Question:
Calculate the following: (-16*y**3 + 32*y)*(3*y**2 - 50*y - 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: -48*y**5 + 800*y**4 + 672*y**3 - 1600*y**2 - 1152*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: (-16*y**3 + 32*y)*(3*y**2 - 50*y - 36)
Expanding the part (-16*y**3 + 32*y) using the distributive property, and we got: (32*y)*(3*y**2 - 50*y - 36) + (-16*y**3)*(3*y**2 - 50*y - 36)
<replace-#Step 1>#Step 2:
Current expression: (32*y)*(3*y**2 - 50*y - 36) + (-16*y**3)*(3*y**2 - 50*y - 36)</replace>
Simplifying the partial expression: (-16*y**3)*(3*y**2 - 50*y - 36)
Expanding the part (3*y**2 - 50*y - 36) using the distributive property, and we got: (-50*y)*(-16*y**3) - (-1)*576*y**3 + (3*y**2)*(-16*y**3)
Replacing (-16*y**3)*(3*y**2 - 50*y - 36) with (-50*y)*(-16*y**3) - (-1)*576*y**3 + (3*y**2)*(-16*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-50*y)*(-16*y**3) - 36*(-16)*y**3 + (32*y)*(3*y**2 - 50*y - 36) + (3*y**2)*(-16*y**3)</replace>
Simplifying the partial expression: (32*y)*(3*y**2 - 50*y - 36)
Expanding the part (3*y**2 - 50*y - 36) using the distributive property, and we got: (-50*y)*(32*y) - 1152*y + (32*y)*(3*y**2)
Replacing (32*y)*(3*y**2 - 50*y - 36) with (-50*y)*(32*y) - 1152*y + (32*y)*(3*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-50*y)*(32*y) + (-50*y)*(-16*y**3) - 36*(-16)*y**3 - 36*32*y + (32*y)*(3*y**2) + (3*y**2)*(-16*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-50*y)*(-16*y**3) = 800*y**4
  (-50*y)*(32*y) = -1600*y**2
  (3*y**2)*(-16*y**3) = -48*y**5
  (3*y**2)*(32*y) = 96*y**3
  -36*-16*y**3 = 576*y**3
  -36*32*y = -1152*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -48*y**5 + 800*y**4 + 96*y**3 + 576*y**3 - 1600*y**2 - 1152*y</replace>
Combining like terms, got -48*y**5 + 800*y**4 + 672*y**3 - 1600*y**2 - 1152*y
<replace-#Step 5>#Step 6:
Current expression: -48*y**5 + 800*y**4 + 672*y**3 - 1600*y**2 - 1152*y</replace>
No more calculations needed.
<answer>-48*y**5 + 800*y**4 + 672*y**3 - 1600*y**2 - 1152*y</answer>


Question:
Calculate the following: 14*y**3 - 672*y**2 - 420*y - 434
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: 14*y**3 - 672*y**2 - 420*y - 434

Let's solve 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**3 - 672*y**2 - 420*y - 434
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: 14*y**3 - 672*y**2 - 420*y - 434</replace>
No more calculations needed.
<answer>14*y**3 - 672*y**2 - 420*y - 434</answer>


Question:
Calculate the following: (48*z**2 + 26)*(19*z**3 + 16*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: 912*z**5 + 768*z**4 + 494*z**3 + 416*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: (48*z**2 + 26)*(19*z**3 + 16*z**2)
Expanding the part (48*z**2 + 26) using the distributive property, and we got: (48*z**2)*(19*z**3 + 16*z**2) + 26*(19*z**3 + 16*z**2)
<replace-#Step 1>#Step 2:
Current expression: (48*z**2)*(19*z**3 + 16*z**2) + 26*(19*z**3 + 16*z**2)</replace>
Simplifying the partial expression: 26*(19*z**3 + 16*z**2)
Expanding the part (19*z**3 + 16*z**2) using the distributive property, and we got: (16*z**2)*26 + (19*z**3)*26
Replacing 26*(19*z**3 + 16*z**2) with (16*z**2)*26 + (19*z**3)*26 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (16*z**2)*26 + (48*z**2)*(19*z**3 + 16*z**2) + (19*z**3)*26</replace>
Simplifying the partial expression: (48*z**2)*(19*z**3 + 16*z**2)
Expanding the part (19*z**3 + 16*z**2) using the distributive property, and we got: (16*z**2)*(48*z**2) + (48*z**2)*(19*z**3)
Replacing (48*z**2)*(19*z**3 + 16*z**2) with (16*z**2)*(48*z**2) + (48*z**2)*(19*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (16*z**2)*(48*z**2) + (16*z**2)*26 + (48*z**2)*(19*z**3) + (19*z**3)*26</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (16*z**2)*26 = 416*z**2
  (16*z**2)*(48*z**2) = 768*z**4
  (19*z**3)*26 = 494*z**3
  (19*z**3)*(48*z**2) = 912*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 912*z**5 + 768*z**4 + 494*z**3 + 416*z**2</replace>
No more calculations needed.
<answer>912*z**5 + 768*z**4 + 494*z**3 + 416*z**2</answer>


Question:
Simplify this expression: -1870*y**3 - 2720*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: -1870*y**3 - 2720*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: -1870*y**3 - 2720*y
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: -1870*y**3 - 2720*y</replace>
No more calculations needed.
<answer>-1870*y**3 - 2720*y</answer>


Question:
Calculate the following: (31 - 25*x**3)*(-35*x**2 - 39*x - 6)
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: 875*x**5 + 975*x**4 + 150*x**3 - 1085*x**2 - 1209*x - 186

Let's solve 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: (31 - 25*x**3)*(-35*x**2 - 39*x - 6)
Expanding the part (31 - 25*x**3) using the distributive property, and we got: (-25*x**3)*(-35*x**2 - 39*x - 6) + 31*(-35*x**2 - 39*x - 6)
<replace-#Step 1>#Step 2:
Current expression: (-25*x**3)*(-35*x**2 - 39*x - 6) + 31*(-35*x**2 - 39*x - 6)</replace>
Simplifying the partial expression: 31*(-35*x**2 - 39*x - 6)
Expanding the part (-35*x**2 - 39*x - 6) using the distributive property, and we got: -39*x*31 - 35*x**2*31 - 6*31
Replacing 31*(-35*x**2 - 39*x - 6) with -39*x*31 - 35*x**2*31 - 6*31 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -39*x*31 - 35*x**2*31 + (-25*x**3)*(-35*x**2 - 39*x - 6) - 186</replace>
Simplifying the partial expression: (-25*x**3)*(-35*x**2 - 39*x - 6)
Expanding the part (-35*x**2 - 39*x - 6) using the distributive property, and we got: (-39*x)*(-25*x**3) - (-1)*150*x**3 + (-35*x**2)*(-25*x**3)
Replacing (-25*x**3)*(-35*x**2 - 39*x - 6) with (-39*x)*(-25*x**3) - (-1)*150*x**3 + (-35*x**2)*(-25*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-39*x)*(-25*x**3) - 39*x*31 - 6*(-25)*x**3 + (-35*x**2)*(-25*x**3) - 35*x**2*31 - 186</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-39*x)*31 = -1209*x
  (-39*x)*(-25*x**3) = 975*x**4
  (-35*x**2)*31 = -1085*x**2
  (-35*x**2)*(-25*x**3) = 875*x**5
  -6*-25*x**3 = 150*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 875*x**5 + 975*x**4 + 150*x**3 - 1085*x**2 - 1209*x - 186</replace>
No more calculations needed.
<answer>875*x**5 + 975*x**4 + 150*x**3 - 1085*x**2 - 1209*x - 186</answer>


Question:
Calculate the following: (46*x**3 - 5*x**2)*(-47*x**3 - 30*x**2 + 16)
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: -2162*x**6 - 1145*x**5 + 150*x**4 + 736*x**3 - 80*x**2


Question:
Simplify this expression: (50*y**3 + 39*y**2)*(-21*y**3 - 4*y**2 + 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: -1050*y**6 - 1019*y**5 - 56*y**4 + 78*y**3


Question:
Calculate the following: (-8*y**2 - 27)*(49*y**3 - 5*y**2 + 33*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: -392*y**5 + 40*y**4 - 1587*y**3 + 135*y**2 - 891*y


Question:
Simplify this expression: (-67*z**3 - 11*z)*(42*z**3 - 23*z**2 - 15*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: -2814*z**6 + 1541*z**5 + 543*z**4 + 253*z**3 + 165*z**2


Question:
Calculate the following: 943*x**2 - 1722
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: 943*x**2 - 1722

Let's solve 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: 943*x**2 - 1722
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: 943*x**2 - 1722</replace>
No more calculations needed.
<answer>943*x**2 - 1722</answer>


Question:
Calculate the following: (y**3 + 92*y**2 - 14*y)*(43*y**3 + 43*y - 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: 43*y**6 + 3956*y**5 - 559*y**4 + 3926*y**3 - 3362*y**2 + 420*y


Question:
Calculate the following: -10*z**2*(-91*z**2 - 7*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: 910*z**4 + 70*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: -10*z**2*(-91*z**2 - 7*z)
Expanding the part (-91*z**2 - 7*z) using the distributive property, and we got: (-7*z)*(-10*z**2) + (-91*z**2)*(-10*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-7*z)*(-10*z**2) + (-91*z**2)*(-10*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-91*z**2)*(-10*z**2) = 910*z**4
  (-7*z)*(-10*z**2) = 70*z**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 910*z**4 + 70*z**3</replace>
No more calculations needed.
<answer>910*z**4 + 70*z**3</answer>


