Question:
Calculate the following: (4 - 39*x**2)*(-56*x**3 - 11)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2184*x**5 - 224*x**3 + 429*x**2 - 44

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (4 - 39*x**2)*(-56*x**3 - 11)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (-56*x**3)*(4 - 39*x**2) - 11*(4 - 39*x**2)</replace>
Simplifying the partial expression: -11*(4 - 39*x**2)
Expanding the part (4 - 39*x**2) using the distributive property, and we got: -39*x**2*(-11) + 4*(-11)
Replacing -11*(4 - 39*x**2) with -39*x**2*(-11) + 4*(-11) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -39*x**2*(-11) + (-56*x**3)*(4 - 39*x**2) - 44</replace>
Simplifying the partial expression: (-56*x**3)*(4 - 39*x**2)
Expanding the part (4 - 39*x**2) using the distributive property, and we got: 4*(-56*x**3) + (-39*x**2)*(-56*x**3)
Replacing (-56*x**3)*(4 - 39*x**2) with 4*(-56*x**3) + (-39*x**2)*(-56*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 4*(-56)*x**3 + (-39*x**2)*(-56*x**3) - 39*x**2*(-11) - 44</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-39*x**2)*-11 = 429*x**2
  (-39*x**2)*(-56*x**3) = 2184*x**5
  4*-56*x**3 = -224*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2184*x**5 - 224*x**3 + 429*x**2 - 44</replace>
No more calculations needed.
<answer>2184*x**5 - 224*x**3 + 429*x**2 - 44</answer>


Question:
Calculate the following: (-17*z**3 - 43*z - 27)*(22*z**3 - 24*z**2 - 25)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -374*z**6 + 408*z**5 - 946*z**4 + 863*z**3 + 648*z**2 + 1075*z + 675


Question:
Simplify this expression: (9*y**3 + 50)*(10*y**3 + 39*y**2 - 22)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 90*y**6 + 351*y**5 + 302*y**3 + 1950*y**2 - 1100

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (9*y**3 + 50)*(10*y**3 + 39*y**2 - 22)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (9*y**3)*(10*y**3 + 39*y**2 - 22) + 50*(10*y**3 + 39*y**2 - 22)</replace>
Simplifying the partial expression: 50*(10*y**3 + 39*y**2 - 22)
Expanding 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
Replacing 50*(10*y**3 + 39*y**2 - 22) with (39*y**2)*50 + (10*y**3)*50 - 22*50 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (39*y**2)*50 + (9*y**3)*(10*y**3 + 39*y**2 - 22) + (10*y**3)*50 - 1100</replace>
Simplifying the partial expression: (9*y**3)*(10*y**3 + 39*y**2 - 22)
Expanding 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)
Replacing (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.
<replace-#Step 3>#Step 4:
Current 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</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (10*y**3)*50 = 500*y**3
  (10*y**3)*(9*y**3) = 90*y**6
  (39*y**2)*50 = 1950*y**2
  (39*y**2)*(9*y**3) = 351*y**5
  -22*9*y**3 = -198*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 90*y**6 + 351*y**5 - 198*y**3 + 500*y**3 + 1950*y**2 - 1100</replace>
Combining like terms, got 90*y**6 + 351*y**5 + 302*y**3 + 1950*y**2 - 1100
<replace-#Step 5>#Step 6:
Current expression: 90*y**6 + 351*y**5 + 302*y**3 + 1950*y**2 - 1100</replace>
No more calculations needed.
<answer>90*y**6 + 351*y**5 + 302*y**3 + 1950*y**2 - 1100</answer>


Question:
Simplify this expression: (45*y**3 - 4*y)*(-47*y**3 - 39*y + 24)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2115*y**6 - 1567*y**4 + 1080*y**3 + 156*y**2 - 96*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (45*y**3 - 4*y)*(-47*y**3 - 39*y + 24)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (-4*y)*(-47*y**3 - 39*y + 24) + (45*y**3)*(-47*y**3 - 39*y + 24)</replace>
Simplifying the partial expression: (-4*y)*(-47*y**3 - 39*y + 24)
Expanding 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)
Replacing (-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.
<replace-#Step 2>#Step 3:
Current expression: (-39*y)*(-4*y) + (-4*y)*(-47*y**3) + 24*(-4)*y + (45*y**3)*(-47*y**3 - 39*y + 24)</replace>
Simplifying the partial expression: (45*y**3)*(-47*y**3 - 39*y + 24)
Expanding 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)
Replacing (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.
<replace-#Step 3>#Step 4:
Current 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)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-47*y**3)*(-4*y) = 188*y**4
  (-47*y**3)*(45*y**3) = -2115*y**6
  (-39*y)*(-4*y) = 156*y**2
  (-39*y)*(45*y**3) = -1755*y**4
  24*-4*y = -96*y
  24*45*y**3 = 1080*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2115*y**6 - 1755*y**4 + 188*y**4 + 1080*y**3 + 156*y**2 - 96*y</replace>
Combining like terms, got -2115*y**6 - 1567*y**4 + 1080*y**3 + 156*y**2 - 96*y
<replace-#Step 5>#Step 6:
Current expression: -2115*y**6 - 1567*y**4 + 1080*y**3 + 156*y**2 - 96*y</replace>
No more calculations needed.
<answer>-2115*y**6 - 1567*y**4 + 1080*y**3 + 156*y**2 - 96*y</answer>


Question:
Calculate the following: (-18*y**3 - 33*y - 1)*(-9*y**3 + 7*y + 38)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 162*y**6 + 171*y**4 - 675*y**3 - 231*y**2 - 1261*y - 38


Question:
Calculate the following: (-35*z**3 + 17*z**2)*(5*z**2 + 38*z - 15)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -175*z**5 - 1245*z**4 + 1171*z**3 - 255*z**2


Question:
Calculate the following: (16*y + 27)*(y**2 - 33)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 16*y**3 + 27*y**2 - 528*y - 891

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (16*y + 27)*(y**2 - 33)
Expanding the part (y**2 - 33) using the distributive property, and we got: y**2*(16*y + 27) - 33*(16*y + 27)
<replace-#Step 1>#Step 2:
Current expression: y**2*(16*y + 27) - 33*(16*y + 27)</replace>
Simplifying the partial expression: -33*(16*y + 27)
Expanding the part (16*y + 27) using the distributive property, and we got: (16*y)*(-33) + 27*(-33)
Replacing -33*(16*y + 27) with (16*y)*(-33) + 27*(-33) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: y**2*(16*y + 27) + (16*y)*(-33) - 891</replace>
Simplifying the partial expression: y**2*(16*y + 27)
Expanding the part (16*y + 27) using the distributive property, and we got: (16*y)*y**2 + 27*y**2
Replacing y**2*(16*y + 27) with (16*y)*y**2 + 27*y**2 in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (16*y)*y**2 + 27*y**2 + (16*y)*(-33) - 891</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (16*y)*-33 = -528*y
  (16*y)*y**2 = 16*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 16*y**3 + 27*y**2 - 528*y - 891</replace>
No more calculations needed.
<answer>16*y**3 + 27*y**2 - 528*y - 891</answer>


Question:
Simplify this expression: (31*z**3 - 46*z**2)*(44*z**3 - 33*z + 48)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1364*z**6 - 2024*z**5 - 1023*z**4 + 3006*z**3 - 2208*z**2


Question:
Simplify this expression: 49*x**3*(33 - 17*x**3)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -833*x**6 + 1617*x**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 49*x**3*(33 - 17*x**3)
Expanding the part (33 - 17*x**3) using the distributive property, and we got: 33*(49*x**3) + (-17*x**3)*(49*x**3)
<replace-#Step 1>#Step 2:
Current expression: 33*(49*x**3) + (-17*x**3)*(49*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  33*(49*x**3) = 1617*x**3
  (-17*x**3)*(49*x**3) = -833*x**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -833*x**6 + 1617*x**3</replace>
No more calculations needed.
<answer>-833*x**6 + 1617*x**3</answer>


