2 + 900*z", "generated_answer": "570*z**4 - 615*z**3 - 1500*z**2 + 900*z", "step_length": 6} {"cot_id": "35371cc11c1845420d4bc031a6bc5ca804207fb4fa29ff4f4f903cce147e6f8e", "datapoint": {"question": "Calculate the following: (28 - 50*y)*(17*y**3 - 43*y**2 - 64*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-850*y**4 + 2626*y**3 + 1996*y**2 - 1792*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1409, "polynomial_expr": "(28 - 50*y)*(17*y**3 - 43*y**2 - 64*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28 - 50*y)*(17*y**3 - 43*y**2 - 64*y)\nExpanding the part (28 - 50*y) using the distributive property, and we got: (-50*y)*(17*y**3 - 43*y**2 - 64*y) + 28*(17*y**3 - 43*y**2 - 64*y)\n#Step 2:\nCurrent expression: (-50*y)*(17*y**3 - 43*y**2 - 64*y) + 28*(17*y**3 - 43*y**2 - 64*y)\nSimplifying the partial expression: 28*(17*y**3 - 43*y**2 - 64*y)\nExpanding the part (17*y**3 - 43*y**2 - 64*y) using the distributive property, and we got: -64*y*28 - 43*y**2*28 + (17*y**3)*28\nReplacing 28*(17*y**3 - 43*y**2 - 64*y) with -64*y*28 - 43*y**2*28 + (17*y**3)*28 in the overall expression.\n#Step 3:\nCurrent expression: -64*y*28 + (-50*y)*(17*y**3 - 43*y**2 - 64*y) - 43*y**2*28 + (17*y**3)*28\nSimplifying the partial expression: (-50*y)*(17*y**3 - 43*y**2 - 64*y)\nExpanding the part (17*y**3 - 43*y**2 - 64*y) using the distributive property, and we got: (-64*y)*(-50*y) + (-50*y)*(-43*y**2) + (-50*y)*(17*y**3)\nReplacing (-50*y)*(17*y**3 - 43*y**2 - 64*y) with (-64*y)*(-50*y) + (-50*y)*(-43*y**2) + (-50*y)*(17*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-64*y)*(-50*y) - 64*y*28 + (-50*y)*(-43*y**2) + (-50*y)*(17*y**3) - 43*y**2*28 + (17*y**3)*28\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-64*y)*28 = -1792*y\n (-64*y)*(-50*y) = 3200*y**2\n (-43*y**2)*28 = -1204*y**2\n (-43*y**2)*(-50*y) = 2150*y**3\n (17*y**3)*28 = 476*y**3\n (17*y**3)*(-50*y) = -850*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -850*y**4 + 476*y**3 + 2150*y**3 - 1204*y**2 + 3200*y**2 - 1792*y\nCombining like terms, got -850*y**4 + 2626*y**3 + 1996*y**2 - 1792*y\n#Step 6:\nCurrent expression: -850*y**4 + 2626*y**3 + 1996*y**2 - 1792*y\nNo more calculations needed.\n-850*y**4 + 2626*y**3 + 1996*y**2 - 1792*y", "generated_answer": "-850*y**4 + 2626*y**3 + 1996*y**2 - 1792*y", "step_length": 6} {"cot_id": "b34603ae805bb0f0f42f8df143437b1a4a83c15036867379f7b9ec67b8926077", "datapoint": {"question": "Simplify this expression: (-15*y**2 + y)*(6*y**3 + 39*y - 26)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-90*y**5 + 6*y**4 - 585*y**3 + 429*y**2 - 26*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1410, "polynomial_expr": "(-15*y**2 + y)*(6*y**3 + 39*y - 26)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-15*y**2 + y)*(6*y**3 + 39*y - 26)\nExpanding the part (-15*y**2 + y) using the distributive property, and we got: y*(6*y**3 + 39*y - 26) + (-15*y**2)*(6*y**3 + 39*y - 26)\n#Step 2:\nCurrent expression: y*(6*y**3 + 39*y - 26) + (-15*y**2)*(6*y**3 + 39*y - 26)\nSimplifying the partial expression: y*(6*y**3 + 39*y - 26)\nExpanding the part (6*y**3 + 39*y - 26) using the distributive property, and we got: y*(39*y) + y*(6*y**3) - 26*y\nReplacing y*(6*y**3 + 39*y - 26) with y*(39*y) + y*(6*y**3) - 26*y in the overall expression.\n#Step 3:\nCurrent expression: y*(39*y) + y*(6*y**3) - 26*y + (-15*y**2)*(6*y**3 + 39*y - 26)\nSimplifying the partial expression: (-15*y**2)*(6*y**3 + 39*y - 26)\nExpanding the part (6*y**3 + 39*y - 26) using the distributive property, and we got: -(-1)*390*y**2 + (39*y)*(-15*y**2) + (-15*y**2)*(6*y**3)\nReplacing (-15*y**2)*(6*y**3 + 39*y - 26) with -(-1)*390*y**2 + (39*y)*(-15*y**2) + (-15*y**2)*(6*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -26*(-15)*y**2 + y*(39*y) + y*(6*y**3) - 26*y + (39*y)*(-15*y**2) + (-15*y**2)*(6*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (6*y**3)*y = 6*y**4\n (6*y**3)*(-15*y**2) = -90*y**5\n (39*y)*y = 39*y**2\n (39*y)*(-15*y**2) = -585*y**3\n -26*-15*y**2 = 390*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -90*y**5 + 6*y**4 - 585*y**3 + 39*y**2 + 390*y**2 - 26*y\nCombining like terms, got -90*y**5 + 6*y**4 - 585*y**3 + 429*y**2 - 26*y\n#Step 6:\nCurrent expression: -90*y**5 + 6*y**4 - 585*y**3 + 429*y**2 - 26*y\nNo more calculations needed.\n-90*y**5 + 6*y**4 - 585*y**3 + 429*y**2 - 26*y", "generated_answer": "-90*y**5 + 6*y**4 - 585*y**3 + 429*y**2 - 26*y", "step_length": 6} {"cot_id": "4022e28f58840d8488d18f0d86f46c81ed199334a08b86e519aa8fa91fb3562a", "datapoint": {"question": "Simplify this expression: (25*y**2 + 27)*(-19*y**3 - 13*y - 22)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-475*y**5 - 838*y**3 - 550*y**2 - 351*y - 594", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1411, "polynomial_expr": "(25*y**2 + 27)*(-19*y**3 - 13*y - 22)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (25*y**2 + 27)*(-19*y**3 - 13*y - 22)\nExpanding the part (25*y**2 + 27) using the distributive property, and we got: (25*y**2)*(-19*y**3 - 13*y - 22) + 27*(-19*y**3 - 13*y - 22)\n#Step 2:\nCurrent expression: (25*y**2)*(-19*y**3 - 13*y - 22) + 27*(-19*y**3 - 13*y - 22)\nSimplifying the partial expression: 27*(-19*y**3 - 13*y - 22)\nExpanding the part (-19*y**3 - 13*y - 22) using the distributive property, and we got: -13*y*27 - 19*y**3*27 - 22*27\nReplacing 27*(-19*y**3 - 13*y - 22) with -13*y*27 - 19*y**3*27 - 22*27 in the overall expression.\n#Step 3:\nCurrent expression: -13*y*27 + (25*y**2)*(-19*y**3 - 13*y - 22) - 19*y**3*27 - 594\nSimplifying the partial expression: (25*y**2)*(-19*y**3 - 13*y - 22)\nExpanding the part (-19*y**3 - 13*y - 22) using the distributive property, and we got: (-13*y)*(25*y**2) - 550*y**2 + (25*y**2)*(-19*y**3)\nReplacing (25*y**2)*(-19*y**3 - 13*y - 22) with (-13*y)*(25*y**2) - 550*y**2 + (25*y**2)*(-19*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-13*y)*(25*y**2) - 13*y*27 - 22*25*y**2 + (25*y**2)*(-19*y**3) - 19*y**3*27 - 594\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*y**3)*27 = -513*y**3\n (-19*y**3)*(25*y**2) = -475*y**5\n (-13*y)*27 = -351*y\n (-13*y)*(25*y**2) = -325*y**3\n -22*25*y**2 = -550*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -475*y**5 - 513*y**3 - 325*y**3 - 550*y**2 - 351*y - 594\nCombining like terms, got -475*y**5 - 838*y**3 - 550*y**2 - 351*y - 594\n#Step 6:\nCurrent expression: -475*y**5 - 838*y**3 - 550*y**2 - 351*y - 594\nNo more calculations needed.\n-475*y**5 - 838*y**3 - 550*y**2 - 351*y - 594", "generated_answer": "-475*y**5 - 838*y**3 - 550*y**2 - 351*y - 594", "step_length": 6} {"cot_id": "e476347242efb0a5aabe0f260d966f15de09856690d5197c3aa393bf0c23001c", "datapoint": {"question": "Calculate the following: (-53*z**2 + 3*z + 37)*(-18*z**2 - 63*z - 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "954*z**4 + 3285*z**3 + 841*z**2 - 2427*z - 1184", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1412, "polynomial_expr": "(-53*z**2 + 3*z + 37)*(-18*z**2 - 63*z - 32)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-53*z**2 + 3*z + 37)*(-18*z**2 - 63*z - 32)\nExpanding the part (-18*z**2 - 63*z - 32) using the distributive property, and we got: (-63*z)*(-53*z**2 + 3*z + 37) + (-18*z**2)*(-53*z**2 + 3*z + 37) - 32*(-53*z**2 + 3*z + 37)\n#Step 2:\nCurrent expression: (-63*z)*(-53*z**2 + 3*z + 37) + (-18*z**2)*(-53*z**2 + 3*z + 37) - 32*(-53*z**2 + 3*z + 37)\nSimplifying the partial expression: -32*(-53*z**2 + 3*z + 37)\nExpanding the part (-53*z**2 + 3*z + 37) using the distributive property, and we got: (3*z)*(-32) - 53*z**2*(-32) + 37*(-32)\nReplacing -32*(-53*z**2 + 3*z + 37) with (3*z)*(-32) - 53*z**2*(-32) + 37*(-32) in the overall expression.\n#Step 3:\nCurrent expression: (-63*z)*(-53*z**2 + 3*z + 37) + (3*z)*(-32) - 53*z**2*(-32) + (-18*z**2)*(-53*z**2 + 3*z + 37) - 1184\nSimplifying the partial expression: (-63*z)*(-53*z**2 + 3*z + 37)\nExpanding the part (-53*z**2 + 3*z + 37) using the distributive property, and we got: (-63*z)*(3*z) + (-63*z)*(-53*z**2) + 37*(-63*z)\nReplacing (-63*z)*(-53*z**2 + 3*z + 37) with (-63*z)*(3*z) + (-63*z)*(-53*z**2) + 37*(-63*z) in the overall expression.\n#Step 4:\nCurrent expression: (-63*z)*(3*z) + (-63*z)*(-53*z**2) + 37*(-63)*z + (3*z)*(-32) - 53*z**2*(-32) + (-18*z**2)*(-53*z**2 + 3*z + 37) - 1184\nSimplifying the partial expression: (-18*z**2)*(-53*z**2 + 3*z + 37)\nExpanding the part (-53*z**2 + 3*z + 37) using the distributive property, and we got: 37*(-18*z**2) + (3*z)*(-18*z**2) + (-53*z**2)*(-18*z**2)\nReplacing (-18*z**2)*(-53*z**2 + 3*z + 37) with 37*(-18*z**2) + (3*z)*(-18*z**2) + (-53*z**2)*(-18*z**2) in the overall expression.\n#Step 5:\nCurrent expression: (-63*z)*(3*z) + (-63*z)*(-53*z**2) + 37*(-18)*z**2 + 37*(-63)*z + (3*z)*(-18*z**2) + (3*z)*(-32) + (-53*z**2)*(-18*z**2) - 53*z**2*(-32) - 1184\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-53*z**2)*-32 = 1696*z**2\n (-53*z**2)*(-63*z) = 3339*z**3\n (-53*z**2)*(-18*z**2) = 954*z**4\n (3*z)*-32 = -96*z\n (3*z)*(-63*z) = -189*z**2\n (3*z)*(-18*z**2) = -54*z**3\n 37*-63*z = -2331*z\n 37*-18*z**2 = -666*z**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 954*z**4 - 54*z**3 + 3339*z**3 - 666*z**2 - 189*z**2 + 1696*z**2 - 2331*z - 96*z - 1184\nCombining like terms, got 954*z**4 + 3285*z**3 + 841*z**2 - 2427*z - 1184\n#Step 7:\nCurrent expression: 954*z**4 + 3285*z**3 + 841*z**2 - 2427*z - 1184\nNo more calculations needed.\n954*z**4 + 3285*z**3 + 841*z**2 - 2427*z - 1184", "generated_answer": "954*z**4 + 3285*z**3 + 841*z**2 - 2427*z - 1184", "step_length": 7} {"cot_id": "ec3128fa819fa062cca3aa6c5fa4e78c6d8ca59393827e64d498a8cf2e771ba3", "datapoint": {"question": "Calculate the following: (22 - 48*z**3)*(47*z**3 + 18*z**2 - 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2256*z**6 - 864*z**5 + 1994*z**3 + 396*z**2 - 440", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1413, "polynomial_expr": "(22 - 48*z**3)*(47*z**3 + 18*z**2 - 20)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (22 - 48*z**3)*(47*z**3 + 18*z**2 - 20)\nExpanding the part (22 - 48*z**3) using the distributive property, and we got: (-48*z**3)*(47*z**3 + 18*z**2 - 20) + 22*(47*z**3 + 18*z**2 - 20)\n#Step 2:\nCurrent expression: (-48*z**3)*(47*z**3 + 18*z**2 - 20) + 22*(47*z**3 + 18*z**2 - 20)\nSimplifying the partial expression: 22*(47*z**3 + 18*z**2 - 20)\nExpanding the part (47*z**3 + 18*z**2 - 20) using the distributive property, and we got: (18*z**2)*22 + (47*z**3)*22 - 20*22\nReplacing 22*(47*z**3 + 18*z**2 - 20) with (18*z**2)*22 + (47*z**3)*22 - 20*22 in the overall expression.\n#Step 3:\nCurrent expression: (18*z**2)*22 + (-48*z**3)*(47*z**3 + 18*z**2 - 20) + (47*z**3)*22 - 440\nSimplifying the partial expression: (-48*z**3)*(47*z**3 + 18*z**2 - 20)\nExpanding the part (47*z**3 + 18*z**2 - 20) using the distributive property, and we got: -(-1)*960*z**3 + (18*z**2)*(-48*z**3) + (-48*z**3)*(47*z**3)\nReplacing (-48*z**3)*(47*z**3 + 18*z**2 - 20) with -(-1)*960*z**3 + (18*z**2)*(-48*z**3) + (-48*z**3)*(47*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -20*(-48)*z**3 + (18*z**2)*(-48*z**3) + (18*z**2)*22 + (-48*z**3)*(47*z**3) + (47*z**3)*22 - 440\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (18*z**2)*22 = 396*z**2\n (18*z**2)*(-48*z**3) = -864*z**5\n (47*z**3)*22 = 1034*z**3\n (47*z**3)*(-48*z**3) = -2256*z**6\n -20*-48*z**3 = 960*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2256*z**6 - 864*z**5 + 960*z**3 + 1034*z**3 + 396*z**2 - 440\nCombining like terms, got -2256*z**6 - 864*z**5 + 1994*z**3 + 396*z**2 - 440\n#Step 6:\nCurrent expression: -2256*z**6 - 864*z**5 + 1994*z**3 + 396*z**2 - 440\nNo more calculations needed.\n-2256*z**6 - 864*z**5 + 1994*z**3 + 396*z**2 - 440", "generated_answer": "-2256*z**6 - 864*z**5 + 1994*z**3 + 396*z**2 - 440", "step_length": 6} {"cot_id": "0a405ddeffd3b07ca4b2c8bb92b3cc8f84fbd38f0d0b918a1350e50fb1121165", "datapoint": {"question": "Calculate the following: (41*y**3 - 14)*(-y**2 + 50*y + 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-41*y**5 + 2050*y**4 + 697*y**3 + 14*y**2 - 700*y - 238", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1414, "polynomial_expr": "(41*y**3 - 14)*(-y**2 + 50*y + 17)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (41*y**3 - 14)*(-y**2 + 50*y + 17)\nExpanding the part (41*y**3 - 14) using the distributive property, and we got: (41*y**3)*(-y**2 + 50*y + 17) - 14*(-y**2 + 50*y + 17)\n#Step 2:\nCurrent expression: (41*y**3)*(-y**2 + 50*y + 17) - 14*(-y**2 + 50*y + 17)\nSimplifying the partial expression: -14*(-y**2 + 50*y + 17)\nExpanding the part (-y**2 + 50*y + 17) using the distributive property, and we got: (50*y)*(-14) - y**2*(-14) + 17*(-14)\nReplacing -14*(-y**2 + 50*y + 17) with (50*y)*(-14) - y**2*(-14) + 17*(-14) in the overall expression.\n#Step 3:\nCurrent expression: (50*y)*(-14) - y**2*(-14) + (41*y**3)*(-y**2 + 50*y + 17) - 238\nSimplifying the partial expression: (41*y**3)*(-y**2 + 50*y + 17)\nExpanding the part (-y**2 + 50*y + 17) using the distributive property, and we got: 17*(41*y**3) + (50*y)*(41*y**3) + (-y**2)*(41*y**3)\nReplacing (41*y**3)*(-y**2 + 50*y + 17) with 17*(41*y**3) + (50*y)*(41*y**3) + (-y**2)*(41*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 17*41*y**3 + (50*y)*(41*y**3) + (50*y)*(-14) + (-y**2)*(41*y**3) - y**2*(-14) - 238\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-y**2)*-14 = 14*y**2\n (-y**2)*(41*y**3) = -41*y**5\n (50*y)*-14 = -700*y\n (50*y)*(41*y**3) = 2050*y**4\n 17*41*y**3 = 697*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -41*y**5 + 2050*y**4 + 697*y**3 + 14*y**2 - 700*y - 238\nNo more calculations needed.\n-41*y**5 + 2050*y**4 + 697*y**3 + 14*y**2 - 700*y - 238", "generated_answer": "-41*y**5 + 2050*y**4 + 697*y**3 + 14*y**2 - 700*y - 238", "step_length": 5} {"cot_id": "4e38b64acaa29ac2c15afbf7e33952a32075f210eb71b564a008dcea9de2dec6", "datapoint": {"question": "Calculate the following: -616*y**3 - 1034*y**2 + 2024\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-616*y**3 - 1034*y**2 + 2024", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1415, "polynomial_expr": "-616*y**3 - 1034*y**2 + 2024", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -616*y**3 - 1034*y**2 + 2024\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -616*y**3 - 1034*y**2 + 2024\nNo more calculations needed.\n-616*y**3 - 1034*y**2 + 2024", "generated_answer": "-616*y**3 - 1034*y**2 + 2024", "step_length": 2} {"cot_id": "4154a58e72fd28a77643a386dab3caddbffad83344993b12dd7e1673db9f0b5a", "datapoint": {"question": "Calculate the following: (3*x**3 - 38)*(76*x**3 - 23*x**2 - 45*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "228*x**6 - 69*x**5 - 135*x**4 - 2888*x**3 + 874*x**2 + 1710*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1416, "polynomial_expr": "(3*x**3 - 38)*(76*x**3 - 23*x**2 - 45*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (3*x**3 - 38)*(76*x**3 - 23*x**2 - 45*x)\nExpanding the part (3*x**3 - 38) using the distributive property, and we got: (3*x**3)*(76*x**3 - 23*x**2 - 45*x) - 38*(76*x**3 - 23*x**2 - 45*x)\n#Step 2:\nCurrent expression: (3*x**3)*(76*x**3 - 23*x**2 - 45*x) - 38*(76*x**3 - 23*x**2 - 45*x)\nSimplifying the partial expression: -38*(76*x**3 - 23*x**2 - 45*x)\nExpanding the part (76*x**3 - 23*x**2 - 45*x) using the distributive property, and we got: -45*x*(-38) - 23*x**2*(-38) + (76*x**3)*(-38)\nReplacing -38*(76*x**3 - 23*x**2 - 45*x) with -45*x*(-38) - 23*x**2*(-38) + (76*x**3)*(-38) in the overall expression.\n#Step 3:\nCurrent expression: -45*x*(-38) - 23*x**2*(-38) + (3*x**3)*(76*x**3 - 23*x**2 - 45*x) + (76*x**3)*(-38)\nSimplifying the partial expression: (3*x**3)*(76*x**3 - 23*x**2 - 45*x)\nExpanding the part (76*x**3 - 23*x**2 - 45*x) using the distributive property, and we got: (-45*x)*(3*x**3) + (-23*x**2)*(3*x**3) + (3*x**3)*(76*x**3)\nReplacing (3*x**3)*(76*x**3 - 23*x**2 - 45*x) with (-45*x)*(3*x**3) + (-23*x**2)*(3*x**3) + (3*x**3)*(76*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-45*x)*(3*x**3) - 45*x*(-38) + (-23*x**2)*(3*x**3) - 23*x**2*(-38) + (3*x**3)*(76*x**3) + (76*x**3)*(-38)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*x)*-38 = 1710*x\n (-45*x)*(3*x**3) = -135*x**4\n (-23*x**2)*-38 = 874*x**2\n (-23*x**2)*(3*x**3) = -69*x**5\n (76*x**3)*-38 = -2888*x**3\n (76*x**3)*(3*x**3) = 228*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 228*x**6 - 69*x**5 - 135*x**4 - 2888*x**3 + 874*x**2 + 1710*x\nNo more calculations needed.\n228*x**6 - 69*x**5 - 135*x**4 - 2888*x**3 + 874*x**2 + 1710*x", "generated_answer": "228*x**6 - 69*x**5 - 135*x**4 - 2888*x**3 + 874*x**2 + 1710*x", "step_length": 5} {"cot_id": "4618fd271504a44c2955b1b117499c7e5f3a0b31f7da663d819395366ad3d716", "datapoint": {"question": "Simplify this expression: (-21*y**3 - 27)*(-45*y**3 - 38*y**2 + 46)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "945*y**6 + 798*y**5 + 249*y**3 + 1026*y**2 - 1242", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1417, "polynomial_expr": "(-21*y**3 - 27)*(-45*y**3 - 38*y**2 + 46)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-21*y**3 - 27)*(-45*y**3 - 38*y**2 + 46)\nExpanding the part (-21*y**3 - 27) using the distributive property, and we got: (-21*y**3)*(-45*y**3 - 38*y**2 + 46) - 27*(-45*y**3 - 38*y**2 + 46)\n#Step 2:\nCurrent expression: (-21*y**3)*(-45*y**3 - 38*y**2 + 46) - 27*(-45*y**3 - 38*y**2 + 46)\nSimplifying the partial expression: -27*(-45*y**3 - 38*y**2 + 46)\nExpanding the part (-45*y**3 - 38*y**2 + 46) using the distributive property, and we got: -38*y**2*(-27) - 45*y**3*(-27) + 46*(-27)\nReplacing -27*(-45*y**3 - 38*y**2 + 46) with -38*y**2*(-27) - 45*y**3*(-27) + 46*(-27) in the overall expression.\n#Step 3:\nCurrent expression: -38*y**2*(-27) - 45*y**3*(-27) + (-21*y**3)*(-45*y**3 - 38*y**2 + 46) - 1242\nSimplifying the partial expression: (-21*y**3)*(-45*y**3 - 38*y**2 + 46)\nExpanding the part (-45*y**3 - 38*y**2 + 46) using the distributive property, and we got: 46*(-21*y**3) + (-38*y**2)*(-21*y**3) + (-45*y**3)*(-21*y**3)\nReplacing (-21*y**3)*(-45*y**3 - 38*y**2 + 46) with 46*(-21*y**3) + (-38*y**2)*(-21*y**3) + (-45*y**3)*(-21*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 46*(-21)*y**3 + (-38*y**2)*(-21*y**3) - 38*y**2*(-27) + (-45*y**3)*(-21*y**3) - 45*y**3*(-27) - 1242\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*y**3)*-27 = 1215*y**3\n (-45*y**3)*(-21*y**3) = 945*y**6\n (-38*y**2)*-27 = 1026*y**2\n (-38*y**2)*(-21*y**3) = 798*y**5\n 46*-21*y**3 = -966*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 945*y**6 + 798*y**5 - 966*y**3 + 1215*y**3 + 1026*y**2 - 1242\nCombining like terms, got 945*y**6 + 798*y**5 + 249*y**3 + 1026*y**2 - 1242\n#Step 6:\nCurrent expression: 945*y**6 + 798*y**5 + 249*y**3 + 1026*y**2 - 1242\nNo more calculations needed.\n945*y**6 + 798*y**5 + 249*y**3 + 1026*y**2 - 1242", "generated_answer": "945*y**6 + 798*y**5 + 249*y**3 + 1026*y**2 - 1242", "step_length": 6} {"cot_id": "4660eec08c3e1eb1d3e81bd0537e08e5736b19e23bc0b2df256bb9ac2293cb1a", "datapoint": {"question": "Simplify this expression: (14*z + 19)*(45*z**3 + 23*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "630*z**4 + 855*z**3 + 322*z**2 + 437*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1418, "polynomial_expr": "(14*z + 19)*(45*z**3 + 23*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14*z + 19)*(45*z**3 + 23*z)\nExpanding the part (14*z + 19) using the distributive property, and we got: (14*z)*(45*z**3 + 23*z) + 19*(45*z**3 + 23*z)\n#Step 2:\nCurrent expression: (14*z)*(45*z**3 + 23*z) + 19*(45*z**3 + 23*z)\nSimplifying the partial expression: 19*(45*z**3 + 23*z)\nExpanding the part (45*z**3 + 23*z) using the distributive property, and we got: (23*z)*19 + (45*z**3)*19\nReplacing 19*(45*z**3 + 23*z) with (23*z)*19 + (45*z**3)*19 in the overall expression.\n#Step 3:\nCurrent expression: (14*z)*(45*z**3 + 23*z) + (23*z)*19 + (45*z**3)*19\nSimplifying the partial expression: (14*z)*(45*z**3 + 23*z)\nExpanding the part (45*z**3 + 23*z) using the distributive property, and we got: (14*z)*(23*z) + (14*z)*(45*z**3)\nReplacing (14*z)*(45*z**3 + 23*z) with (14*z)*(23*z) + (14*z)*(45*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (14*z)*(23*z) + (14*z)*(45*z**3) + (23*z)*19 + (45*z**3)*19\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (23*z)*19 = 437*z\n (23*z)*(14*z) = 322*z**2\n (45*z**3)*19 = 855*z**3\n (45*z**3)*(14*z) = 630*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 630*z**4 + 855*z**3 + 322*z**2 + 437*z\nNo more calculations needed.\n630*z**4 + 855*z**3 + 322*z**2 + 437*z", "generated_answer": "630*z**4 + 855*z**3 + 322*z**2 + 437*z", "step_length": 5} {"cot_id": "b10a0459bc91322e46b6da7c74fc65a51c20859d20ce11eb8d02f6ee2f3b3564", "datapoint": {"question": "Calculate the following: (40*x**2 - 23*x - 27)*(-x**3 + 5*x**2 - 41*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-40*x**5 + 223*x**4 - 1728*x**3 + 808*x**2 + 1107*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1419, "polynomial_expr": "(40*x**2 - 23*x - 27)*(-x**3 + 5*x**2 - 41*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (40*x**2 - 23*x - 27)*(-x**3 + 5*x**2 - 41*x)\nExpanding the part (40*x**2 - 23*x - 27) using the distributive property, and we got: (-23*x)*(-x**3 + 5*x**2 - 41*x) + (40*x**2)*(-x**3 + 5*x**2 - 41*x) - 27*(-x**3 + 5*x**2 - 41*x)\n#Step 2:\nCurrent expression: (-23*x)*(-x**3 + 5*x**2 - 41*x) + (40*x**2)*(-x**3 + 5*x**2 - 41*x) - 27*(-x**3 + 5*x**2 - 41*x)\nSimplifying the partial expression: -27*(-x**3 + 5*x**2 - 41*x)\nExpanding the part (-x**3 + 5*x**2 - 41*x) using the distributive property, and we got: -41*x*(-27) + (5*x**2)*(-27) - x**3*(-27)\nReplacing -27*(-x**3 + 5*x**2 - 41*x) with -41*x*(-27) + (5*x**2)*(-27) - x**3*(-27) in the overall expression.\n#Step 3:\nCurrent expression: -41*x*(-27) + (-23*x)*(-x**3 + 5*x**2 - 41*x) + (5*x**2)*(-27) + (40*x**2)*(-x**3 + 5*x**2 - 41*x) - x**3*(-27)\nSimplifying the partial expression: (-23*x)*(-x**3 + 5*x**2 - 41*x)\nExpanding the part (-x**3 + 5*x**2 - 41*x) using the distributive property, and we got: (-41*x)*(-23*x) + (-23*x)*(5*x**2) + (-23*x)*(-x**3)\nReplacing (-23*x)*(-x**3 + 5*x**2 - 41*x) with (-41*x)*(-23*x) + (-23*x)*(5*x**2) + (-23*x)*(-x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-41*x)*(-23*x) - 41*x*(-27) + (-23*x)*(5*x**2) + (-23*x)*(-x**3) + (5*x**2)*(-27) + (40*x**2)*(-x**3 + 5*x**2 - 41*x) - x**3*(-27)\nSimplifying the partial expression: (40*x**2)*(-x**3 + 5*x**2 - 41*x)\nExpanding the part (-x**3 + 5*x**2 - 41*x) using the distributive property, and we got: (-41*x)*(40*x**2) + (5*x**2)*(40*x**2) + (40*x**2)*(-x**3)\nReplacing (40*x**2)*(-x**3 + 5*x**2 - 41*x) with (-41*x)*(40*x**2) + (5*x**2)*(40*x**2) + (40*x**2)*(-x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-41*x)*(-23*x) + (-41*x)*(40*x**2) - 41*x*(-27) + (-23*x)*(5*x**2) + (-23*x)*(-x**3) + (5*x**2)*(40*x**2) + (5*x**2)*(-27) + (40*x**2)*(-x**3) - x**3*(-27)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-x**3)*-27 = 27*x**3\n (-x**3)*(-23*x) = 23*x**4\n (-x**3)*(40*x**2) = -40*x**5\n (-41*x)*-27 = 1107*x\n (-41*x)*(-23*x) = 943*x**2\n (-41*x)*(40*x**2) = -1640*x**3\n (5*x**2)*-27 = -135*x**2\n (5*x**2)*(-23*x) = -115*x**3\n (5*x**2)*(40*x**2) = 200*x**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -40*x**5 + 23*x**4 + 200*x**4 - 1640*x**3 - 115*x**3 + 27*x**3 - 135*x**2 + 943*x**2 + 1107*x\nCombining like terms, got -40*x**5 + 223*x**4 - 1728*x**3 + 808*x**2 + 1107*x\n#Step 7:\nCurrent expression: -40*x**5 + 223*x**4 - 1728*x**3 + 808*x**2 + 1107*x\nNo more calculations needed.\n-40*x**5 + 223*x**4 - 1728*x**3 + 808*x**2 + 1107*x", "generated_answer": "-40*x**5 + 223*x**4 - 1728*x**3 + 808*x**2 + 1107*x", "step_length": 7} {"cot_id": "5ad302d9278b54d685a4fa9e4722f2811b1bd2bb54c050904e1af72929395e2d", "datapoint": {"question": "Calculate the following: (30 - 26*y**2)*(46*y**2 + 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1196*y**4 + 314*y**2 + 1230", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1420, "polynomial_expr": "(30 - 26*y**2)*(46*y**2 + 41)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (30 - 26*y**2)*(46*y**2 + 41)\nExpanding the part (30 - 26*y**2) using the distributive property, and we got: (-26*y**2)*(46*y**2 + 41) + 30*(46*y**2 + 41)\n#Step 2:\nCurrent expression: (-26*y**2)*(46*y**2 + 41) + 30*(46*y**2 + 41)\nSimplifying the partial expression: 30*(46*y**2 + 41)\nExpanding the part (46*y**2 + 41) using the distributive property, and we got: (46*y**2)*30 + 41*30\nReplacing 30*(46*y**2 + 41) with (46*y**2)*30 + 41*30 in the overall expression.\n#Step 3:\nCurrent expression: (-26*y**2)*(46*y**2 + 41) + (46*y**2)*30 + 1230\nSimplifying the partial expression: (-26*y**2)*(46*y**2 + 41)\nExpanding the part (46*y**2 + 41) using the distributive property, and we got: 41*(-26*y**2) + (-26*y**2)*(46*y**2)\nReplacing (-26*y**2)*(46*y**2 + 41) with 41*(-26*y**2) + (-26*y**2)*(46*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 41*(-26)*y**2 + (-26*y**2)*(46*y**2) + (46*y**2)*30 + 1230\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (46*y**2)*30 = 1380*y**2\n (46*y**2)*(-26*y**2) = -1196*y**4\n 41*-26*y**2 = -1066*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1196*y**4 - 1066*y**2 + 1380*y**2 + 1230\nCombining like terms, got -1196*y**4 + 314*y**2 + 1230\n#Step 6:\nCurrent expression: -1196*y**4 + 314*y**2 + 1230\nNo more calculations needed.\n-1196*y**4 + 314*y**2 + 1230", "generated_answer": "-1196*y**4 + 314*y**2 + 1230", "step_length": 6} {"cot_id": "4238c4d4b1c2d29e7582bcea754ccb8a23fba6a73d02c0414e69527098869b6a", "datapoint": {"question": "Simplify this expression: (-11*z**3 - 16*z**2)*(8*z**2 - 14*z - 43)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-88*z**5 + 26*z**4 + 697*z**3 + 688*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1421, "polynomial_expr": "(-11*z**3 - 16*z**2)*(8*z**2 - 14*z - 43)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-11*z**3 - 16*z**2)*(8*z**2 - 14*z - 43)\nExpanding the part (-11*z**3 - 16*z**2) using the distributive property, and we got: (-16*z**2)*(8*z**2 - 14*z - 43) + (-11*z**3)*(8*z**2 - 14*z - 43)\n#Step 2:\nCurrent expression: (-16*z**2)*(8*z**2 - 14*z - 43) + (-11*z**3)*(8*z**2 - 14*z - 43)\nSimplifying the partial expression: (-16*z**2)*(8*z**2 - 14*z - 43)\nExpanding the part (8*z**2 - 14*z - 43) using the distributive property, and we got: (-14*z)*(-16*z**2) - (-1)*688*z**2 + (-16*z**2)*(8*z**2)\nReplacing (-16*z**2)*(8*z**2 - 14*z - 43) with (-14*z)*(-16*z**2) - (-1)*688*z**2 + (-16*z**2)*(8*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-14*z)*(-16*z**2) - 43*(-16)*z**2 + (-16*z**2)*(8*z**2) + (-11*z**3)*(8*z**2 - 14*z - 43)\nSimplifying the partial expression: (-11*z**3)*(8*z**2 - 14*z - 43)\nExpanding the part (8*z**2 - 14*z - 43) using the distributive property, and we got: (-14*z)*(-11*z**3) - (-1)*473*z**3 + (8*z**2)*(-11*z**3)\nReplacing (-11*z**3)*(8*z**2 - 14*z - 43) with (-14*z)*(-11*z**3) - (-1)*473*z**3 + (8*z**2)*(-11*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-14*z)*(-16*z**2) + (-14*z)*(-11*z**3) - 43*(-11)*z**3 - 43*(-16)*z**2 + (-16*z**2)*(8*z**2) + (8*z**2)*(-11*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-14*z)*(-16*z**2) = 224*z**3\n (-14*z)*(-11*z**3) = 154*z**4\n (8*z**2)*(-16*z**2) = -128*z**4\n (8*z**2)*(-11*z**3) = -88*z**5\n -43*-16*z**2 = 688*z**2\n -43*-11*z**3 = 473*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -88*z**5 - 128*z**4 + 154*z**4 + 224*z**3 + 473*z**3 + 688*z**2\nCombining like terms, got -88*z**5 + 26*z**4 + 697*z**3 + 688*z**2\n#Step 6:\nCurrent expression: -88*z**5 + 26*z**4 + 697*z**3 + 688*z**2\nNo more calculations needed.\n-88*z**5 + 26*z**4 + 697*z**3 + 688*z**2", "generated_answer": "-88*z**5 + 26*z**4 + 697*z**3 + 688*z**2", "step_length": 6} {"cot_id": "f95d9655d1cf41ce1d4f88cab742b162645874838d7436db6bf0d20a4a2932a6", "datapoint": {"question": "Calculate the following: -42*y*(20*y**2 - 45*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-840*y**3 + 1890*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1422, "polynomial_expr": "-42*y*(20*y**2 - 45*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -42*y*(20*y**2 - 45*y)\nExpanding the part (20*y**2 - 45*y) using the distributive property, and we got: (-45*y)*(-42*y) + (-42*y)*(20*y**2)\n#Step 2:\nCurrent expression: (-45*y)*(-42*y) + (-42*y)*(20*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*y)*(-42*y) = 1890*y**2\n (20*y**2)*(-42*y) = -840*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -840*y**3 + 1890*y**2\nNo more calculations needed.\n-840*y**3 + 1890*y**2", "generated_answer": "-840*y**3 + 1890*y**2", "step_length": 3} {"cot_id": "c8af5a661884a059ee8a7182fdae38e276967500dc9ce1dad47270fb7d8f2d71", "datapoint": {"question": "Simplify this expression: (83*x + 47)*(29*x**3 + 4)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2407*x**4 + 1363*x**3 + 332*x + 188", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1423, "polynomial_expr": "(83*x + 47)*(29*x**3 + 4)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (83*x + 47)*(29*x**3 + 4)\nExpanding the part (29*x**3 + 4) using the distributive property, and we got: (29*x**3)*(83*x + 47) + 4*(83*x + 47)\n#Step 2:\nCurrent expression: (29*x**3)*(83*x + 47) + 4*(83*x + 47)\nSimplifying the partial expression: 4*(83*x + 47)\nExpanding the part (83*x + 47) using the distributive property, and we got: (83*x)*4 + 47*4\nReplacing 4*(83*x + 47) with (83*x)*4 + 47*4 in the overall expression.\n#Step 3:\nCurrent expression: (83*x)*4 + (29*x**3)*(83*x + 47) + 188\nSimplifying the partial expression: (29*x**3)*(83*x + 47)\nExpanding the part (83*x + 47) using the distributive property, and we got: 47*(29*x**3) + (83*x)*(29*x**3)\nReplacing (29*x**3)*(83*x + 47) with 47*(29*x**3) + (83*x)*(29*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 47*29*x**3 + (83*x)*(29*x**3) + (83*x)*4 + 188\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (83*x)*4 = 332*x\n (83*x)*(29*x**3) = 2407*x**4\n 47*29*x**3 = 1363*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2407*x**4 + 1363*x**3 + 332*x + 188\nNo more calculations needed.\n2407*x**4 + 1363*x**3 + 332*x + 188", "generated_answer": "2407*x**4 + 1363*x**3 + 332*x + 188", "step_length": 5} {"cot_id": "b79b5d7e5559c2a8fe49c02582ea423fe9f7b42e3d7f1681d02d0ed5783afb0c", "datapoint": {"question": "Calculate the following: (9*z**2 - 13)*(40*z**3 - 32*z**2 - 5*z + 18)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "360*z**5 - 288*z**4 - 565*z**3 + 578*z**2 + 65*z - 234", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1424, "polynomial_expr": "(9*z**2 - 13)*(40*z**3 - 32*z**2 - 5*z + 18)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9*z**2 - 13)*(40*z**3 - 32*z**2 - 5*z + 18)\nExpanding the part (9*z**2 - 13) using the distributive property, and we got: (9*z**2)*(40*z**3 - 32*z**2 - 5*z + 18) - 13*(40*z**3 - 32*z**2 - 5*z + 18)\n#Step 2:\nCurrent expression: (9*z**2)*(40*z**3 - 32*z**2 - 5*z + 18) - 13*(40*z**3 - 32*z**2 - 5*z + 18)\nSimplifying the partial expression: -13*(40*z**3 - 32*z**2 - 5*z + 18)\nExpanding the part (40*z**3 - 32*z**2 - 5*z + 18) using the distributive property, and we got: -5*z*(-13) - 32*z**2*(-13) + (40*z**3)*(-13) + 18*(-13)\nReplacing -13*(40*z**3 - 32*z**2 - 5*z + 18) with -5*z*(-13) - 32*z**2*(-13) + (40*z**3)*(-13) + 18*(-13) in the overall expression.\n#Step 3:\nCurrent expression: -5*z*(-13) - 32*z**2*(-13) + (9*z**2)*(40*z**3 - 32*z**2 - 5*z + 18) + (40*z**3)*(-13) - 234\nSimplifying the partial expression: (9*z**2)*(40*z**3 - 32*z**2 - 5*z + 18)\nExpanding the part (40*z**3 - 32*z**2 - 5*z + 18) using the distributive property, and we got: (-5*z)*(9*z**2) + 18*(9*z**2) + (-32*z**2)*(9*z**2) + (9*z**2)*(40*z**3)\nReplacing (9*z**2)*(40*z**3 - 32*z**2 - 5*z + 18) with (-5*z)*(9*z**2) + 18*(9*z**2) + (-32*z**2)*(9*z**2) + (9*z**2)*(40*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-5*z)*(9*z**2) - 5*z*(-13) + 18*9*z**2 + (-32*z**2)*(9*z**2) - 32*z**2*(-13) + (9*z**2)*(40*z**3) + (40*z**3)*(-13) - 234\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*z**2)*-13 = 416*z**2\n (-32*z**2)*(9*z**2) = -288*z**4\n (-5*z)*-13 = 65*z\n (-5*z)*(9*z**2) = -45*z**3\n (40*z**3)*-13 = -520*z**3\n (40*z**3)*(9*z**2) = 360*z**5\n 18*9*z**2 = 162*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 360*z**5 - 288*z**4 - 520*z**3 - 45*z**3 + 162*z**2 + 416*z**2 + 65*z - 234\nCombining like terms, got 360*z**5 - 288*z**4 - 565*z**3 + 578*z**2 + 65*z - 234\n#Step 6:\nCurrent expression: 360*z**5 - 288*z**4 - 565*z**3 + 578*z**2 + 65*z - 234\nNo more calculations needed.\n360*z**5 - 288*z**4 - 565*z**3 + 578*z**2 + 65*z - 234", "generated_answer": "360*z**5 - 288*z**4 - 565*z**3 + 578*z**2 + 65*z - 234", "step_length": 6} {"cot_id": "4265e0879c13e784ae41dc17f6381d4e8598c1a080bdf50d6e69fa8a09a19392", "datapoint": {"question": "Calculate the following: (-45*z**3 - 3*z**2 + 37)*(-z**3 - 21*z + 5)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "45*z**6 + 3*z**5 + 945*z**4 - 199*z**3 - 15*z**2 - 777*z + 185", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1425, "polynomial_expr": "(-45*z**3 - 3*z**2 + 37)*(-z**3 - 21*z + 5)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-45*z**3 - 3*z**2 + 37)*(-z**3 - 21*z + 5)\nExpanding the part (-z**3 - 21*z + 5) using the distributive property, and we got: (-21*z)*(-45*z**3 - 3*z**2 + 37) + (-z**3)*(-45*z**3 - 3*z**2 + 37) + 5*(-45*z**3 - 3*z**2 + 37)\n#Step 2:\nCurrent expression: (-21*z)*(-45*z**3 - 3*z**2 + 37) + (-z**3)*(-45*z**3 - 3*z**2 + 37) + 5*(-45*z**3 - 3*z**2 + 37)\nSimplifying the partial expression: 5*(-45*z**3 - 3*z**2 + 37)\nExpanding the part (-45*z**3 - 3*z**2 + 37) using the distributive property, and we got: -3*z**2*5 - 45*z**3*5 + 37*5\nReplacing 5*(-45*z**3 - 3*z**2 + 37) with -3*z**2*5 - 45*z**3*5 + 37*5 in the overall expression.\n#Step 3:\nCurrent expression: (-21*z)*(-45*z**3 - 3*z**2 + 37) - 3*z**2*5 - 45*z**3*5 + (-z**3)*(-45*z**3 - 3*z**2 + 37) + 185\nSimplifying the partial expression: (-z**3)*(-45*z**3 - 3*z**2 + 37)\nExpanding the part (-45*z**3 - 3*z**2 + 37) using the distributive property, and we got: 37*(-z**3) + (-3*z**2)*(-z**3) + (-45*z**3)*(-z**3)\nReplacing (-z**3)*(-45*z**3 - 3*z**2 + 37) with 37*(-z**3) + (-3*z**2)*(-z**3) + (-45*z**3)*(-z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-21*z)*(-45*z**3 - 3*z**2 + 37) + 37*(-1)*z**3 + (-3*z**2)*(-z**3) - 3*z**2*5 + (-45*z**3)*(-z**3) - 45*z**3*5 + 185\nSimplifying the partial expression: (-21*z)*(-45*z**3 - 3*z**2 + 37)\nExpanding the part (-45*z**3 - 3*z**2 + 37) using the distributive property, and we got: (-21*z)*(-3*z**2) + (-21*z)*(-45*z**3) + 37*(-21*z)\nReplacing (-21*z)*(-45*z**3 - 3*z**2 + 37) with (-21*z)*(-3*z**2) + (-21*z)*(-45*z**3) + 37*(-21*z) in the overall expression.\n#Step 5:\nCurrent expression: (-21*z)*(-3*z**2) + (-21*z)*(-45*z**3) + 37*(-1)*z**3 + 37*(-21)*z + (-3*z**2)*(-z**3) - 3*z**2*5 + (-45*z**3)*(-z**3) - 45*z**3*5 + 185\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*z**3)*5 = -225*z**3\n (-45*z**3)*(-z**3) = 45*z**6\n (-45*z**3)*(-21*z) = 945*z**4\n (-3*z**2)*5 = -15*z**2\n (-3*z**2)*(-z**3) = 3*z**5\n (-3*z**2)*(-21*z) = 63*z**3\n 37*-1*z**3 = -37*z**3\n 37*-21*z = -777*z\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 45*z**6 + 3*z**5 + 945*z**4 - 225*z**3 - 37*z**3 + 63*z**3 - 15*z**2 - 777*z + 185\nCombining like terms, got 45*z**6 + 3*z**5 + 945*z**4 - 199*z**3 - 15*z**2 - 777*z + 185\n#Step 7:\nCurrent expression: 45*z**6 + 3*z**5 + 945*z**4 - 199*z**3 - 15*z**2 - 777*z + 185\nNo more calculations needed.\n45*z**6 + 3*z**5 + 945*z**4 - 199*z**3 - 15*z**2 - 777*z + 185", "generated_answer": "45*z**6 + 3*z**5 + 945*z**4 - 199*z**3 - 15*z**2 - 777*z + 185", "step_length": 7} {"cot_id": "4e6cfad115da63a28cf06137f0a38b25a0823474c5b185f93518485591495c1f", "datapoint": {"question": "Calculate the following: (42 - 7*z**3)*(44*z**2 - 8)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-308*z**5 + 56*z**3 + 1848*z**2 - 336", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1426, "polynomial_expr": "(42 - 7*z**3)*(44*z**2 - 8)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (42 - 7*z**3)*(44*z**2 - 8)\nExpanding the part (44*z**2 - 8) using the distributive property, and we got: (44*z**2)*(42 - 7*z**3) - 8*(42 - 7*z**3)\n#Step 2:\nCurrent expression: (44*z**2)*(42 - 7*z**3) - 8*(42 - 7*z**3)\nSimplifying the partial expression: -8*(42 - 7*z**3)\nExpanding the part (42 - 7*z**3) using the distributive property, and we got: -7*z**3*(-8) + 42*(-8)\nReplacing -8*(42 - 7*z**3) with -7*z**3*(-8) + 42*(-8) in the overall expression.\n#Step 3:\nCurrent expression: (44*z**2)*(42 - 7*z**3) - 7*z**3*(-8) - 336\nSimplifying the partial expression: (44*z**2)*(42 - 7*z**3)\nExpanding the part (42 - 7*z**3) using the distributive property, and we got: 42*(44*z**2) + (44*z**2)*(-7*z**3)\nReplacing (44*z**2)*(42 - 7*z**3) with 42*(44*z**2) + (44*z**2)*(-7*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 42*44*z**2 + (44*z**2)*(-7*z**3) - 7*z**3*(-8) - 336\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-7*z**3)*-8 = 56*z**3\n (-7*z**3)*(44*z**2) = -308*z**5\n 42*44*z**2 = 1848*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -308*z**5 + 56*z**3 + 1848*z**2 - 336\nNo more calculations needed.\n-308*z**5 + 56*z**3 + 1848*z**2 - 336", "generated_answer": "-308*z**5 + 56*z**3 + 1848*z**2 - 336", "step_length": 5} {"cot_id": "285f9b2443661456dc2556ae7316bd604698fe66614738cb59253e75e43296d2", "datapoint": {"question": "Calculate the following: (-75*x**3 - 40*x**2 - 43)*(23*x**3 - 32*x**2 - 29)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1725*x**6 + 1480*x**5 + 1280*x**4 + 1186*x**3 + 2536*x**2 + 1247", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1427, "polynomial_expr": "(-75*x**3 - 40*x**2 - 43)*(23*x**3 - 32*x**2 - 29)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-75*x**3 - 40*x**2 - 43)*(23*x**3 - 32*x**2 - 29)\nExpanding the part (-75*x**3 - 40*x**2 - 43) using the distributive property, and we got: (-40*x**2)*(23*x**3 - 32*x**2 - 29) + (-75*x**3)*(23*x**3 - 32*x**2 - 29) - 43*(23*x**3 - 32*x**2 - 29)\n#Step 2:\nCurrent expression: (-40*x**2)*(23*x**3 - 32*x**2 - 29) + (-75*x**3)*(23*x**3 - 32*x**2 - 29) - 43*(23*x**3 - 32*x**2 - 29)\nSimplifying the partial expression: -43*(23*x**3 - 32*x**2 - 29)\nExpanding the part (23*x**3 - 32*x**2 - 29) using the distributive property, and we got: -32*x**2*(-43) + (23*x**3)*(-43) - 29*(-43)\nReplacing -43*(23*x**3 - 32*x**2 - 29) with -32*x**2*(-43) + (23*x**3)*(-43) - 29*(-43) in the overall expression.\n#Step 3:\nCurrent expression: (-40*x**2)*(23*x**3 - 32*x**2 - 29) - 32*x**2*(-43) + (-75*x**3)*(23*x**3 - 32*x**2 - 29) + (23*x**3)*(-43) + 1247\nSimplifying the partial expression: (-75*x**3)*(23*x**3 - 32*x**2 - 29)\nExpanding the part (23*x**3 - 32*x**2 - 29) using the distributive property, and we got: -(-1)*2175*x**3 + (-32*x**2)*(-75*x**3) + (-75*x**3)*(23*x**3)\nReplacing (-75*x**3)*(23*x**3 - 32*x**2 - 29) with -(-1)*2175*x**3 + (-32*x**2)*(-75*x**3) + (-75*x**3)*(23*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -29*(-75)*x**3 + (-40*x**2)*(23*x**3 - 32*x**2 - 29) + (-32*x**2)*(-75*x**3) - 32*x**2*(-43) + (-75*x**3)*(23*x**3) + (23*x**3)*(-43) + 1247\nSimplifying the partial expression: (-40*x**2)*(23*x**3 - 32*x**2 - 29)\nExpanding the part (23*x**3 - 32*x**2 - 29) using the distributive property, and we got: -(-1)*1160*x**2 + (-40*x**2)*(-32*x**2) + (-40*x**2)*(23*x**3)\nReplacing (-40*x**2)*(23*x**3 - 32*x**2 - 29) with -(-1)*1160*x**2 + (-40*x**2)*(-32*x**2) + (-40*x**2)*(23*x**3) in the overall expression.\n#Step 5:\nCurrent expression: -29*(-75)*x**3 - 29*(-40)*x**2 + (-40*x**2)*(-32*x**2) + (-40*x**2)*(23*x**3) + (-32*x**2)*(-75*x**3) - 32*x**2*(-43) + (-75*x**3)*(23*x**3) + (23*x**3)*(-43) + 1247\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*x**2)*-43 = 1376*x**2\n (-32*x**2)*(-75*x**3) = 2400*x**5\n (-32*x**2)*(-40*x**2) = 1280*x**4\n (23*x**3)*-43 = -989*x**3\n (23*x**3)*(-75*x**3) = -1725*x**6\n (23*x**3)*(-40*x**2) = -920*x**5\n -29*-75*x**3 = 2175*x**3\n -29*-40*x**2 = 1160*x**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1725*x**6 - 920*x**5 + 2400*x**5 + 1280*x**4 - 989*x**3 + 2175*x**3 + 1160*x**2 + 1376*x**2 + 1247\nCombining like terms, got -1725*x**6 + 1480*x**5 + 1280*x**4 + 1186*x**3 + 2536*x**2 + 1247\n#Step 7:\nCurrent expression: -1725*x**6 + 1480*x**5 + 1280*x**4 + 1186*x**3 + 2536*x**2 + 1247\nNo more calculations needed.\n-1725*x**6 + 1480*x**5 + 1280*x**4 + 1186*x**3 + 2536*x**2 + 1247", "generated_answer": "-1725*x**6 + 1480*x**5 + 1280*x**4 + 1186*x**3 + 2536*x**2 + 1247", "step_length": 7} {"cot_id": "d010045058721cd5dfc9341bd59e16e8d0df6be0365365ab17fbad8d8a9e96f1", "datapoint": {"question": "Simplify this expression: (46 - 34*z**2)*(-87*z - 25)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2958*z**3 + 850*z**2 - 4002*z - 1150", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1428, "polynomial_expr": "(46 - 34*z**2)*(-87*z - 25)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (46 - 34*z**2)*(-87*z - 25)\nExpanding the part (-87*z - 25) using the distributive property, and we got: (-87*z)*(46 - 34*z**2) - 25*(46 - 34*z**2)\n#Step 2:\nCurrent expression: (-87*z)*(46 - 34*z**2) - 25*(46 - 34*z**2)\nSimplifying the partial expression: -25*(46 - 34*z**2)\nExpanding the part (46 - 34*z**2) using the distributive property, and we got: -34*z**2*(-25) + 46*(-25)\nReplacing -25*(46 - 34*z**2) with -34*z**2*(-25) + 46*(-25) in the overall expression.\n#Step 3:\nCurrent expression: (-87*z)*(46 - 34*z**2) - 34*z**2*(-25) - 1150\nSimplifying the partial expression: (-87*z)*(46 - 34*z**2)\nExpanding the part (46 - 34*z**2) using the distributive property, and we got: (-87*z)*(-34*z**2) + 46*(-87*z)\nReplacing (-87*z)*(46 - 34*z**2) with (-87*z)*(-34*z**2) + 46*(-87*z) in the overall expression.\n#Step 4:\nCurrent expression: (-87*z)*(-34*z**2) + 46*(-87)*z - 34*z**2*(-25) - 1150\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*z**2)*-25 = 850*z**2\n (-34*z**2)*(-87*z) = 2958*z**3\n 46*-87*z = -4002*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2958*z**3 + 850*z**2 - 4002*z - 1150\nNo more calculations needed.\n2958*z**3 + 850*z**2 - 4002*z - 1150", "generated_answer": "2958*z**3 + 850*z**2 - 4002*z - 1150", "step_length": 5} {"cot_id": "195295a47236f7b433e0f10f3f82471c55512956669959f2295688f965e03b78", "datapoint": {"question": "Simplify this expression: (-15*x**2 - 5)*(-40*x**2 - 48*x - 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "600*x**4 + 720*x**3 + 500*x**2 + 240*x + 100", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1429, "polynomial_expr": "(-15*x**2 - 5)*(-40*x**2 - 48*x - 20)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-15*x**2 - 5)*(-40*x**2 - 48*x - 20)\nExpanding the part (-15*x**2 - 5) using the distributive property, and we got: (-15*x**2)*(-40*x**2 - 48*x - 20) - 5*(-40*x**2 - 48*x - 20)\n#Step 2:\nCurrent expression: (-15*x**2)*(-40*x**2 - 48*x - 20) - 5*(-40*x**2 - 48*x - 20)\nSimplifying the partial expression: -5*(-40*x**2 - 48*x - 20)\nExpanding the part (-40*x**2 - 48*x - 20) using the distributive property, and we got: -48*x*(-5) - 40*x**2*(-5) - 20*(-5)\nReplacing -5*(-40*x**2 - 48*x - 20) with -48*x*(-5) - 40*x**2*(-5) - 20*(-5) in the overall expression.\n#Step 3:\nCurrent expression: -48*x*(-5) - 40*x**2*(-5) + (-15*x**2)*(-40*x**2 - 48*x - 20) + 100\nSimplifying the partial expression: (-15*x**2)*(-40*x**2 - 48*x - 20)\nExpanding the part (-40*x**2 - 48*x - 20) using the distributive property, and we got: (-48*x)*(-15*x**2) - (-1)*300*x**2 + (-40*x**2)*(-15*x**2)\nReplacing (-15*x**2)*(-40*x**2 - 48*x - 20) with (-48*x)*(-15*x**2) - (-1)*300*x**2 + (-40*x**2)*(-15*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-48*x)*(-15*x**2) - 48*x*(-5) - 20*(-15)*x**2 + (-40*x**2)*(-15*x**2) - 40*x**2*(-5) + 100\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*x)*-5 = 240*x\n (-48*x)*(-15*x**2) = 720*x**3\n (-40*x**2)*-5 = 200*x**2\n (-40*x**2)*(-15*x**2) = 600*x**4\n -20*-15*x**2 = 300*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 600*x**4 + 720*x**3 + 200*x**2 + 300*x**2 + 240*x + 100\nCombining like terms, got 600*x**4 + 720*x**3 + 500*x**2 + 240*x + 100\n#Step 6:\nCurrent expression: 600*x**4 + 720*x**3 + 500*x**2 + 240*x + 100\nNo more calculations needed.\n600*x**4 + 720*x**3 + 500*x**2 + 240*x + 100", "generated_answer": "600*x**4 + 720*x**3 + 500*x**2 + 240*x + 100", "step_length": 6} {"cot_id": "42597d71fb776a312ab815fd6d45f92db18adeab53bf994111ec31f4c64285fb", "datapoint": {"question": "Simplify this expression: (-30*x**2 + 47*x + 48)*(x**2 + 49*x - 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-30*x**4 - 1423*x**3 + 3521*x**2 + 519*x - 1872", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1430, "polynomial_expr": "(-30*x**2 + 47*x + 48)*(x**2 + 49*x - 39)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-30*x**2 + 47*x + 48)*(x**2 + 49*x - 39)\nExpanding the part (x**2 + 49*x - 39) using the distributive property, and we got: x**2*(-30*x**2 + 47*x + 48) + (49*x)*(-30*x**2 + 47*x + 48) - 39*(-30*x**2 + 47*x + 48)\n#Step 2:\nCurrent expression: x**2*(-30*x**2 + 47*x + 48) + (49*x)*(-30*x**2 + 47*x + 48) - 39*(-30*x**2 + 47*x + 48)\nSimplifying the partial expression: -39*(-30*x**2 + 47*x + 48)\nExpanding the part (-30*x**2 + 47*x + 48) using the distributive property, and we got: (47*x)*(-39) - 30*x**2*(-39) + 48*(-39)\nReplacing -39*(-30*x**2 + 47*x + 48) with (47*x)*(-39) - 30*x**2*(-39) + 48*(-39) in the overall expression.\n#Step 3:\nCurrent expression: x**2*(-30*x**2 + 47*x + 48) + (47*x)*(-39) + (49*x)*(-30*x**2 + 47*x + 48) - 30*x**2*(-39) - 1872\nSimplifying the partial expression: x**2*(-30*x**2 + 47*x + 48)\nExpanding the part (-30*x**2 + 47*x + 48) using the distributive property, and we got: (47*x)*x**2 + (-30*x**2)*x**2 + 48*x**2\nReplacing x**2*(-30*x**2 + 47*x + 48) with (47*x)*x**2 + (-30*x**2)*x**2 + 48*x**2 in the overall expression.\n#Step 4:\nCurrent expression: (47*x)*x**2 + (-30*x**2)*x**2 + 48*x**2 + (47*x)*(-39) + (49*x)*(-30*x**2 + 47*x + 48) - 30*x**2*(-39) - 1872\nSimplifying the partial expression: (49*x)*(-30*x**2 + 47*x + 48)\nExpanding the part (-30*x**2 + 47*x + 48) using the distributive property, and we got: 48*(49*x) + (47*x)*(49*x) + (49*x)*(-30*x**2)\nReplacing (49*x)*(-30*x**2 + 47*x + 48) with 48*(49*x) + (47*x)*(49*x) + (49*x)*(-30*x**2) in the overall expression.\n#Step 5:\nCurrent expression: (47*x)*x**2 + (-30*x**2)*x**2 + 48*x**2 + 48*49*x + (47*x)*(49*x) + (47*x)*(-39) + (49*x)*(-30*x**2) - 30*x**2*(-39) - 1872\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*x**2)*-39 = 1170*x**2\n (-30*x**2)*x**2 = -30*x**4\n (-30*x**2)*(49*x) = -1470*x**3\n (47*x)*-39 = -1833*x\n (47*x)*x**2 = 47*x**3\n (47*x)*(49*x) = 2303*x**2\n 48*49*x = 2352*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -30*x**4 - 1470*x**3 + 47*x**3 + 48*x**2 + 1170*x**2 + 2303*x**2 - 1833*x + 2352*x - 1872\nCombining like terms, got -30*x**4 - 1423*x**3 + 3521*x**2 + 519*x - 1872\n#Step 7:\nCurrent expression: -30*x**4 - 1423*x**3 + 3521*x**2 + 519*x - 1872\nNo more calculations needed.\n-30*x**4 - 1423*x**3 + 3521*x**2 + 519*x - 1872", "generated_answer": "-30*x**4 - 1423*x**3 + 3521*x**2 + 519*x - 1872", "step_length": 7} {"cot_id": "9f4fed4044cb0f52baf56843c61f46ca1a8255329cfd07980c1155c9a7c22312", "datapoint": {"question": "Calculate the following: (31*x**3 + 45*x)*(-16*x**3 + 47*x - 45)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-496*x**6 + 737*x**4 - 1395*x**3 + 2115*x**2 - 2025*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1431, "polynomial_expr": "(31*x**3 + 45*x)*(-16*x**3 + 47*x - 45)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31*x**3 + 45*x)*(-16*x**3 + 47*x - 45)\nExpanding the part (31*x**3 + 45*x) using the distributive property, and we got: (45*x)*(-16*x**3 + 47*x - 45) + (31*x**3)*(-16*x**3 + 47*x - 45)\n#Step 2:\nCurrent expression: (45*x)*(-16*x**3 + 47*x - 45) + (31*x**3)*(-16*x**3 + 47*x - 45)\nSimplifying the partial expression: (31*x**3)*(-16*x**3 + 47*x - 45)\nExpanding the part (-16*x**3 + 47*x - 45) using the distributive property, and we got: -1395*x**3 + (47*x)*(31*x**3) + (-16*x**3)*(31*x**3)\nReplacing (31*x**3)*(-16*x**3 + 47*x - 45) with -1395*x**3 + (47*x)*(31*x**3) + (-16*x**3)*(31*x**3) in the overall expression.\n#Step 3:\nCurrent expression: -45*31*x**3 + (45*x)*(-16*x**3 + 47*x - 45) + (47*x)*(31*x**3) + (-16*x**3)*(31*x**3)\nSimplifying the partial expression: (45*x)*(-16*x**3 + 47*x - 45)\nExpanding the part (-16*x**3 + 47*x - 45) using the distributive property, and we got: -2025*x + (45*x)*(47*x) + (45*x)*(-16*x**3)\nReplacing (45*x)*(-16*x**3 + 47*x - 45) with -2025*x + (45*x)*(47*x) + (45*x)*(-16*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -45*31*x**3 - 45*45*x + (45*x)*(47*x) + (45*x)*(-16*x**3) + (47*x)*(31*x**3) + (-16*x**3)*(31*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-16*x**3)*(31*x**3) = -496*x**6\n (-16*x**3)*(45*x) = -720*x**4\n (47*x)*(31*x**3) = 1457*x**4\n (47*x)*(45*x) = 2115*x**2\n -45*31*x**3 = -1395*x**3\n -45*45*x = -2025*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -496*x**6 - 720*x**4 + 1457*x**4 - 1395*x**3 + 2115*x**2 - 2025*x\nCombining like terms, got -496*x**6 + 737*x**4 - 1395*x**3 + 2115*x**2 - 2025*x\n#Step 6:\nCurrent expression: -496*x**6 + 737*x**4 - 1395*x**3 + 2115*x**2 - 2025*x\nNo more calculations needed.\n-496*x**6 + 737*x**4 - 1395*x**3 + 2115*x**2 - 2025*x", "generated_answer": "-496*x**6 + 737*x**4 - 1395*x**3 + 2115*x**2 - 2025*x", "step_length": 6} {"cot_id": "ffd2935862dde771164c9dfa2800062004cdf9e4f7c677ba164f53ac86863486", "datapoint": {"question": "Simplify this expression: (20*x - 6)*(16*x**3 + 28*x**2 + 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "320*x**4 + 464*x**3 - 168*x**2 + 260*x - 78", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1432, "polynomial_expr": "(20*x - 6)*(16*x**3 + 28*x**2 + 13)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (20*x - 6)*(16*x**3 + 28*x**2 + 13)\nExpanding the part (20*x - 6) using the distributive property, and we got: (20*x)*(16*x**3 + 28*x**2 + 13) - 6*(16*x**3 + 28*x**2 + 13)\n#Step 2:\nCurrent expression: (20*x)*(16*x**3 + 28*x**2 + 13) - 6*(16*x**3 + 28*x**2 + 13)\nSimplifying the partial expression: -6*(16*x**3 + 28*x**2 + 13)\nExpanding the part (16*x**3 + 28*x**2 + 13) using the distributive property, and we got: (28*x**2)*(-6) + (16*x**3)*(-6) + 13*(-6)\nReplacing -6*(16*x**3 + 28*x**2 + 13) with (28*x**2)*(-6) + (16*x**3)*(-6) + 13*(-6) in the overall expression.\n#Step 3:\nCurrent expression: (20*x)*(16*x**3 + 28*x**2 + 13) + (28*x**2)*(-6) + (16*x**3)*(-6) - 78\nSimplifying the partial expression: (20*x)*(16*x**3 + 28*x**2 + 13)\nExpanding the part (16*x**3 + 28*x**2 + 13) using the distributive property, and we got: 13*(20*x) + (20*x)*(28*x**2) + (20*x)*(16*x**3)\nReplacing (20*x)*(16*x**3 + 28*x**2 + 13) with 13*(20*x) + (20*x)*(28*x**2) + (20*x)*(16*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 13*20*x + (20*x)*(28*x**2) + (20*x)*(16*x**3) + (28*x**2)*(-6) + (16*x**3)*(-6) - 78\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (16*x**3)*-6 = -96*x**3\n (16*x**3)*(20*x) = 320*x**4\n (28*x**2)*-6 = -168*x**2\n (28*x**2)*(20*x) = 560*x**3\n 13*20*x = 260*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 320*x**4 - 96*x**3 + 560*x**3 - 168*x**2 + 260*x - 78\nCombining like terms, got 320*x**4 + 464*x**3 - 168*x**2 + 260*x - 78\n#Step 6:\nCurrent expression: 320*x**4 + 464*x**3 - 168*x**2 + 260*x - 78\nNo more calculations needed.\n320*x**4 + 464*x**3 - 168*x**2 + 260*x - 78", "generated_answer": "320*x**4 + 464*x**3 - 168*x**2 + 260*x - 78", "step_length": 6} {"cot_id": "6efe399ea4e66d475b3942662ffaae06ff0d6051bd1fa4c3183063d7eced287f", "datapoint": {"question": "Simplify this expression: (41*x**2 - 55)*(35*x**3 + 22*x**2 - 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1435*x**5 + 902*x**4 - 1925*x**3 - 2563*x**2 + 1815", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1433, "polynomial_expr": "(41*x**2 - 55)*(35*x**3 + 22*x**2 - 33)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (41*x**2 - 55)*(35*x**3 + 22*x**2 - 33)\nExpanding the part (41*x**2 - 55) using the distributive property, and we got: (41*x**2)*(35*x**3 + 22*x**2 - 33) - 55*(35*x**3 + 22*x**2 - 33)\n#Step 2:\nCurrent expression: (41*x**2)*(35*x**3 + 22*x**2 - 33) - 55*(35*x**3 + 22*x**2 - 33)\nSimplifying the partial expression: -55*(35*x**3 + 22*x**2 - 33)\nExpanding the part (35*x**3 + 22*x**2 - 33) using the distributive property, and we got: (22*x**2)*(-55) + (35*x**3)*(-55) - 33*(-55)\nReplacing -55*(35*x**3 + 22*x**2 - 33) with (22*x**2)*(-55) + (35*x**3)*(-55) - 33*(-55) in the overall expression.\n#Step 3:\nCurrent expression: (22*x**2)*(-55) + (41*x**2)*(35*x**3 + 22*x**2 - 33) + (35*x**3)*(-55) + 1815\nSimplifying the partial expression: (41*x**2)*(35*x**3 + 22*x**2 - 33)\nExpanding the part (35*x**3 + 22*x**2 - 33) using the distributive property, and we got: -1353*x**2 + (22*x**2)*(41*x**2) + (41*x**2)*(35*x**3)\nReplacing (41*x**2)*(35*x**3 + 22*x**2 - 33) with -1353*x**2 + (22*x**2)*(41*x**2) + (41*x**2)*(35*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -33*41*x**2 + (22*x**2)*(41*x**2) + (22*x**2)*(-55) + (41*x**2)*(35*x**3) + (35*x**3)*(-55) + 1815\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (22*x**2)*-55 = -1210*x**2\n (22*x**2)*(41*x**2) = 902*x**4\n (35*x**3)*-55 = -1925*x**3\n (35*x**3)*(41*x**2) = 1435*x**5\n -33*41*x**2 = -1353*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1435*x**5 + 902*x**4 - 1925*x**3 - 1353*x**2 - 1210*x**2 + 1815\nCombining like terms, got 1435*x**5 + 902*x**4 - 1925*x**3 - 2563*x**2 + 1815\n#Step 6:\nCurrent expression: 1435*x**5 + 902*x**4 - 1925*x**3 - 2563*x**2 + 1815\nNo more calculations needed.\n1435*x**5 + 902*x**4 - 1925*x**3 - 2563*x**2 + 1815", "generated_answer": "1435*x**5 + 902*x**4 - 1925*x**3 - 2563*x**2 + 1815", "step_length": 6} {"cot_id": "079089de5ea6359940b37a9b0777c9832f31847b93d23dfd901fc153fd019e85", "datapoint": {"question": "Calculate the following: (23 - 42*z**2)*(-20*z**2 - 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "840*z**4 + 422*z**2 - 483", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1434, "polynomial_expr": "(23 - 42*z**2)*(-20*z**2 - 21)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (23 - 42*z**2)*(-20*z**2 - 21)\nExpanding the part (-20*z**2 - 21) using the distributive property, and we got: (-20*z**2)*(23 - 42*z**2) - 21*(23 - 42*z**2)\n#Step 2:\nCurrent expression: (-20*z**2)*(23 - 42*z**2) - 21*(23 - 42*z**2)\nSimplifying the partial expression: -21*(23 - 42*z**2)\nExpanding the part (23 - 42*z**2) using the distributive property, and we got: -42*z**2*(-21) + 23*(-21)\nReplacing -21*(23 - 42*z**2) with -42*z**2*(-21) + 23*(-21) in the overall expression.\n#Step 3:\nCurrent expression: -42*z**2*(-21) + (-20*z**2)*(23 - 42*z**2) - 483\nSimplifying the partial expression: (-20*z**2)*(23 - 42*z**2)\nExpanding the part (23 - 42*z**2) using the distributive property, and we got: 23*(-20*z**2) + (-42*z**2)*(-20*z**2)\nReplacing (-20*z**2)*(23 - 42*z**2) with 23*(-20*z**2) + (-42*z**2)*(-20*z**2) in the overall expression.\n#Step 4:\nCurrent expression: 23*(-20)*z**2 + (-42*z**2)*(-20*z**2) - 42*z**2*(-21) - 483\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*z**2)*-21 = 882*z**2\n (-42*z**2)*(-20*z**2) = 840*z**4\n 23*-20*z**2 = -460*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 840*z**4 - 460*z**2 + 882*z**2 - 483\nCombining like terms, got 840*z**4 + 422*z**2 - 483\n#Step 6:\nCurrent expression: 840*z**4 + 422*z**2 - 483\nNo more calculations needed.\n840*z**4 + 422*z**2 - 483", "generated_answer": "840*z**4 + 422*z**2 - 483", "step_length": 6} {"cot_id": "ae611fa55d8b7d6e6c7029b0c31aff233822191eb267bb2dc9f305daa41f811d", "datapoint": {"question": "Calculate the following: (-6*z**3 + 9*z + 12)*(-2*z**3 + 30*z - 64)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "12*z**6 - 198*z**4 + 360*z**3 + 270*z**2 - 216*z - 768", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1435, "polynomial_expr": "(-6*z**3 + 9*z + 12)*(-2*z**3 + 30*z - 64)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-6*z**3 + 9*z + 12)*(-2*z**3 + 30*z - 64)\nExpanding the part (-2*z**3 + 30*z - 64) using the distributive property, and we got: (30*z)*(-6*z**3 + 9*z + 12) + (-2*z**3)*(-6*z**3 + 9*z + 12) - 64*(-6*z**3 + 9*z + 12)\n#Step 2:\nCurrent expression: (30*z)*(-6*z**3 + 9*z + 12) + (-2*z**3)*(-6*z**3 + 9*z + 12) - 64*(-6*z**3 + 9*z + 12)\nSimplifying the partial expression: -64*(-6*z**3 + 9*z + 12)\nExpanding the part (-6*z**3 + 9*z + 12) using the distributive property, and we got: (9*z)*(-64) - 6*z**3*(-64) + 12*(-64)\nReplacing -64*(-6*z**3 + 9*z + 12) with (9*z)*(-64) - 6*z**3*(-64) + 12*(-64) in the overall expression.\n#Step 3:\nCurrent expression: (9*z)*(-64) + (30*z)*(-6*z**3 + 9*z + 12) - 6*z**3*(-64) + (-2*z**3)*(-6*z**3 + 9*z + 12) - 768\nSimplifying the partial expression: (-2*z**3)*(-6*z**3 + 9*z + 12)\nExpanding the part (-6*z**3 + 9*z + 12) using the distributive property, and we got: 12*(-2*z**3) + (9*z)*(-2*z**3) + (-6*z**3)*(-2*z**3)\nReplacing (-2*z**3)*(-6*z**3 + 9*z + 12) with 12*(-2*z**3) + (9*z)*(-2*z**3) + (-6*z**3)*(-2*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 12*(-2)*z**3 + (9*z)*(-2*z**3) + (9*z)*(-64) + (30*z)*(-6*z**3 + 9*z + 12) + (-6*z**3)*(-2*z**3) - 6*z**3*(-64) - 768\nSimplifying the partial expression: (30*z)*(-6*z**3 + 9*z + 12)\nExpanding the part (-6*z**3 + 9*z + 12) using the distributive property, and we got: 12*(30*z) + (9*z)*(30*z) + (30*z)*(-6*z**3)\nReplacing (30*z)*(-6*z**3 + 9*z + 12) with 12*(30*z) + (9*z)*(30*z) + (30*z)*(-6*z**3) in the overall expression.\n#Step 5:\nCurrent expression: 12*(-2)*z**3 + 12*30*z + (9*z)*(30*z) + (9*z)*(-2*z**3) + (9*z)*(-64) + (30*z)*(-6*z**3) + (-6*z**3)*(-2*z**3) - 6*z**3*(-64) - 768\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-6*z**3)*-64 = 384*z**3\n (-6*z**3)*(-2*z**3) = 12*z**6\n (-6*z**3)*(30*z) = -180*z**4\n (9*z)*-64 = -576*z\n (9*z)*(-2*z**3) = -18*z**4\n (9*z)*(30*z) = 270*z**2\n 12*-2*z**3 = -24*z**3\n 12*30*z = 360*z\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 12*z**6 - 180*z**4 - 18*z**4 - 24*z**3 + 384*z**3 + 270*z**2 - 576*z + 360*z - 768\nCombining like terms, got 12*z**6 - 198*z**4 + 360*z**3 + 270*z**2 - 216*z - 768\n#Step 7:\nCurrent expression: 12*z**6 - 198*z**4 + 360*z**3 + 270*z**2 - 216*z - 768\nNo more calculations needed.\n12*z**6 - 198*z**4 + 360*z**3 + 270*z**2 - 216*z - 768", "generated_answer": "12*z**6 - 198*z**4 + 360*z**3 + 270*z**2 - 216*z - 768", "step_length": 7} {"cot_id": "bc25e696cca7127cb577d9644d7bb467f283ba2e6f36253ff0bc65e3c60eef50", "datapoint": {"question": "Simplify this expression: (34*z**2 + 41*z)*(-44*z**3 + 47*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1496*z**5 - 206*z**4 + 1927*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1436, "polynomial_expr": "(34*z**2 + 41*z)*(-44*z**3 + 47*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (34*z**2 + 41*z)*(-44*z**3 + 47*z**2)\nExpanding the part (-44*z**3 + 47*z**2) using the distributive property, and we got: (47*z**2)*(34*z**2 + 41*z) + (-44*z**3)*(34*z**2 + 41*z)\n#Step 2:\nCurrent expression: (47*z**2)*(34*z**2 + 41*z) + (-44*z**3)*(34*z**2 + 41*z)\nSimplifying the partial expression: (-44*z**3)*(34*z**2 + 41*z)\nExpanding the part (34*z**2 + 41*z) using the distributive property, and we got: (41*z)*(-44*z**3) + (34*z**2)*(-44*z**3)\nReplacing (-44*z**3)*(34*z**2 + 41*z) with (41*z)*(-44*z**3) + (34*z**2)*(-44*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (41*z)*(-44*z**3) + (34*z**2)*(-44*z**3) + (47*z**2)*(34*z**2 + 41*z)\nSimplifying the partial expression: (47*z**2)*(34*z**2 + 41*z)\nExpanding the part (34*z**2 + 41*z) using the distributive property, and we got: (41*z)*(47*z**2) + (34*z**2)*(47*z**2)\nReplacing (47*z**2)*(34*z**2 + 41*z) with (41*z)*(47*z**2) + (34*z**2)*(47*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (41*z)*(47*z**2) + (41*z)*(-44*z**3) + (34*z**2)*(47*z**2) + (34*z**2)*(-44*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (34*z**2)*(-44*z**3) = -1496*z**5\n (34*z**2)*(47*z**2) = 1598*z**4\n (41*z)*(-44*z**3) = -1804*z**4\n (41*z)*(47*z**2) = 1927*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1496*z**5 - 1804*z**4 + 1598*z**4 + 1927*z**3\nCombining like terms, got -1496*z**5 - 206*z**4 + 1927*z**3\n#Step 6:\nCurrent expression: -1496*z**5 - 206*z**4 + 1927*z**3\nNo more calculations needed.\n-1496*z**5 - 206*z**4 + 1927*z**3", "generated_answer": "-1496*z**5 - 206*z**4 + 1927*z**3", "step_length": 6} {"cot_id": "12c0abcb655499e9d68b5fca26d20aaf770882fa9eba7c633023ca07e478e215", "datapoint": {"question": "Calculate the following: (25*x**2 - 10)*(-74*x**3 + 17*x - 12)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1850*x**5 + 1165*x**3 - 300*x**2 - 170*x + 120", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1437, "polynomial_expr": "(25*x**2 - 10)*(-74*x**3 + 17*x - 12)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (25*x**2 - 10)*(-74*x**3 + 17*x - 12)\nExpanding the part (25*x**2 - 10) using the distributive property, and we got: (25*x**2)*(-74*x**3 + 17*x - 12) - 10*(-74*x**3 + 17*x - 12)\n#Step 2:\nCurrent expression: (25*x**2)*(-74*x**3 + 17*x - 12) - 10*(-74*x**3 + 17*x - 12)\nSimplifying the partial expression: -10*(-74*x**3 + 17*x - 12)\nExpanding the part (-74*x**3 + 17*x - 12) using the distributive property, and we got: (17*x)*(-10) - 74*x**3*(-10) - 12*(-10)\nReplacing -10*(-74*x**3 + 17*x - 12) with (17*x)*(-10) - 74*x**3*(-10) - 12*(-10) in the overall expression.\n#Step 3:\nCurrent expression: (17*x)*(-10) + (25*x**2)*(-74*x**3 + 17*x - 12) - 74*x**3*(-10) + 120\nSimplifying the partial expression: (25*x**2)*(-74*x**3 + 17*x - 12)\nExpanding the part (-74*x**3 + 17*x - 12) using the distributive property, and we got: -300*x**2 + (17*x)*(25*x**2) + (25*x**2)*(-74*x**3)\nReplacing (25*x**2)*(-74*x**3 + 17*x - 12) with -300*x**2 + (17*x)*(25*x**2) + (25*x**2)*(-74*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -12*25*x**2 + (17*x)*(25*x**2) + (17*x)*(-10) + (25*x**2)*(-74*x**3) - 74*x**3*(-10) + 120\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-74*x**3)*-10 = 740*x**3\n (-74*x**3)*(25*x**2) = -1850*x**5\n (17*x)*-10 = -170*x\n (17*x)*(25*x**2) = 425*x**3\n -12*25*x**2 = -300*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1850*x**5 + 425*x**3 + 740*x**3 - 300*x**2 - 170*x + 120\nCombining like terms, got -1850*x**5 + 1165*x**3 - 300*x**2 - 170*x + 120\n#Step 6:\nCurrent expression: -1850*x**5 + 1165*x**3 - 300*x**2 - 170*x + 120\nNo more calculations needed.\n-1850*x**5 + 1165*x**3 - 300*x**2 - 170*x + 120", "generated_answer": "-1850*x**5 + 1165*x**3 - 300*x**2 - 170*x + 120", "step_length": 6} {"cot_id": "d9a189d878f952de5f00209bfc94b7d745baaa4ca8510f1a5164ecf7a2495dc2", "datapoint": {"question": "Simplify this expression: (50*z**3 - 30)*(-43*z**3 - 33*z**2 - 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2150*z**6 - 1650*z**5 + 290*z**3 + 990*z**2 + 600", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1438, "polynomial_expr": "(50*z**3 - 30)*(-43*z**3 - 33*z**2 - 20)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (50*z**3 - 30)*(-43*z**3 - 33*z**2 - 20)\nExpanding the part (50*z**3 - 30) using the distributive property, and we got: (50*z**3)*(-43*z**3 - 33*z**2 - 20) - 30*(-43*z**3 - 33*z**2 - 20)\n#Step 2:\nCurrent expression: (50*z**3)*(-43*z**3 - 33*z**2 - 20) - 30*(-43*z**3 - 33*z**2 - 20)\nSimplifying the partial expression: -30*(-43*z**3 - 33*z**2 - 20)\nExpanding the part (-43*z**3 - 33*z**2 - 20) using the distributive property, and we got: -33*z**2*(-30) - 43*z**3*(-30) - 20*(-30)\nReplacing -30*(-43*z**3 - 33*z**2 - 20) with -33*z**2*(-30) - 43*z**3*(-30) - 20*(-30) in the overall expression.\n#Step 3:\nCurrent expression: -33*z**2*(-30) - 43*z**3*(-30) + (50*z**3)*(-43*z**3 - 33*z**2 - 20) + 600\nSimplifying the partial expression: (50*z**3)*(-43*z**3 - 33*z**2 - 20)\nExpanding the part (-43*z**3 - 33*z**2 - 20) using the distributive property, and we got: -1000*z**3 + (-33*z**2)*(50*z**3) + (-43*z**3)*(50*z**3)\nReplacing (50*z**3)*(-43*z**3 - 33*z**2 - 20) with -1000*z**3 + (-33*z**2)*(50*z**3) + (-43*z**3)*(50*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -20*50*z**3 + (-33*z**2)*(50*z**3) - 33*z**2*(-30) + (-43*z**3)*(50*z**3) - 43*z**3*(-30) + 600\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-43*z**3)*-30 = 1290*z**3\n (-43*z**3)*(50*z**3) = -2150*z**6\n (-33*z**2)*-30 = 990*z**2\n (-33*z**2)*(50*z**3) = -1650*z**5\n -20*50*z**3 = -1000*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2150*z**6 - 1650*z**5 - 1000*z**3 + 1290*z**3 + 990*z**2 + 600\nCombining like terms, got -2150*z**6 - 1650*z**5 + 290*z**3 + 990*z**2 + 600\n#Step 6:\nCurrent expression: -2150*z**6 - 1650*z**5 + 290*z**3 + 990*z**2 + 600\nNo more calculations needed.\n-2150*z**6 - 1650*z**5 + 290*z**3 + 990*z**2 + 600", "generated_answer": "-2150*z**6 - 1650*z**5 + 290*z**3 + 990*z**2 + 600", "step_length": 6} {"cot_id": "3189e70a3decc98b5883280f8c9df371c04f1813eadab94314361547eb13c8bd", "datapoint": {"question": "Simplify this expression: -27*x*(-17*x**3 - 33*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "459*x**4 + 891*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1439, "polynomial_expr": "-27*x*(-17*x**3 - 33*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -27*x*(-17*x**3 - 33*x**2)\nExpanding the part (-17*x**3 - 33*x**2) using the distributive property, and we got: (-27*x)*(-33*x**2) + (-27*x)*(-17*x**3)\n#Step 2:\nCurrent expression: (-27*x)*(-33*x**2) + (-27*x)*(-17*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*x**2)*(-27*x) = 891*x**3\n (-17*x**3)*(-27*x) = 459*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 459*x**4 + 891*x**3\nNo more calculations needed.\n459*x**4 + 891*x**3", "generated_answer": "459*x**4 + 891*x**3", "step_length": 3} {"cot_id": "ac45507aeb66a964969269c1e71759e8bf93de4d8a5cd0462227e329aa472551", "datapoint": {"question": "Simplify this expression: (46*x**3 - 12)*(-5*x**3 - 14*x**2 + 22*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-230*x**6 - 644*x**5 + 1012*x**4 + 60*x**3 + 168*x**2 - 264*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1440, "polynomial_expr": "(46*x**3 - 12)*(-5*x**3 - 14*x**2 + 22*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (46*x**3 - 12)*(-5*x**3 - 14*x**2 + 22*x)\nExpanding the part (46*x**3 - 12) using the distributive property, and we got: (46*x**3)*(-5*x**3 - 14*x**2 + 22*x) - 12*(-5*x**3 - 14*x**2 + 22*x)\n#Step 2:\nCurrent expression: (46*x**3)*(-5*x**3 - 14*x**2 + 22*x) - 12*(-5*x**3 - 14*x**2 + 22*x)\nSimplifying the partial expression: -12*(-5*x**3 - 14*x**2 + 22*x)\nExpanding the part (-5*x**3 - 14*x**2 + 22*x) using the distributive property, and we got: (22*x)*(-12) - 14*x**2*(-12) - 5*x**3*(-12)\nReplacing -12*(-5*x**3 - 14*x**2 + 22*x) with (22*x)*(-12) - 14*x**2*(-12) - 5*x**3*(-12) in the overall expression.\n#Step 3:\nCurrent expression: (22*x)*(-12) - 14*x**2*(-12) - 5*x**3*(-12) + (46*x**3)*(-5*x**3 - 14*x**2 + 22*x)\nSimplifying the partial expression: (46*x**3)*(-5*x**3 - 14*x**2 + 22*x)\nExpanding the part (-5*x**3 - 14*x**2 + 22*x) using the distributive property, and we got: (22*x)*(46*x**3) + (-14*x**2)*(46*x**3) + (-5*x**3)*(46*x**3)\nReplacing (46*x**3)*(-5*x**3 - 14*x**2 + 22*x) with (22*x)*(46*x**3) + (-14*x**2)*(46*x**3) + (-5*x**3)*(46*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (22*x)*(46*x**3) + (22*x)*(-12) + (-14*x**2)*(46*x**3) - 14*x**2*(-12) + (-5*x**3)*(46*x**3) - 5*x**3*(-12)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-14*x**2)*-12 = 168*x**2\n (-14*x**2)*(46*x**3) = -644*x**5\n (-5*x**3)*-12 = 60*x**3\n (-5*x**3)*(46*x**3) = -230*x**6\n (22*x)*-12 = -264*x\n (22*x)*(46*x**3) = 1012*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -230*x**6 - 644*x**5 + 1012*x**4 + 60*x**3 + 168*x**2 - 264*x\nNo more calculations needed.\n-230*x**6 - 644*x**5 + 1012*x**4 + 60*x**3 + 168*x**2 - 264*x", "generated_answer": "-230*x**6 - 644*x**5 + 1012*x**4 + 60*x**3 + 168*x**2 - 264*x", "step_length": 5} {"cot_id": "a22401976de7b350d4bff7eb51c2b4f682b8137404afddbd66be2c26b1bdc854", "datapoint": {"question": "Calculate the following: (50*z**3 + 52*z**2 + 49)*(60*z**3 + 6*z**2 - 41*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "3000*z**6 + 3420*z**5 - 1738*z**4 + 808*z**3 + 294*z**2 - 2009*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1441, "polynomial_expr": "(50*z**3 + 52*z**2 + 49)*(60*z**3 + 6*z**2 - 41*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (50*z**3 + 52*z**2 + 49)*(60*z**3 + 6*z**2 - 41*z)\nExpanding the part (50*z**3 + 52*z**2 + 49) using the distributive property, and we got: (52*z**2)*(60*z**3 + 6*z**2 - 41*z) + (50*z**3)*(60*z**3 + 6*z**2 - 41*z) + 49*(60*z**3 + 6*z**2 - 41*z)\n#Step 2:\nCurrent expression: (52*z**2)*(60*z**3 + 6*z**2 - 41*z) + (50*z**3)*(60*z**3 + 6*z**2 - 41*z) + 49*(60*z**3 + 6*z**2 - 41*z)\nSimplifying the partial expression: 49*(60*z**3 + 6*z**2 - 41*z)\nExpanding the part (60*z**3 + 6*z**2 - 41*z) using the distributive property, and we got: -41*z*49 + (6*z**2)*49 + (60*z**3)*49\nReplacing 49*(60*z**3 + 6*z**2 - 41*z) with -41*z*49 + (6*z**2)*49 + (60*z**3)*49 in the overall expression.\n#Step 3:\nCurrent expression: -41*z*49 + (6*z**2)*49 + (52*z**2)*(60*z**3 + 6*z**2 - 41*z) + (50*z**3)*(60*z**3 + 6*z**2 - 41*z) + (60*z**3)*49\nSimplifying the partial expression: (50*z**3)*(60*z**3 + 6*z**2 - 41*z)\nExpanding the part (60*z**3 + 6*z**2 - 41*z) using the distributive property, and we got: (-41*z)*(50*z**3) + (6*z**2)*(50*z**3) + (50*z**3)*(60*z**3)\nReplacing (50*z**3)*(60*z**3 + 6*z**2 - 41*z) with (-41*z)*(50*z**3) + (6*z**2)*(50*z**3) + (50*z**3)*(60*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-41*z)*(50*z**3) - 41*z*49 + (6*z**2)*(50*z**3) + (6*z**2)*49 + (52*z**2)*(60*z**3 + 6*z**2 - 41*z) + (50*z**3)*(60*z**3) + (60*z**3)*49\nSimplifying the partial expression: (52*z**2)*(60*z**3 + 6*z**2 - 41*z)\nExpanding the part (60*z**3 + 6*z**2 - 41*z) using the distributive property, and we got: (-41*z)*(52*z**2) + (6*z**2)*(52*z**2) + (52*z**2)*(60*z**3)\nReplacing (52*z**2)*(60*z**3 + 6*z**2 - 41*z) with (-41*z)*(52*z**2) + (6*z**2)*(52*z**2) + (52*z**2)*(60*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-41*z)*(52*z**2) + (-41*z)*(50*z**3) - 41*z*49 + (6*z**2)*(52*z**2) + (6*z**2)*(50*z**3) + (6*z**2)*49 + (52*z**2)*(60*z**3) + (50*z**3)*(60*z**3) + (60*z**3)*49\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*z)*49 = -2009*z\n (-41*z)*(50*z**3) = -2050*z**4\n (-41*z)*(52*z**2) = -2132*z**3\n (6*z**2)*49 = 294*z**2\n (6*z**2)*(50*z**3) = 300*z**5\n (6*z**2)*(52*z**2) = 312*z**4\n (60*z**3)*49 = 2940*z**3\n (60*z**3)*(50*z**3) = 3000*z**6\n (60*z**3)*(52*z**2) = 3120*z**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 3000*z**6 + 300*z**5 + 3120*z**5 - 2050*z**4 + 312*z**4 - 2132*z**3 + 2940*z**3 + 294*z**2 - 2009*z\nCombining like terms, got 3000*z**6 + 3420*z**5 - 1738*z**4 + 808*z**3 + 294*z**2 - 2009*z\n#Step 7:\nCurrent expression: 3000*z**6 + 3420*z**5 - 1738*z**4 + 808*z**3 + 294*z**2 - 2009*z\nNo more calculations needed.\n3000*z**6 + 3420*z**5 - 1738*z**4 + 808*z**3 + 294*z**2 - 2009*z", "generated_answer": "3000*z**6 + 3420*z**5 - 1738*z**4 + 808*z**3 + 294*z**2 - 2009*z", "step_length": 7} {"cot_id": "145fdbb8d498ca80be63cba4e9b8031518d0c72ef955a206ea470bc4d867d2c2", "datapoint": {"question": "Calculate the following: (33 - 36*x**3)*(23*x - 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-828*x**4 + 468*x**3 + 759*x - 429", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1442, "polynomial_expr": "(33 - 36*x**3)*(23*x - 13)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (33 - 36*x**3)*(23*x - 13)\nExpanding the part (23*x - 13) using the distributive property, and we got: (23*x)*(33 - 36*x**3) - 13*(33 - 36*x**3)\n#Step 2:\nCurrent expression: (23*x)*(33 - 36*x**3) - 13*(33 - 36*x**3)\nSimplifying the partial expression: -13*(33 - 36*x**3)\nExpanding the part (33 - 36*x**3) using the distributive property, and we got: -36*x**3*(-13) + 33*(-13)\nReplacing -13*(33 - 36*x**3) with -36*x**3*(-13) + 33*(-13) in the overall expression.\n#Step 3:\nCurrent expression: (23*x)*(33 - 36*x**3) - 36*x**3*(-13) - 429\nSimplifying the partial expression: (23*x)*(33 - 36*x**3)\nExpanding the part (33 - 36*x**3) using the distributive property, and we got: 33*(23*x) + (23*x)*(-36*x**3)\nReplacing (23*x)*(33 - 36*x**3) with 33*(23*x) + (23*x)*(-36*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 33*23*x + (23*x)*(-36*x**3) - 36*x**3*(-13) - 429\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*x**3)*-13 = 468*x**3\n (-36*x**3)*(23*x) = -828*x**4\n 33*23*x = 759*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -828*x**4 + 468*x**3 + 759*x - 429\nNo more calculations needed.\n-828*x**4 + 468*x**3 + 759*x - 429", "generated_answer": "-828*x**4 + 468*x**3 + 759*x - 429", "step_length": 5} {"cot_id": "00d3724e58b32a20828a64319cd8080438b98cdf1f719aa6a76e21cd75548b68", "datapoint": {"question": "Calculate the following: -94*y*(26*y**3 + 30*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2444*y**4 - 2820*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1443, "polynomial_expr": "-94*y*(26*y**3 + 30*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -94*y*(26*y**3 + 30*y)\nExpanding the part (26*y**3 + 30*y) using the distributive property, and we got: (-94*y)*(30*y) + (-94*y)*(26*y**3)\n#Step 2:\nCurrent expression: (-94*y)*(30*y) + (-94*y)*(26*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (26*y**3)*(-94*y) = -2444*y**4\n (30*y)*(-94*y) = -2820*y**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -2444*y**4 - 2820*y**2\nNo more calculations needed.\n-2444*y**4 - 2820*y**2", "generated_answer": "-2444*y**4 - 2820*y**2", "step_length": 3} {"cot_id": "6e8567c2c8d27cc6f8184bc61db3a9a7b9a95b5877f317dc77280d99f7b016e3", "datapoint": {"question": "Calculate the following: (-48*y**3 - 40*y**2 - 21)*(23*y**3 + 43*y**2 - 12*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1104*y**6 - 2984*y**5 - 1144*y**4 - 3*y**3 - 903*y**2 + 252*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1444, "polynomial_expr": "(-48*y**3 - 40*y**2 - 21)*(23*y**3 + 43*y**2 - 12*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-48*y**3 - 40*y**2 - 21)*(23*y**3 + 43*y**2 - 12*y)\nExpanding the part (-48*y**3 - 40*y**2 - 21) using the distributive property, and we got: (-40*y**2)*(23*y**3 + 43*y**2 - 12*y) + (-48*y**3)*(23*y**3 + 43*y**2 - 12*y) - 21*(23*y**3 + 43*y**2 - 12*y)\n#Step 2:\nCurrent expression: (-40*y**2)*(23*y**3 + 43*y**2 - 12*y) + (-48*y**3)*(23*y**3 + 43*y**2 - 12*y) - 21*(23*y**3 + 43*y**2 - 12*y)\nSimplifying the partial expression: -21*(23*y**3 + 43*y**2 - 12*y)\nExpanding the part (23*y**3 + 43*y**2 - 12*y) using the distributive property, and we got: -12*y*(-21) + (43*y**2)*(-21) + (23*y**3)*(-21)\nReplacing -21*(23*y**3 + 43*y**2 - 12*y) with -12*y*(-21) + (43*y**2)*(-21) + (23*y**3)*(-21) in the overall expression.\n#Step 3:\nCurrent expression: -12*y*(-21) + (-40*y**2)*(23*y**3 + 43*y**2 - 12*y) + (43*y**2)*(-21) + (-48*y**3)*(23*y**3 + 43*y**2 - 12*y) + (23*y**3)*(-21)\nSimplifying the partial expression: (-48*y**3)*(23*y**3 + 43*y**2 - 12*y)\nExpanding the part (23*y**3 + 43*y**2 - 12*y) using the distributive property, and we got: (-12*y)*(-48*y**3) + (43*y**2)*(-48*y**3) + (-48*y**3)*(23*y**3)\nReplacing (-48*y**3)*(23*y**3 + 43*y**2 - 12*y) with (-12*y)*(-48*y**3) + (43*y**2)*(-48*y**3) + (-48*y**3)*(23*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-12*y)*(-48*y**3) - 12*y*(-21) + (-40*y**2)*(23*y**3 + 43*y**2 - 12*y) + (43*y**2)*(-48*y**3) + (43*y**2)*(-21) + (-48*y**3)*(23*y**3) + (23*y**3)*(-21)\nSimplifying the partial expression: (-40*y**2)*(23*y**3 + 43*y**2 - 12*y)\nExpanding the part (23*y**3 + 43*y**2 - 12*y) using the distributive property, and we got: (-12*y)*(-40*y**2) + (-40*y**2)*(43*y**2) + (-40*y**2)*(23*y**3)\nReplacing (-40*y**2)*(23*y**3 + 43*y**2 - 12*y) with (-12*y)*(-40*y**2) + (-40*y**2)*(43*y**2) + (-40*y**2)*(23*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-12*y)*(-40*y**2) + (-12*y)*(-48*y**3) - 12*y*(-21) + (-40*y**2)*(43*y**2) + (-40*y**2)*(23*y**3) + (43*y**2)*(-48*y**3) + (43*y**2)*(-21) + (-48*y**3)*(23*y**3) + (23*y**3)*(-21)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*y)*-21 = 252*y\n (-12*y)*(-48*y**3) = 576*y**4\n (-12*y)*(-40*y**2) = 480*y**3\n (23*y**3)*-21 = -483*y**3\n (23*y**3)*(-48*y**3) = -1104*y**6\n (23*y**3)*(-40*y**2) = -920*y**5\n (43*y**2)*-21 = -903*y**2\n (43*y**2)*(-48*y**3) = -2064*y**5\n (43*y**2)*(-40*y**2) = -1720*y**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1104*y**6 - 2064*y**5 - 920*y**5 - 1720*y**4 + 576*y**4 - 483*y**3 + 480*y**3 - 903*y**2 + 252*y\nCombining like terms, got -1104*y**6 - 2984*y**5 - 1144*y**4 - 3*y**3 - 903*y**2 + 252*y\n#Step 7:\nCurrent expression: -1104*y**6 - 2984*y**5 - 1144*y**4 - 3*y**3 - 903*y**2 + 252*y\nNo more calculations needed.\n-1104*y**6 - 2984*y**5 - 1144*y**4 - 3*y**3 - 903*y**2 + 252*y", "generated_answer": "-1104*y**6 - 2984*y**5 - 1144*y**4 - 3*y**3 - 903*y**2 + 252*y", "step_length": 7} {"cot_id": "a4dbd17e6f4e2f13568514bf1a4cfe0fbd028bbd3becf94134b91bc5b67213b4", "datapoint": {"question": "Calculate the following: (30 - 14*x)*(44*x**2 - 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-616*x**3 + 1320*x**2 + 700*x - 1500", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1445, "polynomial_expr": "(30 - 14*x)*(44*x**2 - 50)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (30 - 14*x)*(44*x**2 - 50)\nExpanding the part (44*x**2 - 50) using the distributive property, and we got: (44*x**2)*(30 - 14*x) - 50*(30 - 14*x)\n#Step 2:\nCurrent expression: (44*x**2)*(30 - 14*x) - 50*(30 - 14*x)\nSimplifying the partial expression: -50*(30 - 14*x)\nExpanding the part (30 - 14*x) using the distributive property, and we got: -14*x*(-50) + 30*(-50)\nReplacing -50*(30 - 14*x) with -14*x*(-50) + 30*(-50) in the overall expression.\n#Step 3:\nCurrent expression: -14*x*(-50) + (44*x**2)*(30 - 14*x) - 1500\nSimplifying the partial expression: (44*x**2)*(30 - 14*x)\nExpanding the part (30 - 14*x) using the distributive property, and we got: (-14*x)*(44*x**2) + 30*(44*x**2)\nReplacing (44*x**2)*(30 - 14*x) with (-14*x)*(44*x**2) + 30*(44*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-14*x)*(44*x**2) - 14*x*(-50) + 30*44*x**2 - 1500\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-14*x)*-50 = 700*x\n (-14*x)*(44*x**2) = -616*x**3\n 30*44*x**2 = 1320*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -616*x**3 + 1320*x**2 + 700*x - 1500\nNo more calculations needed.\n-616*x**3 + 1320*x**2 + 700*x - 1500", "generated_answer": "-616*x**3 + 1320*x**2 + 700*x - 1500", "step_length": 5} {"cot_id": "d35bf710d66165175ac88ebfdee837ce9a6b6f95b5a5163c7a38012e843553f4", "datapoint": {"question": "Simplify this expression: (-18*y**2 - 37*y)*(14*y**2 - 49*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-252*y**4 + 364*y**3 + 1813*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1446, "polynomial_expr": "(-18*y**2 - 37*y)*(14*y**2 - 49*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-18*y**2 - 37*y)*(14*y**2 - 49*y)\nExpanding the part (14*y**2 - 49*y) using the distributive property, and we got: (-49*y)*(-18*y**2 - 37*y) + (14*y**2)*(-18*y**2 - 37*y)\n#Step 2:\nCurrent expression: (-49*y)*(-18*y**2 - 37*y) + (14*y**2)*(-18*y**2 - 37*y)\nSimplifying the partial expression: (-49*y)*(-18*y**2 - 37*y)\nExpanding the part (-18*y**2 - 37*y) using the distributive property, and we got: (-49*y)*(-37*y) + (-49*y)*(-18*y**2)\nReplacing (-49*y)*(-18*y**2 - 37*y) with (-49*y)*(-37*y) + (-49*y)*(-18*y**2) in the overall expression.\n#Step 3:\nCurrent expression: (-49*y)*(-37*y) + (-49*y)*(-18*y**2) + (14*y**2)*(-18*y**2 - 37*y)\nSimplifying the partial expression: (14*y**2)*(-18*y**2 - 37*y)\nExpanding the part (-18*y**2 - 37*y) using the distributive property, and we got: (-37*y)*(14*y**2) + (-18*y**2)*(14*y**2)\nReplacing (14*y**2)*(-18*y**2 - 37*y) with (-37*y)*(14*y**2) + (-18*y**2)*(14*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-49*y)*(-37*y) + (-49*y)*(-18*y**2) + (-37*y)*(14*y**2) + (-18*y**2)*(14*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*y)*(-49*y) = 1813*y**2\n (-37*y)*(14*y**2) = -518*y**3\n (-18*y**2)*(-49*y) = 882*y**3\n (-18*y**2)*(14*y**2) = -252*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -252*y**4 - 518*y**3 + 882*y**3 + 1813*y**2\nCombining like terms, got -252*y**4 + 364*y**3 + 1813*y**2\n#Step 6:\nCurrent expression: -252*y**4 + 364*y**3 + 1813*y**2\nNo more calculations needed.\n-252*y**4 + 364*y**3 + 1813*y**2", "generated_answer": "-252*y**4 + 364*y**3 + 1813*y**2", "step_length": 6} {"cot_id": "c9a50255a0e5ae15e7cf300ef9ae8081d57c07ad1d5555bb36f5a7b9d1ff44a8", "datapoint": {"question": "Simplify this expression: (20 - 8*y**3)*(-22*y**3 + 8*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "176*y**6 - 64*y**4 - 440*y**3 + 160*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1447, "polynomial_expr": "(20 - 8*y**3)*(-22*y**3 + 8*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (20 - 8*y**3)*(-22*y**3 + 8*y)\nExpanding the part (20 - 8*y**3) using the distributive property, and we got: (-8*y**3)*(-22*y**3 + 8*y) + 20*(-22*y**3 + 8*y)\n#Step 2:\nCurrent expression: (-8*y**3)*(-22*y**3 + 8*y) + 20*(-22*y**3 + 8*y)\nSimplifying the partial expression: 20*(-22*y**3 + 8*y)\nExpanding the part (-22*y**3 + 8*y) using the distributive property, and we got: (8*y)*20 - 22*y**3*20\nReplacing 20*(-22*y**3 + 8*y) with (8*y)*20 - 22*y**3*20 in the overall expression.\n#Step 3:\nCurrent expression: (8*y)*20 - 22*y**3*20 + (-8*y**3)*(-22*y**3 + 8*y)\nSimplifying the partial expression: (-8*y**3)*(-22*y**3 + 8*y)\nExpanding the part (-22*y**3 + 8*y) using the distributive property, and we got: (8*y)*(-8*y**3) + (-22*y**3)*(-8*y**3)\nReplacing (-8*y**3)*(-22*y**3 + 8*y) with (8*y)*(-8*y**3) + (-22*y**3)*(-8*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (8*y)*(-8*y**3) + (8*y)*20 + (-22*y**3)*(-8*y**3) - 22*y**3*20\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*y**3)*20 = -440*y**3\n (-22*y**3)*(-8*y**3) = 176*y**6\n (8*y)*20 = 160*y\n (8*y)*(-8*y**3) = -64*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 176*y**6 - 64*y**4 - 440*y**3 + 160*y\nNo more calculations needed.\n176*y**6 - 64*y**4 - 440*y**3 + 160*y", "generated_answer": "176*y**6 - 64*y**4 - 440*y**3 + 160*y", "step_length": 5} {"cot_id": "81bb1af72dc3d28e248504e829af1c1851b3df3673deb2ae36daf8fbe7cca76d", "datapoint": {"question": "Calculate the following: 36*z**3*(-43*z**3 + 23*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1548*z**6 + 828*z**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1448, "polynomial_expr": "36*z**3*(-43*z**3 + 23*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 36*z**3*(-43*z**3 + 23*z)\nExpanding the part (-43*z**3 + 23*z) using the distributive property, and we got: (23*z)*(36*z**3) + (-43*z**3)*(36*z**3)\n#Step 2:\nCurrent expression: (23*z)*(36*z**3) + (-43*z**3)*(36*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-43*z**3)*(36*z**3) = -1548*z**6\n (23*z)*(36*z**3) = 828*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1548*z**6 + 828*z**4\nNo more calculations needed.\n-1548*z**6 + 828*z**4", "generated_answer": "-1548*z**6 + 828*z**4", "step_length": 3} {"cot_id": "c47c288e0cca8539768f962e6f0497e25bdd257c90b274d0d2b69769b55a4828", "datapoint": {"question": "Calculate the following: (-28*x**2 + 12*x)*(58*x**3 - 20*x**2 - 45*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1624*x**5 + 1256*x**4 + 1020*x**3 - 540*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1449, "polynomial_expr": "(-28*x**2 + 12*x)*(58*x**3 - 20*x**2 - 45*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-28*x**2 + 12*x)*(58*x**3 - 20*x**2 - 45*x)\nExpanding the part (-28*x**2 + 12*x) using the distributive property, and we got: (12*x)*(58*x**3 - 20*x**2 - 45*x) + (-28*x**2)*(58*x**3 - 20*x**2 - 45*x)\n#Step 2:\nCurrent expression: (12*x)*(58*x**3 - 20*x**2 - 45*x) + (-28*x**2)*(58*x**3 - 20*x**2 - 45*x)\nSimplifying the partial expression: (-28*x**2)*(58*x**3 - 20*x**2 - 45*x)\nExpanding the part (58*x**3 - 20*x**2 - 45*x) using the distributive property, and we got: (-45*x)*(-28*x**2) + (-28*x**2)*(-20*x**2) + (-28*x**2)*(58*x**3)\nReplacing (-28*x**2)*(58*x**3 - 20*x**2 - 45*x) with (-45*x)*(-28*x**2) + (-28*x**2)*(-20*x**2) + (-28*x**2)*(58*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-45*x)*(-28*x**2) + (12*x)*(58*x**3 - 20*x**2 - 45*x) + (-28*x**2)*(-20*x**2) + (-28*x**2)*(58*x**3)\nSimplifying the partial expression: (12*x)*(58*x**3 - 20*x**2 - 45*x)\nExpanding the part (58*x**3 - 20*x**2 - 45*x) using the distributive property, and we got: (-45*x)*(12*x) + (12*x)*(-20*x**2) + (12*x)*(58*x**3)\nReplacing (12*x)*(58*x**3 - 20*x**2 - 45*x) with (-45*x)*(12*x) + (12*x)*(-20*x**2) + (12*x)*(58*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-45*x)*(12*x) + (-45*x)*(-28*x**2) + (12*x)*(-20*x**2) + (12*x)*(58*x**3) + (-28*x**2)*(-20*x**2) + (-28*x**2)*(58*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*x)*(-28*x**2) = 1260*x**3\n (-45*x)*(12*x) = -540*x**2\n (-20*x**2)*(-28*x**2) = 560*x**4\n (-20*x**2)*(12*x) = -240*x**3\n (58*x**3)*(-28*x**2) = -1624*x**5\n (58*x**3)*(12*x) = 696*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1624*x**5 + 560*x**4 + 696*x**4 - 240*x**3 + 1260*x**3 - 540*x**2\nCombining like terms, got -1624*x**5 + 1256*x**4 + 1020*x**3 - 540*x**2\n#Step 6:\nCurrent expression: -1624*x**5 + 1256*x**4 + 1020*x**3 - 540*x**2\nNo more calculations needed.\n-1624*x**5 + 1256*x**4 + 1020*x**3 - 540*x**2", "generated_answer": "-1624*x**5 + 1256*x**4 + 1020*x**3 - 540*x**2", "step_length": 6} {"cot_id": "b6691bd91f37425b2d095d06a9321d2e95e87034ce1ea0752c2d0d600d29c03b", "datapoint": {"question": "Calculate the following: (16*z + 58)*(14*z**2 + 36*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "224*z**3 + 1388*z**2 + 2088*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1450, "polynomial_expr": "(16*z + 58)*(14*z**2 + 36*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (16*z + 58)*(14*z**2 + 36*z)\nExpanding the part (16*z + 58) using the distributive property, and we got: (16*z)*(14*z**2 + 36*z) + 58*(14*z**2 + 36*z)\n#Step 2:\nCurrent expression: (16*z)*(14*z**2 + 36*z) + 58*(14*z**2 + 36*z)\nSimplifying the partial expression: 58*(14*z**2 + 36*z)\nExpanding the part (14*z**2 + 36*z) using the distributive property, and we got: (36*z)*58 + (14*z**2)*58\nReplacing 58*(14*z**2 + 36*z) with (36*z)*58 + (14*z**2)*58 in the overall expression.\n#Step 3:\nCurrent expression: (16*z)*(14*z**2 + 36*z) + (36*z)*58 + (14*z**2)*58\nSimplifying the partial expression: (16*z)*(14*z**2 + 36*z)\nExpanding the part (14*z**2 + 36*z) using the distributive property, and we got: (16*z)*(36*z) + (16*z)*(14*z**2)\nReplacing (16*z)*(14*z**2 + 36*z) with (16*z)*(36*z) + (16*z)*(14*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (16*z)*(36*z) + (16*z)*(14*z**2) + (36*z)*58 + (14*z**2)*58\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (14*z**2)*58 = 812*z**2\n (14*z**2)*(16*z) = 224*z**3\n (36*z)*58 = 2088*z\n (36*z)*(16*z) = 576*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 224*z**3 + 576*z**2 + 812*z**2 + 2088*z\nCombining like terms, got 224*z**3 + 1388*z**2 + 2088*z\n#Step 6:\nCurrent expression: 224*z**3 + 1388*z**2 + 2088*z\nNo more calculations needed.\n224*z**3 + 1388*z**2 + 2088*z", "generated_answer": "224*z**3 + 1388*z**2 + 2088*z", "step_length": 6} {"cot_id": "3ff05ff3203492afad7baaac929fe1b954d476f8f6ede8d02c4e3c7a223c4a61", "datapoint": {"question": "Calculate the following: (x**3 - 4*x**2 - 45)*(32*x**3 - 12*x - 26)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "32*x**6 - 128*x**5 - 12*x**4 - 1418*x**3 + 104*x**2 + 540*x + 1170", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1451, "polynomial_expr": "(x**3 - 4*x**2 - 45)*(32*x**3 - 12*x - 26)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (x**3 - 4*x**2 - 45)*(32*x**3 - 12*x - 26)\nExpanding the part (x**3 - 4*x**2 - 45) using the distributive property, and we got: x**3*(32*x**3 - 12*x - 26) + (-4*x**2)*(32*x**3 - 12*x - 26) - 45*(32*x**3 - 12*x - 26)\n#Step 2:\nCurrent expression: x**3*(32*x**3 - 12*x - 26) + (-4*x**2)*(32*x**3 - 12*x - 26) - 45*(32*x**3 - 12*x - 26)\nSimplifying the partial expression: -45*(32*x**3 - 12*x - 26)\nExpanding the part (32*x**3 - 12*x - 26) using the distributive property, and we got: -12*x*(-45) + (32*x**3)*(-45) - 26*(-45)\nReplacing -45*(32*x**3 - 12*x - 26) with -12*x*(-45) + (32*x**3)*(-45) - 26*(-45) in the overall expression.\n#Step 3:\nCurrent expression: -12*x*(-45) + x**3*(32*x**3 - 12*x - 26) + (-4*x**2)*(32*x**3 - 12*x - 26) + (32*x**3)*(-45) + 1170\nSimplifying the partial expression: x**3*(32*x**3 - 12*x - 26)\nExpanding the part (32*x**3 - 12*x - 26) using the distributive property, and we got: (-12*x)*x**3 + x**3*(32*x**3) - 26*x**3\nReplacing x**3*(32*x**3 - 12*x - 26) with (-12*x)*x**3 + x**3*(32*x**3) - 26*x**3 in the overall expression.\n#Step 4:\nCurrent expression: (-12*x)*x**3 - 12*x*(-45) + x**3*(32*x**3) - 26*x**3 + (-4*x**2)*(32*x**3 - 12*x - 26) + (32*x**3)*(-45) + 1170\nSimplifying the partial expression: (-4*x**2)*(32*x**3 - 12*x - 26)\nExpanding the part (32*x**3 - 12*x - 26) using the distributive property, and we got: (-12*x)*(-4*x**2) - (-1)*104*x**2 + (-4*x**2)*(32*x**3)\nReplacing (-4*x**2)*(32*x**3 - 12*x - 26) with (-12*x)*(-4*x**2) - (-1)*104*x**2 + (-4*x**2)*(32*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-12*x)*x**3 + (-12*x)*(-4*x**2) - 12*x*(-45) + x**3*(32*x**3) - 26*x**3 - 26*(-4)*x**2 + (-4*x**2)*(32*x**3) + (32*x**3)*(-45) + 1170\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*x)*-45 = 540*x\n (-12*x)*x**3 = -12*x**4\n (-12*x)*(-4*x**2) = 48*x**3\n (32*x**3)*-45 = -1440*x**3\n (32*x**3)*x**3 = 32*x**6\n (32*x**3)*(-4*x**2) = -128*x**5\n -26*-4*x**2 = 104*x**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 32*x**6 - 128*x**5 - 12*x**4 - 1440*x**3 - 26*x**3 + 48*x**3 + 104*x**2 + 540*x + 1170\nCombining like terms, got 32*x**6 - 128*x**5 - 12*x**4 - 1418*x**3 + 104*x**2 + 540*x + 1170\n#Step 7:\nCurrent expression: 32*x**6 - 128*x**5 - 12*x**4 - 1418*x**3 + 104*x**2 + 540*x + 1170\nNo more calculations needed.\n32*x**6 - 128*x**5 - 12*x**4 - 1418*x**3 + 104*x**2 + 540*x + 1170", "generated_answer": "32*x**6 - 128*x**5 - 12*x**4 - 1418*x**3 + 104*x**2 + 540*x + 1170", "step_length": 7} {"cot_id": "745def06cb53f4c17d6e38d62816379ba0adaf8425c7df46f214c61d40e4c6df", "datapoint": {"question": "Calculate the following: (44*x**2 + 52*x + 38)*(22*x**3 - 3*x**2 + 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "968*x**5 + 1012*x**4 + 680*x**3 + 458*x**2 + 676*x + 494", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1452, "polynomial_expr": "(44*x**2 + 52*x + 38)*(22*x**3 - 3*x**2 + 13)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (44*x**2 + 52*x + 38)*(22*x**3 - 3*x**2 + 13)\nExpanding the part (22*x**3 - 3*x**2 + 13) using the distributive property, and we got: (-3*x**2)*(44*x**2 + 52*x + 38) + (22*x**3)*(44*x**2 + 52*x + 38) + 13*(44*x**2 + 52*x + 38)\n#Step 2:\nCurrent expression: (-3*x**2)*(44*x**2 + 52*x + 38) + (22*x**3)*(44*x**2 + 52*x + 38) + 13*(44*x**2 + 52*x + 38)\nSimplifying the partial expression: 13*(44*x**2 + 52*x + 38)\nExpanding the part (44*x**2 + 52*x + 38) using the distributive property, and we got: (52*x)*13 + (44*x**2)*13 + 38*13\nReplacing 13*(44*x**2 + 52*x + 38) with (52*x)*13 + (44*x**2)*13 + 38*13 in the overall expression.\n#Step 3:\nCurrent expression: (52*x)*13 + (-3*x**2)*(44*x**2 + 52*x + 38) + (44*x**2)*13 + (22*x**3)*(44*x**2 + 52*x + 38) + 494\nSimplifying the partial expression: (-3*x**2)*(44*x**2 + 52*x + 38)\nExpanding the part (44*x**2 + 52*x + 38) using the distributive property, and we got: 38*(-3*x**2) + (52*x)*(-3*x**2) + (-3*x**2)*(44*x**2)\nReplacing (-3*x**2)*(44*x**2 + 52*x + 38) with 38*(-3*x**2) + (52*x)*(-3*x**2) + (-3*x**2)*(44*x**2) in the overall expression.\n#Step 4:\nCurrent expression: 38*(-3)*x**2 + (52*x)*(-3*x**2) + (52*x)*13 + (-3*x**2)*(44*x**2) + (44*x**2)*13 + (22*x**3)*(44*x**2 + 52*x + 38) + 494\nSimplifying the partial expression: (22*x**3)*(44*x**2 + 52*x + 38)\nExpanding the part (44*x**2 + 52*x + 38) using the distributive property, and we got: 38*(22*x**3) + (52*x)*(22*x**3) + (44*x**2)*(22*x**3)\nReplacing (22*x**3)*(44*x**2 + 52*x + 38) with 38*(22*x**3) + (52*x)*(22*x**3) + (44*x**2)*(22*x**3) in the overall expression.\n#Step 5:\nCurrent expression: 38*22*x**3 + 38*(-3)*x**2 + (52*x)*(-3*x**2) + (52*x)*(22*x**3) + (52*x)*13 + (-3*x**2)*(44*x**2) + (44*x**2)*(22*x**3) + (44*x**2)*13 + 494\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (44*x**2)*13 = 572*x**2\n (44*x**2)*(-3*x**2) = -132*x**4\n (44*x**2)*(22*x**3) = 968*x**5\n (52*x)*13 = 676*x\n (52*x)*(-3*x**2) = -156*x**3\n (52*x)*(22*x**3) = 1144*x**4\n 38*-3*x**2 = -114*x**2\n 38*22*x**3 = 836*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 968*x**5 - 132*x**4 + 1144*x**4 - 156*x**3 + 836*x**3 - 114*x**2 + 572*x**2 + 676*x + 494\nCombining like terms, got 968*x**5 + 1012*x**4 + 680*x**3 + 458*x**2 + 676*x + 494\n#Step 7:\nCurrent expression: 968*x**5 + 1012*x**4 + 680*x**3 + 458*x**2 + 676*x + 494\nNo more calculations needed.\n968*x**5 + 1012*x**4 + 680*x**3 + 458*x**2 + 676*x + 494", "generated_answer": "968*x**5 + 1012*x**4 + 680*x**3 + 458*x**2 + 676*x + 494", "step_length": 7} {"cot_id": "610cba6cb3c034b75b3bcc7564727b3f21618dc05dc5ffb817cb5631fb120a68", "datapoint": {"question": "Calculate the following: (-32*y**2 - 4)*(-40*y**3 + 19*y**2 - 3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1280*y**5 - 608*y**4 + 160*y**3 + 20*y**2 + 12", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1453, "polynomial_expr": "(-32*y**2 - 4)*(-40*y**3 + 19*y**2 - 3)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-32*y**2 - 4)*(-40*y**3 + 19*y**2 - 3)\nExpanding the part (-32*y**2 - 4) using the distributive property, and we got: (-32*y**2)*(-40*y**3 + 19*y**2 - 3) - 4*(-40*y**3 + 19*y**2 - 3)\n#Step 2:\nCurrent expression: (-32*y**2)*(-40*y**3 + 19*y**2 - 3) - 4*(-40*y**3 + 19*y**2 - 3)\nSimplifying the partial expression: -4*(-40*y**3 + 19*y**2 - 3)\nExpanding the part (-40*y**3 + 19*y**2 - 3) using the distributive property, and we got: (19*y**2)*(-4) - 40*y**3*(-4) - 3*(-4)\nReplacing -4*(-40*y**3 + 19*y**2 - 3) with (19*y**2)*(-4) - 40*y**3*(-4) - 3*(-4) in the overall expression.\n#Step 3:\nCurrent expression: (-32*y**2)*(-40*y**3 + 19*y**2 - 3) + (19*y**2)*(-4) - 40*y**3*(-4) + 12\nSimplifying the partial expression: (-32*y**2)*(-40*y**3 + 19*y**2 - 3)\nExpanding the part (-40*y**3 + 19*y**2 - 3) using the distributive property, and we got: -(-1)*96*y**2 + (-32*y**2)*(19*y**2) + (-32*y**2)*(-40*y**3)\nReplacing (-32*y**2)*(-40*y**3 + 19*y**2 - 3) with -(-1)*96*y**2 + (-32*y**2)*(19*y**2) + (-32*y**2)*(-40*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -3*(-32)*y**2 + (-32*y**2)*(19*y**2) + (-32*y**2)*(-40*y**3) + (19*y**2)*(-4) - 40*y**3*(-4) + 12\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*y**3)*-4 = 160*y**3\n (-40*y**3)*(-32*y**2) = 1280*y**5\n (19*y**2)*-4 = -76*y**2\n (19*y**2)*(-32*y**2) = -608*y**4\n -3*-32*y**2 = 96*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1280*y**5 - 608*y**4 + 160*y**3 - 76*y**2 + 96*y**2 + 12\nCombining like terms, got 1280*y**5 - 608*y**4 + 160*y**3 + 20*y**2 + 12\n#Step 6:\nCurrent expression: 1280*y**5 - 608*y**4 + 160*y**3 + 20*y**2 + 12\nNo more calculations needed.\n1280*y**5 - 608*y**4 + 160*y**3 + 20*y**2 + 12", "generated_answer": "1280*y**5 - 608*y**4 + 160*y**3 + 20*y**2 + 12", "step_length": 6} {"cot_id": "0408e035882dffc73d1c47a6da6869ea7b40e9e72f2c429d809223d4c69cab42", "datapoint": {"question": "Calculate the following: (7 - 12*x**2)*(-12*x**2 - 33*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "144*x**4 + 396*x**3 - 84*x**2 - 231*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1454, "polynomial_expr": "(7 - 12*x**2)*(-12*x**2 - 33*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7 - 12*x**2)*(-12*x**2 - 33*x)\nExpanding the part (7 - 12*x**2) using the distributive property, and we got: (-12*x**2)*(-12*x**2 - 33*x) + 7*(-12*x**2 - 33*x)\n#Step 2:\nCurrent expression: (-12*x**2)*(-12*x**2 - 33*x) + 7*(-12*x**2 - 33*x)\nSimplifying the partial expression: 7*(-12*x**2 - 33*x)\nExpanding the part (-12*x**2 - 33*x) using the distributive property, and we got: -33*x*7 - 12*x**2*7\nReplacing 7*(-12*x**2 - 33*x) with -33*x*7 - 12*x**2*7 in the overall expression.\n#Step 3:\nCurrent expression: -33*x*7 + (-12*x**2)*(-12*x**2 - 33*x) - 12*x**2*7\nSimplifying the partial expression: (-12*x**2)*(-12*x**2 - 33*x)\nExpanding the part (-12*x**2 - 33*x) using the distributive property, and we got: (-33*x)*(-12*x**2) + (-12*x**2)*(-12*x**2)\nReplacing (-12*x**2)*(-12*x**2 - 33*x) with (-33*x)*(-12*x**2) + (-12*x**2)*(-12*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-33*x)*(-12*x**2) - 33*x*7 + (-12*x**2)*(-12*x**2) - 12*x**2*7\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*x)*7 = -231*x\n (-33*x)*(-12*x**2) = 396*x**3\n (-12*x**2)*7 = -84*x**2\n (-12*x**2)*(-12*x**2) = 144*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 144*x**4 + 396*x**3 - 84*x**2 - 231*x\nNo more calculations needed.\n144*x**4 + 396*x**3 - 84*x**2 - 231*x", "generated_answer": "144*x**4 + 396*x**3 - 84*x**2 - 231*x", "step_length": 5} {"cot_id": "4013205efff37401ebd24e437f23f2335508a0b275e11317bd2f54537c10dfac", "datapoint": {"question": "Calculate the following: (33*x**3 - 38*x**2 - 9)*(41*x**3 + 79*x**2 - 23)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1353*x**6 + 1049*x**5 - 3002*x**4 - 1128*x**3 + 163*x**2 + 207", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1455, "polynomial_expr": "(33*x**3 - 38*x**2 - 9)*(41*x**3 + 79*x**2 - 23)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (33*x**3 - 38*x**2 - 9)*(41*x**3 + 79*x**2 - 23)\nExpanding the part (41*x**3 + 79*x**2 - 23) using the distributive property, and we got: (79*x**2)*(33*x**3 - 38*x**2 - 9) + (41*x**3)*(33*x**3 - 38*x**2 - 9) - 23*(33*x**3 - 38*x**2 - 9)\n#Step 2:\nCurrent expression: (79*x**2)*(33*x**3 - 38*x**2 - 9) + (41*x**3)*(33*x**3 - 38*x**2 - 9) - 23*(33*x**3 - 38*x**2 - 9)\nSimplifying the partial expression: -23*(33*x**3 - 38*x**2 - 9)\nExpanding the part (33*x**3 - 38*x**2 - 9) using the distributive property, and we got: -38*x**2*(-23) + (33*x**3)*(-23) - 9*(-23)\nReplacing -23*(33*x**3 - 38*x**2 - 9) with -38*x**2*(-23) + (33*x**3)*(-23) - 9*(-23) in the overall expression.\n#Step 3:\nCurrent expression: -38*x**2*(-23) + (79*x**2)*(33*x**3 - 38*x**2 - 9) + (33*x**3)*(-23) + (41*x**3)*(33*x**3 - 38*x**2 - 9) + 207\nSimplifying the partial expression: (41*x**3)*(33*x**3 - 38*x**2 - 9)\nExpanding the part (33*x**3 - 38*x**2 - 9) using the distributive property, and we got: -369*x**3 + (-38*x**2)*(41*x**3) + (33*x**3)*(41*x**3)\nReplacing (41*x**3)*(33*x**3 - 38*x**2 - 9) with -369*x**3 + (-38*x**2)*(41*x**3) + (33*x**3)*(41*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -9*41*x**3 + (-38*x**2)*(41*x**3) - 38*x**2*(-23) + (79*x**2)*(33*x**3 - 38*x**2 - 9) + (33*x**3)*(41*x**3) + (33*x**3)*(-23) + 207\nSimplifying the partial expression: (79*x**2)*(33*x**3 - 38*x**2 - 9)\nExpanding the part (33*x**3 - 38*x**2 - 9) using the distributive property, and we got: -711*x**2 + (-38*x**2)*(79*x**2) + (79*x**2)*(33*x**3)\nReplacing (79*x**2)*(33*x**3 - 38*x**2 - 9) with -711*x**2 + (-38*x**2)*(79*x**2) + (79*x**2)*(33*x**3) in the overall expression.\n#Step 5:\nCurrent expression: -9*41*x**3 - 9*79*x**2 + (-38*x**2)*(79*x**2) + (-38*x**2)*(41*x**3) - 38*x**2*(-23) + (79*x**2)*(33*x**3) + (33*x**3)*(41*x**3) + (33*x**3)*(-23) + 207\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*x**2)*-23 = 874*x**2\n (-38*x**2)*(41*x**3) = -1558*x**5\n (-38*x**2)*(79*x**2) = -3002*x**4\n (33*x**3)*-23 = -759*x**3\n (33*x**3)*(41*x**3) = 1353*x**6\n (33*x**3)*(79*x**2) = 2607*x**5\n -9*41*x**3 = -369*x**3\n -9*79*x**2 = -711*x**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1353*x**6 - 1558*x**5 + 2607*x**5 - 3002*x**4 - 759*x**3 - 369*x**3 - 711*x**2 + 874*x**2 + 207\nCombining like terms, got 1353*x**6 + 1049*x**5 - 3002*x**4 - 1128*x**3 + 163*x**2 + 207\n#Step 7:\nCurrent expression: 1353*x**6 + 1049*x**5 - 3002*x**4 - 1128*x**3 + 163*x**2 + 207\nNo more calculations needed.\n1353*x**6 + 1049*x**5 - 3002*x**4 - 1128*x**3 + 163*x**2 + 207", "generated_answer": "1353*x**6 + 1049*x**5 - 3002*x**4 - 1128*x**3 + 163*x**2 + 207", "step_length": 7} {"cot_id": "99800b4f688e578096917adb3ee3f8102f47b46f31ba47e5a8b939cfb5442a0e", "datapoint": {"question": "Simplify this expression: (29*x**3 - 43*x**2)*(-47*x**3 + 23*x**2 + 10*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1363*x**6 + 2688*x**5 - 699*x**4 - 430*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1456, "polynomial_expr": "(29*x**3 - 43*x**2)*(-47*x**3 + 23*x**2 + 10*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29*x**3 - 43*x**2)*(-47*x**3 + 23*x**2 + 10*x)\nExpanding the part (29*x**3 - 43*x**2) using the distributive property, and we got: (-43*x**2)*(-47*x**3 + 23*x**2 + 10*x) + (29*x**3)*(-47*x**3 + 23*x**2 + 10*x)\n#Step 2:\nCurrent expression: (-43*x**2)*(-47*x**3 + 23*x**2 + 10*x) + (29*x**3)*(-47*x**3 + 23*x**2 + 10*x)\nSimplifying the partial expression: (-43*x**2)*(-47*x**3 + 23*x**2 + 10*x)\nExpanding the part (-47*x**3 + 23*x**2 + 10*x) using the distributive property, and we got: (10*x)*(-43*x**2) + (-43*x**2)*(23*x**2) + (-43*x**2)*(-47*x**3)\nReplacing (-43*x**2)*(-47*x**3 + 23*x**2 + 10*x) with (10*x)*(-43*x**2) + (-43*x**2)*(23*x**2) + (-43*x**2)*(-47*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (10*x)*(-43*x**2) + (-43*x**2)*(23*x**2) + (-43*x**2)*(-47*x**3) + (29*x**3)*(-47*x**3 + 23*x**2 + 10*x)\nSimplifying the partial expression: (29*x**3)*(-47*x**3 + 23*x**2 + 10*x)\nExpanding the part (-47*x**3 + 23*x**2 + 10*x) using the distributive property, and we got: (10*x)*(29*x**3) + (23*x**2)*(29*x**3) + (-47*x**3)*(29*x**3)\nReplacing (29*x**3)*(-47*x**3 + 23*x**2 + 10*x) with (10*x)*(29*x**3) + (23*x**2)*(29*x**3) + (-47*x**3)*(29*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (10*x)*(-43*x**2) + (10*x)*(29*x**3) + (-43*x**2)*(23*x**2) + (-43*x**2)*(-47*x**3) + (23*x**2)*(29*x**3) + (-47*x**3)*(29*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*x**3)*(-43*x**2) = 2021*x**5\n (-47*x**3)*(29*x**3) = -1363*x**6\n (10*x)*(-43*x**2) = -430*x**3\n (10*x)*(29*x**3) = 290*x**4\n (23*x**2)*(-43*x**2) = -989*x**4\n (23*x**2)*(29*x**3) = 667*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1363*x**6 + 667*x**5 + 2021*x**5 - 989*x**4 + 290*x**4 - 430*x**3\nCombining like terms, got -1363*x**6 + 2688*x**5 - 699*x**4 - 430*x**3\n#Step 6:\nCurrent expression: -1363*x**6 + 2688*x**5 - 699*x**4 - 430*x**3\nNo more calculations needed.\n-1363*x**6 + 2688*x**5 - 699*x**4 - 430*x**3", "generated_answer": "-1363*x**6 + 2688*x**5 - 699*x**4 - 430*x**3", "step_length": 6} {"cot_id": "904cb19772b1d2e7c758f0e295daa76aa91dbe7ad5178e1109e6a5188e8d17ec", "datapoint": {"question": "Simplify this expression: (45*y**3 + 24*y)*(46*y**3 - 66*y**2 + 38*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2070*y**6 - 2970*y**5 + 2814*y**4 - 1584*y**3 + 912*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1457, "polynomial_expr": "(45*y**3 + 24*y)*(46*y**3 - 66*y**2 + 38*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (45*y**3 + 24*y)*(46*y**3 - 66*y**2 + 38*y)\nExpanding the part (45*y**3 + 24*y) using the distributive property, and we got: (24*y)*(46*y**3 - 66*y**2 + 38*y) + (45*y**3)*(46*y**3 - 66*y**2 + 38*y)\n#Step 2:\nCurrent expression: (24*y)*(46*y**3 - 66*y**2 + 38*y) + (45*y**3)*(46*y**3 - 66*y**2 + 38*y)\nSimplifying the partial expression: (24*y)*(46*y**3 - 66*y**2 + 38*y)\nExpanding the part (46*y**3 - 66*y**2 + 38*y) using the distributive property, and we got: (24*y)*(38*y) + (24*y)*(-66*y**2) + (24*y)*(46*y**3)\nReplacing (24*y)*(46*y**3 - 66*y**2 + 38*y) with (24*y)*(38*y) + (24*y)*(-66*y**2) + (24*y)*(46*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (24*y)*(38*y) + (24*y)*(-66*y**2) + (24*y)*(46*y**3) + (45*y**3)*(46*y**3 - 66*y**2 + 38*y)\nSimplifying the partial expression: (45*y**3)*(46*y**3 - 66*y**2 + 38*y)\nExpanding the part (46*y**3 - 66*y**2 + 38*y) using the distributive property, and we got: (38*y)*(45*y**3) + (-66*y**2)*(45*y**3) + (45*y**3)*(46*y**3)\nReplacing (45*y**3)*(46*y**3 - 66*y**2 + 38*y) with (38*y)*(45*y**3) + (-66*y**2)*(45*y**3) + (45*y**3)*(46*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (24*y)*(38*y) + (24*y)*(-66*y**2) + (24*y)*(46*y**3) + (38*y)*(45*y**3) + (-66*y**2)*(45*y**3) + (45*y**3)*(46*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-66*y**2)*(24*y) = -1584*y**3\n (-66*y**2)*(45*y**3) = -2970*y**5\n (38*y)*(24*y) = 912*y**2\n (38*y)*(45*y**3) = 1710*y**4\n (46*y**3)*(24*y) = 1104*y**4\n (46*y**3)*(45*y**3) = 2070*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2070*y**6 - 2970*y**5 + 1104*y**4 + 1710*y**4 - 1584*y**3 + 912*y**2\nCombining like terms, got 2070*y**6 - 2970*y**5 + 2814*y**4 - 1584*y**3 + 912*y**2\n#Step 6:\nCurrent expression: 2070*y**6 - 2970*y**5 + 2814*y**4 - 1584*y**3 + 912*y**2\nNo more calculations needed.\n2070*y**6 - 2970*y**5 + 2814*y**4 - 1584*y**3 + 912*y**2", "generated_answer": "2070*y**6 - 2970*y**5 + 2814*y**4 - 1584*y**3 + 912*y**2", "step_length": 6} {"cot_id": "f0893d9fe38f77ba3864a0715d8c628787272163ba877560797ab1ebf3a01099", "datapoint": {"question": "Calculate the following: (2*y**3 - 24)*(-22*y**3 + 50*y + 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-44*y**6 + 100*y**4 + 616*y**3 - 1200*y - 1056", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1458, "polynomial_expr": "(2*y**3 - 24)*(-22*y**3 + 50*y + 44)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2*y**3 - 24)*(-22*y**3 + 50*y + 44)\nExpanding the part (2*y**3 - 24) using the distributive property, and we got: (2*y**3)*(-22*y**3 + 50*y + 44) - 24*(-22*y**3 + 50*y + 44)\n#Step 2:\nCurrent expression: (2*y**3)*(-22*y**3 + 50*y + 44) - 24*(-22*y**3 + 50*y + 44)\nSimplifying the partial expression: -24*(-22*y**3 + 50*y + 44)\nExpanding the part (-22*y**3 + 50*y + 44) using the distributive property, and we got: (50*y)*(-24) - 22*y**3*(-24) + 44*(-24)\nReplacing -24*(-22*y**3 + 50*y + 44) with (50*y)*(-24) - 22*y**3*(-24) + 44*(-24) in the overall expression.\n#Step 3:\nCurrent expression: (50*y)*(-24) - 22*y**3*(-24) + (2*y**3)*(-22*y**3 + 50*y + 44) - 1056\nSimplifying the partial expression: (2*y**3)*(-22*y**3 + 50*y + 44)\nExpanding the part (-22*y**3 + 50*y + 44) using the distributive property, and we got: 44*(2*y**3) + (50*y)*(2*y**3) + (-22*y**3)*(2*y**3)\nReplacing (2*y**3)*(-22*y**3 + 50*y + 44) with 44*(2*y**3) + (50*y)*(2*y**3) + (-22*y**3)*(2*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 44*2*y**3 + (50*y)*(2*y**3) + (50*y)*(-24) + (-22*y**3)*(2*y**3) - 22*y**3*(-24) - 1056\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*y**3)*-24 = 528*y**3\n (-22*y**3)*(2*y**3) = -44*y**6\n (50*y)*-24 = -1200*y\n (50*y)*(2*y**3) = 100*y**4\n 44*2*y**3 = 88*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -44*y**6 + 100*y**4 + 88*y**3 + 528*y**3 - 1200*y - 1056\nCombining like terms, got -44*y**6 + 100*y**4 + 616*y**3 - 1200*y - 1056\n#Step 6:\nCurrent expression: -44*y**6 + 100*y**4 + 616*y**3 - 1200*y - 1056\nNo more calculations needed.\n-44*y**6 + 100*y**4 + 616*y**3 - 1200*y - 1056", "generated_answer": "-44*y**6 + 100*y**4 + 616*y**3 - 1200*y - 1056", "step_length": 6} {"cot_id": "8b91ba73b5fd3ddfb7e58bf6303fb9e19a5e537afaf88f97dda390f7d27d3be2", "datapoint": {"question": "Calculate the following: (-24*z - 18)*(11*z**3 + 69*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-264*z**4 - 198*z**3 - 1656*z**2 - 1242*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1459, "polynomial_expr": "(-24*z - 18)*(11*z**3 + 69*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-24*z - 18)*(11*z**3 + 69*z)\nExpanding the part (-24*z - 18) using the distributive property, and we got: (-24*z)*(11*z**3 + 69*z) - 18*(11*z**3 + 69*z)\n#Step 2:\nCurrent expression: (-24*z)*(11*z**3 + 69*z) - 18*(11*z**3 + 69*z)\nSimplifying the partial expression: -18*(11*z**3 + 69*z)\nExpanding the part (11*z**3 + 69*z) using the distributive property, and we got: (69*z)*(-18) + (11*z**3)*(-18)\nReplacing -18*(11*z**3 + 69*z) with (69*z)*(-18) + (11*z**3)*(-18) in the overall expression.\n#Step 3:\nCurrent expression: (-24*z)*(11*z**3 + 69*z) + (69*z)*(-18) + (11*z**3)*(-18)\nSimplifying the partial expression: (-24*z)*(11*z**3 + 69*z)\nExpanding the part (11*z**3 + 69*z) using the distributive property, and we got: (-24*z)*(69*z) + (-24*z)*(11*z**3)\nReplacing (-24*z)*(11*z**3 + 69*z) with (-24*z)*(69*z) + (-24*z)*(11*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-24*z)*(69*z) + (-24*z)*(11*z**3) + (69*z)*(-18) + (11*z**3)*(-18)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (11*z**3)*-18 = -198*z**3\n (11*z**3)*(-24*z) = -264*z**4\n (69*z)*-18 = -1242*z\n (69*z)*(-24*z) = -1656*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -264*z**4 - 198*z**3 - 1656*z**2 - 1242*z\nNo more calculations needed.\n-264*z**4 - 198*z**3 - 1656*z**2 - 1242*z", "generated_answer": "-264*z**4 - 198*z**3 - 1656*z**2 - 1242*z", "step_length": 5} {"cot_id": "abc653698c3ae2c4bc5a3db5cf382724e48cdd0e5df997ab5baa0d444d425d6c", "datapoint": {"question": "Calculate the following: (-83*x**3 + 28*x**2)*(26*x**3 - 28*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2158*x**6 + 3052*x**5 - 784*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1460, "polynomial_expr": "(-83*x**3 + 28*x**2)*(26*x**3 - 28*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-83*x**3 + 28*x**2)*(26*x**3 - 28*x**2)\nExpanding the part (-83*x**3 + 28*x**2) using the distributive property, and we got: (28*x**2)*(26*x**3 - 28*x**2) + (-83*x**3)*(26*x**3 - 28*x**2)\n#Step 2:\nCurrent expression: (28*x**2)*(26*x**3 - 28*x**2) + (-83*x**3)*(26*x**3 - 28*x**2)\nSimplifying the partial expression: (-83*x**3)*(26*x**3 - 28*x**2)\nExpanding the part (26*x**3 - 28*x**2) using the distributive property, and we got: (-28*x**2)*(-83*x**3) + (-83*x**3)*(26*x**3)\nReplacing (-83*x**3)*(26*x**3 - 28*x**2) with (-28*x**2)*(-83*x**3) + (-83*x**3)*(26*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-28*x**2)*(-83*x**3) + (28*x**2)*(26*x**3 - 28*x**2) + (-83*x**3)*(26*x**3)\nSimplifying the partial expression: (28*x**2)*(26*x**3 - 28*x**2)\nExpanding the part (26*x**3 - 28*x**2) using the distributive property, and we got: (-28*x**2)*(28*x**2) + (28*x**2)*(26*x**3)\nReplacing (28*x**2)*(26*x**3 - 28*x**2) with (-28*x**2)*(28*x**2) + (28*x**2)*(26*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-28*x**2)*(28*x**2) + (-28*x**2)*(-83*x**3) + (28*x**2)*(26*x**3) + (-83*x**3)*(26*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*x**2)*(-83*x**3) = 2324*x**5\n (-28*x**2)*(28*x**2) = -784*x**4\n (26*x**3)*(-83*x**3) = -2158*x**6\n (26*x**3)*(28*x**2) = 728*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2158*x**6 + 728*x**5 + 2324*x**5 - 784*x**4\nCombining like terms, got -2158*x**6 + 3052*x**5 - 784*x**4\n#Step 6:\nCurrent expression: -2158*x**6 + 3052*x**5 - 784*x**4\nNo more calculations needed.\n-2158*x**6 + 3052*x**5 - 784*x**4", "generated_answer": "-2158*x**6 + 3052*x**5 - 784*x**4", "step_length": 6} {"cot_id": "153ff098ec26cf56d4e1122f6836aa9903f15bee01b164d8f37358c54b705859", "datapoint": {"question": "Calculate the following: (23 - 38*y**3)*(5*y**3 + 19*y - 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-190*y**6 - 722*y**4 + 381*y**3 + 437*y - 161", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1461, "polynomial_expr": "(23 - 38*y**3)*(5*y**3 + 19*y - 7)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (23 - 38*y**3)*(5*y**3 + 19*y - 7)\nExpanding the part (23 - 38*y**3) using the distributive property, and we got: (-38*y**3)*(5*y**3 + 19*y - 7) + 23*(5*y**3 + 19*y - 7)\n#Step 2:\nCurrent expression: (-38*y**3)*(5*y**3 + 19*y - 7) + 23*(5*y**3 + 19*y - 7)\nSimplifying the partial expression: 23*(5*y**3 + 19*y - 7)\nExpanding the part (5*y**3 + 19*y - 7) using the distributive property, and we got: (19*y)*23 + (5*y**3)*23 - 7*23\nReplacing 23*(5*y**3 + 19*y - 7) with (19*y)*23 + (5*y**3)*23 - 7*23 in the overall expression.\n#Step 3:\nCurrent expression: (19*y)*23 + (-38*y**3)*(5*y**3 + 19*y - 7) + (5*y**3)*23 - 161\nSimplifying the partial expression: (-38*y**3)*(5*y**3 + 19*y - 7)\nExpanding the part (5*y**3 + 19*y - 7) using the distributive property, and we got: -(-1)*266*y**3 + (19*y)*(-38*y**3) + (-38*y**3)*(5*y**3)\nReplacing (-38*y**3)*(5*y**3 + 19*y - 7) with -(-1)*266*y**3 + (19*y)*(-38*y**3) + (-38*y**3)*(5*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -7*(-38)*y**3 + (19*y)*(-38*y**3) + (19*y)*23 + (-38*y**3)*(5*y**3) + (5*y**3)*23 - 161\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (5*y**3)*23 = 115*y**3\n (5*y**3)*(-38*y**3) = -190*y**6\n (19*y)*23 = 437*y\n (19*y)*(-38*y**3) = -722*y**4\n -7*-38*y**3 = 266*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -190*y**6 - 722*y**4 + 115*y**3 + 266*y**3 + 437*y - 161\nCombining like terms, got -190*y**6 - 722*y**4 + 381*y**3 + 437*y - 161\n#Step 6:\nCurrent expression: -190*y**6 - 722*y**4 + 381*y**3 + 437*y - 161\nNo more calculations needed.\n-190*y**6 - 722*y**4 + 381*y**3 + 437*y - 161", "generated_answer": "-190*y**6 - 722*y**4 + 381*y**3 + 437*y - 161", "step_length": 6} {"cot_id": "5364d6ed26bbe55753aee04af9e4dc8f71c23b1f82cd60cefb3033b72c756434", "datapoint": {"question": "Simplify this expression: -8455*y**2 - 3382*y\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-8455*y**2 - 3382*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1462, "polynomial_expr": "-8455*y**2 - 3382*y", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -8455*y**2 - 3382*y\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -8455*y**2 - 3382*y\nNo more calculations needed.\n-8455*y**2 - 3382*y", "generated_answer": "-8455*y**2 - 3382*y", "step_length": 2} {"cot_id": "9d2968aabbbd3862ef73e5e70eae641eb000ddbe115187b99e03da750ea3a6d7", "datapoint": {"question": "Calculate the following: -63*x**3*(-86*x**3 - 9*x - 46)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "5418*x**6 + 567*x**4 + 2898*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1463, "polynomial_expr": "-63*x**3*(-86*x**3 - 9*x - 46)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -63*x**3*(-86*x**3 - 9*x - 46)\nExpanding the part (-86*x**3 - 9*x - 46) using the distributive property, and we got: (-9*x)*(-63*x**3) - (-1)*2898*x**3 + (-86*x**3)*(-63*x**3)\n#Step 2:\nCurrent expression: (-9*x)*(-63*x**3) - (-1)*2898*x**3 + (-86*x**3)*(-63*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -46*(-63*x**3) = 2898*x**3\n (-86*x**3)*(-63*x**3) = 5418*x**6\n (-9*x)*(-63*x**3) = 567*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 5418*x**6 + 567*x**4 + 2898*x**3\nNo more calculations needed.\n5418*x**6 + 567*x**4 + 2898*x**3", "generated_answer": "5418*x**6 + 567*x**4 + 2898*x**3", "step_length": 3} {"cot_id": "62842e100f7ff10d4438bb083b98cd540690d2c8fcd2b279aea21abe3844ae5e", "datapoint": {"question": "Calculate the following: (40*x**2 + 22*x)*(50*x**3 + 22*x**2 + 20*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2000*x**5 + 1980*x**4 + 1284*x**3 + 440*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1464, "polynomial_expr": "(40*x**2 + 22*x)*(50*x**3 + 22*x**2 + 20*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (40*x**2 + 22*x)*(50*x**3 + 22*x**2 + 20*x)\nExpanding the part (40*x**2 + 22*x) using the distributive property, and we got: (22*x)*(50*x**3 + 22*x**2 + 20*x) + (40*x**2)*(50*x**3 + 22*x**2 + 20*x)\n#Step 2:\nCurrent expression: (22*x)*(50*x**3 + 22*x**2 + 20*x) + (40*x**2)*(50*x**3 + 22*x**2 + 20*x)\nSimplifying the partial expression: (22*x)*(50*x**3 + 22*x**2 + 20*x)\nExpanding the part (50*x**3 + 22*x**2 + 20*x) using the distributive property, and we got: (20*x)*(22*x) + (22*x)*(22*x**2) + (22*x)*(50*x**3)\nReplacing (22*x)*(50*x**3 + 22*x**2 + 20*x) with (20*x)*(22*x) + (22*x)*(22*x**2) + (22*x)*(50*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (20*x)*(22*x) + (22*x)*(22*x**2) + (22*x)*(50*x**3) + (40*x**2)*(50*x**3 + 22*x**2 + 20*x)\nSimplifying the partial expression: (40*x**2)*(50*x**3 + 22*x**2 + 20*x)\nExpanding the part (50*x**3 + 22*x**2 + 20*x) using the distributive property, and we got: (20*x)*(40*x**2) + (22*x**2)*(40*x**2) + (40*x**2)*(50*x**3)\nReplacing (40*x**2)*(50*x**3 + 22*x**2 + 20*x) with (20*x)*(40*x**2) + (22*x**2)*(40*x**2) + (40*x**2)*(50*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (20*x)*(22*x) + (20*x)*(40*x**2) + (22*x)*(22*x**2) + (22*x)*(50*x**3) + (22*x**2)*(40*x**2) + (40*x**2)*(50*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (20*x)*(22*x) = 440*x**2\n (20*x)*(40*x**2) = 800*x**3\n (22*x**2)*(22*x) = 484*x**3\n (22*x**2)*(40*x**2) = 880*x**4\n (50*x**3)*(22*x) = 1100*x**4\n (50*x**3)*(40*x**2) = 2000*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2000*x**5 + 880*x**4 + 1100*x**4 + 484*x**3 + 800*x**3 + 440*x**2\nCombining like terms, got 2000*x**5 + 1980*x**4 + 1284*x**3 + 440*x**2\n#Step 6:\nCurrent expression: 2000*x**5 + 1980*x**4 + 1284*x**3 + 440*x**2\nNo more calculations needed.\n2000*x**5 + 1980*x**4 + 1284*x**3 + 440*x**2", "generated_answer": "2000*x**5 + 1980*x**4 + 1284*x**3 + 440*x**2", "step_length": 6} {"cot_id": "72ad4b6893e8a3ec7cba569450052633f01dfc8924f04afaf23cb551f5dbdfc1", "datapoint": {"question": "Simplify this expression: (28*x - 78)*(41*x**3 - 56*x - 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1148*x**4 - 3198*x**3 - 1568*x**2 + 3892*x + 1326", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1465, "polynomial_expr": "(28*x - 78)*(41*x**3 - 56*x - 17)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28*x - 78)*(41*x**3 - 56*x - 17)\nExpanding the part (28*x - 78) using the distributive property, and we got: (28*x)*(41*x**3 - 56*x - 17) - 78*(41*x**3 - 56*x - 17)\n#Step 2:\nCurrent expression: (28*x)*(41*x**3 - 56*x - 17) - 78*(41*x**3 - 56*x - 17)\nSimplifying the partial expression: -78*(41*x**3 - 56*x - 17)\nExpanding the part (41*x**3 - 56*x - 17) using the distributive property, and we got: -56*x*(-78) + (41*x**3)*(-78) - 17*(-78)\nReplacing -78*(41*x**3 - 56*x - 17) with -56*x*(-78) + (41*x**3)*(-78) - 17*(-78) in the overall expression.\n#Step 3:\nCurrent expression: -56*x*(-78) + (28*x)*(41*x**3 - 56*x - 17) + (41*x**3)*(-78) + 1326\nSimplifying the partial expression: (28*x)*(41*x**3 - 56*x - 17)\nExpanding the part (41*x**3 - 56*x - 17) using the distributive property, and we got: (-56*x)*(28*x) - 476*x + (28*x)*(41*x**3)\nReplacing (28*x)*(41*x**3 - 56*x - 17) with (-56*x)*(28*x) - 476*x + (28*x)*(41*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-56*x)*(28*x) - 56*x*(-78) - 17*28*x + (28*x)*(41*x**3) + (41*x**3)*(-78) + 1326\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-56*x)*-78 = 4368*x\n (-56*x)*(28*x) = -1568*x**2\n (41*x**3)*-78 = -3198*x**3\n (41*x**3)*(28*x) = 1148*x**4\n -17*28*x = -476*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1148*x**4 - 3198*x**3 - 1568*x**2 - 476*x + 4368*x + 1326\nCombining like terms, got 1148*x**4 - 3198*x**3 - 1568*x**2 + 3892*x + 1326\n#Step 6:\nCurrent expression: 1148*x**4 - 3198*x**3 - 1568*x**2 + 3892*x + 1326\nNo more calculations needed.\n1148*x**4 - 3198*x**3 - 1568*x**2 + 3892*x + 1326", "generated_answer": "1148*x**4 - 3198*x**3 - 1568*x**2 + 3892*x + 1326", "step_length": 6} {"cot_id": "08d7df3efe6c48683f02250a86cdfcee75cc66cb535f4d51596384faf6c5b428", "datapoint": {"question": "Simplify this expression: (9 - 45*y)*(24*y**3 + 3*y + 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1080*y**4 + 216*y**3 - 135*y**2 - 1233*y + 252", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1466, "polynomial_expr": "(9 - 45*y)*(24*y**3 + 3*y + 28)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9 - 45*y)*(24*y**3 + 3*y + 28)\nExpanding the part (9 - 45*y) using the distributive property, and we got: (-45*y)*(24*y**3 + 3*y + 28) + 9*(24*y**3 + 3*y + 28)\n#Step 2:\nCurrent expression: (-45*y)*(24*y**3 + 3*y + 28) + 9*(24*y**3 + 3*y + 28)\nSimplifying the partial expression: 9*(24*y**3 + 3*y + 28)\nExpanding the part (24*y**3 + 3*y + 28) using the distributive property, and we got: (3*y)*9 + (24*y**3)*9 + 28*9\nReplacing 9*(24*y**3 + 3*y + 28) with (3*y)*9 + (24*y**3)*9 + 28*9 in the overall expression.\n#Step 3:\nCurrent expression: (-45*y)*(24*y**3 + 3*y + 28) + (3*y)*9 + (24*y**3)*9 + 252\nSimplifying the partial expression: (-45*y)*(24*y**3 + 3*y + 28)\nExpanding the part (24*y**3 + 3*y + 28) using the distributive property, and we got: (-45*y)*(3*y) + (-45*y)*(24*y**3) + 28*(-45*y)\nReplacing (-45*y)*(24*y**3 + 3*y + 28) with (-45*y)*(3*y) + (-45*y)*(24*y**3) + 28*(-45*y) in the overall expression.\n#Step 4:\nCurrent expression: (-45*y)*(3*y) + (-45*y)*(24*y**3) + 28*(-45)*y + (3*y)*9 + (24*y**3)*9 + 252\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (3*y)*9 = 27*y\n (3*y)*(-45*y) = -135*y**2\n (24*y**3)*9 = 216*y**3\n (24*y**3)*(-45*y) = -1080*y**4\n 28*-45*y = -1260*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1080*y**4 + 216*y**3 - 135*y**2 - 1260*y + 27*y + 252\nCombining like terms, got -1080*y**4 + 216*y**3 - 135*y**2 - 1233*y + 252\n#Step 6:\nCurrent expression: -1080*y**4 + 216*y**3 - 135*y**2 - 1233*y + 252\nNo more calculations needed.\n-1080*y**4 + 216*y**3 - 135*y**2 - 1233*y + 252", "generated_answer": "-1080*y**4 + 216*y**3 - 135*y**2 - 1233*y + 252", "step_length": 6} {"cot_id": "12326753a62a2af059aecd8cbf54379c5542738c4f1134f9636396fe83efa780", "datapoint": {"question": "Calculate the following: (-2*y**3 - 29*y + 37)*(40*y**3 - 2*y + 5)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-80*y**6 - 1156*y**4 + 1470*y**3 + 58*y**2 - 219*y + 185", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1467, "polynomial_expr": "(-2*y**3 - 29*y + 37)*(40*y**3 - 2*y + 5)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-2*y**3 - 29*y + 37)*(40*y**3 - 2*y + 5)\nExpanding the part (40*y**3 - 2*y + 5) using the distributive property, and we got: (-2*y)*(-2*y**3 - 29*y + 37) + (40*y**3)*(-2*y**3 - 29*y + 37) + 5*(-2*y**3 - 29*y + 37)\n#Step 2:\nCurrent expression: (-2*y)*(-2*y**3 - 29*y + 37) + (40*y**3)*(-2*y**3 - 29*y + 37) + 5*(-2*y**3 - 29*y + 37)\nSimplifying the partial expression: 5*(-2*y**3 - 29*y + 37)\nExpanding the part (-2*y**3 - 29*y + 37) using the distributive property, and we got: -29*y*5 - 2*y**3*5 + 37*5\nReplacing 5*(-2*y**3 - 29*y + 37) with -29*y*5 - 2*y**3*5 + 37*5 in the overall expression.\n#Step 3:\nCurrent expression: -29*y*5 + (-2*y)*(-2*y**3 - 29*y + 37) - 2*y**3*5 + (40*y**3)*(-2*y**3 - 29*y + 37) + 185\nSimplifying the partial expression: (-2*y)*(-2*y**3 - 29*y + 37)\nExpanding the part (-2*y**3 - 29*y + 37) using the distributive property, and we got: (-29*y)*(-2*y) + (-2*y)*(-2*y**3) + 37*(-2*y)\nReplacing (-2*y)*(-2*y**3 - 29*y + 37) with (-29*y)*(-2*y) + (-2*y)*(-2*y**3) + 37*(-2*y) in the overall expression.\n#Step 4:\nCurrent expression: (-29*y)*(-2*y) - 29*y*5 + (-2*y)*(-2*y**3) + 37*(-2)*y - 2*y**3*5 + (40*y**3)*(-2*y**3 - 29*y + 37) + 185\nSimplifying the partial expression: (40*y**3)*(-2*y**3 - 29*y + 37)\nExpanding the part (-2*y**3 - 29*y + 37) using the distributive property, and we got: (-29*y)*(40*y**3) + 37*(40*y**3) + (-2*y**3)*(40*y**3)\nReplacing (40*y**3)*(-2*y**3 - 29*y + 37) with (-29*y)*(40*y**3) + 37*(40*y**3) + (-2*y**3)*(40*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-29*y)*(-2*y) + (-29*y)*(40*y**3) - 29*y*5 + (-2*y)*(-2*y**3) + 37*40*y**3 + 37*(-2)*y + (-2*y**3)*(40*y**3) - 2*y**3*5 + 185\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*y)*5 = -145*y\n (-29*y)*(-2*y) = 58*y**2\n (-29*y)*(40*y**3) = -1160*y**4\n (-2*y**3)*5 = -10*y**3\n (-2*y**3)*(-2*y) = 4*y**4\n (-2*y**3)*(40*y**3) = -80*y**6\n 37*-2*y = -74*y\n 37*40*y**3 = 1480*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -80*y**6 - 1160*y**4 + 4*y**4 - 10*y**3 + 1480*y**3 + 58*y**2 - 145*y - 74*y + 185\nCombining like terms, got -80*y**6 - 1156*y**4 + 1470*y**3 + 58*y**2 - 219*y + 185\n#Step 7:\nCurrent expression: -80*y**6 - 1156*y**4 + 1470*y**3 + 58*y**2 - 219*y + 185\nNo more calculations needed.\n-80*y**6 - 1156*y**4 + 1470*y**3 + 58*y**2 - 219*y + 185", "generated_answer": "-80*y**6 - 1156*y**4 + 1470*y**3 + 58*y**2 - 219*y + 185", "step_length": 7} {"cot_id": "a8a78845ccf8565b9e49738dcdd3776616c6f252b3edc120f08b3d4d616c474c", "datapoint": {"question": "Simplify this expression: -74*y**2*(29*y**3 + 34*y**2 - 38*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2146*y**5 - 2516*y**4 + 2812*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1468, "polynomial_expr": "-74*y**2*(29*y**3 + 34*y**2 - 38*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -74*y**2*(29*y**3 + 34*y**2 - 38*y)\nExpanding the part (29*y**3 + 34*y**2 - 38*y) using the distributive property, and we got: (-38*y)*(-74*y**2) + (-74*y**2)*(34*y**2) + (-74*y**2)*(29*y**3)\n#Step 2:\nCurrent expression: (-38*y)*(-74*y**2) + (-74*y**2)*(34*y**2) + (-74*y**2)*(29*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*y)*(-74*y**2) = 2812*y**3\n (29*y**3)*(-74*y**2) = -2146*y**5\n (34*y**2)*(-74*y**2) = -2516*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -2146*y**5 - 2516*y**4 + 2812*y**3\nNo more calculations needed.\n-2146*y**5 - 2516*y**4 + 2812*y**3", "generated_answer": "-2146*y**5 - 2516*y**4 + 2812*y**3", "step_length": 3} {"cot_id": "079779a6273316aa2d11007f3b2a8effc65c30c1c37516c9b09f71dd8ac0d9ed", "datapoint": {"question": "Simplify this expression: (3 - 48*x)*(x**3 + 16*x**2 - 20*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-48*x**4 - 765*x**3 + 1008*x**2 - 60*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1469, "polynomial_expr": "(3 - 48*x)*(x**3 + 16*x**2 - 20*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (3 - 48*x)*(x**3 + 16*x**2 - 20*x)\nExpanding the part (3 - 48*x) using the distributive property, and we got: (-48*x)*(x**3 + 16*x**2 - 20*x) + 3*(x**3 + 16*x**2 - 20*x)\n#Step 2:\nCurrent expression: (-48*x)*(x**3 + 16*x**2 - 20*x) + 3*(x**3 + 16*x**2 - 20*x)\nSimplifying the partial expression: 3*(x**3 + 16*x**2 - 20*x)\nExpanding the part (x**3 + 16*x**2 - 20*x) using the distributive property, and we got: -20*x*3 + x**3*3 + (16*x**2)*3\nReplacing 3*(x**3 + 16*x**2 - 20*x) with -20*x*3 + x**3*3 + (16*x**2)*3 in the overall expression.\n#Step 3:\nCurrent expression: (-48*x)*(x**3 + 16*x**2 - 20*x) - 20*x*3 + x**3*3 + (16*x**2)*3\nSimplifying the partial expression: (-48*x)*(x**3 + 16*x**2 - 20*x)\nExpanding the part (x**3 + 16*x**2 - 20*x) using the distributive property, and we got: (-48*x)*(-20*x) + (-48*x)*x**3 + (-48*x)*(16*x**2)\nReplacing (-48*x)*(x**3 + 16*x**2 - 20*x) with (-48*x)*(-20*x) + (-48*x)*x**3 + (-48*x)*(16*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-48*x)*(-20*x) + (-48*x)*x**3 + (-48*x)*(16*x**2) - 20*x*3 + x**3*3 + (16*x**2)*3\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n x**3*3 = 3*x**3\n x**3*(-48*x) = -48*x**4\n (-20*x)*3 = -60*x\n (-20*x)*(-48*x) = 960*x**2\n (16*x**2)*3 = 48*x**2\n (16*x**2)*(-48*x) = -768*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -48*x**4 - 768*x**3 + 3*x**3 + 48*x**2 + 960*x**2 - 60*x\nCombining like terms, got -48*x**4 - 765*x**3 + 1008*x**2 - 60*x\n#Step 6:\nCurrent expression: -48*x**4 - 765*x**3 + 1008*x**2 - 60*x\nNo more calculations needed.\n-48*x**4 - 765*x**3 + 1008*x**2 - 60*x", "generated_answer": "-48*x**4 - 765*x**3 + 1008*x**2 - 60*x", "step_length": 6} {"cot_id": "e588ad9836fc87e29393f38b0a8d13b51ab7c8cef1bd1579c41bba43608a5bd6", "datapoint": {"question": "Calculate the following: (22*y**3 - 40*y**2)*(-27*y**2 + 14*y - 56)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-594*y**5 + 1388*y**4 - 1792*y**3 + 2240*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1470, "polynomial_expr": "(22*y**3 - 40*y**2)*(-27*y**2 + 14*y - 56)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (22*y**3 - 40*y**2)*(-27*y**2 + 14*y - 56)\nExpanding the part (22*y**3 - 40*y**2) using the distributive property, and we got: (-40*y**2)*(-27*y**2 + 14*y - 56) + (22*y**3)*(-27*y**2 + 14*y - 56)\n#Step 2:\nCurrent expression: (-40*y**2)*(-27*y**2 + 14*y - 56) + (22*y**3)*(-27*y**2 + 14*y - 56)\nSimplifying the partial expression: (-40*y**2)*(-27*y**2 + 14*y - 56)\nExpanding the part (-27*y**2 + 14*y - 56) using the distributive property, and we got: -(-1)*2240*y**2 + (14*y)*(-40*y**2) + (-40*y**2)*(-27*y**2)\nReplacing (-40*y**2)*(-27*y**2 + 14*y - 56) with -(-1)*2240*y**2 + (14*y)*(-40*y**2) + (-40*y**2)*(-27*y**2) in the overall expression.\n#Step 3:\nCurrent expression: -56*(-40)*y**2 + (14*y)*(-40*y**2) + (-40*y**2)*(-27*y**2) + (22*y**3)*(-27*y**2 + 14*y - 56)\nSimplifying the partial expression: (22*y**3)*(-27*y**2 + 14*y - 56)\nExpanding the part (-27*y**2 + 14*y - 56) using the distributive property, and we got: -1232*y**3 + (14*y)*(22*y**3) + (-27*y**2)*(22*y**3)\nReplacing (22*y**3)*(-27*y**2 + 14*y - 56) with -1232*y**3 + (14*y)*(22*y**3) + (-27*y**2)*(22*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -56*22*y**3 - 56*(-40)*y**2 + (14*y)*(-40*y**2) + (14*y)*(22*y**3) + (-40*y**2)*(-27*y**2) + (-27*y**2)*(22*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*y**2)*(-40*y**2) = 1080*y**4\n (-27*y**2)*(22*y**3) = -594*y**5\n (14*y)*(-40*y**2) = -560*y**3\n (14*y)*(22*y**3) = 308*y**4\n -56*-40*y**2 = 2240*y**2\n -56*22*y**3 = -1232*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -594*y**5 + 308*y**4 + 1080*y**4 - 1232*y**3 - 560*y**3 + 2240*y**2\nCombining like terms, got -594*y**5 + 1388*y**4 - 1792*y**3 + 2240*y**2\n#Step 6:\nCurrent expression: -594*y**5 + 1388*y**4 - 1792*y**3 + 2240*y**2\nNo more calculations needed.\n-594*y**5 + 1388*y**4 - 1792*y**3 + 2240*y**2", "generated_answer": "-594*y**5 + 1388*y**4 - 1792*y**3 + 2240*y**2", "step_length": 6} {"cot_id": "a205461d5488a996fa363643d2567f9914e5d393d51a4ddfd8e958d1740ad5bc", "datapoint": {"question": "Calculate the following: (39*z**2 - 13*z)*(-87*z**3 + 17*z**2 - 18)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-3393*z**5 + 1794*z**4 - 221*z**3 - 702*z**2 + 234*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1471, "polynomial_expr": "(39*z**2 - 13*z)*(-87*z**3 + 17*z**2 - 18)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (39*z**2 - 13*z)*(-87*z**3 + 17*z**2 - 18)\nExpanding the part (39*z**2 - 13*z) using the distributive property, and we got: (-13*z)*(-87*z**3 + 17*z**2 - 18) + (39*z**2)*(-87*z**3 + 17*z**2 - 18)\n#Step 2:\nCurrent expression: (-13*z)*(-87*z**3 + 17*z**2 - 18) + (39*z**2)*(-87*z**3 + 17*z**2 - 18)\nSimplifying the partial expression: (-13*z)*(-87*z**3 + 17*z**2 - 18)\nExpanding the part (-87*z**3 + 17*z**2 - 18) using the distributive property, and we got: (-13*z)*(17*z**2) + (-13*z)*(-87*z**3) - (-1)*234*z\nReplacing (-13*z)*(-87*z**3 + 17*z**2 - 18) with (-13*z)*(17*z**2) + (-13*z)*(-87*z**3) - (-1)*234*z in the overall expression.\n#Step 3:\nCurrent expression: (-13*z)*(17*z**2) + (-13*z)*(-87*z**3) - 18*(-13)*z + (39*z**2)*(-87*z**3 + 17*z**2 - 18)\nSimplifying the partial expression: (39*z**2)*(-87*z**3 + 17*z**2 - 18)\nExpanding the part (-87*z**3 + 17*z**2 - 18) using the distributive property, and we got: -702*z**2 + (17*z**2)*(39*z**2) + (39*z**2)*(-87*z**3)\nReplacing (39*z**2)*(-87*z**3 + 17*z**2 - 18) with -702*z**2 + (17*z**2)*(39*z**2) + (39*z**2)*(-87*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-13*z)*(17*z**2) + (-13*z)*(-87*z**3) - 18*39*z**2 - 18*(-13)*z + (17*z**2)*(39*z**2) + (39*z**2)*(-87*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-87*z**3)*(-13*z) = 1131*z**4\n (-87*z**3)*(39*z**2) = -3393*z**5\n (17*z**2)*(-13*z) = -221*z**3\n (17*z**2)*(39*z**2) = 663*z**4\n -18*-13*z = 234*z\n -18*39*z**2 = -702*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -3393*z**5 + 663*z**4 + 1131*z**4 - 221*z**3 - 702*z**2 + 234*z\nCombining like terms, got -3393*z**5 + 1794*z**4 - 221*z**3 - 702*z**2 + 234*z\n#Step 6:\nCurrent expression: -3393*z**5 + 1794*z**4 - 221*z**3 - 702*z**2 + 234*z\nNo more calculations needed.\n-3393*z**5 + 1794*z**4 - 221*z**3 - 702*z**2 + 234*z", "generated_answer": "-3393*z**5 + 1794*z**4 - 221*z**3 - 702*z**2 + 234*z", "step_length": 6} {"cot_id": "846c8824bdc11215c82b4d30b4210b921d9ce0656d7c9b8b6164c534756e7b53", "datapoint": {"question": "Simplify this expression: (-6*x**3 - 27*x**2)*(55*x**3 - 27*x**2 + 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-330*x**6 - 1323*x**5 + 729*x**4 - 294*x**3 - 1323*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1472, "polynomial_expr": "(-6*x**3 - 27*x**2)*(55*x**3 - 27*x**2 + 49)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-6*x**3 - 27*x**2)*(55*x**3 - 27*x**2 + 49)\nExpanding the part (-6*x**3 - 27*x**2) using the distributive property, and we got: (-27*x**2)*(55*x**3 - 27*x**2 + 49) + (-6*x**3)*(55*x**3 - 27*x**2 + 49)\n#Step 2:\nCurrent expression: (-27*x**2)*(55*x**3 - 27*x**2 + 49) + (-6*x**3)*(55*x**3 - 27*x**2 + 49)\nSimplifying the partial expression: (-27*x**2)*(55*x**3 - 27*x**2 + 49)\nExpanding the part (55*x**3 - 27*x**2 + 49) using the distributive property, and we got: 49*(-27*x**2) + (-27*x**2)*(55*x**3) + (-27*x**2)*(-27*x**2)\nReplacing (-27*x**2)*(55*x**3 - 27*x**2 + 49) with 49*(-27*x**2) + (-27*x**2)*(55*x**3) + (-27*x**2)*(-27*x**2) in the overall expression.\n#Step 3:\nCurrent expression: 49*(-27)*x**2 + (-27*x**2)*(55*x**3) + (-27*x**2)*(-27*x**2) + (-6*x**3)*(55*x**3 - 27*x**2 + 49)\nSimplifying the partial expression: (-6*x**3)*(55*x**3 - 27*x**2 + 49)\nExpanding the part (55*x**3 - 27*x**2 + 49) using the distributive property, and we got: 49*(-6*x**3) + (-27*x**2)*(-6*x**3) + (-6*x**3)*(55*x**3)\nReplacing (-6*x**3)*(55*x**3 - 27*x**2 + 49) with 49*(-6*x**3) + (-27*x**2)*(-6*x**3) + (-6*x**3)*(55*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 49*(-6)*x**3 + 49*(-27)*x**2 + (-27*x**2)*(-6*x**3) + (-27*x**2)*(55*x**3) + (-27*x**2)*(-27*x**2) + (-6*x**3)*(55*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*x**2)*(-27*x**2) = 729*x**4\n (-27*x**2)*(-6*x**3) = 162*x**5\n (55*x**3)*(-27*x**2) = -1485*x**5\n (55*x**3)*(-6*x**3) = -330*x**6\n 49*-27*x**2 = -1323*x**2\n 49*-6*x**3 = -294*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -330*x**6 - 1485*x**5 + 162*x**5 + 729*x**4 - 294*x**3 - 1323*x**2\nCombining like terms, got -330*x**6 - 1323*x**5 + 729*x**4 - 294*x**3 - 1323*x**2\n#Step 6:\nCurrent expression: -330*x**6 - 1323*x**5 + 729*x**4 - 294*x**3 - 1323*x**2\nNo more calculations needed.\n-330*x**6 - 1323*x**5 + 729*x**4 - 294*x**3 - 1323*x**2", "generated_answer": "-330*x**6 - 1323*x**5 + 729*x**4 - 294*x**3 - 1323*x**2", "step_length": 6} {"cot_id": "3c588cbc4beaf6e90e203543caded1b693c8752f29383d856db70cae3cd1d146", "datapoint": {"question": "Calculate the following: 57*z**2*(-4*z**2 - 15*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-228*z**4 - 855*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1473, "polynomial_expr": "57*z**2*(-4*z**2 - 15*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 57*z**2*(-4*z**2 - 15*z)\nExpanding the part (-4*z**2 - 15*z) using the distributive property, and we got: (-15*z)*(57*z**2) + (-4*z**2)*(57*z**2)\n#Step 2:\nCurrent expression: (-15*z)*(57*z**2) + (-4*z**2)*(57*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-15*z)*(57*z**2) = -855*z**3\n (-4*z**2)*(57*z**2) = -228*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -228*z**4 - 855*z**3\nNo more calculations needed.\n-228*z**4 - 855*z**3", "generated_answer": "-228*z**4 - 855*z**3", "step_length": 3} {"cot_id": "789dc99246280314048d4f18c318b29ed44b0efe8276e965b0ed4690927d6625", "datapoint": {"question": "Calculate the following: 21*x**2*(-22*x**3 + 40*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-462*x**5 + 840*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1474, "polynomial_expr": "21*x**2*(-22*x**3 + 40*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 21*x**2*(-22*x**3 + 40*x)\nExpanding the part (-22*x**3 + 40*x) using the distributive property, and we got: (40*x)*(21*x**2) + (21*x**2)*(-22*x**3)\n#Step 2:\nCurrent expression: (40*x)*(21*x**2) + (21*x**2)*(-22*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*x**3)*(21*x**2) = -462*x**5\n (40*x)*(21*x**2) = 840*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -462*x**5 + 840*x**3\nNo more calculations needed.\n-462*x**5 + 840*x**3", "generated_answer": "-462*x**5 + 840*x**3", "step_length": 3} {"cot_id": "05f6296be9c08139afeed066277782a6fb528eea471375185482cf9e1c45900c", "datapoint": {"question": "Simplify this expression: (20 - 9*y)*(44*y**3 - 15*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-396*y**4 + 1015*y**3 - 300*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1475, "polynomial_expr": "(20 - 9*y)*(44*y**3 - 15*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (20 - 9*y)*(44*y**3 - 15*y**2)\nExpanding the part (20 - 9*y) using the distributive property, and we got: (-9*y)*(44*y**3 - 15*y**2) + 20*(44*y**3 - 15*y**2)\n#Step 2:\nCurrent expression: (-9*y)*(44*y**3 - 15*y**2) + 20*(44*y**3 - 15*y**2)\nSimplifying the partial expression: 20*(44*y**3 - 15*y**2)\nExpanding the part (44*y**3 - 15*y**2) using the distributive property, and we got: -15*y**2*20 + (44*y**3)*20\nReplacing 20*(44*y**3 - 15*y**2) with -15*y**2*20 + (44*y**3)*20 in the overall expression.\n#Step 3:\nCurrent expression: (-9*y)*(44*y**3 - 15*y**2) - 15*y**2*20 + (44*y**3)*20\nSimplifying the partial expression: (-9*y)*(44*y**3 - 15*y**2)\nExpanding the part (44*y**3 - 15*y**2) using the distributive property, and we got: (-9*y)*(-15*y**2) + (-9*y)*(44*y**3)\nReplacing (-9*y)*(44*y**3 - 15*y**2) with (-9*y)*(-15*y**2) + (-9*y)*(44*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-9*y)*(-15*y**2) + (-9*y)*(44*y**3) - 15*y**2*20 + (44*y**3)*20\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-15*y**2)*20 = -300*y**2\n (-15*y**2)*(-9*y) = 135*y**3\n (44*y**3)*20 = 880*y**3\n (44*y**3)*(-9*y) = -396*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -396*y**4 + 135*y**3 + 880*y**3 - 300*y**2\nCombining like terms, got -396*y**4 + 1015*y**3 - 300*y**2\n#Step 6:\nCurrent expression: -396*y**4 + 1015*y**3 - 300*y**2\nNo more calculations needed.\n-396*y**4 + 1015*y**3 - 300*y**2", "generated_answer": "-396*y**4 + 1015*y**3 - 300*y**2", "step_length": 6} {"cot_id": "192c6529fc7365e947d0c301cbf98685917e135860e2763a6321ba6ec4662329", "datapoint": {"question": "Simplify this expression: (-49*x**3 - 23*x)*(-13*x**3 - 28*x**2 - 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "637*x**6 + 1372*x**5 + 299*x**4 + 1281*x**3 + 299*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1476, "polynomial_expr": "(-49*x**3 - 23*x)*(-13*x**3 - 28*x**2 - 13)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-49*x**3 - 23*x)*(-13*x**3 - 28*x**2 - 13)\nExpanding the part (-49*x**3 - 23*x) using the distributive property, and we got: (-23*x)*(-13*x**3 - 28*x**2 - 13) + (-49*x**3)*(-13*x**3 - 28*x**2 - 13)\n#Step 2:\nCurrent expression: (-23*x)*(-13*x**3 - 28*x**2 - 13) + (-49*x**3)*(-13*x**3 - 28*x**2 - 13)\nSimplifying the partial expression: (-49*x**3)*(-13*x**3 - 28*x**2 - 13)\nExpanding the part (-13*x**3 - 28*x**2 - 13) using the distributive property, and we got: -(-1)*637*x**3 + (-28*x**2)*(-49*x**3) + (-49*x**3)*(-13*x**3)\nReplacing (-49*x**3)*(-13*x**3 - 28*x**2 - 13) with -(-1)*637*x**3 + (-28*x**2)*(-49*x**3) + (-49*x**3)*(-13*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-23*x)*(-13*x**3 - 28*x**2 - 13) - 13*(-49)*x**3 + (-28*x**2)*(-49*x**3) + (-49*x**3)*(-13*x**3)\nSimplifying the partial expression: (-23*x)*(-13*x**3 - 28*x**2 - 13)\nExpanding the part (-13*x**3 - 28*x**2 - 13) using the distributive property, and we got: (-23*x)*(-28*x**2) + (-23*x)*(-13*x**3) - (-1)*299*x\nReplacing (-23*x)*(-13*x**3 - 28*x**2 - 13) with (-23*x)*(-28*x**2) + (-23*x)*(-13*x**3) - (-1)*299*x in the overall expression.\n#Step 4:\nCurrent expression: (-23*x)*(-28*x**2) + (-23*x)*(-13*x**3) - 13*(-49)*x**3 - 13*(-23)*x + (-28*x**2)*(-49*x**3) + (-49*x**3)*(-13*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*x**2)*(-49*x**3) = 1372*x**5\n (-28*x**2)*(-23*x) = 644*x**3\n (-13*x**3)*(-49*x**3) = 637*x**6\n (-13*x**3)*(-23*x) = 299*x**4\n -13*-49*x**3 = 637*x**3\n -13*-23*x = 299*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 637*x**6 + 1372*x**5 + 299*x**4 + 637*x**3 + 644*x**3 + 299*x\nCombining like terms, got 637*x**6 + 1372*x**5 + 299*x**4 + 1281*x**3 + 299*x\n#Step 6:\nCurrent expression: 637*x**6 + 1372*x**5 + 299*x**4 + 1281*x**3 + 299*x\nNo more calculations needed.\n637*x**6 + 1372*x**5 + 299*x**4 + 1281*x**3 + 299*x", "generated_answer": "637*x**6 + 1372*x**5 + 299*x**4 + 1281*x**3 + 299*x", "step_length": 6} {"cot_id": "b721129b7adb4eb0d2b8ef97664de8a1ee49366945d16c77ca224473eca92f12", "datapoint": {"question": "Calculate the following: (22*x**2 - 78)*(42*x**3 + 12*x**2 + 3*x - 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "924*x**5 + 264*x**4 - 3210*x**3 - 1728*x**2 - 234*x + 2808", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1477, "polynomial_expr": "(22*x**2 - 78)*(42*x**3 + 12*x**2 + 3*x - 36)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (22*x**2 - 78)*(42*x**3 + 12*x**2 + 3*x - 36)\nExpanding the part (22*x**2 - 78) using the distributive property, and we got: (22*x**2)*(42*x**3 + 12*x**2 + 3*x - 36) - 78*(42*x**3 + 12*x**2 + 3*x - 36)\n#Step 2:\nCurrent expression: (22*x**2)*(42*x**3 + 12*x**2 + 3*x - 36) - 78*(42*x**3 + 12*x**2 + 3*x - 36)\nSimplifying the partial expression: -78*(42*x**3 + 12*x**2 + 3*x - 36)\nExpanding the part (42*x**3 + 12*x**2 + 3*x - 36) using the distributive property, and we got: (3*x)*(-78) + (12*x**2)*(-78) + (42*x**3)*(-78) - 36*(-78)\nReplacing -78*(42*x**3 + 12*x**2 + 3*x - 36) with (3*x)*(-78) + (12*x**2)*(-78) + (42*x**3)*(-78) - 36*(-78) in the overall expression.\n#Step 3:\nCurrent expression: (3*x)*(-78) + (12*x**2)*(-78) + (22*x**2)*(42*x**3 + 12*x**2 + 3*x - 36) + (42*x**3)*(-78) + 2808\nSimplifying the partial expression: (22*x**2)*(42*x**3 + 12*x**2 + 3*x - 36)\nExpanding the part (42*x**3 + 12*x**2 + 3*x - 36) using the distributive property, and we got: -792*x**2 + (3*x)*(22*x**2) + (12*x**2)*(22*x**2) + (22*x**2)*(42*x**3)\nReplacing (22*x**2)*(42*x**3 + 12*x**2 + 3*x - 36) with -792*x**2 + (3*x)*(22*x**2) + (12*x**2)*(22*x**2) + (22*x**2)*(42*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -36*22*x**2 + (3*x)*(22*x**2) + (3*x)*(-78) + (12*x**2)*(22*x**2) + (12*x**2)*(-78) + (22*x**2)*(42*x**3) + (42*x**3)*(-78) + 2808\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (3*x)*-78 = -234*x\n (3*x)*(22*x**2) = 66*x**3\n (12*x**2)*-78 = -936*x**2\n (12*x**2)*(22*x**2) = 264*x**4\n (42*x**3)*-78 = -3276*x**3\n (42*x**3)*(22*x**2) = 924*x**5\n -36*22*x**2 = -792*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 924*x**5 + 264*x**4 - 3276*x**3 + 66*x**3 - 936*x**2 - 792*x**2 - 234*x + 2808\nCombining like terms, got 924*x**5 + 264*x**4 - 3210*x**3 - 1728*x**2 - 234*x + 2808\n#Step 6:\nCurrent expression: 924*x**5 + 264*x**4 - 3210*x**3 - 1728*x**2 - 234*x + 2808\nNo more calculations needed.\n924*x**5 + 264*x**4 - 3210*x**3 - 1728*x**2 - 234*x + 2808", "generated_answer": "924*x**5 + 264*x**4 - 3210*x**3 - 1728*x**2 - 234*x + 2808", "step_length": 6} {"cot_id": "f0a8c71d5a91db69dcc35e9771a0d1f02d9a166e683bbc29c1805c34d99c712b", "datapoint": {"question": "Simplify this expression: (-42*y**3 + 2*y)*(46*y**3 + 48*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1932*y**6 - 2016*y**5 + 92*y**4 + 96*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1478, "polynomial_expr": "(-42*y**3 + 2*y)*(46*y**3 + 48*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-42*y**3 + 2*y)*(46*y**3 + 48*y**2)\nExpanding the part (-42*y**3 + 2*y) using the distributive property, and we got: (2*y)*(46*y**3 + 48*y**2) + (-42*y**3)*(46*y**3 + 48*y**2)\n#Step 2:\nCurrent expression: (2*y)*(46*y**3 + 48*y**2) + (-42*y**3)*(46*y**3 + 48*y**2)\nSimplifying the partial expression: (-42*y**3)*(46*y**3 + 48*y**2)\nExpanding the part (46*y**3 + 48*y**2) using the distributive property, and we got: (48*y**2)*(-42*y**3) + (-42*y**3)*(46*y**3)\nReplacing (-42*y**3)*(46*y**3 + 48*y**2) with (48*y**2)*(-42*y**3) + (-42*y**3)*(46*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (2*y)*(46*y**3 + 48*y**2) + (48*y**2)*(-42*y**3) + (-42*y**3)*(46*y**3)\nSimplifying the partial expression: (2*y)*(46*y**3 + 48*y**2)\nExpanding the part (46*y**3 + 48*y**2) using the distributive property, and we got: (2*y)*(48*y**2) + (2*y)*(46*y**3)\nReplacing (2*y)*(46*y**3 + 48*y**2) with (2*y)*(48*y**2) + (2*y)*(46*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (2*y)*(48*y**2) + (2*y)*(46*y**3) + (48*y**2)*(-42*y**3) + (-42*y**3)*(46*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (46*y**3)*(-42*y**3) = -1932*y**6\n (46*y**3)*(2*y) = 92*y**4\n (48*y**2)*(-42*y**3) = -2016*y**5\n (48*y**2)*(2*y) = 96*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1932*y**6 - 2016*y**5 + 92*y**4 + 96*y**3\nNo more calculations needed.\n-1932*y**6 - 2016*y**5 + 92*y**4 + 96*y**3", "generated_answer": "-1932*y**6 - 2016*y**5 + 92*y**4 + 96*y**3", "step_length": 5} {"cot_id": "cd3129f8c01627dc325e70342c8a90711a769090bd2fe8fb3567cd91ab644306", "datapoint": {"question": "Calculate the following: (-33*x**3 + 4*x)*(-7*x**3 - 12*x - 40)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "231*x**6 + 368*x**4 + 1320*x**3 - 48*x**2 - 160*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1479, "polynomial_expr": "(-33*x**3 + 4*x)*(-7*x**3 - 12*x - 40)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-33*x**3 + 4*x)*(-7*x**3 - 12*x - 40)\nExpanding the part (-33*x**3 + 4*x) using the distributive property, and we got: (4*x)*(-7*x**3 - 12*x - 40) + (-33*x**3)*(-7*x**3 - 12*x - 40)\n#Step 2:\nCurrent expression: (4*x)*(-7*x**3 - 12*x - 40) + (-33*x**3)*(-7*x**3 - 12*x - 40)\nSimplifying the partial expression: (-33*x**3)*(-7*x**3 - 12*x - 40)\nExpanding the part (-7*x**3 - 12*x - 40) using the distributive property, and we got: (-12*x)*(-33*x**3) - (-1)*1320*x**3 + (-33*x**3)*(-7*x**3)\nReplacing (-33*x**3)*(-7*x**3 - 12*x - 40) with (-12*x)*(-33*x**3) - (-1)*1320*x**3 + (-33*x**3)*(-7*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-12*x)*(-33*x**3) - 40*(-33)*x**3 + (4*x)*(-7*x**3 - 12*x - 40) + (-33*x**3)*(-7*x**3)\nSimplifying the partial expression: (4*x)*(-7*x**3 - 12*x - 40)\nExpanding the part (-7*x**3 - 12*x - 40) using the distributive property, and we got: (-12*x)*(4*x) - 160*x + (4*x)*(-7*x**3)\nReplacing (4*x)*(-7*x**3 - 12*x - 40) with (-12*x)*(4*x) - 160*x + (4*x)*(-7*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-12*x)*(4*x) + (-12*x)*(-33*x**3) - 40*(-33)*x**3 - 40*4*x + (4*x)*(-7*x**3) + (-33*x**3)*(-7*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*x)*(-33*x**3) = 396*x**4\n (-12*x)*(4*x) = -48*x**2\n (-7*x**3)*(-33*x**3) = 231*x**6\n (-7*x**3)*(4*x) = -28*x**4\n -40*-33*x**3 = 1320*x**3\n -40*4*x = -160*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 231*x**6 - 28*x**4 + 396*x**4 + 1320*x**3 - 48*x**2 - 160*x\nCombining like terms, got 231*x**6 + 368*x**4 + 1320*x**3 - 48*x**2 - 160*x\n#Step 6:\nCurrent expression: 231*x**6 + 368*x**4 + 1320*x**3 - 48*x**2 - 160*x\nNo more calculations needed.\n231*x**6 + 368*x**4 + 1320*x**3 - 48*x**2 - 160*x", "generated_answer": "231*x**6 + 368*x**4 + 1320*x**3 - 48*x**2 - 160*x", "step_length": 6} {"cot_id": "2223e4c03f7e9399b84663413e8ea63b196ea3091edbe8abc42f1581775ecf06", "datapoint": {"question": "Calculate the following: (29*z**2 + 50*z)*(-6*z**3 + 27*z**2 - 16*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-174*z**5 + 483*z**4 + 886*z**3 - 800*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1480, "polynomial_expr": "(29*z**2 + 50*z)*(-6*z**3 + 27*z**2 - 16*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29*z**2 + 50*z)*(-6*z**3 + 27*z**2 - 16*z)\nExpanding the part (29*z**2 + 50*z) using the distributive property, and we got: (50*z)*(-6*z**3 + 27*z**2 - 16*z) + (29*z**2)*(-6*z**3 + 27*z**2 - 16*z)\n#Step 2:\nCurrent expression: (50*z)*(-6*z**3 + 27*z**2 - 16*z) + (29*z**2)*(-6*z**3 + 27*z**2 - 16*z)\nSimplifying the partial expression: (29*z**2)*(-6*z**3 + 27*z**2 - 16*z)\nExpanding the part (-6*z**3 + 27*z**2 - 16*z) using the distributive property, and we got: (-16*z)*(29*z**2) + (27*z**2)*(29*z**2) + (29*z**2)*(-6*z**3)\nReplacing (29*z**2)*(-6*z**3 + 27*z**2 - 16*z) with (-16*z)*(29*z**2) + (27*z**2)*(29*z**2) + (29*z**2)*(-6*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-16*z)*(29*z**2) + (50*z)*(-6*z**3 + 27*z**2 - 16*z) + (27*z**2)*(29*z**2) + (29*z**2)*(-6*z**3)\nSimplifying the partial expression: (50*z)*(-6*z**3 + 27*z**2 - 16*z)\nExpanding the part (-6*z**3 + 27*z**2 - 16*z) using the distributive property, and we got: (-16*z)*(50*z) + (50*z)*(27*z**2) + (50*z)*(-6*z**3)\nReplacing (50*z)*(-6*z**3 + 27*z**2 - 16*z) with (-16*z)*(50*z) + (50*z)*(27*z**2) + (50*z)*(-6*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-16*z)*(50*z) + (-16*z)*(29*z**2) + (50*z)*(27*z**2) + (50*z)*(-6*z**3) + (27*z**2)*(29*z**2) + (29*z**2)*(-6*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-16*z)*(29*z**2) = -464*z**3\n (-16*z)*(50*z) = -800*z**2\n (-6*z**3)*(29*z**2) = -174*z**5\n (-6*z**3)*(50*z) = -300*z**4\n (27*z**2)*(29*z**2) = 783*z**4\n (27*z**2)*(50*z) = 1350*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -174*z**5 - 300*z**4 + 783*z**4 - 464*z**3 + 1350*z**3 - 800*z**2\nCombining like terms, got -174*z**5 + 483*z**4 + 886*z**3 - 800*z**2\n#Step 6:\nCurrent expression: -174*z**5 + 483*z**4 + 886*z**3 - 800*z**2\nNo more calculations needed.\n-174*z**5 + 483*z**4 + 886*z**3 - 800*z**2", "generated_answer": "-174*z**5 + 483*z**4 + 886*z**3 - 800*z**2", "step_length": 6} {"cot_id": "86cce983359fe90bc1a0174db1c95123fe732b88d27f2f2bfe88899517ea1bd2", "datapoint": {"question": "Calculate the following: (-56*x**3 + 31*x)*(-10*x**2 + 27*x + 2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "560*x**5 - 1512*x**4 - 422*x**3 + 837*x**2 + 62*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1481, "polynomial_expr": "(-56*x**3 + 31*x)*(-10*x**2 + 27*x + 2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-56*x**3 + 31*x)*(-10*x**2 + 27*x + 2)\nExpanding the part (-56*x**3 + 31*x) using the distributive property, and we got: (31*x)*(-10*x**2 + 27*x + 2) + (-56*x**3)*(-10*x**2 + 27*x + 2)\n#Step 2:\nCurrent expression: (31*x)*(-10*x**2 + 27*x + 2) + (-56*x**3)*(-10*x**2 + 27*x + 2)\nSimplifying the partial expression: (-56*x**3)*(-10*x**2 + 27*x + 2)\nExpanding the part (-10*x**2 + 27*x + 2) using the distributive property, and we got: 2*(-56*x**3) + (27*x)*(-56*x**3) + (-10*x**2)*(-56*x**3)\nReplacing (-56*x**3)*(-10*x**2 + 27*x + 2) with 2*(-56*x**3) + (27*x)*(-56*x**3) + (-10*x**2)*(-56*x**3) in the overall expression.\n#Step 3:\nCurrent expression: 2*(-56)*x**3 + (27*x)*(-56*x**3) + (31*x)*(-10*x**2 + 27*x + 2) + (-10*x**2)*(-56*x**3)\nSimplifying the partial expression: (31*x)*(-10*x**2 + 27*x + 2)\nExpanding the part (-10*x**2 + 27*x + 2) using the distributive property, and we got: 2*(31*x) + (27*x)*(31*x) + (31*x)*(-10*x**2)\nReplacing (31*x)*(-10*x**2 + 27*x + 2) with 2*(31*x) + (27*x)*(31*x) + (31*x)*(-10*x**2) in the overall expression.\n#Step 4:\nCurrent expression: 2*(-56)*x**3 + 2*31*x + (27*x)*(31*x) + (27*x)*(-56*x**3) + (31*x)*(-10*x**2) + (-10*x**2)*(-56*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*x**2)*(-56*x**3) = 560*x**5\n (-10*x**2)*(31*x) = -310*x**3\n (27*x)*(-56*x**3) = -1512*x**4\n (27*x)*(31*x) = 837*x**2\n 2*-56*x**3 = -112*x**3\n 2*31*x = 62*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 560*x**5 - 1512*x**4 - 310*x**3 - 112*x**3 + 837*x**2 + 62*x\nCombining like terms, got 560*x**5 - 1512*x**4 - 422*x**3 + 837*x**2 + 62*x\n#Step 6:\nCurrent expression: 560*x**5 - 1512*x**4 - 422*x**3 + 837*x**2 + 62*x\nNo more calculations needed.\n560*x**5 - 1512*x**4 - 422*x**3 + 837*x**2 + 62*x", "generated_answer": "560*x**5 - 1512*x**4 - 422*x**3 + 837*x**2 + 62*x", "step_length": 6} {"cot_id": "5cb101037668731cc1a66c927e4aaadf6afb54dc63b3e7ab0215cac8b9904816", "datapoint": {"question": "Simplify this expression: x*(-2*x - 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2*x**2 - 39*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1482, "polynomial_expr": "x*(-2*x - 39)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: x*(-2*x - 39)\nExpanding the part (-2*x - 39) using the distributive property, and we got: (-2*x)*x - 39*x\n#Step 2:\nCurrent expression: (-2*x)*x - 39*x\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-2*x)*x = -2*x**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -2*x**2 - 39*x\nNo more calculations needed.\n-2*x**2 - 39*x", "generated_answer": "-2*x**2 - 39*x", "step_length": 3} {"cot_id": "336df9a179fb0fae26858aee901fae79cfd2e218bfe22079248e9a1d62181d51", "datapoint": {"question": "Simplify this expression: (28*y**3 + 5)*(-19*y**3 + 42*y**2 + 45*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-532*y**6 + 1176*y**5 + 1260*y**4 - 95*y**3 + 210*y**2 + 225*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1483, "polynomial_expr": "(28*y**3 + 5)*(-19*y**3 + 42*y**2 + 45*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28*y**3 + 5)*(-19*y**3 + 42*y**2 + 45*y)\nExpanding the part (28*y**3 + 5) using the distributive property, and we got: (28*y**3)*(-19*y**3 + 42*y**2 + 45*y) + 5*(-19*y**3 + 42*y**2 + 45*y)\n#Step 2:\nCurrent expression: (28*y**3)*(-19*y**3 + 42*y**2 + 45*y) + 5*(-19*y**3 + 42*y**2 + 45*y)\nSimplifying the partial expression: 5*(-19*y**3 + 42*y**2 + 45*y)\nExpanding the part (-19*y**3 + 42*y**2 + 45*y) using the distributive property, and we got: (45*y)*5 + (42*y**2)*5 - 19*y**3*5\nReplacing 5*(-19*y**3 + 42*y**2 + 45*y) with (45*y)*5 + (42*y**2)*5 - 19*y**3*5 in the overall expression.\n#Step 3:\nCurrent expression: (45*y)*5 + (42*y**2)*5 - 19*y**3*5 + (28*y**3)*(-19*y**3 + 42*y**2 + 45*y)\nSimplifying the partial expression: (28*y**3)*(-19*y**3 + 42*y**2 + 45*y)\nExpanding the part (-19*y**3 + 42*y**2 + 45*y) using the distributive property, and we got: (45*y)*(28*y**3) + (42*y**2)*(28*y**3) + (-19*y**3)*(28*y**3)\nReplacing (28*y**3)*(-19*y**3 + 42*y**2 + 45*y) with (45*y)*(28*y**3) + (42*y**2)*(28*y**3) + (-19*y**3)*(28*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (45*y)*(28*y**3) + (45*y)*5 + (42*y**2)*(28*y**3) + (42*y**2)*5 + (-19*y**3)*(28*y**3) - 19*y**3*5\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*y**3)*5 = -95*y**3\n (-19*y**3)*(28*y**3) = -532*y**6\n (42*y**2)*5 = 210*y**2\n (42*y**2)*(28*y**3) = 1176*y**5\n (45*y)*5 = 225*y\n (45*y)*(28*y**3) = 1260*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -532*y**6 + 1176*y**5 + 1260*y**4 - 95*y**3 + 210*y**2 + 225*y\nNo more calculations needed.\n-532*y**6 + 1176*y**5 + 1260*y**4 - 95*y**3 + 210*y**2 + 225*y", "generated_answer": "-532*y**6 + 1176*y**5 + 1260*y**4 - 95*y**3 + 210*y**2 + 225*y", "step_length": 5} {"cot_id": "d49bb0f61b94bffa8afe4f1233b31fdfae29c05503bc9d8a955c47b157724e5e", "datapoint": {"question": "Calculate the following: (-16*z**2 + 12*z)*(26*z**3 + 29*z - 42)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-416*z**5 + 312*z**4 - 464*z**3 + 1020*z**2 - 504*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1484, "polynomial_expr": "(-16*z**2 + 12*z)*(26*z**3 + 29*z - 42)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-16*z**2 + 12*z)*(26*z**3 + 29*z - 42)\nExpanding the part (-16*z**2 + 12*z) using the distributive property, and we got: (12*z)*(26*z**3 + 29*z - 42) + (-16*z**2)*(26*z**3 + 29*z - 42)\n#Step 2:\nCurrent expression: (12*z)*(26*z**3 + 29*z - 42) + (-16*z**2)*(26*z**3 + 29*z - 42)\nSimplifying the partial expression: (-16*z**2)*(26*z**3 + 29*z - 42)\nExpanding the part (26*z**3 + 29*z - 42) using the distributive property, and we got: -(-1)*672*z**2 + (29*z)*(-16*z**2) + (-16*z**2)*(26*z**3)\nReplacing (-16*z**2)*(26*z**3 + 29*z - 42) with -(-1)*672*z**2 + (29*z)*(-16*z**2) + (-16*z**2)*(26*z**3) in the overall expression.\n#Step 3:\nCurrent expression: -42*(-16)*z**2 + (12*z)*(26*z**3 + 29*z - 42) + (29*z)*(-16*z**2) + (-16*z**2)*(26*z**3)\nSimplifying the partial expression: (12*z)*(26*z**3 + 29*z - 42)\nExpanding the part (26*z**3 + 29*z - 42) using the distributive property, and we got: -504*z + (12*z)*(29*z) + (12*z)*(26*z**3)\nReplacing (12*z)*(26*z**3 + 29*z - 42) with -504*z + (12*z)*(29*z) + (12*z)*(26*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -42*(-16)*z**2 - 42*12*z + (12*z)*(29*z) + (12*z)*(26*z**3) + (29*z)*(-16*z**2) + (-16*z**2)*(26*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (26*z**3)*(-16*z**2) = -416*z**5\n (26*z**3)*(12*z) = 312*z**4\n (29*z)*(-16*z**2) = -464*z**3\n (29*z)*(12*z) = 348*z**2\n -42*-16*z**2 = 672*z**2\n -42*12*z = -504*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -416*z**5 + 312*z**4 - 464*z**3 + 348*z**2 + 672*z**2 - 504*z\nCombining like terms, got -416*z**5 + 312*z**4 - 464*z**3 + 1020*z**2 - 504*z\n#Step 6:\nCurrent expression: -416*z**5 + 312*z**4 - 464*z**3 + 1020*z**2 - 504*z\nNo more calculations needed.\n-416*z**5 + 312*z**4 - 464*z**3 + 1020*z**2 - 504*z", "generated_answer": "-416*z**5 + 312*z**4 - 464*z**3 + 1020*z**2 - 504*z", "step_length": 6} {"cot_id": "b31303fc894c29e43a994710ced927ba1548f959530ec643523586f6761edfc3", "datapoint": {"question": "Calculate the following: (36*z + 1)*(24*z**3 + 45*z**2 + 17*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "864*z**4 + 1644*z**3 + 657*z**2 + 17*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1485, "polynomial_expr": "(36*z + 1)*(24*z**3 + 45*z**2 + 17*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (36*z + 1)*(24*z**3 + 45*z**2 + 17*z)\nExpanding the part (36*z + 1) using the distributive property, and we got: (36*z)*(24*z**3 + 45*z**2 + 17*z) + 1*(24*z**3 + 45*z**2 + 17*z)\n#Step 2:\nCurrent expression: (36*z)*(24*z**3 + 45*z**2 + 17*z) + 1*(24*z**3 + 45*z**2 + 17*z)\nSimplifying the partial expression: 1*(24*z**3 + 45*z**2 + 17*z)\nExpanding the part (24*z**3 + 45*z**2 + 17*z) using the distributive property, and we got: (17*z)*1 + (45*z**2)*1 + (24*z**3)*1\nReplacing 1*(24*z**3 + 45*z**2 + 17*z) with (17*z)*1 + (45*z**2)*1 + (24*z**3)*1 in the overall expression.\n#Step 3:\nCurrent expression: (17*z)*1 + (36*z)*(24*z**3 + 45*z**2 + 17*z) + (45*z**2)*1 + (24*z**3)*1\nSimplifying the partial expression: (36*z)*(24*z**3 + 45*z**2 + 17*z)\nExpanding the part (24*z**3 + 45*z**2 + 17*z) using the distributive property, and we got: (17*z)*(36*z) + (36*z)*(45*z**2) + (36*z)*(24*z**3)\nReplacing (36*z)*(24*z**3 + 45*z**2 + 17*z) with (17*z)*(36*z) + (36*z)*(45*z**2) + (36*z)*(24*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (17*z)*(36*z) + (17*z)*1 + (36*z)*(45*z**2) + (36*z)*(24*z**3) + (45*z**2)*1 + (24*z**3)*1\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (17*z)*1 = 17*z\n (17*z)*(36*z) = 612*z**2\n (24*z**3)*1 = 24*z**3\n (24*z**3)*(36*z) = 864*z**4\n (45*z**2)*1 = 45*z**2\n (45*z**2)*(36*z) = 1620*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 864*z**4 + 24*z**3 + 1620*z**3 + 45*z**2 + 612*z**2 + 17*z\nCombining like terms, got 864*z**4 + 1644*z**3 + 657*z**2 + 17*z\n#Step 6:\nCurrent expression: 864*z**4 + 1644*z**3 + 657*z**2 + 17*z\nNo more calculations needed.\n864*z**4 + 1644*z**3 + 657*z**2 + 17*z", "generated_answer": "864*z**4 + 1644*z**3 + 657*z**2 + 17*z", "step_length": 6} {"cot_id": "4e8f66847f1e82a7b7dcad1d520ee4b613d3a20d02437b44b1efb3e81c843dca", "datapoint": {"question": "Simplify this expression: (37*y - 34)*(-34*y**2 - 28*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1258*y**3 + 120*y**2 + 952*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1486, "polynomial_expr": "(37*y - 34)*(-34*y**2 - 28*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (37*y - 34)*(-34*y**2 - 28*y)\nExpanding the part (37*y - 34) using the distributive property, and we got: (37*y)*(-34*y**2 - 28*y) - 34*(-34*y**2 - 28*y)\n#Step 2:\nCurrent expression: (37*y)*(-34*y**2 - 28*y) - 34*(-34*y**2 - 28*y)\nSimplifying the partial expression: -34*(-34*y**2 - 28*y)\nExpanding the part (-34*y**2 - 28*y) using the distributive property, and we got: -28*y*(-34) - 34*y**2*(-34)\nReplacing -34*(-34*y**2 - 28*y) with -28*y*(-34) - 34*y**2*(-34) in the overall expression.\n#Step 3:\nCurrent expression: -28*y*(-34) + (37*y)*(-34*y**2 - 28*y) - 34*y**2*(-34)\nSimplifying the partial expression: (37*y)*(-34*y**2 - 28*y)\nExpanding the part (-34*y**2 - 28*y) using the distributive property, and we got: (-28*y)*(37*y) + (37*y)*(-34*y**2)\nReplacing (37*y)*(-34*y**2 - 28*y) with (-28*y)*(37*y) + (37*y)*(-34*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-28*y)*(37*y) - 28*y*(-34) + (37*y)*(-34*y**2) - 34*y**2*(-34)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*y**2)*-34 = 1156*y**2\n (-34*y**2)*(37*y) = -1258*y**3\n (-28*y)*-34 = 952*y\n (-28*y)*(37*y) = -1036*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1258*y**3 - 1036*y**2 + 1156*y**2 + 952*y\nCombining like terms, got -1258*y**3 + 120*y**2 + 952*y\n#Step 6:\nCurrent expression: -1258*y**3 + 120*y**2 + 952*y\nNo more calculations needed.\n-1258*y**3 + 120*y**2 + 952*y", "generated_answer": "-1258*y**3 + 120*y**2 + 952*y", "step_length": 6} {"cot_id": "ce2d7e9272a5223336d63355ef88e1ea6afd9ff560299b60a4a602f31ca5b3a2", "datapoint": {"question": "Calculate the following: -282*y**2 + 66*y\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-282*y**2 + 66*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1487, "polynomial_expr": "-282*y**2 + 66*y", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -282*y**2 + 66*y\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -282*y**2 + 66*y\nNo more calculations needed.\n-282*y**2 + 66*y", "generated_answer": "-282*y**2 + 66*y", "step_length": 2} {"cot_id": "f39d20532769aaeb6a98173a6f1edc8d442e4a7586968757dcbafb6624f49f92", "datapoint": {"question": "Calculate the following: (-31*x**3 - 22*x)*(23*x**3 - 30*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-713*x**6 + 424*x**4 + 660*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1488, "polynomial_expr": "(-31*x**3 - 22*x)*(23*x**3 - 30*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-31*x**3 - 22*x)*(23*x**3 - 30*x)\nExpanding the part (-31*x**3 - 22*x) using the distributive property, and we got: (-22*x)*(23*x**3 - 30*x) + (-31*x**3)*(23*x**3 - 30*x)\n#Step 2:\nCurrent expression: (-22*x)*(23*x**3 - 30*x) + (-31*x**3)*(23*x**3 - 30*x)\nSimplifying the partial expression: (-31*x**3)*(23*x**3 - 30*x)\nExpanding the part (23*x**3 - 30*x) using the distributive property, and we got: (-30*x)*(-31*x**3) + (-31*x**3)*(23*x**3)\nReplacing (-31*x**3)*(23*x**3 - 30*x) with (-30*x)*(-31*x**3) + (-31*x**3)*(23*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-30*x)*(-31*x**3) + (-22*x)*(23*x**3 - 30*x) + (-31*x**3)*(23*x**3)\nSimplifying the partial expression: (-22*x)*(23*x**3 - 30*x)\nExpanding the part (23*x**3 - 30*x) using the distributive property, and we got: (-30*x)*(-22*x) + (-22*x)*(23*x**3)\nReplacing (-22*x)*(23*x**3 - 30*x) with (-30*x)*(-22*x) + (-22*x)*(23*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-30*x)*(-22*x) + (-30*x)*(-31*x**3) + (-22*x)*(23*x**3) + (-31*x**3)*(23*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*x)*(-31*x**3) = 930*x**4\n (-30*x)*(-22*x) = 660*x**2\n (23*x**3)*(-31*x**3) = -713*x**6\n (23*x**3)*(-22*x) = -506*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -713*x**6 - 506*x**4 + 930*x**4 + 660*x**2\nCombining like terms, got -713*x**6 + 424*x**4 + 660*x**2\n#Step 6:\nCurrent expression: -713*x**6 + 424*x**4 + 660*x**2\nNo more calculations needed.\n-713*x**6 + 424*x**4 + 660*x**2", "generated_answer": "-713*x**6 + 424*x**4 + 660*x**2", "step_length": 6} {"cot_id": "7840e3be2f22e84fb8ec5572d84e47f377eb4c67df591fb9f3311fe77f534a6d", "datapoint": {"question": "Calculate the following: (48 - 26*z**3)*(37*z**3 + 29)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-962*z**6 + 1022*z**3 + 1392", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1489, "polynomial_expr": "(48 - 26*z**3)*(37*z**3 + 29)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (48 - 26*z**3)*(37*z**3 + 29)\nExpanding the part (37*z**3 + 29) using the distributive property, and we got: (37*z**3)*(48 - 26*z**3) + 29*(48 - 26*z**3)\n#Step 2:\nCurrent expression: (37*z**3)*(48 - 26*z**3) + 29*(48 - 26*z**3)\nSimplifying the partial expression: 29*(48 - 26*z**3)\nExpanding the part (48 - 26*z**3) using the distributive property, and we got: -26*z**3*29 + 48*29\nReplacing 29*(48 - 26*z**3) with -26*z**3*29 + 48*29 in the overall expression.\n#Step 3:\nCurrent expression: -26*z**3*29 + (37*z**3)*(48 - 26*z**3) + 1392\nSimplifying the partial expression: (37*z**3)*(48 - 26*z**3)\nExpanding the part (48 - 26*z**3) using the distributive property, and we got: 48*(37*z**3) + (-26*z**3)*(37*z**3)\nReplacing (37*z**3)*(48 - 26*z**3) with 48*(37*z**3) + (-26*z**3)*(37*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 48*37*z**3 + (-26*z**3)*(37*z**3) - 26*z**3*29 + 1392\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-26*z**3)*29 = -754*z**3\n (-26*z**3)*(37*z**3) = -962*z**6\n 48*37*z**3 = 1776*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -962*z**6 - 754*z**3 + 1776*z**3 + 1392\nCombining like terms, got -962*z**6 + 1022*z**3 + 1392\n#Step 6:\nCurrent expression: -962*z**6 + 1022*z**3 + 1392\nNo more calculations needed.\n-962*z**6 + 1022*z**3 + 1392", "generated_answer": "-962*z**6 + 1022*z**3 + 1392", "step_length": 6} {"cot_id": "ae219a30089f9887dd06fe99030af99270883852c5e2e7a2c8c3bb34eed8fd37", "datapoint": {"question": "Calculate the following: (-5*x**3 + 7*x**2)*(27*x**3 - 7*x**2 + 35*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-135*x**6 + 224*x**5 - 224*x**4 + 245*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1490, "polynomial_expr": "(-5*x**3 + 7*x**2)*(27*x**3 - 7*x**2 + 35*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-5*x**3 + 7*x**2)*(27*x**3 - 7*x**2 + 35*x)\nExpanding the part (-5*x**3 + 7*x**2) using the distributive property, and we got: (7*x**2)*(27*x**3 - 7*x**2 + 35*x) + (-5*x**3)*(27*x**3 - 7*x**2 + 35*x)\n#Step 2:\nCurrent expression: (7*x**2)*(27*x**3 - 7*x**2 + 35*x) + (-5*x**3)*(27*x**3 - 7*x**2 + 35*x)\nSimplifying the partial expression: (-5*x**3)*(27*x**3 - 7*x**2 + 35*x)\nExpanding the part (27*x**3 - 7*x**2 + 35*x) using the distributive property, and we got: (35*x)*(-5*x**3) + (-7*x**2)*(-5*x**3) + (-5*x**3)*(27*x**3)\nReplacing (-5*x**3)*(27*x**3 - 7*x**2 + 35*x) with (35*x)*(-5*x**3) + (-7*x**2)*(-5*x**3) + (-5*x**3)*(27*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (35*x)*(-5*x**3) + (-7*x**2)*(-5*x**3) + (7*x**2)*(27*x**3 - 7*x**2 + 35*x) + (-5*x**3)*(27*x**3)\nSimplifying the partial expression: (7*x**2)*(27*x**3 - 7*x**2 + 35*x)\nExpanding the part (27*x**3 - 7*x**2 + 35*x) using the distributive property, and we got: (35*x)*(7*x**2) + (-7*x**2)*(7*x**2) + (7*x**2)*(27*x**3)\nReplacing (7*x**2)*(27*x**3 - 7*x**2 + 35*x) with (35*x)*(7*x**2) + (-7*x**2)*(7*x**2) + (7*x**2)*(27*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (35*x)*(7*x**2) + (35*x)*(-5*x**3) + (-7*x**2)*(7*x**2) + (-7*x**2)*(-5*x**3) + (7*x**2)*(27*x**3) + (-5*x**3)*(27*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-7*x**2)*(-5*x**3) = 35*x**5\n (-7*x**2)*(7*x**2) = -49*x**4\n (27*x**3)*(-5*x**3) = -135*x**6\n (27*x**3)*(7*x**2) = 189*x**5\n (35*x)*(-5*x**3) = -175*x**4\n (35*x)*(7*x**2) = 245*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -135*x**6 + 35*x**5 + 189*x**5 - 175*x**4 - 49*x**4 + 245*x**3\nCombining like terms, got -135*x**6 + 224*x**5 - 224*x**4 + 245*x**3\n#Step 6:\nCurrent expression: -135*x**6 + 224*x**5 - 224*x**4 + 245*x**3\nNo more calculations needed.\n-135*x**6 + 224*x**5 - 224*x**4 + 245*x**3", "generated_answer": "-135*x**6 + 224*x**5 - 224*x**4 + 245*x**3", "step_length": 6} {"cot_id": "b20f25817f468cbc150644923ec9d90abd8aaa3c2c0d19f0236ef3415bfa827f", "datapoint": {"question": "Simplify this expression: (-12*z**3 + 8*z**2)*(10*z**3 - 15)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-120*z**6 + 80*z**5 + 180*z**3 - 120*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1491, "polynomial_expr": "(-12*z**3 + 8*z**2)*(10*z**3 - 15)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-12*z**3 + 8*z**2)*(10*z**3 - 15)\nExpanding the part (10*z**3 - 15) using the distributive property, and we got: (10*z**3)*(-12*z**3 + 8*z**2) - 15*(-12*z**3 + 8*z**2)\n#Step 2:\nCurrent expression: (10*z**3)*(-12*z**3 + 8*z**2) - 15*(-12*z**3 + 8*z**2)\nSimplifying the partial expression: -15*(-12*z**3 + 8*z**2)\nExpanding the part (-12*z**3 + 8*z**2) using the distributive property, and we got: (8*z**2)*(-15) - 12*z**3*(-15)\nReplacing -15*(-12*z**3 + 8*z**2) with (8*z**2)*(-15) - 12*z**3*(-15) in the overall expression.\n#Step 3:\nCurrent expression: (8*z**2)*(-15) - 12*z**3*(-15) + (10*z**3)*(-12*z**3 + 8*z**2)\nSimplifying the partial expression: (10*z**3)*(-12*z**3 + 8*z**2)\nExpanding the part (-12*z**3 + 8*z**2) using the distributive property, and we got: (8*z**2)*(10*z**3) + (-12*z**3)*(10*z**3)\nReplacing (10*z**3)*(-12*z**3 + 8*z**2) with (8*z**2)*(10*z**3) + (-12*z**3)*(10*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (8*z**2)*(10*z**3) + (8*z**2)*(-15) + (-12*z**3)*(10*z**3) - 12*z**3*(-15)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*z**3)*-15 = 180*z**3\n (-12*z**3)*(10*z**3) = -120*z**6\n (8*z**2)*-15 = -120*z**2\n (8*z**2)*(10*z**3) = 80*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -120*z**6 + 80*z**5 + 180*z**3 - 120*z**2\nNo more calculations needed.\n-120*z**6 + 80*z**5 + 180*z**3 - 120*z**2", "generated_answer": "-120*z**6 + 80*z**5 + 180*z**3 - 120*z**2", "step_length": 5} {"cot_id": "1f3bfa570bb8e29e8b3d4dd2ad95487b628ef44e64b17bc1b1bda407b6cb085b", "datapoint": {"question": "Calculate the following: -248*y**3 + 651*y**2 + 775*y\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-248*y**3 + 651*y**2 + 775*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1492, "polynomial_expr": "-248*y**3 + 651*y**2 + 775*y", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -248*y**3 + 651*y**2 + 775*y\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -248*y**3 + 651*y**2 + 775*y\nNo more calculations needed.\n-248*y**3 + 651*y**2 + 775*y", "generated_answer": "-248*y**3 + 651*y**2 + 775*y", "step_length": 2} {"cot_id": "409dffceec2eb56ae6c1e7b0d24c71d3652a2664cd357860fd7a663cce1d9eec", "datapoint": {"question": "Simplify this expression: 13*y*(42*y**3 + 22*y**2 - 23)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "546*y**4 + 286*y**3 - 299*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1493, "polynomial_expr": "13*y*(42*y**3 + 22*y**2 - 23)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 13*y*(42*y**3 + 22*y**2 - 23)\nExpanding the part (42*y**3 + 22*y**2 - 23) using the distributive property, and we got: -299*y + (13*y)*(22*y**2) + (13*y)*(42*y**3)\n#Step 2:\nCurrent expression: -299*y + (13*y)*(22*y**2) + (13*y)*(42*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -23*(13*y) = -299*y\n (22*y**2)*(13*y) = 286*y**3\n (42*y**3)*(13*y) = 546*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 546*y**4 + 286*y**3 - 299*y\nNo more calculations needed.\n546*y**4 + 286*y**3 - 299*y", "generated_answer": "546*y**4 + 286*y**3 - 299*y", "step_length": 3} {"cot_id": "30edaadebf717326b80466719ead8e582a8b6b9ea5da271ecf711bb897c652d7", "datapoint": {"question": "Simplify this expression: (48*x**2 + 6*x + 48)*(-36*x**3 + 17*x**2 - 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1728*x**5 + 600*x**4 - 1626*x**3 + 336*x**2 - 60*x - 480", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1494, "polynomial_expr": "(48*x**2 + 6*x + 48)*(-36*x**3 + 17*x**2 - 10)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (48*x**2 + 6*x + 48)*(-36*x**3 + 17*x**2 - 10)\nExpanding the part (-36*x**3 + 17*x**2 - 10) using the distributive property, and we got: (17*x**2)*(48*x**2 + 6*x + 48) + (-36*x**3)*(48*x**2 + 6*x + 48) - 10*(48*x**2 + 6*x + 48)\n#Step 2:\nCurrent expression: (17*x**2)*(48*x**2 + 6*x + 48) + (-36*x**3)*(48*x**2 + 6*x + 48) - 10*(48*x**2 + 6*x + 48)\nSimplifying the partial expression: -10*(48*x**2 + 6*x + 48)\nExpanding the part (48*x**2 + 6*x + 48) using the distributive property, and we got: (6*x)*(-10) + (48*x**2)*(-10) + 48*(-10)\nReplacing -10*(48*x**2 + 6*x + 48) with (6*x)*(-10) + (48*x**2)*(-10) + 48*(-10) in the overall expression.\n#Step 3:\nCurrent expression: (6*x)*(-10) + (17*x**2)*(48*x**2 + 6*x + 48) + (48*x**2)*(-10) + (-36*x**3)*(48*x**2 + 6*x + 48) - 480\nSimplifying the partial expression: (-36*x**3)*(48*x**2 + 6*x + 48)\nExpanding the part (48*x**2 + 6*x + 48) using the distributive property, and we got: 48*(-36*x**3) + (6*x)*(-36*x**3) + (48*x**2)*(-36*x**3)\nReplacing (-36*x**3)*(48*x**2 + 6*x + 48) with 48*(-36*x**3) + (6*x)*(-36*x**3) + (48*x**2)*(-36*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 48*(-36)*x**3 + (6*x)*(-36*x**3) + (6*x)*(-10) + (17*x**2)*(48*x**2 + 6*x + 48) + (48*x**2)*(-36*x**3) + (48*x**2)*(-10) - 480\nSimplifying the partial expression: (17*x**2)*(48*x**2 + 6*x + 48)\nExpanding the part (48*x**2 + 6*x + 48) using the distributive property, and we got: 48*(17*x**2) + (6*x)*(17*x**2) + (17*x**2)*(48*x**2)\nReplacing (17*x**2)*(48*x**2 + 6*x + 48) with 48*(17*x**2) + (6*x)*(17*x**2) + (17*x**2)*(48*x**2) in the overall expression.\n#Step 5:\nCurrent expression: 48*(-36)*x**3 + 48*17*x**2 + (6*x)*(17*x**2) + (6*x)*(-36*x**3) + (6*x)*(-10) + (17*x**2)*(48*x**2) + (48*x**2)*(-36*x**3) + (48*x**2)*(-10) - 480\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (6*x)*-10 = -60*x\n (6*x)*(-36*x**3) = -216*x**4\n (6*x)*(17*x**2) = 102*x**3\n (48*x**2)*-10 = -480*x**2\n (48*x**2)*(-36*x**3) = -1728*x**5\n (48*x**2)*(17*x**2) = 816*x**4\n 48*-36*x**3 = -1728*x**3\n 48*17*x**2 = 816*x**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1728*x**5 - 216*x**4 + 816*x**4 - 1728*x**3 + 102*x**3 - 480*x**2 + 816*x**2 - 60*x - 480\nCombining like terms, got -1728*x**5 + 600*x**4 - 1626*x**3 + 336*x**2 - 60*x - 480\n#Step 7:\nCurrent expression: -1728*x**5 + 600*x**4 - 1626*x**3 + 336*x**2 - 60*x - 480\nNo more calculations needed.\n-1728*x**5 + 600*x**4 - 1626*x**3 + 336*x**2 - 60*x - 480", "generated_answer": "-1728*x**5 + 600*x**4 - 1626*x**3 + 336*x**2 - 60*x - 480", "step_length": 7} {"cot_id": "fdbbac1d743ad1428535b08a4ac49868cd7cf6a8203dd2eb6e71112627116c30", "datapoint": {"question": "Simplify this expression: (33*y + 38)*(31*y**2 - y - 9)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1023*y**3 + 1145*y**2 - 335*y - 342", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1495, "polynomial_expr": "(33*y + 38)*(31*y**2 - y - 9)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (33*y + 38)*(31*y**2 - y - 9)\nExpanding the part (33*y + 38) using the distributive property, and we got: (33*y)*(31*y**2 - y - 9) + 38*(31*y**2 - y - 9)\n#Step 2:\nCurrent expression: (33*y)*(31*y**2 - y - 9) + 38*(31*y**2 - y - 9)\nSimplifying the partial expression: 38*(31*y**2 - y - 9)\nExpanding the part (31*y**2 - y - 9) using the distributive property, and we got: -y*38 + (31*y**2)*38 - 9*38\nReplacing 38*(31*y**2 - y - 9) with -y*38 + (31*y**2)*38 - 9*38 in the overall expression.\n#Step 3:\nCurrent expression: -y*38 + (33*y)*(31*y**2 - y - 9) + (31*y**2)*38 - 342\nSimplifying the partial expression: (33*y)*(31*y**2 - y - 9)\nExpanding the part (31*y**2 - y - 9) using the distributive property, and we got: (-y)*(33*y) - 297*y + (33*y)*(31*y**2)\nReplacing (33*y)*(31*y**2 - y - 9) with (-y)*(33*y) - 297*y + (33*y)*(31*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-y)*(33*y) - y*38 - 9*33*y + (33*y)*(31*y**2) + (31*y**2)*38 - 342\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-y)*38 = -38*y\n (-y)*(33*y) = -33*y**2\n (31*y**2)*38 = 1178*y**2\n (31*y**2)*(33*y) = 1023*y**3\n -9*33*y = -297*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1023*y**3 - 33*y**2 + 1178*y**2 - 297*y - 38*y - 342\nCombining like terms, got 1023*y**3 + 1145*y**2 - 335*y - 342\n#Step 6:\nCurrent expression: 1023*y**3 + 1145*y**2 - 335*y - 342\nNo more calculations needed.\n1023*y**3 + 1145*y**2 - 335*y - 342", "generated_answer": "1023*y**3 + 1145*y**2 - 335*y - 342", "step_length": 6} {"cot_id": "7d9bb386ad11c487933613a267dd1699e47154e6277b0c3638a69829b1047c21", "datapoint": {"question": "Calculate the following: (13 - 29*y**3)*(4*y + 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-116*y**4 - 174*y**3 + 52*y + 78", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1496, "polynomial_expr": "(13 - 29*y**3)*(4*y + 6)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (13 - 29*y**3)*(4*y + 6)\nExpanding the part (4*y + 6) using the distributive property, and we got: (4*y)*(13 - 29*y**3) + 6*(13 - 29*y**3)\n#Step 2:\nCurrent expression: (4*y)*(13 - 29*y**3) + 6*(13 - 29*y**3)\nSimplifying the partial expression: 6*(13 - 29*y**3)\nExpanding the part (13 - 29*y**3) using the distributive property, and we got: -29*y**3*6 + 13*6\nReplacing 6*(13 - 29*y**3) with -29*y**3*6 + 13*6 in the overall expression.\n#Step 3:\nCurrent expression: (4*y)*(13 - 29*y**3) - 29*y**3*6 + 78\nSimplifying the partial expression: (4*y)*(13 - 29*y**3)\nExpanding the part (13 - 29*y**3) using the distributive property, and we got: 13*(4*y) + (4*y)*(-29*y**3)\nReplacing (4*y)*(13 - 29*y**3) with 13*(4*y) + (4*y)*(-29*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 13*4*y + (4*y)*(-29*y**3) - 29*y**3*6 + 78\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*y**3)*6 = -174*y**3\n (-29*y**3)*(4*y) = -116*y**4\n 13*4*y = 52*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -116*y**4 - 174*y**3 + 52*y + 78\nNo more calculations needed.\n-116*y**4 - 174*y**3 + 52*y + 78", "generated_answer": "-116*y**4 - 174*y**3 + 52*y + 78", "step_length": 5} {"cot_id": "9237c1fbbf4ddd187fb47971a8e5efad432ce2f17a39b789dabfce13d714bc40", "datapoint": {"question": "Simplify this expression: (30*x**3 - 47*x**2)*(50*x**3 + 3*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1500*x**6 - 2350*x**5 + 90*x**4 - 141*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1497, "polynomial_expr": "(30*x**3 - 47*x**2)*(50*x**3 + 3*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (30*x**3 - 47*x**2)*(50*x**3 + 3*x)\nExpanding the part (30*x**3 - 47*x**2) using the distributive property, and we got: (-47*x**2)*(50*x**3 + 3*x) + (30*x**3)*(50*x**3 + 3*x)\n#Step 2:\nCurrent expression: (-47*x**2)*(50*x**3 + 3*x) + (30*x**3)*(50*x**3 + 3*x)\nSimplifying the partial expression: (-47*x**2)*(50*x**3 + 3*x)\nExpanding the part (50*x**3 + 3*x) using the distributive property, and we got: (3*x)*(-47*x**2) + (-47*x**2)*(50*x**3)\nReplacing (-47*x**2)*(50*x**3 + 3*x) with (3*x)*(-47*x**2) + (-47*x**2)*(50*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (3*x)*(-47*x**2) + (-47*x**2)*(50*x**3) + (30*x**3)*(50*x**3 + 3*x)\nSimplifying the partial expression: (30*x**3)*(50*x**3 + 3*x)\nExpanding the part (50*x**3 + 3*x) using the distributive property, and we got: (3*x)*(30*x**3) + (30*x**3)*(50*x**3)\nReplacing (30*x**3)*(50*x**3 + 3*x) with (3*x)*(30*x**3) + (30*x**3)*(50*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (3*x)*(-47*x**2) + (3*x)*(30*x**3) + (-47*x**2)*(50*x**3) + (30*x**3)*(50*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (3*x)*(-47*x**2) = -141*x**3\n (3*x)*(30*x**3) = 90*x**4\n (50*x**3)*(-47*x**2) = -2350*x**5\n (50*x**3)*(30*x**3) = 1500*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1500*x**6 - 2350*x**5 + 90*x**4 - 141*x**3\nNo more calculations needed.\n1500*x**6 - 2350*x**5 + 90*x**4 - 141*x**3", "generated_answer": "1500*x**6 - 2350*x**5 + 90*x**4 - 141*x**3", "step_length": 5} {"cot_id": "17f5b41d513742e4868ac22369aaceedab62acb96e73f2aad2f47c9f595a4e89", "datapoint": {"question": "Calculate the following: (13 - 60*x)*(-33*x**2 - 27)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1980*x**3 - 429*x**2 + 1620*x - 351", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1498, "polynomial_expr": "(13 - 60*x)*(-33*x**2 - 27)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (13 - 60*x)*(-33*x**2 - 27)\nExpanding the part (-33*x**2 - 27) using the distributive property, and we got: (-33*x**2)*(13 - 60*x) - 27*(13 - 60*x)\n#Step 2:\nCurrent expression: (-33*x**2)*(13 - 60*x) - 27*(13 - 60*x)\nSimplifying the partial expression: -27*(13 - 60*x)\nExpanding the part (13 - 60*x) using the distributive property, and we got: -60*x*(-27) + 13*(-27)\nReplacing -27*(13 - 60*x) with -60*x*(-27) + 13*(-27) in the overall expression.\n#Step 3:\nCurrent expression: -60*x*(-27) + (-33*x**2)*(13 - 60*x) - 351\nSimplifying the partial expression: (-33*x**2)*(13 - 60*x)\nExpanding the part (13 - 60*x) using the distributive property, and we got: (-60*x)*(-33*x**2) + 13*(-33*x**2)\nReplacing (-33*x**2)*(13 - 60*x) with (-60*x)*(-33*x**2) + 13*(-33*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-60*x)*(-33*x**2) - 60*x*(-27) + 13*(-33)*x**2 - 351\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-60*x)*-27 = 1620*x\n (-60*x)*(-33*x**2) = 1980*x**3\n 13*-33*x**2 = -429*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1980*x**3 - 429*x**2 + 1620*x - 351\nNo more calculations needed.\n1980*x**3 - 429*x**2 + 1620*x - 351", "generated_answer": "1980*x**3 - 429*x**2 + 1620*x - 351", "step_length": 5} {"cot_id": "cd02004bc463ab0095993c2259708aaf18a53df6baa4f1d1c70b845a40e757e1", "datapoint": {"question": "Simplify this expression: (9 - y)*(12*y**3 - 59)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-12*y**4 + 108*y**3 + 59*y - 531", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1499, "polynomial_expr": "(9 - y)*(12*y**3 - 59)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9 - y)*(12*y**3 - 59)\nExpanding the part (12*y**3 - 59) using the distributive property, and we got: (12*y**3)*(9 - y) - 59*(9 - y)\n#Step 2:\nCurrent expression: (12*y**3)*(9 - y) - 59*(9 - y)\nSimplifying the partial expression: -59*(9 - y)\nExpanding the part (9 - y) using the distributive property, and we got: -y*(-59) + 9*(-59)\nReplacing -59*(9 - y) with -y*(-59) + 9*(-59) in the overall expression.\n#Step 3:\nCurrent expression: -y*(-59) + (12*y**3)*(9 - y) - 531\nSimplifying the partial expression: (12*y**3)*(9 - y)\nExpanding the part (9 - y) using the distributive property, and we got: (-y)*(12*y**3) + 9*(12*y**3)\nReplacing (12*y**3)*(9 - y) with (-y)*(12*y**3) + 9*(12*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-y)*(12*y**3) - y*(-59) + 9*12*y**3 - 531\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-y)*-59 = 59*y\n (-y)*(12*y**3) = -12*y**4\n 9*12*y**3 = 108*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -12*y**4 + 108*y**3 + 59*y - 531\nNo more calculations needed.\n-12*y**4 + 108*y**3 + 59*y - 531", "generated_answer": "-12*y**4 + 108*y**3 + 59*y - 531", "step_length": 5} {"cot_id": "d54cedbd7d8c1d93938c09cc61326a1d7a1d8aee2e72dd7706379b97ef5c5032", "datapoint": {"question": "Calculate the following: (16 - 56*y**3)*(37*y**3 - 21*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2072*y**6 + 1176*y**4 + 592*y**3 - 336*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1500, "polynomial_expr": "(16 - 56*y**3)*(37*y**3 - 21*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (16 - 56*y**3)*(37*y**3 - 21*y)\nExpanding the part (16 - 56*y**3) using the distributive property, and we got: (-56*y**3)*(37*y**3 - 21*y) + 16*(37*y**3 - 21*y)\n#Step 2:\nCurrent expression: (-56*y**3)*(37*y**3 - 21*y) + 16*(37*y**3 - 21*y)\nSimplifying the partial expression: 16*(37*y**3 - 21*y)\nExpanding the part (37*y**3 - 21*y) using the distributive property, and we got: -21*y*16 + (37*y**3)*16\nReplacing 16*(37*y**3 - 21*y) with -21*y*16 + (37*y**3)*16 in the overall expression.\n#Step 3:\nCurrent expression: -21*y*16 + (-56*y**3)*(37*y**3 - 21*y) + (37*y**3)*16\nSimplifying the partial expression: (-56*y**3)*(37*y**3 - 21*y)\nExpanding the part (37*y**3 - 21*y) using the distributive property, and we got: (-21*y)*(-56*y**3) + (-56*y**3)*(37*y**3)\nReplacing (-56*y**3)*(37*y**3 - 21*y) with (-21*y)*(-56*y**3) + (-56*y**3)*(37*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-21*y)*(-56*y**3) - 21*y*16 + (-56*y**3)*(37*y**3) + (37*y**3)*16\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-21*y)*16 = -336*y\n (-21*y)*(-56*y**3) = 1176*y**4\n (37*y**3)*16 = 592*y**3\n (37*y**3)*(-56*y**3) = -2072*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2072*y**6 + 1176*y**4 + 592*y**3 - 336*y\nNo more calculations needed.\n-2072*y**6 + 1176*y**4 + 592*y**3 - 336*y", "generated_answer": "-2072*y**6 + 1176*y**4 + 592*y**3 - 336*y", "step_length": 5} {"cot_id": "94c8fd690bbb05ede188339c6ca10a3f744e7e86d3472e3a5c4421433fc585b3", "datapoint": {"question": "Calculate the following: 3*x*(3*x**3 - 31*x - 4)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "9*x**4 - 93*x**2 - 12*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1501, "polynomial_expr": "3*x*(3*x**3 - 31*x - 4)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 3*x*(3*x**3 - 31*x - 4)\nExpanding the part (3*x**3 - 31*x - 4) using the distributive property, and we got: (-31*x)*(3*x) - 12*x + (3*x)*(3*x**3)\n#Step 2:\nCurrent expression: (-31*x)*(3*x) - 12*x + (3*x)*(3*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -4*(3*x) = -12*x\n (-31*x)*(3*x) = -93*x**2\n (3*x**3)*(3*x) = 9*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 9*x**4 - 93*x**2 - 12*x\nNo more calculations needed.\n9*x**4 - 93*x**2 - 12*x", "generated_answer": "9*x**4 - 93*x**2 - 12*x", "step_length": 3} {"cot_id": "a90811857f185a1bc1fac0c976425b7177d1b6349cd1df389769cb1e40979a27", "datapoint": {"question": "Calculate the following: (-42*x - 16)*(8*x**2 - 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-336*x**3 - 128*x**2 + 1008*x + 384", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1502, "polynomial_expr": "(-42*x - 16)*(8*x**2 - 24)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-42*x - 16)*(8*x**2 - 24)\nExpanding the part (8*x**2 - 24) using the distributive property, and we got: (8*x**2)*(-42*x - 16) - 24*(-42*x - 16)\n#Step 2:\nCurrent expression: (8*x**2)*(-42*x - 16) - 24*(-42*x - 16)\nSimplifying the partial expression: -24*(-42*x - 16)\nExpanding the part (-42*x - 16) using the distributive property, and we got: -42*x*(-24) - 16*(-24)\nReplacing -24*(-42*x - 16) with -42*x*(-24) - 16*(-24) in the overall expression.\n#Step 3:\nCurrent expression: -42*x*(-24) + (8*x**2)*(-42*x - 16) + 384\nSimplifying the partial expression: (8*x**2)*(-42*x - 16)\nExpanding the part (-42*x - 16) using the distributive property, and we got: (-42*x)*(8*x**2) - 128*x**2\nReplacing (8*x**2)*(-42*x - 16) with (-42*x)*(8*x**2) - 128*x**2 in the overall expression.\n#Step 4:\nCurrent expression: (-42*x)*(8*x**2) - 42*x*(-24) - 16*8*x**2 + 384\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*x)*-24 = 1008*x\n (-42*x)*(8*x**2) = -336*x**3\n -16*8*x**2 = -128*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -336*x**3 - 128*x**2 + 1008*x + 384\nNo more calculations needed.\n-336*x**3 - 128*x**2 + 1008*x + 384", "generated_answer": "-336*x**3 - 128*x**2 + 1008*x + 384", "step_length": 5} {"cot_id": "9fed566494feb309a10f49ef3862d8f8ce245e90e01688d183562e3e59bbdc50", "datapoint": {"question": "Calculate the following: (-20*x - 39)*(-29*x**3 - 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "580*x**4 + 1131*x**3 + 200*x + 390", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1503, "polynomial_expr": "(-20*x - 39)*(-29*x**3 - 10)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-20*x - 39)*(-29*x**3 - 10)\nExpanding the part (-20*x - 39) using the distributive property, and we got: (-20*x)*(-29*x**3 - 10) - 39*(-29*x**3 - 10)\n#Step 2:\nCurrent expression: (-20*x)*(-29*x**3 - 10) - 39*(-29*x**3 - 10)\nSimplifying the partial expression: -39*(-29*x**3 - 10)\nExpanding the part (-29*x**3 - 10) using the distributive property, and we got: -29*x**3*(-39) - 10*(-39)\nReplacing -39*(-29*x**3 - 10) with -29*x**3*(-39) - 10*(-39) in the overall expression.\n#Step 3:\nCurrent expression: (-20*x)*(-29*x**3 - 10) - 29*x**3*(-39) + 390\nSimplifying the partial expression: (-20*x)*(-29*x**3 - 10)\nExpanding the part (-29*x**3 - 10) using the distributive property, and we got: (-20*x)*(-29*x**3) - (-1)*200*x\nReplacing (-20*x)*(-29*x**3 - 10) with (-20*x)*(-29*x**3) - (-1)*200*x in the overall expression.\n#Step 4:\nCurrent expression: (-20*x)*(-29*x**3) - 10*(-20)*x - 29*x**3*(-39) + 390\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*x**3)*-39 = 1131*x**3\n (-29*x**3)*(-20*x) = 580*x**4\n -10*-20*x = 200*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 580*x**4 + 1131*x**3 + 200*x + 390\nNo more calculations needed.\n580*x**4 + 1131*x**3 + 200*x + 390", "generated_answer": "580*x**4 + 1131*x**3 + 200*x + 390", "step_length": 5} {"cot_id": "ea49e81d6864ff99d43c12b708ebd8a48cb96fbdd6f53b6fc9abe3388788034b", "datapoint": {"question": "Calculate the following: (28*x**3 + 2)*(26*x**3 + 14*x**2 + 4*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "728*x**6 + 392*x**5 + 112*x**4 + 52*x**3 + 28*x**2 + 8*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1504, "polynomial_expr": "(28*x**3 + 2)*(26*x**3 + 14*x**2 + 4*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28*x**3 + 2)*(26*x**3 + 14*x**2 + 4*x)\nExpanding the part (28*x**3 + 2) using the distributive property, and we got: (28*x**3)*(26*x**3 + 14*x**2 + 4*x) + 2*(26*x**3 + 14*x**2 + 4*x)\n#Step 2:\nCurrent expression: (28*x**3)*(26*x**3 + 14*x**2 + 4*x) + 2*(26*x**3 + 14*x**2 + 4*x)\nSimplifying the partial expression: 2*(26*x**3 + 14*x**2 + 4*x)\nExpanding the part (26*x**3 + 14*x**2 + 4*x) using the distributive property, and we got: (4*x)*2 + (14*x**2)*2 + (26*x**3)*2\nReplacing 2*(26*x**3 + 14*x**2 + 4*x) with (4*x)*2 + (14*x**2)*2 + (26*x**3)*2 in the overall expression.\n#Step 3:\nCurrent expression: (4*x)*2 + (14*x**2)*2 + (26*x**3)*2 + (28*x**3)*(26*x**3 + 14*x**2 + 4*x)\nSimplifying the partial expression: (28*x**3)*(26*x**3 + 14*x**2 + 4*x)\nExpanding the part (26*x**3 + 14*x**2 + 4*x) using the distributive property, and we got: (4*x)*(28*x**3) + (14*x**2)*(28*x**3) + (26*x**3)*(28*x**3)\nReplacing (28*x**3)*(26*x**3 + 14*x**2 + 4*x) with (4*x)*(28*x**3) + (14*x**2)*(28*x**3) + (26*x**3)*(28*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (4*x)*(28*x**3) + (4*x)*2 + (14*x**2)*(28*x**3) + (14*x**2)*2 + (26*x**3)*(28*x**3) + (26*x**3)*2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (4*x)*2 = 8*x\n (4*x)*(28*x**3) = 112*x**4\n (14*x**2)*2 = 28*x**2\n (14*x**2)*(28*x**3) = 392*x**5\n (26*x**3)*2 = 52*x**3\n (26*x**3)*(28*x**3) = 728*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 728*x**6 + 392*x**5 + 112*x**4 + 52*x**3 + 28*x**2 + 8*x\nNo more calculations needed.