Question:
Calculate the following: 54*y**3*(-10*y**3 - 29*y**2 - 16*y + 11)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -540*y**6 - 1566*y**5 - 864*y**4 + 594*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: 54*y**3*(-10*y**3 - 29*y**2 - 16*y + 11)
Expanding the part (-10*y**3 - 29*y**2 - 16*y + 11) using the distributive property, and we got: (-16*y)*(54*y**3) + 11*(54*y**3) + (-29*y**2)*(54*y**3) + (-10*y**3)*(54*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-16*y)*(54*y**3) + 11*(54*y**3) + (-29*y**2)*(54*y**3) + (-10*y**3)*(54*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  11*(54*y**3) = 594*y**3
  (-29*y**2)*(54*y**3) = -1566*y**5
  (-16*y)*(54*y**3) = -864*y**4
  (-10*y**3)*(54*y**3) = -540*y**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -540*y**6 - 1566*y**5 - 864*y**4 + 594*y**3</replace>
No more calculations needed.
<answer>-540*y**6 - 1566*y**5 - 864*y**4 + 594*y**3</answer>


Question:
Calculate the following: (-11*z**3 - 23)*(-7*z**3 - 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: 77*z**6 + 227*z**3 + 138

Let's solve 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*z**3 - 23)*(-7*z**3 - 6)
Expanding the part (-11*z**3 - 23) using the distributive property, and we got: (-11*z**3)*(-7*z**3 - 6) - 23*(-7*z**3 - 6)
<replace-#Step 1>#Step 2:
Current expression: (-11*z**3)*(-7*z**3 - 6) - 23*(-7*z**3 - 6)</replace>
Simplifying the partial expression: -23*(-7*z**3 - 6)
Expanding the part (-7*z**3 - 6) using the distributive property, and we got: -7*z**3*(-23) - 6*(-23)
Replacing -23*(-7*z**3 - 6) with -7*z**3*(-23) - 6*(-23) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-11*z**3)*(-7*z**3 - 6) - 7*z**3*(-23) + 138</replace>
Simplifying the partial expression: (-11*z**3)*(-7*z**3 - 6)
Expanding the part (-7*z**3 - 6) using the distributive property, and we got: -(-1)*66*z**3 + (-11*z**3)*(-7*z**3)
Replacing (-11*z**3)*(-7*z**3 - 6) with -(-1)*66*z**3 + (-11*z**3)*(-7*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -6*(-11)*z**3 + (-11*z**3)*(-7*z**3) - 7*z**3*(-23) + 138</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-7*z**3)*-23 = 161*z**3
  (-7*z**3)*(-11*z**3) = 77*z**6
  -6*-11*z**3 = 66*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 77*z**6 + 66*z**3 + 161*z**3 + 138</replace>
Combining like terms, got 77*z**6 + 227*z**3 + 138
<replace-#Step 5>#Step 6:
Current expression: 77*z**6 + 227*z**3 + 138</replace>
No more calculations needed.
<answer>77*z**6 + 227*z**3 + 138</answer>


Question:
Calculate the following: 104*z**5
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 104*z**5

Let's solve 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: 104*z**5
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: 104*z**5</replace>
No more calculations needed.
<answer>104*z**5</answer>


Question:
Simplify this expression: (31*y**2 - 21*y)*(-46*y**2 + 3*y + 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: -1426*y**4 + 1059*y**3 + 433*y**2 - 336*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (31*y**2 - 21*y)*(-46*y**2 + 3*y + 16)
Expanding the part (31*y**2 - 21*y) using the distributive property, and we got: (-21*y)*(-46*y**2 + 3*y + 16) + (31*y**2)*(-46*y**2 + 3*y + 16)
<replace-#Step 1>#Step 2:
Current expression: (-21*y)*(-46*y**2 + 3*y + 16) + (31*y**2)*(-46*y**2 + 3*y + 16)</replace>
Simplifying the partial expression: (-21*y)*(-46*y**2 + 3*y + 16)
Expanding the part (-46*y**2 + 3*y + 16) using the distributive property, and we got: (-21*y)*(3*y) + (-21*y)*(-46*y**2) + 16*(-21*y)
Replacing (-21*y)*(-46*y**2 + 3*y + 16) with (-21*y)*(3*y) + (-21*y)*(-46*y**2) + 16*(-21*y) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-21*y)*(3*y) + (-21*y)*(-46*y**2) + 16*(-21)*y + (31*y**2)*(-46*y**2 + 3*y + 16)</replace>
Simplifying the partial expression: (31*y**2)*(-46*y**2 + 3*y + 16)
Expanding the part (-46*y**2 + 3*y + 16) using the distributive property, and we got: 16*(31*y**2) + (3*y)*(31*y**2) + (-46*y**2)*(31*y**2)
Replacing (31*y**2)*(-46*y**2 + 3*y + 16) with 16*(31*y**2) + (3*y)*(31*y**2) + (-46*y**2)*(31*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-21*y)*(3*y) + (-21*y)*(-46*y**2) + 16*31*y**2 + 16*(-21)*y + (3*y)*(31*y**2) + (-46*y**2)*(31*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-46*y**2)*(-21*y) = 966*y**3
  (-46*y**2)*(31*y**2) = -1426*y**4
  (3*y)*(-21*y) = -63*y**2
  (3*y)*(31*y**2) = 93*y**3
  16*-21*y = -336*y
  16*31*y**2 = 496*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1426*y**4 + 93*y**3 + 966*y**3 - 63*y**2 + 496*y**2 - 336*y</replace>
Combining like terms, got -1426*y**4 + 1059*y**3 + 433*y**2 - 336*y
<replace-#Step 5>#Step 6:
Current expression: -1426*y**4 + 1059*y**3 + 433*y**2 - 336*y</replace>
No more calculations needed.
<answer>-1426*y**4 + 1059*y**3 + 433*y**2 - 336*y</answer>


Question:
Calculate the following: (-4*x**3 - 41*x**2)*(20*x**3 + 12*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: -80*x**6 - 868*x**5 - 492*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: (-4*x**3 - 41*x**2)*(20*x**3 + 12*x**2)
Expanding the part (-4*x**3 - 41*x**2) using the distributive property, and we got: (-41*x**2)*(20*x**3 + 12*x**2) + (-4*x**3)*(20*x**3 + 12*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-41*x**2)*(20*x**3 + 12*x**2) + (-4*x**3)*(20*x**3 + 12*x**2)</replace>
Simplifying the partial expression: (-41*x**2)*(20*x**3 + 12*x**2)
Expanding the part (20*x**3 + 12*x**2) using the distributive property, and we got: (-41*x**2)*(12*x**2) + (-41*x**2)*(20*x**3)
Replacing (-41*x**2)*(20*x**3 + 12*x**2) with (-41*x**2)*(12*x**2) + (-41*x**2)*(20*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-41*x**2)*(12*x**2) + (-41*x**2)*(20*x**3) + (-4*x**3)*(20*x**3 + 12*x**2)</replace>
Simplifying the partial expression: (-4*x**3)*(20*x**3 + 12*x**2)
Expanding the part (20*x**3 + 12*x**2) using the distributive property, and we got: (12*x**2)*(-4*x**3) + (-4*x**3)*(20*x**3)
Replacing (-4*x**3)*(20*x**3 + 12*x**2) with (12*x**2)*(-4*x**3) + (-4*x**3)*(20*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-41*x**2)*(12*x**2) + (-41*x**2)*(20*x**3) + (12*x**2)*(-4*x**3) + (-4*x**3)*(20*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (12*x**2)*(-41*x**2) = -492*x**4
  (12*x**2)*(-4*x**3) = -48*x**5
  (20*x**3)*(-41*x**2) = -820*x**5
  (20*x**3)*(-4*x**3) = -80*x**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -80*x**6 - 820*x**5 - 48*x**5 - 492*x**4</replace>
Combining like terms, got -80*x**6 - 868*x**5 - 492*x**4
<replace-#Step 5>#Step 6:
Current expression: -80*x**6 - 868*x**5 - 492*x**4</replace>
No more calculations needed.
<answer>-80*x**6 - 868*x**5 - 492*x**4</answer>


Question:
Calculate the following: (11 - 82*z**2)*(86*z**3 + 50*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: -7052*z**5 - 3154*z**3 + 550*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: (11 - 82*z**2)*(86*z**3 + 50*z)
Expanding the part (11 - 82*z**2) using the distributive property, and we got: (-82*z**2)*(86*z**3 + 50*z) + 11*(86*z**3 + 50*z)
<replace-#Step 1>#Step 2:
Current expression: (-82*z**2)*(86*z**3 + 50*z) + 11*(86*z**3 + 50*z)</replace>
Simplifying the partial expression: 11*(86*z**3 + 50*z)
Expanding the part (86*z**3 + 50*z) using the distributive property, and we got: (50*z)*11 + (86*z**3)*11
Replacing 11*(86*z**3 + 50*z) with (50*z)*11 + (86*z**3)*11 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (50*z)*11 + (-82*z**2)*(86*z**3 + 50*z) + (86*z**3)*11</replace>
Simplifying the partial expression: (-82*z**2)*(86*z**3 + 50*z)
Expanding the part (86*z**3 + 50*z) using the distributive property, and we got: (50*z)*(-82*z**2) + (-82*z**2)*(86*z**3)
Replacing (-82*z**2)*(86*z**3 + 50*z) with (50*z)*(-82*z**2) + (-82*z**2)*(86*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (50*z)*(-82*z**2) + (50*z)*11 + (-82*z**2)*(86*z**3) + (86*z**3)*11</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (50*z)*11 = 550*z
  (50*z)*(-82*z**2) = -4100*z**3
  (86*z**3)*11 = 946*z**3
  (86*z**3)*(-82*z**2) = -7052*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -7052*z**5 - 4100*z**3 + 946*z**3 + 550*z</replace>
Combining like terms, got -7052*z**5 - 3154*z**3 + 550*z
<replace-#Step 5>#Step 6:
Current expression: -7052*z**5 - 3154*z**3 + 550*z</replace>
No more calculations needed.
<answer>-7052*z**5 - 3154*z**3 + 550*z</answer>