Question:
Simplify this expression: (27*z**2 - 20*z)*(4*z**3 - 3*z**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 108*z**5 - 161*z**4 + 60*z**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (27*z**2 - 20*z)*(4*z**3 - 3*z**2)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (-20*z)*(4*z**3 - 3*z**2) + (27*z**2)*(4*z**3 - 3*z**2)</replace>
Simplifying the partial expression: (-20*z)*(4*z**3 - 3*z**2)
Expanding 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)
Replacing (-20*z)*(4*z**3 - 3*z**2) with (-20*z)*(-3*z**2) + (-20*z)*(4*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-20*z)*(-3*z**2) + (-20*z)*(4*z**3) + (27*z**2)*(4*z**3 - 3*z**2)</replace>
Simplifying the partial expression: (27*z**2)*(4*z**3 - 3*z**2)
Expanding 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)
Replacing (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.
<replace-#Step 3>#Step 4:
Current expression: (-20*z)*(-3*z**2) + (-20*z)*(4*z**3) + (-3*z**2)*(27*z**2) + (27*z**2)*(4*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-3*z**2)*(-20*z) = 60*z**3
  (-3*z**2)*(27*z**2) = -81*z**4
  (4*z**3)*(-20*z) = -80*z**4
  (4*z**3)*(27*z**2) = 108*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 108*z**5 - 81*z**4 - 80*z**4 + 60*z**3</replace>
Combining like terms, got 108*z**5 - 161*z**4 + 60*z**3
<replace-#Step 5>#Step 6:
Current expression: 108*z**5 - 161*z**4 + 60*z**3</replace>
No more calculations needed.
<answer>108*z**5 - 161*z**4 + 60*z**3</answer>


Question:
Simplify this expression: (37 - 44*z)*(28*z**2 + 38*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1232*z**3 - 636*z**2 + 1406*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (37 - 44*z)*(28*z**2 + 38*z)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (-44*z)*(28*z**2 + 38*z) + 37*(28*z**2 + 38*z)</replace>
Simplifying the partial expression: 37*(28*z**2 + 38*z)
Expanding the part (28*z**2 + 38*z) using the distributive property, and we got: (38*z)*37 + (28*z**2)*37
Replacing 37*(28*z**2 + 38*z) with (38*z)*37 + (28*z**2)*37 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-44*z)*(28*z**2 + 38*z) + (38*z)*37 + (28*z**2)*37</replace>
Simplifying the partial expression: (-44*z)*(28*z**2 + 38*z)
Expanding the part (28*z**2 + 38*z) using the distributive property, and we got: (-44*z)*(38*z) + (-44*z)*(28*z**2)
Replacing (-44*z)*(28*z**2 + 38*z) with (-44*z)*(38*z) + (-44*z)*(28*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-44*z)*(38*z) + (-44*z)*(28*z**2) + (38*z)*37 + (28*z**2)*37</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (28*z**2)*37 = 1036*z**2
  (28*z**2)*(-44*z) = -1232*z**3
  (38*z)*37 = 1406*z
  (38*z)*(-44*z) = -1672*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1232*z**3 - 1672*z**2 + 1036*z**2 + 1406*z</replace>
Combining like terms, got -1232*z**3 - 636*z**2 + 1406*z
<replace-#Step 5>#Step 6:
Current expression: -1232*z**3 - 636*z**2 + 1406*z</replace>
No more calculations needed.
<answer>-1232*z**3 - 636*z**2 + 1406*z</answer>


Question:
Calculate the following: (-21*x - 41)*(-35*x**3 + 57*x**2 + 49*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 735*x**4 + 238*x**3 - 3366*x**2 - 2009*x


Question:
Simplify this expression: (8*y**3 - 43)*(-47*y**3 - 28*y**2 - 7)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -376*y**6 - 224*y**5 + 1965*y**3 + 1204*y**2 + 301

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (8*y**3 - 43)*(-47*y**3 - 28*y**2 - 7)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (8*y**3)*(-47*y**3 - 28*y**2 - 7) - 43*(-47*y**3 - 28*y**2 - 7)</replace>
Simplifying the partial expression: -43*(-47*y**3 - 28*y**2 - 7)
Expanding 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)
Replacing -43*(-47*y**3 - 28*y**2 - 7) with -28*y**2*(-43) - 47*y**3*(-43) - 7*(-43) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -28*y**2*(-43) - 47*y**3*(-43) + (8*y**3)*(-47*y**3 - 28*y**2 - 7) + 301</replace>
Simplifying the partial expression: (8*y**3)*(-47*y**3 - 28*y**2 - 7)
Expanding 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)
Replacing (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.
<replace-#Step 3>#Step 4:
Current 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</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-47*y**3)*-43 = 2021*y**3
  (-47*y**3)*(8*y**3) = -376*y**6
  (-28*y**2)*-43 = 1204*y**2
  (-28*y**2)*(8*y**3) = -224*y**5
  -7*8*y**3 = -56*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -376*y**6 - 224*y**5 - 56*y**3 + 2021*y**3 + 1204*y**2 + 301</replace>
Combining like terms, got -376*y**6 - 224*y**5 + 1965*y**3 + 1204*y**2 + 301
<replace-#Step 5>#Step 6:
Current expression: -376*y**6 - 224*y**5 + 1965*y**3 + 1204*y**2 + 301</replace>
No more calculations needed.
<answer>-376*y**6 - 224*y**5 + 1965*y**3 + 1204*y**2 + 301</answer>


Question:
Calculate the following: (-45*x**3 + 13*x - 22)*(9*x**3 + 26*x**2 - 16*x - 32)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -405*x**6 - 1170*x**5 + 837*x**4 + 1580*x**3 - 780*x**2 - 64*x + 704


Question:
Simplify this expression: (39*y**2 - 4)*(-19*y**3 + 34*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -741*y**5 + 1402*y**3 - 136*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (39*y**2 - 4)*(-19*y**3 + 34*y)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (39*y**2)*(-19*y**3 + 34*y) - 4*(-19*y**3 + 34*y)</replace>
Simplifying the partial expression: -4*(-19*y**3 + 34*y)
Expanding the part (-19*y**3 + 34*y) using the distributive property, and we got: (34*y)*(-4) - 19*y**3*(-4)
Replacing -4*(-19*y**3 + 34*y) with (34*y)*(-4) - 19*y**3*(-4) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (34*y)*(-4) + (39*y**2)*(-19*y**3 + 34*y) - 19*y**3*(-4)</replace>
Simplifying the partial expression: (39*y**2)*(-19*y**3 + 34*y)
Expanding 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)
Replacing (39*y**2)*(-19*y**3 + 34*y) with (34*y)*(39*y**2) + (39*y**2)*(-19*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (34*y)*(39*y**2) + (34*y)*(-4) + (39*y**2)*(-19*y**3) - 19*y**3*(-4)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-19*y**3)*-4 = 76*y**3
  (-19*y**3)*(39*y**2) = -741*y**5
  (34*y)*-4 = -136*y
  (34*y)*(39*y**2) = 1326*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -741*y**5 + 76*y**3 + 1326*y**3 - 136*y</replace>
Combining like terms, got -741*y**5 + 1402*y**3 - 136*y
<replace-#Step 5>#Step 6:
Current expression: -741*y**5 + 1402*y**3 - 136*y</replace>
No more calculations needed.
<answer>-741*y**5 + 1402*y**3 - 136*y</answer>