\n728*x**6 + 392*x**5 + 112*x**4 + 52*x**3 + 28*x**2 + 8*x", "generated_answer": "728*x**6 + 392*x**5 + 112*x**4 + 52*x**3 + 28*x**2 + 8*x", "step_length": 5} {"cot_id": "aa4c98f6948e59feb3769c18055fe7d7d58548f1570aafd91823fd2b3c1f7b7c", "datapoint": {"question": "Calculate the following: (28*x**2 - 4)*(-34*x**3 + 13*x**2 + 2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-952*x**5 + 364*x**4 + 136*x**3 + 4*x**2 - 8", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1505, "polynomial_expr": "(28*x**2 - 4)*(-34*x**3 + 13*x**2 + 2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28*x**2 - 4)*(-34*x**3 + 13*x**2 + 2)\nExpanding the part (28*x**2 - 4) using the distributive property, and we got: (28*x**2)*(-34*x**3 + 13*x**2 + 2) - 4*(-34*x**3 + 13*x**2 + 2)\n#Step 2:\nCurrent expression: (28*x**2)*(-34*x**3 + 13*x**2 + 2) - 4*(-34*x**3 + 13*x**2 + 2)\nSimplifying the partial expression: -4*(-34*x**3 + 13*x**2 + 2)\nExpanding the part (-34*x**3 + 13*x**2 + 2) using the distributive property, and we got: (13*x**2)*(-4) - 34*x**3*(-4) + 2*(-4)\nReplacing -4*(-34*x**3 + 13*x**2 + 2) with (13*x**2)*(-4) - 34*x**3*(-4) + 2*(-4) in the overall expression.\n#Step 3:\nCurrent expression: (13*x**2)*(-4) + (28*x**2)*(-34*x**3 + 13*x**2 + 2) - 34*x**3*(-4) - 8\nSimplifying the partial expression: (28*x**2)*(-34*x**3 + 13*x**2 + 2)\nExpanding the part (-34*x**3 + 13*x**2 + 2) using the distributive property, and we got: 2*(28*x**2) + (13*x**2)*(28*x**2) + (28*x**2)*(-34*x**3)\nReplacing (28*x**2)*(-34*x**3 + 13*x**2 + 2) with 2*(28*x**2) + (13*x**2)*(28*x**2) + (28*x**2)*(-34*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 2*28*x**2 + (13*x**2)*(28*x**2) + (13*x**2)*(-4) + (28*x**2)*(-34*x**3) - 34*x**3*(-4) - 8\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*x**3)*-4 = 136*x**3\n (-34*x**3)*(28*x**2) = -952*x**5\n (13*x**2)*-4 = -52*x**2\n (13*x**2)*(28*x**2) = 364*x**4\n 2*28*x**2 = 56*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -952*x**5 + 364*x**4 + 136*x**3 - 52*x**2 + 56*x**2 - 8\nCombining like terms, got -952*x**5 + 364*x**4 + 136*x**3 + 4*x**2 - 8\n#Step 6:\nCurrent expression: -952*x**5 + 364*x**4 + 136*x**3 + 4*x**2 - 8\nNo more calculations needed.\n-952*x**5 + 364*x**4 + 136*x**3 + 4*x**2 - 8", "generated_answer": "-952*x**5 + 364*x**4 + 136*x**3 + 4*x**2 - 8", "step_length": 6} {"cot_id": "126411616c6642df3af2c965ff916e4dfdc58c4f7157dc883f027468b11a85f9", "datapoint": {"question": "Simplify this expression: -20*x**3*(42*x**3 + 46*x**2 + 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-840*x**6 - 920*x**5 - 140*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1506, "polynomial_expr": "-20*x**3*(42*x**3 + 46*x**2 + 7)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -20*x**3*(42*x**3 + 46*x**2 + 7)\nExpanding the part (42*x**3 + 46*x**2 + 7) using the distributive property, and we got: 7*(-20*x**3) + (46*x**2)*(-20*x**3) + (-20*x**3)*(42*x**3)\n#Step 2:\nCurrent expression: 7*(-20*x**3) + (46*x**2)*(-20*x**3) + (-20*x**3)*(42*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 7*(-20*x**3) = -140*x**3\n (42*x**3)*(-20*x**3) = -840*x**6\n (46*x**2)*(-20*x**3) = -920*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -840*x**6 - 920*x**5 - 140*x**3\nNo more calculations needed.\n-840*x**6 - 920*x**5 - 140*x**3", "generated_answer": "-840*x**6 - 920*x**5 - 140*x**3", "step_length": 3} {"cot_id": "0de52cd019cbc79f1517e8dba8b262a6867dfd1b2c3904783d33a0269fdaebbb", "datapoint": {"question": "Simplify this expression: (-41*z**2 + 3*z)*(50*z**3 + 11*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2050*z**5 - 301*z**4 + 33*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1507, "polynomial_expr": "(-41*z**2 + 3*z)*(50*z**3 + 11*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-41*z**2 + 3*z)*(50*z**3 + 11*z**2)\nExpanding the part (-41*z**2 + 3*z) using the distributive property, and we got: (3*z)*(50*z**3 + 11*z**2) + (-41*z**2)*(50*z**3 + 11*z**2)\n#Step 2:\nCurrent expression: (3*z)*(50*z**3 + 11*z**2) + (-41*z**2)*(50*z**3 + 11*z**2)\nSimplifying the partial expression: (-41*z**2)*(50*z**3 + 11*z**2)\nExpanding the part (50*z**3 + 11*z**2) using the distributive property, and we got: (-41*z**2)*(11*z**2) + (-41*z**2)*(50*z**3)\nReplacing (-41*z**2)*(50*z**3 + 11*z**2) with (-41*z**2)*(11*z**2) + (-41*z**2)*(50*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (3*z)*(50*z**3 + 11*z**2) + (-41*z**2)*(11*z**2) + (-41*z**2)*(50*z**3)\nSimplifying the partial expression: (3*z)*(50*z**3 + 11*z**2)\nExpanding the part (50*z**3 + 11*z**2) using the distributive property, and we got: (3*z)*(11*z**2) + (3*z)*(50*z**3)\nReplacing (3*z)*(50*z**3 + 11*z**2) with (3*z)*(11*z**2) + (3*z)*(50*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (3*z)*(11*z**2) + (3*z)*(50*z**3) + (-41*z**2)*(11*z**2) + (-41*z**2)*(50*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (11*z**2)*(-41*z**2) = -451*z**4\n (11*z**2)*(3*z) = 33*z**3\n (50*z**3)*(-41*z**2) = -2050*z**5\n (50*z**3)*(3*z) = 150*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2050*z**5 - 451*z**4 + 150*z**4 + 33*z**3\nCombining like terms, got -2050*z**5 - 301*z**4 + 33*z**3\n#Step 6:\nCurrent expression: -2050*z**5 - 301*z**4 + 33*z**3\nNo more calculations needed.\n-2050*z**5 - 301*z**4 + 33*z**3", "generated_answer": "-2050*z**5 - 301*z**4 + 33*z**3", "step_length": 6} {"cot_id": "22d2aecd3ca6fcaf095e7600ada19003e0041fbbefe25386c416291c6f6b7066", "datapoint": {"question": "Simplify this expression: (-39*z**3 - 42*z)*(13*z**3 + 2*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-507*z**6 - 78*z**5 - 546*z**4 - 84*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1508, "polynomial_expr": "(-39*z**3 - 42*z)*(13*z**3 + 2*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-39*z**3 - 42*z)*(13*z**3 + 2*z**2)\nExpanding the part (-39*z**3 - 42*z) using the distributive property, and we got: (-42*z)*(13*z**3 + 2*z**2) + (-39*z**3)*(13*z**3 + 2*z**2)\n#Step 2:\nCurrent expression: (-42*z)*(13*z**3 + 2*z**2) + (-39*z**3)*(13*z**3 + 2*z**2)\nSimplifying the partial expression: (-42*z)*(13*z**3 + 2*z**2)\nExpanding the part (13*z**3 + 2*z**2) using the distributive property, and we got: (-42*z)*(2*z**2) + (-42*z)*(13*z**3)\nReplacing (-42*z)*(13*z**3 + 2*z**2) with (-42*z)*(2*z**2) + (-42*z)*(13*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-42*z)*(2*z**2) + (-42*z)*(13*z**3) + (-39*z**3)*(13*z**3 + 2*z**2)\nSimplifying the partial expression: (-39*z**3)*(13*z**3 + 2*z**2)\nExpanding the part (13*z**3 + 2*z**2) using the distributive property, and we got: (2*z**2)*(-39*z**3) + (-39*z**3)*(13*z**3)\nReplacing (-39*z**3)*(13*z**3 + 2*z**2) with (2*z**2)*(-39*z**3) + (-39*z**3)*(13*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-42*z)*(2*z**2) + (-42*z)*(13*z**3) + (2*z**2)*(-39*z**3) + (-39*z**3)*(13*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (2*z**2)*(-42*z) = -84*z**3\n (2*z**2)*(-39*z**3) = -78*z**5\n (13*z**3)*(-42*z) = -546*z**4\n (13*z**3)*(-39*z**3) = -507*z**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -507*z**6 - 78*z**5 - 546*z**4 - 84*z**3\nNo more calculations needed.\n-507*z**6 - 78*z**5 - 546*z**4 - 84*z**3", "generated_answer": "-507*z**6 - 78*z**5 - 546*z**4 - 84*z**3", "step_length": 5} {"cot_id": "65f81baab59049d2b07f5a02046071c4d1e0c908a20244c86df4c13ce813cc07", "datapoint": {"question": "Calculate the following: (-15*z**3 + 13*z**2 + 26)*(-2*z**3 - 39*z**2 + 7*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "30*z**6 + 559*z**5 - 612*z**4 + 39*z**3 - 1014*z**2 + 182*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1509, "polynomial_expr": "(-15*z**3 + 13*z**2 + 26)*(-2*z**3 - 39*z**2 + 7*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-15*z**3 + 13*z**2 + 26)*(-2*z**3 - 39*z**2 + 7*z)\nExpanding the part (-15*z**3 + 13*z**2 + 26) using the distributive property, and we got: (13*z**2)*(-2*z**3 - 39*z**2 + 7*z) + (-15*z**3)*(-2*z**3 - 39*z**2 + 7*z) + 26*(-2*z**3 - 39*z**2 + 7*z)\n#Step 2:\nCurrent expression: (13*z**2)*(-2*z**3 - 39*z**2 + 7*z) + (-15*z**3)*(-2*z**3 - 39*z**2 + 7*z) + 26*(-2*z**3 - 39*z**2 + 7*z)\nSimplifying the partial expression: 26*(-2*z**3 - 39*z**2 + 7*z)\nExpanding the part (-2*z**3 - 39*z**2 + 7*z) using the distributive property, and we got: (7*z)*26 - 39*z**2*26 - 2*z**3*26\nReplacing 26*(-2*z**3 - 39*z**2 + 7*z) with (7*z)*26 - 39*z**2*26 - 2*z**3*26 in the overall expression.\n#Step 3:\nCurrent expression: (7*z)*26 - 39*z**2*26 + (13*z**2)*(-2*z**3 - 39*z**2 + 7*z) + (-15*z**3)*(-2*z**3 - 39*z**2 + 7*z) - 2*z**3*26\nSimplifying the partial expression: (-15*z**3)*(-2*z**3 - 39*z**2 + 7*z)\nExpanding the part (-2*z**3 - 39*z**2 + 7*z) using the distributive property, and we got: (7*z)*(-15*z**3) + (-39*z**2)*(-15*z**3) + (-15*z**3)*(-2*z**3)\nReplacing (-15*z**3)*(-2*z**3 - 39*z**2 + 7*z) with (7*z)*(-15*z**3) + (-39*z**2)*(-15*z**3) + (-15*z**3)*(-2*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (7*z)*(-15*z**3) + (7*z)*26 + (-39*z**2)*(-15*z**3) - 39*z**2*26 + (13*z**2)*(-2*z**3 - 39*z**2 + 7*z) + (-15*z**3)*(-2*z**3) - 2*z**3*26\nSimplifying the partial expression: (13*z**2)*(-2*z**3 - 39*z**2 + 7*z)\nExpanding the part (-2*z**3 - 39*z**2 + 7*z) using the distributive property, and we got: (7*z)*(13*z**2) + (-39*z**2)*(13*z**2) + (13*z**2)*(-2*z**3)\nReplacing (13*z**2)*(-2*z**3 - 39*z**2 + 7*z) with (7*z)*(13*z**2) + (-39*z**2)*(13*z**2) + (13*z**2)*(-2*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (7*z)*(13*z**2) + (7*z)*(-15*z**3) + (7*z)*26 + (-39*z**2)*(13*z**2) + (-39*z**2)*(-15*z**3) - 39*z**2*26 + (13*z**2)*(-2*z**3) + (-15*z**3)*(-2*z**3) - 2*z**3*26\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*z**2)*26 = -1014*z**2\n (-39*z**2)*(-15*z**3) = 585*z**5\n (-39*z**2)*(13*z**2) = -507*z**4\n (-2*z**3)*26 = -52*z**3\n (-2*z**3)*(-15*z**3) = 30*z**6\n (-2*z**3)*(13*z**2) = -26*z**5\n (7*z)*26 = 182*z\n (7*z)*(-15*z**3) = -105*z**4\n (7*z)*(13*z**2) = 91*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 30*z**6 - 26*z**5 + 585*z**5 - 507*z**4 - 105*z**4 - 52*z**3 + 91*z**3 - 1014*z**2 + 182*z\nCombining like terms, got 30*z**6 + 559*z**5 - 612*z**4 + 39*z**3 - 1014*z**2 + 182*z\n#Step 7:\nCurrent expression: 30*z**6 + 559*z**5 - 612*z**4 + 39*z**3 - 1014*z**2 + 182*z\nNo more calculations needed.\n30*z**6 + 559*z**5 - 612*z**4 + 39*z**3 - 1014*z**2 + 182*z", "generated_answer": "30*z**6 + 559*z**5 - 612*z**4 + 39*z**3 - 1014*z**2 + 182*z", "step_length": 7} {"cot_id": "a78031f0f70f266317da9b2bc5546c9ff7c3c3fc06c7acba0bdd1648ec2541d8", "datapoint": {"question": "Simplify this expression: -42*x*(-4*x**3 - 29*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "168*x**4 + 1218*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1510, "polynomial_expr": "-42*x*(-4*x**3 - 29*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -42*x*(-4*x**3 - 29*x)\nExpanding the part (-4*x**3 - 29*x) using the distributive property, and we got: (-42*x)*(-29*x) + (-42*x)*(-4*x**3)\n#Step 2:\nCurrent expression: (-42*x)*(-29*x) + (-42*x)*(-4*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*x)*(-42*x) = 1218*x**2\n (-4*x**3)*(-42*x) = 168*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 168*x**4 + 1218*x**2\nNo more calculations needed.\n168*x**4 + 1218*x**2", "generated_answer": "168*x**4 + 1218*x**2", "step_length": 3} {"cot_id": "81ba55b82ca809fbe8638f7d9f4ba355802927a562ce0aa8b140c74d8051cea6", "datapoint": {"question": "Calculate the following: (-8*z**2 - 15*z - 28)*(-48*z**3 + 3*z**2 - 24*z + 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "384*z**5 + 696*z**4 + 1491*z**3 + 228*z**2 + 582*z - 168", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1511, "polynomial_expr": "(-8*z**2 - 15*z - 28)*(-48*z**3 + 3*z**2 - 24*z + 6)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-8*z**2 - 15*z - 28)*(-48*z**3 + 3*z**2 - 24*z + 6)\nExpanding the part (-8*z**2 - 15*z - 28) using the distributive property, and we got: (-15*z)*(-48*z**3 + 3*z**2 - 24*z + 6) + (-8*z**2)*(-48*z**3 + 3*z**2 - 24*z + 6) - 28*(-48*z**3 + 3*z**2 - 24*z + 6)\n#Step 2:\nCurrent expression: (-15*z)*(-48*z**3 + 3*z**2 - 24*z + 6) + (-8*z**2)*(-48*z**3 + 3*z**2 - 24*z + 6) - 28*(-48*z**3 + 3*z**2 - 24*z + 6)\nSimplifying the partial expression: -28*(-48*z**3 + 3*z**2 - 24*z + 6)\nExpanding the part (-48*z**3 + 3*z**2 - 24*z + 6) using the distributive property, and we got: -24*z*(-28) + (3*z**2)*(-28) - 48*z**3*(-28) + 6*(-28)\nReplacing -28*(-48*z**3 + 3*z**2 - 24*z + 6) with -24*z*(-28) + (3*z**2)*(-28) - 48*z**3*(-28) + 6*(-28) in the overall expression.\n#Step 3:\nCurrent expression: -24*z*(-28) + (-15*z)*(-48*z**3 + 3*z**2 - 24*z + 6) + (-8*z**2)*(-48*z**3 + 3*z**2 - 24*z + 6) + (3*z**2)*(-28) - 48*z**3*(-28) - 168\nSimplifying the partial expression: (-15*z)*(-48*z**3 + 3*z**2 - 24*z + 6)\nExpanding the part (-48*z**3 + 3*z**2 - 24*z + 6) using the distributive property, and we got: (-24*z)*(-15*z) + (-15*z)*(3*z**2) + (-15*z)*(-48*z**3) + 6*(-15*z)\nReplacing (-15*z)*(-48*z**3 + 3*z**2 - 24*z + 6) with (-24*z)*(-15*z) + (-15*z)*(3*z**2) + (-15*z)*(-48*z**3) + 6*(-15*z) in the overall expression.\n#Step 4:\nCurrent expression: (-24*z)*(-15*z) - 24*z*(-28) + (-15*z)*(3*z**2) + (-15*z)*(-48*z**3) + 6*(-15)*z + (-8*z**2)*(-48*z**3 + 3*z**2 - 24*z + 6) + (3*z**2)*(-28) - 48*z**3*(-28) - 168\nSimplifying the partial expression: (-8*z**2)*(-48*z**3 + 3*z**2 - 24*z + 6)\nExpanding the part (-48*z**3 + 3*z**2 - 24*z + 6) using the distributive property, and we got: (-24*z)*(-8*z**2) + 6*(-8*z**2) + (-8*z**2)*(3*z**2) + (-8*z**2)*(-48*z**3)\nReplacing (-8*z**2)*(-48*z**3 + 3*z**2 - 24*z + 6) with (-24*z)*(-8*z**2) + 6*(-8*z**2) + (-8*z**2)*(3*z**2) + (-8*z**2)*(-48*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-24*z)*(-15*z) + (-24*z)*(-8*z**2) - 24*z*(-28) + (-15*z)*(3*z**2) + (-15*z)*(-48*z**3) + 6*(-8)*z**2 + 6*(-15)*z + (-8*z**2)*(3*z**2) + (-8*z**2)*(-48*z**3) + (3*z**2)*(-28) - 48*z**3*(-28) - 168\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*z**3)*-28 = 1344*z**3\n (-48*z**3)*(-15*z) = 720*z**4\n (-48*z**3)*(-8*z**2) = 384*z**5\n (-24*z)*-28 = 672*z\n (-24*z)*(-15*z) = 360*z**2\n (-24*z)*(-8*z**2) = 192*z**3\n (3*z**2)*-28 = -84*z**2\n (3*z**2)*(-15*z) = -45*z**3\n (3*z**2)*(-8*z**2) = -24*z**4\n 6*-15*z = -90*z\n 6*-8*z**2 = -48*z**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 384*z**5 - 24*z**4 + 720*z**4 - 45*z**3 + 192*z**3 + 1344*z**3 - 84*z**2 - 48*z**2 + 360*z**2 - 90*z + 672*z - 168\nCombining like terms, got 384*z**5 + 696*z**4 + 1491*z**3 + 228*z**2 + 582*z - 168\n#Step 7:\nCurrent expression: 384*z**5 + 696*z**4 + 1491*z**3 + 228*z**2 + 582*z - 168\nNo more calculations needed.\n384*z**5 + 696*z**4 + 1491*z**3 + 228*z**2 + 582*z - 168", "generated_answer": "384*z**5 + 696*z**4 + 1491*z**3 + 228*z**2 + 582*z - 168", "step_length": 7} {"cot_id": "ccfff4e42f1d5e1fed22a24651b303038356bd7acedb4887d9da20fbda20441e", "datapoint": {"question": "Simplify this expression: -1296*y**3 + 243*y**2\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1296*y**3 + 243*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1512, "polynomial_expr": "-1296*y**3 + 243*y**2", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -1296*y**3 + 243*y**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -1296*y**3 + 243*y**2\nNo more calculations needed.\n-1296*y**3 + 243*y**2", "generated_answer": "-1296*y**3 + 243*y**2", "step_length": 2} {"cot_id": "632327b15c152a55252feceeb3770170ad1ecd8938077dd35839775266e3823e", "datapoint": {"question": "Simplify this expression: (5 - 31*y**3)*(-2*y**2 + 7*y - 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "62*y**5 - 217*y**4 + 310*y**3 - 10*y**2 + 35*y - 50", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1513, "polynomial_expr": "(5 - 31*y**3)*(-2*y**2 + 7*y - 10)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (5 - 31*y**3)*(-2*y**2 + 7*y - 10)\nExpanding the part (5 - 31*y**3) using the distributive property, and we got: (-31*y**3)*(-2*y**2 + 7*y - 10) + 5*(-2*y**2 + 7*y - 10)\n#Step 2:\nCurrent expression: (-31*y**3)*(-2*y**2 + 7*y - 10) + 5*(-2*y**2 + 7*y - 10)\nSimplifying the partial expression: 5*(-2*y**2 + 7*y - 10)\nExpanding the part (-2*y**2 + 7*y - 10) using the distributive property, and we got: (7*y)*5 - 2*y**2*5 - 10*5\nReplacing 5*(-2*y**2 + 7*y - 10) with (7*y)*5 - 2*y**2*5 - 10*5 in the overall expression.\n#Step 3:\nCurrent expression: (7*y)*5 - 2*y**2*5 + (-31*y**3)*(-2*y**2 + 7*y - 10) - 50\nSimplifying the partial expression: (-31*y**3)*(-2*y**2 + 7*y - 10)\nExpanding the part (-2*y**2 + 7*y - 10) using the distributive property, and we got: -(-1)*310*y**3 + (7*y)*(-31*y**3) + (-2*y**2)*(-31*y**3)\nReplacing (-31*y**3)*(-2*y**2 + 7*y - 10) with -(-1)*310*y**3 + (7*y)*(-31*y**3) + (-2*y**2)*(-31*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -10*(-31)*y**3 + (7*y)*(-31*y**3) + (7*y)*5 + (-2*y**2)*(-31*y**3) - 2*y**2*5 - 50\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-2*y**2)*5 = -10*y**2\n (-2*y**2)*(-31*y**3) = 62*y**5\n (7*y)*5 = 35*y\n (7*y)*(-31*y**3) = -217*y**4\n -10*-31*y**3 = 310*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 62*y**5 - 217*y**4 + 310*y**3 - 10*y**2 + 35*y - 50\nNo more calculations needed.\n62*y**5 - 217*y**4 + 310*y**3 - 10*y**2 + 35*y - 50", "generated_answer": "62*y**5 - 217*y**4 + 310*y**3 - 10*y**2 + 35*y - 50", "step_length": 5} {"cot_id": "03766eb2595e48f82d8c8b5d9839f83286ac88379613685fd98b215a8793b969", "datapoint": {"question": "Simplify this expression: (50*y - 8)*(16*y**3 + 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "800*y**4 - 128*y**3 + 300*y - 48", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1514, "polynomial_expr": "(50*y - 8)*(16*y**3 + 6)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (50*y - 8)*(16*y**3 + 6)\nExpanding the part (50*y - 8) using the distributive property, and we got: (50*y)*(16*y**3 + 6) - 8*(16*y**3 + 6)\n#Step 2:\nCurrent expression: (50*y)*(16*y**3 + 6) - 8*(16*y**3 + 6)\nSimplifying the partial expression: -8*(16*y**3 + 6)\nExpanding the part (16*y**3 + 6) using the distributive property, and we got: (16*y**3)*(-8) + 6*(-8)\nReplacing -8*(16*y**3 + 6) with (16*y**3)*(-8) + 6*(-8) in the overall expression.\n#Step 3:\nCurrent expression: (50*y)*(16*y**3 + 6) + (16*y**3)*(-8) - 48\nSimplifying the partial expression: (50*y)*(16*y**3 + 6)\nExpanding the part (16*y**3 + 6) using the distributive property, and we got: 6*(50*y) + (50*y)*(16*y**3)\nReplacing (50*y)*(16*y**3 + 6) with 6*(50*y) + (50*y)*(16*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 6*50*y + (50*y)*(16*y**3) + (16*y**3)*(-8) - 48\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (16*y**3)*-8 = -128*y**3\n (16*y**3)*(50*y) = 800*y**4\n 6*50*y = 300*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 800*y**4 - 128*y**3 + 300*y - 48\nNo more calculations needed.\n800*y**4 - 128*y**3 + 300*y - 48", "generated_answer": "800*y**4 - 128*y**3 + 300*y - 48", "step_length": 5} {"cot_id": "4ecd43ae11a2687eb1c36c938af29066b6d4816bf606c7d467c8da5051c18542", "datapoint": {"question": "Calculate the following: (-45*x**3 - 3*x)*(-49*x**3 + 13*x**2 - 49*x + 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2205*x**6 - 585*x**5 + 2352*x**4 - 1884*x**3 + 147*x**2 - 123*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1515, "polynomial_expr": "(-45*x**3 - 3*x)*(-49*x**3 + 13*x**2 - 49*x + 41)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-45*x**3 - 3*x)*(-49*x**3 + 13*x**2 - 49*x + 41)\nExpanding the part (-45*x**3 - 3*x) using the distributive property, and we got: (-3*x)*(-49*x**3 + 13*x**2 - 49*x + 41) + (-45*x**3)*(-49*x**3 + 13*x**2 - 49*x + 41)\n#Step 2:\nCurrent expression: (-3*x)*(-49*x**3 + 13*x**2 - 49*x + 41) + (-45*x**3)*(-49*x**3 + 13*x**2 - 49*x + 41)\nSimplifying the partial expression: (-45*x**3)*(-49*x**3 + 13*x**2 - 49*x + 41)\nExpanding the part (-49*x**3 + 13*x**2 - 49*x + 41) using the distributive property, and we got: (-49*x)*(-45*x**3) + 41*(-45*x**3) + (13*x**2)*(-45*x**3) + (-49*x**3)*(-45*x**3)\nReplacing (-45*x**3)*(-49*x**3 + 13*x**2 - 49*x + 41) with (-49*x)*(-45*x**3) + 41*(-45*x**3) + (13*x**2)*(-45*x**3) + (-49*x**3)*(-45*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-49*x)*(-45*x**3) + (-3*x)*(-49*x**3 + 13*x**2 - 49*x + 41) + 41*(-45)*x**3 + (13*x**2)*(-45*x**3) + (-49*x**3)*(-45*x**3)\nSimplifying the partial expression: (-3*x)*(-49*x**3 + 13*x**2 - 49*x + 41)\nExpanding the part (-49*x**3 + 13*x**2 - 49*x + 41) using the distributive property, and we got: (-49*x)*(-3*x) + (-3*x)*(13*x**2) + (-3*x)*(-49*x**3) + 41*(-3*x)\nReplacing (-3*x)*(-49*x**3 + 13*x**2 - 49*x + 41) with (-49*x)*(-3*x) + (-3*x)*(13*x**2) + (-3*x)*(-49*x**3) + 41*(-3*x) in the overall expression.\n#Step 4:\nCurrent expression: (-49*x)*(-3*x) + (-49*x)*(-45*x**3) + (-3*x)*(13*x**2) + (-3*x)*(-49*x**3) + 41*(-45)*x**3 + 41*(-3)*x + (13*x**2)*(-45*x**3) + (-49*x**3)*(-45*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*x)*(-45*x**3) = 2205*x**4\n (-49*x)*(-3*x) = 147*x**2\n (-49*x**3)*(-45*x**3) = 2205*x**6\n (-49*x**3)*(-3*x) = 147*x**4\n (13*x**2)*(-45*x**3) = -585*x**5\n (13*x**2)*(-3*x) = -39*x**3\n 41*-45*x**3 = -1845*x**3\n 41*-3*x = -123*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2205*x**6 - 585*x**5 + 147*x**4 + 2205*x**4 - 1845*x**3 - 39*x**3 + 147*x**2 - 123*x\nCombining like terms, got 2205*x**6 - 585*x**5 + 2352*x**4 - 1884*x**3 + 147*x**2 - 123*x\n#Step 6:\nCurrent expression: 2205*x**6 - 585*x**5 + 2352*x**4 - 1884*x**3 + 147*x**2 - 123*x\nNo more calculations needed.\n2205*x**6 - 585*x**5 + 2352*x**4 - 1884*x**3 + 147*x**2 - 123*x", "generated_answer": "2205*x**6 - 585*x**5 + 2352*x**4 - 1884*x**3 + 147*x**2 - 123*x", "step_length": 6} {"cot_id": "a8df0bbaa40fddd1a15f0fa37bbc5ff374c85d0a848e3741aa72b0e07b3dfc11", "datapoint": {"question": "Calculate the following: (-61*x**2 + 38*x)*(81*x**3 + 26*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-4941*x**5 + 1492*x**4 + 988*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1516, "polynomial_expr": "(-61*x**2 + 38*x)*(81*x**3 + 26*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-61*x**2 + 38*x)*(81*x**3 + 26*x**2)\nExpanding the part (-61*x**2 + 38*x) using the distributive property, and we got: (38*x)*(81*x**3 + 26*x**2) + (-61*x**2)*(81*x**3 + 26*x**2)\n#Step 2:\nCurrent expression: (38*x)*(81*x**3 + 26*x**2) + (-61*x**2)*(81*x**3 + 26*x**2)\nSimplifying the partial expression: (-61*x**2)*(81*x**3 + 26*x**2)\nExpanding the part (81*x**3 + 26*x**2) using the distributive property, and we got: (-61*x**2)*(26*x**2) + (-61*x**2)*(81*x**3)\nReplacing (-61*x**2)*(81*x**3 + 26*x**2) with (-61*x**2)*(26*x**2) + (-61*x**2)*(81*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (38*x)*(81*x**3 + 26*x**2) + (-61*x**2)*(26*x**2) + (-61*x**2)*(81*x**3)\nSimplifying the partial expression: (38*x)*(81*x**3 + 26*x**2)\nExpanding the part (81*x**3 + 26*x**2) using the distributive property, and we got: (38*x)*(26*x**2) + (38*x)*(81*x**3)\nReplacing (38*x)*(81*x**3 + 26*x**2) with (38*x)*(26*x**2) + (38*x)*(81*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (38*x)*(26*x**2) + (38*x)*(81*x**3) + (-61*x**2)*(26*x**2) + (-61*x**2)*(81*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (26*x**2)*(-61*x**2) = -1586*x**4\n (26*x**2)*(38*x) = 988*x**3\n (81*x**3)*(-61*x**2) = -4941*x**5\n (81*x**3)*(38*x) = 3078*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -4941*x**5 - 1586*x**4 + 3078*x**4 + 988*x**3\nCombining like terms, got -4941*x**5 + 1492*x**4 + 988*x**3\n#Step 6:\nCurrent expression: -4941*x**5 + 1492*x**4 + 988*x**3\nNo more calculations needed.\n-4941*x**5 + 1492*x**4 + 988*x**3", "generated_answer": "-4941*x**5 + 1492*x**4 + 988*x**3", "step_length": 6} {"cot_id": "28400d5675e81209f5238924e730fbff88677f8bfc28e154e9f5815d29a849a9", "datapoint": {"question": "Calculate the following: -26*z**3*(24*z**2 - 49*z - 23)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-624*z**5 + 1274*z**4 + 598*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1517, "polynomial_expr": "-26*z**3*(24*z**2 - 49*z - 23)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -26*z**3*(24*z**2 - 49*z - 23)\nExpanding the part (24*z**2 - 49*z - 23) using the distributive property, and we got: (-49*z)*(-26*z**3) - (-1)*598*z**3 + (24*z**2)*(-26*z**3)\n#Step 2:\nCurrent expression: (-49*z)*(-26*z**3) - (-1)*598*z**3 + (24*z**2)*(-26*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -23*(-26*z**3) = 598*z**3\n (-49*z)*(-26*z**3) = 1274*z**4\n (24*z**2)*(-26*z**3) = -624*z**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -624*z**5 + 1274*z**4 + 598*z**3\nNo more calculations needed.\n-624*z**5 + 1274*z**4 + 598*z**3", "generated_answer": "-624*z**5 + 1274*z**4 + 598*z**3", "step_length": 3} {"cot_id": "3218fe537d1617a9efbf749b3d848a5cbbb09358ac51d5aa2e870ae18ea7a114", "datapoint": {"question": "Calculate the following: -28*z**3 - 1344*z**2 + 56\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-28*z**3 - 1344*z**2 + 56", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1518, "polynomial_expr": "-28*z**3 - 1344*z**2 + 56", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -28*z**3 - 1344*z**2 + 56\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -28*z**3 - 1344*z**2 + 56\nNo more calculations needed.\n-28*z**3 - 1344*z**2 + 56", "generated_answer": "-28*z**3 - 1344*z**2 + 56", "step_length": 2} {"cot_id": "2ddc5a6f61fcf2d7e5e21a6e73d772f7c63745f19e0ab378fa05132901b587e6", "datapoint": {"question": "Simplify this expression: (-20*x**3 - 51*x**2 - 32*x)*(-42*x**3 + 44*x**2 + 32*x - 26)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "840*x**6 + 1262*x**5 - 1540*x**4 - 2520*x**3 + 302*x**2 + 832*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1519, "polynomial_expr": "(-20*x**3 - 51*x**2 - 32*x)*(-42*x**3 + 44*x**2 + 32*x - 26)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-20*x**3 - 51*x**2 - 32*x)*(-42*x**3 + 44*x**2 + 32*x - 26)\nExpanding the part (-20*x**3 - 51*x**2 - 32*x) using the distributive property, and we got: (-32*x)*(-42*x**3 + 44*x**2 + 32*x - 26) + (-51*x**2)*(-42*x**3 + 44*x**2 + 32*x - 26) + (-20*x**3)*(-42*x**3 + 44*x**2 + 32*x - 26)\n#Step 2:\nCurrent expression: (-32*x)*(-42*x**3 + 44*x**2 + 32*x - 26) + (-51*x**2)*(-42*x**3 + 44*x**2 + 32*x - 26) + (-20*x**3)*(-42*x**3 + 44*x**2 + 32*x - 26)\nSimplifying the partial expression: (-51*x**2)*(-42*x**3 + 44*x**2 + 32*x - 26)\nExpanding the part (-42*x**3 + 44*x**2 + 32*x - 26) using the distributive property, and we got: -(-1)*1326*x**2 + (32*x)*(-51*x**2) + (-51*x**2)*(44*x**2) + (-51*x**2)*(-42*x**3)\nReplacing (-51*x**2)*(-42*x**3 + 44*x**2 + 32*x - 26) with -(-1)*1326*x**2 + (32*x)*(-51*x**2) + (-51*x**2)*(44*x**2) + (-51*x**2)*(-42*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-32*x)*(-42*x**3 + 44*x**2 + 32*x - 26) - 26*(-51)*x**2 + (32*x)*(-51*x**2) + (-51*x**2)*(44*x**2) + (-51*x**2)*(-42*x**3) + (-20*x**3)*(-42*x**3 + 44*x**2 + 32*x - 26)\nSimplifying the partial expression: (-32*x)*(-42*x**3 + 44*x**2 + 32*x - 26)\nExpanding the part (-42*x**3 + 44*x**2 + 32*x - 26) using the distributive property, and we got: (-32*x)*(32*x) + (-32*x)*(44*x**2) + (-32*x)*(-42*x**3) - (-1)*832*x\nReplacing (-32*x)*(-42*x**3 + 44*x**2 + 32*x - 26) with (-32*x)*(32*x) + (-32*x)*(44*x**2) + (-32*x)*(-42*x**3) - (-1)*832*x in the overall expression.\n#Step 4:\nCurrent expression: (-32*x)*(32*x) + (-32*x)*(44*x**2) + (-32*x)*(-42*x**3) - 26*(-51)*x**2 - 26*(-32)*x + (32*x)*(-51*x**2) + (-51*x**2)*(44*x**2) + (-51*x**2)*(-42*x**3) + (-20*x**3)*(-42*x**3 + 44*x**2 + 32*x - 26)\nSimplifying the partial expression: (-20*x**3)*(-42*x**3 + 44*x**2 + 32*x - 26)\nExpanding the part (-42*x**3 + 44*x**2 + 32*x - 26) using the distributive property, and we got: -(-1)*520*x**3 + (32*x)*(-20*x**3) + (44*x**2)*(-20*x**3) + (-42*x**3)*(-20*x**3)\nReplacing (-20*x**3)*(-42*x**3 + 44*x**2 + 32*x - 26) with -(-1)*520*x**3 + (32*x)*(-20*x**3) + (44*x**2)*(-20*x**3) + (-42*x**3)*(-20*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-32*x)*(32*x) + (-32*x)*(44*x**2) + (-32*x)*(-42*x**3) - 26*(-20)*x**3 - 26*(-51)*x**2 - 26*(-32)*x + (32*x)*(-51*x**2) + (32*x)*(-20*x**3) + (-51*x**2)*(44*x**2) + (-51*x**2)*(-42*x**3) + (44*x**2)*(-20*x**3) + (-42*x**3)*(-20*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*x**3)*(-51*x**2) = 2142*x**5\n (-42*x**3)*(-32*x) = 1344*x**4\n (-42*x**3)*(-20*x**3) = 840*x**6\n (32*x)*(-51*x**2) = -1632*x**3\n (32*x)*(-32*x) = -1024*x**2\n (32*x)*(-20*x**3) = -640*x**4\n (44*x**2)*(-51*x**2) = -2244*x**4\n (44*x**2)*(-32*x) = -1408*x**3\n (44*x**2)*(-20*x**3) = -880*x**5\n -26*-51*x**2 = 1326*x**2\n -26*-32*x = 832*x\n -26*-20*x**3 = 520*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 840*x**6 - 880*x**5 + 2142*x**5 - 2244*x**4 - 640*x**4 + 1344*x**4 - 1632*x**3 - 1408*x**3 + 520*x**3 - 1024*x**2 + 1326*x**2 + 832*x\nCombining like terms, got 840*x**6 + 1262*x**5 - 1540*x**4 - 2520*x**3 + 302*x**2 + 832*x\n#Step 7:\nCurrent expression: 840*x**6 + 1262*x**5 - 1540*x**4 - 2520*x**3 + 302*x**2 + 832*x\nNo more calculations needed.\n840*x**6 + 1262*x**5 - 1540*x**4 - 2520*x**3 + 302*x**2 + 832*x", "generated_answer": "840*x**6 + 1262*x**5 - 1540*x**4 - 2520*x**3 + 302*x**2 + 832*x", "step_length": 7} {"cot_id": "517c1b6ec28727d311474b50f158e5e190aed50541004dea58f950b03bd83ca7", "datapoint": {"question": "Simplify this expression: (14*y**3 - 21)*(-39*y**3 + 13*y**2 - 15*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-546*y**6 + 182*y**5 - 210*y**4 + 819*y**3 - 273*y**2 + 315*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1520, "polynomial_expr": "(14*y**3 - 21)*(-39*y**3 + 13*y**2 - 15*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14*y**3 - 21)*(-39*y**3 + 13*y**2 - 15*y)\nExpanding the part (14*y**3 - 21) using the distributive property, and we got: (14*y**3)*(-39*y**3 + 13*y**2 - 15*y) - 21*(-39*y**3 + 13*y**2 - 15*y)\n#Step 2:\nCurrent expression: (14*y**3)*(-39*y**3 + 13*y**2 - 15*y) - 21*(-39*y**3 + 13*y**2 - 15*y)\nSimplifying the partial expression: -21*(-39*y**3 + 13*y**2 - 15*y)\nExpanding the part (-39*y**3 + 13*y**2 - 15*y) using the distributive property, and we got: -15*y*(-21) + (13*y**2)*(-21) - 39*y**3*(-21)\nReplacing -21*(-39*y**3 + 13*y**2 - 15*y) with -15*y*(-21) + (13*y**2)*(-21) - 39*y**3*(-21) in the overall expression.\n#Step 3:\nCurrent expression: -15*y*(-21) + (13*y**2)*(-21) - 39*y**3*(-21) + (14*y**3)*(-39*y**3 + 13*y**2 - 15*y)\nSimplifying the partial expression: (14*y**3)*(-39*y**3 + 13*y**2 - 15*y)\nExpanding the part (-39*y**3 + 13*y**2 - 15*y) using the distributive property, and we got: (-15*y)*(14*y**3) + (13*y**2)*(14*y**3) + (-39*y**3)*(14*y**3)\nReplacing (14*y**3)*(-39*y**3 + 13*y**2 - 15*y) with (-15*y)*(14*y**3) + (13*y**2)*(14*y**3) + (-39*y**3)*(14*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-15*y)*(14*y**3) - 15*y*(-21) + (13*y**2)*(14*y**3) + (13*y**2)*(-21) + (-39*y**3)*(14*y**3) - 39*y**3*(-21)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*y**3)*-21 = 819*y**3\n (-39*y**3)*(14*y**3) = -546*y**6\n (-15*y)*-21 = 315*y\n (-15*y)*(14*y**3) = -210*y**4\n (13*y**2)*-21 = -273*y**2\n (13*y**2)*(14*y**3) = 182*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -546*y**6 + 182*y**5 - 210*y**4 + 819*y**3 - 273*y**2 + 315*y\nNo more calculations needed.\n-546*y**6 + 182*y**5 - 210*y**4 + 819*y**3 - 273*y**2 + 315*y", "generated_answer": "-546*y**6 + 182*y**5 - 210*y**4 + 819*y**3 - 273*y**2 + 315*y", "step_length": 5} {"cot_id": "8df86ccf6522c288027f47e0b3941a449e9ca5ac427d74e74d8b91ec6471de29", "datapoint": {"question": "Simplify this expression: (25*z**2 - 24*z)*(23*z**3 + 42)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "575*z**5 - 552*z**4 + 1050*z**2 - 1008*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1521, "polynomial_expr": "(25*z**2 - 24*z)*(23*z**3 + 42)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (25*z**2 - 24*z)*(23*z**3 + 42)\nExpanding the part (23*z**3 + 42) using the distributive property, and we got: (23*z**3)*(25*z**2 - 24*z) + 42*(25*z**2 - 24*z)\n#Step 2:\nCurrent expression: (23*z**3)*(25*z**2 - 24*z) + 42*(25*z**2 - 24*z)\nSimplifying the partial expression: 42*(25*z**2 - 24*z)\nExpanding the part (25*z**2 - 24*z) using the distributive property, and we got: -24*z*42 + (25*z**2)*42\nReplacing 42*(25*z**2 - 24*z) with -24*z*42 + (25*z**2)*42 in the overall expression.\n#Step 3:\nCurrent expression: -24*z*42 + (25*z**2)*42 + (23*z**3)*(25*z**2 - 24*z)\nSimplifying the partial expression: (23*z**3)*(25*z**2 - 24*z)\nExpanding the part (25*z**2 - 24*z) using the distributive property, and we got: (-24*z)*(23*z**3) + (25*z**2)*(23*z**3)\nReplacing (23*z**3)*(25*z**2 - 24*z) with (-24*z)*(23*z**3) + (25*z**2)*(23*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-24*z)*(23*z**3) - 24*z*42 + (25*z**2)*(23*z**3) + (25*z**2)*42\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-24*z)*42 = -1008*z\n (-24*z)*(23*z**3) = -552*z**4\n (25*z**2)*42 = 1050*z**2\n (25*z**2)*(23*z**3) = 575*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 575*z**5 - 552*z**4 + 1050*z**2 - 1008*z\nNo more calculations needed.\n575*z**5 - 552*z**4 + 1050*z**2 - 1008*z", "generated_answer": "575*z**5 - 552*z**4 + 1050*z**2 - 1008*z", "step_length": 5} {"cot_id": "002564df8991cc5c64af3b0dccd2e14d17702a5c251ec5310663f10baa0e08ac", "datapoint": {"question": "Calculate the following: (9*x**3 - 25*x**2 + 25*x)*(37*x**3 - 26*x**2 - 9)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "333*x**6 - 1159*x**5 + 1575*x**4 - 731*x**3 + 225*x**2 - 225*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1522, "polynomial_expr": "(9*x**3 - 25*x**2 + 25*x)*(37*x**3 - 26*x**2 - 9)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9*x**3 - 25*x**2 + 25*x)*(37*x**3 - 26*x**2 - 9)\nExpanding the part (37*x**3 - 26*x**2 - 9) using the distributive property, and we got: (-26*x**2)*(9*x**3 - 25*x**2 + 25*x) + (37*x**3)*(9*x**3 - 25*x**2 + 25*x) - 9*(9*x**3 - 25*x**2 + 25*x)\n#Step 2:\nCurrent expression: (-26*x**2)*(9*x**3 - 25*x**2 + 25*x) + (37*x**3)*(9*x**3 - 25*x**2 + 25*x) - 9*(9*x**3 - 25*x**2 + 25*x)\nSimplifying the partial expression: -9*(9*x**3 - 25*x**2 + 25*x)\nExpanding the part (9*x**3 - 25*x**2 + 25*x) using the distributive property, and we got: (25*x)*(-9) - 25*x**2*(-9) + (9*x**3)*(-9)\nReplacing -9*(9*x**3 - 25*x**2 + 25*x) with (25*x)*(-9) - 25*x**2*(-9) + (9*x**3)*(-9) in the overall expression.\n#Step 3:\nCurrent expression: (25*x)*(-9) + (-26*x**2)*(9*x**3 - 25*x**2 + 25*x) - 25*x**2*(-9) + (9*x**3)*(-9) + (37*x**3)*(9*x**3 - 25*x**2 + 25*x)\nSimplifying the partial expression: (-26*x**2)*(9*x**3 - 25*x**2 + 25*x)\nExpanding the part (9*x**3 - 25*x**2 + 25*x) using the distributive property, and we got: (25*x)*(-26*x**2) + (-26*x**2)*(-25*x**2) + (-26*x**2)*(9*x**3)\nReplacing (-26*x**2)*(9*x**3 - 25*x**2 + 25*x) with (25*x)*(-26*x**2) + (-26*x**2)*(-25*x**2) + (-26*x**2)*(9*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (25*x)*(-26*x**2) + (25*x)*(-9) + (-26*x**2)*(-25*x**2) + (-26*x**2)*(9*x**3) - 25*x**2*(-9) + (9*x**3)*(-9) + (37*x**3)*(9*x**3 - 25*x**2 + 25*x)\nSimplifying the partial expression: (37*x**3)*(9*x**3 - 25*x**2 + 25*x)\nExpanding the part (9*x**3 - 25*x**2 + 25*x) using the distributive property, and we got: (25*x)*(37*x**3) + (-25*x**2)*(37*x**3) + (9*x**3)*(37*x**3)\nReplacing (37*x**3)*(9*x**3 - 25*x**2 + 25*x) with (25*x)*(37*x**3) + (-25*x**2)*(37*x**3) + (9*x**3)*(37*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (25*x)*(-26*x**2) + (25*x)*(37*x**3) + (25*x)*(-9) + (-26*x**2)*(-25*x**2) + (-26*x**2)*(9*x**3) + (-25*x**2)*(37*x**3) - 25*x**2*(-9) + (9*x**3)*(37*x**3) + (9*x**3)*(-9)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*x**2)*-9 = 225*x**2\n (-25*x**2)*(-26*x**2) = 650*x**4\n (-25*x**2)*(37*x**3) = -925*x**5\n (9*x**3)*-9 = -81*x**3\n (9*x**3)*(-26*x**2) = -234*x**5\n (9*x**3)*(37*x**3) = 333*x**6\n (25*x)*-9 = -225*x\n (25*x)*(-26*x**2) = -650*x**3\n (25*x)*(37*x**3) = 925*x**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 333*x**6 - 925*x**5 - 234*x**5 + 650*x**4 + 925*x**4 - 650*x**3 - 81*x**3 + 225*x**2 - 225*x\nCombining like terms, got 333*x**6 - 1159*x**5 + 1575*x**4 - 731*x**3 + 225*x**2 - 225*x\n#Step 7:\nCurrent expression: 333*x**6 - 1159*x**5 + 1575*x**4 - 731*x**3 + 225*x**2 - 225*x\nNo more calculations needed.\n333*x**6 - 1159*x**5 + 1575*x**4 - 731*x**3 + 225*x**2 - 225*x", "generated_answer": "333*x**6 - 1159*x**5 + 1575*x**4 - 731*x**3 + 225*x**2 - 225*x", "step_length": 7} {"cot_id": "49de62a39c1b7318db44eecbe839e56ac42c67bc6bc3aacda7db3e7672adf4ba", "datapoint": {"question": "Calculate the following: (-41*z**3 - 33)*(-30*z**3 - 36*z**2 - 47*z + 45)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1230*z**6 + 1476*z**5 + 1927*z**4 - 855*z**3 + 1188*z**2 + 1551*z - 1485", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1523, "polynomial_expr": "(-41*z**3 - 33)*(-30*z**3 - 36*z**2 - 47*z + 45)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-41*z**3 - 33)*(-30*z**3 - 36*z**2 - 47*z + 45)\nExpanding the part (-41*z**3 - 33) using the distributive property, and we got: (-41*z**3)*(-30*z**3 - 36*z**2 - 47*z + 45) - 33*(-30*z**3 - 36*z**2 - 47*z + 45)\n#Step 2:\nCurrent expression: (-41*z**3)*(-30*z**3 - 36*z**2 - 47*z + 45) - 33*(-30*z**3 - 36*z**2 - 47*z + 45)\nSimplifying the partial expression: -33*(-30*z**3 - 36*z**2 - 47*z + 45)\nExpanding the part (-30*z**3 - 36*z**2 - 47*z + 45) using the distributive property, and we got: -47*z*(-33) - 36*z**2*(-33) - 30*z**3*(-33) + 45*(-33)\nReplacing -33*(-30*z**3 - 36*z**2 - 47*z + 45) with -47*z*(-33) - 36*z**2*(-33) - 30*z**3*(-33) + 45*(-33) in the overall expression.\n#Step 3:\nCurrent expression: -47*z*(-33) - 36*z**2*(-33) + (-41*z**3)*(-30*z**3 - 36*z**2 - 47*z + 45) - 30*z**3*(-33) - 1485\nSimplifying the partial expression: (-41*z**3)*(-30*z**3 - 36*z**2 - 47*z + 45)\nExpanding the part (-30*z**3 - 36*z**2 - 47*z + 45) using the distributive property, and we got: (-47*z)*(-41*z**3) + 45*(-41*z**3) + (-36*z**2)*(-41*z**3) + (-41*z**3)*(-30*z**3)\nReplacing (-41*z**3)*(-30*z**3 - 36*z**2 - 47*z + 45) with (-47*z)*(-41*z**3) + 45*(-41*z**3) + (-36*z**2)*(-41*z**3) + (-41*z**3)*(-30*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-47*z)*(-41*z**3) - 47*z*(-33) + 45*(-41)*z**3 + (-36*z**2)*(-41*z**3) - 36*z**2*(-33) + (-41*z**3)*(-30*z**3) - 30*z**3*(-33) - 1485\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*z)*-33 = 1551*z\n (-47*z)*(-41*z**3) = 1927*z**4\n (-36*z**2)*-33 = 1188*z**2\n (-36*z**2)*(-41*z**3) = 1476*z**5\n (-30*z**3)*-33 = 990*z**3\n (-30*z**3)*(-41*z**3) = 1230*z**6\n 45*-41*z**3 = -1845*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1230*z**6 + 1476*z**5 + 1927*z**4 - 1845*z**3 + 990*z**3 + 1188*z**2 + 1551*z - 1485\nCombining like terms, got 1230*z**6 + 1476*z**5 + 1927*z**4 - 855*z**3 + 1188*z**2 + 1551*z - 1485\n#Step 6:\nCurrent expression: 1230*z**6 + 1476*z**5 + 1927*z**4 - 855*z**3 + 1188*z**2 + 1551*z - 1485\nNo more calculations needed.\n1230*z**6 + 1476*z**5 + 1927*z**4 - 855*z**3 + 1188*z**2 + 1551*z - 1485", "generated_answer": "1230*z**6 + 1476*z**5 + 1927*z**4 - 855*z**3 + 1188*z**2 + 1551*z - 1485", "step_length": 6} {"cot_id": "0d0776ba5231ab9ac402c07982dd406052d34859d7e280c63569313666eef127", "datapoint": {"question": "Calculate the following: (25 - 18*x**2)*(-16*x**3 + 5*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "288*x**5 - 490*x**3 + 125*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1524, "polynomial_expr": "(25 - 18*x**2)*(-16*x**3 + 5*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (25 - 18*x**2)*(-16*x**3 + 5*x)\nExpanding the part (25 - 18*x**2) using the distributive property, and we got: (-18*x**2)*(-16*x**3 + 5*x) + 25*(-16*x**3 + 5*x)\n#Step 2:\nCurrent expression: (-18*x**2)*(-16*x**3 + 5*x) + 25*(-16*x**3 + 5*x)\nSimplifying the partial expression: 25*(-16*x**3 + 5*x)\nExpanding the part (-16*x**3 + 5*x) using the distributive property, and we got: (5*x)*25 - 16*x**3*25\nReplacing 25*(-16*x**3 + 5*x) with (5*x)*25 - 16*x**3*25 in the overall expression.\n#Step 3:\nCurrent expression: (5*x)*25 + (-18*x**2)*(-16*x**3 + 5*x) - 16*x**3*25\nSimplifying the partial expression: (-18*x**2)*(-16*x**3 + 5*x)\nExpanding the part (-16*x**3 + 5*x) using the distributive property, and we got: (5*x)*(-18*x**2) + (-18*x**2)*(-16*x**3)\nReplacing (-18*x**2)*(-16*x**3 + 5*x) with (5*x)*(-18*x**2) + (-18*x**2)*(-16*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (5*x)*(-18*x**2) + (5*x)*25 + (-18*x**2)*(-16*x**3) - 16*x**3*25\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-16*x**3)*25 = -400*x**3\n (-16*x**3)*(-18*x**2) = 288*x**5\n (5*x)*25 = 125*x\n (5*x)*(-18*x**2) = -90*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 288*x**5 - 400*x**3 - 90*x**3 + 125*x\nCombining like terms, got 288*x**5 - 490*x**3 + 125*x\n#Step 6:\nCurrent expression: 288*x**5 - 490*x**3 + 125*x\nNo more calculations needed.\n288*x**5 - 490*x**3 + 125*x", "generated_answer": "288*x**5 - 490*x**3 + 125*x", "step_length": 6} {"cot_id": "b8c443c0b648a85f1f9e6409fa5aea6e9b320eed2fc8ad14cdaa62146686c784", "datapoint": {"question": "Calculate the following: -12*z**3*(7*z**2 - 58)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-84*z**5 + 696*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1525, "polynomial_expr": "-12*z**3*(7*z**2 - 58)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -12*z**3*(7*z**2 - 58)\nExpanding the part (7*z**2 - 58) using the distributive property, and we got: -(-1)*696*z**3 + (7*z**2)*(-12*z**3)\n#Step 2:\nCurrent expression: -(-1)*696*z**3 + (7*z**2)*(-12*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -58*(-12*z**3) = 696*z**3\n (7*z**2)*(-12*z**3) = -84*z**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -84*z**5 + 696*z**3\nNo more calculations needed.\n-84*z**5 + 696*z**3", "generated_answer": "-84*z**5 + 696*z**3", "step_length": 3} {"cot_id": "db6266e5de7e60a7e288ab2f687861179c4579509f054fe1fb1e5edca3d48f1e", "datapoint": {"question": "Calculate the following: 24*y**3*(-77*y**3 + 37*y**2 + 31*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1848*y**6 + 888*y**5 + 744*y**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1526, "polynomial_expr": "24*y**3*(-77*y**3 + 37*y**2 + 31*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 24*y**3*(-77*y**3 + 37*y**2 + 31*y)\nExpanding the part (-77*y**3 + 37*y**2 + 31*y) using the distributive property, and we got: (31*y)*(24*y**3) + (37*y**2)*(24*y**3) + (-77*y**3)*(24*y**3)\n#Step 2:\nCurrent expression: (31*y)*(24*y**3) + (37*y**2)*(24*y**3) + (-77*y**3)*(24*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-77*y**3)*(24*y**3) = -1848*y**6\n (31*y)*(24*y**3) = 744*y**4\n (37*y**2)*(24*y**3) = 888*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1848*y**6 + 888*y**5 + 744*y**4\nNo more calculations needed.\n-1848*y**6 + 888*y**5 + 744*y**4", "generated_answer": "-1848*y**6 + 888*y**5 + 744*y**4", "step_length": 3} {"cot_id": "a9ccfe72c2d45e579e232a23de3fbe7e8e69caa8b9a1a7b064a275206046cec0", "datapoint": {"question": "Simplify this expression: (21*z**2 + 20*z + 27)*(-19*z**3 - 13*z + 42)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-399*z**5 - 380*z**4 - 786*z**3 + 622*z**2 + 489*z + 1134", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1527, "polynomial_expr": "(21*z**2 + 20*z + 27)*(-19*z**3 - 13*z + 42)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21*z**2 + 20*z + 27)*(-19*z**3 - 13*z + 42)\nExpanding the part (21*z**2 + 20*z + 27) using the distributive property, and we got: (20*z)*(-19*z**3 - 13*z + 42) + (21*z**2)*(-19*z**3 - 13*z + 42) + 27*(-19*z**3 - 13*z + 42)\n#Step 2:\nCurrent expression: (20*z)*(-19*z**3 - 13*z + 42) + (21*z**2)*(-19*z**3 - 13*z + 42) + 27*(-19*z**3 - 13*z + 42)\nSimplifying the partial expression: 27*(-19*z**3 - 13*z + 42)\nExpanding the part (-19*z**3 - 13*z + 42) using the distributive property, and we got: -13*z*27 - 19*z**3*27 + 42*27\nReplacing 27*(-19*z**3 - 13*z + 42) with -13*z*27 - 19*z**3*27 + 42*27 in the overall expression.\n#Step 3:\nCurrent expression: -13*z*27 + (20*z)*(-19*z**3 - 13*z + 42) + (21*z**2)*(-19*z**3 - 13*z + 42) - 19*z**3*27 + 1134\nSimplifying the partial expression: (20*z)*(-19*z**3 - 13*z + 42)\nExpanding the part (-19*z**3 - 13*z + 42) using the distributive property, and we got: (-13*z)*(20*z) + 42*(20*z) + (20*z)*(-19*z**3)\nReplacing (20*z)*(-19*z**3 - 13*z + 42) with (-13*z)*(20*z) + 42*(20*z) + (20*z)*(-19*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-13*z)*(20*z) - 13*z*27 + 42*20*z + (20*z)*(-19*z**3) + (21*z**2)*(-19*z**3 - 13*z + 42) - 19*z**3*27 + 1134\nSimplifying the partial expression: (21*z**2)*(-19*z**3 - 13*z + 42)\nExpanding the part (-19*z**3 - 13*z + 42) using the distributive property, and we got: (-13*z)*(21*z**2) + 42*(21*z**2) + (21*z**2)*(-19*z**3)\nReplacing (21*z**2)*(-19*z**3 - 13*z + 42) with (-13*z)*(21*z**2) + 42*(21*z**2) + (21*z**2)*(-19*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-13*z)*(20*z) + (-13*z)*(21*z**2) - 13*z*27 + 42*21*z**2 + 42*20*z + (20*z)*(-19*z**3) + (21*z**2)*(-19*z**3) - 19*z**3*27 + 1134\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*z**3)*27 = -513*z**3\n (-19*z**3)*(20*z) = -380*z**4\n (-19*z**3)*(21*z**2) = -399*z**5\n (-13*z)*27 = -351*z\n (-13*z)*(20*z) = -260*z**2\n (-13*z)*(21*z**2) = -273*z**3\n 42*20*z = 840*z\n 42*21*z**2 = 882*z**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -399*z**5 - 380*z**4 - 513*z**3 - 273*z**3 - 260*z**2 + 882*z**2 - 351*z + 840*z + 1134\nCombining like terms, got -399*z**5 - 380*z**4 - 786*z**3 + 622*z**2 + 489*z + 1134\n#Step 7:\nCurrent expression: -399*z**5 - 380*z**4 - 786*z**3 + 622*z**2 + 489*z + 1134\nNo more calculations needed.\n-399*z**5 - 380*z**4 - 786*z**3 + 622*z**2 + 489*z + 1134", "generated_answer": "-399*z**5 - 380*z**4 - 786*z**3 + 622*z**2 + 489*z + 1134", "step_length": 7} {"cot_id": "eeff7d2eaa29b51c63a9636073ed5873e585388811307cfe1b80d493fded09eb", "datapoint": {"question": "Calculate the following: (10*x - 43)*(20*x**3 + 12*x**2 + 43*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "200*x**4 - 740*x**3 - 86*x**2 - 1849*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1528, "polynomial_expr": "(10*x - 43)*(20*x**3 + 12*x**2 + 43*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (10*x - 43)*(20*x**3 + 12*x**2 + 43*x)\nExpanding the part (10*x - 43) using the distributive property, and we got: (10*x)*(20*x**3 + 12*x**2 + 43*x) - 43*(20*x**3 + 12*x**2 + 43*x)\n#Step 2:\nCurrent expression: (10*x)*(20*x**3 + 12*x**2 + 43*x) - 43*(20*x**3 + 12*x**2 + 43*x)\nSimplifying the partial expression: -43*(20*x**3 + 12*x**2 + 43*x)\nExpanding the part (20*x**3 + 12*x**2 + 43*x) using the distributive property, and we got: (43*x)*(-43) + (12*x**2)*(-43) + (20*x**3)*(-43)\nReplacing -43*(20*x**3 + 12*x**2 + 43*x) with (43*x)*(-43) + (12*x**2)*(-43) + (20*x**3)*(-43) in the overall expression.\n#Step 3:\nCurrent expression: (10*x)*(20*x**3 + 12*x**2 + 43*x) + (43*x)*(-43) + (12*x**2)*(-43) + (20*x**3)*(-43)\nSimplifying the partial expression: (10*x)*(20*x**3 + 12*x**2 + 43*x)\nExpanding the part (20*x**3 + 12*x**2 + 43*x) using the distributive property, and we got: (10*x)*(43*x) + (10*x)*(12*x**2) + (10*x)*(20*x**3)\nReplacing (10*x)*(20*x**3 + 12*x**2 + 43*x) with (10*x)*(43*x) + (10*x)*(12*x**2) + (10*x)*(20*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (10*x)*(43*x) + (10*x)*(12*x**2) + (10*x)*(20*x**3) + (43*x)*(-43) + (12*x**2)*(-43) + (20*x**3)*(-43)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (12*x**2)*-43 = -516*x**2\n (12*x**2)*(10*x) = 120*x**3\n (20*x**3)*-43 = -860*x**3\n (20*x**3)*(10*x) = 200*x**4\n (43*x)*-43 = -1849*x\n (43*x)*(10*x) = 430*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 200*x**4 - 860*x**3 + 120*x**3 - 516*x**2 + 430*x**2 - 1849*x\nCombining like terms, got 200*x**4 - 740*x**3 - 86*x**2 - 1849*x\n#Step 6:\nCurrent expression: 200*x**4 - 740*x**3 - 86*x**2 - 1849*x\nNo more calculations needed.\n200*x**4 - 740*x**3 - 86*x**2 - 1849*x", "generated_answer": "200*x**4 - 740*x**3 - 86*x**2 - 1849*x", "step_length": 6} {"cot_id": "ceb34fb58420e19fbebabd84df1af85a4070408ab7e283cf5eebe41724376140", "datapoint": {"question": "Simplify this expression: 34*x**3*(-27*x**2 + 18*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-918*x**5 + 612*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1529, "polynomial_expr": "34*x**3*(-27*x**2 + 18*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 34*x**3*(-27*x**2 + 18*x)\nExpanding the part (-27*x**2 + 18*x) using the distributive property, and we got: (18*x)*(34*x**3) + (-27*x**2)*(34*x**3)\n#Step 2:\nCurrent expression: (18*x)*(34*x**3) + (-27*x**2)*(34*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*x**2)*(34*x**3) = -918*x**5\n (18*x)*(34*x**3) = 612*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -918*x**5 + 612*x**4\nNo more calculations needed.\n-918*x**5 + 612*x**4", "generated_answer": "-918*x**5 + 612*x**4", "step_length": 3} {"cot_id": "788e1ad8ad864d019eab6d81963d8ea09f3c8c31f22bf0bd6f02fa6c3d6501d9", "datapoint": {"question": "Calculate the following: (-34*z**3 - 44)*(-13*z**3 - 48*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "442*z**6 + 1632*z**5 + 572*z**3 + 2112*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1530, "polynomial_expr": "(-34*z**3 - 44)*(-13*z**3 - 48*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-34*z**3 - 44)*(-13*z**3 - 48*z**2)\nExpanding the part (-34*z**3 - 44) using the distributive property, and we got: (-34*z**3)*(-13*z**3 - 48*z**2) - 44*(-13*z**3 - 48*z**2)\n#Step 2:\nCurrent expression: (-34*z**3)*(-13*z**3 - 48*z**2) - 44*(-13*z**3 - 48*z**2)\nSimplifying the partial expression: -44*(-13*z**3 - 48*z**2)\nExpanding the part (-13*z**3 - 48*z**2) using the distributive property, and we got: -48*z**2*(-44) - 13*z**3*(-44)\nReplacing -44*(-13*z**3 - 48*z**2) with -48*z**2*(-44) - 13*z**3*(-44) in the overall expression.\n#Step 3:\nCurrent expression: -48*z**2*(-44) + (-34*z**3)*(-13*z**3 - 48*z**2) - 13*z**3*(-44)\nSimplifying the partial expression: (-34*z**3)*(-13*z**3 - 48*z**2)\nExpanding the part (-13*z**3 - 48*z**2) using the distributive property, and we got: (-48*z**2)*(-34*z**3) + (-34*z**3)*(-13*z**3)\nReplacing (-34*z**3)*(-13*z**3 - 48*z**2) with (-48*z**2)*(-34*z**3) + (-34*z**3)*(-13*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-48*z**2)*(-34*z**3) - 48*z**2*(-44) + (-34*z**3)*(-13*z**3) - 13*z**3*(-44)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*z**2)*-44 = 2112*z**2\n (-48*z**2)*(-34*z**3) = 1632*z**5\n (-13*z**3)*-44 = 572*z**3\n (-13*z**3)*(-34*z**3) = 442*z**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 442*z**6 + 1632*z**5 + 572*z**3 + 2112*z**2\nNo more calculations needed.\n442*z**6 + 1632*z**5 + 572*z**3 + 2112*z**2", "generated_answer": "442*z**6 + 1632*z**5 + 572*z**3 + 2112*z**2", "step_length": 5} {"cot_id": "858804f4759a79b03cf52315e4498fd9730388ec86518115b68bb699eb806391", "datapoint": {"question": "Simplify this expression: -53*z**3*(-14*z**2 + z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "742*z**5 - 53*z**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1531, "polynomial_expr": "-53*z**3*(-14*z**2 + z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -53*z**3*(-14*z**2 + z)\nExpanding the part (-14*z**2 + z) using the distributive property, and we got: z*(-53*z**3) + (-14*z**2)*(-53*z**3)\n#Step 2:\nCurrent expression: z*(-53*z**3) + (-14*z**2)*(-53*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n z*(-53*z**3) = -53*z**4\n (-14*z**2)*(-53*z**3) = 742*z**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 742*z**5 - 53*z**4\nNo more calculations needed.\n742*z**5 - 53*z**4", "generated_answer": "742*z**5 - 53*z**4", "step_length": 3} {"cot_id": "dea4dda4f00b94271ad2ea3c7e1d02ee9409a4a8a8fb335c79db7d29c52ab6f2", "datapoint": {"question": "Calculate the following: 58*y**2*(13*y**3 + 22*y + 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "754*y**5 + 1276*y**3 + 1798*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1532, "polynomial_expr": "58*y**2*(13*y**3 + 22*y + 31)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 58*y**2*(13*y**3 + 22*y + 31)\nExpanding the part (13*y**3 + 22*y + 31) using the distributive property, and we got: 31*(58*y**2) + (22*y)*(58*y**2) + (58*y**2)*(13*y**3)\n#Step 2:\nCurrent expression: 31*(58*y**2) + (22*y)*(58*y**2) + (58*y**2)*(13*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 31*(58*y**2) = 1798*y**2\n (13*y**3)*(58*y**2) = 754*y**5\n (22*y)*(58*y**2) = 1276*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 754*y**5 + 1276*y**3 + 1798*y**2\nNo more calculations needed.\n754*y**5 + 1276*y**3 + 1798*y**2", "generated_answer": "754*y**5 + 1276*y**3 + 1798*y**2", "step_length": 3} {"cot_id": "a10e76d0aa234630acf048299ada9c8054d8ceab0c08cf79e6e47c9a0d3419fa", "datapoint": {"question": "Calculate the following: (-41*x**2 - 30)*(-29*x**3 - 56*x**2 + 21*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1189*x**5 + 2296*x**4 + 9*x**3 + 1680*x**2 - 630*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1533, "polynomial_expr": "(-41*x**2 - 30)*(-29*x**3 - 56*x**2 + 21*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-41*x**2 - 30)*(-29*x**3 - 56*x**2 + 21*x)\nExpanding the part (-41*x**2 - 30) using the distributive property, and we got: (-41*x**2)*(-29*x**3 - 56*x**2 + 21*x) - 30*(-29*x**3 - 56*x**2 + 21*x)\n#Step 2:\nCurrent expression: (-41*x**2)*(-29*x**3 - 56*x**2 + 21*x) - 30*(-29*x**3 - 56*x**2 + 21*x)\nSimplifying the partial expression: -30*(-29*x**3 - 56*x**2 + 21*x)\nExpanding the part (-29*x**3 - 56*x**2 + 21*x) using the distributive property, and we got: (21*x)*(-30) - 56*x**2*(-30) - 29*x**3*(-30)\nReplacing -30*(-29*x**3 - 56*x**2 + 21*x) with (21*x)*(-30) - 56*x**2*(-30) - 29*x**3*(-30) in the overall expression.\n#Step 3:\nCurrent expression: (21*x)*(-30) - 56*x**2*(-30) + (-41*x**2)*(-29*x**3 - 56*x**2 + 21*x) - 29*x**3*(-30)\nSimplifying the partial expression: (-41*x**2)*(-29*x**3 - 56*x**2 + 21*x)\nExpanding the part (-29*x**3 - 56*x**2 + 21*x) using the distributive property, and we got: (21*x)*(-41*x**2) + (-56*x**2)*(-41*x**2) + (-41*x**2)*(-29*x**3)\nReplacing (-41*x**2)*(-29*x**3 - 56*x**2 + 21*x) with (21*x)*(-41*x**2) + (-56*x**2)*(-41*x**2) + (-41*x**2)*(-29*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (21*x)*(-41*x**2) + (21*x)*(-30) + (-56*x**2)*(-41*x**2) - 56*x**2*(-30) + (-41*x**2)*(-29*x**3) - 29*x**3*(-30)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-56*x**2)*-30 = 1680*x**2\n (-56*x**2)*(-41*x**2) = 2296*x**4\n (-29*x**3)*-30 = 870*x**3\n (-29*x**3)*(-41*x**2) = 1189*x**5\n (21*x)*-30 = -630*x\n (21*x)*(-41*x**2) = -861*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1189*x**5 + 2296*x**4 - 861*x**3 + 870*x**3 + 1680*x**2 - 630*x\nCombining like terms, got 1189*x**5 + 2296*x**4 + 9*x**3 + 1680*x**2 - 630*x\n#Step 6:\nCurrent expression: 1189*x**5 + 2296*x**4 + 9*x**3 + 1680*x**2 - 630*x\nNo more calculations needed.\n1189*x**5 + 2296*x**4 + 9*x**3 + 1680*x**2 - 630*x", "generated_answer": "1189*x**5 + 2296*x**4 + 9*x**3 + 1680*x**2 - 630*x", "step_length": 6} {"cot_id": "8f417776837bc96575a8ec0418ae501f01d3cc22bdeee12a6f4e13960c416ab5", "datapoint": {"question": "Simplify this expression: -540*z**3 + 1260*z\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-540*z**3 + 1260*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1534, "polynomial_expr": "-540*z**3 + 1260*z", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -540*z**3 + 1260*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -540*z**3 + 1260*z\nNo more calculations needed.\n-540*z**3 + 1260*z", "generated_answer": "-540*z**3 + 1260*z", "step_length": 2} {"cot_id": "a40ee7945bdd804a7c4c35e92e531f0fa41eb53f499dd117ab7d60aa1363b17a", "datapoint": {"question": "Calculate the following: (9*y**3 + 9*y**2)*(-39*y**3 - 47*y**2 - 23*y - 22)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-351*y**6 - 774*y**5 - 630*y**4 - 405*y**3 - 198*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1535, "polynomial_expr": "(9*y**3 + 9*y**2)*(-39*y**3 - 47*y**2 - 23*y - 22)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9*y**3 + 9*y**2)*(-39*y**3 - 47*y**2 - 23*y - 22)\nExpanding the part (9*y**3 + 9*y**2) using the distributive property, and we got: (9*y**2)*(-39*y**3 - 47*y**2 - 23*y - 22) + (9*y**3)*(-39*y**3 - 47*y**2 - 23*y - 22)\n#Step 2:\nCurrent expression: (9*y**2)*(-39*y**3 - 47*y**2 - 23*y - 22) + (9*y**3)*(-39*y**3 - 47*y**2 - 23*y - 22)\nSimplifying the partial expression: (9*y**2)*(-39*y**3 - 47*y**2 - 23*y - 22)\nExpanding the part (-39*y**3 - 47*y**2 - 23*y - 22) using the distributive property, and we got: (-23*y)*(9*y**2) - 198*y**2 + (-47*y**2)*(9*y**2) + (9*y**2)*(-39*y**3)\nReplacing (9*y**2)*(-39*y**3 - 47*y**2 - 23*y - 22) with (-23*y)*(9*y**2) - 198*y**2 + (-47*y**2)*(9*y**2) + (9*y**2)*(-39*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-23*y)*(9*y**2) - 22*9*y**2 + (-47*y**2)*(9*y**2) + (9*y**2)*(-39*y**3) + (9*y**3)*(-39*y**3 - 47*y**2 - 23*y - 22)\nSimplifying the partial expression: (9*y**3)*(-39*y**3 - 47*y**2 - 23*y - 22)\nExpanding the part (-39*y**3 - 47*y**2 - 23*y - 22) using the distributive property, and we got: (-23*y)*(9*y**3) - 198*y**3 + (-47*y**2)*(9*y**3) + (-39*y**3)*(9*y**3)\nReplacing (9*y**3)*(-39*y**3 - 47*y**2 - 23*y - 22) with (-23*y)*(9*y**3) - 198*y**3 + (-47*y**2)*(9*y**3) + (-39*y**3)*(9*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-23*y)*(9*y**2) + (-23*y)*(9*y**3) - 22*9*y**3 - 22*9*y**2 + (-47*y**2)*(9*y**2) + (-47*y**2)*(9*y**3) + (9*y**2)*(-39*y**3) + (-39*y**3)*(9*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*y**2)*(9*y**2) = -423*y**4\n (-47*y**2)*(9*y**3) = -423*y**5\n (-39*y**3)*(9*y**2) = -351*y**5\n (-39*y**3)*(9*y**3) = -351*y**6\n (-23*y)*(9*y**2) = -207*y**3\n (-23*y)*(9*y**3) = -207*y**4\n -22*9*y**2 = -198*y**2\n -22*9*y**3 = -198*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -351*y**6 - 423*y**5 - 351*y**5 - 423*y**4 - 207*y**4 - 207*y**3 - 198*y**3 - 198*y**2\nCombining like terms, got -351*y**6 - 774*y**5 - 630*y**4 - 405*y**3 - 198*y**2\n#Step 6:\nCurrent expression: -351*y**6 - 774*y**5 - 630*y**4 - 405*y**3 - 198*y**2\nNo more calculations needed.\n-351*y**6 - 774*y**5 - 630*y**4 - 405*y**3 - 198*y**2", "generated_answer": "-351*y**6 - 774*y**5 - 630*y**4 - 405*y**3 - 198*y**2", "step_length": 6} {"cot_id": "cf86be2d7193f18ae431253f68fee86fadf0bc2304b0002d9d173a71e4107e85", "datapoint": {"question": "Calculate the following: (-44*y**3 + 51*y + 28)*(20*y**3 - 31*y**2 + 28*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-880*y**6 + 1364*y**5 - 212*y**4 - 1021*y**3 + 560*y**2 + 784*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1536, "polynomial_expr": "(-44*y**3 + 51*y + 28)*(20*y**3 - 31*y**2 + 28*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-44*y**3 + 51*y + 28)*(20*y**3 - 31*y**2 + 28*y)\nExpanding the part (-44*y**3 + 51*y + 28) using the distributive property, and we got: (51*y)*(20*y**3 - 31*y**2 + 28*y) + (-44*y**3)*(20*y**3 - 31*y**2 + 28*y) + 28*(20*y**3 - 31*y**2 + 28*y)\n#Step 2:\nCurrent expression: (51*y)*(20*y**3 - 31*y**2 + 28*y) + (-44*y**3)*(20*y**3 - 31*y**2 + 28*y) + 28*(20*y**3 - 31*y**2 + 28*y)\nSimplifying the partial expression: 28*(20*y**3 - 31*y**2 + 28*y)\nExpanding the part (20*y**3 - 31*y**2 + 28*y) using the distributive property, and we got: (28*y)*28 - 31*y**2*28 + (20*y**3)*28\nReplacing 28*(20*y**3 - 31*y**2 + 28*y) with (28*y)*28 - 31*y**2*28 + (20*y**3)*28 in the overall expression.\n#Step 3:\nCurrent expression: (28*y)*28 + (51*y)*(20*y**3 - 31*y**2 + 28*y) - 31*y**2*28 + (-44*y**3)*(20*y**3 - 31*y**2 + 28*y) + (20*y**3)*28\nSimplifying the partial expression: (-44*y**3)*(20*y**3 - 31*y**2 + 28*y)\nExpanding the part (20*y**3 - 31*y**2 + 28*y) using the distributive property, and we got: (28*y)*(-44*y**3) + (-31*y**2)*(-44*y**3) + (-44*y**3)*(20*y**3)\nReplacing (-44*y**3)*(20*y**3 - 31*y**2 + 28*y) with (28*y)*(-44*y**3) + (-31*y**2)*(-44*y**3) + (-44*y**3)*(20*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (28*y)*(-44*y**3) + (28*y)*28 + (51*y)*(20*y**3 - 31*y**2 + 28*y) + (-31*y**2)*(-44*y**3) - 31*y**2*28 + (-44*y**3)*(20*y**3) + (20*y**3)*28\nSimplifying the partial expression: (51*y)*(20*y**3 - 31*y**2 + 28*y)\nExpanding the part (20*y**3 - 31*y**2 + 28*y) using the distributive property, and we got: (28*y)*(51*y) + (51*y)*(-31*y**2) + (51*y)*(20*y**3)\nReplacing (51*y)*(20*y**3 - 31*y**2 + 28*y) with (28*y)*(51*y) + (51*y)*(-31*y**2) + (51*y)*(20*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (28*y)*(51*y) + (28*y)*(-44*y**3) + (28*y)*28 + (51*y)*(-31*y**2) + (51*y)*(20*y**3) + (-31*y**2)*(-44*y**3) - 31*y**2*28 + (-44*y**3)*(20*y**3) + (20*y**3)*28\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-31*y**2)*28 = -868*y**2\n (-31*y**2)*(-44*y**3) = 1364*y**5\n (-31*y**2)*(51*y) = -1581*y**3\n (20*y**3)*28 = 560*y**3\n (20*y**3)*(-44*y**3) = -880*y**6\n (20*y**3)*(51*y) = 1020*y**4\n (28*y)*28 = 784*y\n (28*y)*(-44*y**3) = -1232*y**4\n (28*y)*(51*y) = 1428*y**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -880*y**6 + 1364*y**5 - 1232*y**4 + 1020*y**4 - 1581*y**3 + 560*y**3 - 868*y**2 + 1428*y**2 + 784*y\nCombining like terms, got -880*y**6 + 1364*y**5 - 212*y**4 - 1021*y**3 + 560*y**2 + 784*y\n#Step 7:\nCurrent expression: -880*y**6 + 1364*y**5 - 212*y**4 - 1021*y**3 + 560*y**2 + 784*y\nNo more calculations needed.\n-880*y**6 + 1364*y**5 - 212*y**4 - 1021*y**3 + 560*y**2 + 784*y", "generated_answer": "-880*y**6 + 1364*y**5 - 212*y**4 - 1021*y**3 + 560*y**2 + 784*y", "step_length": 7} {"cot_id": "c96c5af78533e0d16b1da22732aec12837cda516087b0abeba2ad29addf42384", "datapoint": {"question": "Calculate the following: (-62*x**3 - 6)*(-21*x**2 - 28*x - 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1302*x**5 + 1736*x**4 + 868*x**3 + 126*x**2 + 168*x + 84", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1537, "polynomial_expr": "(-62*x**3 - 6)*(-21*x**2 - 28*x - 14)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-62*x**3 - 6)*(-21*x**2 - 28*x - 14)\nExpanding the part (-62*x**3 - 6) using the distributive property, and we got: (-62*x**3)*(-21*x**2 - 28*x - 14) - 6*(-21*x**2 - 28*x - 14)\n#Step 2:\nCurrent expression: (-62*x**3)*(-21*x**2 - 28*x - 14) - 6*(-21*x**2 - 28*x - 14)\nSimplifying the partial expression: -6*(-21*x**2 - 28*x - 14)\nExpanding the part (-21*x**2 - 28*x - 14) using the distributive property, and we got: -28*x*(-6) - 21*x**2*(-6) - 14*(-6)\nReplacing -6*(-21*x**2 - 28*x - 14) with -28*x*(-6) - 21*x**2*(-6) - 14*(-6) in the overall expression.\n#Step 3:\nCurrent expression: -28*x*(-6) - 21*x**2*(-6) + (-62*x**3)*(-21*x**2 - 28*x - 14) + 84\nSimplifying the partial expression: (-62*x**3)*(-21*x**2 - 28*x - 14)\nExpanding the part (-21*x**2 - 28*x - 14) using the distributive property, and we got: (-28*x)*(-62*x**3) - (-1)*868*x**3 + (-21*x**2)*(-62*x**3)\nReplacing (-62*x**3)*(-21*x**2 - 28*x - 14) with (-28*x)*(-62*x**3) - (-1)*868*x**3 + (-21*x**2)*(-62*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-28*x)*(-62*x**3) - 28*x*(-6) - 14*(-62)*x**3 + (-21*x**2)*(-62*x**3) - 21*x**2*(-6) + 84\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*x)*-6 = 168*x\n (-28*x)*(-62*x**3) = 1736*x**4\n (-21*x**2)*-6 = 126*x**2\n (-21*x**2)*(-62*x**3) = 1302*x**5\n -14*-62*x**3 = 868*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1302*x**5 + 1736*x**4 + 868*x**3 + 126*x**2 + 168*x + 84\nNo more calculations needed.\n1302*x**5 + 1736*x**4 + 868*x**3 + 126*x**2 + 168*x + 84", "generated_answer": "1302*x**5 + 1736*x**4 + 868*x**3 + 126*x**2 + 168*x + 84", "step_length": 5} {"cot_id": "6d5ad078dfe497fae0cbec13d4740ca57972ba721f7e74246760a0094d7ef7ef", "datapoint": {"question": "Calculate the following: (29 - 4*x)*(28*x**3 + 7*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-112*x**4 + 784*x**3 + 203*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1538, "polynomial_expr": "(29 - 4*x)*(28*x**3 + 7*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29 - 4*x)*(28*x**3 + 7*x**2)\nExpanding the part (29 - 4*x) using the distributive property, and we got: (-4*x)*(28*x**3 + 7*x**2) + 29*(28*x**3 + 7*x**2)\n#Step 2:\nCurrent expression: (-4*x)*(28*x**3 + 7*x**2) + 29*(28*x**3 + 7*x**2)\nSimplifying the partial expression: 29*(28*x**3 + 7*x**2)\nExpanding the part (28*x**3 + 7*x**2) using the distributive property, and we got: (7*x**2)*29 + (28*x**3)*29\nReplacing 29*(28*x**3 + 7*x**2) with (7*x**2)*29 + (28*x**3)*29 in the overall expression.\n#Step 3:\nCurrent expression: (-4*x)*(28*x**3 + 7*x**2) + (7*x**2)*29 + (28*x**3)*29\nSimplifying the partial expression: (-4*x)*(28*x**3 + 7*x**2)\nExpanding the part (28*x**3 + 7*x**2) using the distributive property, and we got: (-4*x)*(7*x**2) + (-4*x)*(28*x**3)\nReplacing (-4*x)*(28*x**3 + 7*x**2) with (-4*x)*(7*x**2) + (-4*x)*(28*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-4*x)*(7*x**2) + (-4*x)*(28*x**3) + (7*x**2)*29 + (28*x**3)*29\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (7*x**2)*29 = 203*x**2\n (7*x**2)*(-4*x) = -28*x**3\n (28*x**3)*29 = 812*x**3\n (28*x**3)*(-4*x) = -112*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -112*x**4 - 28*x**3 + 812*x**3 + 203*x**2\nCombining like terms, got -112*x**4 + 784*x**3 + 203*x**2\n#Step 6:\nCurrent expression: -112*x**4 + 784*x**3 + 203*x**2\nNo more calculations needed.\n-112*x**4 + 784*x**3 + 203*x**2", "generated_answer": "-112*x**4 + 784*x**3 + 203*x**2", "step_length": 6} {"cot_id": "c0ed319228a02158e9a706964d6a01e44c99dacd0466def6171921cd6b95b9fd", "datapoint": {"question": "Calculate the following: 32*z*(-91*z**3 + 32*z**2 + 4*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2912*z**4 + 1024*z**3 + 128*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1539, "polynomial_expr": "32*z*(-91*z**3 + 32*z**2 + 4*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 32*z*(-91*z**3 + 32*z**2 + 4*z)\nExpanding the part (-91*z**3 + 32*z**2 + 4*z) using the distributive property, and we got: (4*z)*(32*z) + (32*z)*(32*z**2) + (32*z)*(-91*z**3)\n#Step 2:\nCurrent expression: (4*z)*(32*z) + (32*z)*(32*z**2) + (32*z)*(-91*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-91*z**3)*(32*z) = -2912*z**4\n (4*z)*(32*z) = 128*z**2\n (32*z**2)*(32*z) = 1024*z**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -2912*z**4 + 1024*z**3 + 128*z**2\nNo more calculations needed.\n-2912*z**4 + 1024*z**3 + 128*z**2", "generated_answer": "-2912*z**4 + 1024*z**3 + 128*z**2", "step_length": 3} {"cot_id": "bcee4788d10e827cb1a551a0488b60a693a23da9fb3c4a8401ed1530912b2133", "datapoint": {"question": "Simplify this expression: (-31*x**3 + 41*x**2)*(8*x**3 - 3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-248*x**6 + 328*x**5 + 93*x**3 - 123*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1540, "polynomial_expr": "(-31*x**3 + 41*x**2)*(8*x**3 - 3)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-31*x**3 + 41*x**2)*(8*x**3 - 3)\nExpanding the part (8*x**3 - 3) using the distributive property, and we got: (8*x**3)*(-31*x**3 + 41*x**2) - 3*(-31*x**3 + 41*x**2)\n#Step 2:\nCurrent expression: (8*x**3)*(-31*x**3 + 41*x**2) - 3*(-31*x**3 + 41*x**2)\nSimplifying the partial expression: -3*(-31*x**3 + 41*x**2)\nExpanding the part (-31*x**3 + 41*x**2) using the distributive property, and we got: (41*x**2)*(-3) - 31*x**3*(-3)\nReplacing -3*(-31*x**3 + 41*x**2) with (41*x**2)*(-3) - 31*x**3*(-3) in the overall expression.\n#Step 3:\nCurrent expression: (41*x**2)*(-3) - 31*x**3*(-3) + (8*x**3)*(-31*x**3 + 41*x**2)\nSimplifying the partial expression: (8*x**3)*(-31*x**3 + 41*x**2)\nExpanding the part (-31*x**3 + 41*x**2) using the distributive property, and we got: (41*x**2)*(8*x**3) + (-31*x**3)*(8*x**3)\nReplacing (8*x**3)*(-31*x**3 + 41*x**2) with (41*x**2)*(8*x**3) + (-31*x**3)*(8*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (41*x**2)*(8*x**3) + (41*x**2)*(-3) + (-31*x**3)*(8*x**3) - 31*x**3*(-3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-31*x**3)*-3 = 93*x**3\n (-31*x**3)*(8*x**3) = -248*x**6\n (41*x**2)*-3 = -123*x**2\n (41*x**2)*(8*x**3) = 328*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -248*x**6 + 328*x**5 + 93*x**3 - 123*x**2\nNo more calculations needed.\n-248*x**6 + 328*x**5 + 93*x**3 - 123*x**2", "generated_answer": "-248*x**6 + 328*x**5 + 93*x**3 - 123*x**2", "step_length": 5} {"cot_id": "92f6b7f2d7f7e1828a50fc2bc1cf30dfd94b74116a915d3979db175a7e0c200a", "datapoint": {"question": "Simplify this expression: (32 - 3*y**2)*(35*y**3 + 35*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-105*y**5 - 105*y**4 + 1120*y**3 + 1120*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1541, "polynomial_expr": "(32 - 3*y**2)*(35*y**3 + 35*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (32 - 3*y**2)*(35*y**3 + 35*y**2)\nExpanding the part (32 - 3*y**2) using the distributive property, and we got: (-3*y**2)*(35*y**3 + 35*y**2) + 32*(35*y**3 + 35*y**2)\n#Step 2:\nCurrent expression: (-3*y**2)*(35*y**3 + 35*y**2) + 32*(35*y**3 + 35*y**2)\nSimplifying the partial expression: 32*(35*y**3 + 35*y**2)\nExpanding the part (35*y**3 + 35*y**2) using the distributive property, and we got: (35*y**2)*32 + (35*y**3)*32\nReplacing 32*(35*y**3 + 35*y**2) with (35*y**2)*32 + (35*y**3)*32 in the overall expression.\n#Step 3:\nCurrent expression: (-3*y**2)*(35*y**3 + 35*y**2) + (35*y**2)*32 + (35*y**3)*32\nSimplifying the partial expression: (-3*y**2)*(35*y**3 + 35*y**2)\nExpanding the part (35*y**3 + 35*y**2) using the distributive property, and we got: (-3*y**2)*(35*y**2) + (-3*y**2)*(35*y**3)\nReplacing (-3*y**2)*(35*y**3 + 35*y**2) with (-3*y**2)*(35*y**2) + (-3*y**2)*(35*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-3*y**2)*(35*y**2) + (-3*y**2)*(35*y**3) + (35*y**2)*32 + (35*y**3)*32\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (35*y**2)*32 = 1120*y**2\n (35*y**2)*(-3*y**2) = -105*y**4\n (35*y**3)*32 = 1120*y**3\n (35*y**3)*(-3*y**2) = -105*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -105*y**5 - 105*y**4 + 1120*y**3 + 1120*y**2\nNo more calculations needed.\n-105*y**5 - 105*y**4 + 1120*y**3 + 1120*y**2", "generated_answer": "-105*y**5 - 105*y**4 + 1120*y**3 + 1120*y**2", "step_length": 5} {"cot_id": "aca307598d0c708d9cafc73d5d10c79dcbe834c8108b55335ab43129c2b9cae3", "datapoint": {"question": "Calculate the following: -8*y*(43*y + 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-344*y**2 - 128*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1542, "polynomial_expr": "-8*y*(43*y + 16)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -8*y*(43*y + 16)\nExpanding the part (43*y + 16) using the distributive property, and we got: (-8*y)*(43*y) + 16*(-8*y)\n#Step 2:\nCurrent expression: (-8*y)*(43*y) + 16*(-8*y)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 16*(-8*y) = -128*y\n (43*y)*(-8*y) = -344*y**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -344*y**2 - 128*y\nNo more calculations needed.\n-344*y**2 - 128*y", "generated_answer": "-344*y**2 - 128*y", "step_length": 3} {"cot_id": "c55c4e6d35987c09e786daf61ed4cad072234e2bc7bbe53088d3de425555e537", "datapoint": {"question": "Calculate the following: (-43*z**2 - 44*z - 45)*(33*z**3 + 2*z**2 + 12*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1419*z**5 - 1538*z**4 - 2089*z**3 - 618*z**2 - 540*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1543, "polynomial_expr": "(-43*z**2 - 44*z - 45)*(33*z**3 + 2*z**2 + 12*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-43*z**2 - 44*z - 45)*(33*z**3 + 2*z**2 + 12*z)\nExpanding the part (-43*z**2 - 44*z - 45) using the distributive property, and we got: (-44*z)*(33*z**3 + 2*z**2 + 12*z) + (-43*z**2)*(33*z**3 + 2*z**2 + 12*z) - 45*(33*z**3 + 2*z**2 + 12*z)\n#Step 2:\nCurrent expression: (-44*z)*(33*z**3 + 2*z**2 + 12*z) + (-43*z**2)*(33*z**3 + 2*z**2 + 12*z) - 45*(33*z**3 + 2*z**2 + 12*z)\nSimplifying the partial expression: -45*(33*z**3 + 2*z**2 + 12*z)\nExpanding the part (33*z**3 + 2*z**2 + 12*z) using the distributive property, and we got: (12*z)*(-45) + (2*z**2)*(-45) + (33*z**3)*(-45)\nReplacing -45*(33*z**3 + 2*z**2 + 12*z) with (12*z)*(-45) + (2*z**2)*(-45) + (33*z**3)*(-45) in the overall expression.\n#Step 3:\nCurrent expression: (-44*z)*(33*z**3 + 2*z**2 + 12*z) + (12*z)*(-45) + (-43*z**2)*(33*z**3 + 2*z**2 + 12*z) + (2*z**2)*(-45) + (33*z**3)*(-45)\nSimplifying the partial expression: (-44*z)*(33*z**3 + 2*z**2 + 12*z)\nExpanding the part (33*z**3 + 2*z**2 + 12*z) using the distributive property, and we got: (-44*z)*(12*z) + (-44*z)*(2*z**2) + (-44*z)*(33*z**3)\nReplacing (-44*z)*(33*z**3 + 2*z**2 + 12*z) with (-44*z)*(12*z) + (-44*z)*(2*z**2) + (-44*z)*(33*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-44*z)*(12*z) + (-44*z)*(2*z**2) + (-44*z)*(33*z**3) + (12*z)*(-45) + (-43*z**2)*(33*z**3 + 2*z**2 + 12*z) + (2*z**2)*(-45) + (33*z**3)*(-45)\nSimplifying the partial expression: (-43*z**2)*(33*z**3 + 2*z**2 + 12*z)\nExpanding the part (33*z**3 + 2*z**2 + 12*z) using the distributive property, and we got: (12*z)*(-43*z**2) + (-43*z**2)*(2*z**2) + (-43*z**2)*(33*z**3)\nReplacing (-43*z**2)*(33*z**3 + 2*z**2 + 12*z) with (12*z)*(-43*z**2) + (-43*z**2)*(2*z**2) + (-43*z**2)*(33*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-44*z)*(12*z) + (-44*z)*(2*z**2) + (-44*z)*(33*z**3) + (12*z)*(-43*z**2) + (12*z)*(-45) + (-43*z**2)*(2*z**2) + (-43*z**2)*(33*z**3) + (2*z**2)*(-45) + (33*z**3)*(-45)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (2*z**2)*-45 = -90*z**2\n (2*z**2)*(-44*z) = -88*z**3\n (2*z**2)*(-43*z**2) = -86*z**4\n (12*z)*-45 = -540*z\n (12*z)*(-44*z) = -528*z**2\n (12*z)*(-43*z**2) = -516*z**3\n (33*z**3)*-45 = -1485*z**3\n (33*z**3)*(-44*z) = -1452*z**4\n (33*z**3)*(-43*z**2) = -1419*z**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1419*z**5 - 1452*z**4 - 86*z**4 - 1485*z**3 - 516*z**3 - 88*z**3 - 528*z**2 - 90*z**2 - 540*z\nCombining like terms, got -1419*z**5 - 1538*z**4 - 2089*z**3 - 618*z**2 - 540*z\n#Step 7:\nCurrent expression: -1419*z**5 - 1538*z**4 - 2089*z**3 - 618*z**2 - 540*z\nNo more calculations needed.\n-1419*z**5 - 1538*z**4 - 2089*z**3 - 618*z**2 - 540*z", "generated_answer": "-1419*z**5 - 1538*z**4 - 2089*z**3 - 618*z**2 - 540*z", "step_length": 7} {"cot_id": "d02c3ff635fdc32803aecd3b9355481aadd9a8a5efbfcb1bb4afebbf34a3b97e", "datapoint": {"question": "Simplify this expression: 12*y**3*(-15*y**3 - 23*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-180*y**6 - 276*y**5", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1544, "polynomial_expr": "12*y**3*(-15*y**3 - 23*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 12*y**3*(-15*y**3 - 23*y**2)\nExpanding the part (-15*y**3 - 23*y**2) using the distributive property, and we got: (-23*y**2)*(12*y**3) + (-15*y**3)*(12*y**3)\n#Step 2:\nCurrent expression: (-23*y**2)*(12*y**3) + (-15*y**3)*(12*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*y**2)*(12*y**3) = -276*y**5\n (-15*y**3)*(12*y**3) = -180*y**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -180*y**6 - 276*y**5\nNo more calculations needed.\n-180*y**6 - 276*y**5", "generated_answer": "-180*y**6 - 276*y**5", "step_length": 3} {"cot_id": "61b88dbe7bbe57bcd8396f3c8e3cf3b050fd1ef23d210f9ddcff9d8bf9d628f2", "datapoint": {"question": "Simplify this expression: (4 - 5*x**3)*(-35*x**3 + 35*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "175*x**6 - 175*x**5 - 140*x**3 + 140*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1545, "polynomial_expr": "(4 - 5*x**3)*(-35*x**3 + 35*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (4 - 5*x**3)*(-35*x**3 + 35*x**2)\nExpanding the part (4 - 5*x**3) using the distributive property, and we got: (-5*x**3)*(-35*x**3 + 35*x**2) + 4*(-35*x**3 + 35*x**2)\n#Step 2:\nCurrent expression: (-5*x**3)*(-35*x**3 + 35*x**2) + 4*(-35*x**3 + 35*x**2)\nSimplifying the partial expression: 4*(-35*x**3 + 35*x**2)\nExpanding the part (-35*x**3 + 35*x**2) using the distributive property, and we got: (35*x**2)*4 - 35*x**3*4\nReplacing 4*(-35*x**3 + 35*x**2) with (35*x**2)*4 - 35*x**3*4 in the overall expression.\n#Step 3:\nCurrent expression: (35*x**2)*4 - 35*x**3*4 + (-5*x**3)*(-35*x**3 + 35*x**2)\nSimplifying the partial expression: (-5*x**3)*(-35*x**3 + 35*x**2)\nExpanding the part (-35*x**3 + 35*x**2) using the distributive property, and we got: (35*x**2)*(-5*x**3) + (-35*x**3)*(-5*x**3)\nReplacing (-5*x**3)*(-35*x**3 + 35*x**2) with (35*x**2)*(-5*x**3) + (-35*x**3)*(-5*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (35*x**2)*(-5*x**3) + (35*x**2)*4 + (-35*x**3)*(-5*x**3) - 35*x**3*4\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*x**3)*4 = -140*x**3\n (-35*x**3)*(-5*x**3) = 175*x**6\n (35*x**2)*4 = 140*x**2\n (35*x**2)*(-5*x**3) = -175*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 175*x**6 - 175*x**5 - 140*x**3 + 140*x**2\nNo more calculations needed.\n175*x**6 - 175*x**5 - 140*x**3 + 140*x**2", "generated_answer": "175*x**6 - 175*x**5 - 140*x**3 + 140*x**2", "step_length": 5} {"cot_id": "bfd7901ec5e44b0abce20a52d60aa1ad4a06d3030ac7127ed75c4d15f87421ca", "datapoint": {"question": "Simplify this expression: -512*z**3 - 64\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-512*z**3 - 64", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1546, "polynomial_expr": "-512*z**3 - 64", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -512*z**3 - 64\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -512*z**3 - 64\nNo more calculations needed.\n-512*z**3 - 64", "generated_answer": "-512*z**3 - 64", "step_length": 2} {"cot_id": "5397b375e9c70a6919077be260a45abf04f7cbaba52fd2da01aec79796846200", "datapoint": {"question": "Simplify this expression: 49*x**3*(47*x**2 - 35*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2303*x**5 - 1715*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1547, "polynomial_expr": "49*x**3*(47*x**2 - 35*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 49*x**3*(47*x**2 - 35*x)\nExpanding the part (47*x**2 - 35*x) using the distributive property, and we got: (-35*x)*(49*x**3) + (47*x**2)*(49*x**3)\n#Step 2:\nCurrent expression: (-35*x)*(49*x**3) + (47*x**2)*(49*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*x)*(49*x**3) = -1715*x**4\n (47*x**2)*(49*x**3) = 2303*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 2303*x**5 - 1715*x**4\nNo more calculations needed.\n2303*x**5 - 1715*x**4", "generated_answer": "2303*x**5 - 1715*x**4", "step_length": 3} {"cot_id": "6d389d470fb39f92fac5d877474f061df1cab602e4caf69cc7d41ecd08f961f4", "datapoint": {"question": "Calculate the following: (-70*x**3 + 17*x)*(5*x**2 + 19*x - 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-350*x**5 - 1330*x**4 + 575*x**3 + 323*x**2 - 119*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1548, "polynomial_expr": "(-70*x**3 + 17*x)*(5*x**2 + 19*x - 7)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-70*x**3 + 17*x)*(5*x**2 + 19*x - 7)\nExpanding the part (-70*x**3 + 17*x) using the distributive property, and we got: (17*x)*(5*x**2 + 19*x - 7) + (-70*x**3)*(5*x**2 + 19*x - 7)\n#Step 2:\nCurrent expression: (17*x)*(5*x**2 + 19*x - 7) + (-70*x**3)*(5*x**2 + 19*x - 7)\nSimplifying the partial expression: (-70*x**3)*(5*x**2 + 19*x - 7)\nExpanding the part (5*x**2 + 19*x - 7) using the distributive property, and we got: -(-1)*490*x**3 + (19*x)*(-70*x**3) + (5*x**2)*(-70*x**3)\nReplacing (-70*x**3)*(5*x**2 + 19*x - 7) with -(-1)*490*x**3 + (19*x)*(-70*x**3) + (5*x**2)*(-70*x**3) in the overall expression.\n#Step 3:\nCurrent expression: -7*(-70)*x**3 + (17*x)*(5*x**2 + 19*x - 7) + (19*x)*(-70*x**3) + (5*x**2)*(-70*x**3)\nSimplifying the partial expression: (17*x)*(5*x**2 + 19*x - 7)\nExpanding the part (5*x**2 + 19*x - 7) using the distributive property, and we got: -119*x + (17*x)*(19*x) + (17*x)*(5*x**2)\nReplacing (17*x)*(5*x**2 + 19*x - 7) with -119*x + (17*x)*(19*x) + (17*x)*(5*x**2) in the overall expression.\n#Step 4:\nCurrent expression: -7*(-70)*x**3 - 7*17*x + (17*x)*(19*x) + (17*x)*(5*x**2) + (19*x)*(-70*x**3) + (5*x**2)*(-70*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (5*x**2)*(-70*x**3) = -350*x**5\n (5*x**2)*(17*x) = 85*x**3\n (19*x)*(-70*x**3) = -1330*x**4\n (19*x)*(17*x) = 323*x**2\n -7*-70*x**3 = 490*x**3\n -7*17*x = -119*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -350*x**5 - 1330*x**4 + 85*x**3 + 490*x**3 + 323*x**2 - 119*x\nCombining like terms, got -350*x**5 - 1330*x**4 + 575*x**3 + 323*x**2 - 119*x\n#Step 6:\nCurrent expression: -350*x**5 - 1330*x**4 + 575*x**3 + 323*x**2 - 119*x\nNo more calculations needed.\n-350*x**5 - 1330*x**4 + 575*x**3 + 323*x**2 - 119*x", "generated_answer": "-350*x**5 - 1330*x**4 + 575*x**3 + 323*x**2 - 119*x", "step_length": 6} {"cot_id": "6d4e81f24ae44252be25b8a9ab96373eb971dd2cc0a3e2c8d457f690cdf55d04", "datapoint": {"question": "Simplify this expression: (49 - 30*z**3)*(7*z - 34)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-210*z**4 + 1020*z**3 + 343*z - 1666", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1549, "polynomial_expr": "(49 - 30*z**3)*(7*z - 34)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (49 - 30*z**3)*(7*z - 34)\nExpanding the part (7*z - 34) using the distributive property, and we got: (7*z)*(49 - 30*z**3) - 34*(49 - 30*z**3)\n#Step 2:\nCurrent expression: (7*z)*(49 - 30*z**3) - 34*(49 - 30*z**3)\nSimplifying the partial expression: -34*(49 - 30*z**3)\nExpanding the part (49 - 30*z**3) using the distributive property, and we got: -30*z**3*(-34) + 49*(-34)\nReplacing -34*(49 - 30*z**3) with -30*z**3*(-34) + 49*(-34) in the overall expression.\n#Step 3:\nCurrent expression: (7*z)*(49 - 30*z**3) - 30*z**3*(-34) - 1666\nSimplifying the partial expression: (7*z)*(49 - 30*z**3)\nExpanding the part (49 - 30*z**3) using the distributive property, and we got: 49*(7*z) + (7*z)*(-30*z**3)\nReplacing (7*z)*(49 - 30*z**3) with 49*(7*z) + (7*z)*(-30*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 49*7*z + (7*z)*(-30*z**3) - 30*z**3*(-34) - 1666\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*z**3)*-34 = 1020*z**3\n (-30*z**3)*(7*z) = -210*z**4\n 49*7*z = 343*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -210*z**4 + 1020*z**3 + 343*z - 1666\nNo more calculations needed.\n-210*z**4 + 1020*z**3 + 343*z - 1666", "generated_answer": "-210*z**4 + 1020*z**3 + 343*z - 1666", "step_length": 5} {"cot_id": "c0e63be9f5a0d1930f4865255d9f78a6d5a72d8bb39a123bd08163395dd0b3b3", "datapoint": {"question": "Calculate the following: (18*y**2 + 2*y)*(-16*y**3 + 68*y**2 + 36*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-288*y**5 + 1192*y**4 + 784*y**3 + 72*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1550, "polynomial_expr": "(18*y**2 + 2*y)*(-16*y**3 + 68*y**2 + 36*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (18*y**2 + 2*y)*(-16*y**3 + 68*y**2 + 36*y)\nExpanding the part (18*y**2 + 2*y) using the distributive property, and we got: (2*y)*(-16*y**3 + 68*y**2 + 36*y) + (18*y**2)*(-16*y**3 + 68*y**2 + 36*y)\n#Step 2:\nCurrent expression: (2*y)*(-16*y**3 + 68*y**2 + 36*y) + (18*y**2)*(-16*y**3 + 68*y**2 + 36*y)\nSimplifying the partial expression: (2*y)*(-16*y**3 + 68*y**2 + 36*y)\nExpanding the part (-16*y**3 + 68*y**2 + 36*y) using the distributive property, and we got: (2*y)*(36*y) + (2*y)*(68*y**2) + (2*y)*(-16*y**3)\nReplacing (2*y)*(-16*y**3 + 68*y**2 + 36*y) with (2*y)*(36*y) + (2*y)*(68*y**2) + (2*y)*(-16*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (2*y)*(36*y) + (2*y)*(68*y**2) + (2*y)*(-16*y**3) + (18*y**2)*(-16*y**3 + 68*y**2 + 36*y)\nSimplifying the partial expression: (18*y**2)*(-16*y**3 + 68*y**2 + 36*y)\nExpanding the part (-16*y**3 + 68*y**2 + 36*y) using the distributive property, and we got: (36*y)*(18*y**2) + (18*y**2)*(68*y**2) + (18*y**2)*(-16*y**3)\nReplacing (18*y**2)*(-16*y**3 + 68*y**2 + 36*y) with (36*y)*(18*y**2) + (18*y**2)*(68*y**2) + (18*y**2)*(-16*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (2*y)*(36*y) + (2*y)*(68*y**2) + (2*y)*(-16*y**3) + (36*y)*(18*y**2) + (18*y**2)*(68*y**2) + (18*y**2)*(-16*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-16*y**3)*(2*y) = -32*y**4\n (-16*y**3)*(18*y**2) = -288*y**5\n (36*y)*(2*y) = 72*y**2\n (36*y)*(18*y**2) = 648*y**3\n (68*y**2)*(2*y) = 136*y**3\n (68*y**2)*(18*y**2) = 1224*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -288*y**5 - 32*y**4 + 1224*y**4 + 136*y**3 + 648*y**3 + 72*y**2\nCombining like terms, got -288*y**5 + 1192*y**4 + 784*y**3 + 72*y**2\n#Step 6:\nCurrent expression: -288*y**5 + 1192*y**4 + 784*y**3 + 72*y**2\nNo more calculations needed.\n-288*y**5 + 1192*y**4 + 784*y**3 + 72*y**2", "generated_answer": "-288*y**5 + 1192*y**4 + 784*y**3 + 72*y**2", "step_length": 6} {"cot_id": "e04330b87edc1c19917fca6f4fbfcb56d8613bc3ea903d15293acb7d97cf30ed", "datapoint": {"question": "Calculate the following: (29*y + 6)*(-9*y**2 + 44*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-261*y**3 + 1222*y**2 + 264*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1551, "polynomial_expr": "(29*y + 6)*(-9*y**2 + 44*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29*y + 6)*(-9*y**2 + 44*y)\nExpanding the part (29*y + 6) using the distributive property, and we got: (29*y)*(-9*y**2 + 44*y) + 6*(-9*y**2 + 44*y)\n#Step 2:\nCurrent expression: (29*y)*(-9*y**2 + 44*y) + 6*(-9*y**2 + 44*y)\nSimplifying the partial expression: 6*(-9*y**2 + 44*y)\nExpanding the part (-9*y**2 + 44*y) using the distributive property, and we got: (44*y)*6 - 9*y**2*6\nReplacing 6*(-9*y**2 + 44*y) with (44*y)*6 - 9*y**2*6 in the overall expression.\n#Step 3:\nCurrent expression: (29*y)*(-9*y**2 + 44*y) + (44*y)*6 - 9*y**2*6\nSimplifying the partial expression: (29*y)*(-9*y**2 + 44*y)\nExpanding the part (-9*y**2 + 44*y) using the distributive property, and we got: (29*y)*(44*y) + (29*y)*(-9*y**2)\nReplacing (29*y)*(-9*y**2 + 44*y) with (29*y)*(44*y) + (29*y)*(-9*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (29*y)*(44*y) + (29*y)*(-9*y**2) + (44*y)*6 - 9*y**2*6\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-9*y**2)*6 = -54*y**2\n (-9*y**2)*(29*y) = -261*y**3\n (44*y)*6 = 264*y\n (44*y)*(29*y) = 1276*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -261*y**3 - 54*y**2 + 1276*y**2 + 264*y\nCombining like terms, got -261*y**3 + 1222*y**2 + 264*y\n#Step 6:\nCurrent expression: -261*y**3 + 1222*y**2 + 264*y\nNo more calculations needed.\n-261*y**3 + 1222*y**2 + 264*y", "generated_answer": "-261*y**3 + 1222*y**2 + 264*y", "step_length": 6} {"cot_id": "7ffba144b57332c146978345c2336eb95ddecd9e52cc7658b98eb2523575169f", "datapoint": {"question": "Calculate the following: (5*z**2 + 19*z)*(28*z**3 - 46*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "140*z**5 + 302*z**4 - 874*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1552, "polynomial_expr": "(5*z**2 + 19*z)*(28*z**3 - 46*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (5*z**2 + 19*z)*(28*z**3 - 46*z**2)\nExpanding the part (28*z**3 - 46*z**2) using the distributive property, and we got: (-46*z**2)*(5*z**2 + 19*z) + (28*z**3)*(5*z**2 + 19*z)\n#Step 2:\nCurrent expression: (-46*z**2)*(5*z**2 + 19*z) + (28*z**3)*(5*z**2 + 19*z)\nSimplifying the partial expression: (-46*z**2)*(5*z**2 + 19*z)\nExpanding the part (5*z**2 + 19*z) using the distributive property, and we got: (19*z)*(-46*z**2) + (-46*z**2)*(5*z**2)\nReplacing (-46*z**2)*(5*z**2 + 19*z) with (19*z)*(-46*z**2) + (-46*z**2)*(5*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (19*z)*(-46*z**2) + (-46*z**2)*(5*z**2) + (28*z**3)*(5*z**2 + 19*z)\nSimplifying the partial expression: (28*z**3)*(5*z**2 + 19*z)\nExpanding the part (5*z**2 + 19*z) using the distributive property, and we got: (19*z)*(28*z**3) + (5*z**2)*(28*z**3)\nReplacing (28*z**3)*(5*z**2 + 19*z) with (19*z)*(28*z**3) + (5*z**2)*(28*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (19*z)*(-46*z**2) + (19*z)*(28*z**3) + (-46*z**2)*(5*z**2) + (5*z**2)*(28*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (5*z**2)*(-46*z**2) = -230*z**4\n (5*z**2)*(28*z**3) = 140*z**5\n (19*z)*(-46*z**2) = -874*z**3\n (19*z)*(28*z**3) = 532*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 140*z**5 - 230*z**4 + 532*z**4 - 874*z**3\nCombining like terms, got 140*z**5 + 302*z**4 - 874*z**3\n#Step 6:\nCurrent expression: 140*z**5 + 302*z**4 - 874*z**3\nNo more calculations needed.\n140*z**5 + 302*z**4 - 874*z**3", "generated_answer": "140*z**5 + 302*z**4 - 874*z**3", "step_length": 6} {"cot_id": "0810e17f54b99fc2bc2810667a171198ab2d6808dcb5a84fb66483560befbefc", "datapoint": {"question": "Calculate the following: (-26*x**2 + 27*x)*(-27*x**3 - 25*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "702*x**5 - 79*x**4 - 675*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1553, "polynomial_expr": "(-26*x**2 + 27*x)*(-27*x**3 - 25*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-26*x**2 + 27*x)*(-27*x**3 - 25*x**2)\nExpanding the part (-27*x**3 - 25*x**2) using the distributive property, and we got: (-25*x**2)*(-26*x**2 + 27*x) + (-27*x**3)*(-26*x**2 + 27*x)\n#Step 2:\nCurrent expression: (-25*x**2)*(-26*x**2 + 27*x) + (-27*x**3)*(-26*x**2 + 27*x)\nSimplifying the partial expression: (-27*x**3)*(-26*x**2 + 27*x)\nExpanding the part (-26*x**2 + 27*x) using the distributive property, and we got: (27*x)*(-27*x**3) + (-26*x**2)*(-27*x**3)\nReplacing (-27*x**3)*(-26*x**2 + 27*x) with (27*x)*(-27*x**3) + (-26*x**2)*(-27*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (27*x)*(-27*x**3) + (-26*x**2)*(-27*x**3) + (-25*x**2)*(-26*x**2 + 27*x)\nSimplifying the partial expression: (-25*x**2)*(-26*x**2 + 27*x)\nExpanding the part (-26*x**2 + 27*x) using the distributive property, and we got: (27*x)*(-25*x**2) + (-26*x**2)*(-25*x**2)\nReplacing (-25*x**2)*(-26*x**2 + 27*x) with (27*x)*(-25*x**2) + (-26*x**2)*(-25*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (27*x)*(-25*x**2) + (27*x)*(-27*x**3) + (-26*x**2)*(-25*x**2) + (-26*x**2)*(-27*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-26*x**2)*(-27*x**3) = 702*x**5\n (-26*x**2)*(-25*x**2) = 650*x**4\n (27*x)*(-27*x**3) = -729*x**4\n (27*x)*(-25*x**2) = -675*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 702*x**5 - 729*x**4 + 650*x**4 - 675*x**3\nCombining like terms, got 702*x**5 - 79*x**4 - 675*x**3\n#Step 6:\nCurrent expression: 702*x**5 - 79*x**4 - 675*x**3\nNo more calculations needed.\n702*x**5 - 79*x**4 - 675*x**3", "generated_answer": "702*x**5 - 79*x**4 - 675*x**3", "step_length": 6} {"cot_id": "36cfa8c1be52b5f2b24e03888d99f1022d7728f80f1ad30fd7c338c85f38f2ae", "datapoint": {"question": "Calculate the following: (27*x**3 + 73)*(33*x**2 + 2*x - 26)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "891*x**5 + 54*x**4 - 702*x**3 + 2409*x**2 + 146*x - 1898", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1554, "polynomial_expr": "(27*x**3 + 73)*(33*x**2 + 2*x - 26)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*x**3 + 73)*(33*x**2 + 2*x - 26)\nExpanding the part (27*x**3 + 73) using the distributive property, and we got: (27*x**3)*(33*x**2 + 2*x - 26) + 73*(33*x**2 + 2*x - 26)\n#Step 2:\nCurrent expression: (27*x**3)*(33*x**2 + 2*x - 26) + 73*(33*x**2 + 2*x - 26)\nSimplifying the partial expression: 73*(33*x**2 + 2*x - 26)\nExpanding the part (33*x**2 + 2*x - 26) using the distributive property, and we got: (2*x)*73 + (33*x**2)*73 - 26*73\nReplacing 73*(33*x**2 + 2*x - 26) with (2*x)*73 + (33*x**2)*73 - 26*73 in the overall expression.\n#Step 3:\nCurrent expression: (2*x)*73 + (33*x**2)*73 + (27*x**3)*(33*x**2 + 2*x - 26) - 1898\nSimplifying the partial expression: (27*x**3)*(33*x**2 + 2*x - 26)\nExpanding the part (33*x**2 + 2*x - 26) using the distributive property, and we got: -702*x**3 + (2*x)*(27*x**3) + (33*x**2)*(27*x**3)\nReplacing (27*x**3)*(33*x**2 + 2*x - 26) with -702*x**3 + (2*x)*(27*x**3) + (33*x**2)*(27*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -26*27*x**3 + (2*x)*(27*x**3) + (2*x)*73 + (33*x**2)*(27*x**3) + (33*x**2)*73 - 1898\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (2*x)*73 = 146*x\n (2*x)*(27*x**3) = 54*x**4\n (33*x**2)*73 = 2409*x**2\n (33*x**2)*(27*x**3) = 891*x**5\n -26*27*x**3 = -702*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 891*x**5 + 54*x**4 - 702*x**3 + 2409*x**2 + 146*x - 1898\nNo more calculations needed.\n891*x**5 + 54*x**4 - 702*x**3 + 2409*x**2 + 146*x - 1898", "generated_answer": "891*x**5 + 54*x**4 - 702*x**3 + 2409*x**2 + 146*x - 1898", "step_length": 5} {"cot_id": "b698467a98a1a7998ebe02736a097d0be4e9dbbcbd3084d2e21f32d01b3787e6", "datapoint": {"question": "Calculate the following: (28*z - 34)*(42*z**3 + 11*z**2 + 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1176*z**4 - 1120*z**3 - 374*z**2 + 1148*z - 1394", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1555, "polynomial_expr": "(28*z - 34)*(42*z**3 + 11*z**2 + 41)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28*z - 34)*(42*z**3 + 11*z**2 + 41)\nExpanding the part (28*z - 34) using the distributive property, and we got: (28*z)*(42*z**3 + 11*z**2 + 41) - 34*(42*z**3 + 11*z**2 + 41)\n#Step 2:\nCurrent expression: (28*z)*(42*z**3 + 11*z**2 + 41) - 34*(42*z**3 + 11*z**2 + 41)\nSimplifying the partial expression: -34*(42*z**3 + 11*z**2 + 41)\nExpanding the part (42*z**3 + 11*z**2 + 41) using the distributive property, and we got: (11*z**2)*(-34) + (42*z**3)*(-34) + 41*(-34)\nReplacing -34*(42*z**3 + 11*z**2 + 41) with (11*z**2)*(-34) + (42*z**3)*(-34) + 41*(-34) in the overall expression.\n#Step 3:\nCurrent expression: (28*z)*(42*z**3 + 11*z**2 + 41) + (11*z**2)*(-34) + (42*z**3)*(-34) - 1394\nSimplifying the partial expression: (28*z)*(42*z**3 + 11*z**2 + 41)\nExpanding the part (42*z**3 + 11*z**2 + 41) using the distributive property, and we got: 41*(28*z) + (28*z)*(11*z**2) + (28*z)*(42*z**3)\nReplacing (28*z)*(42*z**3 + 11*z**2 + 41) with 41*(28*z) + (28*z)*(11*z**2) + (28*z)*(42*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 41*28*z + (28*z)*(11*z**2) + (28*z)*(42*z**3) + (11*z**2)*(-34) + (42*z**3)*(-34) - 1394\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (11*z**2)*-34 = -374*z**2\n (11*z**2)*(28*z) = 308*z**3\n (42*z**3)*-34 = -1428*z**3\n (42*z**3)*(28*z) = 1176*z**4\n 41*28*z = 1148*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1176*z**4 - 1428*z**3 + 308*z**3 - 374*z**2 + 1148*z - 1394\nCombining like terms, got 1176*z**4 - 1120*z**3 - 374*z**2 + 1148*z - 1394\n#Step 6:\nCurrent expression: 1176*z**4 - 1120*z**3 - 374*z**2 + 1148*z - 1394\nNo more calculations needed.\n1176*z**4 - 1120*z**3 - 374*z**2 + 1148*z - 1394", "generated_answer": "1176*z**4 - 1120*z**3 - 374*z**2 + 1148*z - 1394", "step_length": 6} {"cot_id": "76bbc79669da137c92d318a75891418c0065025d82a5ef05fea07d080cef0607", "datapoint": {"question": "Simplify this expression: (29*y**2 - 25*y - 17)*(-8*y**3 + 24*y**2 - y + 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-232*y**5 + 896*y**4 - 493*y**3 + 226*y**2 - 508*y - 357", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1556, "polynomial_expr": "(29*y**2 - 25*y - 17)*(-8*y**3 + 24*y**2 - y + 21)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29*y**2 - 25*y - 17)*(-8*y**3 + 24*y**2 - y + 21)\nExpanding the part (29*y**2 - 25*y - 17) using the distributive property, and we got: (-25*y)*(-8*y**3 + 24*y**2 - y + 21) + (29*y**2)*(-8*y**3 + 24*y**2 - y + 21) - 17*(-8*y**3 + 24*y**2 - y + 21)\n#Step 2:\nCurrent expression: (-25*y)*(-8*y**3 + 24*y**2 - y + 21) + (29*y**2)*(-8*y**3 + 24*y**2 - y + 21) - 17*(-8*y**3 + 24*y**2 - y + 21)\nSimplifying the partial expression: -17*(-8*y**3 + 24*y**2 - y + 21)\nExpanding the part (-8*y**3 + 24*y**2 - y + 21) using the distributive property, and we got: -y*(-17) + (24*y**2)*(-17) - 8*y**3*(-17) + 21*(-17)\nReplacing -17*(-8*y**3 + 24*y**2 - y + 21) with -y*(-17) + (24*y**2)*(-17) - 8*y**3*(-17) + 21*(-17) in the overall expression.\n#Step 3:\nCurrent expression: (-25*y)*(-8*y**3 + 24*y**2 - y + 21) - y*(-17) + (24*y**2)*(-17) + (29*y**2)*(-8*y**3 + 24*y**2 - y + 21) - 8*y**3*(-17) - 357\nSimplifying the partial expression: (-25*y)*(-8*y**3 + 24*y**2 - y + 21)\nExpanding the part (-8*y**3 + 24*y**2 - y + 21) using the distributive property, and we got: (-25*y)*(-y) + (-25*y)*(24*y**2) + (-25*y)*(-8*y**3) + 21*(-25*y)\nReplacing (-25*y)*(-8*y**3 + 24*y**2 - y + 21) with (-25*y)*(-y) + (-25*y)*(24*y**2) + (-25*y)*(-8*y**3) + 21*(-25*y) in the overall expression.\n#Step 4:\nCurrent expression: (-25*y)*(-y) + (-25*y)*(24*y**2) + (-25*y)*(-8*y**3) - y*(-17) + 21*(-25)*y + (24*y**2)*(-17) + (29*y**2)*(-8*y**3 + 24*y**2 - y + 21) - 8*y**3*(-17) - 357\nSimplifying the partial expression: (29*y**2)*(-8*y**3 + 24*y**2 - y + 21)\nExpanding the part (-8*y**3 + 24*y**2 - y + 21) using the distributive property, and we got: (-y)*(29*y**2) + 21*(29*y**2) + (24*y**2)*(29*y**2) + (29*y**2)*(-8*y**3)\nReplacing (29*y**2)*(-8*y**3 + 24*y**2 - y + 21) with (-y)*(29*y**2) + 21*(29*y**2) + (24*y**2)*(29*y**2) + (29*y**2)*(-8*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-25*y)*(-y) + (-25*y)*(24*y**2) + (-25*y)*(-8*y**3) + (-y)*(29*y**2) - y*(-17) + 21*29*y**2 + 21*(-25)*y + (24*y**2)*(29*y**2) + (24*y**2)*(-17) + (29*y**2)*(-8*y**3) - 8*y**3*(-17) - 357\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-y)*-17 = 17*y\n (-y)*(-25*y) = 25*y**2\n (-y)*(29*y**2) = -29*y**3\n (-8*y**3)*-17 = 136*y**3\n (-8*y**3)*(-25*y) = 200*y**4\n (-8*y**3)*(29*y**2) = -232*y**5\n (24*y**2)*-17 = -408*y**2\n (24*y**2)*(-25*y) = -600*y**3\n (24*y**2)*(29*y**2) = 696*y**4\n 21*-25*y = -525*y\n 21*29*y**2 = 609*y**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -232*y**5 + 200*y**4 + 696*y**4 - 600*y**3 - 29*y**3 + 136*y**3 - 408*y**2 + 25*y**2 + 609*y**2 - 525*y + 17*y - 357\nCombining like terms, got -232*y**5 + 896*y**4 - 493*y**3 + 226*y**2 - 508*y - 357\n#Step 7:\nCurrent expression: -232*y**5 + 896*y**4 - 493*y**3 + 226*y**2 - 508*y - 357\nNo more calculations needed.\n-232*y**5 + 896*y**4 - 493*y**3 + 226*y**2 - 508*y - 357", "generated_answer": "-232*y**5 + 896*y**4 - 493*y**3 + 226*y**2 - 508*y - 357", "step_length": 7} {"cot_id": "088e12434906825258e8a744a71617ea312efa70c387ac20ecb8a311aecf983d", "datapoint": {"question": "Simplify this expression: (-5*z**3 - 14*z**2)*(47*z**2 - z - 18)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-235*z**5 - 653*z**4 + 104*z**3 + 252*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1557, "polynomial_expr": "(-5*z**3 - 14*z**2)*(47*z**2 - z - 18)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-5*z**3 - 14*z**2)*(47*z**2 - z - 18)\nExpanding the part (-5*z**3 - 14*z**2) using the distributive property, and we got: (-14*z**2)*(47*z**2 - z - 18) + (-5*z**3)*(47*z**2 - z - 18)\n#Step 2:\nCurrent expression: (-14*z**2)*(47*z**2 - z - 18) + (-5*z**3)*(47*z**2 - z - 18)\nSimplifying the partial expression: (-14*z**2)*(47*z**2 - z - 18)\nExpanding the part (47*z**2 - z - 18) using the distributive property, and we got: (-z)*(-14*z**2) - (-1)*252*z**2 + (-14*z**2)*(47*z**2)\nReplacing (-14*z**2)*(47*z**2 - z - 18) with (-z)*(-14*z**2) - (-1)*252*z**2 + (-14*z**2)*(47*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-z)*(-14*z**2) - 18*(-14)*z**2 + (-14*z**2)*(47*z**2) + (-5*z**3)*(47*z**2 - z - 18)\nSimplifying the partial expression: (-5*z**3)*(47*z**2 - z - 18)\nExpanding the part (47*z**2 - z - 18) using the distributive property, and we got: (-z)*(-5*z**3) - (-1)*90*z**3 + (47*z**2)*(-5*z**3)\nReplacing (-5*z**3)*(47*z**2 - z - 18) with (-z)*(-5*z**3) - (-1)*90*z**3 + (47*z**2)*(-5*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-z)*(-14*z**2) + (-z)*(-5*z**3) - 18*(-5)*z**3 - 18*(-14)*z**2 + (-14*z**2)*(47*z**2) + (47*z**2)*(-5*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-z)*(-14*z**2) = 14*z**3\n (-z)*(-5*z**3) = 5*z**4\n (47*z**2)*(-14*z**2) = -658*z**4\n (47*z**2)*(-5*z**3) = -235*z**5\n -18*-14*z**2 = 252*z**2\n -18*-5*z**3 = 90*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -235*z**5 - 658*z**4 + 5*z**4 + 14*z**3 + 90*z**3 + 252*z**2\nCombining like terms, got -235*z**5 - 653*z**4 + 104*z**3 + 252*z**2\n#Step 6:\nCurrent expression: -235*z**5 - 653*z**4 + 104*z**3 + 252*z**2\nNo more calculations needed.\n-235*z**5 - 653*z**4 + 104*z**3 + 252*z**2", "generated_answer": "-235*z**5 - 653*z**4 + 104*z**3 + 252*z**2", "step_length": 6} {"cot_id": "f74e9a29d53b44b133b8a37d69a28c2ddb6c35dcef944560aca5b21733447ae8", "datapoint": {"question": "Calculate the following: (28*x**3 + 21*x**2 - 3)*(45*x**3 - 32*x**2 - 13*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1260*x**6 + 49*x**5 - 1036*x**4 - 408*x**3 + 96*x**2 + 39*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1558, "polynomial_expr": "(28*x**3 + 21*x**2 - 3)*(45*x**3 - 32*x**2 - 13*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28*x**3 + 21*x**2 - 3)*(45*x**3 - 32*x**2 - 13*x)\nExpanding the part (28*x**3 + 21*x**2 - 3) using the distributive property, and we got: (21*x**2)*(45*x**3 - 32*x**2 - 13*x) + (28*x**3)*(45*x**3 - 32*x**2 - 13*x) - 3*(45*x**3 - 32*x**2 - 13*x)\n#Step 2:\nCurrent expression: (21*x**2)*(45*x**3 - 32*x**2 - 13*x) + (28*x**3)*(45*x**3 - 32*x**2 - 13*x) - 3*(45*x**3 - 32*x**2 - 13*x)\nSimplifying the partial expression: -3*(45*x**3 - 32*x**2 - 13*x)\nExpanding the part (45*x**3 - 32*x**2 - 13*x) using the distributive property, and we got: -13*x*(-3) - 32*x**2*(-3) + (45*x**3)*(-3)\nReplacing -3*(45*x**3 - 32*x**2 - 13*x) with -13*x*(-3) - 32*x**2*(-3) + (45*x**3)*(-3) in the overall expression.\n#Step 3:\nCurrent expression: -13*x*(-3) - 32*x**2*(-3) + (21*x**2)*(45*x**3 - 32*x**2 - 13*x) + (28*x**3)*(45*x**3 - 32*x**2 - 13*x) + (45*x**3)*(-3)\nSimplifying the partial expression: (21*x**2)*(45*x**3 - 32*x**2 - 13*x)\nExpanding the part (45*x**3 - 32*x**2 - 13*x) using the distributive property, and we got: (-13*x)*(21*x**2) + (-32*x**2)*(21*x**2) + (21*x**2)*(45*x**3)\nReplacing (21*x**2)*(45*x**3 - 32*x**2 - 13*x) with (-13*x)*(21*x**2) + (-32*x**2)*(21*x**2) + (21*x**2)*(45*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-13*x)*(21*x**2) - 13*x*(-3) + (-32*x**2)*(21*x**2) - 32*x**2*(-3) + (21*x**2)*(45*x**3) + (28*x**3)*(45*x**3 - 32*x**2 - 13*x) + (45*x**3)*(-3)\nSimplifying the partial expression: (28*x**3)*(45*x**3 - 32*x**2 - 13*x)\nExpanding the part (45*x**3 - 32*x**2 - 13*x) using the distributive property, and we got: (-13*x)*(28*x**3) + (-32*x**2)*(28*x**3) + (28*x**3)*(45*x**3)\nReplacing (28*x**3)*(45*x**3 - 32*x**2 - 13*x) with (-13*x)*(28*x**3) + (-32*x**2)*(28*x**3) + (28*x**3)*(45*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-13*x)*(21*x**2) + (-13*x)*(28*x**3) - 13*x*(-3) + (-32*x**2)*(21*x**2) + (-32*x**2)*(28*x**3) - 32*x**2*(-3) + (21*x**2)*(45*x**3) + (28*x**3)*(45*x**3) + (45*x**3)*(-3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*x**2)*-3 = 96*x**2\n (-32*x**2)*(21*x**2) = -672*x**4\n (-32*x**2)*(28*x**3) = -896*x**5\n (-13*x)*-3 = 39*x\n (-13*x)*(21*x**2) = -273*x**3\n (-13*x)*(28*x**3) = -364*x**4\n (45*x**3)*-3 = -135*x**3\n (45*x**3)*(21*x**2) = 945*x**5\n (45*x**3)*(28*x**3) = 1260*x**6\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1260*x**6 - 896*x**5 + 945*x**5 - 672*x**4 - 364*x**4 - 273*x**3 - 135*x**3 + 96*x**2 + 39*x\nCombining like terms, got 1260*x**6 + 49*x**5 - 1036*x**4 - 408*x**3 + 96*x**2 + 39*x\n#Step 7:\nCurrent expression: 1260*x**6 + 49*x**5 - 1036*x**4 - 408*x**3 + 96*x**2 + 39*x\nNo more calculations needed.\n1260*x**6 + 49*x**5 - 1036*x**4 - 408*x**3 + 96*x**2 + 39*x", "generated_answer": "1260*x**6 + 49*x**5 - 1036*x**4 - 408*x**3 + 96*x**2 + 39*x", "step_length": 7} {"cot_id": "3858e4f5474c51db74c6091db56a0d9e75db5b3a616317319a0590a4ccab73c8", "datapoint": {"question": "Calculate the following: -15*y**2*(19*y**3 + 18*y**2 + 34*y + 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-285*y**5 - 270*y**4 - 510*y**3 - 300*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1559, "polynomial_expr": "-15*y**2*(19*y**3 + 18*y**2 + 34*y + 20)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -15*y**2*(19*y**3 + 18*y**2 + 34*y + 20)\nExpanding the part (19*y**3 + 18*y**2 + 34*y + 20) using the distributive property, and we got: 20*(-15*y**2) + (34*y)*(-15*y**2) + (-15*y**2)*(18*y**2) + (-15*y**2)*(19*y**3)\n#Step 2:\nCurrent expression: 20*(-15*y**2) + (34*y)*(-15*y**2) + (-15*y**2)*(18*y**2) + (-15*y**2)*(19*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 20*(-15*y**2) = -300*y**2\n (18*y**2)*(-15*y**2) = -270*y**4\n (19*y**3)*(-15*y**2) = -285*y**5\n (34*y)*(-15*y**2) = -510*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -285*y**5 - 270*y**4 - 510*y**3 - 300*y**2\nNo more calculations needed.\n-285*y**5 - 270*y**4 - 510*y**3 - 300*y**2", "generated_answer": "-285*y**5 - 270*y**4 - 510*y**3 - 300*y**2", "step_length": 3} {"cot_id": "5d2650dc9b4887c2b64029b24bfe4256e42e1706c33bba124c7236a87c177fdb", "datapoint": {"question": "Simplify this expression: (-7*y - 42)*(-20*y**3 - 18*y**2 - 30*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "140*y**4 + 966*y**3 + 966*y**2 + 1260*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1560, "polynomial_expr": "(-7*y - 42)*(-20*y**3 - 18*y**2 - 30*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-7*y - 42)*(-20*y**3 - 18*y**2 - 30*y)\nExpanding the part (-7*y - 42) using the distributive property, and we got: (-7*y)*(-20*y**3 - 18*y**2 - 30*y) - 42*(-20*y**3 - 18*y**2 - 30*y)\n#Step 2:\nCurrent expression: (-7*y)*(-20*y**3 - 18*y**2 - 30*y) - 42*(-20*y**3 - 18*y**2 - 30*y)\nSimplifying the partial expression: -42*(-20*y**3 - 18*y**2 - 30*y)\nExpanding the part (-20*y**3 - 18*y**2 - 30*y) using the distributive property, and we got: -30*y*(-42) - 18*y**2*(-42) - 20*y**3*(-42)\nReplacing -42*(-20*y**3 - 18*y**2 - 30*y) with -30*y*(-42) - 18*y**2*(-42) - 20*y**3*(-42) in the overall expression.\n#Step 3:\nCurrent expression: -30*y*(-42) + (-7*y)*(-20*y**3 - 18*y**2 - 30*y) - 18*y**2*(-42) - 20*y**3*(-42)\nSimplifying the partial expression: (-7*y)*(-20*y**3 - 18*y**2 - 30*y)\nExpanding the part (-20*y**3 - 18*y**2 - 30*y) using the distributive property, and we got: (-30*y)*(-7*y) + (-7*y)*(-18*y**2) + (-7*y)*(-20*y**3)\nReplacing (-7*y)*(-20*y**3 - 18*y**2 - 30*y) with (-30*y)*(-7*y) + (-7*y)*(-18*y**2) + (-7*y)*(-20*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-30*y)*(-7*y) - 30*y*(-42) + (-7*y)*(-18*y**2) + (-7*y)*(-20*y**3) - 18*y**2*(-42) - 20*y**3*(-42)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*y)*-42 = 1260*y\n (-30*y)*(-7*y) = 210*y**2\n (-20*y**3)*-42 = 840*y**3\n (-20*y**3)*(-7*y) = 140*y**4\n (-18*y**2)*-42 = 756*y**2\n (-18*y**2)*(-7*y) = 126*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 140*y**4 + 126*y**3 + 840*y**3 + 210*y**2 + 756*y**2 + 1260*y\nCombining like terms, got 140*y**4 + 966*y**3 + 966*y**2 + 1260*y\n#Step 6:\nCurrent expression: 140*y**4 + 966*y**3 + 966*y**2 + 1260*y\nNo more calculations needed.\n140*y**4 + 966*y**3 + 966*y**2 + 1260*y", "generated_answer": "140*y**4 + 966*y**3 + 966*y**2 + 1260*y", "step_length": 6} {"cot_id": "adc31a1debc86a745c1ca357e31fc32e50cda37c9f5f8ab134f04b203d2fc3b9", "datapoint": {"question": "Calculate the following: (-43*z**3 + 46*z**2 + 48)*(27*z**3 + 45*z - 88)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1161*z**6 + 1242*z**5 - 1935*z**4 + 7150*z**3 - 4048*z**2 + 2160*z - 4224", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1561, "polynomial_expr": "(-43*z**3 + 46*z**2 + 48)*(27*z**3 + 45*z - 88)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-43*z**3 + 46*z**2 + 48)*(27*z**3 + 45*z - 88)\nExpanding the part (27*z**3 + 45*z - 88) using the distributive property, and we got: (45*z)*(-43*z**3 + 46*z**2 + 48) + (27*z**3)*(-43*z**3 + 46*z**2 + 48) - 88*(-43*z**3 + 46*z**2 + 48)\n#Step 2:\nCurrent expression: (45*z)*(-43*z**3 + 46*z**2 + 48) + (27*z**3)*(-43*z**3 + 46*z**2 + 48) - 88*(-43*z**3 + 46*z**2 + 48)\nSimplifying the partial expression: -88*(-43*z**3 + 46*z**2 + 48)\nExpanding the part (-43*z**3 + 46*z**2 + 48) using the distributive property, and we got: (46*z**2)*(-88) - 43*z**3*(-88) + 48*(-88)\nReplacing -88*(-43*z**3 + 46*z**2 + 48) with (46*z**2)*(-88) - 43*z**3*(-88) + 48*(-88) in the overall expression.\n#Step 3:\nCurrent expression: (45*z)*(-43*z**3 + 46*z**2 + 48) + (46*z**2)*(-88) - 43*z**3*(-88) + (27*z**3)*(-43*z**3 + 46*z**2 + 48) - 4224\nSimplifying the partial expression: (27*z**3)*(-43*z**3 + 46*z**2 + 48)\nExpanding the part (-43*z**3 + 46*z**2 + 48) using the distributive property, and we got: 48*(27*z**3) + (46*z**2)*(27*z**3) + (-43*z**3)*(27*z**3)\nReplacing (27*z**3)*(-43*z**3 + 46*z**2 + 48) with 48*(27*z**3) + (46*z**2)*(27*z**3) + (-43*z**3)*(27*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 48*27*z**3 + (45*z)*(-43*z**3 + 46*z**2 + 48) + (46*z**2)*(27*z**3) + (46*z**2)*(-88) + (-43*z**3)*(27*z**3) - 43*z**3*(-88) - 4224\nSimplifying the partial expression: (45*z)*(-43*z**3 + 46*z**2 + 48)\nExpanding the part (-43*z**3 + 46*z**2 + 48) using the distributive property, and we got: 48*(45*z) + (45*z)*(46*z**2) + (45*z)*(-43*z**3)\nReplacing (45*z)*(-43*z**3 + 46*z**2 + 48) with 48*(45*z) + (45*z)*(46*z**2) + (45*z)*(-43*z**3) in the overall expression.\n#Step 5:\nCurrent expression: 48*27*z**3 + 48*45*z + (45*z)*(46*z**2) + (45*z)*(-43*z**3) + (46*z**2)*(27*z**3) + (46*z**2)*(-88) + (-43*z**3)*(27*z**3) - 43*z**3*(-88) - 4224\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-43*z**3)*-88 = 3784*z**3\n (-43*z**3)*(27*z**3) = -1161*z**6\n (-43*z**3)*(45*z) = -1935*z**4\n (46*z**2)*-88 = -4048*z**2\n (46*z**2)*(27*z**3) = 1242*z**5\n (46*z**2)*(45*z) = 2070*z**3\n 48*27*z**3 = 1296*z**3\n 48*45*z = 2160*z\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1161*z**6 + 1242*z**5 - 1935*z**4 + 1296*z**3 + 2070*z**3 + 3784*z**3 - 4048*z**2 + 2160*z - 4224\nCombining like terms, got -1161*z**6 + 1242*z**5 - 1935*z**4 + 7150*z**3 - 4048*z**2 + 2160*z - 4224\n#Step 7:\nCurrent expression: -1161*z**6 + 1242*z**5 - 1935*z**4 + 7150*z**3 - 4048*z**2 + 2160*z - 4224\nNo more calculations needed.\n-1161*z**6 + 1242*z**5 - 1935*z**4 + 7150*z**3 - 4048*z**2 + 2160*z - 4224", "generated_answer": "-1161*z**6 + 1242*z**5 - 1935*z**4 + 7150*z**3 - 4048*z**2 + 2160*z - 4224", "step_length": 7} {"cot_id": "ca99391dffd02ecf652035e6eabf227971575804b4879cefe07077e616c7fc33", "datapoint": {"question": "Simplify this expression: (21 - 42*x**2)*(-7*x**3 + 40*x + 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "294*x**5 - 1827*x**3 - 1848*x**2 + 840*x + 924", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1562, "polynomial_expr": "(21 - 42*x**2)*(-7*x**3 + 40*x + 44)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21 - 42*x**2)*(-7*x**3 + 40*x + 44)\nExpanding the part (21 - 42*x**2) using the distributive property, and we got: (-42*x**2)*(-7*x**3 + 40*x + 44) + 21*(-7*x**3 + 40*x + 44)\n#Step 2:\nCurrent expression: (-42*x**2)*(-7*x**3 + 40*x + 44) + 21*(-7*x**3 + 40*x + 44)\nSimplifying the partial expression: 21*(-7*x**3 + 40*x + 44)\nExpanding the part (-7*x**3 + 40*x + 44) using the distributive property, and we got: (40*x)*21 - 7*x**3*21 + 44*21\nReplacing 21*(-7*x**3 + 40*x + 44) with (40*x)*21 - 7*x**3*21 + 44*21 in the overall expression.\n#Step 3:\nCurrent expression: (40*x)*21 + (-42*x**2)*(-7*x**3 + 40*x + 44) - 7*x**3*21 + 924\nSimplifying the partial expression: (-42*x**2)*(-7*x**3 + 40*x + 44)\nExpanding the part (-7*x**3 + 40*x + 44) using the distributive property, and we got: 44*(-42*x**2) + (40*x)*(-42*x**2) + (-42*x**2)*(-7*x**3)\nReplacing (-42*x**2)*(-7*x**3 + 40*x + 44) with 44*(-42*x**2) + (40*x)*(-42*x**2) + (-42*x**2)*(-7*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 44*(-42)*x**2 + (40*x)*(-42*x**2) + (40*x)*21 + (-42*x**2)*(-7*x**3) - 7*x**3*21 + 924\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-7*x**3)*21 = -147*x**3\n (-7*x**3)*(-42*x**2) = 294*x**5\n (40*x)*21 = 840*x\n (40*x)*(-42*x**2) = -1680*x**3\n 44*-42*x**2 = -1848*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 294*x**5 - 1680*x**3 - 147*x**3 - 1848*x**2 + 840*x + 924\nCombining like terms, got 294*x**5 - 1827*x**3 - 1848*x**2 + 840*x + 924\n#Step 6:\nCurrent expression: 294*x**5 - 1827*x**3 - 1848*x**2 + 840*x + 924\nNo more calculations needed.\n294*x**5 - 1827*x**3 - 1848*x**2 + 840*x + 924", "generated_answer": "294*x**5 - 1827*x**3 - 1848*x**2 + 840*x + 924", "step_length": 6} {"cot_id": "e8fb0e0c62be3665f1a952af7d17d6e7c910234d40fbc49f67b08fe2492d7d6f", "datapoint": {"question": "Simplify this expression: 16*x*(15*x**3 + 44*x**2 - 45)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "240*x**4 + 704*x**3 - 720*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1563, "polynomial_expr": "16*x*(15*x**3 + 44*x**2 - 45)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 16*x*(15*x**3 + 44*x**2 - 45)\nExpanding the part (15*x**3 + 44*x**2 - 45) using the distributive property, and we got: -720*x + (16*x)*(44*x**2) + (16*x)*(15*x**3)\n#Step 2:\nCurrent expression: -720*x + (16*x)*(44*x**2) + (16*x)*(15*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -45*(16*x) = -720*x\n (15*x**3)*(16*x) = 240*x**4\n (44*x**2)*(16*x) = 704*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 240*x**4 + 704*x**3 - 720*x\nNo more calculations needed.\n240*x**4 + 704*x**3 - 720*x", "generated_answer": "240*x**4 + 704*x**3 - 720*x", "step_length": 3} {"cot_id": "77059ec06fce79ae7f0372b26b48d062f79c06ca3c269fe61c306c4f720825d4", "datapoint": {"question": "Calculate the following: -3*z**3*(31*z**3 - 61*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-93*z**6 + 183*z**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1564, "polynomial_expr": "-3*z**3*(31*z**3 - 61*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -3*z**3*(31*z**3 - 61*z)\nExpanding the part (31*z**3 - 61*z) using the distributive property, and we got: (-61*z)*(-3*z**3) + (-3*z**3)*(31*z**3)\n#Step 2:\nCurrent expression: (-61*z)*(-3*z**3) + (-3*z**3)*(31*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-61*z)*(-3*z**3) = 183*z**4\n (31*z**3)*(-3*z**3) = -93*z**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -93*z**6 + 183*z**4\nNo more calculations needed.\n-93*z**6 + 183*z**4", "generated_answer": "-93*z**6 + 183*z**4", "step_length": 3} {"cot_id": "bb048d1d43e88c66c1fdef9004d04dce6094b45a18aea0b00ff7012c53ca21ad", "datapoint": {"question": "Calculate the following: (13 - 10*x**2)*(26*x**3 - 31*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-260*x**5 + 310*x**4 + 338*x**3 - 403*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1565, "polynomial_expr": "(13 - 10*x**2)*(26*x**3 - 31*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (13 - 10*x**2)*(26*x**3 - 31*x**2)\nExpanding the part (13 - 10*x**2) using the distributive property, and we got: (-10*x**2)*(26*x**3 - 31*x**2) + 13*(26*x**3 - 31*x**2)\n#Step 2:\nCurrent expression: (-10*x**2)*(26*x**3 - 31*x**2) + 13*(26*x**3 - 31*x**2)\nSimplifying the partial expression: 13*(26*x**3 - 31*x**2)\nExpanding the part (26*x**3 - 31*x**2) using the distributive property, and we got: -31*x**2*13 + (26*x**3)*13\nReplacing 13*(26*x**3 - 31*x**2) with -31*x**2*13 + (26*x**3)*13 in the overall expression.\n#Step 3:\nCurrent expression: -31*x**2*13 + (-10*x**2)*(26*x**3 - 31*x**2) + (26*x**3)*13\nSimplifying the partial expression: (-10*x**2)*(26*x**3 - 31*x**2)\nExpanding the part (26*x**3 - 31*x**2) using the distributive property, and we got: (-31*x**2)*(-10*x**2) + (-10*x**2)*(26*x**3)\nReplacing (-10*x**2)*(26*x**3 - 31*x**2) with (-31*x**2)*(-10*x**2) + (-10*x**2)*(26*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-31*x**2)*(-10*x**2) - 31*x**2*13 + (-10*x**2)*(26*x**3) + (26*x**3)*13\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-31*x**2)*13 = -403*x**2\n (-31*x**2)*(-10*x**2) = 310*x**4\n (26*x**3)*13 = 338*x**3\n (26*x**3)*(-10*x**2) = -260*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -260*x**5 + 310*x**4 + 338*x**3 - 403*x**2\nNo more calculations needed.\n-260*x**5 + 310*x**4 + 338*x**3 - 403*x**2", "generated_answer": "-260*x**5 + 310*x**4 + 338*x**3 - 403*x**2", "step_length": 5} {"cot_id": "b1cd106706b3de82a07b45e39d1dcb0826cda0363e009a068cd1ff7fdcee9653", "datapoint": {"question": "Simplify this expression: -74*x*(-19*x**3 + 24*x**2 - 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1406*x**4 - 1776*x**3 + 1776*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1566, "polynomial_expr": "-74*x*(-19*x**3 + 24*x**2 - 24)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -74*x*(-19*x**3 + 24*x**2 - 24)\nExpanding the part (-19*x**3 + 24*x**2 - 24) using the distributive property, and we got: (-74*x)*(24*x**2) + (-74*x)*(-19*x**3) - (-1)*1776*x\n#Step 2:\nCurrent expression: (-74*x)*(24*x**2) + (-74*x)*(-19*x**3) - (-1)*1776*x\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -24*(-74*x) = 1776*x\n (-19*x**3)*(-74*x) = 1406*x**4\n (24*x**2)*(-74*x) = -1776*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1406*x**4 - 1776*x**3 + 1776*x\nNo more calculations needed.\n1406*x**4 - 1776*x**3 + 1776*x", "generated_answer": "1406*x**4 - 1776*x**3 + 1776*x", "step_length": 3} {"cot_id": "26596a0ba989c862114ec0bcf1310b892b6260198d220f4d103a917e1d0ca4db", "datapoint": {"question": "Simplify this expression: -850*y**2\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-850*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1567, "polynomial_expr": "-850*y**2", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -850*y**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -850*y**2\nNo more calculations needed.\n-850*y**2", "generated_answer": "-850*y**2", "step_length": 2} {"cot_id": "50622bf96a40f2446b6c4b7e9aae4e2e5392411fa559e597321c4b501e44d0ea", "datapoint": {"question": "Calculate the following: (-22*y**3 + 12*y)*(15*y**3 + 45*y**2 - 31*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-330*y**6 - 990*y**5 + 862*y**4 + 540*y**3 - 372*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1568, "polynomial_expr": "(-22*y**3 + 12*y)*(15*y**3 + 45*y**2 - 31*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-22*y**3 + 12*y)*(15*y**3 + 45*y**2 - 31*y)\nExpanding the part (-22*y**3 + 12*y) using the distributive property, and we got: (12*y)*(15*y**3 + 45*y**2 - 31*y) + (-22*y**3)*(15*y**3 + 45*y**2 - 31*y)\n#Step 2:\nCurrent expression: (12*y)*(15*y**3 + 45*y**2 - 31*y) + (-22*y**3)*(15*y**3 + 45*y**2 - 31*y)\nSimplifying the partial expression: (-22*y**3)*(15*y**3 + 45*y**2 - 31*y)\nExpanding the part (15*y**3 + 45*y**2 - 31*y) using the distributive property, and we got: (-31*y)*(-22*y**3) + (45*y**2)*(-22*y**3) + (-22*y**3)*(15*y**3)\nReplacing (-22*y**3)*(15*y**3 + 45*y**2 - 31*y) with (-31*y)*(-22*y**3) + (45*y**2)*(-22*y**3) + (-22*y**3)*(15*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-31*y)*(-22*y**3) + (12*y)*(15*y**3 + 45*y**2 - 31*y) + (45*y**2)*(-22*y**3) + (-22*y**3)*(15*y**3)\nSimplifying the partial expression: (12*y)*(15*y**3 + 45*y**2 - 31*y)\nExpanding the part (15*y**3 + 45*y**2 - 31*y) using the distributive property, and we got: (-31*y)*(12*y) + (12*y)*(45*y**2) + (12*y)*(15*y**3)\nReplacing (12*y)*(15*y**3 + 45*y**2 - 31*y) with (-31*y)*(12*y) + (12*y)*(45*y**2) + (12*y)*(15*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-31*y)*(12*y) + (-31*y)*(-22*y**3) + (12*y)*(45*y**2) + (12*y)*(15*y**3) + (45*y**2)*(-22*y**3) + (-22*y**3)*(15*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-31*y)*(-22*y**3) = 682*y**4\n (-31*y)*(12*y) = -372*y**2\n (15*y**3)*(-22*y**3) = -330*y**6\n (15*y**3)*(12*y) = 180*y**4\n (45*y**2)*(-22*y**3) = -990*y**5\n (45*y**2)*(12*y) = 540*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -330*y**6 - 990*y**5 + 180*y**4 + 682*y**4 + 540*y**3 - 372*y**2\nCombining like terms, got -330*y**6 - 990*y**5 + 862*y**4 + 540*y**3 - 372*y**2\n#Step 6:\nCurrent expression: -330*y**6 - 990*y**5 + 862*y**4 + 540*y**3 - 372*y**2\nNo more calculations needed.\n-330*y**6 - 990*y**5 + 862*y**4 + 540*y**3 - 372*y**2", "generated_answer": "-330*y**6 - 990*y**5 + 862*y**4 + 540*y**3 - 372*y**2", "step_length": 6} {"cot_id": "83045f02b90bb59993be5b0f788935cde5295cf6409326271f58161aa7c89eb8", "datapoint": {"question": "Calculate the following: (7*y**2 + 28*y)*(-6*y**3 - 18)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-42*y**5 - 168*y**4 - 126*y**2 - 504*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1569, "polynomial_expr": "(7*y**2 + 28*y)*(-6*y**3 - 18)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7*y**2 + 28*y)*(-6*y**3 - 18)\nExpanding the part (-6*y**3 - 18) using the distributive property, and we got: (-6*y**3)*(7*y**2 + 28*y) - 18*(7*y**2 + 28*y)\n#Step 2:\nCurrent expression: (-6*y**3)*(7*y**2 + 28*y) - 18*(7*y**2 + 28*y)\nSimplifying the partial expression: -18*(7*y**2 + 28*y)\nExpanding the part (7*y**2 + 28*y) using the distributive property, and we got: (28*y)*(-18) + (7*y**2)*(-18)\nReplacing -18*(7*y**2 + 28*y) with (28*y)*(-18) + (7*y**2)*(-18) in the overall expression.\n#Step 3:\nCurrent expression: (28*y)*(-18) + (7*y**2)*(-18) + (-6*y**3)*(7*y**2 + 28*y)\nSimplifying the partial expression: (-6*y**3)*(7*y**2 + 28*y)\nExpanding the part (7*y**2 + 28*y) using the distributive property, and we got: (28*y)*(-6*y**3) + (7*y**2)*(-6*y**3)\nReplacing (-6*y**3)*(7*y**2 + 28*y) with (28*y)*(-6*y**3) + (7*y**2)*(-6*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (28*y)*(-6*y**3) + (28*y)*(-18) + (7*y**2)*(-6*y**3) + (7*y**2)*(-18)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (7*y**2)*-18 = -126*y**2\n (7*y**2)*(-6*y**3) = -42*y**5\n (28*y)*-18 = -504*y\n (28*y)*(-6*y**3) = -168*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -42*y**5 - 168*y**4 - 126*y**2 - 504*y\nNo more calculations needed.\n-42*y**5 - 168*y**4 - 126*y**2 - 504*y", "generated_answer": "-42*y**5 - 168*y**4 - 126*y**2 - 504*y", "step_length": 5} {"cot_id": "6fc3908ce988e1807e108217219a314c1827efc875ac077b3f4e2027f1bbb668", "datapoint": {"question": "Simplify this expression: 32*x*(-35*x**3 + 4*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1120*x**4 + 128*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1570, "polynomial_expr": "32*x*(-35*x**3 + 4*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 32*x*(-35*x**3 + 4*x**2)\nExpanding the part (-35*x**3 + 4*x**2) using the distributive property, and we got: (32*x)*(4*x**2) + (32*x)*(-35*x**3)\n#Step 2:\nCurrent expression: (32*x)*(4*x**2) + (32*x)*(-35*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*x**3)*(32*x) = -1120*x**4\n (4*x**2)*(32*x) = 128*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1120*x**4 + 128*x**3\nNo more calculations needed.\n-1120*x**4 + 128*x**3", "generated_answer": "-1120*x**4 + 128*x**3", "step_length": 3} {"cot_id": "e93e9bdfbc6bb7f47e9e4693d6c192689e8cd4f6dd14330a4f2bca573755ff82", "datapoint": {"question": "Calculate the following: (42*y**2 - 44*y + 30)*(-9*y**3 - 24*y + 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-378*y**5 + 396*y**4 - 1278*y**3 + 2694*y**2 - 2436*y + 1170", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1571, "polynomial_expr": "(42*y**2 - 44*y + 30)*(-9*y**3 - 24*y + 39)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (42*y**2 - 44*y + 30)*(-9*y**3 - 24*y + 39)\nExpanding the part (42*y**2 - 44*y + 30) using the distributive property, and we got: (-44*y)*(-9*y**3 - 24*y + 39) + (42*y**2)*(-9*y**3 - 24*y + 39) + 30*(-9*y**3 - 24*y + 39)\n#Step 2:\nCurrent expression: (-44*y)*(-9*y**3 - 24*y + 39) + (42*y**2)*(-9*y**3 - 24*y + 39) + 30*(-9*y**3 - 24*y + 39)\nSimplifying the partial expression: 30*(-9*y**3 - 24*y + 39)\nExpanding the part (-9*y**3 - 24*y + 39) using the distributive property, and we got: -24*y*30 - 9*y**3*30 + 39*30\nReplacing 30*(-9*y**3 - 24*y + 39) with -24*y*30 - 9*y**3*30 + 39*30 in the overall expression.\n#Step 3:\nCurrent expression: (-44*y)*(-9*y**3 - 24*y + 39) - 24*y*30 + (42*y**2)*(-9*y**3 - 24*y + 39) - 9*y**3*30 + 1170\nSimplifying the partial expression: (-44*y)*(-9*y**3 - 24*y + 39)\nExpanding the part (-9*y**3 - 24*y + 39) using the distributive property, and we got: (-44*y)*(-24*y) + (-44*y)*(-9*y**3) + 39*(-44*y)\nReplacing (-44*y)*(-9*y**3 - 24*y + 39) with (-44*y)*(-24*y) + (-44*y)*(-9*y**3) + 39*(-44*y) in the overall expression.\n#Step 4:\nCurrent expression: (-44*y)*(-24*y) + (-44*y)*(-9*y**3) - 24*y*30 + 39*(-44)*y + (42*y**2)*(-9*y**3 - 24*y + 39) - 9*y**3*30 + 1170\nSimplifying the partial expression: (42*y**2)*(-9*y**3 - 24*y + 39)\nExpanding the part (-9*y**3 - 24*y + 39) using the distributive property, and we got: (-24*y)*(42*y**2) + 39*(42*y**2) + (42*y**2)*(-9*y**3)\nReplacing (42*y**2)*(-9*y**3 - 24*y + 39) with (-24*y)*(42*y**2) + 39*(42*y**2) + (42*y**2)*(-9*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-44*y)*(-24*y) + (-44*y)*(-9*y**3) + (-24*y)*(42*y**2) - 24*y*30 + 39*42*y**2 + 39*(-44)*y + (42*y**2)*(-9*y**3) - 9*y**3*30 + 1170\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-24*y)*30 = -720*y\n (-24*y)*(-44*y) = 1056*y**2\n (-24*y)*(42*y**2) = -1008*y**3\n (-9*y**3)*30 = -270*y**3\n (-9*y**3)*(-44*y) = 396*y**4\n (-9*y**3)*(42*y**2) = -378*y**5\n 39*-44*y = -1716*y\n 39*42*y**2 = 1638*y**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -378*y**5 + 396*y**4 - 1008*y**3 - 270*y**3 + 1056*y**2 + 1638*y**2 - 1716*y - 720*y + 1170\nCombining like terms, got -378*y**5 + 396*y**4 - 1278*y**3 + 2694*y**2 - 2436*y + 1170\n#Step 7:\nCurrent expression: -378*y**5 + 396*y**4 - 1278*y**3 + 2694*y**2 - 2436*y + 1170\nNo more calculations needed.\n-378*y**5 + 396*y**4 - 1278*y**3 + 2694*y**2 - 2436*y + 1170", "generated_answer": "-378*y**5 + 396*y**4 - 1278*y**3 + 2694*y**2 - 2436*y + 1170", "step_length": 7} {"cot_id": "2a5ff08f45c4f0ea21fb5c8b7d67f52c39022bd9a92494ec781cc9251e19f9ed", "datapoint": {"question": "Simplify this expression: -2623*x**3 - 732*x**2 - 610\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2623*x**3 - 732*x**2 - 610", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1572, "polynomial_expr": "-2623*x**3 - 732*x**2 - 610", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -2623*x**3 - 732*x**2 - 610\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -2623*x**3 - 732*x**2 - 610\nNo more calculations needed.\n-2623*x**3 - 732*x**2 - 610", "generated_answer": "-2623*x**3 - 732*x**2 - 610", "step_length": 2} {"cot_id": "049731a5fa42b3600073b3e8a46e5f9c62f7096b0dae5842b135d0a22cd6078a", "datapoint": {"question": "Calculate the following: (-41*y - 6)*(30*y**2 + 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1230*y**3 - 180*y**2 - 2009*y - 294", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1573, "polynomial_expr": "(-41*y - 6)*(30*y**2 + 49)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-41*y - 6)*(30*y**2 + 49)\nExpanding the part (-41*y - 6) using the distributive property, and we got: (-41*y)*(30*y**2 + 49) - 6*(30*y**2 + 49)\n#Step 2:\nCurrent expression: (-41*y)*(30*y**2 + 49) - 6*(30*y**2 + 49)\nSimplifying the partial expression: -6*(30*y**2 + 49)\nExpanding the part (30*y**2 + 49) using the distributive property, and we got: (30*y**2)*(-6) + 49*(-6)\nReplacing -6*(30*y**2 + 49) with (30*y**2)*(-6) + 49*(-6) in the overall expression.\n#Step 3:\nCurrent expression: (-41*y)*(30*y**2 + 49) + (30*y**2)*(-6) - 294\nSimplifying the partial expression: (-41*y)*(30*y**2 + 49)\nExpanding the part (30*y**2 + 49) using the distributive property, and we got: (-41*y)*(30*y**2) + 49*(-41*y)\nReplacing (-41*y)*(30*y**2 + 49) with (-41*y)*(30*y**2) + 49*(-41*y) in the overall expression.\n#Step 4:\nCurrent expression: (-41*y)*(30*y**2) + 49*(-41)*y + (30*y**2)*(-6) - 294\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (30*y**2)*-6 = -180*y**2\n (30*y**2)*(-41*y) = -1230*y**3\n 49*-41*y = -2009*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1230*y**3 - 180*y**2 - 2009*y - 294\nNo more calculations needed.\n-1230*y**3 - 180*y**2 - 2009*y - 294", "generated_answer": "-1230*y**3 - 180*y**2 - 2009*y - 294", "step_length": 5} {"cot_id": "b87d68e7b1a47b91074c1ecde1e37a5ae72d9d0eb9bc944569985b4bccb7c065", "datapoint": {"question": "Simplify this expression: (-19*z - 21)*(-26*z**2 + 45*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "494*z**3 - 309*z**2 - 945*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1574, "polynomial_expr": "(-19*z - 21)*(-26*z**2 + 45*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-19*z - 21)*(-26*z**2 + 45*z)\nExpanding the part (-19*z - 21) using the distributive property, and we got: (-19*z)*(-26*z**2 + 45*z) - 21*(-26*z**2 + 45*z)\n#Step 2:\nCurrent expression: (-19*z)*(-26*z**2 + 45*z) - 21*(-26*z**2 + 45*z)\nSimplifying the partial expression: -21*(-26*z**2 + 45*z)\nExpanding the part (-26*z**2 + 45*z) using the distributive property, and we got: (45*z)*(-21) - 26*z**2*(-21)\nReplacing -21*(-26*z**2 + 45*z) with (45*z)*(-21) - 26*z**2*(-21) in the overall expression.\n#Step 3:\nCurrent expression: (-19*z)*(-26*z**2 + 45*z) + (45*z)*(-21) - 26*z**2*(-21)\nSimplifying the partial expression: (-19*z)*(-26*z**2 + 45*z)\nExpanding the part (-26*z**2 + 45*z) using the distributive property, and we got: (-19*z)*(45*z) + (-19*z)*(-26*z**2)\nReplacing (-19*z)*(-26*z**2 + 45*z) with (-19*z)*(45*z) + (-19*z)*(-26*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-19*z)*(45*z) + (-19*z)*(-26*z**2) + (45*z)*(-21) - 26*z**2*(-21)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-26*z**2)*-21 = 546*z**2\n (-26*z**2)*(-19*z) = 494*z**3\n (45*z)*-21 = -945*z\n (45*z)*(-19*z) = -855*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 494*z**3 - 855*z**2 + 546*z**2 - 945*z\nCombining like terms, got 494*z**3 - 309*z**2 - 945*z\n#Step 6:\nCurrent expression: 494*z**3 - 309*z**2 - 945*z\nNo more calculations needed.\n494*z**3 - 309*z**2 - 945*z", "generated_answer": "494*z**3 - 309*z**2 - 945*z", "step_length": 6} {"cot_id": "54d812f50934d68d20f7b5589882c8e76e9f2d29abcdfe1a5e841abf4a2799c5", "datapoint": {"question": "Simplify this expression: (-47*y - 59)*(-34*y**2 + 28*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1598*y**3 + 690*y**2 - 1652*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1575, "polynomial_expr": "(-47*y - 59)*(-34*y**2 + 28*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-47*y - 59)*(-34*y**2 + 28*y)\nExpanding the part (-47*y - 59) using the distributive property, and we got: (-47*y)*(-34*y**2 + 28*y) - 59*(-34*y**2 + 28*y)\n#Step 2:\nCurrent expression: (-47*y)*(-34*y**2 + 28*y) - 59*(-34*y**2 + 28*y)\nSimplifying the partial expression: -59*(-34*y**2 + 28*y)\nExpanding the part (-34*y**2 + 28*y) using the distributive property, and we got: (28*y)*(-59) - 34*y**2*(-59)\nReplacing -59*(-34*y**2 + 28*y) with (28*y)*(-59) - 34*y**2*(-59) in the overall expression.\n#Step 3:\nCurrent expression: (-47*y)*(-34*y**2 + 28*y) + (28*y)*(-59) - 34*y**2*(-59)\nSimplifying the partial expression: (-47*y)*(-34*y**2 + 28*y)\nExpanding the part (-34*y**2 + 28*y) using the distributive property, and we got: (-47*y)*(28*y) + (-47*y)*(-34*y**2)\nReplacing (-47*y)*(-34*y**2 + 28*y) with (-47*y)*(28*y) + (-47*y)*(-34*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-47*y)*(28*y) + (-47*y)*(-34*y**2) + (28*y)*(-59) - 34*y**2*(-59)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*y**2)*-59 = 2006*y**2\n (-34*y**2)*(-47*y) = 1598*y**3\n (28*y)*-59 = -1652*y\n (28*y)*(-47*y) = -1316*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1598*y**3 - 1316*y**2 + 2006*y**2 - 1652*y\nCombining like terms, got 1598*y**3 + 690*y**2 - 1652*y\n#Step 6:\nCurrent expression: 1598*y**3 + 690*y**2 - 1652*y\nNo more calculations needed.\n1598*y**3 + 690*y**2 - 1652*y", "generated_answer": "1598*y**3 + 690*y**2 - 1652*y", "step_length": 6} {"cot_id": "c833c03f9784f376ded181b7c16e49adc65b1898d11a6a9c1cd86c747a0da50f", "datapoint": {"question": "Calculate the following: (24*z**3 - 85*z**2)*(-24*z**3 + 15*z**2 + 7*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-576*z**6 + 2400*z**5 - 1107*z**4 - 595*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1576, "polynomial_expr": "(24*z**3 - 85*z**2)*(-24*z**3 + 15*z**2 + 7*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (24*z**3 - 85*z**2)*(-24*z**3 + 15*z**2 + 7*z)\nExpanding the part (24*z**3 - 85*z**2) using the distributive property, and we got: (-85*z**2)*(-24*z**3 + 15*z**2 + 7*z) + (24*z**3)*(-24*z**3 + 15*z**2 + 7*z)\n#Step 2:\nCurrent expression: (-85*z**2)*(-24*z**3 + 15*z**2 + 7*z) + (24*z**3)*(-24*z**3 + 15*z**2 + 7*z)\nSimplifying the partial expression: (-85*z**2)*(-24*z**3 + 15*z**2 + 7*z)\nExpanding the part (-24*z**3 + 15*z**2 + 7*z) using the distributive property, and we got: (7*z)*(-85*z**2) + (-85*z**2)*(15*z**2) + (-85*z**2)*(-24*z**3)\nReplacing (-85*z**2)*(-24*z**3 + 15*z**2 + 7*z) with (7*z)*(-85*z**2) + (-85*z**2)*(15*z**2) + (-85*z**2)*(-24*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (7*z)*(-85*z**2) + (-85*z**2)*(15*z**2) + (-85*z**2)*(-24*z**3) + (24*z**3)*(-24*z**3 + 15*z**2 + 7*z)\nSimplifying the partial expression: (24*z**3)*(-24*z**3 + 15*z**2 + 7*z)\nExpanding the part (-24*z**3 + 15*z**2 + 7*z) using the distributive property, and we got: (7*z)*(24*z**3) + (15*z**2)*(24*z**3) + (-24*z**3)*(24*z**3)\nReplacing (24*z**3)*(-24*z**3 + 15*z**2 + 7*z) with (7*z)*(24*z**3) + (15*z**2)*(24*z**3) + (-24*z**3)*(24*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (7*z)*(-85*z**2) + (7*z)*(24*z**3) + (-85*z**2)*(15*z**2) + (-85*z**2)*(-24*z**3) + (15*z**2)*(24*z**3) + (-24*z**3)*(24*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-24*z**3)*(-85*z**2) = 2040*z**5\n (-24*z**3)*(24*z**3) = -576*z**6\n (7*z)*(-85*z**2) = -595*z**3\n (7*z)*(24*z**3) = 168*z**4\n (15*z**2)*(-85*z**2) = -1275*z**4\n (15*z**2)*(24*z**3) = 360*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -576*z**6 + 360*z**5 + 2040*z**5 - 1275*z**4 + 168*z**4 - 595*z**3\nCombining like terms, got -576*z**6 + 2400*z**5 - 1107*z**4 - 595*z**3\n#Step 6:\nCurrent expression: -576*z**6 + 2400*z**5 - 1107*z**4 - 595*z**3\nNo more calculations needed.\n-576*z**6 + 2400*z**5 - 1107*z**4 - 595*z**3", "generated_answer": "-576*z**6 + 2400*z**5 - 1107*z**4 - 595*z**3", "step_length": 6} {"cot_id": "94c7fece1f6d851eb7e274decbee5c625171e4610c9ffc1e4b45baf3475b2b90", "datapoint": {"question": "Simplify this expression: (24 - x**3)*(27*x**3 - 26*x**2 + 48*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-27*x**6 + 26*x**5 - 48*x**4 + 648*x**3 - 624*x**2 + 1152*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1577, "polynomial_expr": "(24 - x**3)*(27*x**3 - 26*x**2 + 48*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (24 - x**3)*(27*x**3 - 26*x**2 + 48*x)\nExpanding the part (24 - x**3) using the distributive property, and we got: (-x**3)*(27*x**3 - 26*x**2 + 48*x) + 24*(27*x**3 - 26*x**2 + 48*x)\n#Step 2:\nCurrent expression: (-x**3)*(27*x**3 - 26*x**2 + 48*x) + 24*(27*x**3 - 26*x**2 + 48*x)\nSimplifying the partial expression: 24*(27*x**3 - 26*x**2 + 48*x)\nExpanding the part (27*x**3 - 26*x**2 + 48*x) using the distributive property, and we got: (48*x)*24 - 26*x**2*24 + (27*x**3)*24\nReplacing 24*(27*x**3 - 26*x**2 + 48*x) with (48*x)*24 - 26*x**2*24 + (27*x**3)*24 in the overall expression.\n#Step 3:\nCurrent expression: (48*x)*24 - 26*x**2*24 + (-x**3)*(27*x**3 - 26*x**2 + 48*x) + (27*x**3)*24\nSimplifying the partial expression: (-x**3)*(27*x**3 - 26*x**2 + 48*x)\nExpanding the part (27*x**3 - 26*x**2 + 48*x) using the distributive property, and we got: (48*x)*(-x**3) + (-26*x**2)*(-x**3) + (-x**3)*(27*x**3)\nReplacing (-x**3)*(27*x**3 - 26*x**2 + 48*x) with (48*x)*(-x**3) + (-26*x**2)*(-x**3) + (-x**3)*(27*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (48*x)*(-x**3) + (48*x)*24 + (-26*x**2)*(-x**3) - 26*x**2*24 + (-x**3)*(27*x**3) + (27*x**3)*24\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-26*x**2)*24 = -624*x**2\n (-26*x**2)*(-x**3) = 26*x**5\n (27*x**3)*24 = 648*x**3\n (27*x**3)*(-x**3) = -27*x**6\n (48*x)*24 = 1152*x\n (48*x)*(-x**3) = -48*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -27*x**6 + 26*x**5 - 48*x**4 + 648*x**3 - 624*x**2 + 1152*x\nNo more calculations needed.\n-27*x**6 + 26*x**5 - 48*x**4 + 648*x**3 - 624*x**2 + 1152*x", "generated_answer": "-27*x**6 + 26*x**5 - 48*x**4 + 648*x**3 - 624*x**2 + 1152*x", "step_length": 5} {"cot_id": "7fc1894314f62c7878879b6441481d00704f8cf7c514bd8efa7d3e7a4b9b9366", "datapoint": {"question": "Calculate the following: (21*x**3 - 5*x)*(48*x**3 + 37*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1008*x**6 + 777*x**5 - 240*x**4 - 185*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1578, "polynomial_expr": "(21*x**3 - 5*x)*(48*x**3 + 37*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21*x**3 - 5*x)*(48*x**3 + 37*x**2)\nExpanding the part (21*x**3 - 5*x) using the distributive property, and we got: (-5*x)*(48*x**3 + 37*x**2) + (21*x**3)*(48*x**3 + 37*x**2)\n#Step 2:\nCurrent expression: (-5*x)*(48*x**3 + 37*x**2) + (21*x**3)*(48*x**3 + 37*x**2)\nSimplifying the partial expression: (-5*x)*(48*x**3 + 37*x**2)\nExpanding the part (48*x**3 + 37*x**2) using the distributive property, and we got: (-5*x)*(37*x**2) + (-5*x)*(48*x**3)\nReplacing (-5*x)*(48*x**3 + 37*x**2) with (-5*x)*(37*x**2) + (-5*x)*(48*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-5*x)*(37*x**2) + (-5*x)*(48*x**3) + (21*x**3)*(48*x**3 + 37*x**2)\nSimplifying the partial expression: (21*x**3)*(48*x**3 + 37*x**2)\nExpanding the part (48*x**3 + 37*x**2) using the distributive property, and we got: (37*x**2)*(21*x**3) + (21*x**3)*(48*x**3)\nReplacing (21*x**3)*(48*x**3 + 37*x**2) with (37*x**2)*(21*x**3) + (21*x**3)*(48*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-5*x)*(37*x**2) + (-5*x)*(48*x**3) + (37*x**2)*(21*x**3) + (21*x**3)*(48*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (37*x**2)*(-5*x) = -185*x**3\n (37*x**2)*(21*x**3) = 777*x**5\n (48*x**3)*(-5*x) = -240*x**4\n (48*x**3)*(21*x**3) = 1008*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1008*x**6 + 777*x**5 - 240*x**4 - 185*x**3\nNo more calculations needed.\n1008*x**6 + 777*x**5 - 240*x**4 - 185*x**3", "generated_answer": "1008*x**6 + 777*x**5 - 240*x**4 - 185*x**3", "step_length": 5} {"cot_id": "f9f7a002e166fa9a8153b1cde69b3bf57d4d5bb50f568db409c2d98496f8d897", "datapoint": {"question": "Simplify this expression: (20*x**2 - 5)*(15*x**3 - 2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "300*x**5 - 75*x**3 - 40*x**2 + 10", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1579, "polynomial_expr": "(20*x**2 - 5)*(15*x**3 - 2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (20*x**2 - 5)*(15*x**3 - 2)\nExpanding the part (20*x**2 - 5) using the distributive property, and we got: (20*x**2)*(15*x**3 - 2) - 5*(15*x**3 - 2)\n#Step 2:\nCurrent expression: (20*x**2)*(15*x**3 - 2) - 5*(15*x**3 - 2)\nSimplifying the partial expression: -5*(15*x**3 - 2)\nExpanding the part (15*x**3 - 2) using the distributive property, and we got: (15*x**3)*(-5) - 2*(-5)\nReplacing -5*(15*x**3 - 2) with (15*x**3)*(-5) - 2*(-5) in the overall expression.\n#Step 3:\nCurrent expression: (20*x**2)*(15*x**3 - 2) + (15*x**3)*(-5) + 10\nSimplifying the partial expression: (20*x**2)*(15*x**3 - 2)\nExpanding the part (15*x**3 - 2) using the distributive property, and we got: -40*x**2 + (20*x**2)*(15*x**3)\nReplacing (20*x**2)*(15*x**3 - 2) with -40*x**2 + (20*x**2)*(15*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -2*20*x**2 + (20*x**2)*(15*x**3) + (15*x**3)*(-5) + 10\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (15*x**3)*-5 = -75*x**3\n (15*x**3)*(20*x**2) = 300*x**5\n -2*20*x**2 = -40*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 300*x**5 - 75*x**3 - 40*x**2 + 10\nNo more calculations needed.\n300*x**5 - 75*x**3 - 40*x**2 + 10", "generated_answer": "300*x**5 - 75*x**3 - 40*x**2 + 10", "step_length": 5} {"cot_id": "5a9410543369fcbb5879cba80b795e2cacfe933e036fdcd57386077fc920e453", "datapoint": {"question": "Calculate the following: (11*y**3 + 22*y**2)*(-46*y**3 - 39*y - 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-506*y**6 - 1012*y**5 - 429*y**4 - 1287*y**3 - 858*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1580, "polynomial_expr": "(11*y**3 + 22*y**2)*(-46*y**3 - 39*y - 39)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11*y**3 + 22*y**2)*(-46*y**3 - 39*y - 39)\nExpanding the part (11*y**3 + 22*y**2) using the distributive property, and we got: (22*y**2)*(-46*y**3 - 39*y - 39) + (11*y**3)*(-46*y**3 - 39*y - 39)\n#Step 2:\nCurrent expression: (22*y**2)*(-46*y**3 - 39*y - 39) + (11*y**3)*(-46*y**3 - 39*y - 39)\nSimplifying the partial expression: (11*y**3)*(-46*y**3 - 39*y - 39)\nExpanding the part (-46*y**3 - 39*y - 39) using the distributive property, and we got: (-39*y)*(11*y**3) - 429*y**3 + (-46*y**3)*(11*y**3)\nReplacing (11*y**3)*(-46*y**3 - 39*y - 39) with (-39*y)*(11*y**3) - 429*y**3 + (-46*y**3)*(11*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-39*y)*(11*y**3) - 39*11*y**3 + (22*y**2)*(-46*y**3 - 39*y - 39) + (-46*y**3)*(11*y**3)\nSimplifying the partial expression: (22*y**2)*(-46*y**3 - 39*y - 39)\nExpanding the part (-46*y**3 - 39*y - 39) using the distributive property, and we got: (-39*y)*(22*y**2) - 858*y**2 + (22*y**2)*(-46*y**3)\nReplacing (22*y**2)*(-46*y**3 - 39*y - 39) with (-39*y)*(22*y**2) - 858*y**2 + (22*y**2)*(-46*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-39*y)*(22*y**2) + (-39*y)*(11*y**3) - 39*11*y**3 - 39*22*y**2 + (22*y**2)*(-46*y**3) + (-46*y**3)*(11*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*y**3)*(11*y**3) = -506*y**6\n (-46*y**3)*(22*y**2) = -1012*y**5\n (-39*y)*(11*y**3) = -429*y**4\n (-39*y)*(22*y**2) = -858*y**3\n -39*11*y**3 = -429*y**3\n -39*22*y**2 = -858*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -506*y**6 - 1012*y**5 - 429*y**4 - 858*y**3 - 429*y**3 - 858*y**2\nCombining like terms, got -506*y**6 - 1012*y**5 - 429*y**4 - 1287*y**3 - 858*y**2\n#Step 6:\nCurrent expression: -506*y**6 - 1012*y**5 - 429*y**4 - 1287*y**3 - 858*y**2\nNo more calculations needed.\n-506*y**6 - 1012*y**5 - 429*y**4 - 1287*y**3 - 858*y**2", "generated_answer": "-506*y**6 - 1012*y**5 - 429*y**4 - 1287*y**3 - 858*y**2", "step_length": 6} {"cot_id": "0ff1b78518f6b31ef36591fe3125bde9f180d22c61a68266fe66da91332d88ec", "datapoint": {"question": "Calculate the following: (-4*z**3 + 4*z)*(-19*z**3 - 20*z + 25)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "76*z**6 + 4*z**4 - 100*z**3 - 80*z**2 + 100*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1581, "polynomial_expr": "(-4*z**3 + 4*z)*(-19*z**3 - 20*z + 25)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-4*z**3 + 4*z)*(-19*z**3 - 20*z + 25)\nExpanding the part (-4*z**3 + 4*z) using the distributive property, and we got: (4*z)*(-19*z**3 - 20*z + 25) + (-4*z**3)*(-19*z**3 - 20*z + 25)\n#Step 2:\nCurrent expression: (4*z)*(-19*z**3 - 20*z + 25) + (-4*z**3)*(-19*z**3 - 20*z + 25)\nSimplifying the partial expression: (-4*z**3)*(-19*z**3 - 20*z + 25)\nExpanding the part (-19*z**3 - 20*z + 25) using the distributive property, and we got: (-20*z)*(-4*z**3) + 25*(-4*z**3) + (-19*z**3)*(-4*z**3)\nReplacing (-4*z**3)*(-19*z**3 - 20*z + 25) with (-20*z)*(-4*z**3) + 25*(-4*z**3) + (-19*z**3)*(-4*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-20*z)*(-4*z**3) + 25*(-4)*z**3 + (4*z)*(-19*z**3 - 20*z + 25) + (-19*z**3)*(-4*z**3)\nSimplifying the partial expression: (4*z)*(-19*z**3 - 20*z + 25)\nExpanding the part (-19*z**3 - 20*z + 25) using the distributive property, and we got: (-20*z)*(4*z) + 25*(4*z) + (4*z)*(-19*z**3)\nReplacing (4*z)*(-19*z**3 - 20*z + 25) with (-20*z)*(4*z) + 25*(4*z) + (4*z)*(-19*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-20*z)*(4*z) + (-20*z)*(-4*z**3) + 25*(-4)*z**3 + 25*4*z + (4*z)*(-19*z**3) + (-19*z**3)*(-4*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*z)*(-4*z**3) = 80*z**4\n (-20*z)*(4*z) = -80*z**2\n (-19*z**3)*(-4*z**3) = 76*z**6\n (-19*z**3)*(4*z) = -76*z**4\n 25*-4*z**3 = -100*z**3\n 25*4*z = 100*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 76*z**6 - 76*z**4 + 80*z**4 - 100*z**3 - 80*z**2 + 100*z\nCombining like terms, got 76*z**6 + 4*z**4 - 100*z**3 - 80*z**2 + 100*z\n#Step 6:\nCurrent expression: 76*z**6 + 4*z**4 - 100*z**3 - 80*z**2 + 100*z\nNo more calculations needed.\n76*z**6 + 4*z**4 - 100*z**3 - 80*z**2 + 100*z", "generated_answer": "76*z**6 + 4*z**4 - 100*z**3 - 80*z**2 + 100*z", "step_length": 6} {"cot_id": "a1d55bd84182ccd8d422a68518bdd9db093ce99f75c2af5e487a43e44971aebe", "datapoint": {"question": "Calculate the following: -21*x**2*(13*x**2 - 38*x + 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-273*x**4 + 798*x**3 - 294*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1582, "polynomial_expr": "-21*x**2*(13*x**2 - 38*x + 14)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -21*x**2*(13*x**2 - 38*x + 14)\nExpanding the part (13*x**2 - 38*x + 14) using the distributive property, and we got: (-38*x)*(-21*x**2) + 14*(-21*x**2) + (-21*x**2)*(13*x**2)\n#Step 2:\nCurrent expression: (-38*x)*(-21*x**2) + 14*(-21*x**2) + (-21*x**2)*(13*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 14*(-21*x**2) = -294*x**2\n (-38*x)*(-21*x**2) = 798*x**3\n (13*x**2)*(-21*x**2) = -273*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -273*x**4 + 798*x**3 - 294*x**2\nNo more calculations needed.\n-273*x**4 + 798*x**3 - 294*x**2", "generated_answer": "-273*x**4 + 798*x**3 - 294*x**2", "step_length": 3} {"cot_id": "8c438276b049cf1ee779c4bc183d3abd6e597627df60b2e1ccf8667bee7706f2", "datapoint": {"question": "Simplify this expression: (-48*y**3 + 42*y**2)*(47*y**2 - 12*y - 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2256*y**5 + 2550*y**4 + 168*y**3 - 588*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1583, "polynomial_expr": "(-48*y**3 + 42*y**2)*(47*y**2 - 12*y - 14)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-48*y**3 + 42*y**2)*(47*y**2 - 12*y - 14)\nExpanding the part (-48*y**3 + 42*y**2) using the distributive property, and we got: (42*y**2)*(47*y**2 - 12*y - 14) + (-48*y**3)*(47*y**2 - 12*y - 14)\n#Step 2:\nCurrent expression: (42*y**2)*(47*y**2 - 12*y - 14) + (-48*y**3)*(47*y**2 - 12*y - 14)\nSimplifying the partial expression: (-48*y**3)*(47*y**2 - 12*y - 14)\nExpanding the part (47*y**2 - 12*y - 14) using the distributive property, and we got: (-12*y)*(-48*y**3) - (-1)*672*y**3 + (47*y**2)*(-48*y**3)\nReplacing (-48*y**3)*(47*y**2 - 12*y - 14) with (-12*y)*(-48*y**3) - (-1)*672*y**3 + (47*y**2)*(-48*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-12*y)*(-48*y**3) - 14*(-48)*y**3 + (42*y**2)*(47*y**2 - 12*y - 14) + (47*y**2)*(-48*y**3)\nSimplifying the partial expression: (42*y**2)*(47*y**2 - 12*y - 14)\nExpanding the part (47*y**2 - 12*y - 14) using the distributive property, and we got: (-12*y)*(42*y**2) - 588*y**2 + (42*y**2)*(47*y**2)\nReplacing (42*y**2)*(47*y**2 - 12*y - 14) with (-12*y)*(42*y**2) - 588*y**2 + (42*y**2)*(47*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-12*y)*(42*y**2) + (-12*y)*(-48*y**3) - 14*(-48)*y**3 - 14*42*y**2 + (42*y**2)*(47*y**2) + (47*y**2)*(-48*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*y)*(-48*y**3) = 576*y**4\n (-12*y)*(42*y**2) = -504*y**3\n (47*y**2)*(-48*y**3) = -2256*y**5\n (47*y**2)*(42*y**2) = 1974*y**4\n -14*-48*y**3 = 672*y**3\n -14*42*y**2 = -588*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2256*y**5 + 576*y**4 + 1974*y**4 - 504*y**3 + 672*y**3 - 588*y**2\nCombining like terms, got -2256*y**5 + 2550*y**4 + 168*y**3 - 588*y**2\n#Step 6:\nCurrent expression: -2256*y**5 + 2550*y**4 + 168*y**3 - 588*y**2\nNo more calculations needed.\n-2256*y**5 + 2550*y**4 + 168*y**3 - 588*y**2", "generated_answer": "-2256*y**5 + 2550*y**4 + 168*y**3 - 588*y**2", "step_length": 6} {"cot_id": "922d034726f5a293cb01458528b57e53cce28c8ea89f72f943380ebb87ced0c0", "datapoint": {"question": "Calculate the following: (24*y**3 - 9*y)*(-31*y**2 - 16*y + 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-744*y**5 - 384*y**4 + 999*y**3 + 144*y**2 - 270*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1584, "polynomial_expr": "(24*y**3 - 9*y)*(-31*y**2 - 16*y + 30)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (24*y**3 - 9*y)*(-31*y**2 - 16*y + 30)\nExpanding the part (24*y**3 - 9*y) using the distributive property, and we got: (-9*y)*(-31*y**2 - 16*y + 30) + (24*y**3)*(-31*y**2 - 16*y + 30)\n#Step 2:\nCurrent expression: (-9*y)*(-31*y**2 - 16*y + 30) + (24*y**3)*(-31*y**2 - 16*y + 30)\nSimplifying the partial expression: (-9*y)*(-31*y**2 - 16*y + 30)\nExpanding the part (-31*y**2 - 16*y + 30) using the distributive property, and we got: (-16*y)*(-9*y) + (-9*y)*(-31*y**2) + 30*(-9*y)\nReplacing (-9*y)*(-31*y**2 - 16*y + 30) with (-16*y)*(-9*y) + (-9*y)*(-31*y**2) + 30*(-9*y) in the overall expression.\n#Step 3:\nCurrent expression: (-16*y)*(-9*y) + (-9*y)*(-31*y**2) + 30*(-9)*y + (24*y**3)*(-31*y**2 - 16*y + 30)\nSimplifying the partial expression: (24*y**3)*(-31*y**2 - 16*y + 30)\nExpanding the part (-31*y**2 - 16*y + 30) using the distributive property, and we got: (-16*y)*(24*y**3) + 30*(24*y**3) + (-31*y**2)*(24*y**3)\nReplacing (24*y**3)*(-31*y**2 - 16*y + 30) with (-16*y)*(24*y**3) + 30*(24*y**3) + (-31*y**2)*(24*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-16*y)*(-9*y) + (-16*y)*(24*y**3) + (-9*y)*(-31*y**2) + 30*24*y**3 + 30*(-9)*y + (-31*y**2)*(24*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-31*y**2)*(-9*y) = 279*y**3\n (-31*y**2)*(24*y**3) = -744*y**5\n (-16*y)*(-9*y) = 144*y**2\n (-16*y)*(24*y**3) = -384*y**4\n 30*-9*y = -270*y\n 30*24*y**3 = 720*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -744*y**5 - 384*y**4 + 279*y**3 + 720*y**3 + 144*y**2 - 270*y\nCombining like terms, got -744*y**5 - 384*y**4 + 999*y**3 + 144*y**2 - 270*y\n#Step 6:\nCurrent expression: -744*y**5 - 384*y**4 + 999*y**3 + 144*y**2 - 270*y\nNo more calculations needed.\n-744*y**5 - 384*y**4 + 999*y**3 + 144*y**2 - 270*y", "generated_answer": "-744*y**5 - 384*y**4 + 999*y**3 + 144*y**2 - 270*y", "step_length": 6} {"cot_id": "b32831565deb028326931eaf498299a1a8f88a32f4045d69991e3e6bc3b3df81", "datapoint": {"question": "Simplify this expression: (8*y**3 - 16*y**2 - 27*y)*(44*y**3 - 16*y**2 - 48*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "352*y**6 - 832*y**5 - 1316*y**4 + 1200*y**3 + 1296*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1585, "polynomial_expr": "(8*y**3 - 16*y**2 - 27*y)*(44*y**3 - 16*y**2 - 48*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (8*y**3 - 16*y**2 - 27*y)*(44*y**3 - 16*y**2 - 48*y)\nExpanding the part (44*y**3 - 16*y**2 - 48*y) using the distributive property, and we got: (-48*y)*(8*y**3 - 16*y**2 - 27*y) + (-16*y**2)*(8*y**3 - 16*y**2 - 27*y) + (44*y**3)*(8*y**3 - 16*y**2 - 27*y)\n#Step 2:\nCurrent expression: (-48*y)*(8*y**3 - 16*y**2 - 27*y) + (-16*y**2)*(8*y**3 - 16*y**2 - 27*y) + (44*y**3)*(8*y**3 - 16*y**2 - 27*y)\nSimplifying the partial expression: (-48*y)*(8*y**3 - 16*y**2 - 27*y)\nExpanding the part (8*y**3 - 16*y**2 - 27*y) using the distributive property, and we got: (-48*y)*(-27*y) + (-48*y)*(-16*y**2) + (-48*y)*(8*y**3)\nReplacing (-48*y)*(8*y**3 - 16*y**2 - 27*y) with (-48*y)*(-27*y) + (-48*y)*(-16*y**2) + (-48*y)*(8*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-48*y)*(-27*y) + (-48*y)*(-16*y**2) + (-48*y)*(8*y**3) + (-16*y**2)*(8*y**3 - 16*y**2 - 27*y) + (44*y**3)*(8*y**3 - 16*y**2 - 27*y)\nSimplifying the partial expression: (-16*y**2)*(8*y**3 - 16*y**2 - 27*y)\nExpanding the part (8*y**3 - 16*y**2 - 27*y) using the distributive property, and we got: (-27*y)*(-16*y**2) + (-16*y**2)*(8*y**3) + (-16*y**2)*(-16*y**2)\nReplacing (-16*y**2)*(8*y**3 - 16*y**2 - 27*y) with (-27*y)*(-16*y**2) + (-16*y**2)*(8*y**3) + (-16*y**2)*(-16*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-48*y)*(-27*y) + (-48*y)*(-16*y**2) + (-48*y)*(8*y**3) + (-27*y)*(-16*y**2) + (-16*y**2)*(8*y**3) + (-16*y**2)*(-16*y**2) + (44*y**3)*(8*y**3 - 16*y**2 - 27*y)\nSimplifying the partial expression: (44*y**3)*(8*y**3 - 16*y**2 - 27*y)\nExpanding the part (8*y**3 - 16*y**2 - 27*y) using the distributive property, and we got: (-27*y)*(44*y**3) + (-16*y**2)*(44*y**3) + (8*y**3)*(44*y**3)\nReplacing (44*y**3)*(8*y**3 - 16*y**2 - 27*y) with (-27*y)*(44*y**3) + (-16*y**2)*(44*y**3) + (8*y**3)*(44*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-48*y)*(-27*y) + (-48*y)*(-16*y**2) + (-48*y)*(8*y**3) + (-27*y)*(-16*y**2) + (-27*y)*(44*y**3) + (-16*y**2)*(8*y**3) + (-16*y**2)*(44*y**3) + (-16*y**2)*(-16*y**2) + (8*y**3)*(44*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*y)*(-48*y) = 1296*y**2\n (-27*y)*(-16*y**2) = 432*y**3\n (-27*y)*(44*y**3) = -1188*y**4\n (-16*y**2)*(-48*y) = 768*y**3\n (-16*y**2)*(-16*y**2) = 256*y**4\n (-16*y**2)*(44*y**3) = -704*y**5\n (8*y**3)*(-48*y) = -384*y**4\n (8*y**3)*(-16*y**2) = -128*y**5\n (8*y**3)*(44*y**3) = 352*y**6\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 352*y**6 - 704*y**5 - 128*y**5 - 1188*y**4 - 384*y**4 + 256*y**4 + 432*y**3 + 768*y**3 + 1296*y**2\nCombining like terms, got 352*y**6 - 832*y**5 - 1316*y**4 + 1200*y**3 + 1296*y**2\n#Step 7:\nCurrent expression: 352*y**6 - 832*y**5 - 1316*y**4 + 1200*y**3 + 1296*y**2\nNo more calculations needed.\n352*y**6 - 832*y**5 - 1316*y**4 + 1200*y**3 + 1296*y**2", "generated_answer": "352*y**6 - 832*y**5 - 1316*y**4 + 1200*y**3 + 1296*y**2", "step_length": 7} {"cot_id": "2608deb1875725323c739f580d5c0e9b4ec5cf1fd9337980d9f1f07b9349e935", "datapoint": {"question": "Calculate the following: -37*x**2*(5 - 35*x**3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1295*x**5 - 185*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1586, "polynomial_expr": "-37*x**2*(5 - 35*x**3)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -37*x**2*(5 - 35*x**3)\nExpanding the part (5 - 35*x**3) using the distributive property, and we got: 5*(-37*x**2) + (-37*x**2)*(-35*x**3)\n#Step 2:\nCurrent expression: 5*(-37*x**2) + (-37*x**2)*(-35*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 5*(-37*x**2) = -185*x**2\n (-35*x**3)*(-37*x**2) = 1295*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1295*x**5 - 185*x**2\nNo more calculations needed.\n1295*x**5 - 185*x**2", "generated_answer": "1295*x**5 - 185*x**2", "step_length": 3} {"cot_id": "eb00feec69a7bd2ab4aae87fcb69d61490f94e1066195a85271aa8163a0afbd5", "datapoint": {"question": "Calculate the following: (28*z**2 - 17)*(-41*z**3 - 19*z**2 - 7*z + 4)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1148*z**5 - 532*z**4 + 501*z**3 + 435*z**2 + 119*z - 68", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1587, "polynomial_expr": "(28*z**2 - 17)*(-41*z**3 - 19*z**2 - 7*z + 4)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28*z**2 - 17)*(-41*z**3 - 19*z**2 - 7*z + 4)\nExpanding the part (28*z**2 - 17) using the distributive property, and we got: (28*z**2)*(-41*z**3 - 19*z**2 - 7*z + 4) - 17*(-41*z**3 - 19*z**2 - 7*z + 4)\n#Step 2:\nCurrent expression: (28*z**2)*(-41*z**3 - 19*z**2 - 7*z + 4) - 17*(-41*z**3 - 19*z**2 - 7*z + 4)\nSimplifying the partial expression: -17*(-41*z**3 - 19*z**2 - 7*z + 4)\nExpanding the part (-41*z**3 - 19*z**2 - 7*z + 4) using the distributive property, and we got: -7*z*(-17) - 19*z**2*(-17) - 41*z**3*(-17) + 4*(-17)\nReplacing -17*(-41*z**3 - 19*z**2 - 7*z + 4) with -7*z*(-17) - 19*z**2*(-17) - 41*z**3*(-17) + 4*(-17) in the overall expression.\n#Step 3:\nCurrent expression: -7*z*(-17) - 19*z**2*(-17) + (28*z**2)*(-41*z**3 - 19*z**2 - 7*z + 4) - 41*z**3*(-17) - 68\nSimplifying the partial expression: (28*z**2)*(-41*z**3 - 19*z**2 - 7*z + 4)\nExpanding the part (-41*z**3 - 19*z**2 - 7*z + 4) using the distributive property, and we got: (-7*z)*(28*z**2) + 4*(28*z**2) + (-19*z**2)*(28*z**2) + (28*z**2)*(-41*z**3)\nReplacing (28*z**2)*(-41*z**3 - 19*z**2 - 7*z + 4) with (-7*z)*(28*z**2) + 4*(28*z**2) + (-19*z**2)*(28*z**2) + (28*z**2)*(-41*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-7*z)*(28*z**2) - 7*z*(-17) + 4*28*z**2 + (-19*z**2)*(28*z**2) - 19*z**2*(-17) + (28*z**2)*(-41*z**3) - 41*z**3*(-17) - 68\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*z**3)*-17 = 697*z**3\n (-41*z**3)*(28*z**2) = -1148*z**5\n (-19*z**2)*-17 = 323*z**2\n (-19*z**2)*(28*z**2) = -532*z**4\n (-7*z)*-17 = 119*z\n (-7*z)*(28*z**2) = -196*z**3\n 4*28*z**2 = 112*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1148*z**5 - 532*z**4 - 196*z**3 + 697*z**3 + 112*z**2 + 323*z**2 + 119*z - 68\nCombining like terms, got -1148*z**5 - 532*z**4 + 501*z**3 + 435*z**2 + 119*z - 68\n#Step 6:\nCurrent expression: -1148*z**5 - 532*z**4 + 501*z**3 + 435*z**2 + 119*z - 68\nNo more calculations needed.\n-1148*z**5 - 532*z**4 + 501*z**3 + 435*z**2 + 119*z - 68", "generated_answer": "-1148*z**5 - 532*z**4 + 501*z**3 + 435*z**2 + 119*z - 68", "step_length": 6} {"cot_id": "0665e63c53b4f1958b14b1e55fa14d05cdcea45757f7406e311e3100aeb66d81", "datapoint": {"question": "Calculate the following: (45*x**2 + 10)*(-21*x**3 - 5*x**2 - 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-945*x**5 - 225*x**4 - 210*x**3 - 1310*x**2 - 280", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1588, "polynomial_expr": "(45*x**2 + 10)*(-21*x**3 - 5*x**2 - 28)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (45*x**2 + 10)*(-21*x**3 - 5*x**2 - 28)\nExpanding the part (45*x**2 + 10) using the distributive property, and we got: (45*x**2)*(-21*x**3 - 5*x**2 - 28) + 10*(-21*x**3 - 5*x**2 - 28)\n#Step 2:\nCurrent expression: (45*x**2)*(-21*x**3 - 5*x**2 - 28) + 10*(-21*x**3 - 5*x**2 - 28)\nSimplifying the partial expression: 10*(-21*x**3 - 5*x**2 - 28)\nExpanding the part (-21*x**3 - 5*x**2 - 28) using the distributive property, and we got: -5*x**2*10 - 21*x**3*10 - 28*10\nReplacing 10*(-21*x**3 - 5*x**2 - 28) with -5*x**2*10 - 21*x**3*10 - 28*10 in the overall expression.\n#Step 3:\nCurrent expression: -5*x**2*10 + (45*x**2)*(-21*x**3 - 5*x**2 - 28) - 21*x**3*10 - 280\nSimplifying the partial expression: (45*x**2)*(-21*x**3 - 5*x**2 - 28)\nExpanding the part (-21*x**3 - 5*x**2 - 28) using the distributive property, and we got: -1260*x**2 + (-5*x**2)*(45*x**2) + (45*x**2)*(-21*x**3)\nReplacing (45*x**2)*(-21*x**3 - 5*x**2 - 28) with -1260*x**2 + (-5*x**2)*(45*x**2) + (45*x**2)*(-21*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -28*45*x**2 + (-5*x**2)*(45*x**2) - 5*x**2*10 + (45*x**2)*(-21*x**3) - 21*x**3*10 - 280\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-21*x**3)*10 = -210*x**3\n (-21*x**3)*(45*x**2) = -945*x**5\n (-5*x**2)*10 = -50*x**2\n (-5*x**2)*(45*x**2) = -225*x**4\n -28*45*x**2 = -1260*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -945*x**5 - 225*x**4 - 210*x**3 - 1260*x**2 - 50*x**2 - 280\nCombining like terms, got -945*x**5 - 225*x**4 - 210*x**3 - 1310*x**2 - 280\n#Step 6:\nCurrent expression: -945*x**5 - 225*x**4 - 210*x**3 - 1310*x**2 - 280\nNo more calculations needed.\n-945*x**5 - 225*x**4 - 210*x**3 - 1310*x**2 - 280", "generated_answer": "-945*x**5 - 225*x**4 - 210*x**3 - 1310*x**2 - 280", "step_length": 6} {"cot_id": "90d9ee418bbe14279db8d4170628ed79a46e826ef8afda526beac8b54ef583fb", "datapoint": {"question": "Simplify this expression: (44*x**2 + 35*x)*(-24*x**3 + 2*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1056*x**5 - 840*x**4 + 88*x**3 + 70*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1589, "polynomial_expr": "(44*x**2 + 35*x)*(-24*x**3 + 2*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (44*x**2 + 35*x)*(-24*x**3 + 2*x)\nExpanding the part (-24*x**3 + 2*x) using the distributive property, and we got: (2*x)*(44*x**2 + 35*x) + (-24*x**3)*(44*x**2 + 35*x)\n#Step 2:\nCurrent expression: (2*x)*(44*x**2 + 35*x) + (-24*x**3)*(44*x**2 + 35*x)\nSimplifying the partial expression: (-24*x**3)*(44*x**2 + 35*x)\nExpanding the part (44*x**2 + 35*x) using the distributive property, and we got: (35*x)*(-24*x**3) + (44*x**2)*(-24*x**3)\nReplacing (-24*x**3)*(44*x**2 + 35*x) with (35*x)*(-24*x**3) + (44*x**2)*(-24*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (2*x)*(44*x**2 + 35*x) + (35*x)*(-24*x**3) + (44*x**2)*(-24*x**3)\nSimplifying the partial expression: (2*x)*(44*x**2 + 35*x)\nExpanding the part (44*x**2 + 35*x) using the distributive property, and we got: (2*x)*(35*x) + (2*x)*(44*x**2)\nReplacing (2*x)*(44*x**2 + 35*x) with (2*x)*(35*x) + (2*x)*(44*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (2*x)*(35*x) + (2*x)*(44*x**2) + (35*x)*(-24*x**3) + (44*x**2)*(-24*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (35*x)*(-24*x**3) = -840*x**4\n (35*x)*(2*x) = 70*x**2\n (44*x**2)*(-24*x**3) = -1056*x**5\n (44*x**2)*(2*x) = 88*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1056*x**5 - 840*x**4 + 88*x**3 + 70*x**2\nNo more calculations needed.\n-1056*x**5 - 840*x**4 + 88*x**3 + 70*x**2", "generated_answer": "-1056*x**5 - 840*x**4 + 88*x**3 + 70*x**2", "step_length": 5} {"cot_id": "72e7dc130ca9275b4b3d28d7854613f2d6b35704cd3477077e7f6bcfbcc38997", "datapoint": {"question": "Simplify this expression: (12*x**3 - 23*x**2)*(36*x**2 + 18*x - 12)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "432*x**5 - 612*x**4 - 558*x**3 + 276*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1590, "polynomial_expr": "(12*x**3 - 23*x**2)*(36*x**2 + 18*x - 12)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (12*x**3 - 23*x**2)*(36*x**2 + 18*x - 12)\nExpanding the part (12*x**3 - 23*x**2) using the distributive property, and we got: (-23*x**2)*(36*x**2 + 18*x - 12) + (12*x**3)*(36*x**2 + 18*x - 12)\n#Step 2:\nCurrent expression: (-23*x**2)*(36*x**2 + 18*x - 12) + (12*x**3)*(36*x**2 + 18*x - 12)\nSimplifying the partial expression: (-23*x**2)*(36*x**2 + 18*x - 12)\nExpanding the part (36*x**2 + 18*x - 12) using the distributive property, and we got: -(-1)*276*x**2 + (18*x)*(-23*x**2) + (-23*x**2)*(36*x**2)\nReplacing (-23*x**2)*(36*x**2 + 18*x - 12) with -(-1)*276*x**2 + (18*x)*(-23*x**2) + (-23*x**2)*(36*x**2) in the overall expression.\n#Step 3:\nCurrent expression: -12*(-23)*x**2 + (18*x)*(-23*x**2) + (-23*x**2)*(36*x**2) + (12*x**3)*(36*x**2 + 18*x - 12)\nSimplifying the partial expression: (12*x**3)*(36*x**2 + 18*x - 12)\nExpanding the part (36*x**2 + 18*x - 12) using the distributive property, and we got: -144*x**3 + (18*x)*(12*x**3) + (36*x**2)*(12*x**3)\nReplacing (12*x**3)*(36*x**2 + 18*x - 12) with -144*x**3 + (18*x)*(12*x**3) + (36*x**2)*(12*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -12*12*x**3 - 12*(-23)*x**2 + (18*x)*(-23*x**2) + (18*x)*(12*x**3) + (-23*x**2)*(36*x**2) + (36*x**2)*(12*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (18*x)*(-23*x**2) = -414*x**3\n (18*x)*(12*x**3) = 216*x**4\n (36*x**2)*(-23*x**2) = -828*x**4\n (36*x**2)*(12*x**3) = 432*x**5\n -12*-23*x**2 = 276*x**2\n -12*12*x**3 = -144*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 432*x**5 - 828*x**4 + 216*x**4 - 414*x**3 - 144*x**3 + 276*x**2\nCombining like terms, got 432*x**5 - 612*x**4 - 558*x**3 + 276*x**2\n#Step 6:\nCurrent expression: 432*x**5 - 612*x**4 - 558*x**3 + 276*x**2\nNo more calculations needed.\n432*x**5 - 612*x**4 - 558*x**3 + 276*x**2", "generated_answer": "432*x**5 - 612*x**4 - 558*x**3 + 276*x**2", "step_length": 6} {"cot_id": "ef328b983db6a90a61873a5fef04aa79741ab7e1b017df837f764d749259c839", "datapoint": {"question": "Simplify this expression: (29*z**2 - 27*z - 40)*(-21*z**3 + 43*z + 15)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-609*z**5 + 567*z**4 + 2087*z**3 - 726*z**2 - 2125*z - 600", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1591, "polynomial_expr": "(29*z**2 - 27*z - 40)*(-21*z**3 + 43*z + 15)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29*z**2 - 27*z - 40)*(-21*z**3 + 43*z + 15)\nExpanding the part (29*z**2 - 27*z - 40) using the distributive property, and we got: (-27*z)*(-21*z**3 + 43*z + 15) + (29*z**2)*(-21*z**3 + 43*z + 15) - 40*(-21*z**3 + 43*z + 15)\n#Step 2:\nCurrent expression: (-27*z)*(-21*z**3 + 43*z + 15) + (29*z**2)*(-21*z**3 + 43*z + 15) - 40*(-21*z**3 + 43*z + 15)\nSimplifying the partial expression: -40*(-21*z**3 + 43*z + 15)\nExpanding the part (-21*z**3 + 43*z + 15) using the distributive property, and we got: (43*z)*(-40) - 21*z**3*(-40) + 15*(-40)\nReplacing -40*(-21*z**3 + 43*z + 15) with (43*z)*(-40) - 21*z**3*(-40) + 15*(-40) in the overall expression.\n#Step 3:\nCurrent expression: (-27*z)*(-21*z**3 + 43*z + 15) + (43*z)*(-40) + (29*z**2)*(-21*z**3 + 43*z + 15) - 21*z**3*(-40) - 600\nSimplifying the partial expression: (-27*z)*(-21*z**3 + 43*z + 15)\nExpanding the part (-21*z**3 + 43*z + 15) using the distributive property, and we got: (-27*z)*(43*z) + (-27*z)*(-21*z**3) + 15*(-27*z)\nReplacing (-27*z)*(-21*z**3 + 43*z + 15) with (-27*z)*(43*z) + (-27*z)*(-21*z**3) + 15*(-27*z) in the overall expression.\n#Step 4:\nCurrent expression: (-27*z)*(43*z) + (-27*z)*(-21*z**3) + 15*(-27)*z + (43*z)*(-40) + (29*z**2)*(-21*z**3 + 43*z + 15) - 21*z**3*(-40) - 600\nSimplifying the partial expression: (29*z**2)*(-21*z**3 + 43*z + 15)\nExpanding the part (-21*z**3 + 43*z + 15) using the distributive property, and we got: 15*(29*z**2) + (43*z)*(29*z**2) + (29*z**2)*(-21*z**3)\nReplacing (29*z**2)*(-21*z**3 + 43*z + 15) with 15*(29*z**2) + (43*z)*(29*z**2) + (29*z**2)*(-21*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-27*z)*(43*z) + (-27*z)*(-21*z**3) + 15*29*z**2 + 15*(-27)*z + (43*z)*(29*z**2) + (43*z)*(-40) + (29*z**2)*(-21*z**3) - 21*z**3*(-40) - 600\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-21*z**3)*-40 = 840*z**3\n (-21*z**3)*(-27*z) = 567*z**4\n (-21*z**3)*(29*z**2) = -609*z**5\n (43*z)*-40 = -1720*z\n (43*z)*(-27*z) = -1161*z**2\n (43*z)*(29*z**2) = 1247*z**3\n 15*-27*z = -405*z\n 15*29*z**2 = 435*z**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -609*z**5 + 567*z**4 + 840*z**3 + 1247*z**3 - 1161*z**2 + 435*z**2 - 1720*z - 405*z - 600\nCombining like terms, got -609*z**5 + 567*z**4 + 2087*z**3 - 726*z**2 - 2125*z - 600\n#Step 7:\nCurrent expression: -609*z**5 + 567*z**4 + 2087*z**3 - 726*z**2 - 2125*z - 600\nNo more calculations needed.\n-609*z**5 + 567*z**4 + 2087*z**3 - 726*z**2 - 2125*z - 600", "generated_answer": "-609*z**5 + 567*z**4 + 2087*z**3 - 726*z**2 - 2125*z - 600", "step_length": 7} {"cot_id": "69b4fe0788849e7f7b2d9ae11a9c8b189c903685d1b7a02331d36dbc7a0ffd71", "datapoint": {"question": "Simplify this expression: 61*x*(49*x**2 - 49*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2989*x**3 - 2989*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1592, "polynomial_expr": "61*x*(49*x**2 - 49*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 61*x*(49*x**2 - 49*x)\nExpanding the part (49*x**2 - 49*x) using the distributive property, and we got: (-49*x)*(61*x) + (61*x)*(49*x**2)\n#Step 2:\nCurrent expression: (-49*x)*(61*x) + (61*x)*(49*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*x)*(61*x) = -2989*x**2\n (49*x**2)*(61*x) = 2989*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 2989*x**3 - 2989*x**2\nNo more calculations needed.\n2989*x**3 - 2989*x**2", "generated_answer": "2989*x**3 - 2989*x**2", "step_length": 3} {"cot_id": "9352ba8aabe478b60be53bf1a8961220bd8055848215240daf321599e58ea2d4", "datapoint": {"question": "Simplify this expression: (31 - 28*x**2)*(-5*x**3 - 63*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "140*x**5 + 1764*x**4 - 155*x**3 - 1953*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1593, "polynomial_expr": "(31 - 28*x**2)*(-5*x**3 - 63*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31 - 28*x**2)*(-5*x**3 - 63*x**2)\nExpanding the part (31 - 28*x**2) using the distributive property, and we got: (-28*x**2)*(-5*x**3 - 63*x**2) + 31*(-5*x**3 - 63*x**2)\n#Step 2:\nCurrent expression: (-28*x**2)*(-5*x**3 - 63*x**2) + 31*(-5*x**3 - 63*x**2)\nSimplifying the partial expression: 31*(-5*x**3 - 63*x**2)\nExpanding the part (-5*x**3 - 63*x**2) using the distributive property, and we got: -63*x**2*31 - 5*x**3*31\nReplacing 31*(-5*x**3 - 63*x**2) with -63*x**2*31 - 5*x**3*31 in the overall expression.\n#Step 3:\nCurrent expression: -63*x**2*31 + (-28*x**2)*(-5*x**3 - 63*x**2) - 5*x**3*31\nSimplifying the partial expression: (-28*x**2)*(-5*x**3 - 63*x**2)\nExpanding the part (-5*x**3 - 63*x**2) using the distributive property, and we got: (-63*x**2)*(-28*x**2) + (-28*x**2)*(-5*x**3)\nReplacing (-28*x**2)*(-5*x**3 - 63*x**2) with (-63*x**2)*(-28*x**2) + (-28*x**2)*(-5*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-63*x**2)*(-28*x**2) - 63*x**2*31 + (-28*x**2)*(-5*x**3) - 5*x**3*31\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-63*x**2)*31 = -1953*x**2\n (-63*x**2)*(-28*x**2) = 1764*x**4\n (-5*x**3)*31 = -155*x**3\n (-5*x**3)*(-28*x**2) = 140*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 140*x**5 + 1764*x**4 - 155*x**3 - 1953*x**2\nNo more calculations needed.\n140*x**5 + 1764*x**4 - 155*x**3 - 1953*x**2", "generated_answer": "140*x**5 + 1764*x**4 - 155*x**3 - 1953*x**2", "step_length": 5} {"cot_id": "d095322def92fd39e4a1c20ef09882eb8ba49662eed6393ac7b99adb811b1e02", "datapoint": {"question": "Calculate the following: (-34*x**2 + 7*x)*(33*x**2 + 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1122*x**4 + 231*x**3 - 238*x**2 + 49*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1594, "polynomial_expr": "(-34*x**2 + 7*x)*(33*x**2 + 7)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-34*x**2 + 7*x)*(33*x**2 + 7)\nExpanding the part (33*x**2 + 7) using the distributive property, and we got: (33*x**2)*(-34*x**2 + 7*x) + 7*(-34*x**2 + 7*x)\n#Step 2:\nCurrent expression: (33*x**2)*(-34*x**2 + 7*x) + 7*(-34*x**2 + 7*x)\nSimplifying the partial expression: 7*(-34*x**2 + 7*x)\nExpanding the part (-34*x**2 + 7*x) using the distributive property, and we got: (7*x)*7 - 34*x**2*7\nReplacing 7*(-34*x**2 + 7*x) with (7*x)*7 - 34*x**2*7 in the overall expression.\n#Step 3:\nCurrent expression: (7*x)*7 - 34*x**2*7 + (33*x**2)*(-34*x**2 + 7*x)\nSimplifying the partial expression: (33*x**2)*(-34*x**2 + 7*x)\nExpanding the part (-34*x**2 + 7*x) using the distributive property, and we got: (7*x)*(33*x**2) + (-34*x**2)*(33*x**2)\nReplacing (33*x**2)*(-34*x**2 + 7*x) with (7*x)*(33*x**2) + (-34*x**2)*(33*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (7*x)*(33*x**2) + (7*x)*7 + (-34*x**2)*(33*x**2) - 34*x**2*7\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*x**2)*7 = -238*x**2\n (-34*x**2)*(33*x**2) = -1122*x**4\n (7*x)*7 = 49*x\n (7*x)*(33*x**2) = 231*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1122*x**4 + 231*x**3 - 238*x**2 + 49*x\nNo more calculations needed.\n-1122*x**4 + 231*x**3 - 238*x**2 + 49*x", "generated_answer": "-1122*x**4 + 231*x**3 - 238*x**2 + 49*x", "step_length": 5} {"cot_id": "666c1cfbf79208d1182712202330121c20e342a6cd6c7ec207a8a40c1e3d53b6", "datapoint": {"question": "Simplify this expression: (24 - 25*y)*(40*y**3 + 28*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1000*y**4 + 260*y**3 + 672*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1595, "polynomial_expr": "(24 - 25*y)*(40*y**3 + 28*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (24 - 25*y)*(40*y**3 + 28*y**2)\nExpanding the part (24 - 25*y) using the distributive property, and we got: (-25*y)*(40*y**3 + 28*y**2) + 24*(40*y**3 + 28*y**2)\n#Step 2:\nCurrent expression: (-25*y)*(40*y**3 + 28*y**2) + 24*(40*y**3 + 28*y**2)\nSimplifying the partial expression: 24*(40*y**3 + 28*y**2)\nExpanding the part (40*y**3 + 28*y**2) using the distributive property, and we got: (28*y**2)*24 + (40*y**3)*24\nReplacing 24*(40*y**3 + 28*y**2) with (28*y**2)*24 + (40*y**3)*24 in the overall expression.\n#Step 3:\nCurrent expression: (-25*y)*(40*y**3 + 28*y**2) + (28*y**2)*24 + (40*y**3)*24\nSimplifying the partial expression: (-25*y)*(40*y**3 + 28*y**2)\nExpanding the part (40*y**3 + 28*y**2) using the distributive property, and we got: (-25*y)*(28*y**2) + (-25*y)*(40*y**3)\nReplacing (-25*y)*(40*y**3 + 28*y**2) with (-25*y)*(28*y**2) + (-25*y)*(40*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-25*y)*(28*y**2) + (-25*y)*(40*y**3) + (28*y**2)*24 + (40*y**3)*24\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (28*y**2)*24 = 672*y**2\n (28*y**2)*(-25*y) = -700*y**3\n (40*y**3)*24 = 960*y**3\n (40*y**3)*(-25*y) = -1000*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1000*y**4 - 700*y**3 + 960*y**3 + 672*y**2\nCombining like terms, got -1000*y**4 + 260*y**3 + 672*y**2\n#Step 6:\nCurrent expression: -1000*y**4 + 260*y**3 + 672*y**2\nNo more calculations needed.\n-1000*y**4 + 260*y**3 + 672*y**2", "generated_answer": "-1000*y**4 + 260*y**3 + 672*y**2", "step_length": 6} {"cot_id": "3ff1c99b2e4c4c4d41f36fecae5e653ac70f90379633385020af17a3363449d4", "datapoint": {"question": "Calculate the following: (44*z**3 + 42*z**2 - 49)*(46*z**3 + 18*z - 19)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2024*z**6 + 1932*z**5 + 792*z**4 - 2334*z**3 - 798*z**2 - 882*z + 931", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1596, "polynomial_expr": "(44*z**3 + 42*z**2 - 49)*(46*z**3 + 18*z - 19)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (44*z**3 + 42*z**2 - 49)*(46*z**3 + 18*z - 19)\nExpanding the part (44*z**3 + 42*z**2 - 49) using the distributive property, and we got: (42*z**2)*(46*z**3 + 18*z - 19) + (44*z**3)*(46*z**3 + 18*z - 19) - 49*(46*z**3 + 18*z - 19)\n#Step 2:\nCurrent expression: (42*z**2)*(46*z**3 + 18*z - 19) + (44*z**3)*(46*z**3 + 18*z - 19) - 49*(46*z**3 + 18*z - 19)\nSimplifying the partial expression: -49*(46*z**3 + 18*z - 19)\nExpanding the part (46*z**3 + 18*z - 19) using the distributive property, and we got: (18*z)*(-49) + (46*z**3)*(-49) - 19*(-49)\nReplacing -49*(46*z**3 + 18*z - 19) with (18*z)*(-49) + (46*z**3)*(-49) - 19*(-49) in the overall expression.\n#Step 3:\nCurrent expression: (18*z)*(-49) + (42*z**2)*(46*z**3 + 18*z - 19) + (44*z**3)*(46*z**3 + 18*z - 19) + (46*z**3)*(-49) + 931\nSimplifying the partial expression: (42*z**2)*(46*z**3 + 18*z - 19)\nExpanding the part (46*z**3 + 18*z - 19) using the distributive property, and we got: -798*z**2 + (18*z)*(42*z**2) + (42*z**2)*(46*z**3)\nReplacing (42*z**2)*(46*z**3 + 18*z - 19) with -798*z**2 + (18*z)*(42*z**2) + (42*z**2)*(46*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -19*42*z**2 + (18*z)*(42*z**2) + (18*z)*(-49) + (42*z**2)*(46*z**3) + (44*z**3)*(46*z**3 + 18*z - 19) + (46*z**3)*(-49) + 931\nSimplifying the partial expression: (44*z**3)*(46*z**3 + 18*z - 19)\nExpanding the part (46*z**3 + 18*z - 19) using the distributive property, and we got: -836*z**3 + (18*z)*(44*z**3) + (44*z**3)*(46*z**3)\nReplacing (44*z**3)*(46*z**3 + 18*z - 19) with -836*z**3 + (18*z)*(44*z**3) + (44*z**3)*(46*z**3) in the overall expression.\n#Step 5:\nCurrent expression: -19*44*z**3 - 19*42*z**2 + (18*z)*(42*z**2) + (18*z)*(44*z**3) + (18*z)*(-49) + (42*z**2)*(46*z**3) + (44*z**3)*(46*z**3) + (46*z**3)*(-49) + 931\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (18*z)*-49 = -882*z\n (18*z)*(42*z**2) = 756*z**3\n (18*z)*(44*z**3) = 792*z**4\n (46*z**3)*-49 = -2254*z**3\n (46*z**3)*(42*z**2) = 1932*z**5\n (46*z**3)*(44*z**3) = 2024*z**6\n -19*42*z**2 = -798*z**2\n -19*44*z**3 = -836*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 2024*z**6 + 1932*z**5 + 792*z**4 - 2254*z**3 - 836*z**3 + 756*z**3 - 798*z**2 - 882*z + 931\nCombining like terms, got 2024*z**6 + 1932*z**5 + 792*z**4 - 2334*z**3 - 798*z**2 - 882*z + 931\n#Step 7:\nCurrent expression: 2024*z**6 + 1932*z**5 + 792*z**4 - 2334*z**3 - 798*z**2 - 882*z + 931\nNo more calculations needed.\n2024*z**6 + 1932*z**5 + 792*z**4 - 2334*z**3 - 798*z**2 - 882*z + 931", "generated_answer": "2024*z**6 + 1932*z**5 + 792*z**4 - 2334*z**3 - 798*z**2 - 882*z + 931", "step_length": 7} {"cot_id": "91eebce480008fbd43c6fe3d1938a5b4750f71d6971e0bf7583be3d4324f099c", "datapoint": {"question": "Calculate the following: (-16*x**2 - 5)*(22*x**2 - 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-352*x**4 + 2*x**2 + 35", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1597, "polynomial_expr": "(-16*x**2 - 5)*(22*x**2 - 7)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-16*x**2 - 5)*(22*x**2 - 7)\nExpanding the part (22*x**2 - 7) using the distributive property, and we got: (22*x**2)*(-16*x**2 - 5) - 7*(-16*x**2 - 5)\n#Step 2:\nCurrent expression: (22*x**2)*(-16*x**2 - 5) - 7*(-16*x**2 - 5)\nSimplifying the partial expression: -7*(-16*x**2 - 5)\nExpanding the part (-16*x**2 - 5) using the distributive property, and we got: -16*x**2*(-7) - 5*(-7)\nReplacing -7*(-16*x**2 - 5) with -16*x**2*(-7) - 5*(-7) in the overall expression.\n#Step 3:\nCurrent expression: -16*x**2*(-7) + (22*x**2)*(-16*x**2 - 5) + 35\nSimplifying the partial expression: (22*x**2)*(-16*x**2 - 5)\nExpanding the part (-16*x**2 - 5) using the distributive property, and we got: -110*x**2 + (-16*x**2)*(22*x**2)\nReplacing (22*x**2)*(-16*x**2 - 5) with -110*x**2 + (-16*x**2)*(22*x**2) in the overall expression.\n#Step 4:\nCurrent expression: -5*22*x**2 + (-16*x**2)*(22*x**2) - 16*x**2*(-7) + 35\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-16*x**2)*-7 = 112*x**2\n (-16*x**2)*(22*x**2) = -352*x**4\n -5*22*x**2 = -110*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -352*x**4 - 110*x**2 + 112*x**2 + 35\nCombining like terms, got -352*x**4 + 2*x**2 + 35\n#Step 6:\nCurrent expression: -352*x**4 + 2*x**2 + 35\nNo more calculations needed.\n-352*x**4 + 2*x**2 + 35", "generated_answer": "-352*x**4 + 2*x**2 + 35", "step_length": 6} {"cot_id": "ac5e6ca10968573f81a28e598952a298d88ad36796ca01e30c1367aeff3e13fc", "datapoint": {"question": "Simplify this expression: (-65*z**2 + 15*z - 1)*(24*z**3 + 34*z**2 + 12*z - 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1560*z**5 - 1850*z**4 - 294*z**3 + 1446*z**2 - 312*z + 20", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1598, "polynomial_expr": "(-65*z**2 + 15*z - 1)*(24*z**3 + 34*z**2 + 12*z - 20)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-65*z**2 + 15*z - 1)*(24*z**3 + 34*z**2 + 12*z - 20)\nExpanding the part (-65*z**2 + 15*z - 1) using the distributive property, and we got: (15*z)*(24*z**3 + 34*z**2 + 12*z - 20) + (-65*z**2)*(24*z**3 + 34*z**2 + 12*z - 20) - (24*z**3 + 34*z**2 + 12*z - 20)\n#Step 2:\nCurrent expression: (15*z)*(24*z**3 + 34*z**2 + 12*z - 20) + (-65*z**2)*(24*z**3 + 34*z**2 + 12*z - 20) - (24*z**3 + 34*z**2 + 12*z - 20)\nSimplifying the partial expression: -(24*z**3 + 34*z**2 + 12*z - 20)\nExpanding the part (24*z**3 + 34*z**2 + 12*z - 20) using the distributive property, and we got: (12*z)*(-1) + (34*z**2)*(-1) + (24*z**3)*(-1) - 20*(-1)\nReplacing -(24*z**3 + 34*z**2 + 12*z - 20) with (12*z)*(-1) + (34*z**2)*(-1) + (24*z**3)*(-1) - 20*(-1) in the overall expression.\n#Step 3:\nCurrent expression: (12*z)*(-1) + (15*z)*(24*z**3 + 34*z**2 + 12*z - 20) + (-65*z**2)*(24*z**3 + 34*z**2 + 12*z - 20) + (34*z**2)*(-1) + (24*z**3)*(-1) + 20\nSimplifying the partial expression: (-65*z**2)*(24*z**3 + 34*z**2 + 12*z - 20)\nExpanding the part (24*z**3 + 34*z**2 + 12*z - 20) using the distributive property, and we got: -(-1)*1300*z**2 + (12*z)*(-65*z**2) + (-65*z**2)*(34*z**2) + (-65*z**2)*(24*z**3)\nReplacing (-65*z**2)*(24*z**3 + 34*z**2 + 12*z - 20) with -(-1)*1300*z**2 + (12*z)*(-65*z**2) + (-65*z**2)*(34*z**2) + (-65*z**2)*(24*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -20*(-65)*z**2 + (12*z)*(-65*z**2) + (12*z)*(-1) + (15*z)*(24*z**3 + 34*z**2 + 12*z - 20) + (-65*z**2)*(34*z**2) + (-65*z**2)*(24*z**3) + (34*z**2)*(-1) + (24*z**3)*(-1) + 20\nSimplifying the partial expression: (15*z)*(24*z**3 + 34*z**2 + 12*z - 20)\nExpanding the part (24*z**3 + 34*z**2 + 12*z - 20) using the distributive property, and we got: -300*z + (12*z)*(15*z) + (15*z)*(34*z**2) + (15*z)*(24*z**3)\nReplacing (15*z)*(24*z**3 + 34*z**2 + 12*z - 20) with -300*z + (12*z)*(15*z) + (15*z)*(34*z**2) + (15*z)*(24*z**3) in the overall expression.\n#Step 5:\nCurrent expression: -20*(-65)*z**2 - 20*15*z + (12*z)*(15*z) + (12*z)*(-65*z**2) + (12*z)*(-1) + (15*z)*(34*z**2) + (15*z)*(24*z**3) + (-65*z**2)*(34*z**2) + (-65*z**2)*(24*z**3) + (34*z**2)*(-1) + (24*z**3)*(-1) + 20\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (12*z)*-1 = -12*z\n (12*z)*(-65*z**2) = -780*z**3\n (12*z)*(15*z) = 180*z**2\n (24*z**3)*-1 = -24*z**3\n (24*z**3)*(-65*z**2) = -1560*z**5\n (24*z**3)*(15*z) = 360*z**4\n (34*z**2)*-1 = -34*z**2\n (34*z**2)*(-65*z**2) = -2210*z**4\n (34*z**2)*(15*z) = 510*z**3\n -20*-65*z**2 = 1300*z**2\n -20*15*z = -300*z\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1560*z**5 - 2210*z**4 + 360*z**4 - 780*z**3 - 24*z**3 + 510*z**3 - 34*z**2 + 180*z**2 + 1300*z**2 - 300*z - 12*z + 20\nCombining like terms, got -1560*z**5 - 1850*z**4 - 294*z**3 + 1446*z**2 - 312*z + 20\n#Step 7:\nCurrent expression: -1560*z**5 - 1850*z**4 - 294*z**3 + 1446*z**2 - 312*z + 20\nNo more calculations needed.\n-1560*z**5 - 1850*z**4 - 294*z**3 + 1446*z**2 - 312*z + 20", "generated_answer": "-1560*z**5 - 1850*z**4 - 294*z**3 + 1446*z**2 - 312*z + 20", "step_length": 7} {"cot_id": "5d661a170b8d017dbce4d31c2d5aa978d2411761f88fda5b94bcba5afc9163c6", "datapoint": {"question": "Calculate the following: (-54*y**2 - 19)*(42*y**2 + 40)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2268*y**4 - 2958*y**2 - 760", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1599, "polynomial_expr": "(-54*y**2 - 19)*(42*y**2 + 40)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-54*y**2 - 19)*(42*y**2 + 40)\nExpanding the part (-54*y**2 - 19) using the distributive property, and we got: (-54*y**2)*(42*y**2 + 40) - 19*(42*y**2 + 40)\n#Step 2:\nCurrent expression: (-54*y**2)*(42*y**2 + 40) - 19*(42*y**2 + 40)\nSimplifying the partial expression: -19*(42*y**2 + 40)\nExpanding the part (42*y**2 + 40) using the distributive property, and we got: (42*y**2)*(-19) + 40*(-19)\nReplacing -19*(42*y**2 + 40) with (42*y**2)*(-19) + 40*(-19) in the overall expression.\n#Step 3:\nCurrent expression: (-54*y**2)*(42*y**2 + 40) + (42*y**2)*(-19) - 760\nSimplifying the partial expression: (-54*y**2)*(42*y**2 + 40)\nExpanding the part (42*y**2 + 40) using the distributive property, and we got: 40*(-54*y**2) + (-54*y**2)*(42*y**2)\nReplacing (-54*y**2)*(42*y**2 + 40) with 40*(-54*y**2) + (-54*y**2)*(42*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 40*(-54)*y**2 + (-54*y**2)*(42*y**2) + (42*y**2)*(-19) - 760\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (42*y**2)*-19 = -798*y**2\n (42*y**2)*(-54*y**2) = -2268*y**4\n 40*-54*y**2 = -2160*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2268*y**4 - 2160*y**2 - 798*y**2 - 760\nCombining like terms, got -2268*y**4 - 2958*y**2 - 760\n#Step 6:\nCurrent expression: -2268*y**4 - 2958*y**2 - 760\nNo more calculations needed.\n-2268*y**4 - 2958*y**2 - 760", "generated_answer": "-2268*y**4 - 2958*y**2 - 760", "step_length": 6} {"cot_id": "2ca528ecf6539e993f25ad4580012ab90211353c41c288e144742877809487a5", "datapoint": {"question": "Simplify this expression: 21*z**2*(-8*z**3 - 10*z**2 + 53)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-168*z**5 - 210*z**4 + 1113*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1600, "polynomial_expr": "21*z**2*(-8*z**3 - 10*z**2 + 53)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 21*z**2*(-8*z**3 - 10*z**2 + 53)\nExpanding the part (-8*z**3 - 10*z**2 + 53) using the distributive property, and we got: 53*(21*z**2) + (-10*z**2)*(21*z**2) + (21*z**2)*(-8*z**3)\n#Step 2:\nCurrent expression: 53*(21*z**2) + (-10*z**2)*(21*z**2) + (21*z**2)*(-8*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 53*(21*z**2) = 1113*z**2\n (-10*z**2)*(21*z**2) = -210*z**4\n (-8*z**3)*(21*z**2) = -168*z**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -168*z**5 - 210*z**4 + 1113*z**2\nNo more calculations needed.\n-168*z**5 - 210*z**4 + 1113*z**2", "generated_answer": "-168*z**5 - 210*z**4 + 1113*z**2", "step_length": 3} {"cot_id": "1d8b70e6676c831c84fa2d660712c988219879b8461860332b959f89440ad4e2", "datapoint": {"question": "Calculate the following: -6300*y**4\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-6300*y**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1601, "polynomial_expr": "-6300*y**4", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -6300*y**4\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -6300*y**4\nNo more calculations needed.\n-6300*y**4", "generated_answer": "-6300*y**4", "step_length": 2} {"cot_id": "d1c385103521403935f1d7d68e0070df174164cfd40d3d4581afde0392500264", "datapoint": {"question": "Simplify this expression: (-2*y**3 - 18*y)*(6*y**3 + 10*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-12*y**6 - 20*y**5 - 108*y**4 - 180*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1602, "polynomial_expr": "(-2*y**3 - 18*y)*(6*y**3 + 10*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-2*y**3 - 18*y)*(6*y**3 + 10*y**2)\nExpanding the part (-2*y**3 - 18*y) using the distributive property, and we got: (-18*y)*(6*y**3 + 10*y**2) + (-2*y**3)*(6*y**3 + 10*y**2)\n#Step 2:\nCurrent expression: (-18*y)*(6*y**3 + 10*y**2) + (-2*y**3)*(6*y**3 + 10*y**2)\nSimplifying the partial expression: (-18*y)*(6*y**3 + 10*y**2)\nExpanding the part (6*y**3 + 10*y**2) using the distributive property, and we got: (-18*y)*(10*y**2) + (-18*y)*(6*y**3)\nReplacing (-18*y)*(6*y**3 + 10*y**2) with (-18*y)*(10*y**2) + (-18*y)*(6*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-18*y)*(10*y**2) + (-18*y)*(6*y**3) + (-2*y**3)*(6*y**3 + 10*y**2)\nSimplifying the partial expression: (-2*y**3)*(6*y**3 + 10*y**2)\nExpanding the part (6*y**3 + 10*y**2) using the distributive property, and we got: (10*y**2)*(-2*y**3) + (-2*y**3)*(6*y**3)\nReplacing (-2*y**3)*(6*y**3 + 10*y**2) with (10*y**2)*(-2*y**3) + (-2*y**3)*(6*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-18*y)*(10*y**2) + (-18*y)*(6*y**3) + (10*y**2)*(-2*y**3) + (-2*y**3)*(6*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (6*y**3)*(-18*y) = -108*y**4\n (6*y**3)*(-2*y**3) = -12*y**6\n (10*y**2)*(-18*y) = -180*y**3\n (10*y**2)*(-2*y**3) = -20*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -12*y**6 - 20*y**5 - 108*y**4 - 180*y**3\nNo more calculations needed.\n-12*y**6 - 20*y**5 - 108*y**4 - 180*y**3", "generated_answer": "-12*y**6 - 20*y**5 - 108*y**4 - 180*y**3", "step_length": 5} {"cot_id": "8ae192efdbe46d5bf03e0ddfd3c828a4e53606ce0ae5690004e33a467d0ccc89", "datapoint": {"question": "Calculate the following: -105*z*(8*z**2 - 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-840*z**3 + 735*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1603, "polynomial_expr": "-105*z*(8*z**2 - 7)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -105*z*(8*z**2 - 7)\nExpanding the part (8*z**2 - 7) using the distributive property, and we got: (-105*z)*(8*z**2) - (-1)*735*z\n#Step 2:\nCurrent expression: (-105*z)*(8*z**2) - (-1)*735*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -7*(-105*z) = 735*z\n (8*z**2)*(-105*z) = -840*z**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -840*z**3 + 735*z\nNo more calculations needed.\n-840*z**3 + 735*z", "generated_answer": "-840*z**3 + 735*z", "step_length": 3} {"cot_id": "1d4d7ba51fad0c73408463aa553d2639b943dbdd34d465cde53c6b3a8136e905", "datapoint": {"question": "Simplify this expression: (21*y - 27)*(8*y**3 - 41*y**2 + 42*y + 45)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "168*y**4 - 1077*y**3 + 1989*y**2 - 189*y - 1215", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1604, "polynomial_expr": "(21*y - 27)*(8*y**3 - 41*y**2 + 42*y + 45)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21*y - 27)*(8*y**3 - 41*y**2 + 42*y + 45)\nExpanding the part (21*y - 27) using the distributive property, and we got: (21*y)*(8*y**3 - 41*y**2 + 42*y + 45) - 27*(8*y**3 - 41*y**2 + 42*y + 45)\n#Step 2:\nCurrent expression: (21*y)*(8*y**3 - 41*y**2 + 42*y + 45) - 27*(8*y**3 - 41*y**2 + 42*y + 45)\nSimplifying the partial expression: -27*(8*y**3 - 41*y**2 + 42*y + 45)\nExpanding the part (8*y**3 - 41*y**2 + 42*y + 45) using the distributive property, and we got: (42*y)*(-27) - 41*y**2*(-27) + (8*y**3)*(-27) + 45*(-27)\nReplacing -27*(8*y**3 - 41*y**2 + 42*y + 45) with (42*y)*(-27) - 41*y**2*(-27) + (8*y**3)*(-27) + 45*(-27) in the overall expression.\n#Step 3:\nCurrent expression: (21*y)*(8*y**3 - 41*y**2 + 42*y + 45) + (42*y)*(-27) - 41*y**2*(-27) + (8*y**3)*(-27) - 1215\nSimplifying the partial expression: (21*y)*(8*y**3 - 41*y**2 + 42*y + 45)\nExpanding the part (8*y**3 - 41*y**2 + 42*y + 45) using the distributive property, and we got: 45*(21*y) + (21*y)*(42*y) + (21*y)*(-41*y**2) + (21*y)*(8*y**3)\nReplacing (21*y)*(8*y**3 - 41*y**2 + 42*y + 45) with 45*(21*y) + (21*y)*(42*y) + (21*y)*(-41*y**2) + (21*y)*(8*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 45*21*y + (21*y)*(42*y) + (21*y)*(-41*y**2) + (21*y)*(8*y**3) + (42*y)*(-27) - 41*y**2*(-27) + (8*y**3)*(-27) - 1215\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*y**2)*-27 = 1107*y**2\n (-41*y**2)*(21*y) = -861*y**3\n (8*y**3)*-27 = -216*y**3\n (8*y**3)*(21*y) = 168*y**4\n (42*y)*-27 = -1134*y\n (42*y)*(21*y) = 882*y**2\n 45*21*y = 945*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 168*y**4 - 861*y**3 - 216*y**3 + 882*y**2 + 1107*y**2 - 1134*y + 945*y - 1215\nCombining like terms, got 168*y**4 - 1077*y**3 + 1989*y**2 - 189*y - 1215\n#Step 6:\nCurrent expression: 168*y**4 - 1077*y**3 + 1989*y**2 - 189*y - 1215\nNo more calculations needed.\n168*y**4 - 1077*y**3 + 1989*y**2 - 189*y - 1215", "generated_answer": "168*y**4 - 1077*y**3 + 1989*y**2 - 189*y - 1215", "step_length": 6} {"cot_id": "39e94fdf8fa7f159fe31a80958ce96dfaea2d15c452c55975d070e64ad6c7e23", "datapoint": {"question": "Simplify this expression: (47*y - 10)*(-28*y**3 - 15*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1316*y**4 - 425*y**3 + 150*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1605, "polynomial_expr": "(47*y - 10)*(-28*y**3 - 15*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (47*y - 10)*(-28*y**3 - 15*y**2)\nExpanding the part (47*y - 10) using the distributive property, and we got: (47*y)*(-28*y**3 - 15*y**2) - 10*(-28*y**3 - 15*y**2)\n#Step 2:\nCurrent expression: (47*y)*(-28*y**3 - 15*y**2) - 10*(-28*y**3 - 15*y**2)\nSimplifying the partial expression: -10*(-28*y**3 - 15*y**2)\nExpanding the part (-28*y**3 - 15*y**2) using the distributive property, and we got: -15*y**2*(-10) - 28*y**3*(-10)\nReplacing -10*(-28*y**3 - 15*y**2) with -15*y**2*(-10) - 28*y**3*(-10) in the overall expression.\n#Step 3:\nCurrent expression: (47*y)*(-28*y**3 - 15*y**2) - 15*y**2*(-10) - 28*y**3*(-10)\nSimplifying the partial expression: (47*y)*(-28*y**3 - 15*y**2)\nExpanding the part (-28*y**3 - 15*y**2) using the distributive property, and we got: (47*y)*(-15*y**2) + (47*y)*(-28*y**3)\nReplacing (47*y)*(-28*y**3 - 15*y**2) with (47*y)*(-15*y**2) + (47*y)*(-28*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (47*y)*(-15*y**2) + (47*y)*(-28*y**3) - 15*y**2*(-10) - 28*y**3*(-10)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*y**3)*-10 = 280*y**3\n (-28*y**3)*(47*y) = -1316*y**4\n (-15*y**2)*-10 = 150*y**2\n (-15*y**2)*(47*y) = -705*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1316*y**4 - 705*y**3 + 280*y**3 + 150*y**2\nCombining like terms, got -1316*y**4 - 425*y**3 + 150*y**2\n#Step 6:\nCurrent expression: -1316*y**4 - 425*y**3 + 150*y**2\nNo more calculations needed.\n-1316*y**4 - 425*y**3 + 150*y**2", "generated_answer": "-1316*y**4 - 425*y**3 + 150*y**2", "step_length": 6} {"cot_id": "d11ff4069b47b8294db237c72c644630ade033e38331596a92b3acdf4fab873b", "datapoint": {"question": "Calculate the following: (3 - 74*x)*(-33*x**2 + 50*x - 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2442*x**3 - 3799*x**2 + 1112*x - 39", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1606, "polynomial_expr": "(3 - 74*x)*(-33*x**2 + 50*x - 13)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (3 - 74*x)*(-33*x**2 + 50*x - 13)\nExpanding the part (3 - 74*x) using the distributive property, and we got: (-74*x)*(-33*x**2 + 50*x - 13) + 3*(-33*x**2 + 50*x - 13)\n#Step 2:\nCurrent expression: (-74*x)*(-33*x**2 + 50*x - 13) + 3*(-33*x**2 + 50*x - 13)\nSimplifying the partial expression: 3*(-33*x**2 + 50*x - 13)\nExpanding the part (-33*x**2 + 50*x - 13) using the distributive property, and we got: (50*x)*3 - 33*x**2*3 - 13*3\nReplacing 3*(-33*x**2 + 50*x - 13) with (50*x)*3 - 33*x**2*3 - 13*3 in the overall expression.\n#Step 3:\nCurrent expression: (-74*x)*(-33*x**2 + 50*x - 13) + (50*x)*3 - 33*x**2*3 - 39\nSimplifying the partial expression: (-74*x)*(-33*x**2 + 50*x - 13)\nExpanding the part (-33*x**2 + 50*x - 13) using the distributive property, and we got: (-74*x)*(50*x) + (-74*x)*(-33*x**2) - (-1)*962*x\nReplacing (-74*x)*(-33*x**2 + 50*x - 13) with (-74*x)*(50*x) + (-74*x)*(-33*x**2) - (-1)*962*x in the overall expression.