Question:
Simplify this expression: (27*x**3 - 42*x**2)*(-13*x**3 - 40*x**2 - 21*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: -351*x**6 - 534*x**5 + 1113*x**4 + 828*x**3 + 84*x**2


Question:
Calculate the following: (-37*z**3 - 5*z)*(40*z**3 + 12*z**2 - 43)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1480*z**6 - 444*z**5 - 200*z**4 + 1531*z**3 + 215*z


Question:
Calculate the following: 96*x*(30*x**3 - 8*x - 1)
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: 2880*x**4 - 768*x**2 - 96*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: 96*x*(30*x**3 - 8*x - 1)
Expanding the part (30*x**3 - 8*x - 1) using the distributive property, and we got: (-8*x)*(96*x) - 96*x + (96*x)*(30*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-8*x)*(96*x) - 96*x + (96*x)*(30*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -1*(96*x) = -96*x
  (-8*x)*(96*x) = -768*x**2
  (30*x**3)*(96*x) = 2880*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 2880*x**4 - 768*x**2 - 96*x</replace>
No more calculations needed.
<answer>2880*x**4 - 768*x**2 - 96*x</answer>


Question:
Simplify this expression: (34*x**3 + 27*x + 44)*(12*x**3 + 44*x**2 - 28*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: 408*x**6 + 1496*x**5 - 628*x**4 + 1580*x**3 + 1180*x**2 - 1340*x - 176


Question:
Simplify this expression: (13 - 31*x**2)*(11*x**2 - 25*x + 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: -341*x**4 + 775*x**3 - 74*x**2 - 325*x + 91

Let's solve 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: (13 - 31*x**2)*(11*x**2 - 25*x + 7)
Expanding the part (13 - 31*x**2) using the distributive property, and we got: (-31*x**2)*(11*x**2 - 25*x + 7) + 13*(11*x**2 - 25*x + 7)
<replace-#Step 1>#Step 2:
Current expression: (-31*x**2)*(11*x**2 - 25*x + 7) + 13*(11*x**2 - 25*x + 7)</replace>
Simplifying the partial expression: 13*(11*x**2 - 25*x + 7)
Expanding the part (11*x**2 - 25*x + 7) using the distributive property, and we got: -25*x*13 + (11*x**2)*13 + 7*13
Replacing 13*(11*x**2 - 25*x + 7) with -25*x*13 + (11*x**2)*13 + 7*13 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -25*x*13 + (-31*x**2)*(11*x**2 - 25*x + 7) + (11*x**2)*13 + 91</replace>
Simplifying the partial expression: (-31*x**2)*(11*x**2 - 25*x + 7)
Expanding the part (11*x**2 - 25*x + 7) using the distributive property, and we got: (-25*x)*(-31*x**2) + 7*(-31*x**2) + (-31*x**2)*(11*x**2)
Replacing (-31*x**2)*(11*x**2 - 25*x + 7) with (-25*x)*(-31*x**2) + 7*(-31*x**2) + (-31*x**2)*(11*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-25*x)*(-31*x**2) - 25*x*13 + 7*(-31)*x**2 + (-31*x**2)*(11*x**2) + (11*x**2)*13 + 91</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-25*x)*13 = -325*x
  (-25*x)*(-31*x**2) = 775*x**3
  (11*x**2)*13 = 143*x**2
  (11*x**2)*(-31*x**2) = -341*x**4
  7*-31*x**2 = -217*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -341*x**4 + 775*x**3 - 217*x**2 + 143*x**2 - 325*x + 91</replace>
Combining like terms, got -341*x**4 + 775*x**3 - 74*x**2 - 325*x + 91
<replace-#Step 5>#Step 6:
Current expression: -341*x**4 + 775*x**3 - 74*x**2 - 325*x + 91</replace>
No more calculations needed.
<answer>-341*x**4 + 775*x**3 - 74*x**2 - 325*x + 91</answer>


Question:
Calculate the following: (28*x**2 + 84*x)*(49*x**3 + 35*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: 1372*x**5 + 4116*x**4 + 980*x**3 + 2940*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: (28*x**2 + 84*x)*(49*x**3 + 35*x)
Expanding the part (28*x**2 + 84*x) using the distributive property, and we got: (84*x)*(49*x**3 + 35*x) + (28*x**2)*(49*x**3 + 35*x)
<replace-#Step 1>#Step 2:
Current expression: (84*x)*(49*x**3 + 35*x) + (28*x**2)*(49*x**3 + 35*x)</replace>
Simplifying the partial expression: (28*x**2)*(49*x**3 + 35*x)
Expanding the part (49*x**3 + 35*x) using the distributive property, and we got: (35*x)*(28*x**2) + (28*x**2)*(49*x**3)
Replacing (28*x**2)*(49*x**3 + 35*x) with (35*x)*(28*x**2) + (28*x**2)*(49*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (35*x)*(28*x**2) + (84*x)*(49*x**3 + 35*x) + (28*x**2)*(49*x**3)</replace>
Simplifying the partial expression: (84*x)*(49*x**3 + 35*x)
Expanding the part (49*x**3 + 35*x) using the distributive property, and we got: (35*x)*(84*x) + (84*x)*(49*x**3)
Replacing (84*x)*(49*x**3 + 35*x) with (35*x)*(84*x) + (84*x)*(49*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (35*x)*(84*x) + (35*x)*(28*x**2) + (84*x)*(49*x**3) + (28*x**2)*(49*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (35*x)*(28*x**2) = 980*x**3
  (35*x)*(84*x) = 2940*x**2
  (49*x**3)*(28*x**2) = 1372*x**5
  (49*x**3)*(84*x) = 4116*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1372*x**5 + 4116*x**4 + 980*x**3 + 2940*x**2</replace>
No more calculations needed.
<answer>1372*x**5 + 4116*x**4 + 980*x**3 + 2940*x**2</answer>


Question:
Calculate the following: (-27*z - 38)*(-29*z**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: 783*z**3 + 1102*z**2 + 945*z + 1330

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-27*z - 38)*(-29*z**2 - 35)
Expanding the part (-27*z - 38) using the distributive property, and we got: (-27*z)*(-29*z**2 - 35) - 38*(-29*z**2 - 35)
<replace-#Step 1>#Step 2:
Current expression: (-27*z)*(-29*z**2 - 35) - 38*(-29*z**2 - 35)</replace>
Simplifying the partial expression: -38*(-29*z**2 - 35)
Expanding the part (-29*z**2 - 35) using the distributive property, and we got: -29*z**2*(-38) - 35*(-38)
Replacing -38*(-29*z**2 - 35) with -29*z**2*(-38) - 35*(-38) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-27*z)*(-29*z**2 - 35) - 29*z**2*(-38) + 1330</replace>
Simplifying the partial expression: (-27*z)*(-29*z**2 - 35)
Expanding the part (-29*z**2 - 35) using the distributive property, and we got: (-27*z)*(-29*z**2) - (-1)*945*z
Replacing (-27*z)*(-29*z**2 - 35) with (-27*z)*(-29*z**2) - (-1)*945*z in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-27*z)*(-29*z**2) - 35*(-27)*z - 29*z**2*(-38) + 1330</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-29*z**2)*-38 = 1102*z**2
  (-29*z**2)*(-27*z) = 783*z**3
  -35*-27*z = 945*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 783*z**3 + 1102*z**2 + 945*z + 1330</replace>
No more calculations needed.
<answer>783*z**3 + 1102*z**2 + 945*z + 1330</answer>


Question:
Simplify this expression: -2914*y**3 - 558*y**2 + 1426*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: -2914*y**3 - 558*y**2 + 1426*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: -2914*y**3 - 558*y**2 + 1426*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: -2914*y**3 - 558*y**2 + 1426*y</replace>
No more calculations needed.
<answer>-2914*y**3 - 558*y**2 + 1426*y</answer>


Question:
Calculate the following: (-37*y**2 - 30*y - 23)*(-38*y**3 + y**2 - 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: 1406*y**5 + 1103*y**4 + 844*y**3 + 199*y**2 + 180*y + 138


Question:
Simplify this expression: 260*z**2 - 273
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: 260*z**2 - 273

Let's solve 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: 260*z**2 - 273
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: 260*z**2 - 273</replace>
No more calculations needed.
<answer>260*z**2 - 273</answer>