Question:
Calculate the following: (-42*z**2 + 13*z)*(32*z**3 + 17*z**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1344*z**5 - 298*z**4 + 221*z**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-42*z**2 + 13*z)*(32*z**3 + 17*z**2)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (13*z)*(32*z**3 + 17*z**2) + (-42*z**2)*(32*z**3 + 17*z**2)</replace>
Simplifying the partial expression: (-42*z**2)*(32*z**3 + 17*z**2)
Expanding 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)
Replacing (-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.
<replace-#Step 2>#Step 3:
Current expression: (13*z)*(32*z**3 + 17*z**2) + (-42*z**2)*(17*z**2) + (-42*z**2)*(32*z**3)</replace>
Simplifying the partial expression: (13*z)*(32*z**3 + 17*z**2)
Expanding 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)
Replacing (13*z)*(32*z**3 + 17*z**2) with (13*z)*(17*z**2) + (13*z)*(32*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (13*z)*(17*z**2) + (13*z)*(32*z**3) + (-42*z**2)*(17*z**2) + (-42*z**2)*(32*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (17*z**2)*(-42*z**2) = -714*z**4
  (17*z**2)*(13*z) = 221*z**3
  (32*z**3)*(-42*z**2) = -1344*z**5
  (32*z**3)*(13*z) = 416*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1344*z**5 - 714*z**4 + 416*z**4 + 221*z**3</replace>
Combining like terms, got -1344*z**5 - 298*z**4 + 221*z**3
<replace-#Step 5>#Step 6:
Current expression: -1344*z**5 - 298*z**4 + 221*z**3</replace>
No more calculations needed.
<answer>-1344*z**5 - 298*z**4 + 221*z**3</answer>


Question:
Calculate the following: (17*y**3 - 29)*(13*y**3 + 43*y**2 + 30)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 221*y**6 + 731*y**5 + 133*y**3 - 1247*y**2 - 870

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (17*y**3 - 29)*(13*y**3 + 43*y**2 + 30)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (17*y**3)*(13*y**3 + 43*y**2 + 30) - 29*(13*y**3 + 43*y**2 + 30)</replace>
Simplifying the partial expression: -29*(13*y**3 + 43*y**2 + 30)
Expanding 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)
Replacing -29*(13*y**3 + 43*y**2 + 30) with (43*y**2)*(-29) + (13*y**3)*(-29) + 30*(-29) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (43*y**2)*(-29) + (13*y**3)*(-29) + (17*y**3)*(13*y**3 + 43*y**2 + 30) - 870</replace>
Simplifying the partial expression: (17*y**3)*(13*y**3 + 43*y**2 + 30)
Expanding 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)
Replacing (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.
<replace-#Step 3>#Step 4:
Current 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</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (13*y**3)*-29 = -377*y**3
  (13*y**3)*(17*y**3) = 221*y**6
  (43*y**2)*-29 = -1247*y**2
  (43*y**2)*(17*y**3) = 731*y**5
  30*17*y**3 = 510*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 221*y**6 + 731*y**5 - 377*y**3 + 510*y**3 - 1247*y**2 - 870</replace>
Combining like terms, got 221*y**6 + 731*y**5 + 133*y**3 - 1247*y**2 - 870
<replace-#Step 5>#Step 6:
Current expression: 221*y**6 + 731*y**5 + 133*y**3 - 1247*y**2 - 870</replace>
No more calculations needed.
<answer>221*y**6 + 731*y**5 + 133*y**3 - 1247*y**2 - 870</answer>


Question:
Calculate the following: (-21*y**3 - 31*y)*(-7*y**3 - 25*y**2 - 4*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 147*y**6 + 525*y**5 + 301*y**4 + 775*y**3 + 124*y**2


Question:
Simplify this expression: (-34*x**3 - 10*x)*(33*x**3 - 34*x + 42)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1122*x**6 + 826*x**4 - 1428*x**3 + 340*x**2 - 420*x


Question:
Simplify this expression: (-4*y**2 - 7)*(-26*y**3 - 16*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 104*y**5 + 64*y**4 + 182*y**3 + 112*y**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-4*y**2 - 7)*(-26*y**3 - 16*y**2)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (-4*y**2)*(-26*y**3 - 16*y**2) - 7*(-26*y**3 - 16*y**2)</replace>
Simplifying the partial expression: -7*(-26*y**3 - 16*y**2)
Expanding the part (-26*y**3 - 16*y**2) using the distributive property, and we got: -16*y**2*(-7) - 26*y**3*(-7)
Replacing -7*(-26*y**3 - 16*y**2) with -16*y**2*(-7) - 26*y**3*(-7) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -16*y**2*(-7) + (-4*y**2)*(-26*y**3 - 16*y**2) - 26*y**3*(-7)</replace>
Simplifying the partial expression: (-4*y**2)*(-26*y**3 - 16*y**2)
Expanding 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)
Replacing (-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.
<replace-#Step 3>#Step 4:
Current expression: (-16*y**2)*(-4*y**2) - 16*y**2*(-7) + (-4*y**2)*(-26*y**3) - 26*y**3*(-7)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-26*y**3)*-7 = 182*y**3
  (-26*y**3)*(-4*y**2) = 104*y**5
  (-16*y**2)*-7 = 112*y**2
  (-16*y**2)*(-4*y**2) = 64*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 104*y**5 + 64*y**4 + 182*y**3 + 112*y**2</replace>
No more calculations needed.
<answer>104*y**5 + 64*y**4 + 182*y**3 + 112*y**2</answer>


Question:
Simplify this expression: (-11*z**3 + 10*z**2 + 41)*(5*z**3 + 23*z + 21)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -55*z**6 + 50*z**5 - 253*z**4 + 204*z**3 + 210*z**2 + 943*z + 861


Question:
Calculate the following: 2444*x**3 + 4420*x**2 + 468*x
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2444*x**3 + 4420*x**2 + 468*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 2444*x**3 + 4420*x**2 + 468*x
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: 2444*x**3 + 4420*x**2 + 468*x</replace>
No more calculations needed.
<answer>2444*x**3 + 4420*x**2 + 468*x</answer>


Question:
Simplify this expression: (-27*y**2 + 14*y)*(39*y**3 - 24)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1053*y**5 + 546*y**4 + 648*y**2 - 336*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-27*y**2 + 14*y)*(39*y**3 - 24)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (39*y**3)*(-27*y**2 + 14*y) - 24*(-27*y**2 + 14*y)</replace>
Simplifying the partial expression: -24*(-27*y**2 + 14*y)
Expanding the part (-27*y**2 + 14*y) using the distributive property, and we got: (14*y)*(-24) - 27*y**2*(-24)
Replacing -24*(-27*y**2 + 14*y) with (14*y)*(-24) - 27*y**2*(-24) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (14*y)*(-24) - 27*y**2*(-24) + (39*y**3)*(-27*y**2 + 14*y)</replace>
Simplifying the partial expression: (39*y**3)*(-27*y**2 + 14*y)
Expanding 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)
Replacing (39*y**3)*(-27*y**2 + 14*y) with (14*y)*(39*y**3) + (-27*y**2)*(39*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (14*y)*(39*y**3) + (14*y)*(-24) + (-27*y**2)*(39*y**3) - 27*y**2*(-24)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-27*y**2)*-24 = 648*y**2
  (-27*y**2)*(39*y**3) = -1053*y**5
  (14*y)*-24 = -336*y
  (14*y)*(39*y**3) = 546*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1053*y**5 + 546*y**4 + 648*y**2 - 336*y</replace>
No more calculations needed.
<answer>-1053*y**5 + 546*y**4 + 648*y**2 - 336*y</answer>