Question:
Simplify this expression: 73*z*(8*z**2 + 66)
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: 584*z**3 + 4818*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: 73*z*(8*z**2 + 66)
Expanding the part (8*z**2 + 66) using the distributive property, and we got: 66*(73*z) + (73*z)*(8*z**2)
<replace-#Step 1>#Step 2:
Current expression: 66*(73*z) + (73*z)*(8*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  66*(73*z) = 4818*z
  (8*z**2)*(73*z) = 584*z**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 584*z**3 + 4818*z</replace>
No more calculations needed.
<answer>584*z**3 + 4818*z</answer>


Question:
Simplify this expression: (56 - 8*z**3)*(-43*z**3 + 11*z**2 - 30*z - 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: 344*z**6 - 88*z**5 + 240*z**4 - 2112*z**3 + 616*z**2 - 1680*z - 2072


Question:
Calculate the following: (22*z**2 - 24*z + 83)*(26*z**3 + 7*z**2 + 43*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: 572*z**5 - 470*z**4 + 2936*z**3 - 451*z**2 + 3569*z


Question:
Calculate the following: -637*z**3 + 559*z**2 - 455*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: -637*z**3 + 559*z**2 - 455*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: -637*z**3 + 559*z**2 - 455*z
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: -637*z**3 + 559*z**2 - 455*z</replace>
No more calculations needed.
<answer>-637*z**3 + 559*z**2 - 455*z</answer>


Question:
Simplify this expression: (39*z**3 - 69*z**2)*(3*z**3 - 43*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: 117*z**6 - 207*z**5 - 1677*z**4 + 4020*z**3 - 1863*z**2


Question:
Calculate the following: (11*y**2 + 2)*(y**3 - 35*y**2 + 7*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: 11*y**5 - 385*y**4 + 79*y**3 - 70*y**2 + 14*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: (11*y**2 + 2)*(y**3 - 35*y**2 + 7*y)
Expanding the part (11*y**2 + 2) using the distributive property, and we got: (11*y**2)*(y**3 - 35*y**2 + 7*y) + 2*(y**3 - 35*y**2 + 7*y)
<replace-#Step 1>#Step 2:
Current expression: (11*y**2)*(y**3 - 35*y**2 + 7*y) + 2*(y**3 - 35*y**2 + 7*y)</replace>
Simplifying the partial expression: 2*(y**3 - 35*y**2 + 7*y)
Expanding the part (y**3 - 35*y**2 + 7*y) using the distributive property, and we got: y**3*2 + (7*y)*2 - 35*y**2*2
Replacing 2*(y**3 - 35*y**2 + 7*y) with y**3*2 + (7*y)*2 - 35*y**2*2 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: y**3*2 + (7*y)*2 - 35*y**2*2 + (11*y**2)*(y**3 - 35*y**2 + 7*y)</replace>
Simplifying the partial expression: (11*y**2)*(y**3 - 35*y**2 + 7*y)
Expanding the part (y**3 - 35*y**2 + 7*y) using the distributive property, and we got: (11*y**2)*y**3 + (7*y)*(11*y**2) + (-35*y**2)*(11*y**2)
Replacing (11*y**2)*(y**3 - 35*y**2 + 7*y) with (11*y**2)*y**3 + (7*y)*(11*y**2) + (-35*y**2)*(11*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (11*y**2)*y**3 + y**3*2 + (7*y)*(11*y**2) + (7*y)*2 + (-35*y**2)*(11*y**2) - 35*y**2*2</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  y**3*2 = 2*y**3
  y**3*(11*y**2) = 11*y**5
  (-35*y**2)*2 = -70*y**2
  (-35*y**2)*(11*y**2) = -385*y**4
  (7*y)*2 = 14*y
  (7*y)*(11*y**2) = 77*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 11*y**5 - 385*y**4 + 2*y**3 + 77*y**3 - 70*y**2 + 14*y</replace>
Combining like terms, got 11*y**5 - 385*y**4 + 79*y**3 - 70*y**2 + 14*y
<replace-#Step 5>#Step 6:
Current expression: 11*y**5 - 385*y**4 + 79*y**3 - 70*y**2 + 14*y</replace>
No more calculations needed.
<answer>11*y**5 - 385*y**4 + 79*y**3 - 70*y**2 + 14*y</answer>


Question:
Simplify this expression: (11 - 23*y**2)*(-12*y**3 + 19*y**2 - 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: 276*y**5 - 437*y**4 + 121*y**3 + 209*y**2 - 121*y


Question:
Calculate the following: (3*x - 68)*(15*x**3 - 13)
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: 45*x**4 - 1020*x**3 - 39*x + 884

Let's solve 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 - 68)*(15*x**3 - 13)
Expanding the part (3*x - 68) using the distributive property, and we got: (3*x)*(15*x**3 - 13) - 68*(15*x**3 - 13)
<replace-#Step 1>#Step 2:
Current expression: (3*x)*(15*x**3 - 13) - 68*(15*x**3 - 13)</replace>
Simplifying the partial expression: -68*(15*x**3 - 13)
Expanding the part (15*x**3 - 13) using the distributive property, and we got: (15*x**3)*(-68) - 13*(-68)
Replacing -68*(15*x**3 - 13) with (15*x**3)*(-68) - 13*(-68) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (3*x)*(15*x**3 - 13) + (15*x**3)*(-68) + 884</replace>
Simplifying the partial expression: (3*x)*(15*x**3 - 13)
Expanding the part (15*x**3 - 13) using the distributive property, and we got: -39*x + (3*x)*(15*x**3)
Replacing (3*x)*(15*x**3 - 13) with -39*x + (3*x)*(15*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -13*3*x + (3*x)*(15*x**3) + (15*x**3)*(-68) + 884</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (15*x**3)*-68 = -1020*x**3
  (15*x**3)*(3*x) = 45*x**4
  -13*3*x = -39*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 45*x**4 - 1020*x**3 - 39*x + 884</replace>
No more calculations needed.
<answer>45*x**4 - 1020*x**3 - 39*x + 884</answer>


Question:
Calculate the following: (40*y - 44)*(22*y**3 - 16)
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: 880*y**4 - 968*y**3 - 640*y + 704

Let's solve 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: (40*y - 44)*(22*y**3 - 16)
Expanding the part (40*y - 44) using the distributive property, and we got: (40*y)*(22*y**3 - 16) - 44*(22*y**3 - 16)
<replace-#Step 1>#Step 2:
Current expression: (40*y)*(22*y**3 - 16) - 44*(22*y**3 - 16)</replace>
Simplifying the partial expression: -44*(22*y**3 - 16)
Expanding the part (22*y**3 - 16) using the distributive property, and we got: (22*y**3)*(-44) - 16*(-44)
Replacing -44*(22*y**3 - 16) with (22*y**3)*(-44) - 16*(-44) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (40*y)*(22*y**3 - 16) + (22*y**3)*(-44) + 704</replace>
Simplifying the partial expression: (40*y)*(22*y**3 - 16)
Expanding the part (22*y**3 - 16) using the distributive property, and we got: -640*y + (40*y)*(22*y**3)
Replacing (40*y)*(22*y**3 - 16) with -640*y + (40*y)*(22*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -16*40*y + (40*y)*(22*y**3) + (22*y**3)*(-44) + 704</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (22*y**3)*-44 = -968*y**3
  (22*y**3)*(40*y) = 880*y**4
  -16*40*y = -640*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 880*y**4 - 968*y**3 - 640*y + 704</replace>
No more calculations needed.
<answer>880*y**4 - 968*y**3 - 640*y + 704</answer>


Question:
Simplify this expression: (-10*y**2 - 31)*(-48*y**2 + 21*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: 480*y**4 - 210*y**3 + 1198*y**2 - 651*y - 899

Let's solve 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: (-10*y**2 - 31)*(-48*y**2 + 21*y + 29)
Expanding the part (-10*y**2 - 31) using the distributive property, and we got: (-10*y**2)*(-48*y**2 + 21*y + 29) - 31*(-48*y**2 + 21*y + 29)
<replace-#Step 1>#Step 2:
Current expression: (-10*y**2)*(-48*y**2 + 21*y + 29) - 31*(-48*y**2 + 21*y + 29)</replace>
Simplifying the partial expression: -31*(-48*y**2 + 21*y + 29)
Expanding the part (-48*y**2 + 21*y + 29) using the distributive property, and we got: (21*y)*(-31) - 48*y**2*(-31) + 29*(-31)
Replacing -31*(-48*y**2 + 21*y + 29) with (21*y)*(-31) - 48*y**2*(-31) + 29*(-31) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (21*y)*(-31) - 48*y**2*(-31) + (-10*y**2)*(-48*y**2 + 21*y + 29) - 899</replace>
Simplifying the partial expression: (-10*y**2)*(-48*y**2 + 21*y + 29)
Expanding the part (-48*y**2 + 21*y + 29) using the distributive property, and we got: 29*(-10*y**2) + (21*y)*(-10*y**2) + (-48*y**2)*(-10*y**2)
Replacing (-10*y**2)*(-48*y**2 + 21*y + 29) with 29*(-10*y**2) + (21*y)*(-10*y**2) + (-48*y**2)*(-10*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 29*(-10)*y**2 + (21*y)*(-10*y**2) + (21*y)*(-31) + (-48*y**2)*(-10*y**2) - 48*y**2*(-31) - 899</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-48*y**2)*-31 = 1488*y**2
  (-48*y**2)*(-10*y**2) = 480*y**4
  (21*y)*-31 = -651*y
  (21*y)*(-10*y**2) = -210*y**3
  29*-10*y**2 = -290*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 480*y**4 - 210*y**3 - 290*y**2 + 1488*y**2 - 651*y - 899</replace>
Combining like terms, got 480*y**4 - 210*y**3 + 1198*y**2 - 651*y - 899
<replace-#Step 5>#Step 6:
Current expression: 480*y**4 - 210*y**3 + 1198*y**2 - 651*y - 899</replace>
No more calculations needed.
<answer>480*y**4 - 210*y**3 + 1198*y**2 - 651*y - 899</answer>


