Question:
Calculate the following: -33*z*(15*z**2 - 32*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: -495*z**3 + 1056*z**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -33*z*(15*z**2 - 32*z)
Expanding the part (15*z**2 - 32*z) using the distributive property, and we got: (-33*z)*(-32*z) + (-33*z)*(15*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-33*z)*(-32*z) + (-33*z)*(15*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-32*z)*(-33*z) = 1056*z**2
  (15*z**2)*(-33*z) = -495*z**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -495*z**3 + 1056*z**2</replace>
No more calculations needed.
<answer>-495*z**3 + 1056*z**2</answer>


Question:
Simplify this expression: (4*z + 8)*(43*z**3 + 28*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: 172*z**4 + 456*z**3 + 224*z**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (4*z + 8)*(43*z**3 + 28*z**2)
Expanding the part (4*z + 8) using the distributive property, and we got: (4*z)*(43*z**3 + 28*z**2) + 8*(43*z**3 + 28*z**2)
<replace-#Step 1>#Step 2:
Current expression: (4*z)*(43*z**3 + 28*z**2) + 8*(43*z**3 + 28*z**2)</replace>
Simplifying the partial expression: 8*(43*z**3 + 28*z**2)
Expanding the part (43*z**3 + 28*z**2) using the distributive property, and we got: (28*z**2)*8 + (43*z**3)*8
Replacing 8*(43*z**3 + 28*z**2) with (28*z**2)*8 + (43*z**3)*8 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (4*z)*(43*z**3 + 28*z**2) + (28*z**2)*8 + (43*z**3)*8</replace>
Simplifying the partial expression: (4*z)*(43*z**3 + 28*z**2)
Expanding the part (43*z**3 + 28*z**2) using the distributive property, and we got: (4*z)*(28*z**2) + (4*z)*(43*z**3)
Replacing (4*z)*(43*z**3 + 28*z**2) with (4*z)*(28*z**2) + (4*z)*(43*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (4*z)*(28*z**2) + (4*z)*(43*z**3) + (28*z**2)*8 + (43*z**3)*8</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (28*z**2)*8 = 224*z**2
  (28*z**2)*(4*z) = 112*z**3
  (43*z**3)*8 = 344*z**3
  (43*z**3)*(4*z) = 172*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 172*z**4 + 112*z**3 + 344*z**3 + 224*z**2</replace>
Combining like terms, got 172*z**4 + 456*z**3 + 224*z**2
<replace-#Step 5>#Step 6:
Current expression: 172*z**4 + 456*z**3 + 224*z**2</replace>
No more calculations needed.
<answer>172*z**4 + 456*z**3 + 224*z**2</answer>


Question:
Calculate the following: -10*y**2*(33*y**3 - 18*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: -330*y**5 + 180*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: -10*y**2*(33*y**3 - 18*y)
Expanding the part (33*y**3 - 18*y) using the distributive property, and we got: (-18*y)*(-10*y**2) + (-10*y**2)*(33*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-18*y)*(-10*y**2) + (-10*y**2)*(33*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-18*y)*(-10*y**2) = 180*y**3
  (33*y**3)*(-10*y**2) = -330*y**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -330*y**5 + 180*y**3</replace>
No more calculations needed.
<answer>-330*y**5 + 180*y**3</answer>


Question:
Simplify this expression: (1 - 28*y**2)*(34*y**2 - 22*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: -952*y**4 + 616*y**3 - 1310*y**2 - 22*y + 48