Question:
Simplify this expression: -17*y**3*(26*y**2 + 20*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: -442*y**5 - 340*y**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: -17*y**3*(26*y**2 + 20*y)
Expanding the part (26*y**2 + 20*y) using the distributive property, and we got: (20*y)*(-17*y**3) + (26*y**2)*(-17*y**3)
<replace-#Step 1>#Step 2:
Current expression: (20*y)*(-17*y**3) + (26*y**2)*(-17*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (20*y)*(-17*y**3) = -340*y**4
  (26*y**2)*(-17*y**3) = -442*y**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -442*y**5 - 340*y**4</replace>
No more calculations needed.
<answer>-442*y**5 - 340*y**4</answer>


Question:
Calculate the following: (26*y**2 + 51*y)*(-5*y**3 - 10*y + 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: -130*y**5 - 255*y**4 - 260*y**3 + 556*y**2 + 2091*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: (26*y**2 + 51*y)*(-5*y**3 - 10*y + 41)
Expanding the part (26*y**2 + 51*y) using the distributive property, and we got: (51*y)*(-5*y**3 - 10*y + 41) + (26*y**2)*(-5*y**3 - 10*y + 41)
<replace-#Step 1>#Step 2:
Current expression: (51*y)*(-5*y**3 - 10*y + 41) + (26*y**2)*(-5*y**3 - 10*y + 41)</replace>
Simplifying the partial expression: (26*y**2)*(-5*y**3 - 10*y + 41)
Expanding the part (-5*y**3 - 10*y + 41) using the distributive property, and we got: (-10*y)*(26*y**2) + 41*(26*y**2) + (26*y**2)*(-5*y**3)
Replacing (26*y**2)*(-5*y**3 - 10*y + 41) with (-10*y)*(26*y**2) + 41*(26*y**2) + (26*y**2)*(-5*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-10*y)*(26*y**2) + 41*26*y**2 + (51*y)*(-5*y**3 - 10*y + 41) + (26*y**2)*(-5*y**3)</replace>
Simplifying the partial expression: (51*y)*(-5*y**3 - 10*y + 41)
Expanding the part (-5*y**3 - 10*y + 41) using the distributive property, and we got: (-10*y)*(51*y) + 41*(51*y) + (51*y)*(-5*y**3)
Replacing (51*y)*(-5*y**3 - 10*y + 41) with (-10*y)*(51*y) + 41*(51*y) + (51*y)*(-5*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-10*y)*(51*y) + (-10*y)*(26*y**2) + 41*26*y**2 + 41*51*y + (51*y)*(-5*y**3) + (26*y**2)*(-5*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-10*y)*(26*y**2) = -260*y**3
  (-10*y)*(51*y) = -510*y**2
  (-5*y**3)*(26*y**2) = -130*y**5
  (-5*y**3)*(51*y) = -255*y**4
  41*26*y**2 = 1066*y**2
  41*51*y = 2091*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -130*y**5 - 255*y**4 - 260*y**3 - 510*y**2 + 1066*y**2 + 2091*y</replace>
Combining like terms, got -130*y**5 - 255*y**4 - 260*y**3 + 556*y**2 + 2091*y
<replace-#Step 5>#Step 6:
Current expression: -130*y**5 - 255*y**4 - 260*y**3 + 556*y**2 + 2091*y</replace>
No more calculations needed.
<answer>-130*y**5 - 255*y**4 - 260*y**3 + 556*y**2 + 2091*y</answer>


Question:
Simplify this expression: 73*x**2*(-32*x**2 + 16*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: -2336*x**4 + 1168*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: 73*x**2*(-32*x**2 + 16*x)
Expanding the part (-32*x**2 + 16*x) using the distributive property, and we got: (16*x)*(73*x**2) + (-32*x**2)*(73*x**2)
<replace-#Step 1>#Step 2:
Current expression: (16*x)*(73*x**2) + (-32*x**2)*(73*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-32*x**2)*(73*x**2) = -2336*x**4
  (16*x)*(73*x**2) = 1168*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -2336*x**4 + 1168*x**3</replace>
No more calculations needed.
<answer>-2336*x**4 + 1168*x**3</answer>


Question:
Calculate the following: (47 - 39*y**3)*(-30*y**3 - 35*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: 1170*y**6 + 1365*y**4 - 3282*y**3 - 1645*y + 2256

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (47 - 39*y**3)*(-30*y**3 - 35*y + 48)
Expanding the part (47 - 39*y**3) using the distributive property, and we got: (-39*y**3)*(-30*y**3 - 35*y + 48) + 47*(-30*y**3 - 35*y + 48)
<replace-#Step 1>#Step 2:
Current expression: (-39*y**3)*(-30*y**3 - 35*y + 48) + 47*(-30*y**3 - 35*y + 48)</replace>
Simplifying the partial expression: 47*(-30*y**3 - 35*y + 48)
Expanding the part (-30*y**3 - 35*y + 48) using the distributive property, and we got: -35*y*47 - 30*y**3*47 + 48*47
Replacing 47*(-30*y**3 - 35*y + 48) with -35*y*47 - 30*y**3*47 + 48*47 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -35*y*47 + (-39*y**3)*(-30*y**3 - 35*y + 48) - 30*y**3*47 + 2256</replace>
Simplifying the partial expression: (-39*y**3)*(-30*y**3 - 35*y + 48)
Expanding the part (-30*y**3 - 35*y + 48) using the distributive property, and we got: (-35*y)*(-39*y**3) + 48*(-39*y**3) + (-39*y**3)*(-30*y**3)
Replacing (-39*y**3)*(-30*y**3 - 35*y + 48) with (-35*y)*(-39*y**3) + 48*(-39*y**3) + (-39*y**3)*(-30*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-35*y)*(-39*y**3) - 35*y*47 + 48*(-39)*y**3 + (-39*y**3)*(-30*y**3) - 30*y**3*47 + 2256</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-35*y)*47 = -1645*y
  (-35*y)*(-39*y**3) = 1365*y**4
  (-30*y**3)*47 = -1410*y**3
  (-30*y**3)*(-39*y**3) = 1170*y**6
  48*-39*y**3 = -1872*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1170*y**6 + 1365*y**4 - 1872*y**3 - 1410*y**3 - 1645*y + 2256</replace>
Combining like terms, got 1170*y**6 + 1365*y**4 - 3282*y**3 - 1645*y + 2256
<replace-#Step 5>#Step 6:
Current expression: 1170*y**6 + 1365*y**4 - 3282*y**3 - 1645*y + 2256</replace>
No more calculations needed.
<answer>1170*y**6 + 1365*y**4 - 3282*y**3 - 1645*y + 2256</answer>


Question:
Calculate the following: (-4*x**2 - 31*x)*(25*x**2 + 50*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: -100*x**4 - 975*x**3 - 1550*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: (-4*x**2 - 31*x)*(25*x**2 + 50*x)
Expanding the part (-4*x**2 - 31*x) using the distributive property, and we got: (-31*x)*(25*x**2 + 50*x) + (-4*x**2)*(25*x**2 + 50*x)
<replace-#Step 1>#Step 2:
Current expression: (-31*x)*(25*x**2 + 50*x) + (-4*x**2)*(25*x**2 + 50*x)</replace>
Simplifying the partial expression: (-31*x)*(25*x**2 + 50*x)
Expanding the part (25*x**2 + 50*x) using the distributive property, and we got: (-31*x)*(50*x) + (-31*x)*(25*x**2)
Replacing (-31*x)*(25*x**2 + 50*x) with (-31*x)*(50*x) + (-31*x)*(25*x**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-31*x)*(50*x) + (-31*x)*(25*x**2) + (-4*x**2)*(25*x**2 + 50*x)</replace>
Simplifying the partial expression: (-4*x**2)*(25*x**2 + 50*x)
Expanding the part (25*x**2 + 50*x) using the distributive property, and we got: (50*x)*(-4*x**2) + (-4*x**2)*(25*x**2)
Replacing (-4*x**2)*(25*x**2 + 50*x) with (50*x)*(-4*x**2) + (-4*x**2)*(25*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-31*x)*(50*x) + (-31*x)*(25*x**2) + (50*x)*(-4*x**2) + (-4*x**2)*(25*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (25*x**2)*(-31*x) = -775*x**3
  (25*x**2)*(-4*x**2) = -100*x**4
  (50*x)*(-31*x) = -1550*x**2
  (50*x)*(-4*x**2) = -200*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -100*x**4 - 775*x**3 - 200*x**3 - 1550*x**2</replace>
Combining like terms, got -100*x**4 - 975*x**3 - 1550*x**2
<replace-#Step 5>#Step 6:
Current expression: -100*x**4 - 975*x**3 - 1550*x**2</replace>
No more calculations needed.
<answer>-100*x**4 - 975*x**3 - 1550*x**2</answer>


Question:
Calculate the following: (42*x**2 - 26*x + 38)*(24*x**3 + 36*x**2 - 6*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: 1008*x**5 + 888*x**4 - 276*x**3 + 1524*x**2 - 228*x


Question:
Simplify this expression: (7 - 34*x**3)*(-18*x**3 - 15*x**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: 612*x**6 + 510*x**5 - 1112*x**3 - 105*x**2 + 203