Question:
Calculate the following: (-20*y**3 + 25*y**2)*(-12*y**3 + 17*y**2 + 26*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 240*y**6 - 640*y**5 - 95*y**4 + 650*y**3


Question:
Simplify this expression: 2574*x**2 - 3630
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2574*x**2 - 3630

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 2574*x**2 - 3630
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: 2574*x**2 - 3630</replace>
No more calculations needed.
<answer>2574*x**2 - 3630</answer>


Question:
Calculate the following: (-49*y**3 + 16*y)*(-44*y**3 + 29*y - 20)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2156*y**6 - 2125*y**4 + 980*y**3 + 464*y**2 - 320*y


Question:
Calculate the following: 304*x**2
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 304*x**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 304*x**2
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: 304*x**2</replace>
No more calculations needed.
<answer>304*x**2</answer>


Question:
Calculate the following: 44*z**2*(-28*z**2 - 11*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1232*z**4 - 484*z**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 44*z**2*(-28*z**2 - 11*z)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (-11*z)*(44*z**2) + (-28*z**2)*(44*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-28*z**2)*(44*z**2) = -1232*z**4
  (-11*z)*(44*z**2) = -484*z**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1232*z**4 - 484*z**3</replace>
No more calculations needed.
<answer>-1232*z**4 - 484*z**3</answer>


Question:
Calculate the following: (26*y + 3)*(64*y**3 + 37)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1664*y**4 + 192*y**3 + 962*y + 111

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (26*y + 3)*(64*y**3 + 37)
Expanding the part (26*y + 3) using the distributive property, and we got: (26*y)*(64*y**3 + 37) + 3*(64*y**3 + 37)
<replace-#Step 1>#Step 2:
Current expression: (26*y)*(64*y**3 + 37) + 3*(64*y**3 + 37)</replace>
Simplifying the partial expression: 3*(64*y**3 + 37)
Expanding the part (64*y**3 + 37) using the distributive property, and we got: (64*y**3)*3 + 37*3
Replacing 3*(64*y**3 + 37) with (64*y**3)*3 + 37*3 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (26*y)*(64*y**3 + 37) + (64*y**3)*3 + 111</replace>
Simplifying the partial expression: (26*y)*(64*y**3 + 37)
Expanding the part (64*y**3 + 37) using the distributive property, and we got: 37*(26*y) + (26*y)*(64*y**3)
Replacing (26*y)*(64*y**3 + 37) with 37*(26*y) + (26*y)*(64*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 37*26*y + (26*y)*(64*y**3) + (64*y**3)*3 + 111</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (64*y**3)*3 = 192*y**3
  (64*y**3)*(26*y) = 1664*y**4
  37*26*y = 962*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1664*y**4 + 192*y**3 + 962*y + 111</replace>
No more calculations needed.
<answer>1664*y**4 + 192*y**3 + 962*y + 111</answer>


Question:
Calculate the following: (35 - 37*z**3)*(82*z**3 - 7*z**2 - 39*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -3034*z**6 + 259*z**5 + 1443*z**4 + 2870*z**3 - 245*z**2 - 1365*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (35 - 37*z**3)*(82*z**3 - 7*z**2 - 39*z)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (-37*z**3)*(82*z**3 - 7*z**2 - 39*z) + 35*(82*z**3 - 7*z**2 - 39*z)</replace>
Simplifying the partial expression: 35*(82*z**3 - 7*z**2 - 39*z)
Expanding 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
Replacing 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.
<replace-#Step 2>#Step 3:
Current expression: -39*z*35 - 7*z**2*35 + (-37*z**3)*(82*z**3 - 7*z**2 - 39*z) + (82*z**3)*35</replace>
Simplifying the partial expression: (-37*z**3)*(82*z**3 - 7*z**2 - 39*z)
Expanding 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)
Replacing (-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.
<replace-#Step 3>#Step 4:
Current 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</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-39*z)*35 = -1365*z
  (-39*z)*(-37*z**3) = 1443*z**4
  (-7*z**2)*35 = -245*z**2
  (-7*z**2)*(-37*z**3) = 259*z**5
  (82*z**3)*35 = 2870*z**3
  (82*z**3)*(-37*z**3) = -3034*z**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -3034*z**6 + 259*z**5 + 1443*z**4 + 2870*z**3 - 245*z**2 - 1365*z</replace>
No more calculations needed.
<answer>-3034*z**6 + 259*z**5 + 1443*z**4 + 2870*z**3 - 245*z**2 - 1365*z</answer>


Question:
Simplify this expression: 85*y**3*(-24*y**2 + 48*y - 40)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2040*y**5 + 4080*y**4 - 3400*y**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 85*y**3*(-24*y**2 + 48*y - 40)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: -3400*y**3 + (48*y)*(85*y**3) + (-24*y**2)*(85*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -40*(85*y**3) = -3400*y**3
  (-24*y**2)*(85*y**3) = -2040*y**5
  (48*y)*(85*y**3) = 4080*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -2040*y**5 + 4080*y**4 - 3400*y**3</replace>
No more calculations needed.
<answer>-2040*y**5 + 4080*y**4 - 3400*y**3</answer>


Question:
Simplify this expression: -20*x**2*(34*x - 40)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -680*x**3 + 800*x**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -20*x**2*(34*x - 40)
Expanding the part (34*x - 40) using the distributive property, and we got: -(-1)*800*x**2 + (34*x)*(-20*x**2)
<replace-#Step 1>#Step 2:
Current expression: -(-1)*800*x**2 + (34*x)*(-20*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -40*(-20*x**2) = 800*x**2
  (34*x)*(-20*x**2) = -680*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -680*x**3 + 800*x**2</replace>
No more calculations needed.
<answer>-680*x**3 + 800*x**2</answer>


Question:
Calculate the following: 33*x*(28*x**2 + 47)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 924*x**3 + 1551*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 33*x*(28*x**2 + 47)
Expanding the part (28*x**2 + 47) using the distributive property, and we got: 47*(33*x) + (33*x)*(28*x**2)
<replace-#Step 1>#Step 2:
Current expression: 47*(33*x) + (33*x)*(28*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  47*(33*x) = 1551*x
  (28*x**2)*(33*x) = 924*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 924*x**3 + 1551*x</replace>
No more calculations needed.
<answer>924*x**3 + 1551*x</answer>


Question:
Simplify this expression: (42*z + 39)*(-2*z**3 - 48)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -84*z**4 - 78*z**3 - 2016*z - 1872

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (42*z + 39)*(-2*z**3 - 48)
Expanding the part (-2*z**3 - 48) using the distributive property, and we got: (-2*z**3)*(42*z + 39) - 48*(42*z + 39)
<replace-#Step 1>#Step 2:
Current expression: (-2*z**3)*(42*z + 39) - 48*(42*z + 39)</replace>
Simplifying the partial expression: -48*(42*z + 39)
Expanding the part (42*z + 39) using the distributive property, and we got: (42*z)*(-48) + 39*(-48)
Replacing -48*(42*z + 39) with (42*z)*(-48) + 39*(-48) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (42*z)*(-48) + (-2*z**3)*(42*z + 39) - 1872</replace>
Simplifying the partial expression: (-2*z**3)*(42*z + 39)
Expanding the part (42*z + 39) using the distributive property, and we got: 39*(-2*z**3) + (42*z)*(-2*z**3)
Replacing (-2*z**3)*(42*z + 39) with 39*(-2*z**3) + (42*z)*(-2*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 39*(-2)*z**3 + (42*z)*(-2*z**3) + (42*z)*(-48) - 1872</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (42*z)*-48 = -2016*z
  (42*z)*(-2*z**3) = -84*z**4
  39*-2*z**3 = -78*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -84*z**4 - 78*z**3 - 2016*z - 1872</replace>
No more calculations needed.
<answer>-84*z**4 - 78*z**3 - 2016*z - 1872</answer>