\n#Step 4:\nCurrent expression: (-74*x)*(50*x) + (-74*x)*(-33*x**2) - 13*(-74)*x + (50*x)*3 - 33*x**2*3 - 39\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*x**2)*3 = -99*x**2\n (-33*x**2)*(-74*x) = 2442*x**3\n (50*x)*3 = 150*x\n (50*x)*(-74*x) = -3700*x**2\n -13*-74*x = 962*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2442*x**3 - 3700*x**2 - 99*x**2 + 150*x + 962*x - 39\nCombining like terms, got 2442*x**3 - 3799*x**2 + 1112*x - 39\n#Step 6:\nCurrent expression: 2442*x**3 - 3799*x**2 + 1112*x - 39\nNo more calculations needed.\n2442*x**3 - 3799*x**2 + 1112*x - 39", "generated_answer": "2442*x**3 - 3799*x**2 + 1112*x - 39", "step_length": 6} {"cot_id": "f058a666c0793310d11811cb560da19d7cab49193dcb9b3eb95d974000cc68df", "datapoint": {"question": "Calculate the following: (55 - 13*z**3)*(-46*z**3 - 15*z - 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "598*z**6 + 195*z**4 - 2309*z**3 - 825*z - 935", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1607, "polynomial_expr": "(55 - 13*z**3)*(-46*z**3 - 15*z - 17)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (55 - 13*z**3)*(-46*z**3 - 15*z - 17)\nExpanding the part (55 - 13*z**3) using the distributive property, and we got: (-13*z**3)*(-46*z**3 - 15*z - 17) + 55*(-46*z**3 - 15*z - 17)\n#Step 2:\nCurrent expression: (-13*z**3)*(-46*z**3 - 15*z - 17) + 55*(-46*z**3 - 15*z - 17)\nSimplifying the partial expression: 55*(-46*z**3 - 15*z - 17)\nExpanding the part (-46*z**3 - 15*z - 17) using the distributive property, and we got: -15*z*55 - 46*z**3*55 - 17*55\nReplacing 55*(-46*z**3 - 15*z - 17) with -15*z*55 - 46*z**3*55 - 17*55 in the overall expression.\n#Step 3:\nCurrent expression: -15*z*55 - 46*z**3*55 + (-13*z**3)*(-46*z**3 - 15*z - 17) - 935\nSimplifying the partial expression: (-13*z**3)*(-46*z**3 - 15*z - 17)\nExpanding the part (-46*z**3 - 15*z - 17) using the distributive property, and we got: (-15*z)*(-13*z**3) - (-1)*221*z**3 + (-46*z**3)*(-13*z**3)\nReplacing (-13*z**3)*(-46*z**3 - 15*z - 17) with (-15*z)*(-13*z**3) - (-1)*221*z**3 + (-46*z**3)*(-13*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-15*z)*(-13*z**3) - 15*z*55 - 17*(-13)*z**3 + (-46*z**3)*(-13*z**3) - 46*z**3*55 - 935\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*z**3)*55 = -2530*z**3\n (-46*z**3)*(-13*z**3) = 598*z**6\n (-15*z)*55 = -825*z\n (-15*z)*(-13*z**3) = 195*z**4\n -17*-13*z**3 = 221*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 598*z**6 + 195*z**4 - 2530*z**3 + 221*z**3 - 825*z - 935\nCombining like terms, got 598*z**6 + 195*z**4 - 2309*z**3 - 825*z - 935\n#Step 6:\nCurrent expression: 598*z**6 + 195*z**4 - 2309*z**3 - 825*z - 935\nNo more calculations needed.\n598*z**6 + 195*z**4 - 2309*z**3 - 825*z - 935", "generated_answer": "598*z**6 + 195*z**4 - 2309*z**3 - 825*z - 935", "step_length": 6} {"cot_id": "0b744262a56caae847101c1103b688dd92f21eaec767b39dc01a40c2a882e6e8", "datapoint": {"question": "Simplify this expression: -y*(-19*y**3 + 78*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "19*y**4 - 78*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1608, "polynomial_expr": "-y*(-19*y**3 + 78*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -y*(-19*y**3 + 78*y**2)\nExpanding the part (-19*y**3 + 78*y**2) using the distributive property, and we got: (-y)*(78*y**2) + (-y)*(-19*y**3)\n#Step 2:\nCurrent expression: (-y)*(78*y**2) + (-y)*(-19*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*y**3)*(-y) = 19*y**4\n (78*y**2)*(-y) = -78*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 19*y**4 - 78*y**3\nNo more calculations needed.\n19*y**4 - 78*y**3", "generated_answer": "19*y**4 - 78*y**3", "step_length": 3} {"cot_id": "1df1ed802e2f1e06f26f2a727c212a743a78706dcb3a89d8370b78a7fb779a92", "datapoint": {"question": "Simplify this expression: -1026*x**2\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1026*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1609, "polynomial_expr": "-1026*x**2", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -1026*x**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -1026*x**2\nNo more calculations needed.\n-1026*x**2", "generated_answer": "-1026*x**2", "step_length": 2} {"cot_id": "a25118baa8f4e564055907cd651f5f549a9cf4175dd1d1d26002d943c91b65d8", "datapoint": {"question": "Calculate the following: (26 - 87*y**2)*(-32*y**3 - 19)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2784*y**5 - 832*y**3 + 1653*y**2 - 494", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1610, "polynomial_expr": "(26 - 87*y**2)*(-32*y**3 - 19)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (26 - 87*y**2)*(-32*y**3 - 19)\nExpanding the part (-32*y**3 - 19) using the distributive property, and we got: (-32*y**3)*(26 - 87*y**2) - 19*(26 - 87*y**2)\n#Step 2:\nCurrent expression: (-32*y**3)*(26 - 87*y**2) - 19*(26 - 87*y**2)\nSimplifying the partial expression: -19*(26 - 87*y**2)\nExpanding the part (26 - 87*y**2) using the distributive property, and we got: -87*y**2*(-19) + 26*(-19)\nReplacing -19*(26 - 87*y**2) with -87*y**2*(-19) + 26*(-19) in the overall expression.\n#Step 3:\nCurrent expression: -87*y**2*(-19) + (-32*y**3)*(26 - 87*y**2) - 494\nSimplifying the partial expression: (-32*y**3)*(26 - 87*y**2)\nExpanding the part (26 - 87*y**2) using the distributive property, and we got: 26*(-32*y**3) + (-87*y**2)*(-32*y**3)\nReplacing (-32*y**3)*(26 - 87*y**2) with 26*(-32*y**3) + (-87*y**2)*(-32*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 26*(-32)*y**3 + (-87*y**2)*(-32*y**3) - 87*y**2*(-19) - 494\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-87*y**2)*-19 = 1653*y**2\n (-87*y**2)*(-32*y**3) = 2784*y**5\n 26*-32*y**3 = -832*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2784*y**5 - 832*y**3 + 1653*y**2 - 494\nNo more calculations needed.\n2784*y**5 - 832*y**3 + 1653*y**2 - 494", "generated_answer": "2784*y**5 - 832*y**3 + 1653*y**2 - 494", "step_length": 5} {"cot_id": "43ee161cdabc4dfa01e96378cc6c0224702ec07142abb0c9a8721b426141fdbd", "datapoint": {"question": "Calculate the following: (-29*x**3 - 2*x**2 - 5)*(6*x**3 + 3*x - 19)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-174*x**6 - 12*x**5 - 87*x**4 + 515*x**3 + 38*x**2 - 15*x + 95", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1611, "polynomial_expr": "(-29*x**3 - 2*x**2 - 5)*(6*x**3 + 3*x - 19)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-29*x**3 - 2*x**2 - 5)*(6*x**3 + 3*x - 19)\nExpanding the part (6*x**3 + 3*x - 19) using the distributive property, and we got: (3*x)*(-29*x**3 - 2*x**2 - 5) + (6*x**3)*(-29*x**3 - 2*x**2 - 5) - 19*(-29*x**3 - 2*x**2 - 5)\n#Step 2:\nCurrent expression: (3*x)*(-29*x**3 - 2*x**2 - 5) + (6*x**3)*(-29*x**3 - 2*x**2 - 5) - 19*(-29*x**3 - 2*x**2 - 5)\nSimplifying the partial expression: -19*(-29*x**3 - 2*x**2 - 5)\nExpanding the part (-29*x**3 - 2*x**2 - 5) using the distributive property, and we got: -2*x**2*(-19) - 29*x**3*(-19) - 5*(-19)\nReplacing -19*(-29*x**3 - 2*x**2 - 5) with -2*x**2*(-19) - 29*x**3*(-19) - 5*(-19) in the overall expression.\n#Step 3:\nCurrent expression: (3*x)*(-29*x**3 - 2*x**2 - 5) - 2*x**2*(-19) - 29*x**3*(-19) + (6*x**3)*(-29*x**3 - 2*x**2 - 5) + 95\nSimplifying the partial expression: (3*x)*(-29*x**3 - 2*x**2 - 5)\nExpanding the part (-29*x**3 - 2*x**2 - 5) using the distributive property, and we got: -15*x + (3*x)*(-2*x**2) + (3*x)*(-29*x**3)\nReplacing (3*x)*(-29*x**3 - 2*x**2 - 5) with -15*x + (3*x)*(-2*x**2) + (3*x)*(-29*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -5*3*x + (3*x)*(-2*x**2) + (3*x)*(-29*x**3) - 2*x**2*(-19) - 29*x**3*(-19) + (6*x**3)*(-29*x**3 - 2*x**2 - 5) + 95\nSimplifying the partial expression: (6*x**3)*(-29*x**3 - 2*x**2 - 5)\nExpanding the part (-29*x**3 - 2*x**2 - 5) using the distributive property, and we got: -30*x**3 + (-2*x**2)*(6*x**3) + (-29*x**3)*(6*x**3)\nReplacing (6*x**3)*(-29*x**3 - 2*x**2 - 5) with -30*x**3 + (-2*x**2)*(6*x**3) + (-29*x**3)*(6*x**3) in the overall expression.\n#Step 5:\nCurrent expression: -5*6*x**3 - 5*3*x + (3*x)*(-2*x**2) + (3*x)*(-29*x**3) + (-2*x**2)*(6*x**3) - 2*x**2*(-19) + (-29*x**3)*(6*x**3) - 29*x**3*(-19) + 95\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*x**3)*-19 = 551*x**3\n (-29*x**3)*(3*x) = -87*x**4\n (-29*x**3)*(6*x**3) = -174*x**6\n (-2*x**2)*-19 = 38*x**2\n (-2*x**2)*(3*x) = -6*x**3\n (-2*x**2)*(6*x**3) = -12*x**5\n -5*3*x = -15*x\n -5*6*x**3 = -30*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -174*x**6 - 12*x**5 - 87*x**4 - 30*x**3 - 6*x**3 + 551*x**3 + 38*x**2 - 15*x + 95\nCombining like terms, got -174*x**6 - 12*x**5 - 87*x**4 + 515*x**3 + 38*x**2 - 15*x + 95\n#Step 7:\nCurrent expression: -174*x**6 - 12*x**5 - 87*x**4 + 515*x**3 + 38*x**2 - 15*x + 95\nNo more calculations needed.\n-174*x**6 - 12*x**5 - 87*x**4 + 515*x**3 + 38*x**2 - 15*x + 95", "generated_answer": "-174*x**6 - 12*x**5 - 87*x**4 + 515*x**3 + 38*x**2 - 15*x + 95", "step_length": 7} {"cot_id": "6f1d86acda1e2ecfa3e4675946697a7e0620b9332d59eec6b95ef809d722d3b9", "datapoint": {"question": "Simplify this expression: (6 - 53*x**3)*(-12*x**3 + 16*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "636*x**6 - 848*x**5 - 72*x**3 + 96*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1612, "polynomial_expr": "(6 - 53*x**3)*(-12*x**3 + 16*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6 - 53*x**3)*(-12*x**3 + 16*x**2)\nExpanding the part (6 - 53*x**3) using the distributive property, and we got: (-53*x**3)*(-12*x**3 + 16*x**2) + 6*(-12*x**3 + 16*x**2)\n#Step 2:\nCurrent expression: (-53*x**3)*(-12*x**3 + 16*x**2) + 6*(-12*x**3 + 16*x**2)\nSimplifying the partial expression: 6*(-12*x**3 + 16*x**2)\nExpanding the part (-12*x**3 + 16*x**2) using the distributive property, and we got: (16*x**2)*6 - 12*x**3*6\nReplacing 6*(-12*x**3 + 16*x**2) with (16*x**2)*6 - 12*x**3*6 in the overall expression.\n#Step 3:\nCurrent expression: (16*x**2)*6 + (-53*x**3)*(-12*x**3 + 16*x**2) - 12*x**3*6\nSimplifying the partial expression: (-53*x**3)*(-12*x**3 + 16*x**2)\nExpanding the part (-12*x**3 + 16*x**2) using the distributive property, and we got: (16*x**2)*(-53*x**3) + (-53*x**3)*(-12*x**3)\nReplacing (-53*x**3)*(-12*x**3 + 16*x**2) with (16*x**2)*(-53*x**3) + (-53*x**3)*(-12*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (16*x**2)*(-53*x**3) + (16*x**2)*6 + (-53*x**3)*(-12*x**3) - 12*x**3*6\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*x**3)*6 = -72*x**3\n (-12*x**3)*(-53*x**3) = 636*x**6\n (16*x**2)*6 = 96*x**2\n (16*x**2)*(-53*x**3) = -848*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 636*x**6 - 848*x**5 - 72*x**3 + 96*x**2\nNo more calculations needed.\n636*x**6 - 848*x**5 - 72*x**3 + 96*x**2", "generated_answer": "636*x**6 - 848*x**5 - 72*x**3 + 96*x**2", "step_length": 5} {"cot_id": "159b7dad403e1d7cb48cc3d570963a3bbc5d2dd1cd1378ee587b5852168b2d9a", "datapoint": {"question": "Calculate the following: (50*z + 11)*(-8*z**3 + 33*z - 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-400*z**4 - 88*z**3 + 1650*z**2 - 1437*z - 396", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1613, "polynomial_expr": "(50*z + 11)*(-8*z**3 + 33*z - 36)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (50*z + 11)*(-8*z**3 + 33*z - 36)\nExpanding the part (50*z + 11) using the distributive property, and we got: (50*z)*(-8*z**3 + 33*z - 36) + 11*(-8*z**3 + 33*z - 36)\n#Step 2:\nCurrent expression: (50*z)*(-8*z**3 + 33*z - 36) + 11*(-8*z**3 + 33*z - 36)\nSimplifying the partial expression: 11*(-8*z**3 + 33*z - 36)\nExpanding the part (-8*z**3 + 33*z - 36) using the distributive property, and we got: (33*z)*11 - 8*z**3*11 - 36*11\nReplacing 11*(-8*z**3 + 33*z - 36) with (33*z)*11 - 8*z**3*11 - 36*11 in the overall expression.\n#Step 3:\nCurrent expression: (33*z)*11 + (50*z)*(-8*z**3 + 33*z - 36) - 8*z**3*11 - 396\nSimplifying the partial expression: (50*z)*(-8*z**3 + 33*z - 36)\nExpanding the part (-8*z**3 + 33*z - 36) using the distributive property, and we got: -1800*z + (33*z)*(50*z) + (50*z)*(-8*z**3)\nReplacing (50*z)*(-8*z**3 + 33*z - 36) with -1800*z + (33*z)*(50*z) + (50*z)*(-8*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -36*50*z + (33*z)*(50*z) + (33*z)*11 + (50*z)*(-8*z**3) - 8*z**3*11 - 396\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-8*z**3)*11 = -88*z**3\n (-8*z**3)*(50*z) = -400*z**4\n (33*z)*11 = 363*z\n (33*z)*(50*z) = 1650*z**2\n -36*50*z = -1800*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -400*z**4 - 88*z**3 + 1650*z**2 - 1800*z + 363*z - 396\nCombining like terms, got -400*z**4 - 88*z**3 + 1650*z**2 - 1437*z - 396\n#Step 6:\nCurrent expression: -400*z**4 - 88*z**3 + 1650*z**2 - 1437*z - 396\nNo more calculations needed.\n-400*z**4 - 88*z**3 + 1650*z**2 - 1437*z - 396", "generated_answer": "-400*z**4 - 88*z**3 + 1650*z**2 - 1437*z - 396", "step_length": 6} {"cot_id": "0842ea27e0a716552729a667fa2f277915e599f7dc6070cc33dbb3c63cebdd25", "datapoint": {"question": "Simplify this expression: (22*z**2 + 39)*(-38*z**3 + 41*z**2 + 30*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-836*z**5 + 902*z**4 - 822*z**3 + 1599*z**2 + 1170*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1614, "polynomial_expr": "(22*z**2 + 39)*(-38*z**3 + 41*z**2 + 30*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (22*z**2 + 39)*(-38*z**3 + 41*z**2 + 30*z)\nExpanding the part (22*z**2 + 39) using the distributive property, and we got: (22*z**2)*(-38*z**3 + 41*z**2 + 30*z) + 39*(-38*z**3 + 41*z**2 + 30*z)\n#Step 2:\nCurrent expression: (22*z**2)*(-38*z**3 + 41*z**2 + 30*z) + 39*(-38*z**3 + 41*z**2 + 30*z)\nSimplifying the partial expression: 39*(-38*z**3 + 41*z**2 + 30*z)\nExpanding the part (-38*z**3 + 41*z**2 + 30*z) using the distributive property, and we got: (30*z)*39 + (41*z**2)*39 - 38*z**3*39\nReplacing 39*(-38*z**3 + 41*z**2 + 30*z) with (30*z)*39 + (41*z**2)*39 - 38*z**3*39 in the overall expression.\n#Step 3:\nCurrent expression: (30*z)*39 + (22*z**2)*(-38*z**3 + 41*z**2 + 30*z) + (41*z**2)*39 - 38*z**3*39\nSimplifying the partial expression: (22*z**2)*(-38*z**3 + 41*z**2 + 30*z)\nExpanding the part (-38*z**3 + 41*z**2 + 30*z) using the distributive property, and we got: (30*z)*(22*z**2) + (22*z**2)*(41*z**2) + (22*z**2)*(-38*z**3)\nReplacing (22*z**2)*(-38*z**3 + 41*z**2 + 30*z) with (30*z)*(22*z**2) + (22*z**2)*(41*z**2) + (22*z**2)*(-38*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (30*z)*(22*z**2) + (30*z)*39 + (22*z**2)*(41*z**2) + (22*z**2)*(-38*z**3) + (41*z**2)*39 - 38*z**3*39\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*z**3)*39 = -1482*z**3\n (-38*z**3)*(22*z**2) = -836*z**5\n (30*z)*39 = 1170*z\n (30*z)*(22*z**2) = 660*z**3\n (41*z**2)*39 = 1599*z**2\n (41*z**2)*(22*z**2) = 902*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -836*z**5 + 902*z**4 - 1482*z**3 + 660*z**3 + 1599*z**2 + 1170*z\nCombining like terms, got -836*z**5 + 902*z**4 - 822*z**3 + 1599*z**2 + 1170*z\n#Step 6:\nCurrent expression: -836*z**5 + 902*z**4 - 822*z**3 + 1599*z**2 + 1170*z\nNo more calculations needed.\n-836*z**5 + 902*z**4 - 822*z**3 + 1599*z**2 + 1170*z", "generated_answer": "-836*z**5 + 902*z**4 - 822*z**3 + 1599*z**2 + 1170*z", "step_length": 6} {"cot_id": "2ba8f16f51ef1572bd23e03bb63656ae3762190716fc984a20e760785b2c1f99", "datapoint": {"question": "Simplify this expression: (43*z**3 + 14)*(-50*z**3 + 10*z**2 + 37)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2150*z**6 + 430*z**5 + 891*z**3 + 140*z**2 + 518", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1615, "polynomial_expr": "(43*z**3 + 14)*(-50*z**3 + 10*z**2 + 37)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (43*z**3 + 14)*(-50*z**3 + 10*z**2 + 37)\nExpanding the part (43*z**3 + 14) using the distributive property, and we got: (43*z**3)*(-50*z**3 + 10*z**2 + 37) + 14*(-50*z**3 + 10*z**2 + 37)\n#Step 2:\nCurrent expression: (43*z**3)*(-50*z**3 + 10*z**2 + 37) + 14*(-50*z**3 + 10*z**2 + 37)\nSimplifying the partial expression: 14*(-50*z**3 + 10*z**2 + 37)\nExpanding the part (-50*z**3 + 10*z**2 + 37) using the distributive property, and we got: (10*z**2)*14 - 50*z**3*14 + 37*14\nReplacing 14*(-50*z**3 + 10*z**2 + 37) with (10*z**2)*14 - 50*z**3*14 + 37*14 in the overall expression.\n#Step 3:\nCurrent expression: (10*z**2)*14 - 50*z**3*14 + (43*z**3)*(-50*z**3 + 10*z**2 + 37) + 518\nSimplifying the partial expression: (43*z**3)*(-50*z**3 + 10*z**2 + 37)\nExpanding the part (-50*z**3 + 10*z**2 + 37) using the distributive property, and we got: 37*(43*z**3) + (10*z**2)*(43*z**3) + (-50*z**3)*(43*z**3)\nReplacing (43*z**3)*(-50*z**3 + 10*z**2 + 37) with 37*(43*z**3) + (10*z**2)*(43*z**3) + (-50*z**3)*(43*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 37*43*z**3 + (10*z**2)*(43*z**3) + (10*z**2)*14 + (-50*z**3)*(43*z**3) - 50*z**3*14 + 518\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-50*z**3)*14 = -700*z**3\n (-50*z**3)*(43*z**3) = -2150*z**6\n (10*z**2)*14 = 140*z**2\n (10*z**2)*(43*z**3) = 430*z**5\n 37*43*z**3 = 1591*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2150*z**6 + 430*z**5 - 700*z**3 + 1591*z**3 + 140*z**2 + 518\nCombining like terms, got -2150*z**6 + 430*z**5 + 891*z**3 + 140*z**2 + 518\n#Step 6:\nCurrent expression: -2150*z**6 + 430*z**5 + 891*z**3 + 140*z**2 + 518\nNo more calculations needed.\n-2150*z**6 + 430*z**5 + 891*z**3 + 140*z**2 + 518", "generated_answer": "-2150*z**6 + 430*z**5 + 891*z**3 + 140*z**2 + 518", "step_length": 6} {"cot_id": "8a7bb61432c59eb267445f536b09829748dca61dcc01fcaf86c36968389d5b93", "datapoint": {"question": "Calculate the following: (-z - 40)*(-15*z**2 - 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "15*z**3 + 600*z**2 + 16*z + 640", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1616, "polynomial_expr": "(-z - 40)*(-15*z**2 - 16)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-z - 40)*(-15*z**2 - 16)\nExpanding the part (-z - 40) using the distributive property, and we got: (-z)*(-15*z**2 - 16) - 40*(-15*z**2 - 16)\n#Step 2:\nCurrent expression: (-z)*(-15*z**2 - 16) - 40*(-15*z**2 - 16)\nSimplifying the partial expression: -40*(-15*z**2 - 16)\nExpanding the part (-15*z**2 - 16) using the distributive property, and we got: -15*z**2*(-40) - 16*(-40)\nReplacing -40*(-15*z**2 - 16) with -15*z**2*(-40) - 16*(-40) in the overall expression.\n#Step 3:\nCurrent expression: (-z)*(-15*z**2 - 16) - 15*z**2*(-40) + 640\nSimplifying the partial expression: (-z)*(-15*z**2 - 16)\nExpanding the part (-15*z**2 - 16) using the distributive property, and we got: (-z)*(-15*z**2) - (-1)*16*z\nReplacing (-z)*(-15*z**2 - 16) with (-z)*(-15*z**2) - (-1)*16*z in the overall expression.\n#Step 4:\nCurrent expression: (-z)*(-15*z**2) - 16*(-1)*z - 15*z**2*(-40) + 640\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-15*z**2)*-40 = 600*z**2\n (-15*z**2)*(-z) = 15*z**3\n -16*-1*z = 16*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 15*z**3 + 600*z**2 + 16*z + 640\nNo more calculations needed.\n15*z**3 + 600*z**2 + 16*z + 640", "generated_answer": "15*z**3 + 600*z**2 + 16*z + 640", "step_length": 5} {"cot_id": "8ba1effe5adff294cb71e1fbbd332178408b3960ffd9118f7ddb013f91fbd27f", "datapoint": {"question": "Calculate the following: (-7*y**3 - 29*y)*(-9*y**3 - 21*y**2 - 34*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "63*y**6 + 147*y**5 + 499*y**4 + 609*y**3 + 986*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1617, "polynomial_expr": "(-7*y**3 - 29*y)*(-9*y**3 - 21*y**2 - 34*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-7*y**3 - 29*y)*(-9*y**3 - 21*y**2 - 34*y)\nExpanding the part (-7*y**3 - 29*y) using the distributive property, and we got: (-29*y)*(-9*y**3 - 21*y**2 - 34*y) + (-7*y**3)*(-9*y**3 - 21*y**2 - 34*y)\n#Step 2:\nCurrent expression: (-29*y)*(-9*y**3 - 21*y**2 - 34*y) + (-7*y**3)*(-9*y**3 - 21*y**2 - 34*y)\nSimplifying the partial expression: (-29*y)*(-9*y**3 - 21*y**2 - 34*y)\nExpanding the part (-9*y**3 - 21*y**2 - 34*y) using the distributive property, and we got: (-34*y)*(-29*y) + (-29*y)*(-21*y**2) + (-29*y)*(-9*y**3)\nReplacing (-29*y)*(-9*y**3 - 21*y**2 - 34*y) with (-34*y)*(-29*y) + (-29*y)*(-21*y**2) + (-29*y)*(-9*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-34*y)*(-29*y) + (-29*y)*(-21*y**2) + (-29*y)*(-9*y**3) + (-7*y**3)*(-9*y**3 - 21*y**2 - 34*y)\nSimplifying the partial expression: (-7*y**3)*(-9*y**3 - 21*y**2 - 34*y)\nExpanding the part (-9*y**3 - 21*y**2 - 34*y) using the distributive property, and we got: (-34*y)*(-7*y**3) + (-21*y**2)*(-7*y**3) + (-9*y**3)*(-7*y**3)\nReplacing (-7*y**3)*(-9*y**3 - 21*y**2 - 34*y) with (-34*y)*(-7*y**3) + (-21*y**2)*(-7*y**3) + (-9*y**3)*(-7*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-34*y)*(-29*y) + (-34*y)*(-7*y**3) + (-29*y)*(-21*y**2) + (-29*y)*(-9*y**3) + (-21*y**2)*(-7*y**3) + (-9*y**3)*(-7*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*y)*(-29*y) = 986*y**2\n (-34*y)*(-7*y**3) = 238*y**4\n (-21*y**2)*(-29*y) = 609*y**3\n (-21*y**2)*(-7*y**3) = 147*y**5\n (-9*y**3)*(-29*y) = 261*y**4\n (-9*y**3)*(-7*y**3) = 63*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 63*y**6 + 147*y**5 + 238*y**4 + 261*y**4 + 609*y**3 + 986*y**2\nCombining like terms, got 63*y**6 + 147*y**5 + 499*y**4 + 609*y**3 + 986*y**2\n#Step 6:\nCurrent expression: 63*y**6 + 147*y**5 + 499*y**4 + 609*y**3 + 986*y**2\nNo more calculations needed.\n63*y**6 + 147*y**5 + 499*y**4 + 609*y**3 + 986*y**2", "generated_answer": "63*y**6 + 147*y**5 + 499*y**4 + 609*y**3 + 986*y**2", "step_length": 6} {"cot_id": "e706cdfc9325199ea9d1c745d0db8003d835c0e90221ac8365b0ddb59e5de6e3", "datapoint": {"question": "Simplify this expression: (41 - 31*x)*(-30*x**3 + 47*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "930*x**4 - 2687*x**3 + 1927*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1618, "polynomial_expr": "(41 - 31*x)*(-30*x**3 + 47*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (41 - 31*x)*(-30*x**3 + 47*x**2)\nExpanding the part (41 - 31*x) using the distributive property, and we got: (-31*x)*(-30*x**3 + 47*x**2) + 41*(-30*x**3 + 47*x**2)\n#Step 2:\nCurrent expression: (-31*x)*(-30*x**3 + 47*x**2) + 41*(-30*x**3 + 47*x**2)\nSimplifying the partial expression: 41*(-30*x**3 + 47*x**2)\nExpanding the part (-30*x**3 + 47*x**2) using the distributive property, and we got: (47*x**2)*41 - 30*x**3*41\nReplacing 41*(-30*x**3 + 47*x**2) with (47*x**2)*41 - 30*x**3*41 in the overall expression.\n#Step 3:\nCurrent expression: (-31*x)*(-30*x**3 + 47*x**2) + (47*x**2)*41 - 30*x**3*41\nSimplifying the partial expression: (-31*x)*(-30*x**3 + 47*x**2)\nExpanding the part (-30*x**3 + 47*x**2) using the distributive property, and we got: (-31*x)*(47*x**2) + (-31*x)*(-30*x**3)\nReplacing (-31*x)*(-30*x**3 + 47*x**2) with (-31*x)*(47*x**2) + (-31*x)*(-30*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-31*x)*(47*x**2) + (-31*x)*(-30*x**3) + (47*x**2)*41 - 30*x**3*41\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*x**3)*41 = -1230*x**3\n (-30*x**3)*(-31*x) = 930*x**4\n (47*x**2)*41 = 1927*x**2\n (47*x**2)*(-31*x) = -1457*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 930*x**4 - 1457*x**3 - 1230*x**3 + 1927*x**2\nCombining like terms, got 930*x**4 - 2687*x**3 + 1927*x**2\n#Step 6:\nCurrent expression: 930*x**4 - 2687*x**3 + 1927*x**2\nNo more calculations needed.\n930*x**4 - 2687*x**3 + 1927*x**2", "generated_answer": "930*x**4 - 2687*x**3 + 1927*x**2", "step_length": 6} {"cot_id": "957f4a3054f7170e3deb99a7df3e313dfb8857814745f9ad43c71c2c4d2222b5", "datapoint": {"question": "Calculate the following: (-13*y**3 + 38*y**2 - 49*y)*(3*y**3 - 21*y - 5)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-39*y**6 + 114*y**5 + 126*y**4 - 733*y**3 + 839*y**2 + 245*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1619, "polynomial_expr": "(-13*y**3 + 38*y**2 - 49*y)*(3*y**3 - 21*y - 5)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-13*y**3 + 38*y**2 - 49*y)*(3*y**3 - 21*y - 5)\nExpanding the part (3*y**3 - 21*y - 5) using the distributive property, and we got: (-21*y)*(-13*y**3 + 38*y**2 - 49*y) + (3*y**3)*(-13*y**3 + 38*y**2 - 49*y) - 5*(-13*y**3 + 38*y**2 - 49*y)\n#Step 2:\nCurrent expression: (-21*y)*(-13*y**3 + 38*y**2 - 49*y) + (3*y**3)*(-13*y**3 + 38*y**2 - 49*y) - 5*(-13*y**3 + 38*y**2 - 49*y)\nSimplifying the partial expression: -5*(-13*y**3 + 38*y**2 - 49*y)\nExpanding the part (-13*y**3 + 38*y**2 - 49*y) using the distributive property, and we got: -49*y*(-5) + (38*y**2)*(-5) - 13*y**3*(-5)\nReplacing -5*(-13*y**3 + 38*y**2 - 49*y) with -49*y*(-5) + (38*y**2)*(-5) - 13*y**3*(-5) in the overall expression.\n#Step 3:\nCurrent expression: -49*y*(-5) + (-21*y)*(-13*y**3 + 38*y**2 - 49*y) + (38*y**2)*(-5) - 13*y**3*(-5) + (3*y**3)*(-13*y**3 + 38*y**2 - 49*y)\nSimplifying the partial expression: (-21*y)*(-13*y**3 + 38*y**2 - 49*y)\nExpanding the part (-13*y**3 + 38*y**2 - 49*y) using the distributive property, and we got: (-49*y)*(-21*y) + (-21*y)*(38*y**2) + (-21*y)*(-13*y**3)\nReplacing (-21*y)*(-13*y**3 + 38*y**2 - 49*y) with (-49*y)*(-21*y) + (-21*y)*(38*y**2) + (-21*y)*(-13*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-49*y)*(-21*y) - 49*y*(-5) + (-21*y)*(38*y**2) + (-21*y)*(-13*y**3) + (38*y**2)*(-5) - 13*y**3*(-5) + (3*y**3)*(-13*y**3 + 38*y**2 - 49*y)\nSimplifying the partial expression: (3*y**3)*(-13*y**3 + 38*y**2 - 49*y)\nExpanding the part (-13*y**3 + 38*y**2 - 49*y) using the distributive property, and we got: (-49*y)*(3*y**3) + (38*y**2)*(3*y**3) + (-13*y**3)*(3*y**3)\nReplacing (3*y**3)*(-13*y**3 + 38*y**2 - 49*y) with (-49*y)*(3*y**3) + (38*y**2)*(3*y**3) + (-13*y**3)*(3*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-49*y)*(-21*y) + (-49*y)*(3*y**3) - 49*y*(-5) + (-21*y)*(38*y**2) + (-21*y)*(-13*y**3) + (38*y**2)*(3*y**3) + (38*y**2)*(-5) + (-13*y**3)*(3*y**3) - 13*y**3*(-5)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*y)*-5 = 245*y\n (-49*y)*(-21*y) = 1029*y**2\n (-49*y)*(3*y**3) = -147*y**4\n (-13*y**3)*-5 = 65*y**3\n (-13*y**3)*(-21*y) = 273*y**4\n (-13*y**3)*(3*y**3) = -39*y**6\n (38*y**2)*-5 = -190*y**2\n (38*y**2)*(-21*y) = -798*y**3\n (38*y**2)*(3*y**3) = 114*y**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -39*y**6 + 114*y**5 - 147*y**4 + 273*y**4 - 798*y**3 + 65*y**3 - 190*y**2 + 1029*y**2 + 245*y\nCombining like terms, got -39*y**6 + 114*y**5 + 126*y**4 - 733*y**3 + 839*y**2 + 245*y\n#Step 7:\nCurrent expression: -39*y**6 + 114*y**5 + 126*y**4 - 733*y**3 + 839*y**2 + 245*y\nNo more calculations needed.\n-39*y**6 + 114*y**5 + 126*y**4 - 733*y**3 + 839*y**2 + 245*y", "generated_answer": "-39*y**6 + 114*y**5 + 126*y**4 - 733*y**3 + 839*y**2 + 245*y", "step_length": 7} {"cot_id": "bfcbf3d3fba213379f938f4324efff9b11705134c491dedda22b826ea21e8979", "datapoint": {"question": "Calculate the following: (-35*z**3 - 50*z)*(-45*z**3 + 25*z**2 + 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1575*z**6 - 875*z**5 + 2250*z**4 - 2475*z**3 - 1750*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1620, "polynomial_expr": "(-35*z**3 - 50*z)*(-45*z**3 + 25*z**2 + 35)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-35*z**3 - 50*z)*(-45*z**3 + 25*z**2 + 35)\nExpanding the part (-35*z**3 - 50*z) using the distributive property, and we got: (-50*z)*(-45*z**3 + 25*z**2 + 35) + (-35*z**3)*(-45*z**3 + 25*z**2 + 35)\n#Step 2:\nCurrent expression: (-50*z)*(-45*z**3 + 25*z**2 + 35) + (-35*z**3)*(-45*z**3 + 25*z**2 + 35)\nSimplifying the partial expression: (-50*z)*(-45*z**3 + 25*z**2 + 35)\nExpanding the part (-45*z**3 + 25*z**2 + 35) using the distributive property, and we got: (-50*z)*(25*z**2) + (-50*z)*(-45*z**3) + 35*(-50*z)\nReplacing (-50*z)*(-45*z**3 + 25*z**2 + 35) with (-50*z)*(25*z**2) + (-50*z)*(-45*z**3) + 35*(-50*z) in the overall expression.\n#Step 3:\nCurrent expression: (-50*z)*(25*z**2) + (-50*z)*(-45*z**3) + 35*(-50)*z + (-35*z**3)*(-45*z**3 + 25*z**2 + 35)\nSimplifying the partial expression: (-35*z**3)*(-45*z**3 + 25*z**2 + 35)\nExpanding the part (-45*z**3 + 25*z**2 + 35) using the distributive property, and we got: 35*(-35*z**3) + (25*z**2)*(-35*z**3) + (-45*z**3)*(-35*z**3)\nReplacing (-35*z**3)*(-45*z**3 + 25*z**2 + 35) with 35*(-35*z**3) + (25*z**2)*(-35*z**3) + (-45*z**3)*(-35*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-50*z)*(25*z**2) + (-50*z)*(-45*z**3) + 35*(-35)*z**3 + 35*(-50)*z + (25*z**2)*(-35*z**3) + (-45*z**3)*(-35*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*z**3)*(-50*z) = 2250*z**4\n (-45*z**3)*(-35*z**3) = 1575*z**6\n (25*z**2)*(-50*z) = -1250*z**3\n (25*z**2)*(-35*z**3) = -875*z**5\n 35*-50*z = -1750*z\n 35*-35*z**3 = -1225*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1575*z**6 - 875*z**5 + 2250*z**4 - 1250*z**3 - 1225*z**3 - 1750*z\nCombining like terms, got 1575*z**6 - 875*z**5 + 2250*z**4 - 2475*z**3 - 1750*z\n#Step 6:\nCurrent expression: 1575*z**6 - 875*z**5 + 2250*z**4 - 2475*z**3 - 1750*z\nNo more calculations needed.\n1575*z**6 - 875*z**5 + 2250*z**4 - 2475*z**3 - 1750*z", "generated_answer": "1575*z**6 - 875*z**5 + 2250*z**4 - 2475*z**3 - 1750*z", "step_length": 6} {"cot_id": "45c315672bf3bf30d6a0934e51086ad6792d443272c261936668a9734ddd1826", "datapoint": {"question": "Calculate the following: -32*z*(-27*z**3 + 44*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "864*z**4 - 1408*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1621, "polynomial_expr": "-32*z*(-27*z**3 + 44*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -32*z*(-27*z**3 + 44*z**2)\nExpanding the part (-27*z**3 + 44*z**2) using the distributive property, and we got: (-32*z)*(44*z**2) + (-32*z)*(-27*z**3)\n#Step 2:\nCurrent expression: (-32*z)*(44*z**2) + (-32*z)*(-27*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*z**3)*(-32*z) = 864*z**4\n (44*z**2)*(-32*z) = -1408*z**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 864*z**4 - 1408*z**3\nNo more calculations needed.\n864*z**4 - 1408*z**3", "generated_answer": "864*z**4 - 1408*z**3", "step_length": 3} {"cot_id": "ac127a3bba7adb5a1e37c5e53fcf121128b36d1ec33e13fd354304206cba38de", "datapoint": {"question": "Calculate the following: (56*z**3 - 2)*(19*z**3 - 2*z - 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1064*z**6 - 112*z**4 - 2838*z**3 + 4*z + 100", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1622, "polynomial_expr": "(56*z**3 - 2)*(19*z**3 - 2*z - 50)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (56*z**3 - 2)*(19*z**3 - 2*z - 50)\nExpanding the part (56*z**3 - 2) using the distributive property, and we got: (56*z**3)*(19*z**3 - 2*z - 50) - 2*(19*z**3 - 2*z - 50)\n#Step 2:\nCurrent expression: (56*z**3)*(19*z**3 - 2*z - 50) - 2*(19*z**3 - 2*z - 50)\nSimplifying the partial expression: -2*(19*z**3 - 2*z - 50)\nExpanding the part (19*z**3 - 2*z - 50) using the distributive property, and we got: -2*z*(-2) + (19*z**3)*(-2) - 50*(-2)\nReplacing -2*(19*z**3 - 2*z - 50) with -2*z*(-2) + (19*z**3)*(-2) - 50*(-2) in the overall expression.\n#Step 3:\nCurrent expression: -2*z*(-2) + (19*z**3)*(-2) + (56*z**3)*(19*z**3 - 2*z - 50) + 100\nSimplifying the partial expression: (56*z**3)*(19*z**3 - 2*z - 50)\nExpanding the part (19*z**3 - 2*z - 50) using the distributive property, and we got: (-2*z)*(56*z**3) - 2800*z**3 + (19*z**3)*(56*z**3)\nReplacing (56*z**3)*(19*z**3 - 2*z - 50) with (-2*z)*(56*z**3) - 2800*z**3 + (19*z**3)*(56*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-2*z)*(56*z**3) - 2*z*(-2) - 50*56*z**3 + (19*z**3)*(56*z**3) + (19*z**3)*(-2) + 100\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-2*z)*-2 = 4*z\n (-2*z)*(56*z**3) = -112*z**4\n (19*z**3)*-2 = -38*z**3\n (19*z**3)*(56*z**3) = 1064*z**6\n -50*56*z**3 = -2800*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1064*z**6 - 112*z**4 - 2800*z**3 - 38*z**3 + 4*z + 100\nCombining like terms, got 1064*z**6 - 112*z**4 - 2838*z**3 + 4*z + 100\n#Step 6:\nCurrent expression: 1064*z**6 - 112*z**4 - 2838*z**3 + 4*z + 100\nNo more calculations needed.\n1064*z**6 - 112*z**4 - 2838*z**3 + 4*z + 100", "generated_answer": "1064*z**6 - 112*z**4 - 2838*z**3 + 4*z + 100", "step_length": 6} {"cot_id": "948d0722132488dcd745233f6577c5cf0d40bc4059f5d55959fd92ce51eef99b", "datapoint": {"question": "Calculate the following: -47*z**3*(25*z**3 + 52*z + 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1175*z**6 - 2444*z**4 - 2209*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1623, "polynomial_expr": "-47*z**3*(25*z**3 + 52*z + 47)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -47*z**3*(25*z**3 + 52*z + 47)\nExpanding the part (25*z**3 + 52*z + 47) using the distributive property, and we got: 47*(-47*z**3) + (52*z)*(-47*z**3) + (-47*z**3)*(25*z**3)\n#Step 2:\nCurrent expression: 47*(-47*z**3) + (52*z)*(-47*z**3) + (-47*z**3)*(25*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 47*(-47*z**3) = -2209*z**3\n (25*z**3)*(-47*z**3) = -1175*z**6\n (52*z)*(-47*z**3) = -2444*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1175*z**6 - 2444*z**4 - 2209*z**3\nNo more calculations needed.\n-1175*z**6 - 2444*z**4 - 2209*z**3", "generated_answer": "-1175*z**6 - 2444*z**4 - 2209*z**3", "step_length": 3} {"cot_id": "4921c8e82aba9caf5fdba3c228d46643849cc12c2e096043e1f95e5f3cd9b813", "datapoint": {"question": "Simplify this expression: (-29*z**2 - 35*z)*(-18*z**3 + 35*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "522*z**5 + 630*z**4 - 1015*z**3 - 1225*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1624, "polynomial_expr": "(-29*z**2 - 35*z)*(-18*z**3 + 35*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-29*z**2 - 35*z)*(-18*z**3 + 35*z)\nExpanding the part (-29*z**2 - 35*z) using the distributive property, and we got: (-35*z)*(-18*z**3 + 35*z) + (-29*z**2)*(-18*z**3 + 35*z)\n#Step 2:\nCurrent expression: (-35*z)*(-18*z**3 + 35*z) + (-29*z**2)*(-18*z**3 + 35*z)\nSimplifying the partial expression: (-35*z)*(-18*z**3 + 35*z)\nExpanding the part (-18*z**3 + 35*z) using the distributive property, and we got: (-35*z)*(35*z) + (-35*z)*(-18*z**3)\nReplacing (-35*z)*(-18*z**3 + 35*z) with (-35*z)*(35*z) + (-35*z)*(-18*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-35*z)*(35*z) + (-35*z)*(-18*z**3) + (-29*z**2)*(-18*z**3 + 35*z)\nSimplifying the partial expression: (-29*z**2)*(-18*z**3 + 35*z)\nExpanding the part (-18*z**3 + 35*z) using the distributive property, and we got: (35*z)*(-29*z**2) + (-29*z**2)*(-18*z**3)\nReplacing (-29*z**2)*(-18*z**3 + 35*z) with (35*z)*(-29*z**2) + (-29*z**2)*(-18*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-35*z)*(35*z) + (-35*z)*(-18*z**3) + (35*z)*(-29*z**2) + (-29*z**2)*(-18*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-18*z**3)*(-35*z) = 630*z**4\n (-18*z**3)*(-29*z**2) = 522*z**5\n (35*z)*(-35*z) = -1225*z**2\n (35*z)*(-29*z**2) = -1015*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 522*z**5 + 630*z**4 - 1015*z**3 - 1225*z**2\nNo more calculations needed.\n522*z**5 + 630*z**4 - 1015*z**3 - 1225*z**2", "generated_answer": "522*z**5 + 630*z**4 - 1015*z**3 - 1225*z**2", "step_length": 5} {"cot_id": "2630fa9a5cca07f69dea700a0a9b52ce33403e85935d9fce5fe433a1aa746b5b", "datapoint": {"question": "Calculate the following: (-5*y**3 - 2*y)*(65*y**3 + 34*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-325*y**6 - 300*y**4 - 68*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1625, "polynomial_expr": "(-5*y**3 - 2*y)*(65*y**3 + 34*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-5*y**3 - 2*y)*(65*y**3 + 34*y)\nExpanding the part (-5*y**3 - 2*y) using the distributive property, and we got: (-2*y)*(65*y**3 + 34*y) + (-5*y**3)*(65*y**3 + 34*y)\n#Step 2:\nCurrent expression: (-2*y)*(65*y**3 + 34*y) + (-5*y**3)*(65*y**3 + 34*y)\nSimplifying the partial expression: (-5*y**3)*(65*y**3 + 34*y)\nExpanding the part (65*y**3 + 34*y) using the distributive property, and we got: (34*y)*(-5*y**3) + (-5*y**3)*(65*y**3)\nReplacing (-5*y**3)*(65*y**3 + 34*y) with (34*y)*(-5*y**3) + (-5*y**3)*(65*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-2*y)*(65*y**3 + 34*y) + (34*y)*(-5*y**3) + (-5*y**3)*(65*y**3)\nSimplifying the partial expression: (-2*y)*(65*y**3 + 34*y)\nExpanding the part (65*y**3 + 34*y) using the distributive property, and we got: (-2*y)*(34*y) + (-2*y)*(65*y**3)\nReplacing (-2*y)*(65*y**3 + 34*y) with (-2*y)*(34*y) + (-2*y)*(65*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-2*y)*(34*y) + (-2*y)*(65*y**3) + (34*y)*(-5*y**3) + (-5*y**3)*(65*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (34*y)*(-5*y**3) = -170*y**4\n (34*y)*(-2*y) = -68*y**2\n (65*y**3)*(-5*y**3) = -325*y**6\n (65*y**3)*(-2*y) = -130*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -325*y**6 - 170*y**4 - 130*y**4 - 68*y**2\nCombining like terms, got -325*y**6 - 300*y**4 - 68*y**2\n#Step 6:\nCurrent expression: -325*y**6 - 300*y**4 - 68*y**2\nNo more calculations needed.\n-325*y**6 - 300*y**4 - 68*y**2", "generated_answer": "-325*y**6 - 300*y**4 - 68*y**2", "step_length": 6} {"cot_id": "e7317006525a5612da8815701d71628812944193305eb005be9e5943899a0ddf", "datapoint": {"question": "Simplify this expression: (31 - 7*z**3)*(-13*z**3 - 11*z**2 + 18)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "91*z**6 + 77*z**5 - 529*z**3 - 341*z**2 + 558", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1626, "polynomial_expr": "(31 - 7*z**3)*(-13*z**3 - 11*z**2 + 18)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31 - 7*z**3)*(-13*z**3 - 11*z**2 + 18)\nExpanding the part (31 - 7*z**3) using the distributive property, and we got: (-7*z**3)*(-13*z**3 - 11*z**2 + 18) + 31*(-13*z**3 - 11*z**2 + 18)\n#Step 2:\nCurrent expression: (-7*z**3)*(-13*z**3 - 11*z**2 + 18) + 31*(-13*z**3 - 11*z**2 + 18)\nSimplifying the partial expression: 31*(-13*z**3 - 11*z**2 + 18)\nExpanding the part (-13*z**3 - 11*z**2 + 18) using the distributive property, and we got: -11*z**2*31 - 13*z**3*31 + 18*31\nReplacing 31*(-13*z**3 - 11*z**2 + 18) with -11*z**2*31 - 13*z**3*31 + 18*31 in the overall expression.\n#Step 3:\nCurrent expression: -11*z**2*31 - 13*z**3*31 + (-7*z**3)*(-13*z**3 - 11*z**2 + 18) + 558\nSimplifying the partial expression: (-7*z**3)*(-13*z**3 - 11*z**2 + 18)\nExpanding the part (-13*z**3 - 11*z**2 + 18) using the distributive property, and we got: 18*(-7*z**3) + (-11*z**2)*(-7*z**3) + (-13*z**3)*(-7*z**3)\nReplacing (-7*z**3)*(-13*z**3 - 11*z**2 + 18) with 18*(-7*z**3) + (-11*z**2)*(-7*z**3) + (-13*z**3)*(-7*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 18*(-7)*z**3 + (-11*z**2)*(-7*z**3) - 11*z**2*31 + (-13*z**3)*(-7*z**3) - 13*z**3*31 + 558\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*z**3)*31 = -403*z**3\n (-13*z**3)*(-7*z**3) = 91*z**6\n (-11*z**2)*31 = -341*z**2\n (-11*z**2)*(-7*z**3) = 77*z**5\n 18*-7*z**3 = -126*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 91*z**6 + 77*z**5 - 403*z**3 - 126*z**3 - 341*z**2 + 558\nCombining like terms, got 91*z**6 + 77*z**5 - 529*z**3 - 341*z**2 + 558\n#Step 6:\nCurrent expression: 91*z**6 + 77*z**5 - 529*z**3 - 341*z**2 + 558\nNo more calculations needed.\n91*z**6 + 77*z**5 - 529*z**3 - 341*z**2 + 558", "generated_answer": "91*z**6 + 77*z**5 - 529*z**3 - 341*z**2 + 558", "step_length": 6} {"cot_id": "19899cfe0354ee0fa3b60e3b8cc5adf3d275f40094fc12a957c6cd0239acf674", "datapoint": {"question": "Simplify this expression: 3*x**3*(24*x**3 - 29*x - 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "72*x**6 - 87*x**4 - 48*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1627, "polynomial_expr": "3*x**3*(24*x**3 - 29*x - 16)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 3*x**3*(24*x**3 - 29*x - 16)\nExpanding the part (24*x**3 - 29*x - 16) using the distributive property, and we got: (-29*x)*(3*x**3) - 48*x**3 + (3*x**3)*(24*x**3)\n#Step 2:\nCurrent expression: (-29*x)*(3*x**3) - 48*x**3 + (3*x**3)*(24*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -16*(3*x**3) = -48*x**3\n (-29*x)*(3*x**3) = -87*x**4\n (24*x**3)*(3*x**3) = 72*x**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 72*x**6 - 87*x**4 - 48*x**3\nNo more calculations needed.\n72*x**6 - 87*x**4 - 48*x**3", "generated_answer": "72*x**6 - 87*x**4 - 48*x**3", "step_length": 3} {"cot_id": "40a12e0a4cabf7baa2904f12cce3760f1c807c0392cde86bff944e4d6a745d39", "datapoint": {"question": "Calculate the following: (43*y**3 + 4*y)*(2*y**3 + 31*y**2 + 13*y + 26)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "86*y**6 + 1333*y**5 + 567*y**4 + 1242*y**3 + 52*y**2 + 104*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1628, "polynomial_expr": "(43*y**3 + 4*y)*(2*y**3 + 31*y**2 + 13*y + 26)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (43*y**3 + 4*y)*(2*y**3 + 31*y**2 + 13*y + 26)\nExpanding the part (43*y**3 + 4*y) using the distributive property, and we got: (4*y)*(2*y**3 + 31*y**2 + 13*y + 26) + (43*y**3)*(2*y**3 + 31*y**2 + 13*y + 26)\n#Step 2:\nCurrent expression: (4*y)*(2*y**3 + 31*y**2 + 13*y + 26) + (43*y**3)*(2*y**3 + 31*y**2 + 13*y + 26)\nSimplifying the partial expression: (4*y)*(2*y**3 + 31*y**2 + 13*y + 26)\nExpanding the part (2*y**3 + 31*y**2 + 13*y + 26) using the distributive property, and we got: 26*(4*y) + (4*y)*(13*y) + (4*y)*(31*y**2) + (4*y)*(2*y**3)\nReplacing (4*y)*(2*y**3 + 31*y**2 + 13*y + 26) with 26*(4*y) + (4*y)*(13*y) + (4*y)*(31*y**2) + (4*y)*(2*y**3) in the overall expression.\n#Step 3:\nCurrent expression: 26*4*y + (4*y)*(13*y) + (4*y)*(31*y**2) + (4*y)*(2*y**3) + (43*y**3)*(2*y**3 + 31*y**2 + 13*y + 26)\nSimplifying the partial expression: (43*y**3)*(2*y**3 + 31*y**2 + 13*y + 26)\nExpanding the part (2*y**3 + 31*y**2 + 13*y + 26) using the distributive property, and we got: 26*(43*y**3) + (13*y)*(43*y**3) + (31*y**2)*(43*y**3) + (2*y**3)*(43*y**3)\nReplacing (43*y**3)*(2*y**3 + 31*y**2 + 13*y + 26) with 26*(43*y**3) + (13*y)*(43*y**3) + (31*y**2)*(43*y**3) + (2*y**3)*(43*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 26*43*y**3 + 26*4*y + (4*y)*(13*y) + (4*y)*(31*y**2) + (4*y)*(2*y**3) + (13*y)*(43*y**3) + (31*y**2)*(43*y**3) + (2*y**3)*(43*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (2*y**3)*(4*y) = 8*y**4\n (2*y**3)*(43*y**3) = 86*y**6\n (13*y)*(4*y) = 52*y**2\n (13*y)*(43*y**3) = 559*y**4\n (31*y**2)*(4*y) = 124*y**3\n (31*y**2)*(43*y**3) = 1333*y**5\n 26*4*y = 104*y\n 26*43*y**3 = 1118*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 86*y**6 + 1333*y**5 + 8*y**4 + 559*y**4 + 124*y**3 + 1118*y**3 + 52*y**2 + 104*y\nCombining like terms, got 86*y**6 + 1333*y**5 + 567*y**4 + 1242*y**3 + 52*y**2 + 104*y\n#Step 6:\nCurrent expression: 86*y**6 + 1333*y**5 + 567*y**4 + 1242*y**3 + 52*y**2 + 104*y\nNo more calculations needed.\n86*y**6 + 1333*y**5 + 567*y**4 + 1242*y**3 + 52*y**2 + 104*y", "generated_answer": "86*y**6 + 1333*y**5 + 567*y**4 + 1242*y**3 + 52*y**2 + 104*y", "step_length": 6} {"cot_id": "ede370d3974db246eacb960b329c093e0a8021400ac4d95263bb7058d7bd4c97", "datapoint": {"question": "Simplify this expression: (-3*y**3 - 30*y**2 + 4*y)*(25*y**3 + 8*y - 37)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-75*y**6 - 750*y**5 + 76*y**4 - 129*y**3 + 1142*y**2 - 148*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1629, "polynomial_expr": "(-3*y**3 - 30*y**2 + 4*y)*(25*y**3 + 8*y - 37)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-3*y**3 - 30*y**2 + 4*y)*(25*y**3 + 8*y - 37)\nExpanding the part (25*y**3 + 8*y - 37) using the distributive property, and we got: (8*y)*(-3*y**3 - 30*y**2 + 4*y) + (25*y**3)*(-3*y**3 - 30*y**2 + 4*y) - 37*(-3*y**3 - 30*y**2 + 4*y)\n#Step 2:\nCurrent expression: (8*y)*(-3*y**3 - 30*y**2 + 4*y) + (25*y**3)*(-3*y**3 - 30*y**2 + 4*y) - 37*(-3*y**3 - 30*y**2 + 4*y)\nSimplifying the partial expression: -37*(-3*y**3 - 30*y**2 + 4*y)\nExpanding the part (-3*y**3 - 30*y**2 + 4*y) using the distributive property, and we got: (4*y)*(-37) - 30*y**2*(-37) - 3*y**3*(-37)\nReplacing -37*(-3*y**3 - 30*y**2 + 4*y) with (4*y)*(-37) - 30*y**2*(-37) - 3*y**3*(-37) in the overall expression.\n#Step 3:\nCurrent expression: (4*y)*(-37) + (8*y)*(-3*y**3 - 30*y**2 + 4*y) - 30*y**2*(-37) - 3*y**3*(-37) + (25*y**3)*(-3*y**3 - 30*y**2 + 4*y)\nSimplifying the partial expression: (8*y)*(-3*y**3 - 30*y**2 + 4*y)\nExpanding the part (-3*y**3 - 30*y**2 + 4*y) using the distributive property, and we got: (4*y)*(8*y) + (8*y)*(-30*y**2) + (8*y)*(-3*y**3)\nReplacing (8*y)*(-3*y**3 - 30*y**2 + 4*y) with (4*y)*(8*y) + (8*y)*(-30*y**2) + (8*y)*(-3*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (4*y)*(8*y) + (4*y)*(-37) + (8*y)*(-30*y**2) + (8*y)*(-3*y**3) - 30*y**2*(-37) - 3*y**3*(-37) + (25*y**3)*(-3*y**3 - 30*y**2 + 4*y)\nSimplifying the partial expression: (25*y**3)*(-3*y**3 - 30*y**2 + 4*y)\nExpanding the part (-3*y**3 - 30*y**2 + 4*y) using the distributive property, and we got: (4*y)*(25*y**3) + (-30*y**2)*(25*y**3) + (-3*y**3)*(25*y**3)\nReplacing (25*y**3)*(-3*y**3 - 30*y**2 + 4*y) with (4*y)*(25*y**3) + (-30*y**2)*(25*y**3) + (-3*y**3)*(25*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (4*y)*(8*y) + (4*y)*(25*y**3) + (4*y)*(-37) + (8*y)*(-30*y**2) + (8*y)*(-3*y**3) + (-30*y**2)*(25*y**3) - 30*y**2*(-37) + (-3*y**3)*(25*y**3) - 3*y**3*(-37)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*y**2)*-37 = 1110*y**2\n (-30*y**2)*(8*y) = -240*y**3\n (-30*y**2)*(25*y**3) = -750*y**5\n (-3*y**3)*-37 = 111*y**3\n (-3*y**3)*(8*y) = -24*y**4\n (-3*y**3)*(25*y**3) = -75*y**6\n (4*y)*-37 = -148*y\n (4*y)*(8*y) = 32*y**2\n (4*y)*(25*y**3) = 100*y**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -75*y**6 - 750*y**5 - 24*y**4 + 100*y**4 - 240*y**3 + 111*y**3 + 32*y**2 + 1110*y**2 - 148*y\nCombining like terms, got -75*y**6 - 750*y**5 + 76*y**4 - 129*y**3 + 1142*y**2 - 148*y\n#Step 7:\nCurrent expression: -75*y**6 - 750*y**5 + 76*y**4 - 129*y**3 + 1142*y**2 - 148*y\nNo more calculations needed.\n-75*y**6 - 750*y**5 + 76*y**4 - 129*y**3 + 1142*y**2 - 148*y", "generated_answer": "-75*y**6 - 750*y**5 + 76*y**4 - 129*y**3 + 1142*y**2 - 148*y", "step_length": 7} {"cot_id": "919d679d1eb61c8808f25c2c7010c4136b40519d293b43971a5de2e330c736cd", "datapoint": {"question": "Simplify this expression: (-33*z**3 - 6*z)*(-44*z**3 - 32*z**2 - 43*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1452*z**6 + 1056*z**5 + 1683*z**4 + 192*z**3 + 258*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1630, "polynomial_expr": "(-33*z**3 - 6*z)*(-44*z**3 - 32*z**2 - 43*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-33*z**3 - 6*z)*(-44*z**3 - 32*z**2 - 43*z)\nExpanding the part (-33*z**3 - 6*z) using the distributive property, and we got: (-6*z)*(-44*z**3 - 32*z**2 - 43*z) + (-33*z**3)*(-44*z**3 - 32*z**2 - 43*z)\n#Step 2:\nCurrent expression: (-6*z)*(-44*z**3 - 32*z**2 - 43*z) + (-33*z**3)*(-44*z**3 - 32*z**2 - 43*z)\nSimplifying the partial expression: (-33*z**3)*(-44*z**3 - 32*z**2 - 43*z)\nExpanding the part (-44*z**3 - 32*z**2 - 43*z) using the distributive property, and we got: (-43*z)*(-33*z**3) + (-32*z**2)*(-33*z**3) + (-44*z**3)*(-33*z**3)\nReplacing (-33*z**3)*(-44*z**3 - 32*z**2 - 43*z) with (-43*z)*(-33*z**3) + (-32*z**2)*(-33*z**3) + (-44*z**3)*(-33*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-43*z)*(-33*z**3) + (-6*z)*(-44*z**3 - 32*z**2 - 43*z) + (-32*z**2)*(-33*z**3) + (-44*z**3)*(-33*z**3)\nSimplifying the partial expression: (-6*z)*(-44*z**3 - 32*z**2 - 43*z)\nExpanding the part (-44*z**3 - 32*z**2 - 43*z) using the distributive property, and we got: (-43*z)*(-6*z) + (-6*z)*(-32*z**2) + (-6*z)*(-44*z**3)\nReplacing (-6*z)*(-44*z**3 - 32*z**2 - 43*z) with (-43*z)*(-6*z) + (-6*z)*(-32*z**2) + (-6*z)*(-44*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-43*z)*(-6*z) + (-43*z)*(-33*z**3) + (-6*z)*(-32*z**2) + (-6*z)*(-44*z**3) + (-32*z**2)*(-33*z**3) + (-44*z**3)*(-33*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-44*z**3)*(-33*z**3) = 1452*z**6\n (-44*z**3)*(-6*z) = 264*z**4\n (-43*z)*(-33*z**3) = 1419*z**4\n (-43*z)*(-6*z) = 258*z**2\n (-32*z**2)*(-33*z**3) = 1056*z**5\n (-32*z**2)*(-6*z) = 192*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1452*z**6 + 1056*z**5 + 264*z**4 + 1419*z**4 + 192*z**3 + 258*z**2\nCombining like terms, got 1452*z**6 + 1056*z**5 + 1683*z**4 + 192*z**3 + 258*z**2\n#Step 6:\nCurrent expression: 1452*z**6 + 1056*z**5 + 1683*z**4 + 192*z**3 + 258*z**2\nNo more calculations needed.\n1452*z**6 + 1056*z**5 + 1683*z**4 + 192*z**3 + 258*z**2", "generated_answer": "1452*z**6 + 1056*z**5 + 1683*z**4 + 192*z**3 + 258*z**2", "step_length": 6} {"cot_id": "6e66a98f79afc5a2d72e0e983b9835946ef210f12a8fa5e00739b45a96a52776", "datapoint": {"question": "Simplify this expression: 3200*y - 4560\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "3200*y - 4560", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1631, "polynomial_expr": "3200*y - 4560", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 3200*y - 4560\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 3200*y - 4560\nNo more calculations needed.\n3200*y - 4560", "generated_answer": "3200*y - 4560", "step_length": 2} {"cot_id": "f9af82fcdaf51abff935e6be4bb6dc453811d230389c8bc5a4595535143f816a", "datapoint": {"question": "Calculate the following: (45*y + 45)*(-7*y**3 - 36*y**2 - 11*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-315*y**4 - 1935*y**3 - 2115*y**2 - 495*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1632, "polynomial_expr": "(45*y + 45)*(-7*y**3 - 36*y**2 - 11*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (45*y + 45)*(-7*y**3 - 36*y**2 - 11*y)\nExpanding the part (45*y + 45) using the distributive property, and we got: (45*y)*(-7*y**3 - 36*y**2 - 11*y) + 45*(-7*y**3 - 36*y**2 - 11*y)\n#Step 2:\nCurrent expression: (45*y)*(-7*y**3 - 36*y**2 - 11*y) + 45*(-7*y**3 - 36*y**2 - 11*y)\nSimplifying the partial expression: 45*(-7*y**3 - 36*y**2 - 11*y)\nExpanding the part (-7*y**3 - 36*y**2 - 11*y) using the distributive property, and we got: -11*y*45 - 36*y**2*45 - 7*y**3*45\nReplacing 45*(-7*y**3 - 36*y**2 - 11*y) with -11*y*45 - 36*y**2*45 - 7*y**3*45 in the overall expression.\n#Step 3:\nCurrent expression: -11*y*45 + (45*y)*(-7*y**3 - 36*y**2 - 11*y) - 36*y**2*45 - 7*y**3*45\nSimplifying the partial expression: (45*y)*(-7*y**3 - 36*y**2 - 11*y)\nExpanding the part (-7*y**3 - 36*y**2 - 11*y) using the distributive property, and we got: (-11*y)*(45*y) + (45*y)*(-36*y**2) + (45*y)*(-7*y**3)\nReplacing (45*y)*(-7*y**3 - 36*y**2 - 11*y) with (-11*y)*(45*y) + (45*y)*(-36*y**2) + (45*y)*(-7*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-11*y)*(45*y) - 11*y*45 + (45*y)*(-36*y**2) + (45*y)*(-7*y**3) - 36*y**2*45 - 7*y**3*45\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*y**2)*45 = -1620*y**2\n (-36*y**2)*(45*y) = -1620*y**3\n (-11*y)*45 = -495*y\n (-11*y)*(45*y) = -495*y**2\n (-7*y**3)*45 = -315*y**3\n (-7*y**3)*(45*y) = -315*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -315*y**4 - 1620*y**3 - 315*y**3 - 1620*y**2 - 495*y**2 - 495*y\nCombining like terms, got -315*y**4 - 1935*y**3 - 2115*y**2 - 495*y\n#Step 6:\nCurrent expression: -315*y**4 - 1935*y**3 - 2115*y**2 - 495*y\nNo more calculations needed.\n-315*y**4 - 1935*y**3 - 2115*y**2 - 495*y", "generated_answer": "-315*y**4 - 1935*y**3 - 2115*y**2 - 495*y", "step_length": 6} {"cot_id": "33b2b872b33d35872d61e11829f954669d8d0f1e2f7f617612dbab166b7760c6", "datapoint": {"question": "Simplify this expression: (-20*y**2 + 85*y)*(16*y**3 + 14*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-320*y**5 + 1360*y**4 - 280*y**3 + 1190*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1633, "polynomial_expr": "(-20*y**2 + 85*y)*(16*y**3 + 14*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-20*y**2 + 85*y)*(16*y**3 + 14*y)\nExpanding the part (-20*y**2 + 85*y) using the distributive property, and we got: (85*y)*(16*y**3 + 14*y) + (-20*y**2)*(16*y**3 + 14*y)\n#Step 2:\nCurrent expression: (85*y)*(16*y**3 + 14*y) + (-20*y**2)*(16*y**3 + 14*y)\nSimplifying the partial expression: (-20*y**2)*(16*y**3 + 14*y)\nExpanding the part (16*y**3 + 14*y) using the distributive property, and we got: (14*y)*(-20*y**2) + (-20*y**2)*(16*y**3)\nReplacing (-20*y**2)*(16*y**3 + 14*y) with (14*y)*(-20*y**2) + (-20*y**2)*(16*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (14*y)*(-20*y**2) + (85*y)*(16*y**3 + 14*y) + (-20*y**2)*(16*y**3)\nSimplifying the partial expression: (85*y)*(16*y**3 + 14*y)\nExpanding the part (16*y**3 + 14*y) using the distributive property, and we got: (14*y)*(85*y) + (85*y)*(16*y**3)\nReplacing (85*y)*(16*y**3 + 14*y) with (14*y)*(85*y) + (85*y)*(16*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (14*y)*(85*y) + (14*y)*(-20*y**2) + (85*y)*(16*y**3) + (-20*y**2)*(16*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (14*y)*(-20*y**2) = -280*y**3\n (14*y)*(85*y) = 1190*y**2\n (16*y**3)*(-20*y**2) = -320*y**5\n (16*y**3)*(85*y) = 1360*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -320*y**5 + 1360*y**4 - 280*y**3 + 1190*y**2\nNo more calculations needed.\n-320*y**5 + 1360*y**4 - 280*y**3 + 1190*y**2", "generated_answer": "-320*y**5 + 1360*y**4 - 280*y**3 + 1190*y**2", "step_length": 5} {"cot_id": "5feca8005fc10850821ea0b38ae3f077bf5ed28d2e1426e4070ae0c41a277196", "datapoint": {"question": "Calculate the following: (13*x**3 + 7*x)*(43*x**3 + 17*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "559*x**6 + 221*x**5 + 301*x**4 + 119*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1634, "polynomial_expr": "(13*x**3 + 7*x)*(43*x**3 + 17*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (13*x**3 + 7*x)*(43*x**3 + 17*x**2)\nExpanding the part (13*x**3 + 7*x) using the distributive property, and we got: (7*x)*(43*x**3 + 17*x**2) + (13*x**3)*(43*x**3 + 17*x**2)\n#Step 2:\nCurrent expression: (7*x)*(43*x**3 + 17*x**2) + (13*x**3)*(43*x**3 + 17*x**2)\nSimplifying the partial expression: (7*x)*(43*x**3 + 17*x**2)\nExpanding the part (43*x**3 + 17*x**2) using the distributive property, and we got: (7*x)*(17*x**2) + (7*x)*(43*x**3)\nReplacing (7*x)*(43*x**3 + 17*x**2) with (7*x)*(17*x**2) + (7*x)*(43*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (7*x)*(17*x**2) + (7*x)*(43*x**3) + (13*x**3)*(43*x**3 + 17*x**2)\nSimplifying the partial expression: (13*x**3)*(43*x**3 + 17*x**2)\nExpanding the part (43*x**3 + 17*x**2) using the distributive property, and we got: (17*x**2)*(13*x**3) + (13*x**3)*(43*x**3)\nReplacing (13*x**3)*(43*x**3 + 17*x**2) with (17*x**2)*(13*x**3) + (13*x**3)*(43*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (7*x)*(17*x**2) + (7*x)*(43*x**3) + (17*x**2)*(13*x**3) + (13*x**3)*(43*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (17*x**2)*(7*x) = 119*x**3\n (17*x**2)*(13*x**3) = 221*x**5\n (43*x**3)*(7*x) = 301*x**4\n (43*x**3)*(13*x**3) = 559*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 559*x**6 + 221*x**5 + 301*x**4 + 119*x**3\nNo more calculations needed.\n559*x**6 + 221*x**5 + 301*x**4 + 119*x**3", "generated_answer": "559*x**6 + 221*x**5 + 301*x**4 + 119*x**3", "step_length": 5} {"cot_id": "3c7f1717abd0931edf9b7dd2a5745ac89304d38a9319041424d84c604a4dc3c0", "datapoint": {"question": "Calculate the following: (14*z - 24)*(49*z**3 + 4*z**2 - 65*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "686*z**4 - 1120*z**3 - 1006*z**2 + 1560*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1635, "polynomial_expr": "(14*z - 24)*(49*z**3 + 4*z**2 - 65*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14*z - 24)*(49*z**3 + 4*z**2 - 65*z)\nExpanding the part (14*z - 24) using the distributive property, and we got: (14*z)*(49*z**3 + 4*z**2 - 65*z) - 24*(49*z**3 + 4*z**2 - 65*z)\n#Step 2:\nCurrent expression: (14*z)*(49*z**3 + 4*z**2 - 65*z) - 24*(49*z**3 + 4*z**2 - 65*z)\nSimplifying the partial expression: -24*(49*z**3 + 4*z**2 - 65*z)\nExpanding the part (49*z**3 + 4*z**2 - 65*z) using the distributive property, and we got: -65*z*(-24) + (4*z**2)*(-24) + (49*z**3)*(-24)\nReplacing -24*(49*z**3 + 4*z**2 - 65*z) with -65*z*(-24) + (4*z**2)*(-24) + (49*z**3)*(-24) in the overall expression.\n#Step 3:\nCurrent expression: -65*z*(-24) + (14*z)*(49*z**3 + 4*z**2 - 65*z) + (4*z**2)*(-24) + (49*z**3)*(-24)\nSimplifying the partial expression: (14*z)*(49*z**3 + 4*z**2 - 65*z)\nExpanding the part (49*z**3 + 4*z**2 - 65*z) using the distributive property, and we got: (-65*z)*(14*z) + (14*z)*(4*z**2) + (14*z)*(49*z**3)\nReplacing (14*z)*(49*z**3 + 4*z**2 - 65*z) with (-65*z)*(14*z) + (14*z)*(4*z**2) + (14*z)*(49*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-65*z)*(14*z) - 65*z*(-24) + (14*z)*(4*z**2) + (14*z)*(49*z**3) + (4*z**2)*(-24) + (49*z**3)*(-24)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-65*z)*-24 = 1560*z\n (-65*z)*(14*z) = -910*z**2\n (4*z**2)*-24 = -96*z**2\n (4*z**2)*(14*z) = 56*z**3\n (49*z**3)*-24 = -1176*z**3\n (49*z**3)*(14*z) = 686*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 686*z**4 - 1176*z**3 + 56*z**3 - 910*z**2 - 96*z**2 + 1560*z\nCombining like terms, got 686*z**4 - 1120*z**3 - 1006*z**2 + 1560*z\n#Step 6:\nCurrent expression: 686*z**4 - 1120*z**3 - 1006*z**2 + 1560*z\nNo more calculations needed.\n686*z**4 - 1120*z**3 - 1006*z**2 + 1560*z", "generated_answer": "686*z**4 - 1120*z**3 - 1006*z**2 + 1560*z", "step_length": 6} {"cot_id": "b0a1988fb5bd63e84ccdc469de2af2a617b2ba75eda16b3ff2e7a8a8d3c28011", "datapoint": {"question": "Calculate the following: 1911*y**2\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1911*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1636, "polynomial_expr": "1911*y**2", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 1911*y**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 1911*y**2\nNo more calculations needed.\n1911*y**2", "generated_answer": "1911*y**2", "step_length": 2} {"cot_id": "5e2931ef5ab2c84368699eda2b8ad85e0f3adbb871035aca6d2e3d6d25944fc8", "datapoint": {"question": "Simplify this expression: (-18*x**3 - 12*x)*(-3*x**3 - 17*x**2 + 25*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "54*x**6 + 306*x**5 - 414*x**4 + 204*x**3 - 300*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1637, "polynomial_expr": "(-18*x**3 - 12*x)*(-3*x**3 - 17*x**2 + 25*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-18*x**3 - 12*x)*(-3*x**3 - 17*x**2 + 25*x)\nExpanding the part (-18*x**3 - 12*x) using the distributive property, and we got: (-12*x)*(-3*x**3 - 17*x**2 + 25*x) + (-18*x**3)*(-3*x**3 - 17*x**2 + 25*x)\n#Step 2:\nCurrent expression: (-12*x)*(-3*x**3 - 17*x**2 + 25*x) + (-18*x**3)*(-3*x**3 - 17*x**2 + 25*x)\nSimplifying the partial expression: (-18*x**3)*(-3*x**3 - 17*x**2 + 25*x)\nExpanding the part (-3*x**3 - 17*x**2 + 25*x) using the distributive property, and we got: (25*x)*(-18*x**3) + (-17*x**2)*(-18*x**3) + (-18*x**3)*(-3*x**3)\nReplacing (-18*x**3)*(-3*x**3 - 17*x**2 + 25*x) with (25*x)*(-18*x**3) + (-17*x**2)*(-18*x**3) + (-18*x**3)*(-3*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-12*x)*(-3*x**3 - 17*x**2 + 25*x) + (25*x)*(-18*x**3) + (-17*x**2)*(-18*x**3) + (-18*x**3)*(-3*x**3)\nSimplifying the partial expression: (-12*x)*(-3*x**3 - 17*x**2 + 25*x)\nExpanding the part (-3*x**3 - 17*x**2 + 25*x) using the distributive property, and we got: (-12*x)*(25*x) + (-12*x)*(-17*x**2) + (-12*x)*(-3*x**3)\nReplacing (-12*x)*(-3*x**3 - 17*x**2 + 25*x) with (-12*x)*(25*x) + (-12*x)*(-17*x**2) + (-12*x)*(-3*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-12*x)*(25*x) + (-12*x)*(-17*x**2) + (-12*x)*(-3*x**3) + (25*x)*(-18*x**3) + (-17*x**2)*(-18*x**3) + (-18*x**3)*(-3*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-17*x**2)*(-18*x**3) = 306*x**5\n (-17*x**2)*(-12*x) = 204*x**3\n (-3*x**3)*(-18*x**3) = 54*x**6\n (-3*x**3)*(-12*x) = 36*x**4\n (25*x)*(-18*x**3) = -450*x**4\n (25*x)*(-12*x) = -300*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 54*x**6 + 306*x**5 - 450*x**4 + 36*x**4 + 204*x**3 - 300*x**2\nCombining like terms, got 54*x**6 + 306*x**5 - 414*x**4 + 204*x**3 - 300*x**2\n#Step 6:\nCurrent expression: 54*x**6 + 306*x**5 - 414*x**4 + 204*x**3 - 300*x**2\nNo more calculations needed.\n54*x**6 + 306*x**5 - 414*x**4 + 204*x**3 - 300*x**2", "generated_answer": "54*x**6 + 306*x**5 - 414*x**4 + 204*x**3 - 300*x**2", "step_length": 6} {"cot_id": "a147c296a23ba8bf513232f9a0ef7efeb351fc23b5b9537354a46fea7549daa9", "datapoint": {"question": "Simplify this expression: (-18*y**3 - 36*y)*(14*y**3 + 18*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-252*y**6 - 828*y**4 - 648*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1638, "polynomial_expr": "(-18*y**3 - 36*y)*(14*y**3 + 18*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-18*y**3 - 36*y)*(14*y**3 + 18*y)\nExpanding the part (-18*y**3 - 36*y) using the distributive property, and we got: (-36*y)*(14*y**3 + 18*y) + (-18*y**3)*(14*y**3 + 18*y)\n#Step 2:\nCurrent expression: (-36*y)*(14*y**3 + 18*y) + (-18*y**3)*(14*y**3 + 18*y)\nSimplifying the partial expression: (-36*y)*(14*y**3 + 18*y)\nExpanding the part (14*y**3 + 18*y) using the distributive property, and we got: (-36*y)*(18*y) + (-36*y)*(14*y**3)\nReplacing (-36*y)*(14*y**3 + 18*y) with (-36*y)*(18*y) + (-36*y)*(14*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-36*y)*(18*y) + (-36*y)*(14*y**3) + (-18*y**3)*(14*y**3 + 18*y)\nSimplifying the partial expression: (-18*y**3)*(14*y**3 + 18*y)\nExpanding the part (14*y**3 + 18*y) using the distributive property, and we got: (18*y)*(-18*y**3) + (-18*y**3)*(14*y**3)\nReplacing (-18*y**3)*(14*y**3 + 18*y) with (18*y)*(-18*y**3) + (-18*y**3)*(14*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-36*y)*(18*y) + (-36*y)*(14*y**3) + (18*y)*(-18*y**3) + (-18*y**3)*(14*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (14*y**3)*(-36*y) = -504*y**4\n (14*y**3)*(-18*y**3) = -252*y**6\n (18*y)*(-36*y) = -648*y**2\n (18*y)*(-18*y**3) = -324*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -252*y**6 - 504*y**4 - 324*y**4 - 648*y**2\nCombining like terms, got -252*y**6 - 828*y**4 - 648*y**2\n#Step 6:\nCurrent expression: -252*y**6 - 828*y**4 - 648*y**2\nNo more calculations needed.\n-252*y**6 - 828*y**4 - 648*y**2", "generated_answer": "-252*y**6 - 828*y**4 - 648*y**2", "step_length": 6} {"cot_id": "7f4955ebfdd95996977e3b13bbff00ddf5c1ec20819402d9478802b297900de0", "datapoint": {"question": "Calculate the following: (39*y**3 + 17)*(47*y**3 - 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1833*y**6 - 449*y**3 - 544", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1639, "polynomial_expr": "(39*y**3 + 17)*(47*y**3 - 32)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (39*y**3 + 17)*(47*y**3 - 32)\nExpanding the part (47*y**3 - 32) using the distributive property, and we got: (47*y**3)*(39*y**3 + 17) - 32*(39*y**3 + 17)\n#Step 2:\nCurrent expression: (47*y**3)*(39*y**3 + 17) - 32*(39*y**3 + 17)\nSimplifying the partial expression: -32*(39*y**3 + 17)\nExpanding the part (39*y**3 + 17) using the distributive property, and we got: (39*y**3)*(-32) + 17*(-32)\nReplacing -32*(39*y**3 + 17) with (39*y**3)*(-32) + 17*(-32) in the overall expression.\n#Step 3:\nCurrent expression: (39*y**3)*(-32) + (47*y**3)*(39*y**3 + 17) - 544\nSimplifying the partial expression: (47*y**3)*(39*y**3 + 17)\nExpanding the part (39*y**3 + 17) using the distributive property, and we got: 17*(47*y**3) + (39*y**3)*(47*y**3)\nReplacing (47*y**3)*(39*y**3 + 17) with 17*(47*y**3) + (39*y**3)*(47*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 17*47*y**3 + (39*y**3)*(47*y**3) + (39*y**3)*(-32) - 544\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (39*y**3)*-32 = -1248*y**3\n (39*y**3)*(47*y**3) = 1833*y**6\n 17*47*y**3 = 799*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1833*y**6 - 1248*y**3 + 799*y**3 - 544\nCombining like terms, got 1833*y**6 - 449*y**3 - 544\n#Step 6:\nCurrent expression: 1833*y**6 - 449*y**3 - 544\nNo more calculations needed.\n1833*y**6 - 449*y**3 - 544", "generated_answer": "1833*y**6 - 449*y**3 - 544", "step_length": 6} {"cot_id": "0bb64eb8c26c27d4960f73437ac771196ea5de5eb91192aedb9e162ef4c768a4", "datapoint": {"question": "Calculate the following: (35*y**2 + 41*y)*(48*y**2 + 52*y - 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1680*y**4 + 3788*y**3 + 1537*y**2 - 697*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1640, "polynomial_expr": "(35*y**2 + 41*y)*(48*y**2 + 52*y - 17)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (35*y**2 + 41*y)*(48*y**2 + 52*y - 17)\nExpanding the part (35*y**2 + 41*y) using the distributive property, and we got: (41*y)*(48*y**2 + 52*y - 17) + (35*y**2)*(48*y**2 + 52*y - 17)\n#Step 2:\nCurrent expression: (41*y)*(48*y**2 + 52*y - 17) + (35*y**2)*(48*y**2 + 52*y - 17)\nSimplifying the partial expression: (35*y**2)*(48*y**2 + 52*y - 17)\nExpanding the part (48*y**2 + 52*y - 17) using the distributive property, and we got: -595*y**2 + (52*y)*(35*y**2) + (35*y**2)*(48*y**2)\nReplacing (35*y**2)*(48*y**2 + 52*y - 17) with -595*y**2 + (52*y)*(35*y**2) + (35*y**2)*(48*y**2) in the overall expression.\n#Step 3:\nCurrent expression: -17*35*y**2 + (41*y)*(48*y**2 + 52*y - 17) + (52*y)*(35*y**2) + (35*y**2)*(48*y**2)\nSimplifying the partial expression: (41*y)*(48*y**2 + 52*y - 17)\nExpanding the part (48*y**2 + 52*y - 17) using the distributive property, and we got: -697*y + (41*y)*(52*y) + (41*y)*(48*y**2)\nReplacing (41*y)*(48*y**2 + 52*y - 17) with -697*y + (41*y)*(52*y) + (41*y)*(48*y**2) in the overall expression.\n#Step 4:\nCurrent expression: -17*35*y**2 - 17*41*y + (41*y)*(52*y) + (41*y)*(48*y**2) + (52*y)*(35*y**2) + (35*y**2)*(48*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (48*y**2)*(35*y**2) = 1680*y**4\n (48*y**2)*(41*y) = 1968*y**3\n (52*y)*(35*y**2) = 1820*y**3\n (52*y)*(41*y) = 2132*y**2\n -17*35*y**2 = -595*y**2\n -17*41*y = -697*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1680*y**4 + 1820*y**3 + 1968*y**3 - 595*y**2 + 2132*y**2 - 697*y\nCombining like terms, got 1680*y**4 + 3788*y**3 + 1537*y**2 - 697*y\n#Step 6:\nCurrent expression: 1680*y**4 + 3788*y**3 + 1537*y**2 - 697*y\nNo more calculations needed.\n1680*y**4 + 3788*y**3 + 1537*y**2 - 697*y", "generated_answer": "1680*y**4 + 3788*y**3 + 1537*y**2 - 697*y", "step_length": 6} {"cot_id": "d8d0f3f450a86a6ff8a1b7b0fe5f7193843b241af707cf59c01008043e0c29c6", "datapoint": {"question": "Simplify this expression: (12*x + 43)*(47*x**3 + 8*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "564*x**4 + 2117*x**3 + 344*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1641, "polynomial_expr": "(12*x + 43)*(47*x**3 + 8*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (12*x + 43)*(47*x**3 + 8*x**2)\nExpanding the part (12*x + 43) using the distributive property, and we got: (12*x)*(47*x**3 + 8*x**2) + 43*(47*x**3 + 8*x**2)\n#Step 2:\nCurrent expression: (12*x)*(47*x**3 + 8*x**2) + 43*(47*x**3 + 8*x**2)\nSimplifying the partial expression: 43*(47*x**3 + 8*x**2)\nExpanding the part (47*x**3 + 8*x**2) using the distributive property, and we got: (8*x**2)*43 + (47*x**3)*43\nReplacing 43*(47*x**3 + 8*x**2) with (8*x**2)*43 + (47*x**3)*43 in the overall expression.\n#Step 3:\nCurrent expression: (12*x)*(47*x**3 + 8*x**2) + (8*x**2)*43 + (47*x**3)*43\nSimplifying the partial expression: (12*x)*(47*x**3 + 8*x**2)\nExpanding the part (47*x**3 + 8*x**2) using the distributive property, and we got: (12*x)*(8*x**2) + (12*x)*(47*x**3)\nReplacing (12*x)*(47*x**3 + 8*x**2) with (12*x)*(8*x**2) + (12*x)*(47*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (12*x)*(8*x**2) + (12*x)*(47*x**3) + (8*x**2)*43 + (47*x**3)*43\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (8*x**2)*43 = 344*x**2\n (8*x**2)*(12*x) = 96*x**3\n (47*x**3)*43 = 2021*x**3\n (47*x**3)*(12*x) = 564*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 564*x**4 + 96*x**3 + 2021*x**3 + 344*x**2\nCombining like terms, got 564*x**4 + 2117*x**3 + 344*x**2\n#Step 6:\nCurrent expression: 564*x**4 + 2117*x**3 + 344*x**2\nNo more calculations needed.\n564*x**4 + 2117*x**3 + 344*x**2", "generated_answer": "564*x**4 + 2117*x**3 + 344*x**2", "step_length": 6} {"cot_id": "327d07be7b754da93fed9802d013f5f84a3dffb7f4fab74a89c2496c5b9f6b77", "datapoint": {"question": "Simplify this expression: (25*y - 41)*(39*y**3 + y**2 + 24*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "975*y**4 - 1574*y**3 + 559*y**2 - 984*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1642, "polynomial_expr": "(25*y - 41)*(39*y**3 + y**2 + 24*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (25*y - 41)*(39*y**3 + y**2 + 24*y)\nExpanding the part (25*y - 41) using the distributive property, and we got: (25*y)*(39*y**3 + y**2 + 24*y) - 41*(39*y**3 + y**2 + 24*y)\n#Step 2:\nCurrent expression: (25*y)*(39*y**3 + y**2 + 24*y) - 41*(39*y**3 + y**2 + 24*y)\nSimplifying the partial expression: -41*(39*y**3 + y**2 + 24*y)\nExpanding the part (39*y**3 + y**2 + 24*y) using the distributive property, and we got: y**2*(-41) + (24*y)*(-41) + (39*y**3)*(-41)\nReplacing -41*(39*y**3 + y**2 + 24*y) with y**2*(-41) + (24*y)*(-41) + (39*y**3)*(-41) in the overall expression.\n#Step 3:\nCurrent expression: y**2*(-41) + (24*y)*(-41) + (25*y)*(39*y**3 + y**2 + 24*y) + (39*y**3)*(-41)\nSimplifying the partial expression: (25*y)*(39*y**3 + y**2 + 24*y)\nExpanding the part (39*y**3 + y**2 + 24*y) using the distributive property, and we got: (25*y)*y**2 + (24*y)*(25*y) + (25*y)*(39*y**3)\nReplacing (25*y)*(39*y**3 + y**2 + 24*y) with (25*y)*y**2 + (24*y)*(25*y) + (25*y)*(39*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (25*y)*y**2 + y**2*(-41) + (24*y)*(25*y) + (24*y)*(-41) + (25*y)*(39*y**3) + (39*y**3)*(-41)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n y**2*-41 = -41*y**2\n y**2*(25*y) = 25*y**3\n (24*y)*-41 = -984*y\n (24*y)*(25*y) = 600*y**2\n (39*y**3)*-41 = -1599*y**3\n (39*y**3)*(25*y) = 975*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 975*y**4 - 1599*y**3 + 25*y**3 - 41*y**2 + 600*y**2 - 984*y\nCombining like terms, got 975*y**4 - 1574*y**3 + 559*y**2 - 984*y\n#Step 6:\nCurrent expression: 975*y**4 - 1574*y**3 + 559*y**2 - 984*y\nNo more calculations needed.\n975*y**4 - 1574*y**3 + 559*y**2 - 984*y", "generated_answer": "975*y**4 - 1574*y**3 + 559*y**2 - 984*y", "step_length": 6} {"cot_id": "0d61641cb5c704bede4a598904c3080641c668c5431810d32df1e2eadaeb3aba", "datapoint": {"question": "Calculate the following: (-45*z**2 + 47*z - 13)*(-49*z**3 - 24*z**2 - 16*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2205*z**5 - 1223*z**4 + 229*z**3 - 440*z**2 + 208*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1643, "polynomial_expr": "(-45*z**2 + 47*z - 13)*(-49*z**3 - 24*z**2 - 16*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-45*z**2 + 47*z - 13)*(-49*z**3 - 24*z**2 - 16*z)\nExpanding the part (-45*z**2 + 47*z - 13) using the distributive property, and we got: (47*z)*(-49*z**3 - 24*z**2 - 16*z) + (-45*z**2)*(-49*z**3 - 24*z**2 - 16*z) - 13*(-49*z**3 - 24*z**2 - 16*z)\n#Step 2:\nCurrent expression: (47*z)*(-49*z**3 - 24*z**2 - 16*z) + (-45*z**2)*(-49*z**3 - 24*z**2 - 16*z) - 13*(-49*z**3 - 24*z**2 - 16*z)\nSimplifying the partial expression: -13*(-49*z**3 - 24*z**2 - 16*z)\nExpanding the part (-49*z**3 - 24*z**2 - 16*z) using the distributive property, and we got: -16*z*(-13) - 24*z**2*(-13) - 49*z**3*(-13)\nReplacing -13*(-49*z**3 - 24*z**2 - 16*z) with -16*z*(-13) - 24*z**2*(-13) - 49*z**3*(-13) in the overall expression.\n#Step 3:\nCurrent expression: -16*z*(-13) + (47*z)*(-49*z**3 - 24*z**2 - 16*z) + (-45*z**2)*(-49*z**3 - 24*z**2 - 16*z) - 24*z**2*(-13) - 49*z**3*(-13)\nSimplifying the partial expression: (-45*z**2)*(-49*z**3 - 24*z**2 - 16*z)\nExpanding the part (-49*z**3 - 24*z**2 - 16*z) using the distributive property, and we got: (-16*z)*(-45*z**2) + (-45*z**2)*(-24*z**2) + (-45*z**2)*(-49*z**3)\nReplacing (-45*z**2)*(-49*z**3 - 24*z**2 - 16*z) with (-16*z)*(-45*z**2) + (-45*z**2)*(-24*z**2) + (-45*z**2)*(-49*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-16*z)*(-45*z**2) - 16*z*(-13) + (47*z)*(-49*z**3 - 24*z**2 - 16*z) + (-45*z**2)*(-24*z**2) + (-45*z**2)*(-49*z**3) - 24*z**2*(-13) - 49*z**3*(-13)\nSimplifying the partial expression: (47*z)*(-49*z**3 - 24*z**2 - 16*z)\nExpanding the part (-49*z**3 - 24*z**2 - 16*z) using the distributive property, and we got: (-16*z)*(47*z) + (47*z)*(-24*z**2) + (47*z)*(-49*z**3)\nReplacing (47*z)*(-49*z**3 - 24*z**2 - 16*z) with (-16*z)*(47*z) + (47*z)*(-24*z**2) + (47*z)*(-49*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-16*z)*(47*z) + (-16*z)*(-45*z**2) - 16*z*(-13) + (47*z)*(-24*z**2) + (47*z)*(-49*z**3) + (-45*z**2)*(-24*z**2) + (-45*z**2)*(-49*z**3) - 24*z**2*(-13) - 49*z**3*(-13)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*z**3)*-13 = 637*z**3\n (-49*z**3)*(-45*z**2) = 2205*z**5\n (-49*z**3)*(47*z) = -2303*z**4\n (-24*z**2)*-13 = 312*z**2\n (-24*z**2)*(-45*z**2) = 1080*z**4\n (-24*z**2)*(47*z) = -1128*z**3\n (-16*z)*-13 = 208*z\n (-16*z)*(-45*z**2) = 720*z**3\n (-16*z)*(47*z) = -752*z**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 2205*z**5 - 2303*z**4 + 1080*z**4 - 1128*z**3 + 637*z**3 + 720*z**3 - 752*z**2 + 312*z**2 + 208*z\nCombining like terms, got 2205*z**5 - 1223*z**4 + 229*z**3 - 440*z**2 + 208*z\n#Step 7:\nCurrent expression: 2205*z**5 - 1223*z**4 + 229*z**3 - 440*z**2 + 208*z\nNo more calculations needed.\n2205*z**5 - 1223*z**4 + 229*z**3 - 440*z**2 + 208*z", "generated_answer": "2205*z**5 - 1223*z**4 + 229*z**3 - 440*z**2 + 208*z", "step_length": 7} {"cot_id": "9fba8e0b9d2a8b0c71f6c0902b980986021bef971f328e1951bd0cc9623b45ce", "datapoint": {"question": "Calculate the following: (32*x**2 - 37)*(-41*x**3 + 17*x**2 - 15)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1312*x**5 + 544*x**4 + 1517*x**3 - 1109*x**2 + 555", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1644, "polynomial_expr": "(32*x**2 - 37)*(-41*x**3 + 17*x**2 - 15)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (32*x**2 - 37)*(-41*x**3 + 17*x**2 - 15)\nExpanding the part (32*x**2 - 37) using the distributive property, and we got: (32*x**2)*(-41*x**3 + 17*x**2 - 15) - 37*(-41*x**3 + 17*x**2 - 15)\n#Step 2:\nCurrent expression: (32*x**2)*(-41*x**3 + 17*x**2 - 15) - 37*(-41*x**3 + 17*x**2 - 15)\nSimplifying the partial expression: -37*(-41*x**3 + 17*x**2 - 15)\nExpanding the part (-41*x**3 + 17*x**2 - 15) using the distributive property, and we got: (17*x**2)*(-37) - 41*x**3*(-37) - 15*(-37)\nReplacing -37*(-41*x**3 + 17*x**2 - 15) with (17*x**2)*(-37) - 41*x**3*(-37) - 15*(-37) in the overall expression.\n#Step 3:\nCurrent expression: (17*x**2)*(-37) + (32*x**2)*(-41*x**3 + 17*x**2 - 15) - 41*x**3*(-37) + 555\nSimplifying the partial expression: (32*x**2)*(-41*x**3 + 17*x**2 - 15)\nExpanding the part (-41*x**3 + 17*x**2 - 15) using the distributive property, and we got: -480*x**2 + (17*x**2)*(32*x**2) + (32*x**2)*(-41*x**3)\nReplacing (32*x**2)*(-41*x**3 + 17*x**2 - 15) with -480*x**2 + (17*x**2)*(32*x**2) + (32*x**2)*(-41*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -15*32*x**2 + (17*x**2)*(32*x**2) + (17*x**2)*(-37) + (32*x**2)*(-41*x**3) - 41*x**3*(-37) + 555\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*x**3)*-37 = 1517*x**3\n (-41*x**3)*(32*x**2) = -1312*x**5\n (17*x**2)*-37 = -629*x**2\n (17*x**2)*(32*x**2) = 544*x**4\n -15*32*x**2 = -480*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1312*x**5 + 544*x**4 + 1517*x**3 - 629*x**2 - 480*x**2 + 555\nCombining like terms, got -1312*x**5 + 544*x**4 + 1517*x**3 - 1109*x**2 + 555\n#Step 6:\nCurrent expression: -1312*x**5 + 544*x**4 + 1517*x**3 - 1109*x**2 + 555\nNo more calculations needed.\n-1312*x**5 + 544*x**4 + 1517*x**3 - 1109*x**2 + 555", "generated_answer": "-1312*x**5 + 544*x**4 + 1517*x**3 - 1109*x**2 + 555", "step_length": 6} {"cot_id": "46101b32b44c9336c0588bb936cf0095ec7f14c8526e82bdfa34cc89b14f38c4", "datapoint": {"question": "Calculate the following: -33*z*(-16*z**2 - 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "528*z**3 + 1188*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1645, "polynomial_expr": "-33*z*(-16*z**2 - 36)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -33*z*(-16*z**2 - 36)\nExpanding the part (-16*z**2 - 36) using the distributive property, and we got: (-33*z)*(-16*z**2) - (-1)*1188*z\n#Step 2:\nCurrent expression: (-33*z)*(-16*z**2) - (-1)*1188*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -36*(-33*z) = 1188*z\n (-16*z**2)*(-33*z) = 528*z**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 528*z**3 + 1188*z\nNo more calculations needed.\n528*z**3 + 1188*z", "generated_answer": "528*z**3 + 1188*z", "step_length": 3} {"cot_id": "2a62a9251f29984e7a68b2ebac4e5c9eb6526d0b3bf9558232aa30e970763526", "datapoint": {"question": "Simplify this expression: (-34*z**2 + 11*z)*(30*z**3 + 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1020*z**5 + 330*z**4 - 680*z**2 + 220*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1646, "polynomial_expr": "(-34*z**2 + 11*z)*(30*z**3 + 20)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-34*z**2 + 11*z)*(30*z**3 + 20)\nExpanding the part (30*z**3 + 20) using the distributive property, and we got: (30*z**3)*(-34*z**2 + 11*z) + 20*(-34*z**2 + 11*z)\n#Step 2:\nCurrent expression: (30*z**3)*(-34*z**2 + 11*z) + 20*(-34*z**2 + 11*z)\nSimplifying the partial expression: 20*(-34*z**2 + 11*z)\nExpanding the part (-34*z**2 + 11*z) using the distributive property, and we got: (11*z)*20 - 34*z**2*20\nReplacing 20*(-34*z**2 + 11*z) with (11*z)*20 - 34*z**2*20 in the overall expression.\n#Step 3:\nCurrent expression: (11*z)*20 - 34*z**2*20 + (30*z**3)*(-34*z**2 + 11*z)\nSimplifying the partial expression: (30*z**3)*(-34*z**2 + 11*z)\nExpanding the part (-34*z**2 + 11*z) using the distributive property, and we got: (11*z)*(30*z**3) + (-34*z**2)*(30*z**3)\nReplacing (30*z**3)*(-34*z**2 + 11*z) with (11*z)*(30*z**3) + (-34*z**2)*(30*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (11*z)*(30*z**3) + (11*z)*20 + (-34*z**2)*(30*z**3) - 34*z**2*20\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*z**2)*20 = -680*z**2\n (-34*z**2)*(30*z**3) = -1020*z**5\n (11*z)*20 = 220*z\n (11*z)*(30*z**3) = 330*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1020*z**5 + 330*z**4 - 680*z**2 + 220*z\nNo more calculations needed.\n-1020*z**5 + 330*z**4 - 680*z**2 + 220*z", "generated_answer": "-1020*z**5 + 330*z**4 - 680*z**2 + 220*z", "step_length": 5} {"cot_id": "d39bacaaec82873c563d9327778db7a69562be2d8f2037cb614a5e663bf27a6e", "datapoint": {"question": "Simplify this expression: (29*z**3 - 23*z**2 - 34*z)*(37*z**3 + 48*z - 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1073*z**6 - 851*z**5 + 134*z**4 - 1974*z**3 - 942*z**2 + 1020*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1647, "polynomial_expr": "(29*z**3 - 23*z**2 - 34*z)*(37*z**3 + 48*z - 30)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29*z**3 - 23*z**2 - 34*z)*(37*z**3 + 48*z - 30)\nExpanding the part (37*z**3 + 48*z - 30) using the distributive property, and we got: (48*z)*(29*z**3 - 23*z**2 - 34*z) + (37*z**3)*(29*z**3 - 23*z**2 - 34*z) - 30*(29*z**3 - 23*z**2 - 34*z)\n#Step 2:\nCurrent expression: (48*z)*(29*z**3 - 23*z**2 - 34*z) + (37*z**3)*(29*z**3 - 23*z**2 - 34*z) - 30*(29*z**3 - 23*z**2 - 34*z)\nSimplifying the partial expression: -30*(29*z**3 - 23*z**2 - 34*z)\nExpanding the part (29*z**3 - 23*z**2 - 34*z) using the distributive property, and we got: -34*z*(-30) - 23*z**2*(-30) + (29*z**3)*(-30)\nReplacing -30*(29*z**3 - 23*z**2 - 34*z) with -34*z*(-30) - 23*z**2*(-30) + (29*z**3)*(-30) in the overall expression.\n#Step 3:\nCurrent expression: -34*z*(-30) + (48*z)*(29*z**3 - 23*z**2 - 34*z) - 23*z**2*(-30) + (29*z**3)*(-30) + (37*z**3)*(29*z**3 - 23*z**2 - 34*z)\nSimplifying the partial expression: (37*z**3)*(29*z**3 - 23*z**2 - 34*z)\nExpanding the part (29*z**3 - 23*z**2 - 34*z) using the distributive property, and we got: (-34*z)*(37*z**3) + (-23*z**2)*(37*z**3) + (29*z**3)*(37*z**3)\nReplacing (37*z**3)*(29*z**3 - 23*z**2 - 34*z) with (-34*z)*(37*z**3) + (-23*z**2)*(37*z**3) + (29*z**3)*(37*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-34*z)*(37*z**3) - 34*z*(-30) + (48*z)*(29*z**3 - 23*z**2 - 34*z) + (-23*z**2)*(37*z**3) - 23*z**2*(-30) + (29*z**3)*(37*z**3) + (29*z**3)*(-30)\nSimplifying the partial expression: (48*z)*(29*z**3 - 23*z**2 - 34*z)\nExpanding the part (29*z**3 - 23*z**2 - 34*z) using the distributive property, and we got: (-34*z)*(48*z) + (48*z)*(-23*z**2) + (48*z)*(29*z**3)\nReplacing (48*z)*(29*z**3 - 23*z**2 - 34*z) with (-34*z)*(48*z) + (48*z)*(-23*z**2) + (48*z)*(29*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-34*z)*(48*z) + (-34*z)*(37*z**3) - 34*z*(-30) + (48*z)*(-23*z**2) + (48*z)*(29*z**3) + (-23*z**2)*(37*z**3) - 23*z**2*(-30) + (29*z**3)*(37*z**3) + (29*z**3)*(-30)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*z)*-30 = 1020*z\n (-34*z)*(37*z**3) = -1258*z**4\n (-34*z)*(48*z) = -1632*z**2\n (-23*z**2)*-30 = 690*z**2\n (-23*z**2)*(37*z**3) = -851*z**5\n (-23*z**2)*(48*z) = -1104*z**3\n (29*z**3)*-30 = -870*z**3\n (29*z**3)*(37*z**3) = 1073*z**6\n (29*z**3)*(48*z) = 1392*z**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1073*z**6 - 851*z**5 - 1258*z**4 + 1392*z**4 - 1104*z**3 - 870*z**3 - 1632*z**2 + 690*z**2 + 1020*z\nCombining like terms, got 1073*z**6 - 851*z**5 + 134*z**4 - 1974*z**3 - 942*z**2 + 1020*z\n#Step 7:\nCurrent expression: 1073*z**6 - 851*z**5 + 134*z**4 - 1974*z**3 - 942*z**2 + 1020*z\nNo more calculations needed.\n1073*z**6 - 851*z**5 + 134*z**4 - 1974*z**3 - 942*z**2 + 1020*z", "generated_answer": "1073*z**6 - 851*z**5 + 134*z**4 - 1974*z**3 - 942*z**2 + 1020*z", "step_length": 7} {"cot_id": "b0274174e2ff99d993ffb9981dccb4d3cf8318b69ea675092577af870fdbd61c", "datapoint": {"question": "Calculate the following: (17*x**3 + 26*x**2)*(-59*x**3 + 37*x + 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1003*x**6 - 1534*x**5 + 629*x**4 + 1081*x**3 + 182*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1648, "polynomial_expr": "(17*x**3 + 26*x**2)*(-59*x**3 + 37*x + 7)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (17*x**3 + 26*x**2)*(-59*x**3 + 37*x + 7)\nExpanding the part (17*x**3 + 26*x**2) using the distributive property, and we got: (26*x**2)*(-59*x**3 + 37*x + 7) + (17*x**3)*(-59*x**3 + 37*x + 7)\n#Step 2:\nCurrent expression: (26*x**2)*(-59*x**3 + 37*x + 7) + (17*x**3)*(-59*x**3 + 37*x + 7)\nSimplifying the partial expression: (17*x**3)*(-59*x**3 + 37*x + 7)\nExpanding the part (-59*x**3 + 37*x + 7) using the distributive property, and we got: 7*(17*x**3) + (37*x)*(17*x**3) + (-59*x**3)*(17*x**3)\nReplacing (17*x**3)*(-59*x**3 + 37*x + 7) with 7*(17*x**3) + (37*x)*(17*x**3) + (-59*x**3)*(17*x**3) in the overall expression.\n#Step 3:\nCurrent expression: 7*17*x**3 + (37*x)*(17*x**3) + (26*x**2)*(-59*x**3 + 37*x + 7) + (-59*x**3)*(17*x**3)\nSimplifying the partial expression: (26*x**2)*(-59*x**3 + 37*x + 7)\nExpanding the part (-59*x**3 + 37*x + 7) using the distributive property, and we got: 7*(26*x**2) + (37*x)*(26*x**2) + (26*x**2)*(-59*x**3)\nReplacing (26*x**2)*(-59*x**3 + 37*x + 7) with 7*(26*x**2) + (37*x)*(26*x**2) + (26*x**2)*(-59*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 7*17*x**3 + 7*26*x**2 + (37*x)*(26*x**2) + (37*x)*(17*x**3) + (26*x**2)*(-59*x**3) + (-59*x**3)*(17*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-59*x**3)*(17*x**3) = -1003*x**6\n (-59*x**3)*(26*x**2) = -1534*x**5\n (37*x)*(17*x**3) = 629*x**4\n (37*x)*(26*x**2) = 962*x**3\n 7*17*x**3 = 119*x**3\n 7*26*x**2 = 182*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1003*x**6 - 1534*x**5 + 629*x**4 + 119*x**3 + 962*x**3 + 182*x**2\nCombining like terms, got -1003*x**6 - 1534*x**5 + 629*x**4 + 1081*x**3 + 182*x**2\n#Step 6:\nCurrent expression: -1003*x**6 - 1534*x**5 + 629*x**4 + 1081*x**3 + 182*x**2\nNo more calculations needed.\n-1003*x**6 - 1534*x**5 + 629*x**4 + 1081*x**3 + 182*x**2", "generated_answer": "-1003*x**6 - 1534*x**5 + 629*x**4 + 1081*x**3 + 182*x**2", "step_length": 6} {"cot_id": "ea714c7b72ca712aab04f85146a8d6997b05a561d8c54b0c65b4f90581ab2674", "datapoint": {"question": "Simplify this expression: (30 - 36*y**2)*(13*y**2 - 20*y - 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-468*y**4 + 720*y**3 + 1506*y**2 - 600*y - 930", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1649, "polynomial_expr": "(30 - 36*y**2)*(13*y**2 - 20*y - 31)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (30 - 36*y**2)*(13*y**2 - 20*y - 31)\nExpanding the part (30 - 36*y**2) using the distributive property, and we got: (-36*y**2)*(13*y**2 - 20*y - 31) + 30*(13*y**2 - 20*y - 31)\n#Step 2:\nCurrent expression: (-36*y**2)*(13*y**2 - 20*y - 31) + 30*(13*y**2 - 20*y - 31)\nSimplifying the partial expression: 30*(13*y**2 - 20*y - 31)\nExpanding the part (13*y**2 - 20*y - 31) using the distributive property, and we got: -20*y*30 + (13*y**2)*30 - 31*30\nReplacing 30*(13*y**2 - 20*y - 31) with -20*y*30 + (13*y**2)*30 - 31*30 in the overall expression.\n#Step 3:\nCurrent expression: -20*y*30 + (-36*y**2)*(13*y**2 - 20*y - 31) + (13*y**2)*30 - 930\nSimplifying the partial expression: (-36*y**2)*(13*y**2 - 20*y - 31)\nExpanding the part (13*y**2 - 20*y - 31) using the distributive property, and we got: (-20*y)*(-36*y**2) - (-1)*1116*y**2 + (-36*y**2)*(13*y**2)\nReplacing (-36*y**2)*(13*y**2 - 20*y - 31) with (-20*y)*(-36*y**2) - (-1)*1116*y**2 + (-36*y**2)*(13*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-20*y)*(-36*y**2) - 20*y*30 - 31*(-36)*y**2 + (-36*y**2)*(13*y**2) + (13*y**2)*30 - 930\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*y)*30 = -600*y\n (-20*y)*(-36*y**2) = 720*y**3\n (13*y**2)*30 = 390*y**2\n (13*y**2)*(-36*y**2) = -468*y**4\n -31*-36*y**2 = 1116*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -468*y**4 + 720*y**3 + 390*y**2 + 1116*y**2 - 600*y - 930\nCombining like terms, got -468*y**4 + 720*y**3 + 1506*y**2 - 600*y - 930\n#Step 6:\nCurrent expression: -468*y**4 + 720*y**3 + 1506*y**2 - 600*y - 930\nNo more calculations needed.\n-468*y**4 + 720*y**3 + 1506*y**2 - 600*y - 930", "generated_answer": "-468*y**4 + 720*y**3 + 1506*y**2 - 600*y - 930", "step_length": 6} {"cot_id": "3f2888c1c471ec5837f656393c1ccf6198a84a932cb4385e23493e51f84b30b8", "datapoint": {"question": "Simplify this expression: 11*x**2*(52*x - 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "572*x**3 - 451*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1650, "polynomial_expr": "11*x**2*(52*x - 41)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 11*x**2*(52*x - 41)\nExpanding the part (52*x - 41) using the distributive property, and we got: -451*x**2 + (52*x)*(11*x**2)\n#Step 2:\nCurrent expression: -451*x**2 + (52*x)*(11*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -41*(11*x**2) = -451*x**2\n (52*x)*(11*x**2) = 572*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 572*x**3 - 451*x**2\nNo more calculations needed.\n572*x**3 - 451*x**2", "generated_answer": "572*x**3 - 451*x**2", "step_length": 3} {"cot_id": "89515ddaa15cae53a085b7d881239b783356887de19088a0606d5e75bfaeb1ae", "datapoint": {"question": "Calculate the following: (33 - 49*z**2)*(-48*z**3 + 49*z**2 - 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2352*z**5 - 2401*z**4 - 1584*z**3 + 2450*z**2 - 561", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1651, "polynomial_expr": "(33 - 49*z**2)*(-48*z**3 + 49*z**2 - 17)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (33 - 49*z**2)*(-48*z**3 + 49*z**2 - 17)\nExpanding the part (33 - 49*z**2) using the distributive property, and we got: (-49*z**2)*(-48*z**3 + 49*z**2 - 17) + 33*(-48*z**3 + 49*z**2 - 17)\n#Step 2:\nCurrent expression: (-49*z**2)*(-48*z**3 + 49*z**2 - 17) + 33*(-48*z**3 + 49*z**2 - 17)\nSimplifying the partial expression: 33*(-48*z**3 + 49*z**2 - 17)\nExpanding the part (-48*z**3 + 49*z**2 - 17) using the distributive property, and we got: (49*z**2)*33 - 48*z**3*33 - 17*33\nReplacing 33*(-48*z**3 + 49*z**2 - 17) with (49*z**2)*33 - 48*z**3*33 - 17*33 in the overall expression.\n#Step 3:\nCurrent expression: (-49*z**2)*(-48*z**3 + 49*z**2 - 17) + (49*z**2)*33 - 48*z**3*33 - 561\nSimplifying the partial expression: (-49*z**2)*(-48*z**3 + 49*z**2 - 17)\nExpanding the part (-48*z**3 + 49*z**2 - 17) using the distributive property, and we got: -(-1)*833*z**2 + (-49*z**2)*(49*z**2) + (-49*z**2)*(-48*z**3)\nReplacing (-49*z**2)*(-48*z**3 + 49*z**2 - 17) with -(-1)*833*z**2 + (-49*z**2)*(49*z**2) + (-49*z**2)*(-48*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -17*(-49)*z**2 + (-49*z**2)*(49*z**2) + (-49*z**2)*(-48*z**3) + (49*z**2)*33 - 48*z**3*33 - 561\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*z**3)*33 = -1584*z**3\n (-48*z**3)*(-49*z**2) = 2352*z**5\n (49*z**2)*33 = 1617*z**2\n (49*z**2)*(-49*z**2) = -2401*z**4\n -17*-49*z**2 = 833*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2352*z**5 - 2401*z**4 - 1584*z**3 + 833*z**2 + 1617*z**2 - 561\nCombining like terms, got 2352*z**5 - 2401*z**4 - 1584*z**3 + 2450*z**2 - 561\n#Step 6:\nCurrent expression: 2352*z**5 - 2401*z**4 - 1584*z**3 + 2450*z**2 - 561\nNo more calculations needed.\n2352*z**5 - 2401*z**4 - 1584*z**3 + 2450*z**2 - 561", "generated_answer": "2352*z**5 - 2401*z**4 - 1584*z**3 + 2450*z**2 - 561", "step_length": 6} {"cot_id": "791c220937100afdac9aecaf5d2c681213a0262b7ae77003f7ba6b8d8e755171", "datapoint": {"question": "Simplify this expression: -1352*z**3 + 728*z\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1352*z**3 + 728*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1652, "polynomial_expr": "-1352*z**3 + 728*z", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -1352*z**3 + 728*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -1352*z**3 + 728*z\nNo more calculations needed.\n-1352*z**3 + 728*z", "generated_answer": "-1352*z**3 + 728*z", "step_length": 2} {"cot_id": "3d6c3a4ce698a2caa3197313003a5a1dff3c1a172d045ddd60907e0fee286a7a", "datapoint": {"question": "Calculate the following: (38*x**3 - 21*x**2)*(-11*x**2 - 5*x - 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-418*x**5 + 41*x**4 - 1795*x**3 + 1050*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1653, "polynomial_expr": "(38*x**3 - 21*x**2)*(-11*x**2 - 5*x - 50)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (38*x**3 - 21*x**2)*(-11*x**2 - 5*x - 50)\nExpanding the part (38*x**3 - 21*x**2) using the distributive property, and we got: (-21*x**2)*(-11*x**2 - 5*x - 50) + (38*x**3)*(-11*x**2 - 5*x - 50)\n#Step 2:\nCurrent expression: (-21*x**2)*(-11*x**2 - 5*x - 50) + (38*x**3)*(-11*x**2 - 5*x - 50)\nSimplifying the partial expression: (-21*x**2)*(-11*x**2 - 5*x - 50)\nExpanding the part (-11*x**2 - 5*x - 50) using the distributive property, and we got: (-5*x)*(-21*x**2) - (-1)*1050*x**2 + (-21*x**2)*(-11*x**2)\nReplacing (-21*x**2)*(-11*x**2 - 5*x - 50) with (-5*x)*(-21*x**2) - (-1)*1050*x**2 + (-21*x**2)*(-11*x**2) in the overall expression.\n#Step 3:\nCurrent expression: (-5*x)*(-21*x**2) - 50*(-21)*x**2 + (-21*x**2)*(-11*x**2) + (38*x**3)*(-11*x**2 - 5*x - 50)\nSimplifying the partial expression: (38*x**3)*(-11*x**2 - 5*x - 50)\nExpanding the part (-11*x**2 - 5*x - 50) using the distributive property, and we got: (-5*x)*(38*x**3) - 1900*x**3 + (-11*x**2)*(38*x**3)\nReplacing (38*x**3)*(-11*x**2 - 5*x - 50) with (-5*x)*(38*x**3) - 1900*x**3 + (-11*x**2)*(38*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-5*x)*(-21*x**2) + (-5*x)*(38*x**3) - 50*38*x**3 - 50*(-21)*x**2 + (-21*x**2)*(-11*x**2) + (-11*x**2)*(38*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*x**2)*(-21*x**2) = 231*x**4\n (-11*x**2)*(38*x**3) = -418*x**5\n (-5*x)*(-21*x**2) = 105*x**3\n (-5*x)*(38*x**3) = -190*x**4\n -50*-21*x**2 = 1050*x**2\n -50*38*x**3 = -1900*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -418*x**5 - 190*x**4 + 231*x**4 - 1900*x**3 + 105*x**3 + 1050*x**2\nCombining like terms, got -418*x**5 + 41*x**4 - 1795*x**3 + 1050*x**2\n#Step 6:\nCurrent expression: -418*x**5 + 41*x**4 - 1795*x**3 + 1050*x**2\nNo more calculations needed.\n-418*x**5 + 41*x**4 - 1795*x**3 + 1050*x**2", "generated_answer": "-418*x**5 + 41*x**4 - 1795*x**3 + 1050*x**2", "step_length": 6} {"cot_id": "3579d84134e275b4a95c0481d4326d1cf1dda79c9d345872fed6d454d15c88b7", "datapoint": {"question": "Simplify this expression: (-15*x**3 + 7*x**2 + 13*x)*(44*x**3 - 50*x - 23)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-660*x**6 + 308*x**5 + 1322*x**4 - 5*x**3 - 811*x**2 - 299*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1654, "polynomial_expr": "(-15*x**3 + 7*x**2 + 13*x)*(44*x**3 - 50*x - 23)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-15*x**3 + 7*x**2 + 13*x)*(44*x**3 - 50*x - 23)\nExpanding the part (44*x**3 - 50*x - 23) using the distributive property, and we got: (-50*x)*(-15*x**3 + 7*x**2 + 13*x) + (44*x**3)*(-15*x**3 + 7*x**2 + 13*x) - 23*(-15*x**3 + 7*x**2 + 13*x)\n#Step 2:\nCurrent expression: (-50*x)*(-15*x**3 + 7*x**2 + 13*x) + (44*x**3)*(-15*x**3 + 7*x**2 + 13*x) - 23*(-15*x**3 + 7*x**2 + 13*x)\nSimplifying the partial expression: -23*(-15*x**3 + 7*x**2 + 13*x)\nExpanding the part (-15*x**3 + 7*x**2 + 13*x) using the distributive property, and we got: (13*x)*(-23) + (7*x**2)*(-23) - 15*x**3*(-23)\nReplacing -23*(-15*x**3 + 7*x**2 + 13*x) with (13*x)*(-23) + (7*x**2)*(-23) - 15*x**3*(-23) in the overall expression.\n#Step 3:\nCurrent expression: (-50*x)*(-15*x**3 + 7*x**2 + 13*x) + (13*x)*(-23) + (7*x**2)*(-23) - 15*x**3*(-23) + (44*x**3)*(-15*x**3 + 7*x**2 + 13*x)\nSimplifying the partial expression: (-50*x)*(-15*x**3 + 7*x**2 + 13*x)\nExpanding the part (-15*x**3 + 7*x**2 + 13*x) using the distributive property, and we got: (-50*x)*(13*x) + (-50*x)*(7*x**2) + (-50*x)*(-15*x**3)\nReplacing (-50*x)*(-15*x**3 + 7*x**2 + 13*x) with (-50*x)*(13*x) + (-50*x)*(7*x**2) + (-50*x)*(-15*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-50*x)*(13*x) + (-50*x)*(7*x**2) + (-50*x)*(-15*x**3) + (13*x)*(-23) + (7*x**2)*(-23) - 15*x**3*(-23) + (44*x**3)*(-15*x**3 + 7*x**2 + 13*x)\nSimplifying the partial expression: (44*x**3)*(-15*x**3 + 7*x**2 + 13*x)\nExpanding the part (-15*x**3 + 7*x**2 + 13*x) using the distributive property, and we got: (13*x)*(44*x**3) + (7*x**2)*(44*x**3) + (-15*x**3)*(44*x**3)\nReplacing (44*x**3)*(-15*x**3 + 7*x**2 + 13*x) with (13*x)*(44*x**3) + (7*x**2)*(44*x**3) + (-15*x**3)*(44*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-50*x)*(13*x) + (-50*x)*(7*x**2) + (-50*x)*(-15*x**3) + (13*x)*(44*x**3) + (13*x)*(-23) + (7*x**2)*(44*x**3) + (7*x**2)*(-23) + (-15*x**3)*(44*x**3) - 15*x**3*(-23)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-15*x**3)*-23 = 345*x**3\n (-15*x**3)*(-50*x) = 750*x**4\n (-15*x**3)*(44*x**3) = -660*x**6\n (7*x**2)*-23 = -161*x**2\n (7*x**2)*(-50*x) = -350*x**3\n (7*x**2)*(44*x**3) = 308*x**5\n (13*x)*-23 = -299*x\n (13*x)*(-50*x) = -650*x**2\n (13*x)*(44*x**3) = 572*x**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -660*x**6 + 308*x**5 + 572*x**4 + 750*x**4 - 350*x**3 + 345*x**3 - 650*x**2 - 161*x**2 - 299*x\nCombining like terms, got -660*x**6 + 308*x**5 + 1322*x**4 - 5*x**3 - 811*x**2 - 299*x\n#Step 7:\nCurrent expression: -660*x**6 + 308*x**5 + 1322*x**4 - 5*x**3 - 811*x**2 - 299*x\nNo more calculations needed.\n-660*x**6 + 308*x**5 + 1322*x**4 - 5*x**3 - 811*x**2 - 299*x", "generated_answer": "-660*x**6 + 308*x**5 + 1322*x**4 - 5*x**3 - 811*x**2 - 299*x", "step_length": 7} {"cot_id": "d7238df281df72476cc489d107793b3cb32f9ef3addfec73241cd3fc8d1274c2", "datapoint": {"question": "Simplify this expression: -301*z**3 + 4257*z**2 - 2107\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-301*z**3 + 4257*z**2 - 2107", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1655, "polynomial_expr": "-301*z**3 + 4257*z**2 - 2107", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -301*z**3 + 4257*z**2 - 2107\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -301*z**3 + 4257*z**2 - 2107\nNo more calculations needed.\n-301*z**3 + 4257*z**2 - 2107", "generated_answer": "-301*z**3 + 4257*z**2 - 2107", "step_length": 2} {"cot_id": "41b9274fdd1f31ef8148d48b79c08b9ab3c94cff22a543cf14654e3151af7158", "datapoint": {"question": "Calculate the following: (5*y**2 - 36*y)*(26*y**2 - 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "130*y**4 - 936*y**3 - 180*y**2 + 1296*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1656, "polynomial_expr": "(5*y**2 - 36*y)*(26*y**2 - 36)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (5*y**2 - 36*y)*(26*y**2 - 36)\nExpanding the part (26*y**2 - 36) using the distributive property, and we got: (26*y**2)*(5*y**2 - 36*y) - 36*(5*y**2 - 36*y)\n#Step 2:\nCurrent expression: (26*y**2)*(5*y**2 - 36*y) - 36*(5*y**2 - 36*y)\nSimplifying the partial expression: -36*(5*y**2 - 36*y)\nExpanding the part (5*y**2 - 36*y) using the distributive property, and we got: -36*y*(-36) + (5*y**2)*(-36)\nReplacing -36*(5*y**2 - 36*y) with -36*y*(-36) + (5*y**2)*(-36) in the overall expression.\n#Step 3:\nCurrent expression: -36*y*(-36) + (5*y**2)*(-36) + (26*y**2)*(5*y**2 - 36*y)\nSimplifying the partial expression: (26*y**2)*(5*y**2 - 36*y)\nExpanding the part (5*y**2 - 36*y) using the distributive property, and we got: (-36*y)*(26*y**2) + (5*y**2)*(26*y**2)\nReplacing (26*y**2)*(5*y**2 - 36*y) with (-36*y)*(26*y**2) + (5*y**2)*(26*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-36*y)*(26*y**2) - 36*y*(-36) + (5*y**2)*(26*y**2) + (5*y**2)*(-36)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*y)*-36 = 1296*y\n (-36*y)*(26*y**2) = -936*y**3\n (5*y**2)*-36 = -180*y**2\n (5*y**2)*(26*y**2) = 130*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 130*y**4 - 936*y**3 - 180*y**2 + 1296*y\nNo more calculations needed.\n130*y**4 - 936*y**3 - 180*y**2 + 1296*y", "generated_answer": "130*y**4 - 936*y**3 - 180*y**2 + 1296*y", "step_length": 5} {"cot_id": "bb9a0badab7988d23d11de1e13b599ac463f6e432b95bf003fe6a3a835203b5b", "datapoint": {"question": "Calculate the following: -33*y**2*(10*y**2 + 20*y + 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-330*y**4 - 660*y**3 - 561*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1657, "polynomial_expr": "-33*y**2*(10*y**2 + 20*y + 17)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -33*y**2*(10*y**2 + 20*y + 17)\nExpanding the part (10*y**2 + 20*y + 17) using the distributive property, and we got: 17*(-33*y**2) + (20*y)*(-33*y**2) + (-33*y**2)*(10*y**2)\n#Step 2:\nCurrent expression: 17*(-33*y**2) + (20*y)*(-33*y**2) + (-33*y**2)*(10*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 17*(-33*y**2) = -561*y**2\n (10*y**2)*(-33*y**2) = -330*y**4\n (20*y)*(-33*y**2) = -660*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -330*y**4 - 660*y**3 - 561*y**2\nNo more calculations needed.\n-330*y**4 - 660*y**3 - 561*y**2", "generated_answer": "-330*y**4 - 660*y**3 - 561*y**2", "step_length": 3} {"cot_id": "ca393edba5a7f493cebb35fbfe41c95cd4807aeb66459703ec9804129ad62e94", "datapoint": {"question": "Simplify this expression: (17*y + 7)*(26*y**2 - 66)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "442*y**3 + 182*y**2 - 1122*y - 462", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1658, "polynomial_expr": "(17*y + 7)*(26*y**2 - 66)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (17*y + 7)*(26*y**2 - 66)\nExpanding the part (26*y**2 - 66) using the distributive property, and we got: (26*y**2)*(17*y + 7) - 66*(17*y + 7)\n#Step 2:\nCurrent expression: (26*y**2)*(17*y + 7) - 66*(17*y + 7)\nSimplifying the partial expression: -66*(17*y + 7)\nExpanding the part (17*y + 7) using the distributive property, and we got: (17*y)*(-66) + 7*(-66)\nReplacing -66*(17*y + 7) with (17*y)*(-66) + 7*(-66) in the overall expression.\n#Step 3:\nCurrent expression: (17*y)*(-66) + (26*y**2)*(17*y + 7) - 462\nSimplifying the partial expression: (26*y**2)*(17*y + 7)\nExpanding the part (17*y + 7) using the distributive property, and we got: 7*(26*y**2) + (17*y)*(26*y**2)\nReplacing (26*y**2)*(17*y + 7) with 7*(26*y**2) + (17*y)*(26*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 7*26*y**2 + (17*y)*(26*y**2) + (17*y)*(-66) - 462\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (17*y)*-66 = -1122*y\n (17*y)*(26*y**2) = 442*y**3\n 7*26*y**2 = 182*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 442*y**3 + 182*y**2 - 1122*y - 462\nNo more calculations needed.\n442*y**3 + 182*y**2 - 1122*y - 462", "generated_answer": "442*y**3 + 182*y**2 - 1122*y - 462", "step_length": 5} {"cot_id": "8504725fcd5cdd344e38ef189b93d1fd005d737aa649e9d15942af6207b52488", "datapoint": {"question": "Simplify this expression: (12*y**3 + 58)*(-31*y**3 + 11*y + 4)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-372*y**6 + 132*y**4 - 1750*y**3 + 638*y + 232", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1659, "polynomial_expr": "(12*y**3 + 58)*(-31*y**3 + 11*y + 4)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (12*y**3 + 58)*(-31*y**3 + 11*y + 4)\nExpanding the part (12*y**3 + 58) using the distributive property, and we got: (12*y**3)*(-31*y**3 + 11*y + 4) + 58*(-31*y**3 + 11*y + 4)\n#Step 2:\nCurrent expression: (12*y**3)*(-31*y**3 + 11*y + 4) + 58*(-31*y**3 + 11*y + 4)\nSimplifying the partial expression: 58*(-31*y**3 + 11*y + 4)\nExpanding the part (-31*y**3 + 11*y + 4) using the distributive property, and we got: (11*y)*58 - 31*y**3*58 + 4*58\nReplacing 58*(-31*y**3 + 11*y + 4) with (11*y)*58 - 31*y**3*58 + 4*58 in the overall expression.\n#Step 3:\nCurrent expression: (11*y)*58 - 31*y**3*58 + (12*y**3)*(-31*y**3 + 11*y + 4) + 232\nSimplifying the partial expression: (12*y**3)*(-31*y**3 + 11*y + 4)\nExpanding the part (-31*y**3 + 11*y + 4) using the distributive property, and we got: 4*(12*y**3) + (11*y)*(12*y**3) + (-31*y**3)*(12*y**3)\nReplacing (12*y**3)*(-31*y**3 + 11*y + 4) with 4*(12*y**3) + (11*y)*(12*y**3) + (-31*y**3)*(12*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 4*12*y**3 + (11*y)*(12*y**3) + (11*y)*58 + (-31*y**3)*(12*y**3) - 31*y**3*58 + 232\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-31*y**3)*58 = -1798*y**3\n (-31*y**3)*(12*y**3) = -372*y**6\n (11*y)*58 = 638*y\n (11*y)*(12*y**3) = 132*y**4\n 4*12*y**3 = 48*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -372*y**6 + 132*y**4 - 1798*y**3 + 48*y**3 + 638*y + 232\nCombining like terms, got -372*y**6 + 132*y**4 - 1750*y**3 + 638*y + 232\n#Step 6:\nCurrent expression: -372*y**6 + 132*y**4 - 1750*y**3 + 638*y + 232\nNo more calculations needed.\n-372*y**6 + 132*y**4 - 1750*y**3 + 638*y + 232", "generated_answer": "-372*y**6 + 132*y**4 - 1750*y**3 + 638*y + 232", "step_length": 6} {"cot_id": "4a49b3e4fdecf4eb4050269a119aec32eb089dec49cb64f39fcd665af5a8b3d2", "datapoint": {"question": "Simplify this expression: (-35*y - 1)*(23*y**3 - 45*y - 12)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-805*y**4 - 23*y**3 + 1575*y**2 + 465*y + 12", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1660, "polynomial_expr": "(-35*y - 1)*(23*y**3 - 45*y - 12)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-35*y - 1)*(23*y**3 - 45*y - 12)\nExpanding the part (-35*y - 1) using the distributive property, and we got: (-35*y)*(23*y**3 - 45*y - 12) - (23*y**3 - 45*y - 12)\n#Step 2:\nCurrent expression: (-35*y)*(23*y**3 - 45*y - 12) - (23*y**3 - 45*y - 12)\nSimplifying the partial expression: -(23*y**3 - 45*y - 12)\nExpanding the part (23*y**3 - 45*y - 12) using the distributive property, and we got: -45*y*(-1) + (23*y**3)*(-1) - 12*(-1)\nReplacing -(23*y**3 - 45*y - 12) with -45*y*(-1) + (23*y**3)*(-1) - 12*(-1) in the overall expression.\n#Step 3:\nCurrent expression: -45*y*(-1) + (-35*y)*(23*y**3 - 45*y - 12) + (23*y**3)*(-1) + 12\nSimplifying the partial expression: (-35*y)*(23*y**3 - 45*y - 12)\nExpanding the part (23*y**3 - 45*y - 12) using the distributive property, and we got: (-45*y)*(-35*y) + (-35*y)*(23*y**3) - (-1)*420*y\nReplacing (-35*y)*(23*y**3 - 45*y - 12) with (-45*y)*(-35*y) + (-35*y)*(23*y**3) - (-1)*420*y in the overall expression.\n#Step 4:\nCurrent expression: (-45*y)*(-35*y) - 45*y*(-1) + (-35*y)*(23*y**3) - 12*(-35)*y + (23*y**3)*(-1) + 12\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*y)*-1 = 45*y\n (-45*y)*(-35*y) = 1575*y**2\n (23*y**3)*-1 = -23*y**3\n (23*y**3)*(-35*y) = -805*y**4\n -12*-35*y = 420*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -805*y**4 - 23*y**3 + 1575*y**2 + 45*y + 420*y + 12\nCombining like terms, got -805*y**4 - 23*y**3 + 1575*y**2 + 465*y + 12\n#Step 6:\nCurrent expression: -805*y**4 - 23*y**3 + 1575*y**2 + 465*y + 12\nNo more calculations needed.\n-805*y**4 - 23*y**3 + 1575*y**2 + 465*y + 12", "generated_answer": "-805*y**4 - 23*y**3 + 1575*y**2 + 465*y + 12", "step_length": 6} {"cot_id": "8c5edc4d8653a049d46cad046103ee7e55599bfbe04e72680f0072ef9edc8a16", "datapoint": {"question": "Calculate the following: (-50*z - 25)*(-11*z**3 + 3*z + 46)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "550*z**4 + 275*z**3 - 150*z**2 - 2375*z - 1150", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1661, "polynomial_expr": "(-50*z - 25)*(-11*z**3 + 3*z + 46)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-50*z - 25)*(-11*z**3 + 3*z + 46)\nExpanding the part (-50*z - 25) using the distributive property, and we got: (-50*z)*(-11*z**3 + 3*z + 46) - 25*(-11*z**3 + 3*z + 46)\n#Step 2:\nCurrent expression: (-50*z)*(-11*z**3 + 3*z + 46) - 25*(-11*z**3 + 3*z + 46)\nSimplifying the partial expression: -25*(-11*z**3 + 3*z + 46)\nExpanding the part (-11*z**3 + 3*z + 46) using the distributive property, and we got: (3*z)*(-25) - 11*z**3*(-25) + 46*(-25)\nReplacing -25*(-11*z**3 + 3*z + 46) with (3*z)*(-25) - 11*z**3*(-25) + 46*(-25) in the overall expression.\n#Step 3:\nCurrent expression: (-50*z)*(-11*z**3 + 3*z + 46) + (3*z)*(-25) - 11*z**3*(-25) - 1150\nSimplifying the partial expression: (-50*z)*(-11*z**3 + 3*z + 46)\nExpanding the part (-11*z**3 + 3*z + 46) using the distributive property, and we got: (-50*z)*(3*z) + (-50*z)*(-11*z**3) + 46*(-50*z)\nReplacing (-50*z)*(-11*z**3 + 3*z + 46) with (-50*z)*(3*z) + (-50*z)*(-11*z**3) + 46*(-50*z) in the overall expression.\n#Step 4:\nCurrent expression: (-50*z)*(3*z) + (-50*z)*(-11*z**3) + 46*(-50)*z + (3*z)*(-25) - 11*z**3*(-25) - 1150\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*z**3)*-25 = 275*z**3\n (-11*z**3)*(-50*z) = 550*z**4\n (3*z)*-25 = -75*z\n (3*z)*(-50*z) = -150*z**2\n 46*-50*z = -2300*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 550*z**4 + 275*z**3 - 150*z**2 - 2300*z - 75*z - 1150\nCombining like terms, got 550*z**4 + 275*z**3 - 150*z**2 - 2375*z - 1150\n#Step 6:\nCurrent expression: 550*z**4 + 275*z**3 - 150*z**2 - 2375*z - 1150\nNo more calculations needed.\n550*z**4 + 275*z**3 - 150*z**2 - 2375*z - 1150", "generated_answer": "550*z**4 + 275*z**3 - 150*z**2 - 2375*z - 1150", "step_length": 6} {"cot_id": "0481e1859bc02482528908ae1e393e93d98f822aad52052d901620b8b3074c06", "datapoint": {"question": "Simplify this expression: (-45*z**2 - 36*z - 11)*(-13*z**3 + 57*z**2 - 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "585*z**5 - 2097*z**4 - 1909*z**3 + 948*z**2 + 1260*z + 385", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1662, "polynomial_expr": "(-45*z**2 - 36*z - 11)*(-13*z**3 + 57*z**2 - 35)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-45*z**2 - 36*z - 11)*(-13*z**3 + 57*z**2 - 35)\nExpanding the part (-13*z**3 + 57*z**2 - 35) using the distributive property, and we got: (57*z**2)*(-45*z**2 - 36*z - 11) + (-13*z**3)*(-45*z**2 - 36*z - 11) - 35*(-45*z**2 - 36*z - 11)\n#Step 2:\nCurrent expression: (57*z**2)*(-45*z**2 - 36*z - 11) + (-13*z**3)*(-45*z**2 - 36*z - 11) - 35*(-45*z**2 - 36*z - 11)\nSimplifying the partial expression: -35*(-45*z**2 - 36*z - 11)\nExpanding the part (-45*z**2 - 36*z - 11) using the distributive property, and we got: -36*z*(-35) - 45*z**2*(-35) - 11*(-35)\nReplacing -35*(-45*z**2 - 36*z - 11) with -36*z*(-35) - 45*z**2*(-35) - 11*(-35) in the overall expression.\n#Step 3:\nCurrent expression: -36*z*(-35) - 45*z**2*(-35) + (57*z**2)*(-45*z**2 - 36*z - 11) + (-13*z**3)*(-45*z**2 - 36*z - 11) + 385\nSimplifying the partial expression: (-13*z**3)*(-45*z**2 - 36*z - 11)\nExpanding the part (-45*z**2 - 36*z - 11) using the distributive property, and we got: (-36*z)*(-13*z**3) - (-1)*143*z**3 + (-45*z**2)*(-13*z**3)\nReplacing (-13*z**3)*(-45*z**2 - 36*z - 11) with (-36*z)*(-13*z**3) - (-1)*143*z**3 + (-45*z**2)*(-13*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-36*z)*(-13*z**3) - 36*z*(-35) - 11*(-13)*z**3 + (-45*z**2)*(-13*z**3) - 45*z**2*(-35) + (57*z**2)*(-45*z**2 - 36*z - 11) + 385\nSimplifying the partial expression: (57*z**2)*(-45*z**2 - 36*z - 11)\nExpanding the part (-45*z**2 - 36*z - 11) using the distributive property, and we got: (-36*z)*(57*z**2) - 627*z**2 + (-45*z**2)*(57*z**2)\nReplacing (57*z**2)*(-45*z**2 - 36*z - 11) with (-36*z)*(57*z**2) - 627*z**2 + (-45*z**2)*(57*z**2) in the overall expression.\n#Step 5:\nCurrent expression: (-36*z)*(57*z**2) + (-36*z)*(-13*z**3) - 36*z*(-35) - 11*(-13)*z**3 - 11*57*z**2 + (-45*z**2)*(57*z**2) + (-45*z**2)*(-13*z**3) - 45*z**2*(-35) + 385\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*z**2)*-35 = 1575*z**2\n (-45*z**2)*(-13*z**3) = 585*z**5\n (-45*z**2)*(57*z**2) = -2565*z**4\n (-36*z)*-35 = 1260*z\n (-36*z)*(-13*z**3) = 468*z**4\n (-36*z)*(57*z**2) = -2052*z**3\n -11*-13*z**3 = 143*z**3\n -11*57*z**2 = -627*z**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 585*z**5 - 2565*z**4 + 468*z**4 - 2052*z**3 + 143*z**3 - 627*z**2 + 1575*z**2 + 1260*z + 385\nCombining like terms, got 585*z**5 - 2097*z**4 - 1909*z**3 + 948*z**2 + 1260*z + 385\n#Step 7:\nCurrent expression: 585*z**5 - 2097*z**4 - 1909*z**3 + 948*z**2 + 1260*z + 385\nNo more calculations needed.\n585*z**5 - 2097*z**4 - 1909*z**3 + 948*z**2 + 1260*z + 385", "generated_answer": "585*z**5 - 2097*z**4 - 1909*z**3 + 948*z**2 + 1260*z + 385", "step_length": 7} {"cot_id": "d15deede792c40e1b2a4bb23f2628442d7d4232b7aa1575c845ee4b914a0c5c0", "datapoint": {"question": "Calculate the following: 16*z**3*(16*z**3 - 35*z - 9)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "256*z**6 - 560*z**4 - 144*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1663, "polynomial_expr": "16*z**3*(16*z**3 - 35*z - 9)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 16*z**3*(16*z**3 - 35*z - 9)\nExpanding the part (16*z**3 - 35*z - 9) using the distributive property, and we got: (-35*z)*(16*z**3) - 144*z**3 + (16*z**3)*(16*z**3)\n#Step 2:\nCurrent expression: (-35*z)*(16*z**3) - 144*z**3 + (16*z**3)*(16*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -9*(16*z**3) = -144*z**3\n (-35*z)*(16*z**3) = -560*z**4\n (16*z**3)*(16*z**3) = 256*z**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 256*z**6 - 560*z**4 - 144*z**3\nNo more calculations needed.\n256*z**6 - 560*z**4 - 144*z**3", "generated_answer": "256*z**6 - 560*z**4 - 144*z**3", "step_length": 3} {"cot_id": "08d76573ffbf284d943d0ba34118eaf55d06ad011b02eb8c2f94b8dfcc2a2734", "datapoint": {"question": "Calculate the following: (-4*y**3 - 32*y)*(9*y**3 + 30*y**2 - 29*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-36*y**6 - 120*y**5 - 172*y**4 - 960*y**3 + 928*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1664, "polynomial_expr": "(-4*y**3 - 32*y)*(9*y**3 + 30*y**2 - 29*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-4*y**3 - 32*y)*(9*y**3 + 30*y**2 - 29*y)\nExpanding the part (-4*y**3 - 32*y) using the distributive property, and we got: (-32*y)*(9*y**3 + 30*y**2 - 29*y) + (-4*y**3)*(9*y**3 + 30*y**2 - 29*y)\n#Step 2:\nCurrent expression: (-32*y)*(9*y**3 + 30*y**2 - 29*y) + (-4*y**3)*(9*y**3 + 30*y**2 - 29*y)\nSimplifying the partial expression: (-32*y)*(9*y**3 + 30*y**2 - 29*y)\nExpanding the part (9*y**3 + 30*y**2 - 29*y) using the distributive property, and we got: (-32*y)*(-29*y) + (-32*y)*(30*y**2) + (-32*y)*(9*y**3)\nReplacing (-32*y)*(9*y**3 + 30*y**2 - 29*y) with (-32*y)*(-29*y) + (-32*y)*(30*y**2) + (-32*y)*(9*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-32*y)*(-29*y) + (-32*y)*(30*y**2) + (-32*y)*(9*y**3) + (-4*y**3)*(9*y**3 + 30*y**2 - 29*y)\nSimplifying the partial expression: (-4*y**3)*(9*y**3 + 30*y**2 - 29*y)\nExpanding the part (9*y**3 + 30*y**2 - 29*y) using the distributive property, and we got: (-29*y)*(-4*y**3) + (30*y**2)*(-4*y**3) + (-4*y**3)*(9*y**3)\nReplacing (-4*y**3)*(9*y**3 + 30*y**2 - 29*y) with (-29*y)*(-4*y**3) + (30*y**2)*(-4*y**3) + (-4*y**3)*(9*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-32*y)*(-29*y) + (-32*y)*(30*y**2) + (-32*y)*(9*y**3) + (-29*y)*(-4*y**3) + (30*y**2)*(-4*y**3) + (-4*y**3)*(9*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*y)*(-32*y) = 928*y**2\n (-29*y)*(-4*y**3) = 116*y**4\n (9*y**3)*(-32*y) = -288*y**4\n (9*y**3)*(-4*y**3) = -36*y**6\n (30*y**2)*(-32*y) = -960*y**3\n (30*y**2)*(-4*y**3) = -120*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -36*y**6 - 120*y**5 - 288*y**4 + 116*y**4 - 960*y**3 + 928*y**2\nCombining like terms, got -36*y**6 - 120*y**5 - 172*y**4 - 960*y**3 + 928*y**2\n#Step 6:\nCurrent expression: -36*y**6 - 120*y**5 - 172*y**4 - 960*y**3 + 928*y**2\nNo more calculations needed.\n-36*y**6 - 120*y**5 - 172*y**4 - 960*y**3 + 928*y**2", "generated_answer": "-36*y**6 - 120*y**5 - 172*y**4 - 960*y**3 + 928*y**2", "step_length": 6} {"cot_id": "973a30139c5a2d17b7f228857885de86007f36d63310bcd2906ec0ca11cdaed1", "datapoint": {"question": "Simplify this expression: (39*x + 10)*(-22*x**2 - 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-858*x**3 - 220*x**2 - 1170*x - 300", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1665, "polynomial_expr": "(39*x + 10)*(-22*x**2 - 30)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (39*x + 10)*(-22*x**2 - 30)\nExpanding the part (-22*x**2 - 30) using the distributive property, and we got: (-22*x**2)*(39*x + 10) - 30*(39*x + 10)\n#Step 2:\nCurrent expression: (-22*x**2)*(39*x + 10) - 30*(39*x + 10)\nSimplifying the partial expression: -30*(39*x + 10)\nExpanding the part (39*x + 10) using the distributive property, and we got: (39*x)*(-30) + 10*(-30)\nReplacing -30*(39*x + 10) with (39*x)*(-30) + 10*(-30) in the overall expression.\n#Step 3:\nCurrent expression: (39*x)*(-30) + (-22*x**2)*(39*x + 10) - 300\nSimplifying the partial expression: (-22*x**2)*(39*x + 10)\nExpanding the part (39*x + 10) using the distributive property, and we got: 10*(-22*x**2) + (39*x)*(-22*x**2)\nReplacing (-22*x**2)*(39*x + 10) with 10*(-22*x**2) + (39*x)*(-22*x**2) in the overall expression.\n#Step 4:\nCurrent expression: 10*(-22)*x**2 + (39*x)*(-22*x**2) + (39*x)*(-30) - 300\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (39*x)*-30 = -1170*x\n (39*x)*(-22*x**2) = -858*x**3\n 10*-22*x**2 = -220*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -858*x**3 - 220*x**2 - 1170*x - 300\nNo more calculations needed.\n-858*x**3 - 220*x**2 - 1170*x - 300", "generated_answer": "-858*x**3 - 220*x**2 - 1170*x - 300", "step_length": 5} {"cot_id": "86744f8e81c9610e324a99690593eb01f47eff4dad9f2e35aae20ebb42173db0", "datapoint": {"question": "Simplify this expression: (45 - 41*y**3)*(-y - 18)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "41*y**4 + 738*y**3 - 45*y - 810", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1666, "polynomial_expr": "(45 - 41*y**3)*(-y - 18)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (45 - 41*y**3)*(-y - 18)\nExpanding the part (-y - 18) using the distributive property, and we got: (-y)*(45 - 41*y**3) - 18*(45 - 41*y**3)\n#Step 2:\nCurrent expression: (-y)*(45 - 41*y**3) - 18*(45 - 41*y**3)\nSimplifying the partial expression: -18*(45 - 41*y**3)\nExpanding the part (45 - 41*y**3) using the distributive property, and we got: -41*y**3*(-18) + 45*(-18)\nReplacing -18*(45 - 41*y**3) with -41*y**3*(-18) + 45*(-18) in the overall expression.\n#Step 3:\nCurrent expression: (-y)*(45 - 41*y**3) - 41*y**3*(-18) - 810\nSimplifying the partial expression: (-y)*(45 - 41*y**3)\nExpanding the part (45 - 41*y**3) using the distributive property, and we got: (-y)*(-41*y**3) + 45*(-y)\nReplacing (-y)*(45 - 41*y**3) with (-y)*(-41*y**3) + 45*(-y) in the overall expression.\n#Step 4:\nCurrent expression: (-y)*(-41*y**3) + 45*(-1)*y - 41*y**3*(-18) - 810\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*y**3)*-18 = 738*y**3\n (-41*y**3)*(-y) = 41*y**4\n 45*-1*y = -45*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 41*y**4 + 738*y**3 - 45*y - 810\nNo more calculations needed.\n41*y**4 + 738*y**3 - 45*y - 810", "generated_answer": "41*y**4 + 738*y**3 - 45*y - 810", "step_length": 5} {"cot_id": "84f629f083f120c38159f5e4b8bcc1f4ebdfdc0a72952214c8532178117805b6", "datapoint": {"question": "Calculate the following: (27 - 41*z)*(73 - 30*z**3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1230*z**4 - 810*z**3 - 2993*z + 1971", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1667, "polynomial_expr": "(27 - 41*z)*(73 - 30*z**3)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27 - 41*z)*(73 - 30*z**3)\nExpanding the part (27 - 41*z) using the distributive property, and we got: (-41*z)*(73 - 30*z**3) + 27*(73 - 30*z**3)\n#Step 2:\nCurrent expression: (-41*z)*(73 - 30*z**3) + 27*(73 - 30*z**3)\nSimplifying the partial expression: 27*(73 - 30*z**3)\nExpanding the part (73 - 30*z**3) using the distributive property, and we got: -30*z**3*27 + 73*27\nReplacing 27*(73 - 30*z**3) with -30*z**3*27 + 73*27 in the overall expression.\n#Step 3:\nCurrent expression: (-41*z)*(73 - 30*z**3) - 30*z**3*27 + 1971\nSimplifying the partial expression: (-41*z)*(73 - 30*z**3)\nExpanding the part (73 - 30*z**3) using the distributive property, and we got: (-41*z)*(-30*z**3) + 73*(-41*z)\nReplacing (-41*z)*(73 - 30*z**3) with (-41*z)*(-30*z**3) + 73*(-41*z) in the overall expression.\n#Step 4:\nCurrent expression: (-41*z)*(-30*z**3) + 73*(-41)*z - 30*z**3*27 + 1971\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*z**3)*27 = -810*z**3\n (-30*z**3)*(-41*z) = 1230*z**4\n 73*-41*z = -2993*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1230*z**4 - 810*z**3 - 2993*z + 1971\nNo more calculations needed.\n1230*z**4 - 810*z**3 - 2993*z + 1971", "generated_answer": "1230*z**4 - 810*z**3 - 2993*z + 1971", "step_length": 5} {"cot_id": "9379c5d9fbfe3fea5b8687fb1372fc6cb8fb2268b1446be1db9a5f635f95873e", "datapoint": {"question": "Calculate the following: (-44*y**2 + 12*y + 60)*(5*y**3 - 14*y - 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-220*y**5 + 60*y**4 + 916*y**3 + 1284*y**2 - 1236*y - 1980", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1668, "polynomial_expr": "(-44*y**2 + 12*y + 60)*(5*y**3 - 14*y - 33)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-44*y**2 + 12*y + 60)*(5*y**3 - 14*y - 33)\nExpanding the part (5*y**3 - 14*y - 33) using the distributive property, and we got: (-14*y)*(-44*y**2 + 12*y + 60) + (5*y**3)*(-44*y**2 + 12*y + 60) - 33*(-44*y**2 + 12*y + 60)\n#Step 2:\nCurrent expression: (-14*y)*(-44*y**2 + 12*y + 60) + (5*y**3)*(-44*y**2 + 12*y + 60) - 33*(-44*y**2 + 12*y + 60)\nSimplifying the partial expression: -33*(-44*y**2 + 12*y + 60)\nExpanding the part (-44*y**2 + 12*y + 60) using the distributive property, and we got: (12*y)*(-33) - 44*y**2*(-33) + 60*(-33)\nReplacing -33*(-44*y**2 + 12*y + 60) with (12*y)*(-33) - 44*y**2*(-33) + 60*(-33) in the overall expression.\n#Step 3:\nCurrent expression: (-14*y)*(-44*y**2 + 12*y + 60) + (12*y)*(-33) - 44*y**2*(-33) + (5*y**3)*(-44*y**2 + 12*y + 60) - 1980\nSimplifying the partial expression: (-14*y)*(-44*y**2 + 12*y + 60)\nExpanding the part (-44*y**2 + 12*y + 60) using the distributive property, and we got: (-14*y)*(12*y) + (-14*y)*(-44*y**2) + 60*(-14*y)\nReplacing (-14*y)*(-44*y**2 + 12*y + 60) with (-14*y)*(12*y) + (-14*y)*(-44*y**2) + 60*(-14*y) in the overall expression.\n#Step 4:\nCurrent expression: (-14*y)*(12*y) + (-14*y)*(-44*y**2) + 60*(-14)*y + (12*y)*(-33) - 44*y**2*(-33) + (5*y**3)*(-44*y**2 + 12*y + 60) - 1980\nSimplifying the partial expression: (5*y**3)*(-44*y**2 + 12*y + 60)\nExpanding the part (-44*y**2 + 12*y + 60) using the distributive property, and we got: 60*(5*y**3) + (12*y)*(5*y**3) + (-44*y**2)*(5*y**3)\nReplacing (5*y**3)*(-44*y**2 + 12*y + 60) with 60*(5*y**3) + (12*y)*(5*y**3) + (-44*y**2)*(5*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-14*y)*(12*y) + (-14*y)*(-44*y**2) + 60*5*y**3 + 60*(-14)*y + (12*y)*(5*y**3) + (12*y)*(-33) + (-44*y**2)*(5*y**3) - 44*y**2*(-33) - 1980\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-44*y**2)*-33 = 1452*y**2\n (-44*y**2)*(-14*y) = 616*y**3\n (-44*y**2)*(5*y**3) = -220*y**5\n (12*y)*-33 = -396*y\n (12*y)*(-14*y) = -168*y**2\n (12*y)*(5*y**3) = 60*y**4\n 60*-14*y = -840*y\n 60*5*y**3 = 300*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -220*y**5 + 60*y**4 + 300*y**3 + 616*y**3 - 168*y**2 + 1452*y**2 - 840*y - 396*y - 1980\nCombining like terms, got -220*y**5 + 60*y**4 + 916*y**3 + 1284*y**2 - 1236*y - 1980\n#Step 7:\nCurrent expression: -220*y**5 + 60*y**4 + 916*y**3 + 1284*y**2 - 1236*y - 1980\nNo more calculations needed.\n-220*y**5 + 60*y**4 + 916*y**3 + 1284*y**2 - 1236*y - 1980", "generated_answer": "-220*y**5 + 60*y**4 + 916*y**3 + 1284*y**2 - 1236*y - 1980", "step_length": 7} {"cot_id": "cb7f11458b9aec371d3abf08c68d8804b9dbbcc5eb80a943f1bf241df227c014", "datapoint": {"question": "Calculate the following: (57*y**2 + 22*y)*(34*y**2 + 33*y + 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1938*y**4 + 2629*y**3 + 2436*y**2 + 660*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1669, "polynomial_expr": "(57*y**2 + 22*y)*(34*y**2 + 33*y + 30)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (57*y**2 + 22*y)*(34*y**2 + 33*y + 30)\nExpanding the part (57*y**2 + 22*y) using the distributive property, and we got: (22*y)*(34*y**2 + 33*y + 30) + (57*y**2)*(34*y**2 + 33*y + 30)\n#Step 2:\nCurrent expression: (22*y)*(34*y**2 + 33*y + 30) + (57*y**2)*(34*y**2 + 33*y + 30)\nSimplifying the partial expression: (22*y)*(34*y**2 + 33*y + 30)\nExpanding the part (34*y**2 + 33*y + 30) using the distributive property, and we got: 30*(22*y) + (22*y)*(33*y) + (22*y)*(34*y**2)\nReplacing (22*y)*(34*y**2 + 33*y + 30) with 30*(22*y) + (22*y)*(33*y) + (22*y)*(34*y**2) in the overall expression.\n#Step 3:\nCurrent expression: 30*22*y + (22*y)*(33*y) + (22*y)*(34*y**2) + (57*y**2)*(34*y**2 + 33*y + 30)\nSimplifying the partial expression: (57*y**2)*(34*y**2 + 33*y + 30)\nExpanding the part (34*y**2 + 33*y + 30) using the distributive property, and we got: 30*(57*y**2) + (33*y)*(57*y**2) + (34*y**2)*(57*y**2)\nReplacing (57*y**2)*(34*y**2 + 33*y + 30) with 30*(57*y**2) + (33*y)*(57*y**2) + (34*y**2)*(57*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 30*57*y**2 + 30*22*y + (22*y)*(33*y) + (22*y)*(34*y**2) + (33*y)*(57*y**2) + (34*y**2)*(57*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (33*y)*(22*y) = 726*y**2\n (33*y)*(57*y**2) = 1881*y**3\n (34*y**2)*(22*y) = 748*y**3\n (34*y**2)*(57*y**2) = 1938*y**4\n 30*22*y = 660*y\n 30*57*y**2 = 1710*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1938*y**4 + 748*y**3 + 1881*y**3 + 726*y**2 + 1710*y**2 + 660*y\nCombining like terms, got 1938*y**4 + 2629*y**3 + 2436*y**2 + 660*y\n#Step 6:\nCurrent expression: 1938*y**4 + 2629*y**3 + 2436*y**2 + 660*y\nNo more calculations needed.\n1938*y**4 + 2629*y**3 + 2436*y**2 + 660*y", "generated_answer": "1938*y**4 + 2629*y**3 + 2436*y**2 + 660*y", "step_length": 6} {"cot_id": "061fa1f258eb6f99a5f21ca55015929492195fa04bbd9339348bed4cb95f8def", "datapoint": {"question": "Simplify this expression: (-9*z**3 - 6*z)*(29*z**3 - 17*z**2 + 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-261*z**6 + 153*z**5 - 174*z**4 + 93*z**3 - 6*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1670, "polynomial_expr": "(-9*z**3 - 6*z)*(29*z**3 - 17*z**2 + 1)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-9*z**3 - 6*z)*(29*z**3 - 17*z**2 + 1)\nExpanding the part (-9*z**3 - 6*z) using the distributive property, and we got: (-6*z)*(29*z**3 - 17*z**2 + 1) + (-9*z**3)*(29*z**3 - 17*z**2 + 1)\n#Step 2:\nCurrent expression: (-6*z)*(29*z**3 - 17*z**2 + 1) + (-9*z**3)*(29*z**3 - 17*z**2 + 1)\nSimplifying the partial expression: (-9*z**3)*(29*z**3 - 17*z**2 + 1)\nExpanding the part (29*z**3 - 17*z**2 + 1) using the distributive property, and we got: 1*(-9*z**3) + (-17*z**2)*(-9*z**3) + (-9*z**3)*(29*z**3)\nReplacing (-9*z**3)*(29*z**3 - 17*z**2 + 1) with 1*(-9*z**3) + (-17*z**2)*(-9*z**3) + (-9*z**3)*(29*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-6*z)*(29*z**3 - 17*z**2 + 1) - 9*z**3 + (-17*z**2)*(-9*z**3) + (-9*z**3)*(29*z**3)\nSimplifying the partial expression: (-6*z)*(29*z**3 - 17*z**2 + 1)\nExpanding the part (29*z**3 - 17*z**2 + 1) using the distributive property, and we got: (-6*z)*(-17*z**2) + (-6*z)*(29*z**3) + 1*(-6*z)\nReplacing (-6*z)*(29*z**3 - 17*z**2 + 1) with (-6*z)*(-17*z**2) + (-6*z)*(29*z**3) + 1*(-6*z) in the overall expression.\n#Step 4:\nCurrent expression: (-6*z)*(-17*z**2) + (-6*z)*(29*z**3) - 9*z**3 - 6*z + (-17*z**2)*(-9*z**3) + (-9*z**3)*(29*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-17*z**2)*(-9*z**3) = 153*z**5\n (-17*z**2)*(-6*z) = 102*z**3\n (29*z**3)*(-9*z**3) = -261*z**6\n (29*z**3)*(-6*z) = -174*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -261*z**6 + 153*z**5 - 174*z**4 - 9*z**3 + 102*z**3 - 6*z\nCombining like terms, got -261*z**6 + 153*z**5 - 174*z**4 + 93*z**3 - 6*z\n#Step 6:\nCurrent expression: -261*z**6 + 153*z**5 - 174*z**4 + 93*z**3 - 6*z\nNo more calculations needed.\n-261*z**6 + 153*z**5 - 174*z**4 + 93*z**3 - 6*z", "generated_answer": "-261*z**6 + 153*z**5 - 174*z**4 + 93*z**3 - 6*z", "step_length": 6} {"cot_id": "35d72bb6ad56028b229dfa5dd49cef04b41284a39050f3fe7746936a740c42ba", "datapoint": {"question": "Calculate the following: (17 - 14*z**3)*(40*z**2 + 12*z + 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-560*z**5 - 168*z**4 - 182*z**3 + 680*z**2 + 204*z + 221", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1671, "polynomial_expr": "(17 - 14*z**3)*(40*z**2 + 12*z + 13)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (17 - 14*z**3)*(40*z**2 + 12*z + 13)\nExpanding the part (17 - 14*z**3) using the distributive property, and we got: (-14*z**3)*(40*z**2 + 12*z + 13) + 17*(40*z**2 + 12*z + 13)\n#Step 2:\nCurrent expression: (-14*z**3)*(40*z**2 + 12*z + 13) + 17*(40*z**2 + 12*z + 13)\nSimplifying the partial expression: 17*(40*z**2 + 12*z + 13)\nExpanding the part (40*z**2 + 12*z + 13) using the distributive property, and we got: (12*z)*17 + (40*z**2)*17 + 13*17\nReplacing 17*(40*z**2 + 12*z + 13) with (12*z)*17 + (40*z**2)*17 + 13*17 in the overall expression.\n#Step 3:\nCurrent expression: (12*z)*17 + (40*z**2)*17 + (-14*z**3)*(40*z**2 + 12*z + 13) + 221\nSimplifying the partial expression: (-14*z**3)*(40*z**2 + 12*z + 13)\nExpanding the part (40*z**2 + 12*z + 13) using the distributive property, and we got: 13*(-14*z**3) + (12*z)*(-14*z**3) + (40*z**2)*(-14*z**3)\nReplacing (-14*z**3)*(40*z**2 + 12*z + 13) with 13*(-14*z**3) + (12*z)*(-14*z**3) + (40*z**2)*(-14*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 13*(-14)*z**3 + (12*z)*(-14*z**3) + (12*z)*17 + (40*z**2)*(-14*z**3) + (40*z**2)*17 + 221\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (12*z)*17 = 204*z\n (12*z)*(-14*z**3) = -168*z**4\n (40*z**2)*17 = 680*z**2\n (40*z**2)*(-14*z**3) = -560*z**5\n 13*-14*z**3 = -182*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -560*z**5 - 168*z**4 - 182*z**3 + 680*z**2 + 204*z + 221\nNo more calculations needed.\n-560*z**5 - 168*z**4 - 182*z**3 + 680*z**2 + 204*z + 221", "generated_answer": "-560*z**5 - 168*z**4 - 182*z**3 + 680*z**2 + 204*z + 221", "step_length": 5} {"cot_id": "6f9b23181c372203b144d171765f4b4ca976c086631530685ea7b702b75ed0f2", "datapoint": {"question": "Calculate the following: (-54*y**3 - 22*y**2 - 28)*(-29*y**3 + 18*y**2 + 10*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1566*y**6 - 334*y**5 - 936*y**4 + 592*y**3 - 504*y**2 - 280*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1672, "polynomial_expr": "(-54*y**3 - 22*y**2 - 28)*(-29*y**3 + 18*y**2 + 10*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-54*y**3 - 22*y**2 - 28)*(-29*y**3 + 18*y**2 + 10*y)\nExpanding the part (-54*y**3 - 22*y**2 - 28) using the distributive property, and we got: (-22*y**2)*(-29*y**3 + 18*y**2 + 10*y) + (-54*y**3)*(-29*y**3 + 18*y**2 + 10*y) - 28*(-29*y**3 + 18*y**2 + 10*y)\n#Step 2:\nCurrent expression: (-22*y**2)*(-29*y**3 + 18*y**2 + 10*y) + (-54*y**3)*(-29*y**3 + 18*y**2 + 10*y) - 28*(-29*y**3 + 18*y**2 + 10*y)\nSimplifying the partial expression: -28*(-29*y**3 + 18*y**2 + 10*y)\nExpanding the part (-29*y**3 + 18*y**2 + 10*y) using the distributive property, and we got: (10*y)*(-28) + (18*y**2)*(-28) - 29*y**3*(-28)\nReplacing -28*(-29*y**3 + 18*y**2 + 10*y) with (10*y)*(-28) + (18*y**2)*(-28) - 29*y**3*(-28) in the overall expression.\n#Step 3:\nCurrent expression: (10*y)*(-28) + (-22*y**2)*(-29*y**3 + 18*y**2 + 10*y) + (18*y**2)*(-28) + (-54*y**3)*(-29*y**3 + 18*y**2 + 10*y) - 29*y**3*(-28)\nSimplifying the partial expression: (-54*y**3)*(-29*y**3 + 18*y**2 + 10*y)\nExpanding the part (-29*y**3 + 18*y**2 + 10*y) using the distributive property, and we got: (10*y)*(-54*y**3) + (18*y**2)*(-54*y**3) + (-54*y**3)*(-29*y**3)\nReplacing (-54*y**3)*(-29*y**3 + 18*y**2 + 10*y) with (10*y)*(-54*y**3) + (18*y**2)*(-54*y**3) + (-54*y**3)*(-29*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (10*y)*(-54*y**3) + (10*y)*(-28) + (-22*y**2)*(-29*y**3 + 18*y**2 + 10*y) + (18*y**2)*(-54*y**3) + (18*y**2)*(-28) + (-54*y**3)*(-29*y**3) - 29*y**3*(-28)\nSimplifying the partial expression: (-22*y**2)*(-29*y**3 + 18*y**2 + 10*y)\nExpanding the part (-29*y**3 + 18*y**2 + 10*y) using the distributive property, and we got: (10*y)*(-22*y**2) + (-22*y**2)*(18*y**2) + (-22*y**2)*(-29*y**3)\nReplacing (-22*y**2)*(-29*y**3 + 18*y**2 + 10*y) with (10*y)*(-22*y**2) + (-22*y**2)*(18*y**2) + (-22*y**2)*(-29*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (10*y)*(-22*y**2) + (10*y)*(-54*y**3) + (10*y)*(-28) + (-22*y**2)*(18*y**2) + (-22*y**2)*(-29*y**3) + (18*y**2)*(-54*y**3) + (18*y**2)*(-28) + (-54*y**3)*(-29*y**3) - 29*y**3*(-28)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*y**3)*-28 = 812*y**3\n (-29*y**3)*(-54*y**3) = 1566*y**6\n (-29*y**3)*(-22*y**2) = 638*y**5\n (10*y)*-28 = -280*y\n (10*y)*(-54*y**3) = -540*y**4\n (10*y)*(-22*y**2) = -220*y**3\n (18*y**2)*-28 = -504*y**2\n (18*y**2)*(-54*y**3) = -972*y**5\n (18*y**2)*(-22*y**2) = -396*y**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1566*y**6 - 972*y**5 + 638*y**5 - 540*y**4 - 396*y**4 - 220*y**3 + 812*y**3 - 504*y**2 - 280*y\nCombining like terms, got 1566*y**6 - 334*y**5 - 936*y**4 + 592*y**3 - 504*y**2 - 280*y\n#Step 7:\nCurrent expression: 1566*y**6 - 334*y**5 - 936*y**4 + 592*y**3 - 504*y**2 - 280*y\nNo more calculations needed.\n1566*y**6 - 334*y**5 - 936*y**4 + 592*y**3 - 504*y**2 - 280*y", "generated_answer": "1566*y**6 - 334*y**5 - 936*y**4 + 592*y**3 - 504*y**2 - 280*y", "step_length": 7} {"cot_id": "864b201baf2292166419cf5cd57a4269ad047b995e9b2b841475f7e9edf3e2f9", "datapoint": {"question": "Simplify this expression: (11*z**3 + 17*z**2)*(-23*z**3 + 35*z**2 - 26)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-253*z**6 - 6*z**5 + 595*z**4 - 286*z**3 - 442*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1673, "polynomial_expr": "(11*z**3 + 17*z**2)*(-23*z**3 + 35*z**2 - 26)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11*z**3 + 17*z**2)*(-23*z**3 + 35*z**2 - 26)\nExpanding the part (11*z**3 + 17*z**2) using the distributive property, and we got: (17*z**2)*(-23*z**3 + 35*z**2 - 26) + (11*z**3)*(-23*z**3 + 35*z**2 - 26)\n#Step 2:\nCurrent expression: (17*z**2)*(-23*z**3 + 35*z**2 - 26) + (11*z**3)*(-23*z**3 + 35*z**2 - 26)\nSimplifying the partial expression: (11*z**3)*(-23*z**3 + 35*z**2 - 26)\nExpanding the part (-23*z**3 + 35*z**2 - 26) using the distributive property, and we got: -286*z**3 + (35*z**2)*(11*z**3) + (-23*z**3)*(11*z**3)\nReplacing (11*z**3)*(-23*z**3 + 35*z**2 - 26) with -286*z**3 + (35*z**2)*(11*z**3) + (-23*z**3)*(11*z**3) in the overall expression.\n#Step 3:\nCurrent expression: -26*11*z**3 + (17*z**2)*(-23*z**3 + 35*z**2 - 26) + (35*z**2)*(11*z**3) + (-23*z**3)*(11*z**3)\nSimplifying the partial expression: (17*z**2)*(-23*z**3 + 35*z**2 - 26)\nExpanding the part (-23*z**3 + 35*z**2 - 26) using the distributive property, and we got: -442*z**2 + (17*z**2)*(35*z**2) + (17*z**2)*(-23*z**3)\nReplacing (17*z**2)*(-23*z**3 + 35*z**2 - 26) with -442*z**2 + (17*z**2)*(35*z**2) + (17*z**2)*(-23*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -26*11*z**3 - 26*17*z**2 + (17*z**2)*(35*z**2) + (17*z**2)*(-23*z**3) + (35*z**2)*(11*z**3) + (-23*z**3)*(11*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*z**3)*(11*z**3) = -253*z**6\n (-23*z**3)*(17*z**2) = -391*z**5\n (35*z**2)*(11*z**3) = 385*z**5\n (35*z**2)*(17*z**2) = 595*z**4\n -26*11*z**3 = -286*z**3\n -26*17*z**2 = -442*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -253*z**6 - 391*z**5 + 385*z**5 + 595*z**4 - 286*z**3 - 442*z**2\nCombining like terms, got -253*z**6 - 6*z**5 + 595*z**4 - 286*z**3 - 442*z**2\n#Step 6:\nCurrent expression: -253*z**6 - 6*z**5 + 595*z**4 - 286*z**3 - 442*z**2\nNo more calculations needed.\n-253*z**6 - 6*z**5 + 595*z**4 - 286*z**3 - 442*z**2", "generated_answer": "-253*z**6 - 6*z**5 + 595*z**4 - 286*z**3 - 442*z**2", "step_length": 6} {"cot_id": "14d8f4df956f3ca37110d49fe88544a534ddb9b7d7174ef6f26be463aae77606", "datapoint": {"question": "Calculate the following: (30*x**3 + 14*x**2)*(-47*x**3 + 8*x + 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1410*x**6 - 658*x**5 + 240*x**4 + 742*x**3 + 294*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1674, "polynomial_expr": "(30*x**3 + 14*x**2)*(-47*x**3 + 8*x + 21)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (30*x**3 + 14*x**2)*(-47*x**3 + 8*x + 21)\nExpanding the part (30*x**3 + 14*x**2) using the distributive property, and we got: (14*x**2)*(-47*x**3 + 8*x + 21) + (30*x**3)*(-47*x**3 + 8*x + 21)\n#Step 2:\nCurrent expression: (14*x**2)*(-47*x**3 + 8*x + 21) + (30*x**3)*(-47*x**3 + 8*x + 21)\nSimplifying the partial expression: (14*x**2)*(-47*x**3 + 8*x + 21)\nExpanding the part (-47*x**3 + 8*x + 21) using the distributive property, and we got: 21*(14*x**2) + (8*x)*(14*x**2) + (14*x**2)*(-47*x**3)\nReplacing (14*x**2)*(-47*x**3 + 8*x + 21) with 21*(14*x**2) + (8*x)*(14*x**2) + (14*x**2)*(-47*x**3) in the overall expression.\n#Step 3:\nCurrent expression: 21*14*x**2 + (8*x)*(14*x**2) + (14*x**2)*(-47*x**3) + (30*x**3)*(-47*x**3 + 8*x + 21)\nSimplifying the partial expression: (30*x**3)*(-47*x**3 + 8*x + 21)\nExpanding the part (-47*x**3 + 8*x + 21) using the distributive property, and we got: 21*(30*x**3) + (8*x)*(30*x**3) + (-47*x**3)*(30*x**3)\nReplacing (30*x**3)*(-47*x**3 + 8*x + 21) with 21*(30*x**3) + (8*x)*(30*x**3) + (-47*x**3)*(30*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 21*30*x**3 + 21*14*x**2 + (8*x)*(14*x**2) + (8*x)*(30*x**3) + (14*x**2)*(-47*x**3) + (-47*x**3)*(30*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*x**3)*(14*x**2) = -658*x**5\n (-47*x**3)*(30*x**3) = -1410*x**6\n (8*x)*(14*x**2) = 112*x**3\n (8*x)*(30*x**3) = 240*x**4\n 21*14*x**2 = 294*x**2\n 21*30*x**3 = 630*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1410*x**6 - 658*x**5 + 240*x**4 + 112*x**3 + 630*x**3 + 294*x**2\nCombining like terms, got -1410*x**6 - 658*x**5 + 240*x**4 + 742*x**3 + 294*x**2\n#Step 6:\nCurrent expression: -1410*x**6 - 658*x**5 + 240*x**4 + 742*x**3 + 294*x**2\nNo more calculations needed.\n-1410*x**6 - 658*x**5 + 240*x**4 + 742*x**3 + 294*x**2", "generated_answer": "-1410*x**6 - 658*x**5 + 240*x**4 + 742*x**3 + 294*x**2", "step_length": 6} {"cot_id": "a2a4cd9bae9cf59f9b8c5260cf30894b65785d80f4da06234a6958a2e769e0c1", "datapoint": {"question": "Calculate the following: (8*x + 39)*(54*x**3 - 42*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "432*x**4 + 1770*x**3 - 1638*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1675, "polynomial_expr": "(8*x + 39)*(54*x**3 - 42*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (8*x + 39)*(54*x**3 - 42*x**2)\nExpanding the part (8*x + 39) using the distributive property, and we got: (8*x)*(54*x**3 - 42*x**2) + 39*(54*x**3 - 42*x**2)\n#Step 2:\nCurrent expression: (8*x)*(54*x**3 - 42*x**2) + 39*(54*x**3 - 42*x**2)\nSimplifying the partial expression: 39*(54*x**3 - 42*x**2)\nExpanding the part (54*x**3 - 42*x**2) using the distributive property, and we got: -42*x**2*39 + (54*x**3)*39\nReplacing 39*(54*x**3 - 42*x**2) with -42*x**2*39 + (54*x**3)*39 in the overall expression.\n#Step 3:\nCurrent expression: (8*x)*(54*x**3 - 42*x**2) - 42*x**2*39 + (54*x**3)*39\nSimplifying the partial expression: (8*x)*(54*x**3 - 42*x**2)\nExpanding the part (54*x**3 - 42*x**2) using the distributive property, and we got: (8*x)*(-42*x**2) + (8*x)*(54*x**3)\nReplacing (8*x)*(54*x**3 - 42*x**2) with (8*x)*(-42*x**2) + (8*x)*(54*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (8*x)*(-42*x**2) + (8*x)*(54*x**3) - 42*x**2*39 + (54*x**3)*39\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*x**2)*39 = -1638*x**2\n (-42*x**2)*(8*x) = -336*x**3\n (54*x**3)*39 = 2106*x**3\n (54*x**3)*(8*x) = 432*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 432*x**4 - 336*x**3 + 2106*x**3 - 1638*x**2\nCombining like terms, got 432*x**4 + 1770*x**3 - 1638*x**2\n#Step 6:\nCurrent expression: 432*x**4 + 1770*x**3 - 1638*x**2\nNo more calculations needed.\n432*x**4 + 1770*x**3 - 1638*x**2", "generated_answer": "432*x**4 + 1770*x**3 - 1638*x**2", "step_length": 6} {"cot_id": "e0691a42f8db1789701c3248c0c473ce81c029cacef0342e3e42e2841cb9d50d", "datapoint": {"question": "Calculate the following: 54*y*(44*y - 53)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2376*y**2 - 2862*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1676, "polynomial_expr": "54*y*(44*y - 53)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 54*y*(44*y - 53)\nExpanding the part (44*y - 53) using the distributive property, and we got: -2862*y + (44*y)*(54*y)\n#Step 2:\nCurrent expression: -2862*y + (44*y)*(54*y)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -53*(54*y) = -2862*y\n (44*y)*(54*y) = 2376*y**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 2376*y**2 - 2862*y\nNo more calculations needed.\n2376*y**2 - 2862*y", "generated_answer": "2376*y**2 - 2862*y", "step_length": 3} {"cot_id": "6eebb2acf542b36ed79a7c4dddaa487ac1e6493938b69c4430557f24f514baa4", "datapoint": {"question": "Calculate the following: (33*z + 37)*(35*z**3 + 2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1155*z**4 + 1295*z**3 + 66*z + 74", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1677, "polynomial_expr": "(33*z + 37)*(35*z**3 + 2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (33*z + 37)*(35*z**3 + 2)\nExpanding the part (35*z**3 + 2) using the distributive property, and we got: (35*z**3)*(33*z + 37) + 2*(33*z + 37)\n#Step 2:\nCurrent expression: (35*z**3)*(33*z + 37) + 2*(33*z + 37)\nSimplifying the partial expression: 2*(33*z + 37)\nExpanding the part (33*z + 37) using the distributive property, and we got: (33*z)*2 + 37*2\nReplacing 2*(33*z + 37) with (33*z)*2 + 37*2 in the overall expression.\n#Step 3:\nCurrent expression: (33*z)*2 + (35*z**3)*(33*z + 37) + 74\nSimplifying the partial expression: (35*z**3)*(33*z + 37)\nExpanding the part (33*z + 37) using the distributive property, and we got: 37*(35*z**3) + (33*z)*(35*z**3)\nReplacing (35*z**3)*(33*z + 37) with 37*(35*z**3) + (33*z)*(35*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 37*35*z**3 + (33*z)*(35*z**3) + (33*z)*2 + 74\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (33*z)*2 = 66*z\n (33*z)*(35*z**3) = 1155*z**4\n 37*35*z**3 = 1295*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1155*z**4 + 1295*z**3 + 66*z + 74\nNo more calculations needed.\n1155*z**4 + 1295*z**3 + 66*z + 74", "generated_answer": "1155*z**4 + 1295*z**3 + 66*z + 74", "step_length": 5} {"cot_id": "63369ff3b8c8c34cfe729cf286e1e85457fdc13339cb84b26bb1bcb9b7117bdd", "datapoint": {"question": "Calculate the following: (8 - 15*y)*(2*y**3 - 36*y**2 + 40*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-30*y**4 + 556*y**3 - 888*y**2 + 320*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1678, "polynomial_expr": "(8 - 15*y)*(2*y**3 - 36*y**2 + 40*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (8 - 15*y)*(2*y**3 - 36*y**2 + 40*y)\nExpanding the part (8 - 15*y) using the distributive property, and we got: (-15*y)*(2*y**3 - 36*y**2 + 40*y) + 8*(2*y**3 - 36*y**2 + 40*y)\n#Step 2:\nCurrent expression: (-15*y)*(2*y**3 - 36*y**2 + 40*y) + 8*(2*y**3 - 36*y**2 + 40*y)\nSimplifying the partial expression: 8*(2*y**3 - 36*y**2 + 40*y)\nExpanding the part (2*y**3 - 36*y**2 + 40*y) using the distributive property, and we got: (40*y)*8 - 36*y**2*8 + (2*y**3)*8\nReplacing 8*(2*y**3 - 36*y**2 + 40*y) with (40*y)*8 - 36*y**2*8 + (2*y**3)*8 in the overall expression.\n#Step 3:\nCurrent expression: (-15*y)*(2*y**3 - 36*y**2 + 40*y) + (40*y)*8 - 36*y**2*8 + (2*y**3)*8\nSimplifying the partial expression: (-15*y)*(2*y**3 - 36*y**2 + 40*y)\nExpanding the part (2*y**3 - 36*y**2 + 40*y) using the distributive property, and we got: (-15*y)*(40*y) + (-15*y)*(-36*y**2) + (-15*y)*(2*y**3)\nReplacing (-15*y)*(2*y**3 - 36*y**2 + 40*y) with (-15*y)*(40*y) + (-15*y)*(-36*y**2) + (-15*y)*(2*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-15*y)*(40*y) + (-15*y)*(-36*y**2) + (-15*y)*(2*y**3) + (40*y)*8 - 36*y**2*8 + (2*y**3)*8\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*y**2)*8 = -288*y**2\n (-36*y**2)*(-15*y) = 540*y**3\n (2*y**3)*8 = 16*y**3\n (2*y**3)*(-15*y) = -30*y**4\n (40*y)*8 = 320*y\n (40*y)*(-15*y) = -600*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -30*y**4 + 16*y**3 + 540*y**3 - 600*y**2 - 288*y**2 + 320*y\nCombining like terms, got -30*y**4 + 556*y**3 - 888*y**2 + 320*y\n#Step 6:\nCurrent expression: -30*y**4 + 556*y**3 - 888*y**2 + 320*y\nNo more calculations needed.\n-30*y**4 + 556*y**3 - 888*y**2 + 320*y", "generated_answer": "-30*y**4 + 556*y**3 - 888*y**2 + 320*y", "step_length": 6} {"cot_id": "84f30361a3d664eb9227ddff2677c59565d6474605e317b21dc40da3916d5e18", "datapoint": {"question": "Calculate the following: (39*x**3 + 31*x**2)*(86*x**3 - x - 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "3354*x**6 + 2666*x**5 - 39*x**4 - 421*x**3 - 310*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1679, "polynomial_expr": "(39*x**3 + 31*x**2)*(86*x**3 - x - 10)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (39*x**3 + 31*x**2)*(86*x**3 - x - 10)\nExpanding the part (39*x**3 + 31*x**2) using the distributive property, and we got: (31*x**2)*(86*x**3 - x - 10) + (39*x**3)*(86*x**3 - x - 10)\n#Step 2:\nCurrent expression: (31*x**2)*(86*x**3 - x - 10) + (39*x**3)*(86*x**3 - x - 10)\nSimplifying the partial expression: (31*x**2)*(86*x**3 - x - 10)\nExpanding the part (86*x**3 - x - 10) using the distributive property, and we got: (-x)*(31*x**2) - 310*x**2 + (31*x**2)*(86*x**3)\nReplacing (31*x**2)*(86*x**3 - x - 10) with (-x)*(31*x**2) - 310*x**2 + (31*x**2)*(86*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-x)*(31*x**2) - 10*31*x**2 + (31*x**2)*(86*x**3) + (39*x**3)*(86*x**3 - x - 10)\nSimplifying the partial expression: (39*x**3)*(86*x**3 - x - 10)\nExpanding the part (86*x**3 - x - 10) using the distributive property, and we got: (-x)*(39*x**3) - 390*x**3 + (39*x**3)*(86*x**3)\nReplacing (39*x**3)*(86*x**3 - x - 10) with (-x)*(39*x**3) - 390*x**3 + (39*x**3)*(86*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-x)*(31*x**2) + (-x)*(39*x**3) - 10*39*x**3 - 10*31*x**2 + (31*x**2)*(86*x**3) + (39*x**3)*(86*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-x)*(31*x**2) = -31*x**3\n (-x)*(39*x**3) = -39*x**4\n (86*x**3)*(31*x**2) = 2666*x**5\n (86*x**3)*(39*x**3) = 3354*x**6\n -10*31*x**2 = -310*x**2\n -10*39*x**3 = -390*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 3354*x**6 + 2666*x**5 - 39*x**4 - 390*x**3 - 31*x**3 - 310*x**2\nCombining like terms, got 3354*x**6 + 2666*x**5 - 39*x**4 - 421*x**3 - 310*x**2\n#Step 6:\nCurrent expression: 3354*x**6 + 2666*x**5 - 39*x**4 - 421*x**3 - 310*x**2\nNo more calculations needed.\n3354*x**6 + 2666*x**5 - 39*x**4 - 421*x**3 - 310*x**2", "generated_answer": "3354*x**6 + 2666*x**5 - 39*x**4 - 421*x**3 - 310*x**2", "step_length": 6} {"cot_id": "46f366792fa439ae31636b06d75c29b300cc093133f248f71dbe3dcf89b10a20", "datapoint": {"question": "Simplify this expression: (-14*y**2 + 17*y)*(20*y**3 - 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-280*y**5 + 340*y**4 + 336*y**2 - 408*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1680, "polynomial_expr": "(-14*y**2 + 17*y)*(20*y**3 - 24)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-14*y**2 + 17*y)*(20*y**3 - 24)\nExpanding the part (20*y**3 - 24) using the distributive property, and we got: (20*y**3)*(-14*y**2 + 17*y) - 24*(-14*y**2 + 17*y)\n#Step 2:\nCurrent expression: (20*y**3)*(-14*y**2 + 17*y) - 24*(-14*y**2 + 17*y)\nSimplifying the partial expression: -24*(-14*y**2 + 17*y)\nExpanding the part (-14*y**2 + 17*y) using the distributive property, and we got: (17*y)*(-24) - 14*y**2*(-24)\nReplacing -24*(-14*y**2 + 17*y) with (17*y)*(-24) - 14*y**2*(-24) in the overall expression.\n#Step 3:\nCurrent expression: (17*y)*(-24) - 14*y**2*(-24) + (20*y**3)*(-14*y**2 + 17*y)\nSimplifying the partial expression: (20*y**3)*(-14*y**2 + 17*y)\nExpanding the part (-14*y**2 + 17*y) using the distributive property, and we got: (17*y)*(20*y**3) + (-14*y**2)*(20*y**3)\nReplacing (20*y**3)*(-14*y**2 + 17*y) with (17*y)*(20*y**3) + (-14*y**2)*(20*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (17*y)*(20*y**3) + (17*y)*(-24) + (-14*y**2)*(20*y**3) - 14*y**2*(-24)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-14*y**2)*-24 = 336*y**2\n (-14*y**2)*(20*y**3) = -280*y**5\n (17*y)*-24 = -408*y\n (17*y)*(20*y**3) = 340*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -280*y**5 + 340*y**4 + 336*y**2 - 408*y\nNo more calculations needed.\n-280*y**5 + 340*y**4 + 336*y**2 - 408*y", "generated_answer": "-280*y**5 + 340*y**4 + 336*y**2 - 408*y", "step_length": 5} {"cot_id": "6f0092c69eb25d94e139fe05f8c96405d41aca2140614d54d131c7b5c8fedf70", "datapoint": {"question": "Simplify this expression: (15*y**2 - 43*y)*(43*y**3 - 6*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "645*y**5 - 1849*y**4 - 90*y**3 + 258*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1681, "polynomial_expr": "(15*y**2 - 43*y)*(43*y**3 - 6*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (15*y**2 - 43*y)*(43*y**3 - 6*y)\nExpanding the part (15*y**2 - 43*y) using the distributive property, and we got: (-43*y)*(43*y**3 - 6*y) + (15*y**2)*(43*y**3 - 6*y)\n#Step 2:\nCurrent expression: (-43*y)*(43*y**3 - 6*y) + (15*y**2)*(43*y**3 - 6*y)\nSimplifying the partial expression: (-43*y)*(43*y**3 - 6*y)\nExpanding the part (43*y**3 - 6*y) using the distributive property, and we got: (-43*y)*(-6*y) + (-43*y)*(43*y**3)\nReplacing (-43*y)*(43*y**3 - 6*y) with (-43*y)*(-6*y) + (-43*y)*(43*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-43*y)*(-6*y) + (-43*y)*(43*y**3) + (15*y**2)*(43*y**3 - 6*y)\nSimplifying the partial expression: (15*y**2)*(43*y**3 - 6*y)\nExpanding the part (43*y**3 - 6*y) using the distributive property, and we got: (-6*y)*(15*y**2) + (15*y**2)*(43*y**3)\nReplacing (15*y**2)*(43*y**3 - 6*y) with (-6*y)*(15*y**2) + (15*y**2)*(43*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-43*y)*(-6*y) + (-43*y)*(43*y**3) + (-6*y)*(15*y**2) + (15*y**2)*(43*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-6*y)*(-43*y) = 258*y**2\n (-6*y)*(15*y**2) = -90*y**3\n (43*y**3)*(-43*y) = -1849*y**4\n (43*y**3)*(15*y**2) = 645*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 645*y**5 - 1849*y**4 - 90*y**3 + 258*y**2\nNo more calculations needed.\n645*y**5 - 1849*y**4 - 90*y**3 + 258*y**2", "generated_answer": "645*y**5 - 1849*y**4 - 90*y**3 + 258*y**2", "step_length": 5} {"cot_id": "4cb6444a5e37501ac9c9b904c071c95ea10ca790bf89429f723eae9a16eb6678", "datapoint": {"question": "Simplify this expression: (8 - 36*x)*(2*x**2 + 42*x + 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-72*x**3 - 1496*x**2 - 240*x + 128", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1682, "polynomial_expr": "(8 - 36*x)*(2*x**2 + 42*x + 16)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (8 - 36*x)*(2*x**2 + 42*x + 16)\nExpanding the part (8 - 36*x) using the distributive property, and we got: (-36*x)*(2*x**2 + 42*x + 16) + 8*(2*x**2 + 42*x + 16)\n#Step 2:\nCurrent expression: (-36*x)*(2*x**2 + 42*x + 16) + 8*(2*x**2 + 42*x + 16)\nSimplifying the partial expression: 8*(2*x**2 + 42*x + 16)\nExpanding the part (2*x**2 + 42*x + 16) using the distributive property, and we got: (42*x)*8 + (2*x**2)*8 + 16*8\nReplacing 8*(2*x**2 + 42*x + 16) with (42*x)*8 + (2*x**2)*8 + 16*8 in the overall expression.\n#Step 3:\nCurrent expression: (-36*x)*(2*x**2 + 42*x + 16) + (42*x)*8 + (2*x**2)*8 + 128\nSimplifying the partial expression: (-36*x)*(2*x**2 + 42*x + 16)\nExpanding the part (2*x**2 + 42*x + 16) using the distributive property, and we got: (-36*x)*(42*x) + (-36*x)*(2*x**2) + 16*(-36*x)\nReplacing (-36*x)*(2*x**2 + 42*x + 16) with (-36*x)*(42*x) + (-36*x)*(2*x**2) + 16*(-36*x) in the overall expression.\n#Step 4:\nCurrent expression: (-36*x)*(42*x) + (-36*x)*(2*x**2) + 16*(-36)*x + (42*x)*8 + (2*x**2)*8 + 128\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (2*x**2)*8 = 16*x**2\n (2*x**2)*(-36*x) = -72*x**3\n (42*x)*8 = 336*x\n (42*x)*(-36*x) = -1512*x**2\n 16*-36*x = -576*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -72*x**3 - 1512*x**2 + 16*x**2 - 576*x + 336*x + 128\nCombining like terms, got -72*x**3 - 1496*x**2 - 240*x + 128\n#Step 6:\nCurrent expression: -72*x**3 - 1496*x**2 - 240*x + 128\nNo more calculations needed.\n-72*x**3 - 1496*x**2 - 240*x + 128", "generated_answer": "-72*x**3 - 1496*x**2 - 240*x + 128", "step_length": 6} {"cot_id": "1b000726be1c4cff753c5e68ef1f7349e441735a5761d20c6e722cd1727fb61f", "datapoint": {"question": "Calculate the following: (-46*y**3 - 6)*(15*y**3 - 23*y**2 - 14*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-690*y**6 + 1058*y**5 + 644*y**4 - 90*y**3 + 138*y**2 + 84*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1683, "polynomial_expr": "(-46*y**3 - 6)*(15*y**3 - 23*y**2 - 14*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-46*y**3 - 6)*(15*y**3 - 23*y**2 - 14*y)\nExpanding the part (-46*y**3 - 6) using the distributive property, and we got: (-46*y**3)*(15*y**3 - 23*y**2 - 14*y) - 6*(15*y**3 - 23*y**2 - 14*y)\n#Step 2:\nCurrent expression: (-46*y**3)*(15*y**3 - 23*y**2 - 14*y) - 6*(15*y**3 - 23*y**2 - 14*y)\nSimplifying the partial expression: -6*(15*y**3 - 23*y**2 - 14*y)\nExpanding the part (15*y**3 - 23*y**2 - 14*y) using the distributive property, and we got: -14*y*(-6) - 23*y**2*(-6) + (15*y**3)*(-6)\nReplacing -6*(15*y**3 - 23*y**2 - 14*y) with -14*y*(-6) - 23*y**2*(-6) + (15*y**3)*(-6) in the overall expression.\n#Step 3:\nCurrent expression: -14*y*(-6) - 23*y**2*(-6) + (-46*y**3)*(15*y**3 - 23*y**2 - 14*y) + (15*y**3)*(-6)\nSimplifying the partial expression: (-46*y**3)*(15*y**3 - 23*y**2 - 14*y)\nExpanding the part (15*y**3 - 23*y**2 - 14*y) using the distributive property, and we got: (-14*y)*(-46*y**3) + (-23*y**2)*(-46*y**3) + (-46*y**3)*(15*y**3)\nReplacing (-46*y**3)*(15*y**3 - 23*y**2 - 14*y) with (-14*y)*(-46*y**3) + (-23*y**2)*(-46*y**3) + (-46*y**3)*(15*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-14*y)*(-46*y**3) - 14*y*(-6) + (-23*y**2)*(-46*y**3) - 23*y**2*(-6) + (-46*y**3)*(15*y**3) + (15*y**3)*(-6)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*y**2)*-6 = 138*y**2\n (-23*y**2)*(-46*y**3) = 1058*y**5\n (-14*y)*-6 = 84*y\n (-14*y)*(-46*y**3) = 644*y**4\n (15*y**3)*-6 = -90*y**3\n (15*y**3)*(-46*y**3) = -690*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -690*y**6 + 1058*y**5 + 644*y**4 - 90*y**3 + 138*y**2 + 84*y\nNo more calculations needed.\n-690*y**6 + 1058*y**5 + 644*y**4 - 90*y**3 + 138*y**2 + 84*y", "generated_answer": "-690*y**6 + 1058*y**5 + 644*y**4 - 90*y**3 + 138*y**2 + 84*y", "step_length": 5} {"cot_id": "ede0007f112a40dfbca3cd797bf900739490e28b28c3fb5a4f02c866db5b73d2", "datapoint": {"question": "Calculate the following: (-32*x**3 + 39*x**2)*(40*x**3 - 37*x**2 + 22*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1280*x**6 + 2744*x**5 - 2147*x**4 + 858*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1684, "polynomial_expr": "(-32*x**3 + 39*x**2)*(40*x**3 - 37*x**2 + 22*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-32*x**3 + 39*x**2)*(40*x**3 - 37*x**2 + 22*x)\nExpanding the part (-32*x**3 + 39*x**2) using the distributive property, and we got: (39*x**2)*(40*x**3 - 37*x**2 + 22*x) + (-32*x**3)*(40*x**3 - 37*x**2 + 22*x)\n#Step 2:\nCurrent expression: (39*x**2)*(40*x**3 - 37*x**2 + 22*x) + (-32*x**3)*(40*x**3 - 37*x**2 + 22*x)\nSimplifying the partial expression: (-32*x**3)*(40*x**3 - 37*x**2 + 22*x)\nExpanding the part (40*x**3 - 37*x**2 + 22*x) using the distributive property, and we got: (22*x)*(-32*x**3) + (-37*x**2)*(-32*x**3) + (-32*x**3)*(40*x**3)\nReplacing (-32*x**3)*(40*x**3 - 37*x**2 + 22*x) with (22*x)*(-32*x**3) + (-37*x**2)*(-32*x**3) + (-32*x**3)*(40*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (22*x)*(-32*x**3) + (-37*x**2)*(-32*x**3) + (39*x**2)*(40*x**3 - 37*x**2 + 22*x) + (-32*x**3)*(40*x**3)\nSimplifying the partial expression: (39*x**2)*(40*x**3 - 37*x**2 + 22*x)\nExpanding the part (40*x**3 - 37*x**2 + 22*x) using the distributive property, and we got: (22*x)*(39*x**2) + (-37*x**2)*(39*x**2) + (39*x**2)*(40*x**3)\nReplacing (39*x**2)*(40*x**3 - 37*x**2 + 22*x) with (22*x)*(39*x**2) + (-37*x**2)*(39*x**2) + (39*x**2)*(40*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (22*x)*(39*x**2) + (22*x)*(-32*x**3) + (-37*x**2)*(39*x**2) + (-37*x**2)*(-32*x**3) + (39*x**2)*(40*x**3) + (-32*x**3)*(40*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*x**2)*(-32*x**3) = 1184*x**5\n (-37*x**2)*(39*x**2) = -1443*x**4\n (22*x)*(-32*x**3) = -704*x**4\n (22*x)*(39*x**2) = 858*x**3\n (40*x**3)*(-32*x**3) = -1280*x**6\n (40*x**3)*(39*x**2) = 1560*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1280*x**6 + 1184*x**5 + 1560*x**5 - 1443*x**4 - 704*x**4 + 858*x**3\nCombining like terms, got -1280*x**6 + 2744*x**5 - 2147*x**4 + 858*x**3\n#Step 6:\nCurrent expression: -1280*x**6 + 2744*x**5 - 2147*x**4 + 858*x**3\nNo more calculations needed.\n-1280*x**6 + 2744*x**5 - 2147*x**4 + 858*x**3", "generated_answer": "-1280*x**6 + 2744*x**5 - 2147*x**4 + 858*x**3", "step_length": 6} {"cot_id": "5bcec4c97221b25600f0f3e870815d59fc11ffdae5dd010322fe8d4cea473fd6", "datapoint": {"question": "Calculate the following: (-4*z**3 - 34*z**2 - 40)*(62*z**3 - 40*z**2 + 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-248*z**6 - 1948*z**5 + 1360*z**4 - 2624*z**3 + 376*z**2 - 1440", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1685, "polynomial_expr": "(-4*z**3 - 34*z**2 - 40)*(62*z**3 - 40*z**2 + 36)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-4*z**3 - 34*z**2 - 40)*(62*z**3 - 40*z**2 + 36)\nExpanding the part (-4*z**3 - 34*z**2 - 40) using the distributive property, and we got: (-34*z**2)*(62*z**3 - 40*z**2 + 36) + (-4*z**3)*(62*z**3 - 40*z**2 + 36) - 40*(62*z**3 - 40*z**2 + 36)\n#Step 2:\nCurrent expression: (-34*z**2)*(62*z**3 - 40*z**2 + 36) + (-4*z**3)*(62*z**3 - 40*z**2 + 36) - 40*(62*z**3 - 40*z**2 + 36)\nSimplifying the partial expression: -40*(62*z**3 - 40*z**2 + 36)\nExpanding the part (62*z**3 - 40*z**2 + 36) using the distributive property, and we got: -40*z**2*(-40) + (62*z**3)*(-40) + 36*(-40)\nReplacing -40*(62*z**3 - 40*z**2 + 36) with -40*z**2*(-40) + (62*z**3)*(-40) + 36*(-40) in the overall expression.\n#Step 3:\nCurrent expression: -40*z**2*(-40) + (-34*z**2)*(62*z**3 - 40*z**2 + 36) + (-4*z**3)*(62*z**3 - 40*z**2 + 36) + (62*z**3)*(-40) - 1440\nSimplifying the partial expression: (-34*z**2)*(62*z**3 - 40*z**2 + 36)\nExpanding the part (62*z**3 - 40*z**2 + 36) using the distributive property, and we got: 36*(-34*z**2) + (-40*z**2)*(-34*z**2) + (-34*z**2)*(62*z**3)\nReplacing (-34*z**2)*(62*z**3 - 40*z**2 + 36) with 36*(-34*z**2) + (-40*z**2)*(-34*z**2) + (-34*z**2)*(62*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 36*(-34)*z**2 + (-40*z**2)*(-34*z**2) - 40*z**2*(-40) + (-34*z**2)*(62*z**3) + (-4*z**3)*(62*z**3 - 40*z**2 + 36) + (62*z**3)*(-40) - 1440\nSimplifying the partial expression: (-4*z**3)*(62*z**3 - 40*z**2 + 36)\nExpanding the part (62*z**3 - 40*z**2 + 36) using the distributive property, and we got: 36*(-4*z**3) + (-40*z**2)*(-4*z**3) + (-4*z**3)*(62*z**3)\nReplacing (-4*z**3)*(62*z**3 - 40*z**2 + 36) with 36*(-4*z**3) + (-40*z**2)*(-4*z**3) + (-4*z**3)*(62*z**3) in the overall expression.\n#Step 5:\nCurrent expression: 36*(-4)*z**3 + 36*(-34)*z**2 + (-40*z**2)*(-34*z**2) + (-40*z**2)*(-4*z**3) - 40*z**2*(-40) + (-34*z**2)*(62*z**3) + (-4*z**3)*(62*z**3) + (62*z**3)*(-40) - 1440\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*z**2)*-40 = 1600*z**2\n (-40*z**2)*(-34*z**2) = 1360*z**4\n (-40*z**2)*(-4*z**3) = 160*z**5\n (62*z**3)*-40 = -2480*z**3\n (62*z**3)*(-34*z**2) = -2108*z**5\n (62*z**3)*(-4*z**3) = -248*z**6\n 36*-34*z**2 = -1224*z**2\n 36*-4*z**3 = -144*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -248*z**6 - 2108*z**5 + 160*z**5 + 1360*z**4 - 2480*z**3 - 144*z**3 - 1224*z**2 + 1600*z**2 - 1440\nCombining like terms, got -248*z**6 - 1948*z**5 + 1360*z**4 - 2624*z**3 + 376*z**2 - 1440\n#Step 7:\nCurrent expression: -248*z**6 - 1948*z**5 + 1360*z**4 - 2624*z**3 + 376*z**2 - 1440\nNo more calculations needed.\n-248*z**6 - 1948*z**5 + 1360*z**4 - 2624*z**3 + 376*z**2 - 1440", "generated_answer": "-248*z**6 - 1948*z**5 + 1360*z**4 - 2624*z**3 + 376*z**2 - 1440", "step_length": 7} {"cot_id": "95526a95bc68a91b479897c053c11d3486ba9ae3ddf5d7250fdb4978fdbbb751", "datapoint": {"question": "Simplify this expression: (-65*y**3 + 35*y)*(31*y**3 - 35*y**2 + 22*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2015*y**6 + 2275*y**5 - 345*y**4 - 1225*y**3 + 770*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1686, "polynomial_expr": "(-65*y**3 + 35*y)*(31*y**3 - 35*y**2 + 22*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-65*y**3 + 35*y)*(31*y**3 - 35*y**2 + 22*y)\nExpanding the part (-65*y**3 + 35*y) using the distributive property, and we got: (35*y)*(31*y**3 - 35*y**2 + 22*y) + (-65*y**3)*(31*y**3 - 35*y**2 + 22*y)\n#Step 2:\nCurrent expression: (35*y)*(31*y**3 - 35*y**2 + 22*y) + (-65*y**3)*(31*y**3 - 35*y**2 + 22*y)\nSimplifying the partial expression: (-65*y**3)*(31*y**3 - 35*y**2 + 22*y)\nExpanding the part (31*y**3 - 35*y**2 + 22*y) using the distributive property, and we got: (22*y)*(-65*y**3) + (-35*y**2)*(-65*y**3) + (-65*y**3)*(31*y**3)\nReplacing (-65*y**3)*(31*y**3 - 35*y**2 + 22*y) with (22*y)*(-65*y**3) + (-35*y**2)*(-65*y**3) + (-65*y**3)*(31*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (22*y)*(-65*y**3) + (35*y)*(31*y**3 - 35*y**2 + 22*y) + (-35*y**2)*(-65*y**3) + (-65*y**3)*(31*y**3)\nSimplifying the partial expression: (35*y)*(31*y**3 - 35*y**2 + 22*y)\nExpanding the part (31*y**3 - 35*y**2 + 22*y) using the distributive property, and we got: (22*y)*(35*y) + (35*y)*(-35*y**2) + (35*y)*(31*y**3)\nReplacing (35*y)*(31*y**3 - 35*y**2 + 22*y) with (22*y)*(35*y) + (35*y)*(-35*y**2) + (35*y)*(31*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (22*y)*(35*y) + (22*y)*(-65*y**3) + (35*y)*(-35*y**2) + (35*y)*(31*y**3) + (-35*y**2)*(-65*y**3) + (-65*y**3)*(31*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*y**2)*(-65*y**3) = 2275*y**5\n (-35*y**2)*(35*y) = -1225*y**3\n (22*y)*(-65*y**3) = -1430*y**4\n (22*y)*(35*y) = 770*y**2\n (31*y**3)*(-65*y**3) = -2015*y**6\n (31*y**3)*(35*y) = 1085*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2015*y**6 + 2275*y**5 - 1430*y**4 + 1085*y**4 - 1225*y**3 + 770*y**2\nCombining like terms, got -2015*y**6 + 2275*y**5 - 345*y**4 - 1225*y**3 + 770*y**2\n#Step 6:\nCurrent expression: -2015*y**6 + 2275*y**5 - 345*y**4 - 1225*y**3 + 770*y**2\nNo more calculations needed.\n-2015*y**6 + 2275*y**5 - 345*y**4 - 1225*y**3 + 770*y**2", "generated_answer": "-2015*y**6 + 2275*y**5 - 345*y**4 - 1225*y**3 + 770*y**2", "step_length": 6} {"cot_id": "ec40b3de0b9a01203a315ef0eb1e1e401204f8eb9e36d4cf41681edf1b8774c0", "datapoint": {"question": "Calculate the following: (-36*z**2 - 30*z + 14)*(-33*z**2 + 34*z + 4)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1188*z**4 - 234*z**3 - 1626*z**2 + 356*z + 56", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1687, "polynomial_expr": "(-36*z**2 - 30*z + 14)*(-33*z**2 + 34*z + 4)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-36*z**2 - 30*z + 14)*(-33*z**2 + 34*z + 4)\nExpanding the part (-33*z**2 + 34*z + 4) using the distributive property, and we got: (34*z)*(-36*z**2 - 30*z + 14) + (-33*z**2)*(-36*z**2 - 30*z + 14) + 4*(-36*z**2 - 30*z + 14)\n#Step 2:\nCurrent expression: (34*z)*(-36*z**2 - 30*z + 14) + (-33*z**2)*(-36*z**2 - 30*z + 14) + 4*(-36*z**2 - 30*z + 14)\nSimplifying the partial expression: 4*(-36*z**2 - 30*z + 14)\nExpanding the part (-36*z**2 - 30*z + 14) using the distributive property, and we got: -30*z*4 - 36*z**2*4 + 14*4\nReplacing 4*(-36*z**2 - 30*z + 14) with -30*z*4 - 36*z**2*4 + 14*4 in the overall expression.\n#Step 3:\nCurrent expression: -30*z*4 + (34*z)*(-36*z**2 - 30*z + 14) - 36*z**2*4 + (-33*z**2)*(-36*z**2 - 30*z + 14) + 56\nSimplifying the partial expression: (-33*z**2)*(-36*z**2 - 30*z + 14)\nExpanding the part (-36*z**2 - 30*z + 14) using the distributive property, and we got: (-30*z)*(-33*z**2) + 14*(-33*z**2) + (-36*z**2)*(-33*z**2)\nReplacing (-33*z**2)*(-36*z**2 - 30*z + 14) with (-30*z)*(-33*z**2) + 14*(-33*z**2) + (-36*z**2)*(-33*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-30*z)*(-33*z**2) - 30*z*4 + 14*(-33)*z**2 + (34*z)*(-36*z**2 - 30*z + 14) + (-36*z**2)*(-33*z**2) - 36*z**2*4 + 56\nSimplifying the partial expression: (34*z)*(-36*z**2 - 30*z + 14)\nExpanding the part (-36*z**2 - 30*z + 14) using the distributive property, and we got: (-30*z)*(34*z) + 14*(34*z) + (34*z)*(-36*z**2)\nReplacing (34*z)*(-36*z**2 - 30*z + 14) with (-30*z)*(34*z) + 14*(34*z) + (34*z)*(-36*z**2) in the overall expression.\n#Step 5:\nCurrent expression: (-30*z)*(34*z) + (-30*z)*(-33*z**2) - 30*z*4 + 14*(-33)*z**2 + 14*34*z + (34*z)*(-36*z**2) + (-36*z**2)*(-33*z**2) - 36*z**2*4 + 56\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*z**2)*4 = -144*z**2\n (-36*z**2)*(-33*z**2) = 1188*z**4\n (-36*z**2)*(34*z) = -1224*z**3\n (-30*z)*4 = -120*z\n (-30*z)*(-33*z**2) = 990*z**3\n (-30*z)*(34*z) = -1020*z**2\n 14*-33*z**2 = -462*z**2\n 14*34*z = 476*z\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1188*z**4 - 1224*z**3 + 990*z**3 - 1020*z**2 - 462*z**2 - 144*z**2 - 120*z + 476*z + 56\nCombining like terms, got 1188*z**4 - 234*z**3 - 1626*z**2 + 356*z + 56\n#Step 7:\nCurrent expression: 1188*z**4 - 234*z**3 - 1626*z**2 + 356*z + 56\nNo more calculations needed.\n1188*z**4 - 234*z**3 - 1626*z**2 + 356*z + 56", "generated_answer": "1188*z**4 - 234*z**3 - 1626*z**2 + 356*z + 56", "step_length": 7} {"cot_id": "4d5151bf2bdcb14f8ca28aa8886c7393f367eeab80e0a57d8f503687b64ab735", "datapoint": {"question": "Simplify this expression: (33*x**3 + 5)*(-20*x**3 - 8*x - 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-660*x**6 - 264*x**4 - 1717*x**3 - 40*x - 245", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1688, "polynomial_expr": "(33*x**3 + 5)*(-20*x**3 - 8*x - 49)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (33*x**3 + 5)*(-20*x**3 - 8*x - 49)\nExpanding the part (33*x**3 + 5) using the distributive property, and we got: (33*x**3)*(-20*x**3 - 8*x - 49) + 5*(-20*x**3 - 8*x - 49)\n#Step 2:\nCurrent expression: (33*x**3)*(-20*x**3 - 8*x - 49) + 5*(-20*x**3 - 8*x - 49)\nSimplifying the partial expression: 5*(-20*x**3 - 8*x - 49)\nExpanding the part (-20*x**3 - 8*x - 49) using the distributive property, and we got: -8*x*5 - 20*x**3*5 - 49*5\nReplacing 5*(-20*x**3 - 8*x - 49) with -8*x*5 - 20*x**3*5 - 49*5 in the overall expression.\n#Step 3:\nCurrent expression: -8*x*5 - 20*x**3*5 + (33*x**3)*(-20*x**3 - 8*x - 49) - 245\nSimplifying the partial expression: (33*x**3)*(-20*x**3 - 8*x - 49)\nExpanding the part (-20*x**3 - 8*x - 49) using the distributive property, and we got: (-8*x)*(33*x**3) - 1617*x**3 + (-20*x**3)*(33*x**3)\nReplacing (33*x**3)*(-20*x**3 - 8*x - 49) with (-8*x)*(33*x**3) - 1617*x**3 + (-20*x**3)*(33*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-8*x)*(33*x**3) - 8*x*5 - 49*33*x**3 + (-20*x**3)*(33*x**3) - 20*x**3*5 - 245\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*x**3)*5 = -100*x**3\n (-20*x**3)*(33*x**3) = -660*x**6\n (-8*x)*5 = -40*x\n (-8*x)*(33*x**3) = -264*x**4\n -49*33*x**3 = -1617*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -660*x**6 - 264*x**4 - 1617*x**3 - 100*x**3 - 40*x - 245\nCombining like terms, got -660*x**6 - 264*x**4 - 1717*x**3 - 40*x - 245\n#Step 6:\nCurrent expression: -660*x**6 - 264*x**4 - 1717*x**3 - 40*x - 245\nNo more calculations needed.\n-660*x**6 - 264*x**4 - 1717*x**3 - 40*x - 245", "generated_answer": "-660*x**6 - 264*x**4 - 1717*x**3 - 40*x - 245", "step_length": 6} {"cot_id": "fdd6e546721fd2a313f7f6cb305bf5a0abf51eedc46ec66cdcaf4ba391e311fd", "datapoint": {"question": "Calculate the following: (11*y**2 - 34)*(4*y**3 + 52*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "44*y**5 + 572*y**4 - 136*y**3 - 1768*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1689, "polynomial_expr": "(11*y**2 - 34)*(4*y**3 + 52*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11*y**2 - 34)*(4*y**3 + 52*y**2)\nExpanding the part (11*y**2 - 34) using the distributive property, and we got: (11*y**2)*(4*y**3 + 52*y**2) - 34*(4*y**3 + 52*y**2)\n#Step 2:\nCurrent expression: (11*y**2)*(4*y**3 + 52*y**2) - 34*(4*y**3 + 52*y**2)\nSimplifying the partial expression: -34*(4*y**3 + 52*y**2)\nExpanding the part (4*y**3 + 52*y**2) using the distributive property, and we got: (52*y**2)*(-34) + (4*y**3)*(-34)\nReplacing -34*(4*y**3 + 52*y**2) with (52*y**2)*(-34) + (4*y**3)*(-34) in the overall expression.\n#Step 3:\nCurrent expression: (11*y**2)*(4*y**3 + 52*y**2) + (52*y**2)*(-34) + (4*y**3)*(-34)\nSimplifying the partial expression: (11*y**2)*(4*y**3 + 52*y**2)\nExpanding the part (4*y**3 + 52*y**2) using the distributive property, and we got: (11*y**2)*(52*y**2) + (11*y**2)*(4*y**3)\nReplacing (11*y**2)*(4*y**3 + 52*y**2) with (11*y**2)*(52*y**2) + (11*y**2)*(4*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (11*y**2)*(52*y**2) + (11*y**2)*(4*y**3) + (52*y**2)*(-34) + (4*y**3)*(-34)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (4*y**3)*-34 = -136*y**3\n (4*y**3)*(11*y**2) = 44*y**5\n (52*y**2)*-34 = -1768*y**2\n (52*y**2)*(11*y**2) = 572*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 44*y**5 + 572*y**4 - 136*y**3 - 1768*y**2\nNo more calculations needed.\n44*y**5 + 572*y**4 - 136*y**3 - 1768*y**2", "generated_answer": "44*y**5 + 572*y**4 - 136*y**3 - 1768*y**2", "step_length": 5} {"cot_id": "f6aa9786377e1fbc8c5426c6b003db0e3e41ac2e17a4057bc93ff8d30418772a", "datapoint": {"question": "Calculate the following: -2548*x**3 + 539*x**2\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2548*x**3 + 539*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1690, "polynomial_expr": "-2548*x**3 + 539*x**2", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -2548*x**3 + 539*x**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -2548*x**3 + 539*x**2\nNo more calculations needed.\n-2548*x**3 + 539*x**2", "generated_answer": "-2548*x**3 + 539*x**2", "step_length": 2} {"cot_id": "04fab2258dfeafcb6c9b9c52bfec98b705a4bac7b8a89b42c2d5f657144a4c68", "datapoint": {"question": "Simplify this expression: (9*x + 3)*(25*x**2 + 50*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "225*x**3 + 525*x**2 + 150*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1691, "polynomial_expr": "(9*x + 3)*(25*x**2 + 50*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9*x + 3)*(25*x**2 + 50*x)\nExpanding the part (9*x + 3) using the distributive property, and we got: (9*x)*(25*x**2 + 50*x) + 3*(25*x**2 + 50*x)\n#Step 2:\nCurrent expression: (9*x)*(25*x**2 + 50*x) + 3*(25*x**2 + 50*x)\nSimplifying the partial expression: 3*(25*x**2 + 50*x)\nExpanding the part (25*x**2 + 50*x) using the distributive property, and we got: (50*x)*3 + (25*x**2)*3\nReplacing 3*(25*x**2 + 50*x) with (50*x)*3 + (25*x**2)*3 in the overall expression.\n#Step 3:\nCurrent expression: (9*x)*(25*x**2 + 50*x) + (50*x)*3 + (25*x**2)*3\nSimplifying the partial expression: (9*x)*(25*x**2 + 50*x)\nExpanding the part (25*x**2 + 50*x) using the distributive property, and we got: (9*x)*(50*x) + (9*x)*(25*x**2)\nReplacing (9*x)*(25*x**2 + 50*x) with (9*x)*(50*x) + (9*x)*(25*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (9*x)*(50*x) + (9*x)*(25*x**2) + (50*x)*3 + (25*x**2)*3\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (25*x**2)*3 = 75*x**2\n (25*x**2)*(9*x) = 225*x**3\n (50*x)*3 = 150*x\n (50*x)*(9*x) = 450*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 225*x**3 + 75*x**2 + 450*x**2 + 150*x\nCombining like terms, got 225*x**3 + 525*x**2 + 150*x\n#Step 6:\nCurrent expression: 225*x**3 + 525*x**2 + 150*x\nNo more calculations needed.\n225*x**3 + 525*x**2 + 150*x", "generated_answer": "225*x**3 + 525*x**2 + 150*x", "step_length": 6} {"cot_id": "52cb1effb5c5eda439017d373c95866fa8c016fd605bc26835241bd6cb2d40ad", "datapoint": {"question": "Calculate the following: (25 - 4*x**3)*(-4*x**3 + 43*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "16*x**6 - 172*x**5 - 100*x**3 + 1075*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1692, "polynomial_expr": "(25 - 4*x**3)*(-4*x**3 + 43*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (25 - 4*x**3)*(-4*x**3 + 43*x**2)\nExpanding the part (25 - 4*x**3) using the distributive property, and we got: (-4*x**3)*(-4*x**3 + 43*x**2) + 25*(-4*x**3 + 43*x**2)\n#Step 2:\nCurrent expression: (-4*x**3)*(-4*x**3 + 43*x**2) + 25*(-4*x**3 + 43*x**2)\nSimplifying the partial expression: 25*(-4*x**3 + 43*x**2)\nExpanding the part (-4*x**3 + 43*x**2) using the distributive property, and we got: (43*x**2)*25 - 4*x**3*25\nReplacing 25*(-4*x**3 + 43*x**2) with (43*x**2)*25 - 4*x**3*25 in the overall expression.\n#Step 3:\nCurrent expression: (43*x**2)*25 + (-4*x**3)*(-4*x**3 + 43*x**2) - 4*x**3*25\nSimplifying the partial expression: (-4*x**3)*(-4*x**3 + 43*x**2)\nExpanding the part (-4*x**3 + 43*x**2) using the distributive property, and we got: (43*x**2)*(-4*x**3) + (-4*x**3)*(-4*x**3)\nReplacing (-4*x**3)*(-4*x**3 + 43*x**2) with (43*x**2)*(-4*x**3) + (-4*x**3)*(-4*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (43*x**2)*(-4*x**3) + (43*x**2)*25 + (-4*x**3)*(-4*x**3) - 4*x**3*25\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-4*x**3)*25 = -100*x**3\n (-4*x**3)*(-4*x**3) = 16*x**6\n (43*x**2)*25 = 1075*x**2\n (43*x**2)*(-4*x**3) = -172*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 16*x**6 - 172*x**5 - 100*x**3 + 1075*x**2\nNo more calculations needed.\n16*x**6 - 172*x**5 - 100*x**3 + 1075*x**2", "generated_answer": "16*x**6 - 172*x**5 - 100*x**3 + 1075*x**2", "step_length": 5} {"cot_id": "1348846cd48ce63c8ac3f7e26c19930f5179819fe1bb29780e3a374a0c5d7d6b", "datapoint": {"question": "Calculate the following: (-8*y**3 - 71*y**2)*(-6*y**3 - 37*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "48*y**6 + 426*y**5 + 296*y**4 + 2627*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1693, "polynomial_expr": "(-8*y**3 - 71*y**2)*(-6*y**3 - 37*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-8*y**3 - 71*y**2)*(-6*y**3 - 37*y)\nExpanding the part (-8*y**3 - 71*y**2) using the distributive property, and we got: (-71*y**2)*(-6*y**3 - 37*y) + (-8*y**3)*(-6*y**3 - 37*y)\n#Step 2:\nCurrent expression: (-71*y**2)*(-6*y**3 - 37*y) + (-8*y**3)*(-6*y**3 - 37*y)\nSimplifying the partial expression: (-71*y**2)*(-6*y**3 - 37*y)\nExpanding the part (-6*y**3 - 37*y) using the distributive property, and we got: (-37*y)*(-71*y**2) + (-71*y**2)*(-6*y**3)\nReplacing (-71*y**2)*(-6*y**3 - 37*y) with (-37*y)*(-71*y**2) + (-71*y**2)*(-6*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-37*y)*(-71*y**2) + (-71*y**2)*(-6*y**3) + (-8*y**3)*(-6*y**3 - 37*y)\nSimplifying the partial expression: (-8*y**3)*(-6*y**3 - 37*y)\nExpanding the part (-6*y**3 - 37*y) using the distributive property, and we got: (-37*y)*(-8*y**3) + (-8*y**3)*(-6*y**3)\nReplacing (-8*y**3)*(-6*y**3 - 37*y) with (-37*y)*(-8*y**3) + (-8*y**3)*(-6*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-37*y)*(-71*y**2) + (-37*y)*(-8*y**3) + (-71*y**2)*(-6*y**3) + (-8*y**3)*(-6*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*y)*(-71*y**2) = 2627*y**3\n (-37*y)*(-8*y**3) = 296*y**4\n (-6*y**3)*(-71*y**2) = 426*y**5\n (-6*y**3)*(-8*y**3) = 48*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 48*y**6 + 426*y**5 + 296*y**4 + 2627*y**3\nNo more calculations needed.\n48*y**6 + 426*y**5 + 296*y**4 + 2627*y**3", "generated_answer": "48*y**6 + 426*y**5 + 296*y**4 + 2627*y**3", "step_length": 5} {"cot_id": "cb41fcdb3ba2f8d1ff425c6fb8c56c17d7d895ea2087c5ef75eb0d30454890ee", "datapoint": {"question": "Simplify this expression: (7*x**3 - 36)*(38*x**3 - 79*x**2 + 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "266*x**6 - 553*x**5 - 1221*x**3 + 2844*x**2 - 756", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1694, "polynomial_expr": "(7*x**3 - 36)*(38*x**3 - 79*x**2 + 21)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7*x**3 - 36)*(38*x**3 - 79*x**2 + 21)\nExpanding the part (7*x**3 - 36) using the distributive property, and we got: (7*x**3)*(38*x**3 - 79*x**2 + 21) - 36*(38*x**3 - 79*x**2 + 21)\n#Step 2:\nCurrent expression: (7*x**3)*(38*x**3 - 79*x**2 + 21) - 36*(38*x**3 - 79*x**2 + 21)\nSimplifying the partial expression: -36*(38*x**3 - 79*x**2 + 21)\nExpanding the part (38*x**3 - 79*x**2 + 21) using the distributive property, and we got: -79*x**2*(-36) + (38*x**3)*(-36) + 21*(-36)\nReplacing -36*(38*x**3 - 79*x**2 + 21) with -79*x**2*(-36) + (38*x**3)*(-36) + 21*(-36) in the overall expression.\n#Step 3:\nCurrent expression: -79*x**2*(-36) + (7*x**3)*(38*x**3 - 79*x**2 + 21) + (38*x**3)*(-36) - 756\nSimplifying the partial expression: (7*x**3)*(38*x**3 - 79*x**2 + 21)\nExpanding the part (38*x**3 - 79*x**2 + 21) using the distributive property, and we got: 21*(7*x**3) + (-79*x**2)*(7*x**3) + (7*x**3)*(38*x**3)\nReplacing (7*x**3)*(38*x**3 - 79*x**2 + 21) with 21*(7*x**3) + (-79*x**2)*(7*x**3) + (7*x**3)*(38*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 21*7*x**3 + (-79*x**2)*(7*x**3) - 79*x**2*(-36) + (7*x**3)*(38*x**3) + (38*x**3)*(-36) - 756\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-79*x**2)*-36 = 2844*x**2\n (-79*x**2)*(7*x**3) = -553*x**5\n (38*x**3)*-36 = -1368*x**3\n (38*x**3)*(7*x**3) = 266*x**6\n 21*7*x**3 = 147*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 266*x**6 - 553*x**5 - 1368*x**3 + 147*x**3 + 2844*x**2 - 756\nCombining like terms, got 266*x**6 - 553*x**5 - 1221*x**3 + 2844*x**2 - 756\n#Step 6:\nCurrent expression: 266*x**6 - 553*x**5 - 1221*x**3 + 2844*x**2 - 756\nNo more calculations needed.\n266*x**6 - 553*x**5 - 1221*x**3 + 2844*x**2 - 756", "generated_answer": "266*x**6 - 553*x**5 - 1221*x**3 + 2844*x**2 - 756", "step_length": 6} {"cot_id": "5c2557ae0a5eb70f814a3d42ee3fa99b6d5dffdd832256f12ca9a2d2a634d184", "datapoint": {"question": "Simplify this expression: -21*x**3*(4*x**3 - 27*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-84*x**6 + 567*x**5", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1695, "polynomial_expr": "-21*x**3*(4*x**3 - 27*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -21*x**3*(4*x**3 - 27*x**2)\nExpanding the part (4*x**3 - 27*x**2) using the distributive property, and we got: (-27*x**2)*(-21*x**3) + (-21*x**3)*(4*x**3)\n#Step 2:\nCurrent expression: (-27*x**2)*(-21*x**3) + (-21*x**3)*(4*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*x**2)*(-21*x**3) = 567*x**5\n (4*x**3)*(-21*x**3) = -84*x**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -84*x**6 + 567*x**5\nNo more calculations needed.\n-84*x**6 + 567*x**5", "generated_answer": "-84*x**6 + 567*x**5", "step_length": 3} {"cot_id": "000ee0f12e8c7f0cc0958b85725207717fd799508579919fe5bc9f22a34ad326", "datapoint": {"question": "Simplify this expression: (94 - 44*z**2)*(63*z + 43)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2772*z**3 - 1892*z**2 + 5922*z + 4042", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1696, "polynomial_expr": "(94 - 44*z**2)*(63*z + 43)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (94 - 44*z**2)*(63*z + 43)\nExpanding the part (63*z + 43) using the distributive property, and we got: (63*z)*(94 - 44*z**2) + 43*(94 - 44*z**2)\n#Step 2:\nCurrent expression: (63*z)*(94 - 44*z**2) + 43*(94 - 44*z**2)\nSimplifying the partial expression: 43*(94 - 44*z**2)\nExpanding the part (94 - 44*z**2) using the distributive property, and we got: -44*z**2*43 + 94*43\nReplacing 43*(94 - 44*z**2) with -44*z**2*43 + 94*43 in the overall expression.\n#Step 3:\nCurrent expression: (63*z)*(94 - 44*z**2) - 44*z**2*43 + 4042\nSimplifying the partial expression: (63*z)*(94 - 44*z**2)\nExpanding the part (94 - 44*z**2) using the distributive property, and we got: 94*(63*z) + (63*z)*(-44*z**2)\nReplacing (63*z)*(94 - 44*z**2) with 94*(63*z) + (63*z)*(-44*z**2) in the overall expression.\n#Step 4:\nCurrent expression: 94*63*z + (63*z)*(-44*z**2) - 44*z**2*43 + 4042\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-44*z**2)*43 = -1892*z**2\n (-44*z**2)*(63*z) = -2772*z**3\n 94*63*z = 5922*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2772*z**3 - 1892*z**2 + 5922*z + 4042\nNo more calculations needed.\n-2772*z**3 - 1892*z**2 + 5922*z + 4042", "generated_answer": "-2772*z**3 - 1892*z**2 + 5922*z + 4042", "step_length": 5} {"cot_id": "68a6a1c889d5d2015613c3defad80903b8f5053bb97dce27ead0983f298236bd", "datapoint": {"question": "Simplify this expression: (27 - 41*x**3)*(25*x**3 - 15*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1025*x**6 + 615*x**4 + 675*x**3 - 405*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1697, "polynomial_expr": "(27 - 41*x**3)*(25*x**3 - 15*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27 - 41*x**3)*(25*x**3 - 15*x)\nExpanding the part (27 - 41*x**3) using the distributive property, and we got: (-41*x**3)*(25*x**3 - 15*x) + 27*(25*x**3 - 15*x)\n#Step 2:\nCurrent expression: (-41*x**3)*(25*x**3 - 15*x) + 27*(25*x**3 - 15*x)\nSimplifying the partial expression: 27*(25*x**3 - 15*x)\nExpanding the part (25*x**3 - 15*x) using the distributive property, and we got: -15*x*27 + (25*x**3)*27\nReplacing 27*(25*x**3 - 15*x) with -15*x*27 + (25*x**3)*27 in the overall expression.\n#Step 3:\nCurrent expression: -15*x*27 + (-41*x**3)*(25*x**3 - 15*x) + (25*x**3)*27\nSimplifying the partial expression: (-41*x**3)*(25*x**3 - 15*x)\nExpanding the part (25*x**3 - 15*x) using the distributive property, and we got: (-15*x)*(-41*x**3) + (-41*x**3)*(25*x**3)\nReplacing (-41*x**3)*(25*x**3 - 15*x) with (-15*x)*(-41*x**3) + (-41*x**3)*(25*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-15*x)*(-41*x**3) - 15*x*27 + (-41*x**3)*(25*x**3) + (25*x**3)*27\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-15*x)*27 = -405*x\n (-15*x)*(-41*x**3) = 615*x**4\n (25*x**3)*27 = 675*x**3\n (25*x**3)*(-41*x**3) = -1025*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1025*x**6 + 615*x**4 + 675*x**3 - 405*x\nNo more calculations needed.\n-1025*x**6 + 615*x**4 + 675*x**3 - 405*x", "generated_answer": "-1025*x**6 + 615*x**4 + 675*x**3 - 405*x", "step_length": 5} {"cot_id": "e98f02c7b87a8519dc712232e8f101fd0d414cf4a322c226776c1693e19faf15", "datapoint": {"question": "Simplify this expression: -900*z**3 - 460\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-900*z**3 - 460", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1698, "polynomial_expr": "-900*z**3 - 460", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -900*z**3 - 460\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -900*z**3 - 460\nNo more calculations needed.\n-900*z**3 - 460", "generated_answer": "-900*z**3 - 460", "step_length": 2} {"cot_id": "0a46607aec5be0326830e2b7cf84ac2ac3ecb5d10e8e7e37b8f10bb779144d27", "datapoint": {"question": "Calculate the following: (-23*z**3 - 10*z)*(-5*z**3 - 30*z + 80)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "115*z**6 + 740*z**4 - 1840*z**3 + 300*z**2 - 800*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1699, "polynomial_expr": "(-23*z**3 - 10*z)*(-5*z**3 - 30*z + 80)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-23*z**3 - 10*z)*(-5*z**3 - 30*z + 80)\nExpanding the part (-23*z**3 - 10*z) using the distributive property, and we got: (-10*z)*(-5*z**3 - 30*z + 80) + (-23*z**3)*(-5*z**3 - 30*z + 80)\n#Step 2:\nCurrent expression: (-10*z)*(-5*z**3 - 30*z + 80) + (-23*z**3)*(-5*z**3 - 30*z + 80)\nSimplifying the partial expression: (-23*z**3)*(-5*z**3 - 30*z + 80)\nExpanding the part (-5*z**3 - 30*z + 80) using the distributive property, and we got: (-30*z)*(-23*z**3) + 80*(-23*z**3) + (-23*z**3)*(-5*z**3)\nReplacing (-23*z**3)*(-5*z**3 - 30*z + 80) with (-30*z)*(-23*z**3) + 80*(-23*z**3) + (-23*z**3)*(-5*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-30*z)*(-23*z**3) + (-10*z)*(-5*z**3 - 30*z + 80) + 80*(-23)*z**3 + (-23*z**3)*(-5*z**3)\nSimplifying the partial expression: (-10*z)*(-5*z**3 - 30*z + 80)\nExpanding the part (-5*z**3 - 30*z + 80) using the distributive property, and we got: (-30*z)*(-10*z) + (-10*z)*(-5*z**3) + 80*(-10*z)\nReplacing (-10*z)*(-5*z**3 - 30*z + 80) with (-30*z)*(-10*z) + (-10*z)*(-5*z**3) + 80*(-10*z) in the overall expression.\n#Step 4:\nCurrent expression: (-30*z)*(-10*z) + (-30*z)*(-23*z**3) + (-10*z)*(-5*z**3) + 80*(-23)*z**3 + 80*(-10)*z + (-23*z**3)*(-5*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*z)*(-23*z**3) = 690*z**4\n (-30*z)*(-10*z) = 300*z**2\n (-5*z**3)*(-23*z**3) = 115*z**6\n (-5*z**3)*(-10*z) = 50*z**4\n 80*-23*z**3 = -1840*z**3\n 80*-10*z = -800*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 115*z**6 + 50*z**4 + 690*z**4 - 1840*z**3 + 300*z**2 - 800*z\nCombining like terms, got 115*z**6 + 740*z**4 - 1840*z**3 + 300*z**2 - 800*z\n#Step 6:\nCurrent expression: 115*z**6 + 740*z**4 - 1840*z**3 + 300*z**2 - 800*z\nNo more calculations needed.\n115*z**6 + 740*z**4 - 1840*z**3 + 300*z**2 - 800*z", "generated_answer": "115*z**6 + 740*z**4 - 1840*z**3 + 300*z**2 - 800*z", "step_length": 6} {"cot_id": "cf6f5d3db2516fc3ed7f24f3647a66a2e85dcc15215a7434f66111790f1b2226", "datapoint": {"question": "Calculate the following: (17*x**3 + 8*x)*(-20*x**2 + 11*x + 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-340*x**5 + 187*x**4 + 401*x**3 + 88*x**2 + 264*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1700, "polynomial_expr": "(17*x**3 + 8*x)*(-20*x**2 + 11*x + 33)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (17*x**3 + 8*x)*(-20*x**2 + 11*x + 33)\nExpanding the part (17*x**3 + 8*x) using the distributive property, and we got: (8*x)*(-20*x**2 + 11*x + 33) + (17*x**3)*(-20*x**2 + 11*x + 33)\n#Step 2:\nCurrent expression: (8*x)*(-20*x**2 + 11*x + 33) + (17*x**3)*(-20*x**2 + 11*x + 33)\nSimplifying the partial expression: (8*x)*(-20*x**2 + 11*x + 33)\nExpanding the part (-20*x**2 + 11*x + 33) using the distributive property, and we got: 33*(8*x) + (8*x)*(11*x) + (8*x)*(-20*x**2)\nReplacing (8*x)*(-20*x**2 + 11*x + 33) with 33*(8*x) + (8*x)*(11*x) + (8*x)*(-20*x**2) in the overall expression.\n#Step 3:\nCurrent expression: 33*8*x + (8*x)*(11*x) + (8*x)*(-20*x**2) + (17*x**3)*(-20*x**2 + 11*x + 33)\nSimplifying the partial expression: (17*x**3)*(-20*x**2 + 11*x + 33)\nExpanding the part (-20*x**2 + 11*x + 33) using the distributive property, and we got: 33*(17*x**3) + (11*x)*(17*x**3) + (-20*x**2)*(17*x**3)\nReplacing (17*x**3)*(-20*x**2 + 11*x + 33) with 33*(17*x**3) + (11*x)*(17*x**3) + (-20*x**2)*(17*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 33*17*x**3 + 33*8*x + (8*x)*(11*x) + (8*x)*(-20*x**2) + (11*x)*(17*x**3) + (-20*x**2)*(17*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*x**2)*(8*x) = -160*x**3\n (-20*x**2)*(17*x**3) = -340*x**5\n (11*x)*(8*x) = 88*x**2\n (11*x)*(17*x**3) = 187*x**4\n 33*8*x = 264*x\n 33*17*x**3 = 561*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -340*x**5 + 187*x**4 - 160*x**3 + 561*x**3 + 88*x**2 + 264*x\nCombining like terms, got -340*x**5 + 187*x**4 + 401*x**3 + 88*x**2 + 264*x\n#Step 6:\nCurrent expression: -340*x**5 + 187*x**4 + 401*x**3 + 88*x**2 + 264*x\nNo more calculations needed.\n-340*x**5 + 187*x**4 + 401*x**3 + 88*x**2 + 264*x", "generated_answer": "-340*x**5 + 187*x**4 + 401*x**3 + 88*x**2 + 264*x", "step_length": 6} {"cot_id": "fdb9c04fe4623e03e12387fbe130441d082f5367b8db0022d0eb7d67e69c9f9b", "datapoint": {"question": "Simplify this expression: (16*z**3 + 5*z**2)*(49*z**3 - 34*z**2 - 38*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "784*z**6 - 299*z**5 - 778*z**4 - 190*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1701, "polynomial_expr": "(16*z**3 + 5*z**2)*(49*z**3 - 34*z**2 - 38*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (16*z**3 + 5*z**2)*(49*z**3 - 34*z**2 - 38*z)\nExpanding the part (16*z**3 + 5*z**2) using the distributive property, and we got: (5*z**2)*(49*z**3 - 34*z**2 - 38*z) + (16*z**3)*(49*z**3 - 34*z**2 - 38*z)\n#Step 2:\nCurrent expression: (5*z**2)*(49*z**3 - 34*z**2 - 38*z) + (16*z**3)*(49*z**3 - 34*z**2 - 38*z)\nSimplifying the partial expression: (5*z**2)*(49*z**3 - 34*z**2 - 38*z)\nExpanding the part (49*z**3 - 34*z**2 - 38*z) using the distributive property, and we got: (-38*z)*(5*z**2) + (-34*z**2)*(5*z**2) + (5*z**2)*(49*z**3)\nReplacing (5*z**2)*(49*z**3 - 34*z**2 - 38*z) with (-38*z)*(5*z**2) + (-34*z**2)*(5*z**2) + (5*z**2)*(49*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-38*z)*(5*z**2) + (-34*z**2)*(5*z**2) + (5*z**2)*(49*z**3) + (16*z**3)*(49*z**3 - 34*z**2 - 38*z)\nSimplifying the partial expression: (16*z**3)*(49*z**3 - 34*z**2 - 38*z)\nExpanding the part (49*z**3 - 34*z**2 - 38*z) using the distributive property, and we got: (-38*z)*(16*z**3) + (-34*z**2)*(16*z**3) + (16*z**3)*(49*z**3)\nReplacing (16*z**3)*(49*z**3 - 34*z**2 - 38*z) with (-38*z)*(16*z**3) + (-34*z**2)*(16*z**3) + (16*z**3)*(49*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-38*z)*(5*z**2) + (-38*z)*(16*z**3) + (-34*z**2)*(5*z**2) + (-34*z**2)*(16*z**3) + (5*z**2)*(49*z**3) + (16*z**3)*(49*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-38*z)*(5*z**2) = -190*z**3\n (-38*z)*(16*z**3) = -608*z**4\n (-34*z**2)*(5*z**2) = -170*z**4\n (-34*z**2)*(16*z**3) = -544*z**5\n (49*z**3)*(5*z**2) = 245*z**5\n (49*z**3)*(16*z**3) = 784*z**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 784*z**6 - 544*z**5 + 245*z**5 - 608*z**4 - 170*z**4 - 190*z**3\nCombining like terms, got 784*z**6 - 299*z**5 - 778*z**4 - 190*z**3\n#Step 6:\nCurrent expression: 784*z**6 - 299*z**5 - 778*z**4 - 190*z**3\nNo more calculations needed.\n784*z**6 - 299*z**5 - 778*z**4 - 190*z**3", "generated_answer": "784*z**6 - 299*z**5 - 778*z**4 - 190*z**3", "step_length": 6} {"cot_id": "d419a98b7d1e8a3c61d073b51d92c6a2fc716f683670c35a58c935188ce80fe7", "datapoint": {"question": "Simplify this expression: 29*y**3*(32*y + 34)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "928*y**4 + 986*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1702, "polynomial_expr": "29*y**3*(32*y + 34)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 29*y**3*(32*y + 34)\nExpanding the part (32*y + 34) using the distributive property, and we got: 34*(29*y**3) + (32*y)*(29*y**3)\n#Step 2:\nCurrent expression: 34*(29*y**3) + (32*y)*(29*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 34*(29*y**3) = 986*y**3\n (32*y)*(29*y**3) = 928*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 928*y**4 + 986*y**3\nNo more calculations needed.\n928*y**4 + 986*y**3", "generated_answer": "928*y**4 + 986*y**3", "step_length": 3} {"cot_id": "a62da041758e526ea5681fd3f7564246a97ad301fc11d9bde07a90dedc81b423", "datapoint": {"question": "Calculate the following: -52*y**3*(-28*y**3 + 86*y**2 + 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1456*y**6 - 4472*y**5 - 1040*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1703, "polynomial_expr": "-52*y**3*(-28*y**3 + 86*y**2 + 20)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -52*y**3*(-28*y**3 + 86*y**2 + 20)\nExpanding the part (-28*y**3 + 86*y**2 + 20) using the distributive property, and we got: 20*(-52*y**3) + (86*y**2)*(-52*y**3) + (-52*y**3)*(-28*y**3)\n#Step 2:\nCurrent expression: 20*(-52*y**3) + (86*y**2)*(-52*y**3) + (-52*y**3)*(-28*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 20*(-52*y**3) = -1040*y**3\n (-28*y**3)*(-52*y**3) = 1456*y**6\n (86*y**2)*(-52*y**3) = -4472*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1456*y**6 - 4472*y**5 - 1040*y**3\nNo more calculations needed.\n1456*y**6 - 4472*y**5 - 1040*y**3", "generated_answer": "1456*y**6 - 4472*y**5 - 1040*y**3", "step_length": 3} {"cot_id": "46fb0a2dd11558aa070ad0f9295ab015be6eb71a32b15a74efb7b0b35dc78c91", "datapoint": {"question": "Calculate the following: (43*x + 38)*(13*x**3 - 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "559*x**4 + 494*x**3 - 1333*x - 1178", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1704, "polynomial_expr": "(43*x + 38)*(13*x**3 - 31)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (43*x + 38)*(13*x**3 - 31)\nExpanding the part (13*x**3 - 31) using the distributive property, and we got: (13*x**3)*(43*x + 38) - 31*(43*x + 38)\n#Step 2:\nCurrent expression: (13*x**3)*(43*x + 38) - 31*(43*x + 38)\nSimplifying the partial expression: -31*(43*x + 38)\nExpanding the part (43*x + 38) using the distributive property, and we got: (43*x)*(-31) + 38*(-31)\nReplacing -31*(43*x + 38) with (43*x)*(-31) + 38*(-31) in the overall expression.\n#Step 3:\nCurrent expression: (43*x)*(-31) + (13*x**3)*(43*x + 38) - 1178\nSimplifying the partial expression: (13*x**3)*(43*x + 38)\nExpanding the part (43*x + 38) using the distributive property, and we got: 38*(13*x**3) + (43*x)*(13*x**3)\nReplacing (13*x**3)*(43*x + 38) with 38*(13*x**3) + (43*x)*(13*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 38*13*x**3 + (43*x)*(13*x**3) + (43*x)*(-31) - 1178\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (43*x)*-31 = -1333*x\n (43*x)*(13*x**3) = 559*x**4\n 38*13*x**3 = 494*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 559*x**4 + 494*x**3 - 1333*x - 1178\nNo more calculations needed.\n559*x**4 + 494*x**3 - 1333*x - 1178", "generated_answer": "559*x**4 + 494*x**3 - 1333*x - 1178", "step_length": 5} {"cot_id": "1148147ccaa2eb4b0714ae5366a9a3b630fc2555c321e65f0684ea8d8ecbb854", "datapoint": {"question": "Simplify this expression: (10*y - 42)*(7*y**2 - 7*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "70*y**3 - 364*y**2 + 294*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1705, "polynomial_expr": "(10*y - 42)*(7*y**2 - 7*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (10*y - 42)*(7*y**2 - 7*y)\nExpanding the part (10*y - 42) using the distributive property, and we got: (10*y)*(7*y**2 - 7*y) - 42*(7*y**2 - 7*y)\n#Step 2:\nCurrent expression: (10*y)*(7*y**2 - 7*y) - 42*(7*y**2 - 7*y)\nSimplifying the partial expression: -42*(7*y**2 - 7*y)\nExpanding the part (7*y**2 - 7*y) using the distributive property, and we got: -7*y*(-42) + (7*y**2)*(-42)\nReplacing -42*(7*y**2 - 7*y) with -7*y*(-42) + (7*y**2)*(-42) in the overall expression.\n#Step 3:\nCurrent expression: -7*y*(-42) + (10*y)*(7*y**2 - 7*y) + (7*y**2)*(-42)\nSimplifying the partial expression: (10*y)*(7*y**2 - 7*y)\nExpanding the part (7*y**2 - 7*y) using the distributive property, and we got: (-7*y)*(10*y) + (10*y)*(7*y**2)\nReplacing (10*y)*(7*y**2 - 7*y) with (-7*y)*(10*y) + (10*y)*(7*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-7*y)*(10*y) - 7*y*(-42) + (10*y)*(7*y**2) + (7*y**2)*(-42)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-7*y)*-42 = 294*y\n (-7*y)*(10*y) = -70*y**2\n (7*y**2)*-42 = -294*y**2\n (7*y**2)*(10*y) = 70*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 70*y**3 - 294*y**2 - 70*y**2 + 294*y\nCombining like terms, got 70*y**3 - 364*y**2 + 294*y\n#Step 6:\nCurrent expression: 70*y**3 - 364*y**2 + 294*y\nNo more calculations needed.