Let's solve 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 - 34*x**3)*(-18*x**3 - 15*x**2 + 29)
Expanding the part (7 - 34*x**3) using the distributive property, and we got: (-34*x**3)*(-18*x**3 - 15*x**2 + 29) + 7*(-18*x**3 - 15*x**2 + 29)
<replace-#Step 1>#Step 2:
Current expression: (-34*x**3)*(-18*x**3 - 15*x**2 + 29) + 7*(-18*x**3 - 15*x**2 + 29)</replace>
Simplifying the partial expression: 7*(-18*x**3 - 15*x**2 + 29)
Expanding the part (-18*x**3 - 15*x**2 + 29) using the distributive property, and we got: -15*x**2*7 - 18*x**3*7 + 29*7
Replacing 7*(-18*x**3 - 15*x**2 + 29) with -15*x**2*7 - 18*x**3*7 + 29*7 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -15*x**2*7 + (-34*x**3)*(-18*x**3 - 15*x**2 + 29) - 18*x**3*7 + 203</replace>
Simplifying the partial expression: (-34*x**3)*(-18*x**3 - 15*x**2 + 29)
Expanding the part (-18*x**3 - 15*x**2 + 29) using the distributive property, and we got: 29*(-34*x**3) + (-15*x**2)*(-34*x**3) + (-34*x**3)*(-18*x**3)
Replacing (-34*x**3)*(-18*x**3 - 15*x**2 + 29) with 29*(-34*x**3) + (-15*x**2)*(-34*x**3) + (-34*x**3)*(-18*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 29*(-34)*x**3 + (-15*x**2)*(-34*x**3) - 15*x**2*7 + (-34*x**3)*(-18*x**3) - 18*x**3*7 + 203</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-18*x**3)*7 = -126*x**3
  (-18*x**3)*(-34*x**3) = 612*x**6
  (-15*x**2)*7 = -105*x**2
  (-15*x**2)*(-34*x**3) = 510*x**5
  29*-34*x**3 = -986*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 612*x**6 + 510*x**5 - 986*x**3 - 126*x**3 - 105*x**2 + 203</replace>
Combining like terms, got 612*x**6 + 510*x**5 - 1112*x**3 - 105*x**2 + 203
<replace-#Step 5>#Step 6:
Current expression: 612*x**6 + 510*x**5 - 1112*x**3 - 105*x**2 + 203</replace>
No more calculations needed.
<answer>612*x**6 + 510*x**5 - 1112*x**3 - 105*x**2 + 203</answer>


Question:
Simplify this expression: -8*x**2*(-27*x**2 - 13*x - 32)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 216*x**4 + 104*x**3 + 256*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: -8*x**2*(-27*x**2 - 13*x - 32)
Expanding the part (-27*x**2 - 13*x - 32) using the distributive property, and we got: (-13*x)*(-8*x**2) - (-1)*256*x**2 + (-27*x**2)*(-8*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-13*x)*(-8*x**2) - (-1)*256*x**2 + (-27*x**2)*(-8*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -32*(-8*x**2) = 256*x**2
  (-27*x**2)*(-8*x**2) = 216*x**4
  (-13*x)*(-8*x**2) = 104*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 216*x**4 + 104*x**3 + 256*x**2</replace>
No more calculations needed.
<answer>216*x**4 + 104*x**3 + 256*x**2</answer>


Question:
Simplify this expression: (12*x**3 - 42*x)*(-33*x**3 - x**2 - 42*x - 3)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -396*x**6 - 12*x**5 + 882*x**4 + 6*x**3 + 1764*x**2 + 126*x


Question:
Simplify this expression: 71*z*(-16*z**3 + 29*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: -1136*z**4 + 2059*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: 71*z*(-16*z**3 + 29*z**2)
Expanding the part (-16*z**3 + 29*z**2) using the distributive property, and we got: (71*z)*(29*z**2) + (71*z)*(-16*z**3)
<replace-#Step 1>#Step 2:
Current expression: (71*z)*(29*z**2) + (71*z)*(-16*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-16*z**3)*(71*z) = -1136*z**4
  (29*z**2)*(71*z) = 2059*z**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1136*z**4 + 2059*z**3</replace>
No more calculations needed.
<answer>-1136*z**4 + 2059*z**3</answer>


Question:
Simplify this expression: (6*y**3 + 3*y**2)*(19*y**3 - 15*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: 114*y**6 + 57*y**5 - 90*y**4 - 45*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: (6*y**3 + 3*y**2)*(19*y**3 - 15*y)
Expanding the part (19*y**3 - 15*y) using the distributive property, and we got: (-15*y)*(6*y**3 + 3*y**2) + (19*y**3)*(6*y**3 + 3*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-15*y)*(6*y**3 + 3*y**2) + (19*y**3)*(6*y**3 + 3*y**2)</replace>
Simplifying the partial expression: (-15*y)*(6*y**3 + 3*y**2)
Expanding the part (6*y**3 + 3*y**2) using the distributive property, and we got: (-15*y)*(3*y**2) + (-15*y)*(6*y**3)
Replacing (-15*y)*(6*y**3 + 3*y**2) with (-15*y)*(3*y**2) + (-15*y)*(6*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-15*y)*(3*y**2) + (-15*y)*(6*y**3) + (19*y**3)*(6*y**3 + 3*y**2)</replace>
Simplifying the partial expression: (19*y**3)*(6*y**3 + 3*y**2)
Expanding the part (6*y**3 + 3*y**2) using the distributive property, and we got: (3*y**2)*(19*y**3) + (6*y**3)*(19*y**3)
Replacing (19*y**3)*(6*y**3 + 3*y**2) with (3*y**2)*(19*y**3) + (6*y**3)*(19*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-15*y)*(3*y**2) + (-15*y)*(6*y**3) + (3*y**2)*(19*y**3) + (6*y**3)*(19*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (3*y**2)*(-15*y) = -45*y**3
  (3*y**2)*(19*y**3) = 57*y**5
  (6*y**3)*(-15*y) = -90*y**4
  (6*y**3)*(19*y**3) = 114*y**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 114*y**6 + 57*y**5 - 90*y**4 - 45*y**3</replace>
No more calculations needed.
<answer>114*y**6 + 57*y**5 - 90*y**4 - 45*y**3</answer>


Question:
Simplify this expression: (-x**2 + 18*x)*(-27*x**3 - x + 45)
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: 27*x**5 - 486*x**4 + x**3 - 63*x**2 + 810*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: (-x**2 + 18*x)*(-27*x**3 - x + 45)
Expanding the part (-x**2 + 18*x) using the distributive property, and we got: (18*x)*(-27*x**3 - x + 45) + (-x**2)*(-27*x**3 - x + 45)
<replace-#Step 1>#Step 2:
Current expression: (18*x)*(-27*x**3 - x + 45) + (-x**2)*(-27*x**3 - x + 45)</replace>
Simplifying the partial expression: (-x**2)*(-27*x**3 - x + 45)
Expanding the part (-27*x**3 - x + 45) using the distributive property, and we got: (-x)*(-x**2) + 45*(-x**2) + (-x**2)*(-27*x**3)
Replacing (-x**2)*(-27*x**3 - x + 45) with (-x)*(-x**2) + 45*(-x**2) + (-x**2)*(-27*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-x)*(-x**2) + 45*(-1)*x**2 + (18*x)*(-27*x**3 - x + 45) + (-x**2)*(-27*x**3)</replace>
Simplifying the partial expression: (18*x)*(-27*x**3 - x + 45)
Expanding the part (-27*x**3 - x + 45) using the distributive property, and we got: (-x)*(18*x) + 45*(18*x) + (18*x)*(-27*x**3)
Replacing (18*x)*(-27*x**3 - x + 45) with (-x)*(18*x) + 45*(18*x) + (18*x)*(-27*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-x)*(18*x) + (-x)*(-x**2) + 45*(-1)*x**2 + 45*18*x + (18*x)*(-27*x**3) + (-x**2)*(-27*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-x)*(-x**2) = x**3
  (-x)*(18*x) = -18*x**2
  (-27*x**3)*(-x**2) = 27*x**5
  (-27*x**3)*(18*x) = -486*x**4
  45*-1*x**2 = -45*x**2
  45*18*x = 810*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 27*x**5 - 486*x**4 + x**3 - 45*x**2 - 18*x**2 + 810*x</replace>
Combining like terms, got 27*x**5 - 486*x**4 + x**3 - 63*x**2 + 810*x
<replace-#Step 5>#Step 6:
Current expression: 27*x**5 - 486*x**4 + x**3 - 63*x**2 + 810*x</replace>
No more calculations needed.
<answer>27*x**5 - 486*x**4 + x**3 - 63*x**2 + 810*x</answer>


Question:
Simplify this expression: (47 - 45*y)*(-28*y**3 - 18*y + 21)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1260*y**4 - 1316*y**3 + 810*y**2 - 1791*y + 987