Question:
Simplify this expression: (44*x**2 + 47)*(46*x**3 + 32*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: 2024*x**5 + 1408*x**4 + 2162*x**3 + 1504*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: (44*x**2 + 47)*(46*x**3 + 32*x**2)
Expanding the part (44*x**2 + 47) using the distributive property, and we got: (44*x**2)*(46*x**3 + 32*x**2) + 47*(46*x**3 + 32*x**2)
<replace-#Step 1>#Step 2:
Current expression: (44*x**2)*(46*x**3 + 32*x**2) + 47*(46*x**3 + 32*x**2)</replace>
Simplifying the partial expression: 47*(46*x**3 + 32*x**2)
Expanding the part (46*x**3 + 32*x**2) using the distributive property, and we got: (32*x**2)*47 + (46*x**3)*47
Replacing 47*(46*x**3 + 32*x**2) with (32*x**2)*47 + (46*x**3)*47 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (32*x**2)*47 + (44*x**2)*(46*x**3 + 32*x**2) + (46*x**3)*47</replace>
Simplifying the partial expression: (44*x**2)*(46*x**3 + 32*x**2)
Expanding the part (46*x**3 + 32*x**2) using the distributive property, and we got: (32*x**2)*(44*x**2) + (44*x**2)*(46*x**3)
Replacing (44*x**2)*(46*x**3 + 32*x**2) with (32*x**2)*(44*x**2) + (44*x**2)*(46*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (32*x**2)*(44*x**2) + (32*x**2)*47 + (44*x**2)*(46*x**3) + (46*x**3)*47</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (32*x**2)*47 = 1504*x**2
  (32*x**2)*(44*x**2) = 1408*x**4
  (46*x**3)*47 = 2162*x**3
  (46*x**3)*(44*x**2) = 2024*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2024*x**5 + 1408*x**4 + 2162*x**3 + 1504*x**2</replace>
No more calculations needed.
<answer>2024*x**5 + 1408*x**4 + 2162*x**3 + 1504*x**2</answer>


Question:
Calculate the following: (-39*y**3 - 42*y + 6)*(-5*y**3 + 34*y**2 - 26*y + 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: 195*y**6 - 1326*y**5 + 1224*y**4 - 3330*y**3 + 1296*y**2 - 2172*y + 288


Question:
Calculate the following: -1368*y**2 + 1800*y - 792
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: -1368*y**2 + 1800*y - 792

Let's solve 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: -1368*y**2 + 1800*y - 792
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: -1368*y**2 + 1800*y - 792</replace>
No more calculations needed.
<answer>-1368*y**2 + 1800*y - 792</answer>


Question:
Simplify this expression: (-39*y**3 - 30)*(16*y**3 - 37*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: -624*y**6 + 1443*y**4 - 480*y**3 + 1110*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**3 - 30)*(16*y**3 - 37*y)
Expanding the part (-39*y**3 - 30) using the distributive property, and we got: (-39*y**3)*(16*y**3 - 37*y) - 30*(16*y**3 - 37*y)
<replace-#Step 1>#Step 2:
Current expression: (-39*y**3)*(16*y**3 - 37*y) - 30*(16*y**3 - 37*y)</replace>
Simplifying the partial expression: -30*(16*y**3 - 37*y)
Expanding the part (16*y**3 - 37*y) using the distributive property, and we got: -37*y*(-30) + (16*y**3)*(-30)
Replacing -30*(16*y**3 - 37*y) with -37*y*(-30) + (16*y**3)*(-30) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -37*y*(-30) + (-39*y**3)*(16*y**3 - 37*y) + (16*y**3)*(-30)</replace>
Simplifying the partial expression: (-39*y**3)*(16*y**3 - 37*y)
Expanding the part (16*y**3 - 37*y) using the distributive property, and we got: (-37*y)*(-39*y**3) + (-39*y**3)*(16*y**3)
Replacing (-39*y**3)*(16*y**3 - 37*y) with (-37*y)*(-39*y**3) + (-39*y**3)*(16*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-37*y)*(-39*y**3) - 37*y*(-30) + (-39*y**3)*(16*y**3) + (16*y**3)*(-30)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-37*y)*-30 = 1110*y
  (-37*y)*(-39*y**3) = 1443*y**4
  (16*y**3)*-30 = -480*y**3
  (16*y**3)*(-39*y**3) = -624*y**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -624*y**6 + 1443*y**4 - 480*y**3 + 1110*y</replace>
No more calculations needed.
<answer>-624*y**6 + 1443*y**4 - 480*y**3 + 1110*y</answer>


Question:
Simplify this expression: (11*x**3 - 14*x + 17)*(-39*x**3 - 24*x**2 - 45*x - 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: -429*x**6 - 264*x**5 + 51*x**4 - 690*x**3 + 222*x**2 - 303*x - 561


Question:
Simplify this expression: (38*y**3 - 34)*(49*y**3 - 33*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: 1862*y**6 - 1254*y**4 - 1666*y**3 + 1122*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: (38*y**3 - 34)*(49*y**3 - 33*y)
Expanding the part (38*y**3 - 34) using the distributive property, and we got: (38*y**3)*(49*y**3 - 33*y) - 34*(49*y**3 - 33*y)
<replace-#Step 1>#Step 2:
Current expression: (38*y**3)*(49*y**3 - 33*y) - 34*(49*y**3 - 33*y)</replace>
Simplifying the partial expression: -34*(49*y**3 - 33*y)
Expanding the part (49*y**3 - 33*y) using the distributive property, and we got: -33*y*(-34) + (49*y**3)*(-34)
Replacing -34*(49*y**3 - 33*y) with -33*y*(-34) + (49*y**3)*(-34) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -33*y*(-34) + (38*y**3)*(49*y**3 - 33*y) + (49*y**3)*(-34)</replace>
Simplifying the partial expression: (38*y**3)*(49*y**3 - 33*y)
Expanding the part (49*y**3 - 33*y) using the distributive property, and we got: (-33*y)*(38*y**3) + (38*y**3)*(49*y**3)
Replacing (38*y**3)*(49*y**3 - 33*y) with (-33*y)*(38*y**3) + (38*y**3)*(49*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-33*y)*(38*y**3) - 33*y*(-34) + (38*y**3)*(49*y**3) + (49*y**3)*(-34)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-33*y)*-34 = 1122*y
  (-33*y)*(38*y**3) = -1254*y**4
  (49*y**3)*-34 = -1666*y**3
  (49*y**3)*(38*y**3) = 1862*y**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1862*y**6 - 1254*y**4 - 1666*y**3 + 1122*y</replace>
No more calculations needed.
<answer>1862*y**6 - 1254*y**4 - 1666*y**3 + 1122*y</answer>


Question:
Simplify this expression: (37*x**3 + 17)*(43*x**3 + 47*x - 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: 1591*x**6 + 1739*x**4 - 675*x**3 + 799*x - 646

Let's solve 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*x**3 + 17)*(43*x**3 + 47*x - 38)
Expanding the part (37*x**3 + 17) using the distributive property, and we got: (37*x**3)*(43*x**3 + 47*x - 38) + 17*(43*x**3 + 47*x - 38)
<replace-#Step 1>#Step 2:
Current expression: (37*x**3)*(43*x**3 + 47*x - 38) + 17*(43*x**3 + 47*x - 38)</replace>
Simplifying the partial expression: 17*(43*x**3 + 47*x - 38)
Expanding the part (43*x**3 + 47*x - 38) using the distributive property, and we got: (47*x)*17 + (43*x**3)*17 - 38*17
Replacing 17*(43*x**3 + 47*x - 38) with (47*x)*17 + (43*x**3)*17 - 38*17 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (47*x)*17 + (37*x**3)*(43*x**3 + 47*x - 38) + (43*x**3)*17 - 646</replace>
Simplifying the partial expression: (37*x**3)*(43*x**3 + 47*x - 38)
Expanding the part (43*x**3 + 47*x - 38) using the distributive property, and we got: -1406*x**3 + (47*x)*(37*x**3) + (37*x**3)*(43*x**3)
Replacing (37*x**3)*(43*x**3 + 47*x - 38) with -1406*x**3 + (47*x)*(37*x**3) + (37*x**3)*(43*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -38*37*x**3 + (47*x)*(37*x**3) + (47*x)*17 + (37*x**3)*(43*x**3) + (43*x**3)*17 - 646</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (43*x**3)*17 = 731*x**3
  (43*x**3)*(37*x**3) = 1591*x**6
  (47*x)*17 = 799*x
  (47*x)*(37*x**3) = 1739*x**4
  -38*37*x**3 = -1406*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1591*x**6 + 1739*x**4 - 1406*x**3 + 731*x**3 + 799*x - 646</replace>
Combining like terms, got 1591*x**6 + 1739*x**4 - 675*x**3 + 799*x - 646
<replace-#Step 5>#Step 6:
Current expression: 1591*x**6 + 1739*x**4 - 675*x**3 + 799*x - 646</replace>
No more calculations needed.
<answer>1591*x**6 + 1739*x**4 - 675*x**3 + 799*x - 646</answer>