Question:
Calculate the following: (-28*z**3 + 24*z)*(-47*z**3 + 3*z**2 + 3*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1316*z**6 - 84*z**5 - 1212*z**4 + 72*z**3 + 72*z**2


Question:
Calculate the following: (17*y - 37)*(13*y**2 + 50)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 221*y**3 - 481*y**2 + 850*y - 1850

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (17*y - 37)*(13*y**2 + 50)
Expanding the part (17*y - 37) using the distributive property, and we got: (17*y)*(13*y**2 + 50) - 37*(13*y**2 + 50)
<replace-#Step 1>#Step 2:
Current expression: (17*y)*(13*y**2 + 50) - 37*(13*y**2 + 50)</replace>
Simplifying the partial expression: -37*(13*y**2 + 50)
Expanding the part (13*y**2 + 50) using the distributive property, and we got: (13*y**2)*(-37) + 50*(-37)
Replacing -37*(13*y**2 + 50) with (13*y**2)*(-37) + 50*(-37) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (17*y)*(13*y**2 + 50) + (13*y**2)*(-37) - 1850</replace>
Simplifying the partial expression: (17*y)*(13*y**2 + 50)
Expanding the part (13*y**2 + 50) using the distributive property, and we got: 50*(17*y) + (17*y)*(13*y**2)
Replacing (17*y)*(13*y**2 + 50) with 50*(17*y) + (17*y)*(13*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 50*17*y + (17*y)*(13*y**2) + (13*y**2)*(-37) - 1850</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (13*y**2)*-37 = -481*y**2
  (13*y**2)*(17*y) = 221*y**3
  50*17*y = 850*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 221*y**3 - 481*y**2 + 850*y - 1850</replace>
No more calculations needed.
<answer>221*y**3 - 481*y**2 + 850*y - 1850</answer>


Question:
Simplify this expression: (-59*y**2 + 45*y)*(29*y**3 + 3*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1711*y**5 + 1128*y**4 + 135*y**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-59*y**2 + 45*y)*(29*y**3 + 3*y**2)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (45*y)*(29*y**3 + 3*y**2) + (-59*y**2)*(29*y**3 + 3*y**2)</replace>
Simplifying the partial expression: (-59*y**2)*(29*y**3 + 3*y**2)
Expanding 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)
Replacing (-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.
<replace-#Step 2>#Step 3:
Current expression: (45*y)*(29*y**3 + 3*y**2) + (-59*y**2)*(3*y**2) + (-59*y**2)*(29*y**3)</replace>
Simplifying the partial expression: (45*y)*(29*y**3 + 3*y**2)
Expanding 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)
Replacing (45*y)*(29*y**3 + 3*y**2) with (45*y)*(3*y**2) + (45*y)*(29*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (45*y)*(3*y**2) + (45*y)*(29*y**3) + (-59*y**2)*(3*y**2) + (-59*y**2)*(29*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (3*y**2)*(-59*y**2) = -177*y**4
  (3*y**2)*(45*y) = 135*y**3
  (29*y**3)*(-59*y**2) = -1711*y**5
  (29*y**3)*(45*y) = 1305*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1711*y**5 - 177*y**4 + 1305*y**4 + 135*y**3</replace>
Combining like terms, got -1711*y**5 + 1128*y**4 + 135*y**3
<replace-#Step 5>#Step 6:
Current expression: -1711*y**5 + 1128*y**4 + 135*y**3</replace>
No more calculations needed.
<answer>-1711*y**5 + 1128*y**4 + 135*y**3</answer>


Question:
Calculate the following: (11 - 36*x**3)*(-33*x**3 - 45*x**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1188*x**6 + 1620*x**5 - 363*x**3 - 495*x**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (11 - 36*x**3)*(-33*x**3 - 45*x**2)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (-36*x**3)*(-33*x**3 - 45*x**2) + 11*(-33*x**3 - 45*x**2)</replace>
Simplifying the partial expression: 11*(-33*x**3 - 45*x**2)
Expanding the part (-33*x**3 - 45*x**2) using the distributive property, and we got: -45*x**2*11 - 33*x**3*11
Replacing 11*(-33*x**3 - 45*x**2) with -45*x**2*11 - 33*x**3*11 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -45*x**2*11 + (-36*x**3)*(-33*x**3 - 45*x**2) - 33*x**3*11</replace>
Simplifying the partial expression: (-36*x**3)*(-33*x**3 - 45*x**2)
Expanding 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)
Replacing (-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.
<replace-#Step 3>#Step 4:
Current expression: (-45*x**2)*(-36*x**3) - 45*x**2*11 + (-36*x**3)*(-33*x**3) - 33*x**3*11</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-45*x**2)*11 = -495*x**2
  (-45*x**2)*(-36*x**3) = 1620*x**5
  (-33*x**3)*11 = -363*x**3
  (-33*x**3)*(-36*x**3) = 1188*x**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1188*x**6 + 1620*x**5 - 363*x**3 - 495*x**2</replace>
No more calculations needed.
<answer>1188*x**6 + 1620*x**5 - 363*x**3 - 495*x**2</answer>


Question:
Calculate the following: (29*x**2 + 20)*(-9*x**3 + 37*x + 43)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -261*x**5 + 893*x**3 + 1247*x**2 + 740*x + 860

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (29*x**2 + 20)*(-9*x**3 + 37*x + 43)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (29*x**2)*(-9*x**3 + 37*x + 43) + 20*(-9*x**3 + 37*x + 43)</replace>
Simplifying the partial expression: 20*(-9*x**3 + 37*x + 43)
Expanding the part (-9*x**3 + 37*x + 43) using the distributive property, and we got: (37*x)*20 - 9*x**3*20 + 43*20
Replacing 20*(-9*x**3 + 37*x + 43) with (37*x)*20 - 9*x**3*20 + 43*20 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (37*x)*20 + (29*x**2)*(-9*x**3 + 37*x + 43) - 9*x**3*20 + 860</replace>
Simplifying the partial expression: (29*x**2)*(-9*x**3 + 37*x + 43)
Expanding 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)
Replacing (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.
<replace-#Step 3>#Step 4:
Current expression: 43*29*x**2 + (37*x)*(29*x**2) + (37*x)*20 + (29*x**2)*(-9*x**3) - 9*x**3*20 + 860</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-9*x**3)*20 = -180*x**3
  (-9*x**3)*(29*x**2) = -261*x**5
  (37*x)*20 = 740*x
  (37*x)*(29*x**2) = 1073*x**3
  43*29*x**2 = 1247*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -261*x**5 - 180*x**3 + 1073*x**3 + 1247*x**2 + 740*x + 860</replace>
Combining like terms, got -261*x**5 + 893*x**3 + 1247*x**2 + 740*x + 860
<replace-#Step 5>#Step 6:
Current expression: -261*x**5 + 893*x**3 + 1247*x**2 + 740*x + 860</replace>
No more calculations needed.
<answer>-261*x**5 + 893*x**3 + 1247*x**2 + 740*x + 860</answer>