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (47 - 45*y)*(-28*y**3 - 18*y + 21)
Expanding the part (47 - 45*y) using the distributive property, and we got: (-45*y)*(-28*y**3 - 18*y + 21) + 47*(-28*y**3 - 18*y + 21)
<replace-#Step 1>#Step 2:
Current expression: (-45*y)*(-28*y**3 - 18*y + 21) + 47*(-28*y**3 - 18*y + 21)</replace>
Simplifying the partial expression: 47*(-28*y**3 - 18*y + 21)
Expanding the part (-28*y**3 - 18*y + 21) using the distributive property, and we got: -18*y*47 - 28*y**3*47 + 21*47
Replacing 47*(-28*y**3 - 18*y + 21) with -18*y*47 - 28*y**3*47 + 21*47 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-45*y)*(-28*y**3 - 18*y + 21) - 18*y*47 - 28*y**3*47 + 987</replace>
Simplifying the partial expression: (-45*y)*(-28*y**3 - 18*y + 21)
Expanding the part (-28*y**3 - 18*y + 21) using the distributive property, and we got: (-45*y)*(-18*y) + (-45*y)*(-28*y**3) + 21*(-45*y)
Replacing (-45*y)*(-28*y**3 - 18*y + 21) with (-45*y)*(-18*y) + (-45*y)*(-28*y**3) + 21*(-45*y) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-45*y)*(-18*y) + (-45*y)*(-28*y**3) - 18*y*47 + 21*(-45)*y - 28*y**3*47 + 987</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-28*y**3)*47 = -1316*y**3
  (-28*y**3)*(-45*y) = 1260*y**4
  (-18*y)*47 = -846*y
  (-18*y)*(-45*y) = 810*y**2
  21*-45*y = -945*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1260*y**4 - 1316*y**3 + 810*y**2 - 945*y - 846*y + 987</replace>
Combining like terms, got 1260*y**4 - 1316*y**3 + 810*y**2 - 1791*y + 987
<replace-#Step 5>#Step 6:
Current expression: 1260*y**4 - 1316*y**3 + 810*y**2 - 1791*y + 987</replace>
No more calculations needed.
<answer>1260*y**4 - 1316*y**3 + 810*y**2 - 1791*y + 987</answer>


Question:
Calculate the following: (-20*x**3 - 26)*(17*x**3 + 25*x**2 + 52)
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: -340*x**6 - 500*x**5 - 1482*x**3 - 650*x**2 - 1352


Question:
Simplify this expression: (14*y**3 - 31*y**2)*(31*y**3 + 50*y**2 - 16*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: 434*y**6 - 261*y**5 - 1774*y**4 + 496*y**3


Question:
Calculate the following: -19*y*(10*y**3 + 35*y**2 - 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: -190*y**4 - 665*y**3 + 684*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: -19*y*(10*y**3 + 35*y**2 - 36)
Expanding the part (10*y**3 + 35*y**2 - 36) using the distributive property, and we got: (-19*y)*(35*y**2) + (-19*y)*(10*y**3) - (-1)*684*y
<replace-#Step 1>#Step 2:
Current expression: (-19*y)*(35*y**2) + (-19*y)*(10*y**3) - (-1)*684*y</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -36*(-19*y) = 684*y
  (10*y**3)*(-19*y) = -190*y**4
  (35*y**2)*(-19*y) = -665*y**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -190*y**4 - 665*y**3 + 684*y</replace>
No more calculations needed.
<answer>-190*y**4 - 665*y**3 + 684*y</answer>


Question:
Simplify this expression: (7*z**3 - 46*z**2)*(-18*z**2 - 23*z - 1)
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: -126*z**5 + 667*z**4 + 1051*z**3 + 46*z**2


Question:
Simplify this expression: 85*y**3*(-40*y**3 - 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: -3400*y**6 - 255*y**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 85*y**3*(-40*y**3 - 3)
Expanding the part (-40*y**3 - 3) using the distributive property, and we got: -255*y**3 + (-40*y**3)*(85*y**3)
<replace-#Step 1>#Step 2:
Current expression: -255*y**3 + (-40*y**3)*(85*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -3*(85*y**3) = -255*y**3
  (-40*y**3)*(85*y**3) = -3400*y**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -3400*y**6 - 255*y**3</replace>
No more calculations needed.
<answer>-3400*y**6 - 255*y**3</answer>


Question:
Calculate the following: (20*x - 24)*(-37*x**2 + 71*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: -740*x**3 + 2308*x**2 - 1704*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: (20*x - 24)*(-37*x**2 + 71*x)
Expanding the part (20*x - 24) using the distributive property, and we got: (20*x)*(-37*x**2 + 71*x) - 24*(-37*x**2 + 71*x)
<replace-#Step 1>#Step 2:
Current expression: (20*x)*(-37*x**2 + 71*x) - 24*(-37*x**2 + 71*x)</replace>
Simplifying the partial expression: -24*(-37*x**2 + 71*x)
Expanding the part (-37*x**2 + 71*x) using the distributive property, and we got: (71*x)*(-24) - 37*x**2*(-24)
Replacing -24*(-37*x**2 + 71*x) with (71*x)*(-24) - 37*x**2*(-24) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (20*x)*(-37*x**2 + 71*x) + (71*x)*(-24) - 37*x**2*(-24)</replace>
Simplifying the partial expression: (20*x)*(-37*x**2 + 71*x)
Expanding the part (-37*x**2 + 71*x) using the distributive property, and we got: (20*x)*(71*x) + (20*x)*(-37*x**2)
Replacing (20*x)*(-37*x**2 + 71*x) with (20*x)*(71*x) + (20*x)*(-37*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (20*x)*(71*x) + (20*x)*(-37*x**2) + (71*x)*(-24) - 37*x**2*(-24)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-37*x**2)*-24 = 888*x**2
  (-37*x**2)*(20*x) = -740*x**3
  (71*x)*-24 = -1704*x
  (71*x)*(20*x) = 1420*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -740*x**3 + 888*x**2 + 1420*x**2 - 1704*x</replace>
Combining like terms, got -740*x**3 + 2308*x**2 - 1704*x
<replace-#Step 5>#Step 6:
Current expression: -740*x**3 + 2308*x**2 - 1704*x</replace>
No more calculations needed.
<answer>-740*x**3 + 2308*x**2 - 1704*x</answer>


Question:
Simplify this expression: (-8*z**3 - 73*z**2)*(-15*z**3 - 17*z + 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: 120*z**6 + 1095*z**5 + 136*z**4 + 1193*z**3 - 438*z**2


Question:
Calculate the following: -1100*y**2 + 1500*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: -1100*y**2 + 1500*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: -1100*y**2 + 1500*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: -1100*y**2 + 1500*y</replace>
No more calculations needed.
<answer>-1100*y**2 + 1500*y</answer>


Question:
Simplify this expression: (68*z + 35)*(-15*z**3 + 20*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: -1020*z**4 - 525*z**3 + 1360*z**2 + 700*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: (68*z + 35)*(-15*z**3 + 20*z)
Expanding the part (68*z + 35) using the distributive property, and we got: (68*z)*(-15*z**3 + 20*z) + 35*(-15*z**3 + 20*z)
<replace-#Step 1>#Step 2:
Current expression: (68*z)*(-15*z**3 + 20*z) + 35*(-15*z**3 + 20*z)</replace>
Simplifying the partial expression: 35*(-15*z**3 + 20*z)
Expanding the part (-15*z**3 + 20*z) using the distributive property, and we got: (20*z)*35 - 15*z**3*35
Replacing 35*(-15*z**3 + 20*z) with (20*z)*35 - 15*z**3*35 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (20*z)*35 + (68*z)*(-15*z**3 + 20*z) - 15*z**3*35</replace>
Simplifying the partial expression: (68*z)*(-15*z**3 + 20*z)
Expanding the part (-15*z**3 + 20*z) using the distributive property, and we got: (20*z)*(68*z) + (68*z)*(-15*z**3)
Replacing (68*z)*(-15*z**3 + 20*z) with (20*z)*(68*z) + (68*z)*(-15*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (20*z)*(68*z) + (20*z)*35 + (68*z)*(-15*z**3) - 15*z**3*35</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-15*z**3)*35 = -525*z**3
  (-15*z**3)*(68*z) = -1020*z**4
  (20*z)*35 = 700*z
  (20*z)*(68*z) = 1360*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1020*z**4 - 525*z**3 + 1360*z**2 + 700*z</replace>
No more calculations needed.
<answer>-1020*z**4 - 525*z**3 + 1360*z**2 + 700*z</answer>


Question:
Simplify this expression: (-11*z**2 + 30*z + 83)*(46*z**2 - 10*z + 24)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -506*z**4 + 1490*z**3 + 3254*z**2 - 110*z + 1992


Question:
Simplify this expression: (42 - 14*z**2)*(33*z**2 + 24)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -462*z**4 + 1050*z**2 + 1008

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (42 - 14*z**2)*(33*z**2 + 24)
Expanding the part (33*z**2 + 24) using the distributive property, and we got: (33*z**2)*(42 - 14*z**2) + 24*(42 - 14*z**2)
<replace-#Step 1>#Step 2:
Current expression: (33*z**2)*(42 - 14*z**2) + 24*(42 - 14*z**2)</replace>
Simplifying the partial expression: 24*(42 - 14*z**2)
Expanding the part (42 - 14*z**2) using the distributive property, and we got: -14*z**2*24 + 42*24
Replacing 24*(42 - 14*z**2) with -14*z**2*24 + 42*24 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -14*z**2*24 + (33*z**2)*(42 - 14*z**2) + 1008</replace>
Simplifying the partial expression: (33*z**2)*(42 - 14*z**2)
Expanding the part (42 - 14*z**2) using the distributive property, and we got: 42*(33*z**2) + (-14*z**2)*(33*z**2)
Replacing (33*z**2)*(42 - 14*z**2) with 42*(33*z**2) + (-14*z**2)*(33*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 42*33*z**2 + (-14*z**2)*(33*z**2) - 14*z**2*24 + 1008</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-14*z**2)*24 = -336*z**2
  (-14*z**2)*(33*z**2) = -462*z**4
  42*33*z**2 = 1386*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -462*z**4 - 336*z**2 + 1386*z**2 + 1008</replace>
Combining like terms, got -462*z**4 + 1050*z**2 + 1008
<replace-#Step 5>#Step 6:
Current expression: -462*z**4 + 1050*z**2 + 1008</replace>
No more calculations needed.
<answer>-462*z**4 + 1050*z**2 + 1008</answer>