Question:
Calculate the following: (35*y**3 + 3)*(-26*y**3 + 31*y**2 - 9*y + 39)
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: -910*y**6 + 1085*y**5 - 315*y**4 + 1287*y**3 + 93*y**2 - 27*y + 117


Question:
Simplify this expression: (-38*x**2 + 10*x + 22)*(-14*x**3 + 5*x**2 + 63)
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: 532*x**5 - 330*x**4 - 258*x**3 - 2284*x**2 + 630*x + 1386


Question:
Calculate the following: -50*z**2*(31*z**2 - 14)
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: -1550*z**4 + 700*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: -50*z**2*(31*z**2 - 14)
Expanding the part (31*z**2 - 14) using the distributive property, and we got: -(-1)*700*z**2 + (-50*z**2)*(31*z**2)
<replace-#Step 1>#Step 2:
Current expression: -(-1)*700*z**2 + (-50*z**2)*(31*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -14*(-50*z**2) = 700*z**2
  (31*z**2)*(-50*z**2) = -1550*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1550*z**4 + 700*z**2</replace>
No more calculations needed.
<answer>-1550*z**4 + 700*z**2</answer>


Question:
Simplify this expression: (15*z**3 - z)*(-9*z**3 + 3*z**2 - 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*z**6 + 45*z**5 + 9*z**4 - 438*z**3 + 29*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: (15*z**3 - z)*(-9*z**3 + 3*z**2 - 29)
Expanding the part (15*z**3 - z) using the distributive property, and we got: (-z)*(-9*z**3 + 3*z**2 - 29) + (15*z**3)*(-9*z**3 + 3*z**2 - 29)
<replace-#Step 1>#Step 2:
Current expression: (-z)*(-9*z**3 + 3*z**2 - 29) + (15*z**3)*(-9*z**3 + 3*z**2 - 29)</replace>
Simplifying the partial expression: (-z)*(-9*z**3 + 3*z**2 - 29)
Expanding the part (-9*z**3 + 3*z**2 - 29) using the distributive property, and we got: (-z)*(3*z**2) + (-z)*(-9*z**3) - (-1)*29*z
Replacing (-z)*(-9*z**3 + 3*z**2 - 29) with (-z)*(3*z**2) + (-z)*(-9*z**3) - (-1)*29*z in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-z)*(3*z**2) + (-z)*(-9*z**3) - 29*(-1)*z + (15*z**3)*(-9*z**3 + 3*z**2 - 29)</replace>
Simplifying the partial expression: (15*z**3)*(-9*z**3 + 3*z**2 - 29)
Expanding the part (-9*z**3 + 3*z**2 - 29) using the distributive property, and we got: -435*z**3 + (3*z**2)*(15*z**3) + (-9*z**3)*(15*z**3)
Replacing (15*z**3)*(-9*z**3 + 3*z**2 - 29) with -435*z**3 + (3*z**2)*(15*z**3) + (-9*z**3)*(15*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-z)*(3*z**2) + (-z)*(-9*z**3) - 29*15*z**3 - 29*(-1)*z + (3*z**2)*(15*z**3) + (-9*z**3)*(15*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-9*z**3)*(-z) = 9*z**4
  (-9*z**3)*(15*z**3) = -135*z**6
  (3*z**2)*(-z) = -3*z**3
  (3*z**2)*(15*z**3) = 45*z**5
  -29*-1*z = 29*z
  -29*15*z**3 = -435*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -135*z**6 + 45*z**5 + 9*z**4 - 435*z**3 - 3*z**3 + 29*z</replace>
Combining like terms, got -135*z**6 + 45*z**5 + 9*z**4 - 438*z**3 + 29*z
<replace-#Step 5>#Step 6:
Current expression: -135*z**6 + 45*z**5 + 9*z**4 - 438*z**3 + 29*z</replace>
No more calculations needed.
<answer>-135*z**6 + 45*z**5 + 9*z**4 - 438*z**3 + 29*z</answer>


Question:
Calculate the following: (-7*x**2 - 34*x)*(-41*x**2 + 40*x + 9)
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: 287*x**4 + 1114*x**3 - 1423*x**2 - 306*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: (-7*x**2 - 34*x)*(-41*x**2 + 40*x + 9)
Expanding the part (-7*x**2 - 34*x) using the distributive property, and we got: (-34*x)*(-41*x**2 + 40*x + 9) + (-7*x**2)*(-41*x**2 + 40*x + 9)
<replace-#Step 1>#Step 2:
Current expression: (-34*x)*(-41*x**2 + 40*x + 9) + (-7*x**2)*(-41*x**2 + 40*x + 9)</replace>
Simplifying the partial expression: (-34*x)*(-41*x**2 + 40*x + 9)
Expanding the part (-41*x**2 + 40*x + 9) using the distributive property, and we got: (-34*x)*(40*x) + (-34*x)*(-41*x**2) + 9*(-34*x)
Replacing (-34*x)*(-41*x**2 + 40*x + 9) with (-34*x)*(40*x) + (-34*x)*(-41*x**2) + 9*(-34*x) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-34*x)*(40*x) + (-34*x)*(-41*x**2) + 9*(-34)*x + (-7*x**2)*(-41*x**2 + 40*x + 9)</replace>
Simplifying the partial expression: (-7*x**2)*(-41*x**2 + 40*x + 9)
Expanding the part (-41*x**2 + 40*x + 9) using the distributive property, and we got: 9*(-7*x**2) + (40*x)*(-7*x**2) + (-41*x**2)*(-7*x**2)
Replacing (-7*x**2)*(-41*x**2 + 40*x + 9) with 9*(-7*x**2) + (40*x)*(-7*x**2) + (-41*x**2)*(-7*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-34*x)*(40*x) + (-34*x)*(-41*x**2) + 9*(-7)*x**2 + 9*(-34)*x + (40*x)*(-7*x**2) + (-41*x**2)*(-7*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-41*x**2)*(-34*x) = 1394*x**3
  (-41*x**2)*(-7*x**2) = 287*x**4
  (40*x)*(-34*x) = -1360*x**2
  (40*x)*(-7*x**2) = -280*x**3
  9*-34*x = -306*x
  9*-7*x**2 = -63*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 287*x**4 - 280*x**3 + 1394*x**3 - 1360*x**2 - 63*x**2 - 306*x</replace>
Combining like terms, got 287*x**4 + 1114*x**3 - 1423*x**2 - 306*x
<replace-#Step 5>#Step 6:
Current expression: 287*x**4 + 1114*x**3 - 1423*x**2 - 306*x</replace>
No more calculations needed.
<answer>287*x**4 + 1114*x**3 - 1423*x**2 - 306*x</answer>


Question:
Simplify this expression: (43 - 31*z**2)*(14*z**3 - 33*z + 10)
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: -434*z**5 + 1625*z**3 - 310*z**2 - 1419*z + 430

Let's solve 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: (43 - 31*z**2)*(14*z**3 - 33*z + 10)
Expanding the part (43 - 31*z**2) using the distributive property, and we got: (-31*z**2)*(14*z**3 - 33*z + 10) + 43*(14*z**3 - 33*z + 10)
<replace-#Step 1>#Step 2:
Current expression: (-31*z**2)*(14*z**3 - 33*z + 10) + 43*(14*z**3 - 33*z + 10)</replace>
Simplifying the partial expression: 43*(14*z**3 - 33*z + 10)
Expanding the part (14*z**3 - 33*z + 10) using the distributive property, and we got: -33*z*43 + (14*z**3)*43 + 10*43
Replacing 43*(14*z**3 - 33*z + 10) with -33*z*43 + (14*z**3)*43 + 10*43 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -33*z*43 + (-31*z**2)*(14*z**3 - 33*z + 10) + (14*z**3)*43 + 430</replace>
Simplifying the partial expression: (-31*z**2)*(14*z**3 - 33*z + 10)
Expanding the part (14*z**3 - 33*z + 10) using the distributive property, and we got: (-33*z)*(-31*z**2) + 10*(-31*z**2) + (-31*z**2)*(14*z**3)
Replacing (-31*z**2)*(14*z**3 - 33*z + 10) with (-33*z)*(-31*z**2) + 10*(-31*z**2) + (-31*z**2)*(14*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-33*z)*(-31*z**2) - 33*z*43 + 10*(-31)*z**2 + (-31*z**2)*(14*z**3) + (14*z**3)*43 + 430</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-33*z)*43 = -1419*z
  (-33*z)*(-31*z**2) = 1023*z**3
  (14*z**3)*43 = 602*z**3
  (14*z**3)*(-31*z**2) = -434*z**5
  10*-31*z**2 = -310*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -434*z**5 + 602*z**3 + 1023*z**3 - 310*z**2 - 1419*z + 430</replace>
Combining like terms, got -434*z**5 + 1625*z**3 - 310*z**2 - 1419*z + 430
<replace-#Step 5>#Step 6:
Current expression: -434*z**5 + 1625*z**3 - 310*z**2 - 1419*z + 430</replace>
No more calculations needed.
<answer>-434*z**5 + 1625*z**3 - 310*z**2 - 1419*z + 430</answer>