\n70*y**3 - 364*y**2 + 294*y", "generated_answer": "70*y**3 - 364*y**2 + 294*y", "step_length": 6} {"cot_id": "cd2a50223f7afc5cdff0d89b433ef733ff2cd21ed762cafe5edee892ec169067", "datapoint": {"question": "Simplify this expression: (37*z**2 + 17)*(-34*z**3 + 19*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1258*z**5 + 703*z**4 - 578*z**3 + 323*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1706, "polynomial_expr": "(37*z**2 + 17)*(-34*z**3 + 19*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (37*z**2 + 17)*(-34*z**3 + 19*z**2)\nExpanding the part (37*z**2 + 17) using the distributive property, and we got: (37*z**2)*(-34*z**3 + 19*z**2) + 17*(-34*z**3 + 19*z**2)\n#Step 2:\nCurrent expression: (37*z**2)*(-34*z**3 + 19*z**2) + 17*(-34*z**3 + 19*z**2)\nSimplifying the partial expression: 17*(-34*z**3 + 19*z**2)\nExpanding the part (-34*z**3 + 19*z**2) using the distributive property, and we got: (19*z**2)*17 - 34*z**3*17\nReplacing 17*(-34*z**3 + 19*z**2) with (19*z**2)*17 - 34*z**3*17 in the overall expression.\n#Step 3:\nCurrent expression: (19*z**2)*17 + (37*z**2)*(-34*z**3 + 19*z**2) - 34*z**3*17\nSimplifying the partial expression: (37*z**2)*(-34*z**3 + 19*z**2)\nExpanding the part (-34*z**3 + 19*z**2) using the distributive property, and we got: (19*z**2)*(37*z**2) + (37*z**2)*(-34*z**3)\nReplacing (37*z**2)*(-34*z**3 + 19*z**2) with (19*z**2)*(37*z**2) + (37*z**2)*(-34*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (19*z**2)*(37*z**2) + (19*z**2)*17 + (37*z**2)*(-34*z**3) - 34*z**3*17\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*z**3)*17 = -578*z**3\n (-34*z**3)*(37*z**2) = -1258*z**5\n (19*z**2)*17 = 323*z**2\n (19*z**2)*(37*z**2) = 703*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1258*z**5 + 703*z**4 - 578*z**3 + 323*z**2\nNo more calculations needed.\n-1258*z**5 + 703*z**4 - 578*z**3 + 323*z**2", "generated_answer": "-1258*z**5 + 703*z**4 - 578*z**3 + 323*z**2", "step_length": 5} {"cot_id": "857c371de2b150b9b3fb33828abd1153ed9b6756199b2f766fdfc8a94b916e87", "datapoint": {"question": "Simplify this expression: (29*x**2 + 19)*(-11*x**3 - 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-319*x**5 - 209*x**3 - 1363*x**2 - 893", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1707, "polynomial_expr": "(29*x**2 + 19)*(-11*x**3 - 47)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29*x**2 + 19)*(-11*x**3 - 47)\nExpanding the part (-11*x**3 - 47) using the distributive property, and we got: (-11*x**3)*(29*x**2 + 19) - 47*(29*x**2 + 19)\n#Step 2:\nCurrent expression: (-11*x**3)*(29*x**2 + 19) - 47*(29*x**2 + 19)\nSimplifying the partial expression: -47*(29*x**2 + 19)\nExpanding the part (29*x**2 + 19) using the distributive property, and we got: (29*x**2)*(-47) + 19*(-47)\nReplacing -47*(29*x**2 + 19) with (29*x**2)*(-47) + 19*(-47) in the overall expression.\n#Step 3:\nCurrent expression: (29*x**2)*(-47) + (-11*x**3)*(29*x**2 + 19) - 893\nSimplifying the partial expression: (-11*x**3)*(29*x**2 + 19)\nExpanding the part (29*x**2 + 19) using the distributive property, and we got: 19*(-11*x**3) + (29*x**2)*(-11*x**3)\nReplacing (-11*x**3)*(29*x**2 + 19) with 19*(-11*x**3) + (29*x**2)*(-11*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 19*(-11)*x**3 + (29*x**2)*(-11*x**3) + (29*x**2)*(-47) - 893\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (29*x**2)*-47 = -1363*x**2\n (29*x**2)*(-11*x**3) = -319*x**5\n 19*-11*x**3 = -209*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -319*x**5 - 209*x**3 - 1363*x**2 - 893\nNo more calculations needed.\n-319*x**5 - 209*x**3 - 1363*x**2 - 893", "generated_answer": "-319*x**5 - 209*x**3 - 1363*x**2 - 893", "step_length": 5} {"cot_id": "366bfb2fea79e98c71013fff84d826260d43c956bbc7d3d35171f5106f467791", "datapoint": {"question": "Calculate the following: (18 - 26*y**3)*(-12*y**3 - 36*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "312*y**6 + 936*y**4 - 216*y**3 - 648*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1708, "polynomial_expr": "(18 - 26*y**3)*(-12*y**3 - 36*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (18 - 26*y**3)*(-12*y**3 - 36*y)\nExpanding the part (18 - 26*y**3) using the distributive property, and we got: (-26*y**3)*(-12*y**3 - 36*y) + 18*(-12*y**3 - 36*y)\n#Step 2:\nCurrent expression: (-26*y**3)*(-12*y**3 - 36*y) + 18*(-12*y**3 - 36*y)\nSimplifying the partial expression: 18*(-12*y**3 - 36*y)\nExpanding the part (-12*y**3 - 36*y) using the distributive property, and we got: -36*y*18 - 12*y**3*18\nReplacing 18*(-12*y**3 - 36*y) with -36*y*18 - 12*y**3*18 in the overall expression.\n#Step 3:\nCurrent expression: -36*y*18 + (-26*y**3)*(-12*y**3 - 36*y) - 12*y**3*18\nSimplifying the partial expression: (-26*y**3)*(-12*y**3 - 36*y)\nExpanding the part (-12*y**3 - 36*y) using the distributive property, and we got: (-36*y)*(-26*y**3) + (-26*y**3)*(-12*y**3)\nReplacing (-26*y**3)*(-12*y**3 - 36*y) with (-36*y)*(-26*y**3) + (-26*y**3)*(-12*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-36*y)*(-26*y**3) - 36*y*18 + (-26*y**3)*(-12*y**3) - 12*y**3*18\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*y)*18 = -648*y\n (-36*y)*(-26*y**3) = 936*y**4\n (-12*y**3)*18 = -216*y**3\n (-12*y**3)*(-26*y**3) = 312*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 312*y**6 + 936*y**4 - 216*y**3 - 648*y\nNo more calculations needed.\n312*y**6 + 936*y**4 - 216*y**3 - 648*y", "generated_answer": "312*y**6 + 936*y**4 - 216*y**3 - 648*y", "step_length": 5} {"cot_id": "4661a480952cfee39b8a2e3b4cb7488fae3f66f8d013830c622e0a0e0599fe3f", "datapoint": {"question": "Simplify this expression: (29*x**2 - 24*x)*(-10*x**3 - 22)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-290*x**5 + 240*x**4 - 638*x**2 + 528*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1709, "polynomial_expr": "(29*x**2 - 24*x)*(-10*x**3 - 22)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29*x**2 - 24*x)*(-10*x**3 - 22)\nExpanding the part (-10*x**3 - 22) using the distributive property, and we got: (-10*x**3)*(29*x**2 - 24*x) - 22*(29*x**2 - 24*x)\n#Step 2:\nCurrent expression: (-10*x**3)*(29*x**2 - 24*x) - 22*(29*x**2 - 24*x)\nSimplifying the partial expression: -22*(29*x**2 - 24*x)\nExpanding the part (29*x**2 - 24*x) using the distributive property, and we got: -24*x*(-22) + (29*x**2)*(-22)\nReplacing -22*(29*x**2 - 24*x) with -24*x*(-22) + (29*x**2)*(-22) in the overall expression.\n#Step 3:\nCurrent expression: -24*x*(-22) + (29*x**2)*(-22) + (-10*x**3)*(29*x**2 - 24*x)\nSimplifying the partial expression: (-10*x**3)*(29*x**2 - 24*x)\nExpanding the part (29*x**2 - 24*x) using the distributive property, and we got: (-24*x)*(-10*x**3) + (29*x**2)*(-10*x**3)\nReplacing (-10*x**3)*(29*x**2 - 24*x) with (-24*x)*(-10*x**3) + (29*x**2)*(-10*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-24*x)*(-10*x**3) - 24*x*(-22) + (29*x**2)*(-10*x**3) + (29*x**2)*(-22)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-24*x)*-22 = 528*x\n (-24*x)*(-10*x**3) = 240*x**4\n (29*x**2)*-22 = -638*x**2\n (29*x**2)*(-10*x**3) = -290*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -290*x**5 + 240*x**4 - 638*x**2 + 528*x\nNo more calculations needed.\n-290*x**5 + 240*x**4 - 638*x**2 + 528*x", "generated_answer": "-290*x**5 + 240*x**4 - 638*x**2 + 528*x", "step_length": 5} {"cot_id": "e2d5e88bed9c3a2619fb39192c059de611de8ea19ac022409f318f299029f35a", "datapoint": {"question": "Simplify this expression: (-26*x - 13)*(37*x + 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-962*x**2 - 923*x - 221", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1710, "polynomial_expr": "(-26*x - 13)*(37*x + 17)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-26*x - 13)*(37*x + 17)\nExpanding the part (-26*x - 13) using the distributive property, and we got: (-26*x)*(37*x + 17) - 13*(37*x + 17)\n#Step 2:\nCurrent expression: (-26*x)*(37*x + 17) - 13*(37*x + 17)\nSimplifying the partial expression: -13*(37*x + 17)\nExpanding the part (37*x + 17) using the distributive property, and we got: (37*x)*(-13) + 17*(-13)\nReplacing -13*(37*x + 17) with (37*x)*(-13) + 17*(-13) in the overall expression.\n#Step 3:\nCurrent expression: (-26*x)*(37*x + 17) + (37*x)*(-13) - 221\nSimplifying the partial expression: (-26*x)*(37*x + 17)\nExpanding the part (37*x + 17) using the distributive property, and we got: (-26*x)*(37*x) + 17*(-26*x)\nReplacing (-26*x)*(37*x + 17) with (-26*x)*(37*x) + 17*(-26*x) in the overall expression.\n#Step 4:\nCurrent expression: (-26*x)*(37*x) + 17*(-26)*x + (37*x)*(-13) - 221\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (37*x)*-13 = -481*x\n (37*x)*(-26*x) = -962*x**2\n 17*-26*x = -442*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -962*x**2 - 481*x - 442*x - 221\nCombining like terms, got -962*x**2 - 923*x - 221\n#Step 6:\nCurrent expression: -962*x**2 - 923*x - 221\nNo more calculations needed.\n-962*x**2 - 923*x - 221", "generated_answer": "-962*x**2 - 923*x - 221", "step_length": 6} {"cot_id": "df58db2db4249055917642ffa04a0747abd12d6817be3751e9cfd9fb0ecc44db", "datapoint": {"question": "Calculate the following: (45*x**2 + 9)*(11*x**3 + 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "495*x**5 + 99*x**3 + 1710*x**2 + 342", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1711, "polynomial_expr": "(45*x**2 + 9)*(11*x**3 + 38)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (45*x**2 + 9)*(11*x**3 + 38)\nExpanding the part (45*x**2 + 9) using the distributive property, and we got: (45*x**2)*(11*x**3 + 38) + 9*(11*x**3 + 38)\n#Step 2:\nCurrent expression: (45*x**2)*(11*x**3 + 38) + 9*(11*x**3 + 38)\nSimplifying the partial expression: 9*(11*x**3 + 38)\nExpanding the part (11*x**3 + 38) using the distributive property, and we got: (11*x**3)*9 + 38*9\nReplacing 9*(11*x**3 + 38) with (11*x**3)*9 + 38*9 in the overall expression.\n#Step 3:\nCurrent expression: (45*x**2)*(11*x**3 + 38) + (11*x**3)*9 + 342\nSimplifying the partial expression: (45*x**2)*(11*x**3 + 38)\nExpanding the part (11*x**3 + 38) using the distributive property, and we got: 38*(45*x**2) + (45*x**2)*(11*x**3)\nReplacing (45*x**2)*(11*x**3 + 38) with 38*(45*x**2) + (45*x**2)*(11*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 38*45*x**2 + (45*x**2)*(11*x**3) + (11*x**3)*9 + 342\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (11*x**3)*9 = 99*x**3\n (11*x**3)*(45*x**2) = 495*x**5\n 38*45*x**2 = 1710*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 495*x**5 + 99*x**3 + 1710*x**2 + 342\nNo more calculations needed.\n495*x**5 + 99*x**3 + 1710*x**2 + 342", "generated_answer": "495*x**5 + 99*x**3 + 1710*x**2 + 342", "step_length": 5} {"cot_id": "7abb5655cdcd03f33e27ec01509e97ae6cea43369531cf156041a0ba39e15c90", "datapoint": {"question": "Calculate the following: -27*x**3*(-75*x**3 + 32*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2025*x**6 - 864*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1712, "polynomial_expr": "-27*x**3*(-75*x**3 + 32*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -27*x**3*(-75*x**3 + 32*x)\nExpanding the part (-75*x**3 + 32*x) using the distributive property, and we got: (32*x)*(-27*x**3) + (-75*x**3)*(-27*x**3)\n#Step 2:\nCurrent expression: (32*x)*(-27*x**3) + (-75*x**3)*(-27*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-75*x**3)*(-27*x**3) = 2025*x**6\n (32*x)*(-27*x**3) = -864*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 2025*x**6 - 864*x**4\nNo more calculations needed.\n2025*x**6 - 864*x**4", "generated_answer": "2025*x**6 - 864*x**4", "step_length": 3} {"cot_id": "7ccdee37552563aac1997135a625507a5e5860cb957e06394c7da1f7dbdafea3", "datapoint": {"question": "Simplify this expression: (42 - 8*y**2)*(-15*y**3 - 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "120*y**5 - 630*y**3 + 80*y**2 - 420", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1713, "polynomial_expr": "(42 - 8*y**2)*(-15*y**3 - 10)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (42 - 8*y**2)*(-15*y**3 - 10)\nExpanding the part (-15*y**3 - 10) using the distributive property, and we got: (-15*y**3)*(42 - 8*y**2) - 10*(42 - 8*y**2)\n#Step 2:\nCurrent expression: (-15*y**3)*(42 - 8*y**2) - 10*(42 - 8*y**2)\nSimplifying the partial expression: -10*(42 - 8*y**2)\nExpanding the part (42 - 8*y**2) using the distributive property, and we got: -8*y**2*(-10) + 42*(-10)\nReplacing -10*(42 - 8*y**2) with -8*y**2*(-10) + 42*(-10) in the overall expression.\n#Step 3:\nCurrent expression: -8*y**2*(-10) + (-15*y**3)*(42 - 8*y**2) - 420\nSimplifying the partial expression: (-15*y**3)*(42 - 8*y**2)\nExpanding the part (42 - 8*y**2) using the distributive property, and we got: 42*(-15*y**3) + (-8*y**2)*(-15*y**3)\nReplacing (-15*y**3)*(42 - 8*y**2) with 42*(-15*y**3) + (-8*y**2)*(-15*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 42*(-15)*y**3 + (-8*y**2)*(-15*y**3) - 8*y**2*(-10) - 420\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-8*y**2)*-10 = 80*y**2\n (-8*y**2)*(-15*y**3) = 120*y**5\n 42*-15*y**3 = -630*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 120*y**5 - 630*y**3 + 80*y**2 - 420\nNo more calculations needed.\n120*y**5 - 630*y**3 + 80*y**2 - 420", "generated_answer": "120*y**5 - 630*y**3 + 80*y**2 - 420", "step_length": 5} {"cot_id": "c7888703027523c3d3c63e36dc543cd5cad05ed00f9ce95f5dd2f489eabe249b", "datapoint": {"question": "Calculate the following: 29*y**2*(13*y**3 - 21*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "377*y**5 - 609*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1714, "polynomial_expr": "29*y**2*(13*y**3 - 21*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 29*y**2*(13*y**3 - 21*y)\nExpanding the part (13*y**3 - 21*y) using the distributive property, and we got: (-21*y)*(29*y**2) + (29*y**2)*(13*y**3)\n#Step 2:\nCurrent expression: (-21*y)*(29*y**2) + (29*y**2)*(13*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-21*y)*(29*y**2) = -609*y**3\n (13*y**3)*(29*y**2) = 377*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 377*y**5 - 609*y**3\nNo more calculations needed.\n377*y**5 - 609*y**3", "generated_answer": "377*y**5 - 609*y**3", "step_length": 3} {"cot_id": "8444e57e44c598493352bbb80332e21c8d2877b392dba071f6a99828ef30f31d", "datapoint": {"question": "Simplify this expression: -66*z**2*(50*z**3 - 37*z**2 + 3*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-3300*z**5 + 2442*z**4 - 198*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1715, "polynomial_expr": "-66*z**2*(50*z**3 - 37*z**2 + 3*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -66*z**2*(50*z**3 - 37*z**2 + 3*z)\nExpanding the part (50*z**3 - 37*z**2 + 3*z) using the distributive property, and we got: (3*z)*(-66*z**2) + (-66*z**2)*(-37*z**2) + (-66*z**2)*(50*z**3)\n#Step 2:\nCurrent expression: (3*z)*(-66*z**2) + (-66*z**2)*(-37*z**2) + (-66*z**2)*(50*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*z**2)*(-66*z**2) = 2442*z**4\n (3*z)*(-66*z**2) = -198*z**3\n (50*z**3)*(-66*z**2) = -3300*z**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -3300*z**5 + 2442*z**4 - 198*z**3\nNo more calculations needed.\n-3300*z**5 + 2442*z**4 - 198*z**3", "generated_answer": "-3300*z**5 + 2442*z**4 - 198*z**3", "step_length": 3} {"cot_id": "f8806243e2d45bc8838fffedcf2d15c6b58bb5756b3352beef5f1099d3844ef5", "datapoint": {"question": "Calculate the following: -14*x*(36*x**3 + 35*x**2 + 29)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-504*x**4 - 490*x**3 - 406*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1716, "polynomial_expr": "-14*x*(36*x**3 + 35*x**2 + 29)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -14*x*(36*x**3 + 35*x**2 + 29)\nExpanding the part (36*x**3 + 35*x**2 + 29) using the distributive property, and we got: (-14*x)*(35*x**2) + (-14*x)*(36*x**3) + 29*(-14*x)\n#Step 2:\nCurrent expression: (-14*x)*(35*x**2) + (-14*x)*(36*x**3) + 29*(-14*x)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 29*(-14*x) = -406*x\n (35*x**2)*(-14*x) = -490*x**3\n (36*x**3)*(-14*x) = -504*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -504*x**4 - 490*x**3 - 406*x\nNo more calculations needed.\n-504*x**4 - 490*x**3 - 406*x", "generated_answer": "-504*x**4 - 490*x**3 - 406*x", "step_length": 3} {"cot_id": "bec1c84613a8cc3db69c00e9c633550479af37420e16503333e3567e8bd4072f", "datapoint": {"question": "Simplify this expression: (47*y**2 + 4*y)*(20*y**3 - 37*y - 29)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "940*y**5 + 80*y**4 - 1739*y**3 - 1511*y**2 - 116*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1717, "polynomial_expr": "(47*y**2 + 4*y)*(20*y**3 - 37*y - 29)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (47*y**2 + 4*y)*(20*y**3 - 37*y - 29)\nExpanding the part (47*y**2 + 4*y) using the distributive property, and we got: (4*y)*(20*y**3 - 37*y - 29) + (47*y**2)*(20*y**3 - 37*y - 29)\n#Step 2:\nCurrent expression: (4*y)*(20*y**3 - 37*y - 29) + (47*y**2)*(20*y**3 - 37*y - 29)\nSimplifying the partial expression: (4*y)*(20*y**3 - 37*y - 29)\nExpanding the part (20*y**3 - 37*y - 29) using the distributive property, and we got: (-37*y)*(4*y) - 116*y + (4*y)*(20*y**3)\nReplacing (4*y)*(20*y**3 - 37*y - 29) with (-37*y)*(4*y) - 116*y + (4*y)*(20*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-37*y)*(4*y) - 29*4*y + (4*y)*(20*y**3) + (47*y**2)*(20*y**3 - 37*y - 29)\nSimplifying the partial expression: (47*y**2)*(20*y**3 - 37*y - 29)\nExpanding the part (20*y**3 - 37*y - 29) using the distributive property, and we got: (-37*y)*(47*y**2) - 1363*y**2 + (47*y**2)*(20*y**3)\nReplacing (47*y**2)*(20*y**3 - 37*y - 29) with (-37*y)*(47*y**2) - 1363*y**2 + (47*y**2)*(20*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-37*y)*(4*y) + (-37*y)*(47*y**2) - 29*47*y**2 - 29*4*y + (4*y)*(20*y**3) + (47*y**2)*(20*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*y)*(4*y) = -148*y**2\n (-37*y)*(47*y**2) = -1739*y**3\n (20*y**3)*(4*y) = 80*y**4\n (20*y**3)*(47*y**2) = 940*y**5\n -29*4*y = -116*y\n -29*47*y**2 = -1363*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 940*y**5 + 80*y**4 - 1739*y**3 - 1363*y**2 - 148*y**2 - 116*y\nCombining like terms, got 940*y**5 + 80*y**4 - 1739*y**3 - 1511*y**2 - 116*y\n#Step 6:\nCurrent expression: 940*y**5 + 80*y**4 - 1739*y**3 - 1511*y**2 - 116*y\nNo more calculations needed.\n940*y**5 + 80*y**4 - 1739*y**3 - 1511*y**2 - 116*y", "generated_answer": "940*y**5 + 80*y**4 - 1739*y**3 - 1511*y**2 - 116*y", "step_length": 6} {"cot_id": "a55705c9796c05898a70e8eae56399925c728e44d632d6647881222ad4033b9c", "datapoint": {"question": "Calculate the following: (28*z**3 + 31)*(-14*z**3 + 31*z**2 - 23)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-392*z**6 + 868*z**5 - 1078*z**3 + 961*z**2 - 713", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1718, "polynomial_expr": "(28*z**3 + 31)*(-14*z**3 + 31*z**2 - 23)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28*z**3 + 31)*(-14*z**3 + 31*z**2 - 23)\nExpanding the part (28*z**3 + 31) using the distributive property, and we got: (28*z**3)*(-14*z**3 + 31*z**2 - 23) + 31*(-14*z**3 + 31*z**2 - 23)\n#Step 2:\nCurrent expression: (28*z**3)*(-14*z**3 + 31*z**2 - 23) + 31*(-14*z**3 + 31*z**2 - 23)\nSimplifying the partial expression: 31*(-14*z**3 + 31*z**2 - 23)\nExpanding the part (-14*z**3 + 31*z**2 - 23) using the distributive property, and we got: (31*z**2)*31 - 14*z**3*31 - 23*31\nReplacing 31*(-14*z**3 + 31*z**2 - 23) with (31*z**2)*31 - 14*z**3*31 - 23*31 in the overall expression.\n#Step 3:\nCurrent expression: (31*z**2)*31 - 14*z**3*31 + (28*z**3)*(-14*z**3 + 31*z**2 - 23) - 713\nSimplifying the partial expression: (28*z**3)*(-14*z**3 + 31*z**2 - 23)\nExpanding the part (-14*z**3 + 31*z**2 - 23) using the distributive property, and we got: -644*z**3 + (31*z**2)*(28*z**3) + (-14*z**3)*(28*z**3)\nReplacing (28*z**3)*(-14*z**3 + 31*z**2 - 23) with -644*z**3 + (31*z**2)*(28*z**3) + (-14*z**3)*(28*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -23*28*z**3 + (31*z**2)*(28*z**3) + (31*z**2)*31 + (-14*z**3)*(28*z**3) - 14*z**3*31 - 713\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-14*z**3)*31 = -434*z**3\n (-14*z**3)*(28*z**3) = -392*z**6\n (31*z**2)*31 = 961*z**2\n (31*z**2)*(28*z**3) = 868*z**5\n -23*28*z**3 = -644*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -392*z**6 + 868*z**5 - 644*z**3 - 434*z**3 + 961*z**2 - 713\nCombining like terms, got -392*z**6 + 868*z**5 - 1078*z**3 + 961*z**2 - 713\n#Step 6:\nCurrent expression: -392*z**6 + 868*z**5 - 1078*z**3 + 961*z**2 - 713\nNo more calculations needed.\n-392*z**6 + 868*z**5 - 1078*z**3 + 961*z**2 - 713", "generated_answer": "-392*z**6 + 868*z**5 - 1078*z**3 + 961*z**2 - 713", "step_length": 6} {"cot_id": "6a1e3001f95d15190165c4b9e104cbb228a593715cad53ab9eee0322ff2915c0", "datapoint": {"question": "Calculate the following: (-43*x**2 - 24*x)*(30*x**2 - 37*x + 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1290*x**4 + 871*x**3 + 28*x**2 - 480*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1719, "polynomial_expr": "(-43*x**2 - 24*x)*(30*x**2 - 37*x + 20)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-43*x**2 - 24*x)*(30*x**2 - 37*x + 20)\nExpanding the part (-43*x**2 - 24*x) using the distributive property, and we got: (-24*x)*(30*x**2 - 37*x + 20) + (-43*x**2)*(30*x**2 - 37*x + 20)\n#Step 2:\nCurrent expression: (-24*x)*(30*x**2 - 37*x + 20) + (-43*x**2)*(30*x**2 - 37*x + 20)\nSimplifying the partial expression: (-43*x**2)*(30*x**2 - 37*x + 20)\nExpanding the part (30*x**2 - 37*x + 20) using the distributive property, and we got: (-37*x)*(-43*x**2) + 20*(-43*x**2) + (-43*x**2)*(30*x**2)\nReplacing (-43*x**2)*(30*x**2 - 37*x + 20) with (-37*x)*(-43*x**2) + 20*(-43*x**2) + (-43*x**2)*(30*x**2) in the overall expression.\n#Step 3:\nCurrent expression: (-37*x)*(-43*x**2) + (-24*x)*(30*x**2 - 37*x + 20) + 20*(-43)*x**2 + (-43*x**2)*(30*x**2)\nSimplifying the partial expression: (-24*x)*(30*x**2 - 37*x + 20)\nExpanding the part (30*x**2 - 37*x + 20) using the distributive property, and we got: (-37*x)*(-24*x) + (-24*x)*(30*x**2) + 20*(-24*x)\nReplacing (-24*x)*(30*x**2 - 37*x + 20) with (-37*x)*(-24*x) + (-24*x)*(30*x**2) + 20*(-24*x) in the overall expression.\n#Step 4:\nCurrent expression: (-37*x)*(-24*x) + (-37*x)*(-43*x**2) + (-24*x)*(30*x**2) + 20*(-43)*x**2 + 20*(-24)*x + (-43*x**2)*(30*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*x)*(-43*x**2) = 1591*x**3\n (-37*x)*(-24*x) = 888*x**2\n (30*x**2)*(-43*x**2) = -1290*x**4\n (30*x**2)*(-24*x) = -720*x**3\n 20*-43*x**2 = -860*x**2\n 20*-24*x = -480*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1290*x**4 - 720*x**3 + 1591*x**3 - 860*x**2 + 888*x**2 - 480*x\nCombining like terms, got -1290*x**4 + 871*x**3 + 28*x**2 - 480*x\n#Step 6:\nCurrent expression: -1290*x**4 + 871*x**3 + 28*x**2 - 480*x\nNo more calculations needed.\n-1290*x**4 + 871*x**3 + 28*x**2 - 480*x", "generated_answer": "-1290*x**4 + 871*x**3 + 28*x**2 - 480*x", "step_length": 6} {"cot_id": "6ee9c7890932252267c4e106cbc067502fba6b3275412c9c534c94a4bba1bd3d", "datapoint": {"question": "Calculate the following: (31 - 26*y)*(y**3 + 6*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-26*y**4 + 31*y**3 - 156*y**2 + 186*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1720, "polynomial_expr": "(31 - 26*y)*(y**3 + 6*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31 - 26*y)*(y**3 + 6*y)\nExpanding the part (31 - 26*y) using the distributive property, and we got: (-26*y)*(y**3 + 6*y) + 31*(y**3 + 6*y)\n#Step 2:\nCurrent expression: (-26*y)*(y**3 + 6*y) + 31*(y**3 + 6*y)\nSimplifying the partial expression: 31*(y**3 + 6*y)\nExpanding the part (y**3 + 6*y) using the distributive property, and we got: y**3*31 + (6*y)*31\nReplacing 31*(y**3 + 6*y) with y**3*31 + (6*y)*31 in the overall expression.\n#Step 3:\nCurrent expression: (-26*y)*(y**3 + 6*y) + y**3*31 + (6*y)*31\nSimplifying the partial expression: (-26*y)*(y**3 + 6*y)\nExpanding the part (y**3 + 6*y) using the distributive property, and we got: (-26*y)*y**3 + (-26*y)*(6*y)\nReplacing (-26*y)*(y**3 + 6*y) with (-26*y)*y**3 + (-26*y)*(6*y) in the overall expression.\n#Step 4:\nCurrent expression: (-26*y)*y**3 + (-26*y)*(6*y) + y**3*31 + (6*y)*31\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n y**3*31 = 31*y**3\n y**3*(-26*y) = -26*y**4\n (6*y)*31 = 186*y\n (6*y)*(-26*y) = -156*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -26*y**4 + 31*y**3 - 156*y**2 + 186*y\nNo more calculations needed.\n-26*y**4 + 31*y**3 - 156*y**2 + 186*y", "generated_answer": "-26*y**4 + 31*y**3 - 156*y**2 + 186*y", "step_length": 5} {"cot_id": "b561b2051cede17db179eb8b0756456dee4d658c727871becd9a2c1cc0b82c36", "datapoint": {"question": "Calculate the following: -945*z**2 - 385\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-945*z**2 - 385", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1721, "polynomial_expr": "-945*z**2 - 385", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -945*z**2 - 385\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -945*z**2 - 385\nNo more calculations needed.\n-945*z**2 - 385", "generated_answer": "-945*z**2 - 385", "step_length": 2} {"cot_id": "0b8f284fa59880c59c8511b66f24607fed943f72d27767952ecd8d19786194b9", "datapoint": {"question": "Calculate the following: (-54*x**3 + x**2 + 40)*(-25*x**3 - 13*x**2 + 4)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1350*x**6 + 677*x**5 - 13*x**4 - 1216*x**3 - 516*x**2 + 160", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1722, "polynomial_expr": "(-54*x**3 + x**2 + 40)*(-25*x**3 - 13*x**2 + 4)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-54*x**3 + x**2 + 40)*(-25*x**3 - 13*x**2 + 4)\nExpanding the part (-25*x**3 - 13*x**2 + 4) using the distributive property, and we got: (-13*x**2)*(-54*x**3 + x**2 + 40) + (-25*x**3)*(-54*x**3 + x**2 + 40) + 4*(-54*x**3 + x**2 + 40)\n#Step 2:\nCurrent expression: (-13*x**2)*(-54*x**3 + x**2 + 40) + (-25*x**3)*(-54*x**3 + x**2 + 40) + 4*(-54*x**3 + x**2 + 40)\nSimplifying the partial expression: 4*(-54*x**3 + x**2 + 40)\nExpanding the part (-54*x**3 + x**2 + 40) using the distributive property, and we got: x**2*4 - 54*x**3*4 + 40*4\nReplacing 4*(-54*x**3 + x**2 + 40) with x**2*4 - 54*x**3*4 + 40*4 in the overall expression.\n#Step 3:\nCurrent expression: x**2*4 + (-13*x**2)*(-54*x**3 + x**2 + 40) - 54*x**3*4 + (-25*x**3)*(-54*x**3 + x**2 + 40) + 160\nSimplifying the partial expression: (-25*x**3)*(-54*x**3 + x**2 + 40)\nExpanding the part (-54*x**3 + x**2 + 40) using the distributive property, and we got: 40*(-25*x**3) + x**2*(-25*x**3) + (-54*x**3)*(-25*x**3)\nReplacing (-25*x**3)*(-54*x**3 + x**2 + 40) with 40*(-25*x**3) + x**2*(-25*x**3) + (-54*x**3)*(-25*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 40*(-25)*x**3 + x**2*(-25*x**3) + x**2*4 + (-13*x**2)*(-54*x**3 + x**2 + 40) + (-54*x**3)*(-25*x**3) - 54*x**3*4 + 160\nSimplifying the partial expression: (-13*x**2)*(-54*x**3 + x**2 + 40)\nExpanding the part (-54*x**3 + x**2 + 40) using the distributive property, and we got: (-13*x**2)*x**2 + 40*(-13*x**2) + (-13*x**2)*(-54*x**3)\nReplacing (-13*x**2)*(-54*x**3 + x**2 + 40) with (-13*x**2)*x**2 + 40*(-13*x**2) + (-13*x**2)*(-54*x**3) in the overall expression.\n#Step 5:\nCurrent expression: 40*(-25)*x**3 + (-13*x**2)*x**2 + x**2*(-25*x**3) + 40*(-13)*x**2 + x**2*4 + (-13*x**2)*(-54*x**3) + (-54*x**3)*(-25*x**3) - 54*x**3*4 + 160\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n x**2*4 = 4*x**2\n x**2*(-25*x**3) = -25*x**5\n x**2*(-13*x**2) = -13*x**4\n (-54*x**3)*4 = -216*x**3\n (-54*x**3)*(-25*x**3) = 1350*x**6\n (-54*x**3)*(-13*x**2) = 702*x**5\n 40*-25*x**3 = -1000*x**3\n 40*-13*x**2 = -520*x**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1350*x**6 - 25*x**5 + 702*x**5 - 13*x**4 - 1000*x**3 - 216*x**3 - 520*x**2 + 4*x**2 + 160\nCombining like terms, got 1350*x**6 + 677*x**5 - 13*x**4 - 1216*x**3 - 516*x**2 + 160\n#Step 7:\nCurrent expression: 1350*x**6 + 677*x**5 - 13*x**4 - 1216*x**3 - 516*x**2 + 160\nNo more calculations needed.\n1350*x**6 + 677*x**5 - 13*x**4 - 1216*x**3 - 516*x**2 + 160", "generated_answer": "1350*x**6 + 677*x**5 - 13*x**4 - 1216*x**3 - 516*x**2 + 160", "step_length": 7} {"cot_id": "97fafc0aaeee1cd69bd51240c63818c11b91e0f362e747d5dcfd3bd0cc14e2d4", "datapoint": {"question": "Calculate the following: (-32*x**2 - 37*x)*(-52*x**3 - 30*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1664*x**5 + 1924*x**4 + 960*x**3 + 1110*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1723, "polynomial_expr": "(-32*x**2 - 37*x)*(-52*x**3 - 30*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-32*x**2 - 37*x)*(-52*x**3 - 30*x)\nExpanding the part (-52*x**3 - 30*x) using the distributive property, and we got: (-30*x)*(-32*x**2 - 37*x) + (-52*x**3)*(-32*x**2 - 37*x)\n#Step 2:\nCurrent expression: (-30*x)*(-32*x**2 - 37*x) + (-52*x**3)*(-32*x**2 - 37*x)\nSimplifying the partial expression: (-52*x**3)*(-32*x**2 - 37*x)\nExpanding the part (-32*x**2 - 37*x) using the distributive property, and we got: (-37*x)*(-52*x**3) + (-32*x**2)*(-52*x**3)\nReplacing (-52*x**3)*(-32*x**2 - 37*x) with (-37*x)*(-52*x**3) + (-32*x**2)*(-52*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-37*x)*(-52*x**3) + (-30*x)*(-32*x**2 - 37*x) + (-32*x**2)*(-52*x**3)\nSimplifying the partial expression: (-30*x)*(-32*x**2 - 37*x)\nExpanding the part (-32*x**2 - 37*x) using the distributive property, and we got: (-37*x)*(-30*x) + (-30*x)*(-32*x**2)\nReplacing (-30*x)*(-32*x**2 - 37*x) with (-37*x)*(-30*x) + (-30*x)*(-32*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-37*x)*(-30*x) + (-37*x)*(-52*x**3) + (-30*x)*(-32*x**2) + (-32*x**2)*(-52*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*x)*(-52*x**3) = 1924*x**4\n (-37*x)*(-30*x) = 1110*x**2\n (-32*x**2)*(-52*x**3) = 1664*x**5\n (-32*x**2)*(-30*x) = 960*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1664*x**5 + 1924*x**4 + 960*x**3 + 1110*x**2\nNo more calculations needed.\n1664*x**5 + 1924*x**4 + 960*x**3 + 1110*x**2", "generated_answer": "1664*x**5 + 1924*x**4 + 960*x**3 + 1110*x**2", "step_length": 5} {"cot_id": "c18a9660b721c382d0bb7cc185a0812a26876474511fd2b3f33f6d3f4bd2592e", "datapoint": {"question": "Simplify this expression: (-33*x**2 + 40*x - 35)*(42*x**3 + 20*x + 42)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1386*x**5 + 1680*x**4 - 2130*x**3 - 586*x**2 + 980*x - 1470", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1724, "polynomial_expr": "(-33*x**2 + 40*x - 35)*(42*x**3 + 20*x + 42)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-33*x**2 + 40*x - 35)*(42*x**3 + 20*x + 42)\nExpanding the part (-33*x**2 + 40*x - 35) using the distributive property, and we got: (40*x)*(42*x**3 + 20*x + 42) + (-33*x**2)*(42*x**3 + 20*x + 42) - 35*(42*x**3 + 20*x + 42)\n#Step 2:\nCurrent expression: (40*x)*(42*x**3 + 20*x + 42) + (-33*x**2)*(42*x**3 + 20*x + 42) - 35*(42*x**3 + 20*x + 42)\nSimplifying the partial expression: -35*(42*x**3 + 20*x + 42)\nExpanding the part (42*x**3 + 20*x + 42) using the distributive property, and we got: (20*x)*(-35) + (42*x**3)*(-35) + 42*(-35)\nReplacing -35*(42*x**3 + 20*x + 42) with (20*x)*(-35) + (42*x**3)*(-35) + 42*(-35) in the overall expression.\n#Step 3:\nCurrent expression: (20*x)*(-35) + (40*x)*(42*x**3 + 20*x + 42) + (-33*x**2)*(42*x**3 + 20*x + 42) + (42*x**3)*(-35) - 1470\nSimplifying the partial expression: (-33*x**2)*(42*x**3 + 20*x + 42)\nExpanding the part (42*x**3 + 20*x + 42) using the distributive property, and we got: 42*(-33*x**2) + (20*x)*(-33*x**2) + (-33*x**2)*(42*x**3)\nReplacing (-33*x**2)*(42*x**3 + 20*x + 42) with 42*(-33*x**2) + (20*x)*(-33*x**2) + (-33*x**2)*(42*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 42*(-33)*x**2 + (20*x)*(-33*x**2) + (20*x)*(-35) + (40*x)*(42*x**3 + 20*x + 42) + (-33*x**2)*(42*x**3) + (42*x**3)*(-35) - 1470\nSimplifying the partial expression: (40*x)*(42*x**3 + 20*x + 42)\nExpanding the part (42*x**3 + 20*x + 42) using the distributive property, and we got: 42*(40*x) + (20*x)*(40*x) + (40*x)*(42*x**3)\nReplacing (40*x)*(42*x**3 + 20*x + 42) with 42*(40*x) + (20*x)*(40*x) + (40*x)*(42*x**3) in the overall expression.\n#Step 5:\nCurrent expression: 42*(-33)*x**2 + 42*40*x + (20*x)*(40*x) + (20*x)*(-33*x**2) + (20*x)*(-35) + (40*x)*(42*x**3) + (-33*x**2)*(42*x**3) + (42*x**3)*(-35) - 1470\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (20*x)*-35 = -700*x\n (20*x)*(-33*x**2) = -660*x**3\n (20*x)*(40*x) = 800*x**2\n (42*x**3)*-35 = -1470*x**3\n (42*x**3)*(-33*x**2) = -1386*x**5\n (42*x**3)*(40*x) = 1680*x**4\n 42*-33*x**2 = -1386*x**2\n 42*40*x = 1680*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1386*x**5 + 1680*x**4 - 1470*x**3 - 660*x**3 - 1386*x**2 + 800*x**2 - 700*x + 1680*x - 1470\nCombining like terms, got -1386*x**5 + 1680*x**4 - 2130*x**3 - 586*x**2 + 980*x - 1470\n#Step 7:\nCurrent expression: -1386*x**5 + 1680*x**4 - 2130*x**3 - 586*x**2 + 980*x - 1470\nNo more calculations needed.\n-1386*x**5 + 1680*x**4 - 2130*x**3 - 586*x**2 + 980*x - 1470", "generated_answer": "-1386*x**5 + 1680*x**4 - 2130*x**3 - 586*x**2 + 980*x - 1470", "step_length": 7} {"cot_id": "d70313f731dab0a6b2488aa19f82e12c94a6a1555e5d1b8fab0f28572c800e47", "datapoint": {"question": "Simplify this expression: (29*z**3 + 76*z)*(54*z**3 - 19*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1566*z**6 - 551*z**5 + 4104*z**4 - 1444*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1725, "polynomial_expr": "(29*z**3 + 76*z)*(54*z**3 - 19*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29*z**3 + 76*z)*(54*z**3 - 19*z**2)\nExpanding the part (54*z**3 - 19*z**2) using the distributive property, and we got: (-19*z**2)*(29*z**3 + 76*z) + (54*z**3)*(29*z**3 + 76*z)\n#Step 2:\nCurrent expression: (-19*z**2)*(29*z**3 + 76*z) + (54*z**3)*(29*z**3 + 76*z)\nSimplifying the partial expression: (-19*z**2)*(29*z**3 + 76*z)\nExpanding the part (29*z**3 + 76*z) using the distributive property, and we got: (76*z)*(-19*z**2) + (-19*z**2)*(29*z**3)\nReplacing (-19*z**2)*(29*z**3 + 76*z) with (76*z)*(-19*z**2) + (-19*z**2)*(29*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (76*z)*(-19*z**2) + (-19*z**2)*(29*z**3) + (54*z**3)*(29*z**3 + 76*z)\nSimplifying the partial expression: (54*z**3)*(29*z**3 + 76*z)\nExpanding the part (29*z**3 + 76*z) using the distributive property, and we got: (76*z)*(54*z**3) + (29*z**3)*(54*z**3)\nReplacing (54*z**3)*(29*z**3 + 76*z) with (76*z)*(54*z**3) + (29*z**3)*(54*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (76*z)*(-19*z**2) + (76*z)*(54*z**3) + (-19*z**2)*(29*z**3) + (29*z**3)*(54*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (29*z**3)*(-19*z**2) = -551*z**5\n (29*z**3)*(54*z**3) = 1566*z**6\n (76*z)*(-19*z**2) = -1444*z**3\n (76*z)*(54*z**3) = 4104*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1566*z**6 - 551*z**5 + 4104*z**4 - 1444*z**3\nNo more calculations needed.\n1566*z**6 - 551*z**5 + 4104*z**4 - 1444*z**3", "generated_answer": "1566*z**6 - 551*z**5 + 4104*z**4 - 1444*z**3", "step_length": 5} {"cot_id": "9a7e1bd20fcc9637e39baa38a4a37a258640b15157363da045e102076ad08b32", "datapoint": {"question": "Simplify this expression: (-18*x**3 + 15*x - 34)*(-46*x**3 + 34*x**2 - 32*x + 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "828*x**6 - 612*x**5 - 114*x**4 + 1642*x**3 - 1636*x**2 + 1448*x - 816", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1726, "polynomial_expr": "(-18*x**3 + 15*x - 34)*(-46*x**3 + 34*x**2 - 32*x + 24)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-18*x**3 + 15*x - 34)*(-46*x**3 + 34*x**2 - 32*x + 24)\nExpanding the part (-18*x**3 + 15*x - 34) using the distributive property, and we got: (15*x)*(-46*x**3 + 34*x**2 - 32*x + 24) + (-18*x**3)*(-46*x**3 + 34*x**2 - 32*x + 24) - 34*(-46*x**3 + 34*x**2 - 32*x + 24)\n#Step 2:\nCurrent expression: (15*x)*(-46*x**3 + 34*x**2 - 32*x + 24) + (-18*x**3)*(-46*x**3 + 34*x**2 - 32*x + 24) - 34*(-46*x**3 + 34*x**2 - 32*x + 24)\nSimplifying the partial expression: -34*(-46*x**3 + 34*x**2 - 32*x + 24)\nExpanding the part (-46*x**3 + 34*x**2 - 32*x + 24) using the distributive property, and we got: -32*x*(-34) + (34*x**2)*(-34) - 46*x**3*(-34) + 24*(-34)\nReplacing -34*(-46*x**3 + 34*x**2 - 32*x + 24) with -32*x*(-34) + (34*x**2)*(-34) - 46*x**3*(-34) + 24*(-34) in the overall expression.\n#Step 3:\nCurrent expression: -32*x*(-34) + (15*x)*(-46*x**3 + 34*x**2 - 32*x + 24) + (34*x**2)*(-34) - 46*x**3*(-34) + (-18*x**3)*(-46*x**3 + 34*x**2 - 32*x + 24) - 816\nSimplifying the partial expression: (-18*x**3)*(-46*x**3 + 34*x**2 - 32*x + 24)\nExpanding the part (-46*x**3 + 34*x**2 - 32*x + 24) using the distributive property, and we got: (-32*x)*(-18*x**3) + 24*(-18*x**3) + (34*x**2)*(-18*x**3) + (-46*x**3)*(-18*x**3)\nReplacing (-18*x**3)*(-46*x**3 + 34*x**2 - 32*x + 24) with (-32*x)*(-18*x**3) + 24*(-18*x**3) + (34*x**2)*(-18*x**3) + (-46*x**3)*(-18*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-32*x)*(-18*x**3) - 32*x*(-34) + 24*(-18)*x**3 + (15*x)*(-46*x**3 + 34*x**2 - 32*x + 24) + (34*x**2)*(-18*x**3) + (34*x**2)*(-34) + (-46*x**3)*(-18*x**3) - 46*x**3*(-34) - 816\nSimplifying the partial expression: (15*x)*(-46*x**3 + 34*x**2 - 32*x + 24)\nExpanding the part (-46*x**3 + 34*x**2 - 32*x + 24) using the distributive property, and we got: (-32*x)*(15*x) + 24*(15*x) + (15*x)*(34*x**2) + (15*x)*(-46*x**3)\nReplacing (15*x)*(-46*x**3 + 34*x**2 - 32*x + 24) with (-32*x)*(15*x) + 24*(15*x) + (15*x)*(34*x**2) + (15*x)*(-46*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-32*x)*(15*x) + (-32*x)*(-18*x**3) - 32*x*(-34) + 24*(-18)*x**3 + 24*15*x + (15*x)*(34*x**2) + (15*x)*(-46*x**3) + (34*x**2)*(-18*x**3) + (34*x**2)*(-34) + (-46*x**3)*(-18*x**3) - 46*x**3*(-34) - 816\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*x**3)*-34 = 1564*x**3\n (-46*x**3)*(-18*x**3) = 828*x**6\n (-46*x**3)*(15*x) = -690*x**4\n (-32*x)*-34 = 1088*x\n (-32*x)*(-18*x**3) = 576*x**4\n (-32*x)*(15*x) = -480*x**2\n (34*x**2)*-34 = -1156*x**2\n (34*x**2)*(-18*x**3) = -612*x**5\n (34*x**2)*(15*x) = 510*x**3\n 24*-18*x**3 = -432*x**3\n 24*15*x = 360*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 828*x**6 - 612*x**5 - 690*x**4 + 576*x**4 - 432*x**3 + 510*x**3 + 1564*x**3 - 1156*x**2 - 480*x**2 + 360*x + 1088*x - 816\nCombining like terms, got 828*x**6 - 612*x**5 - 114*x**4 + 1642*x**3 - 1636*x**2 + 1448*x - 816\n#Step 7:\nCurrent expression: 828*x**6 - 612*x**5 - 114*x**4 + 1642*x**3 - 1636*x**2 + 1448*x - 816\nNo more calculations needed.\n828*x**6 - 612*x**5 - 114*x**4 + 1642*x**3 - 1636*x**2 + 1448*x - 816", "generated_answer": "828*x**6 - 612*x**5 - 114*x**4 + 1642*x**3 - 1636*x**2 + 1448*x - 816", "step_length": 7} {"cot_id": "73f2cae1a3f63f8c9e17ed8177840ea88f42e2873f87d235d98989767aa8dc2e", "datapoint": {"question": "Simplify this expression: (-40*x**2 + 19*x + 7)*(-13*x**3 + 32*x**2 + 30*x + 8)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "520*x**5 - 1527*x**4 - 683*x**3 + 474*x**2 + 362*x + 56", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1727, "polynomial_expr": "(-40*x**2 + 19*x + 7)*(-13*x**3 + 32*x**2 + 30*x + 8)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-40*x**2 + 19*x + 7)*(-13*x**3 + 32*x**2 + 30*x + 8)\nExpanding the part (-40*x**2 + 19*x + 7) using the distributive property, and we got: (19*x)*(-13*x**3 + 32*x**2 + 30*x + 8) + (-40*x**2)*(-13*x**3 + 32*x**2 + 30*x + 8) + 7*(-13*x**3 + 32*x**2 + 30*x + 8)\n#Step 2:\nCurrent expression: (19*x)*(-13*x**3 + 32*x**2 + 30*x + 8) + (-40*x**2)*(-13*x**3 + 32*x**2 + 30*x + 8) + 7*(-13*x**3 + 32*x**2 + 30*x + 8)\nSimplifying the partial expression: 7*(-13*x**3 + 32*x**2 + 30*x + 8)\nExpanding the part (-13*x**3 + 32*x**2 + 30*x + 8) using the distributive property, and we got: (30*x)*7 + (32*x**2)*7 - 13*x**3*7 + 8*7\nReplacing 7*(-13*x**3 + 32*x**2 + 30*x + 8) with (30*x)*7 + (32*x**2)*7 - 13*x**3*7 + 8*7 in the overall expression.\n#Step 3:\nCurrent expression: (19*x)*(-13*x**3 + 32*x**2 + 30*x + 8) + (30*x)*7 + (-40*x**2)*(-13*x**3 + 32*x**2 + 30*x + 8) + (32*x**2)*7 - 13*x**3*7 + 56\nSimplifying the partial expression: (-40*x**2)*(-13*x**3 + 32*x**2 + 30*x + 8)\nExpanding the part (-13*x**3 + 32*x**2 + 30*x + 8) using the distributive property, and we got: 8*(-40*x**2) + (30*x)*(-40*x**2) + (-40*x**2)*(32*x**2) + (-40*x**2)*(-13*x**3)\nReplacing (-40*x**2)*(-13*x**3 + 32*x**2 + 30*x + 8) with 8*(-40*x**2) + (30*x)*(-40*x**2) + (-40*x**2)*(32*x**2) + (-40*x**2)*(-13*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 8*(-40)*x**2 + (19*x)*(-13*x**3 + 32*x**2 + 30*x + 8) + (30*x)*(-40*x**2) + (30*x)*7 + (-40*x**2)*(32*x**2) + (-40*x**2)*(-13*x**3) + (32*x**2)*7 - 13*x**3*7 + 56\nSimplifying the partial expression: (19*x)*(-13*x**3 + 32*x**2 + 30*x + 8)\nExpanding the part (-13*x**3 + 32*x**2 + 30*x + 8) using the distributive property, and we got: 8*(19*x) + (19*x)*(30*x) + (19*x)*(32*x**2) + (19*x)*(-13*x**3)\nReplacing (19*x)*(-13*x**3 + 32*x**2 + 30*x + 8) with 8*(19*x) + (19*x)*(30*x) + (19*x)*(32*x**2) + (19*x)*(-13*x**3) in the overall expression.\n#Step 5:\nCurrent expression: 8*(-40)*x**2 + 8*19*x + (19*x)*(30*x) + (19*x)*(32*x**2) + (19*x)*(-13*x**3) + (30*x)*(-40*x**2) + (30*x)*7 + (-40*x**2)*(32*x**2) + (-40*x**2)*(-13*x**3) + (32*x**2)*7 - 13*x**3*7 + 56\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*x**3)*7 = -91*x**3\n (-13*x**3)*(-40*x**2) = 520*x**5\n (-13*x**3)*(19*x) = -247*x**4\n (30*x)*7 = 210*x\n (30*x)*(-40*x**2) = -1200*x**3\n (30*x)*(19*x) = 570*x**2\n (32*x**2)*7 = 224*x**2\n (32*x**2)*(-40*x**2) = -1280*x**4\n (32*x**2)*(19*x) = 608*x**3\n 8*-40*x**2 = -320*x**2\n 8*19*x = 152*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 520*x**5 - 1280*x**4 - 247*x**4 - 1200*x**3 - 91*x**3 + 608*x**3 - 320*x**2 + 224*x**2 + 570*x**2 + 152*x + 210*x + 56\nCombining like terms, got 520*x**5 - 1527*x**4 - 683*x**3 + 474*x**2 + 362*x + 56\n#Step 7:\nCurrent expression: 520*x**5 - 1527*x**4 - 683*x**3 + 474*x**2 + 362*x + 56\nNo more calculations needed.\n520*x**5 - 1527*x**4 - 683*x**3 + 474*x**2 + 362*x + 56", "generated_answer": "520*x**5 - 1527*x**4 - 683*x**3 + 474*x**2 + 362*x + 56", "step_length": 7} {"cot_id": "fa33e5668ac926f7f6712bb07d084d8c11e4149c458e94fad99f045d5865f279", "datapoint": {"question": "Calculate the following: (-44*y**2 + 11*y)*(-y**2 + 42*y + 76)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "44*y**4 - 1859*y**3 - 2882*y**2 + 836*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1728, "polynomial_expr": "(-44*y**2 + 11*y)*(-y**2 + 42*y + 76)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-44*y**2 + 11*y)*(-y**2 + 42*y + 76)\nExpanding the part (-44*y**2 + 11*y) using the distributive property, and we got: (11*y)*(-y**2 + 42*y + 76) + (-44*y**2)*(-y**2 + 42*y + 76)\n#Step 2:\nCurrent expression: (11*y)*(-y**2 + 42*y + 76) + (-44*y**2)*(-y**2 + 42*y + 76)\nSimplifying the partial expression: (-44*y**2)*(-y**2 + 42*y + 76)\nExpanding the part (-y**2 + 42*y + 76) using the distributive property, and we got: 76*(-44*y**2) + (42*y)*(-44*y**2) + (-44*y**2)*(-y**2)\nReplacing (-44*y**2)*(-y**2 + 42*y + 76) with 76*(-44*y**2) + (42*y)*(-44*y**2) + (-44*y**2)*(-y**2) in the overall expression.\n#Step 3:\nCurrent expression: 76*(-44)*y**2 + (11*y)*(-y**2 + 42*y + 76) + (42*y)*(-44*y**2) + (-44*y**2)*(-y**2)\nSimplifying the partial expression: (11*y)*(-y**2 + 42*y + 76)\nExpanding the part (-y**2 + 42*y + 76) using the distributive property, and we got: 76*(11*y) + (11*y)*(42*y) + (11*y)*(-y**2)\nReplacing (11*y)*(-y**2 + 42*y + 76) with 76*(11*y) + (11*y)*(42*y) + (11*y)*(-y**2) in the overall expression.\n#Step 4:\nCurrent expression: 76*(-44)*y**2 + 76*11*y + (11*y)*(42*y) + (11*y)*(-y**2) + (42*y)*(-44*y**2) + (-44*y**2)*(-y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-y**2)*(-44*y**2) = 44*y**4\n (-y**2)*(11*y) = -11*y**3\n (42*y)*(-44*y**2) = -1848*y**3\n (42*y)*(11*y) = 462*y**2\n 76*-44*y**2 = -3344*y**2\n 76*11*y = 836*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 44*y**4 - 1848*y**3 - 11*y**3 - 3344*y**2 + 462*y**2 + 836*y\nCombining like terms, got 44*y**4 - 1859*y**3 - 2882*y**2 + 836*y\n#Step 6:\nCurrent expression: 44*y**4 - 1859*y**3 - 2882*y**2 + 836*y\nNo more calculations needed.\n44*y**4 - 1859*y**3 - 2882*y**2 + 836*y", "generated_answer": "44*y**4 - 1859*y**3 - 2882*y**2 + 836*y", "step_length": 6} {"cot_id": "b51a777dfe2581c5c3c339430f600332a963bce90464b31ef3c254b049dfc0ea", "datapoint": {"question": "Simplify this expression: -18*x**2*(-5*x**3 + 43*x**2 + 8)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "90*x**5 - 774*x**4 - 144*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1729, "polynomial_expr": "-18*x**2*(-5*x**3 + 43*x**2 + 8)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -18*x**2*(-5*x**3 + 43*x**2 + 8)\nExpanding the part (-5*x**3 + 43*x**2 + 8) using the distributive property, and we got: 8*(-18*x**2) + (-18*x**2)*(43*x**2) + (-18*x**2)*(-5*x**3)\n#Step 2:\nCurrent expression: 8*(-18*x**2) + (-18*x**2)*(43*x**2) + (-18*x**2)*(-5*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 8*(-18*x**2) = -144*x**2\n (-5*x**3)*(-18*x**2) = 90*x**5\n (43*x**2)*(-18*x**2) = -774*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 90*x**5 - 774*x**4 - 144*x**2\nNo more calculations needed.\n90*x**5 - 774*x**4 - 144*x**2", "generated_answer": "90*x**5 - 774*x**4 - 144*x**2", "step_length": 3} {"cot_id": "5acce8efedbf08223e03d1f0a5fc5ee340efcefb5bcf824a424fb8933ccf909f", "datapoint": {"question": "Simplify this expression: (52*x**2 - 13*x)*(-30*x**3 + 13*x**2 - 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1560*x**5 + 1066*x**4 - 169*x**3 - 52*x**2 + 13*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1730, "polynomial_expr": "(52*x**2 - 13*x)*(-30*x**3 + 13*x**2 - 1)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (52*x**2 - 13*x)*(-30*x**3 + 13*x**2 - 1)\nExpanding the part (52*x**2 - 13*x) using the distributive property, and we got: (-13*x)*(-30*x**3 + 13*x**2 - 1) + (52*x**2)*(-30*x**3 + 13*x**2 - 1)\n#Step 2:\nCurrent expression: (-13*x)*(-30*x**3 + 13*x**2 - 1) + (52*x**2)*(-30*x**3 + 13*x**2 - 1)\nSimplifying the partial expression: (-13*x)*(-30*x**3 + 13*x**2 - 1)\nExpanding the part (-30*x**3 + 13*x**2 - 1) using the distributive property, and we got: (-13*x)*(13*x**2) + (-13*x)*(-30*x**3) - (-1)*13*x\nReplacing (-13*x)*(-30*x**3 + 13*x**2 - 1) with (-13*x)*(13*x**2) + (-13*x)*(-30*x**3) - (-1)*13*x in the overall expression.\n#Step 3:\nCurrent expression: (-13*x)*(13*x**2) + (-13*x)*(-30*x**3) - 1*(-13)*x + (52*x**2)*(-30*x**3 + 13*x**2 - 1)\nSimplifying the partial expression: (52*x**2)*(-30*x**3 + 13*x**2 - 1)\nExpanding the part (-30*x**3 + 13*x**2 - 1) using the distributive property, and we got: -52*x**2 + (13*x**2)*(52*x**2) + (52*x**2)*(-30*x**3)\nReplacing (52*x**2)*(-30*x**3 + 13*x**2 - 1) with -52*x**2 + (13*x**2)*(52*x**2) + (52*x**2)*(-30*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-13*x)*(13*x**2) + (-13*x)*(-30*x**3) - 1*52*x**2 - 1*(-13)*x + (13*x**2)*(52*x**2) + (52*x**2)*(-30*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*x**3)*(-13*x) = 390*x**4\n (-30*x**3)*(52*x**2) = -1560*x**5\n (13*x**2)*(-13*x) = -169*x**3\n (13*x**2)*(52*x**2) = 676*x**4\n -1*-13*x = 13*x\n -1*52*x**2 = -52*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1560*x**5 + 390*x**4 + 676*x**4 - 169*x**3 - 52*x**2 + 13*x\nCombining like terms, got -1560*x**5 + 1066*x**4 - 169*x**3 - 52*x**2 + 13*x\n#Step 6:\nCurrent expression: -1560*x**5 + 1066*x**4 - 169*x**3 - 52*x**2 + 13*x\nNo more calculations needed.\n-1560*x**5 + 1066*x**4 - 169*x**3 - 52*x**2 + 13*x", "generated_answer": "-1560*x**5 + 1066*x**4 - 169*x**3 - 52*x**2 + 13*x", "step_length": 6} {"cot_id": "4689ab80ecc3df2b43d6114703f8e2f56fec6c9a68f6d3ecb54a3f4c7999456e", "datapoint": {"question": "Simplify this expression: (43*y**2 + 40*y + 40)*(29*y**3 - 46*y**2 + 24*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1247*y**5 - 818*y**4 + 352*y**3 - 880*y**2 + 960*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1731, "polynomial_expr": "(43*y**2 + 40*y + 40)*(29*y**3 - 46*y**2 + 24*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (43*y**2 + 40*y + 40)*(29*y**3 - 46*y**2 + 24*y)\nExpanding the part (43*y**2 + 40*y + 40) using the distributive property, and we got: (40*y)*(29*y**3 - 46*y**2 + 24*y) + (43*y**2)*(29*y**3 - 46*y**2 + 24*y) + 40*(29*y**3 - 46*y**2 + 24*y)\n#Step 2:\nCurrent expression: (40*y)*(29*y**3 - 46*y**2 + 24*y) + (43*y**2)*(29*y**3 - 46*y**2 + 24*y) + 40*(29*y**3 - 46*y**2 + 24*y)\nSimplifying the partial expression: 40*(29*y**3 - 46*y**2 + 24*y)\nExpanding the part (29*y**3 - 46*y**2 + 24*y) using the distributive property, and we got: (24*y)*40 - 46*y**2*40 + (29*y**3)*40\nReplacing 40*(29*y**3 - 46*y**2 + 24*y) with (24*y)*40 - 46*y**2*40 + (29*y**3)*40 in the overall expression.\n#Step 3:\nCurrent expression: (24*y)*40 + (40*y)*(29*y**3 - 46*y**2 + 24*y) - 46*y**2*40 + (43*y**2)*(29*y**3 - 46*y**2 + 24*y) + (29*y**3)*40\nSimplifying the partial expression: (40*y)*(29*y**3 - 46*y**2 + 24*y)\nExpanding the part (29*y**3 - 46*y**2 + 24*y) using the distributive property, and we got: (24*y)*(40*y) + (40*y)*(-46*y**2) + (40*y)*(29*y**3)\nReplacing (40*y)*(29*y**3 - 46*y**2 + 24*y) with (24*y)*(40*y) + (40*y)*(-46*y**2) + (40*y)*(29*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (24*y)*(40*y) + (24*y)*40 + (40*y)*(-46*y**2) + (40*y)*(29*y**3) - 46*y**2*40 + (43*y**2)*(29*y**3 - 46*y**2 + 24*y) + (29*y**3)*40\nSimplifying the partial expression: (43*y**2)*(29*y**3 - 46*y**2 + 24*y)\nExpanding the part (29*y**3 - 46*y**2 + 24*y) using the distributive property, and we got: (24*y)*(43*y**2) + (-46*y**2)*(43*y**2) + (43*y**2)*(29*y**3)\nReplacing (43*y**2)*(29*y**3 - 46*y**2 + 24*y) with (24*y)*(43*y**2) + (-46*y**2)*(43*y**2) + (43*y**2)*(29*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (24*y)*(40*y) + (24*y)*(43*y**2) + (24*y)*40 + (40*y)*(-46*y**2) + (40*y)*(29*y**3) + (-46*y**2)*(43*y**2) - 46*y**2*40 + (43*y**2)*(29*y**3) + (29*y**3)*40\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*y**2)*40 = -1840*y**2\n (-46*y**2)*(40*y) = -1840*y**3\n (-46*y**2)*(43*y**2) = -1978*y**4\n (24*y)*40 = 960*y\n (24*y)*(40*y) = 960*y**2\n (24*y)*(43*y**2) = 1032*y**3\n (29*y**3)*40 = 1160*y**3\n (29*y**3)*(40*y) = 1160*y**4\n (29*y**3)*(43*y**2) = 1247*y**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1247*y**5 - 1978*y**4 + 1160*y**4 - 1840*y**3 + 1032*y**3 + 1160*y**3 - 1840*y**2 + 960*y**2 + 960*y\nCombining like terms, got 1247*y**5 - 818*y**4 + 352*y**3 - 880*y**2 + 960*y\n#Step 7:\nCurrent expression: 1247*y**5 - 818*y**4 + 352*y**3 - 880*y**2 + 960*y\nNo more calculations needed.\n1247*y**5 - 818*y**4 + 352*y**3 - 880*y**2 + 960*y", "generated_answer": "1247*y**5 - 818*y**4 + 352*y**3 - 880*y**2 + 960*y", "step_length": 7} {"cot_id": "61e3fc8fc456fda241f3f9f4e3d40c0048674bcdcf8a5bd63a9c7c1ed18494fd", "datapoint": {"question": "Calculate the following: -89*y**2*(41*y**2 - 41*y + 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-3649*y**4 + 3649*y**3 - 3382*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1732, "polynomial_expr": "-89*y**2*(41*y**2 - 41*y + 38)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -89*y**2*(41*y**2 - 41*y + 38)\nExpanding the part (41*y**2 - 41*y + 38) using the distributive property, and we got: (-41*y)*(-89*y**2) + 38*(-89*y**2) + (-89*y**2)*(41*y**2)\n#Step 2:\nCurrent expression: (-41*y)*(-89*y**2) + 38*(-89*y**2) + (-89*y**2)*(41*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 38*(-89*y**2) = -3382*y**2\n (-41*y)*(-89*y**2) = 3649*y**3\n (41*y**2)*(-89*y**2) = -3649*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -3649*y**4 + 3649*y**3 - 3382*y**2\nNo more calculations needed.\n-3649*y**4 + 3649*y**3 - 3382*y**2", "generated_answer": "-3649*y**4 + 3649*y**3 - 3382*y**2", "step_length": 3} {"cot_id": "5e30f0137fc469b9eb733e053540692c2bb09cfffa55ed306d3c3c922453b96d", "datapoint": {"question": "Simplify this expression: (25*y**2 + 39)*(7*y**3 - 5*y**2 - 7*y + 11)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "175*y**5 - 125*y**4 + 98*y**3 + 80*y**2 - 273*y + 429", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1733, "polynomial_expr": "(25*y**2 + 39)*(7*y**3 - 5*y**2 - 7*y + 11)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (25*y**2 + 39)*(7*y**3 - 5*y**2 - 7*y + 11)\nExpanding the part (25*y**2 + 39) using the distributive property, and we got: (25*y**2)*(7*y**3 - 5*y**2 - 7*y + 11) + 39*(7*y**3 - 5*y**2 - 7*y + 11)\n#Step 2:\nCurrent expression: (25*y**2)*(7*y**3 - 5*y**2 - 7*y + 11) + 39*(7*y**3 - 5*y**2 - 7*y + 11)\nSimplifying the partial expression: 39*(7*y**3 - 5*y**2 - 7*y + 11)\nExpanding the part (7*y**3 - 5*y**2 - 7*y + 11) using the distributive property, and we got: -7*y*39 - 5*y**2*39 + (7*y**3)*39 + 11*39\nReplacing 39*(7*y**3 - 5*y**2 - 7*y + 11) with -7*y*39 - 5*y**2*39 + (7*y**3)*39 + 11*39 in the overall expression.\n#Step 3:\nCurrent expression: -7*y*39 - 5*y**2*39 + (25*y**2)*(7*y**3 - 5*y**2 - 7*y + 11) + (7*y**3)*39 + 429\nSimplifying the partial expression: (25*y**2)*(7*y**3 - 5*y**2 - 7*y + 11)\nExpanding the part (7*y**3 - 5*y**2 - 7*y + 11) using the distributive property, and we got: (-7*y)*(25*y**2) + 11*(25*y**2) + (-5*y**2)*(25*y**2) + (25*y**2)*(7*y**3)\nReplacing (25*y**2)*(7*y**3 - 5*y**2 - 7*y + 11) with (-7*y)*(25*y**2) + 11*(25*y**2) + (-5*y**2)*(25*y**2) + (25*y**2)*(7*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-7*y)*(25*y**2) - 7*y*39 + 11*25*y**2 + (-5*y**2)*(25*y**2) - 5*y**2*39 + (25*y**2)*(7*y**3) + (7*y**3)*39 + 429\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-7*y)*39 = -273*y\n (-7*y)*(25*y**2) = -175*y**3\n (-5*y**2)*39 = -195*y**2\n (-5*y**2)*(25*y**2) = -125*y**4\n (7*y**3)*39 = 273*y**3\n (7*y**3)*(25*y**2) = 175*y**5\n 11*25*y**2 = 275*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 175*y**5 - 125*y**4 - 175*y**3 + 273*y**3 - 195*y**2 + 275*y**2 - 273*y + 429\nCombining like terms, got 175*y**5 - 125*y**4 + 98*y**3 + 80*y**2 - 273*y + 429\n#Step 6:\nCurrent expression: 175*y**5 - 125*y**4 + 98*y**3 + 80*y**2 - 273*y + 429\nNo more calculations needed.\n175*y**5 - 125*y**4 + 98*y**3 + 80*y**2 - 273*y + 429", "generated_answer": "175*y**5 - 125*y**4 + 98*y**3 + 80*y**2 - 273*y + 429", "step_length": 6} {"cot_id": "9a3ee54bdf58efac12d3c9ff2bd268e92d9209b5c997f6d6e54c5108b846b425", "datapoint": {"question": "Simplify this expression: (11*z**2 - 37*z)*(47*z**3 - 19*z**2 + 61*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "517*z**5 - 1948*z**4 + 1374*z**3 - 2257*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1734, "polynomial_expr": "(11*z**2 - 37*z)*(47*z**3 - 19*z**2 + 61*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11*z**2 - 37*z)*(47*z**3 - 19*z**2 + 61*z)\nExpanding the part (11*z**2 - 37*z) using the distributive property, and we got: (-37*z)*(47*z**3 - 19*z**2 + 61*z) + (11*z**2)*(47*z**3 - 19*z**2 + 61*z)\n#Step 2:\nCurrent expression: (-37*z)*(47*z**3 - 19*z**2 + 61*z) + (11*z**2)*(47*z**3 - 19*z**2 + 61*z)\nSimplifying the partial expression: (-37*z)*(47*z**3 - 19*z**2 + 61*z)\nExpanding the part (47*z**3 - 19*z**2 + 61*z) using the distributive property, and we got: (-37*z)*(61*z) + (-37*z)*(-19*z**2) + (-37*z)*(47*z**3)\nReplacing (-37*z)*(47*z**3 - 19*z**2 + 61*z) with (-37*z)*(61*z) + (-37*z)*(-19*z**2) + (-37*z)*(47*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-37*z)*(61*z) + (-37*z)*(-19*z**2) + (-37*z)*(47*z**3) + (11*z**2)*(47*z**3 - 19*z**2 + 61*z)\nSimplifying the partial expression: (11*z**2)*(47*z**3 - 19*z**2 + 61*z)\nExpanding the part (47*z**3 - 19*z**2 + 61*z) using the distributive property, and we got: (61*z)*(11*z**2) + (-19*z**2)*(11*z**2) + (11*z**2)*(47*z**3)\nReplacing (11*z**2)*(47*z**3 - 19*z**2 + 61*z) with (61*z)*(11*z**2) + (-19*z**2)*(11*z**2) + (11*z**2)*(47*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-37*z)*(61*z) + (-37*z)*(-19*z**2) + (-37*z)*(47*z**3) + (61*z)*(11*z**2) + (-19*z**2)*(11*z**2) + (11*z**2)*(47*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*z**2)*(-37*z) = 703*z**3\n (-19*z**2)*(11*z**2) = -209*z**4\n (47*z**3)*(-37*z) = -1739*z**4\n (47*z**3)*(11*z**2) = 517*z**5\n (61*z)*(-37*z) = -2257*z**2\n (61*z)*(11*z**2) = 671*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 517*z**5 - 1739*z**4 - 209*z**4 + 671*z**3 + 703*z**3 - 2257*z**2\nCombining like terms, got 517*z**5 - 1948*z**4 + 1374*z**3 - 2257*z**2\n#Step 6:\nCurrent expression: 517*z**5 - 1948*z**4 + 1374*z**3 - 2257*z**2\nNo more calculations needed.\n517*z**5 - 1948*z**4 + 1374*z**3 - 2257*z**2", "generated_answer": "517*z**5 - 1948*z**4 + 1374*z**3 - 2257*z**2", "step_length": 6} {"cot_id": "3aa90271396ffdd9802969861787e3b70b724cc743701721dd241ee268804321", "datapoint": {"question": "Simplify this expression: (-49*z**3 + 3*z**2)*(-3*z**3 + 14*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "147*z**6 - 9*z**5 - 686*z**4 + 42*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1735, "polynomial_expr": "(-49*z**3 + 3*z**2)*(-3*z**3 + 14*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-49*z**3 + 3*z**2)*(-3*z**3 + 14*z)\nExpanding the part (-49*z**3 + 3*z**2) using the distributive property, and we got: (3*z**2)*(-3*z**3 + 14*z) + (-49*z**3)*(-3*z**3 + 14*z)\n#Step 2:\nCurrent expression: (3*z**2)*(-3*z**3 + 14*z) + (-49*z**3)*(-3*z**3 + 14*z)\nSimplifying the partial expression: (-49*z**3)*(-3*z**3 + 14*z)\nExpanding the part (-3*z**3 + 14*z) using the distributive property, and we got: (14*z)*(-49*z**3) + (-49*z**3)*(-3*z**3)\nReplacing (-49*z**3)*(-3*z**3 + 14*z) with (14*z)*(-49*z**3) + (-49*z**3)*(-3*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (14*z)*(-49*z**3) + (3*z**2)*(-3*z**3 + 14*z) + (-49*z**3)*(-3*z**3)\nSimplifying the partial expression: (3*z**2)*(-3*z**3 + 14*z)\nExpanding the part (-3*z**3 + 14*z) using the distributive property, and we got: (14*z)*(3*z**2) + (3*z**2)*(-3*z**3)\nReplacing (3*z**2)*(-3*z**3 + 14*z) with (14*z)*(3*z**2) + (3*z**2)*(-3*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (14*z)*(3*z**2) + (14*z)*(-49*z**3) + (3*z**2)*(-3*z**3) + (-49*z**3)*(-3*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-3*z**3)*(-49*z**3) = 147*z**6\n (-3*z**3)*(3*z**2) = -9*z**5\n (14*z)*(-49*z**3) = -686*z**4\n (14*z)*(3*z**2) = 42*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 147*z**6 - 9*z**5 - 686*z**4 + 42*z**3\nNo more calculations needed.\n147*z**6 - 9*z**5 - 686*z**4 + 42*z**3", "generated_answer": "147*z**6 - 9*z**5 - 686*z**4 + 42*z**3", "step_length": 5} {"cot_id": "6bc67c74332375c792e895216658d55a73e5bd039bc73d364fc931f4f431560d", "datapoint": {"question": "Calculate the following: (43 - 10*x)*(-59*x**2 - 14*x + 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "590*x**3 - 2397*x**2 - 922*x + 1376", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1736, "polynomial_expr": "(43 - 10*x)*(-59*x**2 - 14*x + 32)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (43 - 10*x)*(-59*x**2 - 14*x + 32)\nExpanding the part (43 - 10*x) using the distributive property, and we got: (-10*x)*(-59*x**2 - 14*x + 32) + 43*(-59*x**2 - 14*x + 32)\n#Step 2:\nCurrent expression: (-10*x)*(-59*x**2 - 14*x + 32) + 43*(-59*x**2 - 14*x + 32)\nSimplifying the partial expression: 43*(-59*x**2 - 14*x + 32)\nExpanding the part (-59*x**2 - 14*x + 32) using the distributive property, and we got: -14*x*43 - 59*x**2*43 + 32*43\nReplacing 43*(-59*x**2 - 14*x + 32) with -14*x*43 - 59*x**2*43 + 32*43 in the overall expression.\n#Step 3:\nCurrent expression: -14*x*43 + (-10*x)*(-59*x**2 - 14*x + 32) - 59*x**2*43 + 1376\nSimplifying the partial expression: (-10*x)*(-59*x**2 - 14*x + 32)\nExpanding the part (-59*x**2 - 14*x + 32) using the distributive property, and we got: (-14*x)*(-10*x) + (-10*x)*(-59*x**2) + 32*(-10*x)\nReplacing (-10*x)*(-59*x**2 - 14*x + 32) with (-14*x)*(-10*x) + (-10*x)*(-59*x**2) + 32*(-10*x) in the overall expression.\n#Step 4:\nCurrent expression: (-14*x)*(-10*x) - 14*x*43 + (-10*x)*(-59*x**2) + 32*(-10)*x - 59*x**2*43 + 1376\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-59*x**2)*43 = -2537*x**2\n (-59*x**2)*(-10*x) = 590*x**3\n (-14*x)*43 = -602*x\n (-14*x)*(-10*x) = 140*x**2\n 32*-10*x = -320*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 590*x**3 - 2537*x**2 + 140*x**2 - 602*x - 320*x + 1376\nCombining like terms, got 590*x**3 - 2397*x**2 - 922*x + 1376\n#Step 6:\nCurrent expression: 590*x**3 - 2397*x**2 - 922*x + 1376\nNo more calculations needed.\n590*x**3 - 2397*x**2 - 922*x + 1376", "generated_answer": "590*x**3 - 2397*x**2 - 922*x + 1376", "step_length": 6} {"cot_id": "f3e981372a3afb343cf52fec641604cf671cae1c59fc74457ccd1ffdcc74d320", "datapoint": {"question": "Calculate the following: (42*z**2 - 8*z)*(-25*z**3 + 32*z**2 + 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1050*z**5 + 1544*z**4 - 256*z**3 + 2058*z**2 - 392*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1737, "polynomial_expr": "(42*z**2 - 8*z)*(-25*z**3 + 32*z**2 + 49)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (42*z**2 - 8*z)*(-25*z**3 + 32*z**2 + 49)\nExpanding the part (42*z**2 - 8*z) using the distributive property, and we got: (-8*z)*(-25*z**3 + 32*z**2 + 49) + (42*z**2)*(-25*z**3 + 32*z**2 + 49)\n#Step 2:\nCurrent expression: (-8*z)*(-25*z**3 + 32*z**2 + 49) + (42*z**2)*(-25*z**3 + 32*z**2 + 49)\nSimplifying the partial expression: (-8*z)*(-25*z**3 + 32*z**2 + 49)\nExpanding the part (-25*z**3 + 32*z**2 + 49) using the distributive property, and we got: (-8*z)*(32*z**2) + (-8*z)*(-25*z**3) + 49*(-8*z)\nReplacing (-8*z)*(-25*z**3 + 32*z**2 + 49) with (-8*z)*(32*z**2) + (-8*z)*(-25*z**3) + 49*(-8*z) in the overall expression.\n#Step 3:\nCurrent expression: (-8*z)*(32*z**2) + (-8*z)*(-25*z**3) + 49*(-8)*z + (42*z**2)*(-25*z**3 + 32*z**2 + 49)\nSimplifying the partial expression: (42*z**2)*(-25*z**3 + 32*z**2 + 49)\nExpanding the part (-25*z**3 + 32*z**2 + 49) using the distributive property, and we got: 49*(42*z**2) + (32*z**2)*(42*z**2) + (42*z**2)*(-25*z**3)\nReplacing (42*z**2)*(-25*z**3 + 32*z**2 + 49) with 49*(42*z**2) + (32*z**2)*(42*z**2) + (42*z**2)*(-25*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-8*z)*(32*z**2) + (-8*z)*(-25*z**3) + 49*42*z**2 + 49*(-8)*z + (32*z**2)*(42*z**2) + (42*z**2)*(-25*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*z**3)*(-8*z) = 200*z**4\n (-25*z**3)*(42*z**2) = -1050*z**5\n (32*z**2)*(-8*z) = -256*z**3\n (32*z**2)*(42*z**2) = 1344*z**4\n 49*-8*z = -392*z\n 49*42*z**2 = 2058*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1050*z**5 + 200*z**4 + 1344*z**4 - 256*z**3 + 2058*z**2 - 392*z\nCombining like terms, got -1050*z**5 + 1544*z**4 - 256*z**3 + 2058*z**2 - 392*z\n#Step 6:\nCurrent expression: -1050*z**5 + 1544*z**4 - 256*z**3 + 2058*z**2 - 392*z\nNo more calculations needed.\n-1050*z**5 + 1544*z**4 - 256*z**3 + 2058*z**2 - 392*z", "generated_answer": "-1050*z**5 + 1544*z**4 - 256*z**3 + 2058*z**2 - 392*z", "step_length": 6} {"cot_id": "b07a18e36aa2cc648790c1ca0dbb029a3010556a5317593e811fdda321c1db9d", "datapoint": {"question": "Simplify this expression: (-33*z**3 - 48*z**2 + 45)*(-4*z**3 + 14*z**2 - 36*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "132*z**6 - 270*z**5 + 516*z**4 + 1548*z**3 + 630*z**2 - 1620*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1738, "polynomial_expr": "(-33*z**3 - 48*z**2 + 45)*(-4*z**3 + 14*z**2 - 36*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-33*z**3 - 48*z**2 + 45)*(-4*z**3 + 14*z**2 - 36*z)\nExpanding the part (-33*z**3 - 48*z**2 + 45) using the distributive property, and we got: (-48*z**2)*(-4*z**3 + 14*z**2 - 36*z) + (-33*z**3)*(-4*z**3 + 14*z**2 - 36*z) + 45*(-4*z**3 + 14*z**2 - 36*z)\n#Step 2:\nCurrent expression: (-48*z**2)*(-4*z**3 + 14*z**2 - 36*z) + (-33*z**3)*(-4*z**3 + 14*z**2 - 36*z) + 45*(-4*z**3 + 14*z**2 - 36*z)\nSimplifying the partial expression: 45*(-4*z**3 + 14*z**2 - 36*z)\nExpanding the part (-4*z**3 + 14*z**2 - 36*z) using the distributive property, and we got: -36*z*45 + (14*z**2)*45 - 4*z**3*45\nReplacing 45*(-4*z**3 + 14*z**2 - 36*z) with -36*z*45 + (14*z**2)*45 - 4*z**3*45 in the overall expression.\n#Step 3:\nCurrent expression: -36*z*45 + (-48*z**2)*(-4*z**3 + 14*z**2 - 36*z) + (14*z**2)*45 + (-33*z**3)*(-4*z**3 + 14*z**2 - 36*z) - 4*z**3*45\nSimplifying the partial expression: (-48*z**2)*(-4*z**3 + 14*z**2 - 36*z)\nExpanding the part (-4*z**3 + 14*z**2 - 36*z) using the distributive property, and we got: (-36*z)*(-48*z**2) + (-48*z**2)*(14*z**2) + (-48*z**2)*(-4*z**3)\nReplacing (-48*z**2)*(-4*z**3 + 14*z**2 - 36*z) with (-36*z)*(-48*z**2) + (-48*z**2)*(14*z**2) + (-48*z**2)*(-4*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-36*z)*(-48*z**2) - 36*z*45 + (-48*z**2)*(14*z**2) + (-48*z**2)*(-4*z**3) + (14*z**2)*45 + (-33*z**3)*(-4*z**3 + 14*z**2 - 36*z) - 4*z**3*45\nSimplifying the partial expression: (-33*z**3)*(-4*z**3 + 14*z**2 - 36*z)\nExpanding the part (-4*z**3 + 14*z**2 - 36*z) using the distributive property, and we got: (-36*z)*(-33*z**3) + (14*z**2)*(-33*z**3) + (-33*z**3)*(-4*z**3)\nReplacing (-33*z**3)*(-4*z**3 + 14*z**2 - 36*z) with (-36*z)*(-33*z**3) + (14*z**2)*(-33*z**3) + (-33*z**3)*(-4*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-36*z)*(-48*z**2) + (-36*z)*(-33*z**3) - 36*z*45 + (-48*z**2)*(14*z**2) + (-48*z**2)*(-4*z**3) + (14*z**2)*(-33*z**3) + (14*z**2)*45 + (-33*z**3)*(-4*z**3) - 4*z**3*45\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*z)*45 = -1620*z\n (-36*z)*(-48*z**2) = 1728*z**3\n (-36*z)*(-33*z**3) = 1188*z**4\n (-4*z**3)*45 = -180*z**3\n (-4*z**3)*(-48*z**2) = 192*z**5\n (-4*z**3)*(-33*z**3) = 132*z**6\n (14*z**2)*45 = 630*z**2\n (14*z**2)*(-48*z**2) = -672*z**4\n (14*z**2)*(-33*z**3) = -462*z**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 132*z**6 - 462*z**5 + 192*z**5 - 672*z**4 + 1188*z**4 - 180*z**3 + 1728*z**3 + 630*z**2 - 1620*z\nCombining like terms, got 132*z**6 - 270*z**5 + 516*z**4 + 1548*z**3 + 630*z**2 - 1620*z\n#Step 7:\nCurrent expression: 132*z**6 - 270*z**5 + 516*z**4 + 1548*z**3 + 630*z**2 - 1620*z\nNo more calculations needed.\n132*z**6 - 270*z**5 + 516*z**4 + 1548*z**3 + 630*z**2 - 1620*z", "generated_answer": "132*z**6 - 270*z**5 + 516*z**4 + 1548*z**3 + 630*z**2 - 1620*z", "step_length": 7} {"cot_id": "654c0b90587fe83425f374e4271d0e790dca92b6671cef91dfc19e6f2c2beb3f", "datapoint": {"question": "Simplify this expression: 70*x**3 + 750*x - 10\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "70*x**3 + 750*x - 10", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1739, "polynomial_expr": "70*x**3 + 750*x - 10", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 70*x**3 + 750*x - 10\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 70*x**3 + 750*x - 10\nNo more calculations needed.\n70*x**3 + 750*x - 10", "generated_answer": "70*x**3 + 750*x - 10", "step_length": 2} {"cot_id": "a5d5d1151fd95597730ef55a25aea88ebad8da6960522b04a46631e3db950957", "datapoint": {"question": "Calculate the following: (19 - 34*y**2)*(-42*y**3 + 33*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1428*y**5 - 1920*y**3 + 627*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1740, "polynomial_expr": "(19 - 34*y**2)*(-42*y**3 + 33*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (19 - 34*y**2)*(-42*y**3 + 33*y)\nExpanding the part (19 - 34*y**2) using the distributive property, and we got: (-34*y**2)*(-42*y**3 + 33*y) + 19*(-42*y**3 + 33*y)\n#Step 2:\nCurrent expression: (-34*y**2)*(-42*y**3 + 33*y) + 19*(-42*y**3 + 33*y)\nSimplifying the partial expression: 19*(-42*y**3 + 33*y)\nExpanding the part (-42*y**3 + 33*y) using the distributive property, and we got: (33*y)*19 - 42*y**3*19\nReplacing 19*(-42*y**3 + 33*y) with (33*y)*19 - 42*y**3*19 in the overall expression.\n#Step 3:\nCurrent expression: (33*y)*19 + (-34*y**2)*(-42*y**3 + 33*y) - 42*y**3*19\nSimplifying the partial expression: (-34*y**2)*(-42*y**3 + 33*y)\nExpanding the part (-42*y**3 + 33*y) using the distributive property, and we got: (33*y)*(-34*y**2) + (-34*y**2)*(-42*y**3)\nReplacing (-34*y**2)*(-42*y**3 + 33*y) with (33*y)*(-34*y**2) + (-34*y**2)*(-42*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (33*y)*(-34*y**2) + (33*y)*19 + (-34*y**2)*(-42*y**3) - 42*y**3*19\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*y**3)*19 = -798*y**3\n (-42*y**3)*(-34*y**2) = 1428*y**5\n (33*y)*19 = 627*y\n (33*y)*(-34*y**2) = -1122*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1428*y**5 - 1122*y**3 - 798*y**3 + 627*y\nCombining like terms, got 1428*y**5 - 1920*y**3 + 627*y\n#Step 6:\nCurrent expression: 1428*y**5 - 1920*y**3 + 627*y\nNo more calculations needed.\n1428*y**5 - 1920*y**3 + 627*y", "generated_answer": "1428*y**5 - 1920*y**3 + 627*y", "step_length": 6} {"cot_id": "cbed9a2fa7df80b9565bb4c4403b5f0f72a0df572cba6132de9e177834d8406d", "datapoint": {"question": "Calculate the following: (-78*y**3 - 10*y)*(14*y**3 + 83*y - 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1092*y**6 - 6614*y**4 + 3198*y**3 - 830*y**2 + 410*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1741, "polynomial_expr": "(-78*y**3 - 10*y)*(14*y**3 + 83*y - 41)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-78*y**3 - 10*y)*(14*y**3 + 83*y - 41)\nExpanding the part (-78*y**3 - 10*y) using the distributive property, and we got: (-10*y)*(14*y**3 + 83*y - 41) + (-78*y**3)*(14*y**3 + 83*y - 41)\n#Step 2:\nCurrent expression: (-10*y)*(14*y**3 + 83*y - 41) + (-78*y**3)*(14*y**3 + 83*y - 41)\nSimplifying the partial expression: (-78*y**3)*(14*y**3 + 83*y - 41)\nExpanding the part (14*y**3 + 83*y - 41) using the distributive property, and we got: -(-1)*3198*y**3 + (83*y)*(-78*y**3) + (-78*y**3)*(14*y**3)\nReplacing (-78*y**3)*(14*y**3 + 83*y - 41) with -(-1)*3198*y**3 + (83*y)*(-78*y**3) + (-78*y**3)*(14*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-10*y)*(14*y**3 + 83*y - 41) - 41*(-78)*y**3 + (83*y)*(-78*y**3) + (-78*y**3)*(14*y**3)\nSimplifying the partial expression: (-10*y)*(14*y**3 + 83*y - 41)\nExpanding the part (14*y**3 + 83*y - 41) using the distributive property, and we got: (-10*y)*(83*y) + (-10*y)*(14*y**3) - (-1)*410*y\nReplacing (-10*y)*(14*y**3 + 83*y - 41) with (-10*y)*(83*y) + (-10*y)*(14*y**3) - (-1)*410*y in the overall expression.\n#Step 4:\nCurrent expression: (-10*y)*(83*y) + (-10*y)*(14*y**3) - 41*(-78)*y**3 - 41*(-10)*y + (83*y)*(-78*y**3) + (-78*y**3)*(14*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (14*y**3)*(-78*y**3) = -1092*y**6\n (14*y**3)*(-10*y) = -140*y**4\n (83*y)*(-78*y**3) = -6474*y**4\n (83*y)*(-10*y) = -830*y**2\n -41*-78*y**3 = 3198*y**3\n -41*-10*y = 410*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1092*y**6 - 6474*y**4 - 140*y**4 + 3198*y**3 - 830*y**2 + 410*y\nCombining like terms, got -1092*y**6 - 6614*y**4 + 3198*y**3 - 830*y**2 + 410*y\n#Step 6:\nCurrent expression: -1092*y**6 - 6614*y**4 + 3198*y**3 - 830*y**2 + 410*y\nNo more calculations needed.\n-1092*y**6 - 6614*y**4 + 3198*y**3 - 830*y**2 + 410*y", "generated_answer": "-1092*y**6 - 6614*y**4 + 3198*y**3 - 830*y**2 + 410*y", "step_length": 6} {"cot_id": "a408b93d2b2f51f7ef45650c220d6cbac019b9ab4442217bf0eff8eba7e5fdde", "datapoint": {"question": "Calculate the following: 44*x**2*(44 - 16*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-704*x**3 + 1936*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1742, "polynomial_expr": "44*x**2*(44 - 16*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 44*x**2*(44 - 16*x)\nExpanding the part (44 - 16*x) using the distributive property, and we got: (-16*x)*(44*x**2) + 44*(44*x**2)\n#Step 2:\nCurrent expression: (-16*x)*(44*x**2) + 44*(44*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 44*(44*x**2) = 1936*x**2\n (-16*x)*(44*x**2) = -704*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -704*x**3 + 1936*x**2\nNo more calculations needed.\n-704*x**3 + 1936*x**2", "generated_answer": "-704*x**3 + 1936*x**2", "step_length": 3} {"cot_id": "3f219c870290ac061e62f35287aac06202e47e44c327c99c203b2dce1aa07a07", "datapoint": {"question": "Calculate the following: -5*z*(26*z**3 + 17*z - 4)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-130*z**4 - 85*z**2 + 20*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1743, "polynomial_expr": "-5*z*(26*z**3 + 17*z - 4)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -5*z*(26*z**3 + 17*z - 4)\nExpanding the part (26*z**3 + 17*z - 4) using the distributive property, and we got: (-5*z)*(17*z) + (-5*z)*(26*z**3) - (-1)*20*z\n#Step 2:\nCurrent expression: (-5*z)*(17*z) + (-5*z)*(26*z**3) - (-1)*20*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -4*(-5*z) = 20*z\n (17*z)*(-5*z) = -85*z**2\n (26*z**3)*(-5*z) = -130*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -130*z**4 - 85*z**2 + 20*z\nNo more calculations needed.\n-130*z**4 - 85*z**2 + 20*z", "generated_answer": "-130*z**4 - 85*z**2 + 20*z", "step_length": 3} {"cot_id": "4b4a957f3303f0f12c8f71e3ebc56e63fc682e83c0cc7992839abfc484bed2e1", "datapoint": {"question": "Calculate the following: (-22*z**2 - 17*z + 41)*(-41*z**3 - 41*z - 40)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "902*z**5 + 697*z**4 - 779*z**3 + 1577*z**2 - 1001*z - 1640", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1744, "polynomial_expr": "(-22*z**2 - 17*z + 41)*(-41*z**3 - 41*z - 40)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-22*z**2 - 17*z + 41)*(-41*z**3 - 41*z - 40)\nExpanding the part (-41*z**3 - 41*z - 40) using the distributive property, and we got: (-41*z)*(-22*z**2 - 17*z + 41) + (-41*z**3)*(-22*z**2 - 17*z + 41) - 40*(-22*z**2 - 17*z + 41)\n#Step 2:\nCurrent expression: (-41*z)*(-22*z**2 - 17*z + 41) + (-41*z**3)*(-22*z**2 - 17*z + 41) - 40*(-22*z**2 - 17*z + 41)\nSimplifying the partial expression: -40*(-22*z**2 - 17*z + 41)\nExpanding the part (-22*z**2 - 17*z + 41) using the distributive property, and we got: -17*z*(-40) - 22*z**2*(-40) + 41*(-40)\nReplacing -40*(-22*z**2 - 17*z + 41) with -17*z*(-40) - 22*z**2*(-40) + 41*(-40) in the overall expression.\n#Step 3:\nCurrent expression: (-41*z)*(-22*z**2 - 17*z + 41) - 17*z*(-40) - 22*z**2*(-40) + (-41*z**3)*(-22*z**2 - 17*z + 41) - 1640\nSimplifying the partial expression: (-41*z)*(-22*z**2 - 17*z + 41)\nExpanding the part (-22*z**2 - 17*z + 41) using the distributive property, and we got: (-41*z)*(-17*z) + (-41*z)*(-22*z**2) + 41*(-41*z)\nReplacing (-41*z)*(-22*z**2 - 17*z + 41) with (-41*z)*(-17*z) + (-41*z)*(-22*z**2) + 41*(-41*z) in the overall expression.\n#Step 4:\nCurrent expression: (-41*z)*(-17*z) + (-41*z)*(-22*z**2) - 17*z*(-40) + 41*(-41)*z - 22*z**2*(-40) + (-41*z**3)*(-22*z**2 - 17*z + 41) - 1640\nSimplifying the partial expression: (-41*z**3)*(-22*z**2 - 17*z + 41)\nExpanding the part (-22*z**2 - 17*z + 41) using the distributive property, and we got: (-17*z)*(-41*z**3) + 41*(-41*z**3) + (-22*z**2)*(-41*z**3)\nReplacing (-41*z**3)*(-22*z**2 - 17*z + 41) with (-17*z)*(-41*z**3) + 41*(-41*z**3) + (-22*z**2)*(-41*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-41*z)*(-17*z) + (-41*z)*(-22*z**2) + (-17*z)*(-41*z**3) - 17*z*(-40) + 41*(-41)*z**3 + 41*(-41)*z + (-22*z**2)*(-41*z**3) - 22*z**2*(-40) - 1640\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*z**2)*-40 = 880*z**2\n (-22*z**2)*(-41*z) = 902*z**3\n (-22*z**2)*(-41*z**3) = 902*z**5\n (-17*z)*-40 = 680*z\n (-17*z)*(-41*z) = 697*z**2\n (-17*z)*(-41*z**3) = 697*z**4\n 41*-41*z = -1681*z\n 41*-41*z**3 = -1681*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 902*z**5 + 697*z**4 - 1681*z**3 + 902*z**3 + 697*z**2 + 880*z**2 - 1681*z + 680*z - 1640\nCombining like terms, got 902*z**5 + 697*z**4 - 779*z**3 + 1577*z**2 - 1001*z - 1640\n#Step 7:\nCurrent expression: 902*z**5 + 697*z**4 - 779*z**3 + 1577*z**2 - 1001*z - 1640\nNo more calculations needed.\n902*z**5 + 697*z**4 - 779*z**3 + 1577*z**2 - 1001*z - 1640", "generated_answer": "902*z**5 + 697*z**4 - 779*z**3 + 1577*z**2 - 1001*z - 1640", "step_length": 7} {"cot_id": "53bea9fd07ea0317fe58c17fba937c26903eb80df836ca4a8ab3ce13fa595e0d", "datapoint": {"question": "Calculate the following: 54*x**2*(-10*x**3 - 44*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-540*x**5 - 2376*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1745, "polynomial_expr": "54*x**2*(-10*x**3 - 44*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 54*x**2*(-10*x**3 - 44*x**2)\nExpanding the part (-10*x**3 - 44*x**2) using the distributive property, and we got: (-44*x**2)*(54*x**2) + (54*x**2)*(-10*x**3)\n#Step 2:\nCurrent expression: (-44*x**2)*(54*x**2) + (54*x**2)*(-10*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-44*x**2)*(54*x**2) = -2376*x**4\n (-10*x**3)*(54*x**2) = -540*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -540*x**5 - 2376*x**4\nNo more calculations needed.\n-540*x**5 - 2376*x**4", "generated_answer": "-540*x**5 - 2376*x**4", "step_length": 3} {"cot_id": "326b991244d8cbb11b3fc1a6b697b33b02554b726a8920ed0c752fc74b47bff3", "datapoint": {"question": "Simplify this expression: (5 - 66*x**3)*(-14*x**2 - 5)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "924*x**5 + 330*x**3 - 70*x**2 - 25", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1746, "polynomial_expr": "(5 - 66*x**3)*(-14*x**2 - 5)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (5 - 66*x**3)*(-14*x**2 - 5)\nExpanding the part (-14*x**2 - 5) using the distributive property, and we got: (-14*x**2)*(5 - 66*x**3) - 5*(5 - 66*x**3)\n#Step 2:\nCurrent expression: (-14*x**2)*(5 - 66*x**3) - 5*(5 - 66*x**3)\nSimplifying the partial expression: -5*(5 - 66*x**3)\nExpanding the part (5 - 66*x**3) using the distributive property, and we got: -66*x**3*(-5) + 5*(-5)\nReplacing -5*(5 - 66*x**3) with -66*x**3*(-5) + 5*(-5) in the overall expression.\n#Step 3:\nCurrent expression: (-14*x**2)*(5 - 66*x**3) - 66*x**3*(-5) - 25\nSimplifying the partial expression: (-14*x**2)*(5 - 66*x**3)\nExpanding the part (5 - 66*x**3) using the distributive property, and we got: 5*(-14*x**2) + (-14*x**2)*(-66*x**3)\nReplacing (-14*x**2)*(5 - 66*x**3) with 5*(-14*x**2) + (-14*x**2)*(-66*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 5*(-14)*x**2 + (-14*x**2)*(-66*x**3) - 66*x**3*(-5) - 25\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-66*x**3)*-5 = 330*x**3\n (-66*x**3)*(-14*x**2) = 924*x**5\n 5*-14*x**2 = -70*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 924*x**5 + 330*x**3 - 70*x**2 - 25\nNo more calculations needed.\n924*x**5 + 330*x**3 - 70*x**2 - 25", "generated_answer": "924*x**5 + 330*x**3 - 70*x**2 - 25", "step_length": 5} {"cot_id": "b31e0e2220f4706668d787fd836f7ec913058aeabc0187be903dbada45fade68", "datapoint": {"question": "Simplify this expression: (40*z**3 + 27)*(74*z**3 - 41*z**2 - 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2960*z**6 - 1640*z**5 + 358*z**3 - 1107*z**2 - 1107", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1747, "polynomial_expr": "(40*z**3 + 27)*(74*z**3 - 41*z**2 - 41)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (40*z**3 + 27)*(74*z**3 - 41*z**2 - 41)\nExpanding the part (40*z**3 + 27) using the distributive property, and we got: (40*z**3)*(74*z**3 - 41*z**2 - 41) + 27*(74*z**3 - 41*z**2 - 41)\n#Step 2:\nCurrent expression: (40*z**3)*(74*z**3 - 41*z**2 - 41) + 27*(74*z**3 - 41*z**2 - 41)\nSimplifying the partial expression: 27*(74*z**3 - 41*z**2 - 41)\nExpanding the part (74*z**3 - 41*z**2 - 41) using the distributive property, and we got: -41*z**2*27 + (74*z**3)*27 - 41*27\nReplacing 27*(74*z**3 - 41*z**2 - 41) with -41*z**2*27 + (74*z**3)*27 - 41*27 in the overall expression.\n#Step 3:\nCurrent expression: -41*z**2*27 + (40*z**3)*(74*z**3 - 41*z**2 - 41) + (74*z**3)*27 - 1107\nSimplifying the partial expression: (40*z**3)*(74*z**3 - 41*z**2 - 41)\nExpanding the part (74*z**3 - 41*z**2 - 41) using the distributive property, and we got: -1640*z**3 + (-41*z**2)*(40*z**3) + (40*z**3)*(74*z**3)\nReplacing (40*z**3)*(74*z**3 - 41*z**2 - 41) with -1640*z**3 + (-41*z**2)*(40*z**3) + (40*z**3)*(74*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -41*40*z**3 + (-41*z**2)*(40*z**3) - 41*z**2*27 + (40*z**3)*(74*z**3) + (74*z**3)*27 - 1107\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*z**2)*27 = -1107*z**2\n (-41*z**2)*(40*z**3) = -1640*z**5\n (74*z**3)*27 = 1998*z**3\n (74*z**3)*(40*z**3) = 2960*z**6\n -41*40*z**3 = -1640*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2960*z**6 - 1640*z**5 - 1640*z**3 + 1998*z**3 - 1107*z**2 - 1107\nCombining like terms, got 2960*z**6 - 1640*z**5 + 358*z**3 - 1107*z**2 - 1107\n#Step 6:\nCurrent expression: 2960*z**6 - 1640*z**5 + 358*z**3 - 1107*z**2 - 1107\nNo more calculations needed.\n2960*z**6 - 1640*z**5 + 358*z**3 - 1107*z**2 - 1107", "generated_answer": "2960*z**6 - 1640*z**5 + 358*z**3 - 1107*z**2 - 1107", "step_length": 6} {"cot_id": "7f53400db10e2b71c15120126d7052093f45107498bc4cff9ba36650d54e7b82", "datapoint": {"question": "Calculate the following: (-x**3 - 24*x**2)*(-35*x**3 + 12*x**2 + 9)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "35*x**6 + 828*x**5 - 288*x**4 - 9*x**3 - 216*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1748, "polynomial_expr": "(-x**3 - 24*x**2)*(-35*x**3 + 12*x**2 + 9)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-x**3 - 24*x**2)*(-35*x**3 + 12*x**2 + 9)\nExpanding the part (-x**3 - 24*x**2) using the distributive property, and we got: (-24*x**2)*(-35*x**3 + 12*x**2 + 9) + (-x**3)*(-35*x**3 + 12*x**2 + 9)\n#Step 2:\nCurrent expression: (-24*x**2)*(-35*x**3 + 12*x**2 + 9) + (-x**3)*(-35*x**3 + 12*x**2 + 9)\nSimplifying the partial expression: (-x**3)*(-35*x**3 + 12*x**2 + 9)\nExpanding the part (-35*x**3 + 12*x**2 + 9) using the distributive property, and we got: 9*(-x**3) + (12*x**2)*(-x**3) + (-35*x**3)*(-x**3)\nReplacing (-x**3)*(-35*x**3 + 12*x**2 + 9) with 9*(-x**3) + (12*x**2)*(-x**3) + (-35*x**3)*(-x**3) in the overall expression.\n#Step 3:\nCurrent expression: 9*(-1)*x**3 + (-24*x**2)*(-35*x**3 + 12*x**2 + 9) + (12*x**2)*(-x**3) + (-35*x**3)*(-x**3)\nSimplifying the partial expression: (-24*x**2)*(-35*x**3 + 12*x**2 + 9)\nExpanding the part (-35*x**3 + 12*x**2 + 9) using the distributive property, and we got: 9*(-24*x**2) + (-24*x**2)*(12*x**2) + (-24*x**2)*(-35*x**3)\nReplacing (-24*x**2)*(-35*x**3 + 12*x**2 + 9) with 9*(-24*x**2) + (-24*x**2)*(12*x**2) + (-24*x**2)*(-35*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 9*(-1)*x**3 + 9*(-24)*x**2 + (-24*x**2)*(12*x**2) + (-24*x**2)*(-35*x**3) + (12*x**2)*(-x**3) + (-35*x**3)*(-x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*x**3)*(-x**3) = 35*x**6\n (-35*x**3)*(-24*x**2) = 840*x**5\n (12*x**2)*(-x**3) = -12*x**5\n (12*x**2)*(-24*x**2) = -288*x**4\n 9*-1*x**3 = -9*x**3\n 9*-24*x**2 = -216*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 35*x**6 - 12*x**5 + 840*x**5 - 288*x**4 - 9*x**3 - 216*x**2\nCombining like terms, got 35*x**6 + 828*x**5 - 288*x**4 - 9*x**3 - 216*x**2\n#Step 6:\nCurrent expression: 35*x**6 + 828*x**5 - 288*x**4 - 9*x**3 - 216*x**2\nNo more calculations needed.\n35*x**6 + 828*x**5 - 288*x**4 - 9*x**3 - 216*x**2", "generated_answer": "35*x**6 + 828*x**5 - 288*x**4 - 9*x**3 - 216*x**2", "step_length": 6} {"cot_id": "1eae258ddc4df51c217281fb83adae3572969863a8d2f5964eea1359c2410655", "datapoint": {"question": "Simplify this expression: (-39*y**2 + 3*y)*(19*y**3 + 37)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-741*y**5 + 57*y**4 - 1443*y**2 + 111*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1749, "polynomial_expr": "(-39*y**2 + 3*y)*(19*y**3 + 37)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-39*y**2 + 3*y)*(19*y**3 + 37)\nExpanding the part (19*y**3 + 37) using the distributive property, and we got: (19*y**3)*(-39*y**2 + 3*y) + 37*(-39*y**2 + 3*y)\n#Step 2:\nCurrent expression: (19*y**3)*(-39*y**2 + 3*y) + 37*(-39*y**2 + 3*y)\nSimplifying the partial expression: 37*(-39*y**2 + 3*y)\nExpanding the part (-39*y**2 + 3*y) using the distributive property, and we got: (3*y)*37 - 39*y**2*37\nReplacing 37*(-39*y**2 + 3*y) with (3*y)*37 - 39*y**2*37 in the overall expression.\n#Step 3:\nCurrent expression: (3*y)*37 - 39*y**2*37 + (19*y**3)*(-39*y**2 + 3*y)\nSimplifying the partial expression: (19*y**3)*(-39*y**2 + 3*y)\nExpanding the part (-39*y**2 + 3*y) using the distributive property, and we got: (3*y)*(19*y**3) + (-39*y**2)*(19*y**3)\nReplacing (19*y**3)*(-39*y**2 + 3*y) with (3*y)*(19*y**3) + (-39*y**2)*(19*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (3*y)*(19*y**3) + (3*y)*37 + (-39*y**2)*(19*y**3) - 39*y**2*37\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*y**2)*37 = -1443*y**2\n (-39*y**2)*(19*y**3) = -741*y**5\n (3*y)*37 = 111*y\n (3*y)*(19*y**3) = 57*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -741*y**5 + 57*y**4 - 1443*y**2 + 111*y\nNo more calculations needed.\n-741*y**5 + 57*y**4 - 1443*y**2 + 111*y", "generated_answer": "-741*y**5 + 57*y**4 - 1443*y**2 + 111*y", "step_length": 5} {"cot_id": "a4130b43f9a4ec9e9ecac98a227e553f9764ef89143dd459e68ff1c611e3cde8", "datapoint": {"question": "Calculate the following: (27 - 14*z**2)*(17*z**3 - 49*z - 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-238*z**5 + 1145*z**3 + 14*z**2 - 1323*z - 27", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1750, "polynomial_expr": "(27 - 14*z**2)*(17*z**3 - 49*z - 1)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27 - 14*z**2)*(17*z**3 - 49*z - 1)\nExpanding the part (27 - 14*z**2) using the distributive property, and we got: (-14*z**2)*(17*z**3 - 49*z - 1) + 27*(17*z**3 - 49*z - 1)\n#Step 2:\nCurrent expression: (-14*z**2)*(17*z**3 - 49*z - 1) + 27*(17*z**3 - 49*z - 1)\nSimplifying the partial expression: 27*(17*z**3 - 49*z - 1)\nExpanding the part (17*z**3 - 49*z - 1) using the distributive property, and we got: -49*z*27 + (17*z**3)*27 - 1*27\nReplacing 27*(17*z**3 - 49*z - 1) with -49*z*27 + (17*z**3)*27 - 1*27 in the overall expression.\n#Step 3:\nCurrent expression: -49*z*27 + (-14*z**2)*(17*z**3 - 49*z - 1) + (17*z**3)*27 - 27\nSimplifying the partial expression: (-14*z**2)*(17*z**3 - 49*z - 1)\nExpanding the part (17*z**3 - 49*z - 1) using the distributive property, and we got: (-49*z)*(-14*z**2) - (-1)*14*z**2 + (-14*z**2)*(17*z**3)\nReplacing (-14*z**2)*(17*z**3 - 49*z - 1) with (-49*z)*(-14*z**2) - (-1)*14*z**2 + (-14*z**2)*(17*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-49*z)*(-14*z**2) - 49*z*27 - 1*(-14)*z**2 + (-14*z**2)*(17*z**3) + (17*z**3)*27 - 27\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*z)*27 = -1323*z\n (-49*z)*(-14*z**2) = 686*z**3\n (17*z**3)*27 = 459*z**3\n (17*z**3)*(-14*z**2) = -238*z**5\n -1*-14*z**2 = 14*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -238*z**5 + 459*z**3 + 686*z**3 + 14*z**2 - 1323*z - 27\nCombining like terms, got -238*z**5 + 1145*z**3 + 14*z**2 - 1323*z - 27\n#Step 6:\nCurrent expression: -238*z**5 + 1145*z**3 + 14*z**2 - 1323*z - 27\nNo more calculations needed.\n-238*z**5 + 1145*z**3 + 14*z**2 - 1323*z - 27", "generated_answer": "-238*z**5 + 1145*z**3 + 14*z**2 - 1323*z - 27", "step_length": 6} {"cot_id": "6515dafe8369f46e7ff9024068bb8059e3f7e7f3656e60a5a2af6d4a0f357d07", "datapoint": {"question": "Calculate the following: 7*x**2*(48*x**3 - 20*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "336*x**5 - 140*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1751, "polynomial_expr": "7*x**2*(48*x**3 - 20*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 7*x**2*(48*x**3 - 20*x)\nExpanding the part (48*x**3 - 20*x) using the distributive property, and we got: (-20*x)*(7*x**2) + (7*x**2)*(48*x**3)\n#Step 2:\nCurrent expression: (-20*x)*(7*x**2) + (7*x**2)*(48*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*x)*(7*x**2) = -140*x**3\n (48*x**3)*(7*x**2) = 336*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 336*x**5 - 140*x**3\nNo more calculations needed.\n336*x**5 - 140*x**3", "generated_answer": "336*x**5 - 140*x**3", "step_length": 3} {"cot_id": "69adabcf7b14f73244ac10d244a1894f44da64114f8069856e998190b0dcdb75", "datapoint": {"question": "Simplify this expression: (4*y**3 - 37*y)*(32*y**3 + 3*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "128*y**6 - 1172*y**4 - 111*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1752, "polynomial_expr": "(4*y**3 - 37*y)*(32*y**3 + 3*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (4*y**3 - 37*y)*(32*y**3 + 3*y)\nExpanding the part (4*y**3 - 37*y) using the distributive property, and we got: (-37*y)*(32*y**3 + 3*y) + (4*y**3)*(32*y**3 + 3*y)\n#Step 2:\nCurrent expression: (-37*y)*(32*y**3 + 3*y) + (4*y**3)*(32*y**3 + 3*y)\nSimplifying the partial expression: (-37*y)*(32*y**3 + 3*y)\nExpanding the part (32*y**3 + 3*y) using the distributive property, and we got: (-37*y)*(3*y) + (-37*y)*(32*y**3)\nReplacing (-37*y)*(32*y**3 + 3*y) with (-37*y)*(3*y) + (-37*y)*(32*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-37*y)*(3*y) + (-37*y)*(32*y**3) + (4*y**3)*(32*y**3 + 3*y)\nSimplifying the partial expression: (4*y**3)*(32*y**3 + 3*y)\nExpanding the part (32*y**3 + 3*y) using the distributive property, and we got: (3*y)*(4*y**3) + (4*y**3)*(32*y**3)\nReplacing (4*y**3)*(32*y**3 + 3*y) with (3*y)*(4*y**3) + (4*y**3)*(32*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-37*y)*(3*y) + (-37*y)*(32*y**3) + (3*y)*(4*y**3) + (4*y**3)*(32*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (3*y)*(-37*y) = -111*y**2\n (3*y)*(4*y**3) = 12*y**4\n (32*y**3)*(-37*y) = -1184*y**4\n (32*y**3)*(4*y**3) = 128*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 128*y**6 - 1184*y**4 + 12*y**4 - 111*y**2\nCombining like terms, got 128*y**6 - 1172*y**4 - 111*y**2\n#Step 6:\nCurrent expression: 128*y**6 - 1172*y**4 - 111*y**2\nNo more calculations needed.\n128*y**6 - 1172*y**4 - 111*y**2", "generated_answer": "128*y**6 - 1172*y**4 - 111*y**2", "step_length": 6} {"cot_id": "808d05a2683894dc9aafc7f5d936dd192065564740b5800622736339ccc21cf0", "datapoint": {"question": "Simplify this expression: 34*x*(-30*x - 46)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1020*x**2 - 1564*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1753, "polynomial_expr": "34*x*(-30*x - 46)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 34*x*(-30*x - 46)\nExpanding the part (-30*x - 46) using the distributive property, and we got: (-30*x)*(34*x) - 1564*x\n#Step 2:\nCurrent expression: (-30*x)*(34*x) - 1564*x\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -46*(34*x) = -1564*x\n (-30*x)*(34*x) = -1020*x**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1020*x**2 - 1564*x\nNo more calculations needed.\n-1020*x**2 - 1564*x", "generated_answer": "-1020*x**2 - 1564*x", "step_length": 3} {"cot_id": "7cd11615649cbc1e73d5ed16df645117e7b506801dfc46cc05e2ee2dc46ed0f6", "datapoint": {"question": "Calculate the following: (21*y**2 + 34)*(-11*y**3 - 42*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-231*y**5 - 882*y**4 - 374*y**3 - 1428*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1754, "polynomial_expr": "(21*y**2 + 34)*(-11*y**3 - 42*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (21*y**2 + 34)*(-11*y**3 - 42*y**2)\nExpanding the part (21*y**2 + 34) using the distributive property, and we got: (21*y**2)*(-11*y**3 - 42*y**2) + 34*(-11*y**3 - 42*y**2)\n#Step 2:\nCurrent expression: (21*y**2)*(-11*y**3 - 42*y**2) + 34*(-11*y**3 - 42*y**2)\nSimplifying the partial expression: 34*(-11*y**3 - 42*y**2)\nExpanding the part (-11*y**3 - 42*y**2) using the distributive property, and we got: -42*y**2*34 - 11*y**3*34\nReplacing 34*(-11*y**3 - 42*y**2) with -42*y**2*34 - 11*y**3*34 in the overall expression.\n#Step 3:\nCurrent expression: -42*y**2*34 + (21*y**2)*(-11*y**3 - 42*y**2) - 11*y**3*34\nSimplifying the partial expression: (21*y**2)*(-11*y**3 - 42*y**2)\nExpanding the part (-11*y**3 - 42*y**2) using the distributive property, and we got: (-42*y**2)*(21*y**2) + (21*y**2)*(-11*y**3)\nReplacing (21*y**2)*(-11*y**3 - 42*y**2) with (-42*y**2)*(21*y**2) + (21*y**2)*(-11*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-42*y**2)*(21*y**2) - 42*y**2*34 + (21*y**2)*(-11*y**3) - 11*y**3*34\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*y**2)*34 = -1428*y**2\n (-42*y**2)*(21*y**2) = -882*y**4\n (-11*y**3)*34 = -374*y**3\n (-11*y**3)*(21*y**2) = -231*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -231*y**5 - 882*y**4 - 374*y**3 - 1428*y**2\nNo more calculations needed.\n-231*y**5 - 882*y**4 - 374*y**3 - 1428*y**2", "generated_answer": "-231*y**5 - 882*y**4 - 374*y**3 - 1428*y**2", "step_length": 5} {"cot_id": "422cde9fe1257103a8c210f8ca93ac3b254017fd9c9310e759924a34dbacab9c", "datapoint": {"question": "Simplify this expression: (39*y**2 - 50)*(-27*y**3 - 25*y**2 + 45*y - 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1053*y**5 - 975*y**4 + 3105*y**3 + 860*y**2 - 2250*y + 500", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1755, "polynomial_expr": "(39*y**2 - 50)*(-27*y**3 - 25*y**2 + 45*y - 10)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (39*y**2 - 50)*(-27*y**3 - 25*y**2 + 45*y - 10)\nExpanding the part (39*y**2 - 50) using the distributive property, and we got: (39*y**2)*(-27*y**3 - 25*y**2 + 45*y - 10) - 50*(-27*y**3 - 25*y**2 + 45*y - 10)\n#Step 2:\nCurrent expression: (39*y**2)*(-27*y**3 - 25*y**2 + 45*y - 10) - 50*(-27*y**3 - 25*y**2 + 45*y - 10)\nSimplifying the partial expression: -50*(-27*y**3 - 25*y**2 + 45*y - 10)\nExpanding the part (-27*y**3 - 25*y**2 + 45*y - 10) using the distributive property, and we got: (45*y)*(-50) - 25*y**2*(-50) - 27*y**3*(-50) - 10*(-50)\nReplacing -50*(-27*y**3 - 25*y**2 + 45*y - 10) with (45*y)*(-50) - 25*y**2*(-50) - 27*y**3*(-50) - 10*(-50) in the overall expression.\n#Step 3:\nCurrent expression: (45*y)*(-50) - 25*y**2*(-50) + (39*y**2)*(-27*y**3 - 25*y**2 + 45*y - 10) - 27*y**3*(-50) + 500\nSimplifying the partial expression: (39*y**2)*(-27*y**3 - 25*y**2 + 45*y - 10)\nExpanding the part (-27*y**3 - 25*y**2 + 45*y - 10) using the distributive property, and we got: -390*y**2 + (45*y)*(39*y**2) + (-25*y**2)*(39*y**2) + (39*y**2)*(-27*y**3)\nReplacing (39*y**2)*(-27*y**3 - 25*y**2 + 45*y - 10) with -390*y**2 + (45*y)*(39*y**2) + (-25*y**2)*(39*y**2) + (39*y**2)*(-27*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -10*39*y**2 + (45*y)*(39*y**2) + (45*y)*(-50) + (-25*y**2)*(39*y**2) - 25*y**2*(-50) + (39*y**2)*(-27*y**3) - 27*y**3*(-50) + 500\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*y**3)*-50 = 1350*y**3\n (-27*y**3)*(39*y**2) = -1053*y**5\n (-25*y**2)*-50 = 1250*y**2\n (-25*y**2)*(39*y**2) = -975*y**4\n (45*y)*-50 = -2250*y\n (45*y)*(39*y**2) = 1755*y**3\n -10*39*y**2 = -390*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1053*y**5 - 975*y**4 + 1350*y**3 + 1755*y**3 - 390*y**2 + 1250*y**2 - 2250*y + 500\nCombining like terms, got -1053*y**5 - 975*y**4 + 3105*y**3 + 860*y**2 - 2250*y + 500\n#Step 6:\nCurrent expression: -1053*y**5 - 975*y**4 + 3105*y**3 + 860*y**2 - 2250*y + 500\nNo more calculations needed.\n-1053*y**5 - 975*y**4 + 3105*y**3 + 860*y**2 - 2250*y + 500", "generated_answer": "-1053*y**5 - 975*y**4 + 3105*y**3 + 860*y**2 - 2250*y + 500", "step_length": 6} {"cot_id": "e1e7fcba1f59577f2969ce4808ee2c0dd9a2f6dd20883ecd226a665874aa74f3", "datapoint": {"question": "Simplify this expression: (30 - 10*y)*(50*y**3 + 40*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-500*y**4 + 1100*y**3 + 1200*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1756, "polynomial_expr": "(30 - 10*y)*(50*y**3 + 40*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (30 - 10*y)*(50*y**3 + 40*y**2)\nExpanding the part (30 - 10*y) using the distributive property, and we got: (-10*y)*(50*y**3 + 40*y**2) + 30*(50*y**3 + 40*y**2)\n#Step 2:\nCurrent expression: (-10*y)*(50*y**3 + 40*y**2) + 30*(50*y**3 + 40*y**2)\nSimplifying the partial expression: 30*(50*y**3 + 40*y**2)\nExpanding the part (50*y**3 + 40*y**2) using the distributive property, and we got: (40*y**2)*30 + (50*y**3)*30\nReplacing 30*(50*y**3 + 40*y**2) with (40*y**2)*30 + (50*y**3)*30 in the overall expression.\n#Step 3:\nCurrent expression: (-10*y)*(50*y**3 + 40*y**2) + (40*y**2)*30 + (50*y**3)*30\nSimplifying the partial expression: (-10*y)*(50*y**3 + 40*y**2)\nExpanding the part (50*y**3 + 40*y**2) using the distributive property, and we got: (-10*y)*(40*y**2) + (-10*y)*(50*y**3)\nReplacing (-10*y)*(50*y**3 + 40*y**2) with (-10*y)*(40*y**2) + (-10*y)*(50*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-10*y)*(40*y**2) + (-10*y)*(50*y**3) + (40*y**2)*30 + (50*y**3)*30\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (40*y**2)*30 = 1200*y**2\n (40*y**2)*(-10*y) = -400*y**3\n (50*y**3)*30 = 1500*y**3\n (50*y**3)*(-10*y) = -500*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -500*y**4 - 400*y**3 + 1500*y**3 + 1200*y**2\nCombining like terms, got -500*y**4 + 1100*y**3 + 1200*y**2\n#Step 6:\nCurrent expression: -500*y**4 + 1100*y**3 + 1200*y**2\nNo more calculations needed.\n-500*y**4 + 1100*y**3 + 1200*y**2", "generated_answer": "-500*y**4 + 1100*y**3 + 1200*y**2", "step_length": 6} {"cot_id": "0424d6d3dbc5dd8fb2aa56ffd1c74e77261c769c5db868518c33a92a0f6399ca", "datapoint": {"question": "Simplify this expression: (4*x**2 - 50)*(-22*x**3 + 33*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-88*x**5 + 132*x**4 + 1100*x**3 - 1650*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1757, "polynomial_expr": "(4*x**2 - 50)*(-22*x**3 + 33*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (4*x**2 - 50)*(-22*x**3 + 33*x**2)\nExpanding the part (4*x**2 - 50) using the distributive property, and we got: (4*x**2)*(-22*x**3 + 33*x**2) - 50*(-22*x**3 + 33*x**2)\n#Step 2:\nCurrent expression: (4*x**2)*(-22*x**3 + 33*x**2) - 50*(-22*x**3 + 33*x**2)\nSimplifying the partial expression: -50*(-22*x**3 + 33*x**2)\nExpanding the part (-22*x**3 + 33*x**2) using the distributive property, and we got: (33*x**2)*(-50) - 22*x**3*(-50)\nReplacing -50*(-22*x**3 + 33*x**2) with (33*x**2)*(-50) - 22*x**3*(-50) in the overall expression.\n#Step 3:\nCurrent expression: (4*x**2)*(-22*x**3 + 33*x**2) + (33*x**2)*(-50) - 22*x**3*(-50)\nSimplifying the partial expression: (4*x**2)*(-22*x**3 + 33*x**2)\nExpanding the part (-22*x**3 + 33*x**2) using the distributive property, and we got: (4*x**2)*(33*x**2) + (4*x**2)*(-22*x**3)\nReplacing (4*x**2)*(-22*x**3 + 33*x**2) with (4*x**2)*(33*x**2) + (4*x**2)*(-22*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (4*x**2)*(33*x**2) + (4*x**2)*(-22*x**3) + (33*x**2)*(-50) - 22*x**3*(-50)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*x**3)*-50 = 1100*x**3\n (-22*x**3)*(4*x**2) = -88*x**5\n (33*x**2)*-50 = -1650*x**2\n (33*x**2)*(4*x**2) = 132*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -88*x**5 + 132*x**4 + 1100*x**3 - 1650*x**2\nNo more calculations needed.\n-88*x**5 + 132*x**4 + 1100*x**3 - 1650*x**2", "generated_answer": "-88*x**5 + 132*x**4 + 1100*x**3 - 1650*x**2", "step_length": 5} {"cot_id": "76487215376b5085880e2f1323c085038918b1810affc5117d1df7d066ac6624", "datapoint": {"question": "Simplify this expression: (-45*y**2 + 22*y)*(28*y**3 - 30*y**2 - 2*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1260*y**5 + 1966*y**4 - 570*y**3 - 44*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1758, "polynomial_expr": "(-45*y**2 + 22*y)*(28*y**3 - 30*y**2 - 2*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-45*y**2 + 22*y)*(28*y**3 - 30*y**2 - 2*y)\nExpanding the part (-45*y**2 + 22*y) using the distributive property, and we got: (22*y)*(28*y**3 - 30*y**2 - 2*y) + (-45*y**2)*(28*y**3 - 30*y**2 - 2*y)\n#Step 2:\nCurrent expression: (22*y)*(28*y**3 - 30*y**2 - 2*y) + (-45*y**2)*(28*y**3 - 30*y**2 - 2*y)\nSimplifying the partial expression: (-45*y**2)*(28*y**3 - 30*y**2 - 2*y)\nExpanding the part (28*y**3 - 30*y**2 - 2*y) using the distributive property, and we got: (-2*y)*(-45*y**2) + (-45*y**2)*(-30*y**2) + (-45*y**2)*(28*y**3)\nReplacing (-45*y**2)*(28*y**3 - 30*y**2 - 2*y) with (-2*y)*(-45*y**2) + (-45*y**2)*(-30*y**2) + (-45*y**2)*(28*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-2*y)*(-45*y**2) + (22*y)*(28*y**3 - 30*y**2 - 2*y) + (-45*y**2)*(-30*y**2) + (-45*y**2)*(28*y**3)\nSimplifying the partial expression: (22*y)*(28*y**3 - 30*y**2 - 2*y)\nExpanding the part (28*y**3 - 30*y**2 - 2*y) using the distributive property, and we got: (-2*y)*(22*y) + (22*y)*(-30*y**2) + (22*y)*(28*y**3)\nReplacing (22*y)*(28*y**3 - 30*y**2 - 2*y) with (-2*y)*(22*y) + (22*y)*(-30*y**2) + (22*y)*(28*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-2*y)*(22*y) + (-2*y)*(-45*y**2) + (22*y)*(-30*y**2) + (22*y)*(28*y**3) + (-45*y**2)*(-30*y**2) + (-45*y**2)*(28*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*y**2)*(-45*y**2) = 1350*y**4\n (-30*y**2)*(22*y) = -660*y**3\n (-2*y)*(-45*y**2) = 90*y**3\n (-2*y)*(22*y) = -44*y**2\n (28*y**3)*(-45*y**2) = -1260*y**5\n (28*y**3)*(22*y) = 616*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1260*y**5 + 616*y**4 + 1350*y**4 - 660*y**3 + 90*y**3 - 44*y**2\nCombining like terms, got -1260*y**5 + 1966*y**4 - 570*y**3 - 44*y**2\n#Step 6:\nCurrent expression: -1260*y**5 + 1966*y**4 - 570*y**3 - 44*y**2\nNo more calculations needed.\n-1260*y**5 + 1966*y**4 - 570*y**3 - 44*y**2", "generated_answer": "-1260*y**5 + 1966*y**4 - 570*y**3 - 44*y**2", "step_length": 6} {"cot_id": "7734ab0ba676059bce7deaad9a54236349acf15cf756ad3a8f5d683fa0d3bf86", "datapoint": {"question": "Simplify this expression: (-19*x**3 - 36*x**2)*(20*x**3 + 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-380*x**6 - 720*x**5 - 741*x**3 - 1404*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1759, "polynomial_expr": "(-19*x**3 - 36*x**2)*(20*x**3 + 39)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-19*x**3 - 36*x**2)*(20*x**3 + 39)\nExpanding the part (20*x**3 + 39) using the distributive property, and we got: (20*x**3)*(-19*x**3 - 36*x**2) + 39*(-19*x**3 - 36*x**2)\n#Step 2:\nCurrent expression: (20*x**3)*(-19*x**3 - 36*x**2) + 39*(-19*x**3 - 36*x**2)\nSimplifying the partial expression: 39*(-19*x**3 - 36*x**2)\nExpanding the part (-19*x**3 - 36*x**2) using the distributive property, and we got: -36*x**2*39 - 19*x**3*39\nReplacing 39*(-19*x**3 - 36*x**2) with -36*x**2*39 - 19*x**3*39 in the overall expression.\n#Step 3:\nCurrent expression: -36*x**2*39 - 19*x**3*39 + (20*x**3)*(-19*x**3 - 36*x**2)\nSimplifying the partial expression: (20*x**3)*(-19*x**3 - 36*x**2)\nExpanding the part (-19*x**3 - 36*x**2) using the distributive property, and we got: (-36*x**2)*(20*x**3) + (-19*x**3)*(20*x**3)\nReplacing (20*x**3)*(-19*x**3 - 36*x**2) with (-36*x**2)*(20*x**3) + (-19*x**3)*(20*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-36*x**2)*(20*x**3) - 36*x**2*39 + (-19*x**3)*(20*x**3) - 19*x**3*39\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*x**2)*39 = -1404*x**2\n (-36*x**2)*(20*x**3) = -720*x**5\n (-19*x**3)*39 = -741*x**3\n (-19*x**3)*(20*x**3) = -380*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -380*x**6 - 720*x**5 - 741*x**3 - 1404*x**2\nNo more calculations needed.\n-380*x**6 - 720*x**5 - 741*x**3 - 1404*x**2", "generated_answer": "-380*x**6 - 720*x**5 - 741*x**3 - 1404*x**2", "step_length": 5} {"cot_id": "5586f298472cec5fff97c8e23632d15c812da1308ff27cfa8a82256f0f1a8ac0", "datapoint": {"question": "Simplify this expression: (17 - 33*z**2)*(35*z**3 - 44*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1155*z**5 + 1452*z**4 + 595*z**3 - 748*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1760, "polynomial_expr": "(17 - 33*z**2)*(35*z**3 - 44*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (17 - 33*z**2)*(35*z**3 - 44*z**2)\nExpanding the part (17 - 33*z**2) using the distributive property, and we got: (-33*z**2)*(35*z**3 - 44*z**2) + 17*(35*z**3 - 44*z**2)\n#Step 2:\nCurrent expression: (-33*z**2)*(35*z**3 - 44*z**2) + 17*(35*z**3 - 44*z**2)\nSimplifying the partial expression: 17*(35*z**3 - 44*z**2)\nExpanding the part (35*z**3 - 44*z**2) using the distributive property, and we got: -44*z**2*17 + (35*z**3)*17\nReplacing 17*(35*z**3 - 44*z**2) with -44*z**2*17 + (35*z**3)*17 in the overall expression.\n#Step 3:\nCurrent expression: -44*z**2*17 + (-33*z**2)*(35*z**3 - 44*z**2) + (35*z**3)*17\nSimplifying the partial expression: (-33*z**2)*(35*z**3 - 44*z**2)\nExpanding the part (35*z**3 - 44*z**2) using the distributive property, and we got: (-44*z**2)*(-33*z**2) + (-33*z**2)*(35*z**3)\nReplacing (-33*z**2)*(35*z**3 - 44*z**2) with (-44*z**2)*(-33*z**2) + (-33*z**2)*(35*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-44*z**2)*(-33*z**2) - 44*z**2*17 + (-33*z**2)*(35*z**3) + (35*z**3)*17\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-44*z**2)*17 = -748*z**2\n (-44*z**2)*(-33*z**2) = 1452*z**4\n (35*z**3)*17 = 595*z**3\n (35*z**3)*(-33*z**2) = -1155*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1155*z**5 + 1452*z**4 + 595*z**3 - 748*z**2\nNo more calculations needed.\n-1155*z**5 + 1452*z**4 + 595*z**3 - 748*z**2", "generated_answer": "-1155*z**5 + 1452*z**4 + 595*z**3 - 748*z**2", "step_length": 5} {"cot_id": "2bc96547b9bbe792477adb69f99ee23567f9abf89f59c26916612db79a6cb89a", "datapoint": {"question": "Calculate the following: (25 - 36*z**2)*(-3*z**3 + 55*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "108*z**5 - 2055*z**3 + 1375*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1761, "polynomial_expr": "(25 - 36*z**2)*(-3*z**3 + 55*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (25 - 36*z**2)*(-3*z**3 + 55*z)\nExpanding the part (25 - 36*z**2) using the distributive property, and we got: (-36*z**2)*(-3*z**3 + 55*z) + 25*(-3*z**3 + 55*z)\n#Step 2:\nCurrent expression: (-36*z**2)*(-3*z**3 + 55*z) + 25*(-3*z**3 + 55*z)\nSimplifying the partial expression: 25*(-3*z**3 + 55*z)\nExpanding the part (-3*z**3 + 55*z) using the distributive property, and we got: (55*z)*25 - 3*z**3*25\nReplacing 25*(-3*z**3 + 55*z) with (55*z)*25 - 3*z**3*25 in the overall expression.\n#Step 3:\nCurrent expression: (55*z)*25 + (-36*z**2)*(-3*z**3 + 55*z) - 3*z**3*25\nSimplifying the partial expression: (-36*z**2)*(-3*z**3 + 55*z)\nExpanding the part (-3*z**3 + 55*z) using the distributive property, and we got: (55*z)*(-36*z**2) + (-36*z**2)*(-3*z**3)\nReplacing (-36*z**2)*(-3*z**3 + 55*z) with (55*z)*(-36*z**2) + (-36*z**2)*(-3*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (55*z)*(-36*z**2) + (55*z)*25 + (-36*z**2)*(-3*z**3) - 3*z**3*25\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-3*z**3)*25 = -75*z**3\n (-3*z**3)*(-36*z**2) = 108*z**5\n (55*z)*25 = 1375*z\n (55*z)*(-36*z**2) = -1980*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 108*z**5 - 1980*z**3 - 75*z**3 + 1375*z\nCombining like terms, got 108*z**5 - 2055*z**3 + 1375*z\n#Step 6:\nCurrent expression: 108*z**5 - 2055*z**3 + 1375*z\nNo more calculations needed.\n108*z**5 - 2055*z**3 + 1375*z", "generated_answer": "108*z**5 - 2055*z**3 + 1375*z", "step_length": 6} {"cot_id": "cfcac64b6d8ec61d71759f0e111f7e53ee363f412b26ba2a5a1d6fd1aba9729f", "datapoint": {"question": "Simplify this expression: (-80*z**3 - 43)*(-49*z**3 + 33*z**2 - 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "3920*z**6 - 2640*z**5 + 2667*z**3 - 1419*z**2 + 301", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1762, "polynomial_expr": "(-80*z**3 - 43)*(-49*z**3 + 33*z**2 - 7)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-80*z**3 - 43)*(-49*z**3 + 33*z**2 - 7)\nExpanding the part (-80*z**3 - 43) using the distributive property, and we got: (-80*z**3)*(-49*z**3 + 33*z**2 - 7) - 43*(-49*z**3 + 33*z**2 - 7)\n#Step 2:\nCurrent expression: (-80*z**3)*(-49*z**3 + 33*z**2 - 7) - 43*(-49*z**3 + 33*z**2 - 7)\nSimplifying the partial expression: -43*(-49*z**3 + 33*z**2 - 7)\nExpanding the part (-49*z**3 + 33*z**2 - 7) using the distributive property, and we got: (33*z**2)*(-43) - 49*z**3*(-43) - 7*(-43)\nReplacing -43*(-49*z**3 + 33*z**2 - 7) with (33*z**2)*(-43) - 49*z**3*(-43) - 7*(-43) in the overall expression.\n#Step 3:\nCurrent expression: (33*z**2)*(-43) + (-80*z**3)*(-49*z**3 + 33*z**2 - 7) - 49*z**3*(-43) + 301\nSimplifying the partial expression: (-80*z**3)*(-49*z**3 + 33*z**2 - 7)\nExpanding the part (-49*z**3 + 33*z**2 - 7) using the distributive property, and we got: -(-1)*560*z**3 + (33*z**2)*(-80*z**3) + (-80*z**3)*(-49*z**3)\nReplacing (-80*z**3)*(-49*z**3 + 33*z**2 - 7) with -(-1)*560*z**3 + (33*z**2)*(-80*z**3) + (-80*z**3)*(-49*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -7*(-80)*z**3 + (33*z**2)*(-80*z**3) + (33*z**2)*(-43) + (-80*z**3)*(-49*z**3) - 49*z**3*(-43) + 301\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*z**3)*-43 = 2107*z**3\n (-49*z**3)*(-80*z**3) = 3920*z**6\n (33*z**2)*-43 = -1419*z**2\n (33*z**2)*(-80*z**3) = -2640*z**5\n -7*-80*z**3 = 560*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 3920*z**6 - 2640*z**5 + 560*z**3 + 2107*z**3 - 1419*z**2 + 301\nCombining like terms, got 3920*z**6 - 2640*z**5 + 2667*z**3 - 1419*z**2 + 301\n#Step 6:\nCurrent expression: 3920*z**6 - 2640*z**5 + 2667*z**3 - 1419*z**2 + 301\nNo more calculations needed.\n3920*z**6 - 2640*z**5 + 2667*z**3 - 1419*z**2 + 301", "generated_answer": "3920*z**6 - 2640*z**5 + 2667*z**3 - 1419*z**2 + 301", "step_length": 6} {"cot_id": "c41ae140879cce3c78418c6268ed37efdd434cd6f95bfd5f5334c95021cb8f85", "datapoint": {"question": "Calculate the following: (-45*y**3 + 30*y**2 - 39)*(-13*y**3 - 33*y**2 - 10*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "585*y**6 + 1095*y**5 - 540*y**4 + 207*y**3 + 1287*y**2 + 390*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1763, "polynomial_expr": "(-45*y**3 + 30*y**2 - 39)*(-13*y**3 - 33*y**2 - 10*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-45*y**3 + 30*y**2 - 39)*(-13*y**3 - 33*y**2 - 10*y)\nExpanding the part (-45*y**3 + 30*y**2 - 39) using the distributive property, and we got: (30*y**2)*(-13*y**3 - 33*y**2 - 10*y) + (-45*y**3)*(-13*y**3 - 33*y**2 - 10*y) - 39*(-13*y**3 - 33*y**2 - 10*y)\n#Step 2:\nCurrent expression: (30*y**2)*(-13*y**3 - 33*y**2 - 10*y) + (-45*y**3)*(-13*y**3 - 33*y**2 - 10*y) - 39*(-13*y**3 - 33*y**2 - 10*y)\nSimplifying the partial expression: -39*(-13*y**3 - 33*y**2 - 10*y)\nExpanding the part (-13*y**3 - 33*y**2 - 10*y) using the distributive property, and we got: -10*y*(-39) - 33*y**2*(-39) - 13*y**3*(-39)\nReplacing -39*(-13*y**3 - 33*y**2 - 10*y) with -10*y*(-39) - 33*y**2*(-39) - 13*y**3*(-39) in the overall expression.\n#Step 3:\nCurrent expression: -10*y*(-39) - 33*y**2*(-39) + (30*y**2)*(-13*y**3 - 33*y**2 - 10*y) + (-45*y**3)*(-13*y**3 - 33*y**2 - 10*y) - 13*y**3*(-39)\nSimplifying the partial expression: (-45*y**3)*(-13*y**3 - 33*y**2 - 10*y)\nExpanding the part (-13*y**3 - 33*y**2 - 10*y) using the distributive property, and we got: (-10*y)*(-45*y**3) + (-33*y**2)*(-45*y**3) + (-45*y**3)*(-13*y**3)\nReplacing (-45*y**3)*(-13*y**3 - 33*y**2 - 10*y) with (-10*y)*(-45*y**3) + (-33*y**2)*(-45*y**3) + (-45*y**3)*(-13*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-10*y)*(-45*y**3) - 10*y*(-39) + (-33*y**2)*(-45*y**3) - 33*y**2*(-39) + (30*y**2)*(-13*y**3 - 33*y**2 - 10*y) + (-45*y**3)*(-13*y**3) - 13*y**3*(-39)\nSimplifying the partial expression: (30*y**2)*(-13*y**3 - 33*y**2 - 10*y)\nExpanding the part (-13*y**3 - 33*y**2 - 10*y) using the distributive property, and we got: (-10*y)*(30*y**2) + (-33*y**2)*(30*y**2) + (30*y**2)*(-13*y**3)\nReplacing (30*y**2)*(-13*y**3 - 33*y**2 - 10*y) with (-10*y)*(30*y**2) + (-33*y**2)*(30*y**2) + (30*y**2)*(-13*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-10*y)*(30*y**2) + (-10*y)*(-45*y**3) - 10*y*(-39) + (-33*y**2)*(30*y**2) + (-33*y**2)*(-45*y**3) - 33*y**2*(-39) + (30*y**2)*(-13*y**3) + (-45*y**3)*(-13*y**3) - 13*y**3*(-39)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*y**2)*-39 = 1287*y**2\n (-33*y**2)*(-45*y**3) = 1485*y**5\n (-33*y**2)*(30*y**2) = -990*y**4\n (-13*y**3)*-39 = 507*y**3\n (-13*y**3)*(-45*y**3) = 585*y**6\n (-13*y**3)*(30*y**2) = -390*y**5\n (-10*y)*-39 = 390*y\n (-10*y)*(-45*y**3) = 450*y**4\n (-10*y)*(30*y**2) = -300*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 585*y**6 - 390*y**5 + 1485*y**5 - 990*y**4 + 450*y**4 - 300*y**3 + 507*y**3 + 1287*y**2 + 390*y\nCombining like terms, got 585*y**6 + 1095*y**5 - 540*y**4 + 207*y**3 + 1287*y**2 + 390*y\n#Step 7:\nCurrent expression: 585*y**6 + 1095*y**5 - 540*y**4 + 207*y**3 + 1287*y**2 + 390*y\nNo more calculations needed.\n585*y**6 + 1095*y**5 - 540*y**4 + 207*y**3 + 1287*y**2 + 390*y", "generated_answer": "585*y**6 + 1095*y**5 - 540*y**4 + 207*y**3 + 1287*y**2 + 390*y", "step_length": 7} {"cot_id": "86ca0d0371a83b182b2f989dab401cd8a1c020c4d18f1fe9fe235def786e5bf2", "datapoint": {"question": "Calculate the following: (79 - 34*x**3)*(16*x**2 + 92*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-544*x**5 - 3128*x**4 + 1264*x**2 + 7268*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1764, "polynomial_expr": "(79 - 34*x**3)*(16*x**2 + 92*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (79 - 34*x**3)*(16*x**2 + 92*x)\nExpanding the part (79 - 34*x**3) using the distributive property, and we got: (-34*x**3)*(16*x**2 + 92*x) + 79*(16*x**2 + 92*x)\n#Step 2:\nCurrent expression: (-34*x**3)*(16*x**2 + 92*x) + 79*(16*x**2 + 92*x)\nSimplifying the partial expression: 79*(16*x**2 + 92*x)\nExpanding the part (16*x**2 + 92*x) using the distributive property, and we got: (92*x)*79 + (16*x**2)*79\nReplacing 79*(16*x**2 + 92*x) with (92*x)*79 + (16*x**2)*79 in the overall expression.\n#Step 3:\nCurrent expression: (92*x)*79 + (16*x**2)*79 + (-34*x**3)*(16*x**2 + 92*x)\nSimplifying the partial expression: (-34*x**3)*(16*x**2 + 92*x)\nExpanding the part (16*x**2 + 92*x) using the distributive property, and we got: (92*x)*(-34*x**3) + (16*x**2)*(-34*x**3)\nReplacing (-34*x**3)*(16*x**2 + 92*x) with (92*x)*(-34*x**3) + (16*x**2)*(-34*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (92*x)*(-34*x**3) + (92*x)*79 + (16*x**2)*(-34*x**3) + (16*x**2)*79\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (16*x**2)*79 = 1264*x**2\n (16*x**2)*(-34*x**3) = -544*x**5\n (92*x)*79 = 7268*x\n (92*x)*(-34*x**3) = -3128*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -544*x**5 - 3128*x**4 + 1264*x**2 + 7268*x\nNo more calculations needed.\n-544*x**5 - 3128*x**4 + 1264*x**2 + 7268*x", "generated_answer": "-544*x**5 - 3128*x**4 + 1264*x**2 + 7268*x", "step_length": 5} {"cot_id": "ab2831ceb8d268f3705bedb506703b57a0c87e6f690f42784a0c297c6968bf0f", "datapoint": {"question": "Calculate the following: (-65*z**3 + 38*z)*(12*z**3 - 41*z**2 - 8*z + 5)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-780*z**6 + 2665*z**5 + 976*z**4 - 1883*z**3 - 304*z**2 + 190*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1765, "polynomial_expr": "(-65*z**3 + 38*z)*(12*z**3 - 41*z**2 - 8*z + 5)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-65*z**3 + 38*z)*(12*z**3 - 41*z**2 - 8*z + 5)\nExpanding the part (-65*z**3 + 38*z) using the distributive property, and we got: (38*z)*(12*z**3 - 41*z**2 - 8*z + 5) + (-65*z**3)*(12*z**3 - 41*z**2 - 8*z + 5)\n#Step 2:\nCurrent expression: (38*z)*(12*z**3 - 41*z**2 - 8*z + 5) + (-65*z**3)*(12*z**3 - 41*z**2 - 8*z + 5)\nSimplifying the partial expression: (-65*z**3)*(12*z**3 - 41*z**2 - 8*z + 5)\nExpanding the part (12*z**3 - 41*z**2 - 8*z + 5) using the distributive property, and we got: (-8*z)*(-65*z**3) + 5*(-65*z**3) + (-41*z**2)*(-65*z**3) + (-65*z**3)*(12*z**3)\nReplacing (-65*z**3)*(12*z**3 - 41*z**2 - 8*z + 5) with (-8*z)*(-65*z**3) + 5*(-65*z**3) + (-41*z**2)*(-65*z**3) + (-65*z**3)*(12*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-8*z)*(-65*z**3) + 5*(-65)*z**3 + (38*z)*(12*z**3 - 41*z**2 - 8*z + 5) + (-41*z**2)*(-65*z**3) + (-65*z**3)*(12*z**3)\nSimplifying the partial expression: (38*z)*(12*z**3 - 41*z**2 - 8*z + 5)\nExpanding the part (12*z**3 - 41*z**2 - 8*z + 5) using the distributive property, and we got: (-8*z)*(38*z) + 5*(38*z) + (38*z)*(-41*z**2) + (38*z)*(12*z**3)\nReplacing (38*z)*(12*z**3 - 41*z**2 - 8*z + 5) with (-8*z)*(38*z) + 5*(38*z) + (38*z)*(-41*z**2) + (38*z)*(12*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-8*z)*(38*z) + (-8*z)*(-65*z**3) + 5*(-65)*z**3 + 5*38*z + (38*z)*(-41*z**2) + (38*z)*(12*z**3) + (-41*z**2)*(-65*z**3) + (-65*z**3)*(12*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*z**2)*(-65*z**3) = 2665*z**5\n (-41*z**2)*(38*z) = -1558*z**3\n (-8*z)*(-65*z**3) = 520*z**4\n (-8*z)*(38*z) = -304*z**2\n (12*z**3)*(-65*z**3) = -780*z**6\n (12*z**3)*(38*z) = 456*z**4\n 5*-65*z**3 = -325*z**3\n 5*38*z = 190*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -780*z**6 + 2665*z**5 + 456*z**4 + 520*z**4 - 1558*z**3 - 325*z**3 - 304*z**2 + 190*z\nCombining like terms, got -780*z**6 + 2665*z**5 + 976*z**4 - 1883*z**3 - 304*z**2 + 190*z\n#Step 6:\nCurrent expression: -780*z**6 + 2665*z**5 + 976*z**4 - 1883*z**3 - 304*z**2 + 190*z\nNo more calculations needed.\n-780*z**6 + 2665*z**5 + 976*z**4 - 1883*z**3 - 304*z**2 + 190*z", "generated_answer": "-780*z**6 + 2665*z**5 + 976*z**4 - 1883*z**3 - 304*z**2 + 190*z", "step_length": 6} {"cot_id": "e24886a776609046837f44536b965fb223376ac9b549f1e6125061bd4cfe0004", "datapoint": {"question": "Simplify this expression: (-34*x**2 - 42)*(-10*x**3 - 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "340*x**5 + 420*x**3 + 1700*x**2 + 2100", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1766, "polynomial_expr": "(-34*x**2 - 42)*(-10*x**3 - 50)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-34*x**2 - 42)*(-10*x**3 - 50)\nExpanding the part (-10*x**3 - 50) using the distributive property, and we got: (-10*x**3)*(-34*x**2 - 42) - 50*(-34*x**2 - 42)\n#Step 2:\nCurrent expression: (-10*x**3)*(-34*x**2 - 42) - 50*(-34*x**2 - 42)\nSimplifying the partial expression: -50*(-34*x**2 - 42)\nExpanding the part (-34*x**2 - 42) using the distributive property, and we got: -34*x**2*(-50) - 42*(-50)\nReplacing -50*(-34*x**2 - 42) with -34*x**2*(-50) - 42*(-50) in the overall expression.\n#Step 3:\nCurrent expression: -34*x**2*(-50) + (-10*x**3)*(-34*x**2 - 42) + 2100\nSimplifying the partial expression: (-10*x**3)*(-34*x**2 - 42)\nExpanding the part (-34*x**2 - 42) using the distributive property, and we got: -(-1)*420*x**3 + (-34*x**2)*(-10*x**3)\nReplacing (-10*x**3)*(-34*x**2 - 42) with -(-1)*420*x**3 + (-34*x**2)*(-10*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -42*(-10)*x**3 + (-34*x**2)*(-10*x**3) - 34*x**2*(-50) + 2100\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*x**2)*-50 = 1700*x**2\n (-34*x**2)*(-10*x**3) = 340*x**5\n -42*-10*x**3 = 420*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 340*x**5 + 420*x**3 + 1700*x**2 + 2100\nNo more calculations needed.\n340*x**5 + 420*x**3 + 1700*x**2 + 2100", "generated_answer": "340*x**5 + 420*x**3 + 1700*x**2 + 2100", "step_length": 5} {"cot_id": "c413113907db03be5489c592c0053a23aae4c402a810de329c08806148844ce0", "datapoint": {"question": "Simplify this expression: (34*y + 55)*(36*y + 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1224*y**2 + 2694*y + 1155", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1767, "polynomial_expr": "(34*y + 55)*(36*y + 21)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (34*y + 55)*(36*y + 21)\nExpanding the part (36*y + 21) using the distributive property, and we got: (36*y)*(34*y + 55) + 21*(34*y + 55)\n#Step 2:\nCurrent expression: (36*y)*(34*y + 55) + 21*(34*y + 55)\nSimplifying the partial expression: 21*(34*y + 55)\nExpanding the part (34*y + 55) using the distributive property, and we got: (34*y)*21 + 55*21\nReplacing 21*(34*y + 55) with (34*y)*21 + 55*21 in the overall expression.\n#Step 3:\nCurrent expression: (34*y)*21 + (36*y)*(34*y + 55) + 1155\nSimplifying the partial expression: (36*y)*(34*y + 55)\nExpanding the part (34*y + 55) using the distributive property, and we got: 55*(36*y) + (34*y)*(36*y)\nReplacing (36*y)*(34*y + 55) with 55*(36*y) + (34*y)*(36*y) in the overall expression.\n#Step 4:\nCurrent expression: 55*36*y + (34*y)*(36*y) + (34*y)*21 + 1155\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (34*y)*21 = 714*y\n (34*y)*(36*y) = 1224*y**2\n 55*36*y = 1980*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1224*y**2 + 714*y + 1980*y + 1155\nCombining like terms, got 1224*y**2 + 2694*y + 1155\n#Step 6:\nCurrent expression: 1224*y**2 + 2694*y + 1155\nNo more calculations needed.\n1224*y**2 + 2694*y + 1155", "generated_answer": "1224*y**2 + 2694*y + 1155", "step_length": 6} {"cot_id": "e70202f56e12511160a84d22fb98cfec2451df565aa6c54c65c0a5596c0f8c8c", "datapoint": {"question": "Calculate the following: (10 - 41*x**2)*(93 - 39*x**3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1599*x**5 - 390*x**3 - 3813*x**2 + 930", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1768, "polynomial_expr": "(10 - 41*x**2)*(93 - 39*x**3)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (10 - 41*x**2)*(93 - 39*x**3)\nExpanding the part (10 - 41*x**2) using the distributive property, and we got: (-41*x**2)*(93 - 39*x**3) + 10*(93 - 39*x**3)\n#Step 2:\nCurrent expression: (-41*x**2)*(93 - 39*x**3) + 10*(93 - 39*x**3)\nSimplifying the partial expression: 10*(93 - 39*x**3)\nExpanding the part (93 - 39*x**3) using the distributive property, and we got: -39*x**3*10 + 93*10\nReplacing 10*(93 - 39*x**3) with -39*x**3*10 + 93*10 in the overall expression.\n#Step 3:\nCurrent expression: (-41*x**2)*(93 - 39*x**3) - 39*x**3*10 + 930\nSimplifying the partial expression: (-41*x**2)*(93 - 39*x**3)\nExpanding the part (93 - 39*x**3) using the distributive property, and we got: 93*(-41*x**2) + (-41*x**2)*(-39*x**3)\nReplacing (-41*x**2)*(93 - 39*x**3) with 93*(-41*x**2) + (-41*x**2)*(-39*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 93*(-41)*x**2 + (-41*x**2)*(-39*x**3) - 39*x**3*10 + 930\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*x**3)*10 = -390*x**3\n (-39*x**3)*(-41*x**2) = 1599*x**5\n 93*-41*x**2 = -3813*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1599*x**5 - 390*x**3 - 3813*x**2 + 930\nNo more calculations needed.\n1599*x**5 - 390*x**3 - 3813*x**2 + 930", "generated_answer": "1599*x**5 - 390*x**3 - 3813*x**2 + 930", "step_length": 5} {"cot_id": "3946f88298674241c97406b57d548731a7fe02ed27cc3a4e5af03faa8a34bcfd", "datapoint": {"question": "Calculate the following: (-2*z**3 - 27)*(35*z**3 - 12)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-70*z**6 - 921*z**3 + 324", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1769, "polynomial_expr": "(-2*z**3 - 27)*(35*z**3 - 12)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-2*z**3 - 27)*(35*z**3 - 12)\nExpanding the part (-2*z**3 - 27) using the distributive property, and we got: (-2*z**3)*(35*z**3 - 12) - 27*(35*z**3 - 12)\n#Step 2:\nCurrent expression: (-2*z**3)*(35*z**3 - 12) - 27*(35*z**3 - 12)\nSimplifying the partial expression: -27*(35*z**3 - 12)\nExpanding the part (35*z**3 - 12) using the distributive property, and we got: (35*z**3)*(-27) - 12*(-27)\nReplacing -27*(35*z**3 - 12) with (35*z**3)*(-27) - 12*(-27) in the overall expression.\n#Step 3:\nCurrent expression: (-2*z**3)*(35*z**3 - 12) + (35*z**3)*(-27) + 324\nSimplifying the partial expression: (-2*z**3)*(35*z**3 - 12)\nExpanding the part (35*z**3 - 12) using the distributive property, and we got: -(-1)*24*z**3 + (-2*z**3)*(35*z**3)\nReplacing (-2*z**3)*(35*z**3 - 12) with -(-1)*24*z**3 + (-2*z**3)*(35*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -12*(-2)*z**3 + (-2*z**3)*(35*z**3) + (35*z**3)*(-27) + 324\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (35*z**3)*-27 = -945*z**3\n (35*z**3)*(-2*z**3) = -70*z**6\n -12*-2*z**3 = 24*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -70*z**6 - 945*z**3 + 24*z**3 + 324\nCombining like terms, got -70*z**6 - 921*z**3 + 324\n#Step 6:\nCurrent expression: -70*z**6 - 921*z**3 + 324\nNo more calculations needed.\n-70*z**6 - 921*z**3 + 324", "generated_answer": "-70*z**6 - 921*z**3 + 324", "step_length": 6} {"cot_id": "9c781b732c82d29d16a18c407db09f71e9ebc3157836463550c4abbf92332f66", "datapoint": {"question": "Calculate the following: (-22*z**2 - 10*z - 35)*(49*z**2 + 37*z - 3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1078*z**4 - 1304*z**3 - 2019*z**2 - 1265*z + 105", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1770, "polynomial_expr": "(-22*z**2 - 10*z - 35)*(49*z**2 + 37*z - 3)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-22*z**2 - 10*z - 35)*(49*z**2 + 37*z - 3)\nExpanding the part (-22*z**2 - 10*z - 35) using the distributive property, and we got: (-10*z)*(49*z**2 + 37*z - 3) + (-22*z**2)*(49*z**2 + 37*z - 3) - 35*(49*z**2 + 37*z - 3)\n#Step 2:\nCurrent expression: (-10*z)*(49*z**2 + 37*z - 3) + (-22*z**2)*(49*z**2 + 37*z - 3) - 35*(49*z**2 + 37*z - 3)\nSimplifying the partial expression: -35*(49*z**2 + 37*z - 3)\nExpanding the part (49*z**2 + 37*z - 3) using the distributive property, and we got: (37*z)*(-35) + (49*z**2)*(-35) - 3*(-35)\nReplacing -35*(49*z**2 + 37*z - 3) with (37*z)*(-35) + (49*z**2)*(-35) - 3*(-35) in the overall expression.\n#Step 3:\nCurrent expression: (-10*z)*(49*z**2 + 37*z - 3) + (37*z)*(-35) + (-22*z**2)*(49*z**2 + 37*z - 3) + (49*z**2)*(-35) + 105\nSimplifying the partial expression: (-22*z**2)*(49*z**2 + 37*z - 3)\nExpanding the part (49*z**2 + 37*z - 3) using the distributive property, and we got: -(-1)*66*z**2 + (37*z)*(-22*z**2) + (-22*z**2)*(49*z**2)\nReplacing (-22*z**2)*(49*z**2 + 37*z - 3) with -(-1)*66*z**2 + (37*z)*(-22*z**2) + (-22*z**2)*(49*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-10*z)*(49*z**2 + 37*z - 3) - 3*(-22)*z**2 + (37*z)*(-22*z**2) + (37*z)*(-35) + (-22*z**2)*(49*z**2) + (49*z**2)*(-35) + 105\nSimplifying the partial expression: (-10*z)*(49*z**2 + 37*z - 3)\nExpanding the part (49*z**2 + 37*z - 3) using the distributive property, and we got: (-10*z)*(37*z) + (-10*z)*(49*z**2) - (-1)*30*z\nReplacing (-10*z)*(49*z**2 + 37*z - 3) with (-10*z)*(37*z) + (-10*z)*(49*z**2) - (-1)*30*z in the overall expression.\n#Step 5:\nCurrent expression: (-10*z)*(37*z) + (-10*z)*(49*z**2) - 3*(-22)*z**2 - 3*(-10)*z + (37*z)*(-22*z**2) + (37*z)*(-35) + (-22*z**2)*(49*z**2) + (49*z**2)*(-35) + 105\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (37*z)*-35 = -1295*z\n (37*z)*(-22*z**2) = -814*z**3\n (37*z)*(-10*z) = -370*z**2\n (49*z**2)*-35 = -1715*z**2\n (49*z**2)*(-22*z**2) = -1078*z**4\n (49*z**2)*(-10*z) = -490*z**3\n -3*-22*z**2 = 66*z**2\n -3*-10*z = 30*z\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1078*z**4 - 814*z**3 - 490*z**3 - 1715*z**2 - 370*z**2 + 66*z**2 - 1295*z + 30*z + 105\nCombining like terms, got -1078*z**4 - 1304*z**3 - 2019*z**2 - 1265*z + 105\n#Step 7:\nCurrent expression: -1078*z**4 - 1304*z**3 - 2019*z**2 - 1265*z + 105\nNo more calculations needed.\n-1078*z**4 - 1304*z**3 - 2019*z**2 - 1265*z + 105", "generated_answer": "-1078*z**4 - 1304*z**3 - 2019*z**2 - 1265*z + 105", "step_length": 7} {"cot_id": "b1004c43ef3007e8a02d41e4d767dc5e029e18d1965d4fa2f04ec1ba3c8dde71", "datapoint": {"question": "Simplify this expression: -14*y**2*(47 - 14*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "196*y**3 - 658*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1771, "polynomial_expr": "-14*y**2*(47 - 14*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -14*y**2*(47 - 14*y)\nExpanding the part (47 - 14*y) using the distributive property, and we got: (-14*y)*(-14*y**2) + 47*(-14*y**2)\n#Step 2:\nCurrent expression: (-14*y)*(-14*y**2) + 47*(-14*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 47*(-14*y**2) = -658*y**2\n (-14*y)*(-14*y**2) = 196*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 196*y**3 - 658*y**2\nNo more calculations needed.\n196*y**3 - 658*y**2", "generated_answer": "196*y**3 - 658*y**2", "step_length": 3} {"cot_id": "684e41fad0954904d6e480b9208cf0f88166c23a51fe5e21aeb1436ad6da9c41", "datapoint": {"question": "Simplify this expression: (-5*x**3 + 40*x)*(52*x**2 + 8*x - 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-260*x**5 - 40*x**4 + 2235*x**3 + 320*x**2 - 1240*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1772, "polynomial_expr": "(-5*x**3 + 40*x)*(52*x**2 + 8*x - 31)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-5*x**3 + 40*x)*(52*x**2 + 8*x - 31)\nExpanding the part (-5*x**3 + 40*x) using the distributive property, and we got: (40*x)*(52*x**2 + 8*x - 31) + (-5*x**3)*(52*x**2 + 8*x - 31)\n#Step 2:\nCurrent expression: (40*x)*(52*x**2 + 8*x - 31) + (-5*x**3)*(52*x**2 + 8*x - 31)\nSimplifying the partial expression: (-5*x**3)*(52*x**2 + 8*x - 31)\nExpanding the part (52*x**2 + 8*x - 31) using the distributive property, and we got: -(-1)*155*x**3 + (8*x)*(-5*x**3) + (52*x**2)*(-5*x**3)\nReplacing (-5*x**3)*(52*x**2 + 8*x - 31) with -(-1)*155*x**3 + (8*x)*(-5*x**3) + (52*x**2)*(-5*x**3) in the overall expression.\n#Step 3:\nCurrent expression: -31*(-5)*x**3 + (8*x)*(-5*x**3) + (40*x)*(52*x**2 + 8*x - 31) + (52*x**2)*(-5*x**3)\nSimplifying the partial expression: (40*x)*(52*x**2 + 8*x - 31)\nExpanding the part (52*x**2 + 8*x - 31) using the distributive property, and we got: -1240*x + (8*x)*(40*x) + (40*x)*(52*x**2)\nReplacing (40*x)*(52*x**2 + 8*x - 31) with -1240*x + (8*x)*(40*x) + (40*x)*(52*x**2) in the overall expression.\n#Step 4:\nCurrent expression: -31*(-5)*x**3 - 31*40*x + (8*x)*(40*x) + (8*x)*(-5*x**3) + (40*x)*(52*x**2) + (52*x**2)*(-5*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (8*x)*(-5*x**3) = -40*x**4\n (8*x)*(40*x) = 320*x**2\n (52*x**2)*(-5*x**3) = -260*x**5\n (52*x**2)*(40*x) = 2080*x**3\n -31*-5*x**3 = 155*x**3\n -31*40*x = -1240*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -260*x**5 - 40*x**4 + 155*x**3 + 2080*x**3 + 320*x**2 - 1240*x\nCombining like terms, got -260*x**5 - 40*x**4 + 2235*x**3 + 320*x**2 - 1240*x\n#Step 6:\nCurrent expression: -260*x**5 - 40*x**4 + 2235*x**3 + 320*x**2 - 1240*x\nNo more calculations needed.\n-260*x**5 - 40*x**4 + 2235*x**3 + 320*x**2 - 1240*x", "generated_answer": "-260*x**5 - 40*x**4 + 2235*x**3 + 320*x**2 - 1240*x", "step_length": 6} {"cot_id": "a09b9aea9e3a56670e10fa8e606ac337ab61231f8224e2afa8a0199225d6507e", "datapoint": {"question": "Calculate the following: (22*x**2 + 24)*(44*x**3 + 2*x**2 - 18*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "968*x**5 + 44*x**4 + 660*x**3 + 48*x**2 - 432*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1773, "polynomial_expr": "(22*x**2 + 24)*(44*x**3 + 2*x**2 - 18*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (22*x**2 + 24)*(44*x**3 + 2*x**2 - 18*x)\nExpanding the part (22*x**2 + 24) using the distributive property, and we got: (22*x**2)*(44*x**3 + 2*x**2 - 18*x) + 24*(44*x**3 + 2*x**2 - 18*x)\n#Step 2:\nCurrent expression: (22*x**2)*(44*x**3 + 2*x**2 - 18*x) + 24*(44*x**3 + 2*x**2 - 18*x)\nSimplifying the partial expression: 24*(44*x**3 + 2*x**2 - 18*x)\nExpanding the part (44*x**3 + 2*x**2 - 18*x) using the distributive property, and we got: -18*x*24 + (2*x**2)*24 + (44*x**3)*24\nReplacing 24*(44*x**3 + 2*x**2 - 18*x) with -18*x*24 + (2*x**2)*24 + (44*x**3)*24 in the overall expression.\n#Step 3:\nCurrent expression: -18*x*24 + (2*x**2)*24 + (22*x**2)*(44*x**3 + 2*x**2 - 18*x) + (44*x**3)*24\nSimplifying the partial expression: (22*x**2)*(44*x**3 + 2*x**2 - 18*x)\nExpanding the part (44*x**3 + 2*x**2 - 18*x) using the distributive property, and we got: (-18*x)*(22*x**2) + (2*x**2)*(22*x**2) + (22*x**2)*(44*x**3)\nReplacing (22*x**2)*(44*x**3 + 2*x**2 - 18*x) with (-18*x)*(22*x**2) + (2*x**2)*(22*x**2) + (22*x**2)*(44*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-18*x)*(22*x**2) - 18*x*24 + (2*x**2)*(22*x**2) + (2*x**2)*24 + (22*x**2)*(44*x**3) + (44*x**3)*24\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-18*x)*24 = -432*x\n (-18*x)*(22*x**2) = -396*x**3\n (2*x**2)*24 = 48*x**2\n (2*x**2)*(22*x**2) = 44*x**4\n (44*x**3)*24 = 1056*x**3\n (44*x**3)*(22*x**2) = 968*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 968*x**5 + 44*x**4 - 396*x**3 + 1056*x**3 + 48*x**2 - 432*x\nCombining like terms, got 968*x**5 + 44*x**4 + 660*x**3 + 48*x**2 - 432*x\n#Step 6:\nCurrent expression: 968*x**5 + 44*x**4 + 660*x**3 + 48*x**2 - 432*x\nNo more calculations needed.\n968*x**5 + 44*x**4 + 660*x**3 + 48*x**2 - 432*x", "generated_answer": "968*x**5 + 44*x**4 + 660*x**3 + 48*x**2 - 432*x", "step_length": 6} {"cot_id": "12f2962c6804ff6dd889f22634fa6d832d63382eb5c78ecf30972c88c4c1c8b6", "datapoint": {"question": "Simplify this expression: (55 - 3*y)*(23*y + 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-69*y**2 + 1235*y + 550", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1774, "polynomial_expr": "(55 - 3*y)*(23*y + 10)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (55 - 3*y)*(23*y + 10)\nExpanding the part (23*y + 10) using the distributive property, and we got: (23*y)*(55 - 3*y) + 10*(55 - 3*y)\n#Step 2:\nCurrent expression: (23*y)*(55 - 3*y) + 10*(55 - 3*y)\nSimplifying the partial expression: 10*(55 - 3*y)\nExpanding the part (55 - 3*y) using the distributive property, and we got: -3*y*10 + 55*10\nReplacing 10*(55 - 3*y) with -3*y*10 + 55*10 in the overall expression.\n#Step 3:\nCurrent expression: -3*y*10 + (23*y)*(55 - 3*y) + 550\nSimplifying the partial expression: (23*y)*(55 - 3*y)\nExpanding the part (55 - 3*y) using the distributive property, and we got: (-3*y)*(23*y) + 55*(23*y)\nReplacing (23*y)*(55 - 3*y) with (-3*y)*(23*y) + 55*(23*y) in the overall expression.\n#Step 4:\nCurrent expression: (-3*y)*(23*y) - 3*y*10 + 55*23*y + 550\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-3*y)*10 = -30*y\n (-3*y)*(23*y) = -69*y**2\n 55*23*y = 1265*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -69*y**2 - 30*y + 1265*y + 550\nCombining like terms, got -69*y**2 + 1235*y + 550\n#Step 6:\nCurrent expression: -69*y**2 + 1235*y + 550\nNo more calculations needed.\n-69*y**2 + 1235*y + 550", "generated_answer": "-69*y**2 + 1235*y + 550", "step_length": 6} {"cot_id": "d9fb70518a147e9c14b5695585e678e6cb9a21ff47b012dd4fc92625ff910bb4", "datapoint": {"question": "Calculate the following: (-29*z**3 - 13*z**2)*(-23*z**3 + 108*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "667*z**6 + 299*z**5 - 3132*z**4 - 1404*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1775, "polynomial_expr": "(-29*z**3 - 13*z**2)*(-23*z**3 + 108*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-29*z**3 - 13*z**2)*(-23*z**3 + 108*z)\nExpanding the part (-29*z**3 - 13*z**2) using the distributive property, and we got: (-13*z**2)*(-23*z**3 + 108*z) + (-29*z**3)*(-23*z**3 + 108*z)\n#Step 2:\nCurrent expression: (-13*z**2)*(-23*z**3 + 108*z) + (-29*z**3)*(-23*z**3 + 108*z)\nSimplifying the partial expression: (-29*z**3)*(-23*z**3 + 108*z)\nExpanding the part (-23*z**3 + 108*z) using the distributive property, and we got: (108*z)*(-29*z**3) + (-29*z**3)*(-23*z**3)\nReplacing (-29*z**3)*(-23*z**3 + 108*z) with (108*z)*(-29*z**3) + (-29*z**3)*(-23*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (108*z)*(-29*z**3) + (-13*z**2)*(-23*z**3 + 108*z) + (-29*z**3)*(-23*z**3)\nSimplifying the partial expression: (-13*z**2)*(-23*z**3 + 108*z)\nExpanding the part (-23*z**3 + 108*z) using the distributive property, and we got: (108*z)*(-13*z**2) + (-13*z**2)*(-23*z**3)\nReplacing (-13*z**2)*(-23*z**3 + 108*z) with (108*z)*(-13*z**2) + (-13*z**2)*(-23*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (108*z)*(-13*z**2) + (108*z)*(-29*z**3) + (-13*z**2)*(-23*z**3) + (-29*z**3)*(-23*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*z**3)*(-29*z**3) = 667*z**6\n (-23*z**3)*(-13*z**2) = 299*z**5\n (108*z)*(-29*z**3) = -3132*z**4\n (108*z)*(-13*z**2) = -1404*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 667*z**6 + 299*z**5 - 3132*z**4 - 1404*z**3\nNo more calculations needed.\n667*z**6 + 299*z**5 - 3132*z**4 - 1404*z**3", "generated_answer": "667*z**6 + 299*z**5 - 3132*z**4 - 1404*z**3", "step_length": 5} {"cot_id": "149e0e8212944929afb4e15b06b248a27fd41c5dbf8eccb0c86ce5a66fa28ebe", "datapoint": {"question": "Simplify this expression: (-29*x**2 - 40)*(-25*x**3 + 37*x - 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "725*x**5 - 73*x**3 + 580*x**2 - 1480*x + 800", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1776, "polynomial_expr": "(-29*x**2 - 40)*(-25*x**3 + 37*x - 20)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-29*x**2 - 40)*(-25*x**3 + 37*x - 20)\nExpanding the part (-29*x**2 - 40) using the distributive property, and we got: (-29*x**2)*(-25*x**3 + 37*x - 20) - 40*(-25*x**3 + 37*x - 20)\n#Step 2:\nCurrent expression: (-29*x**2)*(-25*x**3 + 37*x - 20) - 40*(-25*x**3 + 37*x - 20)\nSimplifying the partial expression: -40*(-25*x**3 + 37*x - 20)\nExpanding the part (-25*x**3 + 37*x - 20) using the distributive property, and we got: (37*x)*(-40) - 25*x**3*(-40) - 20*(-40)\nReplacing -40*(-25*x**3 + 37*x - 20) with (37*x)*(-40) - 25*x**3*(-40) - 20*(-40) in the overall expression.\n#Step 3:\nCurrent expression: (37*x)*(-40) + (-29*x**2)*(-25*x**3 + 37*x - 20) - 25*x**3*(-40) + 800\nSimplifying the partial expression: (-29*x**2)*(-25*x**3 + 37*x - 20)\nExpanding the part (-25*x**3 + 37*x - 20) using the distributive property, and we got: -(-1)*580*x**2 + (37*x)*(-29*x**2) + (-29*x**2)*(-25*x**3)\nReplacing (-29*x**2)*(-25*x**3 + 37*x - 20) with -(-1)*580*x**2 + (37*x)*(-29*x**2) + (-29*x**2)*(-25*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -20*(-29)*x**2 + (37*x)*(-29*x**2) + (37*x)*(-40) + (-29*x**2)*(-25*x**3) - 25*x**3*(-40) + 800\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*x**3)*-40 = 1000*x**3\n (-25*x**3)*(-29*x**2) = 725*x**5\n (37*x)*-40 = -1480*x\n (37*x)*(-29*x**2) = -1073*x**3\n -20*-29*x**2 = 580*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 725*x**5 - 1073*x**3 + 1000*x**3 + 580*x**2 - 1480*x + 800\nCombining like terms, got 725*x**5 - 73*x**3 + 580*x**2 - 1480*x + 800\n#Step 6:\nCurrent expression: 725*x**5 - 73*x**3 + 580*x**2 - 1480*x + 800\nNo more calculations needed.\n725*x**5 - 73*x**3 + 580*x**2 - 1480*x + 800", "generated_answer": "725*x**5 - 73*x**3 + 580*x**2 - 1480*x + 800", "step_length": 6} {"cot_id": "b348e1befe853360f794f9af7c689a37c0eeae56bc36fc77e72d14477f7266b6", "datapoint": {"question": "Simplify this expression: 37*y**2*(43*y**3 + 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1591*y**5 + 1776*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1777, "polynomial_expr": "37*y**2*(43*y**3 + 48)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 37*y**2*(43*y**3 + 48)\nExpanding the part (43*y**3 + 48) using the distributive property, and we got: 48*(37*y**2) + (37*y**2)*(43*y**3)\n#Step 2:\nCurrent expression: 48*(37*y**2) + (37*y**2)*(43*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 48*(37*y**2) = 1776*y**2\n (43*y**3)*(37*y**2) = 1591*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1591*y**5 + 1776*y**2\nNo more calculations needed.\n1591*y**5 + 1776*y**2", "generated_answer": "1591*y**5 + 1776*y**2", "step_length": 3} {"cot_id": "42f2cfbe132da1cd5c626d11d185793d0a3385eb101b045eb00b732b77c54d03", "datapoint": {"question": "Simplify this expression: (27*x**2 + 32*x - 33)*(9*x**3 + 28*x**2 + 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "243*x**5 + 1044*x**4 + 599*x**3 + 345*x**2 + 1504*x - 1551", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1778, "polynomial_expr": "(27*x**2 + 32*x - 33)*(9*x**3 + 28*x**2 + 47)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*x**2 + 32*x - 33)*(9*x**3 + 28*x**2 + 47)\nExpanding the part (27*x**2 + 32*x - 33) using the distributive property, and we got: (32*x)*(9*x**3 + 28*x**2 + 47) + (27*x**2)*(9*x**3 + 28*x**2 + 47) - 33*(9*x**3 + 28*x**2 + 47)\n#Step 2:\nCurrent expression: (32*x)*(9*x**3 + 28*x**2 + 47) + (27*x**2)*(9*x**3 + 28*x**2 + 47) - 33*(9*x**3 + 28*x**2 + 47)\nSimplifying the partial expression: -33*(9*x**3 + 28*x**2 + 47)\nExpanding the part (9*x**3 + 28*x**2 + 47) using the distributive property, and we got: (28*x**2)*(-33) + (9*x**3)*(-33) + 47*(-33)\nReplacing -33*(9*x**3 + 28*x**2 + 47) with (28*x**2)*(-33) + (9*x**3)*(-33) + 47*(-33) in the overall expression.\n#Step 3:\nCurrent expression: (32*x)*(9*x**3 + 28*x**2 + 47) + (27*x**2)*(9*x**3 + 28*x**2 + 47) + (28*x**2)*(-33) + (9*x**3)*(-33) - 1551\nSimplifying the partial expression: (27*x**2)*(9*x**3 + 28*x**2 + 47)\nExpanding the part (9*x**3 + 28*x**2 + 47) using the distributive property, and we got: 47*(27*x**2) + (27*x**2)*(28*x**2) + (27*x**2)*(9*x**3)\nReplacing (27*x**2)*(9*x**3 + 28*x**2 + 47) with 47*(27*x**2) + (27*x**2)*(28*x**2) + (27*x**2)*(9*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 47*27*x**2 + (32*x)*(9*x**3 + 28*x**2 + 47) + (27*x**2)*(28*x**2) + (27*x**2)*(9*x**3) + (28*x**2)*(-33) + (9*x**3)*(-33) - 1551\nSimplifying the partial expression: (32*x)*(9*x**3 + 28*x**2 + 47)\nExpanding the part (9*x**3 + 28*x**2 + 47) using the distributive property, and we got: 47*(32*x) + (32*x)*(28*x**2) + (32*x)*(9*x**3)\nReplacing (32*x)*(9*x**3 + 28*x**2 + 47) with 47*(32*x) + (32*x)*(28*x**2) + (32*x)*(9*x**3) in the overall expression.\n#Step 5:\nCurrent expression: 47*27*x**2 + 47*32*x + (32*x)*(28*x**2) + (32*x)*(9*x**3) + (27*x**2)*(28*x**2) + (27*x**2)*(9*x**3) + (28*x**2)*(-33) + (9*x**3)*(-33) - 1551\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (9*x**3)*-33 = -297*x**3\n (9*x**3)*(27*x**2) = 243*x**5\n (9*x**3)*(32*x) = 288*x**4\n (28*x**2)*-33 = -924*x**2\n (28*x**2)*(27*x**2) = 756*x**4\n (28*x**2)*(32*x) = 896*x**3\n 47*27*x**2 = 1269*x**2\n 47*32*x = 1504*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 243*x**5 + 288*x**4 + 756*x**4 - 297*x**3 + 896*x**3 - 924*x**2 + 1269*x**2 + 1504*x - 1551\nCombining like terms, got 243*x**5 + 1044*x**4 + 599*x**3 + 345*x**2 + 1504*x - 1551\n#Step 7:\nCurrent expression: 243*x**5 + 1044*x**4 + 599*x**3 + 345*x**2 + 1504*x - 1551\nNo more calculations needed.\n243*x**5 + 1044*x**4 + 599*x**3 + 345*x**2 + 1504*x - 1551", "generated_answer": "243*x**5 + 1044*x**4 + 599*x**3 + 345*x**2 + 1504*x - 1551", "step_length": 7} {"cot_id": "ecf5990fb5c9c3251ac7c7ecaa5ae8dce08064855308bfec7a58527349edc210", "datapoint": {"question": "Simplify this expression: (4*y - 48)*(44*y**3 - 12*y**2 - 18*y + 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "176*y**4 - 2160*y**3 + 504*y**2 + 1052*y - 2256", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1779, "polynomial_expr": "(4*y - 48)*(44*y**3 - 12*y**2 - 18*y + 47)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (4*y - 48)*(44*y**3 - 12*y**2 - 18*y + 47)\nExpanding the part (4*y - 48) using the distributive property, and we got: (4*y)*(44*y**3 - 12*y**2 - 18*y + 47) - 48*(44*y**3 - 12*y**2 - 18*y + 47)\n#Step 2:\nCurrent expression: (4*y)*(44*y**3 - 12*y**2 - 18*y + 47) - 48*(44*y**3 - 12*y**2 - 18*y + 47)\nSimplifying the partial expression: -48*(44*y**3 - 12*y**2 - 18*y + 47)\nExpanding the part (44*y**3 - 12*y**2 - 18*y + 47) using the distributive property, and we got: -18*y*(-48) - 12*y**2*(-48) + (44*y**3)*(-48) + 47*(-48)\nReplacing -48*(44*y**3 - 12*y**2 - 18*y + 47) with -18*y*(-48) - 12*y**2*(-48) + (44*y**3)*(-48) + 47*(-48) in the overall expression.\n#Step 3:\nCurrent expression: -18*y*(-48) + (4*y)*(44*y**3 - 12*y**2 - 18*y + 47) - 12*y**2*(-48) + (44*y**3)*(-48) - 2256\nSimplifying the partial expression: (4*y)*(44*y**3 - 12*y**2 - 18*y + 47)\nExpanding the part (44*y**3 - 12*y**2 - 18*y + 47) using the distributive property, and we got: (-18*y)*(4*y) + 47*(4*y) + (4*y)*(-12*y**2) + (4*y)*(44*y**3)\nReplacing (4*y)*(44*y**3 - 12*y**2 - 18*y + 47) with (-18*y)*(4*y) + 47*(4*y) + (4*y)*(-12*y**2) + (4*y)*(44*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-18*y)*(4*y) - 18*y*(-48) + 47*4*y + (4*y)*(-12*y**2) + (4*y)*(44*y**3) - 12*y**2*(-48) + (44*y**3)*(-48) - 2256\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-18*y)*-48 = 864*y\n (-18*y)*(4*y) = -72*y**2\n (-12*y**2)*-48 = 576*y**2\n (-12*y**2)*(4*y) = -48*y**3\n (44*y**3)*-48 = -2112*y**3\n (44*y**3)*(4*y) = 176*y**4\n 47*4*y = 188*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 176*y**4 - 2112*y**3 - 48*y**3 - 72*y**2 + 576*y**2 + 188*y + 864*y - 2256\nCombining like terms, got 176*y**4 - 2160*y**3 + 504*y**2 + 1052*y - 2256\n#Step 6:\nCurrent expression: 176*y**4 - 2160*y**3 + 504*y**2 + 1052*y - 2256\nNo more calculations needed.\n176*y**4 - 2160*y**3 + 504*y**2 + 1052*y - 2256", "generated_answer": "176*y**4 - 2160*y**3 + 504*y**2 + 1052*y - 2256", "step_length": 6} {"cot_id": "900b4b29650ff3ab38391dfe7ede367f82941155a9a65809dc28d9ef9ab6e629", "datapoint": {"question": "Simplify this expression: (-34*z**3 + 15*z**2)*(24*z**3 - 24*z - 15)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-816*z**6 + 360*z**5 + 816*z**4 + 150*z**3 - 225*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1780, "polynomial_expr": "(-34*z**3 + 15*z**2)*(24*z**3 - 24*z - 15)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-34*z**3 + 15*z**2)*(24*z**3 - 24*z - 15)\nExpanding the part (-34*z**3 + 15*z**2) using the distributive property, and we got: (15*z**2)*(24*z**3 - 24*z - 15) + (-34*z**3)*(24*z**3 - 24*z - 15)\n#Step 2:\nCurrent expression: (15*z**2)*(24*z**3 - 24*z - 15) + (-34*z**3)*(24*z**3 - 24*z - 15)\nSimplifying the partial expression: (-34*z**3)*(24*z**3 - 24*z - 15)\nExpanding the part (24*z**3 - 24*z - 15) using the distributive property, and we got: (-24*z)*(-34*z**3) - (-1)*510*z**3 + (-34*z**3)*(24*z**3)\nReplacing (-34*z**3)*(24*z**3 - 24*z - 15) with (-24*z)*(-34*z**3) - (-1)*510*z**3 + (-34*z**3)*(24*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-24*z)*(-34*z**3) - 15*(-34)*z**3 + (15*z**2)*(24*z**3 - 24*z - 15) + (-34*z**3)*(24*z**3)\nSimplifying the partial expression: (15*z**2)*(24*z**3 - 24*z - 15)\nExpanding the part (24*z**3 - 24*z - 15) using the distributive property, and we got: (-24*z)*(15*z**2) - 225*z**2 + (15*z**2)*(24*z**3)\nReplacing (15*z**2)*(24*z**3 - 24*z - 15) with (-24*z)*(15*z**2) - 225*z**2 + (15*z**2)*(24*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-24*z)*(15*z**2) + (-24*z)*(-34*z**3) - 15*(-34)*z**3 - 15*15*z**2 + (15*z**2)*(24*z**3) + (-34*z**3)*(24*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-24*z)*(-34*z**3) = 816*z**4\n (-24*z)*(15*z**2) = -360*z**3\n (24*z**3)*(-34*z**3) = -816*z**6\n (24*z**3)*(15*z**2) = 360*z**5\n -15*-34*z**3 = 510*z**3\n -15*15*z**2 = -225*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -816*z**6 + 360*z**5 + 816*z**4 - 360*z**3 + 510*z**3 - 225*z**2\nCombining like terms, got -816*z**6 + 360*z**5 + 816*z**4 + 150*z**3 - 225*z**2\n#Step 6:\nCurrent expression: -816*z**6 + 360*z**5 + 816*z**4 + 150*z**3 - 225*z**2\nNo more calculations needed.\n-816*z**6 + 360*z**5 + 816*z**4 + 150*z**3 - 225*z**2", "generated_answer": "-816*z**6 + 360*z**5 + 816*z**4 + 150*z**3 - 225*z**2", "step_length": 6} {"cot_id": "1e83f8fc4da0dfc602633a232ce4221836eb17f65536f1743434af54ea2725af", "datapoint": {"question": "Calculate the following: 1804 - 1886*y**3\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1804 - 1886*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1781, "polynomial_expr": "1804 - 1886*y**3", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 1804 - 1886*y**3\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 1804 - 1886*y**3\nNo more calculations needed.\n1804 - 1886*y**3", "generated_answer": "1804 - 1886*y**3", "step_length": 2} {"cot_id": "8760beb3e0ea49769cd210ff0cc2698b7f618e2391363afa6429b64205e3ae2c", "datapoint": {"question": "Calculate the following: (34*x**2 + 28*x)*(37*x**3 - 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1258*x**5 + 1036*x**4 - 1496*x**2 - 1232*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1782, "polynomial_expr": "(34*x**2 + 28*x)*(37*x**3 - 44)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (34*x**2 + 28*x)*(37*x**3 - 44)\nExpanding the part (37*x**3 - 44) using the distributive property, and we got: (37*x**3)*(34*x**2 + 28*x) - 44*(34*x**2 + 28*x)\n#Step 2:\nCurrent expression: (37*x**3)*(34*x**2 + 28*x) - 44*(34*x**2 + 28*x)\nSimplifying the partial expression: -44*(34*x**2 + 28*x)\nExpanding the part (34*x**2 + 28*x) using the distributive property, and we got: (28*x)*(-44) + (34*x**2)*(-44)\nReplacing -44*(34*x**2 + 28*x) with (28*x)*(-44) + (34*x**2)*(-44) in the overall expression.\n#Step 3:\nCurrent expression: (28*x)*(-44) + (34*x**2)*(-44) + (37*x**3)*(34*x**2 + 28*x)\nSimplifying the partial expression: (37*x**3)*(34*x**2 + 28*x)\nExpanding the part (34*x**2 + 28*x) using the distributive property, and we got: (28*x)*(37*x**3) + (34*x**2)*(37*x**3)\nReplacing (37*x**3)*(34*x**2 + 28*x) with (28*x)*(37*x**3) + (34*x**2)*(37*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (28*x)*(37*x**3) + (28*x)*(-44) + (34*x**2)*(37*x**3) + (34*x**2)*(-44)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (28*x)*-44 = -1232*x\n (28*x)*(37*x**3) = 1036*x**4\n (34*x**2)*-44 = -1496*x**2\n (34*x**2)*(37*x**3) = 1258*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1258*x**5 + 1036*x**4 - 1496*x**2 - 1232*x\nNo more calculations needed.\n1258*x**5 + 1036*x**4 - 1496*x**2 - 1232*x", "generated_answer": "1258*x**5 + 1036*x**4 - 1496*x**2 - 1232*x", "step_length": 5} {"cot_id": "02d06f4263766ae541b82147626a9a133d578e814e22363fa9668faadb4c3084", "datapoint": {"question": "Simplify this expression: -22*x*(11*x - 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-242*x**2 + 792*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1783, "polynomial_expr": "-22*x*(11*x - 36)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -22*x*(11*x - 36)\nExpanding the part (11*x - 36) using the distributive property, and we got: (-22*x)*(11*x) - (-1)*792*x\n#Step 2:\nCurrent expression: (-22*x)*(11*x) - (-1)*792*x\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -36*(-22*x) = 792*x\n (11*x)*(-22*x) = -242*x**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -242*x**2 + 792*x\nNo more calculations needed.\n-242*x**2 + 792*x", "generated_answer": "-242*x**2 + 792*x", "step_length": 3} {"cot_id": "790499285b8eacfbfd2e87c317a65c45026f40f94432745dd6f384bf12175fbb", "datapoint": {"question": "Calculate the following: (-49*z - 38)*(-32*z**3 - 41*z**2 + 27*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1568*z**4 + 3225*z**3 + 235*z**2 - 1026*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1784, "polynomial_expr": "(-49*z - 38)*(-32*z**3 - 41*z**2 + 27*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-49*z - 38)*(-32*z**3 - 41*z**2 + 27*z)\nExpanding the part (-49*z - 38) using the distributive property, and we got: (-49*z)*(-32*z**3 - 41*z**2 + 27*z) - 38*(-32*z**3 - 41*z**2 + 27*z)\n#Step 2:\nCurrent expression: (-49*z)*(-32*z**3 - 41*z**2 + 27*z) - 38*(-32*z**3 - 41*z**2 + 27*z)\nSimplifying the partial expression: -38*(-32*z**3 - 41*z**2 + 27*z)\nExpanding the part (-32*z**3 - 41*z**2 + 27*z) using the distributive property, and we got: (27*z)*(-38) - 41*z**2*(-38) - 32*z**3*(-38)\nReplacing -38*(-32*z**3 - 41*z**2 + 27*z) with (27*z)*(-38) - 41*z**2*(-38) - 32*z**3*(-38) in the overall expression.\n#Step 3:\nCurrent expression: (-49*z)*(-32*z**3 - 41*z**2 + 27*z) + (27*z)*(-38) - 41*z**2*(-38) - 32*z**3*(-38)\nSimplifying the partial expression: (-49*z)*(-32*z**3 - 41*z**2 + 27*z)\nExpanding the part (-32*z**3 - 41*z**2 + 27*z) using the distributive property, and we got: (-49*z)*(27*z) + (-49*z)*(-41*z**2) + (-49*z)*(-32*z**3)\nReplacing (-49*z)*(-32*z**3 - 41*z**2 + 27*z) with (-49*z)*(27*z) + (-49*z)*(-41*z**2) + (-49*z)*(-32*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-49*z)*(27*z) + (-49*z)*(-41*z**2) + (-49*z)*(-32*z**3) + (27*z)*(-38) - 41*z**2*(-38) - 32*z**3*(-38)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*z**2)*-38 = 1558*z**2\n (-41*z**2)*(-49*z) = 2009*z**3\n (-32*z**3)*-38 = 1216*z**3\n (-32*z**3)*(-49*z) = 1568*z**4\n (27*z)*-38 = -1026*z\n (27*z)*(-49*z) = -1323*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1568*z**4 + 1216*z**3 + 2009*z**3 - 1323*z**2 + 1558*z**2 - 1026*z\nCombining like terms, got 1568*z**4 + 3225*z**3 + 235*z**2 - 1026*z\n#Step 6:\nCurrent expression: 1568*z**4 + 3225*z**3 + 235*z**2 - 1026*z\nNo more calculations needed.\n1568*z**4 + 3225*z**3 + 235*z**2 - 1026*z", "generated_answer": "1568*z**4 + 3225*z**3 + 235*z**2 - 1026*z", "step_length": 6} {"cot_id": "40cc15ddc21238f94f3457dc930380f8cd78cd9372811773a9dcfe441f02a3a0", "datapoint": {"question": "Calculate the following: (66 - 27*y**3)*(29*y**2 - 59*y - 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-783*y**5 + 1593*y**4 + 1107*y**3 + 1914*y**2 - 3894*y - 2706", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1785, "polynomial_expr": "(66 - 27*y**3)*(29*y**2 - 59*y - 41)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (66 - 27*y**3)*(29*y**2 - 59*y - 41)\nExpanding the part (66 - 27*y**3) using the distributive property, and we got: (-27*y**3)*(29*y**2 - 59*y - 41) + 66*(29*y**2 - 59*y - 41)\n#Step 2:\nCurrent expression: (-27*y**3)*(29*y**2 - 59*y - 41) + 66*(29*y**2 - 59*y - 41)\nSimplifying the partial expression: 66*(29*y**2 - 59*y - 41)\nExpanding the part (29*y**2 - 59*y - 41) using the distributive property, and we got: -59*y*66 + (29*y**2)*66 - 41*66\nReplacing 66*(29*y**2 - 59*y - 41) with -59*y*66 + (29*y**2)*66 - 41*66 in the overall expression.\n#Step 3:\nCurrent expression: -59*y*66 + (29*y**2)*66 + (-27*y**3)*(29*y**2 - 59*y - 41) - 2706\nSimplifying the partial expression: (-27*y**3)*(29*y**2 - 59*y - 41)\nExpanding the part (29*y**2 - 59*y - 41) using the distributive property, and we got: (-59*y)*(-27*y**3) - (-1)*1107*y**3 + (29*y**2)*(-27*y**3)\nReplacing (-27*y**3)*(29*y**2 - 59*y - 41) with (-59*y)*(-27*y**3) - (-1)*1107*y**3 + (29*y**2)*(-27*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-59*y)*(-27*y**3) - 59*y*66 - 41*(-27)*y**3 + (29*y**2)*(-27*y**3) + (29*y**2)*66 - 2706\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-59*y)*66 = -3894*y\n (-59*y)*(-27*y**3) = 1593*y**4\n (29*y**2)*66 = 1914*y**2\n (29*y**2)*(-27*y**3) = -783*y**5\n -41*-27*y**3 = 1107*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -783*y**5 + 1593*y**4 + 1107*y**3 + 1914*y**2 - 3894*y - 2706\nNo more calculations needed.\n-783*y**5 + 1593*y**4 + 1107*y**3 + 1914*y**2 - 3894*y - 2706", "generated_answer": "-783*y**5 + 1593*y**4 + 1107*y**3 + 1914*y**2 - 3894*y - 2706", "step_length": 5} {"cot_id": "0fd4bf8484169b7620bf5141a531580ce0be1be1545b68bbfcb390cdf198a774", "datapoint": {"question": "Calculate the following: (39*z**2 + 53*z)*(-14*z**3 + 92*z**2 - 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-546*z**5 + 2846*z**4 + 4876*z**3 - 780*z**2 - 1060*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1786, "polynomial_expr": "(39*z**2 + 53*z)*(-14*z**3 + 92*z**2 - 20)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (39*z**2 + 53*z)*(-14*z**3 + 92*z**2 - 20)\nExpanding the part (39*z**2 + 53*z) using the distributive property, and we got: (53*z)*(-14*z**3 + 92*z**2 - 20) + (39*z**2)*(-14*z**3 + 92*z**2 - 20)\n#Step 2:\nCurrent expression: (53*z)*(-14*z**3 + 92*z**2 - 20) + (39*z**2)*(-14*z**3 + 92*z**2 - 20)\nSimplifying the partial expression: (39*z**2)*(-14*z**3 + 92*z**2 - 20)\nExpanding the part (-14*z**3 + 92*z**2 - 20) using the distributive property, and we got: -780*z**2 + (39*z**2)*(92*z**2) + (39*z**2)*(-14*z**3)\nReplacing (39*z**2)*(-14*z**3 + 92*z**2 - 20) with -780*z**2 + (39*z**2)*(92*z**2) + (39*z**2)*(-14*z**3) in the overall expression.\n#Step 3:\nCurrent expression: -20*39*z**2 + (53*z)*(-14*z**3 + 92*z**2 - 20) + (39*z**2)*(92*z**2) + (39*z**2)*(-14*z**3)\nSimplifying the partial expression: (53*z)*(-14*z**3 + 92*z**2 - 20)\nExpanding the part (-14*z**3 + 92*z**2 - 20) using the distributive property, and we got: -1060*z + (53*z)*(92*z**2) + (53*z)*(-14*z**3)\nReplacing (53*z)*(-14*z**3 + 92*z**2 - 20) with -1060*z + (53*z)*(92*z**2) + (53*z)*(-14*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -20*39*z**2 - 20*53*z + (53*z)*(92*z**2) + (53*z)*(-14*z**3) + (39*z**2)*(92*z**2) + (39*z**2)*(-14*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-14*z**3)*(39*z**2) = -546*z**5\n (-14*z**3)*(53*z) = -742*z**4\n (92*z**2)*(39*z**2) = 3588*z**4\n (92*z**2)*(53*z) = 4876*z**3\n -20*39*z**2 = -780*z**2\n -20*53*z = -1060*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -546*z**5 - 742*z**4 + 3588*z**4 + 4876*z**3 - 780*z**2 - 1060*z\nCombining like terms, got -546*z**5 + 2846*z**4 + 4876*z**3 - 780*z**2 - 1060*z\n#Step 6:\nCurrent expression: -546*z**5 + 2846*z**4 + 4876*z**3 - 780*z**2 - 1060*z\nNo more calculations needed.\n-546*z**5 + 2846*z**4 + 4876*z**3 - 780*z**2 - 1060*z", "generated_answer": "-546*z**5 + 2846*z**4 + 4876*z**3 - 780*z**2 - 1060*z", "step_length": 6} {"cot_id": "7cd49865f68395ec036a39dd4e5b9195956299c24dec8136d2fd24a59bc30db1", "datapoint": {"question": "Calculate the following: 56*y*(32*y**3 + 18*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1792*y**4 + 1008*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1787, "polynomial_expr": "56*y*(32*y**3 + 18*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 56*y*(32*y**3 + 18*y**2)\nExpanding the part (32*y**3 + 18*y**2) using the distributive property, and we got: (56*y)*(18*y**2) + (56*y)*(32*y**3)\n#Step 2:\nCurrent expression: (56*y)*(18*y**2) + (56*y)*(32*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (18*y**2)*(56*y) = 1008*y**3\n (32*y**3)*(56*y) = 1792*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1792*y**4 + 1008*y**3\nNo more calculations needed.\n1792*y**4 + 1008*y**3", "generated_answer": "1792*y**4 + 1008*y**3", "step_length": 3} {"cot_id": "20990705367fa773f3f9f34ca8bd053928f6a4dca9b673adcfdeded1bfdff285", "datapoint": {"question": "Simplify this expression: (8*z**3 - 48*z**2 - 28*z)*(31*z**3 - 15*z**2 + 42)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "248*z**6 - 1608*z**5 - 148*z**4 + 756*z**3 - 2016*z**2 - 1176*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1788, "polynomial_expr": "(8*z**3 - 48*z**2 - 28*z)*(31*z**3 - 15*z**2 + 42)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (8*z**3 - 48*z**2 - 28*z)*(31*z**3 - 15*z**2 + 42)\nExpanding the part (31*z**3 - 15*z**2 + 42) using the distributive property, and we got: (-15*z**2)*(8*z**3 - 48*z**2 - 28*z) + (31*z**3)*(8*z**3 - 48*z**2 - 28*z) + 42*(8*z**3 - 48*z**2 - 28*z)\n#Step 2:\nCurrent expression: (-15*z**2)*(8*z**3 - 48*z**2 - 28*z) + (31*z**3)*(8*z**3 - 48*z**2 - 28*z) + 42*(8*z**3 - 48*z**2 - 28*z)\nSimplifying the partial expression: 42*(8*z**3 - 48*z**2 - 28*z)\nExpanding the part (8*z**3 - 48*z**2 - 28*z) using the distributive property, and we got: -28*z*42 - 48*z**2*42 + (8*z**3)*42\nReplacing 42*(8*z**3 - 48*z**2 - 28*z) with -28*z*42 - 48*z**2*42 + (8*z**3)*42 in the overall expression.\n#Step 3:\nCurrent expression: -28*z*42 - 48*z**2*42 + (-15*z**2)*(8*z**3 - 48*z**2 - 28*z) + (8*z**3)*42 + (31*z**3)*(8*z**3 - 48*z**2 - 28*z)\nSimplifying the partial expression: (-15*z**2)*(8*z**3 - 48*z**2 - 28*z)\nExpanding the part (8*z**3 - 48*z**2 - 28*z) using the distributive property, and we got: (-28*z)*(-15*z**2) + (-48*z**2)*(-15*z**2) + (-15*z**2)*(8*z**3)\nReplacing (-15*z**2)*(8*z**3 - 48*z**2 - 28*z) with (-28*z)*(-15*z**2) + (-48*z**2)*(-15*z**2) + (-15*z**2)*(8*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-28*z)*(-15*z**2) - 28*z*42 + (-48*z**2)*(-15*z**2) - 48*z**2*42 + (-15*z**2)*(8*z**3) + (8*z**3)*42 + (31*z**3)*(8*z**3 - 48*z**2 - 28*z)\nSimplifying the partial expression: (31*z**3)*(8*z**3 - 48*z**2 - 28*z)\nExpanding the part (8*z**3 - 48*z**2 - 28*z) using the distributive property, and we got: (-28*z)*(31*z**3) + (-48*z**2)*(31*z**3) + (8*z**3)*(31*z**3)\nReplacing (31*z**3)*(8*z**3 - 48*z**2 - 28*z) with (-28*z)*(31*z**3) + (-48*z**2)*(31*z**3) + (8*z**3)*(31*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-28*z)*(-15*z**2) + (-28*z)*(31*z**3) - 28*z*42 + (-48*z**2)*(-15*z**2) + (-48*z**2)*(31*z**3) - 48*z**2*42 + (-15*z**2)*(8*z**3) + (8*z**3)*(31*z**3) + (8*z**3)*42\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*z**2)*42 = -2016*z**2\n (-48*z**2)*(-15*z**2) = 720*z**4\n (-48*z**2)*(31*z**3) = -1488*z**5\n (-28*z)*42 = -1176*z\n (-28*z)*(-15*z**2) = 420*z**3\n (-28*z)*(31*z**3) = -868*z**4\n (8*z**3)*42 = 336*z**3\n (8*z**3)*(-15*z**2) = -120*z**5\n (8*z**3)*(31*z**3) = 248*z**6\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 248*z**6 - 1488*z**5 - 120*z**5 - 868*z**4 + 720*z**4 + 336*z**3 + 420*z**3 - 2016*z**2 - 1176*z\nCombining like terms, got 248*z**6 - 1608*z**5 - 148*z**4 + 756*z**3 - 2016*z**2 - 1176*z\n#Step 7:\nCurrent expression: 248*z**6 - 1608*z**5 - 148*z**4 + 756*z**3 - 2016*z**2 - 1176*z\nNo more calculations needed.\n248*z**6 - 1608*z**5 - 148*z**4 + 756*z**3 - 2016*z**2 - 1176*z", "generated_answer": "248*z**6 - 1608*z**5 - 148*z**4 + 756*z**3 - 2016*z**2 - 1176*z", "step_length": 7} {"cot_id": "77bc9023f58d0e223ece829ca2cf05398db4245973c30454e1471f3b3b4df806", "datapoint": {"question": "Calculate the following: -47*z*(14*z**3 + 41*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-658*z**4 - 1927*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1789, "polynomial_expr": "-47*z*(14*z**3 + 41*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -47*z*(14*z**3 + 41*z)\nExpanding the part (14*z**3 + 41*z) using the distributive property, and we got: (-47*z)*(41*z) + (-47*z)*(14*z**3)\n#Step 2:\nCurrent expression: (-47*z)*(41*z) + (-47*z)*(14*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (14*z**3)*(-47*z) = -658*z**4\n (41*z)*(-47*z) = -1927*z**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -658*z**4 - 1927*z**2\nNo more calculations needed.\n-658*z**4 - 1927*z**2", "generated_answer": "-658*z**4 - 1927*z**2", "step_length": 3} {"cot_id": "30c49eed90e8fe3a5108ab0e5d52f9c7d363f87d02ff8074e024da808acb499c", "datapoint": {"question": "Calculate the following: (57*y - 14)*(-47*y**3 + 18*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2679*y**4 + 1684*y**3 - 252*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1790, "polynomial_expr": "(57*y - 14)*(-47*y**3 + 18*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (57*y - 14)*(-47*y**3 + 18*y**2)\nExpanding the part (57*y - 14) using the distributive property, and we got: (57*y)*(-47*y**3 + 18*y**2) - 14*(-47*y**3 + 18*y**2)\n#Step 2:\nCurrent expression: (57*y)*(-47*y**3 + 18*y**2) - 14*(-47*y**3 + 18*y**2)\nSimplifying the partial expression: -14*(-47*y**3 + 18*y**2)\nExpanding the part (-47*y**3 + 18*y**2) using the distributive property, and we got: (18*y**2)*(-14) - 47*y**3*(-14)\nReplacing -14*(-47*y**3 + 18*y**2) with (18*y**2)*(-14) - 47*y**3*(-14) in the overall expression.\n#Step 3:\nCurrent expression: (57*y)*(-47*y**3 + 18*y**2) + (18*y**2)*(-14) - 47*y**3*(-14)\nSimplifying the partial expression: (57*y)*(-47*y**3 + 18*y**2)\nExpanding the part (-47*y**3 + 18*y**2) using the distributive property, and we got: (57*y)*(18*y**2) + (57*y)*(-47*y**3)\nReplacing (57*y)*(-47*y**3 + 18*y**2) with (57*y)*(18*y**2) + (57*y)*(-47*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (57*y)*(18*y**2) + (57*y)*(-47*y**3) + (18*y**2)*(-14) - 47*y**3*(-14)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*y**3)*-14 = 658*y**3\n (-47*y**3)*(57*y) = -2679*y**4\n (18*y**2)*-14 = -252*y**2\n (18*y**2)*(57*y) = 1026*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2679*y**4 + 658*y**3 + 1026*y**3 - 252*y**2\nCombining like terms, got -2679*y**4 + 1684*y**3 - 252*y**2\n#Step 6:\nCurrent expression: -2679*y**4 + 1684*y**3 - 252*y**2\nNo more calculations needed.\n-2679*y**4 + 1684*y**3 - 252*y**2", "generated_answer": "-2679*y**4 + 1684*y**3 - 252*y**2", "step_length": 6} {"cot_id": "919025b0d11e88a13b4e0d66270589fd8d9bf2f8a7d2fc3576bf367fb2b76d29", "datapoint": {"question": "Simplify this expression: (31 - 29*z**2)*(z**3 + 27*z**2 - 30*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-29*z**5 - 783*z**4 + 901*z**3 + 837*z**2 - 930*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1791, "polynomial_expr": "(31 - 29*z**2)*(z**3 + 27*z**2 - 30*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31 - 29*z**2)*(z**3 + 27*z**2 - 30*z)\nExpanding the part (31 - 29*z**2) using the distributive property, and we got: (-29*z**2)*(z**3 + 27*z**2 - 30*z) + 31*(z**3 + 27*z**2 - 30*z)\n#Step 2:\nCurrent expression: (-29*z**2)*(z**3 + 27*z**2 - 30*z) + 31*(z**3 + 27*z**2 - 30*z)\nSimplifying the partial expression: 31*(z**3 + 27*z**2 - 30*z)\nExpanding the part (z**3 + 27*z**2 - 30*z) using the distributive property, and we got: -30*z*31 + z**3*31 + (27*z**2)*31\nReplacing 31*(z**3 + 27*z**2 - 30*z) with -30*z*31 + z**3*31 + (27*z**2)*31 in the overall expression.\n#Step 3:\nCurrent expression: -30*z*31 + z**3*31 + (-29*z**2)*(z**3 + 27*z**2 - 30*z) + (27*z**2)*31\nSimplifying the partial expression: (-29*z**2)*(z**3 + 27*z**2 - 30*z)\nExpanding the part (z**3 + 27*z**2 - 30*z) using the distributive property, and we got: (-30*z)*(-29*z**2) + (-29*z**2)*z**3 + (-29*z**2)*(27*z**2)\nReplacing (-29*z**2)*(z**3 + 27*z**2 - 30*z) with (-30*z)*(-29*z**2) + (-29*z**2)*z**3 + (-29*z**2)*(27*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-30*z)*(-29*z**2) - 30*z*31 + (-29*z**2)*z**3 + z**3*31 + (-29*z**2)*(27*z**2) + (27*z**2)*31\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n z**3*31 = 31*z**3\n z**3*(-29*z**2) = -29*z**5\n (-30*z)*31 = -930*z\n (-30*z)*(-29*z**2) = 870*z**3\n (27*z**2)*31 = 837*z**2\n (27*z**2)*(-29*z**2) = -783*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -29*z**5 - 783*z**4 + 31*z**3 + 870*z**3 + 837*z**2 - 930*z\nCombining like terms, got -29*z**5 - 783*z**4 + 901*z**3 + 837*z**2 - 930*z\n#Step 6:\nCurrent expression: -29*z**5 - 783*z**4 + 901*z**3 + 837*z**2 - 930*z\nNo more calculations needed.\n-29*z**5 - 783*z**4 + 901*z**3 + 837*z**2 - 930*z", "generated_answer": "-29*z**5 - 783*z**4 + 901*z**3 + 837*z**2 - 930*z", "step_length": 6} {"cot_id": "c8f22ca40c4b2bc791b3fab9b4898107bcc2c27e05c0bc763c7966e022de049e", "datapoint": {"question": "Simplify this expression: (48 - 17*y**3)*(31*y**3 + 59)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-527*y**6 + 485*y**3 + 2832", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1792, "polynomial_expr": "(48 - 17*y**3)*(31*y**3 + 59)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (48 - 17*y**3)*(31*y**3 + 59)\nExpanding the part (48 - 17*y**3) using the distributive property, and we got: (-17*y**3)*(31*y**3 + 59) + 48*(31*y**3 + 59)\n#Step 2:\nCurrent expression: (-17*y**3)*(31*y**3 + 59) + 48*(31*y**3 + 59)\nSimplifying the partial expression: 48*(31*y**3 + 59)\nExpanding the part (31*y**3 + 59) using the distributive property, and we got: (31*y**3)*48 + 59*48\nReplacing 48*(31*y**3 + 59) with (31*y**3)*48 + 59*48 in the overall expression.\n#Step 3:\nCurrent expression: (-17*y**3)*(31*y**3 + 59) + (31*y**3)*48 + 2832\nSimplifying the partial expression: (-17*y**3)*(31*y**3 + 59)\nExpanding the part (31*y**3 + 59) using the distributive property, and we got: 59*(-17*y**3) + (-17*y**3)*(31*y**3)\nReplacing (-17*y**3)*(31*y**3 + 59) with 59*(-17*y**3) + (-17*y**3)*(31*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 59*(-17)*y**3 + (-17*y**3)*(31*y**3) + (31*y**3)*48 + 2832\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (31*y**3)*48 = 1488*y**3\n (31*y**3)*(-17*y**3) = -527*y**6\n 59*-17*y**3 = -1003*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -527*y**6 - 1003*y**3 + 1488*y**3 + 2832\nCombining like terms, got -527*y**6 + 485*y**3 + 2832\n#Step 6:\nCurrent expression: -527*y**6 + 485*y**3 + 2832\nNo more calculations needed.\n-527*y**6 + 485*y**3 + 2832", "generated_answer": "-527*y**6 + 485*y**3 + 2832", "step_length": 6} {"cot_id": "5ccfb3402b777660ba8885d68aea328acf30d021653f488180feb816aaf9f346", "datapoint": {"question": "Calculate the following: (39 - 19*z)*(-50*z**2 + 33*z - 23)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "950*z**3 - 2577*z**2 + 1724*z - 897", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1793, "polynomial_expr": "(39 - 19*z)*(-50*z**2 + 33*z - 23)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (39 - 19*z)*(-50*z**2 + 33*z - 23)\nExpanding the part (39 - 19*z) using the distributive property, and we got: (-19*z)*(-50*z**2 + 33*z - 23) + 39*(-50*z**2 + 33*z - 23)\n#Step 2:\nCurrent expression: (-19*z)*(-50*z**2 + 33*z - 23) + 39*(-50*z**2 + 33*z - 23)\nSimplifying the partial expression: 39*(-50*z**2 + 33*z - 23)\nExpanding the part (-50*z**2 + 33*z - 23) using the distributive property, and we got: (33*z)*39 - 50*z**2*39 - 23*39\nReplacing 39*(-50*z**2 + 33*z - 23) with (33*z)*39 - 50*z**2*39 - 23*39 in the overall expression.\n#Step 3:\nCurrent expression: (-19*z)*(-50*z**2 + 33*z - 23) + (33*z)*39 - 50*z**2*39 - 897\nSimplifying the partial expression: (-19*z)*(-50*z**2 + 33*z - 23)\nExpanding the part (-50*z**2 + 33*z - 23) using the distributive property, and we got: (-19*z)*(33*z) + (-19*z)*(-50*z**2) - (-1)*437*z\nReplacing (-19*z)*(-50*z**2 + 33*z - 23) with (-19*z)*(33*z) + (-19*z)*(-50*z**2) - (-1)*437*z in the overall expression.\n#Step 4:\nCurrent expression: (-19*z)*(33*z) + (-19*z)*(-50*z**2) - 23*(-19)*z + (33*z)*39 - 50*z**2*39 - 897\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-50*z**2)*39 = -1950*z**2\n (-50*z**2)*(-19*z) = 950*z**3\n (33*z)*39 = 1287*z\n (33*z)*(-19*z) = -627*z**2\n -23*-19*z = 437*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 950*z**3 - 1950*z**2 - 627*z**2 + 437*z + 1287*z - 897\nCombining like terms, got 950*z**3 - 2577*z**2 + 1724*z - 897\n#Step 6:\nCurrent expression: 950*z**3 - 2577*z**2 + 1724*z - 897\nNo more calculations needed.\n950*z**3 - 2577*z**2 + 1724*z - 897", "generated_answer": "950*z**3 - 2577*z**2 + 1724*z - 897", "step_length": 6} {"cot_id": "9c83ebe5fd5f1116bfb3574de6ee1745690ab0eee0ac3cc487d0a2928598347c", "datapoint": {"question": "Simplify this expression: (46 - 6*x**3)*(45*x**2 + 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-270*x**5 - 186*x**3 + 2070*x**2 + 1426", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1794, "polynomial_expr": "(46 - 6*x**3)*(45*x**2 + 31)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (46 - 6*x**3)*(45*x**2 + 31)\nExpanding the part (45*x**2 + 31) using the distributive property, and we got: (45*x**2)*(46 - 6*x**3) + 31*(46 - 6*x**3)\n#Step 2:\nCurrent expression: (45*x**2)*(46 - 6*x**3) + 31*(46 - 6*x**3)\nSimplifying the partial expression: 31*(46 - 6*x**3)\nExpanding the part (46 - 6*x**3) using the distributive property, and we got: -6*x**3*31 + 46*31\nReplacing 31*(46 - 6*x**3) with -6*x**3*31 + 46*31 in the overall expression.\n#Step 3:\nCurrent expression: (45*x**2)*(46 - 6*x**3) - 6*x**3*31 + 1426\nSimplifying the partial expression: (45*x**2)*(46 - 6*x**3)\nExpanding the part (46 - 6*x**3) using the distributive property, and we got: 46*(45*x**2) + (45*x**2)*(-6*x**3)\nReplacing (45*x**2)*(46 - 6*x**3) with 46*(45*x**2) + (45*x**2)*(-6*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 46*45*x**2 + (45*x**2)*(-6*x**3) - 6*x**3*31 + 1426\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-6*x**3)*31 = -186*x**3\n (-6*x**3)*(45*x**2) = -270*x**5\n 46*45*x**2 = 2070*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -270*x**5 - 186*x**3 + 2070*x**2 + 1426\nNo more calculations needed.\n-270*x**5 - 186*x**3 + 2070*x**2 + 1426", "generated_answer": "-270*x**5 - 186*x**3 + 2070*x**2 + 1426", "step_length": 5} {"cot_id": "73de07468cb2db6cbba532b9acccc29537e4e5d252b45dcf8582928e22a544f8", "datapoint": {"question": "Simplify this expression: (-14*z**2 - 40*z)*(34*z**3 + 49*z**2 + 12)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-476*z**5 - 2046*z**4 - 1960*z**3 - 168*z**2 - 480*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1795, "polynomial_expr": "(-14*z**2 - 40*z)*(34*z**3 + 49*z**2 + 12)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-14*z**2 - 40*z)*(34*z**3 + 49*z**2 + 12)\nExpanding the part (-14*z**2 - 40*z) using the distributive property, and we got: (-40*z)*(34*z**3 + 49*z**2 + 12) + (-14*z**2)*(34*z**3 + 49*z**2 + 12)\n#Step 2:\nCurrent expression: (-40*z)*(34*z**3 + 49*z**2 + 12) + (-14*z**2)*(34*z**3 + 49*z**2 + 12)\nSimplifying the partial expression: (-40*z)*(34*z**3 + 49*z**2 + 12)\nExpanding the part (34*z**3 + 49*z**2 + 12) using the distributive property, and we got: (-40*z)*(49*z**2) + (-40*z)*(34*z**3) + 12*(-40*z)\nReplacing (-40*z)*(34*z**3 + 49*z**2 + 12) with (-40*z)*(49*z**2) + (-40*z)*(34*z**3) + 12*(-40*z) in the overall expression.\n#Step 3:\nCurrent expression: (-40*z)*(49*z**2) + (-40*z)*(34*z**3) + 12*(-40)*z + (-14*z**2)*(34*z**3 + 49*z**2 + 12)\nSimplifying the partial expression: (-14*z**2)*(34*z**3 + 49*z**2 + 12)\nExpanding the part (34*z**3 + 49*z**2 + 12) using the distributive property, and we got: 12*(-14*z**2) + (-14*z**2)*(49*z**2) + (-14*z**2)*(34*z**3)\nReplacing (-14*z**2)*(34*z**3 + 49*z**2 + 12) with 12*(-14*z**2) + (-14*z**2)*(49*z**2) + (-14*z**2)*(34*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-40*z)*(49*z**2) + (-40*z)*(34*z**3) + 12*(-14)*z**2 + 12*(-40)*z + (-14*z**2)*(49*z**2) + (-14*z**2)*(34*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (34*z**3)*(-40*z) = -1360*z**4\n (34*z**3)*(-14*z**2) = -476*z**5\n (49*z**2)*(-40*z) = -1960*z**3\n (49*z**2)*(-14*z**2) = -686*z**4\n 12*-40*z = -480*z\n 12*-14*z**2 = -168*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -476*z**5 - 1360*z**4 - 686*z**4 - 1960*z**3 - 168*z**2 - 480*z\nCombining like terms, got -476*z**5 - 2046*z**4 - 1960*z**3 - 168*z**2 - 480*z\n#Step 6:\nCurrent expression: -476*z**5 - 2046*z**4 - 1960*z**3 - 168*z**2 - 480*z\nNo more calculations needed.\n-476*z**5 - 2046*z**4 - 1960*z**3 - 168*z**2 - 480*z", "generated_answer": "-476*z**5 - 2046*z**4 - 1960*z**3 - 168*z**2 - 480*z", "step_length": 6} {"cot_id": "bc178323c3ed521ca7459a07cffa27923a94147f2859e3e87de5bd449366eb80", "datapoint": {"question": "Simplify this expression: (-24*x - 12)*(-5*x**3 + 32*x**2 - 41*x - 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "120*x**4 - 708*x**3 + 600*x**2 + 1356*x + 432", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1796, "polynomial_expr": "(-24*x - 12)*(-5*x**3 + 32*x**2 - 41*x - 36)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-24*x - 12)*(-5*x**3 + 32*x**2 - 41*x - 36)\nExpanding the part (-24*x - 12) using the distributive property, and we got: (-24*x)*(-5*x**3 + 32*x**2 - 41*x - 36) - 12*(-5*x**3 + 32*x**2 - 41*x - 36)\n#Step 2:\nCurrent expression: (-24*x)*(-5*x**3 + 32*x**2 - 41*x - 36) - 12*(-5*x**3 + 32*x**2 - 41*x - 36)\nSimplifying the partial expression: -12*(-5*x**3 + 32*x**2 - 41*x - 36)\nExpanding the part (-5*x**3 + 32*x**2 - 41*x - 36) using the distributive property, and we got: -41*x*(-12) + (32*x**2)*(-12) - 5*x**3*(-12) - 36*(-12)\nReplacing -12*(-5*x**3 + 32*x**2 - 41*x - 36) with -41*x*(-12) + (32*x**2)*(-12) - 5*x**3*(-12) - 36*(-12) in the overall expression.\n#Step 3:\nCurrent expression: -41*x*(-12) + (-24*x)*(-5*x**3 + 32*x**2 - 41*x - 36) + (32*x**2)*(-12) - 5*x**3*(-12) + 432\nSimplifying the partial expression: (-24*x)*(-5*x**3 + 32*x**2 - 41*x - 36)\nExpanding the part (-5*x**3 + 32*x**2 - 41*x - 36) using the distributive property, and we got: (-41*x)*(-24*x) + (-24*x)*(32*x**2) + (-24*x)*(-5*x**3) - (-1)*864*x\nReplacing (-24*x)*(-5*x**3 + 32*x**2 - 41*x - 36) with (-41*x)*(-24*x) + (-24*x)*(32*x**2) + (-24*x)*(-5*x**3) - (-1)*864*x in the overall expression.\n#Step 4:\nCurrent expression: (-41*x)*(-24*x) - 41*x*(-12) + (-24*x)*(32*x**2) + (-24*x)*(-5*x**3) - 36*(-24)*x + (32*x**2)*(-12) - 5*x**3*(-12) + 432\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*x)*-12 = 492*x\n (-41*x)*(-24*x) = 984*x**2\n (-5*x**3)*-12 = 60*x**3\n (-5*x**3)*(-24*x) = 120*x**4\n (32*x**2)*-12 = -384*x**2\n (32*x**2)*(-24*x) = -768*x**3\n -36*-24*x = 864*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 120*x**4 - 768*x**3 + 60*x**3 - 384*x**2 + 984*x**2 + 492*x + 864*x + 432\nCombining like terms, got 120*x**4 - 708*x**3 + 600*x**2 + 1356*x + 432\n#Step 6:\nCurrent expression: 120*x**4 - 708*x**3 + 600*x**2 + 1356*x + 432\nNo more calculations needed.\n120*x**4 - 708*x**3 + 600*x**2 + 1356*x + 432", "generated_answer": "120*x**4 - 708*x**3 + 600*x**2 + 1356*x + 432", "step_length": 6} {"cot_id": "c779acc9dcc54a68f2eaeeb0cc5fa67f13cd1b83033d6d7d6ec520f6e1c5df58", "datapoint": {"question": "Calculate the following: (41*x**3 + 7*x**2)*(2*x**2 - 4*x + 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "82*x**5 - 150*x**4 + 1530*x**3 + 266*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1797, "polynomial_expr": "(41*x**3 + 7*x**2)*(2*x**2 - 4*x + 38)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (41*x**3 + 7*x**2)*(2*x**2 - 4*x + 38)\nExpanding the part (41*x**3 + 7*x**2) using the distributive property, and we got: (7*x**2)*(2*x**2 - 4*x + 38) + (41*x**3)*(2*x**2 - 4*x + 38)\n#Step 2:\nCurrent expression: (7*x**2)*(2*x**2 - 4*x + 38) + (41*x**3)*(2*x**2 - 4*x + 38)\nSimplifying the partial expression: (7*x**2)*(2*x**2 - 4*x + 38)\nExpanding the part (2*x**2 - 4*x + 38) using the distributive property, and we got: (-4*x)*(7*x**2) + 38*(7*x**2) + (2*x**2)*(7*x**2)\nReplacing (7*x**2)*(2*x**2 - 4*x + 38) with (-4*x)*(7*x**2) + 38*(7*x**2) + (2*x**2)*(7*x**2) in the overall expression.\n#Step 3:\nCurrent expression: (-4*x)*(7*x**2) + 38*7*x**2 + (2*x**2)*(7*x**2) + (41*x**3)*(2*x**2 - 4*x + 38)\nSimplifying the partial expression: (41*x**3)*(2*x**2 - 4*x + 38)\nExpanding the part (2*x**2 - 4*x + 38) using the distributive property, and we got: (-4*x)*(41*x**3) + 38*(41*x**3) + (2*x**2)*(41*x**3)\nReplacing (41*x**3)*(2*x**2 - 4*x + 38) with (-4*x)*(41*x**3) + 38*(41*x**3) + (2*x**2)*(41*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-4*x)*(7*x**2) + (-4*x)*(41*x**3) + 38*41*x**3 + 38*7*x**2 + (2*x**2)*(7*x**2) + (2*x**2)*(41*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-4*x)*(7*x**2) = -28*x**3\n (-4*x)*(41*x**3) = -164*x**4\n (2*x**2)*(7*x**2) = 14*x**4\n (2*x**2)*(41*x**3) = 82*x**5\n 38*7*x**2 = 266*x**2\n 38*41*x**3 = 1558*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 82*x**5 - 164*x**4 + 14*x**4 - 28*x**3 + 1558*x**3 + 266*x**2\nCombining like terms, got 82*x**5 - 150*x**4 + 1530*x**3 + 266*x**2\n#Step 6:\nCurrent expression: 82*x**5 - 150*x**4 + 1530*x**3 + 266*x**2\nNo more calculations needed.\n82*x**5 - 150*x**4 + 1530*x**3 + 266*x**2", "generated_answer": "82*x**5 - 150*x**4 + 1530*x**3 + 266*x**2", "step_length": 6} {"cot_id": "2574e2adc4108e888bc30be80db2936321e299a20519c57d03c67c718aeedd69", "datapoint": {"question": "Simplify this expression: (-21*y**3 - 8)*(8*y**3 + 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-168*y**6 - 799*y**3 - 280", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1798, "polynomial_expr": "(-21*y**3 - 8)*(8*y**3 + 35)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-21*y**3 - 8)*(8*y**3 + 35)\nExpanding the part (-21*y**3 - 8) using the distributive property, and we got: (-21*y**3)*(8*y**3 + 35) - 8*(8*y**3 + 35)\n#Step 2:\nCurrent expression: (-21*y**3)*(8*y**3 + 35) - 8*(8*y**3 + 35)\nSimplifying the partial expression: -8*(8*y**3 + 35)\nExpanding the part (8*y**3 + 35) using the distributive property, and we got: (8*y**3)*(-8) + 35*(-8)\nReplacing -8*(8*y**3 + 35) with (8*y**3)*(-8) + 35*(-8) in the overall expression.\n#Step 3:\nCurrent expression: (-21*y**3)*(8*y**3 + 35) + (8*y**3)*(-8) - 280\nSimplifying the partial expression: (-21*y**3)*(8*y**3 + 35)\nExpanding the part (8*y**3 + 35) using the distributive property, and we got: 35*(-21*y**3) + (-21*y**3)*(8*y**3)\nReplacing (-21*y**3)*(8*y**3 + 35) with 35*(-21*y**3) + (-21*y**3)*(8*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 35*(-21)*y**3 + (-21*y**3)*(8*y**3) + (8*y**3)*(-8) - 280\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (8*y**3)*-8 = -64*y**3\n (8*y**3)*(-21*y**3) = -168*y**6\n 35*-21*y**3 = -735*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -168*y**6 - 735*y**3 - 64*y**3 - 280\nCombining like terms, got -168*y**6 - 799*y**3 - 280\n#Step 6:\nCurrent expression: -168*y**6 - 799*y**3 - 280\nNo more calculations needed.\n-168*y**6 - 799*y**3 - 280", "generated_answer": "-168*y**6 - 799*y**3 - 280", "step_length": 6} {"cot_id": "770ad19c1a76e44bd8b96a97d3c8f4b23a10c101d08c4007aff067451f246cfa", "datapoint": {"question": "Simplify this expression: (16 - 11*z)*(20*z**3 - 22)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-220*z**4 + 320*z**3 + 242*z - 352", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1799, "polynomial_expr": "(16 - 11*z)*(20*z**3 - 22)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (16 - 11*z)*(20*z**3 - 22)\nExpanding the part (20*z**3 - 22) using the distributive property, and we got: (20*z**3)*(16 - 11*z) - 22*(16 - 11*z)\n#Step 2:\nCurrent expression: (20*z**3)*(16 - 11*z) - 22*(16 - 11*z)\nSimplifying the partial expression: -22*(16 - 11*z)\nExpanding the part (16 - 11*z) using the distributive property, and we got: -11*z*(-22) + 16*(-22)\nReplacing -22*(16 - 11*z) with -11*z*(-22) + 16*(-22) in the overall expression.\n#Step 3:\nCurrent expression: -11*z*(-22) + (20*z**3)*(16 - 11*z) - 352\nSimplifying the partial expression: (20*z**3)*(16 - 11*z)\nExpanding the part (16 - 11*z) using the distributive property, and we got: (-11*z)*(20*z**3) + 16*(20*z**3)\nReplacing (20*z**3)*(16 - 11*z) with (-11*z)*(20*z**3) + 16*(20*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-11*z)*(20*z**3) - 11*z*(-22) + 16*20*z**3 - 352\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*z)*-22 = 242*z\n (-11*z)*(20*z**3) = -220*z**4\n 16*20*z**3 = 320*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -220*z**4 + 320*z**3 + 242*z - 352\nNo more calculations needed.\n-220*z**4 + 320*z**3 + 242*z - 352", "generated_answer": "-220*z**4 + 320*z**3 + 242*z - 352", "step_length": 5} {"cot_id": "d005bb53986cd5281e088cc912cdd2d612922024ad27bd49b1436d9398b0bab6", "datapoint": {"question": "Calculate the following: (16*x**2 + 47)*(-9*x**3 + 12*x**2 - 18)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-144*x**5 + 192*x**4 - 423*x**3 + 276*x**2 - 846", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1800, "polynomial_expr": "(16*x**2 + 47)*(-9*x**3 + 12*x**2 - 18)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (16*x**2 + 47)*(-9*x**3 + 12*x**2 - 18)\nExpanding the part (16*x**2 + 47) using the distributive property, and we got: (16*x**2)*(-9*x**3 + 12*x**2 - 18) + 47*(-9*x**3 + 12*x**2 - 18)\n#Step 2:\nCurrent expression: (16*x**2)*(-9*x**3 + 12*x**2 - 18) + 47*(-9*x**3 + 12*x**2 - 18)\nSimplifying the partial expression: 47*(-9*x**3 + 12*x**2 - 18)\nExpanding the part (-9*x**3 + 12*x**2 - 18) using the distributive property, and we got: (12*x**2)*47 - 9*x**3*47 - 18*47\nReplacing 47*(-9*x**3 + 12*x**2 - 18) with (12*x**2)*47 - 9*x**3*47 - 18*47 in the overall expression.\n#Step 3:\nCurrent expression: (12*x**2)*47 + (16*x**2)*(-9*x**3 + 12*x**2 - 18) - 9*x**3*47 - 846\nSimplifying the partial expression: (16*x**2)*(-9*x**3 + 12*x**2 - 18)\nExpanding the part (-9*x**3 + 12*x**2 - 18) using the distributive property, and we got: -288*x**2 + (12*x**2)*(16*x**2) + (16*x**2)*(-9*x**3)\nReplacing (16*x**2)*(-9*x**3 + 12*x**2 - 18) with -288*x**2 + (12*x**2)*(16*x**2) + (16*x**2)*(-9*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -18*16*x**2 + (12*x**2)*(16*x**2) + (12*x**2)*47 + (16*x**2)*(-9*x**3) - 9*x**3*47 - 846\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-9*x**3)*47 = -423*x**3\n (-9*x**3)*(16*x**2) = -144*x**5\n (12*x**2)*47 = 564*x**2\n (12*x**2)*(16*x**2) = 192*x**4\n -18*16*x**2 = -288*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -144*x**5 + 192*x**4 - 423*x**3 - 288*x**2 + 564*x**2 - 846\nCombining like terms, got -144*x**5 + 192*x**4 - 423*x**3 + 276*x**2 - 846\n#Step 6:\nCurrent expression: -144*x**5 + 192*x**4 - 423*x**3 + 276*x**2 - 846\nNo more calculations needed.\n-144*x**5 + 192*x**4 - 423*x**3 + 276*x**2 - 846", "generated_answer": "-144*x**5 + 192*x**4 - 423*x**3 + 276*x**2 - 846", "step_length": 6} {"cot_id": "961846d1417207e1e69b10d6a8c29a41376c61df86966628f4fedcd4882f2eb6", "datapoint": {"question": "Simplify this expression: (-38*y**3 + 40*y)*(-19*y**3 + 10*y - 29)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "722*y**6 - 1140*y**4 + 1102*y**3 + 400*y**2 - 1160*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1801, "polynomial_expr": "(-38*y**3 + 40*y)*(-19*y**3 + 10*y - 29)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-38*y**3 + 40*y)*(-19*y**3 + 10*y - 29)\nExpanding the part (-38*y**3 + 40*y) using the distributive property, and we got: (40*y)*(-19*y**3 + 10*y - 29) + (-38*y**3)*(-19*y**3 + 10*y - 29)\n#Step 2:\nCurrent expression: (40*y)*(-19*y**3 + 10*y - 29) + (-38*y**3)*(-19*y**3 + 10*y - 29)\nSimplifying the partial expression: (-38*y**3)*(-19*y**3 + 10*y - 29)\nExpanding the part (-19*y**3 + 10*y - 29) using the distributive property, and we got: -(-1)*1102*y**3 + (10*y)*(-38*y**3) + (-38*y**3)*(-19*y**3)\nReplacing (-38*y**3)*(-19*y**3 + 10*y - 29) with -(-1)*1102*y**3 + (10*y)*(-38*y**3) + (-38*y**3)*(-19*y**3) in the overall expression.\n#Step 3:\nCurrent expression: -29*(-38)*y**3 + (10*y)*(-38*y**3) + (40*y)*(-19*y**3 + 10*y - 29) + (-38*y**3)*(-19*y**3)\nSimplifying the partial expression: (40*y)*(-19*y**3 + 10*y - 29)\nExpanding the part (-19*y**3 + 10*y - 29) using the distributive property, and we got: -1160*y + (10*y)*(40*y) + (40*y)*(-19*y**3)\nReplacing (40*y)*(-19*y**3 + 10*y - 29) with -1160*y + (10*y)*(40*y) + (40*y)*(-19*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -29*(-38)*y**3 - 29*40*y + (10*y)*(40*y) + (10*y)*(-38*y**3) + (40*y)*(-19*y**3) + (-38*y**3)*(-19*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*y**3)*(-38*y**3) = 722*y**6\n (-19*y**3)*(40*y) = -760*y**4\n (10*y)*(-38*y**3) = -380*y**4\n (10*y)*(40*y) = 400*y**2\n -29*-38*y**3 = 1102*y**3\n -29*40*y = -1160*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 722*y**6 - 760*y**4 - 380*y**4 + 1102*y**3 + 400*y**2 - 1160*y\nCombining like terms, got 722*y**6 - 1140*y**4 + 1102*y**3 + 400*y**2 - 1160*y\n#Step 6:\nCurrent expression: 722*y**6 - 1140*y**4 + 1102*y**3 + 400*y**2 - 1160*y\nNo more calculations needed.\n722*y**6 - 1140*y**4 + 1102*y**3 + 400*y**2 - 1160*y", "generated_answer": "722*y**6 - 1140*y**4 + 1102*y**3 + 400*y**2 - 1160*y", "step_length": 6} {"cot_id": "f034b82f9283ab6db2341c127c379d621cc4688690dc6e6194ff076bb1978b9e", "datapoint": {"question": "Simplify this expression: (-2*z**3 + 23*z**2 + 7)*(47*z**3 - 44*z**2 - 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-94*z**6 + 1169*z**5 - 1012*z**4 + 389*z**3 - 998*z**2 - 210", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1802, "polynomial_expr": "(-2*z**3 + 23*z**2 + 7)*(47*z**3 - 44*z**2 - 30)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-2*z**3 + 23*z**2 + 7)*(47*z**3 - 44*z**2 - 30)\nExpanding the part (47*z**3 - 44*z**2 - 30) using the distributive property, and we got: (-44*z**2)*(-2*z**3 + 23*z**2 + 7) + (47*z**3)*(-2*z**3 + 23*z**2 + 7) - 30*(-2*z**3 + 23*z**2 + 7)\n#Step 2:\nCurrent expression: (-44*z**2)*(-2*z**3 + 23*z**2 + 7) + (47*z**3)*(-2*z**3 + 23*z**2 + 7) - 30*(-2*z**3 + 23*z**2 + 7)\nSimplifying the partial expression: -30*(-2*z**3 + 23*z**2 + 7)\nExpanding the part (-2*z**3 + 23*z**2 + 7) using the distributive property, and we got: (23*z**2)*(-30) - 2*z**3*(-30) + 7*(-30)\nReplacing -30*(-2*z**3 + 23*z**2 + 7) with (23*z**2)*(-30) - 2*z**3*(-30) + 7*(-30) in the overall expression.\n#Step 3:\nCurrent expression: (-44*z**2)*(-2*z**3 + 23*z**2 + 7) + (23*z**2)*(-30) - 2*z**3*(-30) + (47*z**3)*(-2*z**3 + 23*z**2 + 7) - 210\nSimplifying the partial expression: (-44*z**2)*(-2*z**3 + 23*z**2 + 7)\nExpanding the part (-2*z**3 + 23*z**2 + 7) using the distributive property, and we got: 7*(-44*z**2) + (-44*z**2)*(23*z**2) + (-44*z**2)*(-2*z**3)\nReplacing (-44*z**2)*(-2*z**3 + 23*z**2 + 7) with 7*(-44*z**2) + (-44*z**2)*(23*z**2) + (-44*z**2)*(-2*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 7*(-44)*z**2 + (-44*z**2)*(23*z**2) + (-44*z**2)*(-2*z**3) + (23*z**2)*(-30) - 2*z**3*(-30) + (47*z**3)*(-2*z**3 + 23*z**2 + 7) - 210\nSimplifying the partial expression: (47*z**3)*(-2*z**3 + 23*z**2 + 7)\nExpanding the part (-2*z**3 + 23*z**2 + 7) using the distributive property, and we got: 7*(47*z**3) + (23*z**2)*(47*z**3) + (-2*z**3)*(47*z**3)\nReplacing (47*z**3)*(-2*z**3 + 23*z**2 + 7) with 7*(47*z**3) + (23*z**2)*(47*z**3) + (-2*z**3)*(47*z**3) in the overall expression.\n#Step 5:\nCurrent expression: 7*47*z**3 + 7*(-44)*z**2 + (-44*z**2)*(23*z**2) + (-44*z**2)*(-2*z**3) + (23*z**2)*(47*z**3) + (23*z**2)*(-30) + (-2*z**3)*(47*z**3) - 2*z**3*(-30) - 210\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-2*z**3)*-30 = 60*z**3\n (-2*z**3)*(-44*z**2) = 88*z**5\n (-2*z**3)*(47*z**3) = -94*z**6\n (23*z**2)*-30 = -690*z**2\n (23*z**2)*(-44*z**2) = -1012*z**4\n (23*z**2)*(47*z**3) = 1081*z**5\n 7*-44*z**2 = -308*z**2\n 7*47*z**3 = 329*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -94*z**6 + 88*z**5 + 1081*z**5 - 1012*z**4 + 60*z**3 + 329*z**3 - 690*z**2 - 308*z**2 - 210\nCombining like terms, got -94*z**6 + 1169*z**5 - 1012*z**4 + 389*z**3 - 998*z**2 - 210\n#Step 7:\nCurrent expression: -94*z**6 + 1169*z**5 - 1012*z**4 + 389*z**3 - 998*z**2 - 210\nNo more calculations needed.\n-94*z**6 + 1169*z**5 - 1012*z**4 + 389*z**3 - 998*z**2 - 210", "generated_answer": "-94*z**6 + 1169*z**5 - 1012*z**4 + 389*z**3 - 998*z**2 - 210", "step_length": 7} {"cot_id": "d542ef37100480e62d008a6fe019df19bb52e586deb4d59641473b566532be6e", "datapoint": {"question": "Calculate the following: (20*x**3 + 102*x)*(4*x**2 + 22*x - 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "80*x**5 + 440*x**4 + 148*x**3 + 2244*x**2 - 1326*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1803, "polynomial_expr": "(20*x**3 + 102*x)*(4*x**2 + 22*x - 13)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (20*x**3 + 102*x)*(4*x**2 + 22*x - 13)\nExpanding the part (20*x**3 + 102*x) using the distributive property, and we got: (102*x)*(4*x**2 + 22*x - 13) + (20*x**3)*(4*x**2 + 22*x - 13)\n#Step 2:\nCurrent expression: (102*x)*(4*x**2 + 22*x - 13) + (20*x**3)*(4*x**2 + 22*x - 13)\nSimplifying the partial expression: (20*x**3)*(4*x**2 + 22*x - 13)\nExpanding the part (4*x**2 + 22*x - 13) using the distributive property, and we got: -260*x**3 + (22*x)*(20*x**3) + (4*x**2)*(20*x**3)\nReplacing (20*x**3)*(4*x**2 + 22*x - 13) with -260*x**3 + (22*x)*(20*x**3) + (4*x**2)*(20*x**3) in the overall expression.\n#Step 3:\nCurrent expression: -13*20*x**3 + (22*x)*(20*x**3) + (102*x)*(4*x**2 + 22*x - 13) + (4*x**2)*(20*x**3)\nSimplifying the partial expression: (102*x)*(4*x**2 + 22*x - 13)\nExpanding the part (4*x**2 + 22*x - 13) using the distributive property, and we got: -1326*x + (22*x)*(102*x) + (102*x)*(4*x**2)\nReplacing (102*x)*(4*x**2 + 22*x - 13) with -1326*x + (22*x)*(102*x) + (102*x)*(4*x**2) in the overall expression.\n#Step 4:\nCurrent expression: -13*20*x**3 - 13*102*x + (22*x)*(102*x) + (22*x)*(20*x**3) + (102*x)*(4*x**2) + (4*x**2)*(20*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (4*x**2)*(20*x**3) = 80*x**5\n (4*x**2)*(102*x) = 408*x**3\n (22*x)*(20*x**3) = 440*x**4\n (22*x)*(102*x) = 2244*x**2\n -13*20*x**3 = -260*x**3\n -13*102*x = -1326*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 80*x**5 + 440*x**4 - 260*x**3 + 408*x**3 + 2244*x**2 - 1326*x\nCombining like terms, got 80*x**5 + 440*x**4 + 148*x**3 + 2244*x**2 - 1326*x\n#Step 6:\nCurrent expression: 80*x**5 + 440*x**4 + 148*x**3 + 2244*x**2 - 1326*x\nNo more calculations needed.\n80*x**5 + 440*x**4 + 148*x**3 + 2244*x**2 - 1326*x", "generated_answer": "80*x**5 + 440*x**4 + 148*x**3 + 2244*x**2 - 1326*x", "step_length": 6} {"cot_id": "990839763368411b518e67df9f629c4cfdfd2c1335272584f460840f011db1a8", "datapoint": {"question": "Calculate the following: 47*y*(27*y**3 - 34*y - 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1269*y**4 - 1598*y**2 - 799*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1804, "polynomial_expr": "47*y*(27*y**3 - 34*y - 17)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 47*y*(27*y**3 - 34*y - 17)\nExpanding the part (27*y**3 - 34*y - 17) using the distributive property, and we got: (-34*y)*(47*y) - 799*y + (47*y)*(27*y**3)\n#Step 2:\nCurrent expression: (-34*y)*(47*y) - 799*y + (47*y)*(27*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -17*(47*y) = -799*y\n (-34*y)*(47*y) = -1598*y**2\n (27*y**3)*(47*y) = 1269*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1269*y**4 - 1598*y**2 - 799*y\nNo more calculations needed.