Question:
Calculate the following: (5*z**2 + 65*z)*(21*z**3 + 50*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: 105*z**5 + 1615*z**4 + 3250*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: (5*z**2 + 65*z)*(21*z**3 + 50*z**2)
Expanding the part (5*z**2 + 65*z) using the distributive property, and we got: (65*z)*(21*z**3 + 50*z**2) + (5*z**2)*(21*z**3 + 50*z**2)
<replace-#Step 1>#Step 2:
Current expression: (65*z)*(21*z**3 + 50*z**2) + (5*z**2)*(21*z**3 + 50*z**2)</replace>
Simplifying the partial expression: (5*z**2)*(21*z**3 + 50*z**2)
Expanding the part (21*z**3 + 50*z**2) using the distributive property, and we got: (5*z**2)*(50*z**2) + (5*z**2)*(21*z**3)
Replacing (5*z**2)*(21*z**3 + 50*z**2) with (5*z**2)*(50*z**2) + (5*z**2)*(21*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (65*z)*(21*z**3 + 50*z**2) + (5*z**2)*(50*z**2) + (5*z**2)*(21*z**3)</replace>
Simplifying the partial expression: (65*z)*(21*z**3 + 50*z**2)
Expanding the part (21*z**3 + 50*z**2) using the distributive property, and we got: (65*z)*(50*z**2) + (65*z)*(21*z**3)
Replacing (65*z)*(21*z**3 + 50*z**2) with (65*z)*(50*z**2) + (65*z)*(21*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (65*z)*(50*z**2) + (65*z)*(21*z**3) + (5*z**2)*(50*z**2) + (5*z**2)*(21*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (21*z**3)*(5*z**2) = 105*z**5
  (21*z**3)*(65*z) = 1365*z**4
  (50*z**2)*(5*z**2) = 250*z**4
  (50*z**2)*(65*z) = 3250*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 105*z**5 + 250*z**4 + 1365*z**4 + 3250*z**3</replace>
Combining like terms, got 105*z**5 + 1615*z**4 + 3250*z**3
<replace-#Step 5>#Step 6:
Current expression: 105*z**5 + 1615*z**4 + 3250*z**3</replace>
No more calculations needed.
<answer>105*z**5 + 1615*z**4 + 3250*z**3</answer>


Question:
Calculate the following: -27*z**3*(30*z**3 + 38*z**2 - 44)
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: -810*z**6 - 1026*z**5 + 1188*z**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -27*z**3*(30*z**3 + 38*z**2 - 44)
Expanding the part (30*z**3 + 38*z**2 - 44) using the distributive property, and we got: -(-1)*1188*z**3 + (38*z**2)*(-27*z**3) + (-27*z**3)*(30*z**3)
<replace-#Step 1>#Step 2:
Current expression: -(-1)*1188*z**3 + (38*z**2)*(-27*z**3) + (-27*z**3)*(30*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -44*(-27*z**3) = 1188*z**3
  (30*z**3)*(-27*z**3) = -810*z**6
  (38*z**2)*(-27*z**3) = -1026*z**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -810*z**6 - 1026*z**5 + 1188*z**3</replace>
No more calculations needed.
<answer>-810*z**6 - 1026*z**5 + 1188*z**3</answer>


Question:
Simplify this expression: (-35*x**2 + 25*x)*(-43*x**3 - 34*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: 1505*x**5 + 115*x**4 - 850*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: (-35*x**2 + 25*x)*(-43*x**3 - 34*x**2)
Expanding the part (-43*x**3 - 34*x**2) using the distributive property, and we got: (-34*x**2)*(-35*x**2 + 25*x) + (-43*x**3)*(-35*x**2 + 25*x)
<replace-#Step 1>#Step 2:
Current expression: (-34*x**2)*(-35*x**2 + 25*x) + (-43*x**3)*(-35*x**2 + 25*x)</replace>
Simplifying the partial expression: (-43*x**3)*(-35*x**2 + 25*x)
Expanding the part (-35*x**2 + 25*x) using the distributive property, and we got: (25*x)*(-43*x**3) + (-35*x**2)*(-43*x**3)
Replacing (-43*x**3)*(-35*x**2 + 25*x) with (25*x)*(-43*x**3) + (-35*x**2)*(-43*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (25*x)*(-43*x**3) + (-35*x**2)*(-43*x**3) + (-34*x**2)*(-35*x**2 + 25*x)</replace>
Simplifying the partial expression: (-34*x**2)*(-35*x**2 + 25*x)
Expanding the part (-35*x**2 + 25*x) using the distributive property, and we got: (25*x)*(-34*x**2) + (-35*x**2)*(-34*x**2)
Replacing (-34*x**2)*(-35*x**2 + 25*x) with (25*x)*(-34*x**2) + (-35*x**2)*(-34*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (25*x)*(-34*x**2) + (25*x)*(-43*x**3) + (-35*x**2)*(-34*x**2) + (-35*x**2)*(-43*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-35*x**2)*(-43*x**3) = 1505*x**5
  (-35*x**2)*(-34*x**2) = 1190*x**4
  (25*x)*(-43*x**3) = -1075*x**4
  (25*x)*(-34*x**2) = -850*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1505*x**5 - 1075*x**4 + 1190*x**4 - 850*x**3</replace>
Combining like terms, got 1505*x**5 + 115*x**4 - 850*x**3
<replace-#Step 5>#Step 6:
Current expression: 1505*x**5 + 115*x**4 - 850*x**3</replace>
No more calculations needed.
<answer>1505*x**5 + 115*x**4 - 850*x**3</answer>


Question:
Calculate the following: -38*y*(-17*y**2 + 45*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: 646*y**3 - 1710*y**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -38*y*(-17*y**2 + 45*y)
Expanding the part (-17*y**2 + 45*y) using the distributive property, and we got: (-38*y)*(45*y) + (-38*y)*(-17*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-38*y)*(45*y) + (-38*y)*(-17*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-17*y**2)*(-38*y) = 646*y**3
  (45*y)*(-38*y) = -1710*y**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 646*y**3 - 1710*y**2</replace>
No more calculations needed.
<answer>646*y**3 - 1710*y**2</answer>


Question:
Simplify this expression: (-45*x**3 - 13*x)*(-29*x**2 - 28*x + 46)
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: 1305*x**5 + 1260*x**4 - 1693*x**3 + 364*x**2 - 598*x


Question:
Simplify this expression: (27*x**3 - x**2)*(-77*x**3 - 13*x + 15)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2079*x**6 + 77*x**5 - 351*x**4 + 418*x**3 - 15*x**2


Question:
Calculate the following: (27 - 21*y**2)*(29*y**3 - 4*y**2 + 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: -609*y**5 + 84*y**4 + 783*y**3 - 381*y**2 + 351

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (27 - 21*y**2)*(29*y**3 - 4*y**2 + 13)
Expanding the part (27 - 21*y**2) using the distributive property, and we got: (-21*y**2)*(29*y**3 - 4*y**2 + 13) + 27*(29*y**3 - 4*y**2 + 13)
<replace-#Step 1>#Step 2:
Current expression: (-21*y**2)*(29*y**3 - 4*y**2 + 13) + 27*(29*y**3 - 4*y**2 + 13)</replace>
Simplifying the partial expression: 27*(29*y**3 - 4*y**2 + 13)
Expanding the part (29*y**3 - 4*y**2 + 13) using the distributive property, and we got: -4*y**2*27 + (29*y**3)*27 + 13*27
Replacing 27*(29*y**3 - 4*y**2 + 13) with -4*y**2*27 + (29*y**3)*27 + 13*27 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-21*y**2)*(29*y**3 - 4*y**2 + 13) - 4*y**2*27 + (29*y**3)*27 + 351</replace>
Simplifying the partial expression: (-21*y**2)*(29*y**3 - 4*y**2 + 13)
Expanding the part (29*y**3 - 4*y**2 + 13) using the distributive property, and we got: 13*(-21*y**2) + (-21*y**2)*(-4*y**2) + (-21*y**2)*(29*y**3)
Replacing (-21*y**2)*(29*y**3 - 4*y**2 + 13) with 13*(-21*y**2) + (-21*y**2)*(-4*y**2) + (-21*y**2)*(29*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 13*(-21)*y**2 + (-21*y**2)*(-4*y**2) + (-21*y**2)*(29*y**3) - 4*y**2*27 + (29*y**3)*27 + 351</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-4*y**2)*27 = -108*y**2
  (-4*y**2)*(-21*y**2) = 84*y**4
  (29*y**3)*27 = 783*y**3
  (29*y**3)*(-21*y**2) = -609*y**5
  13*-21*y**2 = -273*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -609*y**5 + 84*y**4 + 783*y**3 - 273*y**2 - 108*y**2 + 351</replace>
Combining like terms, got -609*y**5 + 84*y**4 + 783*y**3 - 381*y**2 + 351
<replace-#Step 5>#Step 6:
Current expression: -609*y**5 + 84*y**4 + 783*y**3 - 381*y**2 + 351</replace>
No more calculations needed.
<answer>-609*y**5 + 84*y**4 + 783*y**3 - 381*y**2 + 351</answer>