Question:
Simplify this expression: (36*x + 66)*(32*x**2 + 29*x - 26)
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: 1152*x**3 + 3156*x**2 + 978*x - 1716

Let's solve 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: (36*x + 66)*(32*x**2 + 29*x - 26)
Expanding the part (36*x + 66) using the distributive property, and we got: (36*x)*(32*x**2 + 29*x - 26) + 66*(32*x**2 + 29*x - 26)
<replace-#Step 1>#Step 2:
Current expression: (36*x)*(32*x**2 + 29*x - 26) + 66*(32*x**2 + 29*x - 26)</replace>
Simplifying the partial expression: 66*(32*x**2 + 29*x - 26)
Expanding the part (32*x**2 + 29*x - 26) using the distributive property, and we got: (29*x)*66 + (32*x**2)*66 - 26*66
Replacing 66*(32*x**2 + 29*x - 26) with (29*x)*66 + (32*x**2)*66 - 26*66 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (29*x)*66 + (36*x)*(32*x**2 + 29*x - 26) + (32*x**2)*66 - 1716</replace>
Simplifying the partial expression: (36*x)*(32*x**2 + 29*x - 26)
Expanding the part (32*x**2 + 29*x - 26) using the distributive property, and we got: -936*x + (29*x)*(36*x) + (36*x)*(32*x**2)
Replacing (36*x)*(32*x**2 + 29*x - 26) with -936*x + (29*x)*(36*x) + (36*x)*(32*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -26*36*x + (29*x)*(36*x) + (29*x)*66 + (36*x)*(32*x**2) + (32*x**2)*66 - 1716</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (29*x)*66 = 1914*x
  (29*x)*(36*x) = 1044*x**2
  (32*x**2)*66 = 2112*x**2
  (32*x**2)*(36*x) = 1152*x**3
  -26*36*x = -936*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1152*x**3 + 1044*x**2 + 2112*x**2 - 936*x + 1914*x - 1716</replace>
Combining like terms, got 1152*x**3 + 3156*x**2 + 978*x - 1716
<replace-#Step 5>#Step 6:
Current expression: 1152*x**3 + 3156*x**2 + 978*x - 1716</replace>
No more calculations needed.
<answer>1152*x**3 + 3156*x**2 + 978*x - 1716</answer>


Question:
Calculate the following: (-8*y**3 + 31*y)*(-15*y**3 + 12*y**2 + 31)
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: 120*y**6 - 96*y**5 - 465*y**4 + 124*y**3 + 961*y


Question:
Simplify this expression: (-4*z**3 + 24*z - 44)*(46*z**3 + 32*z - 14)
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: -184*z**6 + 976*z**4 - 1968*z**3 + 768*z**2 - 1744*z + 616


Question:
Calculate the following: 28*x*(3*x**3 + 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: 84*x**4 + 1008*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: 28*x*(3*x**3 + 36)
Expanding the part (3*x**3 + 36) using the distributive property, and we got: 36*(28*x) + (28*x)*(3*x**3)
<replace-#Step 1>#Step 2:
Current expression: 36*(28*x) + (28*x)*(3*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  36*(28*x) = 1008*x
  (3*x**3)*(28*x) = 84*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 84*x**4 + 1008*x</replace>
No more calculations needed.
<answer>84*x**4 + 1008*x</answer>


Question:
Calculate the following: 57*x*(-20*x**3 + 17*x**2 - 35)
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: -1140*x**4 + 969*x**3 - 1995*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: 57*x*(-20*x**3 + 17*x**2 - 35)
Expanding the part (-20*x**3 + 17*x**2 - 35) using the distributive property, and we got: -1995*x + (57*x)*(17*x**2) + (57*x)*(-20*x**3)
<replace-#Step 1>#Step 2:
Current expression: -1995*x + (57*x)*(17*x**2) + (57*x)*(-20*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -35*(57*x) = -1995*x
  (-20*x**3)*(57*x) = -1140*x**4
  (17*x**2)*(57*x) = 969*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1140*x**4 + 969*x**3 - 1995*x</replace>
No more calculations needed.
<answer>-1140*x**4 + 969*x**3 - 1995*x</answer>


Question:
Simplify this expression: (-5*x**2 + 8*x + 29)*(32*x**3 - 49*x**2 - 20*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: -160*x**5 + 501*x**4 + 636*x**3 - 1581*x**2 - 580*x


Question:
Calculate the following: (-11*x**3 - 11*x)*(37*x**3 + 57*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: -407*x**6 - 627*x**5 - 407*x**4 - 627*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: (-11*x**3 - 11*x)*(37*x**3 + 57*x**2)
Expanding the part (-11*x**3 - 11*x) using the distributive property, and we got: (-11*x)*(37*x**3 + 57*x**2) + (-11*x**3)*(37*x**3 + 57*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-11*x)*(37*x**3 + 57*x**2) + (-11*x**3)*(37*x**3 + 57*x**2)</replace>
Simplifying the partial expression: (-11*x)*(37*x**3 + 57*x**2)
Expanding the part (37*x**3 + 57*x**2) using the distributive property, and we got: (-11*x)*(57*x**2) + (-11*x)*(37*x**3)
Replacing (-11*x)*(37*x**3 + 57*x**2) with (-11*x)*(57*x**2) + (-11*x)*(37*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-11*x)*(57*x**2) + (-11*x)*(37*x**3) + (-11*x**3)*(37*x**3 + 57*x**2)</replace>
Simplifying the partial expression: (-11*x**3)*(37*x**3 + 57*x**2)
Expanding the part (37*x**3 + 57*x**2) using the distributive property, and we got: (57*x**2)*(-11*x**3) + (-11*x**3)*(37*x**3)
Replacing (-11*x**3)*(37*x**3 + 57*x**2) with (57*x**2)*(-11*x**3) + (-11*x**3)*(37*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-11*x)*(57*x**2) + (-11*x)*(37*x**3) + (57*x**2)*(-11*x**3) + (-11*x**3)*(37*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (37*x**3)*(-11*x) = -407*x**4
  (37*x**3)*(-11*x**3) = -407*x**6
  (57*x**2)*(-11*x) = -627*x**3
  (57*x**2)*(-11*x**3) = -627*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -407*x**6 - 627*x**5 - 407*x**4 - 627*x**3</replace>
No more calculations needed.
<answer>-407*x**6 - 627*x**5 - 407*x**4 - 627*x**3</answer>


Question:
Simplify this expression: (36 - 27*y**2)*(-16*y**3 - 33*y + 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: 432*y**5 + 315*y**3 - 891*y**2 - 1188*y + 1188

Let's solve 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: (36 - 27*y**2)*(-16*y**3 - 33*y + 33)
Expanding the part (36 - 27*y**2) using the distributive property, and we got: (-27*y**2)*(-16*y**3 - 33*y + 33) + 36*(-16*y**3 - 33*y + 33)
<replace-#Step 1>#Step 2:
Current expression: (-27*y**2)*(-16*y**3 - 33*y + 33) + 36*(-16*y**3 - 33*y + 33)</replace>
Simplifying the partial expression: 36*(-16*y**3 - 33*y + 33)
Expanding the part (-16*y**3 - 33*y + 33) using the distributive property, and we got: -33*y*36 - 16*y**3*36 + 33*36
Replacing 36*(-16*y**3 - 33*y + 33) with -33*y*36 - 16*y**3*36 + 33*36 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -33*y*36 + (-27*y**2)*(-16*y**3 - 33*y + 33) - 16*y**3*36 + 1188</replace>
Simplifying the partial expression: (-27*y**2)*(-16*y**3 - 33*y + 33)
Expanding the part (-16*y**3 - 33*y + 33) using the distributive property, and we got: (-33*y)*(-27*y**2) + 33*(-27*y**2) + (-27*y**2)*(-16*y**3)
Replacing (-27*y**2)*(-16*y**3 - 33*y + 33) with (-33*y)*(-27*y**2) + 33*(-27*y**2) + (-27*y**2)*(-16*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-33*y)*(-27*y**2) - 33*y*36 + 33*(-27)*y**2 + (-27*y**2)*(-16*y**3) - 16*y**3*36 + 1188</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-33*y)*36 = -1188*y
  (-33*y)*(-27*y**2) = 891*y**3
  (-16*y**3)*36 = -576*y**3
  (-16*y**3)*(-27*y**2) = 432*y**5
  33*-27*y**2 = -891*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 432*y**5 - 576*y**3 + 891*y**3 - 891*y**2 - 1188*y + 1188</replace>
Combining like terms, got 432*y**5 + 315*y**3 - 891*y**2 - 1188*y + 1188
<replace-#Step 5>#Step 6:
Current expression: 432*y**5 + 315*y**3 - 891*y**2 - 1188*y + 1188</replace>
No more calculations needed.
<answer>432*y**5 + 315*y**3 - 891*y**2 - 1188*y + 1188</answer>