Question:
Simplify this expression: (-49*y**2 - 41)*(29*y**3 - 2*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1421*y**5 - 1091*y**3 + 82*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-49*y**2 - 41)*(29*y**3 - 2*y)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (-49*y**2)*(29*y**3 - 2*y) - 41*(29*y**3 - 2*y)</replace>
Simplifying the partial expression: -41*(29*y**3 - 2*y)
Expanding the part (29*y**3 - 2*y) using the distributive property, and we got: -2*y*(-41) + (29*y**3)*(-41)
Replacing -41*(29*y**3 - 2*y) with -2*y*(-41) + (29*y**3)*(-41) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -2*y*(-41) + (-49*y**2)*(29*y**3 - 2*y) + (29*y**3)*(-41)</replace>
Simplifying the partial expression: (-49*y**2)*(29*y**3 - 2*y)
Expanding 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)
Replacing (-49*y**2)*(29*y**3 - 2*y) with (-2*y)*(-49*y**2) + (-49*y**2)*(29*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-2*y)*(-49*y**2) - 2*y*(-41) + (-49*y**2)*(29*y**3) + (29*y**3)*(-41)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-2*y)*-41 = 82*y
  (-2*y)*(-49*y**2) = 98*y**3
  (29*y**3)*-41 = -1189*y**3
  (29*y**3)*(-49*y**2) = -1421*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1421*y**5 - 1189*y**3 + 98*y**3 + 82*y</replace>
Combining like terms, got -1421*y**5 - 1091*y**3 + 82*y
<replace-#Step 5>#Step 6:
Current expression: -1421*y**5 - 1091*y**3 + 82*y</replace>
No more calculations needed.
<answer>-1421*y**5 - 1091*y**3 + 82*y</answer>


Question:
Simplify this expression: (y**2 + 30)*(-32*y**3 - 11*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -32*y**5 - 971*y**3 - 330*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (y**2 + 30)*(-32*y**3 - 11*y)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: y**2*(-32*y**3 - 11*y) + 30*(-32*y**3 - 11*y)</replace>
Simplifying the partial expression: 30*(-32*y**3 - 11*y)
Expanding the part (-32*y**3 - 11*y) using the distributive property, and we got: -11*y*30 - 32*y**3*30
Replacing 30*(-32*y**3 - 11*y) with -11*y*30 - 32*y**3*30 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -11*y*30 + y**2*(-32*y**3 - 11*y) - 32*y**3*30</replace>
Simplifying the partial expression: y**2*(-32*y**3 - 11*y)
Expanding the part (-32*y**3 - 11*y) using the distributive property, and we got: (-11*y)*y**2 + y**2*(-32*y**3)
Replacing y**2*(-32*y**3 - 11*y) with (-11*y)*y**2 + y**2*(-32*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-11*y)*y**2 - 11*y*30 + y**2*(-32*y**3) - 32*y**3*30</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-32*y**3)*30 = -960*y**3
  (-32*y**3)*y**2 = -32*y**5
  (-11*y)*30 = -330*y
  (-11*y)*y**2 = -11*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -32*y**5 - 960*y**3 - 11*y**3 - 330*y</replace>
Combining like terms, got -32*y**5 - 971*y**3 - 330*y
<replace-#Step 5>#Step 6:
Current expression: -32*y**5 - 971*y**3 - 330*y</replace>
No more calculations needed.
<answer>-32*y**5 - 971*y**3 - 330*y</answer>


Question:
Calculate the following: (-3*x**2 - 25*x)*(-31*x**3 + 25*x**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 93*x**5 + 700*x**4 - 625*x**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-3*x**2 - 25*x)*(-31*x**3 + 25*x**2)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (25*x**2)*(-3*x**2 - 25*x) + (-31*x**3)*(-3*x**2 - 25*x)</replace>
Simplifying the partial expression: (-31*x**3)*(-3*x**2 - 25*x)
Expanding 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)
Replacing (-31*x**3)*(-3*x**2 - 25*x) with (-25*x)*(-31*x**3) + (-3*x**2)*(-31*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-25*x)*(-31*x**3) + (-3*x**2)*(-31*x**3) + (25*x**2)*(-3*x**2 - 25*x)</replace>
Simplifying the partial expression: (25*x**2)*(-3*x**2 - 25*x)
Expanding 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)
Replacing (25*x**2)*(-3*x**2 - 25*x) with (-25*x)*(25*x**2) + (-3*x**2)*(25*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-25*x)*(25*x**2) + (-25*x)*(-31*x**3) + (-3*x**2)*(25*x**2) + (-3*x**2)*(-31*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-25*x)*(-31*x**3) = 775*x**4
  (-25*x)*(25*x**2) = -625*x**3
  (-3*x**2)*(-31*x**3) = 93*x**5
  (-3*x**2)*(25*x**2) = -75*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 93*x**5 - 75*x**4 + 775*x**4 - 625*x**3</replace>
Combining like terms, got 93*x**5 + 700*x**4 - 625*x**3
<replace-#Step 5>#Step 6:
Current expression: 93*x**5 + 700*x**4 - 625*x**3</replace>
No more calculations needed.
<answer>93*x**5 + 700*x**4 - 625*x**3</answer>


Question:
Simplify this expression: (74 - 13*z**3)*(5*z**2 + 14*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -65*z**5 - 182*z**4 + 370*z**2 + 1036*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (74 - 13*z**3)*(5*z**2 + 14*z)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (-13*z**3)*(5*z**2 + 14*z) + 74*(5*z**2 + 14*z)</replace>
Simplifying the partial expression: 74*(5*z**2 + 14*z)
Expanding the part (5*z**2 + 14*z) using the distributive property, and we got: (14*z)*74 + (5*z**2)*74
Replacing 74*(5*z**2 + 14*z) with (14*z)*74 + (5*z**2)*74 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (14*z)*74 + (5*z**2)*74 + (-13*z**3)*(5*z**2 + 14*z)</replace>
Simplifying the partial expression: (-13*z**3)*(5*z**2 + 14*z)
Expanding 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)
Replacing (-13*z**3)*(5*z**2 + 14*z) with (14*z)*(-13*z**3) + (5*z**2)*(-13*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (14*z)*(-13*z**3) + (14*z)*74 + (5*z**2)*(-13*z**3) + (5*z**2)*74</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (5*z**2)*74 = 370*z**2
  (5*z**2)*(-13*z**3) = -65*z**5
  (14*z)*74 = 1036*z
  (14*z)*(-13*z**3) = -182*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -65*z**5 - 182*z**4 + 370*z**2 + 1036*z</replace>
No more calculations needed.
<answer>-65*z**5 - 182*z**4 + 370*z**2 + 1036*z</answer>


Question:
Simplify this expression: (15 - 42*z**2)*(-30*z**3 + 40*z**2 - 27)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1260*z**5 - 1680*z**4 - 450*z**3 + 1734*z**2 - 405

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (15 - 42*z**2)*(-30*z**3 + 40*z**2 - 27)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (-42*z**2)*(-30*z**3 + 40*z**2 - 27) + 15*(-30*z**3 + 40*z**2 - 27)</replace>
Simplifying the partial expression: 15*(-30*z**3 + 40*z**2 - 27)
Expanding 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
Replacing 15*(-30*z**3 + 40*z**2 - 27) with (40*z**2)*15 - 30*z**3*15 - 27*15 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-42*z**2)*(-30*z**3 + 40*z**2 - 27) + (40*z**2)*15 - 30*z**3*15 - 405</replace>
Simplifying the partial expression: (-42*z**2)*(-30*z**3 + 40*z**2 - 27)
Expanding 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)
Replacing (-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.
<replace-#Step 3>#Step 4:
Current 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</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-30*z**3)*15 = -450*z**3
  (-30*z**3)*(-42*z**2) = 1260*z**5
  (40*z**2)*15 = 600*z**2
  (40*z**2)*(-42*z**2) = -1680*z**4
  -27*-42*z**2 = 1134*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1260*z**5 - 1680*z**4 - 450*z**3 + 600*z**2 + 1134*z**2 - 405</replace>
Combining like terms, got 1260*z**5 - 1680*z**4 - 450*z**3 + 1734*z**2 - 405
<replace-#Step 5>#Step 6:
Current expression: 1260*z**5 - 1680*z**4 - 450*z**3 + 1734*z**2 - 405</replace>
No more calculations needed.
<answer>1260*z**5 - 1680*z**4 - 450*z**3 + 1734*z**2 - 405</answer>