Question:
Calculate the following: (48*x**2 + 33*x)*(39*x**2 + 47*x - 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: 1872*x**4 + 3543*x**3 - 321*x**2 - 1287*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: (48*x**2 + 33*x)*(39*x**2 + 47*x - 39)
Expanding the part (48*x**2 + 33*x) using the distributive property, and we got: (33*x)*(39*x**2 + 47*x - 39) + (48*x**2)*(39*x**2 + 47*x - 39)
<replace-#Step 1>#Step 2:
Current expression: (33*x)*(39*x**2 + 47*x - 39) + (48*x**2)*(39*x**2 + 47*x - 39)</replace>
Simplifying the partial expression: (33*x)*(39*x**2 + 47*x - 39)
Expanding the part (39*x**2 + 47*x - 39) using the distributive property, and we got: -1287*x + (33*x)*(47*x) + (33*x)*(39*x**2)
Replacing (33*x)*(39*x**2 + 47*x - 39) with -1287*x + (33*x)*(47*x) + (33*x)*(39*x**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -39*33*x + (33*x)*(47*x) + (33*x)*(39*x**2) + (48*x**2)*(39*x**2 + 47*x - 39)</replace>
Simplifying the partial expression: (48*x**2)*(39*x**2 + 47*x - 39)
Expanding the part (39*x**2 + 47*x - 39) using the distributive property, and we got: -1872*x**2 + (47*x)*(48*x**2) + (39*x**2)*(48*x**2)
Replacing (48*x**2)*(39*x**2 + 47*x - 39) with -1872*x**2 + (47*x)*(48*x**2) + (39*x**2)*(48*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -39*48*x**2 - 39*33*x + (33*x)*(47*x) + (33*x)*(39*x**2) + (47*x)*(48*x**2) + (39*x**2)*(48*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (39*x**2)*(33*x) = 1287*x**3
  (39*x**2)*(48*x**2) = 1872*x**4
  (47*x)*(33*x) = 1551*x**2
  (47*x)*(48*x**2) = 2256*x**3
  -39*33*x = -1287*x
  -39*48*x**2 = -1872*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1872*x**4 + 1287*x**3 + 2256*x**3 - 1872*x**2 + 1551*x**2 - 1287*x</replace>
Combining like terms, got 1872*x**4 + 3543*x**3 - 321*x**2 - 1287*x
<replace-#Step 5>#Step 6:
Current expression: 1872*x**4 + 3543*x**3 - 321*x**2 - 1287*x</replace>
No more calculations needed.
<answer>1872*x**4 + 3543*x**3 - 321*x**2 - 1287*x</answer>


Question:
Calculate the following: (-20*y**2 + 34*y - 26)*(22*y**3 - 5*y**2 + 11*y - 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: -440*y**5 + 848*y**4 - 962*y**3 + 784*y**2 - 762*y + 364


Question:
Simplify this expression: (95*y + 44)*(-7*y**2 - 51)
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: -665*y**3 - 308*y**2 - 4845*y - 2244

Let's solve 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: (95*y + 44)*(-7*y**2 - 51)
Expanding the part (-7*y**2 - 51) using the distributive property, and we got: (-7*y**2)*(95*y + 44) - 51*(95*y + 44)
<replace-#Step 1>#Step 2:
Current expression: (-7*y**2)*(95*y + 44) - 51*(95*y + 44)</replace>
Simplifying the partial expression: -51*(95*y + 44)
Expanding the part (95*y + 44) using the distributive property, and we got: (95*y)*(-51) + 44*(-51)
Replacing -51*(95*y + 44) with (95*y)*(-51) + 44*(-51) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (95*y)*(-51) + (-7*y**2)*(95*y + 44) - 2244</replace>
Simplifying the partial expression: (-7*y**2)*(95*y + 44)
Expanding the part (95*y + 44) using the distributive property, and we got: 44*(-7*y**2) + (95*y)*(-7*y**2)
Replacing (-7*y**2)*(95*y + 44) with 44*(-7*y**2) + (95*y)*(-7*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 44*(-7)*y**2 + (95*y)*(-7*y**2) + (95*y)*(-51) - 2244</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (95*y)*-51 = -4845*y
  (95*y)*(-7*y**2) = -665*y**3
  44*-7*y**2 = -308*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -665*y**3 - 308*y**2 - 4845*y - 2244</replace>
No more calculations needed.
<answer>-665*y**3 - 308*y**2 - 4845*y - 2244</answer>


Question:
Calculate the following: 2200*x**3 - 450
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: 2200*x**3 - 450

Let's solve 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: 2200*x**3 - 450
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: 2200*x**3 - 450</replace>
No more calculations needed.
<answer>2200*x**3 - 450</answer>


Question:
Calculate the following: (5*z**3 + 14)*(10*z**3 - 17)
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: 50*z**6 + 55*z**3 - 238

Let's solve 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*z**3 + 14)*(10*z**3 - 17)
Expanding the part (10*z**3 - 17) using the distributive property, and we got: (10*z**3)*(5*z**3 + 14) - 17*(5*z**3 + 14)
<replace-#Step 1>#Step 2:
Current expression: (10*z**3)*(5*z**3 + 14) - 17*(5*z**3 + 14)</replace>
Simplifying the partial expression: -17*(5*z**3 + 14)
Expanding the part (5*z**3 + 14) using the distributive property, and we got: (5*z**3)*(-17) + 14*(-17)
Replacing -17*(5*z**3 + 14) with (5*z**3)*(-17) + 14*(-17) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (5*z**3)*(-17) + (10*z**3)*(5*z**3 + 14) - 238</replace>
Simplifying the partial expression: (10*z**3)*(5*z**3 + 14)
Expanding the part (5*z**3 + 14) using the distributive property, and we got: 14*(10*z**3) + (5*z**3)*(10*z**3)
Replacing (10*z**3)*(5*z**3 + 14) with 14*(10*z**3) + (5*z**3)*(10*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 14*10*z**3 + (5*z**3)*(10*z**3) + (5*z**3)*(-17) - 238</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (5*z**3)*-17 = -85*z**3
  (5*z**3)*(10*z**3) = 50*z**6
  14*10*z**3 = 140*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 50*z**6 - 85*z**3 + 140*z**3 - 238</replace>
Combining like terms, got 50*z**6 + 55*z**3 - 238
<replace-#Step 5>#Step 6:
Current expression: 50*z**6 + 55*z**3 - 238</replace>
No more calculations needed.
<answer>50*z**6 + 55*z**3 - 238</answer>


Question:
Simplify this expression: (32 - 68*y**2)*(-40*y**2 + 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: 2720*y**4 - 2516*y**3 - 1280*y**2 + 1184*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: (32 - 68*y**2)*(-40*y**2 + 37*y)
Expanding the part (32 - 68*y**2) using the distributive property, and we got: (-68*y**2)*(-40*y**2 + 37*y) + 32*(-40*y**2 + 37*y)
<replace-#Step 1>#Step 2:
Current expression: (-68*y**2)*(-40*y**2 + 37*y) + 32*(-40*y**2 + 37*y)</replace>
Simplifying the partial expression: 32*(-40*y**2 + 37*y)
Expanding the part (-40*y**2 + 37*y) using the distributive property, and we got: (37*y)*32 - 40*y**2*32
Replacing 32*(-40*y**2 + 37*y) with (37*y)*32 - 40*y**2*32 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (37*y)*32 + (-68*y**2)*(-40*y**2 + 37*y) - 40*y**2*32</replace>
Simplifying the partial expression: (-68*y**2)*(-40*y**2 + 37*y)
Expanding the part (-40*y**2 + 37*y) using the distributive property, and we got: (37*y)*(-68*y**2) + (-68*y**2)*(-40*y**2)
Replacing (-68*y**2)*(-40*y**2 + 37*y) with (37*y)*(-68*y**2) + (-68*y**2)*(-40*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (37*y)*(-68*y**2) + (37*y)*32 + (-68*y**2)*(-40*y**2) - 40*y**2*32</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-40*y**2)*32 = -1280*y**2
  (-40*y**2)*(-68*y**2) = 2720*y**4
  (37*y)*32 = 1184*y
  (37*y)*(-68*y**2) = -2516*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2720*y**4 - 2516*y**3 - 1280*y**2 + 1184*y</replace>
No more calculations needed.
<answer>2720*y**4 - 2516*y**3 - 1280*y**2 + 1184*y</answer>


Question:
Simplify this expression: -925*z - 1100
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: -925*z - 1100

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -925*z - 1100
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: -925*z - 1100</replace>
No more calculations needed.
<answer>-925*z - 1100</answer>