\n1269*y**4 - 1598*y**2 - 799*y", "generated_answer": "1269*y**4 - 1598*y**2 - 799*y", "step_length": 3} {"cot_id": "ea966368bde542658b55f34bb4c4e6ed29a3c6263ad5ec7802036df8239847e1", "datapoint": {"question": "Simplify this expression: (40*x**3 - 16)*(-16*x**3 - 39*x**2 + 6*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-640*x**6 - 1560*x**5 + 240*x**4 + 256*x**3 + 624*x**2 - 96*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1805, "polynomial_expr": "(40*x**3 - 16)*(-16*x**3 - 39*x**2 + 6*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (40*x**3 - 16)*(-16*x**3 - 39*x**2 + 6*x)\nExpanding the part (40*x**3 - 16) using the distributive property, and we got: (40*x**3)*(-16*x**3 - 39*x**2 + 6*x) - 16*(-16*x**3 - 39*x**2 + 6*x)\n#Step 2:\nCurrent expression: (40*x**3)*(-16*x**3 - 39*x**2 + 6*x) - 16*(-16*x**3 - 39*x**2 + 6*x)\nSimplifying the partial expression: -16*(-16*x**3 - 39*x**2 + 6*x)\nExpanding the part (-16*x**3 - 39*x**2 + 6*x) using the distributive property, and we got: (6*x)*(-16) - 39*x**2*(-16) - 16*x**3*(-16)\nReplacing -16*(-16*x**3 - 39*x**2 + 6*x) with (6*x)*(-16) - 39*x**2*(-16) - 16*x**3*(-16) in the overall expression.\n#Step 3:\nCurrent expression: (6*x)*(-16) - 39*x**2*(-16) - 16*x**3*(-16) + (40*x**3)*(-16*x**3 - 39*x**2 + 6*x)\nSimplifying the partial expression: (40*x**3)*(-16*x**3 - 39*x**2 + 6*x)\nExpanding the part (-16*x**3 - 39*x**2 + 6*x) using the distributive property, and we got: (6*x)*(40*x**3) + (-39*x**2)*(40*x**3) + (-16*x**3)*(40*x**3)\nReplacing (40*x**3)*(-16*x**3 - 39*x**2 + 6*x) with (6*x)*(40*x**3) + (-39*x**2)*(40*x**3) + (-16*x**3)*(40*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (6*x)*(40*x**3) + (6*x)*(-16) + (-39*x**2)*(40*x**3) - 39*x**2*(-16) + (-16*x**3)*(40*x**3) - 16*x**3*(-16)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*x**2)*-16 = 624*x**2\n (-39*x**2)*(40*x**3) = -1560*x**5\n (-16*x**3)*-16 = 256*x**3\n (-16*x**3)*(40*x**3) = -640*x**6\n (6*x)*-16 = -96*x\n (6*x)*(40*x**3) = 240*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -640*x**6 - 1560*x**5 + 240*x**4 + 256*x**3 + 624*x**2 - 96*x\nNo more calculations needed.\n-640*x**6 - 1560*x**5 + 240*x**4 + 256*x**3 + 624*x**2 - 96*x", "generated_answer": "-640*x**6 - 1560*x**5 + 240*x**4 + 256*x**3 + 624*x**2 - 96*x", "step_length": 5} {"cot_id": "87463367bcd804c8b550b2f830ebb2cec51b5837db98e3b752314f7f3b389131", "datapoint": {"question": "Simplify this expression: (-25*y**2 - y)*(11*y**2 - 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-275*y**4 - 11*y**3 + 25*y**2 + y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1806, "polynomial_expr": "(-25*y**2 - y)*(11*y**2 - 1)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-25*y**2 - y)*(11*y**2 - 1)\nExpanding the part (11*y**2 - 1) using the distributive property, and we got: (11*y**2)*(-25*y**2 - y) - (-25*y**2 - y)\n#Step 2:\nCurrent expression: (11*y**2)*(-25*y**2 - y) - (-25*y**2 - y)\nSimplifying the partial expression: -(-25*y**2 - y)\nExpanding the part (-25*y**2 - y) using the distributive property, and we got: -y*(-1) - 25*y**2*(-1)\nReplacing -(-25*y**2 - y) with -y*(-1) - 25*y**2*(-1) in the overall expression.\n#Step 3:\nCurrent expression: -y*(-1) - 25*y**2*(-1) + (11*y**2)*(-25*y**2 - y)\nSimplifying the partial expression: (11*y**2)*(-25*y**2 - y)\nExpanding the part (-25*y**2 - y) using the distributive property, and we got: (-y)*(11*y**2) + (-25*y**2)*(11*y**2)\nReplacing (11*y**2)*(-25*y**2 - y) with (-y)*(11*y**2) + (-25*y**2)*(11*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-y)*(11*y**2) - y*(-1) + (-25*y**2)*(11*y**2) - 25*y**2*(-1)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-y)*-1 = y\n (-y)*(11*y**2) = -11*y**3\n (-25*y**2)*-1 = 25*y**2\n (-25*y**2)*(11*y**2) = -275*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -275*y**4 - 11*y**3 + 25*y**2 + y\nNo more calculations needed.\n-275*y**4 - 11*y**3 + 25*y**2 + y", "generated_answer": "-275*y**4 - 11*y**3 + 25*y**2 + y", "step_length": 5} {"cot_id": "5e3e08ced9b1505776542ee514bbc22fbe775ef7140eb9255dfb98e7aa872bff", "datapoint": {"question": "Simplify this expression: 4826*y**5\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "4826*y**5", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1807, "polynomial_expr": "4826*y**5", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 4826*y**5\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 4826*y**5\nNo more calculations needed.\n4826*y**5", "generated_answer": "4826*y**5", "step_length": 2} {"cot_id": "9cb5d35aed09209b3d8e980f330c5fde5fccb253fafa84a8612bcb6fccdeebae", "datapoint": {"question": "Simplify this expression: (-41*z**3 - 2*z)*(-40*z**3 + 34*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1640*z**6 - 1314*z**4 - 68*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1808, "polynomial_expr": "(-41*z**3 - 2*z)*(-40*z**3 + 34*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-41*z**3 - 2*z)*(-40*z**3 + 34*z)\nExpanding the part (-41*z**3 - 2*z) using the distributive property, and we got: (-2*z)*(-40*z**3 + 34*z) + (-41*z**3)*(-40*z**3 + 34*z)\n#Step 2:\nCurrent expression: (-2*z)*(-40*z**3 + 34*z) + (-41*z**3)*(-40*z**3 + 34*z)\nSimplifying the partial expression: (-41*z**3)*(-40*z**3 + 34*z)\nExpanding the part (-40*z**3 + 34*z) using the distributive property, and we got: (34*z)*(-41*z**3) + (-41*z**3)*(-40*z**3)\nReplacing (-41*z**3)*(-40*z**3 + 34*z) with (34*z)*(-41*z**3) + (-41*z**3)*(-40*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-2*z)*(-40*z**3 + 34*z) + (34*z)*(-41*z**3) + (-41*z**3)*(-40*z**3)\nSimplifying the partial expression: (-2*z)*(-40*z**3 + 34*z)\nExpanding the part (-40*z**3 + 34*z) using the distributive property, and we got: (-2*z)*(34*z) + (-2*z)*(-40*z**3)\nReplacing (-2*z)*(-40*z**3 + 34*z) with (-2*z)*(34*z) + (-2*z)*(-40*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-2*z)*(34*z) + (-2*z)*(-40*z**3) + (34*z)*(-41*z**3) + (-41*z**3)*(-40*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*z**3)*(-41*z**3) = 1640*z**6\n (-40*z**3)*(-2*z) = 80*z**4\n (34*z)*(-41*z**3) = -1394*z**4\n (34*z)*(-2*z) = -68*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1640*z**6 - 1394*z**4 + 80*z**4 - 68*z**2\nCombining like terms, got 1640*z**6 - 1314*z**4 - 68*z**2\n#Step 6:\nCurrent expression: 1640*z**6 - 1314*z**4 - 68*z**2\nNo more calculations needed.\n1640*z**6 - 1314*z**4 - 68*z**2", "generated_answer": "1640*z**6 - 1314*z**4 - 68*z**2", "step_length": 6} {"cot_id": "57bbd0a3372ab0d408a55754c33d2e3df3675fd09167aa64bc6af7b1106b1018", "datapoint": {"question": "Simplify this expression: 23*y**2*(-31*y**3 - 55*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-713*y**5 - 1265*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1809, "polynomial_expr": "23*y**2*(-31*y**3 - 55*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 23*y**2*(-31*y**3 - 55*y)\nExpanding the part (-31*y**3 - 55*y) using the distributive property, and we got: (-55*y)*(23*y**2) + (23*y**2)*(-31*y**3)\n#Step 2:\nCurrent expression: (-55*y)*(23*y**2) + (23*y**2)*(-31*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-55*y)*(23*y**2) = -1265*y**3\n (-31*y**3)*(23*y**2) = -713*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -713*y**5 - 1265*y**3\nNo more calculations needed.\n-713*y**5 - 1265*y**3", "generated_answer": "-713*y**5 - 1265*y**3", "step_length": 3} {"cot_id": "8d0c84e4b61a8ed070e54e88ef355b57237f822a9a79e424fc5e61107c94250a", "datapoint": {"question": "Calculate the following: 14*x**2*(-41*x**2 - 46*x + 37)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-574*x**4 - 644*x**3 + 518*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1810, "polynomial_expr": "14*x**2*(-41*x**2 - 46*x + 37)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 14*x**2*(-41*x**2 - 46*x + 37)\nExpanding the part (-41*x**2 - 46*x + 37) using the distributive property, and we got: (-46*x)*(14*x**2) + 37*(14*x**2) + (-41*x**2)*(14*x**2)\n#Step 2:\nCurrent expression: (-46*x)*(14*x**2) + 37*(14*x**2) + (-41*x**2)*(14*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 37*(14*x**2) = 518*x**2\n (-46*x)*(14*x**2) = -644*x**3\n (-41*x**2)*(14*x**2) = -574*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -574*x**4 - 644*x**3 + 518*x**2\nNo more calculations needed.\n-574*x**4 - 644*x**3 + 518*x**2", "generated_answer": "-574*x**4 - 644*x**3 + 518*x**2", "step_length": 3} {"cot_id": "fff853727af7efbaa0334222740ac09e6727d2d14c3a68fc1173af2c8e77f56c", "datapoint": {"question": "Simplify this expression: (-5*x - 40)*(19*x**3 + 42*x**2 + 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-95*x**4 - 970*x**3 - 1680*x**2 - 220*x - 1760", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1811, "polynomial_expr": "(-5*x - 40)*(19*x**3 + 42*x**2 + 44)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-5*x - 40)*(19*x**3 + 42*x**2 + 44)\nExpanding the part (-5*x - 40) using the distributive property, and we got: (-5*x)*(19*x**3 + 42*x**2 + 44) - 40*(19*x**3 + 42*x**2 + 44)\n#Step 2:\nCurrent expression: (-5*x)*(19*x**3 + 42*x**2 + 44) - 40*(19*x**3 + 42*x**2 + 44)\nSimplifying the partial expression: -40*(19*x**3 + 42*x**2 + 44)\nExpanding the part (19*x**3 + 42*x**2 + 44) using the distributive property, and we got: (42*x**2)*(-40) + (19*x**3)*(-40) + 44*(-40)\nReplacing -40*(19*x**3 + 42*x**2 + 44) with (42*x**2)*(-40) + (19*x**3)*(-40) + 44*(-40) in the overall expression.\n#Step 3:\nCurrent expression: (-5*x)*(19*x**3 + 42*x**2 + 44) + (42*x**2)*(-40) + (19*x**3)*(-40) - 1760\nSimplifying the partial expression: (-5*x)*(19*x**3 + 42*x**2 + 44)\nExpanding the part (19*x**3 + 42*x**2 + 44) using the distributive property, and we got: (-5*x)*(42*x**2) + (-5*x)*(19*x**3) + 44*(-5*x)\nReplacing (-5*x)*(19*x**3 + 42*x**2 + 44) with (-5*x)*(42*x**2) + (-5*x)*(19*x**3) + 44*(-5*x) in the overall expression.\n#Step 4:\nCurrent expression: (-5*x)*(42*x**2) + (-5*x)*(19*x**3) + 44*(-5)*x + (42*x**2)*(-40) + (19*x**3)*(-40) - 1760\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (19*x**3)*-40 = -760*x**3\n (19*x**3)*(-5*x) = -95*x**4\n (42*x**2)*-40 = -1680*x**2\n (42*x**2)*(-5*x) = -210*x**3\n 44*-5*x = -220*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -95*x**4 - 760*x**3 - 210*x**3 - 1680*x**2 - 220*x - 1760\nCombining like terms, got -95*x**4 - 970*x**3 - 1680*x**2 - 220*x - 1760\n#Step 6:\nCurrent expression: -95*x**4 - 970*x**3 - 1680*x**2 - 220*x - 1760\nNo more calculations needed.\n-95*x**4 - 970*x**3 - 1680*x**2 - 220*x - 1760", "generated_answer": "-95*x**4 - 970*x**3 - 1680*x**2 - 220*x - 1760", "step_length": 6} {"cot_id": "4818e5e3efb3f301a89005334c6500b49ac40d5a100920d6a81a88655e526dfd", "datapoint": {"question": "Calculate the following: (7 - 42*y**2)*(35*y - 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1470*y**3 + 546*y**2 + 245*y - 91", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1812, "polynomial_expr": "(7 - 42*y**2)*(35*y - 13)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7 - 42*y**2)*(35*y - 13)\nExpanding the part (35*y - 13) using the distributive property, and we got: (35*y)*(7 - 42*y**2) - 13*(7 - 42*y**2)\n#Step 2:\nCurrent expression: (35*y)*(7 - 42*y**2) - 13*(7 - 42*y**2)\nSimplifying the partial expression: -13*(7 - 42*y**2)\nExpanding the part (7 - 42*y**2) using the distributive property, and we got: -42*y**2*(-13) + 7*(-13)\nReplacing -13*(7 - 42*y**2) with -42*y**2*(-13) + 7*(-13) in the overall expression.\n#Step 3:\nCurrent expression: (35*y)*(7 - 42*y**2) - 42*y**2*(-13) - 91\nSimplifying the partial expression: (35*y)*(7 - 42*y**2)\nExpanding the part (7 - 42*y**2) using the distributive property, and we got: 7*(35*y) + (35*y)*(-42*y**2)\nReplacing (35*y)*(7 - 42*y**2) with 7*(35*y) + (35*y)*(-42*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 7*35*y + (35*y)*(-42*y**2) - 42*y**2*(-13) - 91\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*y**2)*-13 = 546*y**2\n (-42*y**2)*(35*y) = -1470*y**3\n 7*35*y = 245*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1470*y**3 + 546*y**2 + 245*y - 91\nNo more calculations needed.\n-1470*y**3 + 546*y**2 + 245*y - 91", "generated_answer": "-1470*y**3 + 546*y**2 + 245*y - 91", "step_length": 5} {"cot_id": "9501bc7005c372735e64d4c70e070fd3ce0b8a832d6dbc59856da1598e3c6f2f", "datapoint": {"question": "Simplify this expression: (-37*y**3 - 17*y**2)*(-43*y**3 - 84*y**2 - 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1591*y**6 + 3839*y**5 + 1428*y**4 + 1739*y**3 + 799*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1813, "polynomial_expr": "(-37*y**3 - 17*y**2)*(-43*y**3 - 84*y**2 - 47)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-37*y**3 - 17*y**2)*(-43*y**3 - 84*y**2 - 47)\nExpanding the part (-37*y**3 - 17*y**2) using the distributive property, and we got: (-17*y**2)*(-43*y**3 - 84*y**2 - 47) + (-37*y**3)*(-43*y**3 - 84*y**2 - 47)\n#Step 2:\nCurrent expression: (-17*y**2)*(-43*y**3 - 84*y**2 - 47) + (-37*y**3)*(-43*y**3 - 84*y**2 - 47)\nSimplifying the partial expression: (-37*y**3)*(-43*y**3 - 84*y**2 - 47)\nExpanding the part (-43*y**3 - 84*y**2 - 47) using the distributive property, and we got: -(-1)*1739*y**3 + (-84*y**2)*(-37*y**3) + (-43*y**3)*(-37*y**3)\nReplacing (-37*y**3)*(-43*y**3 - 84*y**2 - 47) with -(-1)*1739*y**3 + (-84*y**2)*(-37*y**3) + (-43*y**3)*(-37*y**3) in the overall expression.\n#Step 3:\nCurrent expression: -47*(-37)*y**3 + (-84*y**2)*(-37*y**3) + (-17*y**2)*(-43*y**3 - 84*y**2 - 47) + (-43*y**3)*(-37*y**3)\nSimplifying the partial expression: (-17*y**2)*(-43*y**3 - 84*y**2 - 47)\nExpanding the part (-43*y**3 - 84*y**2 - 47) using the distributive property, and we got: -(-1)*799*y**2 + (-84*y**2)*(-17*y**2) + (-17*y**2)*(-43*y**3)\nReplacing (-17*y**2)*(-43*y**3 - 84*y**2 - 47) with -(-1)*799*y**2 + (-84*y**2)*(-17*y**2) + (-17*y**2)*(-43*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -47*(-37)*y**3 - 47*(-17)*y**2 + (-84*y**2)*(-17*y**2) + (-84*y**2)*(-37*y**3) + (-17*y**2)*(-43*y**3) + (-43*y**3)*(-37*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-84*y**2)*(-37*y**3) = 3108*y**5\n (-84*y**2)*(-17*y**2) = 1428*y**4\n (-43*y**3)*(-37*y**3) = 1591*y**6\n (-43*y**3)*(-17*y**2) = 731*y**5\n -47*-37*y**3 = 1739*y**3\n -47*-17*y**2 = 799*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1591*y**6 + 731*y**5 + 3108*y**5 + 1428*y**4 + 1739*y**3 + 799*y**2\nCombining like terms, got 1591*y**6 + 3839*y**5 + 1428*y**4 + 1739*y**3 + 799*y**2\n#Step 6:\nCurrent expression: 1591*y**6 + 3839*y**5 + 1428*y**4 + 1739*y**3 + 799*y**2\nNo more calculations needed.\n1591*y**6 + 3839*y**5 + 1428*y**4 + 1739*y**3 + 799*y**2", "generated_answer": "1591*y**6 + 3839*y**5 + 1428*y**4 + 1739*y**3 + 799*y**2", "step_length": 6} {"cot_id": "5ca2197a2aec8d4738b7bf1f4d9e854599b55744c856f5fdbd9605eaaccb4d23", "datapoint": {"question": "Simplify this expression: (27*z**2 - 14)*(38*z**3 - 9*z**2 + 35*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1026*z**5 - 243*z**4 + 413*z**3 + 126*z**2 - 490*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1814, "polynomial_expr": "(27*z**2 - 14)*(38*z**3 - 9*z**2 + 35*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*z**2 - 14)*(38*z**3 - 9*z**2 + 35*z)\nExpanding the part (27*z**2 - 14) using the distributive property, and we got: (27*z**2)*(38*z**3 - 9*z**2 + 35*z) - 14*(38*z**3 - 9*z**2 + 35*z)\n#Step 2:\nCurrent expression: (27*z**2)*(38*z**3 - 9*z**2 + 35*z) - 14*(38*z**3 - 9*z**2 + 35*z)\nSimplifying the partial expression: -14*(38*z**3 - 9*z**2 + 35*z)\nExpanding the part (38*z**3 - 9*z**2 + 35*z) using the distributive property, and we got: (35*z)*(-14) - 9*z**2*(-14) + (38*z**3)*(-14)\nReplacing -14*(38*z**3 - 9*z**2 + 35*z) with (35*z)*(-14) - 9*z**2*(-14) + (38*z**3)*(-14) in the overall expression.\n#Step 3:\nCurrent expression: (35*z)*(-14) - 9*z**2*(-14) + (27*z**2)*(38*z**3 - 9*z**2 + 35*z) + (38*z**3)*(-14)\nSimplifying the partial expression: (27*z**2)*(38*z**3 - 9*z**2 + 35*z)\nExpanding the part (38*z**3 - 9*z**2 + 35*z) using the distributive property, and we got: (35*z)*(27*z**2) + (-9*z**2)*(27*z**2) + (27*z**2)*(38*z**3)\nReplacing (27*z**2)*(38*z**3 - 9*z**2 + 35*z) with (35*z)*(27*z**2) + (-9*z**2)*(27*z**2) + (27*z**2)*(38*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (35*z)*(27*z**2) + (35*z)*(-14) + (-9*z**2)*(27*z**2) - 9*z**2*(-14) + (27*z**2)*(38*z**3) + (38*z**3)*(-14)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-9*z**2)*-14 = 126*z**2\n (-9*z**2)*(27*z**2) = -243*z**4\n (35*z)*-14 = -490*z\n (35*z)*(27*z**2) = 945*z**3\n (38*z**3)*-14 = -532*z**3\n (38*z**3)*(27*z**2) = 1026*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1026*z**5 - 243*z**4 - 532*z**3 + 945*z**3 + 126*z**2 - 490*z\nCombining like terms, got 1026*z**5 - 243*z**4 + 413*z**3 + 126*z**2 - 490*z\n#Step 6:\nCurrent expression: 1026*z**5 - 243*z**4 + 413*z**3 + 126*z**2 - 490*z\nNo more calculations needed.\n1026*z**5 - 243*z**4 + 413*z**3 + 126*z**2 - 490*z", "generated_answer": "1026*z**5 - 243*z**4 + 413*z**3 + 126*z**2 - 490*z", "step_length": 6} {"cot_id": "44eed2910c69a4dc735f05be8396e2e9a85334c3b2191f9ca22297cf5ab12922", "datapoint": {"question": "Calculate the following: (12 - 43*x**2)*(-10*x**3 - 22*x**2 - 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "430*x**5 + 946*x**4 - 120*x**3 + 1413*x**2 - 468", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1815, "polynomial_expr": "(12 - 43*x**2)*(-10*x**3 - 22*x**2 - 39)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (12 - 43*x**2)*(-10*x**3 - 22*x**2 - 39)\nExpanding the part (12 - 43*x**2) using the distributive property, and we got: (-43*x**2)*(-10*x**3 - 22*x**2 - 39) + 12*(-10*x**3 - 22*x**2 - 39)\n#Step 2:\nCurrent expression: (-43*x**2)*(-10*x**3 - 22*x**2 - 39) + 12*(-10*x**3 - 22*x**2 - 39)\nSimplifying the partial expression: 12*(-10*x**3 - 22*x**2 - 39)\nExpanding the part (-10*x**3 - 22*x**2 - 39) using the distributive property, and we got: -22*x**2*12 - 10*x**3*12 - 39*12\nReplacing 12*(-10*x**3 - 22*x**2 - 39) with -22*x**2*12 - 10*x**3*12 - 39*12 in the overall expression.\n#Step 3:\nCurrent expression: (-43*x**2)*(-10*x**3 - 22*x**2 - 39) - 22*x**2*12 - 10*x**3*12 - 468\nSimplifying the partial expression: (-43*x**2)*(-10*x**3 - 22*x**2 - 39)\nExpanding the part (-10*x**3 - 22*x**2 - 39) using the distributive property, and we got: -(-1)*1677*x**2 + (-43*x**2)*(-22*x**2) + (-43*x**2)*(-10*x**3)\nReplacing (-43*x**2)*(-10*x**3 - 22*x**2 - 39) with -(-1)*1677*x**2 + (-43*x**2)*(-22*x**2) + (-43*x**2)*(-10*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -39*(-43)*x**2 + (-43*x**2)*(-22*x**2) + (-43*x**2)*(-10*x**3) - 22*x**2*12 - 10*x**3*12 - 468\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*x**2)*12 = -264*x**2\n (-22*x**2)*(-43*x**2) = 946*x**4\n (-10*x**3)*12 = -120*x**3\n (-10*x**3)*(-43*x**2) = 430*x**5\n -39*-43*x**2 = 1677*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 430*x**5 + 946*x**4 - 120*x**3 - 264*x**2 + 1677*x**2 - 468\nCombining like terms, got 430*x**5 + 946*x**4 - 120*x**3 + 1413*x**2 - 468\n#Step 6:\nCurrent expression: 430*x**5 + 946*x**4 - 120*x**3 + 1413*x**2 - 468\nNo more calculations needed.\n430*x**5 + 946*x**4 - 120*x**3 + 1413*x**2 - 468", "generated_answer": "430*x**5 + 946*x**4 - 120*x**3 + 1413*x**2 - 468", "step_length": 6} {"cot_id": "f91ac0ac98df993836e5b6548d13810e17a0a6ee4af0ef39594906f320dab8ae", "datapoint": {"question": "Calculate the following: (-17*z**2 - 40)*(-17*z**2 + z + 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "289*z**4 - 17*z**3 + 578*z**2 - 40*z - 240", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1816, "polynomial_expr": "(-17*z**2 - 40)*(-17*z**2 + z + 6)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-17*z**2 - 40)*(-17*z**2 + z + 6)\nExpanding the part (-17*z**2 - 40) using the distributive property, and we got: (-17*z**2)*(-17*z**2 + z + 6) - 40*(-17*z**2 + z + 6)\n#Step 2:\nCurrent expression: (-17*z**2)*(-17*z**2 + z + 6) - 40*(-17*z**2 + z + 6)\nSimplifying the partial expression: -40*(-17*z**2 + z + 6)\nExpanding the part (-17*z**2 + z + 6) using the distributive property, and we got: z*(-40) - 17*z**2*(-40) + 6*(-40)\nReplacing -40*(-17*z**2 + z + 6) with z*(-40) - 17*z**2*(-40) + 6*(-40) in the overall expression.\n#Step 3:\nCurrent expression: z*(-40) + (-17*z**2)*(-17*z**2 + z + 6) - 17*z**2*(-40) - 240\nSimplifying the partial expression: (-17*z**2)*(-17*z**2 + z + 6)\nExpanding the part (-17*z**2 + z + 6) using the distributive property, and we got: 6*(-17*z**2) + z*(-17*z**2) + (-17*z**2)*(-17*z**2)\nReplacing (-17*z**2)*(-17*z**2 + z + 6) with 6*(-17*z**2) + z*(-17*z**2) + (-17*z**2)*(-17*z**2) in the overall expression.\n#Step 4:\nCurrent expression: 6*(-17)*z**2 + z*(-17*z**2) + z*(-40) - 17*z**2*(-40) + (-17*z**2)*(-17*z**2) - 240\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n z*-40 = -40*z\n z*(-17*z**2) = -17*z**3\n (-17*z**2)*-40 = 680*z**2\n (-17*z**2)*(-17*z**2) = 289*z**4\n 6*-17*z**2 = -102*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 289*z**4 - 17*z**3 - 102*z**2 + 680*z**2 - 40*z - 240\nCombining like terms, got 289*z**4 - 17*z**3 + 578*z**2 - 40*z - 240\n#Step 6:\nCurrent expression: 289*z**4 - 17*z**3 + 578*z**2 - 40*z - 240\nNo more calculations needed.\n289*z**4 - 17*z**3 + 578*z**2 - 40*z - 240", "generated_answer": "289*z**4 - 17*z**3 + 578*z**2 - 40*z - 240", "step_length": 6} {"cot_id": "ea4bb0afe4e60b4bf3f9eecb073017d150c7f2989dd871c1396a3c14c73edd17", "datapoint": {"question": "Calculate the following: (47 - 92*z**2)*(49*z**3 - 17*z + 15)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-4508*z**5 + 3867*z**3 - 1380*z**2 - 799*z + 705", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1817, "polynomial_expr": "(47 - 92*z**2)*(49*z**3 - 17*z + 15)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (47 - 92*z**2)*(49*z**3 - 17*z + 15)\nExpanding the part (47 - 92*z**2) using the distributive property, and we got: (-92*z**2)*(49*z**3 - 17*z + 15) + 47*(49*z**3 - 17*z + 15)\n#Step 2:\nCurrent expression: (-92*z**2)*(49*z**3 - 17*z + 15) + 47*(49*z**3 - 17*z + 15)\nSimplifying the partial expression: 47*(49*z**3 - 17*z + 15)\nExpanding the part (49*z**3 - 17*z + 15) using the distributive property, and we got: -17*z*47 + (49*z**3)*47 + 15*47\nReplacing 47*(49*z**3 - 17*z + 15) with -17*z*47 + (49*z**3)*47 + 15*47 in the overall expression.\n#Step 3:\nCurrent expression: -17*z*47 + (-92*z**2)*(49*z**3 - 17*z + 15) + (49*z**3)*47 + 705\nSimplifying the partial expression: (-92*z**2)*(49*z**3 - 17*z + 15)\nExpanding the part (49*z**3 - 17*z + 15) using the distributive property, and we got: (-17*z)*(-92*z**2) + 15*(-92*z**2) + (-92*z**2)*(49*z**3)\nReplacing (-92*z**2)*(49*z**3 - 17*z + 15) with (-17*z)*(-92*z**2) + 15*(-92*z**2) + (-92*z**2)*(49*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-17*z)*(-92*z**2) - 17*z*47 + 15*(-92)*z**2 + (-92*z**2)*(49*z**3) + (49*z**3)*47 + 705\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-17*z)*47 = -799*z\n (-17*z)*(-92*z**2) = 1564*z**3\n (49*z**3)*47 = 2303*z**3\n (49*z**3)*(-92*z**2) = -4508*z**5\n 15*-92*z**2 = -1380*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -4508*z**5 + 1564*z**3 + 2303*z**3 - 1380*z**2 - 799*z + 705\nCombining like terms, got -4508*z**5 + 3867*z**3 - 1380*z**2 - 799*z + 705\n#Step 6:\nCurrent expression: -4508*z**5 + 3867*z**3 - 1380*z**2 - 799*z + 705\nNo more calculations needed.\n-4508*z**5 + 3867*z**3 - 1380*z**2 - 799*z + 705", "generated_answer": "-4508*z**5 + 3867*z**3 - 1380*z**2 - 799*z + 705", "step_length": 6} {"cot_id": "4249ea57b18a1c2d48981b1cfc16aebe5edbb34d9589baaf1c4d96eac5b1aedd", "datapoint": {"question": "Calculate the following: (17*z**2 - 45)*(-50*z**3 + 16*z**2 - 4*z - 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-850*z**5 + 272*z**4 + 2182*z**3 - 1128*z**2 + 180*z + 1080", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1818, "polynomial_expr": "(17*z**2 - 45)*(-50*z**3 + 16*z**2 - 4*z - 24)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (17*z**2 - 45)*(-50*z**3 + 16*z**2 - 4*z - 24)\nExpanding the part (17*z**2 - 45) using the distributive property, and we got: (17*z**2)*(-50*z**3 + 16*z**2 - 4*z - 24) - 45*(-50*z**3 + 16*z**2 - 4*z - 24)\n#Step 2:\nCurrent expression: (17*z**2)*(-50*z**3 + 16*z**2 - 4*z - 24) - 45*(-50*z**3 + 16*z**2 - 4*z - 24)\nSimplifying the partial expression: -45*(-50*z**3 + 16*z**2 - 4*z - 24)\nExpanding the part (-50*z**3 + 16*z**2 - 4*z - 24) using the distributive property, and we got: -4*z*(-45) + (16*z**2)*(-45) - 50*z**3*(-45) - 24*(-45)\nReplacing -45*(-50*z**3 + 16*z**2 - 4*z - 24) with -4*z*(-45) + (16*z**2)*(-45) - 50*z**3*(-45) - 24*(-45) in the overall expression.\n#Step 3:\nCurrent expression: -4*z*(-45) + (16*z**2)*(-45) + (17*z**2)*(-50*z**3 + 16*z**2 - 4*z - 24) - 50*z**3*(-45) + 1080\nSimplifying the partial expression: (17*z**2)*(-50*z**3 + 16*z**2 - 4*z - 24)\nExpanding the part (-50*z**3 + 16*z**2 - 4*z - 24) using the distributive property, and we got: (-4*z)*(17*z**2) - 408*z**2 + (16*z**2)*(17*z**2) + (17*z**2)*(-50*z**3)\nReplacing (17*z**2)*(-50*z**3 + 16*z**2 - 4*z - 24) with (-4*z)*(17*z**2) - 408*z**2 + (16*z**2)*(17*z**2) + (17*z**2)*(-50*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-4*z)*(17*z**2) - 4*z*(-45) - 24*17*z**2 + (16*z**2)*(17*z**2) + (16*z**2)*(-45) + (17*z**2)*(-50*z**3) - 50*z**3*(-45) + 1080\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-50*z**3)*-45 = 2250*z**3\n (-50*z**3)*(17*z**2) = -850*z**5\n (-4*z)*-45 = 180*z\n (-4*z)*(17*z**2) = -68*z**3\n (16*z**2)*-45 = -720*z**2\n (16*z**2)*(17*z**2) = 272*z**4\n -24*17*z**2 = -408*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -850*z**5 + 272*z**4 - 68*z**3 + 2250*z**3 - 720*z**2 - 408*z**2 + 180*z + 1080\nCombining like terms, got -850*z**5 + 272*z**4 + 2182*z**3 - 1128*z**2 + 180*z + 1080\n#Step 6:\nCurrent expression: -850*z**5 + 272*z**4 + 2182*z**3 - 1128*z**2 + 180*z + 1080\nNo more calculations needed.\n-850*z**5 + 272*z**4 + 2182*z**3 - 1128*z**2 + 180*z + 1080", "generated_answer": "-850*z**5 + 272*z**4 + 2182*z**3 - 1128*z**2 + 180*z + 1080", "step_length": 6} {"cot_id": "962eb839b15e4d45bfe21d89ef0e48e248c2b4d6cf9ffca0023f28af06241e9f", "datapoint": {"question": "Calculate the following: (13 - 29*z)*(69*z**3 - 33*z - 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2001*z**4 + 897*z**3 + 957*z**2 - 226*z - 91", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1819, "polynomial_expr": "(13 - 29*z)*(69*z**3 - 33*z - 7)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (13 - 29*z)*(69*z**3 - 33*z - 7)\nExpanding the part (13 - 29*z) using the distributive property, and we got: (-29*z)*(69*z**3 - 33*z - 7) + 13*(69*z**3 - 33*z - 7)\n#Step 2:\nCurrent expression: (-29*z)*(69*z**3 - 33*z - 7) + 13*(69*z**3 - 33*z - 7)\nSimplifying the partial expression: 13*(69*z**3 - 33*z - 7)\nExpanding the part (69*z**3 - 33*z - 7) using the distributive property, and we got: -33*z*13 + (69*z**3)*13 - 7*13\nReplacing 13*(69*z**3 - 33*z - 7) with -33*z*13 + (69*z**3)*13 - 7*13 in the overall expression.\n#Step 3:\nCurrent expression: -33*z*13 + (-29*z)*(69*z**3 - 33*z - 7) + (69*z**3)*13 - 91\nSimplifying the partial expression: (-29*z)*(69*z**3 - 33*z - 7)\nExpanding the part (69*z**3 - 33*z - 7) using the distributive property, and we got: (-33*z)*(-29*z) + (-29*z)*(69*z**3) - (-1)*203*z\nReplacing (-29*z)*(69*z**3 - 33*z - 7) with (-33*z)*(-29*z) + (-29*z)*(69*z**3) - (-1)*203*z in the overall expression.\n#Step 4:\nCurrent expression: (-33*z)*(-29*z) - 33*z*13 + (-29*z)*(69*z**3) - 7*(-29)*z + (69*z**3)*13 - 91\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*z)*13 = -429*z\n (-33*z)*(-29*z) = 957*z**2\n (69*z**3)*13 = 897*z**3\n (69*z**3)*(-29*z) = -2001*z**4\n -7*-29*z = 203*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2001*z**4 + 897*z**3 + 957*z**2 - 429*z + 203*z - 91\nCombining like terms, got -2001*z**4 + 897*z**3 + 957*z**2 - 226*z - 91\n#Step 6:\nCurrent expression: -2001*z**4 + 897*z**3 + 957*z**2 - 226*z - 91\nNo more calculations needed.\n-2001*z**4 + 897*z**3 + 957*z**2 - 226*z - 91", "generated_answer": "-2001*z**4 + 897*z**3 + 957*z**2 - 226*z - 91", "step_length": 6} {"cot_id": "a0571d3fc96f7c38a51bdfcf7a072d1cf253abe59538c911ce97bcf890cfdf71", "datapoint": {"question": "Simplify this expression: (6*y**2 + 10*y - 22)*(-41*y**3 + 37*y - 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-246*y**5 - 410*y**4 + 1124*y**3 + 190*y**2 - 1114*y + 660", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1820, "polynomial_expr": "(6*y**2 + 10*y - 22)*(-41*y**3 + 37*y - 30)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6*y**2 + 10*y - 22)*(-41*y**3 + 37*y - 30)\nExpanding the part (-41*y**3 + 37*y - 30) using the distributive property, and we got: (37*y)*(6*y**2 + 10*y - 22) + (-41*y**3)*(6*y**2 + 10*y - 22) - 30*(6*y**2 + 10*y - 22)\n#Step 2:\nCurrent expression: (37*y)*(6*y**2 + 10*y - 22) + (-41*y**3)*(6*y**2 + 10*y - 22) - 30*(6*y**2 + 10*y - 22)\nSimplifying the partial expression: -30*(6*y**2 + 10*y - 22)\nExpanding the part (6*y**2 + 10*y - 22) using the distributive property, and we got: (10*y)*(-30) + (6*y**2)*(-30) - 22*(-30)\nReplacing -30*(6*y**2 + 10*y - 22) with (10*y)*(-30) + (6*y**2)*(-30) - 22*(-30) in the overall expression.\n#Step 3:\nCurrent expression: (10*y)*(-30) + (37*y)*(6*y**2 + 10*y - 22) + (6*y**2)*(-30) + (-41*y**3)*(6*y**2 + 10*y - 22) + 660\nSimplifying the partial expression: (-41*y**3)*(6*y**2 + 10*y - 22)\nExpanding the part (6*y**2 + 10*y - 22) using the distributive property, and we got: -(-1)*902*y**3 + (10*y)*(-41*y**3) + (6*y**2)*(-41*y**3)\nReplacing (-41*y**3)*(6*y**2 + 10*y - 22) with -(-1)*902*y**3 + (10*y)*(-41*y**3) + (6*y**2)*(-41*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -22*(-41)*y**3 + (10*y)*(-41*y**3) + (10*y)*(-30) + (37*y)*(6*y**2 + 10*y - 22) + (6*y**2)*(-41*y**3) + (6*y**2)*(-30) + 660\nSimplifying the partial expression: (37*y)*(6*y**2 + 10*y - 22)\nExpanding the part (6*y**2 + 10*y - 22) using the distributive property, and we got: -814*y + (10*y)*(37*y) + (37*y)*(6*y**2)\nReplacing (37*y)*(6*y**2 + 10*y - 22) with -814*y + (10*y)*(37*y) + (37*y)*(6*y**2) in the overall expression.\n#Step 5:\nCurrent expression: -22*(-41)*y**3 - 22*37*y + (10*y)*(37*y) + (10*y)*(-41*y**3) + (10*y)*(-30) + (37*y)*(6*y**2) + (6*y**2)*(-41*y**3) + (6*y**2)*(-30) + 660\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (6*y**2)*-30 = -180*y**2\n (6*y**2)*(-41*y**3) = -246*y**5\n (6*y**2)*(37*y) = 222*y**3\n (10*y)*-30 = -300*y\n (10*y)*(-41*y**3) = -410*y**4\n (10*y)*(37*y) = 370*y**2\n -22*-41*y**3 = 902*y**3\n -22*37*y = -814*y\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -246*y**5 - 410*y**4 + 222*y**3 + 902*y**3 - 180*y**2 + 370*y**2 - 814*y - 300*y + 660\nCombining like terms, got -246*y**5 - 410*y**4 + 1124*y**3 + 190*y**2 - 1114*y + 660\n#Step 7:\nCurrent expression: -246*y**5 - 410*y**4 + 1124*y**3 + 190*y**2 - 1114*y + 660\nNo more calculations needed.\n-246*y**5 - 410*y**4 + 1124*y**3 + 190*y**2 - 1114*y + 660", "generated_answer": "-246*y**5 - 410*y**4 + 1124*y**3 + 190*y**2 - 1114*y + 660", "step_length": 7} {"cot_id": "5b4921f59d62d091bedb9df9bd3a09066e5b95fbfbb5af6419fe42e6de7464e4", "datapoint": {"question": "Calculate the following: 15*y*(29*y**2 + 88*y - 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "435*y**3 + 1320*y**2 - 240*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1821, "polynomial_expr": "15*y*(29*y**2 + 88*y - 16)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 15*y*(29*y**2 + 88*y - 16)\nExpanding the part (29*y**2 + 88*y - 16) using the distributive property, and we got: -240*y + (15*y)*(88*y) + (15*y)*(29*y**2)\n#Step 2:\nCurrent expression: -240*y + (15*y)*(88*y) + (15*y)*(29*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -16*(15*y) = -240*y\n (29*y**2)*(15*y) = 435*y**3\n (88*y)*(15*y) = 1320*y**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 435*y**3 + 1320*y**2 - 240*y\nNo more calculations needed.\n435*y**3 + 1320*y**2 - 240*y", "generated_answer": "435*y**3 + 1320*y**2 - 240*y", "step_length": 3} {"cot_id": "efd35365e27507a2afffa6a43010bd4395c49a2d6f1082a1f57612073867dc9a", "datapoint": {"question": "Simplify this expression: (-66*x - 45)*(-20*x - 43)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1320*x**2 + 3738*x + 1935", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1822, "polynomial_expr": "(-66*x - 45)*(-20*x - 43)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-66*x - 45)*(-20*x - 43)\nExpanding the part (-66*x - 45) using the distributive property, and we got: (-66*x)*(-20*x - 43) - 45*(-20*x - 43)\n#Step 2:\nCurrent expression: (-66*x)*(-20*x - 43) - 45*(-20*x - 43)\nSimplifying the partial expression: -45*(-20*x - 43)\nExpanding the part (-20*x - 43) using the distributive property, and we got: -20*x*(-45) - 43*(-45)\nReplacing -45*(-20*x - 43) with -20*x*(-45) - 43*(-45) in the overall expression.\n#Step 3:\nCurrent expression: (-66*x)*(-20*x - 43) - 20*x*(-45) + 1935\nSimplifying the partial expression: (-66*x)*(-20*x - 43)\nExpanding the part (-20*x - 43) using the distributive property, and we got: (-66*x)*(-20*x) - (-1)*2838*x\nReplacing (-66*x)*(-20*x - 43) with (-66*x)*(-20*x) - (-1)*2838*x in the overall expression.\n#Step 4:\nCurrent expression: (-66*x)*(-20*x) - 20*x*(-45) - 43*(-66)*x + 1935\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*x)*-45 = 900*x\n (-20*x)*(-66*x) = 1320*x**2\n -43*-66*x = 2838*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1320*x**2 + 900*x + 2838*x + 1935\nCombining like terms, got 1320*x**2 + 3738*x + 1935\n#Step 6:\nCurrent expression: 1320*x**2 + 3738*x + 1935\nNo more calculations needed.\n1320*x**2 + 3738*x + 1935", "generated_answer": "1320*x**2 + 3738*x + 1935", "step_length": 6} {"cot_id": "d918a2b82aebc1551966e6fb21d227a5014454cc0f6e21b9b66a169a101e82db", "datapoint": {"question": "Calculate the following: (62*z**3 - 3)*(-4*z**3 + 39*z**2 - 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-248*z**6 + 2418*z**5 - 1724*z**3 - 117*z**2 + 84", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1823, "polynomial_expr": "(62*z**3 - 3)*(-4*z**3 + 39*z**2 - 28)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (62*z**3 - 3)*(-4*z**3 + 39*z**2 - 28)\nExpanding the part (62*z**3 - 3) using the distributive property, and we got: (62*z**3)*(-4*z**3 + 39*z**2 - 28) - 3*(-4*z**3 + 39*z**2 - 28)\n#Step 2:\nCurrent expression: (62*z**3)*(-4*z**3 + 39*z**2 - 28) - 3*(-4*z**3 + 39*z**2 - 28)\nSimplifying the partial expression: -3*(-4*z**3 + 39*z**2 - 28)\nExpanding the part (-4*z**3 + 39*z**2 - 28) using the distributive property, and we got: (39*z**2)*(-3) - 4*z**3*(-3) - 28*(-3)\nReplacing -3*(-4*z**3 + 39*z**2 - 28) with (39*z**2)*(-3) - 4*z**3*(-3) - 28*(-3) in the overall expression.\n#Step 3:\nCurrent expression: (39*z**2)*(-3) - 4*z**3*(-3) + (62*z**3)*(-4*z**3 + 39*z**2 - 28) + 84\nSimplifying the partial expression: (62*z**3)*(-4*z**3 + 39*z**2 - 28)\nExpanding the part (-4*z**3 + 39*z**2 - 28) using the distributive property, and we got: -1736*z**3 + (39*z**2)*(62*z**3) + (-4*z**3)*(62*z**3)\nReplacing (62*z**3)*(-4*z**3 + 39*z**2 - 28) with -1736*z**3 + (39*z**2)*(62*z**3) + (-4*z**3)*(62*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -28*62*z**3 + (39*z**2)*(62*z**3) + (39*z**2)*(-3) + (-4*z**3)*(62*z**3) - 4*z**3*(-3) + 84\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-4*z**3)*-3 = 12*z**3\n (-4*z**3)*(62*z**3) = -248*z**6\n (39*z**2)*-3 = -117*z**2\n (39*z**2)*(62*z**3) = 2418*z**5\n -28*62*z**3 = -1736*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -248*z**6 + 2418*z**5 - 1736*z**3 + 12*z**3 - 117*z**2 + 84\nCombining like terms, got -248*z**6 + 2418*z**5 - 1724*z**3 - 117*z**2 + 84\n#Step 6:\nCurrent expression: -248*z**6 + 2418*z**5 - 1724*z**3 - 117*z**2 + 84\nNo more calculations needed.\n-248*z**6 + 2418*z**5 - 1724*z**3 - 117*z**2 + 84", "generated_answer": "-248*z**6 + 2418*z**5 - 1724*z**3 - 117*z**2 + 84", "step_length": 6} {"cot_id": "ed983e90274124d878eba642585c4e8acb2bcf0a67467e3f74fd0ac72c812f57", "datapoint": {"question": "Simplify this expression: (z**2 - 45)*(22*z**2 - 13*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "22*z**4 - 13*z**3 - 990*z**2 + 585*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1824, "polynomial_expr": "(z**2 - 45)*(22*z**2 - 13*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (z**2 - 45)*(22*z**2 - 13*z)\nExpanding the part (z**2 - 45) using the distributive property, and we got: z**2*(22*z**2 - 13*z) - 45*(22*z**2 - 13*z)\n#Step 2:\nCurrent expression: z**2*(22*z**2 - 13*z) - 45*(22*z**2 - 13*z)\nSimplifying the partial expression: -45*(22*z**2 - 13*z)\nExpanding the part (22*z**2 - 13*z) using the distributive property, and we got: -13*z*(-45) + (22*z**2)*(-45)\nReplacing -45*(22*z**2 - 13*z) with -13*z*(-45) + (22*z**2)*(-45) in the overall expression.\n#Step 3:\nCurrent expression: -13*z*(-45) + z**2*(22*z**2 - 13*z) + (22*z**2)*(-45)\nSimplifying the partial expression: z**2*(22*z**2 - 13*z)\nExpanding the part (22*z**2 - 13*z) using the distributive property, and we got: (-13*z)*z**2 + z**2*(22*z**2)\nReplacing z**2*(22*z**2 - 13*z) with (-13*z)*z**2 + z**2*(22*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-13*z)*z**2 - 13*z*(-45) + z**2*(22*z**2) + (22*z**2)*(-45)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*z)*-45 = 585*z\n (-13*z)*z**2 = -13*z**3\n (22*z**2)*-45 = -990*z**2\n (22*z**2)*z**2 = 22*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 22*z**4 - 13*z**3 - 990*z**2 + 585*z\nNo more calculations needed.\n22*z**4 - 13*z**3 - 990*z**2 + 585*z", "generated_answer": "22*z**4 - 13*z**3 - 990*z**2 + 585*z", "step_length": 5} {"cot_id": "74b9166db7482a7c41175e69f56daebcc6574ca32074654f13e021cdd0f4f102", "datapoint": {"question": "Simplify this expression: -22*z**3*(66 - 12*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "264*z**4 - 1452*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1825, "polynomial_expr": "-22*z**3*(66 - 12*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -22*z**3*(66 - 12*z)\nExpanding the part (66 - 12*z) using the distributive property, and we got: (-12*z)*(-22*z**3) + 66*(-22*z**3)\n#Step 2:\nCurrent expression: (-12*z)*(-22*z**3) + 66*(-22*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 66*(-22*z**3) = -1452*z**3\n (-12*z)*(-22*z**3) = 264*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 264*z**4 - 1452*z**3\nNo more calculations needed.\n264*z**4 - 1452*z**3", "generated_answer": "264*z**4 - 1452*z**3", "step_length": 3} {"cot_id": "e5935b963b881a68a7e9c7835c4695401b14c811da41ee9e8e0981794584bb99", "datapoint": {"question": "Simplify this expression: (27*z**3 - 2*z**2 + z)*(17*z**3 - 47*z**2 + 11*z - 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "459*z**6 - 1303*z**5 + 408*z**4 - 609*z**3 + 51*z**2 - 20*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1826, "polynomial_expr": "(27*z**3 - 2*z**2 + z)*(17*z**3 - 47*z**2 + 11*z - 20)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*z**3 - 2*z**2 + z)*(17*z**3 - 47*z**2 + 11*z - 20)\nExpanding the part (27*z**3 - 2*z**2 + z) using the distributive property, and we got: z*(17*z**3 - 47*z**2 + 11*z - 20) + (-2*z**2)*(17*z**3 - 47*z**2 + 11*z - 20) + (27*z**3)*(17*z**3 - 47*z**2 + 11*z - 20)\n#Step 2:\nCurrent expression: z*(17*z**3 - 47*z**2 + 11*z - 20) + (-2*z**2)*(17*z**3 - 47*z**2 + 11*z - 20) + (27*z**3)*(17*z**3 - 47*z**2 + 11*z - 20)\nSimplifying the partial expression: z*(17*z**3 - 47*z**2 + 11*z - 20)\nExpanding the part (17*z**3 - 47*z**2 + 11*z - 20) using the distributive property, and we got: z*(11*z) + z*(-47*z**2) + z*(17*z**3) - 20*z\nReplacing z*(17*z**3 - 47*z**2 + 11*z - 20) with z*(11*z) + z*(-47*z**2) + z*(17*z**3) - 20*z in the overall expression.\n#Step 3:\nCurrent expression: z*(11*z) + z*(-47*z**2) + z*(17*z**3) - 20*z + (-2*z**2)*(17*z**3 - 47*z**2 + 11*z - 20) + (27*z**3)*(17*z**3 - 47*z**2 + 11*z - 20)\nSimplifying the partial expression: (-2*z**2)*(17*z**3 - 47*z**2 + 11*z - 20)\nExpanding the part (17*z**3 - 47*z**2 + 11*z - 20) using the distributive property, and we got: -(-1)*40*z**2 + (11*z)*(-2*z**2) + (-47*z**2)*(-2*z**2) + (-2*z**2)*(17*z**3)\nReplacing (-2*z**2)*(17*z**3 - 47*z**2 + 11*z - 20) with -(-1)*40*z**2 + (11*z)*(-2*z**2) + (-47*z**2)*(-2*z**2) + (-2*z**2)*(17*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -20*(-2)*z**2 + z*(11*z) + z*(-47*z**2) + z*(17*z**3) - 20*z + (11*z)*(-2*z**2) + (-47*z**2)*(-2*z**2) + (-2*z**2)*(17*z**3) + (27*z**3)*(17*z**3 - 47*z**2 + 11*z - 20)\nSimplifying the partial expression: (27*z**3)*(17*z**3 - 47*z**2 + 11*z - 20)\nExpanding the part (17*z**3 - 47*z**2 + 11*z - 20) using the distributive property, and we got: -540*z**3 + (11*z)*(27*z**3) + (-47*z**2)*(27*z**3) + (17*z**3)*(27*z**3)\nReplacing (27*z**3)*(17*z**3 - 47*z**2 + 11*z - 20) with -540*z**3 + (11*z)*(27*z**3) + (-47*z**2)*(27*z**3) + (17*z**3)*(27*z**3) in the overall expression.\n#Step 5:\nCurrent expression: -20*27*z**3 - 20*(-2)*z**2 + z*(11*z) + z*(-47*z**2) + z*(17*z**3) - 20*z + (11*z)*(-2*z**2) + (11*z)*(27*z**3) + (-47*z**2)*(-2*z**2) + (-47*z**2)*(27*z**3) + (-2*z**2)*(17*z**3) + (17*z**3)*(27*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*z**2)*z = -47*z**3\n (-47*z**2)*(-2*z**2) = 94*z**4\n (-47*z**2)*(27*z**3) = -1269*z**5\n (11*z)*z = 11*z**2\n (11*z)*(-2*z**2) = -22*z**3\n (11*z)*(27*z**3) = 297*z**4\n (17*z**3)*z = 17*z**4\n (17*z**3)*(-2*z**2) = -34*z**5\n (17*z**3)*(27*z**3) = 459*z**6\n -20*-2*z**2 = 40*z**2\n -20*27*z**3 = -540*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 459*z**6 - 1269*z**5 - 34*z**5 + 17*z**4 + 94*z**4 + 297*z**4 - 540*z**3 - 47*z**3 - 22*z**3 + 11*z**2 + 40*z**2 - 20*z\nCombining like terms, got 459*z**6 - 1303*z**5 + 408*z**4 - 609*z**3 + 51*z**2 - 20*z\n#Step 7:\nCurrent expression: 459*z**6 - 1303*z**5 + 408*z**4 - 609*z**3 + 51*z**2 - 20*z\nNo more calculations needed.\n459*z**6 - 1303*z**5 + 408*z**4 - 609*z**3 + 51*z**2 - 20*z", "generated_answer": "459*z**6 - 1303*z**5 + 408*z**4 - 609*z**3 + 51*z**2 - 20*z", "step_length": 7} {"cot_id": "3358625cee103b24e90cc6331c5458d03b0bac134974cc37986685e78e67539b", "datapoint": {"question": "Simplify this expression: (-5*x**3 + 42*x**2 + 14*x)*(21*x**3 - 61*x**2 + 9*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-105*x**6 + 1187*x**5 - 2313*x**4 - 476*x**3 + 126*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1827, "polynomial_expr": "(-5*x**3 + 42*x**2 + 14*x)*(21*x**3 - 61*x**2 + 9*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-5*x**3 + 42*x**2 + 14*x)*(21*x**3 - 61*x**2 + 9*x)\nExpanding the part (21*x**3 - 61*x**2 + 9*x) using the distributive property, and we got: (9*x)*(-5*x**3 + 42*x**2 + 14*x) + (-61*x**2)*(-5*x**3 + 42*x**2 + 14*x) + (21*x**3)*(-5*x**3 + 42*x**2 + 14*x)\n#Step 2:\nCurrent expression: (9*x)*(-5*x**3 + 42*x**2 + 14*x) + (-61*x**2)*(-5*x**3 + 42*x**2 + 14*x) + (21*x**3)*(-5*x**3 + 42*x**2 + 14*x)\nSimplifying the partial expression: (-61*x**2)*(-5*x**3 + 42*x**2 + 14*x)\nExpanding the part (-5*x**3 + 42*x**2 + 14*x) using the distributive property, and we got: (14*x)*(-61*x**2) + (-61*x**2)*(42*x**2) + (-61*x**2)*(-5*x**3)\nReplacing (-61*x**2)*(-5*x**3 + 42*x**2 + 14*x) with (14*x)*(-61*x**2) + (-61*x**2)*(42*x**2) + (-61*x**2)*(-5*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (9*x)*(-5*x**3 + 42*x**2 + 14*x) + (14*x)*(-61*x**2) + (-61*x**2)*(42*x**2) + (-61*x**2)*(-5*x**3) + (21*x**3)*(-5*x**3 + 42*x**2 + 14*x)\nSimplifying the partial expression: (9*x)*(-5*x**3 + 42*x**2 + 14*x)\nExpanding the part (-5*x**3 + 42*x**2 + 14*x) using the distributive property, and we got: (9*x)*(14*x) + (9*x)*(42*x**2) + (9*x)*(-5*x**3)\nReplacing (9*x)*(-5*x**3 + 42*x**2 + 14*x) with (9*x)*(14*x) + (9*x)*(42*x**2) + (9*x)*(-5*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (9*x)*(14*x) + (9*x)*(42*x**2) + (9*x)*(-5*x**3) + (14*x)*(-61*x**2) + (-61*x**2)*(42*x**2) + (-61*x**2)*(-5*x**3) + (21*x**3)*(-5*x**3 + 42*x**2 + 14*x)\nSimplifying the partial expression: (21*x**3)*(-5*x**3 + 42*x**2 + 14*x)\nExpanding the part (-5*x**3 + 42*x**2 + 14*x) using the distributive property, and we got: (14*x)*(21*x**3) + (42*x**2)*(21*x**3) + (-5*x**3)*(21*x**3)\nReplacing (21*x**3)*(-5*x**3 + 42*x**2 + 14*x) with (14*x)*(21*x**3) + (42*x**2)*(21*x**3) + (-5*x**3)*(21*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (9*x)*(14*x) + (9*x)*(42*x**2) + (9*x)*(-5*x**3) + (14*x)*(-61*x**2) + (14*x)*(21*x**3) + (-61*x**2)*(42*x**2) + (-61*x**2)*(-5*x**3) + (42*x**2)*(21*x**3) + (-5*x**3)*(21*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-5*x**3)*(-61*x**2) = 305*x**5\n (-5*x**3)*(9*x) = -45*x**4\n (-5*x**3)*(21*x**3) = -105*x**6\n (14*x)*(-61*x**2) = -854*x**3\n (14*x)*(9*x) = 126*x**2\n (14*x)*(21*x**3) = 294*x**4\n (42*x**2)*(-61*x**2) = -2562*x**4\n (42*x**2)*(9*x) = 378*x**3\n (42*x**2)*(21*x**3) = 882*x**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -105*x**6 + 305*x**5 + 882*x**5 - 2562*x**4 - 45*x**4 + 294*x**4 - 854*x**3 + 378*x**3 + 126*x**2\nCombining like terms, got -105*x**6 + 1187*x**5 - 2313*x**4 - 476*x**3 + 126*x**2\n#Step 7:\nCurrent expression: -105*x**6 + 1187*x**5 - 2313*x**4 - 476*x**3 + 126*x**2\nNo more calculations needed.\n-105*x**6 + 1187*x**5 - 2313*x**4 - 476*x**3 + 126*x**2", "generated_answer": "-105*x**6 + 1187*x**5 - 2313*x**4 - 476*x**3 + 126*x**2", "step_length": 7} {"cot_id": "e6f12bd8b05d3174feb253ed65e1231382ae727aba43be0da49f493241d8373e", "datapoint": {"question": "Calculate the following: (-6*y**3 - 18)*(3*y**3 + 18*y**2 + 19*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-18*y**6 - 108*y**5 - 114*y**4 - 54*y**3 - 324*y**2 - 342*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1828, "polynomial_expr": "(-6*y**3 - 18)*(3*y**3 + 18*y**2 + 19*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-6*y**3 - 18)*(3*y**3 + 18*y**2 + 19*y)\nExpanding the part (-6*y**3 - 18) using the distributive property, and we got: (-6*y**3)*(3*y**3 + 18*y**2 + 19*y) - 18*(3*y**3 + 18*y**2 + 19*y)\n#Step 2:\nCurrent expression: (-6*y**3)*(3*y**3 + 18*y**2 + 19*y) - 18*(3*y**3 + 18*y**2 + 19*y)\nSimplifying the partial expression: -18*(3*y**3 + 18*y**2 + 19*y)\nExpanding the part (3*y**3 + 18*y**2 + 19*y) using the distributive property, and we got: (19*y)*(-18) + (18*y**2)*(-18) + (3*y**3)*(-18)\nReplacing -18*(3*y**3 + 18*y**2 + 19*y) with (19*y)*(-18) + (18*y**2)*(-18) + (3*y**3)*(-18) in the overall expression.\n#Step 3:\nCurrent expression: (19*y)*(-18) + (18*y**2)*(-18) + (-6*y**3)*(3*y**3 + 18*y**2 + 19*y) + (3*y**3)*(-18)\nSimplifying the partial expression: (-6*y**3)*(3*y**3 + 18*y**2 + 19*y)\nExpanding the part (3*y**3 + 18*y**2 + 19*y) using the distributive property, and we got: (19*y)*(-6*y**3) + (18*y**2)*(-6*y**3) + (-6*y**3)*(3*y**3)\nReplacing (-6*y**3)*(3*y**3 + 18*y**2 + 19*y) with (19*y)*(-6*y**3) + (18*y**2)*(-6*y**3) + (-6*y**3)*(3*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (19*y)*(-6*y**3) + (19*y)*(-18) + (18*y**2)*(-6*y**3) + (18*y**2)*(-18) + (-6*y**3)*(3*y**3) + (3*y**3)*(-18)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (3*y**3)*-18 = -54*y**3\n (3*y**3)*(-6*y**3) = -18*y**6\n (18*y**2)*-18 = -324*y**2\n (18*y**2)*(-6*y**3) = -108*y**5\n (19*y)*-18 = -342*y\n (19*y)*(-6*y**3) = -114*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -18*y**6 - 108*y**5 - 114*y**4 - 54*y**3 - 324*y**2 - 342*y\nNo more calculations needed.\n-18*y**6 - 108*y**5 - 114*y**4 - 54*y**3 - 324*y**2 - 342*y", "generated_answer": "-18*y**6 - 108*y**5 - 114*y**4 - 54*y**3 - 324*y**2 - 342*y", "step_length": 5} {"cot_id": "cf8a138910f4c154d792c40040c96770394f5bf5d2a2b85d62c7aff62bc9d5b5", "datapoint": {"question": "Simplify this expression: (y**2 + 33)*(-50*y**3 + 2*y + 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-50*y**5 - 1648*y**3 + 36*y**2 + 66*y + 1188", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1829, "polynomial_expr": "(y**2 + 33)*(-50*y**3 + 2*y + 36)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (y**2 + 33)*(-50*y**3 + 2*y + 36)\nExpanding the part (y**2 + 33) using the distributive property, and we got: y**2*(-50*y**3 + 2*y + 36) + 33*(-50*y**3 + 2*y + 36)\n#Step 2:\nCurrent expression: y**2*(-50*y**3 + 2*y + 36) + 33*(-50*y**3 + 2*y + 36)\nSimplifying the partial expression: 33*(-50*y**3 + 2*y + 36)\nExpanding the part (-50*y**3 + 2*y + 36) using the distributive property, and we got: (2*y)*33 - 50*y**3*33 + 36*33\nReplacing 33*(-50*y**3 + 2*y + 36) with (2*y)*33 - 50*y**3*33 + 36*33 in the overall expression.\n#Step 3:\nCurrent expression: y**2*(-50*y**3 + 2*y + 36) + (2*y)*33 - 50*y**3*33 + 1188\nSimplifying the partial expression: y**2*(-50*y**3 + 2*y + 36)\nExpanding the part (-50*y**3 + 2*y + 36) using the distributive property, and we got: (2*y)*y**2 + y**2*(-50*y**3) + 36*y**2\nReplacing y**2*(-50*y**3 + 2*y + 36) with (2*y)*y**2 + y**2*(-50*y**3) + 36*y**2 in the overall expression.\n#Step 4:\nCurrent expression: (2*y)*y**2 + y**2*(-50*y**3) + 36*y**2 + (2*y)*33 - 50*y**3*33 + 1188\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-50*y**3)*33 = -1650*y**3\n (-50*y**3)*y**2 = -50*y**5\n (2*y)*33 = 66*y\n (2*y)*y**2 = 2*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -50*y**5 - 1650*y**3 + 2*y**3 + 36*y**2 + 66*y + 1188\nCombining like terms, got -50*y**5 - 1648*y**3 + 36*y**2 + 66*y + 1188\n#Step 6:\nCurrent expression: -50*y**5 - 1648*y**3 + 36*y**2 + 66*y + 1188\nNo more calculations needed.\n-50*y**5 - 1648*y**3 + 36*y**2 + 66*y + 1188", "generated_answer": "-50*y**5 - 1648*y**3 + 36*y**2 + 66*y + 1188", "step_length": 6} {"cot_id": "6b3bf7f9136530a77225a3a99ae92620fb158b72af6e7696071ecce94f32c4b5", "datapoint": {"question": "Simplify this expression: (-50*y**2 - 71*y)*(27*y**3 + 49*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1350*y**5 - 1917*y**4 - 2450*y**3 - 3479*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1830, "polynomial_expr": "(-50*y**2 - 71*y)*(27*y**3 + 49*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-50*y**2 - 71*y)*(27*y**3 + 49*y)\nExpanding the part (-50*y**2 - 71*y) using the distributive property, and we got: (-71*y)*(27*y**3 + 49*y) + (-50*y**2)*(27*y**3 + 49*y)\n#Step 2:\nCurrent expression: (-71*y)*(27*y**3 + 49*y) + (-50*y**2)*(27*y**3 + 49*y)\nSimplifying the partial expression: (-71*y)*(27*y**3 + 49*y)\nExpanding the part (27*y**3 + 49*y) using the distributive property, and we got: (-71*y)*(49*y) + (-71*y)*(27*y**3)\nReplacing (-71*y)*(27*y**3 + 49*y) with (-71*y)*(49*y) + (-71*y)*(27*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-71*y)*(49*y) + (-71*y)*(27*y**3) + (-50*y**2)*(27*y**3 + 49*y)\nSimplifying the partial expression: (-50*y**2)*(27*y**3 + 49*y)\nExpanding the part (27*y**3 + 49*y) using the distributive property, and we got: (49*y)*(-50*y**2) + (-50*y**2)*(27*y**3)\nReplacing (-50*y**2)*(27*y**3 + 49*y) with (49*y)*(-50*y**2) + (-50*y**2)*(27*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-71*y)*(49*y) + (-71*y)*(27*y**3) + (49*y)*(-50*y**2) + (-50*y**2)*(27*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (27*y**3)*(-71*y) = -1917*y**4\n (27*y**3)*(-50*y**2) = -1350*y**5\n (49*y)*(-71*y) = -3479*y**2\n (49*y)*(-50*y**2) = -2450*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1350*y**5 - 1917*y**4 - 2450*y**3 - 3479*y**2\nNo more calculations needed.\n-1350*y**5 - 1917*y**4 - 2450*y**3 - 3479*y**2", "generated_answer": "-1350*y**5 - 1917*y**4 - 2450*y**3 - 3479*y**2", "step_length": 5} {"cot_id": "537cec2f227aab717b1b175228733e01fe9111cfb11c572d299188b79c5608e2", "datapoint": {"question": "Calculate the following: (-50*z**3 + 11*z**2 + 13*z)*(31*z**3 - 14*z**2 + 43*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1550*z**6 + 1041*z**5 - 1901*z**4 + 291*z**3 + 559*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1831, "polynomial_expr": "(-50*z**3 + 11*z**2 + 13*z)*(31*z**3 - 14*z**2 + 43*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-50*z**3 + 11*z**2 + 13*z)*(31*z**3 - 14*z**2 + 43*z)\nExpanding the part (-50*z**3 + 11*z**2 + 13*z) using the distributive property, and we got: (13*z)*(31*z**3 - 14*z**2 + 43*z) + (11*z**2)*(31*z**3 - 14*z**2 + 43*z) + (-50*z**3)*(31*z**3 - 14*z**2 + 43*z)\n#Step 2:\nCurrent expression: (13*z)*(31*z**3 - 14*z**2 + 43*z) + (11*z**2)*(31*z**3 - 14*z**2 + 43*z) + (-50*z**3)*(31*z**3 - 14*z**2 + 43*z)\nSimplifying the partial expression: (-50*z**3)*(31*z**3 - 14*z**2 + 43*z)\nExpanding the part (31*z**3 - 14*z**2 + 43*z) using the distributive property, and we got: (43*z)*(-50*z**3) + (-14*z**2)*(-50*z**3) + (-50*z**3)*(31*z**3)\nReplacing (-50*z**3)*(31*z**3 - 14*z**2 + 43*z) with (43*z)*(-50*z**3) + (-14*z**2)*(-50*z**3) + (-50*z**3)*(31*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (13*z)*(31*z**3 - 14*z**2 + 43*z) + (43*z)*(-50*z**3) + (-14*z**2)*(-50*z**3) + (11*z**2)*(31*z**3 - 14*z**2 + 43*z) + (-50*z**3)*(31*z**3)\nSimplifying the partial expression: (11*z**2)*(31*z**3 - 14*z**2 + 43*z)\nExpanding the part (31*z**3 - 14*z**2 + 43*z) using the distributive property, and we got: (43*z)*(11*z**2) + (-14*z**2)*(11*z**2) + (11*z**2)*(31*z**3)\nReplacing (11*z**2)*(31*z**3 - 14*z**2 + 43*z) with (43*z)*(11*z**2) + (-14*z**2)*(11*z**2) + (11*z**2)*(31*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (13*z)*(31*z**3 - 14*z**2 + 43*z) + (43*z)*(11*z**2) + (43*z)*(-50*z**3) + (-14*z**2)*(11*z**2) + (-14*z**2)*(-50*z**3) + (11*z**2)*(31*z**3) + (-50*z**3)*(31*z**3)\nSimplifying the partial expression: (13*z)*(31*z**3 - 14*z**2 + 43*z)\nExpanding the part (31*z**3 - 14*z**2 + 43*z) using the distributive property, and we got: (13*z)*(43*z) + (13*z)*(-14*z**2) + (13*z)*(31*z**3)\nReplacing (13*z)*(31*z**3 - 14*z**2 + 43*z) with (13*z)*(43*z) + (13*z)*(-14*z**2) + (13*z)*(31*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (13*z)*(43*z) + (13*z)*(-14*z**2) + (13*z)*(31*z**3) + (43*z)*(11*z**2) + (43*z)*(-50*z**3) + (-14*z**2)*(11*z**2) + (-14*z**2)*(-50*z**3) + (11*z**2)*(31*z**3) + (-50*z**3)*(31*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-14*z**2)*(-50*z**3) = 700*z**5\n (-14*z**2)*(11*z**2) = -154*z**4\n (-14*z**2)*(13*z) = -182*z**3\n (31*z**3)*(-50*z**3) = -1550*z**6\n (31*z**3)*(11*z**2) = 341*z**5\n (31*z**3)*(13*z) = 403*z**4\n (43*z)*(-50*z**3) = -2150*z**4\n (43*z)*(11*z**2) = 473*z**3\n (43*z)*(13*z) = 559*z**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1550*z**6 + 341*z**5 + 700*z**5 - 2150*z**4 - 154*z**4 + 403*z**4 - 182*z**3 + 473*z**3 + 559*z**2\nCombining like terms, got -1550*z**6 + 1041*z**5 - 1901*z**4 + 291*z**3 + 559*z**2\n#Step 7:\nCurrent expression: -1550*z**6 + 1041*z**5 - 1901*z**4 + 291*z**3 + 559*z**2\nNo more calculations needed.\n-1550*z**6 + 1041*z**5 - 1901*z**4 + 291*z**3 + 559*z**2", "generated_answer": "-1550*z**6 + 1041*z**5 - 1901*z**4 + 291*z**3 + 559*z**2", "step_length": 7} {"cot_id": "c7e90639b16c2f66ceb1113cfd95e464ec9d4e756ae89374474b14355e8d1d3e", "datapoint": {"question": "Calculate the following: (-32*z**3 - 23)*(-11*z**2 + 36*z - 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "352*z**5 - 1152*z**4 + 1408*z**3 + 253*z**2 - 828*z + 1012", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1832, "polynomial_expr": "(-32*z**3 - 23)*(-11*z**2 + 36*z - 44)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-32*z**3 - 23)*(-11*z**2 + 36*z - 44)\nExpanding the part (-32*z**3 - 23) using the distributive property, and we got: (-32*z**3)*(-11*z**2 + 36*z - 44) - 23*(-11*z**2 + 36*z - 44)\n#Step 2:\nCurrent expression: (-32*z**3)*(-11*z**2 + 36*z - 44) - 23*(-11*z**2 + 36*z - 44)\nSimplifying the partial expression: -23*(-11*z**2 + 36*z - 44)\nExpanding the part (-11*z**2 + 36*z - 44) using the distributive property, and we got: (36*z)*(-23) - 11*z**2*(-23) - 44*(-23)\nReplacing -23*(-11*z**2 + 36*z - 44) with (36*z)*(-23) - 11*z**2*(-23) - 44*(-23) in the overall expression.\n#Step 3:\nCurrent expression: (36*z)*(-23) - 11*z**2*(-23) + (-32*z**3)*(-11*z**2 + 36*z - 44) + 1012\nSimplifying the partial expression: (-32*z**3)*(-11*z**2 + 36*z - 44)\nExpanding the part (-11*z**2 + 36*z - 44) using the distributive property, and we got: -(-1)*1408*z**3 + (36*z)*(-32*z**3) + (-11*z**2)*(-32*z**3)\nReplacing (-32*z**3)*(-11*z**2 + 36*z - 44) with -(-1)*1408*z**3 + (36*z)*(-32*z**3) + (-11*z**2)*(-32*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -44*(-32)*z**3 + (36*z)*(-32*z**3) + (36*z)*(-23) + (-11*z**2)*(-32*z**3) - 11*z**2*(-23) + 1012\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*z**2)*-23 = 253*z**2\n (-11*z**2)*(-32*z**3) = 352*z**5\n (36*z)*-23 = -828*z\n (36*z)*(-32*z**3) = -1152*z**4\n -44*-32*z**3 = 1408*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 352*z**5 - 1152*z**4 + 1408*z**3 + 253*z**2 - 828*z + 1012\nNo more calculations needed.\n352*z**5 - 1152*z**4 + 1408*z**3 + 253*z**2 - 828*z + 1012", "generated_answer": "352*z**5 - 1152*z**4 + 1408*z**3 + 253*z**2 - 828*z + 1012", "step_length": 5} {"cot_id": "b7c5b57e5e94264cb1bb462cc8c46a58c8795d40b4307aa49170c83afd6ff638", "datapoint": {"question": "Simplify this expression: (7*x**3 + 48*x**2 + 23)*(9*x**3 - 21*x**2 - 5)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "63*x**6 + 285*x**5 - 1008*x**4 + 172*x**3 - 723*x**2 - 115", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1833, "polynomial_expr": "(7*x**3 + 48*x**2 + 23)*(9*x**3 - 21*x**2 - 5)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7*x**3 + 48*x**2 + 23)*(9*x**3 - 21*x**2 - 5)\nExpanding the part (9*x**3 - 21*x**2 - 5) using the distributive property, and we got: (-21*x**2)*(7*x**3 + 48*x**2 + 23) + (9*x**3)*(7*x**3 + 48*x**2 + 23) - 5*(7*x**3 + 48*x**2 + 23)\n#Step 2:\nCurrent expression: (-21*x**2)*(7*x**3 + 48*x**2 + 23) + (9*x**3)*(7*x**3 + 48*x**2 + 23) - 5*(7*x**3 + 48*x**2 + 23)\nSimplifying the partial expression: -5*(7*x**3 + 48*x**2 + 23)\nExpanding the part (7*x**3 + 48*x**2 + 23) using the distributive property, and we got: (48*x**2)*(-5) + (7*x**3)*(-5) + 23*(-5)\nReplacing -5*(7*x**3 + 48*x**2 + 23) with (48*x**2)*(-5) + (7*x**3)*(-5) + 23*(-5) in the overall expression.\n#Step 3:\nCurrent expression: (-21*x**2)*(7*x**3 + 48*x**2 + 23) + (48*x**2)*(-5) + (7*x**3)*(-5) + (9*x**3)*(7*x**3 + 48*x**2 + 23) - 115\nSimplifying the partial expression: (-21*x**2)*(7*x**3 + 48*x**2 + 23)\nExpanding the part (7*x**3 + 48*x**2 + 23) using the distributive property, and we got: 23*(-21*x**2) + (-21*x**2)*(48*x**2) + (-21*x**2)*(7*x**3)\nReplacing (-21*x**2)*(7*x**3 + 48*x**2 + 23) with 23*(-21*x**2) + (-21*x**2)*(48*x**2) + (-21*x**2)*(7*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 23*(-21)*x**2 + (-21*x**2)*(48*x**2) + (-21*x**2)*(7*x**3) + (48*x**2)*(-5) + (7*x**3)*(-5) + (9*x**3)*(7*x**3 + 48*x**2 + 23) - 115\nSimplifying the partial expression: (9*x**3)*(7*x**3 + 48*x**2 + 23)\nExpanding the part (7*x**3 + 48*x**2 + 23) using the distributive property, and we got: 23*(9*x**3) + (48*x**2)*(9*x**3) + (7*x**3)*(9*x**3)\nReplacing (9*x**3)*(7*x**3 + 48*x**2 + 23) with 23*(9*x**3) + (48*x**2)*(9*x**3) + (7*x**3)*(9*x**3) in the overall expression.\n#Step 5:\nCurrent expression: 23*9*x**3 + 23*(-21)*x**2 + (-21*x**2)*(48*x**2) + (-21*x**2)*(7*x**3) + (48*x**2)*(9*x**3) + (48*x**2)*(-5) + (7*x**3)*(9*x**3) + (7*x**3)*(-5) - 115\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (7*x**3)*-5 = -35*x**3\n (7*x**3)*(-21*x**2) = -147*x**5\n (7*x**3)*(9*x**3) = 63*x**6\n (48*x**2)*-5 = -240*x**2\n (48*x**2)*(-21*x**2) = -1008*x**4\n (48*x**2)*(9*x**3) = 432*x**5\n 23*-21*x**2 = -483*x**2\n 23*9*x**3 = 207*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 63*x**6 - 147*x**5 + 432*x**5 - 1008*x**4 - 35*x**3 + 207*x**3 - 483*x**2 - 240*x**2 - 115\nCombining like terms, got 63*x**6 + 285*x**5 - 1008*x**4 + 172*x**3 - 723*x**2 - 115\n#Step 7:\nCurrent expression: 63*x**6 + 285*x**5 - 1008*x**4 + 172*x**3 - 723*x**2 - 115\nNo more calculations needed.\n63*x**6 + 285*x**5 - 1008*x**4 + 172*x**3 - 723*x**2 - 115", "generated_answer": "63*x**6 + 285*x**5 - 1008*x**4 + 172*x**3 - 723*x**2 - 115", "step_length": 7} {"cot_id": "2aca338d1f07f131b4c8fb9fd75b8184dafd9f10287c592914d48e92169c0aec", "datapoint": {"question": "Simplify this expression: (7*y**2 - 7*y + 46)*(24*y**3 - 7*y**2 + 21*y - 19)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "168*y**5 - 217*y**4 + 1300*y**3 - 602*y**2 + 1099*y - 874", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1834, "polynomial_expr": "(7*y**2 - 7*y + 46)*(24*y**3 - 7*y**2 + 21*y - 19)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7*y**2 - 7*y + 46)*(24*y**3 - 7*y**2 + 21*y - 19)\nExpanding the part (7*y**2 - 7*y + 46) using the distributive property, and we got: (-7*y)*(24*y**3 - 7*y**2 + 21*y - 19) + (7*y**2)*(24*y**3 - 7*y**2 + 21*y - 19) + 46*(24*y**3 - 7*y**2 + 21*y - 19)\n#Step 2:\nCurrent expression: (-7*y)*(24*y**3 - 7*y**2 + 21*y - 19) + (7*y**2)*(24*y**3 - 7*y**2 + 21*y - 19) + 46*(24*y**3 - 7*y**2 + 21*y - 19)\nSimplifying the partial expression: 46*(24*y**3 - 7*y**2 + 21*y - 19)\nExpanding the part (24*y**3 - 7*y**2 + 21*y - 19) using the distributive property, and we got: (21*y)*46 - 7*y**2*46 + (24*y**3)*46 - 19*46\nReplacing 46*(24*y**3 - 7*y**2 + 21*y - 19) with (21*y)*46 - 7*y**2*46 + (24*y**3)*46 - 19*46 in the overall expression.\n#Step 3:\nCurrent expression: (-7*y)*(24*y**3 - 7*y**2 + 21*y - 19) + (21*y)*46 - 7*y**2*46 + (7*y**2)*(24*y**3 - 7*y**2 + 21*y - 19) + (24*y**3)*46 - 874\nSimplifying the partial expression: (-7*y)*(24*y**3 - 7*y**2 + 21*y - 19)\nExpanding the part (24*y**3 - 7*y**2 + 21*y - 19) using the distributive property, and we got: (-7*y)*(21*y) + (-7*y)*(-7*y**2) + (-7*y)*(24*y**3) - (-1)*133*y\nReplacing (-7*y)*(24*y**3 - 7*y**2 + 21*y - 19) with (-7*y)*(21*y) + (-7*y)*(-7*y**2) + (-7*y)*(24*y**3) - (-1)*133*y in the overall expression.\n#Step 4:\nCurrent expression: (-7*y)*(21*y) + (-7*y)*(-7*y**2) + (-7*y)*(24*y**3) - 19*(-7)*y + (21*y)*46 - 7*y**2*46 + (7*y**2)*(24*y**3 - 7*y**2 + 21*y - 19) + (24*y**3)*46 - 874\nSimplifying the partial expression: (7*y**2)*(24*y**3 - 7*y**2 + 21*y - 19)\nExpanding the part (24*y**3 - 7*y**2 + 21*y - 19) using the distributive property, and we got: -133*y**2 + (21*y)*(7*y**2) + (-7*y**2)*(7*y**2) + (7*y**2)*(24*y**3)\nReplacing (7*y**2)*(24*y**3 - 7*y**2 + 21*y - 19) with -133*y**2 + (21*y)*(7*y**2) + (-7*y**2)*(7*y**2) + (7*y**2)*(24*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-7*y)*(21*y) + (-7*y)*(-7*y**2) + (-7*y)*(24*y**3) - 19*7*y**2 - 19*(-7)*y + (21*y)*(7*y**2) + (21*y)*46 + (-7*y**2)*(7*y**2) - 7*y**2*46 + (7*y**2)*(24*y**3) + (24*y**3)*46 - 874\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-7*y**2)*46 = -322*y**2\n (-7*y**2)*(-7*y) = 49*y**3\n (-7*y**2)*(7*y**2) = -49*y**4\n (21*y)*46 = 966*y\n (21*y)*(-7*y) = -147*y**2\n (21*y)*(7*y**2) = 147*y**3\n (24*y**3)*46 = 1104*y**3\n (24*y**3)*(-7*y) = -168*y**4\n (24*y**3)*(7*y**2) = 168*y**5\n -19*-7*y = 133*y\n -19*7*y**2 = -133*y**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 168*y**5 - 168*y**4 - 49*y**4 + 49*y**3 + 147*y**3 + 1104*y**3 - 322*y**2 - 147*y**2 - 133*y**2 + 133*y + 966*y - 874\nCombining like terms, got 168*y**5 - 217*y**4 + 1300*y**3 - 602*y**2 + 1099*y - 874\n#Step 7:\nCurrent expression: 168*y**5 - 217*y**4 + 1300*y**3 - 602*y**2 + 1099*y - 874\nNo more calculations needed.\n168*y**5 - 217*y**4 + 1300*y**3 - 602*y**2 + 1099*y - 874", "generated_answer": "168*y**5 - 217*y**4 + 1300*y**3 - 602*y**2 + 1099*y - 874", "step_length": 7} {"cot_id": "48de997d5bf1aa4059409db9d88a3dd4521ffbfb40c1791682111ae3d40c3b98", "datapoint": {"question": "Calculate the following: (-25*x**3 + 5*x**2 - 42)*(23*x**3 + 11*x**2 + 18)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-575*x**6 - 160*x**5 + 55*x**4 - 1416*x**3 - 372*x**2 - 756", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1835, "polynomial_expr": "(-25*x**3 + 5*x**2 - 42)*(23*x**3 + 11*x**2 + 18)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-25*x**3 + 5*x**2 - 42)*(23*x**3 + 11*x**2 + 18)\nExpanding the part (-25*x**3 + 5*x**2 - 42) using the distributive property, and we got: (5*x**2)*(23*x**3 + 11*x**2 + 18) + (-25*x**3)*(23*x**3 + 11*x**2 + 18) - 42*(23*x**3 + 11*x**2 + 18)\n#Step 2:\nCurrent expression: (5*x**2)*(23*x**3 + 11*x**2 + 18) + (-25*x**3)*(23*x**3 + 11*x**2 + 18) - 42*(23*x**3 + 11*x**2 + 18)\nSimplifying the partial expression: -42*(23*x**3 + 11*x**2 + 18)\nExpanding the part (23*x**3 + 11*x**2 + 18) using the distributive property, and we got: (11*x**2)*(-42) + (23*x**3)*(-42) + 18*(-42)\nReplacing -42*(23*x**3 + 11*x**2 + 18) with (11*x**2)*(-42) + (23*x**3)*(-42) + 18*(-42) in the overall expression.\n#Step 3:\nCurrent expression: (5*x**2)*(23*x**3 + 11*x**2 + 18) + (11*x**2)*(-42) + (-25*x**3)*(23*x**3 + 11*x**2 + 18) + (23*x**3)*(-42) - 756\nSimplifying the partial expression: (-25*x**3)*(23*x**3 + 11*x**2 + 18)\nExpanding the part (23*x**3 + 11*x**2 + 18) using the distributive property, and we got: 18*(-25*x**3) + (11*x**2)*(-25*x**3) + (-25*x**3)*(23*x**3)\nReplacing (-25*x**3)*(23*x**3 + 11*x**2 + 18) with 18*(-25*x**3) + (11*x**2)*(-25*x**3) + (-25*x**3)*(23*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 18*(-25)*x**3 + (5*x**2)*(23*x**3 + 11*x**2 + 18) + (11*x**2)*(-25*x**3) + (11*x**2)*(-42) + (-25*x**3)*(23*x**3) + (23*x**3)*(-42) - 756\nSimplifying the partial expression: (5*x**2)*(23*x**3 + 11*x**2 + 18)\nExpanding the part (23*x**3 + 11*x**2 + 18) using the distributive property, and we got: 18*(5*x**2) + (5*x**2)*(11*x**2) + (5*x**2)*(23*x**3)\nReplacing (5*x**2)*(23*x**3 + 11*x**2 + 18) with 18*(5*x**2) + (5*x**2)*(11*x**2) + (5*x**2)*(23*x**3) in the overall expression.\n#Step 5:\nCurrent expression: 18*(-25)*x**3 + 18*5*x**2 + (5*x**2)*(11*x**2) + (5*x**2)*(23*x**3) + (11*x**2)*(-25*x**3) + (11*x**2)*(-42) + (-25*x**3)*(23*x**3) + (23*x**3)*(-42) - 756\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (11*x**2)*-42 = -462*x**2\n (11*x**2)*(-25*x**3) = -275*x**5\n (11*x**2)*(5*x**2) = 55*x**4\n (23*x**3)*-42 = -966*x**3\n (23*x**3)*(-25*x**3) = -575*x**6\n (23*x**3)*(5*x**2) = 115*x**5\n 18*-25*x**3 = -450*x**3\n 18*5*x**2 = 90*x**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -575*x**6 - 275*x**5 + 115*x**5 + 55*x**4 - 966*x**3 - 450*x**3 - 462*x**2 + 90*x**2 - 756\nCombining like terms, got -575*x**6 - 160*x**5 + 55*x**4 - 1416*x**3 - 372*x**2 - 756\n#Step 7:\nCurrent expression: -575*x**6 - 160*x**5 + 55*x**4 - 1416*x**3 - 372*x**2 - 756\nNo more calculations needed.\n-575*x**6 - 160*x**5 + 55*x**4 - 1416*x**3 - 372*x**2 - 756", "generated_answer": "-575*x**6 - 160*x**5 + 55*x**4 - 1416*x**3 - 372*x**2 - 756", "step_length": 7} {"cot_id": "a20f72c39367217d449f97805ca6846f3351333640150dfb24b0ad0c717101ef", "datapoint": {"question": "Calculate the following: -73*z*(-19*z**3 - 53*z + 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1387*z**4 + 3869*z**2 - 3431*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1836, "polynomial_expr": "-73*z*(-19*z**3 - 53*z + 47)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -73*z*(-19*z**3 - 53*z + 47)\nExpanding the part (-19*z**3 - 53*z + 47) using the distributive property, and we got: (-73*z)*(-53*z) + (-73*z)*(-19*z**3) + 47*(-73*z)\n#Step 2:\nCurrent expression: (-73*z)*(-53*z) + (-73*z)*(-19*z**3) + 47*(-73*z)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 47*(-73*z) = -3431*z\n (-53*z)*(-73*z) = 3869*z**2\n (-19*z**3)*(-73*z) = 1387*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1387*z**4 + 3869*z**2 - 3431*z\nNo more calculations needed.\n1387*z**4 + 3869*z**2 - 3431*z", "generated_answer": "1387*z**4 + 3869*z**2 - 3431*z", "step_length": 3} {"cot_id": "fc91aa7d2f45a4833e9fdb6ebbedad306fc0c08fd9c77c3e237d4b0da2d8cbed", "datapoint": {"question": "Calculate the following: -92*z**3*(-36*z**3 - 23*z**2 + 35*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "3312*z**6 + 2116*z**5 - 3220*z**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1837, "polynomial_expr": "-92*z**3*(-36*z**3 - 23*z**2 + 35*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -92*z**3*(-36*z**3 - 23*z**2 + 35*z)\nExpanding the part (-36*z**3 - 23*z**2 + 35*z) using the distributive property, and we got: (35*z)*(-92*z**3) + (-23*z**2)*(-92*z**3) + (-92*z**3)*(-36*z**3)\n#Step 2:\nCurrent expression: (35*z)*(-92*z**3) + (-23*z**2)*(-92*z**3) + (-92*z**3)*(-36*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*z**3)*(-92*z**3) = 3312*z**6\n (-23*z**2)*(-92*z**3) = 2116*z**5\n (35*z)*(-92*z**3) = -3220*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 3312*z**6 + 2116*z**5 - 3220*z**4\nNo more calculations needed.\n3312*z**6 + 2116*z**5 - 3220*z**4", "generated_answer": "3312*z**6 + 2116*z**5 - 3220*z**4", "step_length": 3} {"cot_id": "4f1bb45117bccf4ed15549ca1c7015d5d363562a1a732dfeb088db2fc4b73879", "datapoint": {"question": "Simplify this expression: (-56*z**3 - 4*z)*(23*z**2 + 31*z - 80)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1288*z**5 - 1736*z**4 + 4388*z**3 - 124*z**2 + 320*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1838, "polynomial_expr": "(-56*z**3 - 4*z)*(23*z**2 + 31*z - 80)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-56*z**3 - 4*z)*(23*z**2 + 31*z - 80)\nExpanding the part (-56*z**3 - 4*z) using the distributive property, and we got: (-4*z)*(23*z**2 + 31*z - 80) + (-56*z**3)*(23*z**2 + 31*z - 80)\n#Step 2:\nCurrent expression: (-4*z)*(23*z**2 + 31*z - 80) + (-56*z**3)*(23*z**2 + 31*z - 80)\nSimplifying the partial expression: (-56*z**3)*(23*z**2 + 31*z - 80)\nExpanding the part (23*z**2 + 31*z - 80) using the distributive property, and we got: -(-1)*4480*z**3 + (31*z)*(-56*z**3) + (23*z**2)*(-56*z**3)\nReplacing (-56*z**3)*(23*z**2 + 31*z - 80) with -(-1)*4480*z**3 + (31*z)*(-56*z**3) + (23*z**2)*(-56*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-4*z)*(23*z**2 + 31*z - 80) - 80*(-56)*z**3 + (31*z)*(-56*z**3) + (23*z**2)*(-56*z**3)\nSimplifying the partial expression: (-4*z)*(23*z**2 + 31*z - 80)\nExpanding the part (23*z**2 + 31*z - 80) using the distributive property, and we got: (-4*z)*(31*z) + (-4*z)*(23*z**2) - (-1)*320*z\nReplacing (-4*z)*(23*z**2 + 31*z - 80) with (-4*z)*(31*z) + (-4*z)*(23*z**2) - (-1)*320*z in the overall expression.\n#Step 4:\nCurrent expression: (-4*z)*(31*z) + (-4*z)*(23*z**2) - 80*(-56)*z**3 - 80*(-4)*z + (31*z)*(-56*z**3) + (23*z**2)*(-56*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (23*z**2)*(-56*z**3) = -1288*z**5\n (23*z**2)*(-4*z) = -92*z**3\n (31*z)*(-56*z**3) = -1736*z**4\n (31*z)*(-4*z) = -124*z**2\n -80*-56*z**3 = 4480*z**3\n -80*-4*z = 320*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1288*z**5 - 1736*z**4 - 92*z**3 + 4480*z**3 - 124*z**2 + 320*z\nCombining like terms, got -1288*z**5 - 1736*z**4 + 4388*z**3 - 124*z**2 + 320*z\n#Step 6:\nCurrent expression: -1288*z**5 - 1736*z**4 + 4388*z**3 - 124*z**2 + 320*z\nNo more calculations needed.\n-1288*z**5 - 1736*z**4 + 4388*z**3 - 124*z**2 + 320*z", "generated_answer": "-1288*z**5 - 1736*z**4 + 4388*z**3 - 124*z**2 + 320*z", "step_length": 6} {"cot_id": "225f0476f73e1c04bb359d677b71dde9fba68935cc31854320d6917ec20894de", "datapoint": {"question": "Calculate the following: (-27*y**3 - 37*y**2 - 55*y)*(-7*y**3 - 20*y - 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "189*y**6 + 259*y**5 + 925*y**4 + 1604*y**3 + 2284*y**2 + 1760*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1839, "polynomial_expr": "(-27*y**3 - 37*y**2 - 55*y)*(-7*y**3 - 20*y - 32)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-27*y**3 - 37*y**2 - 55*y)*(-7*y**3 - 20*y - 32)\nExpanding the part (-7*y**3 - 20*y - 32) using the distributive property, and we got: (-20*y)*(-27*y**3 - 37*y**2 - 55*y) + (-7*y**3)*(-27*y**3 - 37*y**2 - 55*y) - 32*(-27*y**3 - 37*y**2 - 55*y)\n#Step 2:\nCurrent expression: (-20*y)*(-27*y**3 - 37*y**2 - 55*y) + (-7*y**3)*(-27*y**3 - 37*y**2 - 55*y) - 32*(-27*y**3 - 37*y**2 - 55*y)\nSimplifying the partial expression: -32*(-27*y**3 - 37*y**2 - 55*y)\nExpanding the part (-27*y**3 - 37*y**2 - 55*y) using the distributive property, and we got: -55*y*(-32) - 37*y**2*(-32) - 27*y**3*(-32)\nReplacing -32*(-27*y**3 - 37*y**2 - 55*y) with -55*y*(-32) - 37*y**2*(-32) - 27*y**3*(-32) in the overall expression.\n#Step 3:\nCurrent expression: -55*y*(-32) + (-20*y)*(-27*y**3 - 37*y**2 - 55*y) - 37*y**2*(-32) - 27*y**3*(-32) + (-7*y**3)*(-27*y**3 - 37*y**2 - 55*y)\nSimplifying the partial expression: (-20*y)*(-27*y**3 - 37*y**2 - 55*y)\nExpanding the part (-27*y**3 - 37*y**2 - 55*y) using the distributive property, and we got: (-55*y)*(-20*y) + (-20*y)*(-37*y**2) + (-20*y)*(-27*y**3)\nReplacing (-20*y)*(-27*y**3 - 37*y**2 - 55*y) with (-55*y)*(-20*y) + (-20*y)*(-37*y**2) + (-20*y)*(-27*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-55*y)*(-20*y) - 55*y*(-32) + (-20*y)*(-37*y**2) + (-20*y)*(-27*y**3) - 37*y**2*(-32) - 27*y**3*(-32) + (-7*y**3)*(-27*y**3 - 37*y**2 - 55*y)\nSimplifying the partial expression: (-7*y**3)*(-27*y**3 - 37*y**2 - 55*y)\nExpanding the part (-27*y**3 - 37*y**2 - 55*y) using the distributive property, and we got: (-55*y)*(-7*y**3) + (-37*y**2)*(-7*y**3) + (-27*y**3)*(-7*y**3)\nReplacing (-7*y**3)*(-27*y**3 - 37*y**2 - 55*y) with (-55*y)*(-7*y**3) + (-37*y**2)*(-7*y**3) + (-27*y**3)*(-7*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-55*y)*(-20*y) + (-55*y)*(-7*y**3) - 55*y*(-32) + (-20*y)*(-37*y**2) + (-20*y)*(-27*y**3) + (-37*y**2)*(-7*y**3) - 37*y**2*(-32) + (-27*y**3)*(-7*y**3) - 27*y**3*(-32)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-55*y)*-32 = 1760*y\n (-55*y)*(-20*y) = 1100*y**2\n (-55*y)*(-7*y**3) = 385*y**4\n (-37*y**2)*-32 = 1184*y**2\n (-37*y**2)*(-20*y) = 740*y**3\n (-37*y**2)*(-7*y**3) = 259*y**5\n (-27*y**3)*-32 = 864*y**3\n (-27*y**3)*(-20*y) = 540*y**4\n (-27*y**3)*(-7*y**3) = 189*y**6\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 189*y**6 + 259*y**5 + 385*y**4 + 540*y**4 + 740*y**3 + 864*y**3 + 1100*y**2 + 1184*y**2 + 1760*y\nCombining like terms, got 189*y**6 + 259*y**5 + 925*y**4 + 1604*y**3 + 2284*y**2 + 1760*y\n#Step 7:\nCurrent expression: 189*y**6 + 259*y**5 + 925*y**4 + 1604*y**3 + 2284*y**2 + 1760*y\nNo more calculations needed.\n189*y**6 + 259*y**5 + 925*y**4 + 1604*y**3 + 2284*y**2 + 1760*y", "generated_answer": "189*y**6 + 259*y**5 + 925*y**4 + 1604*y**3 + 2284*y**2 + 1760*y", "step_length": 7} {"cot_id": "e02c92f43cbd45f313ecf30330e9b5a1e2c60200822a87688e5b07fc0128359a", "datapoint": {"question": "Calculate the following: (-7*y**2 - 41*y)*(-16*y**3 - 46*y**2 + 9)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "112*y**5 + 978*y**4 + 1886*y**3 - 63*y**2 - 369*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1840, "polynomial_expr": "(-7*y**2 - 41*y)*(-16*y**3 - 46*y**2 + 9)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-7*y**2 - 41*y)*(-16*y**3 - 46*y**2 + 9)\nExpanding the part (-7*y**2 - 41*y) using the distributive property, and we got: (-41*y)*(-16*y**3 - 46*y**2 + 9) + (-7*y**2)*(-16*y**3 - 46*y**2 + 9)\n#Step 2:\nCurrent expression: (-41*y)*(-16*y**3 - 46*y**2 + 9) + (-7*y**2)*(-16*y**3 - 46*y**2 + 9)\nSimplifying the partial expression: (-41*y)*(-16*y**3 - 46*y**2 + 9)\nExpanding the part (-16*y**3 - 46*y**2 + 9) using the distributive property, and we got: (-41*y)*(-46*y**2) + (-41*y)*(-16*y**3) + 9*(-41*y)\nReplacing (-41*y)*(-16*y**3 - 46*y**2 + 9) with (-41*y)*(-46*y**2) + (-41*y)*(-16*y**3) + 9*(-41*y) in the overall expression.\n#Step 3:\nCurrent expression: (-41*y)*(-46*y**2) + (-41*y)*(-16*y**3) + 9*(-41)*y + (-7*y**2)*(-16*y**3 - 46*y**2 + 9)\nSimplifying the partial expression: (-7*y**2)*(-16*y**3 - 46*y**2 + 9)\nExpanding the part (-16*y**3 - 46*y**2 + 9) using the distributive property, and we got: 9*(-7*y**2) + (-46*y**2)*(-7*y**2) + (-7*y**2)*(-16*y**3)\nReplacing (-7*y**2)*(-16*y**3 - 46*y**2 + 9) with 9*(-7*y**2) + (-46*y**2)*(-7*y**2) + (-7*y**2)*(-16*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-41*y)*(-46*y**2) + (-41*y)*(-16*y**3) + 9*(-7)*y**2 + 9*(-41)*y + (-46*y**2)*(-7*y**2) + (-7*y**2)*(-16*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*y**2)*(-41*y) = 1886*y**3\n (-46*y**2)*(-7*y**2) = 322*y**4\n (-16*y**3)*(-41*y) = 656*y**4\n (-16*y**3)*(-7*y**2) = 112*y**5\n 9*-41*y = -369*y\n 9*-7*y**2 = -63*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 112*y**5 + 322*y**4 + 656*y**4 + 1886*y**3 - 63*y**2 - 369*y\nCombining like terms, got 112*y**5 + 978*y**4 + 1886*y**3 - 63*y**2 - 369*y\n#Step 6:\nCurrent expression: 112*y**5 + 978*y**4 + 1886*y**3 - 63*y**2 - 369*y\nNo more calculations needed.\n112*y**5 + 978*y**4 + 1886*y**3 - 63*y**2 - 369*y", "generated_answer": "112*y**5 + 978*y**4 + 1886*y**3 - 63*y**2 - 369*y", "step_length": 6} {"cot_id": "9fd5f7267861fc7de94cd71c07d5bffa2c826f1e52149b3d2daef05c543249ed", "datapoint": {"question": "Calculate the following: 68*z*(-34*z**3 - 12*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2312*z**4 - 816*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1841, "polynomial_expr": "68*z*(-34*z**3 - 12*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 68*z*(-34*z**3 - 12*z)\nExpanding the part (-34*z**3 - 12*z) using the distributive property, and we got: (-12*z)*(68*z) + (68*z)*(-34*z**3)\n#Step 2:\nCurrent expression: (-12*z)*(68*z) + (68*z)*(-34*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*z**3)*(68*z) = -2312*z**4\n (-12*z)*(68*z) = -816*z**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -2312*z**4 - 816*z**2\nNo more calculations needed.\n-2312*z**4 - 816*z**2", "generated_answer": "-2312*z**4 - 816*z**2", "step_length": 3} {"cot_id": "22b837a456476d621fa9fbf8f8bd3fdce3c8d72a360857b61d86d19025813881", "datapoint": {"question": "Simplify this expression: (55 - 31*x**2)*(11*x**2 + 19*x + 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-341*x**4 - 589*x**3 - 263*x**2 + 1045*x + 1540", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1842, "polynomial_expr": "(55 - 31*x**2)*(11*x**2 + 19*x + 28)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (55 - 31*x**2)*(11*x**2 + 19*x + 28)\nExpanding the part (55 - 31*x**2) using the distributive property, and we got: (-31*x**2)*(11*x**2 + 19*x + 28) + 55*(11*x**2 + 19*x + 28)\n#Step 2:\nCurrent expression: (-31*x**2)*(11*x**2 + 19*x + 28) + 55*(11*x**2 + 19*x + 28)\nSimplifying the partial expression: 55*(11*x**2 + 19*x + 28)\nExpanding the part (11*x**2 + 19*x + 28) using the distributive property, and we got: (19*x)*55 + (11*x**2)*55 + 28*55\nReplacing 55*(11*x**2 + 19*x + 28) with (19*x)*55 + (11*x**2)*55 + 28*55 in the overall expression.\n#Step 3:\nCurrent expression: (19*x)*55 + (-31*x**2)*(11*x**2 + 19*x + 28) + (11*x**2)*55 + 1540\nSimplifying the partial expression: (-31*x**2)*(11*x**2 + 19*x + 28)\nExpanding the part (11*x**2 + 19*x + 28) using the distributive property, and we got: 28*(-31*x**2) + (19*x)*(-31*x**2) + (-31*x**2)*(11*x**2)\nReplacing (-31*x**2)*(11*x**2 + 19*x + 28) with 28*(-31*x**2) + (19*x)*(-31*x**2) + (-31*x**2)*(11*x**2) in the overall expression.\n#Step 4:\nCurrent expression: 28*(-31)*x**2 + (19*x)*(-31*x**2) + (19*x)*55 + (-31*x**2)*(11*x**2) + (11*x**2)*55 + 1540\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (11*x**2)*55 = 605*x**2\n (11*x**2)*(-31*x**2) = -341*x**4\n (19*x)*55 = 1045*x\n (19*x)*(-31*x**2) = -589*x**3\n 28*-31*x**2 = -868*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -341*x**4 - 589*x**3 - 868*x**2 + 605*x**2 + 1045*x + 1540\nCombining like terms, got -341*x**4 - 589*x**3 - 263*x**2 + 1045*x + 1540\n#Step 6:\nCurrent expression: -341*x**4 - 589*x**3 - 263*x**2 + 1045*x + 1540\nNo more calculations needed.\n-341*x**4 - 589*x**3 - 263*x**2 + 1045*x + 1540", "generated_answer": "-341*x**4 - 589*x**3 - 263*x**2 + 1045*x + 1540", "step_length": 6} {"cot_id": "7dab6fc580d3a10bff88bd17286b4aa5c74c79dc482f8bfb6a05ac1de6eebfe5", "datapoint": {"question": "Calculate the following: (20*z**3 + z)*(24*z**3 + 42*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "480*z**6 + 864*z**4 + 42*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1843, "polynomial_expr": "(20*z**3 + z)*(24*z**3 + 42*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (20*z**3 + z)*(24*z**3 + 42*z)\nExpanding the part (20*z**3 + z) using the distributive property, and we got: z*(24*z**3 + 42*z) + (20*z**3)*(24*z**3 + 42*z)\n#Step 2:\nCurrent expression: z*(24*z**3 + 42*z) + (20*z**3)*(24*z**3 + 42*z)\nSimplifying the partial expression: z*(24*z**3 + 42*z)\nExpanding the part (24*z**3 + 42*z) using the distributive property, and we got: z*(42*z) + z*(24*z**3)\nReplacing z*(24*z**3 + 42*z) with z*(42*z) + z*(24*z**3) in the overall expression.\n#Step 3:\nCurrent expression: z*(42*z) + z*(24*z**3) + (20*z**3)*(24*z**3 + 42*z)\nSimplifying the partial expression: (20*z**3)*(24*z**3 + 42*z)\nExpanding the part (24*z**3 + 42*z) using the distributive property, and we got: (42*z)*(20*z**3) + (20*z**3)*(24*z**3)\nReplacing (20*z**3)*(24*z**3 + 42*z) with (42*z)*(20*z**3) + (20*z**3)*(24*z**3) in the overall expression.\n#Step 4:\nCurrent expression: z*(42*z) + z*(24*z**3) + (42*z)*(20*z**3) + (20*z**3)*(24*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (24*z**3)*z = 24*z**4\n (24*z**3)*(20*z**3) = 480*z**6\n (42*z)*z = 42*z**2\n (42*z)*(20*z**3) = 840*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 480*z**6 + 24*z**4 + 840*z**4 + 42*z**2\nCombining like terms, got 480*z**6 + 864*z**4 + 42*z**2\n#Step 6:\nCurrent expression: 480*z**6 + 864*z**4 + 42*z**2\nNo more calculations needed.\n480*z**6 + 864*z**4 + 42*z**2", "generated_answer": "480*z**6 + 864*z**4 + 42*z**2", "step_length": 6} {"cot_id": "31d473f76668568c3220e7c3d408d28cc1c35debf2107fa6b7e46b75e90563b3", "datapoint": {"question": "Calculate the following: (24*x**3 + 30*x)*(-30*x**3 - 10*x**2 - 13*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-720*x**6 - 240*x**5 - 1212*x**4 - 300*x**3 - 390*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1844, "polynomial_expr": "(24*x**3 + 30*x)*(-30*x**3 - 10*x**2 - 13*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (24*x**3 + 30*x)*(-30*x**3 - 10*x**2 - 13*x)\nExpanding the part (24*x**3 + 30*x) using the distributive property, and we got: (30*x)*(-30*x**3 - 10*x**2 - 13*x) + (24*x**3)*(-30*x**3 - 10*x**2 - 13*x)\n#Step 2:\nCurrent expression: (30*x)*(-30*x**3 - 10*x**2 - 13*x) + (24*x**3)*(-30*x**3 - 10*x**2 - 13*x)\nSimplifying the partial expression: (24*x**3)*(-30*x**3 - 10*x**2 - 13*x)\nExpanding the part (-30*x**3 - 10*x**2 - 13*x) using the distributive property, and we got: (-13*x)*(24*x**3) + (-10*x**2)*(24*x**3) + (-30*x**3)*(24*x**3)\nReplacing (24*x**3)*(-30*x**3 - 10*x**2 - 13*x) with (-13*x)*(24*x**3) + (-10*x**2)*(24*x**3) + (-30*x**3)*(24*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-13*x)*(24*x**3) + (30*x)*(-30*x**3 - 10*x**2 - 13*x) + (-10*x**2)*(24*x**3) + (-30*x**3)*(24*x**3)\nSimplifying the partial expression: (30*x)*(-30*x**3 - 10*x**2 - 13*x)\nExpanding the part (-30*x**3 - 10*x**2 - 13*x) using the distributive property, and we got: (-13*x)*(30*x) + (30*x)*(-10*x**2) + (30*x)*(-30*x**3)\nReplacing (30*x)*(-30*x**3 - 10*x**2 - 13*x) with (-13*x)*(30*x) + (30*x)*(-10*x**2) + (30*x)*(-30*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-13*x)*(30*x) + (-13*x)*(24*x**3) + (30*x)*(-10*x**2) + (30*x)*(-30*x**3) + (-10*x**2)*(24*x**3) + (-30*x**3)*(24*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*x**3)*(24*x**3) = -720*x**6\n (-30*x**3)*(30*x) = -900*x**4\n (-13*x)*(24*x**3) = -312*x**4\n (-13*x)*(30*x) = -390*x**2\n (-10*x**2)*(24*x**3) = -240*x**5\n (-10*x**2)*(30*x) = -300*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -720*x**6 - 240*x**5 - 900*x**4 - 312*x**4 - 300*x**3 - 390*x**2\nCombining like terms, got -720*x**6 - 240*x**5 - 1212*x**4 - 300*x**3 - 390*x**2\n#Step 6:\nCurrent expression: -720*x**6 - 240*x**5 - 1212*x**4 - 300*x**3 - 390*x**2\nNo more calculations needed.\n-720*x**6 - 240*x**5 - 1212*x**4 - 300*x**3 - 390*x**2", "generated_answer": "-720*x**6 - 240*x**5 - 1212*x**4 - 300*x**3 - 390*x**2", "step_length": 6} {"cot_id": "043e58dc721362d6a739cb81a9a338411d07672ea9b87f448eec118e8704091a", "datapoint": {"question": "Simplify this expression: -5*y*(-34*y**3 - 20*y**2 - 18*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "170*y**4 + 100*y**3 + 90*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1845, "polynomial_expr": "-5*y*(-34*y**3 - 20*y**2 - 18*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -5*y*(-34*y**3 - 20*y**2 - 18*y)\nExpanding the part (-34*y**3 - 20*y**2 - 18*y) using the distributive property, and we got: (-18*y)*(-5*y) + (-5*y)*(-20*y**2) + (-5*y)*(-34*y**3)\n#Step 2:\nCurrent expression: (-18*y)*(-5*y) + (-5*y)*(-20*y**2) + (-5*y)*(-34*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*y**3)*(-5*y) = 170*y**4\n (-20*y**2)*(-5*y) = 100*y**3\n (-18*y)*(-5*y) = 90*y**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 170*y**4 + 100*y**3 + 90*y**2\nNo more calculations needed.\n170*y**4 + 100*y**3 + 90*y**2", "generated_answer": "170*y**4 + 100*y**3 + 90*y**2", "step_length": 3} {"cot_id": "05811badfac6251c4d231d5648617aaf55e31c754e504615196b8394370845d4", "datapoint": {"question": "Calculate the following: (-10*z**2 - 11*z)*(-6*z**3 - 36*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "60*z**5 + 66*z**4 + 360*z**3 + 396*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1846, "polynomial_expr": "(-10*z**2 - 11*z)*(-6*z**3 - 36*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-10*z**2 - 11*z)*(-6*z**3 - 36*z)\nExpanding the part (-6*z**3 - 36*z) using the distributive property, and we got: (-36*z)*(-10*z**2 - 11*z) + (-6*z**3)*(-10*z**2 - 11*z)\n#Step 2:\nCurrent expression: (-36*z)*(-10*z**2 - 11*z) + (-6*z**3)*(-10*z**2 - 11*z)\nSimplifying the partial expression: (-36*z)*(-10*z**2 - 11*z)\nExpanding the part (-10*z**2 - 11*z) using the distributive property, and we got: (-36*z)*(-11*z) + (-36*z)*(-10*z**2)\nReplacing (-36*z)*(-10*z**2 - 11*z) with (-36*z)*(-11*z) + (-36*z)*(-10*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-36*z)*(-11*z) + (-36*z)*(-10*z**2) + (-6*z**3)*(-10*z**2 - 11*z)\nSimplifying the partial expression: (-6*z**3)*(-10*z**2 - 11*z)\nExpanding the part (-10*z**2 - 11*z) using the distributive property, and we got: (-11*z)*(-6*z**3) + (-10*z**2)*(-6*z**3)\nReplacing (-6*z**3)*(-10*z**2 - 11*z) with (-11*z)*(-6*z**3) + (-10*z**2)*(-6*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-36*z)*(-11*z) + (-36*z)*(-10*z**2) + (-11*z)*(-6*z**3) + (-10*z**2)*(-6*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*z)*(-36*z) = 396*z**2\n (-11*z)*(-6*z**3) = 66*z**4\n (-10*z**2)*(-36*z) = 360*z**3\n (-10*z**2)*(-6*z**3) = 60*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 60*z**5 + 66*z**4 + 360*z**3 + 396*z**2\nNo more calculations needed.\n60*z**5 + 66*z**4 + 360*z**3 + 396*z**2", "generated_answer": "60*z**5 + 66*z**4 + 360*z**3 + 396*z**2", "step_length": 5} {"cot_id": "8308b846c11af9c2d81e5fcaf45e8e5bf6ee9bb26da8dc69b089ec0800dfefa1", "datapoint": {"question": "Calculate the following: -44*y*(-36*y**3 - 2*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1584*y**4 + 88*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1847, "polynomial_expr": "-44*y*(-36*y**3 - 2*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -44*y*(-36*y**3 - 2*y**2)\nExpanding the part (-36*y**3 - 2*y**2) using the distributive property, and we got: (-44*y)*(-2*y**2) + (-44*y)*(-36*y**3)\n#Step 2:\nCurrent expression: (-44*y)*(-2*y**2) + (-44*y)*(-36*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*y**3)*(-44*y) = 1584*y**4\n (-2*y**2)*(-44*y) = 88*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1584*y**4 + 88*y**3\nNo more calculations needed.\n1584*y**4 + 88*y**3", "generated_answer": "1584*y**4 + 88*y**3", "step_length": 3} {"cot_id": "48893c6ea7266b4f636b9255910e0d31aac55591af7c0788d6b104c28d351461", "datapoint": {"question": "Simplify this expression: (-16*y - 23)*(20*y**2 - 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-320*y**3 - 460*y**2 + 224*y + 322", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1848, "polynomial_expr": "(-16*y - 23)*(20*y**2 - 14)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-16*y - 23)*(20*y**2 - 14)\nExpanding the part (-16*y - 23) using the distributive property, and we got: (-16*y)*(20*y**2 - 14) - 23*(20*y**2 - 14)\n#Step 2:\nCurrent expression: (-16*y)*(20*y**2 - 14) - 23*(20*y**2 - 14)\nSimplifying the partial expression: -23*(20*y**2 - 14)\nExpanding the part (20*y**2 - 14) using the distributive property, and we got: (20*y**2)*(-23) - 14*(-23)\nReplacing -23*(20*y**2 - 14) with (20*y**2)*(-23) - 14*(-23) in the overall expression.\n#Step 3:\nCurrent expression: (-16*y)*(20*y**2 - 14) + (20*y**2)*(-23) + 322\nSimplifying the partial expression: (-16*y)*(20*y**2 - 14)\nExpanding the part (20*y**2 - 14) using the distributive property, and we got: (-16*y)*(20*y**2) - (-1)*224*y\nReplacing (-16*y)*(20*y**2 - 14) with (-16*y)*(20*y**2) - (-1)*224*y in the overall expression.\n#Step 4:\nCurrent expression: (-16*y)*(20*y**2) - 14*(-16)*y + (20*y**2)*(-23) + 322\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (20*y**2)*-23 = -460*y**2\n (20*y**2)*(-16*y) = -320*y**3\n -14*-16*y = 224*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -320*y**3 - 460*y**2 + 224*y + 322\nNo more calculations needed.\n-320*y**3 - 460*y**2 + 224*y + 322", "generated_answer": "-320*y**3 - 460*y**2 + 224*y + 322", "step_length": 5} {"cot_id": "4f726bb3324cc57311be298f1b679333eeeda01aa529bba270bca62cea31e334", "datapoint": {"question": "Simplify this expression: (40 - 20*z**2)*(51*z**3 + 36*z**2 + 5)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1020*z**5 - 720*z**4 + 2040*z**3 + 1340*z**2 + 200", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1849, "polynomial_expr": "(40 - 20*z**2)*(51*z**3 + 36*z**2 + 5)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (40 - 20*z**2)*(51*z**3 + 36*z**2 + 5)\nExpanding the part (40 - 20*z**2) using the distributive property, and we got: (-20*z**2)*(51*z**3 + 36*z**2 + 5) + 40*(51*z**3 + 36*z**2 + 5)\n#Step 2:\nCurrent expression: (-20*z**2)*(51*z**3 + 36*z**2 + 5) + 40*(51*z**3 + 36*z**2 + 5)\nSimplifying the partial expression: 40*(51*z**3 + 36*z**2 + 5)\nExpanding the part (51*z**3 + 36*z**2 + 5) using the distributive property, and we got: (36*z**2)*40 + (51*z**3)*40 + 5*40\nReplacing 40*(51*z**3 + 36*z**2 + 5) with (36*z**2)*40 + (51*z**3)*40 + 5*40 in the overall expression.\n#Step 3:\nCurrent expression: (-20*z**2)*(51*z**3 + 36*z**2 + 5) + (36*z**2)*40 + (51*z**3)*40 + 200\nSimplifying the partial expression: (-20*z**2)*(51*z**3 + 36*z**2 + 5)\nExpanding the part (51*z**3 + 36*z**2 + 5) using the distributive property, and we got: 5*(-20*z**2) + (-20*z**2)*(36*z**2) + (-20*z**2)*(51*z**3)\nReplacing (-20*z**2)*(51*z**3 + 36*z**2 + 5) with 5*(-20*z**2) + (-20*z**2)*(36*z**2) + (-20*z**2)*(51*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 5*(-20)*z**2 + (-20*z**2)*(36*z**2) + (-20*z**2)*(51*z**3) + (36*z**2)*40 + (51*z**3)*40 + 200\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (36*z**2)*40 = 1440*z**2\n (36*z**2)*(-20*z**2) = -720*z**4\n (51*z**3)*40 = 2040*z**3\n (51*z**3)*(-20*z**2) = -1020*z**5\n 5*-20*z**2 = -100*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1020*z**5 - 720*z**4 + 2040*z**3 - 100*z**2 + 1440*z**2 + 200\nCombining like terms, got -1020*z**5 - 720*z**4 + 2040*z**3 + 1340*z**2 + 200\n#Step 6:\nCurrent expression: -1020*z**5 - 720*z**4 + 2040*z**3 + 1340*z**2 + 200\nNo more calculations needed.\n-1020*z**5 - 720*z**4 + 2040*z**3 + 1340*z**2 + 200", "generated_answer": "-1020*z**5 - 720*z**4 + 2040*z**3 + 1340*z**2 + 200", "step_length": 6} {"cot_id": "fb99247a7b9269343d361b33599606c2022560798cccbeb99ed4365fb7da5925", "datapoint": {"question": "Simplify this expression: (41*z**3 + 8)*(-3*z**3 + 17*z**2 - 46*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-123*z**6 + 697*z**5 - 1886*z**4 - 24*z**3 + 136*z**2 - 368*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1850, "polynomial_expr": "(41*z**3 + 8)*(-3*z**3 + 17*z**2 - 46*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (41*z**3 + 8)*(-3*z**3 + 17*z**2 - 46*z)\nExpanding the part (41*z**3 + 8) using the distributive property, and we got: (41*z**3)*(-3*z**3 + 17*z**2 - 46*z) + 8*(-3*z**3 + 17*z**2 - 46*z)\n#Step 2:\nCurrent expression: (41*z**3)*(-3*z**3 + 17*z**2 - 46*z) + 8*(-3*z**3 + 17*z**2 - 46*z)\nSimplifying the partial expression: 8*(-3*z**3 + 17*z**2 - 46*z)\nExpanding the part (-3*z**3 + 17*z**2 - 46*z) using the distributive property, and we got: -46*z*8 + (17*z**2)*8 - 3*z**3*8\nReplacing 8*(-3*z**3 + 17*z**2 - 46*z) with -46*z*8 + (17*z**2)*8 - 3*z**3*8 in the overall expression.\n#Step 3:\nCurrent expression: -46*z*8 + (17*z**2)*8 - 3*z**3*8 + (41*z**3)*(-3*z**3 + 17*z**2 - 46*z)\nSimplifying the partial expression: (41*z**3)*(-3*z**3 + 17*z**2 - 46*z)\nExpanding the part (-3*z**3 + 17*z**2 - 46*z) using the distributive property, and we got: (-46*z)*(41*z**3) + (17*z**2)*(41*z**3) + (-3*z**3)*(41*z**3)\nReplacing (41*z**3)*(-3*z**3 + 17*z**2 - 46*z) with (-46*z)*(41*z**3) + (17*z**2)*(41*z**3) + (-3*z**3)*(41*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-46*z)*(41*z**3) - 46*z*8 + (17*z**2)*(41*z**3) + (17*z**2)*8 + (-3*z**3)*(41*z**3) - 3*z**3*8\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*z)*8 = -368*z\n (-46*z)*(41*z**3) = -1886*z**4\n (-3*z**3)*8 = -24*z**3\n (-3*z**3)*(41*z**3) = -123*z**6\n (17*z**2)*8 = 136*z**2\n (17*z**2)*(41*z**3) = 697*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -123*z**6 + 697*z**5 - 1886*z**4 - 24*z**3 + 136*z**2 - 368*z\nNo more calculations needed.\n-123*z**6 + 697*z**5 - 1886*z**4 - 24*z**3 + 136*z**2 - 368*z", "generated_answer": "-123*z**6 + 697*z**5 - 1886*z**4 - 24*z**3 + 136*z**2 - 368*z", "step_length": 5} {"cot_id": "eafc772b5a920d679f0df337886166bdf29ba501244199d2c667e5e93b3e6f1b", "datapoint": {"question": "Calculate the following: (-29*z - 20)*(6*z + 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-174*z**2 - 294*z - 120", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1851, "polynomial_expr": "(-29*z - 20)*(6*z + 6)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-29*z - 20)*(6*z + 6)\nExpanding the part (-29*z - 20) using the distributive property, and we got: (-29*z)*(6*z + 6) - 20*(6*z + 6)\n#Step 2:\nCurrent expression: (-29*z)*(6*z + 6) - 20*(6*z + 6)\nSimplifying the partial expression: -20*(6*z + 6)\nExpanding the part (6*z + 6) using the distributive property, and we got: (6*z)*(-20) + 6*(-20)\nReplacing -20*(6*z + 6) with (6*z)*(-20) + 6*(-20) in the overall expression.\n#Step 3:\nCurrent expression: (-29*z)*(6*z + 6) + (6*z)*(-20) - 120\nSimplifying the partial expression: (-29*z)*(6*z + 6)\nExpanding the part (6*z + 6) using the distributive property, and we got: (-29*z)*(6*z) + 6*(-29*z)\nReplacing (-29*z)*(6*z + 6) with (-29*z)*(6*z) + 6*(-29*z) in the overall expression.\n#Step 4:\nCurrent expression: (-29*z)*(6*z) + 6*(-29)*z + (6*z)*(-20) - 120\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (6*z)*-20 = -120*z\n (6*z)*(-29*z) = -174*z**2\n 6*-29*z = -174*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -174*z**2 - 174*z - 120*z - 120\nCombining like terms, got -174*z**2 - 294*z - 120\n#Step 6:\nCurrent expression: -174*z**2 - 294*z - 120\nNo more calculations needed.\n-174*z**2 - 294*z - 120", "generated_answer": "-174*z**2 - 294*z - 120", "step_length": 6} {"cot_id": "1d6ba040c596926fef0d09e716de6f333a8bb5bc777c2f81d480f02076aed423", "datapoint": {"question": "Calculate the following: (z**2 - 13)*(10*z**3 - 7*z**2 - 33*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "10*z**5 - 7*z**4 - 163*z**3 + 91*z**2 + 429*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1852, "polynomial_expr": "(z**2 - 13)*(10*z**3 - 7*z**2 - 33*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (z**2 - 13)*(10*z**3 - 7*z**2 - 33*z)\nExpanding the part (z**2 - 13) using the distributive property, and we got: z**2*(10*z**3 - 7*z**2 - 33*z) - 13*(10*z**3 - 7*z**2 - 33*z)\n#Step 2:\nCurrent expression: z**2*(10*z**3 - 7*z**2 - 33*z) - 13*(10*z**3 - 7*z**2 - 33*z)\nSimplifying the partial expression: -13*(10*z**3 - 7*z**2 - 33*z)\nExpanding the part (10*z**3 - 7*z**2 - 33*z) using the distributive property, and we got: -33*z*(-13) - 7*z**2*(-13) + (10*z**3)*(-13)\nReplacing -13*(10*z**3 - 7*z**2 - 33*z) with -33*z*(-13) - 7*z**2*(-13) + (10*z**3)*(-13) in the overall expression.\n#Step 3:\nCurrent expression: -33*z*(-13) + z**2*(10*z**3 - 7*z**2 - 33*z) - 7*z**2*(-13) + (10*z**3)*(-13)\nSimplifying the partial expression: z**2*(10*z**3 - 7*z**2 - 33*z)\nExpanding the part (10*z**3 - 7*z**2 - 33*z) using the distributive property, and we got: (-33*z)*z**2 + (-7*z**2)*z**2 + z**2*(10*z**3)\nReplacing z**2*(10*z**3 - 7*z**2 - 33*z) with (-33*z)*z**2 + (-7*z**2)*z**2 + z**2*(10*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-33*z)*z**2 - 33*z*(-13) + (-7*z**2)*z**2 + z**2*(10*z**3) - 7*z**2*(-13) + (10*z**3)*(-13)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*z)*-13 = 429*z\n (-33*z)*z**2 = -33*z**3\n (-7*z**2)*-13 = 91*z**2\n (-7*z**2)*z**2 = -7*z**4\n (10*z**3)*-13 = -130*z**3\n (10*z**3)*z**2 = 10*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 10*z**5 - 7*z**4 - 130*z**3 - 33*z**3 + 91*z**2 + 429*z\nCombining like terms, got 10*z**5 - 7*z**4 - 163*z**3 + 91*z**2 + 429*z\n#Step 6:\nCurrent expression: 10*z**5 - 7*z**4 - 163*z**3 + 91*z**2 + 429*z\nNo more calculations needed.\n10*z**5 - 7*z**4 - 163*z**3 + 91*z**2 + 429*z", "generated_answer": "10*z**5 - 7*z**4 - 163*z**3 + 91*z**2 + 429*z", "step_length": 6} {"cot_id": "2100325db92290d9b33321285bd90bf14cda2102f3dba835894ad5329d29bf3b", "datapoint": {"question": "Simplify this expression: (-y**2 - 82*y)*(32*y**3 + 50*y + 40)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-32*y**5 - 2624*y**4 - 50*y**3 - 4140*y**2 - 3280*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1853, "polynomial_expr": "(-y**2 - 82*y)*(32*y**3 + 50*y + 40)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-y**2 - 82*y)*(32*y**3 + 50*y + 40)\nExpanding the part (-y**2 - 82*y) using the distributive property, and we got: (-82*y)*(32*y**3 + 50*y + 40) + (-y**2)*(32*y**3 + 50*y + 40)\n#Step 2:\nCurrent expression: (-82*y)*(32*y**3 + 50*y + 40) + (-y**2)*(32*y**3 + 50*y + 40)\nSimplifying the partial expression: (-y**2)*(32*y**3 + 50*y + 40)\nExpanding the part (32*y**3 + 50*y + 40) using the distributive property, and we got: 40*(-y**2) + (50*y)*(-y**2) + (-y**2)*(32*y**3)\nReplacing (-y**2)*(32*y**3 + 50*y + 40) with 40*(-y**2) + (50*y)*(-y**2) + (-y**2)*(32*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-82*y)*(32*y**3 + 50*y + 40) + 40*(-1)*y**2 + (50*y)*(-y**2) + (-y**2)*(32*y**3)\nSimplifying the partial expression: (-82*y)*(32*y**3 + 50*y + 40)\nExpanding the part (32*y**3 + 50*y + 40) using the distributive property, and we got: (-82*y)*(50*y) + (-82*y)*(32*y**3) + 40*(-82*y)\nReplacing (-82*y)*(32*y**3 + 50*y + 40) with (-82*y)*(50*y) + (-82*y)*(32*y**3) + 40*(-82*y) in the overall expression.\n#Step 4:\nCurrent expression: (-82*y)*(50*y) + (-82*y)*(32*y**3) + 40*(-1)*y**2 + 40*(-82)*y + (50*y)*(-y**2) + (-y**2)*(32*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (32*y**3)*(-y**2) = -32*y**5\n (32*y**3)*(-82*y) = -2624*y**4\n (50*y)*(-y**2) = -50*y**3\n (50*y)*(-82*y) = -4100*y**2\n 40*-1*y**2 = -40*y**2\n 40*-82*y = -3280*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -32*y**5 - 2624*y**4 - 50*y**3 - 4100*y**2 - 40*y**2 - 3280*y\nCombining like terms, got -32*y**5 - 2624*y**4 - 50*y**3 - 4140*y**2 - 3280*y\n#Step 6:\nCurrent expression: -32*y**5 - 2624*y**4 - 50*y**3 - 4140*y**2 - 3280*y\nNo more calculations needed.\n-32*y**5 - 2624*y**4 - 50*y**3 - 4140*y**2 - 3280*y", "generated_answer": "-32*y**5 - 2624*y**4 - 50*y**3 - 4140*y**2 - 3280*y", "step_length": 6} {"cot_id": "61a52d5e5d14496d2a29ad32511f23e0e59ac87a6196db5ee9de590f9438e84f", "datapoint": {"question": "Calculate the following: -71*z*(-4*z**3 - 42*z - 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "284*z**4 + 2982*z**2 + 1136*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1854, "polynomial_expr": "-71*z*(-4*z**3 - 42*z - 16)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -71*z*(-4*z**3 - 42*z - 16)\nExpanding the part (-4*z**3 - 42*z - 16) using the distributive property, and we got: (-71*z)*(-42*z) + (-71*z)*(-4*z**3) - (-1)*1136*z\n#Step 2:\nCurrent expression: (-71*z)*(-42*z) + (-71*z)*(-4*z**3) - (-1)*1136*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -16*(-71*z) = 1136*z\n (-42*z)*(-71*z) = 2982*z**2\n (-4*z**3)*(-71*z) = 284*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 284*z**4 + 2982*z**2 + 1136*z\nNo more calculations needed.\n284*z**4 + 2982*z**2 + 1136*z", "generated_answer": "284*z**4 + 2982*z**2 + 1136*z", "step_length": 3} {"cot_id": "996ae270f28f6f8c69f99c50f973269b0b7fc6550c996c04ae4943149dd3856d", "datapoint": {"question": "Simplify this expression: -25*y*(32*y**3 + 33*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-800*y**4 - 825*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1855, "polynomial_expr": "-25*y*(32*y**3 + 33*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -25*y*(32*y**3 + 33*y**2)\nExpanding the part (32*y**3 + 33*y**2) using the distributive property, and we got: (-25*y)*(33*y**2) + (-25*y)*(32*y**3)\n#Step 2:\nCurrent expression: (-25*y)*(33*y**2) + (-25*y)*(32*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (32*y**3)*(-25*y) = -800*y**4\n (33*y**2)*(-25*y) = -825*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -800*y**4 - 825*y**3\nNo more calculations needed.\n-800*y**4 - 825*y**3", "generated_answer": "-800*y**4 - 825*y**3", "step_length": 3} {"cot_id": "427b0209dd192d6f90cb9c7ef0ddfc48da0d51c4eb6db1a4cfbb83e27e091874", "datapoint": {"question": "Calculate the following: (28*y**3 + 15*y)*(-37*y**3 + 10*y**2 - 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1036*y**6 + 280*y**5 - 555*y**4 - 1222*y**3 - 735*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1856, "polynomial_expr": "(28*y**3 + 15*y)*(-37*y**3 + 10*y**2 - 49)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28*y**3 + 15*y)*(-37*y**3 + 10*y**2 - 49)\nExpanding the part (28*y**3 + 15*y) using the distributive property, and we got: (15*y)*(-37*y**3 + 10*y**2 - 49) + (28*y**3)*(-37*y**3 + 10*y**2 - 49)\n#Step 2:\nCurrent expression: (15*y)*(-37*y**3 + 10*y**2 - 49) + (28*y**3)*(-37*y**3 + 10*y**2 - 49)\nSimplifying the partial expression: (15*y)*(-37*y**3 + 10*y**2 - 49)\nExpanding the part (-37*y**3 + 10*y**2 - 49) using the distributive property, and we got: -735*y + (15*y)*(10*y**2) + (15*y)*(-37*y**3)\nReplacing (15*y)*(-37*y**3 + 10*y**2 - 49) with -735*y + (15*y)*(10*y**2) + (15*y)*(-37*y**3) in the overall expression.\n#Step 3:\nCurrent expression: -49*15*y + (15*y)*(10*y**2) + (15*y)*(-37*y**3) + (28*y**3)*(-37*y**3 + 10*y**2 - 49)\nSimplifying the partial expression: (28*y**3)*(-37*y**3 + 10*y**2 - 49)\nExpanding the part (-37*y**3 + 10*y**2 - 49) using the distributive property, and we got: -1372*y**3 + (10*y**2)*(28*y**3) + (-37*y**3)*(28*y**3)\nReplacing (28*y**3)*(-37*y**3 + 10*y**2 - 49) with -1372*y**3 + (10*y**2)*(28*y**3) + (-37*y**3)*(28*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -49*28*y**3 - 49*15*y + (15*y)*(10*y**2) + (15*y)*(-37*y**3) + (10*y**2)*(28*y**3) + (-37*y**3)*(28*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*y**3)*(15*y) = -555*y**4\n (-37*y**3)*(28*y**3) = -1036*y**6\n (10*y**2)*(15*y) = 150*y**3\n (10*y**2)*(28*y**3) = 280*y**5\n -49*15*y = -735*y\n -49*28*y**3 = -1372*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1036*y**6 + 280*y**5 - 555*y**4 - 1372*y**3 + 150*y**3 - 735*y\nCombining like terms, got -1036*y**6 + 280*y**5 - 555*y**4 - 1222*y**3 - 735*y\n#Step 6:\nCurrent expression: -1036*y**6 + 280*y**5 - 555*y**4 - 1222*y**3 - 735*y\nNo more calculations needed.\n-1036*y**6 + 280*y**5 - 555*y**4 - 1222*y**3 - 735*y", "generated_answer": "-1036*y**6 + 280*y**5 - 555*y**4 - 1222*y**3 - 735*y", "step_length": 6} {"cot_id": "1f24442fedf411f2a6d56f28fd88875fa8f6ebdfc8c3b4851e8d4d66dbdfd36d", "datapoint": {"question": "Calculate the following: -29*x*(46*x**2 + 53)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1334*x**3 - 1537*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1857, "polynomial_expr": "-29*x*(46*x**2 + 53)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -29*x*(46*x**2 + 53)\nExpanding the part (46*x**2 + 53) using the distributive property, and we got: (-29*x)*(46*x**2) + 53*(-29*x)\n#Step 2:\nCurrent expression: (-29*x)*(46*x**2) + 53*(-29*x)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 53*(-29*x) = -1537*x\n (46*x**2)*(-29*x) = -1334*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1334*x**3 - 1537*x\nNo more calculations needed.\n-1334*x**3 - 1537*x", "generated_answer": "-1334*x**3 - 1537*x", "step_length": 3} {"cot_id": "611bc94afb8a1deff381156b946cdde36281f79fe1d2e1f26f2754077aa74a43", "datapoint": {"question": "Calculate the following: (-40*x**2 + 75*x)*(7*x**3 - 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-280*x**5 + 525*x**4 + 1760*x**2 - 3300*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1858, "polynomial_expr": "(-40*x**2 + 75*x)*(7*x**3 - 44)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-40*x**2 + 75*x)*(7*x**3 - 44)\nExpanding the part (7*x**3 - 44) using the distributive property, and we got: (7*x**3)*(-40*x**2 + 75*x) - 44*(-40*x**2 + 75*x)\n#Step 2:\nCurrent expression: (7*x**3)*(-40*x**2 + 75*x) - 44*(-40*x**2 + 75*x)\nSimplifying the partial expression: -44*(-40*x**2 + 75*x)\nExpanding the part (-40*x**2 + 75*x) using the distributive property, and we got: (75*x)*(-44) - 40*x**2*(-44)\nReplacing -44*(-40*x**2 + 75*x) with (75*x)*(-44) - 40*x**2*(-44) in the overall expression.\n#Step 3:\nCurrent expression: (75*x)*(-44) - 40*x**2*(-44) + (7*x**3)*(-40*x**2 + 75*x)\nSimplifying the partial expression: (7*x**3)*(-40*x**2 + 75*x)\nExpanding the part (-40*x**2 + 75*x) using the distributive property, and we got: (75*x)*(7*x**3) + (-40*x**2)*(7*x**3)\nReplacing (7*x**3)*(-40*x**2 + 75*x) with (75*x)*(7*x**3) + (-40*x**2)*(7*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (75*x)*(7*x**3) + (75*x)*(-44) + (-40*x**2)*(7*x**3) - 40*x**2*(-44)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*x**2)*-44 = 1760*x**2\n (-40*x**2)*(7*x**3) = -280*x**5\n (75*x)*-44 = -3300*x\n (75*x)*(7*x**3) = 525*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -280*x**5 + 525*x**4 + 1760*x**2 - 3300*x\nNo more calculations needed.\n-280*x**5 + 525*x**4 + 1760*x**2 - 3300*x", "generated_answer": "-280*x**5 + 525*x**4 + 1760*x**2 - 3300*x", "step_length": 5} {"cot_id": "b00dbbd11c6d3af2f55f9692008818f1c79f574d03bce36382e1a2f4fc9a22f3", "datapoint": {"question": "Simplify this expression: (-24*z**3 + 67*z**2)*(32*z**3 - 3*z**2 + 3*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-768*z**6 + 2216*z**5 - 273*z**4 + 201*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1859, "polynomial_expr": "(-24*z**3 + 67*z**2)*(32*z**3 - 3*z**2 + 3*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-24*z**3 + 67*z**2)*(32*z**3 - 3*z**2 + 3*z)\nExpanding the part (-24*z**3 + 67*z**2) using the distributive property, and we got: (67*z**2)*(32*z**3 - 3*z**2 + 3*z) + (-24*z**3)*(32*z**3 - 3*z**2 + 3*z)\n#Step 2:\nCurrent expression: (67*z**2)*(32*z**3 - 3*z**2 + 3*z) + (-24*z**3)*(32*z**3 - 3*z**2 + 3*z)\nSimplifying the partial expression: (-24*z**3)*(32*z**3 - 3*z**2 + 3*z)\nExpanding the part (32*z**3 - 3*z**2 + 3*z) using the distributive property, and we got: (3*z)*(-24*z**3) + (-3*z**2)*(-24*z**3) + (-24*z**3)*(32*z**3)\nReplacing (-24*z**3)*(32*z**3 - 3*z**2 + 3*z) with (3*z)*(-24*z**3) + (-3*z**2)*(-24*z**3) + (-24*z**3)*(32*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (3*z)*(-24*z**3) + (-3*z**2)*(-24*z**3) + (67*z**2)*(32*z**3 - 3*z**2 + 3*z) + (-24*z**3)*(32*z**3)\nSimplifying the partial expression: (67*z**2)*(32*z**3 - 3*z**2 + 3*z)\nExpanding the part (32*z**3 - 3*z**2 + 3*z) using the distributive property, and we got: (3*z)*(67*z**2) + (-3*z**2)*(67*z**2) + (67*z**2)*(32*z**3)\nReplacing (67*z**2)*(32*z**3 - 3*z**2 + 3*z) with (3*z)*(67*z**2) + (-3*z**2)*(67*z**2) + (67*z**2)*(32*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (3*z)*(67*z**2) + (3*z)*(-24*z**3) + (-3*z**2)*(67*z**2) + (-3*z**2)*(-24*z**3) + (67*z**2)*(32*z**3) + (-24*z**3)*(32*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-3*z**2)*(-24*z**3) = 72*z**5\n (-3*z**2)*(67*z**2) = -201*z**4\n (3*z)*(-24*z**3) = -72*z**4\n (3*z)*(67*z**2) = 201*z**3\n (32*z**3)*(-24*z**3) = -768*z**6\n (32*z**3)*(67*z**2) = 2144*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -768*z**6 + 72*z**5 + 2144*z**5 - 201*z**4 - 72*z**4 + 201*z**3\nCombining like terms, got -768*z**6 + 2216*z**5 - 273*z**4 + 201*z**3\n#Step 6:\nCurrent expression: -768*z**6 + 2216*z**5 - 273*z**4 + 201*z**3\nNo more calculations needed.\n-768*z**6 + 2216*z**5 - 273*z**4 + 201*z**3", "generated_answer": "-768*z**6 + 2216*z**5 - 273*z**4 + 201*z**3", "step_length": 6} {"cot_id": "da23824ea151b8f7f10d39022cc0c911d39a0c86fb669ef6b29ca733fa347234", "datapoint": {"question": "Simplify this expression: -39*x**2*(-33*x**3 - 8*x**2 + 3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1287*x**5 + 312*x**4 - 117*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1860, "polynomial_expr": "-39*x**2*(-33*x**3 - 8*x**2 + 3)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -39*x**2*(-33*x**3 - 8*x**2 + 3)\nExpanding the part (-33*x**3 - 8*x**2 + 3) using the distributive property, and we got: 3*(-39*x**2) + (-39*x**2)*(-8*x**2) + (-39*x**2)*(-33*x**3)\n#Step 2:\nCurrent expression: 3*(-39*x**2) + (-39*x**2)*(-8*x**2) + (-39*x**2)*(-33*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 3*(-39*x**2) = -117*x**2\n (-33*x**3)*(-39*x**2) = 1287*x**5\n (-8*x**2)*(-39*x**2) = 312*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1287*x**5 + 312*x**4 - 117*x**2\nNo more calculations needed.\n1287*x**5 + 312*x**4 - 117*x**2", "generated_answer": "1287*x**5 + 312*x**4 - 117*x**2", "step_length": 3} {"cot_id": "55337538b5065361c9fc5b839d87bd57414fe7aece1273c242a51153da5972de", "datapoint": {"question": "Calculate the following: (5*z**2 + 10)*(41*z**3 + 32*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "205*z**5 + 160*z**4 + 410*z**3 + 320*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1861, "polynomial_expr": "(5*z**2 + 10)*(41*z**3 + 32*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (5*z**2 + 10)*(41*z**3 + 32*z**2)\nExpanding the part (5*z**2 + 10) using the distributive property, and we got: (5*z**2)*(41*z**3 + 32*z**2) + 10*(41*z**3 + 32*z**2)\n#Step 2:\nCurrent expression: (5*z**2)*(41*z**3 + 32*z**2) + 10*(41*z**3 + 32*z**2)\nSimplifying the partial expression: 10*(41*z**3 + 32*z**2)\nExpanding the part (41*z**3 + 32*z**2) using the distributive property, and we got: (32*z**2)*10 + (41*z**3)*10\nReplacing 10*(41*z**3 + 32*z**2) with (32*z**2)*10 + (41*z**3)*10 in the overall expression.\n#Step 3:\nCurrent expression: (5*z**2)*(41*z**3 + 32*z**2) + (32*z**2)*10 + (41*z**3)*10\nSimplifying the partial expression: (5*z**2)*(41*z**3 + 32*z**2)\nExpanding the part (41*z**3 + 32*z**2) using the distributive property, and we got: (5*z**2)*(32*z**2) + (5*z**2)*(41*z**3)\nReplacing (5*z**2)*(41*z**3 + 32*z**2) with (5*z**2)*(32*z**2) + (5*z**2)*(41*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (5*z**2)*(32*z**2) + (5*z**2)*(41*z**3) + (32*z**2)*10 + (41*z**3)*10\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (32*z**2)*10 = 320*z**2\n (32*z**2)*(5*z**2) = 160*z**4\n (41*z**3)*10 = 410*z**3\n (41*z**3)*(5*z**2) = 205*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 205*z**5 + 160*z**4 + 410*z**3 + 320*z**2\nNo more calculations needed.\n205*z**5 + 160*z**4 + 410*z**3 + 320*z**2", "generated_answer": "205*z**5 + 160*z**4 + 410*z**3 + 320*z**2", "step_length": 5} {"cot_id": "99a12e23ac938889ccd4f25c80569ae62ce06f0fd12134013f9d7b8f025e62a6", "datapoint": {"question": "Calculate the following: (9*y**3 + 42)*(-4*y**3 - 5*y**2 + y + 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-36*y**6 - 45*y**5 + 9*y**4 + 201*y**3 - 210*y**2 + 42*y + 1722", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1862, "polynomial_expr": "(9*y**3 + 42)*(-4*y**3 - 5*y**2 + y + 41)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9*y**3 + 42)*(-4*y**3 - 5*y**2 + y + 41)\nExpanding the part (9*y**3 + 42) using the distributive property, and we got: (9*y**3)*(-4*y**3 - 5*y**2 + y + 41) + 42*(-4*y**3 - 5*y**2 + y + 41)\n#Step 2:\nCurrent expression: (9*y**3)*(-4*y**3 - 5*y**2 + y + 41) + 42*(-4*y**3 - 5*y**2 + y + 41)\nSimplifying the partial expression: 42*(-4*y**3 - 5*y**2 + y + 41)\nExpanding the part (-4*y**3 - 5*y**2 + y + 41) using the distributive property, and we got: y*42 - 5*y**2*42 - 4*y**3*42 + 41*42\nReplacing 42*(-4*y**3 - 5*y**2 + y + 41) with y*42 - 5*y**2*42 - 4*y**3*42 + 41*42 in the overall expression.\n#Step 3:\nCurrent expression: y*42 - 5*y**2*42 - 4*y**3*42 + (9*y**3)*(-4*y**3 - 5*y**2 + y + 41) + 1722\nSimplifying the partial expression: (9*y**3)*(-4*y**3 - 5*y**2 + y + 41)\nExpanding the part (-4*y**3 - 5*y**2 + y + 41) using the distributive property, and we got: 41*(9*y**3) + y*(9*y**3) + (-5*y**2)*(9*y**3) + (-4*y**3)*(9*y**3)\nReplacing (9*y**3)*(-4*y**3 - 5*y**2 + y + 41) with 41*(9*y**3) + y*(9*y**3) + (-5*y**2)*(9*y**3) + (-4*y**3)*(9*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 41*9*y**3 + y*(9*y**3) + y*42 + (-5*y**2)*(9*y**3) - 5*y**2*42 + (-4*y**3)*(9*y**3) - 4*y**3*42 + 1722\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n y*42 = 42*y\n y*(9*y**3) = 9*y**4\n (-5*y**2)*42 = -210*y**2\n (-5*y**2)*(9*y**3) = -45*y**5\n (-4*y**3)*42 = -168*y**3\n (-4*y**3)*(9*y**3) = -36*y**6\n 41*9*y**3 = 369*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -36*y**6 - 45*y**5 + 9*y**4 - 168*y**3 + 369*y**3 - 210*y**2 + 42*y + 1722\nCombining like terms, got -36*y**6 - 45*y**5 + 9*y**4 + 201*y**3 - 210*y**2 + 42*y + 1722\n#Step 6:\nCurrent expression: -36*y**6 - 45*y**5 + 9*y**4 + 201*y**3 - 210*y**2 + 42*y + 1722\nNo more calculations needed.\n-36*y**6 - 45*y**5 + 9*y**4 + 201*y**3 - 210*y**2 + 42*y + 1722", "generated_answer": "-36*y**6 - 45*y**5 + 9*y**4 + 201*y**3 - 210*y**2 + 42*y + 1722", "step_length": 6} {"cot_id": "0a1dd61903adc0ce4335ccd0dc5e41c48a7c4c83d5452edbb004f64dc21d7c6a", "datapoint": {"question": "Simplify this expression: 20*x*(-9*x**3 - 50*x - 23)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-180*x**4 - 1000*x**2 - 460*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1863, "polynomial_expr": "20*x*(-9*x**3 - 50*x - 23)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 20*x*(-9*x**3 - 50*x - 23)\nExpanding the part (-9*x**3 - 50*x - 23) using the distributive property, and we got: (-50*x)*(20*x) - 460*x + (20*x)*(-9*x**3)\n#Step 2:\nCurrent expression: (-50*x)*(20*x) - 460*x + (20*x)*(-9*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -23*(20*x) = -460*x\n (-50*x)*(20*x) = -1000*x**2\n (-9*x**3)*(20*x) = -180*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -180*x**4 - 1000*x**2 - 460*x\nNo more calculations needed.\n-180*x**4 - 1000*x**2 - 460*x", "generated_answer": "-180*x**4 - 1000*x**2 - 460*x", "step_length": 3} {"cot_id": "94e022141d9b3f2160ffc6148335bb05306ffa74a560c81898462b04c8375761", "datapoint": {"question": "Simplify this expression: (45 - 32*x)*(-19*x**2 + 21*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "608*x**3 - 1527*x**2 + 945*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1864, "polynomial_expr": "(45 - 32*x)*(-19*x**2 + 21*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (45 - 32*x)*(-19*x**2 + 21*x)\nExpanding the part (45 - 32*x) using the distributive property, and we got: (-32*x)*(-19*x**2 + 21*x) + 45*(-19*x**2 + 21*x)\n#Step 2:\nCurrent expression: (-32*x)*(-19*x**2 + 21*x) + 45*(-19*x**2 + 21*x)\nSimplifying the partial expression: 45*(-19*x**2 + 21*x)\nExpanding the part (-19*x**2 + 21*x) using the distributive property, and we got: (21*x)*45 - 19*x**2*45\nReplacing 45*(-19*x**2 + 21*x) with (21*x)*45 - 19*x**2*45 in the overall expression.\n#Step 3:\nCurrent expression: (-32*x)*(-19*x**2 + 21*x) + (21*x)*45 - 19*x**2*45\nSimplifying the partial expression: (-32*x)*(-19*x**2 + 21*x)\nExpanding the part (-19*x**2 + 21*x) using the distributive property, and we got: (-32*x)*(21*x) + (-32*x)*(-19*x**2)\nReplacing (-32*x)*(-19*x**2 + 21*x) with (-32*x)*(21*x) + (-32*x)*(-19*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-32*x)*(21*x) + (-32*x)*(-19*x**2) + (21*x)*45 - 19*x**2*45\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*x**2)*45 = -855*x**2\n (-19*x**2)*(-32*x) = 608*x**3\n (21*x)*45 = 945*x\n (21*x)*(-32*x) = -672*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 608*x**3 - 855*x**2 - 672*x**2 + 945*x\nCombining like terms, got 608*x**3 - 1527*x**2 + 945*x\n#Step 6:\nCurrent expression: 608*x**3 - 1527*x**2 + 945*x\nNo more calculations needed.\n608*x**3 - 1527*x**2 + 945*x", "generated_answer": "608*x**3 - 1527*x**2 + 945*x", "step_length": 6} {"cot_id": "82e72879a1cb8ebb90599d11a942eebc0bfa6d1b361a8949292597160400c9a5", "datapoint": {"question": "Calculate the following: (-30*x**3 + 9*x**2 - 22)*(14*x**3 + 44*x**2 - 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-420*x**6 - 1194*x**5 + 396*x**4 + 1102*x**3 - 1391*x**2 + 1034", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1865, "polynomial_expr": "(-30*x**3 + 9*x**2 - 22)*(14*x**3 + 44*x**2 - 47)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-30*x**3 + 9*x**2 - 22)*(14*x**3 + 44*x**2 - 47)\nExpanding the part (14*x**3 + 44*x**2 - 47) using the distributive property, and we got: (44*x**2)*(-30*x**3 + 9*x**2 - 22) + (14*x**3)*(-30*x**3 + 9*x**2 - 22) - 47*(-30*x**3 + 9*x**2 - 22)\n#Step 2:\nCurrent expression: (44*x**2)*(-30*x**3 + 9*x**2 - 22) + (14*x**3)*(-30*x**3 + 9*x**2 - 22) - 47*(-30*x**3 + 9*x**2 - 22)\nSimplifying the partial expression: -47*(-30*x**3 + 9*x**2 - 22)\nExpanding the part (-30*x**3 + 9*x**2 - 22) using the distributive property, and we got: (9*x**2)*(-47) - 30*x**3*(-47) - 22*(-47)\nReplacing -47*(-30*x**3 + 9*x**2 - 22) with (9*x**2)*(-47) - 30*x**3*(-47) - 22*(-47) in the overall expression.\n#Step 3:\nCurrent expression: (9*x**2)*(-47) + (44*x**2)*(-30*x**3 + 9*x**2 - 22) - 30*x**3*(-47) + (14*x**3)*(-30*x**3 + 9*x**2 - 22) + 1034\nSimplifying the partial expression: (14*x**3)*(-30*x**3 + 9*x**2 - 22)\nExpanding the part (-30*x**3 + 9*x**2 - 22) using the distributive property, and we got: -308*x**3 + (9*x**2)*(14*x**3) + (-30*x**3)*(14*x**3)\nReplacing (14*x**3)*(-30*x**3 + 9*x**2 - 22) with -308*x**3 + (9*x**2)*(14*x**3) + (-30*x**3)*(14*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -22*14*x**3 + (9*x**2)*(14*x**3) + (9*x**2)*(-47) + (44*x**2)*(-30*x**3 + 9*x**2 - 22) + (-30*x**3)*(14*x**3) - 30*x**3*(-47) + 1034\nSimplifying the partial expression: (44*x**2)*(-30*x**3 + 9*x**2 - 22)\nExpanding the part (-30*x**3 + 9*x**2 - 22) using the distributive property, and we got: -968*x**2 + (9*x**2)*(44*x**2) + (44*x**2)*(-30*x**3)\nReplacing (44*x**2)*(-30*x**3 + 9*x**2 - 22) with -968*x**2 + (9*x**2)*(44*x**2) + (44*x**2)*(-30*x**3) in the overall expression.\n#Step 5:\nCurrent expression: -22*14*x**3 - 22*44*x**2 + (9*x**2)*(44*x**2) + (9*x**2)*(14*x**3) + (9*x**2)*(-47) + (44*x**2)*(-30*x**3) + (-30*x**3)*(14*x**3) - 30*x**3*(-47) + 1034\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*x**3)*-47 = 1410*x**3\n (-30*x**3)*(14*x**3) = -420*x**6\n (-30*x**3)*(44*x**2) = -1320*x**5\n (9*x**2)*-47 = -423*x**2\n (9*x**2)*(14*x**3) = 126*x**5\n (9*x**2)*(44*x**2) = 396*x**4\n -22*14*x**3 = -308*x**3\n -22*44*x**2 = -968*x**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -420*x**6 - 1320*x**5 + 126*x**5 + 396*x**4 - 308*x**3 + 1410*x**3 - 968*x**2 - 423*x**2 + 1034\nCombining like terms, got -420*x**6 - 1194*x**5 + 396*x**4 + 1102*x**3 - 1391*x**2 + 1034\n#Step 7:\nCurrent expression: -420*x**6 - 1194*x**5 + 396*x**4 + 1102*x**3 - 1391*x**2 + 1034\nNo more calculations needed.\n-420*x**6 - 1194*x**5 + 396*x**4 + 1102*x**3 - 1391*x**2 + 1034", "generated_answer": "-420*x**6 - 1194*x**5 + 396*x**4 + 1102*x**3 - 1391*x**2 + 1034", "step_length": 7} {"cot_id": "0cfdea069703a804a5a76d87e197a969f711030844233acd8c382216e7eba820", "datapoint": {"question": "Calculate the following: 255*x**3 - 204*x**2 + 782*x + 187\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "255*x**3 - 204*x**2 + 782*x + 187", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1866, "polynomial_expr": "255*x**3 - 204*x**2 + 782*x + 187", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 255*x**3 - 204*x**2 + 782*x + 187\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 255*x**3 - 204*x**2 + 782*x + 187\nNo more calculations needed.\n255*x**3 - 204*x**2 + 782*x + 187", "generated_answer": "255*x**3 - 204*x**2 + 782*x + 187", "step_length": 2} {"cot_id": "ebc0c34d9222c53ca99455a62f571fc7b3deb10de86a2e4dfb66fa6d6dbbd60c", "datapoint": {"question": "Simplify this expression: (-35*y**3 + 87*y**2 + 25*y)*(-2*y**3 + 2*y**2 - 11*y + 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "70*y**6 - 244*y**5 + 509*y**4 - 1397*y**3 + 943*y**2 + 350*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1867, "polynomial_expr": "(-35*y**3 + 87*y**2 + 25*y)*(-2*y**3 + 2*y**2 - 11*y + 14)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-35*y**3 + 87*y**2 + 25*y)*(-2*y**3 + 2*y**2 - 11*y + 14)\nExpanding the part (-35*y**3 + 87*y**2 + 25*y) using the distributive property, and we got: (25*y)*(-2*y**3 + 2*y**2 - 11*y + 14) + (87*y**2)*(-2*y**3 + 2*y**2 - 11*y + 14) + (-35*y**3)*(-2*y**3 + 2*y**2 - 11*y + 14)\n#Step 2:\nCurrent expression: (25*y)*(-2*y**3 + 2*y**2 - 11*y + 14) + (87*y**2)*(-2*y**3 + 2*y**2 - 11*y + 14) + (-35*y**3)*(-2*y**3 + 2*y**2 - 11*y + 14)\nSimplifying the partial expression: (-35*y**3)*(-2*y**3 + 2*y**2 - 11*y + 14)\nExpanding the part (-2*y**3 + 2*y**2 - 11*y + 14) using the distributive property, and we got: (-11*y)*(-35*y**3) + 14*(-35*y**3) + (2*y**2)*(-35*y**3) + (-35*y**3)*(-2*y**3)\nReplacing (-35*y**3)*(-2*y**3 + 2*y**2 - 11*y + 14) with (-11*y)*(-35*y**3) + 14*(-35*y**3) + (2*y**2)*(-35*y**3) + (-35*y**3)*(-2*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-11*y)*(-35*y**3) + 14*(-35)*y**3 + (25*y)*(-2*y**3 + 2*y**2 - 11*y + 14) + (2*y**2)*(-35*y**3) + (87*y**2)*(-2*y**3 + 2*y**2 - 11*y + 14) + (-35*y**3)*(-2*y**3)\nSimplifying the partial expression: (25*y)*(-2*y**3 + 2*y**2 - 11*y + 14)\nExpanding the part (-2*y**3 + 2*y**2 - 11*y + 14) using the distributive property, and we got: (-11*y)*(25*y) + 14*(25*y) + (25*y)*(2*y**2) + (25*y)*(-2*y**3)\nReplacing (25*y)*(-2*y**3 + 2*y**2 - 11*y + 14) with (-11*y)*(25*y) + 14*(25*y) + (25*y)*(2*y**2) + (25*y)*(-2*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-11*y)*(25*y) + (-11*y)*(-35*y**3) + 14*(-35)*y**3 + 14*25*y + (25*y)*(2*y**2) + (25*y)*(-2*y**3) + (2*y**2)*(-35*y**3) + (87*y**2)*(-2*y**3 + 2*y**2 - 11*y + 14) + (-35*y**3)*(-2*y**3)\nSimplifying the partial expression: (87*y**2)*(-2*y**3 + 2*y**2 - 11*y + 14)\nExpanding the part (-2*y**3 + 2*y**2 - 11*y + 14) using the distributive property, and we got: (-11*y)*(87*y**2) + 14*(87*y**2) + (2*y**2)*(87*y**2) + (87*y**2)*(-2*y**3)\nReplacing (87*y**2)*(-2*y**3 + 2*y**2 - 11*y + 14) with (-11*y)*(87*y**2) + 14*(87*y**2) + (2*y**2)*(87*y**2) + (87*y**2)*(-2*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-11*y)*(25*y) + (-11*y)*(87*y**2) + (-11*y)*(-35*y**3) + 14*(-35)*y**3 + 14*87*y**2 + 14*25*y + (25*y)*(2*y**2) + (25*y)*(-2*y**3) + (2*y**2)*(87*y**2) + (2*y**2)*(-35*y**3) + (87*y**2)*(-2*y**3) + (-35*y**3)*(-2*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*y)*(-35*y**3) = 385*y**4\n (-11*y)*(25*y) = -275*y**2\n (-11*y)*(87*y**2) = -957*y**3\n (-2*y**3)*(-35*y**3) = 70*y**6\n (-2*y**3)*(25*y) = -50*y**4\n (-2*y**3)*(87*y**2) = -174*y**5\n (2*y**2)*(-35*y**3) = -70*y**5\n (2*y**2)*(25*y) = 50*y**3\n (2*y**2)*(87*y**2) = 174*y**4\n 14*-35*y**3 = -490*y**3\n 14*25*y = 350*y\n 14*87*y**2 = 1218*y**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 70*y**6 - 174*y**5 - 70*y**5 - 50*y**4 + 174*y**4 + 385*y**4 - 957*y**3 - 490*y**3 + 50*y**3 - 275*y**2 + 1218*y**2 + 350*y\nCombining like terms, got 70*y**6 - 244*y**5 + 509*y**4 - 1397*y**3 + 943*y**2 + 350*y\n#Step 7:\nCurrent expression: 70*y**6 - 244*y**5 + 509*y**4 - 1397*y**3 + 943*y**2 + 350*y\nNo more calculations needed.\n70*y**6 - 244*y**5 + 509*y**4 - 1397*y**3 + 943*y**2 + 350*y", "generated_answer": "70*y**6 - 244*y**5 + 509*y**4 - 1397*y**3 + 943*y**2 + 350*y", "step_length": 7} {"cot_id": "80edf8fe16c742c15b4158a5bfc0cb649f973a58050843fe9c998f53458f2edb", "datapoint": {"question": "Simplify this expression: (49 - 50*x)*(4*x + 94)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-200*x**2 - 4504*x + 4606", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1868, "polynomial_expr": "(49 - 50*x)*(4*x + 94)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (49 - 50*x)*(4*x + 94)\nExpanding the part (49 - 50*x) using the distributive property, and we got: (-50*x)*(4*x + 94) + 49*(4*x + 94)\n#Step 2:\nCurrent expression: (-50*x)*(4*x + 94) + 49*(4*x + 94)\nSimplifying the partial expression: 49*(4*x + 94)\nExpanding the part (4*x + 94) using the distributive property, and we got: (4*x)*49 + 94*49\nReplacing 49*(4*x + 94) with (4*x)*49 + 94*49 in the overall expression.\n#Step 3:\nCurrent expression: (-50*x)*(4*x + 94) + (4*x)*49 + 4606\nSimplifying the partial expression: (-50*x)*(4*x + 94)\nExpanding the part (4*x + 94) using the distributive property, and we got: (-50*x)*(4*x) + 94*(-50*x)\nReplacing (-50*x)*(4*x + 94) with (-50*x)*(4*x) + 94*(-50*x) in the overall expression.\n#Step 4:\nCurrent expression: (-50*x)*(4*x) + 94*(-50)*x + (4*x)*49 + 4606\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (4*x)*49 = 196*x\n (4*x)*(-50*x) = -200*x**2\n 94*-50*x = -4700*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -200*x**2 - 4700*x + 196*x + 4606\nCombining like terms, got -200*x**2 - 4504*x + 4606\n#Step 6:\nCurrent expression: -200*x**2 - 4504*x + 4606\nNo more calculations needed.\n-200*x**2 - 4504*x + 4606", "generated_answer": "-200*x**2 - 4504*x + 4606", "step_length": 6} {"cot_id": "d8078b24908a973d2bd3c67b21910166a5db71caafaa4ccb665c3f2e7f03f0f3", "datapoint": {"question": "Simplify this expression: (-17*y**3 - 44)*(-44*y**3 + 11*y + 43)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "748*y**6 - 187*y**4 + 1205*y**3 - 484*y - 1892", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1869, "polynomial_expr": "(-17*y**3 - 44)*(-44*y**3 + 11*y + 43)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-17*y**3 - 44)*(-44*y**3 + 11*y + 43)\nExpanding the part (-17*y**3 - 44) using the distributive property, and we got: (-17*y**3)*(-44*y**3 + 11*y + 43) - 44*(-44*y**3 + 11*y + 43)\n#Step 2:\nCurrent expression: (-17*y**3)*(-44*y**3 + 11*y + 43) - 44*(-44*y**3 + 11*y + 43)\nSimplifying the partial expression: -44*(-44*y**3 + 11*y + 43)\nExpanding the part (-44*y**3 + 11*y + 43) using the distributive property, and we got: (11*y)*(-44) - 44*y**3*(-44) + 43*(-44)\nReplacing -44*(-44*y**3 + 11*y + 43) with (11*y)*(-44) - 44*y**3*(-44) + 43*(-44) in the overall expression.\n#Step 3:\nCurrent expression: (11*y)*(-44) - 44*y**3*(-44) + (-17*y**3)*(-44*y**3 + 11*y + 43) - 1892\nSimplifying the partial expression: (-17*y**3)*(-44*y**3 + 11*y + 43)\nExpanding the part (-44*y**3 + 11*y + 43) using the distributive property, and we got: 43*(-17*y**3) + (11*y)*(-17*y**3) + (-44*y**3)*(-17*y**3)\nReplacing (-17*y**3)*(-44*y**3 + 11*y + 43) with 43*(-17*y**3) + (11*y)*(-17*y**3) + (-44*y**3)*(-17*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 43*(-17)*y**3 + (11*y)*(-17*y**3) + (11*y)*(-44) + (-44*y**3)*(-17*y**3) - 44*y**3*(-44) - 1892\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-44*y**3)*-44 = 1936*y**3\n (-44*y**3)*(-17*y**3) = 748*y**6\n (11*y)*-44 = -484*y\n (11*y)*(-17*y**3) = -187*y**4\n 43*-17*y**3 = -731*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 748*y**6 - 187*y**4 - 731*y**3 + 1936*y**3 - 484*y - 1892\nCombining like terms, got 748*y**6 - 187*y**4 + 1205*y**3 - 484*y - 1892\n#Step 6:\nCurrent expression: 748*y**6 - 187*y**4 + 1205*y**3 - 484*y - 1892\nNo more calculations needed.\n748*y**6 - 187*y**4 + 1205*y**3 - 484*y - 1892", "generated_answer": "748*y**6 - 187*y**4 + 1205*y**3 - 484*y - 1892", "step_length": 6} {"cot_id": "c248dcf939093be228ddd311c5229c3f64074c1d51060362b73190a2a8979fa6", "datapoint": {"question": "Simplify this expression: (-19*x**2 - 85*x)*(24*x**3 + 87*x + 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-456*x**5 - 2040*x**4 - 1653*x**3 - 7661*x**2 - 1190*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1870, "polynomial_expr": "(-19*x**2 - 85*x)*(24*x**3 + 87*x + 14)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-19*x**2 - 85*x)*(24*x**3 + 87*x + 14)\nExpanding the part (-19*x**2 - 85*x) using the distributive property, and we got: (-85*x)*(24*x**3 + 87*x + 14) + (-19*x**2)*(24*x**3 + 87*x + 14)\n#Step 2:\nCurrent expression: (-85*x)*(24*x**3 + 87*x + 14) + (-19*x**2)*(24*x**3 + 87*x + 14)\nSimplifying the partial expression: (-85*x)*(24*x**3 + 87*x + 14)\nExpanding the part (24*x**3 + 87*x + 14) using the distributive property, and we got: (-85*x)*(87*x) + (-85*x)*(24*x**3) + 14*(-85*x)\nReplacing (-85*x)*(24*x**3 + 87*x + 14) with (-85*x)*(87*x) + (-85*x)*(24*x**3) + 14*(-85*x) in the overall expression.\n#Step 3:\nCurrent expression: (-85*x)*(87*x) + (-85*x)*(24*x**3) + 14*(-85)*x + (-19*x**2)*(24*x**3 + 87*x + 14)\nSimplifying the partial expression: (-19*x**2)*(24*x**3 + 87*x + 14)\nExpanding the part (24*x**3 + 87*x + 14) using the distributive property, and we got: 14*(-19*x**2) + (87*x)*(-19*x**2) + (-19*x**2)*(24*x**3)\nReplacing (-19*x**2)*(24*x**3 + 87*x + 14) with 14*(-19*x**2) + (87*x)*(-19*x**2) + (-19*x**2)*(24*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-85*x)*(87*x) + (-85*x)*(24*x**3) + 14*(-19)*x**2 + 14*(-85)*x + (87*x)*(-19*x**2) + (-19*x**2)*(24*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (24*x**3)*(-85*x) = -2040*x**4\n (24*x**3)*(-19*x**2) = -456*x**5\n (87*x)*(-85*x) = -7395*x**2\n (87*x)*(-19*x**2) = -1653*x**3\n 14*-85*x = -1190*x\n 14*-19*x**2 = -266*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -456*x**5 - 2040*x**4 - 1653*x**3 - 7395*x**2 - 266*x**2 - 1190*x\nCombining like terms, got -456*x**5 - 2040*x**4 - 1653*x**3 - 7661*x**2 - 1190*x\n#Step 6:\nCurrent expression: -456*x**5 - 2040*x**4 - 1653*x**3 - 7661*x**2 - 1190*x\nNo more calculations needed.\n-456*x**5 - 2040*x**4 - 1653*x**3 - 7661*x**2 - 1190*x", "generated_answer": "-456*x**5 - 2040*x**4 - 1653*x**3 - 7661*x**2 - 1190*x", "step_length": 6} {"cot_id": "73fe72b1b7d902976df16c8589402724ee0e99dde73f185d95d5b56e26eedc4d", "datapoint": {"question": "Simplify this expression: (9*z + 24)*(9*z**2 + 26*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "81*z**3 + 450*z**2 + 624*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1871, "polynomial_expr": "(9*z + 24)*(9*z**2 + 26*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9*z + 24)*(9*z**2 + 26*z)\nExpanding the part (9*z + 24) using the distributive property, and we got: (9*z)*(9*z**2 + 26*z) + 24*(9*z**2 + 26*z)\n#Step 2:\nCurrent expression: (9*z)*(9*z**2 + 26*z) + 24*(9*z**2 + 26*z)\nSimplifying the partial expression: 24*(9*z**2 + 26*z)\nExpanding the part (9*z**2 + 26*z) using the distributive property, and we got: (26*z)*24 + (9*z**2)*24\nReplacing 24*(9*z**2 + 26*z) with (26*z)*24 + (9*z**2)*24 in the overall expression.\n#Step 3:\nCurrent expression: (9*z)*(9*z**2 + 26*z) + (26*z)*24 + (9*z**2)*24\nSimplifying the partial expression: (9*z)*(9*z**2 + 26*z)\nExpanding the part (9*z**2 + 26*z) using the distributive property, and we got: (9*z)*(26*z) + (9*z)*(9*z**2)\nReplacing (9*z)*(9*z**2 + 26*z) with (9*z)*(26*z) + (9*z)*(9*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (9*z)*(26*z) + (9*z)*(9*z**2) + (26*z)*24 + (9*z**2)*24\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (9*z**2)*24 = 216*z**2\n (9*z**2)*(9*z) = 81*z**3\n (26*z)*24 = 624*z\n (26*z)*(9*z) = 234*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 81*z**3 + 216*z**2 + 234*z**2 + 624*z\nCombining like terms, got 81*z**3 + 450*z**2 + 624*z\n#Step 6:\nCurrent expression: 81*z**3 + 450*z**2 + 624*z\nNo more calculations needed.\n81*z**3 + 450*z**2 + 624*z", "generated_answer": "81*z**3 + 450*z**2 + 624*z", "step_length": 6} {"cot_id": "a44a6ddfc9d770e955aba376f9e25df196a5aebe8fac7f290f1517d1f271a492", "datapoint": {"question": "Calculate the following: (-10*x**2 + 48*x - 22)*(2*x**2 + 31*x + 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-20*x**4 - 214*x**3 + 1114*x**2 + 902*x - 726", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1872, "polynomial_expr": "(-10*x**2 + 48*x - 22)*(2*x**2 + 31*x + 33)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-10*x**2 + 48*x - 22)*(2*x**2 + 31*x + 33)\nExpanding the part (-10*x**2 + 48*x - 22) using the distributive property, and we got: (48*x)*(2*x**2 + 31*x + 33) + (-10*x**2)*(2*x**2 + 31*x + 33) - 22*(2*x**2 + 31*x + 33)\n#Step 2:\nCurrent expression: (48*x)*(2*x**2 + 31*x + 33) + (-10*x**2)*(2*x**2 + 31*x + 33) - 22*(2*x**2 + 31*x + 33)\nSimplifying the partial expression: -22*(2*x**2 + 31*x + 33)\nExpanding the part (2*x**2 + 31*x + 33) using the distributive property, and we got: (31*x)*(-22) + (2*x**2)*(-22) + 33*(-22)\nReplacing -22*(2*x**2 + 31*x + 33) with (31*x)*(-22) + (2*x**2)*(-22) + 33*(-22) in the overall expression.\n#Step 3:\nCurrent expression: (31*x)*(-22) + (48*x)*(2*x**2 + 31*x + 33) + (-10*x**2)*(2*x**2 + 31*x + 33) + (2*x**2)*(-22) - 726\nSimplifying the partial expression: (-10*x**2)*(2*x**2 + 31*x + 33)\nExpanding the part (2*x**2 + 31*x + 33) using the distributive property, and we got: 33*(-10*x**2) + (31*x)*(-10*x**2) + (-10*x**2)*(2*x**2)\nReplacing (-10*x**2)*(2*x**2 + 31*x + 33) with 33*(-10*x**2) + (31*x)*(-10*x**2) + (-10*x**2)*(2*x**2) in the overall expression.\n#Step 4:\nCurrent expression: 33*(-10)*x**2 + (31*x)*(-10*x**2) + (31*x)*(-22) + (48*x)*(2*x**2 + 31*x + 33) + (-10*x**2)*(2*x**2) + (2*x**2)*(-22) - 726\nSimplifying the partial expression: (48*x)*(2*x**2 + 31*x + 33)\nExpanding the part (2*x**2 + 31*x + 33) using the distributive property, and we got: 33*(48*x) + (31*x)*(48*x) + (48*x)*(2*x**2)\nReplacing (48*x)*(2*x**2 + 31*x + 33) with 33*(48*x) + (31*x)*(48*x) + (48*x)*(2*x**2) in the overall expression.\n#Step 5:\nCurrent expression: 33*(-10)*x**2 + 33*48*x + (31*x)*(48*x) + (31*x)*(-10*x**2) + (31*x)*(-22) + (48*x)*(2*x**2) + (-10*x**2)*(2*x**2) + (2*x**2)*(-22) - 726\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (2*x**2)*-22 = -44*x**2\n (2*x**2)*(-10*x**2) = -20*x**4\n (2*x**2)*(48*x) = 96*x**3\n (31*x)*-22 = -682*x\n (31*x)*(-10*x**2) = -310*x**3\n (31*x)*(48*x) = 1488*x**2\n 33*-10*x**2 = -330*x**2\n 33*48*x = 1584*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -20*x**4 - 310*x**3 + 96*x**3 - 330*x**2 - 44*x**2 + 1488*x**2 - 682*x + 1584*x - 726\nCombining like terms, got -20*x**4 - 214*x**3 + 1114*x**2 + 902*x - 726\n#Step 7:\nCurrent expression: -20*x**4 - 214*x**3 + 1114*x**2 + 902*x - 726\nNo more calculations needed.\n-20*x**4 - 214*x**3 + 1114*x**2 + 902*x - 726", "generated_answer": "-20*x**4 - 214*x**3 + 1114*x**2 + 902*x - 726", "step_length": 7} {"cot_id": "c00b46e203a00bf0b67ba8665519962aee7c7e97c8b1098529f7413a2ca9b4d1", "datapoint": {"question": "Simplify this expression: 583*z**3 - 159*z**2 + 2067*z\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "583*z**3 - 159*z**2 + 2067*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1873, "polynomial_expr": "583*z**3 - 159*z**2 + 2067*z", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 583*z**3 - 159*z**2 + 2067*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 583*z**3 - 159*z**2 + 2067*z\nNo more calculations needed.\n583*z**3 - 159*z**2 + 2067*z", "generated_answer": "583*z**3 - 159*z**2 + 2067*z", "step_length": 2} {"cot_id": "9eb6756dc33c484e9096486224b1fbf75013499695b3044f5e2afadf82650698", "datapoint": {"question": "Simplify this expression: (6 - 44*x)*(50 - 45*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1980*x**2 - 2470*x + 300", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1874, "polynomial_expr": "(6 - 44*x)*(50 - 45*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6 - 44*x)*(50 - 45*x)\nExpanding the part (6 - 44*x) using the distributive property, and we got: (-44*x)*(50 - 45*x) + 6*(50 - 45*x)\n#Step 2:\nCurrent expression: (-44*x)*(50 - 45*x) + 6*(50 - 45*x)\nSimplifying the partial expression: 6*(50 - 45*x)\nExpanding the part (50 - 45*x) using the distributive property, and we got: -45*x*6 + 50*6\nReplacing 6*(50 - 45*x) with -45*x*6 + 50*6 in the overall expression.\n#Step 3:\nCurrent expression: -45*x*6 + (-44*x)*(50 - 45*x) + 300\nSimplifying the partial expression: (-44*x)*(50 - 45*x)\nExpanding the part (50 - 45*x) using the distributive property, and we got: (-45*x)*(-44*x) + 50*(-44*x)\nReplacing (-44*x)*(50 - 45*x) with (-45*x)*(-44*x) + 50*(-44*x) in the overall expression.\n#Step 4:\nCurrent expression: (-45*x)*(-44*x) - 45*x*6 + 50*(-44)*x + 300\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*x)*6 = -270*x\n (-45*x)*(-44*x) = 1980*x**2\n 50*-44*x = -2200*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1980*x**2 - 2200*x - 270*x + 300\nCombining like terms, got 1980*x**2 - 2470*x + 300\n#Step 6:\nCurrent expression: 1980*x**2 - 2470*x + 300\nNo more calculations needed.\n1980*x**2 - 2470*x + 300", "generated_answer": "1980*x**2 - 2470*x + 300", "step_length": 6} {"cot_id": "f0569e9a1df58380ca30b3de4672f2d77d2bb5e8ccc4aa06f8d0203450c6bc97", "datapoint": {"question": "Calculate the following: -972*x\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-972*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1875, "polynomial_expr": "-972*x", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -972*x\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -972*x\nNo more calculations needed.\n-972*x", "generated_answer": "-972*x", "step_length": 2} {"cot_id": "ef810ebce67d5a92f6adaa5ade211b8c79d89a8919fdbc52f5c9c73e5d450881", "datapoint": {"question": "Simplify this expression: (-24*x**2 + 47*x - 9)*(-24*x**3 + 25*x**2 - 18)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "576*x**5 - 1728*x**4 + 1391*x**3 + 207*x**2 - 846*x + 162", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1876, "polynomial_expr": "(-24*x**2 + 47*x - 9)*(-24*x**3 + 25*x**2 - 18)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-24*x**2 + 47*x - 9)*(-24*x**3 + 25*x**2 - 18)\nExpanding the part (-24*x**3 + 25*x**2 - 18) using the distributive property, and we got: (25*x**2)*(-24*x**2 + 47*x - 9) + (-24*x**3)*(-24*x**2 + 47*x - 9) - 18*(-24*x**2 + 47*x - 9)\n#Step 2:\nCurrent expression: (25*x**2)*(-24*x**2 + 47*x - 9) + (-24*x**3)*(-24*x**2 + 47*x - 9) - 18*(-24*x**2 + 47*x - 9)\nSimplifying the partial expression: -18*(-24*x**2 + 47*x - 9)\nExpanding the part (-24*x**2 + 47*x - 9) using the distributive property, and we got: (47*x)*(-18) - 24*x**2*(-18) - 9*(-18)\nReplacing -18*(-24*x**2 + 47*x - 9) with (47*x)*(-18) - 24*x**2*(-18) - 9*(-18) in the overall expression.\n#Step 3:\nCurrent expression: (47*x)*(-18) - 24*x**2*(-18) + (25*x**2)*(-24*x**2 + 47*x - 9) + (-24*x**3)*(-24*x**2 + 47*x - 9) + 162\nSimplifying the partial expression: (-24*x**3)*(-24*x**2 + 47*x - 9)\nExpanding the part (-24*x**2 + 47*x - 9) using the distributive property, and we got: -(-1)*216*x**3 + (47*x)*(-24*x**3) + (-24*x**2)*(-24*x**3)\nReplacing (-24*x**3)*(-24*x**2 + 47*x - 9) with -(-1)*216*x**3 + (47*x)*(-24*x**3) + (-24*x**2)*(-24*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -9*(-24)*x**3 + (47*x)*(-24*x**3) + (47*x)*(-18) + (-24*x**2)*(-24*x**3) - 24*x**2*(-18) + (25*x**2)*(-24*x**2 + 47*x - 9) + 162\nSimplifying the partial expression: (25*x**2)*(-24*x**2 + 47*x - 9)\nExpanding the part (-24*x**2 + 47*x - 9) using the distributive property, and we got: -225*x**2 + (47*x)*(25*x**2) + (-24*x**2)*(25*x**2)\nReplacing (25*x**2)*(-24*x**2 + 47*x - 9) with -225*x**2 + (47*x)*(25*x**2) + (-24*x**2)*(25*x**2) in the overall expression.\n#Step 5:\nCurrent expression: -9*(-24)*x**3 - 9*25*x**2 + (47*x)*(25*x**2) + (47*x)*(-24*x**3) + (47*x)*(-18) + (-24*x**2)*(25*x**2) + (-24*x**2)*(-24*x**3) - 24*x**2*(-18) + 162\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-24*x**2)*-18 = 432*x**2\n (-24*x**2)*(-24*x**3) = 576*x**5\n (-24*x**2)*(25*x**2) = -600*x**4\n (47*x)*-18 = -846*x\n (47*x)*(-24*x**3) = -1128*x**4\n (47*x)*(25*x**2) = 1175*x**3\n -9*-24*x**3 = 216*x**3\n -9*25*x**2 = -225*x**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 576*x**5 - 1128*x**4 - 600*x**4 + 216*x**3 + 1175*x**3 - 225*x**2 + 432*x**2 - 846*x + 162\nCombining like terms, got 576*x**5 - 1728*x**4 + 1391*x**3 + 207*x**2 - 846*x + 162\n#Step 7:\nCurrent expression: 576*x**5 - 1728*x**4 + 1391*x**3 + 207*x**2 - 846*x + 162\nNo more calculations needed.\n576*x**5 - 1728*x**4 + 1391*x**3 + 207*x**2 - 846*x + 162", "generated_answer": "576*x**5 - 1728*x**4 + 1391*x**3 + 207*x**2 - 846*x + 162", "step_length": 7} {"cot_id": "8030f841031335cb0b552b3b9c9ddd48f8a8f650307563d316d555d3ba90891f", "datapoint": {"question": "Calculate the following: (18*y**2 - 19)*(-7*y**2 - 47*y - 40)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-126*y**4 - 846*y**3 - 587*y**2 + 893*y + 760", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1877, "polynomial_expr": "(18*y**2 - 19)*(-7*y**2 - 47*y - 40)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (18*y**2 - 19)*(-7*y**2 - 47*y - 40)\nExpanding the part (18*y**2 - 19) using the distributive property, and we got: (18*y**2)*(-7*y**2 - 47*y - 40) - 19*(-7*y**2 - 47*y - 40)\n#Step 2:\nCurrent expression: (18*y**2)*(-7*y**2 - 47*y - 40) - 19*(-7*y**2 - 47*y - 40)\nSimplifying the partial expression: -19*(-7*y**2 - 47*y - 40)\nExpanding the part (-7*y**2 - 47*y - 40) using the distributive property, and we got: -47*y*(-19) - 7*y**2*(-19) - 40*(-19)\nReplacing -19*(-7*y**2 - 47*y - 40) with -47*y*(-19) - 7*y**2*(-19) - 40*(-19) in the overall expression.\n#Step 3:\nCurrent expression: -47*y*(-19) - 7*y**2*(-19) + (18*y**2)*(-7*y**2 - 47*y - 40) + 760\nSimplifying the partial expression: (18*y**2)*(-7*y**2 - 47*y - 40)\nExpanding the part (-7*y**2 - 47*y - 40) using the distributive property, and we got: (-47*y)*(18*y**2) - 720*y**2 + (-7*y**2)*(18*y**2)\nReplacing (18*y**2)*(-7*y**2 - 47*y - 40) with (-47*y)*(18*y**2) - 720*y**2 + (-7*y**2)*(18*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-47*y)*(18*y**2) - 47*y*(-19) - 40*18*y**2 + (-7*y**2)*(18*y**2) - 7*y**2*(-19) + 760\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*y)*-19 = 893*y\n (-47*y)*(18*y**2) = -846*y**3\n (-7*y**2)*-19 = 133*y**2\n (-7*y**2)*(18*y**2) = -126*y**4\n -40*18*y**2 = -720*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -126*y**4 - 846*y**3 - 720*y**2 + 133*y**2 + 893*y + 760\nCombining like terms, got -126*y**4 - 846*y**3 - 587*y**2 + 893*y + 760\n#Step 6:\nCurrent expression: -126*y**4 - 846*y**3 - 587*y**2 + 893*y + 760\nNo more calculations needed.\n-126*y**4 - 846*y**3 - 587*y**2 + 893*y + 760", "generated_answer": "-126*y**4 - 846*y**3 - 587*y**2 + 893*y + 760", "step_length": 6} {"cot_id": "42b741af6f43294fc8aa33975a6cf3b1aad8613f8af71503337b352e244f501b", "datapoint": {"question": "Calculate the following: 81*y**2*(-25*y**3 + 20*y + 34)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2025*y**5 + 1620*y**3 + 2754*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1878, "polynomial_expr": "81*y**2*(-25*y**3 + 20*y + 34)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 81*y**2*(-25*y**3 + 20*y + 34)\nExpanding the part (-25*y**3 + 20*y + 34) using the distributive property, and we got: 34*(81*y**2) + (20*y)*(81*y**2) + (81*y**2)*(-25*y**3)\n#Step 2:\nCurrent expression: 34*(81*y**2) + (20*y)*(81*y**2) + (81*y**2)*(-25*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 34*(81*y**2) = 2754*y**2\n (-25*y**3)*(81*y**2) = -2025*y**5\n (20*y)*(81*y**2) = 1620*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -2025*y**5 + 1620*y**3 + 2754*y**2\nNo more calculations needed.\n-2025*y**5 + 1620*y**3 + 2754*y**2", "generated_answer": "-2025*y**5 + 1620*y**3 + 2754*y**2", "step_length": 3} {"cot_id": "6431d197779b0e6bb8aa88ea05710372bdd96945973bf94ed4142b434513d1bb", "datapoint": {"question": "Simplify this expression: -77*z**3*(-19*z**3 - 11*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1463*z**6 + 847*z**5", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1879, "polynomial_expr": "-77*z**3*(-19*z**3 - 11*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -77*z**3*(-19*z**3 - 11*z**2)\nExpanding the part (-19*z**3 - 11*z**2) using the distributive property, and we got: (-11*z**2)*(-77*z**3) + (-77*z**3)*(-19*z**3)\n#Step 2:\nCurrent expression: (-11*z**2)*(-77*z**3) + (-77*z**3)*(-19*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*z**3)*(-77*z**3) = 1463*z**6\n (-11*z**2)*(-77*z**3) = 847*z**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1463*z**6 + 847*z**5\nNo more calculations needed.\n1463*z**6 + 847*z**5", "generated_answer": "1463*z**6 + 847*z**5", "step_length": 3} {"cot_id": "0dc53609893bd6673b2f26bee8154339fc8f9dc13f6f53dc06d331d6cbb229e3", "datapoint": {"question": "Simplify this expression: (16*x**2 + 15*x)*(-3*x**3 - 9*x + 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-48*x**5 - 45*x**4 - 144*x**3 + 393*x**2 + 495*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1880, "polynomial_expr": "(16*x**2 + 15*x)*(-3*x**3 - 9*x + 33)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (16*x**2 + 15*x)*(-3*x**3 - 9*x + 33)\nExpanding the part (16*x**2 + 15*x) using the distributive property, and we got: (15*x)*(-3*x**3 - 9*x + 33) + (16*x**2)*(-3*x**3 - 9*x + 33)\n#Step 2:\nCurrent expression: (15*x)*(-3*x**3 - 9*x + 33) + (16*x**2)*(-3*x**3 - 9*x + 33)\nSimplifying the partial expression: (15*x)*(-3*x**3 - 9*x + 33)\nExpanding the part (-3*x**3 - 9*x + 33) using the distributive property, and we got: (-9*x)*(15*x) + 33*(15*x) + (15*x)*(-3*x**3)\nReplacing (15*x)*(-3*x**3 - 9*x + 33) with (-9*x)*(15*x) + 33*(15*x) + (15*x)*(-3*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-9*x)*(15*x) + 33*15*x + (15*x)*(-3*x**3) + (16*x**2)*(-3*x**3 - 9*x + 33)\nSimplifying the partial expression: (16*x**2)*(-3*x**3 - 9*x + 33)\nExpanding the part (-3*x**3 - 9*x + 33) using the distributive property, and we got: (-9*x)*(16*x**2) + 33*(16*x**2) + (16*x**2)*(-3*x**3)\nReplacing (16*x**2)*(-3*x**3 - 9*x + 33) with (-9*x)*(16*x**2) + 33*(16*x**2) + (16*x**2)*(-3*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-9*x)*(15*x) + (-9*x)*(16*x**2) + 33*16*x**2 + 33*15*x + (15*x)*(-3*x**3) + (16*x**2)*(-3*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-9*x)*(15*x) = -135*x**2\n (-9*x)*(16*x**2) = -144*x**3\n (-3*x**3)*(15*x) = -45*x**4\n (-3*x**3)*(16*x**2) = -48*x**5\n 33*15*x = 495*x\n 33*16*x**2 = 528*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -48*x**5 - 45*x**4 - 144*x**3 - 135*x**2 + 528*x**2 + 495*x\nCombining like terms, got -48*x**5 - 45*x**4 - 144*x**3 + 393*x**2 + 495*x\n#Step 6:\nCurrent expression: -48*x**5 - 45*x**4 - 144*x**3 + 393*x**2 + 495*x\nNo more calculations needed.\n-48*x**5 - 45*x**4 - 144*x**3 + 393*x**2 + 495*x", "generated_answer": "-48*x**5 - 45*x**4 - 144*x**3 + 393*x**2 + 495*x", "step_length": 6} {"cot_id": "45856efe6c125b724b9a8a137421e0f0aeb65616fdfabff3ed923a57d6169116", "datapoint": {"question": "Simplify this expression: (-46*y**3 - 26)*(-34*y**3 + 9*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1564*y**6 - 414*y**5 + 884*y**3 - 234*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1881, "polynomial_expr": "(-46*y**3 - 26)*(-34*y**3 + 9*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-46*y**3 - 26)*(-34*y**3 + 9*y**2)\nExpanding the part (-46*y**3 - 26) using the distributive property, and we got: (-46*y**3)*(-34*y**3 + 9*y**2) - 26*(-34*y**3 + 9*y**2)\n#Step 2:\nCurrent expression: (-46*y**3)*(-34*y**3 + 9*y**2) - 26*(-34*y**3 + 9*y**2)\nSimplifying the partial expression: -26*(-34*y**3 + 9*y**2)\nExpanding the part (-34*y**3 + 9*y**2) using the distributive property, and we got: (9*y**2)*(-26) - 34*y**3*(-26)\nReplacing -26*(-34*y**3 + 9*y**2) with (9*y**2)*(-26) - 34*y**3*(-26) in the overall expression.\n#Step 3:\nCurrent expression: (9*y**2)*(-26) + (-46*y**3)*(-34*y**3 + 9*y**2) - 34*y**3*(-26)\nSimplifying the partial expression: (-46*y**3)*(-34*y**3 + 9*y**2)\nExpanding the part (-34*y**3 + 9*y**2) using the distributive property, and we got: (9*y**2)*(-46*y**3) + (-46*y**3)*(-34*y**3)\nReplacing (-46*y**3)*(-34*y**3 + 9*y**2) with (9*y**2)*(-46*y**3) + (-46*y**3)*(-34*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (9*y**2)*(-46*y**3) + (9*y**2)*(-26) + (-46*y**3)*(-34*y**3) - 34*y**3*(-26)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*y**3)*-26 = 884*y**3\n (-34*y**3)*(-46*y**3) = 1564*y**6\n (9*y**2)*-26 = -234*y**2\n (9*y**2)*(-46*y**3) = -414*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1564*y**6 - 414*y**5 + 884*y**3 - 234*y**2\nNo more calculations needed.\n1564*y**6 - 414*y**5 + 884*y**3 - 234*y**2", "generated_answer": "1564*y**6 - 414*y**5 + 884*y**3 - 234*y**2", "step_length": 5} {"cot_id": "4cc494ecb0d2df8f0d2e4ab207a2b3fd648002bdb05b4907eb90302dfe304a32", "datapoint": {"question": "Simplify this expression: (-48*y**3 - 35*y**2)*(27*y**3 - 49*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1296*y**6 + 1407*y**5 + 1715*y**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1882, "polynomial_expr": "(-48*y**3 - 35*y**2)*(27*y**3 - 49*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-48*y**3 - 35*y**2)*(27*y**3 - 49*y**2)\nExpanding the part (27*y**3 - 49*y**2) using the distributive property, and we got: (-49*y**2)*(-48*y**3 - 35*y**2) + (27*y**3)*(-48*y**3 - 35*y**2)\n#Step 2:\nCurrent expression: (-49*y**2)*(-48*y**3 - 35*y**2) + (27*y**3)*(-48*y**3 - 35*y**2)\nSimplifying the partial expression: (-49*y**2)*(-48*y**3 - 35*y**2)\nExpanding the part (-48*y**3 - 35*y**2) using the distributive property, and we got: (-49*y**2)*(-35*y**2) + (-49*y**2)*(-48*y**3)\nReplacing (-49*y**2)*(-48*y**3 - 35*y**2) with (-49*y**2)*(-35*y**2) + (-49*y**2)*(-48*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-49*y**2)*(-35*y**2) + (-49*y**2)*(-48*y**3) + (27*y**3)*(-48*y**3 - 35*y**2)\nSimplifying the partial expression: (27*y**3)*(-48*y**3 - 35*y**2)\nExpanding the part (-48*y**3 - 35*y**2) using the distributive property, and we got: (-35*y**2)*(27*y**3) + (-48*y**3)*(27*y**3)\nReplacing (27*y**3)*(-48*y**3 - 35*y**2) with (-35*y**2)*(27*y**3) + (-48*y**3)*(27*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-49*y**2)*(-35*y**2) + (-49*y**2)*(-48*y**3) + (-35*y**2)*(27*y**3) + (-48*y**3)*(27*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*y**3)*(-49*y**2) = 2352*y**5\n (-48*y**3)*(27*y**3) = -1296*y**6\n (-35*y**2)*(-49*y**2) = 1715*y**4\n (-35*y**2)*(27*y**3) = -945*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1296*y**6 - 945*y**5 + 2352*y**5 + 1715*y**4\nCombining like terms, got -1296*y**6 + 1407*y**5 + 1715*y**4\n#Step 6:\nCurrent expression: -1296*y**6 + 1407*y**5 + 1715*y**4\nNo more calculations needed.\n-1296*y**6 + 1407*y**5 + 1715*y**4", "generated_answer": "-1296*y**6 + 1407*y**5 + 1715*y**4", "step_length": 6} {"cot_id": "cd10d43f7904f590edeb566ac23bd9783325b3f055af9e487a318dcdab1c33e8", "datapoint": {"question": "Simplify this expression: 3*x*(35*x**3 + 37*x**2 - 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "105*x**4 + 111*x**3 - 63*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1883, "polynomial_expr": "3*x*(35*x**3 + 37*x**2 - 21)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 3*x*(35*x**3 + 37*x**2 - 21)\nExpanding the part (35*x**3 + 37*x**2 - 21) using the distributive property, and we got: -63*x + (3*x)*(37*x**2) + (3*x)*(35*x**3)\n#Step 2:\nCurrent expression: -63*x + (3*x)*(37*x**2) + (3*x)*(35*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -21*(3*x) = -63*x\n (35*x**3)*(3*x) = 105*x**4\n (37*x**2)*(3*x) = 111*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 105*x**4 + 111*x**3 - 63*x\nNo more calculations needed.\n105*x**4 + 111*x**3 - 63*x", "generated_answer": "105*x**4 + 111*x**3 - 63*x", "step_length": 3} {"cot_id": "8397e77708d2f54b1c2d1b814844914214ab233fc963df9247564355823b7729", "datapoint": {"question": "Calculate the following: (-38*z**2 - 116*z)*(-2*z**3 - 45*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "76*z**5 + 1942*z**4 + 5220*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1884, "polynomial_expr": "(-38*z**2 - 116*z)*(-2*z**3 - 45*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-38*z**2 - 116*z)*(-2*z**3 - 45*z**2)\nExpanding the part (-38*z**2 - 116*z) using the distributive property, and we got: (-116*z)*(-2*z**3 - 45*z**2) + (-38*z**2)*(-2*z**3 - 45*z**2)\n#Step 2:\nCurrent expression: (-116*z)*(-2*z**3 - 45*z**2) + (-38*z**2)*(-2*z**3 - 45*z**2)\nSimplifying the partial expression: (-116*z)*(-2*z**3 - 45*z**2)\nExpanding the part (-2*z**3 - 45*z**2) using the distributive property, and we got: (-116*z)*(-45*z**2) + (-116*z)*(-2*z**3)\nReplacing (-116*z)*(-2*z**3 - 45*z**2) with (-116*z)*(-45*z**2) + (-116*z)*(-2*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-116*z)*(-45*z**2) + (-116*z)*(-2*z**3) + (-38*z**2)*(-2*z**3 - 45*z**2)\nSimplifying the partial expression: (-38*z**2)*(-2*z**3 - 45*z**2)\nExpanding the part (-2*z**3 - 45*z**2) using the distributive property, and we got: (-45*z**2)*(-38*z**2) + (-38*z**2)*(-2*z**3)\nReplacing (-38*z**2)*(-2*z**3 - 45*z**2) with (-45*z**2)*(-38*z**2) + (-38*z**2)*(-2*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-116*z)*(-45*z**2) + (-116*z)*(-2*z**3) + (-45*z**2)*(-38*z**2) + (-38*z**2)*(-2*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*z**2)*(-116*z) = 5220*z**3\n (-45*z**2)*(-38*z**2) = 1710*z**4\n (-2*z**3)*(-116*z) = 232*z**4\n (-2*z**3)*(-38*z**2) = 76*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 76*z**5 + 232*z**4 + 1710*z**4 + 5220*z**3\nCombining like terms, got 76*z**5 + 1942*z**4 + 5220*z**3\n#Step 6:\nCurrent expression: 76*z**5 + 1942*z**4 + 5220*z**3\nNo more calculations needed.\n76*z**5 + 1942*z**4 + 5220*z**3", "generated_answer": "76*z**5 + 1942*z**4 + 5220*z**3", "step_length": 6} {"cot_id": "056a99ab8daed5c86015b00a63e3f67f839d3a8b108656e1ffb19daea25ff456", "datapoint": {"question": "Simplify this expression: (9*z**2 + 24)*(-28*z**3 - 23*z**2 + 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-252*z**5 - 207*z**4 - 672*z**3 - 228*z**2 + 864", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1885, "polynomial_expr": "(9*z**2 + 24)*(-28*z**3 - 23*z**2 + 36)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9*z**2 + 24)*(-28*z**3 - 23*z**2 + 36)\nExpanding the part (9*z**2 + 24) using the distributive property, and we got: (9*z**2)*(-28*z**3 - 23*z**2 + 36) + 24*(-28*z**3 - 23*z**2 + 36)\n#Step 2:\nCurrent expression: (9*z**2)*(-28*z**3 - 23*z**2 + 36) + 24*(-28*z**3 - 23*z**2 + 36)\nSimplifying the partial expression: 24*(-28*z**3 - 23*z**2 + 36)\nExpanding the part (-28*z**3 - 23*z**2 + 36) using the distributive property, and we got: -23*z**2*24 - 28*z**3*24 + 36*24\nReplacing 24*(-28*z**3 - 23*z**2 + 36) with -23*z**2*24 - 28*z**3*24 + 36*24 in the overall expression.\n#Step 3:\nCurrent expression: -23*z**2*24 + (9*z**2)*(-28*z**3 - 23*z**2 + 36) - 28*z**3*24 + 864\nSimplifying the partial expression: (9*z**2)*(-28*z**3 - 23*z**2 + 36)\nExpanding the part (-28*z**3 - 23*z**2 + 36) using the distributive property, and we got: 36*(9*z**2) + (-23*z**2)*(9*z**2) + (9*z**2)*(-28*z**3)\nReplacing (9*z**2)*(-28*z**3 - 23*z**2 + 36) with 36*(9*z**2) + (-23*z**2)*(9*z**2) + (9*z**2)*(-28*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 36*9*z**2 + (-23*z**2)*(9*z**2) - 23*z**2*24 + (9*z**2)*(-28*z**3) - 28*z**3*24 + 864\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*z**3)*24 = -672*z**3\n (-28*z**3)*(9*z**2) = -252*z**5\n (-23*z**2)*24 = -552*z**2\n (-23*z**2)*(9*z**2) = -207*z**4\n 36*9*z**2 = 324*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -252*z**5 - 207*z**4 - 672*z**3 - 552*z**2 + 324*z**2 + 864\nCombining like terms, got -252*z**5 - 207*z**4 - 672*z**3 - 228*z**2 + 864\n#Step 6:\nCurrent expression: -252*z**5 - 207*z**4 - 672*z**3 - 228*z**2 + 864\nNo more calculations needed.\n-252*z**5 - 207*z**4 - 672*z**3 - 228*z**2 + 864", "generated_answer": "-252*z**5 - 207*z**4 - 672*z**3 - 228*z**2 + 864", "step_length": 6} {"cot_id": "e317bb3afa0e04ef95ed45065cbbe3b540bbd4440f720049db50228d96e95439", "datapoint": {"question": "Simplify this expression: x*(29*x**3 - 29*x**2 + 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "29*x**4 - 29*x**3 + 24*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1886, "polynomial_expr": "x*(29*x**3 - 29*x**2 + 24)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: x*(29*x**3 - 29*x**2 + 24)\nExpanding the part (29*x**3 - 29*x**2 + 24) using the distributive property, and we got: x*(-29*x**2) + x*(29*x**3) + 24*x\n#Step 2:\nCurrent expression: x*(-29*x**2) + x*(29*x**3) + 24*x\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*x**2)*x = -29*x**3\n (29*x**3)*x = 29*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 29*x**4 - 29*x**3 + 24*x\nNo more calculations needed.\n29*x**4 - 29*x**3 + 24*x", "generated_answer": "29*x**4 - 29*x**3 + 24*x", "step_length": 3} {"cot_id": "5613117b1385b4631925fb51ab0b19732c3f9aa8e6100854d1543e722e9fb6a7", "datapoint": {"question": "Simplify this expression: (50*z**2 + 9)*(-46*z**3 + 12*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2300*z**5 + 600*z**4 - 414*z**3 + 108*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1887, "polynomial_expr": "(50*z**2 + 9)*(-46*z**3 + 12*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (50*z**2 + 9)*(-46*z**3 + 12*z**2)\nExpanding the part (50*z**2 + 9) using the distributive property, and we got: (50*z**2)*(-46*z**3 + 12*z**2) + 9*(-46*z**3 + 12*z**2)\n#Step 2:\nCurrent expression: (50*z**2)*(-46*z**3 + 12*z**2) + 9*(-46*z**3 + 12*z**2)\nSimplifying the partial expression: 9*(-46*z**3 + 12*z**2)\nExpanding the part (-46*z**3 + 12*z**2) using the distributive property, and we got: (12*z**2)*9 - 46*z**3*9\nReplacing 9*(-46*z**3 + 12*z**2) with (12*z**2)*9 - 46*z**3*9 in the overall expression.\n#Step 3:\nCurrent expression: (12*z**2)*9 + (50*z**2)*(-46*z**3 + 12*z**2) - 46*z**3*9\nSimplifying the partial expression: (50*z**2)*(-46*z**3 + 12*z**2)\nExpanding the part (-46*z**3 + 12*z**2) using the distributive property, and we got: (12*z**2)*(50*z**2) + (50*z**2)*(-46*z**3)\nReplacing (50*z**2)*(-46*z**3 + 12*z**2) with (12*z**2)*(50*z**2) + (50*z**2)*(-46*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (12*z**2)*(50*z**2) + (12*z**2)*9 + (50*z**2)*(-46*z**3) - 46*z**3*9\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*z**3)*9 = -414*z**3\n (-46*z**3)*(50*z**2) = -2300*z**5\n (12*z**2)*9 = 108*z**2\n (12*z**2)*(50*z**2) = 600*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2300*z**5 + 600*z**4 - 414*z**3 + 108*z**2\nNo more calculations needed.\n-2300*z**5 + 600*z**4 - 414*z**3 + 108*z**2", "generated_answer": "-2300*z**5 + 600*z**4 - 414*z**3 + 108*z**2", "step_length": 5} {"cot_id": "bb0488aab2855af75f0bb72d224426d444b8d243170392aef2ba2f5ec5d4e294", "datapoint": {"question": "Calculate the following: 69*x*(104*x**3 + 19*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "7176*x**4 + 1311*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1888, "polynomial_expr": "69*x*(104*x**3 + 19*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 69*x*(104*x**3 + 19*x**2)\nExpanding the part (104*x**3 + 19*x**2) using the distributive property, and we got: (69*x)*(19*x**2) + (69*x)*(104*x**3)\n#Step 2:\nCurrent expression: (69*x)*(19*x**2) + (69*x)*(104*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (19*x**2)*(69*x) = 1311*x**3\n (104*x**3)*(69*x) = 7176*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 7176*x**4 + 1311*x**3\nNo more calculations needed.\n7176*x**4 + 1311*x**3", "generated_answer": "7176*x**4 + 1311*x**3", "step_length": 3} {"cot_id": "497151f21204280ba4b1972c1070a4da7a08f8ef6694e901a55c142e44613465", "datapoint": {"question": "Calculate the following: (7 - 47*y**3)*(-27*y**3 + 20*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1269*y**6 - 940*y**4 - 189*y**3 + 140*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1889, "polynomial_expr": "(7 - 47*y**3)*(-27*y**3 + 20*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7 - 47*y**3)*(-27*y**3 + 20*y)\nExpanding the part (7 - 47*y**3) using the distributive property, and we got: (-47*y**3)*(-27*y**3 + 20*y) + 7*(-27*y**3 + 20*y)\n#Step 2:\nCurrent expression: (-47*y**3)*(-27*y**3 + 20*y) + 7*(-27*y**3 + 20*y)\nSimplifying the partial expression: 7*(-27*y**3 + 20*y)\nExpanding the part (-27*y**3 + 20*y) using the distributive property, and we got: (20*y)*7 - 27*y**3*7\nReplacing 7*(-27*y**3 + 20*y) with (20*y)*7 - 27*y**3*7 in the overall expression.\n#Step 3:\nCurrent expression: (20*y)*7 + (-47*y**3)*(-27*y**3 + 20*y) - 27*y**3*7\nSimplifying the partial expression: (-47*y**3)*(-27*y**3 + 20*y)\nExpanding the part (-27*y**3 + 20*y) using the distributive property, and we got: (20*y)*(-47*y**3) + (-47*y**3)*(-27*y**3)\nReplacing (-47*y**3)*(-27*y**3 + 20*y) with (20*y)*(-47*y**3) + (-47*y**3)*(-27*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (20*y)*(-47*y**3) + (20*y)*7 + (-47*y**3)*(-27*y**3) - 27*y**3*7\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*y**3)*7 = -189*y**3\n (-27*y**3)*(-47*y**3) = 1269*y**6\n (20*y)*7 = 140*y\n (20*y)*(-47*y**3) = -940*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1269*y**6 - 940*y**4 - 189*y**3 + 140*y\nNo more calculations needed.\n1269*y**6 - 940*y**4 - 189*y**3 + 140*y", "generated_answer": "1269*y**6 - 940*y**4 - 189*y**3 + 140*y", "step_length": 5} {"cot_id": "8d48f09252b4e914b0426aaf114a3c32d99af9e6d292c55e8806ae7b1e8ad987", "datapoint": {"question": "Calculate the following: (36*y**2 - 30*y)*(-4*y**3 - 38*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-144*y**5 - 1248*y**4 + 1140*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1890, "polynomial_expr": "(36*y**2 - 30*y)*(-4*y**3 - 38*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (36*y**2 - 30*y)*(-4*y**3 - 38*y**2)\nExpanding the part (-4*y**3 - 38*y**2) using the distributive property, and we got: (-38*y**2)*(36*y**2 - 30*y) + (-4*y**3)*(36*y**2 - 30*y)\n#Step 2:\nCurrent expression: (-38*y**2)*(36*y**2 - 30*y) + (-4*y**3)*(36*y**2 - 30*y)\nSimplifying the partial expression: (-38*y**2)*(36*y**2 - 30*y)\nExpanding the part (36*y**2 - 30*y) using the distributive property, and we got: (-30*y)*(-38*y**2) + (-38*y**2)*(36*y**2)\nReplacing (-38*y**2)*(36*y**2 - 30*y) with (-30*y)*(-38*y**2) + (-38*y**2)*(36*y**2) in the overall expression.\n#Step 3:\nCurrent expression: (-30*y)*(-38*y**2) + (-38*y**2)*(36*y**2) + (-4*y**3)*(36*y**2 - 30*y)\nSimplifying the partial expression: (-4*y**3)*(36*y**2 - 30*y)\nExpanding the part (36*y**2 - 30*y) using the distributive property, and we got: (-30*y)*(-4*y**3) + (36*y**2)*(-4*y**3)\nReplacing (-4*y**3)*(36*y**2 - 30*y) with (-30*y)*(-4*y**3) + (36*y**2)*(-4*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-30*y)*(-38*y**2) + (-30*y)*(-4*y**3) + (-38*y**2)*(36*y**2) + (36*y**2)*(-4*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*y)*(-38*y**2) = 1140*y**3\n (-30*y)*(-4*y**3) = 120*y**4\n (36*y**2)*(-38*y**2) = -1368*y**4\n (36*y**2)*(-4*y**3) = -144*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -144*y**5 - 1368*y**4 + 120*y**4 + 1140*y**3\nCombining like terms, got -144*y**5 - 1248*y**4 + 1140*y**3\n#Step 6:\nCurrent expression: -144*y**5 - 1248*y**4 + 1140*y**3\nNo more calculations needed.\n-144*y**5 - 1248*y**4 + 1140*y**3", "generated_answer": "-144*y**5 - 1248*y**4 + 1140*y**3", "step_length": 6} {"cot_id": "67c3dcdacfe9d320a61e89dec3ff11469fc3203bb7bc5bfb6baa63632696361a", "datapoint": {"question": "Calculate the following: (46 - 9*y)*(2*y**2 + 6*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-18*y**3 + 38*y**2 + 276*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1891, "polynomial_expr": "(46 - 9*y)*(2*y**2 + 6*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (46 - 9*y)*(2*y**2 + 6*y)\nExpanding the part (46 - 9*y) using the distributive property, and we got: (-9*y)*(2*y**2 + 6*y) + 46*(2*y**2 + 6*y)\n#Step 2:\nCurrent expression: (-9*y)*(2*y**2 + 6*y) + 46*(2*y**2 + 6*y)\nSimplifying the partial expression: 46*(2*y**2 + 6*y)\nExpanding the part (2*y**2 + 6*y) using the distributive property, and we got: (6*y)*46 + (2*y**2)*46\nReplacing 46*(2*y**2 + 6*y) with (6*y)*46 + (2*y**2)*46 in the overall expression.\n#Step 3:\nCurrent expression: (-9*y)*(2*y**2 + 6*y) + (6*y)*46 + (2*y**2)*46\nSimplifying the partial expression: (-9*y)*(2*y**2 + 6*y)\nExpanding the part (2*y**2 + 6*y) using the distributive property, and we got: (-9*y)*(6*y) + (-9*y)*(2*y**2)\nReplacing (-9*y)*(2*y**2 + 6*y) with (-9*y)*(6*y) + (-9*y)*(2*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-9*y)*(6*y) + (-9*y)*(2*y**2) + (6*y)*46 + (2*y**2)*46\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (2*y**2)*46 = 92*y**2\n (2*y**2)*(-9*y) = -18*y**3\n (6*y)*46 = 276*y\n (6*y)*(-9*y) = -54*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -18*y**3 - 54*y**2 + 92*y**2 + 276*y\nCombining like terms, got -18*y**3 + 38*y**2 + 276*y\n#Step 6:\nCurrent expression: -18*y**3 + 38*y**2 + 276*y\nNo more calculations needed.\n-18*y**3 + 38*y**2 + 276*y", "generated_answer": "-18*y**3 + 38*y**2 + 276*y", "step_length": 6} {"cot_id": "6406031c583d47e7ea90cace569e3969039aa07a026797a422e3a513cd6926f0", "datapoint": {"question": "Simplify this expression: (-10*y - 3)*(20*y**3 + 19*y**2 + 78)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-200*y**4 - 250*y**3 - 57*y**2 - 780*y - 234", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1892, "polynomial_expr": "(-10*y - 3)*(20*y**3 + 19*y**2 + 78)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-10*y - 3)*(20*y**3 + 19*y**2 + 78)\nExpanding the part (-10*y - 3) using the distributive property, and we got: (-10*y)*(20*y**3 + 19*y**2 + 78) - 3*(20*y**3 + 19*y**2 + 78)\n#Step 2:\nCurrent expression: (-10*y)*(20*y**3 + 19*y**2 + 78) - 3*(20*y**3 + 19*y**2 + 78)\nSimplifying the partial expression: -3*(20*y**3 + 19*y**2 + 78)\nExpanding the part (20*y**3 + 19*y**2 + 78) using the distributive property, and we got: (19*y**2)*(-3) + (20*y**3)*(-3) + 78*(-3)\nReplacing -3*(20*y**3 + 19*y**2 + 78) with (19*y**2)*(-3) + (20*y**3)*(-3) + 78*(-3) in the overall expression.\n#Step 3:\nCurrent expression: (-10*y)*(20*y**3 + 19*y**2 + 78) + (19*y**2)*(-3) + (20*y**3)*(-3) - 234\nSimplifying the partial expression: (-10*y)*(20*y**3 + 19*y**2 + 78)\nExpanding the part (20*y**3 + 19*y**2 + 78) using the distributive property, and we got: (-10*y)*(19*y**2) + (-10*y)*(20*y**3) + 78*(-10*y)\nReplacing (-10*y)*(20*y**3 + 19*y**2 + 78) with (-10*y)*(19*y**2) + (-10*y)*(20*y**3) + 78*(-10*y) in the overall expression.\n#Step 4:\nCurrent expression: (-10*y)*(19*y**2) + (-10*y)*(20*y**3) + 78*(-10)*y + (19*y**2)*(-3) + (20*y**3)*(-3) - 234\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (19*y**2)*-3 = -57*y**2\n (19*y**2)*(-10*y) = -190*y**3\n (20*y**3)*-3 = -60*y**3\n (20*y**3)*(-10*y) = -200*y**4\n 78*-10*y = -780*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -200*y**4 - 190*y**3 - 60*y**3 - 57*y**2 - 780*y - 234\nCombining like terms, got -200*y**4 - 250*y**3 - 57*y**2 - 780*y - 234\n#Step 6:\nCurrent expression: -200*y**4 - 250*y**3 - 57*y**2 - 780*y - 234\nNo more calculations needed.\n-200*y**4 - 250*y**3 - 57*y**2 - 780*y - 234", "generated_answer": "-200*y**4 - 250*y**3 - 57*y**2 - 780*y - 234", "step_length": 6} {"cot_id": "5c043293430e309a6aa3e026b539dbd53f0cec6ff52b46f51104d22269b56b8d", "datapoint": {"question": "Calculate the following: (-26*x**3 - 8*x + 42)*(10*x**3 - 54*x**2 + 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-260*x**6 + 1404*x**5 - 80*x**4 + 46*x**3 - 2268*x**2 - 248*x + 1302", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1893, "polynomial_expr": "(-26*x**3 - 8*x + 42)*(10*x**3 - 54*x**2 + 31)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-26*x**3 - 8*x + 42)*(10*x**3 - 54*x**2 + 31)\nExpanding the part (10*x**3 - 54*x**2 + 31) using the distributive property, and we got: (-54*x**2)*(-26*x**3 - 8*x + 42) + (10*x**3)*(-26*x**3 - 8*x + 42) + 31*(-26*x**3 - 8*x + 42)\n#Step 2:\nCurrent expression: (-54*x**2)*(-26*x**3 - 8*x + 42) + (10*x**3)*(-26*x**3 - 8*x + 42) + 31*(-26*x**3 - 8*x + 42)\nSimplifying the partial expression: 31*(-26*x**3 - 8*x + 42)\nExpanding the part (-26*x**3 - 8*x + 42) using the distributive property, and we got: -8*x*31 - 26*x**3*31 + 42*31\nReplacing 31*(-26*x**3 - 8*x + 42) with -8*x*31 - 26*x**3*31 + 42*31 in the overall expression.\n#Step 3:\nCurrent expression: -8*x*31 + (-54*x**2)*(-26*x**3 - 8*x + 42) - 26*x**3*31 + (10*x**3)*(-26*x**3 - 8*x + 42) + 1302\nSimplifying the partial expression: (-54*x**2)*(-26*x**3 - 8*x + 42)\nExpanding the part (-26*x**3 - 8*x + 42) using the distributive property, and we got: (-8*x)*(-54*x**2) + 42*(-54*x**2) + (-54*x**2)*(-26*x**3)\nReplacing (-54*x**2)*(-26*x**3 - 8*x + 42) with (-8*x)*(-54*x**2) + 42*(-54*x**2) + (-54*x**2)*(-26*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-8*x)*(-54*x**2) - 8*x*31 + 42*(-54)*x**2 + (-54*x**2)*(-26*x**3) - 26*x**3*31 + (10*x**3)*(-26*x**3 - 8*x + 42) + 1302\nSimplifying the partial expression: (10*x**3)*(-26*x**3 - 8*x + 42)\nExpanding the part (-26*x**3 - 8*x + 42) using the distributive property, and we got: (-8*x)*(10*x**3) + 42*(10*x**3) + (-26*x**3)*(10*x**3)\nReplacing (10*x**3)*(-26*x**3 - 8*x + 42) with (-8*x)*(10*x**3) + 42*(10*x**3) + (-26*x**3)*(10*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-8*x)*(-54*x**2) + (-8*x)*(10*x**3) - 8*x*31 + 42*10*x**3 + 42*(-54)*x**2 + (-54*x**2)*(-26*x**3) + (-26*x**3)*(10*x**3) - 26*x**3*31 + 1302\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-26*x**3)*31 = -806*x**3\n (-26*x**3)*(-54*x**2) = 1404*x**5\n (-26*x**3)*(10*x**3) = -260*x**6\n (-8*x)*31 = -248*x\n (-8*x)*(-54*x**2) = 432*x**3\n (-8*x)*(10*x**3) = -80*x**4\n 42*-54*x**2 = -2268*x**2\n 42*10*x**3 = 420*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -260*x**6 + 1404*x**5 - 80*x**4 - 806*x**3 + 420*x**3 + 432*x**3 - 2268*x**2 - 248*x + 1302\nCombining like terms, got -260*x**6 + 1404*x**5 - 80*x**4 + 46*x**3 - 2268*x**2 - 248*x + 1302\n#Step 7:\nCurrent expression: -260*x**6 + 1404*x**5 - 80*x**4 + 46*x**3 - 2268*x**2 - 248*x + 1302\nNo more calculations needed.\n-260*x**6 + 1404*x**5 - 80*x**4 + 46*x**3 - 2268*x**2 - 248*x + 1302", "generated_answer": "-260*x**6 + 1404*x**5 - 80*x**4 + 46*x**3 - 2268*x**2 - 248*x + 1302", "step_length": 7} {"cot_id": "da90684864caa567484f2ae9cce76193c4bbb1095390e336d9142cf1145a518a", "datapoint": {"question": "Calculate the following: (26 - 26*y)*(y**3 - 33*y + 2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-26*y**4 + 26*y**3 + 858*y**2 - 910*y + 52", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1894, "polynomial_expr": "(26 - 26*y)*(y**3 - 33*y + 2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (26 - 26*y)*(y**3 - 33*y + 2)\nExpanding the part (26 - 26*y) using the distributive property, and we got: (-26*y)*(y**3 - 33*y + 2) + 26*(y**3 - 33*y + 2)\n#Step 2:\nCurrent expression: (-26*y)*(y**3 - 33*y + 2) + 26*(y**3 - 33*y + 2)\nSimplifying the partial expression: 26*(y**3 - 33*y + 2)\nExpanding the part (y**3 - 33*y + 2) using the distributive property, and we got: -33*y*26 + y**3*26 + 2*26\nReplacing 26*(y**3 - 33*y + 2) with -33*y*26 + y**3*26 + 2*26 in the overall expression.\n#Step 3:\nCurrent expression: -33*y*26 + (-26*y)*(y**3 - 33*y + 2) + y**3*26 + 52\nSimplifying the partial expression: (-26*y)*(y**3 - 33*y + 2)\nExpanding the part (y**3 - 33*y + 2) using the distributive property, and we got: (-33*y)*(-26*y) + (-26*y)*y**3 + 2*(-26*y)\nReplacing (-26*y)*(y**3 - 33*y + 2) with (-33*y)*(-26*y) + (-26*y)*y**3 + 2*(-26*y) in the overall expression.\n#Step 4:\nCurrent expression: (-33*y)*(-26*y) - 33*y*26 + (-26*y)*y**3 + y**3*26 + 2*(-26)*y + 52\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n y**3*26 = 26*y**3\n y**3*(-26*y) = -26*y**4\n (-33*y)*26 = -858*y\n (-33*y)*(-26*y) = 858*y**2\n 2*-26*y = -52*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -26*y**4 + 26*y**3 + 858*y**2 - 858*y - 52*y + 52\nCombining like terms, got -26*y**4 + 26*y**3 + 858*y**2 - 910*y + 52\n#Step 6:\nCurrent expression: -26*y**4 + 26*y**3 + 858*y**2 - 910*y + 52\nNo more calculations needed.\n-26*y**4 + 26*y**3 + 858*y**2 - 910*y + 52", "generated_answer": "-26*y**4 + 26*y**3 + 858*y**2 - 910*y + 52", "step_length": 6} {"cot_id": "b71c8d7d377f39c43d7e60e1df2f662c385baddffcb354ac9ceff673f9c49ada", "datapoint": {"question": "Simplify this expression: 19*z**2*(-37*z**3 + 25*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-703*z**5 + 475*z**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1895, "polynomial_expr": "19*z**2*(-37*z**3 + 25*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 19*z**2*(-37*z**3 + 25*z**2)\nExpanding the part (-37*z**3 + 25*z**2) using the distributive property, and we got: (19*z**2)*(25*z**2) + (19*z**2)*(-37*z**3)\n#Step 2:\nCurrent expression: (19*z**2)*(25*z**2) + (19*z**2)*(-37*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*z**3)*(19*z**2) = -703*z**5\n (25*z**2)*(19*z**2) = 475*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -703*z**5 + 475*z**4\nNo more calculations needed.\n-703*z**5 + 475*z**4", "generated_answer": "-703*z**5 + 475*z**4", "step_length": 3} {"cot_id": "4e571ee26af6f6162cd39115aa30ba005f72eab566ceef3212d1f43f8a1b2456", "datapoint": {"question": "Calculate the following: (22*z**3 - 25)*(-36*z**3 + 27*z**2 + 39*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-792*z**6 + 594*z**5 + 858*z**4 + 900*z**3 - 675*z**2 - 975*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1896, "polynomial_expr": "(22*z**3 - 25)*(-36*z**3 + 27*z**2 + 39*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (22*z**3 - 25)*(-36*z**3 + 27*z**2 + 39*z)\nExpanding the part (22*z**3 - 25) using the distributive property, and we got: (22*z**3)*(-36*z**3 + 27*z**2 + 39*z) - 25*(-36*z**3 + 27*z**2 + 39*z)\n#Step 2:\nCurrent expression: (22*z**3)*(-36*z**3 + 27*z**2 + 39*z) - 25*(-36*z**3 + 27*z**2 + 39*z)\nSimplifying the partial expression: -25*(-36*z**3 + 27*z**2 + 39*z)\nExpanding the part (-36*z**3 + 27*z**2 + 39*z) using the distributive property, and we got: (39*z)*(-25) + (27*z**2)*(-25) - 36*z**3*(-25)\nReplacing -25*(-36*z**3 + 27*z**2 + 39*z) with (39*z)*(-25) + (27*z**2)*(-25) - 36*z**3*(-25) in the overall expression.\n#Step 3:\nCurrent expression: (39*z)*(-25) + (27*z**2)*(-25) - 36*z**3*(-25) + (22*z**3)*(-36*z**3 + 27*z**2 + 39*z)\nSimplifying the partial expression: (22*z**3)*(-36*z**3 + 27*z**2 + 39*z)\nExpanding the part (-36*z**3 + 27*z**2 + 39*z) using the distributive property, and we got: (39*z)*(22*z**3) + (27*z**2)*(22*z**3) + (-36*z**3)*(22*z**3)\nReplacing (22*z**3)*(-36*z**3 + 27*z**2 + 39*z) with (39*z)*(22*z**3) + (27*z**2)*(22*z**3) + (-36*z**3)*(22*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (39*z)*(22*z**3) + (39*z)*(-25) + (27*z**2)*(22*z**3) + (27*z**2)*(-25) + (-36*z**3)*(22*z**3) - 36*z**3*(-25)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*z**3)*-25 = 900*z**3\n (-36*z**3)*(22*z**3) = -792*z**6\n (27*z**2)*-25 = -675*z**2\n (27*z**2)*(22*z**3) = 594*z**5\n (39*z)*-25 = -975*z\n (39*z)*(22*z**3) = 858*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -792*z**6 + 594*z**5 + 858*z**4 + 900*z**3 - 675*z**2 - 975*z\nNo more calculations needed.\n-792*z**6 + 594*z**5 + 858*z**4 + 900*z**3 - 675*z**2 - 975*z", "generated_answer": "-792*z**6 + 594*z**5 + 858*z**4 + 900*z**3 - 675*z**2 - 975*z", "step_length": 5} {"cot_id": "b5edebfb91ed5ea7766a4a3761e6419ad7b0c06e69ee0d8e1ae77aa421b501b0", "datapoint": {"question": "Calculate the following: (-36*z**3 + 12*z)*(2*z**3 + 6*z + 11)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-72*z**6 - 192*z**4 - 396*z**3 + 72*z**2 + 132*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1897, "polynomial_expr": "(-36*z**3 + 12*z)*(2*z**3 + 6*z + 11)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-36*z**3 + 12*z)*(2*z**3 + 6*z + 11)\nExpanding the part (-36*z**3 + 12*z) using the distributive property, and we got: (12*z)*(2*z**3 + 6*z + 11) + (-36*z**3)*(2*z**3 + 6*z + 11)\n#Step 2:\nCurrent expression: (12*z)*(2*z**3 + 6*z + 11) + (-36*z**3)*(2*z**3 + 6*z + 11)\nSimplifying the partial expression: (-36*z**3)*(2*z**3 + 6*z + 11)\nExpanding the part (2*z**3 + 6*z + 11) using the distributive property, and we got: 11*(-36*z**3) + (6*z)*(-36*z**3) + (-36*z**3)*(2*z**3)\nReplacing (-36*z**3)*(2*z**3 + 6*z + 11) with 11*(-36*z**3) + (6*z)*(-36*z**3) + (-36*z**3)*(2*z**3) in the overall expression.\n#Step 3:\nCurrent expression: 11*(-36)*z**3 + (6*z)*(-36*z**3) + (12*z)*(2*z**3 + 6*z + 11) + (-36*z**3)*(2*z**3)\nSimplifying the partial expression: (12*z)*(2*z**3 + 6*z + 11)\nExpanding the part (2*z**3 + 6*z + 11) using the distributive property, and we got: 11*(12*z) + (6*z)*(12*z) + (12*z)*(2*z**3)\nReplacing (12*z)*(2*z**3 + 6*z + 11) with 11*(12*z) + (6*z)*(12*z) + (12*z)*(2*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 11*(-36)*z**3 + 11*12*z + (6*z)*(12*z) + (6*z)*(-36*z**3) + (12*z)*(2*z**3) + (-36*z**3)*(2*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (2*z**3)*(-36*z**3) = -72*z**6\n (2*z**3)*(12*z) = 24*z**4\n (6*z)*(-36*z**3) = -216*z**4\n (6*z)*(12*z) = 72*z**2\n 11*-36*z**3 = -396*z**3\n 11*12*z = 132*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -72*z**6 - 216*z**4 + 24*z**4 - 396*z**3 + 72*z**2 + 132*z\nCombining like terms, got -72*z**6 - 192*z**4 - 396*z**3 + 72*z**2 + 132*z\n#Step 6:\nCurrent expression: -72*z**6 - 192*z**4 - 396*z**3 + 72*z**2 + 132*z\nNo more calculations needed.\n-72*z**6 - 192*z**4 - 396*z**3 + 72*z**2 + 132*z", "generated_answer": "-72*z**6 - 192*z**4 - 396*z**3 + 72*z**2 + 132*z", "step_length": 6} {"cot_id": "ca63985cd690da325e74bed3519f894fe903bd5a49a97a8c536690a6957cc031", "datapoint": {"question": "Calculate the following: (2*z**3 - 6*z)*(14*z**2 - 54*z - 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "28*z**5 - 108*z**4 - 146*z**3 + 324*z**2 + 186*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1898, "polynomial_expr": "(2*z**3 - 6*z)*(14*z**2 - 54*z - 31)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2*z**3 - 6*z)*(14*z**2 - 54*z - 31)\nExpanding the part (2*z**3 - 6*z) using the distributive property, and we got: (-6*z)*(14*z**2 - 54*z - 31) + (2*z**3)*(14*z**2 - 54*z - 31)\n#Step 2:\nCurrent expression: (-6*z)*(14*z**2 - 54*z - 31) + (2*z**3)*(14*z**2 - 54*z - 31)\nSimplifying the partial expression: (-6*z)*(14*z**2 - 54*z - 31)\nExpanding the part (14*z**2 - 54*z - 31) using the distributive property, and we got: (-54*z)*(-6*z) + (-6*z)*(14*z**2) - (-1)*186*z\nReplacing (-6*z)*(14*z**2 - 54*z - 31) with (-54*z)*(-6*z) + (-6*z)*(14*z**2) - (-1)*186*z in the overall expression.\n#Step 3:\nCurrent expression: (-54*z)*(-6*z) + (-6*z)*(14*z**2) - 31*(-6)*z + (2*z**3)*(14*z**2 - 54*z - 31)\nSimplifying the partial expression: (2*z**3)*(14*z**2 - 54*z - 31)\nExpanding the part (14*z**2 - 54*z - 31) using the distributive property, and we got: (-54*z)*(2*z**3) - 62*z**3 + (14*z**2)*(2*z**3)\nReplacing (2*z**3)*(14*z**2 - 54*z - 31) with (-54*z)*(2*z**3) - 62*z**3 + (14*z**2)*(2*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-54*z)*(-6*z) + (-54*z)*(2*z**3) + (-6*z)*(14*z**2) - 31*2*z**3 - 31*(-6)*z + (14*z**2)*(2*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-54*z)*(-6*z) = 324*z**2\n (-54*z)*(2*z**3) = -108*z**4\n (14*z**2)*(-6*z) = -84*z**3\n (14*z**2)*(2*z**3) = 28*z**5\n -31*-6*z = 186*z\n -31*2*z**3 = -62*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 28*z**5 - 108*z**4 - 84*z**3 - 62*z**3 + 324*z**2 + 186*z\nCombining like terms, got 28*z**5 - 108*z**4 - 146*z**3 + 324*z**2 + 186*z\n#Step 6:\nCurrent expression: 28*z**5 - 108*z**4 - 146*z**3 + 324*z**2 + 186*z\nNo more calculations needed.\n28*z**5 - 108*z**4 - 146*z**3 + 324*z**2 + 186*z", "generated_answer": "28*z**5 - 108*z**4 - 146*z**3 + 324*z**2 + 186*z", "step_length": 6} {"cot_id": "534b229da2ea19b517d72fe3c1f973e98960f3a11f8393602a27034e4a0a6cec", "datapoint": {"question": "Calculate the following: (-15*y**2 - 29)*(-29*y**3 - 50*y + 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "435*y**5 + 1591*y**3 - 615*y**2 + 1450*y - 1189", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1899, "polynomial_expr": "(-15*y**2 - 29)*(-29*y**3 - 50*y + 41)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-15*y**2 - 29)*(-29*y**3 - 50*y + 41)\nExpanding the part (-15*y**2 - 29) using the distributive property, and we got: (-15*y**2)*(-29*y**3 - 50*y + 41) - 29*(-29*y**3 - 50*y + 41)\n#Step 2:\nCurrent expression: (-15*y**2)*(-29*y**3 - 50*y + 41) - 29*(-29*y**3 - 50*y + 41)\nSimplifying the partial expression: -29*(-29*y**3 - 50*y + 41)\nExpanding the part (-29*y**3 - 50*y + 41) using the distributive property, and we got: -50*y*(-29) - 29*y**3*(-29) + 41*(-29)\nReplacing -29*(-29*y**3 - 50*y + 41) with -50*y*(-29) - 29*y**3*(-29) + 41*(-29) in the overall expression.\n#Step 3:\nCurrent expression: -50*y*(-29) + (-15*y**2)*(-29*y**3 - 50*y + 41) - 29*y**3*(-29) - 1189\nSimplifying the partial expression: (-15*y**2)*(-29*y**3 - 50*y + 41)\nExpanding the part (-29*y**3 - 50*y + 41) using the distributive property, and we got: (-50*y)*(-15*y**2) + 41*(-15*y**2) + (-15*y**2)*(-29*y**3)\nReplacing (-15*y**2)*(-29*y**3 - 50*y + 41) with (-50*y)*(-15*y**2) + 41*(-15*y**2) + (-15*y**2)*(-29*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-50*y)*(-15*y**2) - 50*y*(-29) + 41*(-15)*y**2 + (-15*y**2)*(-29*y**3) - 29*y**3*(-29) - 1189\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-50*y)*-29 = 1450*y\n (-50*y)*(-15*y**2) = 750*y**3\n (-29*y**3)*-29 = 841*y**3\n (-29*y**3)*(-15*y**2) = 435*y**5\n 41*-15*y**2 = -615*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 435*y**5 + 750*y**3 + 841*y**3 - 615*y**2 + 1450*y - 1189\nCombining like terms, got 435*y**5 + 1591*y**3 - 615*y**2 + 1450*y - 1189\n#Step 6:\nCurrent expression: 435*y**5 + 1591*y**3 - 615*y**2 + 1450*y - 1189\nNo more calculations needed.\n435*y**5 + 1591*y**3 - 615*y**2 + 1450*y - 1189", "generated_answer": "435*y**5 + 1591*y**3 - 615*y**2 + 1450*y - 1189", "step_length": 6} {"cot_id": "fa577b2d67022604f7b24672797576ea05da66c445f0d71b4773441c55c54d49", "datapoint": {"question": "Calculate the following: -51*y**3*(39 - 49*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2499*y**5 - 1989*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1900, "polynomial_expr": "-51*y**3*(39 - 49*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -51*y**3*(39 - 49*y**2)\nExpanding the part (39 - 49*y**2) using the distributive property, and we got: 39*(-51*y**3) + (-49*y**2)*(-51*y**3)\n#Step 2:\nCurrent expression: 39*(-51*y**3) + (-49*y**2)*(-51*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 39*(-51*y**3) = -1989*y**3\n (-49*y**2)*(-51*y**3) = 2499*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 2499*y**5 - 1989*y**3\nNo more calculations needed.\n2499*y**5 - 1989*y**3", "generated_answer": "2499*y**5 - 1989*y**3", "step_length": 3} {"cot_id": "0f8d7cf40c687f1bfd2d74aa35d22c6a3b8b6adcfbcb031b82cefdb1eff6842a", "datapoint": {"question": "Calculate the following: (42*z - 23)*(14*z**2 + 51)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "588*z**3 - 322*z**2 + 2142*z - 1173", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1901, "polynomial_expr": "(42*z - 23)*(14*z**2 + 51)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (42*z - 23)*(14*z**2 + 51)\nExpanding the part (42*z - 23) using the distributive property, and we got: (42*z)*(14*z**2 + 51) - 23*(14*z**2 + 51)\n#Step 2:\nCurrent expression: (42*z)*(14*z**2 + 51) - 23*(14*z**2 + 51)\nSimplifying the partial expression: -23*(14*z**2 + 51)\nExpanding the part (14*z**2 + 51) using the distributive property, and we got: (14*z**2)*(-23) + 51*(-23)\nReplacing -23*(14*z**2 + 51) with (14*z**2)*(-23) + 51*(-23) in the overall expression.\n#Step 3:\nCurrent expression: (42*z)*(14*z**2 + 51) + (14*z**2)*(-23) - 1173\nSimplifying the partial expression: (42*z)*(14*z**2 + 51)\nExpanding the part (14*z**2 + 51) using the distributive property, and we got: 51*(42*z) + (42*z)*(14*z**2)\nReplacing (42*z)*(14*z**2 + 51) with 51*(42*z) + (42*z)*(14*z**2) in the overall expression.\n#Step 4:\nCurrent expression: 51*42*z + (42*z)*(14*z**2) + (14*z**2)*(-23) - 1173\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (14*z**2)*-23 = -322*z**2\n (14*z**2)*(42*z) = 588*z**3\n 51*42*z = 2142*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 588*z**3 - 322*z**2 + 2142*z - 1173\nNo more calculations needed.\n588*z**3 - 322*z**2 + 2142*z - 1173", "generated_answer": "588*z**3 - 322*z**2 + 2142*z - 1173", "step_length": 5} {"cot_id": "2cb1dce2d0133dc440efd00e6c04d13946ed8d34657cd62cb8a1defffa67e74b", "datapoint": {"question": "Simplify this expression: (15*x**2 - 48)*(-24*x**3 + 21*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-360*x**5 + 315*x**4 + 1152*x**3 - 1008*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1902, "polynomial_expr": "(15*x**2 - 48)*(-24*x**3 + 21*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (15*x**2 - 48)*(-24*x**3 + 21*x**2)\nExpanding the part (15*x**2 - 48) using the distributive property, and we got: (15*x**2)*(-24*x**3 + 21*x**2) - 48*(-24*x**3 + 21*x**2)\n#Step 2:\nCurrent expression: (15*x**2)*(-24*x**3 + 21*x**2) - 48*(-24*x**3 + 21*x**2)\nSimplifying the partial expression: -48*(-24*x**3 + 21*x**2)\nExpanding the part (-24*x**3 + 21*x**2) using the distributive property, and we got: (21*x**2)*(-48) - 24*x**3*(-48)\nReplacing -48*(-24*x**3 + 21*x**2) with (21*x**2)*(-48) - 24*x**3*(-48) in the overall expression.\n#Step 3:\nCurrent expression: (15*x**2)*(-24*x**3 + 21*x**2) + (21*x**2)*(-48) - 24*x**3*(-48)\nSimplifying the partial expression: (15*x**2)*(-24*x**3 + 21*x**2)\nExpanding the part (-24*x**3 + 21*x**2) using the distributive property, and we got: (15*x**2)*(21*x**2) + (15*x**2)*(-24*x**3)\nReplacing (15*x**2)*(-24*x**3 + 21*x**2) with (15*x**2)*(21*x**2) + (15*x**2)*(-24*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (15*x**2)*(21*x**2) + (15*x**2)*(-24*x**3) + (21*x**2)*(-48) - 24*x**3*(-48)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-24*x**3)*-48 = 1152*x**3\n (-24*x**3)*(15*x**2) = -360*x**5\n (21*x**2)*-48 = -1008*x**2\n (21*x**2)*(15*x**2) = 315*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -360*x**5 + 315*x**4 + 1152*x**3 - 1008*x**2\nNo more calculations needed.\n-360*x**5 + 315*x**4 + 1152*x**3 - 1008*x**2", "generated_answer": "-360*x**5 + 315*x**4 + 1152*x**3 - 1008*x**2", "step_length": 5} {"cot_id": "de87b380320d85c4162d8cff72b5a01d6d7f3758c2bb5007a29731f5e5bdbe1c", "datapoint": {"question": "Calculate the following: (-24*y**2 - 40*y)*(44*y**3 - 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1056*y**5 - 1760*y**4 + 744*y**2 + 1240*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1903, "polynomial_expr": "(-24*y**2 - 40*y)*(44*y**3 - 31)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-24*y**2 - 40*y)*(44*y**3 - 31)\nExpanding the part (44*y**3 - 31) using the distributive property, and we got: (44*y**3)*(-24*y**2 - 40*y) - 31*(-24*y**2 - 40*y)\n#Step 2:\nCurrent expression: (44*y**3)*(-24*y**2 - 40*y) - 31*(-24*y**2 - 40*y)\nSimplifying the partial expression: -31*(-24*y**2 - 40*y)\nExpanding the part (-24*y**2 - 40*y) using the distributive property, and we got: -40*y*(-31) - 24*y**2*(-31)\nReplacing -31*(-24*y**2 - 40*y) with -40*y*(-31) - 24*y**2*(-31) in the overall expression.\n#Step 3:\nCurrent expression: -40*y*(-31) - 24*y**2*(-31) + (44*y**3)*(-24*y**2 - 40*y)\nSimplifying the partial expression: (44*y**3)*(-24*y**2 - 40*y)\nExpanding the part (-24*y**2 - 40*y) using the distributive property, and we got: (-40*y)*(44*y**3) + (-24*y**2)*(44*y**3)\nReplacing (44*y**3)*(-24*y**2 - 40*y) with (-40*y)*(44*y**3) + (-24*y**2)*(44*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-40*y)*(44*y**3) - 40*y*(-31) + (-24*y**2)*(44*y**3) - 24*y**2*(-31)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*y)*-31 = 1240*y\n (-40*y)*(44*y**3) = -1760*y**4\n (-24*y**2)*-31 = 744*y**2\n (-24*y**2)*(44*y**3) = -1056*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1056*y**5 - 1760*y**4 + 744*y**2 + 1240*y\nNo more calculations needed.\n-1056*y**5 - 1760*y**4 + 744*y**2 + 1240*y", "generated_answer": "-1056*y**5 - 1760*y**4 + 744*y**2 + 1240*y", "step_length": 5} {"cot_id": "9f0870b8e09179f3c8ed3afaeeaf0768944dc1e3fea50c9de847456647735cdf", "datapoint": {"question": "Calculate the following: -24*x**3*(30*x**3 + 34*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-720*x**6 - 816*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1904, "polynomial_expr": "-24*x**3*(30*x**3 + 34*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -24*x**3*(30*x**3 + 34*x)\nExpanding the part (30*x**3 + 34*x) using the distributive property, and we got: (34*x)*(-24*x**3) + (-24*x**3)*(30*x**3)\n#Step 2:\nCurrent expression: (34*x)*(-24*x**3) + (-24*x**3)*(30*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (30*x**3)*(-24*x**3) = -720*x**6\n (34*x)*(-24*x**3) = -816*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -720*x**6 - 816*x**4\nNo more calculations needed.\n-720*x**6 - 816*x**4", "generated_answer": "-720*x**6 - 816*x**4", "step_length": 3} {"cot_id": "5ec2445dfed71093ac07d1e71747b4450044fe13cfc29b474a5a2cd1eb2075de", "datapoint": {"question": "Calculate the following: (-z**3 - 19)*(35*z**2 - 24*z + 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-35*z**5 + 24*z**4 - 7*z**3 - 665*z**2 + 456*z - 133", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1905, "polynomial_expr": "(-z**3 - 19)*(35*z**2 - 24*z + 7)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-z**3 - 19)*(35*z**2 - 24*z + 7)\nExpanding the part (-z**3 - 19) using the distributive property, and we got: (-z**3)*(35*z**2 - 24*z + 7) - 19*(35*z**2 - 24*z + 7)\n#Step 2:\nCurrent expression: (-z**3)*(35*z**2 - 24*z + 7) - 19*(35*z**2 - 24*z + 7)\nSimplifying the partial expression: -19*(35*z**2 - 24*z + 7)\nExpanding the part (35*z**2 - 24*z + 7) using the distributive property, and we got: -24*z*(-19) + (35*z**2)*(-19) + 7*(-19)\nReplacing -19*(35*z**2 - 24*z + 7) with -24*z*(-19) + (35*z**2)*(-19) + 7*(-19) in the overall expression.\n#Step 3:\nCurrent expression: -24*z*(-19) + (35*z**2)*(-19) + (-z**3)*(35*z**2 - 24*z + 7) - 133\nSimplifying the partial expression: (-z**3)*(35*z**2 - 24*z + 7)\nExpanding the part (35*z**2 - 24*z + 7) using the distributive property, and we got: (-24*z)*(-z**3) + 7*(-z**3) + (35*z**2)*(-z**3)\nReplacing (-z**3)*(35*z**2 - 24*z + 7) with (-24*z)*(-z**3) + 7*(-z**3) + (35*z**2)*(-z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-24*z)*(-z**3) - 24*z*(-19) + 7*(-1)*z**3 + (35*z**2)*(-z**3) + (35*z**2)*(-19) - 133\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-24*z)*-19 = 456*z\n (-24*z)*(-z**3) = 24*z**4\n (35*z**2)*-19 = -665*z**2\n (35*z**2)*(-z**3) = -35*z**5\n 7*-1*z**3 = -7*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -35*z**5 + 24*z**4 - 7*z**3 - 665*z**2 + 456*z - 133\nNo more calculations needed.