Let's solve 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: (1 - 28*y**2)*(34*y**2 - 22*y + 48)
Expanding the part (1 - 28*y**2) using the distributive property, and we got: (-28*y**2)*(34*y**2 - 22*y + 48) + 1*(34*y**2 - 22*y + 48)
<replace-#Step 1>#Step 2:
Current expression: (-28*y**2)*(34*y**2 - 22*y + 48) + 1*(34*y**2 - 22*y + 48)</replace>
Simplifying the partial expression: 1*(34*y**2 - 22*y + 48)
Expanding the part (34*y**2 - 22*y + 48) using the distributive property, and we got: -22*y*1 + (34*y**2)*1 + 48*1
Replacing 1*(34*y**2 - 22*y + 48) with -22*y*1 + (34*y**2)*1 + 48*1 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -22*y*1 + (-28*y**2)*(34*y**2 - 22*y + 48) + (34*y**2)*1 + 48</replace>
Simplifying the partial expression: (-28*y**2)*(34*y**2 - 22*y + 48)
Expanding the part (34*y**2 - 22*y + 48) using the distributive property, and we got: (-22*y)*(-28*y**2) + 48*(-28*y**2) + (-28*y**2)*(34*y**2)
Replacing (-28*y**2)*(34*y**2 - 22*y + 48) with (-22*y)*(-28*y**2) + 48*(-28*y**2) + (-28*y**2)*(34*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-22*y)*(-28*y**2) - 22*y*1 + 48*(-28)*y**2 + (-28*y**2)*(34*y**2) + (34*y**2)*1 + 48</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-22*y)*1 = -22*y
  (-22*y)*(-28*y**2) = 616*y**3
  (34*y**2)*1 = 34*y**2
  (34*y**2)*(-28*y**2) = -952*y**4
  48*-28*y**2 = -1344*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -952*y**4 + 616*y**3 - 1344*y**2 + 34*y**2 - 22*y + 48</replace>
Combining like terms, got -952*y**4 + 616*y**3 - 1310*y**2 - 22*y + 48
<replace-#Step 5>#Step 6:
Current expression: -952*y**4 + 616*y**3 - 1310*y**2 - 22*y + 48</replace>
No more calculations needed.
<answer>-952*y**4 + 616*y**3 - 1310*y**2 - 22*y + 48</answer>


Question:
Calculate the following: (5*y**3 - 41*y**2)*(9*y**3 + 18*y**2 + 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: 45*y**6 - 279*y**5 - 738*y**4 + 105*y**3 - 861*y**2


Question:
Simplify this expression: 50*y**2*(15*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: 750*y**3 + 700*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: 50*y**2*(15*y + 14)
Expanding the part (15*y + 14) using the distributive property, and we got: 14*(50*y**2) + (15*y)*(50*y**2)
<replace-#Step 1>#Step 2:
Current expression: 14*(50*y**2) + (15*y)*(50*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  14*(50*y**2) = 700*y**2
  (15*y)*(50*y**2) = 750*y**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 750*y**3 + 700*y**2</replace>
No more calculations needed.
<answer>750*y**3 + 700*y**2</answer>


Question:
Calculate the following: (-23*z**2 + 27*z)*(-15*z**3 - 31*z**2 - 47*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: 345*z**5 + 308*z**4 + 244*z**3 - 1269*z**2


Question:
Calculate the following: (-15*y**3 - 9*y**2 - 37*y)*(19*y**3 + 40*y - 38)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -285*y**6 - 171*y**5 - 1303*y**4 + 210*y**3 - 1138*y**2 + 1406*y


Question:
Simplify this expression: (17 - 11*z**3)*(-7*z**3 + 44*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: 77*z**6 - 484*z**4 - 119*z**3 + 748*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (17 - 11*z**3)*(-7*z**3 + 44*z)
Expanding the part (17 - 11*z**3) using the distributive property, and we got: (-11*z**3)*(-7*z**3 + 44*z) + 17*(-7*z**3 + 44*z)
<replace-#Step 1>#Step 2:
Current expression: (-11*z**3)*(-7*z**3 + 44*z) + 17*(-7*z**3 + 44*z)</replace>
Simplifying the partial expression: 17*(-7*z**3 + 44*z)
Expanding the part (-7*z**3 + 44*z) using the distributive property, and we got: (44*z)*17 - 7*z**3*17
Replacing 17*(-7*z**3 + 44*z) with (44*z)*17 - 7*z**3*17 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (44*z)*17 + (-11*z**3)*(-7*z**3 + 44*z) - 7*z**3*17</replace>
Simplifying the partial expression: (-11*z**3)*(-7*z**3 + 44*z)
Expanding the part (-7*z**3 + 44*z) using the distributive property, and we got: (44*z)*(-11*z**3) + (-11*z**3)*(-7*z**3)
Replacing (-11*z**3)*(-7*z**3 + 44*z) with (44*z)*(-11*z**3) + (-11*z**3)*(-7*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (44*z)*(-11*z**3) + (44*z)*17 + (-11*z**3)*(-7*z**3) - 7*z**3*17</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-7*z**3)*17 = -119*z**3
  (-7*z**3)*(-11*z**3) = 77*z**6
  (44*z)*17 = 748*z
  (44*z)*(-11*z**3) = -484*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 77*z**6 - 484*z**4 - 119*z**3 + 748*z</replace>
No more calculations needed.
<answer>77*z**6 - 484*z**4 - 119*z**3 + 748*z</answer>