Question:
Simplify this expression: (-40*x**3 - 32)*(15*x**3 - 20*x**2 + 26*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -600*x**6 + 800*x**5 - 1040*x**4 - 480*x**3 + 640*x**2 - 832*x


Question:
Simplify this expression: -73*z**3*(22*z + 27)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1606*z**4 - 1971*z**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -73*z**3*(22*z + 27)
Expanding the part (22*z + 27) using the distributive property, and we got: 27*(-73*z**3) + (22*z)*(-73*z**3)
<replace-#Step 1>#Step 2:
Current expression: 27*(-73*z**3) + (22*z)*(-73*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  27*(-73*z**3) = -1971*z**3
  (22*z)*(-73*z**3) = -1606*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1606*z**4 - 1971*z**3</replace>
No more calculations needed.
<answer>-1606*z**4 - 1971*z**3</answer>


Question:
Simplify this expression: (46*y**2 + 45)*(-25*y**3 + 12*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1150*y**5 + 552*y**4 - 1125*y**3 + 540*y**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (46*y**2 + 45)*(-25*y**3 + 12*y**2)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (46*y**2)*(-25*y**3 + 12*y**2) + 45*(-25*y**3 + 12*y**2)</replace>
Simplifying the partial expression: 45*(-25*y**3 + 12*y**2)
Expanding the part (-25*y**3 + 12*y**2) using the distributive property, and we got: (12*y**2)*45 - 25*y**3*45
Replacing 45*(-25*y**3 + 12*y**2) with (12*y**2)*45 - 25*y**3*45 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (12*y**2)*45 + (46*y**2)*(-25*y**3 + 12*y**2) - 25*y**3*45</replace>
Simplifying the partial expression: (46*y**2)*(-25*y**3 + 12*y**2)
Expanding 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)
Replacing (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.
<replace-#Step 3>#Step 4:
Current expression: (12*y**2)*(46*y**2) + (12*y**2)*45 + (46*y**2)*(-25*y**3) - 25*y**3*45</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-25*y**3)*45 = -1125*y**3
  (-25*y**3)*(46*y**2) = -1150*y**5
  (12*y**2)*45 = 540*y**2
  (12*y**2)*(46*y**2) = 552*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1150*y**5 + 552*y**4 - 1125*y**3 + 540*y**2</replace>
No more calculations needed.
<answer>-1150*y**5 + 552*y**4 - 1125*y**3 + 540*y**2</answer>


Question:
Simplify this expression: (35 - 43*x**3)*(-37*x**3 - 38*x**2 - 37)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1591*x**6 + 1634*x**5 + 296*x**3 - 1330*x**2 - 1295


Question:
Calculate the following: (-21*z**3 - 13)*(41*z**3 + 36*z**2 + 21*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -861*z**6 - 756*z**5 - 441*z**4 - 533*z**3 - 468*z**2 - 273*z


Question:
Calculate the following: (22*x**3 + 15*x**2 - 48*x)*(49*x**3 - 23*x**2 + 7*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1078*x**6 + 229*x**5 - 2543*x**4 + 1209*x**3 - 336*x**2


Question:
Calculate the following: (-14*y - 37)*(20*y**3 - 44*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -280*y**4 - 124*y**3 + 1628*y**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-14*y - 37)*(20*y**3 - 44*y**2)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (-14*y)*(20*y**3 - 44*y**2) - 37*(20*y**3 - 44*y**2)</replace>
Simplifying the partial expression: -37*(20*y**3 - 44*y**2)
Expanding the part (20*y**3 - 44*y**2) using the distributive property, and we got: -44*y**2*(-37) + (20*y**3)*(-37)
Replacing -37*(20*y**3 - 44*y**2) with -44*y**2*(-37) + (20*y**3)*(-37) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-14*y)*(20*y**3 - 44*y**2) - 44*y**2*(-37) + (20*y**3)*(-37)</replace>
Simplifying the partial expression: (-14*y)*(20*y**3 - 44*y**2)
Expanding 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)
Replacing (-14*y)*(20*y**3 - 44*y**2) with (-14*y)*(-44*y**2) + (-14*y)*(20*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-14*y)*(-44*y**2) + (-14*y)*(20*y**3) - 44*y**2*(-37) + (20*y**3)*(-37)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-44*y**2)*-37 = 1628*y**2
  (-44*y**2)*(-14*y) = 616*y**3
  (20*y**3)*-37 = -740*y**3
  (20*y**3)*(-14*y) = -280*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -280*y**4 - 740*y**3 + 616*y**3 + 1628*y**2</replace>
Combining like terms, got -280*y**4 - 124*y**3 + 1628*y**2
<replace-#Step 5>#Step 6:
Current expression: -280*y**4 - 124*y**3 + 1628*y**2</replace>
No more calculations needed.
<answer>-280*y**4 - 124*y**3 + 1628*y**2</answer>


Question:
Simplify this expression: -15*y**3*(9*y**2 + 24*y - 29)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -135*y**5 - 360*y**4 + 435*y**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -15*y**3*(9*y**2 + 24*y - 29)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: -(-1)*435*y**3 + (24*y)*(-15*y**3) + (9*y**2)*(-15*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -29*(-15*y**3) = 435*y**3
  (9*y**2)*(-15*y**3) = -135*y**5
  (24*y)*(-15*y**3) = -360*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -135*y**5 - 360*y**4 + 435*y**3</replace>
No more calculations needed.
<answer>-135*y**5 - 360*y**4 + 435*y**3</answer>


Question:
Calculate the following: (8 - 15*x)*(41*x**3 + 32*x**2 + 18*x + 36)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -615*x**4 - 152*x**3 - 14*x**2 - 396*x + 288


Question:
Simplify this expression: (-47*y**2 - 50)*(-68*y**2 + 33*y + 19)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 3196*y**4 - 1551*y**3 + 2507*y**2 - 1650*y - 950

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-47*y**2 - 50)*(-68*y**2 + 33*y + 19)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (-47*y**2)*(-68*y**2 + 33*y + 19) - 50*(-68*y**2 + 33*y + 19)</replace>
Simplifying the partial expression: -50*(-68*y**2 + 33*y + 19)
Expanding the part (-68*y**2 + 33*y + 19) using the distributive property, and we got: (33*y)*(-50) - 68*y**2*(-50) + 19*(-50)
Replacing -50*(-68*y**2 + 33*y + 19) with (33*y)*(-50) - 68*y**2*(-50) + 19*(-50) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (33*y)*(-50) - 68*y**2*(-50) + (-47*y**2)*(-68*y**2 + 33*y + 19) - 950</replace>
Simplifying the partial expression: (-47*y**2)*(-68*y**2 + 33*y + 19)
Expanding 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)
Replacing (-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.
<replace-#Step 3>#Step 4:
Current expression: 19*(-47)*y**2 + (33*y)*(-47*y**2) + (33*y)*(-50) + (-68*y**2)*(-47*y**2) - 68*y**2*(-50) - 950</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-68*y**2)*-50 = 3400*y**2
  (-68*y**2)*(-47*y**2) = 3196*y**4
  (33*y)*-50 = -1650*y
  (33*y)*(-47*y**2) = -1551*y**3
  19*-47*y**2 = -893*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 3196*y**4 - 1551*y**3 - 893*y**2 + 3400*y**2 - 1650*y - 950</replace>
Combining like terms, got 3196*y**4 - 1551*y**3 + 2507*y**2 - 1650*y - 950
<replace-#Step 5>#Step 6:
Current expression: 3196*y**4 - 1551*y**3 + 2507*y**2 - 1650*y - 950</replace>
No more calculations needed.
<answer>3196*y**4 - 1551*y**3 + 2507*y**2 - 1650*y - 950</answer>