\n-35*z**5 + 24*z**4 - 7*z**3 - 665*z**2 + 456*z - 133", "generated_answer": "-35*z**5 + 24*z**4 - 7*z**3 - 665*z**2 + 456*z - 133", "step_length": 5} {"cot_id": "3e2044128c34d52cbd2cbfdf154883aba987ed348dd23f2279b4c24af191854a", "datapoint": {"question": "Simplify this expression: (3*y**2 - 44)*(70*y**3 - 2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "210*y**5 - 3080*y**3 - 6*y**2 + 88", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1906, "polynomial_expr": "(3*y**2 - 44)*(70*y**3 - 2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (3*y**2 - 44)*(70*y**3 - 2)\nExpanding the part (3*y**2 - 44) using the distributive property, and we got: (3*y**2)*(70*y**3 - 2) - 44*(70*y**3 - 2)\n#Step 2:\nCurrent expression: (3*y**2)*(70*y**3 - 2) - 44*(70*y**3 - 2)\nSimplifying the partial expression: -44*(70*y**3 - 2)\nExpanding the part (70*y**3 - 2) using the distributive property, and we got: (70*y**3)*(-44) - 2*(-44)\nReplacing -44*(70*y**3 - 2) with (70*y**3)*(-44) - 2*(-44) in the overall expression.\n#Step 3:\nCurrent expression: (3*y**2)*(70*y**3 - 2) + (70*y**3)*(-44) + 88\nSimplifying the partial expression: (3*y**2)*(70*y**3 - 2)\nExpanding the part (70*y**3 - 2) using the distributive property, and we got: -6*y**2 + (3*y**2)*(70*y**3)\nReplacing (3*y**2)*(70*y**3 - 2) with -6*y**2 + (3*y**2)*(70*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -2*3*y**2 + (3*y**2)*(70*y**3) + (70*y**3)*(-44) + 88\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (70*y**3)*-44 = -3080*y**3\n (70*y**3)*(3*y**2) = 210*y**5\n -2*3*y**2 = -6*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 210*y**5 - 3080*y**3 - 6*y**2 + 88\nNo more calculations needed.\n210*y**5 - 3080*y**3 - 6*y**2 + 88", "generated_answer": "210*y**5 - 3080*y**3 - 6*y**2 + 88", "step_length": 5} {"cot_id": "ab5608ddcf93ac3bf02d8d7fa0b8070401886da31d4ed8e5547791d1f95f8cd3", "datapoint": {"question": "Calculate the following: (31*z**2 - 10*z)*(-13*z**3 + 5*z**2 + 55*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-403*z**5 + 285*z**4 + 1655*z**3 - 550*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1907, "polynomial_expr": "(31*z**2 - 10*z)*(-13*z**3 + 5*z**2 + 55*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (31*z**2 - 10*z)*(-13*z**3 + 5*z**2 + 55*z)\nExpanding the part (31*z**2 - 10*z) using the distributive property, and we got: (-10*z)*(-13*z**3 + 5*z**2 + 55*z) + (31*z**2)*(-13*z**3 + 5*z**2 + 55*z)\n#Step 2:\nCurrent expression: (-10*z)*(-13*z**3 + 5*z**2 + 55*z) + (31*z**2)*(-13*z**3 + 5*z**2 + 55*z)\nSimplifying the partial expression: (-10*z)*(-13*z**3 + 5*z**2 + 55*z)\nExpanding the part (-13*z**3 + 5*z**2 + 55*z) using the distributive property, and we got: (-10*z)*(55*z) + (-10*z)*(5*z**2) + (-10*z)*(-13*z**3)\nReplacing (-10*z)*(-13*z**3 + 5*z**2 + 55*z) with (-10*z)*(55*z) + (-10*z)*(5*z**2) + (-10*z)*(-13*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-10*z)*(55*z) + (-10*z)*(5*z**2) + (-10*z)*(-13*z**3) + (31*z**2)*(-13*z**3 + 5*z**2 + 55*z)\nSimplifying the partial expression: (31*z**2)*(-13*z**3 + 5*z**2 + 55*z)\nExpanding the part (-13*z**3 + 5*z**2 + 55*z) using the distributive property, and we got: (55*z)*(31*z**2) + (5*z**2)*(31*z**2) + (31*z**2)*(-13*z**3)\nReplacing (31*z**2)*(-13*z**3 + 5*z**2 + 55*z) with (55*z)*(31*z**2) + (5*z**2)*(31*z**2) + (31*z**2)*(-13*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-10*z)*(55*z) + (-10*z)*(5*z**2) + (-10*z)*(-13*z**3) + (55*z)*(31*z**2) + (5*z**2)*(31*z**2) + (31*z**2)*(-13*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*z**3)*(-10*z) = 130*z**4\n (-13*z**3)*(31*z**2) = -403*z**5\n (5*z**2)*(-10*z) = -50*z**3\n (5*z**2)*(31*z**2) = 155*z**4\n (55*z)*(-10*z) = -550*z**2\n (55*z)*(31*z**2) = 1705*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -403*z**5 + 130*z**4 + 155*z**4 - 50*z**3 + 1705*z**3 - 550*z**2\nCombining like terms, got -403*z**5 + 285*z**4 + 1655*z**3 - 550*z**2\n#Step 6:\nCurrent expression: -403*z**5 + 285*z**4 + 1655*z**3 - 550*z**2\nNo more calculations needed.\n-403*z**5 + 285*z**4 + 1655*z**3 - 550*z**2", "generated_answer": "-403*z**5 + 285*z**4 + 1655*z**3 - 550*z**2", "step_length": 6} {"cot_id": "b243216cb86844651c65bac9ca74502340c0678c08c6509cbb5814ccf8d77ba7", "datapoint": {"question": "Simplify this expression: (62 - 3*x**2)*(20*x**3 - 34*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-60*x**5 + 102*x**4 + 1240*x**3 - 2108*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1908, "polynomial_expr": "(62 - 3*x**2)*(20*x**3 - 34*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (62 - 3*x**2)*(20*x**3 - 34*x**2)\nExpanding the part (62 - 3*x**2) using the distributive property, and we got: (-3*x**2)*(20*x**3 - 34*x**2) + 62*(20*x**3 - 34*x**2)\n#Step 2:\nCurrent expression: (-3*x**2)*(20*x**3 - 34*x**2) + 62*(20*x**3 - 34*x**2)\nSimplifying the partial expression: 62*(20*x**3 - 34*x**2)\nExpanding the part (20*x**3 - 34*x**2) using the distributive property, and we got: -34*x**2*62 + (20*x**3)*62\nReplacing 62*(20*x**3 - 34*x**2) with -34*x**2*62 + (20*x**3)*62 in the overall expression.\n#Step 3:\nCurrent expression: -34*x**2*62 + (-3*x**2)*(20*x**3 - 34*x**2) + (20*x**3)*62\nSimplifying the partial expression: (-3*x**2)*(20*x**3 - 34*x**2)\nExpanding the part (20*x**3 - 34*x**2) using the distributive property, and we got: (-34*x**2)*(-3*x**2) + (-3*x**2)*(20*x**3)\nReplacing (-3*x**2)*(20*x**3 - 34*x**2) with (-34*x**2)*(-3*x**2) + (-3*x**2)*(20*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-34*x**2)*(-3*x**2) - 34*x**2*62 + (-3*x**2)*(20*x**3) + (20*x**3)*62\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*x**2)*62 = -2108*x**2\n (-34*x**2)*(-3*x**2) = 102*x**4\n (20*x**3)*62 = 1240*x**3\n (20*x**3)*(-3*x**2) = -60*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -60*x**5 + 102*x**4 + 1240*x**3 - 2108*x**2\nNo more calculations needed.\n-60*x**5 + 102*x**4 + 1240*x**3 - 2108*x**2", "generated_answer": "-60*x**5 + 102*x**4 + 1240*x**3 - 2108*x**2", "step_length": 5} {"cot_id": "072779969a7e88c29b612228013730588e7e8a516f39230c2bf6a8ad6661d3af", "datapoint": {"question": "Simplify this expression: 735*x**2 - 945*x\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "735*x**2 - 945*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1909, "polynomial_expr": "735*x**2 - 945*x", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 735*x**2 - 945*x\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 735*x**2 - 945*x\nNo more calculations needed.\n735*x**2 - 945*x", "generated_answer": "735*x**2 - 945*x", "step_length": 2} {"cot_id": "91ee627d5accfec6f8e6c0fd77395ac0df96ca53b329f8d9f8907fb5e30cbd66", "datapoint": {"question": "Simplify this expression: -5*z**3*(19*z**3 - 50*z**2 + 47*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-95*z**6 + 250*z**5 - 235*z**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1910, "polynomial_expr": "-5*z**3*(19*z**3 - 50*z**2 + 47*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -5*z**3*(19*z**3 - 50*z**2 + 47*z)\nExpanding the part (19*z**3 - 50*z**2 + 47*z) using the distributive property, and we got: (47*z)*(-5*z**3) + (-50*z**2)*(-5*z**3) + (-5*z**3)*(19*z**3)\n#Step 2:\nCurrent expression: (47*z)*(-5*z**3) + (-50*z**2)*(-5*z**3) + (-5*z**3)*(19*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-50*z**2)*(-5*z**3) = 250*z**5\n (19*z**3)*(-5*z**3) = -95*z**6\n (47*z)*(-5*z**3) = -235*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -95*z**6 + 250*z**5 - 235*z**4\nNo more calculations needed.\n-95*z**6 + 250*z**5 - 235*z**4", "generated_answer": "-95*z**6 + 250*z**5 - 235*z**4", "step_length": 3} {"cot_id": "2d4b2ead409fbeb6c6b5ff09d915f3def20ab191f1194842624b31ff111e33db", "datapoint": {"question": "Calculate the following: (6*z + 15)*(38*z**3 + 50*z**2 - 77*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "228*z**4 + 870*z**3 + 288*z**2 - 1155*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1911, "polynomial_expr": "(6*z + 15)*(38*z**3 + 50*z**2 - 77*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6*z + 15)*(38*z**3 + 50*z**2 - 77*z)\nExpanding the part (6*z + 15) using the distributive property, and we got: (6*z)*(38*z**3 + 50*z**2 - 77*z) + 15*(38*z**3 + 50*z**2 - 77*z)\n#Step 2:\nCurrent expression: (6*z)*(38*z**3 + 50*z**2 - 77*z) + 15*(38*z**3 + 50*z**2 - 77*z)\nSimplifying the partial expression: 15*(38*z**3 + 50*z**2 - 77*z)\nExpanding the part (38*z**3 + 50*z**2 - 77*z) using the distributive property, and we got: -77*z*15 + (50*z**2)*15 + (38*z**3)*15\nReplacing 15*(38*z**3 + 50*z**2 - 77*z) with -77*z*15 + (50*z**2)*15 + (38*z**3)*15 in the overall expression.\n#Step 3:\nCurrent expression: -77*z*15 + (6*z)*(38*z**3 + 50*z**2 - 77*z) + (50*z**2)*15 + (38*z**3)*15\nSimplifying the partial expression: (6*z)*(38*z**3 + 50*z**2 - 77*z)\nExpanding the part (38*z**3 + 50*z**2 - 77*z) using the distributive property, and we got: (-77*z)*(6*z) + (6*z)*(50*z**2) + (6*z)*(38*z**3)\nReplacing (6*z)*(38*z**3 + 50*z**2 - 77*z) with (-77*z)*(6*z) + (6*z)*(50*z**2) + (6*z)*(38*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-77*z)*(6*z) - 77*z*15 + (6*z)*(50*z**2) + (6*z)*(38*z**3) + (50*z**2)*15 + (38*z**3)*15\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-77*z)*15 = -1155*z\n (-77*z)*(6*z) = -462*z**2\n (38*z**3)*15 = 570*z**3\n (38*z**3)*(6*z) = 228*z**4\n (50*z**2)*15 = 750*z**2\n (50*z**2)*(6*z) = 300*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 228*z**4 + 300*z**3 + 570*z**3 - 462*z**2 + 750*z**2 - 1155*z\nCombining like terms, got 228*z**4 + 870*z**3 + 288*z**2 - 1155*z\n#Step 6:\nCurrent expression: 228*z**4 + 870*z**3 + 288*z**2 - 1155*z\nNo more calculations needed.\n228*z**4 + 870*z**3 + 288*z**2 - 1155*z", "generated_answer": "228*z**4 + 870*z**3 + 288*z**2 - 1155*z", "step_length": 6} {"cot_id": "41396db6ae7729b3ecadf6155337ff23bf7337edba4d3edaff21518ccfd86afb", "datapoint": {"question": "Calculate the following: (-18*z**2 - 39)*(39*z**2 + 58)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-702*z**4 - 2565*z**2 - 2262", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1912, "polynomial_expr": "(-18*z**2 - 39)*(39*z**2 + 58)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-18*z**2 - 39)*(39*z**2 + 58)\nExpanding the part (-18*z**2 - 39) using the distributive property, and we got: (-18*z**2)*(39*z**2 + 58) - 39*(39*z**2 + 58)\n#Step 2:\nCurrent expression: (-18*z**2)*(39*z**2 + 58) - 39*(39*z**2 + 58)\nSimplifying the partial expression: -39*(39*z**2 + 58)\nExpanding the part (39*z**2 + 58) using the distributive property, and we got: (39*z**2)*(-39) + 58*(-39)\nReplacing -39*(39*z**2 + 58) with (39*z**2)*(-39) + 58*(-39) in the overall expression.\n#Step 3:\nCurrent expression: (-18*z**2)*(39*z**2 + 58) + (39*z**2)*(-39) - 2262\nSimplifying the partial expression: (-18*z**2)*(39*z**2 + 58)\nExpanding the part (39*z**2 + 58) using the distributive property, and we got: 58*(-18*z**2) + (-18*z**2)*(39*z**2)\nReplacing (-18*z**2)*(39*z**2 + 58) with 58*(-18*z**2) + (-18*z**2)*(39*z**2) in the overall expression.\n#Step 4:\nCurrent expression: 58*(-18)*z**2 + (-18*z**2)*(39*z**2) + (39*z**2)*(-39) - 2262\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (39*z**2)*-39 = -1521*z**2\n (39*z**2)*(-18*z**2) = -702*z**4\n 58*-18*z**2 = -1044*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -702*z**4 - 1521*z**2 - 1044*z**2 - 2262\nCombining like terms, got -702*z**4 - 2565*z**2 - 2262\n#Step 6:\nCurrent expression: -702*z**4 - 2565*z**2 - 2262\nNo more calculations needed.\n-702*z**4 - 2565*z**2 - 2262", "generated_answer": "-702*z**4 - 2565*z**2 - 2262", "step_length": 6} {"cot_id": "148399377c17ad6ed11f1c5151fa95725e02e6f6ad2b82290c4d5e617de6042f", "datapoint": {"question": "Calculate the following: (-40*z**2 - 5)*(24*z**3 + 35*z - 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-960*z**5 - 1520*z**3 + 400*z**2 - 175*z + 50", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1913, "polynomial_expr": "(-40*z**2 - 5)*(24*z**3 + 35*z - 10)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-40*z**2 - 5)*(24*z**3 + 35*z - 10)\nExpanding the part (-40*z**2 - 5) using the distributive property, and we got: (-40*z**2)*(24*z**3 + 35*z - 10) - 5*(24*z**3 + 35*z - 10)\n#Step 2:\nCurrent expression: (-40*z**2)*(24*z**3 + 35*z - 10) - 5*(24*z**3 + 35*z - 10)\nSimplifying the partial expression: -5*(24*z**3 + 35*z - 10)\nExpanding the part (24*z**3 + 35*z - 10) using the distributive property, and we got: (35*z)*(-5) + (24*z**3)*(-5) - 10*(-5)\nReplacing -5*(24*z**3 + 35*z - 10) with (35*z)*(-5) + (24*z**3)*(-5) - 10*(-5) in the overall expression.\n#Step 3:\nCurrent expression: (35*z)*(-5) + (-40*z**2)*(24*z**3 + 35*z - 10) + (24*z**3)*(-5) + 50\nSimplifying the partial expression: (-40*z**2)*(24*z**3 + 35*z - 10)\nExpanding the part (24*z**3 + 35*z - 10) using the distributive property, and we got: -(-1)*400*z**2 + (35*z)*(-40*z**2) + (-40*z**2)*(24*z**3)\nReplacing (-40*z**2)*(24*z**3 + 35*z - 10) with -(-1)*400*z**2 + (35*z)*(-40*z**2) + (-40*z**2)*(24*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -10*(-40)*z**2 + (35*z)*(-40*z**2) + (35*z)*(-5) + (-40*z**2)*(24*z**3) + (24*z**3)*(-5) + 50\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (24*z**3)*-5 = -120*z**3\n (24*z**3)*(-40*z**2) = -960*z**5\n (35*z)*-5 = -175*z\n (35*z)*(-40*z**2) = -1400*z**3\n -10*-40*z**2 = 400*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -960*z**5 - 1400*z**3 - 120*z**3 + 400*z**2 - 175*z + 50\nCombining like terms, got -960*z**5 - 1520*z**3 + 400*z**2 - 175*z + 50\n#Step 6:\nCurrent expression: -960*z**5 - 1520*z**3 + 400*z**2 - 175*z + 50\nNo more calculations needed.\n-960*z**5 - 1520*z**3 + 400*z**2 - 175*z + 50", "generated_answer": "-960*z**5 - 1520*z**3 + 400*z**2 - 175*z + 50", "step_length": 6} {"cot_id": "1db5000ee4c8f93fffaf6389dd8a622ccdcc71997c8230c5ea1b2cb2f3c00b48", "datapoint": {"question": "Simplify this expression: (35*z - 36)*(119*z**3 + 38*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "4165*z**4 - 4284*z**3 + 1330*z**2 - 1368*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1914, "polynomial_expr": "(35*z - 36)*(119*z**3 + 38*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (35*z - 36)*(119*z**3 + 38*z)\nExpanding the part (35*z - 36) using the distributive property, and we got: (35*z)*(119*z**3 + 38*z) - 36*(119*z**3 + 38*z)\n#Step 2:\nCurrent expression: (35*z)*(119*z**3 + 38*z) - 36*(119*z**3 + 38*z)\nSimplifying the partial expression: -36*(119*z**3 + 38*z)\nExpanding the part (119*z**3 + 38*z) using the distributive property, and we got: (38*z)*(-36) + (119*z**3)*(-36)\nReplacing -36*(119*z**3 + 38*z) with (38*z)*(-36) + (119*z**3)*(-36) in the overall expression.\n#Step 3:\nCurrent expression: (35*z)*(119*z**3 + 38*z) + (38*z)*(-36) + (119*z**3)*(-36)\nSimplifying the partial expression: (35*z)*(119*z**3 + 38*z)\nExpanding the part (119*z**3 + 38*z) using the distributive property, and we got: (35*z)*(38*z) + (35*z)*(119*z**3)\nReplacing (35*z)*(119*z**3 + 38*z) with (35*z)*(38*z) + (35*z)*(119*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (35*z)*(38*z) + (35*z)*(119*z**3) + (38*z)*(-36) + (119*z**3)*(-36)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (38*z)*-36 = -1368*z\n (38*z)*(35*z) = 1330*z**2\n (119*z**3)*-36 = -4284*z**3\n (119*z**3)*(35*z) = 4165*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 4165*z**4 - 4284*z**3 + 1330*z**2 - 1368*z\nNo more calculations needed.\n4165*z**4 - 4284*z**3 + 1330*z**2 - 1368*z", "generated_answer": "4165*z**4 - 4284*z**3 + 1330*z**2 - 1368*z", "step_length": 5} {"cot_id": "1f5462f2b8bfe8c43c020be7845f4e62491e1da1f6c47321df09977e2fb7d306", "datapoint": {"question": "Simplify this expression: -6*y**2*(-21*y**3 + 5*y**2 + 19)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "126*y**5 - 30*y**4 - 114*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1915, "polynomial_expr": "-6*y**2*(-21*y**3 + 5*y**2 + 19)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -6*y**2*(-21*y**3 + 5*y**2 + 19)\nExpanding the part (-21*y**3 + 5*y**2 + 19) using the distributive property, and we got: 19*(-6*y**2) + (-6*y**2)*(5*y**2) + (-6*y**2)*(-21*y**3)\n#Step 2:\nCurrent expression: 19*(-6*y**2) + (-6*y**2)*(5*y**2) + (-6*y**2)*(-21*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 19*(-6*y**2) = -114*y**2\n (-21*y**3)*(-6*y**2) = 126*y**5\n (5*y**2)*(-6*y**2) = -30*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 126*y**5 - 30*y**4 - 114*y**2\nNo more calculations needed.\n126*y**5 - 30*y**4 - 114*y**2", "generated_answer": "126*y**5 - 30*y**4 - 114*y**2", "step_length": 3} {"cot_id": "0fe62887db663deb6ef8a3c741019791ce6eb32959bd8e8c06e5a438c8abb40d", "datapoint": {"question": "Calculate the following: (29*z**2 + 19)*(33*z**3 + 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "957*z**5 + 627*z**3 + 1015*z**2 + 665", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1916, "polynomial_expr": "(29*z**2 + 19)*(33*z**3 + 35)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29*z**2 + 19)*(33*z**3 + 35)\nExpanding the part (29*z**2 + 19) using the distributive property, and we got: (29*z**2)*(33*z**3 + 35) + 19*(33*z**3 + 35)\n#Step 2:\nCurrent expression: (29*z**2)*(33*z**3 + 35) + 19*(33*z**3 + 35)\nSimplifying the partial expression: 19*(33*z**3 + 35)\nExpanding the part (33*z**3 + 35) using the distributive property, and we got: (33*z**3)*19 + 35*19\nReplacing 19*(33*z**3 + 35) with (33*z**3)*19 + 35*19 in the overall expression.\n#Step 3:\nCurrent expression: (29*z**2)*(33*z**3 + 35) + (33*z**3)*19 + 665\nSimplifying the partial expression: (29*z**2)*(33*z**3 + 35)\nExpanding the part (33*z**3 + 35) using the distributive property, and we got: 35*(29*z**2) + (29*z**2)*(33*z**3)\nReplacing (29*z**2)*(33*z**3 + 35) with 35*(29*z**2) + (29*z**2)*(33*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 35*29*z**2 + (29*z**2)*(33*z**3) + (33*z**3)*19 + 665\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (33*z**3)*19 = 627*z**3\n (33*z**3)*(29*z**2) = 957*z**5\n 35*29*z**2 = 1015*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 957*z**5 + 627*z**3 + 1015*z**2 + 665\nNo more calculations needed.\n957*z**5 + 627*z**3 + 1015*z**2 + 665", "generated_answer": "957*z**5 + 627*z**3 + 1015*z**2 + 665", "step_length": 5} {"cot_id": "26cb562aa031f044a3e710bca026554e9d583bb2efc644f04877cb8a8a0c54c0", "datapoint": {"question": "Calculate the following: (-12*z**3 - 21*z - 21)*(-3*z**3 + 48*z**2 - 20*z + 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "36*z**6 - 576*z**5 + 303*z**4 - 957*z**3 - 588*z**2 + 399*z - 21", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1917, "polynomial_expr": "(-12*z**3 - 21*z - 21)*(-3*z**3 + 48*z**2 - 20*z + 1)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-12*z**3 - 21*z - 21)*(-3*z**3 + 48*z**2 - 20*z + 1)\nExpanding the part (-12*z**3 - 21*z - 21) using the distributive property, and we got: (-21*z)*(-3*z**3 + 48*z**2 - 20*z + 1) + (-12*z**3)*(-3*z**3 + 48*z**2 - 20*z + 1) - 21*(-3*z**3 + 48*z**2 - 20*z + 1)\n#Step 2:\nCurrent expression: (-21*z)*(-3*z**3 + 48*z**2 - 20*z + 1) + (-12*z**3)*(-3*z**3 + 48*z**2 - 20*z + 1) - 21*(-3*z**3 + 48*z**2 - 20*z + 1)\nSimplifying the partial expression: -21*(-3*z**3 + 48*z**2 - 20*z + 1)\nExpanding the part (-3*z**3 + 48*z**2 - 20*z + 1) using the distributive property, and we got: -20*z*(-21) + (48*z**2)*(-21) - 3*z**3*(-21) + 1*(-21)\nReplacing -21*(-3*z**3 + 48*z**2 - 20*z + 1) with -20*z*(-21) + (48*z**2)*(-21) - 3*z**3*(-21) + 1*(-21) in the overall expression.\n#Step 3:\nCurrent expression: (-21*z)*(-3*z**3 + 48*z**2 - 20*z + 1) - 20*z*(-21) + (48*z**2)*(-21) + (-12*z**3)*(-3*z**3 + 48*z**2 - 20*z + 1) - 3*z**3*(-21) - 21\nSimplifying the partial expression: (-21*z)*(-3*z**3 + 48*z**2 - 20*z + 1)\nExpanding the part (-3*z**3 + 48*z**2 - 20*z + 1) using the distributive property, and we got: (-21*z)*(-20*z) + (-21*z)*(48*z**2) + (-21*z)*(-3*z**3) + 1*(-21*z)\nReplacing (-21*z)*(-3*z**3 + 48*z**2 - 20*z + 1) with (-21*z)*(-20*z) + (-21*z)*(48*z**2) + (-21*z)*(-3*z**3) + 1*(-21*z) in the overall expression.\n#Step 4:\nCurrent expression: (-21*z)*(-20*z) + (-21*z)*(48*z**2) + (-21*z)*(-3*z**3) - 20*z*(-21) - 21*z + (48*z**2)*(-21) + (-12*z**3)*(-3*z**3 + 48*z**2 - 20*z + 1) - 3*z**3*(-21) - 21\nSimplifying the partial expression: (-12*z**3)*(-3*z**3 + 48*z**2 - 20*z + 1)\nExpanding the part (-3*z**3 + 48*z**2 - 20*z + 1) using the distributive property, and we got: (-20*z)*(-12*z**3) + 1*(-12*z**3) + (48*z**2)*(-12*z**3) + (-12*z**3)*(-3*z**3)\nReplacing (-12*z**3)*(-3*z**3 + 48*z**2 - 20*z + 1) with (-20*z)*(-12*z**3) + 1*(-12*z**3) + (48*z**2)*(-12*z**3) + (-12*z**3)*(-3*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-21*z)*(-20*z) + (-21*z)*(48*z**2) + (-21*z)*(-3*z**3) + (-20*z)*(-12*z**3) - 20*z*(-21) - 12*z**3 - 21*z + (48*z**2)*(-12*z**3) + (48*z**2)*(-21) + (-12*z**3)*(-3*z**3) - 3*z**3*(-21) - 21\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*z)*-21 = 420*z\n (-20*z)*(-21*z) = 420*z**2\n (-20*z)*(-12*z**3) = 240*z**4\n (-3*z**3)*-21 = 63*z**3\n (-3*z**3)*(-21*z) = 63*z**4\n (-3*z**3)*(-12*z**3) = 36*z**6\n (48*z**2)*-21 = -1008*z**2\n (48*z**2)*(-21*z) = -1008*z**3\n (48*z**2)*(-12*z**3) = -576*z**5\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 36*z**6 - 576*z**5 + 63*z**4 + 240*z**4 - 1008*z**3 - 12*z**3 + 63*z**3 - 1008*z**2 + 420*z**2 - 21*z + 420*z - 21\nCombining like terms, got 36*z**6 - 576*z**5 + 303*z**4 - 957*z**3 - 588*z**2 + 399*z - 21\n#Step 7:\nCurrent expression: 36*z**6 - 576*z**5 + 303*z**4 - 957*z**3 - 588*z**2 + 399*z - 21\nNo more calculations needed.\n36*z**6 - 576*z**5 + 303*z**4 - 957*z**3 - 588*z**2 + 399*z - 21", "generated_answer": "36*z**6 - 576*z**5 + 303*z**4 - 957*z**3 - 588*z**2 + 399*z - 21", "step_length": 7} {"cot_id": "45a85757b4d24e95a6a9bcf8989d0381d5b1d7a57c4b92c20c8862f926b148cd", "datapoint": {"question": "Simplify this expression: (-111*y**3 - 5)*(-y**2 + 22*y + 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "111*y**5 - 2442*y**4 - 5439*y**3 + 5*y**2 - 110*y - 245", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1918, "polynomial_expr": "(-111*y**3 - 5)*(-y**2 + 22*y + 49)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-111*y**3 - 5)*(-y**2 + 22*y + 49)\nExpanding the part (-111*y**3 - 5) using the distributive property, and we got: (-111*y**3)*(-y**2 + 22*y + 49) - 5*(-y**2 + 22*y + 49)\n#Step 2:\nCurrent expression: (-111*y**3)*(-y**2 + 22*y + 49) - 5*(-y**2 + 22*y + 49)\nSimplifying the partial expression: -5*(-y**2 + 22*y + 49)\nExpanding the part (-y**2 + 22*y + 49) using the distributive property, and we got: (22*y)*(-5) - y**2*(-5) + 49*(-5)\nReplacing -5*(-y**2 + 22*y + 49) with (22*y)*(-5) - y**2*(-5) + 49*(-5) in the overall expression.\n#Step 3:\nCurrent expression: (22*y)*(-5) - y**2*(-5) + (-111*y**3)*(-y**2 + 22*y + 49) - 245\nSimplifying the partial expression: (-111*y**3)*(-y**2 + 22*y + 49)\nExpanding the part (-y**2 + 22*y + 49) using the distributive property, and we got: 49*(-111*y**3) + (22*y)*(-111*y**3) + (-y**2)*(-111*y**3)\nReplacing (-111*y**3)*(-y**2 + 22*y + 49) with 49*(-111*y**3) + (22*y)*(-111*y**3) + (-y**2)*(-111*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 49*(-111)*y**3 + (22*y)*(-111*y**3) + (22*y)*(-5) + (-y**2)*(-111*y**3) - y**2*(-5) - 245\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-y**2)*-5 = 5*y**2\n (-y**2)*(-111*y**3) = 111*y**5\n (22*y)*-5 = -110*y\n (22*y)*(-111*y**3) = -2442*y**4\n 49*-111*y**3 = -5439*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 111*y**5 - 2442*y**4 - 5439*y**3 + 5*y**2 - 110*y - 245\nNo more calculations needed.\n111*y**5 - 2442*y**4 - 5439*y**3 + 5*y**2 - 110*y - 245", "generated_answer": "111*y**5 - 2442*y**4 - 5439*y**3 + 5*y**2 - 110*y - 245", "step_length": 5} {"cot_id": "4222f58f0f5d8f7a0ea4e50cdcd3226bd31a7f49902171f4fec64f317036feab", "datapoint": {"question": "Calculate the following: (2*z**2 - 48*z)*(9*z**3 - 39*z**2 + 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "18*z**5 - 510*z**4 + 1872*z**3 + 12*z**2 - 288*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1919, "polynomial_expr": "(2*z**2 - 48*z)*(9*z**3 - 39*z**2 + 6)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2*z**2 - 48*z)*(9*z**3 - 39*z**2 + 6)\nExpanding the part (2*z**2 - 48*z) using the distributive property, and we got: (-48*z)*(9*z**3 - 39*z**2 + 6) + (2*z**2)*(9*z**3 - 39*z**2 + 6)\n#Step 2:\nCurrent expression: (-48*z)*(9*z**3 - 39*z**2 + 6) + (2*z**2)*(9*z**3 - 39*z**2 + 6)\nSimplifying the partial expression: (-48*z)*(9*z**3 - 39*z**2 + 6)\nExpanding the part (9*z**3 - 39*z**2 + 6) using the distributive property, and we got: (-48*z)*(-39*z**2) + (-48*z)*(9*z**3) + 6*(-48*z)\nReplacing (-48*z)*(9*z**3 - 39*z**2 + 6) with (-48*z)*(-39*z**2) + (-48*z)*(9*z**3) + 6*(-48*z) in the overall expression.\n#Step 3:\nCurrent expression: (-48*z)*(-39*z**2) + (-48*z)*(9*z**3) + 6*(-48)*z + (2*z**2)*(9*z**3 - 39*z**2 + 6)\nSimplifying the partial expression: (2*z**2)*(9*z**3 - 39*z**2 + 6)\nExpanding the part (9*z**3 - 39*z**2 + 6) using the distributive property, and we got: 6*(2*z**2) + (-39*z**2)*(2*z**2) + (2*z**2)*(9*z**3)\nReplacing (2*z**2)*(9*z**3 - 39*z**2 + 6) with 6*(2*z**2) + (-39*z**2)*(2*z**2) + (2*z**2)*(9*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-48*z)*(-39*z**2) + (-48*z)*(9*z**3) + 6*2*z**2 + 6*(-48)*z + (-39*z**2)*(2*z**2) + (2*z**2)*(9*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*z**2)*(-48*z) = 1872*z**3\n (-39*z**2)*(2*z**2) = -78*z**4\n (9*z**3)*(-48*z) = -432*z**4\n (9*z**3)*(2*z**2) = 18*z**5\n 6*-48*z = -288*z\n 6*2*z**2 = 12*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 18*z**5 - 432*z**4 - 78*z**4 + 1872*z**3 + 12*z**2 - 288*z\nCombining like terms, got 18*z**5 - 510*z**4 + 1872*z**3 + 12*z**2 - 288*z\n#Step 6:\nCurrent expression: 18*z**5 - 510*z**4 + 1872*z**3 + 12*z**2 - 288*z\nNo more calculations needed.\n18*z**5 - 510*z**4 + 1872*z**3 + 12*z**2 - 288*z", "generated_answer": "18*z**5 - 510*z**4 + 1872*z**3 + 12*z**2 - 288*z", "step_length": 6} {"cot_id": "18f9094a3dc51943db02818694232f625d15fcdb69e021b14e8689e6bfc24195", "datapoint": {"question": "Calculate the following: (-49*x**2 + 5*x + 17)*(33*x**3 - 10*x**2 + 4*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1617*x**5 + 655*x**4 + 315*x**3 - 150*x**2 + 68*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1920, "polynomial_expr": "(-49*x**2 + 5*x + 17)*(33*x**3 - 10*x**2 + 4*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-49*x**2 + 5*x + 17)*(33*x**3 - 10*x**2 + 4*x)\nExpanding the part (-49*x**2 + 5*x + 17) using the distributive property, and we got: (5*x)*(33*x**3 - 10*x**2 + 4*x) + (-49*x**2)*(33*x**3 - 10*x**2 + 4*x) + 17*(33*x**3 - 10*x**2 + 4*x)\n#Step 2:\nCurrent expression: (5*x)*(33*x**3 - 10*x**2 + 4*x) + (-49*x**2)*(33*x**3 - 10*x**2 + 4*x) + 17*(33*x**3 - 10*x**2 + 4*x)\nSimplifying the partial expression: 17*(33*x**3 - 10*x**2 + 4*x)\nExpanding the part (33*x**3 - 10*x**2 + 4*x) using the distributive property, and we got: (4*x)*17 - 10*x**2*17 + (33*x**3)*17\nReplacing 17*(33*x**3 - 10*x**2 + 4*x) with (4*x)*17 - 10*x**2*17 + (33*x**3)*17 in the overall expression.\n#Step 3:\nCurrent expression: (4*x)*17 + (5*x)*(33*x**3 - 10*x**2 + 4*x) + (-49*x**2)*(33*x**3 - 10*x**2 + 4*x) - 10*x**2*17 + (33*x**3)*17\nSimplifying the partial expression: (-49*x**2)*(33*x**3 - 10*x**2 + 4*x)\nExpanding the part (33*x**3 - 10*x**2 + 4*x) using the distributive property, and we got: (4*x)*(-49*x**2) + (-49*x**2)*(-10*x**2) + (-49*x**2)*(33*x**3)\nReplacing (-49*x**2)*(33*x**3 - 10*x**2 + 4*x) with (4*x)*(-49*x**2) + (-49*x**2)*(-10*x**2) + (-49*x**2)*(33*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (4*x)*(-49*x**2) + (4*x)*17 + (5*x)*(33*x**3 - 10*x**2 + 4*x) + (-49*x**2)*(-10*x**2) + (-49*x**2)*(33*x**3) - 10*x**2*17 + (33*x**3)*17\nSimplifying the partial expression: (5*x)*(33*x**3 - 10*x**2 + 4*x)\nExpanding the part (33*x**3 - 10*x**2 + 4*x) using the distributive property, and we got: (4*x)*(5*x) + (5*x)*(-10*x**2) + (5*x)*(33*x**3)\nReplacing (5*x)*(33*x**3 - 10*x**2 + 4*x) with (4*x)*(5*x) + (5*x)*(-10*x**2) + (5*x)*(33*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (4*x)*(5*x) + (4*x)*(-49*x**2) + (4*x)*17 + (5*x)*(-10*x**2) + (5*x)*(33*x**3) + (-49*x**2)*(-10*x**2) + (-49*x**2)*(33*x**3) - 10*x**2*17 + (33*x**3)*17\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*x**2)*17 = -170*x**2\n (-10*x**2)*(-49*x**2) = 490*x**4\n (-10*x**2)*(5*x) = -50*x**3\n (4*x)*17 = 68*x\n (4*x)*(-49*x**2) = -196*x**3\n (4*x)*(5*x) = 20*x**2\n (33*x**3)*17 = 561*x**3\n (33*x**3)*(-49*x**2) = -1617*x**5\n (33*x**3)*(5*x) = 165*x**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1617*x**5 + 165*x**4 + 490*x**4 - 196*x**3 - 50*x**3 + 561*x**3 - 170*x**2 + 20*x**2 + 68*x\nCombining like terms, got -1617*x**5 + 655*x**4 + 315*x**3 - 150*x**2 + 68*x\n#Step 7:\nCurrent expression: -1617*x**5 + 655*x**4 + 315*x**3 - 150*x**2 + 68*x\nNo more calculations needed.\n-1617*x**5 + 655*x**4 + 315*x**3 - 150*x**2 + 68*x", "generated_answer": "-1617*x**5 + 655*x**4 + 315*x**3 - 150*x**2 + 68*x", "step_length": 7} {"cot_id": "3c3e1f1b1954ed9213ff5b9972838d51eb06fbd6df6715d911ea2b46ba155fba", "datapoint": {"question": "Simplify this expression: (3*z**3 + 62*z)*(9*z**3 - z - 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "27*z**6 + 555*z**4 - 108*z**3 - 62*z**2 - 2232*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1921, "polynomial_expr": "(3*z**3 + 62*z)*(9*z**3 - z - 36)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (3*z**3 + 62*z)*(9*z**3 - z - 36)\nExpanding the part (3*z**3 + 62*z) using the distributive property, and we got: (62*z)*(9*z**3 - z - 36) + (3*z**3)*(9*z**3 - z - 36)\n#Step 2:\nCurrent expression: (62*z)*(9*z**3 - z - 36) + (3*z**3)*(9*z**3 - z - 36)\nSimplifying the partial expression: (3*z**3)*(9*z**3 - z - 36)\nExpanding the part (9*z**3 - z - 36) using the distributive property, and we got: (-z)*(3*z**3) - 108*z**3 + (3*z**3)*(9*z**3)\nReplacing (3*z**3)*(9*z**3 - z - 36) with (-z)*(3*z**3) - 108*z**3 + (3*z**3)*(9*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-z)*(3*z**3) - 36*3*z**3 + (62*z)*(9*z**3 - z - 36) + (3*z**3)*(9*z**3)\nSimplifying the partial expression: (62*z)*(9*z**3 - z - 36)\nExpanding the part (9*z**3 - z - 36) using the distributive property, and we got: (-z)*(62*z) - 2232*z + (62*z)*(9*z**3)\nReplacing (62*z)*(9*z**3 - z - 36) with (-z)*(62*z) - 2232*z + (62*z)*(9*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-z)*(62*z) + (-z)*(3*z**3) - 36*3*z**3 - 36*62*z + (62*z)*(9*z**3) + (3*z**3)*(9*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-z)*(3*z**3) = -3*z**4\n (-z)*(62*z) = -62*z**2\n (9*z**3)*(3*z**3) = 27*z**6\n (9*z**3)*(62*z) = 558*z**4\n -36*3*z**3 = -108*z**3\n -36*62*z = -2232*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 27*z**6 - 3*z**4 + 558*z**4 - 108*z**3 - 62*z**2 - 2232*z\nCombining like terms, got 27*z**6 + 555*z**4 - 108*z**3 - 62*z**2 - 2232*z\n#Step 6:\nCurrent expression: 27*z**6 + 555*z**4 - 108*z**3 - 62*z**2 - 2232*z\nNo more calculations needed.\n27*z**6 + 555*z**4 - 108*z**3 - 62*z**2 - 2232*z", "generated_answer": "27*z**6 + 555*z**4 - 108*z**3 - 62*z**2 - 2232*z", "step_length": 6} {"cot_id": "66cdac01f261c714292e224d3cf08247c8d55aa6d9a63e503d9ad033dd9ec77e", "datapoint": {"question": "Calculate the following: (27*z**2 + 40)*(-29*z**3 + 70*z + 12)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-783*z**5 + 730*z**3 + 324*z**2 + 2800*z + 480", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1922, "polynomial_expr": "(27*z**2 + 40)*(-29*z**3 + 70*z + 12)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*z**2 + 40)*(-29*z**3 + 70*z + 12)\nExpanding the part (27*z**2 + 40) using the distributive property, and we got: (27*z**2)*(-29*z**3 + 70*z + 12) + 40*(-29*z**3 + 70*z + 12)\n#Step 2:\nCurrent expression: (27*z**2)*(-29*z**3 + 70*z + 12) + 40*(-29*z**3 + 70*z + 12)\nSimplifying the partial expression: 40*(-29*z**3 + 70*z + 12)\nExpanding the part (-29*z**3 + 70*z + 12) using the distributive property, and we got: (70*z)*40 - 29*z**3*40 + 12*40\nReplacing 40*(-29*z**3 + 70*z + 12) with (70*z)*40 - 29*z**3*40 + 12*40 in the overall expression.\n#Step 3:\nCurrent expression: (70*z)*40 + (27*z**2)*(-29*z**3 + 70*z + 12) - 29*z**3*40 + 480\nSimplifying the partial expression: (27*z**2)*(-29*z**3 + 70*z + 12)\nExpanding the part (-29*z**3 + 70*z + 12) using the distributive property, and we got: 12*(27*z**2) + (70*z)*(27*z**2) + (27*z**2)*(-29*z**3)\nReplacing (27*z**2)*(-29*z**3 + 70*z + 12) with 12*(27*z**2) + (70*z)*(27*z**2) + (27*z**2)*(-29*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 12*27*z**2 + (70*z)*(27*z**2) + (70*z)*40 + (27*z**2)*(-29*z**3) - 29*z**3*40 + 480\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*z**3)*40 = -1160*z**3\n (-29*z**3)*(27*z**2) = -783*z**5\n (70*z)*40 = 2800*z\n (70*z)*(27*z**2) = 1890*z**3\n 12*27*z**2 = 324*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -783*z**5 - 1160*z**3 + 1890*z**3 + 324*z**2 + 2800*z + 480\nCombining like terms, got -783*z**5 + 730*z**3 + 324*z**2 + 2800*z + 480\n#Step 6:\nCurrent expression: -783*z**5 + 730*z**3 + 324*z**2 + 2800*z + 480\nNo more calculations needed.\n-783*z**5 + 730*z**3 + 324*z**2 + 2800*z + 480", "generated_answer": "-783*z**5 + 730*z**3 + 324*z**2 + 2800*z + 480", "step_length": 6} {"cot_id": "40252a3c3cf7196f049043c959ce37773dd728c5fd4d6a86576807cb2d461679", "datapoint": {"question": "Calculate the following: -99*x*(4 - 25*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2475*x**3 - 396*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1924, "polynomial_expr": "-99*x*(4 - 25*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -99*x*(4 - 25*x**2)\nExpanding the part (4 - 25*x**2) using the distributive property, and we got: (-99*x)*(-25*x**2) + 4*(-99*x)\n#Step 2:\nCurrent expression: (-99*x)*(-25*x**2) + 4*(-99*x)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 4*(-99*x) = -396*x\n (-25*x**2)*(-99*x) = 2475*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 2475*x**3 - 396*x\nNo more calculations needed.\n2475*x**3 - 396*x", "generated_answer": "2475*x**3 - 396*x", "step_length": 3} {"cot_id": "32ed914aedc8751f6056c13d323c820252192142664dc576b198e2f65dc3bbbb", "datapoint": {"question": "Simplify this expression: (7*z**2 - 33*z)*(26*z**3 - 10*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "182*z**5 - 858*z**4 - 70*z**3 + 330*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1925, "polynomial_expr": "(7*z**2 - 33*z)*(26*z**3 - 10*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7*z**2 - 33*z)*(26*z**3 - 10*z)\nExpanding the part (7*z**2 - 33*z) using the distributive property, and we got: (-33*z)*(26*z**3 - 10*z) + (7*z**2)*(26*z**3 - 10*z)\n#Step 2:\nCurrent expression: (-33*z)*(26*z**3 - 10*z) + (7*z**2)*(26*z**3 - 10*z)\nSimplifying the partial expression: (-33*z)*(26*z**3 - 10*z)\nExpanding the part (26*z**3 - 10*z) using the distributive property, and we got: (-33*z)*(-10*z) + (-33*z)*(26*z**3)\nReplacing (-33*z)*(26*z**3 - 10*z) with (-33*z)*(-10*z) + (-33*z)*(26*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-33*z)*(-10*z) + (-33*z)*(26*z**3) + (7*z**2)*(26*z**3 - 10*z)\nSimplifying the partial expression: (7*z**2)*(26*z**3 - 10*z)\nExpanding the part (26*z**3 - 10*z) using the distributive property, and we got: (-10*z)*(7*z**2) + (7*z**2)*(26*z**3)\nReplacing (7*z**2)*(26*z**3 - 10*z) with (-10*z)*(7*z**2) + (7*z**2)*(26*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-33*z)*(-10*z) + (-33*z)*(26*z**3) + (-10*z)*(7*z**2) + (7*z**2)*(26*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*z)*(-33*z) = 330*z**2\n (-10*z)*(7*z**2) = -70*z**3\n (26*z**3)*(-33*z) = -858*z**4\n (26*z**3)*(7*z**2) = 182*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 182*z**5 - 858*z**4 - 70*z**3 + 330*z**2\nNo more calculations needed.\n182*z**5 - 858*z**4 - 70*z**3 + 330*z**2", "generated_answer": "182*z**5 - 858*z**4 - 70*z**3 + 330*z**2", "step_length": 5} {"cot_id": "c0e573476af63c81838fce6beafeeedcb96b4985d66e1076803c3e0c4b3372b6", "datapoint": {"question": "Simplify this expression: (46 - 33*z**2)*(-21*z**3 + 3*z**2 + 3*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "693*z**5 - 99*z**4 - 1065*z**3 + 138*z**2 + 138*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1926, "polynomial_expr": "(46 - 33*z**2)*(-21*z**3 + 3*z**2 + 3*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (46 - 33*z**2)*(-21*z**3 + 3*z**2 + 3*z)\nExpanding the part (46 - 33*z**2) using the distributive property, and we got: (-33*z**2)*(-21*z**3 + 3*z**2 + 3*z) + 46*(-21*z**3 + 3*z**2 + 3*z)\n#Step 2:\nCurrent expression: (-33*z**2)*(-21*z**3 + 3*z**2 + 3*z) + 46*(-21*z**3 + 3*z**2 + 3*z)\nSimplifying the partial expression: 46*(-21*z**3 + 3*z**2 + 3*z)\nExpanding the part (-21*z**3 + 3*z**2 + 3*z) using the distributive property, and we got: (3*z)*46 + (3*z**2)*46 - 21*z**3*46\nReplacing 46*(-21*z**3 + 3*z**2 + 3*z) with (3*z)*46 + (3*z**2)*46 - 21*z**3*46 in the overall expression.\n#Step 3:\nCurrent expression: (3*z)*46 + (-33*z**2)*(-21*z**3 + 3*z**2 + 3*z) + (3*z**2)*46 - 21*z**3*46\nSimplifying the partial expression: (-33*z**2)*(-21*z**3 + 3*z**2 + 3*z)\nExpanding the part (-21*z**3 + 3*z**2 + 3*z) using the distributive property, and we got: (3*z)*(-33*z**2) + (-33*z**2)*(3*z**2) + (-33*z**2)*(-21*z**3)\nReplacing (-33*z**2)*(-21*z**3 + 3*z**2 + 3*z) with (3*z)*(-33*z**2) + (-33*z**2)*(3*z**2) + (-33*z**2)*(-21*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (3*z)*(-33*z**2) + (3*z)*46 + (-33*z**2)*(3*z**2) + (-33*z**2)*(-21*z**3) + (3*z**2)*46 - 21*z**3*46\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-21*z**3)*46 = -966*z**3\n (-21*z**3)*(-33*z**2) = 693*z**5\n (3*z)*46 = 138*z\n (3*z)*(-33*z**2) = -99*z**3\n (3*z**2)*46 = 138*z**2\n (3*z**2)*(-33*z**2) = -99*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 693*z**5 - 99*z**4 - 966*z**3 - 99*z**3 + 138*z**2 + 138*z\nCombining like terms, got 693*z**5 - 99*z**4 - 1065*z**3 + 138*z**2 + 138*z\n#Step 6:\nCurrent expression: 693*z**5 - 99*z**4 - 1065*z**3 + 138*z**2 + 138*z\nNo more calculations needed.\n693*z**5 - 99*z**4 - 1065*z**3 + 138*z**2 + 138*z", "generated_answer": "693*z**5 - 99*z**4 - 1065*z**3 + 138*z**2 + 138*z", "step_length": 6} {"cot_id": "a145c7fedec8eae152f9f1cfc3b595ae39d9b84c3c562bd3e34e83f35700c83d", "datapoint": {"question": "Simplify this expression: -54*y**3*(15*y**3 + 12*y + 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-810*y**6 - 648*y**4 - 1674*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1927, "polynomial_expr": "-54*y**3*(15*y**3 + 12*y + 31)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -54*y**3*(15*y**3 + 12*y + 31)\nExpanding the part (15*y**3 + 12*y + 31) using the distributive property, and we got: 31*(-54*y**3) + (12*y)*(-54*y**3) + (-54*y**3)*(15*y**3)\n#Step 2:\nCurrent expression: 31*(-54*y**3) + (12*y)*(-54*y**3) + (-54*y**3)*(15*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 31*(-54*y**3) = -1674*y**3\n (12*y)*(-54*y**3) = -648*y**4\n (15*y**3)*(-54*y**3) = -810*y**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -810*y**6 - 648*y**4 - 1674*y**3\nNo more calculations needed.\n-810*y**6 - 648*y**4 - 1674*y**3", "generated_answer": "-810*y**6 - 648*y**4 - 1674*y**3", "step_length": 3} {"cot_id": "c2fe159bb0ea3309d4d701c03116e345a7cadfe7fcdd59f8430c656218e02ec2", "datapoint": {"question": "Simplify this expression: (x + 8)*(-75*x**2 - 3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-75*x**3 - 600*x**2 - 3*x - 24", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1928, "polynomial_expr": "(x + 8)*(-75*x**2 - 3)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (x + 8)*(-75*x**2 - 3)\nExpanding the part (-75*x**2 - 3) using the distributive property, and we got: (-75*x**2)*(x + 8) - 3*(x + 8)\n#Step 2:\nCurrent expression: (-75*x**2)*(x + 8) - 3*(x + 8)\nSimplifying the partial expression: -3*(x + 8)\nExpanding the part (x + 8) using the distributive property, and we got: x*(-3) + 8*(-3)\nReplacing -3*(x + 8) with x*(-3) + 8*(-3) in the overall expression.\n#Step 3:\nCurrent expression: x*(-3) + (-75*x**2)*(x + 8) - 24\nSimplifying the partial expression: (-75*x**2)*(x + 8)\nExpanding the part (x + 8) using the distributive property, and we got: 8*(-75*x**2) + x*(-75*x**2)\nReplacing (-75*x**2)*(x + 8) with 8*(-75*x**2) + x*(-75*x**2) in the overall expression.\n#Step 4:\nCurrent expression: 8*(-75)*x**2 + x*(-75*x**2) + x*(-3) - 24\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n x*-3 = -3*x\n x*(-75*x**2) = -75*x**3\n 8*-75*x**2 = -600*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -75*x**3 - 600*x**2 - 3*x - 24\nNo more calculations needed.\n-75*x**3 - 600*x**2 - 3*x - 24", "generated_answer": "-75*x**3 - 600*x**2 - 3*x - 24", "step_length": 5} {"cot_id": "f38c0cefefcd5f44dd48d96e00c15afe120667b9384090924485e1ceeb798823", "datapoint": {"question": "Calculate the following: (-13*x**3 - 48)*(47*x**3 + 38*x**2 + 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-611*x**6 - 494*x**5 - 2893*x**3 - 1824*x**2 - 2352", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1929, "polynomial_expr": "(-13*x**3 - 48)*(47*x**3 + 38*x**2 + 49)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-13*x**3 - 48)*(47*x**3 + 38*x**2 + 49)\nExpanding the part (-13*x**3 - 48) using the distributive property, and we got: (-13*x**3)*(47*x**3 + 38*x**2 + 49) - 48*(47*x**3 + 38*x**2 + 49)\n#Step 2:\nCurrent expression: (-13*x**3)*(47*x**3 + 38*x**2 + 49) - 48*(47*x**3 + 38*x**2 + 49)\nSimplifying the partial expression: -48*(47*x**3 + 38*x**2 + 49)\nExpanding the part (47*x**3 + 38*x**2 + 49) using the distributive property, and we got: (38*x**2)*(-48) + (47*x**3)*(-48) + 49*(-48)\nReplacing -48*(47*x**3 + 38*x**2 + 49) with (38*x**2)*(-48) + (47*x**3)*(-48) + 49*(-48) in the overall expression.\n#Step 3:\nCurrent expression: (38*x**2)*(-48) + (-13*x**3)*(47*x**3 + 38*x**2 + 49) + (47*x**3)*(-48) - 2352\nSimplifying the partial expression: (-13*x**3)*(47*x**3 + 38*x**2 + 49)\nExpanding the part (47*x**3 + 38*x**2 + 49) using the distributive property, and we got: 49*(-13*x**3) + (38*x**2)*(-13*x**3) + (-13*x**3)*(47*x**3)\nReplacing (-13*x**3)*(47*x**3 + 38*x**2 + 49) with 49*(-13*x**3) + (38*x**2)*(-13*x**3) + (-13*x**3)*(47*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 49*(-13)*x**3 + (38*x**2)*(-13*x**3) + (38*x**2)*(-48) + (-13*x**3)*(47*x**3) + (47*x**3)*(-48) - 2352\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (38*x**2)*-48 = -1824*x**2\n (38*x**2)*(-13*x**3) = -494*x**5\n (47*x**3)*-48 = -2256*x**3\n (47*x**3)*(-13*x**3) = -611*x**6\n 49*-13*x**3 = -637*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -611*x**6 - 494*x**5 - 2256*x**3 - 637*x**3 - 1824*x**2 - 2352\nCombining like terms, got -611*x**6 - 494*x**5 - 2893*x**3 - 1824*x**2 - 2352\n#Step 6:\nCurrent expression: -611*x**6 - 494*x**5 - 2893*x**3 - 1824*x**2 - 2352\nNo more calculations needed.\n-611*x**6 - 494*x**5 - 2893*x**3 - 1824*x**2 - 2352", "generated_answer": "-611*x**6 - 494*x**5 - 2893*x**3 - 1824*x**2 - 2352", "step_length": 6} {"cot_id": "7301456acc2671a66ccf2af0b3630e25cc54929293577c5cbc0c808c5c5610d7", "datapoint": {"question": "Simplify this expression: (1 - 2*z**3)*(-43*z**3 - 21*z**2 - 45*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "86*z**6 + 42*z**5 + 90*z**4 - 43*z**3 - 21*z**2 - 45*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1930, "polynomial_expr": "(1 - 2*z**3)*(-43*z**3 - 21*z**2 - 45*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (1 - 2*z**3)*(-43*z**3 - 21*z**2 - 45*z)\nExpanding the part (1 - 2*z**3) using the distributive property, and we got: (-2*z**3)*(-43*z**3 - 21*z**2 - 45*z) + 1*(-43*z**3 - 21*z**2 - 45*z)\n#Step 2:\nCurrent expression: (-2*z**3)*(-43*z**3 - 21*z**2 - 45*z) + 1*(-43*z**3 - 21*z**2 - 45*z)\nSimplifying the partial expression: 1*(-43*z**3 - 21*z**2 - 45*z)\nExpanding the part (-43*z**3 - 21*z**2 - 45*z) using the distributive property, and we got: -45*z*1 - 21*z**2*1 - 43*z**3*1\nReplacing 1*(-43*z**3 - 21*z**2 - 45*z) with -45*z*1 - 21*z**2*1 - 43*z**3*1 in the overall expression.\n#Step 3:\nCurrent expression: -45*z*1 - 21*z**2*1 - 43*z**3*1 + (-2*z**3)*(-43*z**3 - 21*z**2 - 45*z)\nSimplifying the partial expression: (-2*z**3)*(-43*z**3 - 21*z**2 - 45*z)\nExpanding the part (-43*z**3 - 21*z**2 - 45*z) using the distributive property, and we got: (-45*z)*(-2*z**3) + (-21*z**2)*(-2*z**3) + (-43*z**3)*(-2*z**3)\nReplacing (-2*z**3)*(-43*z**3 - 21*z**2 - 45*z) with (-45*z)*(-2*z**3) + (-21*z**2)*(-2*z**3) + (-43*z**3)*(-2*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-45*z)*(-2*z**3) - 45*z*1 + (-21*z**2)*(-2*z**3) - 21*z**2*1 + (-43*z**3)*(-2*z**3) - 43*z**3*1\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*z)*1 = -45*z\n (-45*z)*(-2*z**3) = 90*z**4\n (-43*z**3)*1 = -43*z**3\n (-43*z**3)*(-2*z**3) = 86*z**6\n (-21*z**2)*1 = -21*z**2\n (-21*z**2)*(-2*z**3) = 42*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 86*z**6 + 42*z**5 + 90*z**4 - 43*z**3 - 21*z**2 - 45*z\nNo more calculations needed.\n86*z**6 + 42*z**5 + 90*z**4 - 43*z**3 - 21*z**2 - 45*z", "generated_answer": "86*z**6 + 42*z**5 + 90*z**4 - 43*z**3 - 21*z**2 - 45*z", "step_length": 5} {"cot_id": "2168d30b94383335d6741cc8ce6b6b8fb84ce596409e26e00a2d1464b4fddd32", "datapoint": {"question": "Simplify this expression: 36*x**2*(-16*x**3 + 25*x**2 + 28*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-576*x**5 + 900*x**4 + 1008*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1931, "polynomial_expr": "36*x**2*(-16*x**3 + 25*x**2 + 28*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 36*x**2*(-16*x**3 + 25*x**2 + 28*x)\nExpanding the part (-16*x**3 + 25*x**2 + 28*x) using the distributive property, and we got: (28*x)*(36*x**2) + (25*x**2)*(36*x**2) + (36*x**2)*(-16*x**3)\n#Step 2:\nCurrent expression: (28*x)*(36*x**2) + (25*x**2)*(36*x**2) + (36*x**2)*(-16*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-16*x**3)*(36*x**2) = -576*x**5\n (25*x**2)*(36*x**2) = 900*x**4\n (28*x)*(36*x**2) = 1008*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -576*x**5 + 900*x**4 + 1008*x**3\nNo more calculations needed.\n-576*x**5 + 900*x**4 + 1008*x**3", "generated_answer": "-576*x**5 + 900*x**4 + 1008*x**3", "step_length": 3} {"cot_id": "1abd8a6fa29b3ee394e4b5355d06c3ad93b993fca771a39896f18f6a325a86da", "datapoint": {"question": "Simplify this expression: (10*x + 55)*(98*x**3 + 16*x - 37)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "980*x**4 + 5390*x**3 + 160*x**2 + 510*x - 2035", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1932, "polynomial_expr": "(10*x + 55)*(98*x**3 + 16*x - 37)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (10*x + 55)*(98*x**3 + 16*x - 37)\nExpanding the part (10*x + 55) using the distributive property, and we got: (10*x)*(98*x**3 + 16*x - 37) + 55*(98*x**3 + 16*x - 37)\n#Step 2:\nCurrent expression: (10*x)*(98*x**3 + 16*x - 37) + 55*(98*x**3 + 16*x - 37)\nSimplifying the partial expression: 55*(98*x**3 + 16*x - 37)\nExpanding the part (98*x**3 + 16*x - 37) using the distributive property, and we got: (16*x)*55 + (98*x**3)*55 - 37*55\nReplacing 55*(98*x**3 + 16*x - 37) with (16*x)*55 + (98*x**3)*55 - 37*55 in the overall expression.\n#Step 3:\nCurrent expression: (10*x)*(98*x**3 + 16*x - 37) + (16*x)*55 + (98*x**3)*55 - 2035\nSimplifying the partial expression: (10*x)*(98*x**3 + 16*x - 37)\nExpanding the part (98*x**3 + 16*x - 37) using the distributive property, and we got: -370*x + (10*x)*(16*x) + (10*x)*(98*x**3)\nReplacing (10*x)*(98*x**3 + 16*x - 37) with -370*x + (10*x)*(16*x) + (10*x)*(98*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -37*10*x + (10*x)*(16*x) + (10*x)*(98*x**3) + (16*x)*55 + (98*x**3)*55 - 2035\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (16*x)*55 = 880*x\n (16*x)*(10*x) = 160*x**2\n (98*x**3)*55 = 5390*x**3\n (98*x**3)*(10*x) = 980*x**4\n -37*10*x = -370*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 980*x**4 + 5390*x**3 + 160*x**2 - 370*x + 880*x - 2035\nCombining like terms, got 980*x**4 + 5390*x**3 + 160*x**2 + 510*x - 2035\n#Step 6:\nCurrent expression: 980*x**4 + 5390*x**3 + 160*x**2 + 510*x - 2035\nNo more calculations needed.\n980*x**4 + 5390*x**3 + 160*x**2 + 510*x - 2035", "generated_answer": "980*x**4 + 5390*x**3 + 160*x**2 + 510*x - 2035", "step_length": 6} {"cot_id": "f4c976b4639b633cc38cf47f8e0a1c3ad24766073e2a48625b6945025cdf4243", "datapoint": {"question": "Calculate the following: -26*z*(-31*z**3 - 3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "806*z**4 + 78*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1933, "polynomial_expr": "-26*z*(-31*z**3 - 3)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -26*z*(-31*z**3 - 3)\nExpanding the part (-31*z**3 - 3) using the distributive property, and we got: (-26*z)*(-31*z**3) - (-1)*78*z\n#Step 2:\nCurrent expression: (-26*z)*(-31*z**3) - (-1)*78*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -3*(-26*z) = 78*z\n (-31*z**3)*(-26*z) = 806*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 806*z**4 + 78*z\nNo more calculations needed.\n806*z**4 + 78*z", "generated_answer": "806*z**4 + 78*z", "step_length": 3} {"cot_id": "51e002b9b71670b18d02997e5ddc45c3bb1f99e205b1fe62a94ef9ef28a1d878", "datapoint": {"question": "Calculate the following: (19 - 39*x**3)*(94*x**2 + 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-3666*x**5 - 273*x**3 + 1786*x**2 + 133", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1934, "polynomial_expr": "(19 - 39*x**3)*(94*x**2 + 7)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (19 - 39*x**3)*(94*x**2 + 7)\nExpanding the part (94*x**2 + 7) using the distributive property, and we got: (94*x**2)*(19 - 39*x**3) + 7*(19 - 39*x**3)\n#Step 2:\nCurrent expression: (94*x**2)*(19 - 39*x**3) + 7*(19 - 39*x**3)\nSimplifying the partial expression: 7*(19 - 39*x**3)\nExpanding the part (19 - 39*x**3) using the distributive property, and we got: -39*x**3*7 + 19*7\nReplacing 7*(19 - 39*x**3) with -39*x**3*7 + 19*7 in the overall expression.\n#Step 3:\nCurrent expression: (94*x**2)*(19 - 39*x**3) - 39*x**3*7 + 133\nSimplifying the partial expression: (94*x**2)*(19 - 39*x**3)\nExpanding the part (19 - 39*x**3) using the distributive property, and we got: 19*(94*x**2) + (94*x**2)*(-39*x**3)\nReplacing (94*x**2)*(19 - 39*x**3) with 19*(94*x**2) + (94*x**2)*(-39*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 19*94*x**2 + (94*x**2)*(-39*x**3) - 39*x**3*7 + 133\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*x**3)*7 = -273*x**3\n (-39*x**3)*(94*x**2) = -3666*x**5\n 19*94*x**2 = 1786*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -3666*x**5 - 273*x**3 + 1786*x**2 + 133\nNo more calculations needed.\n-3666*x**5 - 273*x**3 + 1786*x**2 + 133", "generated_answer": "-3666*x**5 - 273*x**3 + 1786*x**2 + 133", "step_length": 5} {"cot_id": "0ab4ba9e7f92982299a8bba29d600e774f980ef2330c09b2d44fc3aa36301a6a", "datapoint": {"question": "Calculate the following: -580*y**2\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-580*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1935, "polynomial_expr": "-580*y**2", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -580*y**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -580*y**2\nNo more calculations needed.\n-580*y**2", "generated_answer": "-580*y**2", "step_length": 2} {"cot_id": "18c719c9c4586abcc63a87c3116c7f8952746d1ffa2b1075a98db8200a3b6a37", "datapoint": {"question": "Simplify this expression: (6*x**3 + 28)*(15*x**3 - 19*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "90*x**6 - 114*x**4 + 420*x**3 - 532*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1936, "polynomial_expr": "(6*x**3 + 28)*(15*x**3 - 19*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6*x**3 + 28)*(15*x**3 - 19*x)\nExpanding the part (6*x**3 + 28) using the distributive property, and we got: (6*x**3)*(15*x**3 - 19*x) + 28*(15*x**3 - 19*x)\n#Step 2:\nCurrent expression: (6*x**3)*(15*x**3 - 19*x) + 28*(15*x**3 - 19*x)\nSimplifying the partial expression: 28*(15*x**3 - 19*x)\nExpanding the part (15*x**3 - 19*x) using the distributive property, and we got: -19*x*28 + (15*x**3)*28\nReplacing 28*(15*x**3 - 19*x) with -19*x*28 + (15*x**3)*28 in the overall expression.\n#Step 3:\nCurrent expression: -19*x*28 + (6*x**3)*(15*x**3 - 19*x) + (15*x**3)*28\nSimplifying the partial expression: (6*x**3)*(15*x**3 - 19*x)\nExpanding the part (15*x**3 - 19*x) using the distributive property, and we got: (-19*x)*(6*x**3) + (6*x**3)*(15*x**3)\nReplacing (6*x**3)*(15*x**3 - 19*x) with (-19*x)*(6*x**3) + (6*x**3)*(15*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-19*x)*(6*x**3) - 19*x*28 + (6*x**3)*(15*x**3) + (15*x**3)*28\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*x)*28 = -532*x\n (-19*x)*(6*x**3) = -114*x**4\n (15*x**3)*28 = 420*x**3\n (15*x**3)*(6*x**3) = 90*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 90*x**6 - 114*x**4 + 420*x**3 - 532*x\nNo more calculations needed.\n90*x**6 - 114*x**4 + 420*x**3 - 532*x", "generated_answer": "90*x**6 - 114*x**4 + 420*x**3 - 532*x", "step_length": 5} {"cot_id": "c357c74132e285bad87791d50d119979689e2dda30e702da1a6be673eefdc5a6", "datapoint": {"question": "Calculate the following: 43*x*(17 - 66*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2838*x**3 + 731*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1937, "polynomial_expr": "43*x*(17 - 66*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 43*x*(17 - 66*x**2)\nExpanding the part (17 - 66*x**2) using the distributive property, and we got: 17*(43*x) + (43*x)*(-66*x**2)\n#Step 2:\nCurrent expression: 17*(43*x) + (43*x)*(-66*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 17*(43*x) = 731*x\n (-66*x**2)*(43*x) = -2838*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -2838*x**3 + 731*x\nNo more calculations needed.\n-2838*x**3 + 731*x", "generated_answer": "-2838*x**3 + 731*x", "step_length": 3} {"cot_id": "48287151af38220d42a5ee42e4295b2448874d7bc475fff3a2f3cbf3fd013d5a", "datapoint": {"question": "Simplify this expression: (-33*x**3 - 26*x)*(32*x**3 - 19*x**2 + 42*x + 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1056*x**6 + 627*x**5 - 2218*x**4 - 1090*x**3 - 1092*x**2 - 1248*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1938, "polynomial_expr": "(-33*x**3 - 26*x)*(32*x**3 - 19*x**2 + 42*x + 48)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-33*x**3 - 26*x)*(32*x**3 - 19*x**2 + 42*x + 48)\nExpanding the part (-33*x**3 - 26*x) using the distributive property, and we got: (-26*x)*(32*x**3 - 19*x**2 + 42*x + 48) + (-33*x**3)*(32*x**3 - 19*x**2 + 42*x + 48)\n#Step 2:\nCurrent expression: (-26*x)*(32*x**3 - 19*x**2 + 42*x + 48) + (-33*x**3)*(32*x**3 - 19*x**2 + 42*x + 48)\nSimplifying the partial expression: (-33*x**3)*(32*x**3 - 19*x**2 + 42*x + 48)\nExpanding the part (32*x**3 - 19*x**2 + 42*x + 48) using the distributive property, and we got: 48*(-33*x**3) + (42*x)*(-33*x**3) + (-19*x**2)*(-33*x**3) + (-33*x**3)*(32*x**3)\nReplacing (-33*x**3)*(32*x**3 - 19*x**2 + 42*x + 48) with 48*(-33*x**3) + (42*x)*(-33*x**3) + (-19*x**2)*(-33*x**3) + (-33*x**3)*(32*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-26*x)*(32*x**3 - 19*x**2 + 42*x + 48) + 48*(-33)*x**3 + (42*x)*(-33*x**3) + (-19*x**2)*(-33*x**3) + (-33*x**3)*(32*x**3)\nSimplifying the partial expression: (-26*x)*(32*x**3 - 19*x**2 + 42*x + 48)\nExpanding the part (32*x**3 - 19*x**2 + 42*x + 48) using the distributive property, and we got: (-26*x)*(42*x) + (-26*x)*(-19*x**2) + (-26*x)*(32*x**3) + 48*(-26*x)\nReplacing (-26*x)*(32*x**3 - 19*x**2 + 42*x + 48) with (-26*x)*(42*x) + (-26*x)*(-19*x**2) + (-26*x)*(32*x**3) + 48*(-26*x) in the overall expression.\n#Step 4:\nCurrent expression: (-26*x)*(42*x) + (-26*x)*(-19*x**2) + (-26*x)*(32*x**3) + 48*(-33)*x**3 + 48*(-26)*x + (42*x)*(-33*x**3) + (-19*x**2)*(-33*x**3) + (-33*x**3)*(32*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*x**2)*(-33*x**3) = 627*x**5\n (-19*x**2)*(-26*x) = 494*x**3\n (32*x**3)*(-33*x**3) = -1056*x**6\n (32*x**3)*(-26*x) = -832*x**4\n (42*x)*(-33*x**3) = -1386*x**4\n (42*x)*(-26*x) = -1092*x**2\n 48*-33*x**3 = -1584*x**3\n 48*-26*x = -1248*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1056*x**6 + 627*x**5 - 1386*x**4 - 832*x**4 - 1584*x**3 + 494*x**3 - 1092*x**2 - 1248*x\nCombining like terms, got -1056*x**6 + 627*x**5 - 2218*x**4 - 1090*x**3 - 1092*x**2 - 1248*x\n#Step 6:\nCurrent expression: -1056*x**6 + 627*x**5 - 2218*x**4 - 1090*x**3 - 1092*x**2 - 1248*x\nNo more calculations needed.\n-1056*x**6 + 627*x**5 - 2218*x**4 - 1090*x**3 - 1092*x**2 - 1248*x", "generated_answer": "-1056*x**6 + 627*x**5 - 2218*x**4 - 1090*x**3 - 1092*x**2 - 1248*x", "step_length": 6} {"cot_id": "b8c2498a49198dd050e6fb589539c13eaff9a8abdb7f793eb436c9b0b32e18de", "datapoint": {"question": "Calculate the following: (14*x**2 + 47)*(49*x**3 + 8*x - 3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "686*x**5 + 2415*x**3 - 42*x**2 + 376*x - 141", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1939, "polynomial_expr": "(14*x**2 + 47)*(49*x**3 + 8*x - 3)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14*x**2 + 47)*(49*x**3 + 8*x - 3)\nExpanding the part (14*x**2 + 47) using the distributive property, and we got: (14*x**2)*(49*x**3 + 8*x - 3) + 47*(49*x**3 + 8*x - 3)\n#Step 2:\nCurrent expression: (14*x**2)*(49*x**3 + 8*x - 3) + 47*(49*x**3 + 8*x - 3)\nSimplifying the partial expression: 47*(49*x**3 + 8*x - 3)\nExpanding the part (49*x**3 + 8*x - 3) using the distributive property, and we got: (8*x)*47 + (49*x**3)*47 - 3*47\nReplacing 47*(49*x**3 + 8*x - 3) with (8*x)*47 + (49*x**3)*47 - 3*47 in the overall expression.\n#Step 3:\nCurrent expression: (8*x)*47 + (14*x**2)*(49*x**3 + 8*x - 3) + (49*x**3)*47 - 141\nSimplifying the partial expression: (14*x**2)*(49*x**3 + 8*x - 3)\nExpanding the part (49*x**3 + 8*x - 3) using the distributive property, and we got: -42*x**2 + (8*x)*(14*x**2) + (14*x**2)*(49*x**3)\nReplacing (14*x**2)*(49*x**3 + 8*x - 3) with -42*x**2 + (8*x)*(14*x**2) + (14*x**2)*(49*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -3*14*x**2 + (8*x)*(14*x**2) + (8*x)*47 + (14*x**2)*(49*x**3) + (49*x**3)*47 - 141\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (8*x)*47 = 376*x\n (8*x)*(14*x**2) = 112*x**3\n (49*x**3)*47 = 2303*x**3\n (49*x**3)*(14*x**2) = 686*x**5\n -3*14*x**2 = -42*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 686*x**5 + 112*x**3 + 2303*x**3 - 42*x**2 + 376*x - 141\nCombining like terms, got 686*x**5 + 2415*x**3 - 42*x**2 + 376*x - 141\n#Step 6:\nCurrent expression: 686*x**5 + 2415*x**3 - 42*x**2 + 376*x - 141\nNo more calculations needed.\n686*x**5 + 2415*x**3 - 42*x**2 + 376*x - 141", "generated_answer": "686*x**5 + 2415*x**3 - 42*x**2 + 376*x - 141", "step_length": 6} {"cot_id": "7dac7b06d5c079999d476c5ff6b096cd05d8f6f61bc226c21626dd6f1ec217ce", "datapoint": {"question": "Calculate the following: (-19*x**3 - 34*x**2 + 25)*(38*x**3 + 34*x**2 + 29)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-722*x**6 - 1938*x**5 - 1156*x**4 + 399*x**3 - 136*x**2 + 725", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1940, "polynomial_expr": "(-19*x**3 - 34*x**2 + 25)*(38*x**3 + 34*x**2 + 29)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-19*x**3 - 34*x**2 + 25)*(38*x**3 + 34*x**2 + 29)\nExpanding the part (-19*x**3 - 34*x**2 + 25) using the distributive property, and we got: (-34*x**2)*(38*x**3 + 34*x**2 + 29) + (-19*x**3)*(38*x**3 + 34*x**2 + 29) + 25*(38*x**3 + 34*x**2 + 29)\n#Step 2:\nCurrent expression: (-34*x**2)*(38*x**3 + 34*x**2 + 29) + (-19*x**3)*(38*x**3 + 34*x**2 + 29) + 25*(38*x**3 + 34*x**2 + 29)\nSimplifying the partial expression: 25*(38*x**3 + 34*x**2 + 29)\nExpanding the part (38*x**3 + 34*x**2 + 29) using the distributive property, and we got: (34*x**2)*25 + (38*x**3)*25 + 29*25\nReplacing 25*(38*x**3 + 34*x**2 + 29) with (34*x**2)*25 + (38*x**3)*25 + 29*25 in the overall expression.\n#Step 3:\nCurrent expression: (-34*x**2)*(38*x**3 + 34*x**2 + 29) + (34*x**2)*25 + (-19*x**3)*(38*x**3 + 34*x**2 + 29) + (38*x**3)*25 + 725\nSimplifying the partial expression: (-34*x**2)*(38*x**3 + 34*x**2 + 29)\nExpanding the part (38*x**3 + 34*x**2 + 29) using the distributive property, and we got: 29*(-34*x**2) + (-34*x**2)*(34*x**2) + (-34*x**2)*(38*x**3)\nReplacing (-34*x**2)*(38*x**3 + 34*x**2 + 29) with 29*(-34*x**2) + (-34*x**2)*(34*x**2) + (-34*x**2)*(38*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 29*(-34)*x**2 + (-34*x**2)*(34*x**2) + (-34*x**2)*(38*x**3) + (34*x**2)*25 + (-19*x**3)*(38*x**3 + 34*x**2 + 29) + (38*x**3)*25 + 725\nSimplifying the partial expression: (-19*x**3)*(38*x**3 + 34*x**2 + 29)\nExpanding the part (38*x**3 + 34*x**2 + 29) using the distributive property, and we got: 29*(-19*x**3) + (34*x**2)*(-19*x**3) + (-19*x**3)*(38*x**3)\nReplacing (-19*x**3)*(38*x**3 + 34*x**2 + 29) with 29*(-19*x**3) + (34*x**2)*(-19*x**3) + (-19*x**3)*(38*x**3) in the overall expression.\n#Step 5:\nCurrent expression: 29*(-19)*x**3 + 29*(-34)*x**2 + (-34*x**2)*(34*x**2) + (-34*x**2)*(38*x**3) + (34*x**2)*(-19*x**3) + (34*x**2)*25 + (-19*x**3)*(38*x**3) + (38*x**3)*25 + 725\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (34*x**2)*25 = 850*x**2\n (34*x**2)*(-34*x**2) = -1156*x**4\n (34*x**2)*(-19*x**3) = -646*x**5\n (38*x**3)*25 = 950*x**3\n (38*x**3)*(-34*x**2) = -1292*x**5\n (38*x**3)*(-19*x**3) = -722*x**6\n 29*-34*x**2 = -986*x**2\n 29*-19*x**3 = -551*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -722*x**6 - 1292*x**5 - 646*x**5 - 1156*x**4 - 551*x**3 + 950*x**3 - 986*x**2 + 850*x**2 + 725\nCombining like terms, got -722*x**6 - 1938*x**5 - 1156*x**4 + 399*x**3 - 136*x**2 + 725\n#Step 7:\nCurrent expression: -722*x**6 - 1938*x**5 - 1156*x**4 + 399*x**3 - 136*x**2 + 725\nNo more calculations needed.\n-722*x**6 - 1938*x**5 - 1156*x**4 + 399*x**3 - 136*x**2 + 725", "generated_answer": "-722*x**6 - 1938*x**5 - 1156*x**4 + 399*x**3 - 136*x**2 + 725", "step_length": 7} {"cot_id": "93639ed3a9732eb57ed0c0998081eceac2674d31fd517fbc220813c186e8b225", "datapoint": {"question": "Calculate the following: (-43*z**3 - 79)*(35*z**3 + 61*z + 2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1505*z**6 - 2623*z**4 - 2851*z**3 - 4819*z - 158", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1941, "polynomial_expr": "(-43*z**3 - 79)*(35*z**3 + 61*z + 2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-43*z**3 - 79)*(35*z**3 + 61*z + 2)\nExpanding the part (-43*z**3 - 79) using the distributive property, and we got: (-43*z**3)*(35*z**3 + 61*z + 2) - 79*(35*z**3 + 61*z + 2)\n#Step 2:\nCurrent expression: (-43*z**3)*(35*z**3 + 61*z + 2) - 79*(35*z**3 + 61*z + 2)\nSimplifying the partial expression: -79*(35*z**3 + 61*z + 2)\nExpanding the part (35*z**3 + 61*z + 2) using the distributive property, and we got: (61*z)*(-79) + (35*z**3)*(-79) + 2*(-79)\nReplacing -79*(35*z**3 + 61*z + 2) with (61*z)*(-79) + (35*z**3)*(-79) + 2*(-79) in the overall expression.\n#Step 3:\nCurrent expression: (61*z)*(-79) + (-43*z**3)*(35*z**3 + 61*z + 2) + (35*z**3)*(-79) - 158\nSimplifying the partial expression: (-43*z**3)*(35*z**3 + 61*z + 2)\nExpanding the part (35*z**3 + 61*z + 2) using the distributive property, and we got: 2*(-43*z**3) + (61*z)*(-43*z**3) + (-43*z**3)*(35*z**3)\nReplacing (-43*z**3)*(35*z**3 + 61*z + 2) with 2*(-43*z**3) + (61*z)*(-43*z**3) + (-43*z**3)*(35*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 2*(-43)*z**3 + (61*z)*(-43*z**3) + (61*z)*(-79) + (-43*z**3)*(35*z**3) + (35*z**3)*(-79) - 158\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (35*z**3)*-79 = -2765*z**3\n (35*z**3)*(-43*z**3) = -1505*z**6\n (61*z)*-79 = -4819*z\n (61*z)*(-43*z**3) = -2623*z**4\n 2*-43*z**3 = -86*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1505*z**6 - 2623*z**4 - 2765*z**3 - 86*z**3 - 4819*z - 158\nCombining like terms, got -1505*z**6 - 2623*z**4 - 2851*z**3 - 4819*z - 158\n#Step 6:\nCurrent expression: -1505*z**6 - 2623*z**4 - 2851*z**3 - 4819*z - 158\nNo more calculations needed.\n-1505*z**6 - 2623*z**4 - 2851*z**3 - 4819*z - 158", "generated_answer": "-1505*z**6 - 2623*z**4 - 2851*z**3 - 4819*z - 158", "step_length": 6} {"cot_id": "2d5f158789db88eff04dc6e6d80cce6d5fd2e112a9f2f6f0ef27466982e6f4b9", "datapoint": {"question": "Simplify this expression: (-34*y**2 - 13)*(-41*y**2 - 46*y + 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1394*y**4 + 1564*y**3 - 147*y**2 + 598*y - 260", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1942, "polynomial_expr": "(-34*y**2 - 13)*(-41*y**2 - 46*y + 20)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-34*y**2 - 13)*(-41*y**2 - 46*y + 20)\nExpanding the part (-34*y**2 - 13) using the distributive property, and we got: (-34*y**2)*(-41*y**2 - 46*y + 20) - 13*(-41*y**2 - 46*y + 20)\n#Step 2:\nCurrent expression: (-34*y**2)*(-41*y**2 - 46*y + 20) - 13*(-41*y**2 - 46*y + 20)\nSimplifying the partial expression: -13*(-41*y**2 - 46*y + 20)\nExpanding the part (-41*y**2 - 46*y + 20) using the distributive property, and we got: -46*y*(-13) - 41*y**2*(-13) + 20*(-13)\nReplacing -13*(-41*y**2 - 46*y + 20) with -46*y*(-13) - 41*y**2*(-13) + 20*(-13) in the overall expression.\n#Step 3:\nCurrent expression: -46*y*(-13) - 41*y**2*(-13) + (-34*y**2)*(-41*y**2 - 46*y + 20) - 260\nSimplifying the partial expression: (-34*y**2)*(-41*y**2 - 46*y + 20)\nExpanding the part (-41*y**2 - 46*y + 20) using the distributive property, and we got: (-46*y)*(-34*y**2) + 20*(-34*y**2) + (-41*y**2)*(-34*y**2)\nReplacing (-34*y**2)*(-41*y**2 - 46*y + 20) with (-46*y)*(-34*y**2) + 20*(-34*y**2) + (-41*y**2)*(-34*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-46*y)*(-34*y**2) - 46*y*(-13) + 20*(-34)*y**2 + (-41*y**2)*(-34*y**2) - 41*y**2*(-13) - 260\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*y)*-13 = 598*y\n (-46*y)*(-34*y**2) = 1564*y**3\n (-41*y**2)*-13 = 533*y**2\n (-41*y**2)*(-34*y**2) = 1394*y**4\n 20*-34*y**2 = -680*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1394*y**4 + 1564*y**3 - 680*y**2 + 533*y**2 + 598*y - 260\nCombining like terms, got 1394*y**4 + 1564*y**3 - 147*y**2 + 598*y - 260\n#Step 6:\nCurrent expression: 1394*y**4 + 1564*y**3 - 147*y**2 + 598*y - 260\nNo more calculations needed.\n1394*y**4 + 1564*y**3 - 147*y**2 + 598*y - 260", "generated_answer": "1394*y**4 + 1564*y**3 - 147*y**2 + 598*y - 260", "step_length": 6} {"cot_id": "fa7b57242ce243f711c03c936c12278e41d38298020557c3671ad1ec1d7d37e1", "datapoint": {"question": "Calculate the following: (-40*y - 35)*(-33*y**3 - 20*y**2 - 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1320*y**4 + 1955*y**3 + 700*y**2 + 1640*y + 1435", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1943, "polynomial_expr": "(-40*y - 35)*(-33*y**3 - 20*y**2 - 41)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-40*y - 35)*(-33*y**3 - 20*y**2 - 41)\nExpanding the part (-40*y - 35) using the distributive property, and we got: (-40*y)*(-33*y**3 - 20*y**2 - 41) - 35*(-33*y**3 - 20*y**2 - 41)\n#Step 2:\nCurrent expression: (-40*y)*(-33*y**3 - 20*y**2 - 41) - 35*(-33*y**3 - 20*y**2 - 41)\nSimplifying the partial expression: -35*(-33*y**3 - 20*y**2 - 41)\nExpanding the part (-33*y**3 - 20*y**2 - 41) using the distributive property, and we got: -20*y**2*(-35) - 33*y**3*(-35) - 41*(-35)\nReplacing -35*(-33*y**3 - 20*y**2 - 41) with -20*y**2*(-35) - 33*y**3*(-35) - 41*(-35) in the overall expression.\n#Step 3:\nCurrent expression: (-40*y)*(-33*y**3 - 20*y**2 - 41) - 20*y**2*(-35) - 33*y**3*(-35) + 1435\nSimplifying the partial expression: (-40*y)*(-33*y**3 - 20*y**2 - 41)\nExpanding the part (-33*y**3 - 20*y**2 - 41) using the distributive property, and we got: (-40*y)*(-20*y**2) + (-40*y)*(-33*y**3) - (-1)*1640*y\nReplacing (-40*y)*(-33*y**3 - 20*y**2 - 41) with (-40*y)*(-20*y**2) + (-40*y)*(-33*y**3) - (-1)*1640*y in the overall expression.\n#Step 4:\nCurrent expression: (-40*y)*(-20*y**2) + (-40*y)*(-33*y**3) - 41*(-40)*y - 20*y**2*(-35) - 33*y**3*(-35) + 1435\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*y**3)*-35 = 1155*y**3\n (-33*y**3)*(-40*y) = 1320*y**4\n (-20*y**2)*-35 = 700*y**2\n (-20*y**2)*(-40*y) = 800*y**3\n -41*-40*y = 1640*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1320*y**4 + 800*y**3 + 1155*y**3 + 700*y**2 + 1640*y + 1435\nCombining like terms, got 1320*y**4 + 1955*y**3 + 700*y**2 + 1640*y + 1435\n#Step 6:\nCurrent expression: 1320*y**4 + 1955*y**3 + 700*y**2 + 1640*y + 1435\nNo more calculations needed.\n1320*y**4 + 1955*y**3 + 700*y**2 + 1640*y + 1435", "generated_answer": "1320*y**4 + 1955*y**3 + 700*y**2 + 1640*y + 1435", "step_length": 6} {"cot_id": "f045ef3de8662c092c70b147ed208283993c395bc6880da06d1bf952f56b5531", "datapoint": {"question": "Calculate the following: (40*y**2 - 43*y)*(-31*y**3 + 41*y - 5)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1240*y**5 + 1333*y**4 + 1640*y**3 - 1963*y**2 + 215*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1944, "polynomial_expr": "(40*y**2 - 43*y)*(-31*y**3 + 41*y - 5)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (40*y**2 - 43*y)*(-31*y**3 + 41*y - 5)\nExpanding the part (40*y**2 - 43*y) using the distributive property, and we got: (-43*y)*(-31*y**3 + 41*y - 5) + (40*y**2)*(-31*y**3 + 41*y - 5)\n#Step 2:\nCurrent expression: (-43*y)*(-31*y**3 + 41*y - 5) + (40*y**2)*(-31*y**3 + 41*y - 5)\nSimplifying the partial expression: (-43*y)*(-31*y**3 + 41*y - 5)\nExpanding the part (-31*y**3 + 41*y - 5) using the distributive property, and we got: (-43*y)*(41*y) + (-43*y)*(-31*y**3) - (-1)*215*y\nReplacing (-43*y)*(-31*y**3 + 41*y - 5) with (-43*y)*(41*y) + (-43*y)*(-31*y**3) - (-1)*215*y in the overall expression.\n#Step 3:\nCurrent expression: (-43*y)*(41*y) + (-43*y)*(-31*y**3) - 5*(-43)*y + (40*y**2)*(-31*y**3 + 41*y - 5)\nSimplifying the partial expression: (40*y**2)*(-31*y**3 + 41*y - 5)\nExpanding the part (-31*y**3 + 41*y - 5) using the distributive property, and we got: -200*y**2 + (41*y)*(40*y**2) + (40*y**2)*(-31*y**3)\nReplacing (40*y**2)*(-31*y**3 + 41*y - 5) with -200*y**2 + (41*y)*(40*y**2) + (40*y**2)*(-31*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-43*y)*(41*y) + (-43*y)*(-31*y**3) - 5*40*y**2 - 5*(-43)*y + (41*y)*(40*y**2) + (40*y**2)*(-31*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-31*y**3)*(-43*y) = 1333*y**4\n (-31*y**3)*(40*y**2) = -1240*y**5\n (41*y)*(-43*y) = -1763*y**2\n (41*y)*(40*y**2) = 1640*y**3\n -5*-43*y = 215*y\n -5*40*y**2 = -200*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1240*y**5 + 1333*y**4 + 1640*y**3 - 1763*y**2 - 200*y**2 + 215*y\nCombining like terms, got -1240*y**5 + 1333*y**4 + 1640*y**3 - 1963*y**2 + 215*y\n#Step 6:\nCurrent expression: -1240*y**5 + 1333*y**4 + 1640*y**3 - 1963*y**2 + 215*y\nNo more calculations needed.\n-1240*y**5 + 1333*y**4 + 1640*y**3 - 1963*y**2 + 215*y", "generated_answer": "-1240*y**5 + 1333*y**4 + 1640*y**3 - 1963*y**2 + 215*y", "step_length": 6} {"cot_id": "170f90304bf77576e961260220521d0e17f04d3a413f97147eb6e2b9b5edd792", "datapoint": {"question": "Calculate the following: (47*y**2 + 19*y - 45)*(29*y**3 - 18*y**2 + 73*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1363*y**5 - 295*y**4 + 1784*y**3 + 2197*y**2 - 3285*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1945, "polynomial_expr": "(47*y**2 + 19*y - 45)*(29*y**3 - 18*y**2 + 73*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (47*y**2 + 19*y - 45)*(29*y**3 - 18*y**2 + 73*y)\nExpanding the part (47*y**2 + 19*y - 45) using the distributive property, and we got: (19*y)*(29*y**3 - 18*y**2 + 73*y) + (47*y**2)*(29*y**3 - 18*y**2 + 73*y) - 45*(29*y**3 - 18*y**2 + 73*y)\n#Step 2:\nCurrent expression: (19*y)*(29*y**3 - 18*y**2 + 73*y) + (47*y**2)*(29*y**3 - 18*y**2 + 73*y) - 45*(29*y**3 - 18*y**2 + 73*y)\nSimplifying the partial expression: -45*(29*y**3 - 18*y**2 + 73*y)\nExpanding the part (29*y**3 - 18*y**2 + 73*y) using the distributive property, and we got: (73*y)*(-45) - 18*y**2*(-45) + (29*y**3)*(-45)\nReplacing -45*(29*y**3 - 18*y**2 + 73*y) with (73*y)*(-45) - 18*y**2*(-45) + (29*y**3)*(-45) in the overall expression.\n#Step 3:\nCurrent expression: (19*y)*(29*y**3 - 18*y**2 + 73*y) + (73*y)*(-45) - 18*y**2*(-45) + (47*y**2)*(29*y**3 - 18*y**2 + 73*y) + (29*y**3)*(-45)\nSimplifying the partial expression: (19*y)*(29*y**3 - 18*y**2 + 73*y)\nExpanding the part (29*y**3 - 18*y**2 + 73*y) using the distributive property, and we got: (19*y)*(73*y) + (19*y)*(-18*y**2) + (19*y)*(29*y**3)\nReplacing (19*y)*(29*y**3 - 18*y**2 + 73*y) with (19*y)*(73*y) + (19*y)*(-18*y**2) + (19*y)*(29*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (19*y)*(73*y) + (19*y)*(-18*y**2) + (19*y)*(29*y**3) + (73*y)*(-45) - 18*y**2*(-45) + (47*y**2)*(29*y**3 - 18*y**2 + 73*y) + (29*y**3)*(-45)\nSimplifying the partial expression: (47*y**2)*(29*y**3 - 18*y**2 + 73*y)\nExpanding the part (29*y**3 - 18*y**2 + 73*y) using the distributive property, and we got: (73*y)*(47*y**2) + (-18*y**2)*(47*y**2) + (47*y**2)*(29*y**3)\nReplacing (47*y**2)*(29*y**3 - 18*y**2 + 73*y) with (73*y)*(47*y**2) + (-18*y**2)*(47*y**2) + (47*y**2)*(29*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (19*y)*(73*y) + (19*y)*(-18*y**2) + (19*y)*(29*y**3) + (73*y)*(47*y**2) + (73*y)*(-45) + (-18*y**2)*(47*y**2) - 18*y**2*(-45) + (47*y**2)*(29*y**3) + (29*y**3)*(-45)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-18*y**2)*-45 = 810*y**2\n (-18*y**2)*(19*y) = -342*y**3\n (-18*y**2)*(47*y**2) = -846*y**4\n (29*y**3)*-45 = -1305*y**3\n (29*y**3)*(19*y) = 551*y**4\n (29*y**3)*(47*y**2) = 1363*y**5\n (73*y)*-45 = -3285*y\n (73*y)*(19*y) = 1387*y**2\n (73*y)*(47*y**2) = 3431*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1363*y**5 - 846*y**4 + 551*y**4 - 1305*y**3 - 342*y**3 + 3431*y**3 + 810*y**2 + 1387*y**2 - 3285*y\nCombining like terms, got 1363*y**5 - 295*y**4 + 1784*y**3 + 2197*y**2 - 3285*y\n#Step 7:\nCurrent expression: 1363*y**5 - 295*y**4 + 1784*y**3 + 2197*y**2 - 3285*y\nNo more calculations needed.\n1363*y**5 - 295*y**4 + 1784*y**3 + 2197*y**2 - 3285*y", "generated_answer": "1363*y**5 - 295*y**4 + 1784*y**3 + 2197*y**2 - 3285*y", "step_length": 7} {"cot_id": "77746f3889ee9b13a63eb10c1c8e653a364584f05a53348332bcd2fd864cdcfc", "datapoint": {"question": "Simplify this expression: (-31*z**2 + 13*z - 5)*(32*z**2 - 52*z - 40)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-992*z**4 + 2028*z**3 + 404*z**2 - 260*z + 200", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1946, "polynomial_expr": "(-31*z**2 + 13*z - 5)*(32*z**2 - 52*z - 40)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-31*z**2 + 13*z - 5)*(32*z**2 - 52*z - 40)\nExpanding the part (32*z**2 - 52*z - 40) using the distributive property, and we got: (-52*z)*(-31*z**2 + 13*z - 5) + (32*z**2)*(-31*z**2 + 13*z - 5) - 40*(-31*z**2 + 13*z - 5)\n#Step 2:\nCurrent expression: (-52*z)*(-31*z**2 + 13*z - 5) + (32*z**2)*(-31*z**2 + 13*z - 5) - 40*(-31*z**2 + 13*z - 5)\nSimplifying the partial expression: -40*(-31*z**2 + 13*z - 5)\nExpanding the part (-31*z**2 + 13*z - 5) using the distributive property, and we got: (13*z)*(-40) - 31*z**2*(-40) - 5*(-40)\nReplacing -40*(-31*z**2 + 13*z - 5) with (13*z)*(-40) - 31*z**2*(-40) - 5*(-40) in the overall expression.\n#Step 3:\nCurrent expression: (-52*z)*(-31*z**2 + 13*z - 5) + (13*z)*(-40) - 31*z**2*(-40) + (32*z**2)*(-31*z**2 + 13*z - 5) + 200\nSimplifying the partial expression: (-52*z)*(-31*z**2 + 13*z - 5)\nExpanding the part (-31*z**2 + 13*z - 5) using the distributive property, and we got: (-52*z)*(13*z) + (-52*z)*(-31*z**2) - (-1)*260*z\nReplacing (-52*z)*(-31*z**2 + 13*z - 5) with (-52*z)*(13*z) + (-52*z)*(-31*z**2) - (-1)*260*z in the overall expression.\n#Step 4:\nCurrent expression: (-52*z)*(13*z) + (-52*z)*(-31*z**2) - 5*(-52)*z + (13*z)*(-40) - 31*z**2*(-40) + (32*z**2)*(-31*z**2 + 13*z - 5) + 200\nSimplifying the partial expression: (32*z**2)*(-31*z**2 + 13*z - 5)\nExpanding the part (-31*z**2 + 13*z - 5) using the distributive property, and we got: -160*z**2 + (13*z)*(32*z**2) + (-31*z**2)*(32*z**2)\nReplacing (32*z**2)*(-31*z**2 + 13*z - 5) with -160*z**2 + (13*z)*(32*z**2) + (-31*z**2)*(32*z**2) in the overall expression.\n#Step 5:\nCurrent expression: (-52*z)*(13*z) + (-52*z)*(-31*z**2) - 5*32*z**2 - 5*(-52)*z + (13*z)*(32*z**2) + (13*z)*(-40) + (-31*z**2)*(32*z**2) - 31*z**2*(-40) + 200\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-31*z**2)*-40 = 1240*z**2\n (-31*z**2)*(-52*z) = 1612*z**3\n (-31*z**2)*(32*z**2) = -992*z**4\n (13*z)*-40 = -520*z\n (13*z)*(-52*z) = -676*z**2\n (13*z)*(32*z**2) = 416*z**3\n -5*-52*z = 260*z\n -5*32*z**2 = -160*z**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -992*z**4 + 416*z**3 + 1612*z**3 - 676*z**2 - 160*z**2 + 1240*z**2 - 520*z + 260*z + 200\nCombining like terms, got -992*z**4 + 2028*z**3 + 404*z**2 - 260*z + 200\n#Step 7:\nCurrent expression: -992*z**4 + 2028*z**3 + 404*z**2 - 260*z + 200\nNo more calculations needed.\n-992*z**4 + 2028*z**3 + 404*z**2 - 260*z + 200", "generated_answer": "-992*z**4 + 2028*z**3 + 404*z**2 - 260*z + 200", "step_length": 7} {"cot_id": "e0a545fe7e3f6192e58a35e631a646f5b88881527a7cd048473163f124a70e82", "datapoint": {"question": "Calculate the following: 53*z*(8*z**2 - 11*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "424*z**3 - 583*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1947, "polynomial_expr": "53*z*(8*z**2 - 11*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 53*z*(8*z**2 - 11*z)\nExpanding the part (8*z**2 - 11*z) using the distributive property, and we got: (-11*z)*(53*z) + (53*z)*(8*z**2)\n#Step 2:\nCurrent expression: (-11*z)*(53*z) + (53*z)*(8*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*z)*(53*z) = -583*z**2\n (8*z**2)*(53*z) = 424*z**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 424*z**3 - 583*z**2\nNo more calculations needed.\n424*z**3 - 583*z**2", "generated_answer": "424*z**3 - 583*z**2", "step_length": 3} {"cot_id": "3775659f32e88154ada723e8a290280b3d1355dbf50cb8b9a78e8af590747848", "datapoint": {"question": "Simplify this expression: x*(52*x**3 + 19*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "52*x**4 + 19*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1948, "polynomial_expr": "x*(52*x**3 + 19*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: x*(52*x**3 + 19*x)\nExpanding the part (52*x**3 + 19*x) using the distributive property, and we got: x*(19*x) + x*(52*x**3)\n#Step 2:\nCurrent expression: x*(19*x) + x*(52*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (19*x)*x = 19*x**2\n (52*x**3)*x = 52*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 52*x**4 + 19*x**2\nNo more calculations needed.\n52*x**4 + 19*x**2", "generated_answer": "52*x**4 + 19*x**2", "step_length": 3} {"cot_id": "bfa051735562cf5924001f76f32c1189e05d72d8207c1deb8d2956ba21a0b779", "datapoint": {"question": "Calculate the following: (-30*z**3 - 30*z)*(-32*z**3 + 47*z + 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "960*z**6 - 450*z**4 - 1470*z**3 - 1410*z**2 - 1470*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1949, "polynomial_expr": "(-30*z**3 - 30*z)*(-32*z**3 + 47*z + 49)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-30*z**3 - 30*z)*(-32*z**3 + 47*z + 49)\nExpanding the part (-30*z**3 - 30*z) using the distributive property, and we got: (-30*z)*(-32*z**3 + 47*z + 49) + (-30*z**3)*(-32*z**3 + 47*z + 49)\n#Step 2:\nCurrent expression: (-30*z)*(-32*z**3 + 47*z + 49) + (-30*z**3)*(-32*z**3 + 47*z + 49)\nSimplifying the partial expression: (-30*z)*(-32*z**3 + 47*z + 49)\nExpanding the part (-32*z**3 + 47*z + 49) using the distributive property, and we got: (-30*z)*(47*z) + (-30*z)*(-32*z**3) + 49*(-30*z)\nReplacing (-30*z)*(-32*z**3 + 47*z + 49) with (-30*z)*(47*z) + (-30*z)*(-32*z**3) + 49*(-30*z) in the overall expression.\n#Step 3:\nCurrent expression: (-30*z)*(47*z) + (-30*z)*(-32*z**3) + 49*(-30)*z + (-30*z**3)*(-32*z**3 + 47*z + 49)\nSimplifying the partial expression: (-30*z**3)*(-32*z**3 + 47*z + 49)\nExpanding the part (-32*z**3 + 47*z + 49) using the distributive property, and we got: 49*(-30*z**3) + (47*z)*(-30*z**3) + (-32*z**3)*(-30*z**3)\nReplacing (-30*z**3)*(-32*z**3 + 47*z + 49) with 49*(-30*z**3) + (47*z)*(-30*z**3) + (-32*z**3)*(-30*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-30*z)*(47*z) + (-30*z)*(-32*z**3) + 49*(-30)*z**3 + 49*(-30)*z + (47*z)*(-30*z**3) + (-32*z**3)*(-30*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*z**3)*(-30*z) = 960*z**4\n (-32*z**3)*(-30*z**3) = 960*z**6\n (47*z)*(-30*z) = -1410*z**2\n (47*z)*(-30*z**3) = -1410*z**4\n 49*-30*z = -1470*z\n 49*-30*z**3 = -1470*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 960*z**6 - 1410*z**4 + 960*z**4 - 1470*z**3 - 1410*z**2 - 1470*z\nCombining like terms, got 960*z**6 - 450*z**4 - 1470*z**3 - 1410*z**2 - 1470*z\n#Step 6:\nCurrent expression: 960*z**6 - 450*z**4 - 1470*z**3 - 1410*z**2 - 1470*z\nNo more calculations needed.\n960*z**6 - 450*z**4 - 1470*z**3 - 1410*z**2 - 1470*z", "generated_answer": "960*z**6 - 450*z**4 - 1470*z**3 - 1410*z**2 - 1470*z", "step_length": 6} {"cot_id": "5c5db6c1dd2637602dc0c9eecc23056a29ae41e2ae8ff2238e7754bf8a4f33d1", "datapoint": {"question": "Calculate the following: (z + 17)*(71*z**2 - 20)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "71*z**3 + 1207*z**2 - 20*z - 340", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1950, "polynomial_expr": "(z + 17)*(71*z**2 - 20)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (z + 17)*(71*z**2 - 20)\nExpanding the part (71*z**2 - 20) using the distributive property, and we got: (71*z**2)*(z + 17) - 20*(z + 17)\n#Step 2:\nCurrent expression: (71*z**2)*(z + 17) - 20*(z + 17)\nSimplifying the partial expression: -20*(z + 17)\nExpanding the part (z + 17) using the distributive property, and we got: z*(-20) + 17*(-20)\nReplacing -20*(z + 17) with z*(-20) + 17*(-20) in the overall expression.\n#Step 3:\nCurrent expression: z*(-20) + (71*z**2)*(z + 17) - 340\nSimplifying the partial expression: (71*z**2)*(z + 17)\nExpanding the part (z + 17) using the distributive property, and we got: 17*(71*z**2) + z*(71*z**2)\nReplacing (71*z**2)*(z + 17) with 17*(71*z**2) + z*(71*z**2) in the overall expression.\n#Step 4:\nCurrent expression: 17*71*z**2 + z*(71*z**2) + z*(-20) - 340\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n z*-20 = -20*z\n z*(71*z**2) = 71*z**3\n 17*71*z**2 = 1207*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 71*z**3 + 1207*z**2 - 20*z - 340\nNo more calculations needed.\n71*z**3 + 1207*z**2 - 20*z - 340", "generated_answer": "71*z**3 + 1207*z**2 - 20*z - 340", "step_length": 5} {"cot_id": "fa89e80b1c5a8aa2a603e679a83c2f478877ae1613268847ebaa3b50f6f68878", "datapoint": {"question": "Simplify this expression: (3*y**3 - 59*y)*(15*y**3 + 18*y + 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "45*y**6 - 831*y**4 + 3*y**3 - 1062*y**2 - 59*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1951, "polynomial_expr": "(3*y**3 - 59*y)*(15*y**3 + 18*y + 1)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (3*y**3 - 59*y)*(15*y**3 + 18*y + 1)\nExpanding the part (3*y**3 - 59*y) using the distributive property, and we got: (-59*y)*(15*y**3 + 18*y + 1) + (3*y**3)*(15*y**3 + 18*y + 1)\n#Step 2:\nCurrent expression: (-59*y)*(15*y**3 + 18*y + 1) + (3*y**3)*(15*y**3 + 18*y + 1)\nSimplifying the partial expression: (-59*y)*(15*y**3 + 18*y + 1)\nExpanding the part (15*y**3 + 18*y + 1) using the distributive property, and we got: (-59*y)*(18*y) + (-59*y)*(15*y**3) + 1*(-59*y)\nReplacing (-59*y)*(15*y**3 + 18*y + 1) with (-59*y)*(18*y) + (-59*y)*(15*y**3) + 1*(-59*y) in the overall expression.\n#Step 3:\nCurrent expression: (-59*y)*(18*y) + (-59*y)*(15*y**3) - 59*y + (3*y**3)*(15*y**3 + 18*y + 1)\nSimplifying the partial expression: (3*y**3)*(15*y**3 + 18*y + 1)\nExpanding the part (15*y**3 + 18*y + 1) using the distributive property, and we got: 1*(3*y**3) + (18*y)*(3*y**3) + (3*y**3)*(15*y**3)\nReplacing (3*y**3)*(15*y**3 + 18*y + 1) with 1*(3*y**3) + (18*y)*(3*y**3) + (3*y**3)*(15*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-59*y)*(18*y) + (-59*y)*(15*y**3) + 3*y**3 - 59*y + (18*y)*(3*y**3) + (3*y**3)*(15*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (15*y**3)*(-59*y) = -885*y**4\n (15*y**3)*(3*y**3) = 45*y**6\n (18*y)*(-59*y) = -1062*y**2\n (18*y)*(3*y**3) = 54*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 45*y**6 - 885*y**4 + 54*y**4 + 3*y**3 - 1062*y**2 - 59*y\nCombining like terms, got 45*y**6 - 831*y**4 + 3*y**3 - 1062*y**2 - 59*y\n#Step 6:\nCurrent expression: 45*y**6 - 831*y**4 + 3*y**3 - 1062*y**2 - 59*y\nNo more calculations needed.\n45*y**6 - 831*y**4 + 3*y**3 - 1062*y**2 - 59*y", "generated_answer": "45*y**6 - 831*y**4 + 3*y**3 - 1062*y**2 - 59*y", "step_length": 6} {"cot_id": "b451151933e01e2382fbf5a244be173f45c0ca57cee177b9f54b8a05893b1f5f", "datapoint": {"question": "Calculate the following: (34 - 2*y**3)*(-59*y**3 - 19*y**2 + 17*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "118*y**6 + 38*y**5 - 34*y**4 - 2006*y**3 - 646*y**2 + 578*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1952, "polynomial_expr": "(34 - 2*y**3)*(-59*y**3 - 19*y**2 + 17*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (34 - 2*y**3)*(-59*y**3 - 19*y**2 + 17*y)\nExpanding the part (34 - 2*y**3) using the distributive property, and we got: (-2*y**3)*(-59*y**3 - 19*y**2 + 17*y) + 34*(-59*y**3 - 19*y**2 + 17*y)\n#Step 2:\nCurrent expression: (-2*y**3)*(-59*y**3 - 19*y**2 + 17*y) + 34*(-59*y**3 - 19*y**2 + 17*y)\nSimplifying the partial expression: 34*(-59*y**3 - 19*y**2 + 17*y)\nExpanding the part (-59*y**3 - 19*y**2 + 17*y) using the distributive property, and we got: (17*y)*34 - 19*y**2*34 - 59*y**3*34\nReplacing 34*(-59*y**3 - 19*y**2 + 17*y) with (17*y)*34 - 19*y**2*34 - 59*y**3*34 in the overall expression.\n#Step 3:\nCurrent expression: (17*y)*34 - 19*y**2*34 - 59*y**3*34 + (-2*y**3)*(-59*y**3 - 19*y**2 + 17*y)\nSimplifying the partial expression: (-2*y**3)*(-59*y**3 - 19*y**2 + 17*y)\nExpanding the part (-59*y**3 - 19*y**2 + 17*y) using the distributive property, and we got: (17*y)*(-2*y**3) + (-19*y**2)*(-2*y**3) + (-59*y**3)*(-2*y**3)\nReplacing (-2*y**3)*(-59*y**3 - 19*y**2 + 17*y) with (17*y)*(-2*y**3) + (-19*y**2)*(-2*y**3) + (-59*y**3)*(-2*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (17*y)*(-2*y**3) + (17*y)*34 + (-19*y**2)*(-2*y**3) - 19*y**2*34 + (-59*y**3)*(-2*y**3) - 59*y**3*34\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-59*y**3)*34 = -2006*y**3\n (-59*y**3)*(-2*y**3) = 118*y**6\n (-19*y**2)*34 = -646*y**2\n (-19*y**2)*(-2*y**3) = 38*y**5\n (17*y)*34 = 578*y\n (17*y)*(-2*y**3) = -34*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 118*y**6 + 38*y**5 - 34*y**4 - 2006*y**3 - 646*y**2 + 578*y\nNo more calculations needed.\n118*y**6 + 38*y**5 - 34*y**4 - 2006*y**3 - 646*y**2 + 578*y", "generated_answer": "118*y**6 + 38*y**5 - 34*y**4 - 2006*y**3 - 646*y**2 + 578*y", "step_length": 5} {"cot_id": "f4d95afa5274195a9c03e381f15220d16734ba67b0cc27b5a75fb0729eab86ae", "datapoint": {"question": "Calculate the following: (-13*z - 20)*(41*z**3 - 29*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-533*z**4 - 820*z**3 + 377*z**2 + 580*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1953, "polynomial_expr": "(-13*z - 20)*(41*z**3 - 29*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-13*z - 20)*(41*z**3 - 29*z)\nExpanding the part (-13*z - 20) using the distributive property, and we got: (-13*z)*(41*z**3 - 29*z) - 20*(41*z**3 - 29*z)\n#Step 2:\nCurrent expression: (-13*z)*(41*z**3 - 29*z) - 20*(41*z**3 - 29*z)\nSimplifying the partial expression: -20*(41*z**3 - 29*z)\nExpanding the part (41*z**3 - 29*z) using the distributive property, and we got: -29*z*(-20) + (41*z**3)*(-20)\nReplacing -20*(41*z**3 - 29*z) with -29*z*(-20) + (41*z**3)*(-20) in the overall expression.\n#Step 3:\nCurrent expression: -29*z*(-20) + (-13*z)*(41*z**3 - 29*z) + (41*z**3)*(-20)\nSimplifying the partial expression: (-13*z)*(41*z**3 - 29*z)\nExpanding the part (41*z**3 - 29*z) using the distributive property, and we got: (-29*z)*(-13*z) + (-13*z)*(41*z**3)\nReplacing (-13*z)*(41*z**3 - 29*z) with (-29*z)*(-13*z) + (-13*z)*(41*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-29*z)*(-13*z) - 29*z*(-20) + (-13*z)*(41*z**3) + (41*z**3)*(-20)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*z)*-20 = 580*z\n (-29*z)*(-13*z) = 377*z**2\n (41*z**3)*-20 = -820*z**3\n (41*z**3)*(-13*z) = -533*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -533*z**4 - 820*z**3 + 377*z**2 + 580*z\nNo more calculations needed.\n-533*z**4 - 820*z**3 + 377*z**2 + 580*z", "generated_answer": "-533*z**4 - 820*z**3 + 377*z**2 + 580*z", "step_length": 5} {"cot_id": "945bf98963e4c41f371bcf78b0e7fb89566b8555f6610c92d2825d5a0209db18", "datapoint": {"question": "Calculate the following: (-35*z**2 + 53*z)*(-69*z**3 - 11*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2415*z**5 - 3657*z**4 + 385*z**3 - 583*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1954, "polynomial_expr": "(-35*z**2 + 53*z)*(-69*z**3 - 11*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-35*z**2 + 53*z)*(-69*z**3 - 11*z)\nExpanding the part (-69*z**3 - 11*z) using the distributive property, and we got: (-11*z)*(-35*z**2 + 53*z) + (-69*z**3)*(-35*z**2 + 53*z)\n#Step 2:\nCurrent expression: (-11*z)*(-35*z**2 + 53*z) + (-69*z**3)*(-35*z**2 + 53*z)\nSimplifying the partial expression: (-69*z**3)*(-35*z**2 + 53*z)\nExpanding the part (-35*z**2 + 53*z) using the distributive property, and we got: (53*z)*(-69*z**3) + (-35*z**2)*(-69*z**3)\nReplacing (-69*z**3)*(-35*z**2 + 53*z) with (53*z)*(-69*z**3) + (-35*z**2)*(-69*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-11*z)*(-35*z**2 + 53*z) + (53*z)*(-69*z**3) + (-35*z**2)*(-69*z**3)\nSimplifying the partial expression: (-11*z)*(-35*z**2 + 53*z)\nExpanding the part (-35*z**2 + 53*z) using the distributive property, and we got: (-11*z)*(53*z) + (-11*z)*(-35*z**2)\nReplacing (-11*z)*(-35*z**2 + 53*z) with (-11*z)*(53*z) + (-11*z)*(-35*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-11*z)*(53*z) + (-11*z)*(-35*z**2) + (53*z)*(-69*z**3) + (-35*z**2)*(-69*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*z**2)*(-69*z**3) = 2415*z**5\n (-35*z**2)*(-11*z) = 385*z**3\n (53*z)*(-69*z**3) = -3657*z**4\n (53*z)*(-11*z) = -583*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2415*z**5 - 3657*z**4 + 385*z**3 - 583*z**2\nNo more calculations needed.\n2415*z**5 - 3657*z**4 + 385*z**3 - 583*z**2", "generated_answer": "2415*z**5 - 3657*z**4 + 385*z**3 - 583*z**2", "step_length": 5} {"cot_id": "ff4a1e4661311afe0c04eb11f4221dc667374ab477fba187e5bcb6d2fd698d78", "datapoint": {"question": "Simplify this expression: (4*x**3 - 48*x**2)*(22*x**3 - 9)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "88*x**6 - 1056*x**5 - 36*x**3 + 432*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1955, "polynomial_expr": "(4*x**3 - 48*x**2)*(22*x**3 - 9)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (4*x**3 - 48*x**2)*(22*x**3 - 9)\nExpanding the part (22*x**3 - 9) using the distributive property, and we got: (22*x**3)*(4*x**3 - 48*x**2) - 9*(4*x**3 - 48*x**2)\n#Step 2:\nCurrent expression: (22*x**3)*(4*x**3 - 48*x**2) - 9*(4*x**3 - 48*x**2)\nSimplifying the partial expression: -9*(4*x**3 - 48*x**2)\nExpanding the part (4*x**3 - 48*x**2) using the distributive property, and we got: -48*x**2*(-9) + (4*x**3)*(-9)\nReplacing -9*(4*x**3 - 48*x**2) with -48*x**2*(-9) + (4*x**3)*(-9) in the overall expression.\n#Step 3:\nCurrent expression: -48*x**2*(-9) + (4*x**3)*(-9) + (22*x**3)*(4*x**3 - 48*x**2)\nSimplifying the partial expression: (22*x**3)*(4*x**3 - 48*x**2)\nExpanding the part (4*x**3 - 48*x**2) using the distributive property, and we got: (-48*x**2)*(22*x**3) + (4*x**3)*(22*x**3)\nReplacing (22*x**3)*(4*x**3 - 48*x**2) with (-48*x**2)*(22*x**3) + (4*x**3)*(22*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-48*x**2)*(22*x**3) - 48*x**2*(-9) + (4*x**3)*(22*x**3) + (4*x**3)*(-9)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*x**2)*-9 = 432*x**2\n (-48*x**2)*(22*x**3) = -1056*x**5\n (4*x**3)*-9 = -36*x**3\n (4*x**3)*(22*x**3) = 88*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 88*x**6 - 1056*x**5 - 36*x**3 + 432*x**2\nNo more calculations needed.\n88*x**6 - 1056*x**5 - 36*x**3 + 432*x**2", "generated_answer": "88*x**6 - 1056*x**5 - 36*x**3 + 432*x**2", "step_length": 5} {"cot_id": "dc092000edd7b56200f6d1d14f568c7831062944078463956f436b1101a73583", "datapoint": {"question": "Simplify this expression: (19*z - 24)*(37*z**2 - 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "703*z**3 - 888*z**2 - 247*z + 312", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1956, "polynomial_expr": "(19*z - 24)*(37*z**2 - 13)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (19*z - 24)*(37*z**2 - 13)\nExpanding the part (19*z - 24) using the distributive property, and we got: (19*z)*(37*z**2 - 13) - 24*(37*z**2 - 13)\n#Step 2:\nCurrent expression: (19*z)*(37*z**2 - 13) - 24*(37*z**2 - 13)\nSimplifying the partial expression: -24*(37*z**2 - 13)\nExpanding the part (37*z**2 - 13) using the distributive property, and we got: (37*z**2)*(-24) - 13*(-24)\nReplacing -24*(37*z**2 - 13) with (37*z**2)*(-24) - 13*(-24) in the overall expression.\n#Step 3:\nCurrent expression: (19*z)*(37*z**2 - 13) + (37*z**2)*(-24) + 312\nSimplifying the partial expression: (19*z)*(37*z**2 - 13)\nExpanding the part (37*z**2 - 13) using the distributive property, and we got: -247*z + (19*z)*(37*z**2)\nReplacing (19*z)*(37*z**2 - 13) with -247*z + (19*z)*(37*z**2) in the overall expression.\n#Step 4:\nCurrent expression: -13*19*z + (19*z)*(37*z**2) + (37*z**2)*(-24) + 312\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (37*z**2)*-24 = -888*z**2\n (37*z**2)*(19*z) = 703*z**3\n -13*19*z = -247*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 703*z**3 - 888*z**2 - 247*z + 312\nNo more calculations needed.\n703*z**3 - 888*z**2 - 247*z + 312", "generated_answer": "703*z**3 - 888*z**2 - 247*z + 312", "step_length": 5} {"cot_id": "b6b68433a96e0bf5772f30d0bb4d20028abfbee73707294a6325b97415d7d23c", "datapoint": {"question": "Calculate the following: -48*x*(47*x**3 - 40)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2256*x**4 + 1920*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1957, "polynomial_expr": "-48*x*(47*x**3 - 40)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -48*x*(47*x**3 - 40)\nExpanding the part (47*x**3 - 40) using the distributive property, and we got: (-48*x)*(47*x**3) - (-1)*1920*x\n#Step 2:\nCurrent expression: (-48*x)*(47*x**3) - (-1)*1920*x\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -40*(-48*x) = 1920*x\n (47*x**3)*(-48*x) = -2256*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -2256*x**4 + 1920*x\nNo more calculations needed.\n-2256*x**4 + 1920*x", "generated_answer": "-2256*x**4 + 1920*x", "step_length": 3} {"cot_id": "08acaa84ccf364dee380ee743c6230ccbaff270b61a0f4825a08c42cff507a8d", "datapoint": {"question": "Calculate the following: (50*y + 38)*(-23*y**3 - y**2 - 10*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1150*y**4 - 924*y**3 - 538*y**2 - 380*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1958, "polynomial_expr": "(50*y + 38)*(-23*y**3 - y**2 - 10*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (50*y + 38)*(-23*y**3 - y**2 - 10*y)\nExpanding the part (50*y + 38) using the distributive property, and we got: (50*y)*(-23*y**3 - y**2 - 10*y) + 38*(-23*y**3 - y**2 - 10*y)\n#Step 2:\nCurrent expression: (50*y)*(-23*y**3 - y**2 - 10*y) + 38*(-23*y**3 - y**2 - 10*y)\nSimplifying the partial expression: 38*(-23*y**3 - y**2 - 10*y)\nExpanding the part (-23*y**3 - y**2 - 10*y) using the distributive property, and we got: -10*y*38 - y**2*38 - 23*y**3*38\nReplacing 38*(-23*y**3 - y**2 - 10*y) with -10*y*38 - y**2*38 - 23*y**3*38 in the overall expression.\n#Step 3:\nCurrent expression: -10*y*38 + (50*y)*(-23*y**3 - y**2 - 10*y) - y**2*38 - 23*y**3*38\nSimplifying the partial expression: (50*y)*(-23*y**3 - y**2 - 10*y)\nExpanding the part (-23*y**3 - y**2 - 10*y) using the distributive property, and we got: (-10*y)*(50*y) + (50*y)*(-y**2) + (50*y)*(-23*y**3)\nReplacing (50*y)*(-23*y**3 - y**2 - 10*y) with (-10*y)*(50*y) + (50*y)*(-y**2) + (50*y)*(-23*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-10*y)*(50*y) - 10*y*38 + (50*y)*(-y**2) + (50*y)*(-23*y**3) - y**2*38 - 23*y**3*38\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-y**2)*38 = -38*y**2\n (-y**2)*(50*y) = -50*y**3\n (-23*y**3)*38 = -874*y**3\n (-23*y**3)*(50*y) = -1150*y**4\n (-10*y)*38 = -380*y\n (-10*y)*(50*y) = -500*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1150*y**4 - 874*y**3 - 50*y**3 - 500*y**2 - 38*y**2 - 380*y\nCombining like terms, got -1150*y**4 - 924*y**3 - 538*y**2 - 380*y\n#Step 6:\nCurrent expression: -1150*y**4 - 924*y**3 - 538*y**2 - 380*y\nNo more calculations needed.\n-1150*y**4 - 924*y**3 - 538*y**2 - 380*y", "generated_answer": "-1150*y**4 - 924*y**3 - 538*y**2 - 380*y", "step_length": 6} {"cot_id": "8f432ec8f3eb696d333fb9146efe5f7c4470eea4ec588d36dee66cd86d1f9116", "datapoint": {"question": "Calculate the following: (42*z**3 + 48)*(-28*z**3 - 11*z**2 - 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1176*z**6 - 462*z**5 - 2604*z**3 - 528*z**2 - 1440", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1959, "polynomial_expr": "(42*z**3 + 48)*(-28*z**3 - 11*z**2 - 30)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (42*z**3 + 48)*(-28*z**3 - 11*z**2 - 30)\nExpanding the part (42*z**3 + 48) using the distributive property, and we got: (42*z**3)*(-28*z**3 - 11*z**2 - 30) + 48*(-28*z**3 - 11*z**2 - 30)\n#Step 2:\nCurrent expression: (42*z**3)*(-28*z**3 - 11*z**2 - 30) + 48*(-28*z**3 - 11*z**2 - 30)\nSimplifying the partial expression: 48*(-28*z**3 - 11*z**2 - 30)\nExpanding the part (-28*z**3 - 11*z**2 - 30) using the distributive property, and we got: -11*z**2*48 - 28*z**3*48 - 30*48\nReplacing 48*(-28*z**3 - 11*z**2 - 30) with -11*z**2*48 - 28*z**3*48 - 30*48 in the overall expression.\n#Step 3:\nCurrent expression: -11*z**2*48 - 28*z**3*48 + (42*z**3)*(-28*z**3 - 11*z**2 - 30) - 1440\nSimplifying the partial expression: (42*z**3)*(-28*z**3 - 11*z**2 - 30)\nExpanding the part (-28*z**3 - 11*z**2 - 30) using the distributive property, and we got: -1260*z**3 + (-11*z**2)*(42*z**3) + (-28*z**3)*(42*z**3)\nReplacing (42*z**3)*(-28*z**3 - 11*z**2 - 30) with -1260*z**3 + (-11*z**2)*(42*z**3) + (-28*z**3)*(42*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -30*42*z**3 + (-11*z**2)*(42*z**3) - 11*z**2*48 + (-28*z**3)*(42*z**3) - 28*z**3*48 - 1440\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*z**3)*48 = -1344*z**3\n (-28*z**3)*(42*z**3) = -1176*z**6\n (-11*z**2)*48 = -528*z**2\n (-11*z**2)*(42*z**3) = -462*z**5\n -30*42*z**3 = -1260*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1176*z**6 - 462*z**5 - 1344*z**3 - 1260*z**3 - 528*z**2 - 1440\nCombining like terms, got -1176*z**6 - 462*z**5 - 2604*z**3 - 528*z**2 - 1440\n#Step 6:\nCurrent expression: -1176*z**6 - 462*z**5 - 2604*z**3 - 528*z**2 - 1440\nNo more calculations needed.\n-1176*z**6 - 462*z**5 - 2604*z**3 - 528*z**2 - 1440", "generated_answer": "-1176*z**6 - 462*z**5 - 2604*z**3 - 528*z**2 - 1440", "step_length": 6} {"cot_id": "7205ab94f7c6b9de83d9dd9a0260222eb3494da04ce89cf955bd434b0f856f72", "datapoint": {"question": "Calculate the following: 49*z**2*(2*z**3 + 37*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "98*z**5 + 1813*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1960, "polynomial_expr": "49*z**2*(2*z**3 + 37*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 49*z**2*(2*z**3 + 37*z)\nExpanding the part (2*z**3 + 37*z) using the distributive property, and we got: (37*z)*(49*z**2) + (49*z**2)*(2*z**3)\n#Step 2:\nCurrent expression: (37*z)*(49*z**2) + (49*z**2)*(2*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (2*z**3)*(49*z**2) = 98*z**5\n (37*z)*(49*z**2) = 1813*z**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 98*z**5 + 1813*z**3\nNo more calculations needed.\n98*z**5 + 1813*z**3", "generated_answer": "98*z**5 + 1813*z**3", "step_length": 3} {"cot_id": "4ff402c888671201d900e9cd7e0e62aa3f134fb2ce9070549c950dd88b1f91bb", "datapoint": {"question": "Calculate the following: (-38*x**3 + 2*x**2 + 25)*(20*x**3 - 22*x**2 + 46*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-760*x**6 + 876*x**5 - 1792*x**4 + 592*x**3 - 550*x**2 + 1150*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1961, "polynomial_expr": "(-38*x**3 + 2*x**2 + 25)*(20*x**3 - 22*x**2 + 46*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-38*x**3 + 2*x**2 + 25)*(20*x**3 - 22*x**2 + 46*x)\nExpanding the part (-38*x**3 + 2*x**2 + 25) using the distributive property, and we got: (2*x**2)*(20*x**3 - 22*x**2 + 46*x) + (-38*x**3)*(20*x**3 - 22*x**2 + 46*x) + 25*(20*x**3 - 22*x**2 + 46*x)\n#Step 2:\nCurrent expression: (2*x**2)*(20*x**3 - 22*x**2 + 46*x) + (-38*x**3)*(20*x**3 - 22*x**2 + 46*x) + 25*(20*x**3 - 22*x**2 + 46*x)\nSimplifying the partial expression: 25*(20*x**3 - 22*x**2 + 46*x)\nExpanding the part (20*x**3 - 22*x**2 + 46*x) using the distributive property, and we got: (46*x)*25 - 22*x**2*25 + (20*x**3)*25\nReplacing 25*(20*x**3 - 22*x**2 + 46*x) with (46*x)*25 - 22*x**2*25 + (20*x**3)*25 in the overall expression.\n#Step 3:\nCurrent expression: (46*x)*25 - 22*x**2*25 + (2*x**2)*(20*x**3 - 22*x**2 + 46*x) + (-38*x**3)*(20*x**3 - 22*x**2 + 46*x) + (20*x**3)*25\nSimplifying the partial expression: (-38*x**3)*(20*x**3 - 22*x**2 + 46*x)\nExpanding the part (20*x**3 - 22*x**2 + 46*x) using the distributive property, and we got: (46*x)*(-38*x**3) + (-22*x**2)*(-38*x**3) + (-38*x**3)*(20*x**3)\nReplacing (-38*x**3)*(20*x**3 - 22*x**2 + 46*x) with (46*x)*(-38*x**3) + (-22*x**2)*(-38*x**3) + (-38*x**3)*(20*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (46*x)*(-38*x**3) + (46*x)*25 + (-22*x**2)*(-38*x**3) - 22*x**2*25 + (2*x**2)*(20*x**3 - 22*x**2 + 46*x) + (-38*x**3)*(20*x**3) + (20*x**3)*25\nSimplifying the partial expression: (2*x**2)*(20*x**3 - 22*x**2 + 46*x)\nExpanding the part (20*x**3 - 22*x**2 + 46*x) using the distributive property, and we got: (46*x)*(2*x**2) + (-22*x**2)*(2*x**2) + (2*x**2)*(20*x**3)\nReplacing (2*x**2)*(20*x**3 - 22*x**2 + 46*x) with (46*x)*(2*x**2) + (-22*x**2)*(2*x**2) + (2*x**2)*(20*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (46*x)*(2*x**2) + (46*x)*(-38*x**3) + (46*x)*25 + (-22*x**2)*(2*x**2) + (-22*x**2)*(-38*x**3) - 22*x**2*25 + (2*x**2)*(20*x**3) + (-38*x**3)*(20*x**3) + (20*x**3)*25\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*x**2)*25 = -550*x**2\n (-22*x**2)*(-38*x**3) = 836*x**5\n (-22*x**2)*(2*x**2) = -44*x**4\n (20*x**3)*25 = 500*x**3\n (20*x**3)*(-38*x**3) = -760*x**6\n (20*x**3)*(2*x**2) = 40*x**5\n (46*x)*25 = 1150*x\n (46*x)*(-38*x**3) = -1748*x**4\n (46*x)*(2*x**2) = 92*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -760*x**6 + 40*x**5 + 836*x**5 - 1748*x**4 - 44*x**4 + 92*x**3 + 500*x**3 - 550*x**2 + 1150*x\nCombining like terms, got -760*x**6 + 876*x**5 - 1792*x**4 + 592*x**3 - 550*x**2 + 1150*x\n#Step 7:\nCurrent expression: -760*x**6 + 876*x**5 - 1792*x**4 + 592*x**3 - 550*x**2 + 1150*x\nNo more calculations needed.\n-760*x**6 + 876*x**5 - 1792*x**4 + 592*x**3 - 550*x**2 + 1150*x", "generated_answer": "-760*x**6 + 876*x**5 - 1792*x**4 + 592*x**3 - 550*x**2 + 1150*x", "step_length": 7} {"cot_id": "322a73aae653c5de7bc5799fb80b02c0f230fe70e41ec434747d40b80dfeb2e5", "datapoint": {"question": "Simplify this expression: (12*z + 51)*(64*z**2 - 11*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "768*z**3 + 3132*z**2 - 561*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1962, "polynomial_expr": "(12*z + 51)*(64*z**2 - 11*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (12*z + 51)*(64*z**2 - 11*z)\nExpanding the part (12*z + 51) using the distributive property, and we got: (12*z)*(64*z**2 - 11*z) + 51*(64*z**2 - 11*z)\n#Step 2:\nCurrent expression: (12*z)*(64*z**2 - 11*z) + 51*(64*z**2 - 11*z)\nSimplifying the partial expression: 51*(64*z**2 - 11*z)\nExpanding the part (64*z**2 - 11*z) using the distributive property, and we got: -11*z*51 + (64*z**2)*51\nReplacing 51*(64*z**2 - 11*z) with -11*z*51 + (64*z**2)*51 in the overall expression.\n#Step 3:\nCurrent expression: -11*z*51 + (12*z)*(64*z**2 - 11*z) + (64*z**2)*51\nSimplifying the partial expression: (12*z)*(64*z**2 - 11*z)\nExpanding the part (64*z**2 - 11*z) using the distributive property, and we got: (-11*z)*(12*z) + (12*z)*(64*z**2)\nReplacing (12*z)*(64*z**2 - 11*z) with (-11*z)*(12*z) + (12*z)*(64*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-11*z)*(12*z) - 11*z*51 + (12*z)*(64*z**2) + (64*z**2)*51\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*z)*51 = -561*z\n (-11*z)*(12*z) = -132*z**2\n (64*z**2)*51 = 3264*z**2\n (64*z**2)*(12*z) = 768*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 768*z**3 - 132*z**2 + 3264*z**2 - 561*z\nCombining like terms, got 768*z**3 + 3132*z**2 - 561*z\n#Step 6:\nCurrent expression: 768*z**3 + 3132*z**2 - 561*z\nNo more calculations needed.\n768*z**3 + 3132*z**2 - 561*z", "generated_answer": "768*z**3 + 3132*z**2 - 561*z", "step_length": 6} {"cot_id": "b386d121af6b6e41db9cd7135708c8af038a84a37d443686ac99bd0d29fc90af", "datapoint": {"question": "Calculate the following: (-42*y**3 - y)*(-28*y**3 - 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1176*y**6 + 28*y**4 + 1344*y**3 + 32*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1963, "polynomial_expr": "(-42*y**3 - y)*(-28*y**3 - 32)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-42*y**3 - y)*(-28*y**3 - 32)\nExpanding the part (-28*y**3 - 32) using the distributive property, and we got: (-28*y**3)*(-42*y**3 - y) - 32*(-42*y**3 - y)\n#Step 2:\nCurrent expression: (-28*y**3)*(-42*y**3 - y) - 32*(-42*y**3 - y)\nSimplifying the partial expression: -32*(-42*y**3 - y)\nExpanding the part (-42*y**3 - y) using the distributive property, and we got: -y*(-32) - 42*y**3*(-32)\nReplacing -32*(-42*y**3 - y) with -y*(-32) - 42*y**3*(-32) in the overall expression.\n#Step 3:\nCurrent expression: -y*(-32) - 42*y**3*(-32) + (-28*y**3)*(-42*y**3 - y)\nSimplifying the partial expression: (-28*y**3)*(-42*y**3 - y)\nExpanding the part (-42*y**3 - y) using the distributive property, and we got: (-y)*(-28*y**3) + (-42*y**3)*(-28*y**3)\nReplacing (-28*y**3)*(-42*y**3 - y) with (-y)*(-28*y**3) + (-42*y**3)*(-28*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-y)*(-28*y**3) - y*(-32) + (-42*y**3)*(-28*y**3) - 42*y**3*(-32)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-y)*-32 = 32*y\n (-y)*(-28*y**3) = 28*y**4\n (-42*y**3)*-32 = 1344*y**3\n (-42*y**3)*(-28*y**3) = 1176*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1176*y**6 + 28*y**4 + 1344*y**3 + 32*y\nNo more calculations needed.\n1176*y**6 + 28*y**4 + 1344*y**3 + 32*y", "generated_answer": "1176*y**6 + 28*y**4 + 1344*y**3 + 32*y", "step_length": 5} {"cot_id": "5bfabb0a75536d41bcde6da12a51b5e88d3b8bb6f30114ad06f53f7bc77265a6", "datapoint": {"question": "Simplify this expression: -6*z**3*(-36*z**2 - 29*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "216*z**5 + 174*z**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1964, "polynomial_expr": "-6*z**3*(-36*z**2 - 29*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -6*z**3*(-36*z**2 - 29*z)\nExpanding the part (-36*z**2 - 29*z) using the distributive property, and we got: (-29*z)*(-6*z**3) + (-36*z**2)*(-6*z**3)\n#Step 2:\nCurrent expression: (-29*z)*(-6*z**3) + (-36*z**2)*(-6*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-36*z**2)*(-6*z**3) = 216*z**5\n (-29*z)*(-6*z**3) = 174*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 216*z**5 + 174*z**4\nNo more calculations needed.\n216*z**5 + 174*z**4", "generated_answer": "216*z**5 + 174*z**4", "step_length": 3} {"cot_id": "f5cd327d18a5dadd1fb68d5ab81920f8e0894816c844cecf9f31bd11c6804e9d", "datapoint": {"question": "Calculate the following: -59*x**2*(-40*x**2 - 46*x + 46)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2360*x**4 + 2714*x**3 - 2714*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1965, "polynomial_expr": "-59*x**2*(-40*x**2 - 46*x + 46)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -59*x**2*(-40*x**2 - 46*x + 46)\nExpanding the part (-40*x**2 - 46*x + 46) using the distributive property, and we got: (-46*x)*(-59*x**2) + 46*(-59*x**2) + (-59*x**2)*(-40*x**2)\n#Step 2:\nCurrent expression: (-46*x)*(-59*x**2) + 46*(-59*x**2) + (-59*x**2)*(-40*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 46*(-59*x**2) = -2714*x**2\n (-46*x)*(-59*x**2) = 2714*x**3\n (-40*x**2)*(-59*x**2) = 2360*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 2360*x**4 + 2714*x**3 - 2714*x**2\nNo more calculations needed.\n2360*x**4 + 2714*x**3 - 2714*x**2", "generated_answer": "2360*x**4 + 2714*x**3 - 2714*x**2", "step_length": 3} {"cot_id": "9954e54d98896005f3861432fd7e7751596cb43d781e5faef6b98b0919f7e772", "datapoint": {"question": "Simplify this expression: (24*x**2 + 15)*(-4*x**3 + 10*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-96*x**5 + 240*x**4 - 60*x**3 + 150*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1966, "polynomial_expr": "(24*x**2 + 15)*(-4*x**3 + 10*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (24*x**2 + 15)*(-4*x**3 + 10*x**2)\nExpanding the part (24*x**2 + 15) using the distributive property, and we got: (24*x**2)*(-4*x**3 + 10*x**2) + 15*(-4*x**3 + 10*x**2)\n#Step 2:\nCurrent expression: (24*x**2)*(-4*x**3 + 10*x**2) + 15*(-4*x**3 + 10*x**2)\nSimplifying the partial expression: 15*(-4*x**3 + 10*x**2)\nExpanding the part (-4*x**3 + 10*x**2) using the distributive property, and we got: (10*x**2)*15 - 4*x**3*15\nReplacing 15*(-4*x**3 + 10*x**2) with (10*x**2)*15 - 4*x**3*15 in the overall expression.\n#Step 3:\nCurrent expression: (10*x**2)*15 + (24*x**2)*(-4*x**3 + 10*x**2) - 4*x**3*15\nSimplifying the partial expression: (24*x**2)*(-4*x**3 + 10*x**2)\nExpanding the part (-4*x**3 + 10*x**2) using the distributive property, and we got: (10*x**2)*(24*x**2) + (24*x**2)*(-4*x**3)\nReplacing (24*x**2)*(-4*x**3 + 10*x**2) with (10*x**2)*(24*x**2) + (24*x**2)*(-4*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (10*x**2)*(24*x**2) + (10*x**2)*15 + (24*x**2)*(-4*x**3) - 4*x**3*15\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-4*x**3)*15 = -60*x**3\n (-4*x**3)*(24*x**2) = -96*x**5\n (10*x**2)*15 = 150*x**2\n (10*x**2)*(24*x**2) = 240*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -96*x**5 + 240*x**4 - 60*x**3 + 150*x**2\nNo more calculations needed.\n-96*x**5 + 240*x**4 - 60*x**3 + 150*x**2", "generated_answer": "-96*x**5 + 240*x**4 - 60*x**3 + 150*x**2", "step_length": 5} {"cot_id": "a316e9405beade7a2a1033f91cf4e5f506be9bd864ef7bd9d90f4f92c14bf0d6", "datapoint": {"question": "Simplify this expression: (-32*y**3 + 39*y**2 + 5)*(-18*y**3 - 4*y + 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "576*y**6 - 702*y**5 + 128*y**4 - 694*y**3 + 546*y**2 - 20*y + 70", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1967, "polynomial_expr": "(-32*y**3 + 39*y**2 + 5)*(-18*y**3 - 4*y + 14)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-32*y**3 + 39*y**2 + 5)*(-18*y**3 - 4*y + 14)\nExpanding the part (-32*y**3 + 39*y**2 + 5) using the distributive property, and we got: (39*y**2)*(-18*y**3 - 4*y + 14) + (-32*y**3)*(-18*y**3 - 4*y + 14) + 5*(-18*y**3 - 4*y + 14)\n#Step 2:\nCurrent expression: (39*y**2)*(-18*y**3 - 4*y + 14) + (-32*y**3)*(-18*y**3 - 4*y + 14) + 5*(-18*y**3 - 4*y + 14)\nSimplifying the partial expression: 5*(-18*y**3 - 4*y + 14)\nExpanding the part (-18*y**3 - 4*y + 14) using the distributive property, and we got: -4*y*5 - 18*y**3*5 + 14*5\nReplacing 5*(-18*y**3 - 4*y + 14) with -4*y*5 - 18*y**3*5 + 14*5 in the overall expression.\n#Step 3:\nCurrent expression: -4*y*5 + (39*y**2)*(-18*y**3 - 4*y + 14) + (-32*y**3)*(-18*y**3 - 4*y + 14) - 18*y**3*5 + 70\nSimplifying the partial expression: (-32*y**3)*(-18*y**3 - 4*y + 14)\nExpanding the part (-18*y**3 - 4*y + 14) using the distributive property, and we got: (-4*y)*(-32*y**3) + 14*(-32*y**3) + (-32*y**3)*(-18*y**3)\nReplacing (-32*y**3)*(-18*y**3 - 4*y + 14) with (-4*y)*(-32*y**3) + 14*(-32*y**3) + (-32*y**3)*(-18*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-4*y)*(-32*y**3) - 4*y*5 + 14*(-32)*y**3 + (39*y**2)*(-18*y**3 - 4*y + 14) + (-32*y**3)*(-18*y**3) - 18*y**3*5 + 70\nSimplifying the partial expression: (39*y**2)*(-18*y**3 - 4*y + 14)\nExpanding the part (-18*y**3 - 4*y + 14) using the distributive property, and we got: (-4*y)*(39*y**2) + 14*(39*y**2) + (39*y**2)*(-18*y**3)\nReplacing (39*y**2)*(-18*y**3 - 4*y + 14) with (-4*y)*(39*y**2) + 14*(39*y**2) + (39*y**2)*(-18*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-4*y)*(39*y**2) + (-4*y)*(-32*y**3) - 4*y*5 + 14*(-32)*y**3 + 14*39*y**2 + (39*y**2)*(-18*y**3) + (-32*y**3)*(-18*y**3) - 18*y**3*5 + 70\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-18*y**3)*5 = -90*y**3\n (-18*y**3)*(-32*y**3) = 576*y**6\n (-18*y**3)*(39*y**2) = -702*y**5\n (-4*y)*5 = -20*y\n (-4*y)*(-32*y**3) = 128*y**4\n (-4*y)*(39*y**2) = -156*y**3\n 14*-32*y**3 = -448*y**3\n 14*39*y**2 = 546*y**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 576*y**6 - 702*y**5 + 128*y**4 - 448*y**3 - 156*y**3 - 90*y**3 + 546*y**2 - 20*y + 70\nCombining like terms, got 576*y**6 - 702*y**5 + 128*y**4 - 694*y**3 + 546*y**2 - 20*y + 70\n#Step 7:\nCurrent expression: 576*y**6 - 702*y**5 + 128*y**4 - 694*y**3 + 546*y**2 - 20*y + 70\nNo more calculations needed.\n576*y**6 - 702*y**5 + 128*y**4 - 694*y**3 + 546*y**2 - 20*y + 70", "generated_answer": "576*y**6 - 702*y**5 + 128*y**4 - 694*y**3 + 546*y**2 - 20*y + 70", "step_length": 7} {"cot_id": "1a1ea3566a13f8095cb8450d5f16ffc77c6e579f44363790a96df0ea7527aff2", "datapoint": {"question": "Simplify this expression: (-15*x**3 - 66)*(6*x**3 + 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-90*x**6 - 636*x**3 - 1056", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1968, "polynomial_expr": "(-15*x**3 - 66)*(6*x**3 + 16)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-15*x**3 - 66)*(6*x**3 + 16)\nExpanding the part (-15*x**3 - 66) using the distributive property, and we got: (-15*x**3)*(6*x**3 + 16) - 66*(6*x**3 + 16)\n#Step 2:\nCurrent expression: (-15*x**3)*(6*x**3 + 16) - 66*(6*x**3 + 16)\nSimplifying the partial expression: -66*(6*x**3 + 16)\nExpanding the part (6*x**3 + 16) using the distributive property, and we got: (6*x**3)*(-66) + 16*(-66)\nReplacing -66*(6*x**3 + 16) with (6*x**3)*(-66) + 16*(-66) in the overall expression.\n#Step 3:\nCurrent expression: (-15*x**3)*(6*x**3 + 16) + (6*x**3)*(-66) - 1056\nSimplifying the partial expression: (-15*x**3)*(6*x**3 + 16)\nExpanding the part (6*x**3 + 16) using the distributive property, and we got: 16*(-15*x**3) + (-15*x**3)*(6*x**3)\nReplacing (-15*x**3)*(6*x**3 + 16) with 16*(-15*x**3) + (-15*x**3)*(6*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 16*(-15)*x**3 + (-15*x**3)*(6*x**3) + (6*x**3)*(-66) - 1056\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (6*x**3)*-66 = -396*x**3\n (6*x**3)*(-15*x**3) = -90*x**6\n 16*-15*x**3 = -240*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -90*x**6 - 396*x**3 - 240*x**3 - 1056\nCombining like terms, got -90*x**6 - 636*x**3 - 1056\n#Step 6:\nCurrent expression: -90*x**6 - 636*x**3 - 1056\nNo more calculations needed.\n-90*x**6 - 636*x**3 - 1056", "generated_answer": "-90*x**6 - 636*x**3 - 1056", "step_length": 6} {"cot_id": "35c1130b49b28d9c24e8b910ee71a25a702e1caeaf988bf71e49ffa209d94444", "datapoint": {"question": "Simplify this expression: (14 - 31*z)*(33*z**2 - 12*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1023*z**3 + 834*z**2 - 168*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1969, "polynomial_expr": "(14 - 31*z)*(33*z**2 - 12*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14 - 31*z)*(33*z**2 - 12*z)\nExpanding the part (14 - 31*z) using the distributive property, and we got: (-31*z)*(33*z**2 - 12*z) + 14*(33*z**2 - 12*z)\n#Step 2:\nCurrent expression: (-31*z)*(33*z**2 - 12*z) + 14*(33*z**2 - 12*z)\nSimplifying the partial expression: 14*(33*z**2 - 12*z)\nExpanding the part (33*z**2 - 12*z) using the distributive property, and we got: -12*z*14 + (33*z**2)*14\nReplacing 14*(33*z**2 - 12*z) with -12*z*14 + (33*z**2)*14 in the overall expression.\n#Step 3:\nCurrent expression: (-31*z)*(33*z**2 - 12*z) - 12*z*14 + (33*z**2)*14\nSimplifying the partial expression: (-31*z)*(33*z**2 - 12*z)\nExpanding the part (33*z**2 - 12*z) using the distributive property, and we got: (-31*z)*(-12*z) + (-31*z)*(33*z**2)\nReplacing (-31*z)*(33*z**2 - 12*z) with (-31*z)*(-12*z) + (-31*z)*(33*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-31*z)*(-12*z) + (-31*z)*(33*z**2) - 12*z*14 + (33*z**2)*14\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*z)*14 = -168*z\n (-12*z)*(-31*z) = 372*z**2\n (33*z**2)*14 = 462*z**2\n (33*z**2)*(-31*z) = -1023*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1023*z**3 + 372*z**2 + 462*z**2 - 168*z\nCombining like terms, got -1023*z**3 + 834*z**2 - 168*z\n#Step 6:\nCurrent expression: -1023*z**3 + 834*z**2 - 168*z\nNo more calculations needed.\n-1023*z**3 + 834*z**2 - 168*z", "generated_answer": "-1023*z**3 + 834*z**2 - 168*z", "step_length": 6} {"cot_id": "bdbe224a30801560454cc39806f7fae5bb637c5c4ce18b5c6baf7e2a46221a82", "datapoint": {"question": "Calculate the following: -767*x**4\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-767*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1970, "polynomial_expr": "-767*x**4", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -767*x**4\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -767*x**4\nNo more calculations needed.\n-767*x**4", "generated_answer": "-767*x**4", "step_length": 2} {"cot_id": "71411ac4ee116b03b77fd7a73f8b7e0d38875147b3c39f11a44d30d75df3397b", "datapoint": {"question": "Simplify this expression: (50 - 7*y**2)*(51*y**2 + 48*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-357*y**4 - 336*y**3 + 2550*y**2 + 2400*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1971, "polynomial_expr": "(50 - 7*y**2)*(51*y**2 + 48*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (50 - 7*y**2)*(51*y**2 + 48*y)\nExpanding the part (50 - 7*y**2) using the distributive property, and we got: (-7*y**2)*(51*y**2 + 48*y) + 50*(51*y**2 + 48*y)\n#Step 2:\nCurrent expression: (-7*y**2)*(51*y**2 + 48*y) + 50*(51*y**2 + 48*y)\nSimplifying the partial expression: 50*(51*y**2 + 48*y)\nExpanding the part (51*y**2 + 48*y) using the distributive property, and we got: (48*y)*50 + (51*y**2)*50\nReplacing 50*(51*y**2 + 48*y) with (48*y)*50 + (51*y**2)*50 in the overall expression.\n#Step 3:\nCurrent expression: (48*y)*50 + (-7*y**2)*(51*y**2 + 48*y) + (51*y**2)*50\nSimplifying the partial expression: (-7*y**2)*(51*y**2 + 48*y)\nExpanding the part (51*y**2 + 48*y) using the distributive property, and we got: (48*y)*(-7*y**2) + (-7*y**2)*(51*y**2)\nReplacing (-7*y**2)*(51*y**2 + 48*y) with (48*y)*(-7*y**2) + (-7*y**2)*(51*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (48*y)*(-7*y**2) + (48*y)*50 + (-7*y**2)*(51*y**2) + (51*y**2)*50\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (48*y)*50 = 2400*y\n (48*y)*(-7*y**2) = -336*y**3\n (51*y**2)*50 = 2550*y**2\n (51*y**2)*(-7*y**2) = -357*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -357*y**4 - 336*y**3 + 2550*y**2 + 2400*y\nNo more calculations needed.\n-357*y**4 - 336*y**3 + 2550*y**2 + 2400*y", "generated_answer": "-357*y**4 - 336*y**3 + 2550*y**2 + 2400*y", "step_length": 5} {"cot_id": "34e73e779b08e2d7a6ad71b7f56d5418e0eb4a4001feee6836d2502bbe4415f5", "datapoint": {"question": "Simplify this expression: (-45*y**2 - 22)*(-42*y**2 - 14*y + 23)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1890*y**4 + 630*y**3 - 111*y**2 + 308*y - 506", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1972, "polynomial_expr": "(-45*y**2 - 22)*(-42*y**2 - 14*y + 23)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-45*y**2 - 22)*(-42*y**2 - 14*y + 23)\nExpanding the part (-45*y**2 - 22) using the distributive property, and we got: (-45*y**2)*(-42*y**2 - 14*y + 23) - 22*(-42*y**2 - 14*y + 23)\n#Step 2:\nCurrent expression: (-45*y**2)*(-42*y**2 - 14*y + 23) - 22*(-42*y**2 - 14*y + 23)\nSimplifying the partial expression: -22*(-42*y**2 - 14*y + 23)\nExpanding the part (-42*y**2 - 14*y + 23) using the distributive property, and we got: -14*y*(-22) - 42*y**2*(-22) + 23*(-22)\nReplacing -22*(-42*y**2 - 14*y + 23) with -14*y*(-22) - 42*y**2*(-22) + 23*(-22) in the overall expression.\n#Step 3:\nCurrent expression: -14*y*(-22) + (-45*y**2)*(-42*y**2 - 14*y + 23) - 42*y**2*(-22) - 506\nSimplifying the partial expression: (-45*y**2)*(-42*y**2 - 14*y + 23)\nExpanding the part (-42*y**2 - 14*y + 23) using the distributive property, and we got: (-14*y)*(-45*y**2) + 23*(-45*y**2) + (-45*y**2)*(-42*y**2)\nReplacing (-45*y**2)*(-42*y**2 - 14*y + 23) with (-14*y)*(-45*y**2) + 23*(-45*y**2) + (-45*y**2)*(-42*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-14*y)*(-45*y**2) - 14*y*(-22) + 23*(-45)*y**2 + (-45*y**2)*(-42*y**2) - 42*y**2*(-22) - 506\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*y**2)*-22 = 924*y**2\n (-42*y**2)*(-45*y**2) = 1890*y**4\n (-14*y)*-22 = 308*y\n (-14*y)*(-45*y**2) = 630*y**3\n 23*-45*y**2 = -1035*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1890*y**4 + 630*y**3 - 1035*y**2 + 924*y**2 + 308*y - 506\nCombining like terms, got 1890*y**4 + 630*y**3 - 111*y**2 + 308*y - 506\n#Step 6:\nCurrent expression: 1890*y**4 + 630*y**3 - 111*y**2 + 308*y - 506\nNo more calculations needed.\n1890*y**4 + 630*y**3 - 111*y**2 + 308*y - 506", "generated_answer": "1890*y**4 + 630*y**3 - 111*y**2 + 308*y - 506", "step_length": 6} {"cot_id": "44b3dd6be7377416fe2bfd3c4f1e13d6d50d178e39818ab74aac7ba977263244", "datapoint": {"question": "Simplify this expression: (-z**3 + 42*z**2)*(37*z**3 + z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-37*z**6 + 1553*z**5 + 42*z**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1973, "polynomial_expr": "(-z**3 + 42*z**2)*(37*z**3 + z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-z**3 + 42*z**2)*(37*z**3 + z**2)\nExpanding the part (37*z**3 + z**2) using the distributive property, and we got: z**2*(-z**3 + 42*z**2) + (37*z**3)*(-z**3 + 42*z**2)\n#Step 2:\nCurrent expression: z**2*(-z**3 + 42*z**2) + (37*z**3)*(-z**3 + 42*z**2)\nSimplifying the partial expression: z**2*(-z**3 + 42*z**2)\nExpanding the part (-z**3 + 42*z**2) using the distributive property, and we got: z**2*(42*z**2) + z**2*(-z**3)\nReplacing z**2*(-z**3 + 42*z**2) with z**2*(42*z**2) + z**2*(-z**3) in the overall expression.\n#Step 3:\nCurrent expression: z**2*(42*z**2) + z**2*(-z**3) + (37*z**3)*(-z**3 + 42*z**2)\nSimplifying the partial expression: (37*z**3)*(-z**3 + 42*z**2)\nExpanding the part (-z**3 + 42*z**2) using the distributive property, and we got: (42*z**2)*(37*z**3) + (-z**3)*(37*z**3)\nReplacing (37*z**3)*(-z**3 + 42*z**2) with (42*z**2)*(37*z**3) + (-z**3)*(37*z**3) in the overall expression.\n#Step 4:\nCurrent expression: z**2*(42*z**2) + z**2*(-z**3) + (42*z**2)*(37*z**3) + (-z**3)*(37*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-z**3)*z**2 = -z**5\n (-z**3)*(37*z**3) = -37*z**6\n (42*z**2)*z**2 = 42*z**4\n (42*z**2)*(37*z**3) = 1554*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -37*z**6 - z**5 + 1554*z**5 + 42*z**4\nCombining like terms, got -37*z**6 + 1553*z**5 + 42*z**4\n#Step 6:\nCurrent expression: -37*z**6 + 1553*z**5 + 42*z**4\nNo more calculations needed.\n-37*z**6 + 1553*z**5 + 42*z**4", "generated_answer": "-37*z**6 + 1553*z**5 + 42*z**4", "step_length": 6} {"cot_id": "e0f94f02206153a4b17ab26ba42f73daf994c73a7fd6765e4efec175f447caef", "datapoint": {"question": "Simplify this expression: (-46*z - 16)*(-5*z**3 - 10*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "230*z**4 + 80*z**3 + 460*z**2 + 160*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1974, "polynomial_expr": "(-46*z - 16)*(-5*z**3 - 10*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-46*z - 16)*(-5*z**3 - 10*z)\nExpanding the part (-46*z - 16) using the distributive property, and we got: (-46*z)*(-5*z**3 - 10*z) - 16*(-5*z**3 - 10*z)\n#Step 2:\nCurrent expression: (-46*z)*(-5*z**3 - 10*z) - 16*(-5*z**3 - 10*z)\nSimplifying the partial expression: -16*(-5*z**3 - 10*z)\nExpanding the part (-5*z**3 - 10*z) using the distributive property, and we got: -10*z*(-16) - 5*z**3*(-16)\nReplacing -16*(-5*z**3 - 10*z) with -10*z*(-16) - 5*z**3*(-16) in the overall expression.\n#Step 3:\nCurrent expression: (-46*z)*(-5*z**3 - 10*z) - 10*z*(-16) - 5*z**3*(-16)\nSimplifying the partial expression: (-46*z)*(-5*z**3 - 10*z)\nExpanding the part (-5*z**3 - 10*z) using the distributive property, and we got: (-46*z)*(-10*z) + (-46*z)*(-5*z**3)\nReplacing (-46*z)*(-5*z**3 - 10*z) with (-46*z)*(-10*z) + (-46*z)*(-5*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-46*z)*(-10*z) + (-46*z)*(-5*z**3) - 10*z*(-16) - 5*z**3*(-16)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*z)*-16 = 160*z\n (-10*z)*(-46*z) = 460*z**2\n (-5*z**3)*-16 = 80*z**3\n (-5*z**3)*(-46*z) = 230*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 230*z**4 + 80*z**3 + 460*z**2 + 160*z\nNo more calculations needed.\n230*z**4 + 80*z**3 + 460*z**2 + 160*z", "generated_answer": "230*z**4 + 80*z**3 + 460*z**2 + 160*z", "step_length": 5} {"cot_id": "88bd640fa56eb8ff30271a4489ffc9c762e1d02b149bb097df276a2c53cd9c46", "datapoint": {"question": "Simplify this expression: (2 - 6*x**2)*(33*x**3 + 29)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-198*x**5 + 66*x**3 - 174*x**2 + 58", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1975, "polynomial_expr": "(2 - 6*x**2)*(33*x**3 + 29)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2 - 6*x**2)*(33*x**3 + 29)\nExpanding the part (2 - 6*x**2) using the distributive property, and we got: (-6*x**2)*(33*x**3 + 29) + 2*(33*x**3 + 29)\n#Step 2:\nCurrent expression: (-6*x**2)*(33*x**3 + 29) + 2*(33*x**3 + 29)\nSimplifying the partial expression: 2*(33*x**3 + 29)\nExpanding the part (33*x**3 + 29) using the distributive property, and we got: (33*x**3)*2 + 29*2\nReplacing 2*(33*x**3 + 29) with (33*x**3)*2 + 29*2 in the overall expression.\n#Step 3:\nCurrent expression: (-6*x**2)*(33*x**3 + 29) + (33*x**3)*2 + 58\nSimplifying the partial expression: (-6*x**2)*(33*x**3 + 29)\nExpanding the part (33*x**3 + 29) using the distributive property, and we got: 29*(-6*x**2) + (-6*x**2)*(33*x**3)\nReplacing (-6*x**2)*(33*x**3 + 29) with 29*(-6*x**2) + (-6*x**2)*(33*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 29*(-6)*x**2 + (-6*x**2)*(33*x**3) + (33*x**3)*2 + 58\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (33*x**3)*2 = 66*x**3\n (33*x**3)*(-6*x**2) = -198*x**5\n 29*-6*x**2 = -174*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -198*x**5 + 66*x**3 - 174*x**2 + 58\nNo more calculations needed.\n-198*x**5 + 66*x**3 - 174*x**2 + 58", "generated_answer": "-198*x**5 + 66*x**3 - 174*x**2 + 58", "step_length": 5} {"cot_id": "f9ee944f48f020092daac59e8826975bc91e153c28f50e4b251e2c5919b69e30", "datapoint": {"question": "Simplify this expression: 8*z**2*(-26*z - 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-208*z**3 - 280*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1976, "polynomial_expr": "8*z**2*(-26*z - 35)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 8*z**2*(-26*z - 35)\nExpanding the part (-26*z - 35) using the distributive property, and we got: (-26*z)*(8*z**2) - 280*z**2\n#Step 2:\nCurrent expression: (-26*z)*(8*z**2) - 280*z**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -35*(8*z**2) = -280*z**2\n (-26*z)*(8*z**2) = -208*z**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -208*z**3 - 280*z**2\nNo more calculations needed.\n-208*z**3 - 280*z**2", "generated_answer": "-208*z**3 - 280*z**2", "step_length": 3} {"cot_id": "b292d848a8c5f2ffab70d25edfade64e37ce651933173551eceec2f5b900dd63", "datapoint": {"question": "Calculate the following: (x**2 + 11)*(-48*x**3 + 43*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-48*x**5 + 43*x**4 - 528*x**3 + 473*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1977, "polynomial_expr": "(x**2 + 11)*(-48*x**3 + 43*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (x**2 + 11)*(-48*x**3 + 43*x**2)\nExpanding the part (x**2 + 11) using the distributive property, and we got: x**2*(-48*x**3 + 43*x**2) + 11*(-48*x**3 + 43*x**2)\n#Step 2:\nCurrent expression: x**2*(-48*x**3 + 43*x**2) + 11*(-48*x**3 + 43*x**2)\nSimplifying the partial expression: 11*(-48*x**3 + 43*x**2)\nExpanding the part (-48*x**3 + 43*x**2) using the distributive property, and we got: (43*x**2)*11 - 48*x**3*11\nReplacing 11*(-48*x**3 + 43*x**2) with (43*x**2)*11 - 48*x**3*11 in the overall expression.\n#Step 3:\nCurrent expression: x**2*(-48*x**3 + 43*x**2) + (43*x**2)*11 - 48*x**3*11\nSimplifying the partial expression: x**2*(-48*x**3 + 43*x**2)\nExpanding the part (-48*x**3 + 43*x**2) using the distributive property, and we got: x**2*(43*x**2) + x**2*(-48*x**3)\nReplacing x**2*(-48*x**3 + 43*x**2) with x**2*(43*x**2) + x**2*(-48*x**3) in the overall expression.\n#Step 4:\nCurrent expression: x**2*(43*x**2) + x**2*(-48*x**3) + (43*x**2)*11 - 48*x**3*11\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*x**3)*11 = -528*x**3\n (-48*x**3)*x**2 = -48*x**5\n (43*x**2)*11 = 473*x**2\n (43*x**2)*x**2 = 43*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -48*x**5 + 43*x**4 - 528*x**3 + 473*x**2\nNo more calculations needed.\n-48*x**5 + 43*x**4 - 528*x**3 + 473*x**2", "generated_answer": "-48*x**5 + 43*x**4 - 528*x**3 + 473*x**2", "step_length": 5} {"cot_id": "e58b09e19e84d21004088f261c07111fe5c1edb5a08015a24c735d95a0423112", "datapoint": {"question": "Calculate the following: -31*z**2*(50*z**2 + 31*z + 65)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1550*z**4 - 961*z**3 - 2015*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1978, "polynomial_expr": "-31*z**2*(50*z**2 + 31*z + 65)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -31*z**2*(50*z**2 + 31*z + 65)\nExpanding the part (50*z**2 + 31*z + 65) using the distributive property, and we got: 65*(-31*z**2) + (31*z)*(-31*z**2) + (-31*z**2)*(50*z**2)\n#Step 2:\nCurrent expression: 65*(-31*z**2) + (31*z)*(-31*z**2) + (-31*z**2)*(50*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 65*(-31*z**2) = -2015*z**2\n (31*z)*(-31*z**2) = -961*z**3\n (50*z**2)*(-31*z**2) = -1550*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1550*z**4 - 961*z**3 - 2015*z**2\nNo more calculations needed.\n-1550*z**4 - 961*z**3 - 2015*z**2", "generated_answer": "-1550*z**4 - 961*z**3 - 2015*z**2", "step_length": 3} {"cot_id": "f968778d78bd492a90f528d4f06eff8444e6fb7dce1e55a7d46294044ea838b3", "datapoint": {"question": "Calculate the following: 10*y**3*(79*y**3 + 11)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "790*y**6 + 110*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1979, "polynomial_expr": "10*y**3*(79*y**3 + 11)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 10*y**3*(79*y**3 + 11)\nExpanding the part (79*y**3 + 11) using the distributive property, and we got: 11*(10*y**3) + (10*y**3)*(79*y**3)\n#Step 2:\nCurrent expression: 11*(10*y**3) + (10*y**3)*(79*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 11*(10*y**3) = 110*y**3\n (79*y**3)*(10*y**3) = 790*y**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 790*y**6 + 110*y**3\nNo more calculations needed.\n790*y**6 + 110*y**3", "generated_answer": "790*y**6 + 110*y**3", "step_length": 3} {"cot_id": "b52669e49a755dc75b0f0bbe52e01a98a6f63098203064c5ab650fa3d54292ec", "datapoint": {"question": "Calculate the following: (51*z**3 + 20*z**2)*(21*z**3 + 34*z**2 + 35*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1071*z**6 + 2154*z**5 + 2465*z**4 + 700*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1980, "polynomial_expr": "(51*z**3 + 20*z**2)*(21*z**3 + 34*z**2 + 35*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (51*z**3 + 20*z**2)*(21*z**3 + 34*z**2 + 35*z)\nExpanding the part (51*z**3 + 20*z**2) using the distributive property, and we got: (20*z**2)*(21*z**3 + 34*z**2 + 35*z) + (51*z**3)*(21*z**3 + 34*z**2 + 35*z)\n#Step 2:\nCurrent expression: (20*z**2)*(21*z**3 + 34*z**2 + 35*z) + (51*z**3)*(21*z**3 + 34*z**2 + 35*z)\nSimplifying the partial expression: (20*z**2)*(21*z**3 + 34*z**2 + 35*z)\nExpanding the part (21*z**3 + 34*z**2 + 35*z) using the distributive property, and we got: (35*z)*(20*z**2) + (20*z**2)*(34*z**2) + (20*z**2)*(21*z**3)\nReplacing (20*z**2)*(21*z**3 + 34*z**2 + 35*z) with (35*z)*(20*z**2) + (20*z**2)*(34*z**2) + (20*z**2)*(21*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (35*z)*(20*z**2) + (20*z**2)*(34*z**2) + (20*z**2)*(21*z**3) + (51*z**3)*(21*z**3 + 34*z**2 + 35*z)\nSimplifying the partial expression: (51*z**3)*(21*z**3 + 34*z**2 + 35*z)\nExpanding the part (21*z**3 + 34*z**2 + 35*z) using the distributive property, and we got: (35*z)*(51*z**3) + (34*z**2)*(51*z**3) + (21*z**3)*(51*z**3)\nReplacing (51*z**3)*(21*z**3 + 34*z**2 + 35*z) with (35*z)*(51*z**3) + (34*z**2)*(51*z**3) + (21*z**3)*(51*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (35*z)*(20*z**2) + (35*z)*(51*z**3) + (20*z**2)*(34*z**2) + (20*z**2)*(21*z**3) + (34*z**2)*(51*z**3) + (21*z**3)*(51*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (21*z**3)*(20*z**2) = 420*z**5\n (21*z**3)*(51*z**3) = 1071*z**6\n (34*z**2)*(20*z**2) = 680*z**4\n (34*z**2)*(51*z**3) = 1734*z**5\n (35*z)*(20*z**2) = 700*z**3\n (35*z)*(51*z**3) = 1785*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1071*z**6 + 420*z**5 + 1734*z**5 + 680*z**4 + 1785*z**4 + 700*z**3\nCombining like terms, got 1071*z**6 + 2154*z**5 + 2465*z**4 + 700*z**3\n#Step 6:\nCurrent expression: 1071*z**6 + 2154*z**5 + 2465*z**4 + 700*z**3\nNo more calculations needed.\n1071*z**6 + 2154*z**5 + 2465*z**4 + 700*z**3", "generated_answer": "1071*z**6 + 2154*z**5 + 2465*z**4 + 700*z**3", "step_length": 6} {"cot_id": "c6d5b30b4f7faa7b392255cca743c808c44eeff105d9873340588e497a021a9f", "datapoint": {"question": "Simplify this expression: -6*y*(5 - 41*y**3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "246*y**4 - 30*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1981, "polynomial_expr": "-6*y*(5 - 41*y**3)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -6*y*(5 - 41*y**3)\nExpanding the part (5 - 41*y**3) using the distributive property, and we got: (-6*y)*(-41*y**3) + 5*(-6*y)\n#Step 2:\nCurrent expression: (-6*y)*(-41*y**3) + 5*(-6*y)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 5*(-6*y) = -30*y\n (-41*y**3)*(-6*y) = 246*y**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 246*y**4 - 30*y\nNo more calculations needed.\n246*y**4 - 30*y", "generated_answer": "246*y**4 - 30*y", "step_length": 3} {"cot_id": "e9f72035fdedf81f643e0d70dbbb85f5e8cb4d2beaf9ed8734053eb2a4c08901", "datapoint": {"question": "Simplify this expression: (6*y**2 + 11*y)*(47*y**2 + 46*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "282*y**4 + 793*y**3 + 506*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1982, "polynomial_expr": "(6*y**2 + 11*y)*(47*y**2 + 46*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6*y**2 + 11*y)*(47*y**2 + 46*y)\nExpanding the part (6*y**2 + 11*y) using the distributive property, and we got: (11*y)*(47*y**2 + 46*y) + (6*y**2)*(47*y**2 + 46*y)\n#Step 2:\nCurrent expression: (11*y)*(47*y**2 + 46*y) + (6*y**2)*(47*y**2 + 46*y)\nSimplifying the partial expression: (6*y**2)*(47*y**2 + 46*y)\nExpanding the part (47*y**2 + 46*y) using the distributive property, and we got: (46*y)*(6*y**2) + (6*y**2)*(47*y**2)\nReplacing (6*y**2)*(47*y**2 + 46*y) with (46*y)*(6*y**2) + (6*y**2)*(47*y**2) in the overall expression.\n#Step 3:\nCurrent expression: (11*y)*(47*y**2 + 46*y) + (46*y)*(6*y**2) + (6*y**2)*(47*y**2)\nSimplifying the partial expression: (11*y)*(47*y**2 + 46*y)\nExpanding the part (47*y**2 + 46*y) using the distributive property, and we got: (11*y)*(46*y) + (11*y)*(47*y**2)\nReplacing (11*y)*(47*y**2 + 46*y) with (11*y)*(46*y) + (11*y)*(47*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (11*y)*(46*y) + (11*y)*(47*y**2) + (46*y)*(6*y**2) + (6*y**2)*(47*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (46*y)*(6*y**2) = 276*y**3\n (46*y)*(11*y) = 506*y**2\n (47*y**2)*(6*y**2) = 282*y**4\n (47*y**2)*(11*y) = 517*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 282*y**4 + 276*y**3 + 517*y**3 + 506*y**2\nCombining like terms, got 282*y**4 + 793*y**3 + 506*y**2\n#Step 6:\nCurrent expression: 282*y**4 + 793*y**3 + 506*y**2\nNo more calculations needed.\n282*y**4 + 793*y**3 + 506*y**2", "generated_answer": "282*y**4 + 793*y**3 + 506*y**2", "step_length": 6} {"cot_id": "c3556290743daa6e178af1d56ae0825289ba399341151ed2374c8f647b5c7da0", "datapoint": {"question": "Simplify this expression: (2*z**3 - 7*z**2 - 13)*(3*z**3 + 19*z**2 + 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "6*z**6 + 17*z**5 - 133*z**4 + 23*z**3 - 464*z**2 - 403", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1983, "polynomial_expr": "(2*z**3 - 7*z**2 - 13)*(3*z**3 + 19*z**2 + 31)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2*z**3 - 7*z**2 - 13)*(3*z**3 + 19*z**2 + 31)\nExpanding the part (2*z**3 - 7*z**2 - 13) using the distributive property, and we got: (-7*z**2)*(3*z**3 + 19*z**2 + 31) + (2*z**3)*(3*z**3 + 19*z**2 + 31) - 13*(3*z**3 + 19*z**2 + 31)\n#Step 2:\nCurrent expression: (-7*z**2)*(3*z**3 + 19*z**2 + 31) + (2*z**3)*(3*z**3 + 19*z**2 + 31) - 13*(3*z**3 + 19*z**2 + 31)\nSimplifying the partial expression: -13*(3*z**3 + 19*z**2 + 31)\nExpanding the part (3*z**3 + 19*z**2 + 31) using the distributive property, and we got: (19*z**2)*(-13) + (3*z**3)*(-13) + 31*(-13)\nReplacing -13*(3*z**3 + 19*z**2 + 31) with (19*z**2)*(-13) + (3*z**3)*(-13) + 31*(-13) in the overall expression.\n#Step 3:\nCurrent expression: (-7*z**2)*(3*z**3 + 19*z**2 + 31) + (19*z**2)*(-13) + (2*z**3)*(3*z**3 + 19*z**2 + 31) + (3*z**3)*(-13) - 403\nSimplifying the partial expression: (-7*z**2)*(3*z**3 + 19*z**2 + 31)\nExpanding the part (3*z**3 + 19*z**2 + 31) using the distributive property, and we got: 31*(-7*z**2) + (-7*z**2)*(19*z**2) + (-7*z**2)*(3*z**3)\nReplacing (-7*z**2)*(3*z**3 + 19*z**2 + 31) with 31*(-7*z**2) + (-7*z**2)*(19*z**2) + (-7*z**2)*(3*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 31*(-7)*z**2 + (-7*z**2)*(19*z**2) + (-7*z**2)*(3*z**3) + (19*z**2)*(-13) + (2*z**3)*(3*z**3 + 19*z**2 + 31) + (3*z**3)*(-13) - 403\nSimplifying the partial expression: (2*z**3)*(3*z**3 + 19*z**2 + 31)\nExpanding the part (3*z**3 + 19*z**2 + 31) using the distributive property, and we got: 31*(2*z**3) + (19*z**2)*(2*z**3) + (2*z**3)*(3*z**3)\nReplacing (2*z**3)*(3*z**3 + 19*z**2 + 31) with 31*(2*z**3) + (19*z**2)*(2*z**3) + (2*z**3)*(3*z**3) in the overall expression.\n#Step 5:\nCurrent expression: 31*2*z**3 + 31*(-7)*z**2 + (-7*z**2)*(19*z**2) + (-7*z**2)*(3*z**3) + (19*z**2)*(2*z**3) + (19*z**2)*(-13) + (2*z**3)*(3*z**3) + (3*z**3)*(-13) - 403\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (3*z**3)*-13 = -39*z**3\n (3*z**3)*(-7*z**2) = -21*z**5\n (3*z**3)*(2*z**3) = 6*z**6\n (19*z**2)*-13 = -247*z**2\n (19*z**2)*(-7*z**2) = -133*z**4\n (19*z**2)*(2*z**3) = 38*z**5\n 31*-7*z**2 = -217*z**2\n 31*2*z**3 = 62*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 6*z**6 - 21*z**5 + 38*z**5 - 133*z**4 - 39*z**3 + 62*z**3 - 247*z**2 - 217*z**2 - 403\nCombining like terms, got 6*z**6 + 17*z**5 - 133*z**4 + 23*z**3 - 464*z**2 - 403\n#Step 7:\nCurrent expression: 6*z**6 + 17*z**5 - 133*z**4 + 23*z**3 - 464*z**2 - 403\nNo more calculations needed.\n6*z**6 + 17*z**5 - 133*z**4 + 23*z**3 - 464*z**2 - 403", "generated_answer": "6*z**6 + 17*z**5 - 133*z**4 + 23*z**3 - 464*z**2 - 403", "step_length": 7} {"cot_id": "ae0350a7f6b0d64c73906e7368ad8bf72bad8444c382872f0077d5d69f6f008b", "datapoint": {"question": "Calculate the following: (23*x**3 - 6*x)*(37*x**3 + 33*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "851*x**6 + 537*x**4 - 198*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1984, "polynomial_expr": "(23*x**3 - 6*x)*(37*x**3 + 33*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (23*x**3 - 6*x)*(37*x**3 + 33*x)\nExpanding the part (23*x**3 - 6*x) using the distributive property, and we got: (-6*x)*(37*x**3 + 33*x) + (23*x**3)*(37*x**3 + 33*x)\n#Step 2:\nCurrent expression: (-6*x)*(37*x**3 + 33*x) + (23*x**3)*(37*x**3 + 33*x)\nSimplifying the partial expression: (-6*x)*(37*x**3 + 33*x)\nExpanding the part (37*x**3 + 33*x) using the distributive property, and we got: (-6*x)*(33*x) + (-6*x)*(37*x**3)\nReplacing (-6*x)*(37*x**3 + 33*x) with (-6*x)*(33*x) + (-6*x)*(37*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-6*x)*(33*x) + (-6*x)*(37*x**3) + (23*x**3)*(37*x**3 + 33*x)\nSimplifying the partial expression: (23*x**3)*(37*x**3 + 33*x)\nExpanding the part (37*x**3 + 33*x) using the distributive property, and we got: (33*x)*(23*x**3) + (23*x**3)*(37*x**3)\nReplacing (23*x**3)*(37*x**3 + 33*x) with (33*x)*(23*x**3) + (23*x**3)*(37*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-6*x)*(33*x) + (-6*x)*(37*x**3) + (33*x)*(23*x**3) + (23*x**3)*(37*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (33*x)*(-6*x) = -198*x**2\n (33*x)*(23*x**3) = 759*x**4\n (37*x**3)*(-6*x) = -222*x**4\n (37*x**3)*(23*x**3) = 851*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 851*x**6 - 222*x**4 + 759*x**4 - 198*x**2\nCombining like terms, got 851*x**6 + 537*x**4 - 198*x**2\n#Step 6:\nCurrent expression: 851*x**6 + 537*x**4 - 198*x**2\nNo more calculations needed.\n851*x**6 + 537*x**4 - 198*x**2", "generated_answer": "851*x**6 + 537*x**4 - 198*x**2", "step_length": 6} {"cot_id": "1a98d083c2810d509aa1e1d8e762b2409feece660afefddcdacf591b49a10c41", "datapoint": {"question": "Calculate the following: (x**2 - 41)*(-22*x**2 + 44*x - 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-22*x**4 + 44*x**3 + 863*x**2 - 1804*x + 1599", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1985, "polynomial_expr": "(x**2 - 41)*(-22*x**2 + 44*x - 39)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (x**2 - 41)*(-22*x**2 + 44*x - 39)\nExpanding the part (x**2 - 41) using the distributive property, and we got: x**2*(-22*x**2 + 44*x - 39) - 41*(-22*x**2 + 44*x - 39)\n#Step 2:\nCurrent expression: x**2*(-22*x**2 + 44*x - 39) - 41*(-22*x**2 + 44*x - 39)\nSimplifying the partial expression: -41*(-22*x**2 + 44*x - 39)\nExpanding the part (-22*x**2 + 44*x - 39) using the distributive property, and we got: (44*x)*(-41) - 22*x**2*(-41) - 39*(-41)\nReplacing -41*(-22*x**2 + 44*x - 39) with (44*x)*(-41) - 22*x**2*(-41) - 39*(-41) in the overall expression.\n#Step 3:\nCurrent expression: x**2*(-22*x**2 + 44*x - 39) + (44*x)*(-41) - 22*x**2*(-41) + 1599\nSimplifying the partial expression: x**2*(-22*x**2 + 44*x - 39)\nExpanding the part (-22*x**2 + 44*x - 39) using the distributive property, and we got: (44*x)*x**2 + (-22*x**2)*x**2 - 39*x**2\nReplacing x**2*(-22*x**2 + 44*x - 39) with (44*x)*x**2 + (-22*x**2)*x**2 - 39*x**2 in the overall expression.\n#Step 4:\nCurrent expression: (44*x)*x**2 + (-22*x**2)*x**2 - 39*x**2 + (44*x)*(-41) - 22*x**2*(-41) + 1599\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*x**2)*-41 = 902*x**2\n (-22*x**2)*x**2 = -22*x**4\n (44*x)*-41 = -1804*x\n (44*x)*x**2 = 44*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -22*x**4 + 44*x**3 - 39*x**2 + 902*x**2 - 1804*x + 1599\nCombining like terms, got -22*x**4 + 44*x**3 + 863*x**2 - 1804*x + 1599\n#Step 6:\nCurrent expression: -22*x**4 + 44*x**3 + 863*x**2 - 1804*x + 1599\nNo more calculations needed.\n-22*x**4 + 44*x**3 + 863*x**2 - 1804*x + 1599", "generated_answer": "-22*x**4 + 44*x**3 + 863*x**2 - 1804*x + 1599", "step_length": 6} {"cot_id": "22f5646232be7e12c6e27717548336473f5c0e33ba4332e0eade6dafc97e2cda", "datapoint": {"question": "Simplify this expression: (-y**3 - 38)*(26*y**3 + 38*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-26*y**6 - 38*y**4 - 988*y**3 - 1444*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1986, "polynomial_expr": "(-y**3 - 38)*(26*y**3 + 38*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-y**3 - 38)*(26*y**3 + 38*y)\nExpanding the part (-y**3 - 38) using the distributive property, and we got: (-y**3)*(26*y**3 + 38*y) - 38*(26*y**3 + 38*y)\n#Step 2:\nCurrent expression: (-y**3)*(26*y**3 + 38*y) - 38*(26*y**3 + 38*y)\nSimplifying the partial expression: -38*(26*y**3 + 38*y)\nExpanding the part (26*y**3 + 38*y) using the distributive property, and we got: (38*y)*(-38) + (26*y**3)*(-38)\nReplacing -38*(26*y**3 + 38*y) with (38*y)*(-38) + (26*y**3)*(-38) in the overall expression.\n#Step 3:\nCurrent expression: (38*y)*(-38) + (-y**3)*(26*y**3 + 38*y) + (26*y**3)*(-38)\nSimplifying the partial expression: (-y**3)*(26*y**3 + 38*y)\nExpanding the part (26*y**3 + 38*y) using the distributive property, and we got: (38*y)*(-y**3) + (-y**3)*(26*y**3)\nReplacing (-y**3)*(26*y**3 + 38*y) with (38*y)*(-y**3) + (-y**3)*(26*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (38*y)*(-y**3) + (38*y)*(-38) + (-y**3)*(26*y**3) + (26*y**3)*(-38)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (26*y**3)*-38 = -988*y**3\n (26*y**3)*(-y**3) = -26*y**6\n (38*y)*-38 = -1444*y\n (38*y)*(-y**3) = -38*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -26*y**6 - 38*y**4 - 988*y**3 - 1444*y\nNo more calculations needed.\n-26*y**6 - 38*y**4 - 988*y**3 - 1444*y", "generated_answer": "-26*y**6 - 38*y**4 - 988*y**3 - 1444*y", "step_length": 5} {"cot_id": "ac261c813265bd3bcc7d717990db27295dd6a916d9295c9cbea7f7c2ba35e17b", "datapoint": {"question": "Simplify this expression: (47*z**2 - 15)*(11*z**3 - 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "517*z**5 - 165*z**3 - 1504*z**2 + 480", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1987, "polynomial_expr": "(47*z**2 - 15)*(11*z**3 - 32)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (47*z**2 - 15)*(11*z**3 - 32)\nExpanding the part (11*z**3 - 32) using the distributive property, and we got: (11*z**3)*(47*z**2 - 15) - 32*(47*z**2 - 15)\n#Step 2:\nCurrent expression: (11*z**3)*(47*z**2 - 15) - 32*(47*z**2 - 15)\nSimplifying the partial expression: -32*(47*z**2 - 15)\nExpanding the part (47*z**2 - 15) using the distributive property, and we got: (47*z**2)*(-32) - 15*(-32)\nReplacing -32*(47*z**2 - 15) with (47*z**2)*(-32) - 15*(-32) in the overall expression.\n#Step 3:\nCurrent expression: (47*z**2)*(-32) + (11*z**3)*(47*z**2 - 15) + 480\nSimplifying the partial expression: (11*z**3)*(47*z**2 - 15)\nExpanding the part (47*z**2 - 15) using the distributive property, and we got: -165*z**3 + (47*z**2)*(11*z**3)\nReplacing (11*z**3)*(47*z**2 - 15) with -165*z**3 + (47*z**2)*(11*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -15*11*z**3 + (47*z**2)*(11*z**3) + (47*z**2)*(-32) + 480\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (47*z**2)*-32 = -1504*z**2\n (47*z**2)*(11*z**3) = 517*z**5\n -15*11*z**3 = -165*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 517*z**5 - 165*z**3 - 1504*z**2 + 480\nNo more calculations needed.\n517*z**5 - 165*z**3 - 1504*z**2 + 480", "generated_answer": "517*z**5 - 165*z**3 - 1504*z**2 + 480", "step_length": 5} {"cot_id": "5398093bf7b2b3b4a3c52dd480ece659f073c3d65afc9a7c4dcccd66461e3c88", "datapoint": {"question": "Simplify this expression: (-33*y**3 - 30*y**2 + 9*y)*(28*y**3 - 20*y**2 - 25*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-924*y**6 - 180*y**5 + 1677*y**4 + 570*y**3 - 225*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1988, "polynomial_expr": "(-33*y**3 - 30*y**2 + 9*y)*(28*y**3 - 20*y**2 - 25*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-33*y**3 - 30*y**2 + 9*y)*(28*y**3 - 20*y**2 - 25*y)\nExpanding the part (-33*y**3 - 30*y**2 + 9*y) using the distributive property, and we got: (9*y)*(28*y**3 - 20*y**2 - 25*y) + (-30*y**2)*(28*y**3 - 20*y**2 - 25*y) + (-33*y**3)*(28*y**3 - 20*y**2 - 25*y)\n#Step 2:\nCurrent expression: (9*y)*(28*y**3 - 20*y**2 - 25*y) + (-30*y**2)*(28*y**3 - 20*y**2 - 25*y) + (-33*y**3)*(28*y**3 - 20*y**2 - 25*y)\nSimplifying the partial expression: (-33*y**3)*(28*y**3 - 20*y**2 - 25*y)\nExpanding the part (28*y**3 - 20*y**2 - 25*y) using the distributive property, and we got: (-25*y)*(-33*y**3) + (-20*y**2)*(-33*y**3) + (-33*y**3)*(28*y**3)\nReplacing (-33*y**3)*(28*y**3 - 20*y**2 - 25*y) with (-25*y)*(-33*y**3) + (-20*y**2)*(-33*y**3) + (-33*y**3)*(28*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-25*y)*(-33*y**3) + (9*y)*(28*y**3 - 20*y**2 - 25*y) + (-30*y**2)*(28*y**3 - 20*y**2 - 25*y) + (-20*y**2)*(-33*y**3) + (-33*y**3)*(28*y**3)\nSimplifying the partial expression: (-30*y**2)*(28*y**3 - 20*y**2 - 25*y)\nExpanding the part (28*y**3 - 20*y**2 - 25*y) using the distributive property, and we got: (-25*y)*(-30*y**2) + (-30*y**2)*(-20*y**2) + (-30*y**2)*(28*y**3)\nReplacing (-30*y**2)*(28*y**3 - 20*y**2 - 25*y) with (-25*y)*(-30*y**2) + (-30*y**2)*(-20*y**2) + (-30*y**2)*(28*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-25*y)*(-30*y**2) + (-25*y)*(-33*y**3) + (9*y)*(28*y**3 - 20*y**2 - 25*y) + (-30*y**2)*(-20*y**2) + (-30*y**2)*(28*y**3) + (-20*y**2)*(-33*y**3) + (-33*y**3)*(28*y**3)\nSimplifying the partial expression: (9*y)*(28*y**3 - 20*y**2 - 25*y)\nExpanding the part (28*y**3 - 20*y**2 - 25*y) using the distributive property, and we got: (-25*y)*(9*y) + (9*y)*(-20*y**2) + (9*y)*(28*y**3)\nReplacing (9*y)*(28*y**3 - 20*y**2 - 25*y) with (-25*y)*(9*y) + (9*y)*(-20*y**2) + (9*y)*(28*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-25*y)*(9*y) + (-25*y)*(-30*y**2) + (-25*y)*(-33*y**3) + (9*y)*(-20*y**2) + (9*y)*(28*y**3) + (-30*y**2)*(-20*y**2) + (-30*y**2)*(28*y**3) + (-20*y**2)*(-33*y**3) + (-33*y**3)*(28*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-25*y)*(-33*y**3) = 825*y**4\n (-25*y)*(-30*y**2) = 750*y**3\n (-25*y)*(9*y) = -225*y**2\n (-20*y**2)*(-33*y**3) = 660*y**5\n (-20*y**2)*(-30*y**2) = 600*y**4\n (-20*y**2)*(9*y) = -180*y**3\n (28*y**3)*(-33*y**3) = -924*y**6\n (28*y**3)*(-30*y**2) = -840*y**5\n (28*y**3)*(9*y) = 252*y**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -924*y**6 - 840*y**5 + 660*y**5 + 252*y**4 + 600*y**4 + 825*y**4 - 180*y**3 + 750*y**3 - 225*y**2\nCombining like terms, got -924*y**6 - 180*y**5 + 1677*y**4 + 570*y**3 - 225*y**2\n#Step 7:\nCurrent expression: -924*y**6 - 180*y**5 + 1677*y**4 + 570*y**3 - 225*y**2\nNo more calculations needed.\n-924*y**6 - 180*y**5 + 1677*y**4 + 570*y**3 - 225*y**2", "generated_answer": "-924*y**6 - 180*y**5 + 1677*y**4 + 570*y**3 - 225*y**2", "step_length": 7} {"cot_id": "5ad328359107b6ec007d00f0e440b5f713675f0acce670df55853dba737d2ef2", "datapoint": {"question": "Calculate the following: (-13*z**2 - 13*z)*(-19*z**2 + 24*z - 29)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "247*z**4 - 65*z**3 + 65*z**2 + 377*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1989, "polynomial_expr": "(-13*z**2 - 13*z)*(-19*z**2 + 24*z - 29)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-13*z**2 - 13*z)*(-19*z**2 + 24*z - 29)\nExpanding the part (-13*z**2 - 13*z) using the distributive property, and we got: (-13*z)*(-19*z**2 + 24*z - 29) + (-13*z**2)*(-19*z**2 + 24*z - 29)\n#Step 2:\nCurrent expression: (-13*z)*(-19*z**2 + 24*z - 29) + (-13*z**2)*(-19*z**2 + 24*z - 29)\nSimplifying the partial expression: (-13*z)*(-19*z**2 + 24*z - 29)\nExpanding the part (-19*z**2 + 24*z - 29) using the distributive property, and we got: (-13*z)*(24*z) + (-13*z)*(-19*z**2) - (-1)*377*z\nReplacing (-13*z)*(-19*z**2 + 24*z - 29) with (-13*z)*(24*z) + (-13*z)*(-19*z**2) - (-1)*377*z in the overall expression.\n#Step 3:\nCurrent expression: (-13*z)*(24*z) + (-13*z)*(-19*z**2) - 29*(-13)*z + (-13*z**2)*(-19*z**2 + 24*z - 29)\nSimplifying the partial expression: (-13*z**2)*(-19*z**2 + 24*z - 29)\nExpanding the part (-19*z**2 + 24*z - 29) using the distributive property, and we got: -(-1)*377*z**2 + (24*z)*(-13*z**2) + (-19*z**2)*(-13*z**2)\nReplacing (-13*z**2)*(-19*z**2 + 24*z - 29) with -(-1)*377*z**2 + (24*z)*(-13*z**2) + (-19*z**2)*(-13*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-13*z)*(24*z) + (-13*z)*(-19*z**2) - 29*(-13)*z**2 - 29*(-13)*z + (24*z)*(-13*z**2) + (-19*z**2)*(-13*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*z**2)*(-13*z) = 247*z**3\n (-19*z**2)*(-13*z**2) = 247*z**4\n (24*z)*(-13*z) = -312*z**2\n (24*z)*(-13*z**2) = -312*z**3\n -29*-13*z = 377*z\n -29*-13*z**2 = 377*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 247*z**4 - 312*z**3 + 247*z**3 - 312*z**2 + 377*z**2 + 377*z\nCombining like terms, got 247*z**4 - 65*z**3 + 65*z**2 + 377*z\n#Step 6:\nCurrent expression: 247*z**4 - 65*z**3 + 65*z**2 + 377*z\nNo more calculations needed.\n247*z**4 - 65*z**3 + 65*z**2 + 377*z", "generated_answer": "247*z**4 - 65*z**3 + 65*z**2 + 377*z", "step_length": 6} {"cot_id": "8f74fb46e0b1c28fe56628d3872e6acec0cd386d1b330a824f92b807bb841add", "datapoint": {"question": "Calculate the following: -546*x**2 - 234\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-546*x**2 - 234", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1990, "polynomial_expr": "-546*x**2 - 234", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -546*x**2 - 234\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -546*x**2 - 234\nNo more calculations needed.\n-546*x**2 - 234", "generated_answer": "-546*x**2 - 234", "step_length": 2} {"cot_id": "7d1748a659a9ffc1b1846338f0ee9b5b3f3ad03d4a382848d9d32dab8da24ab2", "datapoint": {"question": "Simplify this expression: (48*y + 26)*(56*y**3 + 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2688*y**4 + 1456*y**3 + 288*y + 156", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1991, "polynomial_expr": "(48*y + 26)*(56*y**3 + 6)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (48*y + 26)*(56*y**3 + 6)\nExpanding the part (56*y**3 + 6) using the distributive property, and we got: (56*y**3)*(48*y + 26) + 6*(48*y + 26)\n#Step 2:\nCurrent expression: (56*y**3)*(48*y + 26) + 6*(48*y + 26)\nSimplifying the partial expression: 6*(48*y + 26)\nExpanding the part (48*y + 26) using the distributive property, and we got: (48*y)*6 + 26*6\nReplacing 6*(48*y + 26) with (48*y)*6 + 26*6 in the overall expression.\n#Step 3:\nCurrent expression: (48*y)*6 + (56*y**3)*(48*y + 26) + 156\nSimplifying the partial expression: (56*y**3)*(48*y + 26)\nExpanding the part (48*y + 26) using the distributive property, and we got: 26*(56*y**3) + (48*y)*(56*y**3)\nReplacing (56*y**3)*(48*y + 26) with 26*(56*y**3) + (48*y)*(56*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 26*56*y**3 + (48*y)*(56*y**3) + (48*y)*6 + 156\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (48*y)*6 = 288*y\n (48*y)*(56*y**3) = 2688*y**4\n 26*56*y**3 = 1456*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2688*y**4 + 1456*y**3 + 288*y + 156\nNo more calculations needed.\n2688*y**4 + 1456*y**3 + 288*y + 156", "generated_answer": "2688*y**4 + 1456*y**3 + 288*y + 156", "step_length": 5} {"cot_id": "b711edbbe1b8fc2886669910facd3ee720de5faed42cdd9cdf33527a524028ff", "datapoint": {"question": "Calculate the following: (x**2 + 14*x)*(x**3 - 59*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "x**5 + 14*x**4 - 59*x**3 - 826*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1992, "polynomial_expr": "(x**2 + 14*x)*(x**3 - 59*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (x**2 + 14*x)*(x**3 - 59*x)\nExpanding the part (x**2 + 14*x) using the distributive property, and we got: x**2*(x**3 - 59*x) + (14*x)*(x**3 - 59*x)\n#Step 2:\nCurrent expression: x**2*(x**3 - 59*x) + (14*x)*(x**3 - 59*x)\nSimplifying the partial expression: x**2*(x**3 - 59*x)\nExpanding the part (x**3 - 59*x) using the distributive property, and we got: (-59*x)*x**2 + x**2*x**3\nReplacing x**2*(x**3 - 59*x) with (-59*x)*x**2 + x**2*x**3 in the overall expression.\n#Step 3:\nCurrent expression: (-59*x)*x**2 + x**2*x**3 + (14*x)*(x**3 - 59*x)\nSimplifying the partial expression: (14*x)*(x**3 - 59*x)\nExpanding the part (x**3 - 59*x) using the distributive property, and we got: (-59*x)*(14*x) + (14*x)*x**3\nReplacing (14*x)*(x**3 - 59*x) with (-59*x)*(14*x) + (14*x)*x**3 in the overall expression.\n#Step 4:\nCurrent expression: (-59*x)*x**2 + (-59*x)*(14*x) + (14*x)*x**3 + x**2*x**3\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n x**3*x**2 = x**5\n x**3*(14*x) = 14*x**4\n (-59*x)*x**2 = -59*x**3\n (-59*x)*(14*x) = -826*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: x**5 + 14*x**4 - 59*x**3 - 826*x**2\nNo more calculations needed.\nx**5 + 14*x**4 - 59*x**3 - 826*x**2", "generated_answer": "x**5 + 14*x**4 - 59*x**3 - 826*x**2", "step_length": 5} {"cot_id": "ed295c911cd45b4c8a99bcc5945d7c4fc978a1ba0ebe1ef8a8e4c2f222058c4d", "datapoint": {"question": "Calculate the following: (-47*y**3 + 3*y**2)*(32*y**3 + 5*y - 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1504*y**6 + 96*y**5 - 235*y**4 + 1472*y**3 - 93*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1993, "polynomial_expr": "(-47*y**3 + 3*y**2)*(32*y**3 + 5*y - 31)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-47*y**3 + 3*y**2)*(32*y**3 + 5*y - 31)\nExpanding the part (-47*y**3 + 3*y**2) using the distributive property, and we got: (3*y**2)*(32*y**3 + 5*y - 31) + (-47*y**3)*(32*y**3 + 5*y - 31)\n#Step 2:\nCurrent expression: (3*y**2)*(32*y**3 + 5*y - 31) + (-47*y**3)*(32*y**3 + 5*y - 31)\nSimplifying the partial expression: (-47*y**3)*(32*y**3 + 5*y - 31)\nExpanding the part (32*y**3 + 5*y - 31) using the distributive property, and we got: -(-1)*1457*y**3 + (5*y)*(-47*y**3) + (-47*y**3)*(32*y**3)\nReplacing (-47*y**3)*(32*y**3 + 5*y - 31) with -(-1)*1457*y**3 + (5*y)*(-47*y**3) + (-47*y**3)*(32*y**3) in the overall expression.\n#Step 3:\nCurrent expression: -31*(-47)*y**3 + (5*y)*(-47*y**3) + (3*y**2)*(32*y**3 + 5*y - 31) + (-47*y**3)*(32*y**3)\nSimplifying the partial expression: (3*y**2)*(32*y**3 + 5*y - 31)\nExpanding the part (32*y**3 + 5*y - 31) using the distributive property, and we got: -93*y**2 + (5*y)*(3*y**2) + (3*y**2)*(32*y**3)\nReplacing (3*y**2)*(32*y**3 + 5*y - 31) with -93*y**2 + (5*y)*(3*y**2) + (3*y**2)*(32*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -31*(-47)*y**3 - 31*3*y**2 + (5*y)*(3*y**2) + (5*y)*(-47*y**3) + (3*y**2)*(32*y**3) + (-47*y**3)*(32*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (5*y)*(-47*y**3) = -235*y**4\n (5*y)*(3*y**2) = 15*y**3\n (32*y**3)*(-47*y**3) = -1504*y**6\n (32*y**3)*(3*y**2) = 96*y**5\n -31*-47*y**3 = 1457*y**3\n -31*3*y**2 = -93*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1504*y**6 + 96*y**5 - 235*y**4 + 15*y**3 + 1457*y**3 - 93*y**2\nCombining like terms, got -1504*y**6 + 96*y**5 - 235*y**4 + 1472*y**3 - 93*y**2\n#Step 6:\nCurrent expression: -1504*y**6 + 96*y**5 - 235*y**4 + 1472*y**3 - 93*y**2\nNo more calculations needed.\n-1504*y**6 + 96*y**5 - 235*y**4 + 1472*y**3 - 93*y**2", "generated_answer": "-1504*y**6 + 96*y**5 - 235*y**4 + 1472*y**3 - 93*y**2", "step_length": 6} {"cot_id": "4352d5ebe608d0eca9dd71acb0932f525e6307796f33e35842f7fb44d1b02f97", "datapoint": {"question": "Simplify this expression: -4*x*(-6*x**3 - 44*x - 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "24*x**4 + 176*x**2 + 56*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1994, "polynomial_expr": "-4*x*(-6*x**3 - 44*x - 14)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -4*x*(-6*x**3 - 44*x - 14)\nExpanding the part (-6*x**3 - 44*x - 14) using the distributive property, and we got: (-44*x)*(-4*x) + (-4*x)*(-6*x**3) - (-1)*56*x\n#Step 2:\nCurrent expression: (-44*x)*(-4*x) + (-4*x)*(-6*x**3) - (-1)*56*x\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -14*(-4*x) = 56*x\n (-44*x)*(-4*x) = 176*x**2\n (-6*x**3)*(-4*x) = 24*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 24*x**4 + 176*x**2 + 56*x\nNo more calculations needed.\n24*x**4 + 176*x**2 + 56*x", "generated_answer": "24*x**4 + 176*x**2 + 56*x", "step_length": 3} {"cot_id": "8a1923ab64346f104aad4e0b4d1f03d4442bd9d7238da8d8feba431c9f654b29", "datapoint": {"question": "Calculate the following: (25*y**3 + 18*y**2 - 30)*(30*y**3 + 12*y - 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "750*y**6 + 540*y**5 + 300*y**4 - 1859*y**3 - 846*y**2 - 360*y + 1410", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1995, "polynomial_expr": "(25*y**3 + 18*y**2 - 30)*(30*y**3 + 12*y - 47)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (25*y**3 + 18*y**2 - 30)*(30*y**3 + 12*y - 47)\nExpanding the part (30*y**3 + 12*y - 47) using the distributive property, and we got: (12*y)*(25*y**3 + 18*y**2 - 30) + (30*y**3)*(25*y**3 + 18*y**2 - 30) - 47*(25*y**3 + 18*y**2 - 30)\n#Step 2:\nCurrent expression: (12*y)*(25*y**3 + 18*y**2 - 30) + (30*y**3)*(25*y**3 + 18*y**2 - 30) - 47*(25*y**3 + 18*y**2 - 30)\nSimplifying the partial expression: -47*(25*y**3 + 18*y**2 - 30)\nExpanding the part (25*y**3 + 18*y**2 - 30) using the distributive property, and we got: (18*y**2)*(-47) + (25*y**3)*(-47) - 30*(-47)\nReplacing -47*(25*y**3 + 18*y**2 - 30) with (18*y**2)*(-47) + (25*y**3)*(-47) - 30*(-47) in the overall expression.\n#Step 3:\nCurrent expression: (12*y)*(25*y**3 + 18*y**2 - 30) + (18*y**2)*(-47) + (25*y**3)*(-47) + (30*y**3)*(25*y**3 + 18*y**2 - 30) + 1410\nSimplifying the partial expression: (12*y)*(25*y**3 + 18*y**2 - 30)\nExpanding the part (25*y**3 + 18*y**2 - 30) using the distributive property, and we got: -360*y + (12*y)*(18*y**2) + (12*y)*(25*y**3)\nReplacing (12*y)*(25*y**3 + 18*y**2 - 30) with -360*y + (12*y)*(18*y**2) + (12*y)*(25*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -30*12*y + (12*y)*(18*y**2) + (12*y)*(25*y**3) + (18*y**2)*(-47) + (25*y**3)*(-47) + (30*y**3)*(25*y**3 + 18*y**2 - 30) + 1410\nSimplifying the partial expression: (30*y**3)*(25*y**3 + 18*y**2 - 30)\nExpanding the part (25*y**3 + 18*y**2 - 30) using the distributive property, and we got: -900*y**3 + (18*y**2)*(30*y**3) + (25*y**3)*(30*y**3)\nReplacing (30*y**3)*(25*y**3 + 18*y**2 - 30) with -900*y**3 + (18*y**2)*(30*y**3) + (25*y**3)*(30*y**3) in the overall expression.\n#Step 5:\nCurrent expression: -30*30*y**3 - 30*12*y + (12*y)*(18*y**2) + (12*y)*(25*y**3) + (18*y**2)*(30*y**3) + (18*y**2)*(-47) + (25*y**3)*(30*y**3) + (25*y**3)*(-47) + 1410\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (18*y**2)*-47 = -846*y**2\n (18*y**2)*(12*y) = 216*y**3\n (18*y**2)*(30*y**3) = 540*y**5\n (25*y**3)*-47 = -1175*y**3\n (25*y**3)*(12*y) = 300*y**4\n (25*y**3)*(30*y**3) = 750*y**6\n -30*12*y = -360*y\n -30*30*y**3 = -900*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 750*y**6 + 540*y**5 + 300*y**4 - 1175*y**3 - 900*y**3 + 216*y**3 - 846*y**2 - 360*y + 1410\nCombining like terms, got 750*y**6 + 540*y**5 + 300*y**4 - 1859*y**3 - 846*y**2 - 360*y + 1410\n#Step 7:\nCurrent expression: 750*y**6 + 540*y**5 + 300*y**4 - 1859*y**3 - 846*y**2 - 360*y + 1410\nNo more calculations needed.\n750*y**6 + 540*y**5 + 300*y**4 - 1859*y**3 - 846*y**2 - 360*y + 1410", "generated_answer": "750*y**6 + 540*y**5 + 300*y**4 - 1859*y**3 - 846*y**2 - 360*y + 1410", "step_length": 7} {"cot_id": "b9fcce7e46695a175c6f2ea4f5b5baaef713ca5a193aaa5f86f03bb7ea5c93b2", "datapoint": {"question": "Calculate the following: 19*x**3*(-11*x**2 + 7*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-209*x**5 + 133*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1996, "polynomial_expr": "19*x**3*(-11*x**2 + 7*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 19*x**3*(-11*x**2 + 7*x)\nExpanding the part (-11*x**2 + 7*x) using the distributive property, and we got: (7*x)*(19*x**3) + (-11*x**2)*(19*x**3)\n#Step 2:\nCurrent expression: (7*x)*(19*x**3) + (-11*x**2)*(19*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*x**2)*(19*x**3) = -209*x**5\n (7*x)*(19*x**3) = 133*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -209*x**5 + 133*x**4\nNo more calculations needed.\n-209*x**5 + 133*x**4", "generated_answer": "-209*x**5 + 133*x**4", "step_length": 3} {"cot_id": "4bab45d96cf337f09bad81f99705713ee5a1b2e05e71ac14dc19750e53167402", "datapoint": {"question": "Calculate the following: (-46*z**2 + 47*z)*(21*z**3 - z - 82)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-966*z**5 + 987*z**4 + 46*z**3 + 3725*z**2 - 3854*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1997, "polynomial_expr": "(-46*z**2 + 47*z)*(21*z**3 - z - 82)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-46*z**2 + 47*z)*(21*z**3 - z - 82)\nExpanding the part (-46*z**2 + 47*z) using the distributive property, and we got: (47*z)*(21*z**3 - z - 82) + (-46*z**2)*(21*z**3 - z - 82)\n#Step 2:\nCurrent expression: (47*z)*(21*z**3 - z - 82) + (-46*z**2)*(21*z**3 - z - 82)\nSimplifying the partial expression: (-46*z**2)*(21*z**3 - z - 82)\nExpanding the part (21*z**3 - z - 82) using the distributive property, and we got: (-z)*(-46*z**2) - (-1)*3772*z**2 + (-46*z**2)*(21*z**3)\nReplacing (-46*z**2)*(21*z**3 - z - 82) with (-z)*(-46*z**2) - (-1)*3772*z**2 + (-46*z**2)*(21*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-z)*(-46*z**2) - 82*(-46)*z**2 + (47*z)*(21*z**3 - z - 82) + (-46*z**2)*(21*z**3)\nSimplifying the partial expression: (47*z)*(21*z**3 - z - 82)\nExpanding the part (21*z**3 - z - 82) using the distributive property, and we got: (-z)*(47*z) - 3854*z + (47*z)*(21*z**3)\nReplacing (47*z)*(21*z**3 - z - 82) with (-z)*(47*z) - 3854*z + (47*z)*(21*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-z)*(47*z) + (-z)*(-46*z**2) - 82*(-46)*z**2 - 82*47*z + (47*z)*(21*z**3) + (-46*z**2)*(21*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-z)*(-46*z**2) = 46*z**3\n (-z)*(47*z) = -47*z**2\n (21*z**3)*(-46*z**2) = -966*z**5\n (21*z**3)*(47*z) = 987*z**4\n -82*-46*z**2 = 3772*z**2\n -82*47*z = -3854*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -966*z**5 + 987*z**4 + 46*z**3 - 47*z**2 + 3772*z**2 - 3854*z\nCombining like terms, got -966*z**5 + 987*z**4 + 46*z**3 + 3725*z**2 - 3854*z\n#Step 6:\nCurrent expression: -966*z**5 + 987*z**4 + 46*z**3 + 3725*z**2 - 3854*z\nNo more calculations needed.\n-966*z**5 + 987*z**4 + 46*z**3 + 3725*z**2 - 3854*z", "generated_answer": "-966*z**5 + 987*z**4 + 46*z**3 + 3725*z**2 - 3854*z", "step_length": 6} {"cot_id": "0783e99a9d1fd5d505ec712c85078b2ce31580e3977cff1a225bbbed6f3dadd4", "datapoint": {"question": "Calculate the following: (-11*y**3 + 17*y**2 - 33*y)*(y**3 - 23*y + 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-11*y**6 + 17*y**5 + 220*y**4 - 622*y**3 + 1116*y**2 - 693*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1998, "polynomial_expr": "(-11*y**3 + 17*y**2 - 33*y)*(y**3 - 23*y + 21)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-11*y**3 + 17*y**2 - 33*y)*(y**3 - 23*y + 21)\nExpanding the part (y**3 - 23*y + 21) using the distributive property, and we got: (-23*y)*(-11*y**3 + 17*y**2 - 33*y) + y**3*(-11*y**3 + 17*y**2 - 33*y) + 21*(-11*y**3 + 17*y**2 - 33*y)\n#Step 2:\nCurrent expression: (-23*y)*(-11*y**3 + 17*y**2 - 33*y) + y**3*(-11*y**3 + 17*y**2 - 33*y) + 21*(-11*y**3 + 17*y**2 - 33*y)\nSimplifying the partial expression: 21*(-11*y**3 + 17*y**2 - 33*y)\nExpanding the part (-11*y**3 + 17*y**2 - 33*y) using the distributive property, and we got: -33*y*21 + (17*y**2)*21 - 11*y**3*21\nReplacing 21*(-11*y**3 + 17*y**2 - 33*y) with -33*y*21 + (17*y**2)*21 - 11*y**3*21 in the overall expression.\n#Step 3:\nCurrent expression: -33*y*21 + (-23*y)*(-11*y**3 + 17*y**2 - 33*y) + y**3*(-11*y**3 + 17*y**2 - 33*y) + (17*y**2)*21 - 11*y**3*21\nSimplifying the partial expression: y**3*(-11*y**3 + 17*y**2 - 33*y)\nExpanding the part (-11*y**3 + 17*y**2 - 33*y) using the distributive property, and we got: (-33*y)*y**3 + (17*y**2)*y**3 + (-11*y**3)*y**3\nReplacing y**3*(-11*y**3 + 17*y**2 - 33*y) with (-33*y)*y**3 + (17*y**2)*y**3 + (-11*y**3)*y**3 in the overall expression.\n#Step 4:\nCurrent expression: (-33*y)*y**3 - 33*y*21 + (-23*y)*(-11*y**3 + 17*y**2 - 33*y) + (17*y**2)*y**3 + (-11*y**3)*y**3 + (17*y**2)*21 - 11*y**3*21\nSimplifying the partial expression: (-23*y)*(-11*y**3 + 17*y**2 - 33*y)\nExpanding the part (-11*y**3 + 17*y**2 - 33*y) using the distributive property, and we got: (-33*y)*(-23*y) + (-23*y)*(17*y**2) + (-23*y)*(-11*y**3)\nReplacing (-23*y)*(-11*y**3 + 17*y**2 - 33*y) with (-33*y)*(-23*y) + (-23*y)*(17*y**2) + (-23*y)*(-11*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-33*y)*(-23*y) + (-33*y)*y**3 - 33*y*21 + (-23*y)*(17*y**2) + (-23*y)*(-11*y**3) + (17*y**2)*y**3 + (-11*y**3)*y**3 + (17*y**2)*21 - 11*y**3*21\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*y)*21 = -693*y\n (-33*y)*y**3 = -33*y**4\n (-33*y)*(-23*y) = 759*y**2\n (-11*y**3)*21 = -231*y**3\n (-11*y**3)*y**3 = -11*y**6\n (-11*y**3)*(-23*y) = 253*y**4\n (17*y**2)*21 = 357*y**2\n (17*y**2)*y**3 = 17*y**5\n (17*y**2)*(-23*y) = -391*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -11*y**6 + 17*y**5 - 33*y**4 + 253*y**4 - 391*y**3 - 231*y**3 + 357*y**2 + 759*y**2 - 693*y\nCombining like terms, got -11*y**6 + 17*y**5 + 220*y**4 - 622*y**3 + 1116*y**2 - 693*y\n#Step 7:\nCurrent expression: -11*y**6 + 17*y**5 + 220*y**4 - 622*y**3 + 1116*y**2 - 693*y\nNo more calculations needed.\n-11*y**6 + 17*y**5 + 220*y**4 - 622*y**3 + 1116*y**2 - 693*y", "generated_answer": "-11*y**6 + 17*y**5 + 220*y**4 - 622*y**3 + 1116*y**2 - 693*y", "step_length": 7} {"cot_id": "269c73fbaaae524b348c1f7e3c19aadbfc12a937996c399c39ea7d804ea95a01", "datapoint": {"question": "Calculate the following: (17*x**2 - 66)*(25*x**3 + 18*x**2 + 34)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "425*x**5 + 306*x**4 - 1650*x**3 - 610*x**2 - 2244", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 1999, "polynomial_expr": "(17*x**2 - 66)*(25*x**3 + 18*x**2 + 34)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (17*x**2 - 66)*(25*x**3 + 18*x**2 + 34)\nExpanding the part (17*x**2 - 66) using the distributive property, and we got: (17*x**2)*(25*x**3 + 18*x**2 + 34) - 66*(25*x**3 + 18*x**2 + 34)\n#Step 2:\nCurrent expression: (17*x**2)*(25*x**3 + 18*x**2 + 34) - 66*(25*x**3 + 18*x**2 + 34)\nSimplifying the partial expression: -66*(25*x**3 + 18*x**2 + 34)\nExpanding the part (25*x**3 + 18*x**2 + 34) using the distributive property, and we got: (18*x**2)*(-66) + (25*x**3)*(-66) + 34*(-66)\nReplacing -66*(25*x**3 + 18*x**2 + 34) with (18*x**2)*(-66) + (25*x**3)*(-66) + 34*(-66) in the overall expression.\n#Step 3:\nCurrent expression: (17*x**2)*(25*x**3 + 18*x**2 + 34) + (18*x**2)*(-66) + (25*x**3)*(-66) - 2244\nSimplifying the partial expression: (17*x**2)*(25*x**3 + 18*x**2 + 34)\nExpanding the part (25*x**3 + 18*x**2 + 34) using the distributive property, and we got: 34*(17*x**2) + (17*x**2)*(18*x**2) + (17*x**2)*(25*x**3)\nReplacing (17*x**2)*(25*x**3 + 18*x**2 + 34) with 34*(17*x**2) + (17*x**2)*(18*x**2) + (17*x**2)*(25*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 34*17*x**2 + (17*x**2)*(18*x**2) + (17*x**2)*(25*x**3) + (18*x**2)*(-66) + (25*x**3)*(-66) - 2244\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (18*x**2)*-66 = -1188*x**2\n (18*x**2)*(17*x**2) = 306*x**4\n (25*x**3)*-66 = -1650*x**3\n (25*x**3)*(17*x**2) = 425*x**5\n 34*17*x**2 = 578*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 425*x**5 + 306*x**4 - 1650*x**3 - 1188*x**2 + 578*x**2 - 2244\nCombining like terms, got 425*x**5 + 306*x**4 - 1650*x**3 - 610*x**2 - 2244\n#Step 6:\nCurrent expression: 425*x**5 + 306*x**4 - 1650*x**3 - 610*x**2 - 2244\nNo more calculations needed.\n425*x**5 + 306*x**4 - 1650*x**3 - 610*x**2 - 2244", "generated_answer": "425*x**5 + 306*x**4 - 1650*x**3 - 610*x**2 - 2244", "step_length": 6} {"cot_id": "aa688d4f64385bd8058903c04490522e59fcc6dc4b077e63376918d77535f8d8", "datapoint": {"question": "Calculate the following: (22*y**2 + 45*y + 20)*(-45*y**3 - 13*y**2 - 10*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-990*y**5 - 2311*y**4 - 1705*y**3 - 710*y**2 - 200*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2000, "polynomial_expr": "(22*y**2 + 45*y + 20)*(-45*y**3 - 13*y**2 - 10*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (22*y**2 + 45*y + 20)*(-45*y**3 - 13*y**2 - 10*y)\nExpanding the part (22*y**2 + 45*y + 20) using the distributive property, and we got: (45*y)*(-45*y**3 - 13*y**2 - 10*y) + (22*y**2)*(-45*y**3 - 13*y**2 - 10*y) + 20*(-45*y**3 - 13*y**2 - 10*y)\n#Step 2:\nCurrent expression: (45*y)*(-45*y**3 - 13*y**2 - 10*y) + (22*y**2)*(-45*y**3 - 13*y**2 - 10*y) + 20*(-45*y**3 - 13*y**2 - 10*y)\nSimplifying the partial expression: 20*(-45*y**3 - 13*y**2 - 10*y)\nExpanding the part (-45*y**3 - 13*y**2 - 10*y) using the distributive property, and we got: -10*y*20 - 13*y**2*20 - 45*y**3*20\nReplacing 20*(-45*y**3 - 13*y**2 - 10*y) with -10*y*20 - 13*y**2*20 - 45*y**3*20 in the overall expression.\n#Step 3:\nCurrent expression: -10*y*20 + (45*y)*(-45*y**3 - 13*y**2 - 10*y) - 13*y**2*20 + (22*y**2)*(-45*y**3 - 13*y**2 - 10*y) - 45*y**3*20\nSimplifying the partial expression: (22*y**2)*(-45*y**3 - 13*y**2 - 10*y)\nExpanding the part (-45*y**3 - 13*y**2 - 10*y) using the distributive property, and we got: (-10*y)*(22*y**2) + (-13*y**2)*(22*y**2) + (22*y**2)*(-45*y**3)\nReplacing (22*y**2)*(-45*y**3 - 13*y**2 - 10*y) with (-10*y)*(22*y**2) + (-13*y**2)*(22*y**2) + (22*y**2)*(-45*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-10*y)*(22*y**2) - 10*y*20 + (45*y)*(-45*y**3 - 13*y**2 - 10*y) + (-13*y**2)*(22*y**2) - 13*y**2*20 + (22*y**2)*(-45*y**3) - 45*y**3*20\nSimplifying the partial expression: (45*y)*(-45*y**3 - 13*y**2 - 10*y)\nExpanding the part (-45*y**3 - 13*y**2 - 10*y) using the distributive property, and we got: (-10*y)*(45*y) + (45*y)*(-13*y**2) + (45*y)*(-45*y**3)\nReplacing (45*y)*(-45*y**3 - 13*y**2 - 10*y) with (-10*y)*(45*y) + (45*y)*(-13*y**2) + (45*y)*(-45*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-10*y)*(45*y) + (-10*y)*(22*y**2) - 10*y*20 + (45*y)*(-13*y**2) + (45*y)*(-45*y**3) + (-13*y**2)*(22*y**2) - 13*y**2*20 + (22*y**2)*(-45*y**3) - 45*y**3*20\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*y**3)*20 = -900*y**3\n (-45*y**3)*(22*y**2) = -990*y**5\n (-45*y**3)*(45*y) = -2025*y**4\n (-13*y**2)*20 = -260*y**2\n (-13*y**2)*(22*y**2) = -286*y**4\n (-13*y**2)*(45*y) = -585*y**3\n (-10*y)*20 = -200*y\n (-10*y)*(22*y**2) = -220*y**3\n (-10*y)*(45*y) = -450*y**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -990*y**5 - 2025*y**4 - 286*y**4 - 900*y**3 - 585*y**3 - 220*y**3 - 450*y**2 - 260*y**2 - 200*y\nCombining like terms, got -990*y**5 - 2311*y**4 - 1705*y**3 - 710*y**2 - 200*y\n#Step 7:\nCurrent expression: -990*y**5 - 2311*y**4 - 1705*y**3 - 710*y**2 - 200*y\nNo more calculations needed.\n-990*y**5 - 2311*y**4 - 1705*y**3 - 710*y**2 - 200*y", "generated_answer": "-990*y**5 - 2311*y**4 - 1705*y**3 - 710*y**2 - 200*y", "step_length": 7} {"cot_id": "471e414c37a92594ad1dbfa324c7de3e5c9f1faeec572cdf709b6453b4f0845f", "datapoint": {"question": "Simplify this expression: (-20*y**2 + 30*y + 33)*(43*y**3 - 28*y**2 - 43)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-860*y**5 + 1850*y**4 + 579*y**3 - 64*y**2 - 1290*y - 1419", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2001, "polynomial_expr": "(-20*y**2 + 30*y + 33)*(43*y**3 - 28*y**2 - 43)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-20*y**2 + 30*y + 33)*(43*y**3 - 28*y**2 - 43)\nExpanding the part (43*y**3 - 28*y**2 - 43) using the distributive property, and we got: (-28*y**2)*(-20*y**2 + 30*y + 33) + (43*y**3)*(-20*y**2 + 30*y + 33) - 43*(-20*y**2 + 30*y + 33)\n#Step 2:\nCurrent expression: (-28*y**2)*(-20*y**2 + 30*y + 33) + (43*y**3)*(-20*y**2 + 30*y + 33) - 43*(-20*y**2 + 30*y + 33)\nSimplifying the partial expression: -43*(-20*y**2 + 30*y + 33)\nExpanding the part (-20*y**2 + 30*y + 33) using the distributive property, and we got: (30*y)*(-43) - 20*y**2*(-43) + 33*(-43)\nReplacing -43*(-20*y**2 + 30*y + 33) with (30*y)*(-43) - 20*y**2*(-43) + 33*(-43) in the overall expression.\n#Step 3:\nCurrent expression: (30*y)*(-43) + (-28*y**2)*(-20*y**2 + 30*y + 33) - 20*y**2*(-43) + (43*y**3)*(-20*y**2 + 30*y + 33) - 1419\nSimplifying the partial expression: (-28*y**2)*(-20*y**2 + 30*y + 33)\nExpanding the part (-20*y**2 + 30*y + 33) using the distributive property, and we got: 33*(-28*y**2) + (30*y)*(-28*y**2) + (-28*y**2)*(-20*y**2)\nReplacing (-28*y**2)*(-20*y**2 + 30*y + 33) with 33*(-28*y**2) + (30*y)*(-28*y**2) + (-28*y**2)*(-20*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 33*(-28)*y**2 + (30*y)*(-28*y**2) + (30*y)*(-43) + (-28*y**2)*(-20*y**2) - 20*y**2*(-43) + (43*y**3)*(-20*y**2 + 30*y + 33) - 1419\nSimplifying the partial expression: (43*y**3)*(-20*y**2 + 30*y + 33)\nExpanding the part (-20*y**2 + 30*y + 33) using the distributive property, and we got: 33*(43*y**3) + (30*y)*(43*y**3) + (-20*y**2)*(43*y**3)\nReplacing (43*y**3)*(-20*y**2 + 30*y + 33) with 33*(43*y**3) + (30*y)*(43*y**3) + (-20*y**2)*(43*y**3) in the overall expression.\n#Step 5:\nCurrent expression: 33*43*y**3 + 33*(-28)*y**2 + (30*y)*(-28*y**2) + (30*y)*(43*y**3) + (30*y)*(-43) + (-28*y**2)*(-20*y**2) + (-20*y**2)*(43*y**3) - 20*y**2*(-43) - 1419\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*y**2)*-43 = 860*y**2\n (-20*y**2)*(-28*y**2) = 560*y**4\n (-20*y**2)*(43*y**3) = -860*y**5\n (30*y)*-43 = -1290*y\n (30*y)*(-28*y**2) = -840*y**3\n (30*y)*(43*y**3) = 1290*y**4\n 33*-28*y**2 = -924*y**2\n 33*43*y**3 = 1419*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -860*y**5 + 560*y**4 + 1290*y**4 - 840*y**3 + 1419*y**3 - 924*y**2 + 860*y**2 - 1290*y - 1419\nCombining like terms, got -860*y**5 + 1850*y**4 + 579*y**3 - 64*y**2 - 1290*y - 1419\n#Step 7:\nCurrent expression: -860*y**5 + 1850*y**4 + 579*y**3 - 64*y**2 - 1290*y - 1419\nNo more calculations needed.\n-860*y**5 + 1850*y**4 + 579*y**3 - 64*y**2 - 1290*y - 1419", "generated_answer": "-860*y**5 + 1850*y**4 + 579*y**3 - 64*y**2 - 1290*y - 1419", "step_length": 7} {"cot_id": "3dc16f056ebaaa7f8225ceb9c071aac22bbc10c0a3ee080bcf39fa6417097a0c", "datapoint": {"question": "Calculate the following: (-34*x**2 + 4*x)*(39*x**3 - 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1326*x**5 + 156*x**4 + 442*x**2 - 52*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2002, "polynomial_expr": "(-34*x**2 + 4*x)*(39*x**3 - 13)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-34*x**2 + 4*x)*(39*x**3 - 13)\nExpanding the part (39*x**3 - 13) using the distributive property, and we got: (39*x**3)*(-34*x**2 + 4*x) - 13*(-34*x**2 + 4*x)\n#Step 2:\nCurrent expression: (39*x**3)*(-34*x**2 + 4*x) - 13*(-34*x**2 + 4*x)\nSimplifying the partial expression: -13*(-34*x**2 + 4*x)\nExpanding the part (-34*x**2 + 4*x) using the distributive property, and we got: (4*x)*(-13) - 34*x**2*(-13)\nReplacing -13*(-34*x**2 + 4*x) with (4*x)*(-13) - 34*x**2*(-13) in the overall expression.\n#Step 3:\nCurrent expression: (4*x)*(-13) - 34*x**2*(-13) + (39*x**3)*(-34*x**2 + 4*x)\nSimplifying the partial expression: (39*x**3)*(-34*x**2 + 4*x)\nExpanding the part (-34*x**2 + 4*x) using the distributive property, and we got: (4*x)*(39*x**3) + (-34*x**2)*(39*x**3)\nReplacing (39*x**3)*(-34*x**2 + 4*x) with (4*x)*(39*x**3) + (-34*x**2)*(39*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (4*x)*(39*x**3) + (4*x)*(-13) + (-34*x**2)*(39*x**3) - 34*x**2*(-13)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*x**2)*-13 = 442*x**2\n (-34*x**2)*(39*x**3) = -1326*x**5\n (4*x)*-13 = -52*x\n (4*x)*(39*x**3) = 156*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1326*x**5 + 156*x**4 + 442*x**2 - 52*x\nNo more calculations needed.\n-1326*x**5 + 156*x**4 + 442*x**2 - 52*x", "generated_answer": "-1326*x**5 + 156*x**4 + 442*x**2 - 52*x", "step_length": 5} {"cot_id": "0f2f32b15fd60f3c8023479dc459a0a56452e65cbec171a61391db22b11ad965", "datapoint": {"question": "Simplify this expression: -495*x**3 + 88*x**2 - 385*x\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-495*x**3 + 88*x**2 - 385*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2003, "polynomial_expr": "-495*x**3 + 88*x**2 - 385*x", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -495*x**3 + 88*x**2 - 385*x\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -495*x**3 + 88*x**2 - 385*x\nNo more calculations needed.\n-495*x**3 + 88*x**2 - 385*x", "generated_answer": "-495*x**3 + 88*x**2 - 385*x", "step_length": 2} {"cot_id": "d8bc53868847c300cf7d8ceff4d5a5eaa876877a4a70648a8b55babca30ec88c", "datapoint": {"question": "Simplify this expression: (2*z**2 - 35*z)*(-50*z**3 - 40*z**2 + z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-100*z**5 + 1670*z**4 + 1402*z**3 - 35*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2004, "polynomial_expr": "(2*z**2 - 35*z)*(-50*z**3 - 40*z**2 + z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2*z**2 - 35*z)*(-50*z**3 - 40*z**2 + z)\nExpanding the part (2*z**2 - 35*z) using the distributive property, and we got: (-35*z)*(-50*z**3 - 40*z**2 + z) + (2*z**2)*(-50*z**3 - 40*z**2 + z)\n#Step 2:\nCurrent expression: (-35*z)*(-50*z**3 - 40*z**2 + z) + (2*z**2)*(-50*z**3 - 40*z**2 + z)\nSimplifying the partial expression: (-35*z)*(-50*z**3 - 40*z**2 + z)\nExpanding the part (-50*z**3 - 40*z**2 + z) using the distributive property, and we got: (-35*z)*z + (-35*z)*(-40*z**2) + (-35*z)*(-50*z**3)\nReplacing (-35*z)*(-50*z**3 - 40*z**2 + z) with (-35*z)*z + (-35*z)*(-40*z**2) + (-35*z)*(-50*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-35*z)*z + (-35*z)*(-40*z**2) + (-35*z)*(-50*z**3) + (2*z**2)*(-50*z**3 - 40*z**2 + z)\nSimplifying the partial expression: (2*z**2)*(-50*z**3 - 40*z**2 + z)\nExpanding the part (-50*z**3 - 40*z**2 + z) using the distributive property, and we got: z*(2*z**2) + (-40*z**2)*(2*z**2) + (2*z**2)*(-50*z**3)\nReplacing (2*z**2)*(-50*z**3 - 40*z**2 + z) with z*(2*z**2) + (-40*z**2)*(2*z**2) + (2*z**2)*(-50*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-35*z)*z + (-35*z)*(-40*z**2) + (-35*z)*(-50*z**3) + z*(2*z**2) + (-40*z**2)*(2*z**2) + (2*z**2)*(-50*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n z*(-35*z) = -35*z**2\n z*(2*z**2) = 2*z**3\n (-50*z**3)*(-35*z) = 1750*z**4\n (-50*z**3)*(2*z**2) = -100*z**5\n (-40*z**2)*(-35*z) = 1400*z**3\n (-40*z**2)*(2*z**2) = -80*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -100*z**5 - 80*z**4 + 1750*z**4 + 2*z**3 + 1400*z**3 - 35*z**2\nCombining like terms, got -100*z**5 + 1670*z**4 + 1402*z**3 - 35*z**2\n#Step 6:\nCurrent expression: -100*z**5 + 1670*z**4 + 1402*z**3 - 35*z**2\nNo more calculations needed.\n-100*z**5 + 1670*z**4 + 1402*z**3 - 35*z**2", "generated_answer": "-100*z**5 + 1670*z**4 + 1402*z**3 - 35*z**2", "step_length": 6} {"cot_id": "fa65c3e700925911815636d34aace23a0a477b56005c31715522f3126cfb435f", "datapoint": {"question": "Simplify this expression: (-36*z**3 + 24*z**2)*(-29*z**3 - 9*z**2 - 11)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1044*z**6 - 372*z**5 - 216*z**4 + 396*z**3 - 264*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2005, "polynomial_expr": "(-36*z**3 + 24*z**2)*(-29*z**3 - 9*z**2 - 11)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-36*z**3 + 24*z**2)*(-29*z**3 - 9*z**2 - 11)\nExpanding the part (-36*z**3 + 24*z**2) using the distributive property, and we got: (24*z**2)*(-29*z**3 - 9*z**2 - 11) + (-36*z**3)*(-29*z**3 - 9*z**2 - 11)\n#Step 2:\nCurrent expression: (24*z**2)*(-29*z**3 - 9*z**2 - 11) + (-36*z**3)*(-29*z**3 - 9*z**2 - 11)\nSimplifying the partial expression: (-36*z**3)*(-29*z**3 - 9*z**2 - 11)\nExpanding the part (-29*z**3 - 9*z**2 - 11) using the distributive property, and we got: -(-1)*396*z**3 + (-9*z**2)*(-36*z**3) + (-36*z**3)*(-29*z**3)\nReplacing (-36*z**3)*(-29*z**3 - 9*z**2 - 11) with -(-1)*396*z**3 + (-9*z**2)*(-36*z**3) + (-36*z**3)*(-29*z**3) in the overall expression.\n#Step 3:\nCurrent expression: -11*(-36)*z**3 + (-9*z**2)*(-36*z**3) + (24*z**2)*(-29*z**3 - 9*z**2 - 11) + (-36*z**3)*(-29*z**3)\nSimplifying the partial expression: (24*z**2)*(-29*z**3 - 9*z**2 - 11)\nExpanding the part (-29*z**3 - 9*z**2 - 11) using the distributive property, and we got: -264*z**2 + (-9*z**2)*(24*z**2) + (24*z**2)*(-29*z**3)\nReplacing (24*z**2)*(-29*z**3 - 9*z**2 - 11) with -264*z**2 + (-9*z**2)*(24*z**2) + (24*z**2)*(-29*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -11*(-36)*z**3 - 11*24*z**2 + (-9*z**2)*(24*z**2) + (-9*z**2)*(-36*z**3) + (24*z**2)*(-29*z**3) + (-36*z**3)*(-29*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*z**3)*(-36*z**3) = 1044*z**6\n (-29*z**3)*(24*z**2) = -696*z**5\n (-9*z**2)*(-36*z**3) = 324*z**5\n (-9*z**2)*(24*z**2) = -216*z**4\n -11*-36*z**3 = 396*z**3\n -11*24*z**2 = -264*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1044*z**6 - 696*z**5 + 324*z**5 - 216*z**4 + 396*z**3 - 264*z**2\nCombining like terms, got 1044*z**6 - 372*z**5 - 216*z**4 + 396*z**3 - 264*z**2\n#Step 6:\nCurrent expression: 1044*z**6 - 372*z**5 - 216*z**4 + 396*z**3 - 264*z**2\nNo more calculations needed.\n1044*z**6 - 372*z**5 - 216*z**4 + 396*z**3 - 264*z**2", "generated_answer": "1044*z**6 - 372*z**5 - 216*z**4 + 396*z**3 - 264*z**2", "step_length": 6} {"cot_id": "ccca97f06ca664f805ef9e27bb515b964c4e2e0e30ed7a392645555157753fa7", "datapoint": {"question": "Calculate the following: (14*y**2 - 47*y)*(14*y**3 + 25*y + 42)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "196*y**5 - 658*y**4 + 350*y**3 - 587*y**2 - 1974*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2006, "polynomial_expr": "(14*y**2 - 47*y)*(14*y**3 + 25*y + 42)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14*y**2 - 47*y)*(14*y**3 + 25*y + 42)\nExpanding the part (14*y**2 - 47*y) using the distributive property, and we got: (-47*y)*(14*y**3 + 25*y + 42) + (14*y**2)*(14*y**3 + 25*y + 42)\n#Step 2:\nCurrent expression: (-47*y)*(14*y**3 + 25*y + 42) + (14*y**2)*(14*y**3 + 25*y + 42)\nSimplifying the partial expression: (-47*y)*(14*y**3 + 25*y + 42)\nExpanding the part (14*y**3 + 25*y + 42) using the distributive property, and we got: (-47*y)*(25*y) + (-47*y)*(14*y**3) + 42*(-47*y)\nReplacing (-47*y)*(14*y**3 + 25*y + 42) with (-47*y)*(25*y) + (-47*y)*(14*y**3) + 42*(-47*y) in the overall expression.\n#Step 3:\nCurrent expression: (-47*y)*(25*y) + (-47*y)*(14*y**3) + 42*(-47)*y + (14*y**2)*(14*y**3 + 25*y + 42)\nSimplifying the partial expression: (14*y**2)*(14*y**3 + 25*y + 42)\nExpanding the part (14*y**3 + 25*y + 42) using the distributive property, and we got: 42*(14*y**2) + (25*y)*(14*y**2) + (14*y**2)*(14*y**3)\nReplacing (14*y**2)*(14*y**3 + 25*y + 42) with 42*(14*y**2) + (25*y)*(14*y**2) + (14*y**2)*(14*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-47*y)*(25*y) + (-47*y)*(14*y**3) + 42*14*y**2 + 42*(-47)*y + (25*y)*(14*y**2) + (14*y**2)*(14*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (14*y**3)*(-47*y) = -658*y**4\n (14*y**3)*(14*y**2) = 196*y**5\n (25*y)*(-47*y) = -1175*y**2\n (25*y)*(14*y**2) = 350*y**3\n 42*-47*y = -1974*y\n 42*14*y**2 = 588*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 196*y**5 - 658*y**4 + 350*y**3 - 1175*y**2 + 588*y**2 - 1974*y\nCombining like terms, got 196*y**5 - 658*y**4 + 350*y**3 - 587*y**2 - 1974*y\n#Step 6:\nCurrent expression: 196*y**5 - 658*y**4 + 350*y**3 - 587*y**2 - 1974*y\nNo more calculations needed.\n196*y**5 - 658*y**4 + 350*y**3 - 587*y**2 - 1974*y", "generated_answer": "196*y**5 - 658*y**4 + 350*y**3 - 587*y**2 - 1974*y", "step_length": 6} {"cot_id": "78bbb1e0584c7970cbf48f68d46872397f5aa95e38d2dbc96461d0c6689b6f0d", "datapoint": {"question": "Simplify this expression: (-39*z**3 + 44*z**2)*(-20*z**3 - 35*z**2 - 40)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "780*z**6 + 485*z**5 - 1540*z**4 + 1560*z**3 - 1760*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2007, "polynomial_expr": "(-39*z**3 + 44*z**2)*(-20*z**3 - 35*z**2 - 40)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-39*z**3 + 44*z**2)*(-20*z**3 - 35*z**2 - 40)\nExpanding the part (-39*z**3 + 44*z**2) using the distributive property, and we got: (44*z**2)*(-20*z**3 - 35*z**2 - 40) + (-39*z**3)*(-20*z**3 - 35*z**2 - 40)\n#Step 2:\nCurrent expression: (44*z**2)*(-20*z**3 - 35*z**2 - 40) + (-39*z**3)*(-20*z**3 - 35*z**2 - 40)\nSimplifying the partial expression: (-39*z**3)*(-20*z**3 - 35*z**2 - 40)\nExpanding the part (-20*z**3 - 35*z**2 - 40) using the distributive property, and we got: -(-1)*1560*z**3 + (-35*z**2)*(-39*z**3) + (-39*z**3)*(-20*z**3)\nReplacing (-39*z**3)*(-20*z**3 - 35*z**2 - 40) with -(-1)*1560*z**3 + (-35*z**2)*(-39*z**3) + (-39*z**3)*(-20*z**3) in the overall expression.\n#Step 3:\nCurrent expression: -40*(-39)*z**3 + (-35*z**2)*(-39*z**3) + (44*z**2)*(-20*z**3 - 35*z**2 - 40) + (-39*z**3)*(-20*z**3)\nSimplifying the partial expression: (44*z**2)*(-20*z**3 - 35*z**2 - 40)\nExpanding the part (-20*z**3 - 35*z**2 - 40) using the distributive property, and we got: -1760*z**2 + (-35*z**2)*(44*z**2) + (44*z**2)*(-20*z**3)\nReplacing (44*z**2)*(-20*z**3 - 35*z**2 - 40) with -1760*z**2 + (-35*z**2)*(44*z**2) + (44*z**2)*(-20*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -40*(-39)*z**3 - 40*44*z**2 + (-35*z**2)*(44*z**2) + (-35*z**2)*(-39*z**3) + (44*z**2)*(-20*z**3) + (-39*z**3)*(-20*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*z**2)*(-39*z**3) = 1365*z**5\n (-35*z**2)*(44*z**2) = -1540*z**4\n (-20*z**3)*(-39*z**3) = 780*z**6\n (-20*z**3)*(44*z**2) = -880*z**5\n -40*-39*z**3 = 1560*z**3\n -40*44*z**2 = -1760*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 780*z**6 - 880*z**5 + 1365*z**5 - 1540*z**4 + 1560*z**3 - 1760*z**2\nCombining like terms, got 780*z**6 + 485*z**5 - 1540*z**4 + 1560*z**3 - 1760*z**2\n#Step 6:\nCurrent expression: 780*z**6 + 485*z**5 - 1540*z**4 + 1560*z**3 - 1760*z**2\nNo more calculations needed.\n780*z**6 + 485*z**5 - 1540*z**4 + 1560*z**3 - 1760*z**2", "generated_answer": "780*z**6 + 485*z**5 - 1540*z**4 + 1560*z**3 - 1760*z**2", "step_length": 6} {"cot_id": "d4fcde4344efa3e005fd0af91938d964ac566923d79aec701a70ce2376800d2c", "datapoint": {"question": "Calculate the following: 52*z*(-28*z**2 + 43*z - 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1456*z**3 + 2236*z**2 - 1976*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2008, "polynomial_expr": "52*z*(-28*z**2 + 43*z - 38)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 52*z*(-28*z**2 + 43*z - 38)\nExpanding the part (-28*z**2 + 43*z - 38) using the distributive property, and we got: -1976*z + (43*z)*(52*z) + (52*z)*(-28*z**2)\n#Step 2:\nCurrent expression: -1976*z + (43*z)*(52*z) + (52*z)*(-28*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -38*(52*z) = -1976*z\n (-28*z**2)*(52*z) = -1456*z**3\n (43*z)*(52*z) = 2236*z**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1456*z**3 + 2236*z**2 - 1976*z\nNo more calculations needed.\n-1456*z**3 + 2236*z**2 - 1976*z", "generated_answer": "-1456*z**3 + 2236*z**2 - 1976*z", "step_length": 3} {"cot_id": "b6cac969048aa11bbd8e28eed18b6f8c6c273a51982a8ab210a58aa2ca850966", "datapoint": {"question": "Simplify this expression: (-6*x**3 + 31*x)*(-12*x**3 - 40*x**2 + 34*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "72*x**6 + 240*x**5 - 576*x**4 - 1240*x**3 + 1054*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2009, "polynomial_expr": "(-6*x**3 + 31*x)*(-12*x**3 - 40*x**2 + 34*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-6*x**3 + 31*x)*(-12*x**3 - 40*x**2 + 34*x)\nExpanding the part (-6*x**3 + 31*x) using the distributive property, and we got: (31*x)*(-12*x**3 - 40*x**2 + 34*x) + (-6*x**3)*(-12*x**3 - 40*x**2 + 34*x)\n#Step 2:\nCurrent expression: (31*x)*(-12*x**3 - 40*x**2 + 34*x) + (-6*x**3)*(-12*x**3 - 40*x**2 + 34*x)\nSimplifying the partial expression: (-6*x**3)*(-12*x**3 - 40*x**2 + 34*x)\nExpanding the part (-12*x**3 - 40*x**2 + 34*x) using the distributive property, and we got: (34*x)*(-6*x**3) + (-40*x**2)*(-6*x**3) + (-12*x**3)*(-6*x**3)\nReplacing (-6*x**3)*(-12*x**3 - 40*x**2 + 34*x) with (34*x)*(-6*x**3) + (-40*x**2)*(-6*x**3) + (-12*x**3)*(-6*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (31*x)*(-12*x**3 - 40*x**2 + 34*x) + (34*x)*(-6*x**3) + (-40*x**2)*(-6*x**3) + (-12*x**3)*(-6*x**3)\nSimplifying the partial expression: (31*x)*(-12*x**3 - 40*x**2 + 34*x)\nExpanding the part (-12*x**3 - 40*x**2 + 34*x) using the distributive property, and we got: (31*x)*(34*x) + (31*x)*(-40*x**2) + (31*x)*(-12*x**3)\nReplacing (31*x)*(-12*x**3 - 40*x**2 + 34*x) with (31*x)*(34*x) + (31*x)*(-40*x**2) + (31*x)*(-12*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (31*x)*(34*x) + (31*x)*(-40*x**2) + (31*x)*(-12*x**3) + (34*x)*(-6*x**3) + (-40*x**2)*(-6*x**3) + (-12*x**3)*(-6*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*x**2)*(-6*x**3) = 240*x**5\n (-40*x**2)*(31*x) = -1240*x**3\n (-12*x**3)*(-6*x**3) = 72*x**6\n (-12*x**3)*(31*x) = -372*x**4\n (34*x)*(-6*x**3) = -204*x**4\n (34*x)*(31*x) = 1054*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 72*x**6 + 240*x**5 - 372*x**4 - 204*x**4 - 1240*x**3 + 1054*x**2\nCombining like terms, got 72*x**6 + 240*x**5 - 576*x**4 - 1240*x**3 + 1054*x**2\n#Step 6:\nCurrent expression: 72*x**6 + 240*x**5 - 576*x**4 - 1240*x**3 + 1054*x**2\nNo more calculations needed.