Question:
Calculate the following: (-36*z**2 + 37*z)*(3*z**3 - 14*z**2 + 8)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -108*z**5 + 615*z**4 - 518*z**3 - 288*z**2 + 296*z


Question:
Simplify this expression: (-26*x**3 + 29*x**2)*(45*x**3 - 32*x - 25)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1170*x**6 + 1305*x**5 + 832*x**4 - 278*x**3 - 725*x**2


Question:
Calculate the following: 1443*x**3 - 975*x**2 - 780*x + 741
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: 1443*x**3 - 975*x**2 - 780*x + 741

Let's solve 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: 1443*x**3 - 975*x**2 - 780*x + 741
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: 1443*x**3 - 975*x**2 - 780*x + 741</replace>
No more calculations needed.
<answer>1443*x**3 - 975*x**2 - 780*x + 741</answer>


Question:
Simplify this expression: (50*z**2 - 9*z)*(28*z**3 - 2*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: 1400*z**5 - 352*z**4 + 18*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: (50*z**2 - 9*z)*(28*z**3 - 2*z**2)
Expanding the part (50*z**2 - 9*z) using the distributive property, and we got: (-9*z)*(28*z**3 - 2*z**2) + (50*z**2)*(28*z**3 - 2*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-9*z)*(28*z**3 - 2*z**2) + (50*z**2)*(28*z**3 - 2*z**2)</replace>
Simplifying the partial expression: (-9*z)*(28*z**3 - 2*z**2)
Expanding the part (28*z**3 - 2*z**2) using the distributive property, and we got: (-9*z)*(-2*z**2) + (-9*z)*(28*z**3)
Replacing (-9*z)*(28*z**3 - 2*z**2) with (-9*z)*(-2*z**2) + (-9*z)*(28*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-9*z)*(-2*z**2) + (-9*z)*(28*z**3) + (50*z**2)*(28*z**3 - 2*z**2)</replace>
Simplifying the partial expression: (50*z**2)*(28*z**3 - 2*z**2)
Expanding the part (28*z**3 - 2*z**2) using the distributive property, and we got: (-2*z**2)*(50*z**2) + (50*z**2)*(28*z**3)
Replacing (50*z**2)*(28*z**3 - 2*z**2) with (-2*z**2)*(50*z**2) + (50*z**2)*(28*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-9*z)*(-2*z**2) + (-9*z)*(28*z**3) + (-2*z**2)*(50*z**2) + (50*z**2)*(28*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-2*z**2)*(-9*z) = 18*z**3
  (-2*z**2)*(50*z**2) = -100*z**4
  (28*z**3)*(-9*z) = -252*z**4
  (28*z**3)*(50*z**2) = 1400*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1400*z**5 - 252*z**4 - 100*z**4 + 18*z**3</replace>
Combining like terms, got 1400*z**5 - 352*z**4 + 18*z**3
<replace-#Step 5>#Step 6:
Current expression: 1400*z**5 - 352*z**4 + 18*z**3</replace>
No more calculations needed.
<answer>1400*z**5 - 352*z**4 + 18*z**3</answer>


Question:
Simplify this expression: (-14*x**2 - 45*x - 14)*(-77*x**3 - 41*x - 37)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1078*x**5 + 3465*x**4 + 1652*x**3 + 2363*x**2 + 2239*x + 518


Question:
Simplify this expression: -7*y**2*(30*y**2 - 38)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -210*y**4 + 266*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: -7*y**2*(30*y**2 - 38)
Expanding the part (30*y**2 - 38) using the distributive property, and we got: -(-1)*266*y**2 + (-7*y**2)*(30*y**2)
<replace-#Step 1>#Step 2:
Current expression: -(-1)*266*y**2 + (-7*y**2)*(30*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -38*(-7*y**2) = 266*y**2
  (30*y**2)*(-7*y**2) = -210*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -210*y**4 + 266*y**2</replace>
No more calculations needed.
<answer>-210*y**4 + 266*y**2</answer>


Question:
Simplify this expression: (21*y**3 - 45)*(2*y**3 + 17*y + 50)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 42*y**6 + 357*y**4 + 960*y**3 - 765*y - 2250