Question:
Calculate the following: (-44*y**2 + 40*y)*(-29*y**3 + 48*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1276*y**5 - 3272*y**4 + 1920*y**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-44*y**2 + 40*y)*(-29*y**3 + 48*y**2)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (40*y)*(-29*y**3 + 48*y**2) + (-44*y**2)*(-29*y**3 + 48*y**2)</replace>
Simplifying the partial expression: (-44*y**2)*(-29*y**3 + 48*y**2)
Expanding 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)
Replacing (-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.
<replace-#Step 2>#Step 3:
Current expression: (40*y)*(-29*y**3 + 48*y**2) + (-44*y**2)*(48*y**2) + (-44*y**2)*(-29*y**3)</replace>
Simplifying the partial expression: (40*y)*(-29*y**3 + 48*y**2)
Expanding 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)
Replacing (40*y)*(-29*y**3 + 48*y**2) with (40*y)*(48*y**2) + (40*y)*(-29*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (40*y)*(48*y**2) + (40*y)*(-29*y**3) + (-44*y**2)*(48*y**2) + (-44*y**2)*(-29*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-29*y**3)*(-44*y**2) = 1276*y**5
  (-29*y**3)*(40*y) = -1160*y**4
  (48*y**2)*(-44*y**2) = -2112*y**4
  (48*y**2)*(40*y) = 1920*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1276*y**5 - 2112*y**4 - 1160*y**4 + 1920*y**3</replace>
Combining like terms, got 1276*y**5 - 3272*y**4 + 1920*y**3
<replace-#Step 5>#Step 6:
Current expression: 1276*y**5 - 3272*y**4 + 1920*y**3</replace>
No more calculations needed.
<answer>1276*y**5 - 3272*y**4 + 1920*y**3</answer>


Question:
Calculate the following: 30*x**3*(73 - 20*x**3)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -600*x**6 + 2190*x**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 30*x**3*(73 - 20*x**3)
Expanding the part (73 - 20*x**3) using the distributive property, and we got: 73*(30*x**3) + (-20*x**3)*(30*x**3)
<replace-#Step 1>#Step 2:
Current expression: 73*(30*x**3) + (-20*x**3)*(30*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  73*(30*x**3) = 2190*x**3
  (-20*x**3)*(30*x**3) = -600*x**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -600*x**6 + 2190*x**3</replace>
No more calculations needed.
<answer>-600*x**6 + 2190*x**3</answer>


Question:
Simplify this expression: 16*z**2*(-48*z**2 - 49)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -768*z**4 - 784*z**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 16*z**2*(-48*z**2 - 49)
Expanding the part (-48*z**2 - 49) using the distributive property, and we got: -784*z**2 + (-48*z**2)*(16*z**2)
<replace-#Step 1>#Step 2:
Current expression: -784*z**2 + (-48*z**2)*(16*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -49*(16*z**2) = -784*z**2
  (-48*z**2)*(16*z**2) = -768*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -768*z**4 - 784*z**2</replace>
No more calculations needed.
<answer>-768*z**4 - 784*z**2</answer>


Question:
Calculate the following: (-3*z**3 - z + 32)*(26*z**3 + 43*z**2 + 5*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -78*z**6 - 129*z**5 - 41*z**4 + 789*z**3 + 1371*z**2 + 160*z


Question:
Calculate the following: (30 - 36*x)*(37*x**2 - 35*x + 41)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1332*x**3 + 2370*x**2 - 2526*x + 1230

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (30 - 36*x)*(37*x**2 - 35*x + 41)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (-36*x)*(37*x**2 - 35*x + 41) + 30*(37*x**2 - 35*x + 41)</replace>
Simplifying the partial expression: 30*(37*x**2 - 35*x + 41)
Expanding the part (37*x**2 - 35*x + 41) using the distributive property, and we got: -35*x*30 + (37*x**2)*30 + 41*30
Replacing 30*(37*x**2 - 35*x + 41) with -35*x*30 + (37*x**2)*30 + 41*30 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-36*x)*(37*x**2 - 35*x + 41) - 35*x*30 + (37*x**2)*30 + 1230</replace>
Simplifying the partial expression: (-36*x)*(37*x**2 - 35*x + 41)
Expanding 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)
Replacing (-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.
<replace-#Step 3>#Step 4:
Current expression: (-36*x)*(-35*x) + (-36*x)*(37*x**2) - 35*x*30 + 41*(-36)*x + (37*x**2)*30 + 1230</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-35*x)*30 = -1050*x
  (-35*x)*(-36*x) = 1260*x**2
  (37*x**2)*30 = 1110*x**2
  (37*x**2)*(-36*x) = -1332*x**3
  41*-36*x = -1476*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1332*x**3 + 1110*x**2 + 1260*x**2 - 1476*x - 1050*x + 1230</replace>
Combining like terms, got -1332*x**3 + 2370*x**2 - 2526*x + 1230
<replace-#Step 5>#Step 6:
Current expression: -1332*x**3 + 2370*x**2 - 2526*x + 1230</replace>
No more calculations needed.
<answer>-1332*x**3 + 2370*x**2 - 2526*x + 1230</answer>


Question:
Calculate the following: 2*z**3*(8*z**3 + 42*z - 50)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 16*z**6 + 84*z**4 - 100*z**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 2*z**3*(8*z**3 + 42*z - 50)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: -100*z**3 + (42*z)*(2*z**3) + (2*z**3)*(8*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -50*(2*z**3) = -100*z**3
  (8*z**3)*(2*z**3) = 16*z**6
  (42*z)*(2*z**3) = 84*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 16*z**6 + 84*z**4 - 100*z**3</replace>
No more calculations needed.
<answer>16*z**6 + 84*z**4 - 100*z**3</answer>


Question:
Simplify this expression: (12 - 41*x)*(-46*x**3 - 33*x**2 - 34*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1886*x**4 + 801*x**3 + 998*x**2 - 408*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (12 - 41*x)*(-46*x**3 - 33*x**2 - 34*x)
Expanding 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)
<replace-#Step 1>#Step 2:
Current expression: (-41*x)*(-46*x**3 - 33*x**2 - 34*x) + 12*(-46*x**3 - 33*x**2 - 34*x)</replace>
Simplifying the partial expression: 12*(-46*x**3 - 33*x**2 - 34*x)
Expanding 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
Replacing 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.
<replace-#Step 2>#Step 3:
Current expression: (-41*x)*(-46*x**3 - 33*x**2 - 34*x) - 34*x*12 - 33*x**2*12 - 46*x**3*12</replace>
Simplifying the partial expression: (-41*x)*(-46*x**3 - 33*x**2 - 34*x)
Expanding 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)
Replacing (-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.
<replace-#Step 3>#Step 4:
Current 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</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-46*x**3)*12 = -552*x**3
  (-46*x**3)*(-41*x) = 1886*x**4
  (-34*x)*12 = -408*x
  (-34*x)*(-41*x) = 1394*x**2
  (-33*x**2)*12 = -396*x**2
  (-33*x**2)*(-41*x) = 1353*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1886*x**4 - 552*x**3 + 1353*x**3 - 396*x**2 + 1394*x**2 - 408*x</replace>
Combining like terms, got 1886*x**4 + 801*x**3 + 998*x**2 - 408*x
<replace-#Step 5>#Step 6:
Current expression: 1886*x**4 + 801*x**3 + 998*x**2 - 408*x</replace>
No more calculations needed.
<answer>1886*x**4 + 801*x**3 + 998*x**2 - 408*x</answer>