\n72*x**6 + 240*x**5 - 576*x**4 - 1240*x**3 + 1054*x**2", "generated_answer": "72*x**6 + 240*x**5 - 576*x**4 - 1240*x**3 + 1054*x**2", "step_length": 6} {"cot_id": "4ed9b20a2d0316a372a747ce2955112feacaf11cd027f13a1e3f80032b20399d", "datapoint": {"question": "Simplify this expression: -215*z**3 - 45*z**2\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-215*z**3 - 45*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2010, "polynomial_expr": "-215*z**3 - 45*z**2", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -215*z**3 - 45*z**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -215*z**3 - 45*z**2\nNo more calculations needed.\n-215*z**3 - 45*z**2", "generated_answer": "-215*z**3 - 45*z**2", "step_length": 2} {"cot_id": "df783325278ca3b2b5aea6139ff2fc4f2c24f93d06c9cac4e1571b4e61035dfb", "datapoint": {"question": "Calculate the following: -1200*y**2 - 225\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1200*y**2 - 225", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2011, "polynomial_expr": "-1200*y**2 - 225", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -1200*y**2 - 225\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -1200*y**2 - 225\nNo more calculations needed.\n-1200*y**2 - 225", "generated_answer": "-1200*y**2 - 225", "step_length": 2} {"cot_id": "d5ecabaf8cce1dfff3ccb7d9b16ecf77cde374f4221545640acb515556308ed4", "datapoint": {"question": "Simplify this expression: (46*x**2 - 26)*(-42*x**3 + 40*x - 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1932*x**5 + 2932*x**3 - 2024*x**2 - 1040*x + 1144", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2012, "polynomial_expr": "(46*x**2 - 26)*(-42*x**3 + 40*x - 44)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (46*x**2 - 26)*(-42*x**3 + 40*x - 44)\nExpanding the part (46*x**2 - 26) using the distributive property, and we got: (46*x**2)*(-42*x**3 + 40*x - 44) - 26*(-42*x**3 + 40*x - 44)\n#Step 2:\nCurrent expression: (46*x**2)*(-42*x**3 + 40*x - 44) - 26*(-42*x**3 + 40*x - 44)\nSimplifying the partial expression: -26*(-42*x**3 + 40*x - 44)\nExpanding the part (-42*x**3 + 40*x - 44) using the distributive property, and we got: (40*x)*(-26) - 42*x**3*(-26) - 44*(-26)\nReplacing -26*(-42*x**3 + 40*x - 44) with (40*x)*(-26) - 42*x**3*(-26) - 44*(-26) in the overall expression.\n#Step 3:\nCurrent expression: (40*x)*(-26) + (46*x**2)*(-42*x**3 + 40*x - 44) - 42*x**3*(-26) + 1144\nSimplifying the partial expression: (46*x**2)*(-42*x**3 + 40*x - 44)\nExpanding the part (-42*x**3 + 40*x - 44) using the distributive property, and we got: -2024*x**2 + (40*x)*(46*x**2) + (46*x**2)*(-42*x**3)\nReplacing (46*x**2)*(-42*x**3 + 40*x - 44) with -2024*x**2 + (40*x)*(46*x**2) + (46*x**2)*(-42*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -44*46*x**2 + (40*x)*(46*x**2) + (40*x)*(-26) + (46*x**2)*(-42*x**3) - 42*x**3*(-26) + 1144\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*x**3)*-26 = 1092*x**3\n (-42*x**3)*(46*x**2) = -1932*x**5\n (40*x)*-26 = -1040*x\n (40*x)*(46*x**2) = 1840*x**3\n -44*46*x**2 = -2024*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1932*x**5 + 1092*x**3 + 1840*x**3 - 2024*x**2 - 1040*x + 1144\nCombining like terms, got -1932*x**5 + 2932*x**3 - 2024*x**2 - 1040*x + 1144\n#Step 6:\nCurrent expression: -1932*x**5 + 2932*x**3 - 2024*x**2 - 1040*x + 1144\nNo more calculations needed.\n-1932*x**5 + 2932*x**3 - 2024*x**2 - 1040*x + 1144", "generated_answer": "-1932*x**5 + 2932*x**3 - 2024*x**2 - 1040*x + 1144", "step_length": 6} {"cot_id": "95b95fe1a7cb74289428a76ad3c53cb2e40770f85c50356cf226ce989f8292c2", "datapoint": {"question": "Calculate the following: (11 - 29*x)*(-53*x**3 + 13*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1537*x**4 - 583*x**3 - 377*x**2 + 143*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2013, "polynomial_expr": "(11 - 29*x)*(-53*x**3 + 13*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11 - 29*x)*(-53*x**3 + 13*x)\nExpanding the part (11 - 29*x) using the distributive property, and we got: (-29*x)*(-53*x**3 + 13*x) + 11*(-53*x**3 + 13*x)\n#Step 2:\nCurrent expression: (-29*x)*(-53*x**3 + 13*x) + 11*(-53*x**3 + 13*x)\nSimplifying the partial expression: 11*(-53*x**3 + 13*x)\nExpanding the part (-53*x**3 + 13*x) using the distributive property, and we got: (13*x)*11 - 53*x**3*11\nReplacing 11*(-53*x**3 + 13*x) with (13*x)*11 - 53*x**3*11 in the overall expression.\n#Step 3:\nCurrent expression: (-29*x)*(-53*x**3 + 13*x) + (13*x)*11 - 53*x**3*11\nSimplifying the partial expression: (-29*x)*(-53*x**3 + 13*x)\nExpanding the part (-53*x**3 + 13*x) using the distributive property, and we got: (-29*x)*(13*x) + (-29*x)*(-53*x**3)\nReplacing (-29*x)*(-53*x**3 + 13*x) with (-29*x)*(13*x) + (-29*x)*(-53*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-29*x)*(13*x) + (-29*x)*(-53*x**3) + (13*x)*11 - 53*x**3*11\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-53*x**3)*11 = -583*x**3\n (-53*x**3)*(-29*x) = 1537*x**4\n (13*x)*11 = 143*x\n (13*x)*(-29*x) = -377*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1537*x**4 - 583*x**3 - 377*x**2 + 143*x\nNo more calculations needed.\n1537*x**4 - 583*x**3 - 377*x**2 + 143*x", "generated_answer": "1537*x**4 - 583*x**3 - 377*x**2 + 143*x", "step_length": 5} {"cot_id": "ae274a63b98589db7d5f411b89d315c5a283efc4ead741aa93e402e94a306b7a", "datapoint": {"question": "Calculate the following: (z**3 + 33*z)*(47*z**3 - 32*z**2 - 25)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "47*z**6 - 32*z**5 + 1551*z**4 - 1081*z**3 - 825*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2014, "polynomial_expr": "(z**3 + 33*z)*(47*z**3 - 32*z**2 - 25)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (z**3 + 33*z)*(47*z**3 - 32*z**2 - 25)\nExpanding the part (z**3 + 33*z) using the distributive property, and we got: z**3*(47*z**3 - 32*z**2 - 25) + (33*z)*(47*z**3 - 32*z**2 - 25)\n#Step 2:\nCurrent expression: z**3*(47*z**3 - 32*z**2 - 25) + (33*z)*(47*z**3 - 32*z**2 - 25)\nSimplifying the partial expression: z**3*(47*z**3 - 32*z**2 - 25)\nExpanding the part (47*z**3 - 32*z**2 - 25) using the distributive property, and we got: (-32*z**2)*z**3 + z**3*(47*z**3) - 25*z**3\nReplacing z**3*(47*z**3 - 32*z**2 - 25) with (-32*z**2)*z**3 + z**3*(47*z**3) - 25*z**3 in the overall expression.\n#Step 3:\nCurrent expression: (-32*z**2)*z**3 + z**3*(47*z**3) - 25*z**3 + (33*z)*(47*z**3 - 32*z**2 - 25)\nSimplifying the partial expression: (33*z)*(47*z**3 - 32*z**2 - 25)\nExpanding the part (47*z**3 - 32*z**2 - 25) using the distributive property, and we got: -825*z + (33*z)*(-32*z**2) + (33*z)*(47*z**3)\nReplacing (33*z)*(47*z**3 - 32*z**2 - 25) with -825*z + (33*z)*(-32*z**2) + (33*z)*(47*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-32*z**2)*z**3 + z**3*(47*z**3) - 25*z**3 - 25*33*z + (33*z)*(-32*z**2) + (33*z)*(47*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*z**2)*z**3 = -32*z**5\n (-32*z**2)*(33*z) = -1056*z**3\n (47*z**3)*z**3 = 47*z**6\n (47*z**3)*(33*z) = 1551*z**4\n -25*33*z = -825*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 47*z**6 - 32*z**5 + 1551*z**4 - 1056*z**3 - 25*z**3 - 825*z\nCombining like terms, got 47*z**6 - 32*z**5 + 1551*z**4 - 1081*z**3 - 825*z\n#Step 6:\nCurrent expression: 47*z**6 - 32*z**5 + 1551*z**4 - 1081*z**3 - 825*z\nNo more calculations needed.\n47*z**6 - 32*z**5 + 1551*z**4 - 1081*z**3 - 825*z", "generated_answer": "47*z**6 - 32*z**5 + 1551*z**4 - 1081*z**3 - 825*z", "step_length": 6} {"cot_id": "4043ea52dc272ce80d7538b4bc316a6cfd0c20376638bde55344e7ac29980e40", "datapoint": {"question": "Simplify this expression: (45*z**3 - 37*z)*(84*z**3 + 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "3780*z**6 - 3108*z**4 + 1980*z**3 - 1628*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2015, "polynomial_expr": "(45*z**3 - 37*z)*(84*z**3 + 44)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (45*z**3 - 37*z)*(84*z**3 + 44)\nExpanding the part (84*z**3 + 44) using the distributive property, and we got: (84*z**3)*(45*z**3 - 37*z) + 44*(45*z**3 - 37*z)\n#Step 2:\nCurrent expression: (84*z**3)*(45*z**3 - 37*z) + 44*(45*z**3 - 37*z)\nSimplifying the partial expression: 44*(45*z**3 - 37*z)\nExpanding the part (45*z**3 - 37*z) using the distributive property, and we got: -37*z*44 + (45*z**3)*44\nReplacing 44*(45*z**3 - 37*z) with -37*z*44 + (45*z**3)*44 in the overall expression.\n#Step 3:\nCurrent expression: -37*z*44 + (45*z**3)*44 + (84*z**3)*(45*z**3 - 37*z)\nSimplifying the partial expression: (84*z**3)*(45*z**3 - 37*z)\nExpanding the part (45*z**3 - 37*z) using the distributive property, and we got: (-37*z)*(84*z**3) + (45*z**3)*(84*z**3)\nReplacing (84*z**3)*(45*z**3 - 37*z) with (-37*z)*(84*z**3) + (45*z**3)*(84*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-37*z)*(84*z**3) - 37*z*44 + (45*z**3)*(84*z**3) + (45*z**3)*44\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*z)*44 = -1628*z\n (-37*z)*(84*z**3) = -3108*z**4\n (45*z**3)*44 = 1980*z**3\n (45*z**3)*(84*z**3) = 3780*z**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 3780*z**6 - 3108*z**4 + 1980*z**3 - 1628*z\nNo more calculations needed.\n3780*z**6 - 3108*z**4 + 1980*z**3 - 1628*z", "generated_answer": "3780*z**6 - 3108*z**4 + 1980*z**3 - 1628*z", "step_length": 5} {"cot_id": "cc5d4ef218523b5cded5b5fb5f42895b2f6e0637460d7e5715049870bc73ae55", "datapoint": {"question": "Calculate the following: (-18*x**3 - 16*x)*(45*x**3 - 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-810*x**6 - 720*x**4 + 378*x**3 + 336*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2016, "polynomial_expr": "(-18*x**3 - 16*x)*(45*x**3 - 21)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-18*x**3 - 16*x)*(45*x**3 - 21)\nExpanding the part (45*x**3 - 21) using the distributive property, and we got: (45*x**3)*(-18*x**3 - 16*x) - 21*(-18*x**3 - 16*x)\n#Step 2:\nCurrent expression: (45*x**3)*(-18*x**3 - 16*x) - 21*(-18*x**3 - 16*x)\nSimplifying the partial expression: -21*(-18*x**3 - 16*x)\nExpanding the part (-18*x**3 - 16*x) using the distributive property, and we got: -16*x*(-21) - 18*x**3*(-21)\nReplacing -21*(-18*x**3 - 16*x) with -16*x*(-21) - 18*x**3*(-21) in the overall expression.\n#Step 3:\nCurrent expression: -16*x*(-21) - 18*x**3*(-21) + (45*x**3)*(-18*x**3 - 16*x)\nSimplifying the partial expression: (45*x**3)*(-18*x**3 - 16*x)\nExpanding the part (-18*x**3 - 16*x) using the distributive property, and we got: (-16*x)*(45*x**3) + (-18*x**3)*(45*x**3)\nReplacing (45*x**3)*(-18*x**3 - 16*x) with (-16*x)*(45*x**3) + (-18*x**3)*(45*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-16*x)*(45*x**3) - 16*x*(-21) + (-18*x**3)*(45*x**3) - 18*x**3*(-21)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-18*x**3)*-21 = 378*x**3\n (-18*x**3)*(45*x**3) = -810*x**6\n (-16*x)*-21 = 336*x\n (-16*x)*(45*x**3) = -720*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -810*x**6 - 720*x**4 + 378*x**3 + 336*x\nNo more calculations needed.\n-810*x**6 - 720*x**4 + 378*x**3 + 336*x", "generated_answer": "-810*x**6 - 720*x**4 + 378*x**3 + 336*x", "step_length": 5} {"cot_id": "b532257e1cdd0efa9f7559751e53a315a735403be5da9bbaf5eacb0a38880a97", "datapoint": {"question": "Simplify this expression: (-31*y**3 + 27*y - 13)*(-11*y**3 + 5*y**2 + 20*y - 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "341*y**6 - 155*y**5 - 917*y**4 + 588*y**3 + 475*y**2 - 530*y + 130", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2017, "polynomial_expr": "(-31*y**3 + 27*y - 13)*(-11*y**3 + 5*y**2 + 20*y - 10)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-31*y**3 + 27*y - 13)*(-11*y**3 + 5*y**2 + 20*y - 10)\nExpanding the part (-31*y**3 + 27*y - 13) using the distributive property, and we got: (27*y)*(-11*y**3 + 5*y**2 + 20*y - 10) + (-31*y**3)*(-11*y**3 + 5*y**2 + 20*y - 10) - 13*(-11*y**3 + 5*y**2 + 20*y - 10)\n#Step 2:\nCurrent expression: (27*y)*(-11*y**3 + 5*y**2 + 20*y - 10) + (-31*y**3)*(-11*y**3 + 5*y**2 + 20*y - 10) - 13*(-11*y**3 + 5*y**2 + 20*y - 10)\nSimplifying the partial expression: -13*(-11*y**3 + 5*y**2 + 20*y - 10)\nExpanding the part (-11*y**3 + 5*y**2 + 20*y - 10) using the distributive property, and we got: (20*y)*(-13) + (5*y**2)*(-13) - 11*y**3*(-13) - 10*(-13)\nReplacing -13*(-11*y**3 + 5*y**2 + 20*y - 10) with (20*y)*(-13) + (5*y**2)*(-13) - 11*y**3*(-13) - 10*(-13) in the overall expression.\n#Step 3:\nCurrent expression: (20*y)*(-13) + (27*y)*(-11*y**3 + 5*y**2 + 20*y - 10) + (5*y**2)*(-13) + (-31*y**3)*(-11*y**3 + 5*y**2 + 20*y - 10) - 11*y**3*(-13) + 130\nSimplifying the partial expression: (-31*y**3)*(-11*y**3 + 5*y**2 + 20*y - 10)\nExpanding the part (-11*y**3 + 5*y**2 + 20*y - 10) using the distributive property, and we got: -(-1)*310*y**3 + (20*y)*(-31*y**3) + (5*y**2)*(-31*y**3) + (-31*y**3)*(-11*y**3)\nReplacing (-31*y**3)*(-11*y**3 + 5*y**2 + 20*y - 10) with -(-1)*310*y**3 + (20*y)*(-31*y**3) + (5*y**2)*(-31*y**3) + (-31*y**3)*(-11*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -10*(-31)*y**3 + (20*y)*(-31*y**3) + (20*y)*(-13) + (27*y)*(-11*y**3 + 5*y**2 + 20*y - 10) + (5*y**2)*(-31*y**3) + (5*y**2)*(-13) + (-31*y**3)*(-11*y**3) - 11*y**3*(-13) + 130\nSimplifying the partial expression: (27*y)*(-11*y**3 + 5*y**2 + 20*y - 10)\nExpanding the part (-11*y**3 + 5*y**2 + 20*y - 10) using the distributive property, and we got: -270*y + (20*y)*(27*y) + (27*y)*(5*y**2) + (27*y)*(-11*y**3)\nReplacing (27*y)*(-11*y**3 + 5*y**2 + 20*y - 10) with -270*y + (20*y)*(27*y) + (27*y)*(5*y**2) + (27*y)*(-11*y**3) in the overall expression.\n#Step 5:\nCurrent expression: -10*(-31)*y**3 - 10*27*y + (20*y)*(27*y) + (20*y)*(-31*y**3) + (20*y)*(-13) + (27*y)*(5*y**2) + (27*y)*(-11*y**3) + (5*y**2)*(-31*y**3) + (5*y**2)*(-13) + (-31*y**3)*(-11*y**3) - 11*y**3*(-13) + 130\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*y**3)*-13 = 143*y**3\n (-11*y**3)*(-31*y**3) = 341*y**6\n (-11*y**3)*(27*y) = -297*y**4\n (5*y**2)*-13 = -65*y**2\n (5*y**2)*(-31*y**3) = -155*y**5\n (5*y**2)*(27*y) = 135*y**3\n (20*y)*-13 = -260*y\n (20*y)*(-31*y**3) = -620*y**4\n (20*y)*(27*y) = 540*y**2\n -10*-31*y**3 = 310*y**3\n -10*27*y = -270*y\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 341*y**6 - 155*y**5 - 620*y**4 - 297*y**4 + 135*y**3 + 143*y**3 + 310*y**3 - 65*y**2 + 540*y**2 - 270*y - 260*y + 130\nCombining like terms, got 341*y**6 - 155*y**5 - 917*y**4 + 588*y**3 + 475*y**2 - 530*y + 130\n#Step 7:\nCurrent expression: 341*y**6 - 155*y**5 - 917*y**4 + 588*y**3 + 475*y**2 - 530*y + 130\nNo more calculations needed.\n341*y**6 - 155*y**5 - 917*y**4 + 588*y**3 + 475*y**2 - 530*y + 130", "generated_answer": "341*y**6 - 155*y**5 - 917*y**4 + 588*y**3 + 475*y**2 - 530*y + 130", "step_length": 7} {"cot_id": "0bf14b61d333cb7b5530a8ab982a886f1198035adc1968bca69ca86a59b2842f", "datapoint": {"question": "Simplify this expression: (40*z**2 + 15*z)*(-36*z**3 + 31*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1440*z**5 + 700*z**4 + 465*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2018, "polynomial_expr": "(40*z**2 + 15*z)*(-36*z**3 + 31*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (40*z**2 + 15*z)*(-36*z**3 + 31*z**2)\nExpanding the part (-36*z**3 + 31*z**2) using the distributive property, and we got: (31*z**2)*(40*z**2 + 15*z) + (-36*z**3)*(40*z**2 + 15*z)\n#Step 2:\nCurrent expression: (31*z**2)*(40*z**2 + 15*z) + (-36*z**3)*(40*z**2 + 15*z)\nSimplifying the partial expression: (-36*z**3)*(40*z**2 + 15*z)\nExpanding the part (40*z**2 + 15*z) using the distributive property, and we got: (15*z)*(-36*z**3) + (40*z**2)*(-36*z**3)\nReplacing (-36*z**3)*(40*z**2 + 15*z) with (15*z)*(-36*z**3) + (40*z**2)*(-36*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (15*z)*(-36*z**3) + (31*z**2)*(40*z**2 + 15*z) + (40*z**2)*(-36*z**3)\nSimplifying the partial expression: (31*z**2)*(40*z**2 + 15*z)\nExpanding the part (40*z**2 + 15*z) using the distributive property, and we got: (15*z)*(31*z**2) + (31*z**2)*(40*z**2)\nReplacing (31*z**2)*(40*z**2 + 15*z) with (15*z)*(31*z**2) + (31*z**2)*(40*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (15*z)*(31*z**2) + (15*z)*(-36*z**3) + (31*z**2)*(40*z**2) + (40*z**2)*(-36*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (15*z)*(-36*z**3) = -540*z**4\n (15*z)*(31*z**2) = 465*z**3\n (40*z**2)*(-36*z**3) = -1440*z**5\n (40*z**2)*(31*z**2) = 1240*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1440*z**5 - 540*z**4 + 1240*z**4 + 465*z**3\nCombining like terms, got -1440*z**5 + 700*z**4 + 465*z**3\n#Step 6:\nCurrent expression: -1440*z**5 + 700*z**4 + 465*z**3\nNo more calculations needed.\n-1440*z**5 + 700*z**4 + 465*z**3", "generated_answer": "-1440*z**5 + 700*z**4 + 465*z**3", "step_length": 6} {"cot_id": "b19a78e3d0ccefa1947aa89b9edf016a7cf14a5eee3427492b1cda593a809d2f", "datapoint": {"question": "Calculate the following: (10 - 50*y**3)*(32*y**2 - 8*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1600*y**5 + 400*y**4 + 320*y**2 - 80*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2019, "polynomial_expr": "(10 - 50*y**3)*(32*y**2 - 8*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (10 - 50*y**3)*(32*y**2 - 8*y)\nExpanding the part (10 - 50*y**3) using the distributive property, and we got: (-50*y**3)*(32*y**2 - 8*y) + 10*(32*y**2 - 8*y)\n#Step 2:\nCurrent expression: (-50*y**3)*(32*y**2 - 8*y) + 10*(32*y**2 - 8*y)\nSimplifying the partial expression: 10*(32*y**2 - 8*y)\nExpanding the part (32*y**2 - 8*y) using the distributive property, and we got: -8*y*10 + (32*y**2)*10\nReplacing 10*(32*y**2 - 8*y) with -8*y*10 + (32*y**2)*10 in the overall expression.\n#Step 3:\nCurrent expression: -8*y*10 + (32*y**2)*10 + (-50*y**3)*(32*y**2 - 8*y)\nSimplifying the partial expression: (-50*y**3)*(32*y**2 - 8*y)\nExpanding the part (32*y**2 - 8*y) using the distributive property, and we got: (-8*y)*(-50*y**3) + (32*y**2)*(-50*y**3)\nReplacing (-50*y**3)*(32*y**2 - 8*y) with (-8*y)*(-50*y**3) + (32*y**2)*(-50*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-8*y)*(-50*y**3) - 8*y*10 + (32*y**2)*(-50*y**3) + (32*y**2)*10\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-8*y)*10 = -80*y\n (-8*y)*(-50*y**3) = 400*y**4\n (32*y**2)*10 = 320*y**2\n (32*y**2)*(-50*y**3) = -1600*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1600*y**5 + 400*y**4 + 320*y**2 - 80*y\nNo more calculations needed.\n-1600*y**5 + 400*y**4 + 320*y**2 - 80*y", "generated_answer": "-1600*y**5 + 400*y**4 + 320*y**2 - 80*y", "step_length": 5} {"cot_id": "21f6b01649d81420f51f2a4707ef843167b58db858b6d95eae8d322728529381", "datapoint": {"question": "Simplify this expression: (30*y**2 + y)*(-24*y**2 - 47*y + 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-720*y**4 - 1434*y**3 + 1363*y**2 + 47*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2020, "polynomial_expr": "(30*y**2 + y)*(-24*y**2 - 47*y + 47)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (30*y**2 + y)*(-24*y**2 - 47*y + 47)\nExpanding the part (30*y**2 + y) using the distributive property, and we got: y*(-24*y**2 - 47*y + 47) + (30*y**2)*(-24*y**2 - 47*y + 47)\n#Step 2:\nCurrent expression: y*(-24*y**2 - 47*y + 47) + (30*y**2)*(-24*y**2 - 47*y + 47)\nSimplifying the partial expression: y*(-24*y**2 - 47*y + 47)\nExpanding the part (-24*y**2 - 47*y + 47) using the distributive property, and we got: (-47*y)*y + y*(-24*y**2) + 47*y\nReplacing y*(-24*y**2 - 47*y + 47) with (-47*y)*y + y*(-24*y**2) + 47*y in the overall expression.\n#Step 3:\nCurrent expression: (-47*y)*y + y*(-24*y**2) + 47*y + (30*y**2)*(-24*y**2 - 47*y + 47)\nSimplifying the partial expression: (30*y**2)*(-24*y**2 - 47*y + 47)\nExpanding the part (-24*y**2 - 47*y + 47) using the distributive property, and we got: (-47*y)*(30*y**2) + 47*(30*y**2) + (-24*y**2)*(30*y**2)\nReplacing (30*y**2)*(-24*y**2 - 47*y + 47) with (-47*y)*(30*y**2) + 47*(30*y**2) + (-24*y**2)*(30*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-47*y)*y + (-47*y)*(30*y**2) + 47*30*y**2 + y*(-24*y**2) + 47*y + (-24*y**2)*(30*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*y)*y = -47*y**2\n (-47*y)*(30*y**2) = -1410*y**3\n (-24*y**2)*y = -24*y**3\n (-24*y**2)*(30*y**2) = -720*y**4\n 47*30*y**2 = 1410*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -720*y**4 - 1410*y**3 - 24*y**3 - 47*y**2 + 1410*y**2 + 47*y\nCombining like terms, got -720*y**4 - 1434*y**3 + 1363*y**2 + 47*y\n#Step 6:\nCurrent expression: -720*y**4 - 1434*y**3 + 1363*y**2 + 47*y\nNo more calculations needed.\n-720*y**4 - 1434*y**3 + 1363*y**2 + 47*y", "generated_answer": "-720*y**4 - 1434*y**3 + 1363*y**2 + 47*y", "step_length": 6} {"cot_id": "9392ea1e6aa68376ba88543a43be8d57b1d077bc799b60f6b4ddc373dd6e7bef", "datapoint": {"question": "Calculate the following: (-31*x**3 - 31*x**2)*(-29*x**2 + 24*x - 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "899*x**5 + 155*x**4 + 775*x**3 + 1519*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2021, "polynomial_expr": "(-31*x**3 - 31*x**2)*(-29*x**2 + 24*x - 49)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-31*x**3 - 31*x**2)*(-29*x**2 + 24*x - 49)\nExpanding the part (-31*x**3 - 31*x**2) using the distributive property, and we got: (-31*x**2)*(-29*x**2 + 24*x - 49) + (-31*x**3)*(-29*x**2 + 24*x - 49)\n#Step 2:\nCurrent expression: (-31*x**2)*(-29*x**2 + 24*x - 49) + (-31*x**3)*(-29*x**2 + 24*x - 49)\nSimplifying the partial expression: (-31*x**2)*(-29*x**2 + 24*x - 49)\nExpanding the part (-29*x**2 + 24*x - 49) using the distributive property, and we got: -(-1)*1519*x**2 + (24*x)*(-31*x**2) + (-31*x**2)*(-29*x**2)\nReplacing (-31*x**2)*(-29*x**2 + 24*x - 49) with -(-1)*1519*x**2 + (24*x)*(-31*x**2) + (-31*x**2)*(-29*x**2) in the overall expression.\n#Step 3:\nCurrent expression: -49*(-31)*x**2 + (24*x)*(-31*x**2) + (-31*x**2)*(-29*x**2) + (-31*x**3)*(-29*x**2 + 24*x - 49)\nSimplifying the partial expression: (-31*x**3)*(-29*x**2 + 24*x - 49)\nExpanding the part (-29*x**2 + 24*x - 49) using the distributive property, and we got: -(-1)*1519*x**3 + (24*x)*(-31*x**3) + (-29*x**2)*(-31*x**3)\nReplacing (-31*x**3)*(-29*x**2 + 24*x - 49) with -(-1)*1519*x**3 + (24*x)*(-31*x**3) + (-29*x**2)*(-31*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -49*(-31)*x**3 - 49*(-31)*x**2 + (24*x)*(-31*x**2) + (24*x)*(-31*x**3) + (-31*x**2)*(-29*x**2) + (-29*x**2)*(-31*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-29*x**2)*(-31*x**2) = 899*x**4\n (-29*x**2)*(-31*x**3) = 899*x**5\n (24*x)*(-31*x**2) = -744*x**3\n (24*x)*(-31*x**3) = -744*x**4\n -49*-31*x**2 = 1519*x**2\n -49*-31*x**3 = 1519*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 899*x**5 - 744*x**4 + 899*x**4 - 744*x**3 + 1519*x**3 + 1519*x**2\nCombining like terms, got 899*x**5 + 155*x**4 + 775*x**3 + 1519*x**2\n#Step 6:\nCurrent expression: 899*x**5 + 155*x**4 + 775*x**3 + 1519*x**2\nNo more calculations needed.\n899*x**5 + 155*x**4 + 775*x**3 + 1519*x**2", "generated_answer": "899*x**5 + 155*x**4 + 775*x**3 + 1519*x**2", "step_length": 6} {"cot_id": "ad151f7419b7560e4767c2a506c527f83b0292071d9cec14210b5be3bfb2fe11", "datapoint": {"question": "Calculate the following: (-18*z**3 + 30*z)*(28*z**3 + 49*z**2 - 14*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-504*z**6 - 882*z**5 + 1092*z**4 + 1470*z**3 - 420*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2022, "polynomial_expr": "(-18*z**3 + 30*z)*(28*z**3 + 49*z**2 - 14*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-18*z**3 + 30*z)*(28*z**3 + 49*z**2 - 14*z)\nExpanding the part (-18*z**3 + 30*z) using the distributive property, and we got: (30*z)*(28*z**3 + 49*z**2 - 14*z) + (-18*z**3)*(28*z**3 + 49*z**2 - 14*z)\n#Step 2:\nCurrent expression: (30*z)*(28*z**3 + 49*z**2 - 14*z) + (-18*z**3)*(28*z**3 + 49*z**2 - 14*z)\nSimplifying the partial expression: (-18*z**3)*(28*z**3 + 49*z**2 - 14*z)\nExpanding the part (28*z**3 + 49*z**2 - 14*z) using the distributive property, and we got: (-14*z)*(-18*z**3) + (49*z**2)*(-18*z**3) + (-18*z**3)*(28*z**3)\nReplacing (-18*z**3)*(28*z**3 + 49*z**2 - 14*z) with (-14*z)*(-18*z**3) + (49*z**2)*(-18*z**3) + (-18*z**3)*(28*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-14*z)*(-18*z**3) + (30*z)*(28*z**3 + 49*z**2 - 14*z) + (49*z**2)*(-18*z**3) + (-18*z**3)*(28*z**3)\nSimplifying the partial expression: (30*z)*(28*z**3 + 49*z**2 - 14*z)\nExpanding the part (28*z**3 + 49*z**2 - 14*z) using the distributive property, and we got: (-14*z)*(30*z) + (30*z)*(49*z**2) + (30*z)*(28*z**3)\nReplacing (30*z)*(28*z**3 + 49*z**2 - 14*z) with (-14*z)*(30*z) + (30*z)*(49*z**2) + (30*z)*(28*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-14*z)*(30*z) + (-14*z)*(-18*z**3) + (30*z)*(49*z**2) + (30*z)*(28*z**3) + (49*z**2)*(-18*z**3) + (-18*z**3)*(28*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-14*z)*(-18*z**3) = 252*z**4\n (-14*z)*(30*z) = -420*z**2\n (28*z**3)*(-18*z**3) = -504*z**6\n (28*z**3)*(30*z) = 840*z**4\n (49*z**2)*(-18*z**3) = -882*z**5\n (49*z**2)*(30*z) = 1470*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -504*z**6 - 882*z**5 + 252*z**4 + 840*z**4 + 1470*z**3 - 420*z**2\nCombining like terms, got -504*z**6 - 882*z**5 + 1092*z**4 + 1470*z**3 - 420*z**2\n#Step 6:\nCurrent expression: -504*z**6 - 882*z**5 + 1092*z**4 + 1470*z**3 - 420*z**2\nNo more calculations needed.\n-504*z**6 - 882*z**5 + 1092*z**4 + 1470*z**3 - 420*z**2", "generated_answer": "-504*z**6 - 882*z**5 + 1092*z**4 + 1470*z**3 - 420*z**2", "step_length": 6} {"cot_id": "c4efa329321a474525c0a2172e307fd83c77a4c2ac9d8282c7f6482519c93131", "datapoint": {"question": "Simplify this expression: (-3*z**2 - 14)*(15*z**2 + 39*z - 3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-45*z**4 - 117*z**3 - 201*z**2 - 546*z + 42", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2023, "polynomial_expr": "(-3*z**2 - 14)*(15*z**2 + 39*z - 3)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-3*z**2 - 14)*(15*z**2 + 39*z - 3)\nExpanding the part (-3*z**2 - 14) using the distributive property, and we got: (-3*z**2)*(15*z**2 + 39*z - 3) - 14*(15*z**2 + 39*z - 3)\n#Step 2:\nCurrent expression: (-3*z**2)*(15*z**2 + 39*z - 3) - 14*(15*z**2 + 39*z - 3)\nSimplifying the partial expression: -14*(15*z**2 + 39*z - 3)\nExpanding the part (15*z**2 + 39*z - 3) using the distributive property, and we got: (39*z)*(-14) + (15*z**2)*(-14) - 3*(-14)\nReplacing -14*(15*z**2 + 39*z - 3) with (39*z)*(-14) + (15*z**2)*(-14) - 3*(-14) in the overall expression.\n#Step 3:\nCurrent expression: (39*z)*(-14) + (-3*z**2)*(15*z**2 + 39*z - 3) + (15*z**2)*(-14) + 42\nSimplifying the partial expression: (-3*z**2)*(15*z**2 + 39*z - 3)\nExpanding the part (15*z**2 + 39*z - 3) using the distributive property, and we got: -(-1)*9*z**2 + (39*z)*(-3*z**2) + (-3*z**2)*(15*z**2)\nReplacing (-3*z**2)*(15*z**2 + 39*z - 3) with -(-1)*9*z**2 + (39*z)*(-3*z**2) + (-3*z**2)*(15*z**2) in the overall expression.\n#Step 4:\nCurrent expression: -3*(-3)*z**2 + (39*z)*(-3*z**2) + (39*z)*(-14) + (-3*z**2)*(15*z**2) + (15*z**2)*(-14) + 42\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (15*z**2)*-14 = -210*z**2\n (15*z**2)*(-3*z**2) = -45*z**4\n (39*z)*-14 = -546*z\n (39*z)*(-3*z**2) = -117*z**3\n -3*-3*z**2 = 9*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -45*z**4 - 117*z**3 - 210*z**2 + 9*z**2 - 546*z + 42\nCombining like terms, got -45*z**4 - 117*z**3 - 201*z**2 - 546*z + 42\n#Step 6:\nCurrent expression: -45*z**4 - 117*z**3 - 201*z**2 - 546*z + 42\nNo more calculations needed.\n-45*z**4 - 117*z**3 - 201*z**2 - 546*z + 42", "generated_answer": "-45*z**4 - 117*z**3 - 201*z**2 - 546*z + 42", "step_length": 6} {"cot_id": "199dec788e916f95e65c508e3b71f5e84de40f102aa6e55641abb950c56c7d6d", "datapoint": {"question": "Calculate the following: (34*z - 33)*(-15*z**2 + 29*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-510*z**3 + 1481*z**2 - 957*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2024, "polynomial_expr": "(34*z - 33)*(-15*z**2 + 29*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (34*z - 33)*(-15*z**2 + 29*z)\nExpanding the part (34*z - 33) using the distributive property, and we got: (34*z)*(-15*z**2 + 29*z) - 33*(-15*z**2 + 29*z)\n#Step 2:\nCurrent expression: (34*z)*(-15*z**2 + 29*z) - 33*(-15*z**2 + 29*z)\nSimplifying the partial expression: -33*(-15*z**2 + 29*z)\nExpanding the part (-15*z**2 + 29*z) using the distributive property, and we got: (29*z)*(-33) - 15*z**2*(-33)\nReplacing -33*(-15*z**2 + 29*z) with (29*z)*(-33) - 15*z**2*(-33) in the overall expression.\n#Step 3:\nCurrent expression: (29*z)*(-33) + (34*z)*(-15*z**2 + 29*z) - 15*z**2*(-33)\nSimplifying the partial expression: (34*z)*(-15*z**2 + 29*z)\nExpanding the part (-15*z**2 + 29*z) using the distributive property, and we got: (29*z)*(34*z) + (34*z)*(-15*z**2)\nReplacing (34*z)*(-15*z**2 + 29*z) with (29*z)*(34*z) + (34*z)*(-15*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (29*z)*(34*z) + (29*z)*(-33) + (34*z)*(-15*z**2) - 15*z**2*(-33)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-15*z**2)*-33 = 495*z**2\n (-15*z**2)*(34*z) = -510*z**3\n (29*z)*-33 = -957*z\n (29*z)*(34*z) = 986*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -510*z**3 + 495*z**2 + 986*z**2 - 957*z\nCombining like terms, got -510*z**3 + 1481*z**2 - 957*z\n#Step 6:\nCurrent expression: -510*z**3 + 1481*z**2 - 957*z\nNo more calculations needed.\n-510*z**3 + 1481*z**2 - 957*z", "generated_answer": "-510*z**3 + 1481*z**2 - 957*z", "step_length": 6} {"cot_id": "b3acf79f10c9c48f961861bcd80f7e8dd3ff9aa191dd0d9c1455f8b67860fc50", "datapoint": {"question": "Calculate the following: (-50*x**3 - 44)*(-39*x**3 - 23*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1950*x**6 + 1150*x**4 + 1716*x**3 + 1012*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2025, "polynomial_expr": "(-50*x**3 - 44)*(-39*x**3 - 23*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-50*x**3 - 44)*(-39*x**3 - 23*x)\nExpanding the part (-50*x**3 - 44) using the distributive property, and we got: (-50*x**3)*(-39*x**3 - 23*x) - 44*(-39*x**3 - 23*x)\n#Step 2:\nCurrent expression: (-50*x**3)*(-39*x**3 - 23*x) - 44*(-39*x**3 - 23*x)\nSimplifying the partial expression: -44*(-39*x**3 - 23*x)\nExpanding the part (-39*x**3 - 23*x) using the distributive property, and we got: -23*x*(-44) - 39*x**3*(-44)\nReplacing -44*(-39*x**3 - 23*x) with -23*x*(-44) - 39*x**3*(-44) in the overall expression.\n#Step 3:\nCurrent expression: -23*x*(-44) + (-50*x**3)*(-39*x**3 - 23*x) - 39*x**3*(-44)\nSimplifying the partial expression: (-50*x**3)*(-39*x**3 - 23*x)\nExpanding the part (-39*x**3 - 23*x) using the distributive property, and we got: (-23*x)*(-50*x**3) + (-50*x**3)*(-39*x**3)\nReplacing (-50*x**3)*(-39*x**3 - 23*x) with (-23*x)*(-50*x**3) + (-50*x**3)*(-39*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-23*x)*(-50*x**3) - 23*x*(-44) + (-50*x**3)*(-39*x**3) - 39*x**3*(-44)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*x**3)*-44 = 1716*x**3\n (-39*x**3)*(-50*x**3) = 1950*x**6\n (-23*x)*-44 = 1012*x\n (-23*x)*(-50*x**3) = 1150*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1950*x**6 + 1150*x**4 + 1716*x**3 + 1012*x\nNo more calculations needed.\n1950*x**6 + 1150*x**4 + 1716*x**3 + 1012*x", "generated_answer": "1950*x**6 + 1150*x**4 + 1716*x**3 + 1012*x", "step_length": 5} {"cot_id": "dc84e5f1affc499cd93141351df5ca1858e6172e1463d274530ee651d12a5f5d", "datapoint": {"question": "Simplify this expression: (7*z**3 + 8*z**2)*(57*z**3 + 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "399*z**6 + 456*z**5 + 336*z**3 + 384*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2026, "polynomial_expr": "(7*z**3 + 8*z**2)*(57*z**3 + 48)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7*z**3 + 8*z**2)*(57*z**3 + 48)\nExpanding the part (57*z**3 + 48) using the distributive property, and we got: (57*z**3)*(7*z**3 + 8*z**2) + 48*(7*z**3 + 8*z**2)\n#Step 2:\nCurrent expression: (57*z**3)*(7*z**3 + 8*z**2) + 48*(7*z**3 + 8*z**2)\nSimplifying the partial expression: 48*(7*z**3 + 8*z**2)\nExpanding the part (7*z**3 + 8*z**2) using the distributive property, and we got: (8*z**2)*48 + (7*z**3)*48\nReplacing 48*(7*z**3 + 8*z**2) with (8*z**2)*48 + (7*z**3)*48 in the overall expression.\n#Step 3:\nCurrent expression: (8*z**2)*48 + (7*z**3)*48 + (57*z**3)*(7*z**3 + 8*z**2)\nSimplifying the partial expression: (57*z**3)*(7*z**3 + 8*z**2)\nExpanding the part (7*z**3 + 8*z**2) using the distributive property, and we got: (8*z**2)*(57*z**3) + (7*z**3)*(57*z**3)\nReplacing (57*z**3)*(7*z**3 + 8*z**2) with (8*z**2)*(57*z**3) + (7*z**3)*(57*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (8*z**2)*(57*z**3) + (8*z**2)*48 + (7*z**3)*(57*z**3) + (7*z**3)*48\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (7*z**3)*48 = 336*z**3\n (7*z**3)*(57*z**3) = 399*z**6\n (8*z**2)*48 = 384*z**2\n (8*z**2)*(57*z**3) = 456*z**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 399*z**6 + 456*z**5 + 336*z**3 + 384*z**2\nNo more calculations needed.\n399*z**6 + 456*z**5 + 336*z**3 + 384*z**2", "generated_answer": "399*z**6 + 456*z**5 + 336*z**3 + 384*z**2", "step_length": 5} {"cot_id": "5cebcb55603f3a4e4e02f69bc7fa958e4ea603ea64ae481c92b782ec02f5c8b8", "datapoint": {"question": "Calculate the following: -30*y**2 + 190*y - 220\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-30*y**2 + 190*y - 220", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2027, "polynomial_expr": "-30*y**2 + 190*y - 220", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -30*y**2 + 190*y - 220\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -30*y**2 + 190*y - 220\nNo more calculations needed.\n-30*y**2 + 190*y - 220", "generated_answer": "-30*y**2 + 190*y - 220", "step_length": 2} {"cot_id": "2c0360120ba272c6a9c155d423e64e54c06e4721658b97b30860d3987d6d006e", "datapoint": {"question": "Calculate the following: (-6*y**3 + 6*y)*(-3*y**3 + 34*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "18*y**6 - 204*y**5 - 18*y**4 + 204*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2028, "polynomial_expr": "(-6*y**3 + 6*y)*(-3*y**3 + 34*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-6*y**3 + 6*y)*(-3*y**3 + 34*y**2)\nExpanding the part (-6*y**3 + 6*y) using the distributive property, and we got: (6*y)*(-3*y**3 + 34*y**2) + (-6*y**3)*(-3*y**3 + 34*y**2)\n#Step 2:\nCurrent expression: (6*y)*(-3*y**3 + 34*y**2) + (-6*y**3)*(-3*y**3 + 34*y**2)\nSimplifying the partial expression: (-6*y**3)*(-3*y**3 + 34*y**2)\nExpanding the part (-3*y**3 + 34*y**2) using the distributive property, and we got: (34*y**2)*(-6*y**3) + (-6*y**3)*(-3*y**3)\nReplacing (-6*y**3)*(-3*y**3 + 34*y**2) with (34*y**2)*(-6*y**3) + (-6*y**3)*(-3*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (6*y)*(-3*y**3 + 34*y**2) + (34*y**2)*(-6*y**3) + (-6*y**3)*(-3*y**3)\nSimplifying the partial expression: (6*y)*(-3*y**3 + 34*y**2)\nExpanding the part (-3*y**3 + 34*y**2) using the distributive property, and we got: (6*y)*(34*y**2) + (6*y)*(-3*y**3)\nReplacing (6*y)*(-3*y**3 + 34*y**2) with (6*y)*(34*y**2) + (6*y)*(-3*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (6*y)*(34*y**2) + (6*y)*(-3*y**3) + (34*y**2)*(-6*y**3) + (-6*y**3)*(-3*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-3*y**3)*(-6*y**3) = 18*y**6\n (-3*y**3)*(6*y) = -18*y**4\n (34*y**2)*(-6*y**3) = -204*y**5\n (34*y**2)*(6*y) = 204*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 18*y**6 - 204*y**5 - 18*y**4 + 204*y**3\nNo more calculations needed.\n18*y**6 - 204*y**5 - 18*y**4 + 204*y**3", "generated_answer": "18*y**6 - 204*y**5 - 18*y**4 + 204*y**3", "step_length": 5} {"cot_id": "120c6f82b51a6f9c6f4bb45243f55c385e7c19f3488392a843cd42f88b6b19ce", "datapoint": {"question": "Simplify this expression: (22*x**2 + 2)*(33*x**3 + 30*x**2 + 56*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "726*x**5 + 660*x**4 + 1298*x**3 + 60*x**2 + 112*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2029, "polynomial_expr": "(22*x**2 + 2)*(33*x**3 + 30*x**2 + 56*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (22*x**2 + 2)*(33*x**3 + 30*x**2 + 56*x)\nExpanding the part (22*x**2 + 2) using the distributive property, and we got: (22*x**2)*(33*x**3 + 30*x**2 + 56*x) + 2*(33*x**3 + 30*x**2 + 56*x)\n#Step 2:\nCurrent expression: (22*x**2)*(33*x**3 + 30*x**2 + 56*x) + 2*(33*x**3 + 30*x**2 + 56*x)\nSimplifying the partial expression: 2*(33*x**3 + 30*x**2 + 56*x)\nExpanding the part (33*x**3 + 30*x**2 + 56*x) using the distributive property, and we got: (56*x)*2 + (30*x**2)*2 + (33*x**3)*2\nReplacing 2*(33*x**3 + 30*x**2 + 56*x) with (56*x)*2 + (30*x**2)*2 + (33*x**3)*2 in the overall expression.\n#Step 3:\nCurrent expression: (56*x)*2 + (22*x**2)*(33*x**3 + 30*x**2 + 56*x) + (30*x**2)*2 + (33*x**3)*2\nSimplifying the partial expression: (22*x**2)*(33*x**3 + 30*x**2 + 56*x)\nExpanding the part (33*x**3 + 30*x**2 + 56*x) using the distributive property, and we got: (56*x)*(22*x**2) + (22*x**2)*(30*x**2) + (22*x**2)*(33*x**3)\nReplacing (22*x**2)*(33*x**3 + 30*x**2 + 56*x) with (56*x)*(22*x**2) + (22*x**2)*(30*x**2) + (22*x**2)*(33*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (56*x)*(22*x**2) + (56*x)*2 + (22*x**2)*(30*x**2) + (22*x**2)*(33*x**3) + (30*x**2)*2 + (33*x**3)*2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (30*x**2)*2 = 60*x**2\n (30*x**2)*(22*x**2) = 660*x**4\n (33*x**3)*2 = 66*x**3\n (33*x**3)*(22*x**2) = 726*x**5\n (56*x)*2 = 112*x\n (56*x)*(22*x**2) = 1232*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 726*x**5 + 660*x**4 + 66*x**3 + 1232*x**3 + 60*x**2 + 112*x\nCombining like terms, got 726*x**5 + 660*x**4 + 1298*x**3 + 60*x**2 + 112*x\n#Step 6:\nCurrent expression: 726*x**5 + 660*x**4 + 1298*x**3 + 60*x**2 + 112*x\nNo more calculations needed.\n726*x**5 + 660*x**4 + 1298*x**3 + 60*x**2 + 112*x", "generated_answer": "726*x**5 + 660*x**4 + 1298*x**3 + 60*x**2 + 112*x", "step_length": 6} {"cot_id": "e688c839ea828b05dd4d14954150d140d88a148fa019654a99d05032f588cdde", "datapoint": {"question": "Calculate the following: 34*y**2*(-37*y - 11)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1258*y**3 - 374*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2030, "polynomial_expr": "34*y**2*(-37*y - 11)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 34*y**2*(-37*y - 11)\nExpanding the part (-37*y - 11) using the distributive property, and we got: (-37*y)*(34*y**2) - 374*y**2\n#Step 2:\nCurrent expression: (-37*y)*(34*y**2) - 374*y**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -11*(34*y**2) = -374*y**2\n (-37*y)*(34*y**2) = -1258*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1258*y**3 - 374*y**2\nNo more calculations needed.\n-1258*y**3 - 374*y**2", "generated_answer": "-1258*y**3 - 374*y**2", "step_length": 3} {"cot_id": "c47ced694bdc8c32a7f92b2647c1ad7ef122692c1044d3fb97c9066a5ecffd6b", "datapoint": {"question": "Simplify this expression: (6 - 18*x**3)*(-4*x**3 - 45*x**2 - 30*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "72*x**6 + 810*x**5 + 540*x**4 - 24*x**3 - 270*x**2 - 180*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2031, "polynomial_expr": "(6 - 18*x**3)*(-4*x**3 - 45*x**2 - 30*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6 - 18*x**3)*(-4*x**3 - 45*x**2 - 30*x)\nExpanding the part (6 - 18*x**3) using the distributive property, and we got: (-18*x**3)*(-4*x**3 - 45*x**2 - 30*x) + 6*(-4*x**3 - 45*x**2 - 30*x)\n#Step 2:\nCurrent expression: (-18*x**3)*(-4*x**3 - 45*x**2 - 30*x) + 6*(-4*x**3 - 45*x**2 - 30*x)\nSimplifying the partial expression: 6*(-4*x**3 - 45*x**2 - 30*x)\nExpanding the part (-4*x**3 - 45*x**2 - 30*x) using the distributive property, and we got: -30*x*6 - 45*x**2*6 - 4*x**3*6\nReplacing 6*(-4*x**3 - 45*x**2 - 30*x) with -30*x*6 - 45*x**2*6 - 4*x**3*6 in the overall expression.\n#Step 3:\nCurrent expression: -30*x*6 - 45*x**2*6 + (-18*x**3)*(-4*x**3 - 45*x**2 - 30*x) - 4*x**3*6\nSimplifying the partial expression: (-18*x**3)*(-4*x**3 - 45*x**2 - 30*x)\nExpanding the part (-4*x**3 - 45*x**2 - 30*x) using the distributive property, and we got: (-30*x)*(-18*x**3) + (-45*x**2)*(-18*x**3) + (-18*x**3)*(-4*x**3)\nReplacing (-18*x**3)*(-4*x**3 - 45*x**2 - 30*x) with (-30*x)*(-18*x**3) + (-45*x**2)*(-18*x**3) + (-18*x**3)*(-4*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-30*x)*(-18*x**3) - 30*x*6 + (-45*x**2)*(-18*x**3) - 45*x**2*6 + (-18*x**3)*(-4*x**3) - 4*x**3*6\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*x**2)*6 = -270*x**2\n (-45*x**2)*(-18*x**3) = 810*x**5\n (-30*x)*6 = -180*x\n (-30*x)*(-18*x**3) = 540*x**4\n (-4*x**3)*6 = -24*x**3\n (-4*x**3)*(-18*x**3) = 72*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 72*x**6 + 810*x**5 + 540*x**4 - 24*x**3 - 270*x**2 - 180*x\nNo more calculations needed.\n72*x**6 + 810*x**5 + 540*x**4 - 24*x**3 - 270*x**2 - 180*x", "generated_answer": "72*x**6 + 810*x**5 + 540*x**4 - 24*x**3 - 270*x**2 - 180*x", "step_length": 5} {"cot_id": "2ca438c52d4d5a91ece9749b347eab048f49bafaf0ad15567248c6f0d9bee744", "datapoint": {"question": "Calculate the following: (41*z - 34)*(-14*z**3 + 6*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-574*z**4 + 476*z**3 + 246*z**2 - 204*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2032, "polynomial_expr": "(41*z - 34)*(-14*z**3 + 6*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (41*z - 34)*(-14*z**3 + 6*z)\nExpanding the part (41*z - 34) using the distributive property, and we got: (41*z)*(-14*z**3 + 6*z) - 34*(-14*z**3 + 6*z)\n#Step 2:\nCurrent expression: (41*z)*(-14*z**3 + 6*z) - 34*(-14*z**3 + 6*z)\nSimplifying the partial expression: -34*(-14*z**3 + 6*z)\nExpanding the part (-14*z**3 + 6*z) using the distributive property, and we got: (6*z)*(-34) - 14*z**3*(-34)\nReplacing -34*(-14*z**3 + 6*z) with (6*z)*(-34) - 14*z**3*(-34) in the overall expression.\n#Step 3:\nCurrent expression: (6*z)*(-34) + (41*z)*(-14*z**3 + 6*z) - 14*z**3*(-34)\nSimplifying the partial expression: (41*z)*(-14*z**3 + 6*z)\nExpanding the part (-14*z**3 + 6*z) using the distributive property, and we got: (6*z)*(41*z) + (41*z)*(-14*z**3)\nReplacing (41*z)*(-14*z**3 + 6*z) with (6*z)*(41*z) + (41*z)*(-14*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (6*z)*(41*z) + (6*z)*(-34) + (41*z)*(-14*z**3) - 14*z**3*(-34)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-14*z**3)*-34 = 476*z**3\n (-14*z**3)*(41*z) = -574*z**4\n (6*z)*-34 = -204*z\n (6*z)*(41*z) = 246*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -574*z**4 + 476*z**3 + 246*z**2 - 204*z\nNo more calculations needed.\n-574*z**4 + 476*z**3 + 246*z**2 - 204*z", "generated_answer": "-574*z**4 + 476*z**3 + 246*z**2 - 204*z", "step_length": 5} {"cot_id": "9bc4de27ba2369c2b426fcf81e44d8568ecf83cecdbd8a88ceafbe5f5d3615ad", "datapoint": {"question": "Calculate the following: (-19*z**2 - 10)*(13*z**3 - 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-247*z**5 - 130*z**3 + 608*z**2 + 320", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2033, "polynomial_expr": "(-19*z**2 - 10)*(13*z**3 - 32)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-19*z**2 - 10)*(13*z**3 - 32)\nExpanding the part (13*z**3 - 32) using the distributive property, and we got: (13*z**3)*(-19*z**2 - 10) - 32*(-19*z**2 - 10)\n#Step 2:\nCurrent expression: (13*z**3)*(-19*z**2 - 10) - 32*(-19*z**2 - 10)\nSimplifying the partial expression: -32*(-19*z**2 - 10)\nExpanding the part (-19*z**2 - 10) using the distributive property, and we got: -19*z**2*(-32) - 10*(-32)\nReplacing -32*(-19*z**2 - 10) with -19*z**2*(-32) - 10*(-32) in the overall expression.\n#Step 3:\nCurrent expression: -19*z**2*(-32) + (13*z**3)*(-19*z**2 - 10) + 320\nSimplifying the partial expression: (13*z**3)*(-19*z**2 - 10)\nExpanding the part (-19*z**2 - 10) using the distributive property, and we got: -130*z**3 + (-19*z**2)*(13*z**3)\nReplacing (13*z**3)*(-19*z**2 - 10) with -130*z**3 + (-19*z**2)*(13*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -10*13*z**3 + (-19*z**2)*(13*z**3) - 19*z**2*(-32) + 320\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*z**2)*-32 = 608*z**2\n (-19*z**2)*(13*z**3) = -247*z**5\n -10*13*z**3 = -130*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -247*z**5 - 130*z**3 + 608*z**2 + 320\nNo more calculations needed.\n-247*z**5 - 130*z**3 + 608*z**2 + 320", "generated_answer": "-247*z**5 - 130*z**3 + 608*z**2 + 320", "step_length": 5} {"cot_id": "b9078da2264b3a9e2fe055b30a19880c7a80c015ca516077ff2ecdc111926a46", "datapoint": {"question": "Calculate the following: (14*x**3 + 50*x**2 - 22)*(5*x**3 + 47*x**2 - 44*x - 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "70*x**6 + 908*x**5 + 1734*x**4 - 2772*x**3 - 2684*x**2 + 968*x + 726", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2034, "polynomial_expr": "(14*x**3 + 50*x**2 - 22)*(5*x**3 + 47*x**2 - 44*x - 33)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14*x**3 + 50*x**2 - 22)*(5*x**3 + 47*x**2 - 44*x - 33)\nExpanding the part (14*x**3 + 50*x**2 - 22) using the distributive property, and we got: (50*x**2)*(5*x**3 + 47*x**2 - 44*x - 33) + (14*x**3)*(5*x**3 + 47*x**2 - 44*x - 33) - 22*(5*x**3 + 47*x**2 - 44*x - 33)\n#Step 2:\nCurrent expression: (50*x**2)*(5*x**3 + 47*x**2 - 44*x - 33) + (14*x**3)*(5*x**3 + 47*x**2 - 44*x - 33) - 22*(5*x**3 + 47*x**2 - 44*x - 33)\nSimplifying the partial expression: -22*(5*x**3 + 47*x**2 - 44*x - 33)\nExpanding the part (5*x**3 + 47*x**2 - 44*x - 33) using the distributive property, and we got: -44*x*(-22) + (47*x**2)*(-22) + (5*x**3)*(-22) - 33*(-22)\nReplacing -22*(5*x**3 + 47*x**2 - 44*x - 33) with -44*x*(-22) + (47*x**2)*(-22) + (5*x**3)*(-22) - 33*(-22) in the overall expression.\n#Step 3:\nCurrent expression: -44*x*(-22) + (47*x**2)*(-22) + (50*x**2)*(5*x**3 + 47*x**2 - 44*x - 33) + (5*x**3)*(-22) + (14*x**3)*(5*x**3 + 47*x**2 - 44*x - 33) + 726\nSimplifying the partial expression: (14*x**3)*(5*x**3 + 47*x**2 - 44*x - 33)\nExpanding the part (5*x**3 + 47*x**2 - 44*x - 33) using the distributive property, and we got: (-44*x)*(14*x**3) - 462*x**3 + (47*x**2)*(14*x**3) + (5*x**3)*(14*x**3)\nReplacing (14*x**3)*(5*x**3 + 47*x**2 - 44*x - 33) with (-44*x)*(14*x**3) - 462*x**3 + (47*x**2)*(14*x**3) + (5*x**3)*(14*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-44*x)*(14*x**3) - 44*x*(-22) - 33*14*x**3 + (47*x**2)*(14*x**3) + (47*x**2)*(-22) + (50*x**2)*(5*x**3 + 47*x**2 - 44*x - 33) + (5*x**3)*(14*x**3) + (5*x**3)*(-22) + 726\nSimplifying the partial expression: (50*x**2)*(5*x**3 + 47*x**2 - 44*x - 33)\nExpanding the part (5*x**3 + 47*x**2 - 44*x - 33) using the distributive property, and we got: (-44*x)*(50*x**2) - 1650*x**2 + (47*x**2)*(50*x**2) + (50*x**2)*(5*x**3)\nReplacing (50*x**2)*(5*x**3 + 47*x**2 - 44*x - 33) with (-44*x)*(50*x**2) - 1650*x**2 + (47*x**2)*(50*x**2) + (50*x**2)*(5*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-44*x)*(50*x**2) + (-44*x)*(14*x**3) - 44*x*(-22) - 33*14*x**3 - 33*50*x**2 + (47*x**2)*(50*x**2) + (47*x**2)*(14*x**3) + (47*x**2)*(-22) + (50*x**2)*(5*x**3) + (5*x**3)*(14*x**3) + (5*x**3)*(-22) + 726\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-44*x)*-22 = 968*x\n (-44*x)*(14*x**3) = -616*x**4\n (-44*x)*(50*x**2) = -2200*x**3\n (5*x**3)*-22 = -110*x**3\n (5*x**3)*(14*x**3) = 70*x**6\n (5*x**3)*(50*x**2) = 250*x**5\n (47*x**2)*-22 = -1034*x**2\n (47*x**2)*(14*x**3) = 658*x**5\n (47*x**2)*(50*x**2) = 2350*x**4\n -33*14*x**3 = -462*x**3\n -33*50*x**2 = -1650*x**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 70*x**6 + 250*x**5 + 658*x**5 - 616*x**4 + 2350*x**4 - 2200*x**3 - 462*x**3 - 110*x**3 - 1650*x**2 - 1034*x**2 + 968*x + 726\nCombining like terms, got 70*x**6 + 908*x**5 + 1734*x**4 - 2772*x**3 - 2684*x**2 + 968*x + 726\n#Step 7:\nCurrent expression: 70*x**6 + 908*x**5 + 1734*x**4 - 2772*x**3 - 2684*x**2 + 968*x + 726\nNo more calculations needed.\n70*x**6 + 908*x**5 + 1734*x**4 - 2772*x**3 - 2684*x**2 + 968*x + 726", "generated_answer": "70*x**6 + 908*x**5 + 1734*x**4 - 2772*x**3 - 2684*x**2 + 968*x + 726", "step_length": 7} {"cot_id": "22c3cfd5462c180f133b1a15edf2a8914c981b0a2022d55a352d6221349f79dc", "datapoint": {"question": "Calculate the following: (36 - 21*y)*(-3*y**2 + y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "63*y**3 - 129*y**2 + 36*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2035, "polynomial_expr": "(36 - 21*y)*(-3*y**2 + y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (36 - 21*y)*(-3*y**2 + y)\nExpanding the part (36 - 21*y) using the distributive property, and we got: (-21*y)*(-3*y**2 + y) + 36*(-3*y**2 + y)\n#Step 2:\nCurrent expression: (-21*y)*(-3*y**2 + y) + 36*(-3*y**2 + y)\nSimplifying the partial expression: 36*(-3*y**2 + y)\nExpanding the part (-3*y**2 + y) using the distributive property, and we got: y*36 - 3*y**2*36\nReplacing 36*(-3*y**2 + y) with y*36 - 3*y**2*36 in the overall expression.\n#Step 3:\nCurrent expression: (-21*y)*(-3*y**2 + y) + y*36 - 3*y**2*36\nSimplifying the partial expression: (-21*y)*(-3*y**2 + y)\nExpanding the part (-3*y**2 + y) using the distributive property, and we got: (-21*y)*y + (-21*y)*(-3*y**2)\nReplacing (-21*y)*(-3*y**2 + y) with (-21*y)*y + (-21*y)*(-3*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (-21*y)*y + (-21*y)*(-3*y**2) + y*36 - 3*y**2*36\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n y*36 = 36*y\n y*(-21*y) = -21*y**2\n (-3*y**2)*36 = -108*y**2\n (-3*y**2)*(-21*y) = 63*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 63*y**3 - 108*y**2 - 21*y**2 + 36*y\nCombining like terms, got 63*y**3 - 129*y**2 + 36*y\n#Step 6:\nCurrent expression: 63*y**3 - 129*y**2 + 36*y\nNo more calculations needed.\n63*y**3 - 129*y**2 + 36*y", "generated_answer": "63*y**3 - 129*y**2 + 36*y", "step_length": 6} {"cot_id": "5a3ea116604954022ae13ebbc177202aaf26011d81a19e9041d1624cf1a2da52", "datapoint": {"question": "Calculate the following: 78*x**2*(4*x**3 - 12*x**2 + 23*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "312*x**5 - 936*x**4 + 1794*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2036, "polynomial_expr": "78*x**2*(4*x**3 - 12*x**2 + 23*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 78*x**2*(4*x**3 - 12*x**2 + 23*x)\nExpanding the part (4*x**3 - 12*x**2 + 23*x) using the distributive property, and we got: (23*x)*(78*x**2) + (-12*x**2)*(78*x**2) + (78*x**2)*(4*x**3)\n#Step 2:\nCurrent expression: (23*x)*(78*x**2) + (-12*x**2)*(78*x**2) + (78*x**2)*(4*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*x**2)*(78*x**2) = -936*x**4\n (4*x**3)*(78*x**2) = 312*x**5\n (23*x)*(78*x**2) = 1794*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 312*x**5 - 936*x**4 + 1794*x**3\nNo more calculations needed.\n312*x**5 - 936*x**4 + 1794*x**3", "generated_answer": "312*x**5 - 936*x**4 + 1794*x**3", "step_length": 3} {"cot_id": "e5948907a57e1dee601e0685688e9815dadd7ec9a9f04d2e726ffea195e3caa4", "datapoint": {"question": "Simplify this expression: (28 - 5*y)*(39 - 12*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "60*y**3 - 336*y**2 - 195*y + 1092", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2037, "polynomial_expr": "(28 - 5*y)*(39 - 12*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28 - 5*y)*(39 - 12*y**2)\nExpanding the part (28 - 5*y) using the distributive property, and we got: (-5*y)*(39 - 12*y**2) + 28*(39 - 12*y**2)\n#Step 2:\nCurrent expression: (-5*y)*(39 - 12*y**2) + 28*(39 - 12*y**2)\nSimplifying the partial expression: 28*(39 - 12*y**2)\nExpanding the part (39 - 12*y**2) using the distributive property, and we got: -12*y**2*28 + 39*28\nReplacing 28*(39 - 12*y**2) with -12*y**2*28 + 39*28 in the overall expression.\n#Step 3:\nCurrent expression: (-5*y)*(39 - 12*y**2) - 12*y**2*28 + 1092\nSimplifying the partial expression: (-5*y)*(39 - 12*y**2)\nExpanding the part (39 - 12*y**2) using the distributive property, and we got: (-5*y)*(-12*y**2) + 39*(-5*y)\nReplacing (-5*y)*(39 - 12*y**2) with (-5*y)*(-12*y**2) + 39*(-5*y) in the overall expression.\n#Step 4:\nCurrent expression: (-5*y)*(-12*y**2) + 39*(-5)*y - 12*y**2*28 + 1092\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*y**2)*28 = -336*y**2\n (-12*y**2)*(-5*y) = 60*y**3\n 39*-5*y = -195*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 60*y**3 - 336*y**2 - 195*y + 1092\nNo more calculations needed.\n60*y**3 - 336*y**2 - 195*y + 1092", "generated_answer": "60*y**3 - 336*y**2 - 195*y + 1092", "step_length": 5} {"cot_id": "39ad019fcaad7d1e82788ab0095f372a921c5d1c6bf4c79c3d58cdce10d8f4c3", "datapoint": {"question": "Simplify this expression: (-27*x**3 + 35*x**2)*(-21*x**3 - 41)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "567*x**6 - 735*x**5 + 1107*x**3 - 1435*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2038, "polynomial_expr": "(-27*x**3 + 35*x**2)*(-21*x**3 - 41)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-27*x**3 + 35*x**2)*(-21*x**3 - 41)\nExpanding the part (-21*x**3 - 41) using the distributive property, and we got: (-21*x**3)*(-27*x**3 + 35*x**2) - 41*(-27*x**3 + 35*x**2)\n#Step 2:\nCurrent expression: (-21*x**3)*(-27*x**3 + 35*x**2) - 41*(-27*x**3 + 35*x**2)\nSimplifying the partial expression: -41*(-27*x**3 + 35*x**2)\nExpanding the part (-27*x**3 + 35*x**2) using the distributive property, and we got: (35*x**2)*(-41) - 27*x**3*(-41)\nReplacing -41*(-27*x**3 + 35*x**2) with (35*x**2)*(-41) - 27*x**3*(-41) in the overall expression.\n#Step 3:\nCurrent expression: (35*x**2)*(-41) - 27*x**3*(-41) + (-21*x**3)*(-27*x**3 + 35*x**2)\nSimplifying the partial expression: (-21*x**3)*(-27*x**3 + 35*x**2)\nExpanding the part (-27*x**3 + 35*x**2) using the distributive property, and we got: (35*x**2)*(-21*x**3) + (-27*x**3)*(-21*x**3)\nReplacing (-21*x**3)*(-27*x**3 + 35*x**2) with (35*x**2)*(-21*x**3) + (-27*x**3)*(-21*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (35*x**2)*(-21*x**3) + (35*x**2)*(-41) + (-27*x**3)*(-21*x**3) - 27*x**3*(-41)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-27*x**3)*-41 = 1107*x**3\n (-27*x**3)*(-21*x**3) = 567*x**6\n (35*x**2)*-41 = -1435*x**2\n (35*x**2)*(-21*x**3) = -735*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 567*x**6 - 735*x**5 + 1107*x**3 - 1435*x**2\nNo more calculations needed.\n567*x**6 - 735*x**5 + 1107*x**3 - 1435*x**2", "generated_answer": "567*x**6 - 735*x**5 + 1107*x**3 - 1435*x**2", "step_length": 5} {"cot_id": "fa5ad6a8b18ceabd9dd8847ed2840d4cb4949a53e8ecc12dc71fb82b77809865", "datapoint": {"question": "Simplify this expression: (-95*y**2 + 14*y)*(53*y**2 + 12*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-5035*y**4 - 398*y**3 + 168*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2039, "polynomial_expr": "(-95*y**2 + 14*y)*(53*y**2 + 12*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-95*y**2 + 14*y)*(53*y**2 + 12*y)\nExpanding the part (-95*y**2 + 14*y) using the distributive property, and we got: (14*y)*(53*y**2 + 12*y) + (-95*y**2)*(53*y**2 + 12*y)\n#Step 2:\nCurrent expression: (14*y)*(53*y**2 + 12*y) + (-95*y**2)*(53*y**2 + 12*y)\nSimplifying the partial expression: (-95*y**2)*(53*y**2 + 12*y)\nExpanding the part (53*y**2 + 12*y) using the distributive property, and we got: (12*y)*(-95*y**2) + (-95*y**2)*(53*y**2)\nReplacing (-95*y**2)*(53*y**2 + 12*y) with (12*y)*(-95*y**2) + (-95*y**2)*(53*y**2) in the overall expression.\n#Step 3:\nCurrent expression: (12*y)*(-95*y**2) + (14*y)*(53*y**2 + 12*y) + (-95*y**2)*(53*y**2)\nSimplifying the partial expression: (14*y)*(53*y**2 + 12*y)\nExpanding the part (53*y**2 + 12*y) using the distributive property, and we got: (12*y)*(14*y) + (14*y)*(53*y**2)\nReplacing (14*y)*(53*y**2 + 12*y) with (12*y)*(14*y) + (14*y)*(53*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (12*y)*(14*y) + (12*y)*(-95*y**2) + (14*y)*(53*y**2) + (-95*y**2)*(53*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (12*y)*(-95*y**2) = -1140*y**3\n (12*y)*(14*y) = 168*y**2\n (53*y**2)*(-95*y**2) = -5035*y**4\n (53*y**2)*(14*y) = 742*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -5035*y**4 - 1140*y**3 + 742*y**3 + 168*y**2\nCombining like terms, got -5035*y**4 - 398*y**3 + 168*y**2\n#Step 6:\nCurrent expression: -5035*y**4 - 398*y**3 + 168*y**2\nNo more calculations needed.\n-5035*y**4 - 398*y**3 + 168*y**2", "generated_answer": "-5035*y**4 - 398*y**3 + 168*y**2", "step_length": 6} {"cot_id": "2bc280d9830e0df07c29be22d3455f4ed94788cdf3774675e9e810fa2e466ba2", "datapoint": {"question": "Simplify this expression: (-34*z - 47)*(27*z**3 - 41*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-918*z**4 - 1269*z**3 + 1394*z**2 + 1927*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2040, "polynomial_expr": "(-34*z - 47)*(27*z**3 - 41*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-34*z - 47)*(27*z**3 - 41*z)\nExpanding the part (-34*z - 47) using the distributive property, and we got: (-34*z)*(27*z**3 - 41*z) - 47*(27*z**3 - 41*z)\n#Step 2:\nCurrent expression: (-34*z)*(27*z**3 - 41*z) - 47*(27*z**3 - 41*z)\nSimplifying the partial expression: -47*(27*z**3 - 41*z)\nExpanding the part (27*z**3 - 41*z) using the distributive property, and we got: -41*z*(-47) + (27*z**3)*(-47)\nReplacing -47*(27*z**3 - 41*z) with -41*z*(-47) + (27*z**3)*(-47) in the overall expression.\n#Step 3:\nCurrent expression: -41*z*(-47) + (-34*z)*(27*z**3 - 41*z) + (27*z**3)*(-47)\nSimplifying the partial expression: (-34*z)*(27*z**3 - 41*z)\nExpanding the part (27*z**3 - 41*z) using the distributive property, and we got: (-41*z)*(-34*z) + (-34*z)*(27*z**3)\nReplacing (-34*z)*(27*z**3 - 41*z) with (-41*z)*(-34*z) + (-34*z)*(27*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-41*z)*(-34*z) - 41*z*(-47) + (-34*z)*(27*z**3) + (27*z**3)*(-47)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*z)*-47 = 1927*z\n (-41*z)*(-34*z) = 1394*z**2\n (27*z**3)*-47 = -1269*z**3\n (27*z**3)*(-34*z) = -918*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -918*z**4 - 1269*z**3 + 1394*z**2 + 1927*z\nNo more calculations needed.\n-918*z**4 - 1269*z**3 + 1394*z**2 + 1927*z", "generated_answer": "-918*z**4 - 1269*z**3 + 1394*z**2 + 1927*z", "step_length": 5} {"cot_id": "a332db343bfdd436e256d48971f2b5e5506e5183ddaa1b1c9b7b50085b3b01f7", "datapoint": {"question": "Simplify this expression: (18*x**2 - 4)*(-55*x**3 + 43*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-990*x**5 + 994*x**3 - 172*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2041, "polynomial_expr": "(18*x**2 - 4)*(-55*x**3 + 43*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (18*x**2 - 4)*(-55*x**3 + 43*x)\nExpanding the part (18*x**2 - 4) using the distributive property, and we got: (18*x**2)*(-55*x**3 + 43*x) - 4*(-55*x**3 + 43*x)\n#Step 2:\nCurrent expression: (18*x**2)*(-55*x**3 + 43*x) - 4*(-55*x**3 + 43*x)\nSimplifying the partial expression: -4*(-55*x**3 + 43*x)\nExpanding the part (-55*x**3 + 43*x) using the distributive property, and we got: (43*x)*(-4) - 55*x**3*(-4)\nReplacing -4*(-55*x**3 + 43*x) with (43*x)*(-4) - 55*x**3*(-4) in the overall expression.\n#Step 3:\nCurrent expression: (43*x)*(-4) + (18*x**2)*(-55*x**3 + 43*x) - 55*x**3*(-4)\nSimplifying the partial expression: (18*x**2)*(-55*x**3 + 43*x)\nExpanding the part (-55*x**3 + 43*x) using the distributive property, and we got: (43*x)*(18*x**2) + (18*x**2)*(-55*x**3)\nReplacing (18*x**2)*(-55*x**3 + 43*x) with (43*x)*(18*x**2) + (18*x**2)*(-55*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (43*x)*(18*x**2) + (43*x)*(-4) + (18*x**2)*(-55*x**3) - 55*x**3*(-4)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-55*x**3)*-4 = 220*x**3\n (-55*x**3)*(18*x**2) = -990*x**5\n (43*x)*-4 = -172*x\n (43*x)*(18*x**2) = 774*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -990*x**5 + 220*x**3 + 774*x**3 - 172*x\nCombining like terms, got -990*x**5 + 994*x**3 - 172*x\n#Step 6:\nCurrent expression: -990*x**5 + 994*x**3 - 172*x\nNo more calculations needed.\n-990*x**5 + 994*x**3 - 172*x", "generated_answer": "-990*x**5 + 994*x**3 - 172*x", "step_length": 6} {"cot_id": "735163b927b5e07a7530bbb0d82382ab9f7e0114e42e674111ae3fe1e450d028", "datapoint": {"question": "Simplify this expression: (10*y + 44)*(-3*y**3 - 21*y - 80)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-30*y**4 - 132*y**3 - 210*y**2 - 1724*y - 3520", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2042, "polynomial_expr": "(10*y + 44)*(-3*y**3 - 21*y - 80)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (10*y + 44)*(-3*y**3 - 21*y - 80)\nExpanding the part (10*y + 44) using the distributive property, and we got: (10*y)*(-3*y**3 - 21*y - 80) + 44*(-3*y**3 - 21*y - 80)\n#Step 2:\nCurrent expression: (10*y)*(-3*y**3 - 21*y - 80) + 44*(-3*y**3 - 21*y - 80)\nSimplifying the partial expression: 44*(-3*y**3 - 21*y - 80)\nExpanding the part (-3*y**3 - 21*y - 80) using the distributive property, and we got: -21*y*44 - 3*y**3*44 - 80*44\nReplacing 44*(-3*y**3 - 21*y - 80) with -21*y*44 - 3*y**3*44 - 80*44 in the overall expression.\n#Step 3:\nCurrent expression: -21*y*44 + (10*y)*(-3*y**3 - 21*y - 80) - 3*y**3*44 - 3520\nSimplifying the partial expression: (10*y)*(-3*y**3 - 21*y - 80)\nExpanding the part (-3*y**3 - 21*y - 80) using the distributive property, and we got: (-21*y)*(10*y) - 800*y + (10*y)*(-3*y**3)\nReplacing (10*y)*(-3*y**3 - 21*y - 80) with (-21*y)*(10*y) - 800*y + (10*y)*(-3*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-21*y)*(10*y) - 21*y*44 - 80*10*y + (10*y)*(-3*y**3) - 3*y**3*44 - 3520\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-21*y)*44 = -924*y\n (-21*y)*(10*y) = -210*y**2\n (-3*y**3)*44 = -132*y**3\n (-3*y**3)*(10*y) = -30*y**4\n -80*10*y = -800*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -30*y**4 - 132*y**3 - 210*y**2 - 924*y - 800*y - 3520\nCombining like terms, got -30*y**4 - 132*y**3 - 210*y**2 - 1724*y - 3520\n#Step 6:\nCurrent expression: -30*y**4 - 132*y**3 - 210*y**2 - 1724*y - 3520\nNo more calculations needed.\n-30*y**4 - 132*y**3 - 210*y**2 - 1724*y - 3520", "generated_answer": "-30*y**4 - 132*y**3 - 210*y**2 - 1724*y - 3520", "step_length": 6} {"cot_id": "087c4dd613f4b663a3f73b112d805cbad1ae1e78738a51e7e28d295c8ca01139", "datapoint": {"question": "Calculate the following: (-7*x**2 - 54)*(6*x**2 - 34*x + 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-42*x**4 + 238*x**3 - 590*x**2 + 1836*x - 2052", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2043, "polynomial_expr": "(-7*x**2 - 54)*(6*x**2 - 34*x + 38)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-7*x**2 - 54)*(6*x**2 - 34*x + 38)\nExpanding the part (-7*x**2 - 54) using the distributive property, and we got: (-7*x**2)*(6*x**2 - 34*x + 38) - 54*(6*x**2 - 34*x + 38)\n#Step 2:\nCurrent expression: (-7*x**2)*(6*x**2 - 34*x + 38) - 54*(6*x**2 - 34*x + 38)\nSimplifying the partial expression: -54*(6*x**2 - 34*x + 38)\nExpanding the part (6*x**2 - 34*x + 38) using the distributive property, and we got: -34*x*(-54) + (6*x**2)*(-54) + 38*(-54)\nReplacing -54*(6*x**2 - 34*x + 38) with -34*x*(-54) + (6*x**2)*(-54) + 38*(-54) in the overall expression.\n#Step 3:\nCurrent expression: -34*x*(-54) + (-7*x**2)*(6*x**2 - 34*x + 38) + (6*x**2)*(-54) - 2052\nSimplifying the partial expression: (-7*x**2)*(6*x**2 - 34*x + 38)\nExpanding the part (6*x**2 - 34*x + 38) using the distributive property, and we got: (-34*x)*(-7*x**2) + 38*(-7*x**2) + (-7*x**2)*(6*x**2)\nReplacing (-7*x**2)*(6*x**2 - 34*x + 38) with (-34*x)*(-7*x**2) + 38*(-7*x**2) + (-7*x**2)*(6*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-34*x)*(-7*x**2) - 34*x*(-54) + 38*(-7)*x**2 + (-7*x**2)*(6*x**2) + (6*x**2)*(-54) - 2052\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*x)*-54 = 1836*x\n (-34*x)*(-7*x**2) = 238*x**3\n (6*x**2)*-54 = -324*x**2\n (6*x**2)*(-7*x**2) = -42*x**4\n 38*-7*x**2 = -266*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -42*x**4 + 238*x**3 - 324*x**2 - 266*x**2 + 1836*x - 2052\nCombining like terms, got -42*x**4 + 238*x**3 - 590*x**2 + 1836*x - 2052\n#Step 6:\nCurrent expression: -42*x**4 + 238*x**3 - 590*x**2 + 1836*x - 2052\nNo more calculations needed.\n-42*x**4 + 238*x**3 - 590*x**2 + 1836*x - 2052", "generated_answer": "-42*x**4 + 238*x**3 - 590*x**2 + 1836*x - 2052", "step_length": 6} {"cot_id": "f02a9d512bbb49d78571d1d54acbf0b72eca48d77b4b91d526b3002efa001e6e", "datapoint": {"question": "Calculate the following: (3 - 2*z)*(14*z**2 + 44*z - 95)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-28*z**3 - 46*z**2 + 322*z - 285", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2044, "polynomial_expr": "(3 - 2*z)*(14*z**2 + 44*z - 95)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (3 - 2*z)*(14*z**2 + 44*z - 95)\nExpanding the part (3 - 2*z) using the distributive property, and we got: (-2*z)*(14*z**2 + 44*z - 95) + 3*(14*z**2 + 44*z - 95)\n#Step 2:\nCurrent expression: (-2*z)*(14*z**2 + 44*z - 95) + 3*(14*z**2 + 44*z - 95)\nSimplifying the partial expression: 3*(14*z**2 + 44*z - 95)\nExpanding the part (14*z**2 + 44*z - 95) using the distributive property, and we got: (44*z)*3 + (14*z**2)*3 - 95*3\nReplacing 3*(14*z**2 + 44*z - 95) with (44*z)*3 + (14*z**2)*3 - 95*3 in the overall expression.\n#Step 3:\nCurrent expression: (-2*z)*(14*z**2 + 44*z - 95) + (44*z)*3 + (14*z**2)*3 - 285\nSimplifying the partial expression: (-2*z)*(14*z**2 + 44*z - 95)\nExpanding the part (14*z**2 + 44*z - 95) using the distributive property, and we got: (-2*z)*(44*z) + (-2*z)*(14*z**2) - (-1)*190*z\nReplacing (-2*z)*(14*z**2 + 44*z - 95) with (-2*z)*(44*z) + (-2*z)*(14*z**2) - (-1)*190*z in the overall expression.\n#Step 4:\nCurrent expression: (-2*z)*(44*z) + (-2*z)*(14*z**2) - 95*(-2)*z + (44*z)*3 + (14*z**2)*3 - 285\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (14*z**2)*3 = 42*z**2\n (14*z**2)*(-2*z) = -28*z**3\n (44*z)*3 = 132*z\n (44*z)*(-2*z) = -88*z**2\n -95*-2*z = 190*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -28*z**3 - 88*z**2 + 42*z**2 + 132*z + 190*z - 285\nCombining like terms, got -28*z**3 - 46*z**2 + 322*z - 285\n#Step 6:\nCurrent expression: -28*z**3 - 46*z**2 + 322*z - 285\nNo more calculations needed.\n-28*z**3 - 46*z**2 + 322*z - 285", "generated_answer": "-28*z**3 - 46*z**2 + 322*z - 285", "step_length": 6} {"cot_id": "5585b9e5dbced18bd3413bc92fbb14ec786b490471a16f2cbbf9376eb2bbe790", "datapoint": {"question": "Calculate the following: (6 - 43*x**3)*(7*x**3 - 45*x**2 + 40*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-301*x**6 + 1935*x**5 - 1720*x**4 + 42*x**3 - 270*x**2 + 240*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2045, "polynomial_expr": "(6 - 43*x**3)*(7*x**3 - 45*x**2 + 40*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6 - 43*x**3)*(7*x**3 - 45*x**2 + 40*x)\nExpanding the part (6 - 43*x**3) using the distributive property, and we got: (-43*x**3)*(7*x**3 - 45*x**2 + 40*x) + 6*(7*x**3 - 45*x**2 + 40*x)\n#Step 2:\nCurrent expression: (-43*x**3)*(7*x**3 - 45*x**2 + 40*x) + 6*(7*x**3 - 45*x**2 + 40*x)\nSimplifying the partial expression: 6*(7*x**3 - 45*x**2 + 40*x)\nExpanding the part (7*x**3 - 45*x**2 + 40*x) using the distributive property, and we got: (40*x)*6 - 45*x**2*6 + (7*x**3)*6\nReplacing 6*(7*x**3 - 45*x**2 + 40*x) with (40*x)*6 - 45*x**2*6 + (7*x**3)*6 in the overall expression.\n#Step 3:\nCurrent expression: (40*x)*6 - 45*x**2*6 + (-43*x**3)*(7*x**3 - 45*x**2 + 40*x) + (7*x**3)*6\nSimplifying the partial expression: (-43*x**3)*(7*x**3 - 45*x**2 + 40*x)\nExpanding the part (7*x**3 - 45*x**2 + 40*x) using the distributive property, and we got: (40*x)*(-43*x**3) + (-45*x**2)*(-43*x**3) + (-43*x**3)*(7*x**3)\nReplacing (-43*x**3)*(7*x**3 - 45*x**2 + 40*x) with (40*x)*(-43*x**3) + (-45*x**2)*(-43*x**3) + (-43*x**3)*(7*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (40*x)*(-43*x**3) + (40*x)*6 + (-45*x**2)*(-43*x**3) - 45*x**2*6 + (-43*x**3)*(7*x**3) + (7*x**3)*6\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*x**2)*6 = -270*x**2\n (-45*x**2)*(-43*x**3) = 1935*x**5\n (7*x**3)*6 = 42*x**3\n (7*x**3)*(-43*x**3) = -301*x**6\n (40*x)*6 = 240*x\n (40*x)*(-43*x**3) = -1720*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -301*x**6 + 1935*x**5 - 1720*x**4 + 42*x**3 - 270*x**2 + 240*x\nNo more calculations needed.\n-301*x**6 + 1935*x**5 - 1720*x**4 + 42*x**3 - 270*x**2 + 240*x", "generated_answer": "-301*x**6 + 1935*x**5 - 1720*x**4 + 42*x**3 - 270*x**2 + 240*x", "step_length": 5} {"cot_id": "6db93e42669cc833e04cc45d5f22f74e69171ebf11e3bd2a4f3bdef03c5bac81", "datapoint": {"question": "Simplify this expression: (75 - 23*z**3)*(16*z**2 + 7)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-368*z**5 - 161*z**3 + 1200*z**2 + 525", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2046, "polynomial_expr": "(75 - 23*z**3)*(16*z**2 + 7)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (75 - 23*z**3)*(16*z**2 + 7)\nExpanding the part (16*z**2 + 7) using the distributive property, and we got: (16*z**2)*(75 - 23*z**3) + 7*(75 - 23*z**3)\n#Step 2:\nCurrent expression: (16*z**2)*(75 - 23*z**3) + 7*(75 - 23*z**3)\nSimplifying the partial expression: 7*(75 - 23*z**3)\nExpanding the part (75 - 23*z**3) using the distributive property, and we got: -23*z**3*7 + 75*7\nReplacing 7*(75 - 23*z**3) with -23*z**3*7 + 75*7 in the overall expression.\n#Step 3:\nCurrent expression: (16*z**2)*(75 - 23*z**3) - 23*z**3*7 + 525\nSimplifying the partial expression: (16*z**2)*(75 - 23*z**3)\nExpanding the part (75 - 23*z**3) using the distributive property, and we got: 75*(16*z**2) + (16*z**2)*(-23*z**3)\nReplacing (16*z**2)*(75 - 23*z**3) with 75*(16*z**2) + (16*z**2)*(-23*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 75*16*z**2 + (16*z**2)*(-23*z**3) - 23*z**3*7 + 525\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*z**3)*7 = -161*z**3\n (-23*z**3)*(16*z**2) = -368*z**5\n 75*16*z**2 = 1200*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -368*z**5 - 161*z**3 + 1200*z**2 + 525\nNo more calculations needed.\n-368*z**5 - 161*z**3 + 1200*z**2 + 525", "generated_answer": "-368*z**5 - 161*z**3 + 1200*z**2 + 525", "step_length": 5} {"cot_id": "2872f2a7b7a391fafe351517ccbdcd7acf1f0bb1d4b3c398984c650adb883c6e", "datapoint": {"question": "Simplify this expression: (37 - y**2)*(12*y**3 + 8*y**2 - 35*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-12*y**5 - 8*y**4 + 479*y**3 + 296*y**2 - 1295*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2047, "polynomial_expr": "(37 - y**2)*(12*y**3 + 8*y**2 - 35*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (37 - y**2)*(12*y**3 + 8*y**2 - 35*y)\nExpanding the part (37 - y**2) using the distributive property, and we got: (-y**2)*(12*y**3 + 8*y**2 - 35*y) + 37*(12*y**3 + 8*y**2 - 35*y)\n#Step 2:\nCurrent expression: (-y**2)*(12*y**3 + 8*y**2 - 35*y) + 37*(12*y**3 + 8*y**2 - 35*y)\nSimplifying the partial expression: 37*(12*y**3 + 8*y**2 - 35*y)\nExpanding the part (12*y**3 + 8*y**2 - 35*y) using the distributive property, and we got: -35*y*37 + (8*y**2)*37 + (12*y**3)*37\nReplacing 37*(12*y**3 + 8*y**2 - 35*y) with -35*y*37 + (8*y**2)*37 + (12*y**3)*37 in the overall expression.\n#Step 3:\nCurrent expression: -35*y*37 + (-y**2)*(12*y**3 + 8*y**2 - 35*y) + (8*y**2)*37 + (12*y**3)*37\nSimplifying the partial expression: (-y**2)*(12*y**3 + 8*y**2 - 35*y)\nExpanding the part (12*y**3 + 8*y**2 - 35*y) using the distributive property, and we got: (-35*y)*(-y**2) + (-y**2)*(8*y**2) + (-y**2)*(12*y**3)\nReplacing (-y**2)*(12*y**3 + 8*y**2 - 35*y) with (-35*y)*(-y**2) + (-y**2)*(8*y**2) + (-y**2)*(12*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-35*y)*(-y**2) - 35*y*37 + (-y**2)*(8*y**2) + (-y**2)*(12*y**3) + (8*y**2)*37 + (12*y**3)*37\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*y)*37 = -1295*y\n (-35*y)*(-y**2) = 35*y**3\n (8*y**2)*37 = 296*y**2\n (8*y**2)*(-y**2) = -8*y**4\n (12*y**3)*37 = 444*y**3\n (12*y**3)*(-y**2) = -12*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -12*y**5 - 8*y**4 + 35*y**3 + 444*y**3 + 296*y**2 - 1295*y\nCombining like terms, got -12*y**5 - 8*y**4 + 479*y**3 + 296*y**2 - 1295*y\n#Step 6:\nCurrent expression: -12*y**5 - 8*y**4 + 479*y**3 + 296*y**2 - 1295*y\nNo more calculations needed.\n-12*y**5 - 8*y**4 + 479*y**3 + 296*y**2 - 1295*y", "generated_answer": "-12*y**5 - 8*y**4 + 479*y**3 + 296*y**2 - 1295*y", "step_length": 6} {"cot_id": "ecc9a3e2d9e0341cb5467e612d4db0fc0c31cf20a78d2ac20acae9a97639445b", "datapoint": {"question": "Simplify this expression: (-23*x**3 - 36*x**2)*(13*x**3 + 10*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-299*x**6 - 468*x**5 - 230*x**4 - 360*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2048, "polynomial_expr": "(-23*x**3 - 36*x**2)*(13*x**3 + 10*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-23*x**3 - 36*x**2)*(13*x**3 + 10*x)\nExpanding the part (-23*x**3 - 36*x**2) using the distributive property, and we got: (-36*x**2)*(13*x**3 + 10*x) + (-23*x**3)*(13*x**3 + 10*x)\n#Step 2:\nCurrent expression: (-36*x**2)*(13*x**3 + 10*x) + (-23*x**3)*(13*x**3 + 10*x)\nSimplifying the partial expression: (-36*x**2)*(13*x**3 + 10*x)\nExpanding the part (13*x**3 + 10*x) using the distributive property, and we got: (10*x)*(-36*x**2) + (-36*x**2)*(13*x**3)\nReplacing (-36*x**2)*(13*x**3 + 10*x) with (10*x)*(-36*x**2) + (-36*x**2)*(13*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (10*x)*(-36*x**2) + (-36*x**2)*(13*x**3) + (-23*x**3)*(13*x**3 + 10*x)\nSimplifying the partial expression: (-23*x**3)*(13*x**3 + 10*x)\nExpanding the part (13*x**3 + 10*x) using the distributive property, and we got: (10*x)*(-23*x**3) + (-23*x**3)*(13*x**3)\nReplacing (-23*x**3)*(13*x**3 + 10*x) with (10*x)*(-23*x**3) + (-23*x**3)*(13*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (10*x)*(-36*x**2) + (10*x)*(-23*x**3) + (-36*x**2)*(13*x**3) + (-23*x**3)*(13*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (10*x)*(-36*x**2) = -360*x**3\n (10*x)*(-23*x**3) = -230*x**4\n (13*x**3)*(-36*x**2) = -468*x**5\n (13*x**3)*(-23*x**3) = -299*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -299*x**6 - 468*x**5 - 230*x**4 - 360*x**3\nNo more calculations needed.\n-299*x**6 - 468*x**5 - 230*x**4 - 360*x**3", "generated_answer": "-299*x**6 - 468*x**5 - 230*x**4 - 360*x**3", "step_length": 5} {"cot_id": "290d256077c9bf6f0e4c63aff01d0c6dde2018c8480359d972b54fc3fd52f11e", "datapoint": {"question": "Simplify this expression: (10*y**3 - 31)*(-19*y**2 + 27*y + 25)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-190*y**5 + 270*y**4 + 250*y**3 + 589*y**2 - 837*y - 775", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2049, "polynomial_expr": "(10*y**3 - 31)*(-19*y**2 + 27*y + 25)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (10*y**3 - 31)*(-19*y**2 + 27*y + 25)\nExpanding the part (10*y**3 - 31) using the distributive property, and we got: (10*y**3)*(-19*y**2 + 27*y + 25) - 31*(-19*y**2 + 27*y + 25)\n#Step 2:\nCurrent expression: (10*y**3)*(-19*y**2 + 27*y + 25) - 31*(-19*y**2 + 27*y + 25)\nSimplifying the partial expression: -31*(-19*y**2 + 27*y + 25)\nExpanding the part (-19*y**2 + 27*y + 25) using the distributive property, and we got: (27*y)*(-31) - 19*y**2*(-31) + 25*(-31)\nReplacing -31*(-19*y**2 + 27*y + 25) with (27*y)*(-31) - 19*y**2*(-31) + 25*(-31) in the overall expression.\n#Step 3:\nCurrent expression: (27*y)*(-31) - 19*y**2*(-31) + (10*y**3)*(-19*y**2 + 27*y + 25) - 775\nSimplifying the partial expression: (10*y**3)*(-19*y**2 + 27*y + 25)\nExpanding the part (-19*y**2 + 27*y + 25) using the distributive property, and we got: 25*(10*y**3) + (27*y)*(10*y**3) + (-19*y**2)*(10*y**3)\nReplacing (10*y**3)*(-19*y**2 + 27*y + 25) with 25*(10*y**3) + (27*y)*(10*y**3) + (-19*y**2)*(10*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 25*10*y**3 + (27*y)*(10*y**3) + (27*y)*(-31) + (-19*y**2)*(10*y**3) - 19*y**2*(-31) - 775\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*y**2)*-31 = 589*y**2\n (-19*y**2)*(10*y**3) = -190*y**5\n (27*y)*-31 = -837*y\n (27*y)*(10*y**3) = 270*y**4\n 25*10*y**3 = 250*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -190*y**5 + 270*y**4 + 250*y**3 + 589*y**2 - 837*y - 775\nNo more calculations needed.\n-190*y**5 + 270*y**4 + 250*y**3 + 589*y**2 - 837*y - 775", "generated_answer": "-190*y**5 + 270*y**4 + 250*y**3 + 589*y**2 - 837*y - 775", "step_length": 5} {"cot_id": "9e03922dd1319bc19e456234de2fa65c6c2c8a65877eacbfbf3902d0883a4ad5", "datapoint": {"question": "Calculate the following: (19*z + 26)*(33*z**3 - 14*z**2 + 14*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "627*z**4 + 592*z**3 - 98*z**2 + 364*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2050, "polynomial_expr": "(19*z + 26)*(33*z**3 - 14*z**2 + 14*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (19*z + 26)*(33*z**3 - 14*z**2 + 14*z)\nExpanding the part (19*z + 26) using the distributive property, and we got: (19*z)*(33*z**3 - 14*z**2 + 14*z) + 26*(33*z**3 - 14*z**2 + 14*z)\n#Step 2:\nCurrent expression: (19*z)*(33*z**3 - 14*z**2 + 14*z) + 26*(33*z**3 - 14*z**2 + 14*z)\nSimplifying the partial expression: 26*(33*z**3 - 14*z**2 + 14*z)\nExpanding the part (33*z**3 - 14*z**2 + 14*z) using the distributive property, and we got: (14*z)*26 - 14*z**2*26 + (33*z**3)*26\nReplacing 26*(33*z**3 - 14*z**2 + 14*z) with (14*z)*26 - 14*z**2*26 + (33*z**3)*26 in the overall expression.\n#Step 3:\nCurrent expression: (14*z)*26 + (19*z)*(33*z**3 - 14*z**2 + 14*z) - 14*z**2*26 + (33*z**3)*26\nSimplifying the partial expression: (19*z)*(33*z**3 - 14*z**2 + 14*z)\nExpanding the part (33*z**3 - 14*z**2 + 14*z) using the distributive property, and we got: (14*z)*(19*z) + (19*z)*(-14*z**2) + (19*z)*(33*z**3)\nReplacing (19*z)*(33*z**3 - 14*z**2 + 14*z) with (14*z)*(19*z) + (19*z)*(-14*z**2) + (19*z)*(33*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (14*z)*(19*z) + (14*z)*26 + (19*z)*(-14*z**2) + (19*z)*(33*z**3) - 14*z**2*26 + (33*z**3)*26\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-14*z**2)*26 = -364*z**2\n (-14*z**2)*(19*z) = -266*z**3\n (14*z)*26 = 364*z\n (14*z)*(19*z) = 266*z**2\n (33*z**3)*26 = 858*z**3\n (33*z**3)*(19*z) = 627*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 627*z**4 - 266*z**3 + 858*z**3 - 364*z**2 + 266*z**2 + 364*z\nCombining like terms, got 627*z**4 + 592*z**3 - 98*z**2 + 364*z\n#Step 6:\nCurrent expression: 627*z**4 + 592*z**3 - 98*z**2 + 364*z\nNo more calculations needed.\n627*z**4 + 592*z**3 - 98*z**2 + 364*z", "generated_answer": "627*z**4 + 592*z**3 - 98*z**2 + 364*z", "step_length": 6} {"cot_id": "733251ab3f33559d21372a13cebdd85ea93fb9cf8537209c9eff2b210ccee732", "datapoint": {"question": "Simplify this expression: (10*y**2 - 48*y)*(-39*y**3 + 9*y**2 + 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-390*y**5 + 1962*y**4 - 432*y**3 + 330*y**2 - 1584*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2051, "polynomial_expr": "(10*y**2 - 48*y)*(-39*y**3 + 9*y**2 + 33)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (10*y**2 - 48*y)*(-39*y**3 + 9*y**2 + 33)\nExpanding the part (10*y**2 - 48*y) using the distributive property, and we got: (-48*y)*(-39*y**3 + 9*y**2 + 33) + (10*y**2)*(-39*y**3 + 9*y**2 + 33)\n#Step 2:\nCurrent expression: (-48*y)*(-39*y**3 + 9*y**2 + 33) + (10*y**2)*(-39*y**3 + 9*y**2 + 33)\nSimplifying the partial expression: (-48*y)*(-39*y**3 + 9*y**2 + 33)\nExpanding the part (-39*y**3 + 9*y**2 + 33) using the distributive property, and we got: (-48*y)*(9*y**2) + (-48*y)*(-39*y**3) + 33*(-48*y)\nReplacing (-48*y)*(-39*y**3 + 9*y**2 + 33) with (-48*y)*(9*y**2) + (-48*y)*(-39*y**3) + 33*(-48*y) in the overall expression.\n#Step 3:\nCurrent expression: (-48*y)*(9*y**2) + (-48*y)*(-39*y**3) + 33*(-48)*y + (10*y**2)*(-39*y**3 + 9*y**2 + 33)\nSimplifying the partial expression: (10*y**2)*(-39*y**3 + 9*y**2 + 33)\nExpanding the part (-39*y**3 + 9*y**2 + 33) using the distributive property, and we got: 33*(10*y**2) + (9*y**2)*(10*y**2) + (10*y**2)*(-39*y**3)\nReplacing (10*y**2)*(-39*y**3 + 9*y**2 + 33) with 33*(10*y**2) + (9*y**2)*(10*y**2) + (10*y**2)*(-39*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-48*y)*(9*y**2) + (-48*y)*(-39*y**3) + 33*10*y**2 + 33*(-48)*y + (9*y**2)*(10*y**2) + (10*y**2)*(-39*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*y**3)*(-48*y) = 1872*y**4\n (-39*y**3)*(10*y**2) = -390*y**5\n (9*y**2)*(-48*y) = -432*y**3\n (9*y**2)*(10*y**2) = 90*y**4\n 33*-48*y = -1584*y\n 33*10*y**2 = 330*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -390*y**5 + 90*y**4 + 1872*y**4 - 432*y**3 + 330*y**2 - 1584*y\nCombining like terms, got -390*y**5 + 1962*y**4 - 432*y**3 + 330*y**2 - 1584*y\n#Step 6:\nCurrent expression: -390*y**5 + 1962*y**4 - 432*y**3 + 330*y**2 - 1584*y\nNo more calculations needed.\n-390*y**5 + 1962*y**4 - 432*y**3 + 330*y**2 - 1584*y", "generated_answer": "-390*y**5 + 1962*y**4 - 432*y**3 + 330*y**2 - 1584*y", "step_length": 6} {"cot_id": "10886e8792913cea646753c85bcb59205b09c5d7c7f48db2ae5e8e99d11fda5b", "datapoint": {"question": "Calculate the following: (26 - 47*x)*(43*x + 54)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2021*x**2 - 1420*x + 1404", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2052, "polynomial_expr": "(26 - 47*x)*(43*x + 54)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (26 - 47*x)*(43*x + 54)\nExpanding the part (26 - 47*x) using the distributive property, and we got: (-47*x)*(43*x + 54) + 26*(43*x + 54)\n#Step 2:\nCurrent expression: (-47*x)*(43*x + 54) + 26*(43*x + 54)\nSimplifying the partial expression: 26*(43*x + 54)\nExpanding the part (43*x + 54) using the distributive property, and we got: (43*x)*26 + 54*26\nReplacing 26*(43*x + 54) with (43*x)*26 + 54*26 in the overall expression.\n#Step 3:\nCurrent expression: (-47*x)*(43*x + 54) + (43*x)*26 + 1404\nSimplifying the partial expression: (-47*x)*(43*x + 54)\nExpanding the part (43*x + 54) using the distributive property, and we got: (-47*x)*(43*x) + 54*(-47*x)\nReplacing (-47*x)*(43*x + 54) with (-47*x)*(43*x) + 54*(-47*x) in the overall expression.\n#Step 4:\nCurrent expression: (-47*x)*(43*x) + 54*(-47)*x + (43*x)*26 + 1404\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (43*x)*26 = 1118*x\n (43*x)*(-47*x) = -2021*x**2\n 54*-47*x = -2538*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -2021*x**2 - 2538*x + 1118*x + 1404\nCombining like terms, got -2021*x**2 - 1420*x + 1404\n#Step 6:\nCurrent expression: -2021*x**2 - 1420*x + 1404\nNo more calculations needed.\n-2021*x**2 - 1420*x + 1404", "generated_answer": "-2021*x**2 - 1420*x + 1404", "step_length": 6} {"cot_id": "8f50eed0b7ff791d73c4559ef34a5968e3bf32df3e66a7c24314ebb7fd4c9943", "datapoint": {"question": "Calculate the following: (49*z - 77)*(20*z**2 + 36*z - 12)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "980*z**3 + 224*z**2 - 3360*z + 924", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2053, "polynomial_expr": "(49*z - 77)*(20*z**2 + 36*z - 12)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (49*z - 77)*(20*z**2 + 36*z - 12)\nExpanding the part (49*z - 77) using the distributive property, and we got: (49*z)*(20*z**2 + 36*z - 12) - 77*(20*z**2 + 36*z - 12)\n#Step 2:\nCurrent expression: (49*z)*(20*z**2 + 36*z - 12) - 77*(20*z**2 + 36*z - 12)\nSimplifying the partial expression: -77*(20*z**2 + 36*z - 12)\nExpanding the part (20*z**2 + 36*z - 12) using the distributive property, and we got: (36*z)*(-77) + (20*z**2)*(-77) - 12*(-77)\nReplacing -77*(20*z**2 + 36*z - 12) with (36*z)*(-77) + (20*z**2)*(-77) - 12*(-77) in the overall expression.\n#Step 3:\nCurrent expression: (36*z)*(-77) + (49*z)*(20*z**2 + 36*z - 12) + (20*z**2)*(-77) + 924\nSimplifying the partial expression: (49*z)*(20*z**2 + 36*z - 12)\nExpanding the part (20*z**2 + 36*z - 12) using the distributive property, and we got: -588*z + (36*z)*(49*z) + (49*z)*(20*z**2)\nReplacing (49*z)*(20*z**2 + 36*z - 12) with -588*z + (36*z)*(49*z) + (49*z)*(20*z**2) in the overall expression.\n#Step 4:\nCurrent expression: -12*49*z + (36*z)*(49*z) + (36*z)*(-77) + (49*z)*(20*z**2) + (20*z**2)*(-77) + 924\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (20*z**2)*-77 = -1540*z**2\n (20*z**2)*(49*z) = 980*z**3\n (36*z)*-77 = -2772*z\n (36*z)*(49*z) = 1764*z**2\n -12*49*z = -588*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 980*z**3 - 1540*z**2 + 1764*z**2 - 2772*z - 588*z + 924\nCombining like terms, got 980*z**3 + 224*z**2 - 3360*z + 924\n#Step 6:\nCurrent expression: 980*z**3 + 224*z**2 - 3360*z + 924\nNo more calculations needed.\n980*z**3 + 224*z**2 - 3360*z + 924", "generated_answer": "980*z**3 + 224*z**2 - 3360*z + 924", "step_length": 6} {"cot_id": "77015db6e98a90215d9fee8104b072b01db49438bbeed0034f72075bf2490940", "datapoint": {"question": "Simplify this expression: (37*x**2 + 6)*(35*x**3 - 41*x**2 - 45*x - 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1295*x**5 - 1517*x**4 - 1455*x**3 - 1467*x**2 - 270*x - 198", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2054, "polynomial_expr": "(37*x**2 + 6)*(35*x**3 - 41*x**2 - 45*x - 33)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (37*x**2 + 6)*(35*x**3 - 41*x**2 - 45*x - 33)\nExpanding the part (37*x**2 + 6) using the distributive property, and we got: (37*x**2)*(35*x**3 - 41*x**2 - 45*x - 33) + 6*(35*x**3 - 41*x**2 - 45*x - 33)\n#Step 2:\nCurrent expression: (37*x**2)*(35*x**3 - 41*x**2 - 45*x - 33) + 6*(35*x**3 - 41*x**2 - 45*x - 33)\nSimplifying the partial expression: 6*(35*x**3 - 41*x**2 - 45*x - 33)\nExpanding the part (35*x**3 - 41*x**2 - 45*x - 33) using the distributive property, and we got: -45*x*6 - 41*x**2*6 + (35*x**3)*6 - 33*6\nReplacing 6*(35*x**3 - 41*x**2 - 45*x - 33) with -45*x*6 - 41*x**2*6 + (35*x**3)*6 - 33*6 in the overall expression.\n#Step 3:\nCurrent expression: -45*x*6 - 41*x**2*6 + (37*x**2)*(35*x**3 - 41*x**2 - 45*x - 33) + (35*x**3)*6 - 198\nSimplifying the partial expression: (37*x**2)*(35*x**3 - 41*x**2 - 45*x - 33)\nExpanding the part (35*x**3 - 41*x**2 - 45*x - 33) using the distributive property, and we got: (-45*x)*(37*x**2) - 1221*x**2 + (-41*x**2)*(37*x**2) + (37*x**2)*(35*x**3)\nReplacing (37*x**2)*(35*x**3 - 41*x**2 - 45*x - 33) with (-45*x)*(37*x**2) - 1221*x**2 + (-41*x**2)*(37*x**2) + (37*x**2)*(35*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-45*x)*(37*x**2) - 45*x*6 - 33*37*x**2 + (-41*x**2)*(37*x**2) - 41*x**2*6 + (37*x**2)*(35*x**3) + (35*x**3)*6 - 198\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*x)*6 = -270*x\n (-45*x)*(37*x**2) = -1665*x**3\n (-41*x**2)*6 = -246*x**2\n (-41*x**2)*(37*x**2) = -1517*x**4\n (35*x**3)*6 = 210*x**3\n (35*x**3)*(37*x**2) = 1295*x**5\n -33*37*x**2 = -1221*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1295*x**5 - 1517*x**4 - 1665*x**3 + 210*x**3 - 1221*x**2 - 246*x**2 - 270*x - 198\nCombining like terms, got 1295*x**5 - 1517*x**4 - 1455*x**3 - 1467*x**2 - 270*x - 198\n#Step 6:\nCurrent expression: 1295*x**5 - 1517*x**4 - 1455*x**3 - 1467*x**2 - 270*x - 198\nNo more calculations needed.\n1295*x**5 - 1517*x**4 - 1455*x**3 - 1467*x**2 - 270*x - 198", "generated_answer": "1295*x**5 - 1517*x**4 - 1455*x**3 - 1467*x**2 - 270*x - 198", "step_length": 6} {"cot_id": "cdaa1e1cd738570c826d4b7d839ca5ebae540d832d600787f56b9c7d2438fabc", "datapoint": {"question": "Calculate the following: -12*x**3*(-12*x**3 - 18)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "144*x**6 + 216*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2055, "polynomial_expr": "-12*x**3*(-12*x**3 - 18)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -12*x**3*(-12*x**3 - 18)\nExpanding the part (-12*x**3 - 18) using the distributive property, and we got: -(-1)*216*x**3 + (-12*x**3)*(-12*x**3)\n#Step 2:\nCurrent expression: -(-1)*216*x**3 + (-12*x**3)*(-12*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -18*(-12*x**3) = 216*x**3\n (-12*x**3)*(-12*x**3) = 144*x**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 144*x**6 + 216*x**3\nNo more calculations needed.\n144*x**6 + 216*x**3", "generated_answer": "144*x**6 + 216*x**3", "step_length": 3} {"cot_id": "6ea3ffd09e98e4dbdc4bd231272a620c4ae6f543f5474ebfc82c6cdefba9846c", "datapoint": {"question": "Simplify this expression: (7*x**3 - 36)*(16*x**3 + 23*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "112*x**6 + 161*x**4 - 576*x**3 - 828*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2056, "polynomial_expr": "(7*x**3 - 36)*(16*x**3 + 23*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7*x**3 - 36)*(16*x**3 + 23*x)\nExpanding the part (7*x**3 - 36) using the distributive property, and we got: (7*x**3)*(16*x**3 + 23*x) - 36*(16*x**3 + 23*x)\n#Step 2:\nCurrent expression: (7*x**3)*(16*x**3 + 23*x) - 36*(16*x**3 + 23*x)\nSimplifying the partial expression: -36*(16*x**3 + 23*x)\nExpanding the part (16*x**3 + 23*x) using the distributive property, and we got: (23*x)*(-36) + (16*x**3)*(-36)\nReplacing -36*(16*x**3 + 23*x) with (23*x)*(-36) + (16*x**3)*(-36) in the overall expression.\n#Step 3:\nCurrent expression: (23*x)*(-36) + (7*x**3)*(16*x**3 + 23*x) + (16*x**3)*(-36)\nSimplifying the partial expression: (7*x**3)*(16*x**3 + 23*x)\nExpanding the part (16*x**3 + 23*x) using the distributive property, and we got: (23*x)*(7*x**3) + (7*x**3)*(16*x**3)\nReplacing (7*x**3)*(16*x**3 + 23*x) with (23*x)*(7*x**3) + (7*x**3)*(16*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (23*x)*(7*x**3) + (23*x)*(-36) + (7*x**3)*(16*x**3) + (16*x**3)*(-36)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (16*x**3)*-36 = -576*x**3\n (16*x**3)*(7*x**3) = 112*x**6\n (23*x)*-36 = -828*x\n (23*x)*(7*x**3) = 161*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 112*x**6 + 161*x**4 - 576*x**3 - 828*x\nNo more calculations needed.\n112*x**6 + 161*x**4 - 576*x**3 - 828*x", "generated_answer": "112*x**6 + 161*x**4 - 576*x**3 - 828*x", "step_length": 5} {"cot_id": "92e51f030145a49ded88daa7a5d39d9cc44c2f63062591db7211766e909cae41", "datapoint": {"question": "Calculate the following: (23*y**2 + 7*y)*(-18*y**3 + 16*y**2 - 14*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-414*y**5 + 242*y**4 - 210*y**3 - 98*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2057, "polynomial_expr": "(23*y**2 + 7*y)*(-18*y**3 + 16*y**2 - 14*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (23*y**2 + 7*y)*(-18*y**3 + 16*y**2 - 14*y)\nExpanding the part (23*y**2 + 7*y) using the distributive property, and we got: (7*y)*(-18*y**3 + 16*y**2 - 14*y) + (23*y**2)*(-18*y**3 + 16*y**2 - 14*y)\n#Step 2:\nCurrent expression: (7*y)*(-18*y**3 + 16*y**2 - 14*y) + (23*y**2)*(-18*y**3 + 16*y**2 - 14*y)\nSimplifying the partial expression: (7*y)*(-18*y**3 + 16*y**2 - 14*y)\nExpanding the part (-18*y**3 + 16*y**2 - 14*y) using the distributive property, and we got: (-14*y)*(7*y) + (7*y)*(16*y**2) + (7*y)*(-18*y**3)\nReplacing (7*y)*(-18*y**3 + 16*y**2 - 14*y) with (-14*y)*(7*y) + (7*y)*(16*y**2) + (7*y)*(-18*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-14*y)*(7*y) + (7*y)*(16*y**2) + (7*y)*(-18*y**3) + (23*y**2)*(-18*y**3 + 16*y**2 - 14*y)\nSimplifying the partial expression: (23*y**2)*(-18*y**3 + 16*y**2 - 14*y)\nExpanding the part (-18*y**3 + 16*y**2 - 14*y) using the distributive property, and we got: (-14*y)*(23*y**2) + (16*y**2)*(23*y**2) + (23*y**2)*(-18*y**3)\nReplacing (23*y**2)*(-18*y**3 + 16*y**2 - 14*y) with (-14*y)*(23*y**2) + (16*y**2)*(23*y**2) + (23*y**2)*(-18*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-14*y)*(7*y) + (-14*y)*(23*y**2) + (7*y)*(16*y**2) + (7*y)*(-18*y**3) + (16*y**2)*(23*y**2) + (23*y**2)*(-18*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-18*y**3)*(7*y) = -126*y**4\n (-18*y**3)*(23*y**2) = -414*y**5\n (-14*y)*(7*y) = -98*y**2\n (-14*y)*(23*y**2) = -322*y**3\n (16*y**2)*(7*y) = 112*y**3\n (16*y**2)*(23*y**2) = 368*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -414*y**5 - 126*y**4 + 368*y**4 - 322*y**3 + 112*y**3 - 98*y**2\nCombining like terms, got -414*y**5 + 242*y**4 - 210*y**3 - 98*y**2\n#Step 6:\nCurrent expression: -414*y**5 + 242*y**4 - 210*y**3 - 98*y**2\nNo more calculations needed.\n-414*y**5 + 242*y**4 - 210*y**3 - 98*y**2", "generated_answer": "-414*y**5 + 242*y**4 - 210*y**3 - 98*y**2", "step_length": 6} {"cot_id": "958015a815fcbab9742b1e9b0573b1a5feda31b13679b47024a650d987bb3787", "datapoint": {"question": "Calculate the following: (-26*y - 45)*(30*y**3 + 27*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-780*y**4 - 1350*y**3 - 702*y**2 - 1215*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2058, "polynomial_expr": "(-26*y - 45)*(30*y**3 + 27*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-26*y - 45)*(30*y**3 + 27*y)\nExpanding the part (-26*y - 45) using the distributive property, and we got: (-26*y)*(30*y**3 + 27*y) - 45*(30*y**3 + 27*y)\n#Step 2:\nCurrent expression: (-26*y)*(30*y**3 + 27*y) - 45*(30*y**3 + 27*y)\nSimplifying the partial expression: -45*(30*y**3 + 27*y)\nExpanding the part (30*y**3 + 27*y) using the distributive property, and we got: (27*y)*(-45) + (30*y**3)*(-45)\nReplacing -45*(30*y**3 + 27*y) with (27*y)*(-45) + (30*y**3)*(-45) in the overall expression.\n#Step 3:\nCurrent expression: (-26*y)*(30*y**3 + 27*y) + (27*y)*(-45) + (30*y**3)*(-45)\nSimplifying the partial expression: (-26*y)*(30*y**3 + 27*y)\nExpanding the part (30*y**3 + 27*y) using the distributive property, and we got: (-26*y)*(27*y) + (-26*y)*(30*y**3)\nReplacing (-26*y)*(30*y**3 + 27*y) with (-26*y)*(27*y) + (-26*y)*(30*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-26*y)*(27*y) + (-26*y)*(30*y**3) + (27*y)*(-45) + (30*y**3)*(-45)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (27*y)*-45 = -1215*y\n (27*y)*(-26*y) = -702*y**2\n (30*y**3)*-45 = -1350*y**3\n (30*y**3)*(-26*y) = -780*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -780*y**4 - 1350*y**3 - 702*y**2 - 1215*y\nNo more calculations needed.\n-780*y**4 - 1350*y**3 - 702*y**2 - 1215*y", "generated_answer": "-780*y**4 - 1350*y**3 - 702*y**2 - 1215*y", "step_length": 5} {"cot_id": "8afcf86e709e8ec8ac27abc7e23b3331b3db0ef16a1c0d58f9a608d7b09c3c88", "datapoint": {"question": "Calculate the following: (23*z**3 - 32)*(-11*z**3 - 11*z**2 + 13*z + 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-253*z**6 - 253*z**5 + 299*z**4 + 1042*z**3 + 352*z**2 - 416*z - 960", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2059, "polynomial_expr": "(23*z**3 - 32)*(-11*z**3 - 11*z**2 + 13*z + 30)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (23*z**3 - 32)*(-11*z**3 - 11*z**2 + 13*z + 30)\nExpanding the part (23*z**3 - 32) using the distributive property, and we got: (23*z**3)*(-11*z**3 - 11*z**2 + 13*z + 30) - 32*(-11*z**3 - 11*z**2 + 13*z + 30)\n#Step 2:\nCurrent expression: (23*z**3)*(-11*z**3 - 11*z**2 + 13*z + 30) - 32*(-11*z**3 - 11*z**2 + 13*z + 30)\nSimplifying the partial expression: -32*(-11*z**3 - 11*z**2 + 13*z + 30)\nExpanding the part (-11*z**3 - 11*z**2 + 13*z + 30) using the distributive property, and we got: (13*z)*(-32) - 11*z**2*(-32) - 11*z**3*(-32) + 30*(-32)\nReplacing -32*(-11*z**3 - 11*z**2 + 13*z + 30) with (13*z)*(-32) - 11*z**2*(-32) - 11*z**3*(-32) + 30*(-32) in the overall expression.\n#Step 3:\nCurrent expression: (13*z)*(-32) - 11*z**2*(-32) - 11*z**3*(-32) + (23*z**3)*(-11*z**3 - 11*z**2 + 13*z + 30) - 960\nSimplifying the partial expression: (23*z**3)*(-11*z**3 - 11*z**2 + 13*z + 30)\nExpanding the part (-11*z**3 - 11*z**2 + 13*z + 30) using the distributive property, and we got: 30*(23*z**3) + (13*z)*(23*z**3) + (-11*z**2)*(23*z**3) + (-11*z**3)*(23*z**3)\nReplacing (23*z**3)*(-11*z**3 - 11*z**2 + 13*z + 30) with 30*(23*z**3) + (13*z)*(23*z**3) + (-11*z**2)*(23*z**3) + (-11*z**3)*(23*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 30*23*z**3 + (13*z)*(23*z**3) + (13*z)*(-32) + (-11*z**2)*(23*z**3) - 11*z**2*(-32) + (-11*z**3)*(23*z**3) - 11*z**3*(-32) - 960\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*z**2)*-32 = 352*z**2\n (-11*z**2)*(23*z**3) = -253*z**5\n (-11*z**3)*-32 = 352*z**3\n (-11*z**3)*(23*z**3) = -253*z**6\n (13*z)*-32 = -416*z\n (13*z)*(23*z**3) = 299*z**4\n 30*23*z**3 = 690*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -253*z**6 - 253*z**5 + 299*z**4 + 352*z**3 + 690*z**3 + 352*z**2 - 416*z - 960\nCombining like terms, got -253*z**6 - 253*z**5 + 299*z**4 + 1042*z**3 + 352*z**2 - 416*z - 960\n#Step 6:\nCurrent expression: -253*z**6 - 253*z**5 + 299*z**4 + 1042*z**3 + 352*z**2 - 416*z - 960\nNo more calculations needed.\n-253*z**6 - 253*z**5 + 299*z**4 + 1042*z**3 + 352*z**2 - 416*z - 960", "generated_answer": "-253*z**6 - 253*z**5 + 299*z**4 + 1042*z**3 + 352*z**2 - 416*z - 960", "step_length": 6} {"cot_id": "9d9771f5971ce2f1eb5a2ea39154e424aa60d390484810cb236d2e47984cb3b9", "datapoint": {"question": "Simplify this expression: (18*y**3 - 22*y**2)*(11*y**3 - 20*y**2 - 40)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "198*y**6 - 602*y**5 + 440*y**4 - 720*y**3 + 880*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2060, "polynomial_expr": "(18*y**3 - 22*y**2)*(11*y**3 - 20*y**2 - 40)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (18*y**3 - 22*y**2)*(11*y**3 - 20*y**2 - 40)\nExpanding the part (18*y**3 - 22*y**2) using the distributive property, and we got: (-22*y**2)*(11*y**3 - 20*y**2 - 40) + (18*y**3)*(11*y**3 - 20*y**2 - 40)\n#Step 2:\nCurrent expression: (-22*y**2)*(11*y**3 - 20*y**2 - 40) + (18*y**3)*(11*y**3 - 20*y**2 - 40)\nSimplifying the partial expression: (-22*y**2)*(11*y**3 - 20*y**2 - 40)\nExpanding the part (11*y**3 - 20*y**2 - 40) using the distributive property, and we got: -(-1)*880*y**2 + (-22*y**2)*(-20*y**2) + (-22*y**2)*(11*y**3)\nReplacing (-22*y**2)*(11*y**3 - 20*y**2 - 40) with -(-1)*880*y**2 + (-22*y**2)*(-20*y**2) + (-22*y**2)*(11*y**3) in the overall expression.\n#Step 3:\nCurrent expression: -40*(-22)*y**2 + (-22*y**2)*(-20*y**2) + (-22*y**2)*(11*y**3) + (18*y**3)*(11*y**3 - 20*y**2 - 40)\nSimplifying the partial expression: (18*y**3)*(11*y**3 - 20*y**2 - 40)\nExpanding the part (11*y**3 - 20*y**2 - 40) using the distributive property, and we got: -720*y**3 + (-20*y**2)*(18*y**3) + (11*y**3)*(18*y**3)\nReplacing (18*y**3)*(11*y**3 - 20*y**2 - 40) with -720*y**3 + (-20*y**2)*(18*y**3) + (11*y**3)*(18*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -40*18*y**3 - 40*(-22)*y**2 + (-22*y**2)*(-20*y**2) + (-22*y**2)*(11*y**3) + (-20*y**2)*(18*y**3) + (11*y**3)*(18*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*y**2)*(-22*y**2) = 440*y**4\n (-20*y**2)*(18*y**3) = -360*y**5\n (11*y**3)*(-22*y**2) = -242*y**5\n (11*y**3)*(18*y**3) = 198*y**6\n -40*-22*y**2 = 880*y**2\n -40*18*y**3 = -720*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 198*y**6 - 360*y**5 - 242*y**5 + 440*y**4 - 720*y**3 + 880*y**2\nCombining like terms, got 198*y**6 - 602*y**5 + 440*y**4 - 720*y**3 + 880*y**2\n#Step 6:\nCurrent expression: 198*y**6 - 602*y**5 + 440*y**4 - 720*y**3 + 880*y**2\nNo more calculations needed.\n198*y**6 - 602*y**5 + 440*y**4 - 720*y**3 + 880*y**2", "generated_answer": "198*y**6 - 602*y**5 + 440*y**4 - 720*y**3 + 880*y**2", "step_length": 6} {"cot_id": "380d1fd00bdf90bf3640e60fd2a7ff87d00a414947f31f4227bdc9c000c1bb59", "datapoint": {"question": "Simplify this expression: -31*x**3*(-57*x**3 + 26*x**2 - 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1767*x**6 - 806*x**5 + 496*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2061, "polynomial_expr": "-31*x**3*(-57*x**3 + 26*x**2 - 16)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -31*x**3*(-57*x**3 + 26*x**2 - 16)\nExpanding the part (-57*x**3 + 26*x**2 - 16) using the distributive property, and we got: -(-1)*496*x**3 + (26*x**2)*(-31*x**3) + (-57*x**3)*(-31*x**3)\n#Step 2:\nCurrent expression: -(-1)*496*x**3 + (26*x**2)*(-31*x**3) + (-57*x**3)*(-31*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -16*(-31*x**3) = 496*x**3\n (-57*x**3)*(-31*x**3) = 1767*x**6\n (26*x**2)*(-31*x**3) = -806*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1767*x**6 - 806*x**5 + 496*x**3\nNo more calculations needed.\n1767*x**6 - 806*x**5 + 496*x**3", "generated_answer": "1767*x**6 - 806*x**5 + 496*x**3", "step_length": 3} {"cot_id": "a720c54be6f0e53ac319c3c8c762a9298a9711673a9d8d5b5abeddea44cb6356", "datapoint": {"question": "Calculate the following: (6*x**3 - 24*x**2)*(48*x**3 - 11*x**2 - 23)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "288*x**6 - 1218*x**5 + 264*x**4 - 138*x**3 + 552*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2062, "polynomial_expr": "(6*x**3 - 24*x**2)*(48*x**3 - 11*x**2 - 23)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6*x**3 - 24*x**2)*(48*x**3 - 11*x**2 - 23)\nExpanding the part (6*x**3 - 24*x**2) using the distributive property, and we got: (-24*x**2)*(48*x**3 - 11*x**2 - 23) + (6*x**3)*(48*x**3 - 11*x**2 - 23)\n#Step 2:\nCurrent expression: (-24*x**2)*(48*x**3 - 11*x**2 - 23) + (6*x**3)*(48*x**3 - 11*x**2 - 23)\nSimplifying the partial expression: (-24*x**2)*(48*x**3 - 11*x**2 - 23)\nExpanding the part (48*x**3 - 11*x**2 - 23) using the distributive property, and we got: -(-1)*552*x**2 + (-24*x**2)*(-11*x**2) + (-24*x**2)*(48*x**3)\nReplacing (-24*x**2)*(48*x**3 - 11*x**2 - 23) with -(-1)*552*x**2 + (-24*x**2)*(-11*x**2) + (-24*x**2)*(48*x**3) in the overall expression.\n#Step 3:\nCurrent expression: -23*(-24)*x**2 + (-24*x**2)*(-11*x**2) + (-24*x**2)*(48*x**3) + (6*x**3)*(48*x**3 - 11*x**2 - 23)\nSimplifying the partial expression: (6*x**3)*(48*x**3 - 11*x**2 - 23)\nExpanding the part (48*x**3 - 11*x**2 - 23) using the distributive property, and we got: -138*x**3 + (-11*x**2)*(6*x**3) + (6*x**3)*(48*x**3)\nReplacing (6*x**3)*(48*x**3 - 11*x**2 - 23) with -138*x**3 + (-11*x**2)*(6*x**3) + (6*x**3)*(48*x**3) in the overall expression.\n#Step 4:\nCurrent expression: -23*6*x**3 - 23*(-24)*x**2 + (-24*x**2)*(-11*x**2) + (-24*x**2)*(48*x**3) + (-11*x**2)*(6*x**3) + (6*x**3)*(48*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*x**2)*(-24*x**2) = 264*x**4\n (-11*x**2)*(6*x**3) = -66*x**5\n (48*x**3)*(-24*x**2) = -1152*x**5\n (48*x**3)*(6*x**3) = 288*x**6\n -23*-24*x**2 = 552*x**2\n -23*6*x**3 = -138*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 288*x**6 - 1152*x**5 - 66*x**5 + 264*x**4 - 138*x**3 + 552*x**2\nCombining like terms, got 288*x**6 - 1218*x**5 + 264*x**4 - 138*x**3 + 552*x**2\n#Step 6:\nCurrent expression: 288*x**6 - 1218*x**5 + 264*x**4 - 138*x**3 + 552*x**2\nNo more calculations needed.\n288*x**6 - 1218*x**5 + 264*x**4 - 138*x**3 + 552*x**2", "generated_answer": "288*x**6 - 1218*x**5 + 264*x**4 - 138*x**3 + 552*x**2", "step_length": 6} {"cot_id": "4acd20186ce6b8bf097c26d40def01682298e242fd4f44326eecaa1a03d6d729", "datapoint": {"question": "Simplify this expression: -129*x*(4*x**3 - x**2 + 37*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-516*x**4 + 129*x**3 - 4773*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2063, "polynomial_expr": "-129*x*(4*x**3 - x**2 + 37*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -129*x*(4*x**3 - x**2 + 37*x)\nExpanding the part (4*x**3 - x**2 + 37*x) using the distributive property, and we got: (-129*x)*(37*x) + (-129*x)*(-x**2) + (-129*x)*(4*x**3)\n#Step 2:\nCurrent expression: (-129*x)*(37*x) + (-129*x)*(-x**2) + (-129*x)*(4*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-x**2)*(-129*x) = 129*x**3\n (4*x**3)*(-129*x) = -516*x**4\n (37*x)*(-129*x) = -4773*x**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -516*x**4 + 129*x**3 - 4773*x**2\nNo more calculations needed.\n-516*x**4 + 129*x**3 - 4773*x**2", "generated_answer": "-516*x**4 + 129*x**3 - 4773*x**2", "step_length": 3} {"cot_id": "6f3602b3551495c1aafcc92c02ac12d98a0f705ec8251879cb202f2bd110f746", "datapoint": {"question": "Simplify this expression: (47*y**3 - 47)*(-37*y**3 - 11*y**2 - 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1739*y**6 - 517*y**5 - 517*y**3 + 517*y**2 + 2256", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2064, "polynomial_expr": "(47*y**3 - 47)*(-37*y**3 - 11*y**2 - 48)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (47*y**3 - 47)*(-37*y**3 - 11*y**2 - 48)\nExpanding the part (47*y**3 - 47) using the distributive property, and we got: (47*y**3)*(-37*y**3 - 11*y**2 - 48) - 47*(-37*y**3 - 11*y**2 - 48)\n#Step 2:\nCurrent expression: (47*y**3)*(-37*y**3 - 11*y**2 - 48) - 47*(-37*y**3 - 11*y**2 - 48)\nSimplifying the partial expression: -47*(-37*y**3 - 11*y**2 - 48)\nExpanding the part (-37*y**3 - 11*y**2 - 48) using the distributive property, and we got: -11*y**2*(-47) - 37*y**3*(-47) - 48*(-47)\nReplacing -47*(-37*y**3 - 11*y**2 - 48) with -11*y**2*(-47) - 37*y**3*(-47) - 48*(-47) in the overall expression.\n#Step 3:\nCurrent expression: -11*y**2*(-47) - 37*y**3*(-47) + (47*y**3)*(-37*y**3 - 11*y**2 - 48) + 2256\nSimplifying the partial expression: (47*y**3)*(-37*y**3 - 11*y**2 - 48)\nExpanding the part (-37*y**3 - 11*y**2 - 48) using the distributive property, and we got: -2256*y**3 + (-11*y**2)*(47*y**3) + (-37*y**3)*(47*y**3)\nReplacing (47*y**3)*(-37*y**3 - 11*y**2 - 48) with -2256*y**3 + (-11*y**2)*(47*y**3) + (-37*y**3)*(47*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -48*47*y**3 + (-11*y**2)*(47*y**3) - 11*y**2*(-47) + (-37*y**3)*(47*y**3) - 37*y**3*(-47) + 2256\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*y**3)*-47 = 1739*y**3\n (-37*y**3)*(47*y**3) = -1739*y**6\n (-11*y**2)*-47 = 517*y**2\n (-11*y**2)*(47*y**3) = -517*y**5\n -48*47*y**3 = -2256*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1739*y**6 - 517*y**5 - 2256*y**3 + 1739*y**3 + 517*y**2 + 2256\nCombining like terms, got -1739*y**6 - 517*y**5 - 517*y**3 + 517*y**2 + 2256\n#Step 6:\nCurrent expression: -1739*y**6 - 517*y**5 - 517*y**3 + 517*y**2 + 2256\nNo more calculations needed.\n-1739*y**6 - 517*y**5 - 517*y**3 + 517*y**2 + 2256", "generated_answer": "-1739*y**6 - 517*y**5 - 517*y**3 + 517*y**2 + 2256", "step_length": 6} {"cot_id": "2c4ede5e9ecdadd1a028da60e66c55f3a3defbb79f0a97ee26bb96b5b5f3a2ca", "datapoint": {"question": "Simplify this expression: (7*x + 4)*(-49*x**2 + 23*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-343*x**3 - 35*x**2 + 92*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2065, "polynomial_expr": "(7*x + 4)*(-49*x**2 + 23*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7*x + 4)*(-49*x**2 + 23*x)\nExpanding the part (7*x + 4) using the distributive property, and we got: (7*x)*(-49*x**2 + 23*x) + 4*(-49*x**2 + 23*x)\n#Step 2:\nCurrent expression: (7*x)*(-49*x**2 + 23*x) + 4*(-49*x**2 + 23*x)\nSimplifying the partial expression: 4*(-49*x**2 + 23*x)\nExpanding the part (-49*x**2 + 23*x) using the distributive property, and we got: (23*x)*4 - 49*x**2*4\nReplacing 4*(-49*x**2 + 23*x) with (23*x)*4 - 49*x**2*4 in the overall expression.\n#Step 3:\nCurrent expression: (7*x)*(-49*x**2 + 23*x) + (23*x)*4 - 49*x**2*4\nSimplifying the partial expression: (7*x)*(-49*x**2 + 23*x)\nExpanding the part (-49*x**2 + 23*x) using the distributive property, and we got: (7*x)*(23*x) + (7*x)*(-49*x**2)\nReplacing (7*x)*(-49*x**2 + 23*x) with (7*x)*(23*x) + (7*x)*(-49*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (7*x)*(23*x) + (7*x)*(-49*x**2) + (23*x)*4 - 49*x**2*4\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*x**2)*4 = -196*x**2\n (-49*x**2)*(7*x) = -343*x**3\n (23*x)*4 = 92*x\n (23*x)*(7*x) = 161*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -343*x**3 - 196*x**2 + 161*x**2 + 92*x\nCombining like terms, got -343*x**3 - 35*x**2 + 92*x\n#Step 6:\nCurrent expression: -343*x**3 - 35*x**2 + 92*x\nNo more calculations needed.\n-343*x**3 - 35*x**2 + 92*x", "generated_answer": "-343*x**3 - 35*x**2 + 92*x", "step_length": 6} {"cot_id": "a0904306e9cd3bda7f897a967e8b693c7b2669499b3189eb6a5d548ad0935998", "datapoint": {"question": "Calculate the following: (19*y**2 - 38)*(45*y**3 + 46*y**2 + 17)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "855*y**5 + 874*y**4 - 1710*y**3 - 1425*y**2 - 646", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2066, "polynomial_expr": "(19*y**2 - 38)*(45*y**3 + 46*y**2 + 17)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (19*y**2 - 38)*(45*y**3 + 46*y**2 + 17)\nExpanding the part (19*y**2 - 38) using the distributive property, and we got: (19*y**2)*(45*y**3 + 46*y**2 + 17) - 38*(45*y**3 + 46*y**2 + 17)\n#Step 2:\nCurrent expression: (19*y**2)*(45*y**3 + 46*y**2 + 17) - 38*(45*y**3 + 46*y**2 + 17)\nSimplifying the partial expression: -38*(45*y**3 + 46*y**2 + 17)\nExpanding the part (45*y**3 + 46*y**2 + 17) using the distributive property, and we got: (46*y**2)*(-38) + (45*y**3)*(-38) + 17*(-38)\nReplacing -38*(45*y**3 + 46*y**2 + 17) with (46*y**2)*(-38) + (45*y**3)*(-38) + 17*(-38) in the overall expression.\n#Step 3:\nCurrent expression: (19*y**2)*(45*y**3 + 46*y**2 + 17) + (46*y**2)*(-38) + (45*y**3)*(-38) - 646\nSimplifying the partial expression: (19*y**2)*(45*y**3 + 46*y**2 + 17)\nExpanding the part (45*y**3 + 46*y**2 + 17) using the distributive property, and we got: 17*(19*y**2) + (19*y**2)*(46*y**2) + (19*y**2)*(45*y**3)\nReplacing (19*y**2)*(45*y**3 + 46*y**2 + 17) with 17*(19*y**2) + (19*y**2)*(46*y**2) + (19*y**2)*(45*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 17*19*y**2 + (19*y**2)*(46*y**2) + (19*y**2)*(45*y**3) + (46*y**2)*(-38) + (45*y**3)*(-38) - 646\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (45*y**3)*-38 = -1710*y**3\n (45*y**3)*(19*y**2) = 855*y**5\n (46*y**2)*-38 = -1748*y**2\n (46*y**2)*(19*y**2) = 874*y**4\n 17*19*y**2 = 323*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 855*y**5 + 874*y**4 - 1710*y**3 - 1748*y**2 + 323*y**2 - 646\nCombining like terms, got 855*y**5 + 874*y**4 - 1710*y**3 - 1425*y**2 - 646\n#Step 6:\nCurrent expression: 855*y**5 + 874*y**4 - 1710*y**3 - 1425*y**2 - 646\nNo more calculations needed.\n855*y**5 + 874*y**4 - 1710*y**3 - 1425*y**2 - 646", "generated_answer": "855*y**5 + 874*y**4 - 1710*y**3 - 1425*y**2 - 646", "step_length": 6} {"cot_id": "23faf7fbb13da542af902741441534431fe4f1948bf1b08a4269a2f2de25b483", "datapoint": {"question": "Calculate the following: (13*y**3 - 49*y**2)*(-19*y**3 - 35*y - 59)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-247*y**6 + 931*y**5 - 455*y**4 + 948*y**3 + 2891*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2067, "polynomial_expr": "(13*y**3 - 49*y**2)*(-19*y**3 - 35*y - 59)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (13*y**3 - 49*y**2)*(-19*y**3 - 35*y - 59)\nExpanding the part (13*y**3 - 49*y**2) using the distributive property, and we got: (-49*y**2)*(-19*y**3 - 35*y - 59) + (13*y**3)*(-19*y**3 - 35*y - 59)\n#Step 2:\nCurrent expression: (-49*y**2)*(-19*y**3 - 35*y - 59) + (13*y**3)*(-19*y**3 - 35*y - 59)\nSimplifying the partial expression: (-49*y**2)*(-19*y**3 - 35*y - 59)\nExpanding the part (-19*y**3 - 35*y - 59) using the distributive property, and we got: (-35*y)*(-49*y**2) - (-1)*2891*y**2 + (-49*y**2)*(-19*y**3)\nReplacing (-49*y**2)*(-19*y**3 - 35*y - 59) with (-35*y)*(-49*y**2) - (-1)*2891*y**2 + (-49*y**2)*(-19*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (-35*y)*(-49*y**2) - 59*(-49)*y**2 + (-49*y**2)*(-19*y**3) + (13*y**3)*(-19*y**3 - 35*y - 59)\nSimplifying the partial expression: (13*y**3)*(-19*y**3 - 35*y - 59)\nExpanding the part (-19*y**3 - 35*y - 59) using the distributive property, and we got: (-35*y)*(13*y**3) - 767*y**3 + (-19*y**3)*(13*y**3)\nReplacing (13*y**3)*(-19*y**3 - 35*y - 59) with (-35*y)*(13*y**3) - 767*y**3 + (-19*y**3)*(13*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-35*y)*(-49*y**2) + (-35*y)*(13*y**3) - 59*13*y**3 - 59*(-49)*y**2 + (-49*y**2)*(-19*y**3) + (-19*y**3)*(13*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-35*y)*(-49*y**2) = 1715*y**3\n (-35*y)*(13*y**3) = -455*y**4\n (-19*y**3)*(-49*y**2) = 931*y**5\n (-19*y**3)*(13*y**3) = -247*y**6\n -59*-49*y**2 = 2891*y**2\n -59*13*y**3 = -767*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -247*y**6 + 931*y**5 - 455*y**4 - 767*y**3 + 1715*y**3 + 2891*y**2\nCombining like terms, got -247*y**6 + 931*y**5 - 455*y**4 + 948*y**3 + 2891*y**2\n#Step 6:\nCurrent expression: -247*y**6 + 931*y**5 - 455*y**4 + 948*y**3 + 2891*y**2\nNo more calculations needed.\n-247*y**6 + 931*y**5 - 455*y**4 + 948*y**3 + 2891*y**2", "generated_answer": "-247*y**6 + 931*y**5 - 455*y**4 + 948*y**3 + 2891*y**2", "step_length": 6} {"cot_id": "d4f6e17356bba3ffa4b2825e72115f9591cdb711480ec5898ab964d5372244ea", "datapoint": {"question": "Simplify this expression: 44*x**3*(-39*x**3 + 8*x**2 + 11*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1716*x**6 + 352*x**5 + 484*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2068, "polynomial_expr": "44*x**3*(-39*x**3 + 8*x**2 + 11*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 44*x**3*(-39*x**3 + 8*x**2 + 11*x)\nExpanding the part (-39*x**3 + 8*x**2 + 11*x) using the distributive property, and we got: (11*x)*(44*x**3) + (8*x**2)*(44*x**3) + (-39*x**3)*(44*x**3)\n#Step 2:\nCurrent expression: (11*x)*(44*x**3) + (8*x**2)*(44*x**3) + (-39*x**3)*(44*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*x**3)*(44*x**3) = -1716*x**6\n (8*x**2)*(44*x**3) = 352*x**5\n (11*x)*(44*x**3) = 484*x**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1716*x**6 + 352*x**5 + 484*x**4\nNo more calculations needed.\n-1716*x**6 + 352*x**5 + 484*x**4", "generated_answer": "-1716*x**6 + 352*x**5 + 484*x**4", "step_length": 3} {"cot_id": "9b7542c6a22053b244b9553be3bb0b27f950531d6e6cc6757e99105f6c6eda3e", "datapoint": {"question": "Simplify this expression: -16*y**3*(-47*y**3 + 49*y**2 - 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "752*y**6 - 784*y**5 + 768*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2069, "polynomial_expr": "-16*y**3*(-47*y**3 + 49*y**2 - 48)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -16*y**3*(-47*y**3 + 49*y**2 - 48)\nExpanding the part (-47*y**3 + 49*y**2 - 48) using the distributive property, and we got: -(-1)*768*y**3 + (49*y**2)*(-16*y**3) + (-47*y**3)*(-16*y**3)\n#Step 2:\nCurrent expression: -(-1)*768*y**3 + (49*y**2)*(-16*y**3) + (-47*y**3)*(-16*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -48*(-16*y**3) = 768*y**3\n (-47*y**3)*(-16*y**3) = 752*y**6\n (49*y**2)*(-16*y**3) = -784*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 752*y**6 - 784*y**5 + 768*y**3\nNo more calculations needed.\n752*y**6 - 784*y**5 + 768*y**3", "generated_answer": "752*y**6 - 784*y**5 + 768*y**3", "step_length": 3} {"cot_id": "9301024482596364a6f9ef1fac11d0466662d4876e0cc9fe02fd95eb54ebcdd3", "datapoint": {"question": "Simplify this expression: (32*x**3 + 33*x)*(50*x**3 + 7*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1600*x**6 + 1874*x**4 + 231*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2070, "polynomial_expr": "(32*x**3 + 33*x)*(50*x**3 + 7*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (32*x**3 + 33*x)*(50*x**3 + 7*x)\nExpanding the part (50*x**3 + 7*x) using the distributive property, and we got: (7*x)*(32*x**3 + 33*x) + (50*x**3)*(32*x**3 + 33*x)\n#Step 2:\nCurrent expression: (7*x)*(32*x**3 + 33*x) + (50*x**3)*(32*x**3 + 33*x)\nSimplifying the partial expression: (7*x)*(32*x**3 + 33*x)\nExpanding the part (32*x**3 + 33*x) using the distributive property, and we got: (7*x)*(33*x) + (7*x)*(32*x**3)\nReplacing (7*x)*(32*x**3 + 33*x) with (7*x)*(33*x) + (7*x)*(32*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (7*x)*(33*x) + (7*x)*(32*x**3) + (50*x**3)*(32*x**3 + 33*x)\nSimplifying the partial expression: (50*x**3)*(32*x**3 + 33*x)\nExpanding the part (32*x**3 + 33*x) using the distributive property, and we got: (33*x)*(50*x**3) + (32*x**3)*(50*x**3)\nReplacing (50*x**3)*(32*x**3 + 33*x) with (33*x)*(50*x**3) + (32*x**3)*(50*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (7*x)*(33*x) + (7*x)*(32*x**3) + (33*x)*(50*x**3) + (32*x**3)*(50*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (32*x**3)*(7*x) = 224*x**4\n (32*x**3)*(50*x**3) = 1600*x**6\n (33*x)*(7*x) = 231*x**2\n (33*x)*(50*x**3) = 1650*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1600*x**6 + 224*x**4 + 1650*x**4 + 231*x**2\nCombining like terms, got 1600*x**6 + 1874*x**4 + 231*x**2\n#Step 6:\nCurrent expression: 1600*x**6 + 1874*x**4 + 231*x**2\nNo more calculations needed.\n1600*x**6 + 1874*x**4 + 231*x**2", "generated_answer": "1600*x**6 + 1874*x**4 + 231*x**2", "step_length": 6} {"cot_id": "4ab88205a96e87d25a63a489b5a3ac88329e1445aebad14afdc752e23c64b49f", "datapoint": {"question": "Calculate the following: (29*x**2 - 28*x)*(-35*x**2 - 49*x + 45)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1015*x**4 - 441*x**3 + 2677*x**2 - 1260*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2071, "polynomial_expr": "(29*x**2 - 28*x)*(-35*x**2 - 49*x + 45)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29*x**2 - 28*x)*(-35*x**2 - 49*x + 45)\nExpanding the part (29*x**2 - 28*x) using the distributive property, and we got: (-28*x)*(-35*x**2 - 49*x + 45) + (29*x**2)*(-35*x**2 - 49*x + 45)\n#Step 2:\nCurrent expression: (-28*x)*(-35*x**2 - 49*x + 45) + (29*x**2)*(-35*x**2 - 49*x + 45)\nSimplifying the partial expression: (-28*x)*(-35*x**2 - 49*x + 45)\nExpanding the part (-35*x**2 - 49*x + 45) using the distributive property, and we got: (-49*x)*(-28*x) + (-28*x)*(-35*x**2) + 45*(-28*x)\nReplacing (-28*x)*(-35*x**2 - 49*x + 45) with (-49*x)*(-28*x) + (-28*x)*(-35*x**2) + 45*(-28*x) in the overall expression.\n#Step 3:\nCurrent expression: (-49*x)*(-28*x) + (-28*x)*(-35*x**2) + 45*(-28)*x + (29*x**2)*(-35*x**2 - 49*x + 45)\nSimplifying the partial expression: (29*x**2)*(-35*x**2 - 49*x + 45)\nExpanding the part (-35*x**2 - 49*x + 45) using the distributive property, and we got: (-49*x)*(29*x**2) + 45*(29*x**2) + (-35*x**2)*(29*x**2)\nReplacing (29*x**2)*(-35*x**2 - 49*x + 45) with (-49*x)*(29*x**2) + 45*(29*x**2) + (-35*x**2)*(29*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-49*x)*(-28*x) + (-49*x)*(29*x**2) + (-28*x)*(-35*x**2) + 45*29*x**2 + 45*(-28)*x + (-35*x**2)*(29*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*x)*(-28*x) = 1372*x**2\n (-49*x)*(29*x**2) = -1421*x**3\n (-35*x**2)*(-28*x) = 980*x**3\n (-35*x**2)*(29*x**2) = -1015*x**4\n 45*-28*x = -1260*x\n 45*29*x**2 = 1305*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1015*x**4 - 1421*x**3 + 980*x**3 + 1305*x**2 + 1372*x**2 - 1260*x\nCombining like terms, got -1015*x**4 - 441*x**3 + 2677*x**2 - 1260*x\n#Step 6:\nCurrent expression: -1015*x**4 - 441*x**3 + 2677*x**2 - 1260*x\nNo more calculations needed.\n-1015*x**4 - 441*x**3 + 2677*x**2 - 1260*x", "generated_answer": "-1015*x**4 - 441*x**3 + 2677*x**2 - 1260*x", "step_length": 6} {"cot_id": "ef475a1b8c3ea22747296d5829fee4f82e99ad648be7a44d02fc04edd68b6e84", "datapoint": {"question": "Simplify this expression: (20 - 48*x**2)*(-22*x - 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1056*x**3 + 768*x**2 - 440*x - 320", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2072, "polynomial_expr": "(20 - 48*x**2)*(-22*x - 16)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (20 - 48*x**2)*(-22*x - 16)\nExpanding the part (-22*x - 16) using the distributive property, and we got: (-22*x)*(20 - 48*x**2) - 16*(20 - 48*x**2)\n#Step 2:\nCurrent expression: (-22*x)*(20 - 48*x**2) - 16*(20 - 48*x**2)\nSimplifying the partial expression: -16*(20 - 48*x**2)\nExpanding the part (20 - 48*x**2) using the distributive property, and we got: -48*x**2*(-16) + 20*(-16)\nReplacing -16*(20 - 48*x**2) with -48*x**2*(-16) + 20*(-16) in the overall expression.\n#Step 3:\nCurrent expression: (-22*x)*(20 - 48*x**2) - 48*x**2*(-16) - 320\nSimplifying the partial expression: (-22*x)*(20 - 48*x**2)\nExpanding the part (20 - 48*x**2) using the distributive property, and we got: (-22*x)*(-48*x**2) + 20*(-22*x)\nReplacing (-22*x)*(20 - 48*x**2) with (-22*x)*(-48*x**2) + 20*(-22*x) in the overall expression.\n#Step 4:\nCurrent expression: (-22*x)*(-48*x**2) + 20*(-22)*x - 48*x**2*(-16) - 320\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*x**2)*-16 = 768*x**2\n (-48*x**2)*(-22*x) = 1056*x**3\n 20*-22*x = -440*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1056*x**3 + 768*x**2 - 440*x - 320\nNo more calculations needed.\n1056*x**3 + 768*x**2 - 440*x - 320", "generated_answer": "1056*x**3 + 768*x**2 - 440*x - 320", "step_length": 5} {"cot_id": "251dc18f3d811a0d0150e0f14b27a3c23dfd6393a0f52dce1116ce251c2ed3ab", "datapoint": {"question": "Simplify this expression: (18*y + 15)*(-8*y**3 + 3*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-144*y**4 - 66*y**3 + 45*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2073, "polynomial_expr": "(18*y + 15)*(-8*y**3 + 3*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (18*y + 15)*(-8*y**3 + 3*y**2)\nExpanding the part (18*y + 15) using the distributive property, and we got: (18*y)*(-8*y**3 + 3*y**2) + 15*(-8*y**3 + 3*y**2)\n#Step 2:\nCurrent expression: (18*y)*(-8*y**3 + 3*y**2) + 15*(-8*y**3 + 3*y**2)\nSimplifying the partial expression: 15*(-8*y**3 + 3*y**2)\nExpanding the part (-8*y**3 + 3*y**2) using the distributive property, and we got: (3*y**2)*15 - 8*y**3*15\nReplacing 15*(-8*y**3 + 3*y**2) with (3*y**2)*15 - 8*y**3*15 in the overall expression.\n#Step 3:\nCurrent expression: (18*y)*(-8*y**3 + 3*y**2) + (3*y**2)*15 - 8*y**3*15\nSimplifying the partial expression: (18*y)*(-8*y**3 + 3*y**2)\nExpanding the part (-8*y**3 + 3*y**2) using the distributive property, and we got: (18*y)*(3*y**2) + (18*y)*(-8*y**3)\nReplacing (18*y)*(-8*y**3 + 3*y**2) with (18*y)*(3*y**2) + (18*y)*(-8*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (18*y)*(3*y**2) + (18*y)*(-8*y**3) + (3*y**2)*15 - 8*y**3*15\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-8*y**3)*15 = -120*y**3\n (-8*y**3)*(18*y) = -144*y**4\n (3*y**2)*15 = 45*y**2\n (3*y**2)*(18*y) = 54*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -144*y**4 - 120*y**3 + 54*y**3 + 45*y**2\nCombining like terms, got -144*y**4 - 66*y**3 + 45*y**2\n#Step 6:\nCurrent expression: -144*y**4 - 66*y**3 + 45*y**2\nNo more calculations needed.\n-144*y**4 - 66*y**3 + 45*y**2", "generated_answer": "-144*y**4 - 66*y**3 + 45*y**2", "step_length": 6} {"cot_id": "c90b5d830190ceeacd371618cb4962fbd89a44d9c9e004f45361aed6994b1711", "datapoint": {"question": "Simplify this expression: (-29*z - 40)*(45*z**3 - 10*z**2 - 37*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1305*z**4 - 1510*z**3 + 1473*z**2 + 1480*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2074, "polynomial_expr": "(-29*z - 40)*(45*z**3 - 10*z**2 - 37*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-29*z - 40)*(45*z**3 - 10*z**2 - 37*z)\nExpanding the part (-29*z - 40) using the distributive property, and we got: (-29*z)*(45*z**3 - 10*z**2 - 37*z) - 40*(45*z**3 - 10*z**2 - 37*z)\n#Step 2:\nCurrent expression: (-29*z)*(45*z**3 - 10*z**2 - 37*z) - 40*(45*z**3 - 10*z**2 - 37*z)\nSimplifying the partial expression: -40*(45*z**3 - 10*z**2 - 37*z)\nExpanding the part (45*z**3 - 10*z**2 - 37*z) using the distributive property, and we got: -37*z*(-40) - 10*z**2*(-40) + (45*z**3)*(-40)\nReplacing -40*(45*z**3 - 10*z**2 - 37*z) with -37*z*(-40) - 10*z**2*(-40) + (45*z**3)*(-40) in the overall expression.\n#Step 3:\nCurrent expression: -37*z*(-40) + (-29*z)*(45*z**3 - 10*z**2 - 37*z) - 10*z**2*(-40) + (45*z**3)*(-40)\nSimplifying the partial expression: (-29*z)*(45*z**3 - 10*z**2 - 37*z)\nExpanding the part (45*z**3 - 10*z**2 - 37*z) using the distributive property, and we got: (-37*z)*(-29*z) + (-29*z)*(-10*z**2) + (-29*z)*(45*z**3)\nReplacing (-29*z)*(45*z**3 - 10*z**2 - 37*z) with (-37*z)*(-29*z) + (-29*z)*(-10*z**2) + (-29*z)*(45*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-37*z)*(-29*z) - 37*z*(-40) + (-29*z)*(-10*z**2) + (-29*z)*(45*z**3) - 10*z**2*(-40) + (45*z**3)*(-40)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*z)*-40 = 1480*z\n (-37*z)*(-29*z) = 1073*z**2\n (-10*z**2)*-40 = 400*z**2\n (-10*z**2)*(-29*z) = 290*z**3\n (45*z**3)*-40 = -1800*z**3\n (45*z**3)*(-29*z) = -1305*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1305*z**4 - 1800*z**3 + 290*z**3 + 400*z**2 + 1073*z**2 + 1480*z\nCombining like terms, got -1305*z**4 - 1510*z**3 + 1473*z**2 + 1480*z\n#Step 6:\nCurrent expression: -1305*z**4 - 1510*z**3 + 1473*z**2 + 1480*z\nNo more calculations needed.\n-1305*z**4 - 1510*z**3 + 1473*z**2 + 1480*z", "generated_answer": "-1305*z**4 - 1510*z**3 + 1473*z**2 + 1480*z", "step_length": 6} {"cot_id": "126ced3e3dffc9e912a727482388f9e2eb158219f8a692fe68c5c52c66957ec7", "datapoint": {"question": "Simplify this expression: (34*x**3 + x**2)*(-4*x**3 + 27*x + 28)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-136*x**6 - 4*x**5 + 918*x**4 + 979*x**3 + 28*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2075, "polynomial_expr": "(34*x**3 + x**2)*(-4*x**3 + 27*x + 28)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (34*x**3 + x**2)*(-4*x**3 + 27*x + 28)\nExpanding the part (34*x**3 + x**2) using the distributive property, and we got: x**2*(-4*x**3 + 27*x + 28) + (34*x**3)*(-4*x**3 + 27*x + 28)\n#Step 2:\nCurrent expression: x**2*(-4*x**3 + 27*x + 28) + (34*x**3)*(-4*x**3 + 27*x + 28)\nSimplifying the partial expression: x**2*(-4*x**3 + 27*x + 28)\nExpanding the part (-4*x**3 + 27*x + 28) using the distributive property, and we got: (27*x)*x**2 + x**2*(-4*x**3) + 28*x**2\nReplacing x**2*(-4*x**3 + 27*x + 28) with (27*x)*x**2 + x**2*(-4*x**3) + 28*x**2 in the overall expression.\n#Step 3:\nCurrent expression: (27*x)*x**2 + x**2*(-4*x**3) + 28*x**2 + (34*x**3)*(-4*x**3 + 27*x + 28)\nSimplifying the partial expression: (34*x**3)*(-4*x**3 + 27*x + 28)\nExpanding the part (-4*x**3 + 27*x + 28) using the distributive property, and we got: 28*(34*x**3) + (27*x)*(34*x**3) + (-4*x**3)*(34*x**3)\nReplacing (34*x**3)*(-4*x**3 + 27*x + 28) with 28*(34*x**3) + (27*x)*(34*x**3) + (-4*x**3)*(34*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 28*34*x**3 + (27*x)*x**2 + x**2*(-4*x**3) + 28*x**2 + (27*x)*(34*x**3) + (-4*x**3)*(34*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-4*x**3)*x**2 = -4*x**5\n (-4*x**3)*(34*x**3) = -136*x**6\n (27*x)*x**2 = 27*x**3\n (27*x)*(34*x**3) = 918*x**4\n 28*34*x**3 = 952*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -136*x**6 - 4*x**5 + 918*x**4 + 27*x**3 + 952*x**3 + 28*x**2\nCombining like terms, got -136*x**6 - 4*x**5 + 918*x**4 + 979*x**3 + 28*x**2\n#Step 6:\nCurrent expression: -136*x**6 - 4*x**5 + 918*x**4 + 979*x**3 + 28*x**2\nNo more calculations needed.\n-136*x**6 - 4*x**5 + 918*x**4 + 979*x**3 + 28*x**2", "generated_answer": "-136*x**6 - 4*x**5 + 918*x**4 + 979*x**3 + 28*x**2", "step_length": 6} {"cot_id": "868de2fc2f94e1bffa9eee01b4a6b249e73475079784645295157140c433fdb7", "datapoint": {"question": "Simplify this expression: (-37*y**2 - 32*y + 29)*(10*y**3 + 33*y**2 - 13*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-370*y**5 - 1541*y**4 - 285*y**3 + 1373*y**2 - 377*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2076, "polynomial_expr": "(-37*y**2 - 32*y + 29)*(10*y**3 + 33*y**2 - 13*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-37*y**2 - 32*y + 29)*(10*y**3 + 33*y**2 - 13*y)\nExpanding the part (-37*y**2 - 32*y + 29) using the distributive property, and we got: (-32*y)*(10*y**3 + 33*y**2 - 13*y) + (-37*y**2)*(10*y**3 + 33*y**2 - 13*y) + 29*(10*y**3 + 33*y**2 - 13*y)\n#Step 2:\nCurrent expression: (-32*y)*(10*y**3 + 33*y**2 - 13*y) + (-37*y**2)*(10*y**3 + 33*y**2 - 13*y) + 29*(10*y**3 + 33*y**2 - 13*y)\nSimplifying the partial expression: 29*(10*y**3 + 33*y**2 - 13*y)\nExpanding the part (10*y**3 + 33*y**2 - 13*y) using the distributive property, and we got: -13*y*29 + (33*y**2)*29 + (10*y**3)*29\nReplacing 29*(10*y**3 + 33*y**2 - 13*y) with -13*y*29 + (33*y**2)*29 + (10*y**3)*29 in the overall expression.\n#Step 3:\nCurrent expression: (-32*y)*(10*y**3 + 33*y**2 - 13*y) - 13*y*29 + (-37*y**2)*(10*y**3 + 33*y**2 - 13*y) + (33*y**2)*29 + (10*y**3)*29\nSimplifying the partial expression: (-37*y**2)*(10*y**3 + 33*y**2 - 13*y)\nExpanding the part (10*y**3 + 33*y**2 - 13*y) using the distributive property, and we got: (-13*y)*(-37*y**2) + (-37*y**2)*(33*y**2) + (-37*y**2)*(10*y**3)\nReplacing (-37*y**2)*(10*y**3 + 33*y**2 - 13*y) with (-13*y)*(-37*y**2) + (-37*y**2)*(33*y**2) + (-37*y**2)*(10*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-32*y)*(10*y**3 + 33*y**2 - 13*y) + (-13*y)*(-37*y**2) - 13*y*29 + (-37*y**2)*(33*y**2) + (-37*y**2)*(10*y**3) + (33*y**2)*29 + (10*y**3)*29\nSimplifying the partial expression: (-32*y)*(10*y**3 + 33*y**2 - 13*y)\nExpanding the part (10*y**3 + 33*y**2 - 13*y) using the distributive property, and we got: (-32*y)*(-13*y) + (-32*y)*(33*y**2) + (-32*y)*(10*y**3)\nReplacing (-32*y)*(10*y**3 + 33*y**2 - 13*y) with (-32*y)*(-13*y) + (-32*y)*(33*y**2) + (-32*y)*(10*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-32*y)*(-13*y) + (-32*y)*(33*y**2) + (-32*y)*(10*y**3) + (-13*y)*(-37*y**2) - 13*y*29 + (-37*y**2)*(33*y**2) + (-37*y**2)*(10*y**3) + (33*y**2)*29 + (10*y**3)*29\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*y)*29 = -377*y\n (-13*y)*(-37*y**2) = 481*y**3\n (-13*y)*(-32*y) = 416*y**2\n (10*y**3)*29 = 290*y**3\n (10*y**3)*(-37*y**2) = -370*y**5\n (10*y**3)*(-32*y) = -320*y**4\n (33*y**2)*29 = 957*y**2\n (33*y**2)*(-37*y**2) = -1221*y**4\n (33*y**2)*(-32*y) = -1056*y**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -370*y**5 - 1221*y**4 - 320*y**4 - 1056*y**3 + 290*y**3 + 481*y**3 + 416*y**2 + 957*y**2 - 377*y\nCombining like terms, got -370*y**5 - 1541*y**4 - 285*y**3 + 1373*y**2 - 377*y\n#Step 7:\nCurrent expression: -370*y**5 - 1541*y**4 - 285*y**3 + 1373*y**2 - 377*y\nNo more calculations needed.\n-370*y**5 - 1541*y**4 - 285*y**3 + 1373*y**2 - 377*y", "generated_answer": "-370*y**5 - 1541*y**4 - 285*y**3 + 1373*y**2 - 377*y", "step_length": 7} {"cot_id": "ac84ab412d5250f194e7094237eba16403a59c55067e64ab176c4384a52d124b", "datapoint": {"question": "Simplify this expression: (4*x + 1)*(-17*x**3 + 51*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-68*x**4 - 17*x**3 + 204*x**2 + 51*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2077, "polynomial_expr": "(4*x + 1)*(-17*x**3 + 51*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (4*x + 1)*(-17*x**3 + 51*x)\nExpanding the part (4*x + 1) using the distributive property, and we got: (4*x)*(-17*x**3 + 51*x) + 1*(-17*x**3 + 51*x)\n#Step 2:\nCurrent expression: (4*x)*(-17*x**3 + 51*x) + 1*(-17*x**3 + 51*x)\nSimplifying the partial expression: 1*(-17*x**3 + 51*x)\nExpanding the part (-17*x**3 + 51*x) using the distributive property, and we got: (51*x)*1 - 17*x**3*1\nReplacing 1*(-17*x**3 + 51*x) with (51*x)*1 - 17*x**3*1 in the overall expression.\n#Step 3:\nCurrent expression: (4*x)*(-17*x**3 + 51*x) + (51*x)*1 - 17*x**3*1\nSimplifying the partial expression: (4*x)*(-17*x**3 + 51*x)\nExpanding the part (-17*x**3 + 51*x) using the distributive property, and we got: (4*x)*(51*x) + (4*x)*(-17*x**3)\nReplacing (4*x)*(-17*x**3 + 51*x) with (4*x)*(51*x) + (4*x)*(-17*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (4*x)*(51*x) + (4*x)*(-17*x**3) + (51*x)*1 - 17*x**3*1\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-17*x**3)*1 = -17*x**3\n (-17*x**3)*(4*x) = -68*x**4\n (51*x)*1 = 51*x\n (51*x)*(4*x) = 204*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -68*x**4 - 17*x**3 + 204*x**2 + 51*x\nNo more calculations needed.\n-68*x**4 - 17*x**3 + 204*x**2 + 51*x", "generated_answer": "-68*x**4 - 17*x**3 + 204*x**2 + 51*x", "step_length": 5} {"cot_id": "01c65b2b1ae8e0cb160bf07cd9371b68758e1273fb23af9f5e6d3810599c5ebe", "datapoint": {"question": "Simplify this expression: (-8*z**2 + 25*z)*(26*z**2 - 37*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-208*z**4 + 946*z**3 - 925*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2078, "polynomial_expr": "(-8*z**2 + 25*z)*(26*z**2 - 37*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-8*z**2 + 25*z)*(26*z**2 - 37*z)\nExpanding the part (26*z**2 - 37*z) using the distributive property, and we got: (-37*z)*(-8*z**2 + 25*z) + (26*z**2)*(-8*z**2 + 25*z)\n#Step 2:\nCurrent expression: (-37*z)*(-8*z**2 + 25*z) + (26*z**2)*(-8*z**2 + 25*z)\nSimplifying the partial expression: (-37*z)*(-8*z**2 + 25*z)\nExpanding the part (-8*z**2 + 25*z) using the distributive property, and we got: (-37*z)*(25*z) + (-37*z)*(-8*z**2)\nReplacing (-37*z)*(-8*z**2 + 25*z) with (-37*z)*(25*z) + (-37*z)*(-8*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-37*z)*(25*z) + (-37*z)*(-8*z**2) + (26*z**2)*(-8*z**2 + 25*z)\nSimplifying the partial expression: (26*z**2)*(-8*z**2 + 25*z)\nExpanding the part (-8*z**2 + 25*z) using the distributive property, and we got: (25*z)*(26*z**2) + (-8*z**2)*(26*z**2)\nReplacing (26*z**2)*(-8*z**2 + 25*z) with (25*z)*(26*z**2) + (-8*z**2)*(26*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-37*z)*(25*z) + (-37*z)*(-8*z**2) + (25*z)*(26*z**2) + (-8*z**2)*(26*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-8*z**2)*(-37*z) = 296*z**3\n (-8*z**2)*(26*z**2) = -208*z**4\n (25*z)*(-37*z) = -925*z**2\n (25*z)*(26*z**2) = 650*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -208*z**4 + 296*z**3 + 650*z**3 - 925*z**2\nCombining like terms, got -208*z**4 + 946*z**3 - 925*z**2\n#Step 6:\nCurrent expression: -208*z**4 + 946*z**3 - 925*z**2\nNo more calculations needed.\n-208*z**4 + 946*z**3 - 925*z**2", "generated_answer": "-208*z**4 + 946*z**3 - 925*z**2", "step_length": 6} {"cot_id": "f8ee5946d7c8de4ff6701e6b53058f247139240733c5997413cdb22a39ce9858", "datapoint": {"question": "Simplify this expression: (2*x + 2)*(6*x**3 + 44*x**2 + 22)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "12*x**4 + 100*x**3 + 88*x**2 + 44*x + 44", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2079, "polynomial_expr": "(2*x + 2)*(6*x**3 + 44*x**2 + 22)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2*x + 2)*(6*x**3 + 44*x**2 + 22)\nExpanding the part (2*x + 2) using the distributive property, and we got: (2*x)*(6*x**3 + 44*x**2 + 22) + 2*(6*x**3 + 44*x**2 + 22)\n#Step 2:\nCurrent expression: (2*x)*(6*x**3 + 44*x**2 + 22) + 2*(6*x**3 + 44*x**2 + 22)\nSimplifying the partial expression: 2*(6*x**3 + 44*x**2 + 22)\nExpanding the part (6*x**3 + 44*x**2 + 22) using the distributive property, and we got: (44*x**2)*2 + (6*x**3)*2 + 22*2\nReplacing 2*(6*x**3 + 44*x**2 + 22) with (44*x**2)*2 + (6*x**3)*2 + 22*2 in the overall expression.\n#Step 3:\nCurrent expression: (2*x)*(6*x**3 + 44*x**2 + 22) + (44*x**2)*2 + (6*x**3)*2 + 44\nSimplifying the partial expression: (2*x)*(6*x**3 + 44*x**2 + 22)\nExpanding the part (6*x**3 + 44*x**2 + 22) using the distributive property, and we got: 22*(2*x) + (2*x)*(44*x**2) + (2*x)*(6*x**3)\nReplacing (2*x)*(6*x**3 + 44*x**2 + 22) with 22*(2*x) + (2*x)*(44*x**2) + (2*x)*(6*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 22*2*x + (2*x)*(44*x**2) + (2*x)*(6*x**3) + (44*x**2)*2 + (6*x**3)*2 + 44\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (6*x**3)*2 = 12*x**3\n (6*x**3)*(2*x) = 12*x**4\n (44*x**2)*2 = 88*x**2\n (44*x**2)*(2*x) = 88*x**3\n 22*2*x = 44*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 12*x**4 + 12*x**3 + 88*x**3 + 88*x**2 + 44*x + 44\nCombining like terms, got 12*x**4 + 100*x**3 + 88*x**2 + 44*x + 44\n#Step 6:\nCurrent expression: 12*x**4 + 100*x**3 + 88*x**2 + 44*x + 44\nNo more calculations needed.\n12*x**4 + 100*x**3 + 88*x**2 + 44*x + 44", "generated_answer": "12*x**4 + 100*x**3 + 88*x**2 + 44*x + 44", "step_length": 6} {"cot_id": "236f945dd7f548322eb7e5eeda952eba968e9fbff739ca2aed6ad137e0feffff", "datapoint": {"question": "Calculate the following: (-37*y**2 - 12)*(-41*y**3 + 6*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1517*y**5 + 270*y**3 - 72*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2080, "polynomial_expr": "(-37*y**2 - 12)*(-41*y**3 + 6*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-37*y**2 - 12)*(-41*y**3 + 6*y)\nExpanding the part (-37*y**2 - 12) using the distributive property, and we got: (-37*y**2)*(-41*y**3 + 6*y) - 12*(-41*y**3 + 6*y)\n#Step 2:\nCurrent expression: (-37*y**2)*(-41*y**3 + 6*y) - 12*(-41*y**3 + 6*y)\nSimplifying the partial expression: -12*(-41*y**3 + 6*y)\nExpanding the part (-41*y**3 + 6*y) using the distributive property, and we got: (6*y)*(-12) - 41*y**3*(-12)\nReplacing -12*(-41*y**3 + 6*y) with (6*y)*(-12) - 41*y**3*(-12) in the overall expression.\n#Step 3:\nCurrent expression: (6*y)*(-12) + (-37*y**2)*(-41*y**3 + 6*y) - 41*y**3*(-12)\nSimplifying the partial expression: (-37*y**2)*(-41*y**3 + 6*y)\nExpanding the part (-41*y**3 + 6*y) using the distributive property, and we got: (6*y)*(-37*y**2) + (-37*y**2)*(-41*y**3)\nReplacing (-37*y**2)*(-41*y**3 + 6*y) with (6*y)*(-37*y**2) + (-37*y**2)*(-41*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (6*y)*(-37*y**2) + (6*y)*(-12) + (-37*y**2)*(-41*y**3) - 41*y**3*(-12)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*y**3)*-12 = 492*y**3\n (-41*y**3)*(-37*y**2) = 1517*y**5\n (6*y)*-12 = -72*y\n (6*y)*(-37*y**2) = -222*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1517*y**5 - 222*y**3 + 492*y**3 - 72*y\nCombining like terms, got 1517*y**5 + 270*y**3 - 72*y\n#Step 6:\nCurrent expression: 1517*y**5 + 270*y**3 - 72*y\nNo more calculations needed.\n1517*y**5 + 270*y**3 - 72*y", "generated_answer": "1517*y**5 + 270*y**3 - 72*y", "step_length": 6} {"cot_id": "78ca0fcfa9f4581b75ab6430d1e9570ccc6be9f77ec834ebe73d3b24afd5ede8", "datapoint": {"question": "Calculate the following: 54*z**2*(28 - 17*z**3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-918*z**5 + 1512*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2081, "polynomial_expr": "54*z**2*(28 - 17*z**3)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 54*z**2*(28 - 17*z**3)\nExpanding the part (28 - 17*z**3) using the distributive property, and we got: 28*(54*z**2) + (54*z**2)*(-17*z**3)\n#Step 2:\nCurrent expression: 28*(54*z**2) + (54*z**2)*(-17*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 28*(54*z**2) = 1512*z**2\n (-17*z**3)*(54*z**2) = -918*z**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -918*z**5 + 1512*z**2\nNo more calculations needed.\n-918*z**5 + 1512*z**2", "generated_answer": "-918*z**5 + 1512*z**2", "step_length": 3} {"cot_id": "17ffe9941ab0f73b4d52c7c4657b251a265cb52f7e0d879fd78ce66b81f5daa2", "datapoint": {"question": "Simplify this expression: -82*x*(22 - 25*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2050*x**2 - 1804*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2082, "polynomial_expr": "-82*x*(22 - 25*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -82*x*(22 - 25*x)\nExpanding the part (22 - 25*x) using the distributive property, and we got: (-82*x)*(-25*x) + 22*(-82*x)\n#Step 2:\nCurrent expression: (-82*x)*(-25*x) + 22*(-82*x)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 22*(-82*x) = -1804*x\n (-25*x)*(-82*x) = 2050*x**2\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 2050*x**2 - 1804*x\nNo more calculations needed.\n2050*x**2 - 1804*x", "generated_answer": "2050*x**2 - 1804*x", "step_length": 3} {"cot_id": "dab670112dba304e758e2f819b1df6e4b00253b6473164205687186f1d0145b0", "datapoint": {"question": "Calculate the following: 2520*y - 540\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2520*y - 540", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2083, "polynomial_expr": "2520*y - 540", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 2520*y - 540\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 2520*y - 540\nNo more calculations needed.\n2520*y - 540", "generated_answer": "2520*y - 540", "step_length": 2} {"cot_id": "92c6bc003e1b5931b5bde2e02a91a14c5571810913741492dc7797c47ea7f8d6", "datapoint": {"question": "Calculate the following: (19*x**3 - 1)*(-43*x**2 - 68*x + 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-817*x**5 - 1292*x**4 + 589*x**3 + 43*x**2 + 68*x - 31", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2084, "polynomial_expr": "(19*x**3 - 1)*(-43*x**2 - 68*x + 31)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (19*x**3 - 1)*(-43*x**2 - 68*x + 31)\nExpanding the part (19*x**3 - 1) using the distributive property, and we got: (19*x**3)*(-43*x**2 - 68*x + 31) - (-43*x**2 - 68*x + 31)\n#Step 2:\nCurrent expression: (19*x**3)*(-43*x**2 - 68*x + 31) - (-43*x**2 - 68*x + 31)\nSimplifying the partial expression: -(-43*x**2 - 68*x + 31)\nExpanding the part (-43*x**2 - 68*x + 31) using the distributive property, and we got: -68*x*(-1) - 43*x**2*(-1) + 31*(-1)\nReplacing -(-43*x**2 - 68*x + 31) with -68*x*(-1) - 43*x**2*(-1) + 31*(-1) in the overall expression.\n#Step 3:\nCurrent expression: -68*x*(-1) - 43*x**2*(-1) + (19*x**3)*(-43*x**2 - 68*x + 31) - 31\nSimplifying the partial expression: (19*x**3)*(-43*x**2 - 68*x + 31)\nExpanding the part (-43*x**2 - 68*x + 31) using the distributive property, and we got: (-68*x)*(19*x**3) + 31*(19*x**3) + (-43*x**2)*(19*x**3)\nReplacing (19*x**3)*(-43*x**2 - 68*x + 31) with (-68*x)*(19*x**3) + 31*(19*x**3) + (-43*x**2)*(19*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-68*x)*(19*x**3) - 68*x*(-1) + 31*19*x**3 + (-43*x**2)*(19*x**3) - 43*x**2*(-1) - 31\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-68*x)*-1 = 68*x\n (-68*x)*(19*x**3) = -1292*x**4\n (-43*x**2)*-1 = 43*x**2\n (-43*x**2)*(19*x**3) = -817*x**5\n 31*19*x**3 = 589*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -817*x**5 - 1292*x**4 + 589*x**3 + 43*x**2 + 68*x - 31\nNo more calculations needed.\n-817*x**5 - 1292*x**4 + 589*x**3 + 43*x**2 + 68*x - 31", "generated_answer": "-817*x**5 - 1292*x**4 + 589*x**3 + 43*x**2 + 68*x - 31", "step_length": 5} {"cot_id": "9d50b0344ff36037d7f844676d08a6a0d48c037d71de4e1bf1ea32ac4d6f7b0c", "datapoint": {"question": "Calculate the following: (-15*x**2 - 43*x)*(6*x**3 + 6*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-90*x**5 - 348*x**4 - 258*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2085, "polynomial_expr": "(-15*x**2 - 43*x)*(6*x**3 + 6*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-15*x**2 - 43*x)*(6*x**3 + 6*x**2)\nExpanding the part (-15*x**2 - 43*x) using the distributive property, and we got: (-43*x)*(6*x**3 + 6*x**2) + (-15*x**2)*(6*x**3 + 6*x**2)\n#Step 2:\nCurrent expression: (-43*x)*(6*x**3 + 6*x**2) + (-15*x**2)*(6*x**3 + 6*x**2)\nSimplifying the partial expression: (-43*x)*(6*x**3 + 6*x**2)\nExpanding the part (6*x**3 + 6*x**2) using the distributive property, and we got: (-43*x)*(6*x**2) + (-43*x)*(6*x**3)\nReplacing (-43*x)*(6*x**3 + 6*x**2) with (-43*x)*(6*x**2) + (-43*x)*(6*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-43*x)*(6*x**2) + (-43*x)*(6*x**3) + (-15*x**2)*(6*x**3 + 6*x**2)\nSimplifying the partial expression: (-15*x**2)*(6*x**3 + 6*x**2)\nExpanding the part (6*x**3 + 6*x**2) using the distributive property, and we got: (-15*x**2)*(6*x**2) + (-15*x**2)*(6*x**3)\nReplacing (-15*x**2)*(6*x**3 + 6*x**2) with (-15*x**2)*(6*x**2) + (-15*x**2)*(6*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-43*x)*(6*x**2) + (-43*x)*(6*x**3) + (-15*x**2)*(6*x**2) + (-15*x**2)*(6*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (6*x**2)*(-43*x) = -258*x**3\n (6*x**2)*(-15*x**2) = -90*x**4\n (6*x**3)*(-43*x) = -258*x**4\n (6*x**3)*(-15*x**2) = -90*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -90*x**5 - 258*x**4 - 90*x**4 - 258*x**3\nCombining like terms, got -90*x**5 - 348*x**4 - 258*x**3\n#Step 6:\nCurrent expression: -90*x**5 - 348*x**4 - 258*x**3\nNo more calculations needed.\n-90*x**5 - 348*x**4 - 258*x**3", "generated_answer": "-90*x**5 - 348*x**4 - 258*x**3", "step_length": 6} {"cot_id": "0a328e1c4257a97905fba435b866fc3cab0b99a411dc8a4ecb1e28d0912bf86c", "datapoint": {"question": "Simplify this expression: (6*x + 77)*(-47*x**2 + 43*x - 23)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-282*x**3 - 3361*x**2 + 3173*x - 1771", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2086, "polynomial_expr": "(6*x + 77)*(-47*x**2 + 43*x - 23)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (6*x + 77)*(-47*x**2 + 43*x - 23)\nExpanding the part (6*x + 77) using the distributive property, and we got: (6*x)*(-47*x**2 + 43*x - 23) + 77*(-47*x**2 + 43*x - 23)\n#Step 2:\nCurrent expression: (6*x)*(-47*x**2 + 43*x - 23) + 77*(-47*x**2 + 43*x - 23)\nSimplifying the partial expression: 77*(-47*x**2 + 43*x - 23)\nExpanding the part (-47*x**2 + 43*x - 23) using the distributive property, and we got: (43*x)*77 - 47*x**2*77 - 23*77\nReplacing 77*(-47*x**2 + 43*x - 23) with (43*x)*77 - 47*x**2*77 - 23*77 in the overall expression.\n#Step 3:\nCurrent expression: (6*x)*(-47*x**2 + 43*x - 23) + (43*x)*77 - 47*x**2*77 - 1771\nSimplifying the partial expression: (6*x)*(-47*x**2 + 43*x - 23)\nExpanding the part (-47*x**2 + 43*x - 23) using the distributive property, and we got: -138*x + (6*x)*(43*x) + (6*x)*(-47*x**2)\nReplacing (6*x)*(-47*x**2 + 43*x - 23) with -138*x + (6*x)*(43*x) + (6*x)*(-47*x**2) in the overall expression.\n#Step 4:\nCurrent expression: -23*6*x + (6*x)*(43*x) + (6*x)*(-47*x**2) + (43*x)*77 - 47*x**2*77 - 1771\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*x**2)*77 = -3619*x**2\n (-47*x**2)*(6*x) = -282*x**3\n (43*x)*77 = 3311*x\n (43*x)*(6*x) = 258*x**2\n -23*6*x = -138*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -282*x**3 - 3619*x**2 + 258*x**2 - 138*x + 3311*x - 1771\nCombining like terms, got -282*x**3 - 3361*x**2 + 3173*x - 1771\n#Step 6:\nCurrent expression: -282*x**3 - 3361*x**2 + 3173*x - 1771\nNo more calculations needed.\n-282*x**3 - 3361*x**2 + 3173*x - 1771", "generated_answer": "-282*x**3 - 3361*x**2 + 3173*x - 1771", "step_length": 6} {"cot_id": "47b14a8f023b98446e80abb6764397f088d4fe333c2647c7b6ec7dfbaab7cbd0", "datapoint": {"question": "Calculate the following: (2 - 4*x)*(-48*x**3 - 49*x**2 - 42*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "192*x**4 + 100*x**3 + 70*x**2 - 84*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2087, "polynomial_expr": "(2 - 4*x)*(-48*x**3 - 49*x**2 - 42*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2 - 4*x)*(-48*x**3 - 49*x**2 - 42*x)\nExpanding the part (2 - 4*x) using the distributive property, and we got: (-4*x)*(-48*x**3 - 49*x**2 - 42*x) + 2*(-48*x**3 - 49*x**2 - 42*x)\n#Step 2:\nCurrent expression: (-4*x)*(-48*x**3 - 49*x**2 - 42*x) + 2*(-48*x**3 - 49*x**2 - 42*x)\nSimplifying the partial expression: 2*(-48*x**3 - 49*x**2 - 42*x)\nExpanding the part (-48*x**3 - 49*x**2 - 42*x) using the distributive property, and we got: -42*x*2 - 49*x**2*2 - 48*x**3*2\nReplacing 2*(-48*x**3 - 49*x**2 - 42*x) with -42*x*2 - 49*x**2*2 - 48*x**3*2 in the overall expression.\n#Step 3:\nCurrent expression: -42*x*2 + (-4*x)*(-48*x**3 - 49*x**2 - 42*x) - 49*x**2*2 - 48*x**3*2\nSimplifying the partial expression: (-4*x)*(-48*x**3 - 49*x**2 - 42*x)\nExpanding the part (-48*x**3 - 49*x**2 - 42*x) using the distributive property, and we got: (-42*x)*(-4*x) + (-4*x)*(-49*x**2) + (-4*x)*(-48*x**3)\nReplacing (-4*x)*(-48*x**3 - 49*x**2 - 42*x) with (-42*x)*(-4*x) + (-4*x)*(-49*x**2) + (-4*x)*(-48*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-42*x)*(-4*x) - 42*x*2 + (-4*x)*(-49*x**2) + (-4*x)*(-48*x**3) - 49*x**2*2 - 48*x**3*2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*x**2)*2 = -98*x**2\n (-49*x**2)*(-4*x) = 196*x**3\n (-48*x**3)*2 = -96*x**3\n (-48*x**3)*(-4*x) = 192*x**4\n (-42*x)*2 = -84*x\n (-42*x)*(-4*x) = 168*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 192*x**4 - 96*x**3 + 196*x**3 - 98*x**2 + 168*x**2 - 84*x\nCombining like terms, got 192*x**4 + 100*x**3 + 70*x**2 - 84*x\n#Step 6:\nCurrent expression: 192*x**4 + 100*x**3 + 70*x**2 - 84*x\nNo more calculations needed.\n192*x**4 + 100*x**3 + 70*x**2 - 84*x", "generated_answer": "192*x**4 + 100*x**3 + 70*x**2 - 84*x", "step_length": 6} {"cot_id": "92372db6b1c77d7d761e80fa0dc1e9bbc87186e9f4a00c09ac06e38b6ad6ffcd", "datapoint": {"question": "Simplify this expression: (-36*x - 24)*(45*x**3 + 30*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1620*x**4 - 2160*x**3 - 720*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2088, "polynomial_expr": "(-36*x - 24)*(45*x**3 + 30*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-36*x - 24)*(45*x**3 + 30*x**2)\nExpanding the part (-36*x - 24) using the distributive property, and we got: (-36*x)*(45*x**3 + 30*x**2) - 24*(45*x**3 + 30*x**2)\n#Step 2:\nCurrent expression: (-36*x)*(45*x**3 + 30*x**2) - 24*(45*x**3 + 30*x**2)\nSimplifying the partial expression: -24*(45*x**3 + 30*x**2)\nExpanding the part (45*x**3 + 30*x**2) using the distributive property, and we got: (30*x**2)*(-24) + (45*x**3)*(-24)\nReplacing -24*(45*x**3 + 30*x**2) with (30*x**2)*(-24) + (45*x**3)*(-24) in the overall expression.\n#Step 3:\nCurrent expression: (-36*x)*(45*x**3 + 30*x**2) + (30*x**2)*(-24) + (45*x**3)*(-24)\nSimplifying the partial expression: (-36*x)*(45*x**3 + 30*x**2)\nExpanding the part (45*x**3 + 30*x**2) using the distributive property, and we got: (-36*x)*(30*x**2) + (-36*x)*(45*x**3)\nReplacing (-36*x)*(45*x**3 + 30*x**2) with (-36*x)*(30*x**2) + (-36*x)*(45*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-36*x)*(30*x**2) + (-36*x)*(45*x**3) + (30*x**2)*(-24) + (45*x**3)*(-24)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (30*x**2)*-24 = -720*x**2\n (30*x**2)*(-36*x) = -1080*x**3\n (45*x**3)*-24 = -1080*x**3\n (45*x**3)*(-36*x) = -1620*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1620*x**4 - 1080*x**3 - 1080*x**3 - 720*x**2\nCombining like terms, got -1620*x**4 - 2160*x**3 - 720*x**2\n#Step 6:\nCurrent expression: -1620*x**4 - 2160*x**3 - 720*x**2\nNo more calculations needed.\n-1620*x**4 - 2160*x**3 - 720*x**2", "generated_answer": "-1620*x**4 - 2160*x**3 - 720*x**2", "step_length": 6} {"cot_id": "19d85cd5b3eacc8059703e7e7329f0392f6c50e07d23c66da76adbcb06e4c46f", "datapoint": {"question": "Simplify this expression: (26*z**2 - 30*z)*(25*z**2 - 9*z + 23)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "650*z**4 - 984*z**3 + 868*z**2 - 690*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2089, "polynomial_expr": "(26*z**2 - 30*z)*(25*z**2 - 9*z + 23)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (26*z**2 - 30*z)*(25*z**2 - 9*z + 23)\nExpanding the part (26*z**2 - 30*z) using the distributive property, and we got: (-30*z)*(25*z**2 - 9*z + 23) + (26*z**2)*(25*z**2 - 9*z + 23)\n#Step 2:\nCurrent expression: (-30*z)*(25*z**2 - 9*z + 23) + (26*z**2)*(25*z**2 - 9*z + 23)\nSimplifying the partial expression: (-30*z)*(25*z**2 - 9*z + 23)\nExpanding the part (25*z**2 - 9*z + 23) using the distributive property, and we got: (-30*z)*(-9*z) + (-30*z)*(25*z**2) + 23*(-30*z)\nReplacing (-30*z)*(25*z**2 - 9*z + 23) with (-30*z)*(-9*z) + (-30*z)*(25*z**2) + 23*(-30*z) in the overall expression.\n#Step 3:\nCurrent expression: (-30*z)*(-9*z) + (-30*z)*(25*z**2) + 23*(-30)*z + (26*z**2)*(25*z**2 - 9*z + 23)\nSimplifying the partial expression: (26*z**2)*(25*z**2 - 9*z + 23)\nExpanding the part (25*z**2 - 9*z + 23) using the distributive property, and we got: (-9*z)*(26*z**2) + 23*(26*z**2) + (25*z**2)*(26*z**2)\nReplacing (26*z**2)*(25*z**2 - 9*z + 23) with (-9*z)*(26*z**2) + 23*(26*z**2) + (25*z**2)*(26*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-30*z)*(-9*z) + (-30*z)*(25*z**2) + (-9*z)*(26*z**2) + 23*26*z**2 + 23*(-30)*z + (25*z**2)*(26*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-9*z)*(-30*z) = 270*z**2\n (-9*z)*(26*z**2) = -234*z**3\n (25*z**2)*(-30*z) = -750*z**3\n (25*z**2)*(26*z**2) = 650*z**4\n 23*-30*z = -690*z\n 23*26*z**2 = 598*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 650*z**4 - 750*z**3 - 234*z**3 + 270*z**2 + 598*z**2 - 690*z\nCombining like terms, got 650*z**4 - 984*z**3 + 868*z**2 - 690*z\n#Step 6:\nCurrent expression: 650*z**4 - 984*z**3 + 868*z**2 - 690*z\nNo more calculations needed.\n650*z**4 - 984*z**3 + 868*z**2 - 690*z", "generated_answer": "650*z**4 - 984*z**3 + 868*z**2 - 690*z", "step_length": 6} {"cot_id": "132c812d3bb56161e1650a3959ece467fd7e3ab30a9fef45dd68eb3fc9456de3", "datapoint": {"question": "Simplify this expression: (50*y - 40)*(47*y**2 + 6*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2350*y**3 - 1580*y**2 - 240*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2090, "polynomial_expr": "(50*y - 40)*(47*y**2 + 6*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (50*y - 40)*(47*y**2 + 6*y)\nExpanding the part (50*y - 40) using the distributive property, and we got: (50*y)*(47*y**2 + 6*y) - 40*(47*y**2 + 6*y)\n#Step 2:\nCurrent expression: (50*y)*(47*y**2 + 6*y) - 40*(47*y**2 + 6*y)\nSimplifying the partial expression: -40*(47*y**2 + 6*y)\nExpanding the part (47*y**2 + 6*y) using the distributive property, and we got: (6*y)*(-40) + (47*y**2)*(-40)\nReplacing -40*(47*y**2 + 6*y) with (6*y)*(-40) + (47*y**2)*(-40) in the overall expression.\n#Step 3:\nCurrent expression: (6*y)*(-40) + (50*y)*(47*y**2 + 6*y) + (47*y**2)*(-40)\nSimplifying the partial expression: (50*y)*(47*y**2 + 6*y)\nExpanding the part (47*y**2 + 6*y) using the distributive property, and we got: (6*y)*(50*y) + (50*y)*(47*y**2)\nReplacing (50*y)*(47*y**2 + 6*y) with (6*y)*(50*y) + (50*y)*(47*y**2) in the overall expression.\n#Step 4:\nCurrent expression: (6*y)*(50*y) + (6*y)*(-40) + (50*y)*(47*y**2) + (47*y**2)*(-40)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (6*y)*-40 = -240*y\n (6*y)*(50*y) = 300*y**2\n (47*y**2)*-40 = -1880*y**2\n (47*y**2)*(50*y) = 2350*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2350*y**3 - 1880*y**2 + 300*y**2 - 240*y\nCombining like terms, got 2350*y**3 - 1580*y**2 - 240*y\n#Step 6:\nCurrent expression: 2350*y**3 - 1580*y**2 - 240*y\nNo more calculations needed.\n2350*y**3 - 1580*y**2 - 240*y", "generated_answer": "2350*y**3 - 1580*y**2 - 240*y", "step_length": 6} {"cot_id": "0b5bac0108cb219e5e757e08cc1498fae5bd2fcc2b96598273c187aa5949c0bd", "datapoint": {"question": "Calculate the following: -59*x**2*(-2*x - 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "118*x**3 + 2950*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2091, "polynomial_expr": "-59*x**2*(-2*x - 50)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -59*x**2*(-2*x - 50)\nExpanding the part (-2*x - 50) using the distributive property, and we got: (-2*x)*(-59*x**2) - (-1)*2950*x**2\n#Step 2:\nCurrent expression: (-2*x)*(-59*x**2) - (-1)*2950*x**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -50*(-59*x**2) = 2950*x**2\n (-2*x)*(-59*x**2) = 118*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 118*x**3 + 2950*x**2\nNo more calculations needed.\n118*x**3 + 2950*x**2", "generated_answer": "118*x**3 + 2950*x**2", "step_length": 3} {"cot_id": "f0d7ecfcafa2329d0a059178f81f76995f9e5317f28cfde85e1e6ba5767122a0", "datapoint": {"question": "Calculate the following: (35*y**2 + 45*y)*(-10*y**3 - 45*y**2 + 33*y + 49)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-350*y**5 - 2025*y**4 - 870*y**3 + 3200*y**2 + 2205*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2092, "polynomial_expr": "(35*y**2 + 45*y)*(-10*y**3 - 45*y**2 + 33*y + 49)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (35*y**2 + 45*y)*(-10*y**3 - 45*y**2 + 33*y + 49)\nExpanding the part (35*y**2 + 45*y) using the distributive property, and we got: (45*y)*(-10*y**3 - 45*y**2 + 33*y + 49) + (35*y**2)*(-10*y**3 - 45*y**2 + 33*y + 49)\n#Step 2:\nCurrent expression: (45*y)*(-10*y**3 - 45*y**2 + 33*y + 49) + (35*y**2)*(-10*y**3 - 45*y**2 + 33*y + 49)\nSimplifying the partial expression: (35*y**2)*(-10*y**3 - 45*y**2 + 33*y + 49)\nExpanding the part (-10*y**3 - 45*y**2 + 33*y + 49) using the distributive property, and we got: 49*(35*y**2) + (33*y)*(35*y**2) + (-45*y**2)*(35*y**2) + (35*y**2)*(-10*y**3)\nReplacing (35*y**2)*(-10*y**3 - 45*y**2 + 33*y + 49) with 49*(35*y**2) + (33*y)*(35*y**2) + (-45*y**2)*(35*y**2) + (35*y**2)*(-10*y**3) in the overall expression.\n#Step 3:\nCurrent expression: 49*35*y**2 + (33*y)*(35*y**2) + (45*y)*(-10*y**3 - 45*y**2 + 33*y + 49) + (-45*y**2)*(35*y**2) + (35*y**2)*(-10*y**3)\nSimplifying the partial expression: (45*y)*(-10*y**3 - 45*y**2 + 33*y + 49)\nExpanding the part (-10*y**3 - 45*y**2 + 33*y + 49) using the distributive property, and we got: 49*(45*y) + (33*y)*(45*y) + (45*y)*(-45*y**2) + (45*y)*(-10*y**3)\nReplacing (45*y)*(-10*y**3 - 45*y**2 + 33*y + 49) with 49*(45*y) + (33*y)*(45*y) + (45*y)*(-45*y**2) + (45*y)*(-10*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 49*35*y**2 + 49*45*y + (33*y)*(45*y) + (33*y)*(35*y**2) + (45*y)*(-45*y**2) + (45*y)*(-10*y**3) + (-45*y**2)*(35*y**2) + (35*y**2)*(-10*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*y**2)*(35*y**2) = -1575*y**4\n (-45*y**2)*(45*y) = -2025*y**3\n (-10*y**3)*(35*y**2) = -350*y**5\n (-10*y**3)*(45*y) = -450*y**4\n (33*y)*(35*y**2) = 1155*y**3\n (33*y)*(45*y) = 1485*y**2\n 49*35*y**2 = 1715*y**2\n 49*45*y = 2205*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -350*y**5 - 1575*y**4 - 450*y**4 - 2025*y**3 + 1155*y**3 + 1485*y**2 + 1715*y**2 + 2205*y\nCombining like terms, got -350*y**5 - 2025*y**4 - 870*y**3 + 3200*y**2 + 2205*y\n#Step 6:\nCurrent expression: -350*y**5 - 2025*y**4 - 870*y**3 + 3200*y**2 + 2205*y\nNo more calculations needed.\n-350*y**5 - 2025*y**4 - 870*y**3 + 3200*y**2 + 2205*y", "generated_answer": "-350*y**5 - 2025*y**4 - 870*y**3 + 3200*y**2 + 2205*y", "step_length": 6} {"cot_id": "41190adf2f2f4720651b42ce9cac26938fe0db01c0696a05c1eb11796640725c", "datapoint": {"question": "Simplify this expression: 28*z*(49 - 23*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-644*z**3 + 1372*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2093, "polynomial_expr": "28*z*(49 - 23*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 28*z*(49 - 23*z**2)\nExpanding the part (49 - 23*z**2) using the distributive property, and we got: 49*(28*z) + (28*z)*(-23*z**2)\n#Step 2:\nCurrent expression: 49*(28*z) + (28*z)*(-23*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 49*(28*z) = 1372*z\n (-23*z**2)*(28*z) = -644*z**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -644*z**3 + 1372*z\nNo more calculations needed.\n-644*z**3 + 1372*z", "generated_answer": "-644*z**3 + 1372*z", "step_length": 3} {"cot_id": "831ca17e774850ec97fc5830037913a4e5da7b506e1b37840ee1d0cf6a590c24", "datapoint": {"question": "Calculate the following: (17*x**3 - 26)*(26*x**3 - 8*x**2 + 41*x + 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "442*x**6 - 136*x**5 + 697*x**4 - 166*x**3 + 208*x**2 - 1066*x - 780", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2094, "polynomial_expr": "(17*x**3 - 26)*(26*x**3 - 8*x**2 + 41*x + 30)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (17*x**3 - 26)*(26*x**3 - 8*x**2 + 41*x + 30)\nExpanding the part (17*x**3 - 26) using the distributive property, and we got: (17*x**3)*(26*x**3 - 8*x**2 + 41*x + 30) - 26*(26*x**3 - 8*x**2 + 41*x + 30)\n#Step 2:\nCurrent expression: (17*x**3)*(26*x**3 - 8*x**2 + 41*x + 30) - 26*(26*x**3 - 8*x**2 + 41*x + 30)\nSimplifying the partial expression: -26*(26*x**3 - 8*x**2 + 41*x + 30)\nExpanding the part (26*x**3 - 8*x**2 + 41*x + 30) using the distributive property, and we got: (41*x)*(-26) - 8*x**2*(-26) + (26*x**3)*(-26) + 30*(-26)\nReplacing -26*(26*x**3 - 8*x**2 + 41*x + 30) with (41*x)*(-26) - 8*x**2*(-26) + (26*x**3)*(-26) + 30*(-26) in the overall expression.\n#Step 3:\nCurrent expression: (41*x)*(-26) - 8*x**2*(-26) + (17*x**3)*(26*x**3 - 8*x**2 + 41*x + 30) + (26*x**3)*(-26) - 780\nSimplifying the partial expression: (17*x**3)*(26*x**3 - 8*x**2 + 41*x + 30)\nExpanding the part (26*x**3 - 8*x**2 + 41*x + 30) using the distributive property, and we got: 30*(17*x**3) + (41*x)*(17*x**3) + (-8*x**2)*(17*x**3) + (17*x**3)*(26*x**3)\nReplacing (17*x**3)*(26*x**3 - 8*x**2 + 41*x + 30) with 30*(17*x**3) + (41*x)*(17*x**3) + (-8*x**2)*(17*x**3) + (17*x**3)*(26*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 30*17*x**3 + (41*x)*(17*x**3) + (41*x)*(-26) + (-8*x**2)*(17*x**3) - 8*x**2*(-26) + (17*x**3)*(26*x**3) + (26*x**3)*(-26) - 780\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-8*x**2)*-26 = 208*x**2\n (-8*x**2)*(17*x**3) = -136*x**5\n (26*x**3)*-26 = -676*x**3\n (26*x**3)*(17*x**3) = 442*x**6\n (41*x)*-26 = -1066*x\n (41*x)*(17*x**3) = 697*x**4\n 30*17*x**3 = 510*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 442*x**6 - 136*x**5 + 697*x**4 - 676*x**3 + 510*x**3 + 208*x**2 - 1066*x - 780\nCombining like terms, got 442*x**6 - 136*x**5 + 697*x**4 - 166*x**3 + 208*x**2 - 1066*x - 780\n#Step 6:\nCurrent expression: 442*x**6 - 136*x**5 + 697*x**4 - 166*x**3 + 208*x**2 - 1066*x - 780\nNo more calculations needed.\n442*x**6 - 136*x**5 + 697*x**4 - 166*x**3 + 208*x**2 - 1066*x - 780", "generated_answer": "442*x**6 - 136*x**5 + 697*x**4 - 166*x**3 + 208*x**2 - 1066*x - 780", "step_length": 6} {"cot_id": "f6a4f8615a484c926fc84ab254b5cb543db10378ec769782bf8e3e6cbc898444", "datapoint": {"question": "Calculate the following: 1056*z + 16\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1056*z + 16", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2095, "polynomial_expr": "1056*z + 16", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 1056*z + 16\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 1056*z + 16\nNo more calculations needed.\n1056*z + 16", "generated_answer": "1056*z + 16", "step_length": 2} {"cot_id": "1ad199766e989daac202d3a70ab1b702e0560f93d8510921c3caa5bba70ebb7f", "datapoint": {"question": "Calculate the following: (32*z**2 - 24)*(-26*z**3 + 50*z**2 + 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-832*z**5 + 1600*z**4 + 624*z**3 - 176*z**2 - 768", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2096, "polynomial_expr": "(32*z**2 - 24)*(-26*z**3 + 50*z**2 + 32)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (32*z**2 - 24)*(-26*z**3 + 50*z**2 + 32)\nExpanding the part (32*z**2 - 24) using the distributive property, and we got: (32*z**2)*(-26*z**3 + 50*z**2 + 32) - 24*(-26*z**3 + 50*z**2 + 32)\n#Step 2:\nCurrent expression: (32*z**2)*(-26*z**3 + 50*z**2 + 32) - 24*(-26*z**3 + 50*z**2 + 32)\nSimplifying the partial expression: -24*(-26*z**3 + 50*z**2 + 32)\nExpanding the part (-26*z**3 + 50*z**2 + 32) using the distributive property, and we got: (50*z**2)*(-24) - 26*z**3*(-24) + 32*(-24)\nReplacing -24*(-26*z**3 + 50*z**2 + 32) with (50*z**2)*(-24) - 26*z**3*(-24) + 32*(-24) in the overall expression.\n#Step 3:\nCurrent expression: (32*z**2)*(-26*z**3 + 50*z**2 + 32) + (50*z**2)*(-24) - 26*z**3*(-24) - 768\nSimplifying the partial expression: (32*z**2)*(-26*z**3 + 50*z**2 + 32)\nExpanding the part (-26*z**3 + 50*z**2 + 32) using the distributive property, and we got: 32*(32*z**2) + (32*z**2)*(50*z**2) + (32*z**2)*(-26*z**3)\nReplacing (32*z**2)*(-26*z**3 + 50*z**2 + 32) with 32*(32*z**2) + (32*z**2)*(50*z**2) + (32*z**2)*(-26*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 32*32*z**2 + (32*z**2)*(50*z**2) + (32*z**2)*(-26*z**3) + (50*z**2)*(-24) - 26*z**3*(-24) - 768\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-26*z**3)*-24 = 624*z**3\n (-26*z**3)*(32*z**2) = -832*z**5\n (50*z**2)*-24 = -1200*z**2\n (50*z**2)*(32*z**2) = 1600*z**4\n 32*32*z**2 = 1024*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -832*z**5 + 1600*z**4 + 624*z**3 - 1200*z**2 + 1024*z**2 - 768\nCombining like terms, got -832*z**5 + 1600*z**4 + 624*z**3 - 176*z**2 - 768\n#Step 6:\nCurrent expression: -832*z**5 + 1600*z**4 + 624*z**3 - 176*z**2 - 768\nNo more calculations needed.\n-832*z**5 + 1600*z**4 + 624*z**3 - 176*z**2 - 768", "generated_answer": "-832*z**5 + 1600*z**4 + 624*z**3 - 176*z**2 - 768", "step_length": 6} {"cot_id": "621639ce9595d0623a069b0b1d56ab90a501cf7828967fd4edf2639c1f4fe95d", "datapoint": {"question": "Calculate the following: (-3*z**2 + 21*z + 3)*(18*z**3 - 34*z**2 - 50*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-54*z**5 + 480*z**4 - 510*z**3 - 1152*z**2 - 150*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2097, "polynomial_expr": "(-3*z**2 + 21*z + 3)*(18*z**3 - 34*z**2 - 50*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-3*z**2 + 21*z + 3)*(18*z**3 - 34*z**2 - 50*z)\nExpanding the part (-3*z**2 + 21*z + 3) using the distributive property, and we got: (21*z)*(18*z**3 - 34*z**2 - 50*z) + (-3*z**2)*(18*z**3 - 34*z**2 - 50*z) + 3*(18*z**3 - 34*z**2 - 50*z)\n#Step 2:\nCurrent expression: (21*z)*(18*z**3 - 34*z**2 - 50*z) + (-3*z**2)*(18*z**3 - 34*z**2 - 50*z) + 3*(18*z**3 - 34*z**2 - 50*z)\nSimplifying the partial expression: 3*(18*z**3 - 34*z**2 - 50*z)\nExpanding the part (18*z**3 - 34*z**2 - 50*z) using the distributive property, and we got: -50*z*3 - 34*z**2*3 + (18*z**3)*3\nReplacing 3*(18*z**3 - 34*z**2 - 50*z) with -50*z*3 - 34*z**2*3 + (18*z**3)*3 in the overall expression.\n#Step 3:\nCurrent expression: -50*z*3 + (21*z)*(18*z**3 - 34*z**2 - 50*z) - 34*z**2*3 + (-3*z**2)*(18*z**3 - 34*z**2 - 50*z) + (18*z**3)*3\nSimplifying the partial expression: (-3*z**2)*(18*z**3 - 34*z**2 - 50*z)\nExpanding the part (18*z**3 - 34*z**2 - 50*z) using the distributive property, and we got: (-50*z)*(-3*z**2) + (-34*z**2)*(-3*z**2) + (-3*z**2)*(18*z**3)\nReplacing (-3*z**2)*(18*z**3 - 34*z**2 - 50*z) with (-50*z)*(-3*z**2) + (-34*z**2)*(-3*z**2) + (-3*z**2)*(18*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-50*z)*(-3*z**2) - 50*z*3 + (21*z)*(18*z**3 - 34*z**2 - 50*z) + (-34*z**2)*(-3*z**2) - 34*z**2*3 + (-3*z**2)*(18*z**3) + (18*z**3)*3\nSimplifying the partial expression: (21*z)*(18*z**3 - 34*z**2 - 50*z)\nExpanding the part (18*z**3 - 34*z**2 - 50*z) using the distributive property, and we got: (-50*z)*(21*z) + (21*z)*(-34*z**2) + (21*z)*(18*z**3)\nReplacing (21*z)*(18*z**3 - 34*z**2 - 50*z) with (-50*z)*(21*z) + (21*z)*(-34*z**2) + (21*z)*(18*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-50*z)*(21*z) + (-50*z)*(-3*z**2) - 50*z*3 + (21*z)*(-34*z**2) + (21*z)*(18*z**3) + (-34*z**2)*(-3*z**2) - 34*z**2*3 + (-3*z**2)*(18*z**3) + (18*z**3)*3\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-50*z)*3 = -150*z\n (-50*z)*(-3*z**2) = 150*z**3\n (-50*z)*(21*z) = -1050*z**2\n (-34*z**2)*3 = -102*z**2\n (-34*z**2)*(-3*z**2) = 102*z**4\n (-34*z**2)*(21*z) = -714*z**3\n (18*z**3)*3 = 54*z**3\n (18*z**3)*(-3*z**2) = -54*z**5\n (18*z**3)*(21*z) = 378*z**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -54*z**5 + 102*z**4 + 378*z**4 - 714*z**3 + 54*z**3 + 150*z**3 - 1050*z**2 - 102*z**2 - 150*z\nCombining like terms, got -54*z**5 + 480*z**4 - 510*z**3 - 1152*z**2 - 150*z\n#Step 7:\nCurrent expression: -54*z**5 + 480*z**4 - 510*z**3 - 1152*z**2 - 150*z\nNo more calculations needed.\n-54*z**5 + 480*z**4 - 510*z**3 - 1152*z**2 - 150*z", "generated_answer": "-54*z**5 + 480*z**4 - 510*z**3 - 1152*z**2 - 150*z", "step_length": 7} {"cot_id": "ab5d20c5491da684a5c46b739c3849ef8583fce1de9fb9e0d86e4085de121aae", "datapoint": {"question": "Simplify this expression: (-39*z**3 + 42*z - 30)*(-z**3 - z**2 - 23*z - 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "39*z**6 + 39*z**5 + 855*z**4 + 222*z**3 - 936*z**2 + 438*z + 180", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2098, "polynomial_expr": "(-39*z**3 + 42*z - 30)*(-z**3 - z**2 - 23*z - 6)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-39*z**3 + 42*z - 30)*(-z**3 - z**2 - 23*z - 6)\nExpanding the part (-39*z**3 + 42*z - 30) using the distributive property, and we got: (42*z)*(-z**3 - z**2 - 23*z - 6) + (-39*z**3)*(-z**3 - z**2 - 23*z - 6) - 30*(-z**3 - z**2 - 23*z - 6)\n#Step 2:\nCurrent expression: (42*z)*(-z**3 - z**2 - 23*z - 6) + (-39*z**3)*(-z**3 - z**2 - 23*z - 6) - 30*(-z**3 - z**2 - 23*z - 6)\nSimplifying the partial expression: -30*(-z**3 - z**2 - 23*z - 6)\nExpanding the part (-z**3 - z**2 - 23*z - 6) using the distributive property, and we got: -23*z*(-30) - z**2*(-30) - z**3*(-30) - 6*(-30)\nReplacing -30*(-z**3 - z**2 - 23*z - 6) with -23*z*(-30) - z**2*(-30) - z**3*(-30) - 6*(-30) in the overall expression.\n#Step 3:\nCurrent expression: -23*z*(-30) + (42*z)*(-z**3 - z**2 - 23*z - 6) - z**2*(-30) + (-39*z**3)*(-z**3 - z**2 - 23*z - 6) - z**3*(-30) + 180\nSimplifying the partial expression: (-39*z**3)*(-z**3 - z**2 - 23*z - 6)\nExpanding the part (-z**3 - z**2 - 23*z - 6) using the distributive property, and we got: (-23*z)*(-39*z**3) - (-1)*234*z**3 + (-z**2)*(-39*z**3) + (-39*z**3)*(-z**3)\nReplacing (-39*z**3)*(-z**3 - z**2 - 23*z - 6) with (-23*z)*(-39*z**3) - (-1)*234*z**3 + (-z**2)*(-39*z**3) + (-39*z**3)*(-z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-23*z)*(-39*z**3) - 23*z*(-30) - 6*(-39)*z**3 + (42*z)*(-z**3 - z**2 - 23*z - 6) + (-z**2)*(-39*z**3) - z**2*(-30) + (-39*z**3)*(-z**3) - z**3*(-30) + 180\nSimplifying the partial expression: (42*z)*(-z**3 - z**2 - 23*z - 6)\nExpanding the part (-z**3 - z**2 - 23*z - 6) using the distributive property, and we got: (-23*z)*(42*z) - 252*z + (42*z)*(-z**2) + (42*z)*(-z**3)\nReplacing (42*z)*(-z**3 - z**2 - 23*z - 6) with (-23*z)*(42*z) - 252*z + (42*z)*(-z**2) + (42*z)*(-z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-23*z)*(42*z) + (-23*z)*(-39*z**3) - 23*z*(-30) - 6*(-39)*z**3 - 6*42*z + (42*z)*(-z**2) + (42*z)*(-z**3) + (-z**2)*(-39*z**3) - z**2*(-30) + (-39*z**3)*(-z**3) - z**3*(-30) + 180\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-z**2)*-30 = 30*z**2\n (-z**2)*(-39*z**3) = 39*z**5\n (-z**2)*(42*z) = -42*z**3\n (-z**3)*-30 = 30*z**3\n (-z**3)*(-39*z**3) = 39*z**6\n (-z**3)*(42*z) = -42*z**4\n (-23*z)*-30 = 690*z\n (-23*z)*(-39*z**3) = 897*z**4\n (-23*z)*(42*z) = -966*z**2\n -6*-39*z**3 = 234*z**3\n -6*42*z = -252*z\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 39*z**6 + 39*z**5 - 42*z**4 + 897*z**4 - 42*z**3 + 30*z**3 + 234*z**3 - 966*z**2 + 30*z**2 - 252*z + 690*z + 180\nCombining like terms, got 39*z**6 + 39*z**5 + 855*z**4 + 222*z**3 - 936*z**2 + 438*z + 180\n#Step 7:\nCurrent expression: 39*z**6 + 39*z**5 + 855*z**4 + 222*z**3 - 936*z**2 + 438*z + 180\nNo more calculations needed.\n39*z**6 + 39*z**5 + 855*z**4 + 222*z**3 - 936*z**2 + 438*z + 180", "generated_answer": "39*z**6 + 39*z**5 + 855*z**4 + 222*z**3 - 936*z**2 + 438*z + 180", "step_length": 7} {"cot_id": "51f53750ff842d62715f131b571e514c169c14502a8320eb003fde5eeee94623", "datapoint": {"question": "Calculate the following: (10 - 78*y**2)*(45*y**2 + 32)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-3510*y**4 - 2046*y**2 + 320", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2099, "polynomial_expr": "(10 - 78*y**2)*(45*y**2 + 32)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (10 - 78*y**2)*(45*y**2 + 32)\nExpanding the part (10 - 78*y**2) using the distributive property, and we got: (-78*y**2)*(45*y**2 + 32) + 10*(45*y**2 + 32)\n#Step 2:\nCurrent expression: (-78*y**2)*(45*y**2 + 32) + 10*(45*y**2 + 32)\nSimplifying the partial expression: 10*(45*y**2 + 32)\nExpanding the part (45*y**2 + 32) using the distributive property, and we got: (45*y**2)*10 + 32*10\nReplacing 10*(45*y**2 + 32) with (45*y**2)*10 + 32*10 in the overall expression.\n#Step 3:\nCurrent expression: (-78*y**2)*(45*y**2 + 32) + (45*y**2)*10 + 320\nSimplifying the partial expression: (-78*y**2)*(45*y**2 + 32)\nExpanding the part (45*y**2 + 32) using the distributive property, and we got: 32*(-78*y**2) + (-78*y**2)*(45*y**2)\nReplacing (-78*y**2)*(45*y**2 + 32) with 32*(-78*y**2) + (-78*y**2)*(45*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 32*(-78)*y**2 + (-78*y**2)*(45*y**2) + (45*y**2)*10 + 320\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (45*y**2)*10 = 450*y**2\n (45*y**2)*(-78*y**2) = -3510*y**4\n 32*-78*y**2 = -2496*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -3510*y**4 - 2496*y**2 + 450*y**2 + 320\nCombining like terms, got -3510*y**4 - 2046*y**2 + 320\n#Step 6:\nCurrent expression: -3510*y**4 - 2046*y**2 + 320\nNo more calculations needed.\n-3510*y**4 - 2046*y**2 + 320", "generated_answer": "-3510*y**4 - 2046*y**2 + 320", "step_length": 6} {"cot_id": "df77f26e332e38172b38b1957f74b672b1648a9a5f15d72c2ee6a9c931afc379", "datapoint": {"question": "Calculate the following: (-27*z**2 - 63)*(-7*z**3 + 3*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "189*z**5 + 360*z**3 - 189*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2100, "polynomial_expr": "(-27*z**2 - 63)*(-7*z**3 + 3*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-27*z**2 - 63)*(-7*z**3 + 3*z)\nExpanding the part (-27*z**2 - 63) using the distributive property, and we got: (-27*z**2)*(-7*z**3 + 3*z) - 63*(-7*z**3 + 3*z)\n#Step 2:\nCurrent expression: (-27*z**2)*(-7*z**3 + 3*z) - 63*(-7*z**3 + 3*z)\nSimplifying the partial expression: -63*(-7*z**3 + 3*z)\nExpanding the part (-7*z**3 + 3*z) using the distributive property, and we got: (3*z)*(-63) - 7*z**3*(-63)\nReplacing -63*(-7*z**3 + 3*z) with (3*z)*(-63) - 7*z**3*(-63) in the overall expression.\n#Step 3:\nCurrent expression: (3*z)*(-63) + (-27*z**2)*(-7*z**3 + 3*z) - 7*z**3*(-63)\nSimplifying the partial expression: (-27*z**2)*(-7*z**3 + 3*z)\nExpanding the part (-7*z**3 + 3*z) using the distributive property, and we got: (3*z)*(-27*z**2) + (-27*z**2)*(-7*z**3)\nReplacing (-27*z**2)*(-7*z**3 + 3*z) with (3*z)*(-27*z**2) + (-27*z**2)*(-7*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (3*z)*(-27*z**2) + (3*z)*(-63) + (-27*z**2)*(-7*z**3) - 7*z**3*(-63)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-7*z**3)*-63 = 441*z**3\n (-7*z**3)*(-27*z**2) = 189*z**5\n (3*z)*-63 = -189*z\n (3*z)*(-27*z**2) = -81*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 189*z**5 - 81*z**3 + 441*z**3 - 189*z\nCombining like terms, got 189*z**5 + 360*z**3 - 189*z\n#Step 6:\nCurrent expression: 189*z**5 + 360*z**3 - 189*z\nNo more calculations needed.\n189*z**5 + 360*z**3 - 189*z", "generated_answer": "189*z**5 + 360*z**3 - 189*z", "step_length": 6} {"cot_id": "af642f7f1c52fccd5e25052d1543f69576540e999b38f393b54d44992262986c", "datapoint": {"question": "Simplify this expression: (41*z**2 + 44*z)*(16*z**3 - 38)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "656*z**5 + 704*z**4 - 1558*z**2 - 1672*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2101, "polynomial_expr": "(41*z**2 + 44*z)*(16*z**3 - 38)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (41*z**2 + 44*z)*(16*z**3 - 38)\nExpanding the part (16*z**3 - 38) using the distributive property, and we got: (16*z**3)*(41*z**2 + 44*z) - 38*(41*z**2 + 44*z)\n#Step 2:\nCurrent expression: (16*z**3)*(41*z**2 + 44*z) - 38*(41*z**2 + 44*z)\nSimplifying the partial expression: -38*(41*z**2 + 44*z)\nExpanding the part (41*z**2 + 44*z) using the distributive property, and we got: (44*z)*(-38) + (41*z**2)*(-38)\nReplacing -38*(41*z**2 + 44*z) with (44*z)*(-38) + (41*z**2)*(-38) in the overall expression.\n#Step 3:\nCurrent expression: (44*z)*(-38) + (41*z**2)*(-38) + (16*z**3)*(41*z**2 + 44*z)\nSimplifying the partial expression: (16*z**3)*(41*z**2 + 44*z)\nExpanding the part (41*z**2 + 44*z) using the distributive property, and we got: (44*z)*(16*z**3) + (41*z**2)*(16*z**3)\nReplacing (16*z**3)*(41*z**2 + 44*z) with (44*z)*(16*z**3) + (41*z**2)*(16*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (44*z)*(16*z**3) + (44*z)*(-38) + (41*z**2)*(16*z**3) + (41*z**2)*(-38)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (41*z**2)*-38 = -1558*z**2\n (41*z**2)*(16*z**3) = 656*z**5\n (44*z)*-38 = -1672*z\n (44*z)*(16*z**3) = 704*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 656*z**5 + 704*z**4 - 1558*z**2 - 1672*z\nNo more calculations needed.\n656*z**5 + 704*z**4 - 1558*z**2 - 1672*z", "generated_answer": "656*z**5 + 704*z**4 - 1558*z**2 - 1672*z", "step_length": 5} {"cot_id": "6987bfaf6286dab7fc27f12d00f8c66dbd29c4ee0a1d9529d37cb4fb936d8996", "datapoint": {"question": "Simplify this expression: (-45*y**2 - 27)*(-6*y**3 - 7*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "270*y**5 + 477*y**3 + 189*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2102, "polynomial_expr": "(-45*y**2 - 27)*(-6*y**3 - 7*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-45*y**2 - 27)*(-6*y**3 - 7*y)\nExpanding the part (-45*y**2 - 27) using the distributive property, and we got: (-45*y**2)*(-6*y**3 - 7*y) - 27*(-6*y**3 - 7*y)\n#Step 2:\nCurrent expression: (-45*y**2)*(-6*y**3 - 7*y) - 27*(-6*y**3 - 7*y)\nSimplifying the partial expression: -27*(-6*y**3 - 7*y)\nExpanding the part (-6*y**3 - 7*y) using the distributive property, and we got: -7*y*(-27) - 6*y**3*(-27)\nReplacing -27*(-6*y**3 - 7*y) with -7*y*(-27) - 6*y**3*(-27) in the overall expression.\n#Step 3:\nCurrent expression: -7*y*(-27) + (-45*y**2)*(-6*y**3 - 7*y) - 6*y**3*(-27)\nSimplifying the partial expression: (-45*y**2)*(-6*y**3 - 7*y)\nExpanding the part (-6*y**3 - 7*y) using the distributive property, and we got: (-7*y)*(-45*y**2) + (-45*y**2)*(-6*y**3)\nReplacing (-45*y**2)*(-6*y**3 - 7*y) with (-7*y)*(-45*y**2) + (-45*y**2)*(-6*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-7*y)*(-45*y**2) - 7*y*(-27) + (-45*y**2)*(-6*y**3) - 6*y**3*(-27)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-7*y)*-27 = 189*y\n (-7*y)*(-45*y**2) = 315*y**3\n (-6*y**3)*-27 = 162*y**3\n (-6*y**3)*(-45*y**2) = 270*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 270*y**5 + 162*y**3 + 315*y**3 + 189*y\nCombining like terms, got 270*y**5 + 477*y**3 + 189*y\n#Step 6:\nCurrent expression: 270*y**5 + 477*y**3 + 189*y\nNo more calculations needed.\n270*y**5 + 477*y**3 + 189*y", "generated_answer": "270*y**5 + 477*y**3 + 189*y", "step_length": 6} {"cot_id": "75ceb7e4ae443dd998713b0e1395d6098070853e64659a33ae0b2b3241bdc2b9", "datapoint": {"question": "Calculate the following: -4080*y**2\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-4080*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2103, "polynomial_expr": "-4080*y**2", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -4080*y**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -4080*y**2\nNo more calculations needed.\n-4080*y**2", "generated_answer": "-4080*y**2", "step_length": 2} {"cot_id": "b9a30a0df75e4cdda83c299e1fc405cc1d2b6222d9f064f2b2a9776d73d6b588", "datapoint": {"question": "Calculate the following: (12*x**3 + 36*x)*(18*x**3 + 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "216*x**6 + 648*x**4 + 288*x**3 + 864*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2104, "polynomial_expr": "(12*x**3 + 36*x)*(18*x**3 + 24)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (12*x**3 + 36*x)*(18*x**3 + 24)\nExpanding the part (18*x**3 + 24) using the distributive property, and we got: (18*x**3)*(12*x**3 + 36*x) + 24*(12*x**3 + 36*x)\n#Step 2:\nCurrent expression: (18*x**3)*(12*x**3 + 36*x) + 24*(12*x**3 + 36*x)\nSimplifying the partial expression: 24*(12*x**3 + 36*x)\nExpanding the part (12*x**3 + 36*x) using the distributive property, and we got: (36*x)*24 + (12*x**3)*24\nReplacing 24*(12*x**3 + 36*x) with (36*x)*24 + (12*x**3)*24 in the overall expression.\n#Step 3:\nCurrent expression: (36*x)*24 + (12*x**3)*24 + (18*x**3)*(12*x**3 + 36*x)\nSimplifying the partial expression: (18*x**3)*(12*x**3 + 36*x)\nExpanding the part (12*x**3 + 36*x) using the distributive property, and we got: (36*x)*(18*x**3) + (12*x**3)*(18*x**3)\nReplacing (18*x**3)*(12*x**3 + 36*x) with (36*x)*(18*x**3) + (12*x**3)*(18*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (36*x)*(18*x**3) + (36*x)*24 + (12*x**3)*(18*x**3) + (12*x**3)*24\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (12*x**3)*24 = 288*x**3\n (12*x**3)*(18*x**3) = 216*x**6\n (36*x)*24 = 864*x\n (36*x)*(18*x**3) = 648*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 216*x**6 + 648*x**4 + 288*x**3 + 864*x\nNo more calculations needed.\n216*x**6 + 648*x**4 + 288*x**3 + 864*x", "generated_answer": "216*x**6 + 648*x**4 + 288*x**3 + 864*x", "step_length": 5} {"cot_id": "7dc0d46fc4fa5298fa852d425cf3e0d78e47d193c10acc829139096fe283386b", "datapoint": {"question": "Simplify this expression: -8*x**3*(21*x**3 + 23)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-168*x**6 - 184*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2105, "polynomial_expr": "-8*x**3*(21*x**3 + 23)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -8*x**3*(21*x**3 + 23)\nExpanding the part (21*x**3 + 23) using the distributive property, and we got: 23*(-8*x**3) + (-8*x**3)*(21*x**3)\n#Step 2:\nCurrent expression: 23*(-8*x**3) + (-8*x**3)*(21*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 23*(-8*x**3) = -184*x**3\n (21*x**3)*(-8*x**3) = -168*x**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -168*x**6 - 184*x**3\nNo more calculations needed.\n-168*x**6 - 184*x**3", "generated_answer": "-168*x**6 - 184*x**3", "step_length": 3} {"cot_id": "1eadd3d2b3ec60f06cacb8803100fbfafd8ee7bfc3e72aa3ebf634898f613c29", "datapoint": {"question": "Calculate the following: (92*y + 35)*(-41*y**3 + 45*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-3772*y**4 + 2705*y**3 + 1575*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2106, "polynomial_expr": "(92*y + 35)*(-41*y**3 + 45*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (92*y + 35)*(-41*y**3 + 45*y**2)\nExpanding the part (92*y + 35) using the distributive property, and we got: (92*y)*(-41*y**3 + 45*y**2) + 35*(-41*y**3 + 45*y**2)\n#Step 2:\nCurrent expression: (92*y)*(-41*y**3 + 45*y**2) + 35*(-41*y**3 + 45*y**2)\nSimplifying the partial expression: 35*(-41*y**3 + 45*y**2)\nExpanding the part (-41*y**3 + 45*y**2) using the distributive property, and we got: (45*y**2)*35 - 41*y**3*35\nReplacing 35*(-41*y**3 + 45*y**2) with (45*y**2)*35 - 41*y**3*35 in the overall expression.\n#Step 3:\nCurrent expression: (92*y)*(-41*y**3 + 45*y**2) + (45*y**2)*35 - 41*y**3*35\nSimplifying the partial expression: (92*y)*(-41*y**3 + 45*y**2)\nExpanding the part (-41*y**3 + 45*y**2) using the distributive property, and we got: (92*y)*(45*y**2) + (92*y)*(-41*y**3)\nReplacing (92*y)*(-41*y**3 + 45*y**2) with (92*y)*(45*y**2) + (92*y)*(-41*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (92*y)*(45*y**2) + (92*y)*(-41*y**3) + (45*y**2)*35 - 41*y**3*35\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*y**3)*35 = -1435*y**3\n (-41*y**3)*(92*y) = -3772*y**4\n (45*y**2)*35 = 1575*y**2\n (45*y**2)*(92*y) = 4140*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -3772*y**4 - 1435*y**3 + 4140*y**3 + 1575*y**2\nCombining like terms, got -3772*y**4 + 2705*y**3 + 1575*y**2\n#Step 6:\nCurrent expression: -3772*y**4 + 2705*y**3 + 1575*y**2\nNo more calculations needed.\n-3772*y**4 + 2705*y**3 + 1575*y**2", "generated_answer": "-3772*y**4 + 2705*y**3 + 1575*y**2", "step_length": 6} {"cot_id": "ed168dce7ef4bce3e1e89100608abf3ff5bc03f1645f4b9d0c191f0094dccb91", "datapoint": {"question": "Simplify this expression: (2*z - 53)*(-44*z**2 + 19*z - 65)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-88*z**3 + 2370*z**2 - 1137*z + 3445", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2107, "polynomial_expr": "(2*z - 53)*(-44*z**2 + 19*z - 65)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2*z - 53)*(-44*z**2 + 19*z - 65)\nExpanding the part (2*z - 53) using the distributive property, and we got: (2*z)*(-44*z**2 + 19*z - 65) - 53*(-44*z**2 + 19*z - 65)\n#Step 2:\nCurrent expression: (2*z)*(-44*z**2 + 19*z - 65) - 53*(-44*z**2 + 19*z - 65)\nSimplifying the partial expression: -53*(-44*z**2 + 19*z - 65)\nExpanding the part (-44*z**2 + 19*z - 65) using the distributive property, and we got: (19*z)*(-53) - 44*z**2*(-53) - 65*(-53)\nReplacing -53*(-44*z**2 + 19*z - 65) with (19*z)*(-53) - 44*z**2*(-53) - 65*(-53) in the overall expression.\n#Step 3:\nCurrent expression: (2*z)*(-44*z**2 + 19*z - 65) + (19*z)*(-53) - 44*z**2*(-53) + 3445\nSimplifying the partial expression: (2*z)*(-44*z**2 + 19*z - 65)\nExpanding the part (-44*z**2 + 19*z - 65) using the distributive property, and we got: -130*z + (2*z)*(19*z) + (2*z)*(-44*z**2)\nReplacing (2*z)*(-44*z**2 + 19*z - 65) with -130*z + (2*z)*(19*z) + (2*z)*(-44*z**2) in the overall expression.\n#Step 4:\nCurrent expression: -65*2*z + (2*z)*(19*z) + (2*z)*(-44*z**2) + (19*z)*(-53) - 44*z**2*(-53) + 3445\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-44*z**2)*-53 = 2332*z**2\n (-44*z**2)*(2*z) = -88*z**3\n (19*z)*-53 = -1007*z\n (19*z)*(2*z) = 38*z**2\n -65*2*z = -130*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -88*z**3 + 38*z**2 + 2332*z**2 - 1007*z - 130*z + 3445\nCombining like terms, got -88*z**3 + 2370*z**2 - 1137*z + 3445\n#Step 6:\nCurrent expression: -88*z**3 + 2370*z**2 - 1137*z + 3445\nNo more calculations needed.\n-88*z**3 + 2370*z**2 - 1137*z + 3445", "generated_answer": "-88*z**3 + 2370*z**2 - 1137*z + 3445", "step_length": 6} {"cot_id": "0ae1ae454efa7338b3f4aac5dc460b1655ea1e804e323004c699e27742a94f3c", "datapoint": {"question": "Simplify this expression: (-38*y**3 - 27*y + 7)*(62*y**3 + 49*y**2 - 10*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-2356*y**6 - 1862*y**5 - 1294*y**4 - 889*y**3 + 613*y**2 - 70*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2108, "polynomial_expr": "(-38*y**3 - 27*y + 7)*(62*y**3 + 49*y**2 - 10*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-38*y**3 - 27*y + 7)*(62*y**3 + 49*y**2 - 10*y)\nExpanding the part (-38*y**3 - 27*y + 7) using the distributive property, and we got: (-27*y)*(62*y**3 + 49*y**2 - 10*y) + (-38*y**3)*(62*y**3 + 49*y**2 - 10*y) + 7*(62*y**3 + 49*y**2 - 10*y)\n#Step 2:\nCurrent expression: (-27*y)*(62*y**3 + 49*y**2 - 10*y) + (-38*y**3)*(62*y**3 + 49*y**2 - 10*y) + 7*(62*y**3 + 49*y**2 - 10*y)\nSimplifying the partial expression: 7*(62*y**3 + 49*y**2 - 10*y)\nExpanding the part (62*y**3 + 49*y**2 - 10*y) using the distributive property, and we got: -10*y*7 + (49*y**2)*7 + (62*y**3)*7\nReplacing 7*(62*y**3 + 49*y**2 - 10*y) with -10*y*7 + (49*y**2)*7 + (62*y**3)*7 in the overall expression.\n#Step 3:\nCurrent expression: (-27*y)*(62*y**3 + 49*y**2 - 10*y) - 10*y*7 + (49*y**2)*7 + (-38*y**3)*(62*y**3 + 49*y**2 - 10*y) + (62*y**3)*7\nSimplifying the partial expression: (-38*y**3)*(62*y**3 + 49*y**2 - 10*y)\nExpanding the part (62*y**3 + 49*y**2 - 10*y) using the distributive property, and we got: (-10*y)*(-38*y**3) + (49*y**2)*(-38*y**3) + (-38*y**3)*(62*y**3)\nReplacing (-38*y**3)*(62*y**3 + 49*y**2 - 10*y) with (-10*y)*(-38*y**3) + (49*y**2)*(-38*y**3) + (-38*y**3)*(62*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-27*y)*(62*y**3 + 49*y**2 - 10*y) + (-10*y)*(-38*y**3) - 10*y*7 + (49*y**2)*(-38*y**3) + (49*y**2)*7 + (-38*y**3)*(62*y**3) + (62*y**3)*7\nSimplifying the partial expression: (-27*y)*(62*y**3 + 49*y**2 - 10*y)\nExpanding the part (62*y**3 + 49*y**2 - 10*y) using the distributive property, and we got: (-27*y)*(-10*y) + (-27*y)*(49*y**2) + (-27*y)*(62*y**3)\nReplacing (-27*y)*(62*y**3 + 49*y**2 - 10*y) with (-27*y)*(-10*y) + (-27*y)*(49*y**2) + (-27*y)*(62*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-27*y)*(-10*y) + (-27*y)*(49*y**2) + (-27*y)*(62*y**3) + (-10*y)*(-38*y**3) - 10*y*7 + (49*y**2)*(-38*y**3) + (49*y**2)*7 + (-38*y**3)*(62*y**3) + (62*y**3)*7\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*y)*7 = -70*y\n (-10*y)*(-38*y**3) = 380*y**4\n (-10*y)*(-27*y) = 270*y**2\n (49*y**2)*7 = 343*y**2\n (49*y**2)*(-38*y**3) = -1862*y**5\n (49*y**2)*(-27*y) = -1323*y**3\n (62*y**3)*7 = 434*y**3\n (62*y**3)*(-38*y**3) = -2356*y**6\n (62*y**3)*(-27*y) = -1674*y**4\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -2356*y**6 - 1862*y**5 - 1674*y**4 + 380*y**4 - 1323*y**3 + 434*y**3 + 270*y**2 + 343*y**2 - 70*y\nCombining like terms, got -2356*y**6 - 1862*y**5 - 1294*y**4 - 889*y**3 + 613*y**2 - 70*y\n#Step 7:\nCurrent expression: -2356*y**6 - 1862*y**5 - 1294*y**4 - 889*y**3 + 613*y**2 - 70*y\nNo more calculations needed.\n-2356*y**6 - 1862*y**5 - 1294*y**4 - 889*y**3 + 613*y**2 - 70*y", "generated_answer": "-2356*y**6 - 1862*y**5 - 1294*y**4 - 889*y**3 + 613*y**2 - 70*y", "step_length": 7} {"cot_id": "24185eec90db7286e67ce5b86c96cf3fbed9048e97671a5a72c80045f013c0e0", "datapoint": {"question": "Calculate the following: (38*z**3 - 38*z**2 - 5*z)*(44*z**3 - 44*z**2 - 2*z - 43)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1672*z**6 - 3344*z**5 + 1376*z**4 - 1338*z**3 + 1644*z**2 + 215*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2109, "polynomial_expr": "(38*z**3 - 38*z**2 - 5*z)*(44*z**3 - 44*z**2 - 2*z - 43)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (38*z**3 - 38*z**2 - 5*z)*(44*z**3 - 44*z**2 - 2*z - 43)\nExpanding the part (38*z**3 - 38*z**2 - 5*z) using the distributive property, and we got: (-5*z)*(44*z**3 - 44*z**2 - 2*z - 43) + (-38*z**2)*(44*z**3 - 44*z**2 - 2*z - 43) + (38*z**3)*(44*z**3 - 44*z**2 - 2*z - 43)\n#Step 2:\nCurrent expression: (-5*z)*(44*z**3 - 44*z**2 - 2*z - 43) + (-38*z**2)*(44*z**3 - 44*z**2 - 2*z - 43) + (38*z**3)*(44*z**3 - 44*z**2 - 2*z - 43)\nSimplifying the partial expression: (-38*z**2)*(44*z**3 - 44*z**2 - 2*z - 43)\nExpanding the part (44*z**3 - 44*z**2 - 2*z - 43) using the distributive property, and we got: (-2*z)*(-38*z**2) - (-1)*1634*z**2 + (-44*z**2)*(-38*z**2) + (-38*z**2)*(44*z**3)\nReplacing (-38*z**2)*(44*z**3 - 44*z**2 - 2*z - 43) with (-2*z)*(-38*z**2) - (-1)*1634*z**2 + (-44*z**2)*(-38*z**2) + (-38*z**2)*(44*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-5*z)*(44*z**3 - 44*z**2 - 2*z - 43) + (-2*z)*(-38*z**2) - 43*(-38)*z**2 + (-44*z**2)*(-38*z**2) + (-38*z**2)*(44*z**3) + (38*z**3)*(44*z**3 - 44*z**2 - 2*z - 43)\nSimplifying the partial expression: (-5*z)*(44*z**3 - 44*z**2 - 2*z - 43)\nExpanding the part (44*z**3 - 44*z**2 - 2*z - 43) using the distributive property, and we got: (-5*z)*(-2*z) + (-5*z)*(-44*z**2) + (-5*z)*(44*z**3) - (-1)*215*z\nReplacing (-5*z)*(44*z**3 - 44*z**2 - 2*z - 43) with (-5*z)*(-2*z) + (-5*z)*(-44*z**2) + (-5*z)*(44*z**3) - (-1)*215*z in the overall expression.\n#Step 4:\nCurrent expression: (-5*z)*(-2*z) + (-5*z)*(-44*z**2) + (-5*z)*(44*z**3) + (-2*z)*(-38*z**2) - 43*(-38)*z**2 - 43*(-5)*z + (-44*z**2)*(-38*z**2) + (-38*z**2)*(44*z**3) + (38*z**3)*(44*z**3 - 44*z**2 - 2*z - 43)\nSimplifying the partial expression: (38*z**3)*(44*z**3 - 44*z**2 - 2*z - 43)\nExpanding the part (44*z**3 - 44*z**2 - 2*z - 43) using the distributive property, and we got: (-2*z)*(38*z**3) - 1634*z**3 + (-44*z**2)*(38*z**3) + (38*z**3)*(44*z**3)\nReplacing (38*z**3)*(44*z**3 - 44*z**2 - 2*z - 43) with (-2*z)*(38*z**3) - 1634*z**3 + (-44*z**2)*(38*z**3) + (38*z**3)*(44*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-5*z)*(-2*z) + (-5*z)*(-44*z**2) + (-5*z)*(44*z**3) + (-2*z)*(-38*z**2) + (-2*z)*(38*z**3) - 43*38*z**3 - 43*(-38)*z**2 - 43*(-5)*z + (-44*z**2)*(-38*z**2) + (-44*z**2)*(38*z**3) + (-38*z**2)*(44*z**3) + (38*z**3)*(44*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-44*z**2)*(-38*z**2) = 1672*z**4\n (-44*z**2)*(-5*z) = 220*z**3\n (-44*z**2)*(38*z**3) = -1672*z**5\n (-2*z)*(-38*z**2) = 76*z**3\n (-2*z)*(-5*z) = 10*z**2\n (-2*z)*(38*z**3) = -76*z**4\n (44*z**3)*(-38*z**2) = -1672*z**5\n (44*z**3)*(-5*z) = -220*z**4\n (44*z**3)*(38*z**3) = 1672*z**6\n -43*-38*z**2 = 1634*z**2\n -43*-5*z = 215*z\n -43*38*z**3 = -1634*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 1672*z**6 - 1672*z**5 - 1672*z**5 - 220*z**4 - 76*z**4 + 1672*z**4 - 1634*z**3 + 76*z**3 + 220*z**3 + 10*z**2 + 1634*z**2 + 215*z\nCombining like terms, got 1672*z**6 - 3344*z**5 + 1376*z**4 - 1338*z**3 + 1644*z**2 + 215*z\n#Step 7:\nCurrent expression: 1672*z**6 - 3344*z**5 + 1376*z**4 - 1338*z**3 + 1644*z**2 + 215*z\nNo more calculations needed.\n1672*z**6 - 3344*z**5 + 1376*z**4 - 1338*z**3 + 1644*z**2 + 215*z", "generated_answer": "1672*z**6 - 3344*z**5 + 1376*z**4 - 1338*z**3 + 1644*z**2 + 215*z", "step_length": 7} {"cot_id": "bb6e94303faac692e3235be008f3e5508344fd5b0a69b6deb32ed83420e35879", "datapoint": {"question": "Simplify this expression: 72*y**2*(-11*y**2 + 12*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-792*y**4 + 864*y**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2110, "polynomial_expr": "72*y**2*(-11*y**2 + 12*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 72*y**2*(-11*y**2 + 12*y)\nExpanding the part (-11*y**2 + 12*y) using the distributive property, and we got: (12*y)*(72*y**2) + (-11*y**2)*(72*y**2)\n#Step 2:\nCurrent expression: (12*y)*(72*y**2) + (-11*y**2)*(72*y**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*y**2)*(72*y**2) = -792*y**4\n (12*y)*(72*y**2) = 864*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -792*y**4 + 864*y**3\nNo more calculations needed.