Question:
Simplify this expression: -65*z*(30*z**3 - 3*z**2 - 27*z - 34)
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: -1950*z**4 + 195*z**3 + 1755*z**2 + 2210*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: -65*z*(30*z**3 - 3*z**2 - 27*z - 34)
Expanding the part (30*z**3 - 3*z**2 - 27*z - 34) using the distributive property, and we got: (-65*z)*(-27*z) + (-65*z)*(-3*z**2) + (-65*z)*(30*z**3) - (-1)*2210*z
<replace-#Step 1>#Step 2:
Current expression: (-65*z)*(-27*z) + (-65*z)*(-3*z**2) + (-65*z)*(30*z**3) - (-1)*2210*z</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -34*(-65*z) = 2210*z
  (-27*z)*(-65*z) = 1755*z**2
  (-3*z**2)*(-65*z) = 195*z**3
  (30*z**3)*(-65*z) = -1950*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1950*z**4 + 195*z**3 + 1755*z**2 + 2210*z</replace>
No more calculations needed.
<answer>-1950*z**4 + 195*z**3 + 1755*z**2 + 2210*z</answer>


Question:
Calculate the following: -412*y**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: -412*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: -412*y**3
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: -412*y**3</replace>
No more calculations needed.
<answer>-412*y**3</answer>


Question:
Calculate the following: (6*x**2 - 33*x - 40)*(35*x**3 - 46*x**2 - 17*x + 16)
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: 210*x**5 - 1431*x**4 + 16*x**3 + 2497*x**2 + 152*x - 640


Question:
Calculate the following: (-21*z**3 - 43*z)*(-69*z**3 + 46*z**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: 1449*z**6 - 966*z**5 + 2967*z**4 - 1831*z**3 + 301*z


Question:
Simplify this expression: (-49*z**2 + 25*z)*(-40*z**3 + 31*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: 1960*z**5 - 2519*z**4 + 775*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: (-49*z**2 + 25*z)*(-40*z**3 + 31*z**2)
Expanding the part (-49*z**2 + 25*z) using the distributive property, and we got: (25*z)*(-40*z**3 + 31*z**2) + (-49*z**2)*(-40*z**3 + 31*z**2)
<replace-#Step 1>#Step 2:
Current expression: (25*z)*(-40*z**3 + 31*z**2) + (-49*z**2)*(-40*z**3 + 31*z**2)</replace>
Simplifying the partial expression: (-49*z**2)*(-40*z**3 + 31*z**2)
Expanding the part (-40*z**3 + 31*z**2) using the distributive property, and we got: (-49*z**2)*(31*z**2) + (-49*z**2)*(-40*z**3)
Replacing (-49*z**2)*(-40*z**3 + 31*z**2) with (-49*z**2)*(31*z**2) + (-49*z**2)*(-40*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (25*z)*(-40*z**3 + 31*z**2) + (-49*z**2)*(31*z**2) + (-49*z**2)*(-40*z**3)</replace>
Simplifying the partial expression: (25*z)*(-40*z**3 + 31*z**2)
Expanding the part (-40*z**3 + 31*z**2) using the distributive property, and we got: (25*z)*(31*z**2) + (25*z)*(-40*z**3)
Replacing (25*z)*(-40*z**3 + 31*z**2) with (25*z)*(31*z**2) + (25*z)*(-40*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (25*z)*(31*z**2) + (25*z)*(-40*z**3) + (-49*z**2)*(31*z**2) + (-49*z**2)*(-40*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-40*z**3)*(-49*z**2) = 1960*z**5
  (-40*z**3)*(25*z) = -1000*z**4
  (31*z**2)*(-49*z**2) = -1519*z**4
  (31*z**2)*(25*z) = 775*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1960*z**5 - 1519*z**4 - 1000*z**4 + 775*z**3</replace>
Combining like terms, got 1960*z**5 - 2519*z**4 + 775*z**3
<replace-#Step 5>#Step 6:
Current expression: 1960*z**5 - 2519*z**4 + 775*z**3</replace>
No more calculations needed.
<answer>1960*z**5 - 2519*z**4 + 775*z**3</answer>


Question:
Simplify this expression: (35*z**3 - 35*z)*(52*z**3 - 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: 1820*z**6 - 1820*z**4 - 245*z**3 + 245*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*z**3 - 35*z)*(52*z**3 - 7)
Expanding the part (52*z**3 - 7) using the distributive property, and we got: (52*z**3)*(35*z**3 - 35*z) - 7*(35*z**3 - 35*z)
<replace-#Step 1>#Step 2:
Current expression: (52*z**3)*(35*z**3 - 35*z) - 7*(35*z**3 - 35*z)</replace>
Simplifying the partial expression: -7*(35*z**3 - 35*z)
Expanding the part (35*z**3 - 35*z) using the distributive property, and we got: -35*z*(-7) + (35*z**3)*(-7)
Replacing -7*(35*z**3 - 35*z) with -35*z*(-7) + (35*z**3)*(-7) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -35*z*(-7) + (35*z**3)*(-7) + (52*z**3)*(35*z**3 - 35*z)</replace>
Simplifying the partial expression: (52*z**3)*(35*z**3 - 35*z)
Expanding the part (35*z**3 - 35*z) using the distributive property, and we got: (-35*z)*(52*z**3) + (35*z**3)*(52*z**3)
Replacing (52*z**3)*(35*z**3 - 35*z) with (-35*z)*(52*z**3) + (35*z**3)*(52*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-35*z)*(52*z**3) - 35*z*(-7) + (35*z**3)*(52*z**3) + (35*z**3)*(-7)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-35*z)*-7 = 245*z
  (-35*z)*(52*z**3) = -1820*z**4
  (35*z**3)*-7 = -245*z**3
  (35*z**3)*(52*z**3) = 1820*z**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1820*z**6 - 1820*z**4 - 245*z**3 + 245*z</replace>
No more calculations needed.
<answer>1820*z**6 - 1820*z**4 - 245*z**3 + 245*z</answer>


Question:
Simplify this expression: (17*z**2 + 100*z)*(53*z**2 - 48*z + 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: 901*z**4 + 4484*z**3 - 4171*z**2 + 3700*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: (17*z**2 + 100*z)*(53*z**2 - 48*z + 37)
Expanding the part (17*z**2 + 100*z) using the distributive property, and we got: (100*z)*(53*z**2 - 48*z + 37) + (17*z**2)*(53*z**2 - 48*z + 37)
<replace-#Step 1>#Step 2:
Current expression: (100*z)*(53*z**2 - 48*z + 37) + (17*z**2)*(53*z**2 - 48*z + 37)</replace>
Simplifying the partial expression: (17*z**2)*(53*z**2 - 48*z + 37)
Expanding the part (53*z**2 - 48*z + 37) using the distributive property, and we got: (-48*z)*(17*z**2) + 37*(17*z**2) + (17*z**2)*(53*z**2)
Replacing (17*z**2)*(53*z**2 - 48*z + 37) with (-48*z)*(17*z**2) + 37*(17*z**2) + (17*z**2)*(53*z**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-48*z)*(17*z**2) + 37*17*z**2 + (100*z)*(53*z**2 - 48*z + 37) + (17*z**2)*(53*z**2)</replace>
Simplifying the partial expression: (100*z)*(53*z**2 - 48*z + 37)
Expanding the part (53*z**2 - 48*z + 37) using the distributive property, and we got: (-48*z)*(100*z) + 37*(100*z) + (100*z)*(53*z**2)
Replacing (100*z)*(53*z**2 - 48*z + 37) with (-48*z)*(100*z) + 37*(100*z) + (100*z)*(53*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-48*z)*(100*z) + (-48*z)*(17*z**2) + 37*17*z**2 + 37*100*z + (100*z)*(53*z**2) + (17*z**2)*(53*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-48*z)*(17*z**2) = -816*z**3
  (-48*z)*(100*z) = -4800*z**2
  (53*z**2)*(17*z**2) = 901*z**4
  (53*z**2)*(100*z) = 5300*z**3
  37*17*z**2 = 629*z**2
  37*100*z = 3700*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 901*z**4 - 816*z**3 + 5300*z**3 - 4800*z**2 + 629*z**2 + 3700*z</replace>
Combining like terms, got 901*z**4 + 4484*z**3 - 4171*z**2 + 3700*z
<replace-#Step 5>#Step 6:
Current expression: 901*z**4 + 4484*z**3 - 4171*z**2 + 3700*z</replace>
No more calculations needed.
<answer>901*z**4 + 4484*z**3 - 4171*z**2 + 3700*z</answer>


Question:
Calculate the following: 512 - 576*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: 512 - 576*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: 512 - 576*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: 512 - 576*x</replace>
No more calculations needed.
<answer>512 - 576*x</answer>


Question:
Calculate the following: -21*x*(30*x**3 + 93*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: -630*x**4 - 1953*x**2 - 861*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: -21*x*(30*x**3 + 93*x + 41)
Expanding the part (30*x**3 + 93*x + 41) using the distributive property, and we got: (-21*x)*(93*x) + (-21*x)*(30*x**3) + 41*(-21*x)
<replace-#Step 1>#Step 2:
Current expression: (-21*x)*(93*x) + (-21*x)*(30*x**3) + 41*(-21*x)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  41*(-21*x) = -861*x
  (30*x**3)*(-21*x) = -630*x**4
  (93*x)*(-21*x) = -1953*x**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -630*x**4 - 1953*x**2 - 861*x</replace>
No more calculations needed.
<answer>-630*x**4 - 1953*x**2 - 861*x</answer>