Question:
Calculate the following: (-35*y**3 + 42*y**2)*(60*y**3 + 55*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2100*y**6 + 595*y**5 + 2310*y**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: (-35*y**3 + 42*y**2)*(60*y**3 + 55*y**2)
Expanding the part (-35*y**3 + 42*y**2) using the distributive property, and we got: (42*y**2)*(60*y**3 + 55*y**2) + (-35*y**3)*(60*y**3 + 55*y**2)
<replace-#Step 1>#Step 2:
Current expression: (42*y**2)*(60*y**3 + 55*y**2) + (-35*y**3)*(60*y**3 + 55*y**2)</replace>
Simplifying the partial expression: (-35*y**3)*(60*y**3 + 55*y**2)
Expanding the part (60*y**3 + 55*y**2) using the distributive property, and we got: (55*y**2)*(-35*y**3) + (-35*y**3)*(60*y**3)
Replacing (-35*y**3)*(60*y**3 + 55*y**2) with (55*y**2)*(-35*y**3) + (-35*y**3)*(60*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (42*y**2)*(60*y**3 + 55*y**2) + (55*y**2)*(-35*y**3) + (-35*y**3)*(60*y**3)</replace>
Simplifying the partial expression: (42*y**2)*(60*y**3 + 55*y**2)
Expanding the part (60*y**3 + 55*y**2) using the distributive property, and we got: (42*y**2)*(55*y**2) + (42*y**2)*(60*y**3)
Replacing (42*y**2)*(60*y**3 + 55*y**2) with (42*y**2)*(55*y**2) + (42*y**2)*(60*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (42*y**2)*(55*y**2) + (42*y**2)*(60*y**3) + (55*y**2)*(-35*y**3) + (-35*y**3)*(60*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (55*y**2)*(-35*y**3) = -1925*y**5
  (55*y**2)*(42*y**2) = 2310*y**4
  (60*y**3)*(-35*y**3) = -2100*y**6
  (60*y**3)*(42*y**2) = 2520*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2100*y**6 - 1925*y**5 + 2520*y**5 + 2310*y**4</replace>
Combining like terms, got -2100*y**6 + 595*y**5 + 2310*y**4
<replace-#Step 5>#Step 6:
Current expression: -2100*y**6 + 595*y**5 + 2310*y**4</replace>
No more calculations needed.
<answer>-2100*y**6 + 595*y**5 + 2310*y**4</answer>


Question:
Simplify this expression: (11*z**2 + 46*z + 71)*(-16*z**3 + 41*z - 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: -176*z**5 - 736*z**4 - 685*z**3 + 1160*z**2 - 125*z - 4686


Question:
Simplify this expression: -75*y**3*(-38*y**3 + 34*y + 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: 2850*y**6 - 2550*y**4 - 2100*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: -75*y**3*(-38*y**3 + 34*y + 28)
Expanding the part (-38*y**3 + 34*y + 28) using the distributive property, and we got: 28*(-75*y**3) + (34*y)*(-75*y**3) + (-75*y**3)*(-38*y**3)
<replace-#Step 1>#Step 2:
Current expression: 28*(-75*y**3) + (34*y)*(-75*y**3) + (-75*y**3)*(-38*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  28*(-75*y**3) = -2100*y**3
  (-38*y**3)*(-75*y**3) = 2850*y**6
  (34*y)*(-75*y**3) = -2550*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 2850*y**6 - 2550*y**4 - 2100*y**3</replace>
No more calculations needed.
<answer>2850*y**6 - 2550*y**4 - 2100*y**3</answer>


Question:
Simplify this expression: (-35*x**2 - 19*x)*(-36*x**3 + 13*x**2 + 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: 1260*x**5 + 229*x**4 - 247*x**3 - 1190*x**2 - 646*x


Question:
Calculate the following: (53*z**3 + 54*z)*(-27*z**3 + 20*z**2 + 49)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1431*z**6 + 1060*z**5 - 1458*z**4 + 3677*z**3 + 2646*z


Question:
Calculate the following: (-3*x**3 - 19)*(8*x**3 - 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: -24*x**6 - 128*x**3 + 152

Let's solve 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**3 - 19)*(8*x**3 - 8)
Expanding the part (-3*x**3 - 19) using the distributive property, and we got: (-3*x**3)*(8*x**3 - 8) - 19*(8*x**3 - 8)
<replace-#Step 1>#Step 2:
Current expression: (-3*x**3)*(8*x**3 - 8) - 19*(8*x**3 - 8)</replace>
Simplifying the partial expression: -19*(8*x**3 - 8)
Expanding the part (8*x**3 - 8) using the distributive property, and we got: (8*x**3)*(-19) - 8*(-19)
Replacing -19*(8*x**3 - 8) with (8*x**3)*(-19) - 8*(-19) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-3*x**3)*(8*x**3 - 8) + (8*x**3)*(-19) + 152</replace>
Simplifying the partial expression: (-3*x**3)*(8*x**3 - 8)
Expanding the part (8*x**3 - 8) using the distributive property, and we got: -(-1)*24*x**3 + (-3*x**3)*(8*x**3)
Replacing (-3*x**3)*(8*x**3 - 8) with -(-1)*24*x**3 + (-3*x**3)*(8*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -8*(-3)*x**3 + (-3*x**3)*(8*x**3) + (8*x**3)*(-19) + 152</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (8*x**3)*-19 = -152*x**3
  (8*x**3)*(-3*x**3) = -24*x**6
  -8*-3*x**3 = 24*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -24*x**6 - 152*x**3 + 24*x**3 + 152</replace>
Combining like terms, got -24*x**6 - 128*x**3 + 152
<replace-#Step 5>#Step 6:
Current expression: -24*x**6 - 128*x**3 + 152</replace>
No more calculations needed.
<answer>-24*x**6 - 128*x**3 + 152</answer>


Question:
Calculate the following: -23*x*(44*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: -1012*x**4 + 161*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: -23*x*(44*x**3 - 7*x)
Expanding the part (44*x**3 - 7*x) using the distributive property, and we got: (-23*x)*(-7*x) + (-23*x)*(44*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-23*x)*(-7*x) + (-23*x)*(44*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)*(-23*x) = 161*x**2
  (44*x**3)*(-23*x) = -1012*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1012*x**4 + 161*x**2</replace>
No more calculations needed.
<answer>-1012*x**4 + 161*x**2</answer>


Question:
Calculate the following: (10*y - 17)*(4*y**3 + 50*y**2 - 46)
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: 40*y**4 + 432*y**3 - 850*y**2 - 460*y + 782

Let's solve 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 - 17)*(4*y**3 + 50*y**2 - 46)
Expanding the part (10*y - 17) using the distributive property, and we got: (10*y)*(4*y**3 + 50*y**2 - 46) - 17*(4*y**3 + 50*y**2 - 46)
<replace-#Step 1>#Step 2:
Current expression: (10*y)*(4*y**3 + 50*y**2 - 46) - 17*(4*y**3 + 50*y**2 - 46)</replace>
Simplifying the partial expression: -17*(4*y**3 + 50*y**2 - 46)
Expanding the part (4*y**3 + 50*y**2 - 46) using the distributive property, and we got: (50*y**2)*(-17) + (4*y**3)*(-17) - 46*(-17)
Replacing -17*(4*y**3 + 50*y**2 - 46) with (50*y**2)*(-17) + (4*y**3)*(-17) - 46*(-17) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (10*y)*(4*y**3 + 50*y**2 - 46) + (50*y**2)*(-17) + (4*y**3)*(-17) + 782</replace>
Simplifying the partial expression: (10*y)*(4*y**3 + 50*y**2 - 46)
Expanding the part (4*y**3 + 50*y**2 - 46) using the distributive property, and we got: -460*y + (10*y)*(50*y**2) + (10*y)*(4*y**3)
Replacing (10*y)*(4*y**3 + 50*y**2 - 46) with -460*y + (10*y)*(50*y**2) + (10*y)*(4*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -46*10*y + (10*y)*(50*y**2) + (10*y)*(4*y**3) + (50*y**2)*(-17) + (4*y**3)*(-17) + 782</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (4*y**3)*-17 = -68*y**3
  (4*y**3)*(10*y) = 40*y**4
  (50*y**2)*-17 = -850*y**2
  (50*y**2)*(10*y) = 500*y**3
  -46*10*y = -460*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 40*y**4 - 68*y**3 + 500*y**3 - 850*y**2 - 460*y + 782</replace>
Combining like terms, got 40*y**4 + 432*y**3 - 850*y**2 - 460*y + 782
<replace-#Step 5>#Step 6:
Current expression: 40*y**4 + 432*y**3 - 850*y**2 - 460*y + 782</replace>
No more calculations needed.
<answer>40*y**4 + 432*y**3 - 850*y**2 - 460*y + 782</answer>


Question:
Calculate the following: -53*y*(19 - 38*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2014*y**3 - 1007*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: -53*y*(19 - 38*y**2)
Expanding the part (19 - 38*y**2) using the distributive property, and we got: (-53*y)*(-38*y**2) + 19*(-53*y)
<replace-#Step 1>#Step 2:
Current expression: (-53*y)*(-38*y**2) + 19*(-53*y)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  19*(-53*y) = -1007*y
  (-38*y**2)*(-53*y) = 2014*y**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 2014*y**3 - 1007*y</replace>
No more calculations needed.
<answer>2014*y**3 - 1007*y</answer>