\n-792*y**4 + 864*y**3", "generated_answer": "-792*y**4 + 864*y**3", "step_length": 3} {"cot_id": "c74abd1aa219fd3c9e08ef8fc205b4089d235628f005dc052e31f6ed645aafd0", "datapoint": {"question": "Calculate the following: (-33*x**2 - 24)*(-8*x**2 + 37*x + 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "264*x**4 - 1221*x**3 - 1095*x**2 - 888*x - 936", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2111, "polynomial_expr": "(-33*x**2 - 24)*(-8*x**2 + 37*x + 39)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-33*x**2 - 24)*(-8*x**2 + 37*x + 39)\nExpanding the part (-33*x**2 - 24) using the distributive property, and we got: (-33*x**2)*(-8*x**2 + 37*x + 39) - 24*(-8*x**2 + 37*x + 39)\n#Step 2:\nCurrent expression: (-33*x**2)*(-8*x**2 + 37*x + 39) - 24*(-8*x**2 + 37*x + 39)\nSimplifying the partial expression: -24*(-8*x**2 + 37*x + 39)\nExpanding the part (-8*x**2 + 37*x + 39) using the distributive property, and we got: (37*x)*(-24) - 8*x**2*(-24) + 39*(-24)\nReplacing -24*(-8*x**2 + 37*x + 39) with (37*x)*(-24) - 8*x**2*(-24) + 39*(-24) in the overall expression.\n#Step 3:\nCurrent expression: (37*x)*(-24) + (-33*x**2)*(-8*x**2 + 37*x + 39) - 8*x**2*(-24) - 936\nSimplifying the partial expression: (-33*x**2)*(-8*x**2 + 37*x + 39)\nExpanding the part (-8*x**2 + 37*x + 39) using the distributive property, and we got: 39*(-33*x**2) + (37*x)*(-33*x**2) + (-33*x**2)*(-8*x**2)\nReplacing (-33*x**2)*(-8*x**2 + 37*x + 39) with 39*(-33*x**2) + (37*x)*(-33*x**2) + (-33*x**2)*(-8*x**2) in the overall expression.\n#Step 4:\nCurrent expression: 39*(-33)*x**2 + (37*x)*(-33*x**2) + (37*x)*(-24) + (-33*x**2)*(-8*x**2) - 8*x**2*(-24) - 936\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-8*x**2)*-24 = 192*x**2\n (-8*x**2)*(-33*x**2) = 264*x**4\n (37*x)*-24 = -888*x\n (37*x)*(-33*x**2) = -1221*x**3\n 39*-33*x**2 = -1287*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 264*x**4 - 1221*x**3 - 1287*x**2 + 192*x**2 - 888*x - 936\nCombining like terms, got 264*x**4 - 1221*x**3 - 1095*x**2 - 888*x - 936\n#Step 6:\nCurrent expression: 264*x**4 - 1221*x**3 - 1095*x**2 - 888*x - 936\nNo more calculations needed.\n264*x**4 - 1221*x**3 - 1095*x**2 - 888*x - 936", "generated_answer": "264*x**4 - 1221*x**3 - 1095*x**2 - 888*x - 936", "step_length": 6} {"cot_id": "5f58ba60c57cb9b82bb0c467bf6f3df8431b7573f6609e7af6fb72aa34fc7ea9", "datapoint": {"question": "Calculate the following: -62*z**3*(21*z**3 - 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1302*z**6 + 1922*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2112, "polynomial_expr": "-62*z**3*(21*z**3 - 31)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -62*z**3*(21*z**3 - 31)\nExpanding the part (21*z**3 - 31) using the distributive property, and we got: -(-1)*1922*z**3 + (-62*z**3)*(21*z**3)\n#Step 2:\nCurrent expression: -(-1)*1922*z**3 + (-62*z**3)*(21*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -31*(-62*z**3) = 1922*z**3\n (21*z**3)*(-62*z**3) = -1302*z**6\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1302*z**6 + 1922*z**3\nNo more calculations needed.\n-1302*z**6 + 1922*z**3", "generated_answer": "-1302*z**6 + 1922*z**3", "step_length": 3} {"cot_id": "b986f20bc3a96037880123c7cfa4fafb63c23b93b25da324c57ca443337dbb47", "datapoint": {"question": "Calculate the following: (-50*x**3 - 27*x - 3)*(26*x**3 + 45*x - 15)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1300*x**6 - 2952*x**4 + 672*x**3 - 1215*x**2 + 270*x + 45", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2113, "polynomial_expr": "(-50*x**3 - 27*x - 3)*(26*x**3 + 45*x - 15)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-50*x**3 - 27*x - 3)*(26*x**3 + 45*x - 15)\nExpanding the part (26*x**3 + 45*x - 15) using the distributive property, and we got: (45*x)*(-50*x**3 - 27*x - 3) + (26*x**3)*(-50*x**3 - 27*x - 3) - 15*(-50*x**3 - 27*x - 3)\n#Step 2:\nCurrent expression: (45*x)*(-50*x**3 - 27*x - 3) + (26*x**3)*(-50*x**3 - 27*x - 3) - 15*(-50*x**3 - 27*x - 3)\nSimplifying the partial expression: -15*(-50*x**3 - 27*x - 3)\nExpanding the part (-50*x**3 - 27*x - 3) using the distributive property, and we got: -27*x*(-15) - 50*x**3*(-15) - 3*(-15)\nReplacing -15*(-50*x**3 - 27*x - 3) with -27*x*(-15) - 50*x**3*(-15) - 3*(-15) in the overall expression.\n#Step 3:\nCurrent expression: -27*x*(-15) + (45*x)*(-50*x**3 - 27*x - 3) - 50*x**3*(-15) + (26*x**3)*(-50*x**3 - 27*x - 3) + 45\nSimplifying the partial expression: (26*x**3)*(-50*x**3 - 27*x - 3)\nExpanding the part (-50*x**3 - 27*x - 3) using the distributive property, and we got: (-27*x)*(26*x**3) - 78*x**3 + (-50*x**3)*(26*x**3)\nReplacing (26*x**3)*(-50*x**3 - 27*x - 3) with (-27*x)*(26*x**3) - 78*x**3 + (-50*x**3)*(26*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-27*x)*(26*x**3) - 27*x*(-15) - 3*26*x**3 + (45*x)*(-50*x**3 - 27*x - 3) + (-50*x**3)*(26*x**3) - 50*x**3*(-15) + 45\nSimplifying the partial expression: (45*x)*(-50*x**3 - 27*x - 3)\nExpanding the part (-50*x**3 - 27*x - 3) using the distributive property, and we got: (-27*x)*(45*x) - 135*x + (45*x)*(-50*x**3)\nReplacing (45*x)*(-50*x**3 - 27*x - 3) with (-27*x)*(45*x) - 135*x + (45*x)*(-50*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-27*x)*(45*x) + (-27*x)*(26*x**3) - 27*x*(-15) - 3*26*x**3 - 3*45*x + (45*x)*(-50*x**3) + (-50*x**3)*(26*x**3) - 50*x**3*(-15) + 45\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-50*x**3)*-15 = 750*x**3\n (-50*x**3)*(26*x**3) = -1300*x**6\n (-50*x**3)*(45*x) = -2250*x**4\n (-27*x)*-15 = 405*x\n (-27*x)*(26*x**3) = -702*x**4\n (-27*x)*(45*x) = -1215*x**2\n -3*26*x**3 = -78*x**3\n -3*45*x = -135*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1300*x**6 - 2250*x**4 - 702*x**4 - 78*x**3 + 750*x**3 - 1215*x**2 - 135*x + 405*x + 45\nCombining like terms, got -1300*x**6 - 2952*x**4 + 672*x**3 - 1215*x**2 + 270*x + 45\n#Step 7:\nCurrent expression: -1300*x**6 - 2952*x**4 + 672*x**3 - 1215*x**2 + 270*x + 45\nNo more calculations needed.\n-1300*x**6 - 2952*x**4 + 672*x**3 - 1215*x**2 + 270*x + 45", "generated_answer": "-1300*x**6 - 2952*x**4 + 672*x**3 - 1215*x**2 + 270*x + 45", "step_length": 7} {"cot_id": "60a8f5a91c9a7c3d9cc365e7e3d035604c6debc22c5d757d730428de76f1f827", "datapoint": {"question": "Simplify this expression: 41*z**3*(40*z**3 + 44*z + 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1640*z**6 + 1804*z**4 + 1804*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2114, "polynomial_expr": "41*z**3*(40*z**3 + 44*z + 44)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 41*z**3*(40*z**3 + 44*z + 44)\nExpanding the part (40*z**3 + 44*z + 44) using the distributive property, and we got: 44*(41*z**3) + (44*z)*(41*z**3) + (40*z**3)*(41*z**3)\n#Step 2:\nCurrent expression: 44*(41*z**3) + (44*z)*(41*z**3) + (40*z**3)*(41*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 44*(41*z**3) = 1804*z**3\n (40*z**3)*(41*z**3) = 1640*z**6\n (44*z)*(41*z**3) = 1804*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1640*z**6 + 1804*z**4 + 1804*z**3\nNo more calculations needed.\n1640*z**6 + 1804*z**4 + 1804*z**3", "generated_answer": "1640*z**6 + 1804*z**4 + 1804*z**3", "step_length": 3} {"cot_id": "b74c8f7b767b056a507260151d9e89af1d741059d8899959197f19359e62120b", "datapoint": {"question": "Calculate the following: (42*z + 62)*(-32*z**3 + 14*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1344*z**4 - 1396*z**3 + 868*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2115, "polynomial_expr": "(42*z + 62)*(-32*z**3 + 14*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (42*z + 62)*(-32*z**3 + 14*z**2)\nExpanding the part (42*z + 62) using the distributive property, and we got: (42*z)*(-32*z**3 + 14*z**2) + 62*(-32*z**3 + 14*z**2)\n#Step 2:\nCurrent expression: (42*z)*(-32*z**3 + 14*z**2) + 62*(-32*z**3 + 14*z**2)\nSimplifying the partial expression: 62*(-32*z**3 + 14*z**2)\nExpanding the part (-32*z**3 + 14*z**2) using the distributive property, and we got: (14*z**2)*62 - 32*z**3*62\nReplacing 62*(-32*z**3 + 14*z**2) with (14*z**2)*62 - 32*z**3*62 in the overall expression.\n#Step 3:\nCurrent expression: (42*z)*(-32*z**3 + 14*z**2) + (14*z**2)*62 - 32*z**3*62\nSimplifying the partial expression: (42*z)*(-32*z**3 + 14*z**2)\nExpanding the part (-32*z**3 + 14*z**2) using the distributive property, and we got: (42*z)*(14*z**2) + (42*z)*(-32*z**3)\nReplacing (42*z)*(-32*z**3 + 14*z**2) with (42*z)*(14*z**2) + (42*z)*(-32*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (42*z)*(14*z**2) + (42*z)*(-32*z**3) + (14*z**2)*62 - 32*z**3*62\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-32*z**3)*62 = -1984*z**3\n (-32*z**3)*(42*z) = -1344*z**4\n (14*z**2)*62 = 868*z**2\n (14*z**2)*(42*z) = 588*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1344*z**4 - 1984*z**3 + 588*z**3 + 868*z**2\nCombining like terms, got -1344*z**4 - 1396*z**3 + 868*z**2\n#Step 6:\nCurrent expression: -1344*z**4 - 1396*z**3 + 868*z**2\nNo more calculations needed.\n-1344*z**4 - 1396*z**3 + 868*z**2", "generated_answer": "-1344*z**4 - 1396*z**3 + 868*z**2", "step_length": 6} {"cot_id": "261328a294046cef727450808eda62b7604aa94cc0620795f030d284bc668752", "datapoint": {"question": "Simplify this expression: (40*z**2 + 41*z + 31)*(-21*z**3 + 43*z**2 - 53*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-840*z**5 + 859*z**4 - 1008*z**3 - 840*z**2 - 1643*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2116, "polynomial_expr": "(40*z**2 + 41*z + 31)*(-21*z**3 + 43*z**2 - 53*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (40*z**2 + 41*z + 31)*(-21*z**3 + 43*z**2 - 53*z)\nExpanding the part (40*z**2 + 41*z + 31) using the distributive property, and we got: (41*z)*(-21*z**3 + 43*z**2 - 53*z) + (40*z**2)*(-21*z**3 + 43*z**2 - 53*z) + 31*(-21*z**3 + 43*z**2 - 53*z)\n#Step 2:\nCurrent expression: (41*z)*(-21*z**3 + 43*z**2 - 53*z) + (40*z**2)*(-21*z**3 + 43*z**2 - 53*z) + 31*(-21*z**3 + 43*z**2 - 53*z)\nSimplifying the partial expression: 31*(-21*z**3 + 43*z**2 - 53*z)\nExpanding the part (-21*z**3 + 43*z**2 - 53*z) using the distributive property, and we got: -53*z*31 + (43*z**2)*31 - 21*z**3*31\nReplacing 31*(-21*z**3 + 43*z**2 - 53*z) with -53*z*31 + (43*z**2)*31 - 21*z**3*31 in the overall expression.\n#Step 3:\nCurrent expression: -53*z*31 + (41*z)*(-21*z**3 + 43*z**2 - 53*z) + (40*z**2)*(-21*z**3 + 43*z**2 - 53*z) + (43*z**2)*31 - 21*z**3*31\nSimplifying the partial expression: (40*z**2)*(-21*z**3 + 43*z**2 - 53*z)\nExpanding the part (-21*z**3 + 43*z**2 - 53*z) using the distributive property, and we got: (-53*z)*(40*z**2) + (40*z**2)*(43*z**2) + (40*z**2)*(-21*z**3)\nReplacing (40*z**2)*(-21*z**3 + 43*z**2 - 53*z) with (-53*z)*(40*z**2) + (40*z**2)*(43*z**2) + (40*z**2)*(-21*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-53*z)*(40*z**2) - 53*z*31 + (41*z)*(-21*z**3 + 43*z**2 - 53*z) + (40*z**2)*(43*z**2) + (40*z**2)*(-21*z**3) + (43*z**2)*31 - 21*z**3*31\nSimplifying the partial expression: (41*z)*(-21*z**3 + 43*z**2 - 53*z)\nExpanding the part (-21*z**3 + 43*z**2 - 53*z) using the distributive property, and we got: (-53*z)*(41*z) + (41*z)*(43*z**2) + (41*z)*(-21*z**3)\nReplacing (41*z)*(-21*z**3 + 43*z**2 - 53*z) with (-53*z)*(41*z) + (41*z)*(43*z**2) + (41*z)*(-21*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-53*z)*(41*z) + (-53*z)*(40*z**2) - 53*z*31 + (41*z)*(43*z**2) + (41*z)*(-21*z**3) + (40*z**2)*(43*z**2) + (40*z**2)*(-21*z**3) + (43*z**2)*31 - 21*z**3*31\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-53*z)*31 = -1643*z\n (-53*z)*(40*z**2) = -2120*z**3\n (-53*z)*(41*z) = -2173*z**2\n (-21*z**3)*31 = -651*z**3\n (-21*z**3)*(40*z**2) = -840*z**5\n (-21*z**3)*(41*z) = -861*z**4\n (43*z**2)*31 = 1333*z**2\n (43*z**2)*(40*z**2) = 1720*z**4\n (43*z**2)*(41*z) = 1763*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -840*z**5 - 861*z**4 + 1720*z**4 - 2120*z**3 - 651*z**3 + 1763*z**3 - 2173*z**2 + 1333*z**2 - 1643*z\nCombining like terms, got -840*z**5 + 859*z**4 - 1008*z**3 - 840*z**2 - 1643*z\n#Step 7:\nCurrent expression: -840*z**5 + 859*z**4 - 1008*z**3 - 840*z**2 - 1643*z\nNo more calculations needed.\n-840*z**5 + 859*z**4 - 1008*z**3 - 840*z**2 - 1643*z", "generated_answer": "-840*z**5 + 859*z**4 - 1008*z**3 - 840*z**2 - 1643*z", "step_length": 7} {"cot_id": "c661cb372e82b1fc9f6e55cfebd07f70dd5d82a7c36fd40d1e17d34f14cb8a05", "datapoint": {"question": "Simplify this expression: (-37*y**3 + 29*y**2 + 34*y)*(4*y**3 + 47*y + 27)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-148*y**6 + 116*y**5 - 1603*y**4 + 364*y**3 + 2381*y**2 + 918*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2117, "polynomial_expr": "(-37*y**3 + 29*y**2 + 34*y)*(4*y**3 + 47*y + 27)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-37*y**3 + 29*y**2 + 34*y)*(4*y**3 + 47*y + 27)\nExpanding the part (4*y**3 + 47*y + 27) using the distributive property, and we got: (47*y)*(-37*y**3 + 29*y**2 + 34*y) + (4*y**3)*(-37*y**3 + 29*y**2 + 34*y) + 27*(-37*y**3 + 29*y**2 + 34*y)\n#Step 2:\nCurrent expression: (47*y)*(-37*y**3 + 29*y**2 + 34*y) + (4*y**3)*(-37*y**3 + 29*y**2 + 34*y) + 27*(-37*y**3 + 29*y**2 + 34*y)\nSimplifying the partial expression: 27*(-37*y**3 + 29*y**2 + 34*y)\nExpanding the part (-37*y**3 + 29*y**2 + 34*y) using the distributive property, and we got: (34*y)*27 + (29*y**2)*27 - 37*y**3*27\nReplacing 27*(-37*y**3 + 29*y**2 + 34*y) with (34*y)*27 + (29*y**2)*27 - 37*y**3*27 in the overall expression.\n#Step 3:\nCurrent expression: (34*y)*27 + (47*y)*(-37*y**3 + 29*y**2 + 34*y) + (29*y**2)*27 - 37*y**3*27 + (4*y**3)*(-37*y**3 + 29*y**2 + 34*y)\nSimplifying the partial expression: (4*y**3)*(-37*y**3 + 29*y**2 + 34*y)\nExpanding the part (-37*y**3 + 29*y**2 + 34*y) using the distributive property, and we got: (34*y)*(4*y**3) + (29*y**2)*(4*y**3) + (-37*y**3)*(4*y**3)\nReplacing (4*y**3)*(-37*y**3 + 29*y**2 + 34*y) with (34*y)*(4*y**3) + (29*y**2)*(4*y**3) + (-37*y**3)*(4*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (34*y)*(4*y**3) + (34*y)*27 + (47*y)*(-37*y**3 + 29*y**2 + 34*y) + (29*y**2)*(4*y**3) + (29*y**2)*27 + (-37*y**3)*(4*y**3) - 37*y**3*27\nSimplifying the partial expression: (47*y)*(-37*y**3 + 29*y**2 + 34*y)\nExpanding the part (-37*y**3 + 29*y**2 + 34*y) using the distributive property, and we got: (34*y)*(47*y) + (47*y)*(29*y**2) + (47*y)*(-37*y**3)\nReplacing (47*y)*(-37*y**3 + 29*y**2 + 34*y) with (34*y)*(47*y) + (47*y)*(29*y**2) + (47*y)*(-37*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (34*y)*(47*y) + (34*y)*(4*y**3) + (34*y)*27 + (47*y)*(29*y**2) + (47*y)*(-37*y**3) + (29*y**2)*(4*y**3) + (29*y**2)*27 + (-37*y**3)*(4*y**3) - 37*y**3*27\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-37*y**3)*27 = -999*y**3\n (-37*y**3)*(4*y**3) = -148*y**6\n (-37*y**3)*(47*y) = -1739*y**4\n (29*y**2)*27 = 783*y**2\n (29*y**2)*(4*y**3) = 116*y**5\n (29*y**2)*(47*y) = 1363*y**3\n (34*y)*27 = 918*y\n (34*y)*(4*y**3) = 136*y**4\n (34*y)*(47*y) = 1598*y**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -148*y**6 + 116*y**5 - 1739*y**4 + 136*y**4 - 999*y**3 + 1363*y**3 + 783*y**2 + 1598*y**2 + 918*y\nCombining like terms, got -148*y**6 + 116*y**5 - 1603*y**4 + 364*y**3 + 2381*y**2 + 918*y\n#Step 7:\nCurrent expression: -148*y**6 + 116*y**5 - 1603*y**4 + 364*y**3 + 2381*y**2 + 918*y\nNo more calculations needed.\n-148*y**6 + 116*y**5 - 1603*y**4 + 364*y**3 + 2381*y**2 + 918*y", "generated_answer": "-148*y**6 + 116*y**5 - 1603*y**4 + 364*y**3 + 2381*y**2 + 918*y", "step_length": 7} {"cot_id": "9b1b2cf6c4203e6067c4a470cfa0a62ad4e599be96d088d875920ebb826a1277", "datapoint": {"question": "Simplify this expression: (33 - 19*y**2)*(47*y**2 + 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-893*y**4 + 1247*y**2 + 528", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2118, "polynomial_expr": "(33 - 19*y**2)*(47*y**2 + 16)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (33 - 19*y**2)*(47*y**2 + 16)\nExpanding the part (47*y**2 + 16) using the distributive property, and we got: (47*y**2)*(33 - 19*y**2) + 16*(33 - 19*y**2)\n#Step 2:\nCurrent expression: (47*y**2)*(33 - 19*y**2) + 16*(33 - 19*y**2)\nSimplifying the partial expression: 16*(33 - 19*y**2)\nExpanding the part (33 - 19*y**2) using the distributive property, and we got: -19*y**2*16 + 33*16\nReplacing 16*(33 - 19*y**2) with -19*y**2*16 + 33*16 in the overall expression.\n#Step 3:\nCurrent expression: -19*y**2*16 + (47*y**2)*(33 - 19*y**2) + 528\nSimplifying the partial expression: (47*y**2)*(33 - 19*y**2)\nExpanding the part (33 - 19*y**2) using the distributive property, and we got: 33*(47*y**2) + (-19*y**2)*(47*y**2)\nReplacing (47*y**2)*(33 - 19*y**2) with 33*(47*y**2) + (-19*y**2)*(47*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 33*47*y**2 + (-19*y**2)*(47*y**2) - 19*y**2*16 + 528\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-19*y**2)*16 = -304*y**2\n (-19*y**2)*(47*y**2) = -893*y**4\n 33*47*y**2 = 1551*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -893*y**4 - 304*y**2 + 1551*y**2 + 528\nCombining like terms, got -893*y**4 + 1247*y**2 + 528\n#Step 6:\nCurrent expression: -893*y**4 + 1247*y**2 + 528\nNo more calculations needed.\n-893*y**4 + 1247*y**2 + 528", "generated_answer": "-893*y**4 + 1247*y**2 + 528", "step_length": 6} {"cot_id": "bfbd78b8bb2ea1d34ae0e3ef70d3dec481b2e7bc52d49a92acb6c3cb914627b8", "datapoint": {"question": "Simplify this expression: (-40*z**2 + 46*z + 63)*(34*z**3 + 18*z**2 + 29*z - 50)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1360*z**5 + 844*z**4 + 1810*z**3 + 4468*z**2 - 473*z - 3150", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2119, "polynomial_expr": "(-40*z**2 + 46*z + 63)*(34*z**3 + 18*z**2 + 29*z - 50)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-40*z**2 + 46*z + 63)*(34*z**3 + 18*z**2 + 29*z - 50)\nExpanding the part (-40*z**2 + 46*z + 63) using the distributive property, and we got: (46*z)*(34*z**3 + 18*z**2 + 29*z - 50) + (-40*z**2)*(34*z**3 + 18*z**2 + 29*z - 50) + 63*(34*z**3 + 18*z**2 + 29*z - 50)\n#Step 2:\nCurrent expression: (46*z)*(34*z**3 + 18*z**2 + 29*z - 50) + (-40*z**2)*(34*z**3 + 18*z**2 + 29*z - 50) + 63*(34*z**3 + 18*z**2 + 29*z - 50)\nSimplifying the partial expression: 63*(34*z**3 + 18*z**2 + 29*z - 50)\nExpanding the part (34*z**3 + 18*z**2 + 29*z - 50) using the distributive property, and we got: (29*z)*63 + (18*z**2)*63 + (34*z**3)*63 - 50*63\nReplacing 63*(34*z**3 + 18*z**2 + 29*z - 50) with (29*z)*63 + (18*z**2)*63 + (34*z**3)*63 - 50*63 in the overall expression.\n#Step 3:\nCurrent expression: (29*z)*63 + (46*z)*(34*z**3 + 18*z**2 + 29*z - 50) + (-40*z**2)*(34*z**3 + 18*z**2 + 29*z - 50) + (18*z**2)*63 + (34*z**3)*63 - 3150\nSimplifying the partial expression: (-40*z**2)*(34*z**3 + 18*z**2 + 29*z - 50)\nExpanding the part (34*z**3 + 18*z**2 + 29*z - 50) using the distributive property, and we got: -(-1)*2000*z**2 + (29*z)*(-40*z**2) + (-40*z**2)*(18*z**2) + (-40*z**2)*(34*z**3)\nReplacing (-40*z**2)*(34*z**3 + 18*z**2 + 29*z - 50) with -(-1)*2000*z**2 + (29*z)*(-40*z**2) + (-40*z**2)*(18*z**2) + (-40*z**2)*(34*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -50*(-40)*z**2 + (29*z)*(-40*z**2) + (29*z)*63 + (46*z)*(34*z**3 + 18*z**2 + 29*z - 50) + (-40*z**2)*(18*z**2) + (-40*z**2)*(34*z**3) + (18*z**2)*63 + (34*z**3)*63 - 3150\nSimplifying the partial expression: (46*z)*(34*z**3 + 18*z**2 + 29*z - 50)\nExpanding the part (34*z**3 + 18*z**2 + 29*z - 50) using the distributive property, and we got: -2300*z + (29*z)*(46*z) + (46*z)*(18*z**2) + (46*z)*(34*z**3)\nReplacing (46*z)*(34*z**3 + 18*z**2 + 29*z - 50) with -2300*z + (29*z)*(46*z) + (46*z)*(18*z**2) + (46*z)*(34*z**3) in the overall expression.\n#Step 5:\nCurrent expression: -50*(-40)*z**2 - 50*46*z + (29*z)*(46*z) + (29*z)*(-40*z**2) + (29*z)*63 + (46*z)*(18*z**2) + (46*z)*(34*z**3) + (-40*z**2)*(18*z**2) + (-40*z**2)*(34*z**3) + (18*z**2)*63 + (34*z**3)*63 - 3150\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (18*z**2)*63 = 1134*z**2\n (18*z**2)*(-40*z**2) = -720*z**4\n (18*z**2)*(46*z) = 828*z**3\n (29*z)*63 = 1827*z\n (29*z)*(-40*z**2) = -1160*z**3\n (29*z)*(46*z) = 1334*z**2\n (34*z**3)*63 = 2142*z**3\n (34*z**3)*(-40*z**2) = -1360*z**5\n (34*z**3)*(46*z) = 1564*z**4\n -50*-40*z**2 = 2000*z**2\n -50*46*z = -2300*z\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -1360*z**5 - 720*z**4 + 1564*z**4 - 1160*z**3 + 828*z**3 + 2142*z**3 + 1134*z**2 + 1334*z**2 + 2000*z**2 - 2300*z + 1827*z - 3150\nCombining like terms, got -1360*z**5 + 844*z**4 + 1810*z**3 + 4468*z**2 - 473*z - 3150\n#Step 7:\nCurrent expression: -1360*z**5 + 844*z**4 + 1810*z**3 + 4468*z**2 - 473*z - 3150\nNo more calculations needed.\n-1360*z**5 + 844*z**4 + 1810*z**3 + 4468*z**2 - 473*z - 3150", "generated_answer": "-1360*z**5 + 844*z**4 + 1810*z**3 + 4468*z**2 - 473*z - 3150", "step_length": 7} {"cot_id": "caccb195787e55ae62d188a6912b27c6a617cde181e6dd182db0ce9ef54e7a85", "datapoint": {"question": "Calculate the following: (-38*z - 61)*(41*z**2 - 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1558*z**3 - 2501*z**2 + 228*z + 366", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2120, "polynomial_expr": "(-38*z - 61)*(41*z**2 - 6)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-38*z - 61)*(41*z**2 - 6)\nExpanding the part (-38*z - 61) using the distributive property, and we got: (-38*z)*(41*z**2 - 6) - 61*(41*z**2 - 6)\n#Step 2:\nCurrent expression: (-38*z)*(41*z**2 - 6) - 61*(41*z**2 - 6)\nSimplifying the partial expression: -61*(41*z**2 - 6)\nExpanding the part (41*z**2 - 6) using the distributive property, and we got: (41*z**2)*(-61) - 6*(-61)\nReplacing -61*(41*z**2 - 6) with (41*z**2)*(-61) - 6*(-61) in the overall expression.\n#Step 3:\nCurrent expression: (-38*z)*(41*z**2 - 6) + (41*z**2)*(-61) + 366\nSimplifying the partial expression: (-38*z)*(41*z**2 - 6)\nExpanding the part (41*z**2 - 6) using the distributive property, and we got: (-38*z)*(41*z**2) - (-1)*228*z\nReplacing (-38*z)*(41*z**2 - 6) with (-38*z)*(41*z**2) - (-1)*228*z in the overall expression.\n#Step 4:\nCurrent expression: (-38*z)*(41*z**2) - 6*(-38)*z + (41*z**2)*(-61) + 366\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (41*z**2)*-61 = -2501*z**2\n (41*z**2)*(-38*z) = -1558*z**3\n -6*-38*z = 228*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1558*z**3 - 2501*z**2 + 228*z + 366\nNo more calculations needed.\n-1558*z**3 - 2501*z**2 + 228*z + 366", "generated_answer": "-1558*z**3 - 2501*z**2 + 228*z + 366", "step_length": 5} {"cot_id": "4086541bbaf3437c30e760d4f593aff8695c3a17f0759336785f8a979e775eee", "datapoint": {"question": "Simplify this expression: 85*z**2*(35*z**2 - 11)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2975*z**4 - 935*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2121, "polynomial_expr": "85*z**2*(35*z**2 - 11)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 85*z**2*(35*z**2 - 11)\nExpanding the part (35*z**2 - 11) using the distributive property, and we got: -935*z**2 + (35*z**2)*(85*z**2)\n#Step 2:\nCurrent expression: -935*z**2 + (35*z**2)*(85*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -11*(85*z**2) = -935*z**2\n (35*z**2)*(85*z**2) = 2975*z**4\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 2975*z**4 - 935*z**2\nNo more calculations needed.\n2975*z**4 - 935*z**2", "generated_answer": "2975*z**4 - 935*z**2", "step_length": 3} {"cot_id": "731137eb446c427540d865546ce9f0efc4728ec76cd42dfde1046dd5a67a6b45", "datapoint": {"question": "Calculate the following: (11*y**2 - 20*y)*(41*y**3 + 34)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "451*y**5 - 820*y**4 + 374*y**2 - 680*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2122, "polynomial_expr": "(11*y**2 - 20*y)*(41*y**3 + 34)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (11*y**2 - 20*y)*(41*y**3 + 34)\nExpanding the part (41*y**3 + 34) using the distributive property, and we got: (41*y**3)*(11*y**2 - 20*y) + 34*(11*y**2 - 20*y)\n#Step 2:\nCurrent expression: (41*y**3)*(11*y**2 - 20*y) + 34*(11*y**2 - 20*y)\nSimplifying the partial expression: 34*(11*y**2 - 20*y)\nExpanding the part (11*y**2 - 20*y) using the distributive property, and we got: -20*y*34 + (11*y**2)*34\nReplacing 34*(11*y**2 - 20*y) with -20*y*34 + (11*y**2)*34 in the overall expression.\n#Step 3:\nCurrent expression: -20*y*34 + (11*y**2)*34 + (41*y**3)*(11*y**2 - 20*y)\nSimplifying the partial expression: (41*y**3)*(11*y**2 - 20*y)\nExpanding the part (11*y**2 - 20*y) using the distributive property, and we got: (-20*y)*(41*y**3) + (11*y**2)*(41*y**3)\nReplacing (41*y**3)*(11*y**2 - 20*y) with (-20*y)*(41*y**3) + (11*y**2)*(41*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-20*y)*(41*y**3) - 20*y*34 + (11*y**2)*(41*y**3) + (11*y**2)*34\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*y)*34 = -680*y\n (-20*y)*(41*y**3) = -820*y**4\n (11*y**2)*34 = 374*y**2\n (11*y**2)*(41*y**3) = 451*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 451*y**5 - 820*y**4 + 374*y**2 - 680*y\nNo more calculations needed.\n451*y**5 - 820*y**4 + 374*y**2 - 680*y", "generated_answer": "451*y**5 - 820*y**4 + 374*y**2 - 680*y", "step_length": 5} {"cot_id": "04abc9d79a79be755ef82784c9360dbe967d4cfb66b9c4ecc91ffec6247d04b2", "datapoint": {"question": "Simplify this expression: (60*y**2 + 23*y)*(-27*y**3 - 90)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1620*y**5 - 621*y**4 - 5400*y**2 - 2070*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2123, "polynomial_expr": "(60*y**2 + 23*y)*(-27*y**3 - 90)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (60*y**2 + 23*y)*(-27*y**3 - 90)\nExpanding the part (-27*y**3 - 90) using the distributive property, and we got: (-27*y**3)*(60*y**2 + 23*y) - 90*(60*y**2 + 23*y)\n#Step 2:\nCurrent expression: (-27*y**3)*(60*y**2 + 23*y) - 90*(60*y**2 + 23*y)\nSimplifying the partial expression: -90*(60*y**2 + 23*y)\nExpanding the part (60*y**2 + 23*y) using the distributive property, and we got: (23*y)*(-90) + (60*y**2)*(-90)\nReplacing -90*(60*y**2 + 23*y) with (23*y)*(-90) + (60*y**2)*(-90) in the overall expression.\n#Step 3:\nCurrent expression: (23*y)*(-90) + (60*y**2)*(-90) + (-27*y**3)*(60*y**2 + 23*y)\nSimplifying the partial expression: (-27*y**3)*(60*y**2 + 23*y)\nExpanding the part (60*y**2 + 23*y) using the distributive property, and we got: (23*y)*(-27*y**3) + (60*y**2)*(-27*y**3)\nReplacing (-27*y**3)*(60*y**2 + 23*y) with (23*y)*(-27*y**3) + (60*y**2)*(-27*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (23*y)*(-27*y**3) + (23*y)*(-90) + (60*y**2)*(-27*y**3) + (60*y**2)*(-90)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (23*y)*-90 = -2070*y\n (23*y)*(-27*y**3) = -621*y**4\n (60*y**2)*-90 = -5400*y**2\n (60*y**2)*(-27*y**3) = -1620*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1620*y**5 - 621*y**4 - 5400*y**2 - 2070*y\nNo more calculations needed.\n-1620*y**5 - 621*y**4 - 5400*y**2 - 2070*y", "generated_answer": "-1620*y**5 - 621*y**4 - 5400*y**2 - 2070*y", "step_length": 5} {"cot_id": "ed49fef181608f03470c4d121ea7046d680c2ebe71b063d2962ec67aa0f5727b", "datapoint": {"question": "Calculate the following: (23*x**3 + 59)*(-27*x**3 - 48*x**2 - 42*x + 48)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-621*x**6 - 1104*x**5 - 966*x**4 - 489*x**3 - 2832*x**2 - 2478*x + 2832", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2124, "polynomial_expr": "(23*x**3 + 59)*(-27*x**3 - 48*x**2 - 42*x + 48)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (23*x**3 + 59)*(-27*x**3 - 48*x**2 - 42*x + 48)\nExpanding the part (23*x**3 + 59) using the distributive property, and we got: (23*x**3)*(-27*x**3 - 48*x**2 - 42*x + 48) + 59*(-27*x**3 - 48*x**2 - 42*x + 48)\n#Step 2:\nCurrent expression: (23*x**3)*(-27*x**3 - 48*x**2 - 42*x + 48) + 59*(-27*x**3 - 48*x**2 - 42*x + 48)\nSimplifying the partial expression: 59*(-27*x**3 - 48*x**2 - 42*x + 48)\nExpanding the part (-27*x**3 - 48*x**2 - 42*x + 48) using the distributive property, and we got: -42*x*59 - 48*x**2*59 - 27*x**3*59 + 48*59\nReplacing 59*(-27*x**3 - 48*x**2 - 42*x + 48) with -42*x*59 - 48*x**2*59 - 27*x**3*59 + 48*59 in the overall expression.\n#Step 3:\nCurrent expression: -42*x*59 - 48*x**2*59 - 27*x**3*59 + (23*x**3)*(-27*x**3 - 48*x**2 - 42*x + 48) + 2832\nSimplifying the partial expression: (23*x**3)*(-27*x**3 - 48*x**2 - 42*x + 48)\nExpanding the part (-27*x**3 - 48*x**2 - 42*x + 48) using the distributive property, and we got: (-42*x)*(23*x**3) + 48*(23*x**3) + (-48*x**2)*(23*x**3) + (-27*x**3)*(23*x**3)\nReplacing (23*x**3)*(-27*x**3 - 48*x**2 - 42*x + 48) with (-42*x)*(23*x**3) + 48*(23*x**3) + (-48*x**2)*(23*x**3) + (-27*x**3)*(23*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-42*x)*(23*x**3) - 42*x*59 + 48*23*x**3 + (-48*x**2)*(23*x**3) - 48*x**2*59 + (-27*x**3)*(23*x**3) - 27*x**3*59 + 2832\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*x**2)*59 = -2832*x**2\n (-48*x**2)*(23*x**3) = -1104*x**5\n (-42*x)*59 = -2478*x\n (-42*x)*(23*x**3) = -966*x**4\n (-27*x**3)*59 = -1593*x**3\n (-27*x**3)*(23*x**3) = -621*x**6\n 48*23*x**3 = 1104*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -621*x**6 - 1104*x**5 - 966*x**4 - 1593*x**3 + 1104*x**3 - 2832*x**2 - 2478*x + 2832\nCombining like terms, got -621*x**6 - 1104*x**5 - 966*x**4 - 489*x**3 - 2832*x**2 - 2478*x + 2832\n#Step 6:\nCurrent expression: -621*x**6 - 1104*x**5 - 966*x**4 - 489*x**3 - 2832*x**2 - 2478*x + 2832\nNo more calculations needed.\n-621*x**6 - 1104*x**5 - 966*x**4 - 489*x**3 - 2832*x**2 - 2478*x + 2832", "generated_answer": "-621*x**6 - 1104*x**5 - 966*x**4 - 489*x**3 - 2832*x**2 - 2478*x + 2832", "step_length": 6} {"cot_id": "344f8d2bb4e92c8b85fc342efcc17fe635360d6da440f755c6085cba7adb6adc", "datapoint": {"question": "Simplify this expression: (20*z**3 - 26*z)*(34*z**3 + 37*z**2 - 37)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "680*z**6 + 740*z**5 - 884*z**4 - 1702*z**3 + 962*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2125, "polynomial_expr": "(20*z**3 - 26*z)*(34*z**3 + 37*z**2 - 37)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (20*z**3 - 26*z)*(34*z**3 + 37*z**2 - 37)\nExpanding the part (20*z**3 - 26*z) using the distributive property, and we got: (-26*z)*(34*z**3 + 37*z**2 - 37) + (20*z**3)*(34*z**3 + 37*z**2 - 37)\n#Step 2:\nCurrent expression: (-26*z)*(34*z**3 + 37*z**2 - 37) + (20*z**3)*(34*z**3 + 37*z**2 - 37)\nSimplifying the partial expression: (-26*z)*(34*z**3 + 37*z**2 - 37)\nExpanding the part (34*z**3 + 37*z**2 - 37) using the distributive property, and we got: (-26*z)*(37*z**2) + (-26*z)*(34*z**3) - (-1)*962*z\nReplacing (-26*z)*(34*z**3 + 37*z**2 - 37) with (-26*z)*(37*z**2) + (-26*z)*(34*z**3) - (-1)*962*z in the overall expression.\n#Step 3:\nCurrent expression: (-26*z)*(37*z**2) + (-26*z)*(34*z**3) - 37*(-26)*z + (20*z**3)*(34*z**3 + 37*z**2 - 37)\nSimplifying the partial expression: (20*z**3)*(34*z**3 + 37*z**2 - 37)\nExpanding the part (34*z**3 + 37*z**2 - 37) using the distributive property, and we got: -740*z**3 + (37*z**2)*(20*z**3) + (20*z**3)*(34*z**3)\nReplacing (20*z**3)*(34*z**3 + 37*z**2 - 37) with -740*z**3 + (37*z**2)*(20*z**3) + (20*z**3)*(34*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-26*z)*(37*z**2) + (-26*z)*(34*z**3) - 37*20*z**3 - 37*(-26)*z + (37*z**2)*(20*z**3) + (20*z**3)*(34*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (34*z**3)*(-26*z) = -884*z**4\n (34*z**3)*(20*z**3) = 680*z**6\n (37*z**2)*(-26*z) = -962*z**3\n (37*z**2)*(20*z**3) = 740*z**5\n -37*-26*z = 962*z\n -37*20*z**3 = -740*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 680*z**6 + 740*z**5 - 884*z**4 - 962*z**3 - 740*z**3 + 962*z\nCombining like terms, got 680*z**6 + 740*z**5 - 884*z**4 - 1702*z**3 + 962*z\n#Step 6:\nCurrent expression: 680*z**6 + 740*z**5 - 884*z**4 - 1702*z**3 + 962*z\nNo more calculations needed.\n680*z**6 + 740*z**5 - 884*z**4 - 1702*z**3 + 962*z", "generated_answer": "680*z**6 + 740*z**5 - 884*z**4 - 1702*z**3 + 962*z", "step_length": 6} {"cot_id": "89a530de481f84c28c3c73655cc283aa963e256e44f1491c49412731692994ee", "datapoint": {"question": "Calculate the following: (-63*x**3 - 40)*(-23*x**3 + 6*x**2 + 22)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1449*x**6 - 378*x**5 - 466*x**3 - 240*x**2 - 880", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2126, "polynomial_expr": "(-63*x**3 - 40)*(-23*x**3 + 6*x**2 + 22)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-63*x**3 - 40)*(-23*x**3 + 6*x**2 + 22)\nExpanding the part (-63*x**3 - 40) using the distributive property, and we got: (-63*x**3)*(-23*x**3 + 6*x**2 + 22) - 40*(-23*x**3 + 6*x**2 + 22)\n#Step 2:\nCurrent expression: (-63*x**3)*(-23*x**3 + 6*x**2 + 22) - 40*(-23*x**3 + 6*x**2 + 22)\nSimplifying the partial expression: -40*(-23*x**3 + 6*x**2 + 22)\nExpanding the part (-23*x**3 + 6*x**2 + 22) using the distributive property, and we got: (6*x**2)*(-40) - 23*x**3*(-40) + 22*(-40)\nReplacing -40*(-23*x**3 + 6*x**2 + 22) with (6*x**2)*(-40) - 23*x**3*(-40) + 22*(-40) in the overall expression.\n#Step 3:\nCurrent expression: (6*x**2)*(-40) + (-63*x**3)*(-23*x**3 + 6*x**2 + 22) - 23*x**3*(-40) - 880\nSimplifying the partial expression: (-63*x**3)*(-23*x**3 + 6*x**2 + 22)\nExpanding the part (-23*x**3 + 6*x**2 + 22) using the distributive property, and we got: 22*(-63*x**3) + (6*x**2)*(-63*x**3) + (-63*x**3)*(-23*x**3)\nReplacing (-63*x**3)*(-23*x**3 + 6*x**2 + 22) with 22*(-63*x**3) + (6*x**2)*(-63*x**3) + (-63*x**3)*(-23*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 22*(-63)*x**3 + (6*x**2)*(-63*x**3) + (6*x**2)*(-40) + (-63*x**3)*(-23*x**3) - 23*x**3*(-40) - 880\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*x**3)*-40 = 920*x**3\n (-23*x**3)*(-63*x**3) = 1449*x**6\n (6*x**2)*-40 = -240*x**2\n (6*x**2)*(-63*x**3) = -378*x**5\n 22*-63*x**3 = -1386*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1449*x**6 - 378*x**5 - 1386*x**3 + 920*x**3 - 240*x**2 - 880\nCombining like terms, got 1449*x**6 - 378*x**5 - 466*x**3 - 240*x**2 - 880\n#Step 6:\nCurrent expression: 1449*x**6 - 378*x**5 - 466*x**3 - 240*x**2 - 880\nNo more calculations needed.\n1449*x**6 - 378*x**5 - 466*x**3 - 240*x**2 - 880", "generated_answer": "1449*x**6 - 378*x**5 - 466*x**3 - 240*x**2 - 880", "step_length": 6} {"cot_id": "fcdef75942e98b430766100a09614d11dd9d3c9bbf99388aededef1670b6062a", "datapoint": {"question": "Simplify this expression: (14*y**3 - 17*y**2)*(42*y**2 + 30*y + 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "588*y**5 - 294*y**4 - 426*y**3 - 102*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2127, "polynomial_expr": "(14*y**3 - 17*y**2)*(42*y**2 + 30*y + 6)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (14*y**3 - 17*y**2)*(42*y**2 + 30*y + 6)\nExpanding the part (14*y**3 - 17*y**2) using the distributive property, and we got: (-17*y**2)*(42*y**2 + 30*y + 6) + (14*y**3)*(42*y**2 + 30*y + 6)\n#Step 2:\nCurrent expression: (-17*y**2)*(42*y**2 + 30*y + 6) + (14*y**3)*(42*y**2 + 30*y + 6)\nSimplifying the partial expression: (-17*y**2)*(42*y**2 + 30*y + 6)\nExpanding the part (42*y**2 + 30*y + 6) using the distributive property, and we got: 6*(-17*y**2) + (30*y)*(-17*y**2) + (-17*y**2)*(42*y**2)\nReplacing (-17*y**2)*(42*y**2 + 30*y + 6) with 6*(-17*y**2) + (30*y)*(-17*y**2) + (-17*y**2)*(42*y**2) in the overall expression.\n#Step 3:\nCurrent expression: 6*(-17)*y**2 + (30*y)*(-17*y**2) + (-17*y**2)*(42*y**2) + (14*y**3)*(42*y**2 + 30*y + 6)\nSimplifying the partial expression: (14*y**3)*(42*y**2 + 30*y + 6)\nExpanding the part (42*y**2 + 30*y + 6) using the distributive property, and we got: 6*(14*y**3) + (30*y)*(14*y**3) + (42*y**2)*(14*y**3)\nReplacing (14*y**3)*(42*y**2 + 30*y + 6) with 6*(14*y**3) + (30*y)*(14*y**3) + (42*y**2)*(14*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 6*14*y**3 + 6*(-17)*y**2 + (30*y)*(-17*y**2) + (30*y)*(14*y**3) + (-17*y**2)*(42*y**2) + (42*y**2)*(14*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (30*y)*(-17*y**2) = -510*y**3\n (30*y)*(14*y**3) = 420*y**4\n (42*y**2)*(-17*y**2) = -714*y**4\n (42*y**2)*(14*y**3) = 588*y**5\n 6*-17*y**2 = -102*y**2\n 6*14*y**3 = 84*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 588*y**5 - 714*y**4 + 420*y**4 - 510*y**3 + 84*y**3 - 102*y**2\nCombining like terms, got 588*y**5 - 294*y**4 - 426*y**3 - 102*y**2\n#Step 6:\nCurrent expression: 588*y**5 - 294*y**4 - 426*y**3 - 102*y**2\nNo more calculations needed.\n588*y**5 - 294*y**4 - 426*y**3 - 102*y**2", "generated_answer": "588*y**5 - 294*y**4 - 426*y**3 - 102*y**2", "step_length": 6} {"cot_id": "690e9f8e3105765ddc614e191b454aa899f47e901aa8e163f6863597bbbff2b3", "datapoint": {"question": "Calculate the following: (-30*y**3 - 40*y)*(-23*y**3 - y**2 + 35*y - 2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "690*y**6 + 30*y**5 - 130*y**4 + 100*y**3 - 1400*y**2 + 80*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2128, "polynomial_expr": "(-30*y**3 - 40*y)*(-23*y**3 - y**2 + 35*y - 2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-30*y**3 - 40*y)*(-23*y**3 - y**2 + 35*y - 2)\nExpanding the part (-30*y**3 - 40*y) using the distributive property, and we got: (-40*y)*(-23*y**3 - y**2 + 35*y - 2) + (-30*y**3)*(-23*y**3 - y**2 + 35*y - 2)\n#Step 2:\nCurrent expression: (-40*y)*(-23*y**3 - y**2 + 35*y - 2) + (-30*y**3)*(-23*y**3 - y**2 + 35*y - 2)\nSimplifying the partial expression: (-40*y)*(-23*y**3 - y**2 + 35*y - 2)\nExpanding the part (-23*y**3 - y**2 + 35*y - 2) using the distributive property, and we got: (-40*y)*(35*y) + (-40*y)*(-y**2) + (-40*y)*(-23*y**3) - (-1)*80*y\nReplacing (-40*y)*(-23*y**3 - y**2 + 35*y - 2) with (-40*y)*(35*y) + (-40*y)*(-y**2) + (-40*y)*(-23*y**3) - (-1)*80*y in the overall expression.\n#Step 3:\nCurrent expression: (-40*y)*(35*y) + (-40*y)*(-y**2) + (-40*y)*(-23*y**3) - 2*(-40)*y + (-30*y**3)*(-23*y**3 - y**2 + 35*y - 2)\nSimplifying the partial expression: (-30*y**3)*(-23*y**3 - y**2 + 35*y - 2)\nExpanding the part (-23*y**3 - y**2 + 35*y - 2) using the distributive property, and we got: -(-1)*60*y**3 + (35*y)*(-30*y**3) + (-y**2)*(-30*y**3) + (-30*y**3)*(-23*y**3)\nReplacing (-30*y**3)*(-23*y**3 - y**2 + 35*y - 2) with -(-1)*60*y**3 + (35*y)*(-30*y**3) + (-y**2)*(-30*y**3) + (-30*y**3)*(-23*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-40*y)*(35*y) + (-40*y)*(-y**2) + (-40*y)*(-23*y**3) - 2*(-30)*y**3 - 2*(-40)*y + (35*y)*(-30*y**3) + (-y**2)*(-30*y**3) + (-30*y**3)*(-23*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-y**2)*(-40*y) = 40*y**3\n (-y**2)*(-30*y**3) = 30*y**5\n (-23*y**3)*(-40*y) = 920*y**4\n (-23*y**3)*(-30*y**3) = 690*y**6\n (35*y)*(-40*y) = -1400*y**2\n (35*y)*(-30*y**3) = -1050*y**4\n -2*-40*y = 80*y\n -2*-30*y**3 = 60*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 690*y**6 + 30*y**5 - 1050*y**4 + 920*y**4 + 40*y**3 + 60*y**3 - 1400*y**2 + 80*y\nCombining like terms, got 690*y**6 + 30*y**5 - 130*y**4 + 100*y**3 - 1400*y**2 + 80*y\n#Step 6:\nCurrent expression: 690*y**6 + 30*y**5 - 130*y**4 + 100*y**3 - 1400*y**2 + 80*y\nNo more calculations needed.\n690*y**6 + 30*y**5 - 130*y**4 + 100*y**3 - 1400*y**2 + 80*y", "generated_answer": "690*y**6 + 30*y**5 - 130*y**4 + 100*y**3 - 1400*y**2 + 80*y", "step_length": 6} {"cot_id": "43425c3b3f661b800c4324a8dadc360ce6169b0a5cc1686f8b3e1a23b56eb9cc", "datapoint": {"question": "Calculate the following: (-38*x**2 + 34*x - 5)*(x**3 - 25*x**2 - 39*x + 8)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-38*x**5 + 984*x**4 + 627*x**3 - 1505*x**2 + 467*x - 40", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2129, "polynomial_expr": "(-38*x**2 + 34*x - 5)*(x**3 - 25*x**2 - 39*x + 8)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-38*x**2 + 34*x - 5)*(x**3 - 25*x**2 - 39*x + 8)\nExpanding the part (-38*x**2 + 34*x - 5) using the distributive property, and we got: (34*x)*(x**3 - 25*x**2 - 39*x + 8) + (-38*x**2)*(x**3 - 25*x**2 - 39*x + 8) - 5*(x**3 - 25*x**2 - 39*x + 8)\n#Step 2:\nCurrent expression: (34*x)*(x**3 - 25*x**2 - 39*x + 8) + (-38*x**2)*(x**3 - 25*x**2 - 39*x + 8) - 5*(x**3 - 25*x**2 - 39*x + 8)\nSimplifying the partial expression: -5*(x**3 - 25*x**2 - 39*x + 8)\nExpanding the part (x**3 - 25*x**2 - 39*x + 8) using the distributive property, and we got: -39*x*(-5) + x**3*(-5) - 25*x**2*(-5) + 8*(-5)\nReplacing -5*(x**3 - 25*x**2 - 39*x + 8) with -39*x*(-5) + x**3*(-5) - 25*x**2*(-5) + 8*(-5) in the overall expression.\n#Step 3:\nCurrent expression: -39*x*(-5) + x**3*(-5) + (34*x)*(x**3 - 25*x**2 - 39*x + 8) + (-38*x**2)*(x**3 - 25*x**2 - 39*x + 8) - 25*x**2*(-5) - 40\nSimplifying the partial expression: (-38*x**2)*(x**3 - 25*x**2 - 39*x + 8)\nExpanding the part (x**3 - 25*x**2 - 39*x + 8) using the distributive property, and we got: (-39*x)*(-38*x**2) + (-38*x**2)*x**3 + 8*(-38*x**2) + (-38*x**2)*(-25*x**2)\nReplacing (-38*x**2)*(x**3 - 25*x**2 - 39*x + 8) with (-39*x)*(-38*x**2) + (-38*x**2)*x**3 + 8*(-38*x**2) + (-38*x**2)*(-25*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-39*x)*(-38*x**2) - 39*x*(-5) + (-38*x**2)*x**3 + x**3*(-5) + 8*(-38)*x**2 + (34*x)*(x**3 - 25*x**2 - 39*x + 8) + (-38*x**2)*(-25*x**2) - 25*x**2*(-5) - 40\nSimplifying the partial expression: (34*x)*(x**3 - 25*x**2 - 39*x + 8)\nExpanding the part (x**3 - 25*x**2 - 39*x + 8) using the distributive property, and we got: (-39*x)*(34*x) + (34*x)*x**3 + 8*(34*x) + (34*x)*(-25*x**2)\nReplacing (34*x)*(x**3 - 25*x**2 - 39*x + 8) with (-39*x)*(34*x) + (34*x)*x**3 + 8*(34*x) + (34*x)*(-25*x**2) in the overall expression.\n#Step 5:\nCurrent expression: (-39*x)*(34*x) + (-39*x)*(-38*x**2) - 39*x*(-5) + (34*x)*x**3 + (-38*x**2)*x**3 + x**3*(-5) + 8*(-38)*x**2 + 8*34*x + (34*x)*(-25*x**2) + (-38*x**2)*(-25*x**2) - 25*x**2*(-5) - 40\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n x**3*-5 = -5*x**3\n x**3*(-38*x**2) = -38*x**5\n x**3*(34*x) = 34*x**4\n (-39*x)*-5 = 195*x\n (-39*x)*(-38*x**2) = 1482*x**3\n (-39*x)*(34*x) = -1326*x**2\n (-25*x**2)*-5 = 125*x**2\n (-25*x**2)*(-38*x**2) = 950*x**4\n (-25*x**2)*(34*x) = -850*x**3\n 8*-38*x**2 = -304*x**2\n 8*34*x = 272*x\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -38*x**5 + 34*x**4 + 950*x**4 - 850*x**3 - 5*x**3 + 1482*x**3 - 1326*x**2 - 304*x**2 + 125*x**2 + 195*x + 272*x - 40\nCombining like terms, got -38*x**5 + 984*x**4 + 627*x**3 - 1505*x**2 + 467*x - 40\n#Step 7:\nCurrent expression: -38*x**5 + 984*x**4 + 627*x**3 - 1505*x**2 + 467*x - 40\nNo more calculations needed.\n-38*x**5 + 984*x**4 + 627*x**3 - 1505*x**2 + 467*x - 40", "generated_answer": "-38*x**5 + 984*x**4 + 627*x**3 - 1505*x**2 + 467*x - 40", "step_length": 7} {"cot_id": "5b6f9fd41cc59a3da50ac505713ed5c2f26fbbad32dd7a4ed900cf6cbe93066c", "datapoint": {"question": "Simplify this expression: (-47*z**2 - 18*z)*(-40*z**2 - 3*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1880*z**4 + 861*z**3 + 54*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2130, "polynomial_expr": "(-47*z**2 - 18*z)*(-40*z**2 - 3*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-47*z**2 - 18*z)*(-40*z**2 - 3*z)\nExpanding the part (-47*z**2 - 18*z) using the distributive property, and we got: (-18*z)*(-40*z**2 - 3*z) + (-47*z**2)*(-40*z**2 - 3*z)\n#Step 2:\nCurrent expression: (-18*z)*(-40*z**2 - 3*z) + (-47*z**2)*(-40*z**2 - 3*z)\nSimplifying the partial expression: (-47*z**2)*(-40*z**2 - 3*z)\nExpanding the part (-40*z**2 - 3*z) using the distributive property, and we got: (-3*z)*(-47*z**2) + (-47*z**2)*(-40*z**2)\nReplacing (-47*z**2)*(-40*z**2 - 3*z) with (-3*z)*(-47*z**2) + (-47*z**2)*(-40*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (-18*z)*(-40*z**2 - 3*z) + (-3*z)*(-47*z**2) + (-47*z**2)*(-40*z**2)\nSimplifying the partial expression: (-18*z)*(-40*z**2 - 3*z)\nExpanding the part (-40*z**2 - 3*z) using the distributive property, and we got: (-18*z)*(-3*z) + (-18*z)*(-40*z**2)\nReplacing (-18*z)*(-40*z**2 - 3*z) with (-18*z)*(-3*z) + (-18*z)*(-40*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-18*z)*(-3*z) + (-18*z)*(-40*z**2) + (-3*z)*(-47*z**2) + (-47*z**2)*(-40*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-40*z**2)*(-47*z**2) = 1880*z**4\n (-40*z**2)*(-18*z) = 720*z**3\n (-3*z)*(-47*z**2) = 141*z**3\n (-3*z)*(-18*z) = 54*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1880*z**4 + 141*z**3 + 720*z**3 + 54*z**2\nCombining like terms, got 1880*z**4 + 861*z**3 + 54*z**2\n#Step 6:\nCurrent expression: 1880*z**4 + 861*z**3 + 54*z**2\nNo more calculations needed.\n1880*z**4 + 861*z**3 + 54*z**2", "generated_answer": "1880*z**4 + 861*z**3 + 54*z**2", "step_length": 6} {"cot_id": "87bcf471235dd1b4162085328379fa8707abfda6a2328d62f1bfb2e9eb7a98c8", "datapoint": {"question": "Calculate the following: (-3*z**3 - 47*z**2)*(-68*z**3 + 17*z**2 + 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "204*z**6 + 3145*z**5 - 799*z**4 - 18*z**3 - 282*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2131, "polynomial_expr": "(-3*z**3 - 47*z**2)*(-68*z**3 + 17*z**2 + 6)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-3*z**3 - 47*z**2)*(-68*z**3 + 17*z**2 + 6)\nExpanding the part (-3*z**3 - 47*z**2) using the distributive property, and we got: (-47*z**2)*(-68*z**3 + 17*z**2 + 6) + (-3*z**3)*(-68*z**3 + 17*z**2 + 6)\n#Step 2:\nCurrent expression: (-47*z**2)*(-68*z**3 + 17*z**2 + 6) + (-3*z**3)*(-68*z**3 + 17*z**2 + 6)\nSimplifying the partial expression: (-47*z**2)*(-68*z**3 + 17*z**2 + 6)\nExpanding the part (-68*z**3 + 17*z**2 + 6) using the distributive property, and we got: 6*(-47*z**2) + (-47*z**2)*(17*z**2) + (-47*z**2)*(-68*z**3)\nReplacing (-47*z**2)*(-68*z**3 + 17*z**2 + 6) with 6*(-47*z**2) + (-47*z**2)*(17*z**2) + (-47*z**2)*(-68*z**3) in the overall expression.\n#Step 3:\nCurrent expression: 6*(-47)*z**2 + (-47*z**2)*(17*z**2) + (-47*z**2)*(-68*z**3) + (-3*z**3)*(-68*z**3 + 17*z**2 + 6)\nSimplifying the partial expression: (-3*z**3)*(-68*z**3 + 17*z**2 + 6)\nExpanding the part (-68*z**3 + 17*z**2 + 6) using the distributive property, and we got: 6*(-3*z**3) + (17*z**2)*(-3*z**3) + (-68*z**3)*(-3*z**3)\nReplacing (-3*z**3)*(-68*z**3 + 17*z**2 + 6) with 6*(-3*z**3) + (17*z**2)*(-3*z**3) + (-68*z**3)*(-3*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 6*(-3)*z**3 + 6*(-47)*z**2 + (-47*z**2)*(17*z**2) + (-47*z**2)*(-68*z**3) + (17*z**2)*(-3*z**3) + (-68*z**3)*(-3*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-68*z**3)*(-47*z**2) = 3196*z**5\n (-68*z**3)*(-3*z**3) = 204*z**6\n (17*z**2)*(-47*z**2) = -799*z**4\n (17*z**2)*(-3*z**3) = -51*z**5\n 6*-47*z**2 = -282*z**2\n 6*-3*z**3 = -18*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 204*z**6 - 51*z**5 + 3196*z**5 - 799*z**4 - 18*z**3 - 282*z**2\nCombining like terms, got 204*z**6 + 3145*z**5 - 799*z**4 - 18*z**3 - 282*z**2\n#Step 6:\nCurrent expression: 204*z**6 + 3145*z**5 - 799*z**4 - 18*z**3 - 282*z**2\nNo more calculations needed.\n204*z**6 + 3145*z**5 - 799*z**4 - 18*z**3 - 282*z**2", "generated_answer": "204*z**6 + 3145*z**5 - 799*z**4 - 18*z**3 - 282*z**2", "step_length": 6} {"cot_id": "17b5041bd3dadde749d750769566fbd87facab78c57600b6b4183254aa89c8c8", "datapoint": {"question": "Simplify this expression: 46*x**2*(46*x - 40)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2116*x**3 - 1840*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2132, "polynomial_expr": "46*x**2*(46*x - 40)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 46*x**2*(46*x - 40)\nExpanding the part (46*x - 40) using the distributive property, and we got: -1840*x**2 + (46*x)*(46*x**2)\n#Step 2:\nCurrent expression: -1840*x**2 + (46*x)*(46*x**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -40*(46*x**2) = -1840*x**2\n (46*x)*(46*x**2) = 2116*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 2116*x**3 - 1840*x**2\nNo more calculations needed.\n2116*x**3 - 1840*x**2", "generated_answer": "2116*x**3 - 1840*x**2", "step_length": 3} {"cot_id": "2a98cac8db017117c93db989b756a397e28709a56cce9af8654fe4c4ae2e3135", "datapoint": {"question": "Calculate the following: (-16*y**2 + 7*y)*(4*y**3 + 41*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-64*y**5 + 28*y**4 - 656*y**3 + 287*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2133, "polynomial_expr": "(-16*y**2 + 7*y)*(4*y**3 + 41*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-16*y**2 + 7*y)*(4*y**3 + 41*y)\nExpanding the part (-16*y**2 + 7*y) using the distributive property, and we got: (7*y)*(4*y**3 + 41*y) + (-16*y**2)*(4*y**3 + 41*y)\n#Step 2:\nCurrent expression: (7*y)*(4*y**3 + 41*y) + (-16*y**2)*(4*y**3 + 41*y)\nSimplifying the partial expression: (-16*y**2)*(4*y**3 + 41*y)\nExpanding the part (4*y**3 + 41*y) using the distributive property, and we got: (41*y)*(-16*y**2) + (-16*y**2)*(4*y**3)\nReplacing (-16*y**2)*(4*y**3 + 41*y) with (41*y)*(-16*y**2) + (-16*y**2)*(4*y**3) in the overall expression.\n#Step 3:\nCurrent expression: (7*y)*(4*y**3 + 41*y) + (41*y)*(-16*y**2) + (-16*y**2)*(4*y**3)\nSimplifying the partial expression: (7*y)*(4*y**3 + 41*y)\nExpanding the part (4*y**3 + 41*y) using the distributive property, and we got: (7*y)*(41*y) + (7*y)*(4*y**3)\nReplacing (7*y)*(4*y**3 + 41*y) with (7*y)*(41*y) + (7*y)*(4*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (7*y)*(41*y) + (7*y)*(4*y**3) + (41*y)*(-16*y**2) + (-16*y**2)*(4*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (4*y**3)*(-16*y**2) = -64*y**5\n (4*y**3)*(7*y) = 28*y**4\n (41*y)*(-16*y**2) = -656*y**3\n (41*y)*(7*y) = 287*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -64*y**5 + 28*y**4 - 656*y**3 + 287*y**2\nNo more calculations needed.\n-64*y**5 + 28*y**4 - 656*y**3 + 287*y**2", "generated_answer": "-64*y**5 + 28*y**4 - 656*y**3 + 287*y**2", "step_length": 5} {"cot_id": "7a66a970765dab3d2d8a6c9a335dc1d6830615620ddd8753aefaf7430f51bafb", "datapoint": {"question": "Simplify this expression: (-47*x**2 - 1)*(22*x**3 - 23*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1034*x**5 + 1081*x**4 - 22*x**3 + 23*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2134, "polynomial_expr": "(-47*x**2 - 1)*(22*x**3 - 23*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-47*x**2 - 1)*(22*x**3 - 23*x**2)\nExpanding the part (-47*x**2 - 1) using the distributive property, and we got: (-47*x**2)*(22*x**3 - 23*x**2) - (22*x**3 - 23*x**2)\n#Step 2:\nCurrent expression: (-47*x**2)*(22*x**3 - 23*x**2) - (22*x**3 - 23*x**2)\nSimplifying the partial expression: -(22*x**3 - 23*x**2)\nExpanding the part (22*x**3 - 23*x**2) using the distributive property, and we got: -23*x**2*(-1) + (22*x**3)*(-1)\nReplacing -(22*x**3 - 23*x**2) with -23*x**2*(-1) + (22*x**3)*(-1) in the overall expression.\n#Step 3:\nCurrent expression: (-47*x**2)*(22*x**3 - 23*x**2) - 23*x**2*(-1) + (22*x**3)*(-1)\nSimplifying the partial expression: (-47*x**2)*(22*x**3 - 23*x**2)\nExpanding the part (22*x**3 - 23*x**2) using the distributive property, and we got: (-47*x**2)*(-23*x**2) + (-47*x**2)*(22*x**3)\nReplacing (-47*x**2)*(22*x**3 - 23*x**2) with (-47*x**2)*(-23*x**2) + (-47*x**2)*(22*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-47*x**2)*(-23*x**2) + (-47*x**2)*(22*x**3) - 23*x**2*(-1) + (22*x**3)*(-1)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*x**2)*-1 = 23*x**2\n (-23*x**2)*(-47*x**2) = 1081*x**4\n (22*x**3)*-1 = -22*x**3\n (22*x**3)*(-47*x**2) = -1034*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1034*x**5 + 1081*x**4 - 22*x**3 + 23*x**2\nNo more calculations needed.\n-1034*x**5 + 1081*x**4 - 22*x**3 + 23*x**2", "generated_answer": "-1034*x**5 + 1081*x**4 - 22*x**3 + 23*x**2", "step_length": 5} {"cot_id": "7ee33bd3d08cf3546873f189bdf6a6bb18a4b73f7331eb414862498e92de123f", "datapoint": {"question": "Calculate the following: 3950*z\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "3950*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2135, "polynomial_expr": "3950*z", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 3950*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 3950*z\nNo more calculations needed.\n3950*z", "generated_answer": "3950*z", "step_length": 2} {"cot_id": "c419c2fedb9b58b485dc3f09aadfa1fb51b53a47e38ab89f94dde276e0ef062b", "datapoint": {"question": "Simplify this expression: (-23*z - 46)*(32*z**2 + 67*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-736*z**3 - 3013*z**2 - 3082*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2136, "polynomial_expr": "(-23*z - 46)*(32*z**2 + 67*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-23*z - 46)*(32*z**2 + 67*z)\nExpanding the part (-23*z - 46) using the distributive property, and we got: (-23*z)*(32*z**2 + 67*z) - 46*(32*z**2 + 67*z)\n#Step 2:\nCurrent expression: (-23*z)*(32*z**2 + 67*z) - 46*(32*z**2 + 67*z)\nSimplifying the partial expression: -46*(32*z**2 + 67*z)\nExpanding the part (32*z**2 + 67*z) using the distributive property, and we got: (67*z)*(-46) + (32*z**2)*(-46)\nReplacing -46*(32*z**2 + 67*z) with (67*z)*(-46) + (32*z**2)*(-46) in the overall expression.\n#Step 3:\nCurrent expression: (-23*z)*(32*z**2 + 67*z) + (67*z)*(-46) + (32*z**2)*(-46)\nSimplifying the partial expression: (-23*z)*(32*z**2 + 67*z)\nExpanding the part (32*z**2 + 67*z) using the distributive property, and we got: (-23*z)*(67*z) + (-23*z)*(32*z**2)\nReplacing (-23*z)*(32*z**2 + 67*z) with (-23*z)*(67*z) + (-23*z)*(32*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-23*z)*(67*z) + (-23*z)*(32*z**2) + (67*z)*(-46) + (32*z**2)*(-46)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (32*z**2)*-46 = -1472*z**2\n (32*z**2)*(-23*z) = -736*z**3\n (67*z)*-46 = -3082*z\n (67*z)*(-23*z) = -1541*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -736*z**3 - 1541*z**2 - 1472*z**2 - 3082*z\nCombining like terms, got -736*z**3 - 3013*z**2 - 3082*z\n#Step 6:\nCurrent expression: -736*z**3 - 3013*z**2 - 3082*z\nNo more calculations needed.\n-736*z**3 - 3013*z**2 - 3082*z", "generated_answer": "-736*z**3 - 3013*z**2 - 3082*z", "step_length": 6} {"cot_id": "a62d46b0eb01df2e093ff82df15673032880fede7883d9a2bf1b5020ee15ad6f", "datapoint": {"question": "Calculate the following: (41*y**3 + 42)*(-21*y**3 - 48*y**2 + 22*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-861*y**6 - 1968*y**5 + 902*y**4 - 882*y**3 - 2016*y**2 + 924*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2137, "polynomial_expr": "(41*y**3 + 42)*(-21*y**3 - 48*y**2 + 22*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (41*y**3 + 42)*(-21*y**3 - 48*y**2 + 22*y)\nExpanding the part (41*y**3 + 42) using the distributive property, and we got: (41*y**3)*(-21*y**3 - 48*y**2 + 22*y) + 42*(-21*y**3 - 48*y**2 + 22*y)\n#Step 2:\nCurrent expression: (41*y**3)*(-21*y**3 - 48*y**2 + 22*y) + 42*(-21*y**3 - 48*y**2 + 22*y)\nSimplifying the partial expression: 42*(-21*y**3 - 48*y**2 + 22*y)\nExpanding the part (-21*y**3 - 48*y**2 + 22*y) using the distributive property, and we got: (22*y)*42 - 48*y**2*42 - 21*y**3*42\nReplacing 42*(-21*y**3 - 48*y**2 + 22*y) with (22*y)*42 - 48*y**2*42 - 21*y**3*42 in the overall expression.\n#Step 3:\nCurrent expression: (22*y)*42 - 48*y**2*42 - 21*y**3*42 + (41*y**3)*(-21*y**3 - 48*y**2 + 22*y)\nSimplifying the partial expression: (41*y**3)*(-21*y**3 - 48*y**2 + 22*y)\nExpanding the part (-21*y**3 - 48*y**2 + 22*y) using the distributive property, and we got: (22*y)*(41*y**3) + (-48*y**2)*(41*y**3) + (-21*y**3)*(41*y**3)\nReplacing (41*y**3)*(-21*y**3 - 48*y**2 + 22*y) with (22*y)*(41*y**3) + (-48*y**2)*(41*y**3) + (-21*y**3)*(41*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (22*y)*(41*y**3) + (22*y)*42 + (-48*y**2)*(41*y**3) - 48*y**2*42 + (-21*y**3)*(41*y**3) - 21*y**3*42\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*y**2)*42 = -2016*y**2\n (-48*y**2)*(41*y**3) = -1968*y**5\n (-21*y**3)*42 = -882*y**3\n (-21*y**3)*(41*y**3) = -861*y**6\n (22*y)*42 = 924*y\n (22*y)*(41*y**3) = 902*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -861*y**6 - 1968*y**5 + 902*y**4 - 882*y**3 - 2016*y**2 + 924*y\nNo more calculations needed.\n-861*y**6 - 1968*y**5 + 902*y**4 - 882*y**3 - 2016*y**2 + 924*y", "generated_answer": "-861*y**6 - 1968*y**5 + 902*y**4 - 882*y**3 - 2016*y**2 + 924*y", "step_length": 5} {"cot_id": "7cfba93432963937b7eb3cbaae0dababa8219c9f83f0181d576dbb57ce65947f", "datapoint": {"question": "Calculate the following: 18*x**3*(25*x**2 - 22*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "450*x**5 - 396*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2138, "polynomial_expr": "18*x**3*(25*x**2 - 22*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 18*x**3*(25*x**2 - 22*x)\nExpanding the part (25*x**2 - 22*x) using the distributive property, and we got: (-22*x)*(18*x**3) + (25*x**2)*(18*x**3)\n#Step 2:\nCurrent expression: (-22*x)*(18*x**3) + (25*x**2)*(18*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*x)*(18*x**3) = -396*x**4\n (25*x**2)*(18*x**3) = 450*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 450*x**5 - 396*x**4\nNo more calculations needed.\n450*x**5 - 396*x**4", "generated_answer": "450*x**5 - 396*x**4", "step_length": 3} {"cot_id": "11764c76e5edf2ecdc53c1adfd0e44efb77d6cb819634917cc0677900279fa1b", "datapoint": {"question": "Simplify this expression: (-18*x**3 + 17*x)*(-48*x**3 - 18*x**2 + 2*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "864*x**6 + 324*x**5 - 852*x**4 - 306*x**3 + 34*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2139, "polynomial_expr": "(-18*x**3 + 17*x)*(-48*x**3 - 18*x**2 + 2*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-18*x**3 + 17*x)*(-48*x**3 - 18*x**2 + 2*x)\nExpanding the part (-18*x**3 + 17*x) using the distributive property, and we got: (17*x)*(-48*x**3 - 18*x**2 + 2*x) + (-18*x**3)*(-48*x**3 - 18*x**2 + 2*x)\n#Step 2:\nCurrent expression: (17*x)*(-48*x**3 - 18*x**2 + 2*x) + (-18*x**3)*(-48*x**3 - 18*x**2 + 2*x)\nSimplifying the partial expression: (-18*x**3)*(-48*x**3 - 18*x**2 + 2*x)\nExpanding the part (-48*x**3 - 18*x**2 + 2*x) using the distributive property, and we got: (2*x)*(-18*x**3) + (-18*x**2)*(-18*x**3) + (-48*x**3)*(-18*x**3)\nReplacing (-18*x**3)*(-48*x**3 - 18*x**2 + 2*x) with (2*x)*(-18*x**3) + (-18*x**2)*(-18*x**3) + (-48*x**3)*(-18*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (2*x)*(-18*x**3) + (17*x)*(-48*x**3 - 18*x**2 + 2*x) + (-18*x**2)*(-18*x**3) + (-48*x**3)*(-18*x**3)\nSimplifying the partial expression: (17*x)*(-48*x**3 - 18*x**2 + 2*x)\nExpanding the part (-48*x**3 - 18*x**2 + 2*x) using the distributive property, and we got: (2*x)*(17*x) + (17*x)*(-18*x**2) + (17*x)*(-48*x**3)\nReplacing (17*x)*(-48*x**3 - 18*x**2 + 2*x) with (2*x)*(17*x) + (17*x)*(-18*x**2) + (17*x)*(-48*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (2*x)*(17*x) + (2*x)*(-18*x**3) + (17*x)*(-18*x**2) + (17*x)*(-48*x**3) + (-18*x**2)*(-18*x**3) + (-48*x**3)*(-18*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*x**3)*(-18*x**3) = 864*x**6\n (-48*x**3)*(17*x) = -816*x**4\n (-18*x**2)*(-18*x**3) = 324*x**5\n (-18*x**2)*(17*x) = -306*x**3\n (2*x)*(-18*x**3) = -36*x**4\n (2*x)*(17*x) = 34*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 864*x**6 + 324*x**5 - 816*x**4 - 36*x**4 - 306*x**3 + 34*x**2\nCombining like terms, got 864*x**6 + 324*x**5 - 852*x**4 - 306*x**3 + 34*x**2\n#Step 6:\nCurrent expression: 864*x**6 + 324*x**5 - 852*x**4 - 306*x**3 + 34*x**2\nNo more calculations needed.\n864*x**6 + 324*x**5 - 852*x**4 - 306*x**3 + 34*x**2", "generated_answer": "864*x**6 + 324*x**5 - 852*x**4 - 306*x**3 + 34*x**2", "step_length": 6} {"cot_id": "01efe8df52067ed2d020084e6a435282d70e0c0a17e24384a58b51efd2d3152e", "datapoint": {"question": "Simplify this expression: (45*y**2 + 30)*(27*y**3 + 18*y**2 + 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1215*y**5 + 810*y**4 + 810*y**3 + 2025*y**2 + 990", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2140, "polynomial_expr": "(45*y**2 + 30)*(27*y**3 + 18*y**2 + 33)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (45*y**2 + 30)*(27*y**3 + 18*y**2 + 33)\nExpanding the part (45*y**2 + 30) using the distributive property, and we got: (45*y**2)*(27*y**3 + 18*y**2 + 33) + 30*(27*y**3 + 18*y**2 + 33)\n#Step 2:\nCurrent expression: (45*y**2)*(27*y**3 + 18*y**2 + 33) + 30*(27*y**3 + 18*y**2 + 33)\nSimplifying the partial expression: 30*(27*y**3 + 18*y**2 + 33)\nExpanding the part (27*y**3 + 18*y**2 + 33) using the distributive property, and we got: (18*y**2)*30 + (27*y**3)*30 + 33*30\nReplacing 30*(27*y**3 + 18*y**2 + 33) with (18*y**2)*30 + (27*y**3)*30 + 33*30 in the overall expression.\n#Step 3:\nCurrent expression: (18*y**2)*30 + (45*y**2)*(27*y**3 + 18*y**2 + 33) + (27*y**3)*30 + 990\nSimplifying the partial expression: (45*y**2)*(27*y**3 + 18*y**2 + 33)\nExpanding the part (27*y**3 + 18*y**2 + 33) using the distributive property, and we got: 33*(45*y**2) + (18*y**2)*(45*y**2) + (45*y**2)*(27*y**3)\nReplacing (45*y**2)*(27*y**3 + 18*y**2 + 33) with 33*(45*y**2) + (18*y**2)*(45*y**2) + (45*y**2)*(27*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 33*45*y**2 + (18*y**2)*(45*y**2) + (18*y**2)*30 + (45*y**2)*(27*y**3) + (27*y**3)*30 + 990\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (18*y**2)*30 = 540*y**2\n (18*y**2)*(45*y**2) = 810*y**4\n (27*y**3)*30 = 810*y**3\n (27*y**3)*(45*y**2) = 1215*y**5\n 33*45*y**2 = 1485*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1215*y**5 + 810*y**4 + 810*y**3 + 540*y**2 + 1485*y**2 + 990\nCombining like terms, got 1215*y**5 + 810*y**4 + 810*y**3 + 2025*y**2 + 990\n#Step 6:\nCurrent expression: 1215*y**5 + 810*y**4 + 810*y**3 + 2025*y**2 + 990\nNo more calculations needed.\n1215*y**5 + 810*y**4 + 810*y**3 + 2025*y**2 + 990", "generated_answer": "1215*y**5 + 810*y**4 + 810*y**3 + 2025*y**2 + 990", "step_length": 6} {"cot_id": "77232a262a3ac2d7e7af967b2e434e2a0f1f1cdee3a2833d8df199fcdd870f2c", "datapoint": {"question": "Calculate the following: (46 - 3*z)*(69*z**3 + 42*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-207*z**4 + 3048*z**3 + 1932*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2141, "polynomial_expr": "(46 - 3*z)*(69*z**3 + 42*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (46 - 3*z)*(69*z**3 + 42*z**2)\nExpanding the part (46 - 3*z) using the distributive property, and we got: (-3*z)*(69*z**3 + 42*z**2) + 46*(69*z**3 + 42*z**2)\n#Step 2:\nCurrent expression: (-3*z)*(69*z**3 + 42*z**2) + 46*(69*z**3 + 42*z**2)\nSimplifying the partial expression: 46*(69*z**3 + 42*z**2)\nExpanding the part (69*z**3 + 42*z**2) using the distributive property, and we got: (42*z**2)*46 + (69*z**3)*46\nReplacing 46*(69*z**3 + 42*z**2) with (42*z**2)*46 + (69*z**3)*46 in the overall expression.\n#Step 3:\nCurrent expression: (-3*z)*(69*z**3 + 42*z**2) + (42*z**2)*46 + (69*z**3)*46\nSimplifying the partial expression: (-3*z)*(69*z**3 + 42*z**2)\nExpanding the part (69*z**3 + 42*z**2) using the distributive property, and we got: (-3*z)*(42*z**2) + (-3*z)*(69*z**3)\nReplacing (-3*z)*(69*z**3 + 42*z**2) with (-3*z)*(42*z**2) + (-3*z)*(69*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-3*z)*(42*z**2) + (-3*z)*(69*z**3) + (42*z**2)*46 + (69*z**3)*46\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (42*z**2)*46 = 1932*z**2\n (42*z**2)*(-3*z) = -126*z**3\n (69*z**3)*46 = 3174*z**3\n (69*z**3)*(-3*z) = -207*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -207*z**4 - 126*z**3 + 3174*z**3 + 1932*z**2\nCombining like terms, got -207*z**4 + 3048*z**3 + 1932*z**2\n#Step 6:\nCurrent expression: -207*z**4 + 3048*z**3 + 1932*z**2\nNo more calculations needed.\n-207*z**4 + 3048*z**3 + 1932*z**2", "generated_answer": "-207*z**4 + 3048*z**3 + 1932*z**2", "step_length": 6} {"cot_id": "e6d559f9a8feb62819409bd8784b41da55055a5a1af9e3a0cdfa9c26cfcee4cb", "datapoint": {"question": "Simplify this expression: 78*x*(9*x**3 + 45*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "702*x**4 + 3510*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2142, "polynomial_expr": "78*x*(9*x**3 + 45*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 78*x*(9*x**3 + 45*x**2)\nExpanding the part (9*x**3 + 45*x**2) using the distributive property, and we got: (78*x)*(45*x**2) + (78*x)*(9*x**3)\n#Step 2:\nCurrent expression: (78*x)*(45*x**2) + (78*x)*(9*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (9*x**3)*(78*x) = 702*x**4\n (45*x**2)*(78*x) = 3510*x**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 702*x**4 + 3510*x**3\nNo more calculations needed.\n702*x**4 + 3510*x**3", "generated_answer": "702*x**4 + 3510*x**3", "step_length": 3} {"cot_id": "1e9b342500b7d6171e3227787ed6ab231d405e63ed527c7767975f18ca2d75f9", "datapoint": {"question": "Simplify this expression: (15*y**3 - 23*y**2)*(31*y**3 - 25)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "465*y**6 - 713*y**5 - 375*y**3 + 575*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2143, "polynomial_expr": "(15*y**3 - 23*y**2)*(31*y**3 - 25)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (15*y**3 - 23*y**2)*(31*y**3 - 25)\nExpanding the part (31*y**3 - 25) using the distributive property, and we got: (31*y**3)*(15*y**3 - 23*y**2) - 25*(15*y**3 - 23*y**2)\n#Step 2:\nCurrent expression: (31*y**3)*(15*y**3 - 23*y**2) - 25*(15*y**3 - 23*y**2)\nSimplifying the partial expression: -25*(15*y**3 - 23*y**2)\nExpanding the part (15*y**3 - 23*y**2) using the distributive property, and we got: -23*y**2*(-25) + (15*y**3)*(-25)\nReplacing -25*(15*y**3 - 23*y**2) with -23*y**2*(-25) + (15*y**3)*(-25) in the overall expression.\n#Step 3:\nCurrent expression: -23*y**2*(-25) + (15*y**3)*(-25) + (31*y**3)*(15*y**3 - 23*y**2)\nSimplifying the partial expression: (31*y**3)*(15*y**3 - 23*y**2)\nExpanding the part (15*y**3 - 23*y**2) using the distributive property, and we got: (-23*y**2)*(31*y**3) + (15*y**3)*(31*y**3)\nReplacing (31*y**3)*(15*y**3 - 23*y**2) with (-23*y**2)*(31*y**3) + (15*y**3)*(31*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-23*y**2)*(31*y**3) - 23*y**2*(-25) + (15*y**3)*(31*y**3) + (15*y**3)*(-25)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-23*y**2)*-25 = 575*y**2\n (-23*y**2)*(31*y**3) = -713*y**5\n (15*y**3)*-25 = -375*y**3\n (15*y**3)*(31*y**3) = 465*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 465*y**6 - 713*y**5 - 375*y**3 + 575*y**2\nNo more calculations needed.\n465*y**6 - 713*y**5 - 375*y**3 + 575*y**2", "generated_answer": "465*y**6 - 713*y**5 - 375*y**3 + 575*y**2", "step_length": 5} {"cot_id": "0cbf334c95f86518cb8f4a5d34d761ca4a632c6e0c59672a16e11b80b80f37ca", "datapoint": {"question": "Simplify this expression: -1750*x**2 + 1120*x\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1750*x**2 + 1120*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2144, "polynomial_expr": "-1750*x**2 + 1120*x", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -1750*x**2 + 1120*x\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -1750*x**2 + 1120*x\nNo more calculations needed.\n-1750*x**2 + 1120*x", "generated_answer": "-1750*x**2 + 1120*x", "step_length": 2} {"cot_id": "f6073fb812a5f519cbcf0ca6373ef2602f2d978c46bf41253ba97ddd5f19bbf6", "datapoint": {"question": "Simplify this expression: 55*x**2*(29*x**3 - 44)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1595*x**5 - 2420*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2145, "polynomial_expr": "55*x**2*(29*x**3 - 44)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 55*x**2*(29*x**3 - 44)\nExpanding the part (29*x**3 - 44) using the distributive property, and we got: -2420*x**2 + (55*x**2)*(29*x**3)\n#Step 2:\nCurrent expression: -2420*x**2 + (55*x**2)*(29*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -44*(55*x**2) = -2420*x**2\n (29*x**3)*(55*x**2) = 1595*x**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1595*x**5 - 2420*x**2\nNo more calculations needed.\n1595*x**5 - 2420*x**2", "generated_answer": "1595*x**5 - 2420*x**2", "step_length": 3} {"cot_id": "db51ddedef0cee83cb7761125fdeaa18771d25a698f243c8a7ae9b53a13cc4d3", "datapoint": {"question": "Simplify this expression: (15*y**3 - 60*y**2)*(-43*y**3 + 33*y**2 + 11*y + 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-645*y**6 + 3075*y**5 - 1815*y**4 - 645*y**3 - 60*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2146, "polynomial_expr": "(15*y**3 - 60*y**2)*(-43*y**3 + 33*y**2 + 11*y + 1)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (15*y**3 - 60*y**2)*(-43*y**3 + 33*y**2 + 11*y + 1)\nExpanding the part (15*y**3 - 60*y**2) using the distributive property, and we got: (-60*y**2)*(-43*y**3 + 33*y**2 + 11*y + 1) + (15*y**3)*(-43*y**3 + 33*y**2 + 11*y + 1)\n#Step 2:\nCurrent expression: (-60*y**2)*(-43*y**3 + 33*y**2 + 11*y + 1) + (15*y**3)*(-43*y**3 + 33*y**2 + 11*y + 1)\nSimplifying the partial expression: (-60*y**2)*(-43*y**3 + 33*y**2 + 11*y + 1)\nExpanding the part (-43*y**3 + 33*y**2 + 11*y + 1) using the distributive property, and we got: 1*(-60*y**2) + (11*y)*(-60*y**2) + (-60*y**2)*(33*y**2) + (-60*y**2)*(-43*y**3)\nReplacing (-60*y**2)*(-43*y**3 + 33*y**2 + 11*y + 1) with 1*(-60*y**2) + (11*y)*(-60*y**2) + (-60*y**2)*(33*y**2) + (-60*y**2)*(-43*y**3) in the overall expression.\n#Step 3:\nCurrent expression: -60*y**2 + (11*y)*(-60*y**2) + (-60*y**2)*(33*y**2) + (-60*y**2)*(-43*y**3) + (15*y**3)*(-43*y**3 + 33*y**2 + 11*y + 1)\nSimplifying the partial expression: (15*y**3)*(-43*y**3 + 33*y**2 + 11*y + 1)\nExpanding the part (-43*y**3 + 33*y**2 + 11*y + 1) using the distributive property, and we got: 1*(15*y**3) + (11*y)*(15*y**3) + (33*y**2)*(15*y**3) + (-43*y**3)*(15*y**3)\nReplacing (15*y**3)*(-43*y**3 + 33*y**2 + 11*y + 1) with 1*(15*y**3) + (11*y)*(15*y**3) + (33*y**2)*(15*y**3) + (-43*y**3)*(15*y**3) in the overall expression.\n#Step 4:\nCurrent expression: 15*y**3 - 60*y**2 + (11*y)*(-60*y**2) + (11*y)*(15*y**3) + (-60*y**2)*(33*y**2) + (-60*y**2)*(-43*y**3) + (33*y**2)*(15*y**3) + (-43*y**3)*(15*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-43*y**3)*(-60*y**2) = 2580*y**5\n (-43*y**3)*(15*y**3) = -645*y**6\n (11*y)*(-60*y**2) = -660*y**3\n (11*y)*(15*y**3) = 165*y**4\n (33*y**2)*(-60*y**2) = -1980*y**4\n (33*y**2)*(15*y**3) = 495*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -645*y**6 + 495*y**5 + 2580*y**5 - 1980*y**4 + 165*y**4 - 660*y**3 + 15*y**3 - 60*y**2\nCombining like terms, got -645*y**6 + 3075*y**5 - 1815*y**4 - 645*y**3 - 60*y**2\n#Step 6:\nCurrent expression: -645*y**6 + 3075*y**5 - 1815*y**4 - 645*y**3 - 60*y**2\nNo more calculations needed.\n-645*y**6 + 3075*y**5 - 1815*y**4 - 645*y**3 - 60*y**2", "generated_answer": "-645*y**6 + 3075*y**5 - 1815*y**4 - 645*y**3 - 60*y**2", "step_length": 6} {"cot_id": "322650a3062a2f801c309fc3d8ca7b2e6c2f6eb1acebdcf6c173337c272a89e2", "datapoint": {"question": "Calculate the following: (-24*x**2 - 3*x + 8)*(-30*x**3 + 14*x**2 - 62*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "720*x**5 - 246*x**4 + 1206*x**3 + 298*x**2 - 496*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2147, "polynomial_expr": "(-24*x**2 - 3*x + 8)*(-30*x**3 + 14*x**2 - 62*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-24*x**2 - 3*x + 8)*(-30*x**3 + 14*x**2 - 62*x)\nExpanding the part (-24*x**2 - 3*x + 8) using the distributive property, and we got: (-3*x)*(-30*x**3 + 14*x**2 - 62*x) + (-24*x**2)*(-30*x**3 + 14*x**2 - 62*x) + 8*(-30*x**3 + 14*x**2 - 62*x)\n#Step 2:\nCurrent expression: (-3*x)*(-30*x**3 + 14*x**2 - 62*x) + (-24*x**2)*(-30*x**3 + 14*x**2 - 62*x) + 8*(-30*x**3 + 14*x**2 - 62*x)\nSimplifying the partial expression: 8*(-30*x**3 + 14*x**2 - 62*x)\nExpanding the part (-30*x**3 + 14*x**2 - 62*x) using the distributive property, and we got: -62*x*8 + (14*x**2)*8 - 30*x**3*8\nReplacing 8*(-30*x**3 + 14*x**2 - 62*x) with -62*x*8 + (14*x**2)*8 - 30*x**3*8 in the overall expression.\n#Step 3:\nCurrent expression: -62*x*8 + (-3*x)*(-30*x**3 + 14*x**2 - 62*x) + (-24*x**2)*(-30*x**3 + 14*x**2 - 62*x) + (14*x**2)*8 - 30*x**3*8\nSimplifying the partial expression: (-24*x**2)*(-30*x**3 + 14*x**2 - 62*x)\nExpanding the part (-30*x**3 + 14*x**2 - 62*x) using the distributive property, and we got: (-62*x)*(-24*x**2) + (-24*x**2)*(14*x**2) + (-24*x**2)*(-30*x**3)\nReplacing (-24*x**2)*(-30*x**3 + 14*x**2 - 62*x) with (-62*x)*(-24*x**2) + (-24*x**2)*(14*x**2) + (-24*x**2)*(-30*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-62*x)*(-24*x**2) - 62*x*8 + (-3*x)*(-30*x**3 + 14*x**2 - 62*x) + (-24*x**2)*(14*x**2) + (-24*x**2)*(-30*x**3) + (14*x**2)*8 - 30*x**3*8\nSimplifying the partial expression: (-3*x)*(-30*x**3 + 14*x**2 - 62*x)\nExpanding the part (-30*x**3 + 14*x**2 - 62*x) using the distributive property, and we got: (-62*x)*(-3*x) + (-3*x)*(14*x**2) + (-3*x)*(-30*x**3)\nReplacing (-3*x)*(-30*x**3 + 14*x**2 - 62*x) with (-62*x)*(-3*x) + (-3*x)*(14*x**2) + (-3*x)*(-30*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-62*x)*(-3*x) + (-62*x)*(-24*x**2) - 62*x*8 + (-3*x)*(14*x**2) + (-3*x)*(-30*x**3) + (-24*x**2)*(14*x**2) + (-24*x**2)*(-30*x**3) + (14*x**2)*8 - 30*x**3*8\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-62*x)*8 = -496*x\n (-62*x)*(-24*x**2) = 1488*x**3\n (-62*x)*(-3*x) = 186*x**2\n (-30*x**3)*8 = -240*x**3\n (-30*x**3)*(-24*x**2) = 720*x**5\n (-30*x**3)*(-3*x) = 90*x**4\n (14*x**2)*8 = 112*x**2\n (14*x**2)*(-24*x**2) = -336*x**4\n (14*x**2)*(-3*x) = -42*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 720*x**5 - 336*x**4 + 90*x**4 - 240*x**3 - 42*x**3 + 1488*x**3 + 112*x**2 + 186*x**2 - 496*x\nCombining like terms, got 720*x**5 - 246*x**4 + 1206*x**3 + 298*x**2 - 496*x\n#Step 7:\nCurrent expression: 720*x**5 - 246*x**4 + 1206*x**3 + 298*x**2 - 496*x\nNo more calculations needed.\n720*x**5 - 246*x**4 + 1206*x**3 + 298*x**2 - 496*x", "generated_answer": "720*x**5 - 246*x**4 + 1206*x**3 + 298*x**2 - 496*x", "step_length": 7} {"cot_id": "faaecdfddbf12a85202ee7fccffb1638481d705b8c1cba296b46aa5a93dcd078", "datapoint": {"question": "Calculate the following: (36*z - 22)*(-15*z**3 + 27*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-540*z**4 + 1302*z**3 - 594*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2148, "polynomial_expr": "(36*z - 22)*(-15*z**3 + 27*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (36*z - 22)*(-15*z**3 + 27*z**2)\nExpanding the part (36*z - 22) using the distributive property, and we got: (36*z)*(-15*z**3 + 27*z**2) - 22*(-15*z**3 + 27*z**2)\n#Step 2:\nCurrent expression: (36*z)*(-15*z**3 + 27*z**2) - 22*(-15*z**3 + 27*z**2)\nSimplifying the partial expression: -22*(-15*z**3 + 27*z**2)\nExpanding the part (-15*z**3 + 27*z**2) using the distributive property, and we got: (27*z**2)*(-22) - 15*z**3*(-22)\nReplacing -22*(-15*z**3 + 27*z**2) with (27*z**2)*(-22) - 15*z**3*(-22) in the overall expression.\n#Step 3:\nCurrent expression: (36*z)*(-15*z**3 + 27*z**2) + (27*z**2)*(-22) - 15*z**3*(-22)\nSimplifying the partial expression: (36*z)*(-15*z**3 + 27*z**2)\nExpanding the part (-15*z**3 + 27*z**2) using the distributive property, and we got: (36*z)*(27*z**2) + (36*z)*(-15*z**3)\nReplacing (36*z)*(-15*z**3 + 27*z**2) with (36*z)*(27*z**2) + (36*z)*(-15*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (36*z)*(27*z**2) + (36*z)*(-15*z**3) + (27*z**2)*(-22) - 15*z**3*(-22)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-15*z**3)*-22 = 330*z**3\n (-15*z**3)*(36*z) = -540*z**4\n (27*z**2)*-22 = -594*z**2\n (27*z**2)*(36*z) = 972*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -540*z**4 + 330*z**3 + 972*z**3 - 594*z**2\nCombining like terms, got -540*z**4 + 1302*z**3 - 594*z**2\n#Step 6:\nCurrent expression: -540*z**4 + 1302*z**3 - 594*z**2\nNo more calculations needed.\n-540*z**4 + 1302*z**3 - 594*z**2", "generated_answer": "-540*z**4 + 1302*z**3 - 594*z**2", "step_length": 6} {"cot_id": "7a6c1ca18a0c58c86eee5aa74cc088b15731e84f7fd1e45ecc9351f12992da39", "datapoint": {"question": "Calculate the following: (-13*x**2 + 21*x)*(15*x**3 - 72*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-195*x**5 + 1251*x**4 - 1512*x**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2149, "polynomial_expr": "(-13*x**2 + 21*x)*(15*x**3 - 72*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-13*x**2 + 21*x)*(15*x**3 - 72*x**2)\nExpanding the part (15*x**3 - 72*x**2) using the distributive property, and we got: (-72*x**2)*(-13*x**2 + 21*x) + (15*x**3)*(-13*x**2 + 21*x)\n#Step 2:\nCurrent expression: (-72*x**2)*(-13*x**2 + 21*x) + (15*x**3)*(-13*x**2 + 21*x)\nSimplifying the partial expression: (-72*x**2)*(-13*x**2 + 21*x)\nExpanding the part (-13*x**2 + 21*x) using the distributive property, and we got: (21*x)*(-72*x**2) + (-72*x**2)*(-13*x**2)\nReplacing (-72*x**2)*(-13*x**2 + 21*x) with (21*x)*(-72*x**2) + (-72*x**2)*(-13*x**2) in the overall expression.\n#Step 3:\nCurrent expression: (21*x)*(-72*x**2) + (-72*x**2)*(-13*x**2) + (15*x**3)*(-13*x**2 + 21*x)\nSimplifying the partial expression: (15*x**3)*(-13*x**2 + 21*x)\nExpanding the part (-13*x**2 + 21*x) using the distributive property, and we got: (21*x)*(15*x**3) + (-13*x**2)*(15*x**3)\nReplacing (15*x**3)*(-13*x**2 + 21*x) with (21*x)*(15*x**3) + (-13*x**2)*(15*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (21*x)*(-72*x**2) + (21*x)*(15*x**3) + (-72*x**2)*(-13*x**2) + (-13*x**2)*(15*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*x**2)*(-72*x**2) = 936*x**4\n (-13*x**2)*(15*x**3) = -195*x**5\n (21*x)*(-72*x**2) = -1512*x**3\n (21*x)*(15*x**3) = 315*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -195*x**5 + 315*x**4 + 936*x**4 - 1512*x**3\nCombining like terms, got -195*x**5 + 1251*x**4 - 1512*x**3\n#Step 6:\nCurrent expression: -195*x**5 + 1251*x**4 - 1512*x**3\nNo more calculations needed.\n-195*x**5 + 1251*x**4 - 1512*x**3", "generated_answer": "-195*x**5 + 1251*x**4 - 1512*x**3", "step_length": 6} {"cot_id": "9b78db2aa987e972335dd2a94afd569b5a36169705bd75afb372010554a156fd", "datapoint": {"question": "Calculate the following: (28*y**2 + 29*y)*(58*y**3 + 71)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1624*y**5 + 1682*y**4 + 1988*y**2 + 2059*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2150, "polynomial_expr": "(28*y**2 + 29*y)*(58*y**3 + 71)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (28*y**2 + 29*y)*(58*y**3 + 71)\nExpanding the part (58*y**3 + 71) using the distributive property, and we got: (58*y**3)*(28*y**2 + 29*y) + 71*(28*y**2 + 29*y)\n#Step 2:\nCurrent expression: (58*y**3)*(28*y**2 + 29*y) + 71*(28*y**2 + 29*y)\nSimplifying the partial expression: 71*(28*y**2 + 29*y)\nExpanding the part (28*y**2 + 29*y) using the distributive property, and we got: (29*y)*71 + (28*y**2)*71\nReplacing 71*(28*y**2 + 29*y) with (29*y)*71 + (28*y**2)*71 in the overall expression.\n#Step 3:\nCurrent expression: (29*y)*71 + (28*y**2)*71 + (58*y**3)*(28*y**2 + 29*y)\nSimplifying the partial expression: (58*y**3)*(28*y**2 + 29*y)\nExpanding the part (28*y**2 + 29*y) using the distributive property, and we got: (29*y)*(58*y**3) + (28*y**2)*(58*y**3)\nReplacing (58*y**3)*(28*y**2 + 29*y) with (29*y)*(58*y**3) + (28*y**2)*(58*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (29*y)*(58*y**3) + (29*y)*71 + (28*y**2)*(58*y**3) + (28*y**2)*71\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (28*y**2)*71 = 1988*y**2\n (28*y**2)*(58*y**3) = 1624*y**5\n (29*y)*71 = 2059*y\n (29*y)*(58*y**3) = 1682*y**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1624*y**5 + 1682*y**4 + 1988*y**2 + 2059*y\nNo more calculations needed.\n1624*y**5 + 1682*y**4 + 1988*y**2 + 2059*y", "generated_answer": "1624*y**5 + 1682*y**4 + 1988*y**2 + 2059*y", "step_length": 5} {"cot_id": "c1f6fcfb0e170cfe4545b68fe12f105016dc1c6eb2c74d78110d211d5968b612", "datapoint": {"question": "Simplify this expression: -35*z**2*(-40*z**3 + 47*z + 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1400*z**5 - 1645*z**3 - 735*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2151, "polynomial_expr": "-35*z**2*(-40*z**3 + 47*z + 21)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -35*z**2*(-40*z**3 + 47*z + 21)\nExpanding the part (-40*z**3 + 47*z + 21) using the distributive property, and we got: 21*(-35*z**2) + (47*z)*(-35*z**2) + (-35*z**2)*(-40*z**3)\n#Step 2:\nCurrent expression: 21*(-35*z**2) + (47*z)*(-35*z**2) + (-35*z**2)*(-40*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 21*(-35*z**2) = -735*z**2\n (-40*z**3)*(-35*z**2) = 1400*z**5\n (47*z)*(-35*z**2) = -1645*z**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 1400*z**5 - 1645*z**3 - 735*z**2\nNo more calculations needed.\n1400*z**5 - 1645*z**3 - 735*z**2", "generated_answer": "1400*z**5 - 1645*z**3 - 735*z**2", "step_length": 3} {"cot_id": "35b9e6d7e1a95ab60a8152c3a7e518b2017fa481b9047dd63c21069502a76940", "datapoint": {"question": "Calculate the following: (-13*y**3 + 33*y**2)*(5*y**3 + 23)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-65*y**6 + 165*y**5 - 299*y**3 + 759*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2152, "polynomial_expr": "(-13*y**3 + 33*y**2)*(5*y**3 + 23)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-13*y**3 + 33*y**2)*(5*y**3 + 23)\nExpanding the part (5*y**3 + 23) using the distributive property, and we got: (5*y**3)*(-13*y**3 + 33*y**2) + 23*(-13*y**3 + 33*y**2)\n#Step 2:\nCurrent expression: (5*y**3)*(-13*y**3 + 33*y**2) + 23*(-13*y**3 + 33*y**2)\nSimplifying the partial expression: 23*(-13*y**3 + 33*y**2)\nExpanding the part (-13*y**3 + 33*y**2) using the distributive property, and we got: (33*y**2)*23 - 13*y**3*23\nReplacing 23*(-13*y**3 + 33*y**2) with (33*y**2)*23 - 13*y**3*23 in the overall expression.\n#Step 3:\nCurrent expression: (33*y**2)*23 - 13*y**3*23 + (5*y**3)*(-13*y**3 + 33*y**2)\nSimplifying the partial expression: (5*y**3)*(-13*y**3 + 33*y**2)\nExpanding the part (-13*y**3 + 33*y**2) using the distributive property, and we got: (33*y**2)*(5*y**3) + (-13*y**3)*(5*y**3)\nReplacing (5*y**3)*(-13*y**3 + 33*y**2) with (33*y**2)*(5*y**3) + (-13*y**3)*(5*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (33*y**2)*(5*y**3) + (33*y**2)*23 + (-13*y**3)*(5*y**3) - 13*y**3*23\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-13*y**3)*23 = -299*y**3\n (-13*y**3)*(5*y**3) = -65*y**6\n (33*y**2)*23 = 759*y**2\n (33*y**2)*(5*y**3) = 165*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -65*y**6 + 165*y**5 - 299*y**3 + 759*y**2\nNo more calculations needed.\n-65*y**6 + 165*y**5 - 299*y**3 + 759*y**2", "generated_answer": "-65*y**6 + 165*y**5 - 299*y**3 + 759*y**2", "step_length": 5} {"cot_id": "a75cc77bf6cfb417a9ba758d734b7d04998633661691b3d964fbdffc8941f4dd", "datapoint": {"question": "Calculate the following: (29*z - 25)*(-z**2 - 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-29*z**3 + 25*z**2 - 290*z + 250", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2153, "polynomial_expr": "(29*z - 25)*(-z**2 - 10)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (29*z - 25)*(-z**2 - 10)\nExpanding the part (29*z - 25) using the distributive property, and we got: (29*z)*(-z**2 - 10) - 25*(-z**2 - 10)\n#Step 2:\nCurrent expression: (29*z)*(-z**2 - 10) - 25*(-z**2 - 10)\nSimplifying the partial expression: -25*(-z**2 - 10)\nExpanding the part (-z**2 - 10) using the distributive property, and we got: -z**2*(-25) - 10*(-25)\nReplacing -25*(-z**2 - 10) with -z**2*(-25) - 10*(-25) in the overall expression.\n#Step 3:\nCurrent expression: (29*z)*(-z**2 - 10) - z**2*(-25) + 250\nSimplifying the partial expression: (29*z)*(-z**2 - 10)\nExpanding the part (-z**2 - 10) using the distributive property, and we got: -290*z + (29*z)*(-z**2)\nReplacing (29*z)*(-z**2 - 10) with -290*z + (29*z)*(-z**2) in the overall expression.\n#Step 4:\nCurrent expression: -10*29*z + (29*z)*(-z**2) - z**2*(-25) + 250\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-z**2)*-25 = 25*z**2\n (-z**2)*(29*z) = -29*z**3\n -10*29*z = -290*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -29*z**3 + 25*z**2 - 290*z + 250\nNo more calculations needed.\n-29*z**3 + 25*z**2 - 290*z + 250", "generated_answer": "-29*z**3 + 25*z**2 - 290*z + 250", "step_length": 5} {"cot_id": "71cc88329f02f62666330852a5df2fc3042e461e9d0e9a896b49dd560a4e1f51", "datapoint": {"question": "Simplify this expression: (45 - 11*x)*(30*x**3 - 15)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-330*x**4 + 1350*x**3 + 165*x - 675", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2154, "polynomial_expr": "(45 - 11*x)*(30*x**3 - 15)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (45 - 11*x)*(30*x**3 - 15)\nExpanding the part (30*x**3 - 15) using the distributive property, and we got: (30*x**3)*(45 - 11*x) - 15*(45 - 11*x)\n#Step 2:\nCurrent expression: (30*x**3)*(45 - 11*x) - 15*(45 - 11*x)\nSimplifying the partial expression: -15*(45 - 11*x)\nExpanding the part (45 - 11*x) using the distributive property, and we got: -11*x*(-15) + 45*(-15)\nReplacing -15*(45 - 11*x) with -11*x*(-15) + 45*(-15) in the overall expression.\n#Step 3:\nCurrent expression: -11*x*(-15) + (30*x**3)*(45 - 11*x) - 675\nSimplifying the partial expression: (30*x**3)*(45 - 11*x)\nExpanding the part (45 - 11*x) using the distributive property, and we got: (-11*x)*(30*x**3) + 45*(30*x**3)\nReplacing (30*x**3)*(45 - 11*x) with (-11*x)*(30*x**3) + 45*(30*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-11*x)*(30*x**3) - 11*x*(-15) + 45*30*x**3 - 675\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-11*x)*-15 = 165*x\n (-11*x)*(30*x**3) = -330*x**4\n 45*30*x**3 = 1350*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -330*x**4 + 1350*x**3 + 165*x - 675\nNo more calculations needed.\n-330*x**4 + 1350*x**3 + 165*x - 675", "generated_answer": "-330*x**4 + 1350*x**3 + 165*x - 675", "step_length": 5} {"cot_id": "a56ae69dcc48cc2c7500c9e56b69c824a0ac78af978f915f06112f17f2550c00", "datapoint": {"question": "Simplify this expression: 67*z**2\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "67*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2155, "polynomial_expr": "67*z**2", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 67*z**2\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 67*z**2\nNo more calculations needed.\n67*z**2", "generated_answer": "67*z**2", "step_length": 2} {"cot_id": "05306455ed570ee9699475428465796573917974c330b142188eabb190317f94", "datapoint": {"question": "Simplify this expression: (49 - 16*z**2)*(12*z**3 + 4)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-192*z**5 + 588*z**3 - 64*z**2 + 196", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2156, "polynomial_expr": "(49 - 16*z**2)*(12*z**3 + 4)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (49 - 16*z**2)*(12*z**3 + 4)\nExpanding the part (12*z**3 + 4) using the distributive property, and we got: (12*z**3)*(49 - 16*z**2) + 4*(49 - 16*z**2)\n#Step 2:\nCurrent expression: (12*z**3)*(49 - 16*z**2) + 4*(49 - 16*z**2)\nSimplifying the partial expression: 4*(49 - 16*z**2)\nExpanding the part (49 - 16*z**2) using the distributive property, and we got: -16*z**2*4 + 49*4\nReplacing 4*(49 - 16*z**2) with -16*z**2*4 + 49*4 in the overall expression.\n#Step 3:\nCurrent expression: -16*z**2*4 + (12*z**3)*(49 - 16*z**2) + 196\nSimplifying the partial expression: (12*z**3)*(49 - 16*z**2)\nExpanding the part (49 - 16*z**2) using the distributive property, and we got: 49*(12*z**3) + (-16*z**2)*(12*z**3)\nReplacing (12*z**3)*(49 - 16*z**2) with 49*(12*z**3) + (-16*z**2)*(12*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 49*12*z**3 + (-16*z**2)*(12*z**3) - 16*z**2*4 + 196\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-16*z**2)*4 = -64*z**2\n (-16*z**2)*(12*z**3) = -192*z**5\n 49*12*z**3 = 588*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -192*z**5 + 588*z**3 - 64*z**2 + 196\nNo more calculations needed.\n-192*z**5 + 588*z**3 - 64*z**2 + 196", "generated_answer": "-192*z**5 + 588*z**3 - 64*z**2 + 196", "step_length": 5} {"cot_id": "7b683a8c18b2efc2ae3a89b022526fec2123a2b6f99b9fd2fc834bcd0561d27a", "datapoint": {"question": "Calculate the following: (-13*z - 45)*(-10*z**3 - 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "130*z**4 + 450*z**3 + 455*z + 1575", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2157, "polynomial_expr": "(-13*z - 45)*(-10*z**3 - 35)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-13*z - 45)*(-10*z**3 - 35)\nExpanding the part (-13*z - 45) using the distributive property, and we got: (-13*z)*(-10*z**3 - 35) - 45*(-10*z**3 - 35)\n#Step 2:\nCurrent expression: (-13*z)*(-10*z**3 - 35) - 45*(-10*z**3 - 35)\nSimplifying the partial expression: -45*(-10*z**3 - 35)\nExpanding the part (-10*z**3 - 35) using the distributive property, and we got: -10*z**3*(-45) - 35*(-45)\nReplacing -45*(-10*z**3 - 35) with -10*z**3*(-45) - 35*(-45) in the overall expression.\n#Step 3:\nCurrent expression: (-13*z)*(-10*z**3 - 35) - 10*z**3*(-45) + 1575\nSimplifying the partial expression: (-13*z)*(-10*z**3 - 35)\nExpanding the part (-10*z**3 - 35) using the distributive property, and we got: (-13*z)*(-10*z**3) - (-1)*455*z\nReplacing (-13*z)*(-10*z**3 - 35) with (-13*z)*(-10*z**3) - (-1)*455*z in the overall expression.\n#Step 4:\nCurrent expression: (-13*z)*(-10*z**3) - 35*(-13)*z - 10*z**3*(-45) + 1575\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-10*z**3)*-45 = 450*z**3\n (-10*z**3)*(-13*z) = 130*z**4\n -35*-13*z = 455*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 130*z**4 + 450*z**3 + 455*z + 1575\nNo more calculations needed.\n130*z**4 + 450*z**3 + 455*z + 1575", "generated_answer": "130*z**4 + 450*z**3 + 455*z + 1575", "step_length": 5} {"cot_id": "d9ed03c1c7e869d35d8bc177279716b8128c31502a738162f77a5ce48355ea27", "datapoint": {"question": "Simplify this expression: 32*y*(-15*y**3 + 35*y**2 + 8*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-480*y**4 + 1120*y**3 + 256*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2158, "polynomial_expr": "32*y*(-15*y**3 + 35*y**2 + 8*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 32*y*(-15*y**3 + 35*y**2 + 8*y)\nExpanding the part (-15*y**3 + 35*y**2 + 8*y) using the distributive property, and we got: (8*y)*(32*y) + (32*y)*(35*y**2) + (32*y)*(-15*y**3)\n#Step 2:\nCurrent expression: (8*y)*(32*y) + (32*y)*(35*y**2) + (32*y)*(-15*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-15*y**3)*(32*y) = -480*y**4\n (8*y)*(32*y) = 256*y**2\n (35*y**2)*(32*y) = 1120*y**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -480*y**4 + 1120*y**3 + 256*y**2\nNo more calculations needed.\n-480*y**4 + 1120*y**3 + 256*y**2", "generated_answer": "-480*y**4 + 1120*y**3 + 256*y**2", "step_length": 3} {"cot_id": "db1920e2f0a14964b16952e4134f5393031f17ed2e926d6f06c74ae286df7f42", "datapoint": {"question": "Calculate the following: (-13*x**3 - 13*x + 13)*(46*x**3 + 32*x**2 - 28*x + 10)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-598*x**6 - 416*x**5 - 234*x**4 + 52*x**3 + 780*x**2 - 494*x + 130", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2159, "polynomial_expr": "(-13*x**3 - 13*x + 13)*(46*x**3 + 32*x**2 - 28*x + 10)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-13*x**3 - 13*x + 13)*(46*x**3 + 32*x**2 - 28*x + 10)\nExpanding the part (-13*x**3 - 13*x + 13) using the distributive property, and we got: (-13*x)*(46*x**3 + 32*x**2 - 28*x + 10) + (-13*x**3)*(46*x**3 + 32*x**2 - 28*x + 10) + 13*(46*x**3 + 32*x**2 - 28*x + 10)\n#Step 2:\nCurrent expression: (-13*x)*(46*x**3 + 32*x**2 - 28*x + 10) + (-13*x**3)*(46*x**3 + 32*x**2 - 28*x + 10) + 13*(46*x**3 + 32*x**2 - 28*x + 10)\nSimplifying the partial expression: 13*(46*x**3 + 32*x**2 - 28*x + 10)\nExpanding the part (46*x**3 + 32*x**2 - 28*x + 10) using the distributive property, and we got: -28*x*13 + (32*x**2)*13 + (46*x**3)*13 + 10*13\nReplacing 13*(46*x**3 + 32*x**2 - 28*x + 10) with -28*x*13 + (32*x**2)*13 + (46*x**3)*13 + 10*13 in the overall expression.\n#Step 3:\nCurrent expression: -28*x*13 + (-13*x)*(46*x**3 + 32*x**2 - 28*x + 10) + (32*x**2)*13 + (-13*x**3)*(46*x**3 + 32*x**2 - 28*x + 10) + (46*x**3)*13 + 130\nSimplifying the partial expression: (-13*x)*(46*x**3 + 32*x**2 - 28*x + 10)\nExpanding the part (46*x**3 + 32*x**2 - 28*x + 10) using the distributive property, and we got: (-28*x)*(-13*x) + (-13*x)*(32*x**2) + (-13*x)*(46*x**3) + 10*(-13*x)\nReplacing (-13*x)*(46*x**3 + 32*x**2 - 28*x + 10) with (-28*x)*(-13*x) + (-13*x)*(32*x**2) + (-13*x)*(46*x**3) + 10*(-13*x) in the overall expression.\n#Step 4:\nCurrent expression: (-28*x)*(-13*x) - 28*x*13 + (-13*x)*(32*x**2) + (-13*x)*(46*x**3) + 10*(-13)*x + (32*x**2)*13 + (-13*x**3)*(46*x**3 + 32*x**2 - 28*x + 10) + (46*x**3)*13 + 130\nSimplifying the partial expression: (-13*x**3)*(46*x**3 + 32*x**2 - 28*x + 10)\nExpanding the part (46*x**3 + 32*x**2 - 28*x + 10) using the distributive property, and we got: (-28*x)*(-13*x**3) + 10*(-13*x**3) + (32*x**2)*(-13*x**3) + (-13*x**3)*(46*x**3)\nReplacing (-13*x**3)*(46*x**3 + 32*x**2 - 28*x + 10) with (-28*x)*(-13*x**3) + 10*(-13*x**3) + (32*x**2)*(-13*x**3) + (-13*x**3)*(46*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-28*x)*(-13*x) + (-28*x)*(-13*x**3) - 28*x*13 + (-13*x)*(32*x**2) + (-13*x)*(46*x**3) + 10*(-13)*x**3 + 10*(-13)*x + (32*x**2)*(-13*x**3) + (32*x**2)*13 + (-13*x**3)*(46*x**3) + (46*x**3)*13 + 130\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-28*x)*13 = -364*x\n (-28*x)*(-13*x) = 364*x**2\n (-28*x)*(-13*x**3) = 364*x**4\n (32*x**2)*13 = 416*x**2\n (32*x**2)*(-13*x) = -416*x**3\n (32*x**2)*(-13*x**3) = -416*x**5\n (46*x**3)*13 = 598*x**3\n (46*x**3)*(-13*x) = -598*x**4\n (46*x**3)*(-13*x**3) = -598*x**6\n 10*-13*x = -130*x\n 10*-13*x**3 = -130*x**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -598*x**6 - 416*x**5 - 598*x**4 + 364*x**4 - 416*x**3 - 130*x**3 + 598*x**3 + 364*x**2 + 416*x**2 - 364*x - 130*x + 130\nCombining like terms, got -598*x**6 - 416*x**5 - 234*x**4 + 52*x**3 + 780*x**2 - 494*x + 130\n#Step 7:\nCurrent expression: -598*x**6 - 416*x**5 - 234*x**4 + 52*x**3 + 780*x**2 - 494*x + 130\nNo more calculations needed.\n-598*x**6 - 416*x**5 - 234*x**4 + 52*x**3 + 780*x**2 - 494*x + 130", "generated_answer": "-598*x**6 - 416*x**5 - 234*x**4 + 52*x**3 + 780*x**2 - 494*x + 130", "step_length": 7} {"cot_id": "d06180a27daf589781c78338dcc506b13700c5d8db1dcf2330936a43fdb057c1", "datapoint": {"question": "Calculate the following: (3*x**2 - 32*x - 44)*(-18*x**3 + 34*x**2 + 37)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-54*x**5 + 678*x**4 - 296*x**3 - 1385*x**2 - 1184*x - 1628", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2160, "polynomial_expr": "(3*x**2 - 32*x - 44)*(-18*x**3 + 34*x**2 + 37)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (3*x**2 - 32*x - 44)*(-18*x**3 + 34*x**2 + 37)\nExpanding the part (3*x**2 - 32*x - 44) using the distributive property, and we got: (-32*x)*(-18*x**3 + 34*x**2 + 37) + (3*x**2)*(-18*x**3 + 34*x**2 + 37) - 44*(-18*x**3 + 34*x**2 + 37)\n#Step 2:\nCurrent expression: (-32*x)*(-18*x**3 + 34*x**2 + 37) + (3*x**2)*(-18*x**3 + 34*x**2 + 37) - 44*(-18*x**3 + 34*x**2 + 37)\nSimplifying the partial expression: -44*(-18*x**3 + 34*x**2 + 37)\nExpanding the part (-18*x**3 + 34*x**2 + 37) using the distributive property, and we got: (34*x**2)*(-44) - 18*x**3*(-44) + 37*(-44)\nReplacing -44*(-18*x**3 + 34*x**2 + 37) with (34*x**2)*(-44) - 18*x**3*(-44) + 37*(-44) in the overall expression.\n#Step 3:\nCurrent expression: (-32*x)*(-18*x**3 + 34*x**2 + 37) + (3*x**2)*(-18*x**3 + 34*x**2 + 37) + (34*x**2)*(-44) - 18*x**3*(-44) - 1628\nSimplifying the partial expression: (-32*x)*(-18*x**3 + 34*x**2 + 37)\nExpanding the part (-18*x**3 + 34*x**2 + 37) using the distributive property, and we got: (-32*x)*(34*x**2) + (-32*x)*(-18*x**3) + 37*(-32*x)\nReplacing (-32*x)*(-18*x**3 + 34*x**2 + 37) with (-32*x)*(34*x**2) + (-32*x)*(-18*x**3) + 37*(-32*x) in the overall expression.\n#Step 4:\nCurrent expression: (-32*x)*(34*x**2) + (-32*x)*(-18*x**3) + 37*(-32)*x + (3*x**2)*(-18*x**3 + 34*x**2 + 37) + (34*x**2)*(-44) - 18*x**3*(-44) - 1628\nSimplifying the partial expression: (3*x**2)*(-18*x**3 + 34*x**2 + 37)\nExpanding the part (-18*x**3 + 34*x**2 + 37) using the distributive property, and we got: 37*(3*x**2) + (3*x**2)*(34*x**2) + (3*x**2)*(-18*x**3)\nReplacing (3*x**2)*(-18*x**3 + 34*x**2 + 37) with 37*(3*x**2) + (3*x**2)*(34*x**2) + (3*x**2)*(-18*x**3) in the overall expression.\n#Step 5:\nCurrent expression: (-32*x)*(34*x**2) + (-32*x)*(-18*x**3) + 37*3*x**2 + 37*(-32)*x + (3*x**2)*(34*x**2) + (3*x**2)*(-18*x**3) + (34*x**2)*(-44) - 18*x**3*(-44) - 1628\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-18*x**3)*-44 = 792*x**3\n (-18*x**3)*(-32*x) = 576*x**4\n (-18*x**3)*(3*x**2) = -54*x**5\n (34*x**2)*-44 = -1496*x**2\n (34*x**2)*(-32*x) = -1088*x**3\n (34*x**2)*(3*x**2) = 102*x**4\n 37*-32*x = -1184*x\n 37*3*x**2 = 111*x**2\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -54*x**5 + 102*x**4 + 576*x**4 - 1088*x**3 + 792*x**3 - 1496*x**2 + 111*x**2 - 1184*x - 1628\nCombining like terms, got -54*x**5 + 678*x**4 - 296*x**3 - 1385*x**2 - 1184*x - 1628\n#Step 7:\nCurrent expression: -54*x**5 + 678*x**4 - 296*x**3 - 1385*x**2 - 1184*x - 1628\nNo more calculations needed.\n-54*x**5 + 678*x**4 - 296*x**3 - 1385*x**2 - 1184*x - 1628", "generated_answer": "-54*x**5 + 678*x**4 - 296*x**3 - 1385*x**2 - 1184*x - 1628", "step_length": 7} {"cot_id": "b5d8527d30584f1624df678faeb01a73e1bf412d1186515f77c381be3312d817", "datapoint": {"question": "Calculate the following: (-14*z**3 + 41*z**2)*(26*z**3 - 33*z + 36)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-364*z**6 + 1066*z**5 + 462*z**4 - 1857*z**3 + 1476*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2161, "polynomial_expr": "(-14*z**3 + 41*z**2)*(26*z**3 - 33*z + 36)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-14*z**3 + 41*z**2)*(26*z**3 - 33*z + 36)\nExpanding the part (-14*z**3 + 41*z**2) using the distributive property, and we got: (41*z**2)*(26*z**3 - 33*z + 36) + (-14*z**3)*(26*z**3 - 33*z + 36)\n#Step 2:\nCurrent expression: (41*z**2)*(26*z**3 - 33*z + 36) + (-14*z**3)*(26*z**3 - 33*z + 36)\nSimplifying the partial expression: (-14*z**3)*(26*z**3 - 33*z + 36)\nExpanding the part (26*z**3 - 33*z + 36) using the distributive property, and we got: (-33*z)*(-14*z**3) + 36*(-14*z**3) + (-14*z**3)*(26*z**3)\nReplacing (-14*z**3)*(26*z**3 - 33*z + 36) with (-33*z)*(-14*z**3) + 36*(-14*z**3) + (-14*z**3)*(26*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-33*z)*(-14*z**3) + 36*(-14)*z**3 + (41*z**2)*(26*z**3 - 33*z + 36) + (-14*z**3)*(26*z**3)\nSimplifying the partial expression: (41*z**2)*(26*z**3 - 33*z + 36)\nExpanding the part (26*z**3 - 33*z + 36) using the distributive property, and we got: (-33*z)*(41*z**2) + 36*(41*z**2) + (41*z**2)*(26*z**3)\nReplacing (41*z**2)*(26*z**3 - 33*z + 36) with (-33*z)*(41*z**2) + 36*(41*z**2) + (41*z**2)*(26*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-33*z)*(41*z**2) + (-33*z)*(-14*z**3) + 36*(-14)*z**3 + 36*41*z**2 + (41*z**2)*(26*z**3) + (-14*z**3)*(26*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*z)*(-14*z**3) = 462*z**4\n (-33*z)*(41*z**2) = -1353*z**3\n (26*z**3)*(-14*z**3) = -364*z**6\n (26*z**3)*(41*z**2) = 1066*z**5\n 36*-14*z**3 = -504*z**3\n 36*41*z**2 = 1476*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -364*z**6 + 1066*z**5 + 462*z**4 - 1353*z**3 - 504*z**3 + 1476*z**2\nCombining like terms, got -364*z**6 + 1066*z**5 + 462*z**4 - 1857*z**3 + 1476*z**2\n#Step 6:\nCurrent expression: -364*z**6 + 1066*z**5 + 462*z**4 - 1857*z**3 + 1476*z**2\nNo more calculations needed.\n-364*z**6 + 1066*z**5 + 462*z**4 - 1857*z**3 + 1476*z**2", "generated_answer": "-364*z**6 + 1066*z**5 + 462*z**4 - 1857*z**3 + 1476*z**2", "step_length": 6} {"cot_id": "0fed90b6dd94f95bddc11114e4110717670cb8df75ac81205113d8a978c63f53", "datapoint": {"question": "Calculate the following: (4 - 41*x**2)*(11*x**2 - 18*x - 39)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-451*x**4 + 738*x**3 + 1643*x**2 - 72*x - 156", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2162, "polynomial_expr": "(4 - 41*x**2)*(11*x**2 - 18*x - 39)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (4 - 41*x**2)*(11*x**2 - 18*x - 39)\nExpanding the part (4 - 41*x**2) using the distributive property, and we got: (-41*x**2)*(11*x**2 - 18*x - 39) + 4*(11*x**2 - 18*x - 39)\n#Step 2:\nCurrent expression: (-41*x**2)*(11*x**2 - 18*x - 39) + 4*(11*x**2 - 18*x - 39)\nSimplifying the partial expression: 4*(11*x**2 - 18*x - 39)\nExpanding the part (11*x**2 - 18*x - 39) using the distributive property, and we got: -18*x*4 + (11*x**2)*4 - 39*4\nReplacing 4*(11*x**2 - 18*x - 39) with -18*x*4 + (11*x**2)*4 - 39*4 in the overall expression.\n#Step 3:\nCurrent expression: -18*x*4 + (-41*x**2)*(11*x**2 - 18*x - 39) + (11*x**2)*4 - 156\nSimplifying the partial expression: (-41*x**2)*(11*x**2 - 18*x - 39)\nExpanding the part (11*x**2 - 18*x - 39) using the distributive property, and we got: (-18*x)*(-41*x**2) - (-1)*1599*x**2 + (-41*x**2)*(11*x**2)\nReplacing (-41*x**2)*(11*x**2 - 18*x - 39) with (-18*x)*(-41*x**2) - (-1)*1599*x**2 + (-41*x**2)*(11*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (-18*x)*(-41*x**2) - 18*x*4 - 39*(-41)*x**2 + (-41*x**2)*(11*x**2) + (11*x**2)*4 - 156\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-18*x)*4 = -72*x\n (-18*x)*(-41*x**2) = 738*x**3\n (11*x**2)*4 = 44*x**2\n (11*x**2)*(-41*x**2) = -451*x**4\n -39*-41*x**2 = 1599*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -451*x**4 + 738*x**3 + 44*x**2 + 1599*x**2 - 72*x - 156\nCombining like terms, got -451*x**4 + 738*x**3 + 1643*x**2 - 72*x - 156\n#Step 6:\nCurrent expression: -451*x**4 + 738*x**3 + 1643*x**2 - 72*x - 156\nNo more calculations needed.\n-451*x**4 + 738*x**3 + 1643*x**2 - 72*x - 156", "generated_answer": "-451*x**4 + 738*x**3 + 1643*x**2 - 72*x - 156", "step_length": 6} {"cot_id": "68d6e996e7214a897813ddb33f61ba2f159ca08521480b98449c92add1ce3194", "datapoint": {"question": "Calculate the following: (56*z + 54)*(-2*z**3 - 22*z**2 - 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-112*z**4 - 1340*z**3 - 1188*z**2 - 1176*z - 1134", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2163, "polynomial_expr": "(56*z + 54)*(-2*z**3 - 22*z**2 - 21)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (56*z + 54)*(-2*z**3 - 22*z**2 - 21)\nExpanding the part (56*z + 54) using the distributive property, and we got: (56*z)*(-2*z**3 - 22*z**2 - 21) + 54*(-2*z**3 - 22*z**2 - 21)\n#Step 2:\nCurrent expression: (56*z)*(-2*z**3 - 22*z**2 - 21) + 54*(-2*z**3 - 22*z**2 - 21)\nSimplifying the partial expression: 54*(-2*z**3 - 22*z**2 - 21)\nExpanding the part (-2*z**3 - 22*z**2 - 21) using the distributive property, and we got: -22*z**2*54 - 2*z**3*54 - 21*54\nReplacing 54*(-2*z**3 - 22*z**2 - 21) with -22*z**2*54 - 2*z**3*54 - 21*54 in the overall expression.\n#Step 3:\nCurrent expression: (56*z)*(-2*z**3 - 22*z**2 - 21) - 22*z**2*54 - 2*z**3*54 - 1134\nSimplifying the partial expression: (56*z)*(-2*z**3 - 22*z**2 - 21)\nExpanding the part (-2*z**3 - 22*z**2 - 21) using the distributive property, and we got: -1176*z + (56*z)*(-22*z**2) + (56*z)*(-2*z**3)\nReplacing (56*z)*(-2*z**3 - 22*z**2 - 21) with -1176*z + (56*z)*(-22*z**2) + (56*z)*(-2*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -21*56*z + (56*z)*(-22*z**2) + (56*z)*(-2*z**3) - 22*z**2*54 - 2*z**3*54 - 1134\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-22*z**2)*54 = -1188*z**2\n (-22*z**2)*(56*z) = -1232*z**3\n (-2*z**3)*54 = -108*z**3\n (-2*z**3)*(56*z) = -112*z**4\n -21*56*z = -1176*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -112*z**4 - 1232*z**3 - 108*z**3 - 1188*z**2 - 1176*z - 1134\nCombining like terms, got -112*z**4 - 1340*z**3 - 1188*z**2 - 1176*z - 1134\n#Step 6:\nCurrent expression: -112*z**4 - 1340*z**3 - 1188*z**2 - 1176*z - 1134\nNo more calculations needed.\n-112*z**4 - 1340*z**3 - 1188*z**2 - 1176*z - 1134", "generated_answer": "-112*z**4 - 1340*z**3 - 1188*z**2 - 1176*z - 1134", "step_length": 6} {"cot_id": "a469ec42ac5023ab5949f127557db1cc625f58dca30ba10ac9853488d9116dfd", "datapoint": {"question": "Calculate the following: (37 - 18*y**3)*(25*y**2 - 39*y + 16)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-450*y**5 + 702*y**4 - 288*y**3 + 925*y**2 - 1443*y + 592", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2164, "polynomial_expr": "(37 - 18*y**3)*(25*y**2 - 39*y + 16)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (37 - 18*y**3)*(25*y**2 - 39*y + 16)\nExpanding the part (37 - 18*y**3) using the distributive property, and we got: (-18*y**3)*(25*y**2 - 39*y + 16) + 37*(25*y**2 - 39*y + 16)\n#Step 2:\nCurrent expression: (-18*y**3)*(25*y**2 - 39*y + 16) + 37*(25*y**2 - 39*y + 16)\nSimplifying the partial expression: 37*(25*y**2 - 39*y + 16)\nExpanding the part (25*y**2 - 39*y + 16) using the distributive property, and we got: -39*y*37 + (25*y**2)*37 + 16*37\nReplacing 37*(25*y**2 - 39*y + 16) with -39*y*37 + (25*y**2)*37 + 16*37 in the overall expression.\n#Step 3:\nCurrent expression: -39*y*37 + (25*y**2)*37 + (-18*y**3)*(25*y**2 - 39*y + 16) + 592\nSimplifying the partial expression: (-18*y**3)*(25*y**2 - 39*y + 16)\nExpanding the part (25*y**2 - 39*y + 16) using the distributive property, and we got: (-39*y)*(-18*y**3) + 16*(-18*y**3) + (25*y**2)*(-18*y**3)\nReplacing (-18*y**3)*(25*y**2 - 39*y + 16) with (-39*y)*(-18*y**3) + 16*(-18*y**3) + (25*y**2)*(-18*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-39*y)*(-18*y**3) - 39*y*37 + 16*(-18)*y**3 + (25*y**2)*(-18*y**3) + (25*y**2)*37 + 592\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-39*y)*37 = -1443*y\n (-39*y)*(-18*y**3) = 702*y**4\n (25*y**2)*37 = 925*y**2\n (25*y**2)*(-18*y**3) = -450*y**5\n 16*-18*y**3 = -288*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -450*y**5 + 702*y**4 - 288*y**3 + 925*y**2 - 1443*y + 592\nNo more calculations needed.\n-450*y**5 + 702*y**4 - 288*y**3 + 925*y**2 - 1443*y + 592", "generated_answer": "-450*y**5 + 702*y**4 - 288*y**3 + 925*y**2 - 1443*y + 592", "step_length": 5} {"cot_id": "1061a296400e31ef39503bddeb7577bc5c124e2c2980578d116ed818f69c6719", "datapoint": {"question": "Simplify this expression: (34 - 38*z**3)*(27*z**3 + 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1026*z**6 - 412*z**3 + 1190", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2165, "polynomial_expr": "(34 - 38*z**3)*(27*z**3 + 35)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (34 - 38*z**3)*(27*z**3 + 35)\nExpanding the part (34 - 38*z**3) using the distributive property, and we got: (-38*z**3)*(27*z**3 + 35) + 34*(27*z**3 + 35)\n#Step 2:\nCurrent expression: (-38*z**3)*(27*z**3 + 35) + 34*(27*z**3 + 35)\nSimplifying the partial expression: 34*(27*z**3 + 35)\nExpanding the part (27*z**3 + 35) using the distributive property, and we got: (27*z**3)*34 + 35*34\nReplacing 34*(27*z**3 + 35) with (27*z**3)*34 + 35*34 in the overall expression.\n#Step 3:\nCurrent expression: (-38*z**3)*(27*z**3 + 35) + (27*z**3)*34 + 1190\nSimplifying the partial expression: (-38*z**3)*(27*z**3 + 35)\nExpanding the part (27*z**3 + 35) using the distributive property, and we got: 35*(-38*z**3) + (-38*z**3)*(27*z**3)\nReplacing (-38*z**3)*(27*z**3 + 35) with 35*(-38*z**3) + (-38*z**3)*(27*z**3) in the overall expression.\n#Step 4:\nCurrent expression: 35*(-38)*z**3 + (-38*z**3)*(27*z**3) + (27*z**3)*34 + 1190\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (27*z**3)*34 = 918*z**3\n (27*z**3)*(-38*z**3) = -1026*z**6\n 35*-38*z**3 = -1330*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1026*z**6 - 1330*z**3 + 918*z**3 + 1190\nCombining like terms, got -1026*z**6 - 412*z**3 + 1190\n#Step 6:\nCurrent expression: -1026*z**6 - 412*z**3 + 1190\nNo more calculations needed.\n-1026*z**6 - 412*z**3 + 1190", "generated_answer": "-1026*z**6 - 412*z**3 + 1190", "step_length": 6} {"cot_id": "3536d97a375a58440e4df224a4ccb22d3d4af497e9e16b8ddd455932595d6d3e", "datapoint": {"question": "Calculate the following: (-2*x**3 - 46*x)*(14*x**3 + 4)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-28*x**6 - 644*x**4 - 8*x**3 - 184*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2166, "polynomial_expr": "(-2*x**3 - 46*x)*(14*x**3 + 4)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-2*x**3 - 46*x)*(14*x**3 + 4)\nExpanding the part (14*x**3 + 4) using the distributive property, and we got: (14*x**3)*(-2*x**3 - 46*x) + 4*(-2*x**3 - 46*x)\n#Step 2:\nCurrent expression: (14*x**3)*(-2*x**3 - 46*x) + 4*(-2*x**3 - 46*x)\nSimplifying the partial expression: 4*(-2*x**3 - 46*x)\nExpanding the part (-2*x**3 - 46*x) using the distributive property, and we got: -46*x*4 - 2*x**3*4\nReplacing 4*(-2*x**3 - 46*x) with -46*x*4 - 2*x**3*4 in the overall expression.\n#Step 3:\nCurrent expression: -46*x*4 - 2*x**3*4 + (14*x**3)*(-2*x**3 - 46*x)\nSimplifying the partial expression: (14*x**3)*(-2*x**3 - 46*x)\nExpanding the part (-2*x**3 - 46*x) using the distributive property, and we got: (-46*x)*(14*x**3) + (-2*x**3)*(14*x**3)\nReplacing (14*x**3)*(-2*x**3 - 46*x) with (-46*x)*(14*x**3) + (-2*x**3)*(14*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-46*x)*(14*x**3) - 46*x*4 + (-2*x**3)*(14*x**3) - 2*x**3*4\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-46*x)*4 = -184*x\n (-46*x)*(14*x**3) = -644*x**4\n (-2*x**3)*4 = -8*x**3\n (-2*x**3)*(14*x**3) = -28*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -28*x**6 - 644*x**4 - 8*x**3 - 184*x\nNo more calculations needed.\n-28*x**6 - 644*x**4 - 8*x**3 - 184*x", "generated_answer": "-28*x**6 - 644*x**4 - 8*x**3 - 184*x", "step_length": 5} {"cot_id": "4546e436830a5fd99632ed39d643bc459ac99aa68cf127a5c93f8331748cad8c", "datapoint": {"question": "Calculate the following: (7 - 15*x**2)*(22 - 12*x**3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "180*x**5 - 84*x**3 - 330*x**2 + 154", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2167, "polynomial_expr": "(7 - 15*x**2)*(22 - 12*x**3)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (7 - 15*x**2)*(22 - 12*x**3)\nExpanding the part (7 - 15*x**2) using the distributive property, and we got: (-15*x**2)*(22 - 12*x**3) + 7*(22 - 12*x**3)\n#Step 2:\nCurrent expression: (-15*x**2)*(22 - 12*x**3) + 7*(22 - 12*x**3)\nSimplifying the partial expression: 7*(22 - 12*x**3)\nExpanding the part (22 - 12*x**3) using the distributive property, and we got: -12*x**3*7 + 22*7\nReplacing 7*(22 - 12*x**3) with -12*x**3*7 + 22*7 in the overall expression.\n#Step 3:\nCurrent expression: (-15*x**2)*(22 - 12*x**3) - 12*x**3*7 + 154\nSimplifying the partial expression: (-15*x**2)*(22 - 12*x**3)\nExpanding the part (22 - 12*x**3) using the distributive property, and we got: 22*(-15*x**2) + (-15*x**2)*(-12*x**3)\nReplacing (-15*x**2)*(22 - 12*x**3) with 22*(-15*x**2) + (-15*x**2)*(-12*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 22*(-15)*x**2 + (-15*x**2)*(-12*x**3) - 12*x**3*7 + 154\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-12*x**3)*7 = -84*x**3\n (-12*x**3)*(-15*x**2) = 180*x**5\n 22*-15*x**2 = -330*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 180*x**5 - 84*x**3 - 330*x**2 + 154\nNo more calculations needed.\n180*x**5 - 84*x**3 - 330*x**2 + 154", "generated_answer": "180*x**5 - 84*x**3 - 330*x**2 + 154", "step_length": 5} {"cot_id": "3fff64a2f5ad5c72b01b1639e55966dae25f5223008f815dd3e115df48125f47", "datapoint": {"question": "Simplify this expression: 1470 - 1078*z\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1470 - 1078*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2168, "polynomial_expr": "1470 - 1078*z", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 1470 - 1078*z\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 1470 - 1078*z\nNo more calculations needed.\n1470 - 1078*z", "generated_answer": "1470 - 1078*z", "step_length": 2} {"cot_id": "f6bad03e61b02ec657feab774916471b339d3458a92e698b19c15495cd5f8e75", "datapoint": {"question": "Simplify this expression: (-9*z**2 - 30*z + 56)*(-8*z**3 - z**2 + 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "72*z**5 + 249*z**4 - 418*z**3 - 65*z**2 - 30*z + 56", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2169, "polynomial_expr": "(-9*z**2 - 30*z + 56)*(-8*z**3 - z**2 + 1)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-9*z**2 - 30*z + 56)*(-8*z**3 - z**2 + 1)\nExpanding the part (-8*z**3 - z**2 + 1) using the distributive property, and we got: (-z**2)*(-9*z**2 - 30*z + 56) + (-8*z**3)*(-9*z**2 - 30*z + 56) + 1*(-9*z**2 - 30*z + 56)\n#Step 2:\nCurrent expression: (-z**2)*(-9*z**2 - 30*z + 56) + (-8*z**3)*(-9*z**2 - 30*z + 56) + 1*(-9*z**2 - 30*z + 56)\nSimplifying the partial expression: 1*(-9*z**2 - 30*z + 56)\nExpanding the part (-9*z**2 - 30*z + 56) using the distributive property, and we got: -30*z*1 - 9*z**2*1 + 56*1\nReplacing 1*(-9*z**2 - 30*z + 56) with -30*z*1 - 9*z**2*1 + 56*1 in the overall expression.\n#Step 3:\nCurrent expression: -30*z*1 - 9*z**2*1 + (-z**2)*(-9*z**2 - 30*z + 56) + (-8*z**3)*(-9*z**2 - 30*z + 56) + 56\nSimplifying the partial expression: (-z**2)*(-9*z**2 - 30*z + 56)\nExpanding the part (-9*z**2 - 30*z + 56) using the distributive property, and we got: (-30*z)*(-z**2) + 56*(-z**2) + (-9*z**2)*(-z**2)\nReplacing (-z**2)*(-9*z**2 - 30*z + 56) with (-30*z)*(-z**2) + 56*(-z**2) + (-9*z**2)*(-z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-30*z)*(-z**2) - 30*z*1 + 56*(-1)*z**2 + (-9*z**2)*(-z**2) - 9*z**2*1 + (-8*z**3)*(-9*z**2 - 30*z + 56) + 56\nSimplifying the partial expression: (-8*z**3)*(-9*z**2 - 30*z + 56)\nExpanding the part (-9*z**2 - 30*z + 56) using the distributive property, and we got: (-30*z)*(-8*z**3) + 56*(-8*z**3) + (-9*z**2)*(-8*z**3)\nReplacing (-8*z**3)*(-9*z**2 - 30*z + 56) with (-30*z)*(-8*z**3) + 56*(-8*z**3) + (-9*z**2)*(-8*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-30*z)*(-z**2) + (-30*z)*(-8*z**3) - 30*z*1 + 56*(-8)*z**3 + 56*(-1)*z**2 + (-9*z**2)*(-z**2) + (-9*z**2)*(-8*z**3) - 9*z**2*1 + 56\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-30*z)*1 = -30*z\n (-30*z)*(-z**2) = 30*z**3\n (-30*z)*(-8*z**3) = 240*z**4\n (-9*z**2)*1 = -9*z**2\n (-9*z**2)*(-z**2) = 9*z**4\n (-9*z**2)*(-8*z**3) = 72*z**5\n 56*-1*z**2 = -56*z**2\n 56*-8*z**3 = -448*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 72*z**5 + 9*z**4 + 240*z**4 - 448*z**3 + 30*z**3 - 56*z**2 - 9*z**2 - 30*z + 56\nCombining like terms, got 72*z**5 + 249*z**4 - 418*z**3 - 65*z**2 - 30*z + 56\n#Step 7:\nCurrent expression: 72*z**5 + 249*z**4 - 418*z**3 - 65*z**2 - 30*z + 56\nNo more calculations needed.\n72*z**5 + 249*z**4 - 418*z**3 - 65*z**2 - 30*z + 56", "generated_answer": "72*z**5 + 249*z**4 - 418*z**3 - 65*z**2 - 30*z + 56", "step_length": 7} {"cot_id": "276c602cf26fcda554a49974e89e024f2d65fb41f593e4caf25fc55a2320907f", "datapoint": {"question": "Calculate the following: (5*z**2 + 28*z)*(62*z**3 - 6*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "310*z**5 + 1706*z**4 - 168*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2170, "polynomial_expr": "(5*z**2 + 28*z)*(62*z**3 - 6*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (5*z**2 + 28*z)*(62*z**3 - 6*z**2)\nExpanding the part (62*z**3 - 6*z**2) using the distributive property, and we got: (-6*z**2)*(5*z**2 + 28*z) + (62*z**3)*(5*z**2 + 28*z)\n#Step 2:\nCurrent expression: (-6*z**2)*(5*z**2 + 28*z) + (62*z**3)*(5*z**2 + 28*z)\nSimplifying the partial expression: (-6*z**2)*(5*z**2 + 28*z)\nExpanding the part (5*z**2 + 28*z) using the distributive property, and we got: (28*z)*(-6*z**2) + (-6*z**2)*(5*z**2)\nReplacing (-6*z**2)*(5*z**2 + 28*z) with (28*z)*(-6*z**2) + (-6*z**2)*(5*z**2) in the overall expression.\n#Step 3:\nCurrent expression: (28*z)*(-6*z**2) + (-6*z**2)*(5*z**2) + (62*z**3)*(5*z**2 + 28*z)\nSimplifying the partial expression: (62*z**3)*(5*z**2 + 28*z)\nExpanding the part (5*z**2 + 28*z) using the distributive property, and we got: (28*z)*(62*z**3) + (5*z**2)*(62*z**3)\nReplacing (62*z**3)*(5*z**2 + 28*z) with (28*z)*(62*z**3) + (5*z**2)*(62*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (28*z)*(-6*z**2) + (28*z)*(62*z**3) + (-6*z**2)*(5*z**2) + (5*z**2)*(62*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (5*z**2)*(-6*z**2) = -30*z**4\n (5*z**2)*(62*z**3) = 310*z**5\n (28*z)*(-6*z**2) = -168*z**3\n (28*z)*(62*z**3) = 1736*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 310*z**5 - 30*z**4 + 1736*z**4 - 168*z**3\nCombining like terms, got 310*z**5 + 1706*z**4 - 168*z**3\n#Step 6:\nCurrent expression: 310*z**5 + 1706*z**4 - 168*z**3\nNo more calculations needed.\n310*z**5 + 1706*z**4 - 168*z**3", "generated_answer": "310*z**5 + 1706*z**4 - 168*z**3", "step_length": 6} {"cot_id": "0d71593e1fcfa24eac163964d05a3866fdf140a962cca9d09c63c9a0a26b35d1", "datapoint": {"question": "Calculate the following: 37*y**2*(-30*y**3 - 21)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1110*y**5 - 777*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2171, "polynomial_expr": "37*y**2*(-30*y**3 - 21)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 37*y**2*(-30*y**3 - 21)\nExpanding the part (-30*y**3 - 21) using the distributive property, and we got: -777*y**2 + (37*y**2)*(-30*y**3)\n#Step 2:\nCurrent expression: -777*y**2 + (37*y**2)*(-30*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -21*(37*y**2) = -777*y**2\n (-30*y**3)*(37*y**2) = -1110*y**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -1110*y**5 - 777*y**2\nNo more calculations needed.\n-1110*y**5 - 777*y**2", "generated_answer": "-1110*y**5 - 777*y**2", "step_length": 3} {"cot_id": "06c4ad2648eaa54727224c82562ac012c7cd11493334aa9400a492463c62dc01", "datapoint": {"question": "Calculate the following: (16*y**2 - 29)*(74*y**3 + 61*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1184*y**5 - 1170*y**3 - 1769*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2172, "polynomial_expr": "(16*y**2 - 29)*(74*y**3 + 61*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (16*y**2 - 29)*(74*y**3 + 61*y)\nExpanding the part (16*y**2 - 29) using the distributive property, and we got: (16*y**2)*(74*y**3 + 61*y) - 29*(74*y**3 + 61*y)\n#Step 2:\nCurrent expression: (16*y**2)*(74*y**3 + 61*y) - 29*(74*y**3 + 61*y)\nSimplifying the partial expression: -29*(74*y**3 + 61*y)\nExpanding the part (74*y**3 + 61*y) using the distributive property, and we got: (61*y)*(-29) + (74*y**3)*(-29)\nReplacing -29*(74*y**3 + 61*y) with (61*y)*(-29) + (74*y**3)*(-29) in the overall expression.\n#Step 3:\nCurrent expression: (61*y)*(-29) + (16*y**2)*(74*y**3 + 61*y) + (74*y**3)*(-29)\nSimplifying the partial expression: (16*y**2)*(74*y**3 + 61*y)\nExpanding the part (74*y**3 + 61*y) using the distributive property, and we got: (61*y)*(16*y**2) + (16*y**2)*(74*y**3)\nReplacing (16*y**2)*(74*y**3 + 61*y) with (61*y)*(16*y**2) + (16*y**2)*(74*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (61*y)*(16*y**2) + (61*y)*(-29) + (16*y**2)*(74*y**3) + (74*y**3)*(-29)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (61*y)*-29 = -1769*y\n (61*y)*(16*y**2) = 976*y**3\n (74*y**3)*-29 = -2146*y**3\n (74*y**3)*(16*y**2) = 1184*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1184*y**5 - 2146*y**3 + 976*y**3 - 1769*y\nCombining like terms, got 1184*y**5 - 1170*y**3 - 1769*y\n#Step 6:\nCurrent expression: 1184*y**5 - 1170*y**3 - 1769*y\nNo more calculations needed.\n1184*y**5 - 1170*y**3 - 1769*y", "generated_answer": "1184*y**5 - 1170*y**3 - 1769*y", "step_length": 6} {"cot_id": "680c66a434e43ca706c29a699e4f0deec55ec17d368a2b4bf3361c92808458e8", "datapoint": {"question": "Calculate the following: (-28*x**3 - 19*x**2)*(27*x**3 + 8*x + 51)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-756*x**6 - 513*x**5 - 224*x**4 - 1580*x**3 - 969*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2173, "polynomial_expr": "(-28*x**3 - 19*x**2)*(27*x**3 + 8*x + 51)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-28*x**3 - 19*x**2)*(27*x**3 + 8*x + 51)\nExpanding the part (-28*x**3 - 19*x**2) using the distributive property, and we got: (-19*x**2)*(27*x**3 + 8*x + 51) + (-28*x**3)*(27*x**3 + 8*x + 51)\n#Step 2:\nCurrent expression: (-19*x**2)*(27*x**3 + 8*x + 51) + (-28*x**3)*(27*x**3 + 8*x + 51)\nSimplifying the partial expression: (-28*x**3)*(27*x**3 + 8*x + 51)\nExpanding the part (27*x**3 + 8*x + 51) using the distributive property, and we got: 51*(-28*x**3) + (8*x)*(-28*x**3) + (-28*x**3)*(27*x**3)\nReplacing (-28*x**3)*(27*x**3 + 8*x + 51) with 51*(-28*x**3) + (8*x)*(-28*x**3) + (-28*x**3)*(27*x**3) in the overall expression.\n#Step 3:\nCurrent expression: 51*(-28)*x**3 + (8*x)*(-28*x**3) + (-19*x**2)*(27*x**3 + 8*x + 51) + (-28*x**3)*(27*x**3)\nSimplifying the partial expression: (-19*x**2)*(27*x**3 + 8*x + 51)\nExpanding the part (27*x**3 + 8*x + 51) using the distributive property, and we got: 51*(-19*x**2) + (8*x)*(-19*x**2) + (-19*x**2)*(27*x**3)\nReplacing (-19*x**2)*(27*x**3 + 8*x + 51) with 51*(-19*x**2) + (8*x)*(-19*x**2) + (-19*x**2)*(27*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 51*(-28)*x**3 + 51*(-19)*x**2 + (8*x)*(-19*x**2) + (8*x)*(-28*x**3) + (-19*x**2)*(27*x**3) + (-28*x**3)*(27*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (8*x)*(-28*x**3) = -224*x**4\n (8*x)*(-19*x**2) = -152*x**3\n (27*x**3)*(-28*x**3) = -756*x**6\n (27*x**3)*(-19*x**2) = -513*x**5\n 51*-28*x**3 = -1428*x**3\n 51*-19*x**2 = -969*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -756*x**6 - 513*x**5 - 224*x**4 - 1428*x**3 - 152*x**3 - 969*x**2\nCombining like terms, got -756*x**6 - 513*x**5 - 224*x**4 - 1580*x**3 - 969*x**2\n#Step 6:\nCurrent expression: -756*x**6 - 513*x**5 - 224*x**4 - 1580*x**3 - 969*x**2\nNo more calculations needed.\n-756*x**6 - 513*x**5 - 224*x**4 - 1580*x**3 - 969*x**2", "generated_answer": "-756*x**6 - 513*x**5 - 224*x**4 - 1580*x**3 - 969*x**2", "step_length": 6} {"cot_id": "56871aab3125bc3a40f04e17225b154f556563783aa7862f51e08781ecd4b96d", "datapoint": {"question": "Simplify this expression: (9*z**2 + 54*z)*(36*z**2 + 27)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "324*z**4 + 1944*z**3 + 243*z**2 + 1458*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2174, "polynomial_expr": "(9*z**2 + 54*z)*(36*z**2 + 27)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (9*z**2 + 54*z)*(36*z**2 + 27)\nExpanding the part (36*z**2 + 27) using the distributive property, and we got: (36*z**2)*(9*z**2 + 54*z) + 27*(9*z**2 + 54*z)\n#Step 2:\nCurrent expression: (36*z**2)*(9*z**2 + 54*z) + 27*(9*z**2 + 54*z)\nSimplifying the partial expression: 27*(9*z**2 + 54*z)\nExpanding the part (9*z**2 + 54*z) using the distributive property, and we got: (54*z)*27 + (9*z**2)*27\nReplacing 27*(9*z**2 + 54*z) with (54*z)*27 + (9*z**2)*27 in the overall expression.\n#Step 3:\nCurrent expression: (54*z)*27 + (9*z**2)*27 + (36*z**2)*(9*z**2 + 54*z)\nSimplifying the partial expression: (36*z**2)*(9*z**2 + 54*z)\nExpanding the part (9*z**2 + 54*z) using the distributive property, and we got: (54*z)*(36*z**2) + (9*z**2)*(36*z**2)\nReplacing (36*z**2)*(9*z**2 + 54*z) with (54*z)*(36*z**2) + (9*z**2)*(36*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (54*z)*(36*z**2) + (54*z)*27 + (9*z**2)*(36*z**2) + (9*z**2)*27\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (9*z**2)*27 = 243*z**2\n (9*z**2)*(36*z**2) = 324*z**4\n (54*z)*27 = 1458*z\n (54*z)*(36*z**2) = 1944*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 324*z**4 + 1944*z**3 + 243*z**2 + 1458*z\nNo more calculations needed.\n324*z**4 + 1944*z**3 + 243*z**2 + 1458*z", "generated_answer": "324*z**4 + 1944*z**3 + 243*z**2 + 1458*z", "step_length": 5} {"cot_id": "ad025f6bc3553e227707bd234eb4683e23f2d9141043a9b5011ef389afc912be", "datapoint": {"question": "Calculate the following: (49 - 9*x**2)*(22*x**2 + 13*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-198*x**4 - 117*x**3 + 1078*x**2 + 637*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2175, "polynomial_expr": "(49 - 9*x**2)*(22*x**2 + 13*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (49 - 9*x**2)*(22*x**2 + 13*x)\nExpanding the part (49 - 9*x**2) using the distributive property, and we got: (-9*x**2)*(22*x**2 + 13*x) + 49*(22*x**2 + 13*x)\n#Step 2:\nCurrent expression: (-9*x**2)*(22*x**2 + 13*x) + 49*(22*x**2 + 13*x)\nSimplifying the partial expression: 49*(22*x**2 + 13*x)\nExpanding the part (22*x**2 + 13*x) using the distributive property, and we got: (13*x)*49 + (22*x**2)*49\nReplacing 49*(22*x**2 + 13*x) with (13*x)*49 + (22*x**2)*49 in the overall expression.\n#Step 3:\nCurrent expression: (13*x)*49 + (-9*x**2)*(22*x**2 + 13*x) + (22*x**2)*49\nSimplifying the partial expression: (-9*x**2)*(22*x**2 + 13*x)\nExpanding the part (22*x**2 + 13*x) using the distributive property, and we got: (13*x)*(-9*x**2) + (-9*x**2)*(22*x**2)\nReplacing (-9*x**2)*(22*x**2 + 13*x) with (13*x)*(-9*x**2) + (-9*x**2)*(22*x**2) in the overall expression.\n#Step 4:\nCurrent expression: (13*x)*(-9*x**2) + (13*x)*49 + (-9*x**2)*(22*x**2) + (22*x**2)*49\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (13*x)*49 = 637*x\n (13*x)*(-9*x**2) = -117*x**3\n (22*x**2)*49 = 1078*x**2\n (22*x**2)*(-9*x**2) = -198*x**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -198*x**4 - 117*x**3 + 1078*x**2 + 637*x\nNo more calculations needed.\n-198*x**4 - 117*x**3 + 1078*x**2 + 637*x", "generated_answer": "-198*x**4 - 117*x**3 + 1078*x**2 + 637*x", "step_length": 5} {"cot_id": "f505f6e6729ac8ca80e03576771ddff0f305ec11a413dfa41b179683ff9f3bb6", "datapoint": {"question": "Calculate the following: (27*x**3 - 10)*(-42*x**3 + 36*x**2 + 50*x + 9)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1134*x**6 + 972*x**5 + 1350*x**4 + 663*x**3 - 360*x**2 - 500*x - 90", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2176, "polynomial_expr": "(27*x**3 - 10)*(-42*x**3 + 36*x**2 + 50*x + 9)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*x**3 - 10)*(-42*x**3 + 36*x**2 + 50*x + 9)\nExpanding the part (27*x**3 - 10) using the distributive property, and we got: (27*x**3)*(-42*x**3 + 36*x**2 + 50*x + 9) - 10*(-42*x**3 + 36*x**2 + 50*x + 9)\n#Step 2:\nCurrent expression: (27*x**3)*(-42*x**3 + 36*x**2 + 50*x + 9) - 10*(-42*x**3 + 36*x**2 + 50*x + 9)\nSimplifying the partial expression: -10*(-42*x**3 + 36*x**2 + 50*x + 9)\nExpanding the part (-42*x**3 + 36*x**2 + 50*x + 9) using the distributive property, and we got: (50*x)*(-10) + (36*x**2)*(-10) - 42*x**3*(-10) + 9*(-10)\nReplacing -10*(-42*x**3 + 36*x**2 + 50*x + 9) with (50*x)*(-10) + (36*x**2)*(-10) - 42*x**3*(-10) + 9*(-10) in the overall expression.\n#Step 3:\nCurrent expression: (50*x)*(-10) + (36*x**2)*(-10) - 42*x**3*(-10) + (27*x**3)*(-42*x**3 + 36*x**2 + 50*x + 9) - 90\nSimplifying the partial expression: (27*x**3)*(-42*x**3 + 36*x**2 + 50*x + 9)\nExpanding the part (-42*x**3 + 36*x**2 + 50*x + 9) using the distributive property, and we got: 9*(27*x**3) + (50*x)*(27*x**3) + (36*x**2)*(27*x**3) + (-42*x**3)*(27*x**3)\nReplacing (27*x**3)*(-42*x**3 + 36*x**2 + 50*x + 9) with 9*(27*x**3) + (50*x)*(27*x**3) + (36*x**2)*(27*x**3) + (-42*x**3)*(27*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 9*27*x**3 + (50*x)*(27*x**3) + (50*x)*(-10) + (36*x**2)*(27*x**3) + (36*x**2)*(-10) + (-42*x**3)*(27*x**3) - 42*x**3*(-10) - 90\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*x**3)*-10 = 420*x**3\n (-42*x**3)*(27*x**3) = -1134*x**6\n (36*x**2)*-10 = -360*x**2\n (36*x**2)*(27*x**3) = 972*x**5\n (50*x)*-10 = -500*x\n (50*x)*(27*x**3) = 1350*x**4\n 9*27*x**3 = 243*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1134*x**6 + 972*x**5 + 1350*x**4 + 243*x**3 + 420*x**3 - 360*x**2 - 500*x - 90\nCombining like terms, got -1134*x**6 + 972*x**5 + 1350*x**4 + 663*x**3 - 360*x**2 - 500*x - 90\n#Step 6:\nCurrent expression: -1134*x**6 + 972*x**5 + 1350*x**4 + 663*x**3 - 360*x**2 - 500*x - 90\nNo more calculations needed.\n-1134*x**6 + 972*x**5 + 1350*x**4 + 663*x**3 - 360*x**2 - 500*x - 90", "generated_answer": "-1134*x**6 + 972*x**5 + 1350*x**4 + 663*x**3 - 360*x**2 - 500*x - 90", "step_length": 6} {"cot_id": "b6a333c8ce1759dc369544326b5c071e94e03343a61f10fa7c1e9721c083b5a2", "datapoint": {"question": "Calculate the following: (-46*z**3 - 11*z)*(-45*z**3 + 42*z**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "2070*z**6 - 1932*z**5 + 495*z**4 - 462*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2177, "polynomial_expr": "(-46*z**3 - 11*z)*(-45*z**3 + 42*z**2)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-46*z**3 - 11*z)*(-45*z**3 + 42*z**2)\nExpanding the part (-46*z**3 - 11*z) using the distributive property, and we got: (-11*z)*(-45*z**3 + 42*z**2) + (-46*z**3)*(-45*z**3 + 42*z**2)\n#Step 2:\nCurrent expression: (-11*z)*(-45*z**3 + 42*z**2) + (-46*z**3)*(-45*z**3 + 42*z**2)\nSimplifying the partial expression: (-46*z**3)*(-45*z**3 + 42*z**2)\nExpanding the part (-45*z**3 + 42*z**2) using the distributive property, and we got: (42*z**2)*(-46*z**3) + (-46*z**3)*(-45*z**3)\nReplacing (-46*z**3)*(-45*z**3 + 42*z**2) with (42*z**2)*(-46*z**3) + (-46*z**3)*(-45*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-11*z)*(-45*z**3 + 42*z**2) + (42*z**2)*(-46*z**3) + (-46*z**3)*(-45*z**3)\nSimplifying the partial expression: (-11*z)*(-45*z**3 + 42*z**2)\nExpanding the part (-45*z**3 + 42*z**2) using the distributive property, and we got: (-11*z)*(42*z**2) + (-11*z)*(-45*z**3)\nReplacing (-11*z)*(-45*z**3 + 42*z**2) with (-11*z)*(42*z**2) + (-11*z)*(-45*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-11*z)*(42*z**2) + (-11*z)*(-45*z**3) + (42*z**2)*(-46*z**3) + (-46*z**3)*(-45*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-45*z**3)*(-46*z**3) = 2070*z**6\n (-45*z**3)*(-11*z) = 495*z**4\n (42*z**2)*(-46*z**3) = -1932*z**5\n (42*z**2)*(-11*z) = -462*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 2070*z**6 - 1932*z**5 + 495*z**4 - 462*z**3\nNo more calculations needed.\n2070*z**6 - 1932*z**5 + 495*z**4 - 462*z**3", "generated_answer": "2070*z**6 - 1932*z**5 + 495*z**4 - 462*z**3", "step_length": 5} {"cot_id": "b742190c200daefbcb2d5a8398bf00a65888cf8da43a15a848d4388a5f695d9a", "datapoint": {"question": "Calculate the following: -43*z**2*(22*z**3 - 34*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-946*z**5 + 1462*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2178, "polynomial_expr": "-43*z**2*(22*z**3 - 34*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -43*z**2*(22*z**3 - 34*z)\nExpanding the part (22*z**3 - 34*z) using the distributive property, and we got: (-34*z)*(-43*z**2) + (-43*z**2)*(22*z**3)\n#Step 2:\nCurrent expression: (-34*z)*(-43*z**2) + (-43*z**2)*(22*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-34*z)*(-43*z**2) = 1462*z**3\n (22*z**3)*(-43*z**2) = -946*z**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -946*z**5 + 1462*z**3\nNo more calculations needed.\n-946*z**5 + 1462*z**3", "generated_answer": "-946*z**5 + 1462*z**3", "step_length": 3} {"cot_id": "2078dd6e30bb45942e51580ffbeed0665cba281a3aafd34bc11eb51a53897ad2", "datapoint": {"question": "Simplify this expression: (-31*z - 34)*(50*z**2 - 8*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1550*z**3 - 1452*z**2 + 272*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2179, "polynomial_expr": "(-31*z - 34)*(50*z**2 - 8*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-31*z - 34)*(50*z**2 - 8*z)\nExpanding the part (-31*z - 34) using the distributive property, and we got: (-31*z)*(50*z**2 - 8*z) - 34*(50*z**2 - 8*z)\n#Step 2:\nCurrent expression: (-31*z)*(50*z**2 - 8*z) - 34*(50*z**2 - 8*z)\nSimplifying the partial expression: -34*(50*z**2 - 8*z)\nExpanding the part (50*z**2 - 8*z) using the distributive property, and we got: -8*z*(-34) + (50*z**2)*(-34)\nReplacing -34*(50*z**2 - 8*z) with -8*z*(-34) + (50*z**2)*(-34) in the overall expression.\n#Step 3:\nCurrent expression: (-31*z)*(50*z**2 - 8*z) - 8*z*(-34) + (50*z**2)*(-34)\nSimplifying the partial expression: (-31*z)*(50*z**2 - 8*z)\nExpanding the part (50*z**2 - 8*z) using the distributive property, and we got: (-31*z)*(-8*z) + (-31*z)*(50*z**2)\nReplacing (-31*z)*(50*z**2 - 8*z) with (-31*z)*(-8*z) + (-31*z)*(50*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-31*z)*(-8*z) + (-31*z)*(50*z**2) - 8*z*(-34) + (50*z**2)*(-34)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-8*z)*-34 = 272*z\n (-8*z)*(-31*z) = 248*z**2\n (50*z**2)*-34 = -1700*z**2\n (50*z**2)*(-31*z) = -1550*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1550*z**3 - 1700*z**2 + 248*z**2 + 272*z\nCombining like terms, got -1550*z**3 - 1452*z**2 + 272*z\n#Step 6:\nCurrent expression: -1550*z**3 - 1452*z**2 + 272*z\nNo more calculations needed.\n-1550*z**3 - 1452*z**2 + 272*z", "generated_answer": "-1550*z**3 - 1452*z**2 + 272*z", "step_length": 6} {"cot_id": "997fce591af247f16001a0a4dafa488a832998182db72326930be751d6b96590", "datapoint": {"question": "Simplify this expression: (-9*x**2 - 6*x)*(-17*x**3 - 18*x + 3)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "153*x**5 + 102*x**4 + 162*x**3 + 81*x**2 - 18*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2180, "polynomial_expr": "(-9*x**2 - 6*x)*(-17*x**3 - 18*x + 3)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-9*x**2 - 6*x)*(-17*x**3 - 18*x + 3)\nExpanding the part (-9*x**2 - 6*x) using the distributive property, and we got: (-6*x)*(-17*x**3 - 18*x + 3) + (-9*x**2)*(-17*x**3 - 18*x + 3)\n#Step 2:\nCurrent expression: (-6*x)*(-17*x**3 - 18*x + 3) + (-9*x**2)*(-17*x**3 - 18*x + 3)\nSimplifying the partial expression: (-9*x**2)*(-17*x**3 - 18*x + 3)\nExpanding the part (-17*x**3 - 18*x + 3) using the distributive property, and we got: (-18*x)*(-9*x**2) + 3*(-9*x**2) + (-9*x**2)*(-17*x**3)\nReplacing (-9*x**2)*(-17*x**3 - 18*x + 3) with (-18*x)*(-9*x**2) + 3*(-9*x**2) + (-9*x**2)*(-17*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-18*x)*(-9*x**2) + (-6*x)*(-17*x**3 - 18*x + 3) + 3*(-9)*x**2 + (-9*x**2)*(-17*x**3)\nSimplifying the partial expression: (-6*x)*(-17*x**3 - 18*x + 3)\nExpanding the part (-17*x**3 - 18*x + 3) using the distributive property, and we got: (-18*x)*(-6*x) + (-6*x)*(-17*x**3) + 3*(-6*x)\nReplacing (-6*x)*(-17*x**3 - 18*x + 3) with (-18*x)*(-6*x) + (-6*x)*(-17*x**3) + 3*(-6*x) in the overall expression.\n#Step 4:\nCurrent expression: (-18*x)*(-6*x) + (-18*x)*(-9*x**2) + (-6*x)*(-17*x**3) + 3*(-9)*x**2 + 3*(-6)*x + (-9*x**2)*(-17*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-18*x)*(-9*x**2) = 162*x**3\n (-18*x)*(-6*x) = 108*x**2\n (-17*x**3)*(-9*x**2) = 153*x**5\n (-17*x**3)*(-6*x) = 102*x**4\n 3*-9*x**2 = -27*x**2\n 3*-6*x = -18*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 153*x**5 + 102*x**4 + 162*x**3 - 27*x**2 + 108*x**2 - 18*x\nCombining like terms, got 153*x**5 + 102*x**4 + 162*x**3 + 81*x**2 - 18*x\n#Step 6:\nCurrent expression: 153*x**5 + 102*x**4 + 162*x**3 + 81*x**2 - 18*x\nNo more calculations needed.\n153*x**5 + 102*x**4 + 162*x**3 + 81*x**2 - 18*x", "generated_answer": "153*x**5 + 102*x**4 + 162*x**3 + 81*x**2 - 18*x", "step_length": 6} {"cot_id": "d0c2fe1490c7bef6e3e1fbbcefdb6730ce4ad9a12b3ac8af2b03d49c29659a3a", "datapoint": {"question": "Calculate the following: (-74*z**2 + 17*z)*(44*z**2 - 31)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-3256*z**4 + 748*z**3 + 2294*z**2 - 527*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2181, "polynomial_expr": "(-74*z**2 + 17*z)*(44*z**2 - 31)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-74*z**2 + 17*z)*(44*z**2 - 31)\nExpanding the part (44*z**2 - 31) using the distributive property, and we got: (44*z**2)*(-74*z**2 + 17*z) - 31*(-74*z**2 + 17*z)\n#Step 2:\nCurrent expression: (44*z**2)*(-74*z**2 + 17*z) - 31*(-74*z**2 + 17*z)\nSimplifying the partial expression: -31*(-74*z**2 + 17*z)\nExpanding the part (-74*z**2 + 17*z) using the distributive property, and we got: (17*z)*(-31) - 74*z**2*(-31)\nReplacing -31*(-74*z**2 + 17*z) with (17*z)*(-31) - 74*z**2*(-31) in the overall expression.\n#Step 3:\nCurrent expression: (17*z)*(-31) - 74*z**2*(-31) + (44*z**2)*(-74*z**2 + 17*z)\nSimplifying the partial expression: (44*z**2)*(-74*z**2 + 17*z)\nExpanding the part (-74*z**2 + 17*z) using the distributive property, and we got: (17*z)*(44*z**2) + (-74*z**2)*(44*z**2)\nReplacing (44*z**2)*(-74*z**2 + 17*z) with (17*z)*(44*z**2) + (-74*z**2)*(44*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (17*z)*(44*z**2) + (17*z)*(-31) + (-74*z**2)*(44*z**2) - 74*z**2*(-31)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-74*z**2)*-31 = 2294*z**2\n (-74*z**2)*(44*z**2) = -3256*z**4\n (17*z)*-31 = -527*z\n (17*z)*(44*z**2) = 748*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -3256*z**4 + 748*z**3 + 2294*z**2 - 527*z\nNo more calculations needed.\n-3256*z**4 + 748*z**3 + 2294*z**2 - 527*z", "generated_answer": "-3256*z**4 + 748*z**3 + 2294*z**2 - 527*z", "step_length": 5} {"cot_id": "a8375d759e8fa699dd72f83241089f3ef8dbc0e78588f0cb7e0e26555979aec5", "datapoint": {"question": "Calculate the following: (34*z**2 + 1)*(48*z**2 + 1)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1632*z**4 + 82*z**2 + 1", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2182, "polynomial_expr": "(34*z**2 + 1)*(48*z**2 + 1)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (34*z**2 + 1)*(48*z**2 + 1)\nExpanding the part (34*z**2 + 1) using the distributive property, and we got: (34*z**2)*(48*z**2 + 1) + 1*(48*z**2 + 1)\n#Step 2:\nCurrent expression: (34*z**2)*(48*z**2 + 1) + 1*(48*z**2 + 1)\nSimplifying the partial expression: 1*(48*z**2 + 1)\nExpanding the part (48*z**2 + 1) using the distributive property, and we got: (48*z**2)*1 + 1*1\nReplacing 1*(48*z**2 + 1) with (48*z**2)*1 + 1*1 in the overall expression.\n#Step 3:\nCurrent expression: (34*z**2)*(48*z**2 + 1) + (48*z**2)*1 + 1\nSimplifying the partial expression: (34*z**2)*(48*z**2 + 1)\nExpanding the part (48*z**2 + 1) using the distributive property, and we got: 1*(34*z**2) + (34*z**2)*(48*z**2)\nReplacing (34*z**2)*(48*z**2 + 1) with 1*(34*z**2) + (34*z**2)*(48*z**2) in the overall expression.\n#Step 4:\nCurrent expression: 34*z**2 + (34*z**2)*(48*z**2) + (48*z**2)*1 + 1\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (48*z**2)*1 = 48*z**2\n (48*z**2)*(34*z**2) = 1632*z**4\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1632*z**4 + 34*z**2 + 48*z**2 + 1\nCombining like terms, got 1632*z**4 + 82*z**2 + 1\n#Step 6:\nCurrent expression: 1632*z**4 + 82*z**2 + 1\nNo more calculations needed.\n1632*z**4 + 82*z**2 + 1", "generated_answer": "1632*z**4 + 82*z**2 + 1", "step_length": 6} {"cot_id": "544a46ab95b4fe8909c00eb628450cefc3e45f727c20b0dac26a9f54a11bcc6f", "datapoint": {"question": "Calculate the following: (-18*x**3 + 22*x)*(-47*x**3 + 29*x**2 + 25*x)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "846*x**6 - 522*x**5 - 1484*x**4 + 638*x**3 + 550*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2183, "polynomial_expr": "(-18*x**3 + 22*x)*(-47*x**3 + 29*x**2 + 25*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-18*x**3 + 22*x)*(-47*x**3 + 29*x**2 + 25*x)\nExpanding the part (-18*x**3 + 22*x) using the distributive property, and we got: (22*x)*(-47*x**3 + 29*x**2 + 25*x) + (-18*x**3)*(-47*x**3 + 29*x**2 + 25*x)\n#Step 2:\nCurrent expression: (22*x)*(-47*x**3 + 29*x**2 + 25*x) + (-18*x**3)*(-47*x**3 + 29*x**2 + 25*x)\nSimplifying the partial expression: (-18*x**3)*(-47*x**3 + 29*x**2 + 25*x)\nExpanding the part (-47*x**3 + 29*x**2 + 25*x) using the distributive property, and we got: (25*x)*(-18*x**3) + (29*x**2)*(-18*x**3) + (-47*x**3)*(-18*x**3)\nReplacing (-18*x**3)*(-47*x**3 + 29*x**2 + 25*x) with (25*x)*(-18*x**3) + (29*x**2)*(-18*x**3) + (-47*x**3)*(-18*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (22*x)*(-47*x**3 + 29*x**2 + 25*x) + (25*x)*(-18*x**3) + (29*x**2)*(-18*x**3) + (-47*x**3)*(-18*x**3)\nSimplifying the partial expression: (22*x)*(-47*x**3 + 29*x**2 + 25*x)\nExpanding the part (-47*x**3 + 29*x**2 + 25*x) using the distributive property, and we got: (22*x)*(25*x) + (22*x)*(29*x**2) + (22*x)*(-47*x**3)\nReplacing (22*x)*(-47*x**3 + 29*x**2 + 25*x) with (22*x)*(25*x) + (22*x)*(29*x**2) + (22*x)*(-47*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (22*x)*(25*x) + (22*x)*(29*x**2) + (22*x)*(-47*x**3) + (25*x)*(-18*x**3) + (29*x**2)*(-18*x**3) + (-47*x**3)*(-18*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-47*x**3)*(-18*x**3) = 846*x**6\n (-47*x**3)*(22*x) = -1034*x**4\n (25*x)*(-18*x**3) = -450*x**4\n (25*x)*(22*x) = 550*x**2\n (29*x**2)*(-18*x**3) = -522*x**5\n (29*x**2)*(22*x) = 638*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 846*x**6 - 522*x**5 - 1034*x**4 - 450*x**4 + 638*x**3 + 550*x**2\nCombining like terms, got 846*x**6 - 522*x**5 - 1484*x**4 + 638*x**3 + 550*x**2\n#Step 6:\nCurrent expression: 846*x**6 - 522*x**5 - 1484*x**4 + 638*x**3 + 550*x**2\nNo more calculations needed.\n846*x**6 - 522*x**5 - 1484*x**4 + 638*x**3 + 550*x**2", "generated_answer": "846*x**6 - 522*x**5 - 1484*x**4 + 638*x**3 + 550*x**2", "step_length": 6} {"cot_id": "c33b0c49ee33fe6ad8f6fa3fd12bf52b43767acebaa39551d6ac6d98e7383e62", "datapoint": {"question": "Simplify this expression: (2*x**2 - 15)*(-48*x**3 - 48*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-96*x**5 - 96*x**4 + 720*x**3 + 720*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2184, "polynomial_expr": "(2*x**2 - 15)*(-48*x**3 - 48*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (2*x**2 - 15)*(-48*x**3 - 48*x**2)\nExpanding the part (2*x**2 - 15) using the distributive property, and we got: (2*x**2)*(-48*x**3 - 48*x**2) - 15*(-48*x**3 - 48*x**2)\n#Step 2:\nCurrent expression: (2*x**2)*(-48*x**3 - 48*x**2) - 15*(-48*x**3 - 48*x**2)\nSimplifying the partial expression: -15*(-48*x**3 - 48*x**2)\nExpanding the part (-48*x**3 - 48*x**2) using the distributive property, and we got: -48*x**2*(-15) - 48*x**3*(-15)\nReplacing -15*(-48*x**3 - 48*x**2) with -48*x**2*(-15) - 48*x**3*(-15) in the overall expression.\n#Step 3:\nCurrent expression: -48*x**2*(-15) + (2*x**2)*(-48*x**3 - 48*x**2) - 48*x**3*(-15)\nSimplifying the partial expression: (2*x**2)*(-48*x**3 - 48*x**2)\nExpanding the part (-48*x**3 - 48*x**2) using the distributive property, and we got: (-48*x**2)*(2*x**2) + (2*x**2)*(-48*x**3)\nReplacing (2*x**2)*(-48*x**3 - 48*x**2) with (-48*x**2)*(2*x**2) + (2*x**2)*(-48*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-48*x**2)*(2*x**2) - 48*x**2*(-15) + (2*x**2)*(-48*x**3) - 48*x**3*(-15)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*x**2)*-15 = 720*x**2\n (-48*x**2)*(2*x**2) = -96*x**4\n (-48*x**3)*-15 = 720*x**3\n (-48*x**3)*(2*x**2) = -96*x**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -96*x**5 - 96*x**4 + 720*x**3 + 720*x**2\nNo more calculations needed.\n-96*x**5 - 96*x**4 + 720*x**3 + 720*x**2", "generated_answer": "-96*x**5 - 96*x**4 + 720*x**3 + 720*x**2", "step_length": 5} {"cot_id": "e2d0035a4e5ad51b5813d7d6322f5bb49bd288f67ac0ef7d68a6caac40447dfa", "datapoint": {"question": "Simplify this expression: 1127*z**3 + 392*z - 2352\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1127*z**3 + 392*z - 2352", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2185, "polynomial_expr": "1127*z**3 + 392*z - 2352", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 1127*z**3 + 392*z - 2352\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: 1127*z**3 + 392*z - 2352\nNo more calculations needed.\n1127*z**3 + 392*z - 2352", "generated_answer": "1127*z**3 + 392*z - 2352", "step_length": 2} {"cot_id": "0c5a4e636b394170208492f78cb54779c5f025a8d3d9bd2b4b707ea91a96c2ed", "datapoint": {"question": "Simplify this expression: (32 - 47*y**3)*(32*y**3 - 2*y**2 - 33)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1504*y**6 + 94*y**5 + 2575*y**3 - 64*y**2 - 1056", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2186, "polynomial_expr": "(32 - 47*y**3)*(32*y**3 - 2*y**2 - 33)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (32 - 47*y**3)*(32*y**3 - 2*y**2 - 33)\nExpanding the part (32 - 47*y**3) using the distributive property, and we got: (-47*y**3)*(32*y**3 - 2*y**2 - 33) + 32*(32*y**3 - 2*y**2 - 33)\n#Step 2:\nCurrent expression: (-47*y**3)*(32*y**3 - 2*y**2 - 33) + 32*(32*y**3 - 2*y**2 - 33)\nSimplifying the partial expression: 32*(32*y**3 - 2*y**2 - 33)\nExpanding the part (32*y**3 - 2*y**2 - 33) using the distributive property, and we got: -2*y**2*32 + (32*y**3)*32 - 33*32\nReplacing 32*(32*y**3 - 2*y**2 - 33) with -2*y**2*32 + (32*y**3)*32 - 33*32 in the overall expression.\n#Step 3:\nCurrent expression: -2*y**2*32 + (-47*y**3)*(32*y**3 - 2*y**2 - 33) + (32*y**3)*32 - 1056\nSimplifying the partial expression: (-47*y**3)*(32*y**3 - 2*y**2 - 33)\nExpanding the part (32*y**3 - 2*y**2 - 33) using the distributive property, and we got: -(-1)*1551*y**3 + (-2*y**2)*(-47*y**3) + (-47*y**3)*(32*y**3)\nReplacing (-47*y**3)*(32*y**3 - 2*y**2 - 33) with -(-1)*1551*y**3 + (-2*y**2)*(-47*y**3) + (-47*y**3)*(32*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -33*(-47)*y**3 + (-2*y**2)*(-47*y**3) - 2*y**2*32 + (-47*y**3)*(32*y**3) + (32*y**3)*32 - 1056\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-2*y**2)*32 = -64*y**2\n (-2*y**2)*(-47*y**3) = 94*y**5\n (32*y**3)*32 = 1024*y**3\n (32*y**3)*(-47*y**3) = -1504*y**6\n -33*-47*y**3 = 1551*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1504*y**6 + 94*y**5 + 1024*y**3 + 1551*y**3 - 64*y**2 - 1056\nCombining like terms, got -1504*y**6 + 94*y**5 + 2575*y**3 - 64*y**2 - 1056\n#Step 6:\nCurrent expression: -1504*y**6 + 94*y**5 + 2575*y**3 - 64*y**2 - 1056\nNo more calculations needed.\n-1504*y**6 + 94*y**5 + 2575*y**3 - 64*y**2 - 1056", "generated_answer": "-1504*y**6 + 94*y**5 + 2575*y**3 - 64*y**2 - 1056", "step_length": 6} {"cot_id": "f6c3196cc41d590a9a0e7d21b2f5b77c2d7d7c9f5d012fa176dfecc752a62ac9", "datapoint": {"question": "Calculate the following: (-23*y**3 - 19)*(21*y**3 - 42*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-483*y**6 + 966*y**5 - 399*y**3 + 798*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2187, "polynomial_expr": "(-23*y**3 - 19)*(21*y**3 - 42*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-23*y**3 - 19)*(21*y**3 - 42*y**2)\nExpanding the part (-23*y**3 - 19) using the distributive property, and we got: (-23*y**3)*(21*y**3 - 42*y**2) - 19*(21*y**3 - 42*y**2)\n#Step 2:\nCurrent expression: (-23*y**3)*(21*y**3 - 42*y**2) - 19*(21*y**3 - 42*y**2)\nSimplifying the partial expression: -19*(21*y**3 - 42*y**2)\nExpanding the part (21*y**3 - 42*y**2) using the distributive property, and we got: -42*y**2*(-19) + (21*y**3)*(-19)\nReplacing -19*(21*y**3 - 42*y**2) with -42*y**2*(-19) + (21*y**3)*(-19) in the overall expression.\n#Step 3:\nCurrent expression: -42*y**2*(-19) + (-23*y**3)*(21*y**3 - 42*y**2) + (21*y**3)*(-19)\nSimplifying the partial expression: (-23*y**3)*(21*y**3 - 42*y**2)\nExpanding the part (21*y**3 - 42*y**2) using the distributive property, and we got: (-42*y**2)*(-23*y**3) + (-23*y**3)*(21*y**3)\nReplacing (-23*y**3)*(21*y**3 - 42*y**2) with (-42*y**2)*(-23*y**3) + (-23*y**3)*(21*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-42*y**2)*(-23*y**3) - 42*y**2*(-19) + (-23*y**3)*(21*y**3) + (21*y**3)*(-19)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*y**2)*-19 = 798*y**2\n (-42*y**2)*(-23*y**3) = 966*y**5\n (21*y**3)*-19 = -399*y**3\n (21*y**3)*(-23*y**3) = -483*y**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -483*y**6 + 966*y**5 - 399*y**3 + 798*y**2\nNo more calculations needed.\n-483*y**6 + 966*y**5 - 399*y**3 + 798*y**2", "generated_answer": "-483*y**6 + 966*y**5 - 399*y**3 + 798*y**2", "step_length": 5} {"cot_id": "d0791b2d7aa3b4ba4802e09413432e14b304ca6d746f8be3bd06ec9b83b6fea7", "datapoint": {"question": "Calculate the following: (23*x**3 - 33*x**2)*(73*x**3 - 35*x**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "1679*x**6 - 3214*x**5 + 1155*x**4", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2188, "polynomial_expr": "(23*x**3 - 33*x**2)*(73*x**3 - 35*x**2)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (23*x**3 - 33*x**2)*(73*x**3 - 35*x**2)\nExpanding the part (73*x**3 - 35*x**2) using the distributive property, and we got: (-35*x**2)*(23*x**3 - 33*x**2) + (73*x**3)*(23*x**3 - 33*x**2)\n#Step 2:\nCurrent expression: (-35*x**2)*(23*x**3 - 33*x**2) + (73*x**3)*(23*x**3 - 33*x**2)\nSimplifying the partial expression: (-35*x**2)*(23*x**3 - 33*x**2)\nExpanding the part (23*x**3 - 33*x**2) using the distributive property, and we got: (-35*x**2)*(-33*x**2) + (-35*x**2)*(23*x**3)\nReplacing (-35*x**2)*(23*x**3 - 33*x**2) with (-35*x**2)*(-33*x**2) + (-35*x**2)*(23*x**3) in the overall expression.\n#Step 3:\nCurrent expression: (-35*x**2)*(-33*x**2) + (-35*x**2)*(23*x**3) + (73*x**3)*(23*x**3 - 33*x**2)\nSimplifying the partial expression: (73*x**3)*(23*x**3 - 33*x**2)\nExpanding the part (23*x**3 - 33*x**2) using the distributive property, and we got: (-33*x**2)*(73*x**3) + (23*x**3)*(73*x**3)\nReplacing (73*x**3)*(23*x**3 - 33*x**2) with (-33*x**2)*(73*x**3) + (23*x**3)*(73*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-35*x**2)*(-33*x**2) + (-35*x**2)*(23*x**3) + (-33*x**2)*(73*x**3) + (23*x**3)*(73*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-33*x**2)*(-35*x**2) = 1155*x**4\n (-33*x**2)*(73*x**3) = -2409*x**5\n (23*x**3)*(-35*x**2) = -805*x**5\n (23*x**3)*(73*x**3) = 1679*x**6\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 1679*x**6 - 2409*x**5 - 805*x**5 + 1155*x**4\nCombining like terms, got 1679*x**6 - 3214*x**5 + 1155*x**4\n#Step 6:\nCurrent expression: 1679*x**6 - 3214*x**5 + 1155*x**4\nNo more calculations needed.\n1679*x**6 - 3214*x**5 + 1155*x**4", "generated_answer": "1679*x**6 - 3214*x**5 + 1155*x**4", "step_length": 6} {"cot_id": "55afed4d2d5825ddf0b3e4d2b4b235cbeaecddfcdebe37d3a31fe05d4a48b8a9", "datapoint": {"question": "Simplify this expression: (-46*x**3 + 28*x)*(-21*x**3 + 15*x**2 + 52)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "966*x**6 - 690*x**5 - 588*x**4 - 1972*x**3 + 1456*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2189, "polynomial_expr": "(-46*x**3 + 28*x)*(-21*x**3 + 15*x**2 + 52)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-46*x**3 + 28*x)*(-21*x**3 + 15*x**2 + 52)\nExpanding the part (-46*x**3 + 28*x) using the distributive property, and we got: (28*x)*(-21*x**3 + 15*x**2 + 52) + (-46*x**3)*(-21*x**3 + 15*x**2 + 52)\n#Step 2:\nCurrent expression: (28*x)*(-21*x**3 + 15*x**2 + 52) + (-46*x**3)*(-21*x**3 + 15*x**2 + 52)\nSimplifying the partial expression: (-46*x**3)*(-21*x**3 + 15*x**2 + 52)\nExpanding the part (-21*x**3 + 15*x**2 + 52) using the distributive property, and we got: 52*(-46*x**3) + (15*x**2)*(-46*x**3) + (-46*x**3)*(-21*x**3)\nReplacing (-46*x**3)*(-21*x**3 + 15*x**2 + 52) with 52*(-46*x**3) + (15*x**2)*(-46*x**3) + (-46*x**3)*(-21*x**3) in the overall expression.\n#Step 3:\nCurrent expression: 52*(-46)*x**3 + (28*x)*(-21*x**3 + 15*x**2 + 52) + (15*x**2)*(-46*x**3) + (-46*x**3)*(-21*x**3)\nSimplifying the partial expression: (28*x)*(-21*x**3 + 15*x**2 + 52)\nExpanding the part (-21*x**3 + 15*x**2 + 52) using the distributive property, and we got: 52*(28*x) + (28*x)*(15*x**2) + (28*x)*(-21*x**3)\nReplacing (28*x)*(-21*x**3 + 15*x**2 + 52) with 52*(28*x) + (28*x)*(15*x**2) + (28*x)*(-21*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 52*(-46)*x**3 + 52*28*x + (28*x)*(15*x**2) + (28*x)*(-21*x**3) + (15*x**2)*(-46*x**3) + (-46*x**3)*(-21*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-21*x**3)*(-46*x**3) = 966*x**6\n (-21*x**3)*(28*x) = -588*x**4\n (15*x**2)*(-46*x**3) = -690*x**5\n (15*x**2)*(28*x) = 420*x**3\n 52*-46*x**3 = -2392*x**3\n 52*28*x = 1456*x\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 966*x**6 - 690*x**5 - 588*x**4 - 2392*x**3 + 420*x**3 + 1456*x\nCombining like terms, got 966*x**6 - 690*x**5 - 588*x**4 - 1972*x**3 + 1456*x\n#Step 6:\nCurrent expression: 966*x**6 - 690*x**5 - 588*x**4 - 1972*x**3 + 1456*x\nNo more calculations needed.\n966*x**6 - 690*x**5 - 588*x**4 - 1972*x**3 + 1456*x", "generated_answer": "966*x**6 - 690*x**5 - 588*x**4 - 1972*x**3 + 1456*x", "step_length": 6} {"cot_id": "e55c289253787b48fa8aa6465f9e60e12d659b98e63c97731996e579c5866a26", "datapoint": {"question": "Calculate the following: (-8*z**2 + 34*z)*(38*z**3 - 48*z - 26)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-304*z**5 + 1292*z**4 + 384*z**3 - 1424*z**2 - 884*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2190, "polynomial_expr": "(-8*z**2 + 34*z)*(38*z**3 - 48*z - 26)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-8*z**2 + 34*z)*(38*z**3 - 48*z - 26)\nExpanding the part (-8*z**2 + 34*z) using the distributive property, and we got: (34*z)*(38*z**3 - 48*z - 26) + (-8*z**2)*(38*z**3 - 48*z - 26)\n#Step 2:\nCurrent expression: (34*z)*(38*z**3 - 48*z - 26) + (-8*z**2)*(38*z**3 - 48*z - 26)\nSimplifying the partial expression: (-8*z**2)*(38*z**3 - 48*z - 26)\nExpanding the part (38*z**3 - 48*z - 26) using the distributive property, and we got: (-48*z)*(-8*z**2) - (-1)*208*z**2 + (-8*z**2)*(38*z**3)\nReplacing (-8*z**2)*(38*z**3 - 48*z - 26) with (-48*z)*(-8*z**2) - (-1)*208*z**2 + (-8*z**2)*(38*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-48*z)*(-8*z**2) - 26*(-8)*z**2 + (34*z)*(38*z**3 - 48*z - 26) + (-8*z**2)*(38*z**3)\nSimplifying the partial expression: (34*z)*(38*z**3 - 48*z - 26)\nExpanding the part (38*z**3 - 48*z - 26) using the distributive property, and we got: (-48*z)*(34*z) - 884*z + (34*z)*(38*z**3)\nReplacing (34*z)*(38*z**3 - 48*z - 26) with (-48*z)*(34*z) - 884*z + (34*z)*(38*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-48*z)*(34*z) + (-48*z)*(-8*z**2) - 26*(-8)*z**2 - 26*34*z + (34*z)*(38*z**3) + (-8*z**2)*(38*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*z)*(-8*z**2) = 384*z**3\n (-48*z)*(34*z) = -1632*z**2\n (38*z**3)*(-8*z**2) = -304*z**5\n (38*z**3)*(34*z) = 1292*z**4\n -26*-8*z**2 = 208*z**2\n -26*34*z = -884*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -304*z**5 + 1292*z**4 + 384*z**3 - 1632*z**2 + 208*z**2 - 884*z\nCombining like terms, got -304*z**5 + 1292*z**4 + 384*z**3 - 1424*z**2 - 884*z\n#Step 6:\nCurrent expression: -304*z**5 + 1292*z**4 + 384*z**3 - 1424*z**2 - 884*z\nNo more calculations needed.\n-304*z**5 + 1292*z**4 + 384*z**3 - 1424*z**2 - 884*z", "generated_answer": "-304*z**5 + 1292*z**4 + 384*z**3 - 1424*z**2 - 884*z", "step_length": 6} {"cot_id": "73a1c41e31ae19cffecb3cd559be79c82134772efba1dfdbb2dc6f204d653094", "datapoint": {"question": "Calculate the following: -3*z**2*(9 - 31*z)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "93*z**3 - 27*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2191, "polynomial_expr": "-3*z**2*(9 - 31*z)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -3*z**2*(9 - 31*z)\nExpanding the part (9 - 31*z) using the distributive property, and we got: (-31*z)*(-3*z**2) + 9*(-3*z**2)\n#Step 2:\nCurrent expression: (-31*z)*(-3*z**2) + 9*(-3*z**2)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n 9*(-3*z**2) = -27*z**2\n (-31*z)*(-3*z**2) = 93*z**3\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: 93*z**3 - 27*z**2\nNo more calculations needed.\n93*z**3 - 27*z**2", "generated_answer": "93*z**3 - 27*z**2", "step_length": 3} {"cot_id": "c3627238bdf397b9b3f6b71752e387948003b5986e62cb4205c34ea15e8f73de", "datapoint": {"question": "Simplify this expression: (-26*z**3 - 34)*(-z**3 + 46*z + 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "26*z**6 - 1196*z**4 - 1188*z**3 - 1564*z - 1598", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2192, "polynomial_expr": "(-26*z**3 - 34)*(-z**3 + 46*z + 47)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-26*z**3 - 34)*(-z**3 + 46*z + 47)\nExpanding the part (-26*z**3 - 34) using the distributive property, and we got: (-26*z**3)*(-z**3 + 46*z + 47) - 34*(-z**3 + 46*z + 47)\n#Step 2:\nCurrent expression: (-26*z**3)*(-z**3 + 46*z + 47) - 34*(-z**3 + 46*z + 47)\nSimplifying the partial expression: -34*(-z**3 + 46*z + 47)\nExpanding the part (-z**3 + 46*z + 47) using the distributive property, and we got: (46*z)*(-34) - z**3*(-34) + 47*(-34)\nReplacing -34*(-z**3 + 46*z + 47) with (46*z)*(-34) - z**3*(-34) + 47*(-34) in the overall expression.\n#Step 3:\nCurrent expression: (46*z)*(-34) + (-26*z**3)*(-z**3 + 46*z + 47) - z**3*(-34) - 1598\nSimplifying the partial expression: (-26*z**3)*(-z**3 + 46*z + 47)\nExpanding the part (-z**3 + 46*z + 47) using the distributive property, and we got: 47*(-26*z**3) + (46*z)*(-26*z**3) + (-26*z**3)*(-z**3)\nReplacing (-26*z**3)*(-z**3 + 46*z + 47) with 47*(-26*z**3) + (46*z)*(-26*z**3) + (-26*z**3)*(-z**3) in the overall expression.\n#Step 4:\nCurrent expression: 47*(-26)*z**3 + (46*z)*(-26*z**3) + (46*z)*(-34) + (-26*z**3)*(-z**3) - z**3*(-34) - 1598\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-z**3)*-34 = 34*z**3\n (-z**3)*(-26*z**3) = 26*z**6\n (46*z)*-34 = -1564*z\n (46*z)*(-26*z**3) = -1196*z**4\n 47*-26*z**3 = -1222*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 26*z**6 - 1196*z**4 - 1222*z**3 + 34*z**3 - 1564*z - 1598\nCombining like terms, got 26*z**6 - 1196*z**4 - 1188*z**3 - 1564*z - 1598\n#Step 6:\nCurrent expression: 26*z**6 - 1196*z**4 - 1188*z**3 - 1564*z - 1598\nNo more calculations needed.\n26*z**6 - 1196*z**4 - 1188*z**3 - 1564*z - 1598", "generated_answer": "26*z**6 - 1196*z**4 - 1188*z**3 - 1564*z - 1598", "step_length": 6} {"cot_id": "0b67e3799efa2566967210a3b376ec7505ead0152349457ff2a79bc9cb2506ca", "datapoint": {"question": "Simplify this expression: (-21*y**3 - 52)*(-21*y**3 - 8*y**2)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "441*y**6 + 168*y**5 + 1092*y**3 + 416*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2193, "polynomial_expr": "(-21*y**3 - 52)*(-21*y**3 - 8*y**2)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-21*y**3 - 52)*(-21*y**3 - 8*y**2)\nExpanding the part (-21*y**3 - 52) using the distributive property, and we got: (-21*y**3)*(-21*y**3 - 8*y**2) - 52*(-21*y**3 - 8*y**2)\n#Step 2:\nCurrent expression: (-21*y**3)*(-21*y**3 - 8*y**2) - 52*(-21*y**3 - 8*y**2)\nSimplifying the partial expression: -52*(-21*y**3 - 8*y**2)\nExpanding the part (-21*y**3 - 8*y**2) using the distributive property, and we got: -8*y**2*(-52) - 21*y**3*(-52)\nReplacing -52*(-21*y**3 - 8*y**2) with -8*y**2*(-52) - 21*y**3*(-52) in the overall expression.\n#Step 3:\nCurrent expression: -8*y**2*(-52) + (-21*y**3)*(-21*y**3 - 8*y**2) - 21*y**3*(-52)\nSimplifying the partial expression: (-21*y**3)*(-21*y**3 - 8*y**2)\nExpanding the part (-21*y**3 - 8*y**2) using the distributive property, and we got: (-8*y**2)*(-21*y**3) + (-21*y**3)*(-21*y**3)\nReplacing (-21*y**3)*(-21*y**3 - 8*y**2) with (-8*y**2)*(-21*y**3) + (-21*y**3)*(-21*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-8*y**2)*(-21*y**3) - 8*y**2*(-52) - 21*y**3*(-52) + (-21*y**3)*(-21*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-21*y**3)*-52 = 1092*y**3\n (-21*y**3)*(-21*y**3) = 441*y**6\n (-8*y**2)*-52 = 416*y**2\n (-8*y**2)*(-21*y**3) = 168*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 441*y**6 + 168*y**5 + 1092*y**3 + 416*y**2\nNo more calculations needed.\n441*y**6 + 168*y**5 + 1092*y**3 + 416*y**2", "generated_answer": "441*y**6 + 168*y**5 + 1092*y**3 + 416*y**2", "step_length": 5} {"cot_id": "63429f96830d5d8e898f2b8b48159c1ce36c348631e01c46057a26c8bcb4a73b", "datapoint": {"question": "Simplify this expression: (13*z**3 - 7*z**2 - 19*z)*(-16*z**3 - 6*z**2 + 11*z - 47)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-208*z**6 + 34*z**5 + 489*z**4 - 574*z**3 + 120*z**2 + 893*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2194, "polynomial_expr": "(13*z**3 - 7*z**2 - 19*z)*(-16*z**3 - 6*z**2 + 11*z - 47)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (13*z**3 - 7*z**2 - 19*z)*(-16*z**3 - 6*z**2 + 11*z - 47)\nExpanding the part (13*z**3 - 7*z**2 - 19*z) using the distributive property, and we got: (-19*z)*(-16*z**3 - 6*z**2 + 11*z - 47) + (-7*z**2)*(-16*z**3 - 6*z**2 + 11*z - 47) + (13*z**3)*(-16*z**3 - 6*z**2 + 11*z - 47)\n#Step 2:\nCurrent expression: (-19*z)*(-16*z**3 - 6*z**2 + 11*z - 47) + (-7*z**2)*(-16*z**3 - 6*z**2 + 11*z - 47) + (13*z**3)*(-16*z**3 - 6*z**2 + 11*z - 47)\nSimplifying the partial expression: (-19*z)*(-16*z**3 - 6*z**2 + 11*z - 47)\nExpanding the part (-16*z**3 - 6*z**2 + 11*z - 47) using the distributive property, and we got: (-19*z)*(11*z) + (-19*z)*(-6*z**2) + (-19*z)*(-16*z**3) - (-1)*893*z\nReplacing (-19*z)*(-16*z**3 - 6*z**2 + 11*z - 47) with (-19*z)*(11*z) + (-19*z)*(-6*z**2) + (-19*z)*(-16*z**3) - (-1)*893*z in the overall expression.\n#Step 3:\nCurrent expression: (-19*z)*(11*z) + (-19*z)*(-6*z**2) + (-19*z)*(-16*z**3) - 47*(-19)*z + (-7*z**2)*(-16*z**3 - 6*z**2 + 11*z - 47) + (13*z**3)*(-16*z**3 - 6*z**2 + 11*z - 47)\nSimplifying the partial expression: (-7*z**2)*(-16*z**3 - 6*z**2 + 11*z - 47)\nExpanding the part (-16*z**3 - 6*z**2 + 11*z - 47) using the distributive property, and we got: -(-1)*329*z**2 + (11*z)*(-7*z**2) + (-7*z**2)*(-6*z**2) + (-7*z**2)*(-16*z**3)\nReplacing (-7*z**2)*(-16*z**3 - 6*z**2 + 11*z - 47) with -(-1)*329*z**2 + (11*z)*(-7*z**2) + (-7*z**2)*(-6*z**2) + (-7*z**2)*(-16*z**3) in the overall expression.\n#Step 4:\nCurrent expression: (-19*z)*(11*z) + (-19*z)*(-6*z**2) + (-19*z)*(-16*z**3) - 47*(-7)*z**2 - 47*(-19)*z + (11*z)*(-7*z**2) + (-7*z**2)*(-6*z**2) + (-7*z**2)*(-16*z**3) + (13*z**3)*(-16*z**3 - 6*z**2 + 11*z - 47)\nSimplifying the partial expression: (13*z**3)*(-16*z**3 - 6*z**2 + 11*z - 47)\nExpanding the part (-16*z**3 - 6*z**2 + 11*z - 47) using the distributive property, and we got: -611*z**3 + (11*z)*(13*z**3) + (-6*z**2)*(13*z**3) + (-16*z**3)*(13*z**3)\nReplacing (13*z**3)*(-16*z**3 - 6*z**2 + 11*z - 47) with -611*z**3 + (11*z)*(13*z**3) + (-6*z**2)*(13*z**3) + (-16*z**3)*(13*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-19*z)*(11*z) + (-19*z)*(-6*z**2) + (-19*z)*(-16*z**3) - 47*13*z**3 - 47*(-7)*z**2 - 47*(-19)*z + (11*z)*(-7*z**2) + (11*z)*(13*z**3) + (-7*z**2)*(-6*z**2) + (-7*z**2)*(-16*z**3) + (-6*z**2)*(13*z**3) + (-16*z**3)*(13*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-16*z**3)*(-19*z) = 304*z**4\n (-16*z**3)*(-7*z**2) = 112*z**5\n (-16*z**3)*(13*z**3) = -208*z**6\n (-6*z**2)*(-19*z) = 114*z**3\n (-6*z**2)*(-7*z**2) = 42*z**4\n (-6*z**2)*(13*z**3) = -78*z**5\n (11*z)*(-19*z) = -209*z**2\n (11*z)*(-7*z**2) = -77*z**3\n (11*z)*(13*z**3) = 143*z**4\n -47*-19*z = 893*z\n -47*-7*z**2 = 329*z**2\n -47*13*z**3 = -611*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: -208*z**6 - 78*z**5 + 112*z**5 + 42*z**4 + 143*z**4 + 304*z**4 - 611*z**3 - 77*z**3 + 114*z**3 - 209*z**2 + 329*z**2 + 893*z\nCombining like terms, got -208*z**6 + 34*z**5 + 489*z**4 - 574*z**3 + 120*z**2 + 893*z\n#Step 7:\nCurrent expression: -208*z**6 + 34*z**5 + 489*z**4 - 574*z**3 + 120*z**2 + 893*z\nNo more calculations needed.\n-208*z**6 + 34*z**5 + 489*z**4 - 574*z**3 + 120*z**2 + 893*z", "generated_answer": "-208*z**6 + 34*z**5 + 489*z**4 - 574*z**3 + 120*z**2 + 893*z", "step_length": 7} {"cot_id": "41535faceacd8ce77c9e4808f448df5b059260fc1ca9b3d004b45e7837e8106d", "datapoint": {"question": "Calculate the following: (35*x**3 - 22*x**2)*(-48*x**3 + 8*x**2 + 35)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1680*x**6 + 1336*x**5 - 176*x**4 + 1225*x**3 - 770*x**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2195, "polynomial_expr": "(35*x**3 - 22*x**2)*(-48*x**3 + 8*x**2 + 35)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (35*x**3 - 22*x**2)*(-48*x**3 + 8*x**2 + 35)\nExpanding the part (35*x**3 - 22*x**2) using the distributive property, and we got: (-22*x**2)*(-48*x**3 + 8*x**2 + 35) + (35*x**3)*(-48*x**3 + 8*x**2 + 35)\n#Step 2:\nCurrent expression: (-22*x**2)*(-48*x**3 + 8*x**2 + 35) + (35*x**3)*(-48*x**3 + 8*x**2 + 35)\nSimplifying the partial expression: (-22*x**2)*(-48*x**3 + 8*x**2 + 35)\nExpanding the part (-48*x**3 + 8*x**2 + 35) using the distributive property, and we got: 35*(-22*x**2) + (-22*x**2)*(8*x**2) + (-22*x**2)*(-48*x**3)\nReplacing (-22*x**2)*(-48*x**3 + 8*x**2 + 35) with 35*(-22*x**2) + (-22*x**2)*(8*x**2) + (-22*x**2)*(-48*x**3) in the overall expression.\n#Step 3:\nCurrent expression: 35*(-22)*x**2 + (-22*x**2)*(8*x**2) + (-22*x**2)*(-48*x**3) + (35*x**3)*(-48*x**3 + 8*x**2 + 35)\nSimplifying the partial expression: (35*x**3)*(-48*x**3 + 8*x**2 + 35)\nExpanding the part (-48*x**3 + 8*x**2 + 35) using the distributive property, and we got: 35*(35*x**3) + (8*x**2)*(35*x**3) + (-48*x**3)*(35*x**3)\nReplacing (35*x**3)*(-48*x**3 + 8*x**2 + 35) with 35*(35*x**3) + (8*x**2)*(35*x**3) + (-48*x**3)*(35*x**3) in the overall expression.\n#Step 4:\nCurrent expression: 35*35*x**3 + 35*(-22)*x**2 + (-22*x**2)*(8*x**2) + (-22*x**2)*(-48*x**3) + (8*x**2)*(35*x**3) + (-48*x**3)*(35*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-48*x**3)*(-22*x**2) = 1056*x**5\n (-48*x**3)*(35*x**3) = -1680*x**6\n (8*x**2)*(-22*x**2) = -176*x**4\n (8*x**2)*(35*x**3) = 280*x**5\n 35*-22*x**2 = -770*x**2\n 35*35*x**3 = 1225*x**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1680*x**6 + 280*x**5 + 1056*x**5 - 176*x**4 + 1225*x**3 - 770*x**2\nCombining like terms, got -1680*x**6 + 1336*x**5 - 176*x**4 + 1225*x**3 - 770*x**2\n#Step 6:\nCurrent expression: -1680*x**6 + 1336*x**5 - 176*x**4 + 1225*x**3 - 770*x**2\nNo more calculations needed.\n-1680*x**6 + 1336*x**5 - 176*x**4 + 1225*x**3 - 770*x**2", "generated_answer": "-1680*x**6 + 1336*x**5 - 176*x**4 + 1225*x**3 - 770*x**2", "step_length": 6} {"cot_id": "fe91f6ac644c0005d5b7cd4f94721b109a1d3c0823a9b40716b95f412e5a158b", "datapoint": {"question": "Simplify this expression: -3*z**3 - 171*z - 123\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-3*z**3 - 171*z - 123", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2196, "polynomial_expr": "-3*z**3 - 171*z - 123", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: -3*z**3 - 171*z - 123\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n \nReplacing them in the overall expression.\n#Step 2:\nCurrent expression: -3*z**3 - 171*z - 123\nNo more calculations needed.\n-3*z**3 - 171*z - 123", "generated_answer": "-3*z**3 - 171*z - 123", "step_length": 2} {"cot_id": "7d03355cfd325ab561c66debfc0734c8dba5608dc4c970bc32c808945edf03b1", "datapoint": {"question": "Calculate the following: (27*y**2 + 3*y)*(-57*y**3 + 23*y**2 - 14)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-1539*y**5 + 450*y**4 + 69*y**3 - 378*y**2 - 42*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2197, "polynomial_expr": "(27*y**2 + 3*y)*(-57*y**3 + 23*y**2 - 14)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (27*y**2 + 3*y)*(-57*y**3 + 23*y**2 - 14)\nExpanding the part (27*y**2 + 3*y) using the distributive property, and we got: (3*y)*(-57*y**3 + 23*y**2 - 14) + (27*y**2)*(-57*y**3 + 23*y**2 - 14)\n#Step 2:\nCurrent expression: (3*y)*(-57*y**3 + 23*y**2 - 14) + (27*y**2)*(-57*y**3 + 23*y**2 - 14)\nSimplifying the partial expression: (3*y)*(-57*y**3 + 23*y**2 - 14)\nExpanding the part (-57*y**3 + 23*y**2 - 14) using the distributive property, and we got: -42*y + (3*y)*(23*y**2) + (3*y)*(-57*y**3)\nReplacing (3*y)*(-57*y**3 + 23*y**2 - 14) with -42*y + (3*y)*(23*y**2) + (3*y)*(-57*y**3) in the overall expression.\n#Step 3:\nCurrent expression: -14*3*y + (3*y)*(23*y**2) + (3*y)*(-57*y**3) + (27*y**2)*(-57*y**3 + 23*y**2 - 14)\nSimplifying the partial expression: (27*y**2)*(-57*y**3 + 23*y**2 - 14)\nExpanding the part (-57*y**3 + 23*y**2 - 14) using the distributive property, and we got: -378*y**2 + (23*y**2)*(27*y**2) + (27*y**2)*(-57*y**3)\nReplacing (27*y**2)*(-57*y**3 + 23*y**2 - 14) with -378*y**2 + (23*y**2)*(27*y**2) + (27*y**2)*(-57*y**3) in the overall expression.\n#Step 4:\nCurrent expression: -14*27*y**2 - 14*3*y + (3*y)*(23*y**2) + (3*y)*(-57*y**3) + (23*y**2)*(27*y**2) + (27*y**2)*(-57*y**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-57*y**3)*(3*y) = -171*y**4\n (-57*y**3)*(27*y**2) = -1539*y**5\n (23*y**2)*(3*y) = 69*y**3\n (23*y**2)*(27*y**2) = 621*y**4\n -14*3*y = -42*y\n -14*27*y**2 = -378*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -1539*y**5 - 171*y**4 + 621*y**4 + 69*y**3 - 378*y**2 - 42*y\nCombining like terms, got -1539*y**5 + 450*y**4 + 69*y**3 - 378*y**2 - 42*y\n#Step 6:\nCurrent expression: -1539*y**5 + 450*y**4 + 69*y**3 - 378*y**2 - 42*y\nNo more calculations needed.\n-1539*y**5 + 450*y**4 + 69*y**3 - 378*y**2 - 42*y", "generated_answer": "-1539*y**5 + 450*y**4 + 69*y**3 - 378*y**2 - 42*y", "step_length": 6} {"cot_id": "b611d2273ed24af5e77b544e88d11ca22d4890943248914c8778b43f12d90d74", "datapoint": {"question": "Simplify this expression: (16*y**3 + 38*y - 52)*(27*y**3 - 24*y**2 - 49*y - 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "432*y**6 - 384*y**5 + 242*y**4 - 2412*y**3 - 614*y**2 + 2320*y + 312", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2198, "polynomial_expr": "(16*y**3 + 38*y - 52)*(27*y**3 - 24*y**2 - 49*y - 6)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (16*y**3 + 38*y - 52)*(27*y**3 - 24*y**2 - 49*y - 6)\nExpanding the part (16*y**3 + 38*y - 52) using the distributive property, and we got: (38*y)*(27*y**3 - 24*y**2 - 49*y - 6) + (16*y**3)*(27*y**3 - 24*y**2 - 49*y - 6) - 52*(27*y**3 - 24*y**2 - 49*y - 6)\n#Step 2:\nCurrent expression: (38*y)*(27*y**3 - 24*y**2 - 49*y - 6) + (16*y**3)*(27*y**3 - 24*y**2 - 49*y - 6) - 52*(27*y**3 - 24*y**2 - 49*y - 6)\nSimplifying the partial expression: -52*(27*y**3 - 24*y**2 - 49*y - 6)\nExpanding the part (27*y**3 - 24*y**2 - 49*y - 6) using the distributive property, and we got: -49*y*(-52) - 24*y**2*(-52) + (27*y**3)*(-52) - 6*(-52)\nReplacing -52*(27*y**3 - 24*y**2 - 49*y - 6) with -49*y*(-52) - 24*y**2*(-52) + (27*y**3)*(-52) - 6*(-52) in the overall expression.\n#Step 3:\nCurrent expression: -49*y*(-52) + (38*y)*(27*y**3 - 24*y**2 - 49*y - 6) - 24*y**2*(-52) + (16*y**3)*(27*y**3 - 24*y**2 - 49*y - 6) + (27*y**3)*(-52) + 312\nSimplifying the partial expression: (16*y**3)*(27*y**3 - 24*y**2 - 49*y - 6)\nExpanding the part (27*y**3 - 24*y**2 - 49*y - 6) using the distributive property, and we got: (-49*y)*(16*y**3) - 96*y**3 + (-24*y**2)*(16*y**3) + (16*y**3)*(27*y**3)\nReplacing (16*y**3)*(27*y**3 - 24*y**2 - 49*y - 6) with (-49*y)*(16*y**3) - 96*y**3 + (-24*y**2)*(16*y**3) + (16*y**3)*(27*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-49*y)*(16*y**3) - 49*y*(-52) - 6*16*y**3 + (38*y)*(27*y**3 - 24*y**2 - 49*y - 6) + (-24*y**2)*(16*y**3) - 24*y**2*(-52) + (16*y**3)*(27*y**3) + (27*y**3)*(-52) + 312\nSimplifying the partial expression: (38*y)*(27*y**3 - 24*y**2 - 49*y - 6)\nExpanding the part (27*y**3 - 24*y**2 - 49*y - 6) using the distributive property, and we got: (-49*y)*(38*y) - 228*y + (38*y)*(-24*y**2) + (38*y)*(27*y**3)\nReplacing (38*y)*(27*y**3 - 24*y**2 - 49*y - 6) with (-49*y)*(38*y) - 228*y + (38*y)*(-24*y**2) + (38*y)*(27*y**3) in the overall expression.\n#Step 5:\nCurrent expression: (-49*y)*(38*y) + (-49*y)*(16*y**3) - 49*y*(-52) - 6*16*y**3 - 6*38*y + (38*y)*(-24*y**2) + (38*y)*(27*y**3) + (-24*y**2)*(16*y**3) - 24*y**2*(-52) + (16*y**3)*(27*y**3) + (27*y**3)*(-52) + 312\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-49*y)*-52 = 2548*y\n (-49*y)*(16*y**3) = -784*y**4\n (-49*y)*(38*y) = -1862*y**2\n (-24*y**2)*-52 = 1248*y**2\n (-24*y**2)*(16*y**3) = -384*y**5\n (-24*y**2)*(38*y) = -912*y**3\n (27*y**3)*-52 = -1404*y**3\n (27*y**3)*(16*y**3) = 432*y**6\n (27*y**3)*(38*y) = 1026*y**4\n -6*16*y**3 = -96*y**3\n -6*38*y = -228*y\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 432*y**6 - 384*y**5 - 784*y**4 + 1026*y**4 - 1404*y**3 - 912*y**3 - 96*y**3 - 1862*y**2 + 1248*y**2 - 228*y + 2548*y + 312\nCombining like terms, got 432*y**6 - 384*y**5 + 242*y**4 - 2412*y**3 - 614*y**2 + 2320*y + 312\n#Step 7:\nCurrent expression: 432*y**6 - 384*y**5 + 242*y**4 - 2412*y**3 - 614*y**2 + 2320*y + 312\nNo more calculations needed.\n432*y**6 - 384*y**5 + 242*y**4 - 2412*y**3 - 614*y**2 + 2320*y + 312", "generated_answer": "432*y**6 - 384*y**5 + 242*y**4 - 2412*y**3 - 614*y**2 + 2320*y + 312", "step_length": 7} {"cot_id": "b04292a0394e55dd39e3874fc81a2791935da5a2b284a4e878c1f1354976afa6", "datapoint": {"question": "Calculate the following: (-41*z**2 - 2*z + 42)*(-18*z**3 - 57*z**2 - 13)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "738*z**5 + 2373*z**4 - 642*z**3 - 1861*z**2 + 26*z - 546", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2199, "polynomial_expr": "(-41*z**2 - 2*z + 42)*(-18*z**3 - 57*z**2 - 13)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-41*z**2 - 2*z + 42)*(-18*z**3 - 57*z**2 - 13)\nExpanding the part (-18*z**3 - 57*z**2 - 13) using the distributive property, and we got: (-57*z**2)*(-41*z**2 - 2*z + 42) + (-18*z**3)*(-41*z**2 - 2*z + 42) - 13*(-41*z**2 - 2*z + 42)\n#Step 2:\nCurrent expression: (-57*z**2)*(-41*z**2 - 2*z + 42) + (-18*z**3)*(-41*z**2 - 2*z + 42) - 13*(-41*z**2 - 2*z + 42)\nSimplifying the partial expression: -13*(-41*z**2 - 2*z + 42)\nExpanding the part (-41*z**2 - 2*z + 42) using the distributive property, and we got: -2*z*(-13) - 41*z**2*(-13) + 42*(-13)\nReplacing -13*(-41*z**2 - 2*z + 42) with -2*z*(-13) - 41*z**2*(-13) + 42*(-13) in the overall expression.\n#Step 3:\nCurrent expression: -2*z*(-13) + (-57*z**2)*(-41*z**2 - 2*z + 42) - 41*z**2*(-13) + (-18*z**3)*(-41*z**2 - 2*z + 42) - 546\nSimplifying the partial expression: (-57*z**2)*(-41*z**2 - 2*z + 42)\nExpanding the part (-41*z**2 - 2*z + 42) using the distributive property, and we got: (-2*z)*(-57*z**2) + 42*(-57*z**2) + (-57*z**2)*(-41*z**2)\nReplacing (-57*z**2)*(-41*z**2 - 2*z + 42) with (-2*z)*(-57*z**2) + 42*(-57*z**2) + (-57*z**2)*(-41*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-2*z)*(-57*z**2) - 2*z*(-13) + 42*(-57)*z**2 + (-57*z**2)*(-41*z**2) - 41*z**2*(-13) + (-18*z**3)*(-41*z**2 - 2*z + 42) - 546\nSimplifying the partial expression: (-18*z**3)*(-41*z**2 - 2*z + 42)\nExpanding the part (-41*z**2 - 2*z + 42) using the distributive property, and we got: (-2*z)*(-18*z**3) + 42*(-18*z**3) + (-41*z**2)*(-18*z**3)\nReplacing (-18*z**3)*(-41*z**2 - 2*z + 42) with (-2*z)*(-18*z**3) + 42*(-18*z**3) + (-41*z**2)*(-18*z**3) in the overall expression.\n#Step 5:\nCurrent expression: (-2*z)*(-57*z**2) + (-2*z)*(-18*z**3) - 2*z*(-13) + 42*(-18)*z**3 + 42*(-57)*z**2 + (-57*z**2)*(-41*z**2) + (-41*z**2)*(-18*z**3) - 41*z**2*(-13) - 546\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-41*z**2)*-13 = 533*z**2\n (-41*z**2)*(-57*z**2) = 2337*z**4\n (-41*z**2)*(-18*z**3) = 738*z**5\n (-2*z)*-13 = 26*z\n (-2*z)*(-57*z**2) = 114*z**3\n (-2*z)*(-18*z**3) = 36*z**4\n 42*-57*z**2 = -2394*z**2\n 42*-18*z**3 = -756*z**3\nReplacing them in the overall expression.\n#Step 6:\nCurrent expression: 738*z**5 + 36*z**4 + 2337*z**4 - 756*z**3 + 114*z**3 - 2394*z**2 + 533*z**2 + 26*z - 546\nCombining like terms, got 738*z**5 + 2373*z**4 - 642*z**3 - 1861*z**2 + 26*z - 546\n#Step 7:\nCurrent expression: 738*z**5 + 2373*z**4 - 642*z**3 - 1861*z**2 + 26*z - 546\nNo more calculations needed.\n738*z**5 + 2373*z**4 - 642*z**3 - 1861*z**2 + 26*z - 546", "generated_answer": "738*z**5 + 2373*z**4 - 642*z**3 - 1861*z**2 + 26*z - 546", "step_length": 7} {"cot_id": "3c038c517d21a3727947428403c99cd01cc1432f1d77ef68f1ad7fd8bed0c18d", "datapoint": {"question": "Calculate the following: (4*z**3 - 6*z**2)*(44*z**3 - 42*z**2 - 18)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "176*z**6 - 432*z**5 + 252*z**4 - 72*z**3 + 108*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2200, "polynomial_expr": "(4*z**3 - 6*z**2)*(44*z**3 - 42*z**2 - 18)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (4*z**3 - 6*z**2)*(44*z**3 - 42*z**2 - 18)\nExpanding the part (4*z**3 - 6*z**2) using the distributive property, and we got: (-6*z**2)*(44*z**3 - 42*z**2 - 18) + (4*z**3)*(44*z**3 - 42*z**2 - 18)\n#Step 2:\nCurrent expression: (-6*z**2)*(44*z**3 - 42*z**2 - 18) + (4*z**3)*(44*z**3 - 42*z**2 - 18)\nSimplifying the partial expression: (-6*z**2)*(44*z**3 - 42*z**2 - 18)\nExpanding the part (44*z**3 - 42*z**2 - 18) using the distributive property, and we got: -(-1)*108*z**2 + (-42*z**2)*(-6*z**2) + (-6*z**2)*(44*z**3)\nReplacing (-6*z**2)*(44*z**3 - 42*z**2 - 18) with -(-1)*108*z**2 + (-42*z**2)*(-6*z**2) + (-6*z**2)*(44*z**3) in the overall expression.\n#Step 3:\nCurrent expression: -18*(-6)*z**2 + (-42*z**2)*(-6*z**2) + (-6*z**2)*(44*z**3) + (4*z**3)*(44*z**3 - 42*z**2 - 18)\nSimplifying the partial expression: (4*z**3)*(44*z**3 - 42*z**2 - 18)\nExpanding the part (44*z**3 - 42*z**2 - 18) using the distributive property, and we got: -72*z**3 + (-42*z**2)*(4*z**3) + (4*z**3)*(44*z**3)\nReplacing (4*z**3)*(44*z**3 - 42*z**2 - 18) with -72*z**3 + (-42*z**2)*(4*z**3) + (4*z**3)*(44*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -18*4*z**3 - 18*(-6)*z**2 + (-42*z**2)*(-6*z**2) + (-42*z**2)*(4*z**3) + (-6*z**2)*(44*z**3) + (4*z**3)*(44*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-42*z**2)*(-6*z**2) = 252*z**4\n (-42*z**2)*(4*z**3) = -168*z**5\n (44*z**3)*(-6*z**2) = -264*z**5\n (44*z**3)*(4*z**3) = 176*z**6\n -18*-6*z**2 = 108*z**2\n -18*4*z**3 = -72*z**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 176*z**6 - 264*z**5 - 168*z**5 + 252*z**4 - 72*z**3 + 108*z**2\nCombining like terms, got 176*z**6 - 432*z**5 + 252*z**4 - 72*z**3 + 108*z**2\n#Step 6:\nCurrent expression: 176*z**6 - 432*z**5 + 252*z**4 - 72*z**3 + 108*z**2\nNo more calculations needed.\n176*z**6 - 432*z**5 + 252*z**4 - 72*z**3 + 108*z**2", "generated_answer": "176*z**6 - 432*z**5 + 252*z**4 - 72*z**3 + 108*z**2", "step_length": 6} {"cot_id": "b0dc3dab55da341b5e64b858ec42e0a7445bd993d4f1e57ab739d3c08e5c354f", "datapoint": {"question": "Simplify this expression: (-20*y**3 + 13*y**2)*(49*y**3 + 77)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-980*y**6 + 637*y**5 - 1540*y**3 + 1001*y**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2201, "polynomial_expr": "(-20*y**3 + 13*y**2)*(49*y**3 + 77)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-20*y**3 + 13*y**2)*(49*y**3 + 77)\nExpanding the part (49*y**3 + 77) using the distributive property, and we got: (49*y**3)*(-20*y**3 + 13*y**2) + 77*(-20*y**3 + 13*y**2)\n#Step 2:\nCurrent expression: (49*y**3)*(-20*y**3 + 13*y**2) + 77*(-20*y**3 + 13*y**2)\nSimplifying the partial expression: 77*(-20*y**3 + 13*y**2)\nExpanding the part (-20*y**3 + 13*y**2) using the distributive property, and we got: (13*y**2)*77 - 20*y**3*77\nReplacing 77*(-20*y**3 + 13*y**2) with (13*y**2)*77 - 20*y**3*77 in the overall expression.\n#Step 3:\nCurrent expression: (13*y**2)*77 - 20*y**3*77 + (49*y**3)*(-20*y**3 + 13*y**2)\nSimplifying the partial expression: (49*y**3)*(-20*y**3 + 13*y**2)\nExpanding the part (-20*y**3 + 13*y**2) using the distributive property, and we got: (13*y**2)*(49*y**3) + (-20*y**3)*(49*y**3)\nReplacing (49*y**3)*(-20*y**3 + 13*y**2) with (13*y**2)*(49*y**3) + (-20*y**3)*(49*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (13*y**2)*(49*y**3) + (13*y**2)*77 + (-20*y**3)*(49*y**3) - 20*y**3*77\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-20*y**3)*77 = -1540*y**3\n (-20*y**3)*(49*y**3) = -980*y**6\n (13*y**2)*77 = 1001*y**2\n (13*y**2)*(49*y**3) = 637*y**5\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -980*y**6 + 637*y**5 - 1540*y**3 + 1001*y**2\nNo more calculations needed.\n-980*y**6 + 637*y**5 - 1540*y**3 + 1001*y**2", "generated_answer": "-980*y**6 + 637*y**5 - 1540*y**3 + 1001*y**2", "step_length": 5} {"cot_id": "dea98bbc96737af903fdc91b025966a4b4b570518d543df68e639d9f59ae3874", "datapoint": {"question": "Calculate the following: (17*z**3 + 45*z**2)*(41*z**3 + 44*z - 6)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "697*z**6 + 1845*z**5 + 748*z**4 + 1878*z**3 - 270*z**2", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2202, "polynomial_expr": "(17*z**3 + 45*z**2)*(41*z**3 + 44*z - 6)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (17*z**3 + 45*z**2)*(41*z**3 + 44*z - 6)\nExpanding the part (17*z**3 + 45*z**2) using the distributive property, and we got: (45*z**2)*(41*z**3 + 44*z - 6) + (17*z**3)*(41*z**3 + 44*z - 6)\n#Step 2:\nCurrent expression: (45*z**2)*(41*z**3 + 44*z - 6) + (17*z**3)*(41*z**3 + 44*z - 6)\nSimplifying the partial expression: (17*z**3)*(41*z**3 + 44*z - 6)\nExpanding the part (41*z**3 + 44*z - 6) using the distributive property, and we got: -102*z**3 + (44*z)*(17*z**3) + (17*z**3)*(41*z**3)\nReplacing (17*z**3)*(41*z**3 + 44*z - 6) with -102*z**3 + (44*z)*(17*z**3) + (17*z**3)*(41*z**3) in the overall expression.\n#Step 3:\nCurrent expression: -6*17*z**3 + (44*z)*(17*z**3) + (45*z**2)*(41*z**3 + 44*z - 6) + (17*z**3)*(41*z**3)\nSimplifying the partial expression: (45*z**2)*(41*z**3 + 44*z - 6)\nExpanding the part (41*z**3 + 44*z - 6) using the distributive property, and we got: -270*z**2 + (44*z)*(45*z**2) + (45*z**2)*(41*z**3)\nReplacing (45*z**2)*(41*z**3 + 44*z - 6) with -270*z**2 + (44*z)*(45*z**2) + (45*z**2)*(41*z**3) in the overall expression.\n#Step 4:\nCurrent expression: -6*17*z**3 - 6*45*z**2 + (44*z)*(45*z**2) + (44*z)*(17*z**3) + (45*z**2)*(41*z**3) + (17*z**3)*(41*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (41*z**3)*(17*z**3) = 697*z**6\n (41*z**3)*(45*z**2) = 1845*z**5\n (44*z)*(17*z**3) = 748*z**4\n (44*z)*(45*z**2) = 1980*z**3\n -6*17*z**3 = -102*z**3\n -6*45*z**2 = -270*z**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 697*z**6 + 1845*z**5 + 748*z**4 - 102*z**3 + 1980*z**3 - 270*z**2\nCombining like terms, got 697*z**6 + 1845*z**5 + 748*z**4 + 1878*z**3 - 270*z**2\n#Step 6:\nCurrent expression: 697*z**6 + 1845*z**5 + 748*z**4 + 1878*z**3 - 270*z**2\nNo more calculations needed.\n697*z**6 + 1845*z**5 + 748*z**4 + 1878*z**3 - 270*z**2", "generated_answer": "697*z**6 + 1845*z**5 + 748*z**4 + 1878*z**3 - 270*z**2", "step_length": 6} {"cot_id": "7fb03b75151abc84501854eb6246007ebe0c6d72720e03f0386b581710f8ee9e", "datapoint": {"question": "Simplify this expression: (15*x**2 - 45*x)*(-3*x**3 + 10*x - 58)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-45*x**5 + 135*x**4 + 150*x**3 - 1320*x**2 + 2610*x", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2203, "polynomial_expr": "(15*x**2 - 45*x)*(-3*x**3 + 10*x - 58)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (15*x**2 - 45*x)*(-3*x**3 + 10*x - 58)\nExpanding the part (15*x**2 - 45*x) using the distributive property, and we got: (-45*x)*(-3*x**3 + 10*x - 58) + (15*x**2)*(-3*x**3 + 10*x - 58)\n#Step 2:\nCurrent expression: (-45*x)*(-3*x**3 + 10*x - 58) + (15*x**2)*(-3*x**3 + 10*x - 58)\nSimplifying the partial expression: (-45*x)*(-3*x**3 + 10*x - 58)\nExpanding the part (-3*x**3 + 10*x - 58) using the distributive property, and we got: (-45*x)*(10*x) + (-45*x)*(-3*x**3) - (-1)*2610*x\nReplacing (-45*x)*(-3*x**3 + 10*x - 58) with (-45*x)*(10*x) + (-45*x)*(-3*x**3) - (-1)*2610*x in the overall expression.\n#Step 3:\nCurrent expression: (-45*x)*(10*x) + (-45*x)*(-3*x**3) - 58*(-45)*x + (15*x**2)*(-3*x**3 + 10*x - 58)\nSimplifying the partial expression: (15*x**2)*(-3*x**3 + 10*x - 58)\nExpanding the part (-3*x**3 + 10*x - 58) using the distributive property, and we got: -870*x**2 + (10*x)*(15*x**2) + (15*x**2)*(-3*x**3)\nReplacing (15*x**2)*(-3*x**3 + 10*x - 58) with -870*x**2 + (10*x)*(15*x**2) + (15*x**2)*(-3*x**3) in the overall expression.\n#Step 4:\nCurrent expression: (-45*x)*(10*x) + (-45*x)*(-3*x**3) - 58*15*x**2 - 58*(-45)*x + (10*x)*(15*x**2) + (15*x**2)*(-3*x**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-3*x**3)*(-45*x) = 135*x**4\n (-3*x**3)*(15*x**2) = -45*x**5\n (10*x)*(-45*x) = -450*x**2\n (10*x)*(15*x**2) = 150*x**3\n -58*-45*x = 2610*x\n -58*15*x**2 = -870*x**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -45*x**5 + 135*x**4 + 150*x**3 - 870*x**2 - 450*x**2 + 2610*x\nCombining like terms, got -45*x**5 + 135*x**4 + 150*x**3 - 1320*x**2 + 2610*x\n#Step 6:\nCurrent expression: -45*x**5 + 135*x**4 + 150*x**3 - 1320*x**2 + 2610*x\nNo more calculations needed.\n-45*x**5 + 135*x**4 + 150*x**3 - 1320*x**2 + 2610*x", "generated_answer": "-45*x**5 + 135*x**4 + 150*x**3 - 1320*x**2 + 2610*x", "step_length": 6} {"cot_id": "8dfe7007d3c2d99ac7caa427d1b25acdecfba8a68c61e572da3fdaf6bdc8af45", "datapoint": {"question": "Calculate the following: (-46*z**3 + 6*z)*(-17*z**2 - 13*z + 30)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "782*z**5 + 598*z**4 - 1482*z**3 - 78*z**2 + 180*z", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2204, "polynomial_expr": "(-46*z**3 + 6*z)*(-17*z**2 - 13*z + 30)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (-46*z**3 + 6*z)*(-17*z**2 - 13*z + 30)\nExpanding the part (-46*z**3 + 6*z) using the distributive property, and we got: (6*z)*(-17*z**2 - 13*z + 30) + (-46*z**3)*(-17*z**2 - 13*z + 30)\n#Step 2:\nCurrent expression: (6*z)*(-17*z**2 - 13*z + 30) + (-46*z**3)*(-17*z**2 - 13*z + 30)\nSimplifying the partial expression: (-46*z**3)*(-17*z**2 - 13*z + 30)\nExpanding the part (-17*z**2 - 13*z + 30) using the distributive property, and we got: (-13*z)*(-46*z**3) + 30*(-46*z**3) + (-17*z**2)*(-46*z**3)\nReplacing (-46*z**3)*(-17*z**2 - 13*z + 30) with (-13*z)*(-46*z**3) + 30*(-46*z**3) + (-17*z**2)*(-46*z**3) in the overall expression.\n#Step 3:\nCurrent expression: (-13*z)*(-46*z**3) + 30*(-46)*z**3 + (6*z)*(-17*z**2 - 13*z + 30) + (-17*z**2)*(-46*z**3)\nSimplifying the partial expression: (6*z)*(-17*z**2 - 13*z + 30)\nExpanding the part (-17*z**2 - 13*z + 30) using the distributive property, and we got: (-13*z)*(6*z) + 30*(6*z) + (6*z)*(-17*z**2)\nReplacing (6*z)*(-17*z**2 - 13*z + 30) with (-13*z)*(6*z) + 30*(6*z) + (6*z)*(-17*z**2) in the overall expression.\n#Step 4:\nCurrent expression: (-13*z)*(6*z) + (-13*z)*(-46*z**3) + 30*(-46)*z**3 + 30*6*z + (6*z)*(-17*z**2) + (-17*z**2)*(-46*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-17*z**2)*(-46*z**3) = 782*z**5\n (-17*z**2)*(6*z) = -102*z**3\n (-13*z)*(-46*z**3) = 598*z**4\n (-13*z)*(6*z) = -78*z**2\n 30*-46*z**3 = -1380*z**3\n 30*6*z = 180*z\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 782*z**5 + 598*z**4 - 1380*z**3 - 102*z**3 - 78*z**2 + 180*z\nCombining like terms, got 782*z**5 + 598*z**4 - 1482*z**3 - 78*z**2 + 180*z\n#Step 6:\nCurrent expression: 782*z**5 + 598*z**4 - 1482*z**3 - 78*z**2 + 180*z\nNo more calculations needed.\n782*z**5 + 598*z**4 - 1482*z**3 - 78*z**2 + 180*z", "generated_answer": "782*z**5 + 598*z**4 - 1482*z**3 - 78*z**2 + 180*z", "step_length": 6} {"cot_id": "8575702e0de790fbb2f2d3512e58968ba6a2c948f0c406357accadde533170be", "datapoint": {"question": "Calculate the following: 47*z**3*(-2*z**2 - 11*z - 40)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-94*z**5 - 517*z**4 - 1880*z**3", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2205, "polynomial_expr": "47*z**3*(-2*z**2 - 11*z - 40)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: 47*z**3*(-2*z**2 - 11*z - 40)\nExpanding the part (-2*z**2 - 11*z - 40) using the distributive property, and we got: (-11*z)*(47*z**3) - 1880*z**3 + (-2*z**2)*(47*z**3)\n#Step 2:\nCurrent expression: (-11*z)*(47*z**3) - 1880*z**3 + (-2*z**2)*(47*z**3)\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n -40*(47*z**3) = -1880*z**3\n (-11*z)*(47*z**3) = -517*z**4\n (-2*z**2)*(47*z**3) = -94*z**5\nReplacing them in the overall expression.\n#Step 3:\nCurrent expression: -94*z**5 - 517*z**4 - 1880*z**3\nNo more calculations needed.\n-94*z**5 - 517*z**4 - 1880*z**3", "generated_answer": "-94*z**5 - 517*z**4 - 1880*z**3", "step_length": 3} {"cot_id": "b1ff054815d03ea1d366834ac20fcdaf629b4823f92d9fd9f7a55b2b26c94da9", "datapoint": {"question": "Simplify this expression: (32*y + 13)*(18*y**2 + 24)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "576*y**3 + 234*y**2 + 768*y + 312", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2206, "polynomial_expr": "(32*y + 13)*(18*y**2 + 24)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (32*y + 13)*(18*y**2 + 24)\nExpanding the part (32*y + 13) using the distributive property, and we got: (32*y)*(18*y**2 + 24) + 13*(18*y**2 + 24)\n#Step 2:\nCurrent expression: (32*y)*(18*y**2 + 24) + 13*(18*y**2 + 24)\nSimplifying the partial expression: 13*(18*y**2 + 24)\nExpanding the part (18*y**2 + 24) using the distributive property, and we got: (18*y**2)*13 + 24*13\nReplacing 13*(18*y**2 + 24) with (18*y**2)*13 + 24*13 in the overall expression.\n#Step 3:\nCurrent expression: (32*y)*(18*y**2 + 24) + (18*y**2)*13 + 312\nSimplifying the partial expression: (32*y)*(18*y**2 + 24)\nExpanding the part (18*y**2 + 24) using the distributive property, and we got: 24*(32*y) + (32*y)*(18*y**2)\nReplacing (32*y)*(18*y**2 + 24) with 24*(32*y) + (32*y)*(18*y**2) in the overall expression.\n#Step 4:\nCurrent expression: 24*32*y + (32*y)*(18*y**2) + (18*y**2)*13 + 312\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (18*y**2)*13 = 234*y**2\n (18*y**2)*(32*y) = 576*y**3\n 24*32*y = 768*y\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 576*y**3 + 234*y**2 + 768*y + 312\nNo more calculations needed.\n576*y**3 + 234*y**2 + 768*y + 312", "generated_answer": "576*y**3 + 234*y**2 + 768*y + 312", "step_length": 5} {"cot_id": "18dae7acbb5725b56d1548efe587a0795ede90557db556cf650a6e477f9ffc35", "datapoint": {"question": "Calculate the following: (12 - 20*y)*(-y**3 - 48*y**2 + 40*y)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "20*y**4 + 948*y**3 - 1376*y**2 + 480*y", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2207, "polynomial_expr": "(12 - 20*y)*(-y**3 - 48*y**2 + 40*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (12 - 20*y)*(-y**3 - 48*y**2 + 40*y)\nExpanding the part (12 - 20*y) using the distributive property, and we got: (-20*y)*(-y**3 - 48*y**2 + 40*y) + 12*(-y**3 - 48*y**2 + 40*y)\n#Step 2:\nCurrent expression: (-20*y)*(-y**3 - 48*y**2 + 40*y) + 12*(-y**3 - 48*y**2 + 40*y)\nSimplifying the partial expression: 12*(-y**3 - 48*y**2 + 40*y)\nExpanding the part (-y**3 - 48*y**2 + 40*y) using the distributive property, and we got: (40*y)*12 - 48*y**2*12 - y**3*12\nReplacing 12*(-y**3 - 48*y**2 + 40*y) with (40*y)*12 - 48*y**2*12 - y**3*12 in the overall expression.\n#Step 3:\nCurrent expression: (-20*y)*(-y**3 - 48*y**2 + 40*y) + (40*y)*12 - 48*y**2*12 - y**3*12\nSimplifying the partial expression: (-20*y)*(-y**3 - 48*y**2 + 40*y)\nExpanding the part (-y**3 - 48*y**2 + 40*y) using the distributive property, and we got: (-20*y)*(40*y) + (-20*y)*(-48*y**2) + (-20*y)*(-y**3)\nReplacing (-20*y)*(-y**3 - 48*y**2 + 40*y) with (-20*y)*(40*y) + (-20*y)*(-48*y**2) + (-20*y)*(-y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-20*y)*(40*y) + (-20*y)*(-48*y**2) + (-20*y)*(-y**3) + (40*y)*12 - 48*y**2*12 - y**3*12\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-y**3)*12 = -12*y**3\n (-y**3)*(-20*y) = 20*y**4\n (-48*y**2)*12 = -576*y**2\n (-48*y**2)*(-20*y) = 960*y**3\n (40*y)*12 = 480*y\n (40*y)*(-20*y) = -800*y**2\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: 20*y**4 - 12*y**3 + 960*y**3 - 800*y**2 - 576*y**2 + 480*y\nCombining like terms, got 20*y**4 + 948*y**3 - 1376*y**2 + 480*y\n#Step 6:\nCurrent expression: 20*y**4 + 948*y**3 - 1376*y**2 + 480*y\nNo more calculations needed.\n20*y**4 + 948*y**3 - 1376*y**2 + 480*y", "generated_answer": "20*y**4 + 948*y**3 - 1376*y**2 + 480*y", "step_length": 6} {"cot_id": "d2c8f76f32aee25523f84259ba1e204beddc1ba60cbbdf4b7adc7543c8ac25a6", "datapoint": {"question": "Simplify this expression: (66 - 18*y)*(34*y**3 + 27)\nWhen performing calculations, please follow these guidelines:\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n", "answer": "-612*y**4 + 2244*y**3 - 486*y + 1782", "metadata": {"source_dataset": "polynomial_multiplication", "source_index": 2208, "polynomial_expr": "(66 - 18*y)*(34*y**3 + 27)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 50, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 2}}}, "cot": "Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:\n#Step 1:\nCurrent expression: (66 - 18*y)*(34*y**3 + 27)\nExpanding the part (34*y**3 + 27) using the distributive property, and we got: (34*y**3)*(66 - 18*y) + 27*(66 - 18*y)\n#Step 2:\nCurrent expression: (34*y**3)*(66 - 18*y) + 27*(66 - 18*y)\nSimplifying the partial expression: 27*(66 - 18*y)\nExpanding the part (66 - 18*y) using the distributive property, and we got: -18*y*27 + 66*27\nReplacing 27*(66 - 18*y) with -18*y*27 + 66*27 in the overall expression.\n#Step 3:\nCurrent expression: -18*y*27 + (34*y**3)*(66 - 18*y) + 1782\nSimplifying the partial expression: (34*y**3)*(66 - 18*y)\nExpanding the part (66 - 18*y) using the distributive property, and we got: (-18*y)*(34*y**3) + 66*(34*y**3)\nReplacing (34*y**3)*(66 - 18*y) with (-18*y)*(34*y**3) + 66*(34*y**3) in the overall expression.\n#Step 4:\nCurrent expression: (-18*y)*(34*y**3) - 18*y*27 + 66*34*y**3 + 1782\nNo partial expression needs using the distributive property to simplify.\nCalculating the product of the terms in the current expression:\n (-18*y)*27 = -486*y\n (-18*y)*(34*y**3) = -612*y**4\n 66*34*y**3 = 2244*y**3\nReplacing them in the overall expression.\n#Step 5:\nCurrent expression: -612*y**4 + 2244*y**3 - 486*y + 1782\nNo more calculations needed.\n-612*y**4 + 2244*y**3 - 486*y + 1782", "generated_answer": "-612*y**4 + 2244*y**3 - 486*y + 1782", "step_length": 5}