Question:
Calculate the following: (-38*x**3 - 29*x**2)*(19*x**3 - 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: -722*x**6 - 551*x**5 + 266*x**4 + 203*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: (-38*x**3 - 29*x**2)*(19*x**3 - 7*x)
Expanding the part (-38*x**3 - 29*x**2) using the distributive property, and we got: (-29*x**2)*(19*x**3 - 7*x) + (-38*x**3)*(19*x**3 - 7*x)
<replace-#Step 1>#Step 2:
Current expression: (-29*x**2)*(19*x**3 - 7*x) + (-38*x**3)*(19*x**3 - 7*x)</replace>
Simplifying the partial expression: (-38*x**3)*(19*x**3 - 7*x)
Expanding the part (19*x**3 - 7*x) using the distributive property, and we got: (-7*x)*(-38*x**3) + (-38*x**3)*(19*x**3)
Replacing (-38*x**3)*(19*x**3 - 7*x) with (-7*x)*(-38*x**3) + (-38*x**3)*(19*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-7*x)*(-38*x**3) + (-29*x**2)*(19*x**3 - 7*x) + (-38*x**3)*(19*x**3)</replace>
Simplifying the partial expression: (-29*x**2)*(19*x**3 - 7*x)
Expanding the part (19*x**3 - 7*x) using the distributive property, and we got: (-7*x)*(-29*x**2) + (-29*x**2)*(19*x**3)
Replacing (-29*x**2)*(19*x**3 - 7*x) with (-7*x)*(-29*x**2) + (-29*x**2)*(19*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-7*x)*(-29*x**2) + (-7*x)*(-38*x**3) + (-29*x**2)*(19*x**3) + (-38*x**3)*(19*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-7*x)*(-38*x**3) = 266*x**4
  (-7*x)*(-29*x**2) = 203*x**3
  (19*x**3)*(-38*x**3) = -722*x**6
  (19*x**3)*(-29*x**2) = -551*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -722*x**6 - 551*x**5 + 266*x**4 + 203*x**3</replace>
No more calculations needed.
<answer>-722*x**6 - 551*x**5 + 266*x**4 + 203*x**3</answer>


Question:
Calculate the following: (-14*y - 32)*(-47*y**3 - 9*y**2 + 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: 658*y**4 + 1630*y**3 - 188*y**2 - 1088*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: (-14*y - 32)*(-47*y**3 - 9*y**2 + 34*y)
Expanding the part (-14*y - 32) using the distributive property, and we got: (-14*y)*(-47*y**3 - 9*y**2 + 34*y) - 32*(-47*y**3 - 9*y**2 + 34*y)
<replace-#Step 1>#Step 2:
Current expression: (-14*y)*(-47*y**3 - 9*y**2 + 34*y) - 32*(-47*y**3 - 9*y**2 + 34*y)</replace>
Simplifying the partial expression: -32*(-47*y**3 - 9*y**2 + 34*y)
Expanding the part (-47*y**3 - 9*y**2 + 34*y) using the distributive property, and we got: (34*y)*(-32) - 9*y**2*(-32) - 47*y**3*(-32)
Replacing -32*(-47*y**3 - 9*y**2 + 34*y) with (34*y)*(-32) - 9*y**2*(-32) - 47*y**3*(-32) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-14*y)*(-47*y**3 - 9*y**2 + 34*y) + (34*y)*(-32) - 9*y**2*(-32) - 47*y**3*(-32)</replace>
Simplifying the partial expression: (-14*y)*(-47*y**3 - 9*y**2 + 34*y)
Expanding the part (-47*y**3 - 9*y**2 + 34*y) using the distributive property, and we got: (-14*y)*(34*y) + (-14*y)*(-9*y**2) + (-14*y)*(-47*y**3)
Replacing (-14*y)*(-47*y**3 - 9*y**2 + 34*y) with (-14*y)*(34*y) + (-14*y)*(-9*y**2) + (-14*y)*(-47*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-14*y)*(34*y) + (-14*y)*(-9*y**2) + (-14*y)*(-47*y**3) + (34*y)*(-32) - 9*y**2*(-32) - 47*y**3*(-32)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-47*y**3)*-32 = 1504*y**3
  (-47*y**3)*(-14*y) = 658*y**4
  (-9*y**2)*-32 = 288*y**2
  (-9*y**2)*(-14*y) = 126*y**3
  (34*y)*-32 = -1088*y
  (34*y)*(-14*y) = -476*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 658*y**4 + 126*y**3 + 1504*y**3 - 476*y**2 + 288*y**2 - 1088*y</replace>
Combining like terms, got 658*y**4 + 1630*y**3 - 188*y**2 - 1088*y
<replace-#Step 5>#Step 6:
Current expression: 658*y**4 + 1630*y**3 - 188*y**2 - 1088*y</replace>
No more calculations needed.
<answer>658*y**4 + 1630*y**3 - 188*y**2 - 1088*y</answer>


Question:
Simplify this expression: 75*x**3*(14*x**3 - 14)
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: 1050*x**6 - 1050*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: 75*x**3*(14*x**3 - 14)
Expanding the part (14*x**3 - 14) using the distributive property, and we got: -1050*x**3 + (14*x**3)*(75*x**3)
<replace-#Step 1>#Step 2:
Current expression: -1050*x**3 + (14*x**3)*(75*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -14*(75*x**3) = -1050*x**3
  (14*x**3)*(75*x**3) = 1050*x**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1050*x**6 - 1050*x**3</replace>
No more calculations needed.
<answer>1050*x**6 - 1050*x**3</answer>


Question:
Simplify this expression: (15 - 20*x**3)*(-36*x**2 - 26)
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: 720*x**5 + 520*x**3 - 540*x**2 - 390

Let's solve 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 - 20*x**3)*(-36*x**2 - 26)
Expanding the part (-36*x**2 - 26) using the distributive property, and we got: (-36*x**2)*(15 - 20*x**3) - 26*(15 - 20*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-36*x**2)*(15 - 20*x**3) - 26*(15 - 20*x**3)</replace>
Simplifying the partial expression: -26*(15 - 20*x**3)
Expanding the part (15 - 20*x**3) using the distributive property, and we got: -20*x**3*(-26) + 15*(-26)
Replacing -26*(15 - 20*x**3) with -20*x**3*(-26) + 15*(-26) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-36*x**2)*(15 - 20*x**3) - 20*x**3*(-26) - 390</replace>
Simplifying the partial expression: (-36*x**2)*(15 - 20*x**3)
Expanding the part (15 - 20*x**3) using the distributive property, and we got: 15*(-36*x**2) + (-36*x**2)*(-20*x**3)
Replacing (-36*x**2)*(15 - 20*x**3) with 15*(-36*x**2) + (-36*x**2)*(-20*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 15*(-36)*x**2 + (-36*x**2)*(-20*x**3) - 20*x**3*(-26) - 390</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-20*x**3)*-26 = 520*x**3
  (-20*x**3)*(-36*x**2) = 720*x**5
  15*-36*x**2 = -540*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 720*x**5 + 520*x**3 - 540*x**2 - 390</replace>
No more calculations needed.
<answer>720*x**5 + 520*x**3 - 540*x**2 - 390</answer>


Question:
Simplify this expression: (46*z**2 + 22*z)*(3*z**3 + 45*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: 138*z**5 + 2136*z**4 + 990*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: (46*z**2 + 22*z)*(3*z**3 + 45*z**2)
Expanding the part (3*z**3 + 45*z**2) using the distributive property, and we got: (45*z**2)*(46*z**2 + 22*z) + (3*z**3)*(46*z**2 + 22*z)
<replace-#Step 1>#Step 2:
Current expression: (45*z**2)*(46*z**2 + 22*z) + (3*z**3)*(46*z**2 + 22*z)</replace>
Simplifying the partial expression: (3*z**3)*(46*z**2 + 22*z)
Expanding the part (46*z**2 + 22*z) using the distributive property, and we got: (22*z)*(3*z**3) + (46*z**2)*(3*z**3)
Replacing (3*z**3)*(46*z**2 + 22*z) with (22*z)*(3*z**3) + (46*z**2)*(3*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (22*z)*(3*z**3) + (45*z**2)*(46*z**2 + 22*z) + (46*z**2)*(3*z**3)</replace>
Simplifying the partial expression: (45*z**2)*(46*z**2 + 22*z)
Expanding the part (46*z**2 + 22*z) using the distributive property, and we got: (22*z)*(45*z**2) + (45*z**2)*(46*z**2)
Replacing (45*z**2)*(46*z**2 + 22*z) with (22*z)*(45*z**2) + (45*z**2)*(46*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (22*z)*(45*z**2) + (22*z)*(3*z**3) + (45*z**2)*(46*z**2) + (46*z**2)*(3*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (22*z)*(3*z**3) = 66*z**4
  (22*z)*(45*z**2) = 990*z**3
  (46*z**2)*(3*z**3) = 138*z**5
  (46*z**2)*(45*z**2) = 2070*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 138*z**5 + 66*z**4 + 2070*z**4 + 990*z**3</replace>
Combining like terms, got 138*z**5 + 2136*z**4 + 990*z**3
<replace-#Step 5>#Step 6:
Current expression: 138*z**5 + 2136*z**4 + 990*z**3</replace>
No more calculations needed.
<answer>138*z**5 + 2136*z**4 + 990*z**3</answer>


Question:
Calculate the following: -115*z**2 + 90*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: -115*z**2 + 90*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: -115*z**2 + 90*z
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: -115*z**2 + 90*z</replace>
No more calculations needed.
<answer>-115*z**2 + 90*z</answer>


Question:
Calculate the following: (18*z**3 + 30*z**2)*(-48*z**3 + 16*z**2 - 4*z - 28)
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: -864*z**6 - 1152*z**5 + 408*z**4 - 624*z**3 - 840*z**2


Question:
Simplify this expression: (9*z**3 + 16*z)*(22*z**3 - 38*z**2 + 30*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: 198*z**6 - 342*z**5 + 622*z**4 - 851*z**3 + 480*z**2 - 432*z


Question:
Simplify this expression: (23*x**3 + 36*x - 50)*(23*x**3 - 61*x**2 - 26)
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: 529*x**6 - 1403*x**5 + 828*x**4 - 3944*x**3 + 3050*x**2 - 936*x + 1300


Question:
Calculate the following: (11 - y**2)*(-32*y**3 + 70*y + 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: 32*y**5 - 422*y**3 - 49*y**2 + 770*y + 539

Let's solve 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 - y**2)*(-32*y**3 + 70*y + 49)
Expanding the part (11 - y**2) using the distributive property, and we got: (-y**2)*(-32*y**3 + 70*y + 49) + 11*(-32*y**3 + 70*y + 49)
<replace-#Step 1>#Step 2:
Current expression: (-y**2)*(-32*y**3 + 70*y + 49) + 11*(-32*y**3 + 70*y + 49)</replace>
Simplifying the partial expression: 11*(-32*y**3 + 70*y + 49)
Expanding the part (-32*y**3 + 70*y + 49) using the distributive property, and we got: (70*y)*11 - 32*y**3*11 + 49*11
Replacing 11*(-32*y**3 + 70*y + 49) with (70*y)*11 - 32*y**3*11 + 49*11 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (70*y)*11 + (-y**2)*(-32*y**3 + 70*y + 49) - 32*y**3*11 + 539</replace>
Simplifying the partial expression: (-y**2)*(-32*y**3 + 70*y + 49)
Expanding the part (-32*y**3 + 70*y + 49) using the distributive property, and we got: 49*(-y**2) + (70*y)*(-y**2) + (-y**2)*(-32*y**3)
Replacing (-y**2)*(-32*y**3 + 70*y + 49) with 49*(-y**2) + (70*y)*(-y**2) + (-y**2)*(-32*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 49*(-1)*y**2 + (70*y)*(-y**2) + (70*y)*11 + (-y**2)*(-32*y**3) - 32*y**3*11 + 539</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-32*y**3)*11 = -352*y**3
  (-32*y**3)*(-y**2) = 32*y**5
  (70*y)*11 = 770*y
  (70*y)*(-y**2) = -70*y**3
  49*-1*y**2 = -49*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 32*y**5 - 352*y**3 - 70*y**3 - 49*y**2 + 770*y + 539</replace>
Combining like terms, got 32*y**5 - 422*y**3 - 49*y**2 + 770*y + 539
<replace-#Step 5>#Step 6:
Current expression: 32*y**5 - 422*y**3 - 49*y**2 + 770*y + 539</replace>
No more calculations needed.
<answer>32*y**5 - 422*y**3 - 49*y**2 + 770*y + 539</answer>


Question:
Calculate the following: (5 - 11*x**3)*(31*x**2 + 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: -341*x**5 - 33*x**3 + 155*x**2 + 15

Let's solve 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: (5 - 11*x**3)*(31*x**2 + 3)
Expanding the part (31*x**2 + 3) using the distributive property, and we got: (31*x**2)*(5 - 11*x**3) + 3*(5 - 11*x**3)
<replace-#Step 1>#Step 2:
Current expression: (31*x**2)*(5 - 11*x**3) + 3*(5 - 11*x**3)</replace>
Simplifying the partial expression: 3*(5 - 11*x**3)
Expanding the part (5 - 11*x**3) using the distributive property, and we got: -11*x**3*3 + 5*3
Replacing 3*(5 - 11*x**3) with -11*x**3*3 + 5*3 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (31*x**2)*(5 - 11*x**3) - 11*x**3*3 + 15</replace>
Simplifying the partial expression: (31*x**2)*(5 - 11*x**3)
Expanding the part (5 - 11*x**3) using the distributive property, and we got: 5*(31*x**2) + (31*x**2)*(-11*x**3)
Replacing (31*x**2)*(5 - 11*x**3) with 5*(31*x**2) + (31*x**2)*(-11*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 5*31*x**2 + (31*x**2)*(-11*x**3) - 11*x**3*3 + 15</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-11*x**3)*3 = -33*x**3
  (-11*x**3)*(31*x**2) = -341*x**5
  5*31*x**2 = 155*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -341*x**5 - 33*x**3 + 155*x**2 + 15</replace>
No more calculations needed.
<answer>-341*x**5 - 33*x**3 + 155*x**2 + 15</answer>


Question:
Calculate the following: (-81*z**3 - 46)*(-22*z**3 - 10*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: 1782*z**6 + 810*z**4 + 1012*z**3 + 460*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: (-81*z**3 - 46)*(-22*z**3 - 10*z)
Expanding the part (-81*z**3 - 46) using the distributive property, and we got: (-81*z**3)*(-22*z**3 - 10*z) - 46*(-22*z**3 - 10*z)
<replace-#Step 1>#Step 2:
Current expression: (-81*z**3)*(-22*z**3 - 10*z) - 46*(-22*z**3 - 10*z)</replace>
Simplifying the partial expression: -46*(-22*z**3 - 10*z)
Expanding the part (-22*z**3 - 10*z) using the distributive property, and we got: -10*z*(-46) - 22*z**3*(-46)
Replacing -46*(-22*z**3 - 10*z) with -10*z*(-46) - 22*z**3*(-46) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -10*z*(-46) + (-81*z**3)*(-22*z**3 - 10*z) - 22*z**3*(-46)</replace>
Simplifying the partial expression: (-81*z**3)*(-22*z**3 - 10*z)
Expanding the part (-22*z**3 - 10*z) using the distributive property, and we got: (-10*z)*(-81*z**3) + (-81*z**3)*(-22*z**3)
Replacing (-81*z**3)*(-22*z**3 - 10*z) with (-10*z)*(-81*z**3) + (-81*z**3)*(-22*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-10*z)*(-81*z**3) - 10*z*(-46) + (-81*z**3)*(-22*z**3) - 22*z**3*(-46)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-22*z**3)*-46 = 1012*z**3
  (-22*z**3)*(-81*z**3) = 1782*z**6
  (-10*z)*-46 = 460*z
  (-10*z)*(-81*z**3) = 810*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1782*z**6 + 810*z**4 + 1012*z**3 + 460*z</replace>
No more calculations needed.
<answer>1782*z**6 + 810*z**4 + 1012*z**3 + 460*z</answer>


Question:
Simplify this expression: (-59*x**3 + 11*x**2)*(42*x**3 - 30*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: -2478*x**6 + 2232*x**5 - 330*x**4

Let's solve 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*x**3 + 11*x**2)*(42*x**3 - 30*x**2)
Expanding the part (-59*x**3 + 11*x**2) using the distributive property, and we got: (11*x**2)*(42*x**3 - 30*x**2) + (-59*x**3)*(42*x**3 - 30*x**2)
<replace-#Step 1>#Step 2:
Current expression: (11*x**2)*(42*x**3 - 30*x**2) + (-59*x**3)*(42*x**3 - 30*x**2)</replace>
Simplifying the partial expression: (-59*x**3)*(42*x**3 - 30*x**2)
Expanding the part (42*x**3 - 30*x**2) using the distributive property, and we got: (-30*x**2)*(-59*x**3) + (-59*x**3)*(42*x**3)
Replacing (-59*x**3)*(42*x**3 - 30*x**2) with (-30*x**2)*(-59*x**3) + (-59*x**3)*(42*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-30*x**2)*(-59*x**3) + (11*x**2)*(42*x**3 - 30*x**2) + (-59*x**3)*(42*x**3)</replace>
Simplifying the partial expression: (11*x**2)*(42*x**3 - 30*x**2)
Expanding the part (42*x**3 - 30*x**2) using the distributive property, and we got: (-30*x**2)*(11*x**2) + (11*x**2)*(42*x**3)
Replacing (11*x**2)*(42*x**3 - 30*x**2) with (-30*x**2)*(11*x**2) + (11*x**2)*(42*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-30*x**2)*(11*x**2) + (-30*x**2)*(-59*x**3) + (11*x**2)*(42*x**3) + (-59*x**3)*(42*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-30*x**2)*(-59*x**3) = 1770*x**5
  (-30*x**2)*(11*x**2) = -330*x**4
  (42*x**3)*(-59*x**3) = -2478*x**6
  (42*x**3)*(11*x**2) = 462*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2478*x**6 + 462*x**5 + 1770*x**5 - 330*x**4</replace>
Combining like terms, got -2478*x**6 + 2232*x**5 - 330*x**4
<replace-#Step 5>#Step 6:
Current expression: -2478*x**6 + 2232*x**5 - 330*x**4</replace>
No more calculations needed.
<answer>-2478*x**6 + 2232*x**5 - 330*x**4</answer>


Question:
Calculate the following: (-22*z**3 + 28*z**2)*(-2*z**3 - 13*z**2 - 8)
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: 44*z**6 + 230*z**5 - 364*z**4 + 176*z**3 - 224*z**2


Question:
Simplify this expression: 6*x**4
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: 6*x**4

Let's solve 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: 6*x**4
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: 6*x**4</replace>
No more calculations needed.
<answer>6*x**4</answer>


Question:
Calculate the following: (-6*x**3 - 38*x**2)*(-16*x**3 - 28*x**2 - 32*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: 96*x**6 + 776*x**5 + 1256*x**4 + 1216*x**3