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (21*y**3 - 45)*(2*y**3 + 17*y + 50)
Expanding the part (21*y**3 - 45) using the distributive property, and we got: (21*y**3)*(2*y**3 + 17*y + 50) - 45*(2*y**3 + 17*y + 50)
<replace-#Step 1>#Step 2:
Current expression: (21*y**3)*(2*y**3 + 17*y + 50) - 45*(2*y**3 + 17*y + 50)</replace>
Simplifying the partial expression: -45*(2*y**3 + 17*y + 50)
Expanding the part (2*y**3 + 17*y + 50) using the distributive property, and we got: (17*y)*(-45) + (2*y**3)*(-45) + 50*(-45)
Replacing -45*(2*y**3 + 17*y + 50) with (17*y)*(-45) + (2*y**3)*(-45) + 50*(-45) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (17*y)*(-45) + (2*y**3)*(-45) + (21*y**3)*(2*y**3 + 17*y + 50) - 2250</replace>
Simplifying the partial expression: (21*y**3)*(2*y**3 + 17*y + 50)
Expanding the part (2*y**3 + 17*y + 50) using the distributive property, and we got: 50*(21*y**3) + (17*y)*(21*y**3) + (2*y**3)*(21*y**3)
Replacing (21*y**3)*(2*y**3 + 17*y + 50) with 50*(21*y**3) + (17*y)*(21*y**3) + (2*y**3)*(21*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 50*21*y**3 + (17*y)*(21*y**3) + (17*y)*(-45) + (2*y**3)*(21*y**3) + (2*y**3)*(-45) - 2250</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (2*y**3)*-45 = -90*y**3
  (2*y**3)*(21*y**3) = 42*y**6
  (17*y)*-45 = -765*y
  (17*y)*(21*y**3) = 357*y**4
  50*21*y**3 = 1050*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 42*y**6 + 357*y**4 - 90*y**3 + 1050*y**3 - 765*y - 2250</replace>
Combining like terms, got 42*y**6 + 357*y**4 + 960*y**3 - 765*y - 2250
<replace-#Step 5>#Step 6:
Current expression: 42*y**6 + 357*y**4 + 960*y**3 - 765*y - 2250</replace>
No more calculations needed.
<answer>42*y**6 + 357*y**4 + 960*y**3 - 765*y - 2250</answer>


Question:
Calculate the following: (-8*y**2 - 4*y)*(24*y**3 + 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: -192*y**5 - 96*y**4 - 312*y**2 - 156*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: (-8*y**2 - 4*y)*(24*y**3 + 39)
Expanding the part (24*y**3 + 39) using the distributive property, and we got: (24*y**3)*(-8*y**2 - 4*y) + 39*(-8*y**2 - 4*y)
<replace-#Step 1>#Step 2:
Current expression: (24*y**3)*(-8*y**2 - 4*y) + 39*(-8*y**2 - 4*y)</replace>
Simplifying the partial expression: 39*(-8*y**2 - 4*y)
Expanding the part (-8*y**2 - 4*y) using the distributive property, and we got: -4*y*39 - 8*y**2*39
Replacing 39*(-8*y**2 - 4*y) with -4*y*39 - 8*y**2*39 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -4*y*39 - 8*y**2*39 + (24*y**3)*(-8*y**2 - 4*y)</replace>
Simplifying the partial expression: (24*y**3)*(-8*y**2 - 4*y)
Expanding the part (-8*y**2 - 4*y) using the distributive property, and we got: (-4*y)*(24*y**3) + (-8*y**2)*(24*y**3)
Replacing (24*y**3)*(-8*y**2 - 4*y) with (-4*y)*(24*y**3) + (-8*y**2)*(24*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-4*y)*(24*y**3) - 4*y*39 + (-8*y**2)*(24*y**3) - 8*y**2*39</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-8*y**2)*39 = -312*y**2
  (-8*y**2)*(24*y**3) = -192*y**5
  (-4*y)*39 = -156*y
  (-4*y)*(24*y**3) = -96*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -192*y**5 - 96*y**4 - 312*y**2 - 156*y</replace>
No more calculations needed.
<answer>-192*y**5 - 96*y**4 - 312*y**2 - 156*y</answer>


Question:
Simplify this expression: (-38*z**2 + 33*z)*(-14*z**2 + 28*z - 27)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 532*z**4 - 1526*z**3 + 1950*z**2 - 891*z


Question:
Calculate the following: (46*x**2 - 23*x)*(6*x**3 + 60*x + 36)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 276*x**5 - 138*x**4 + 2760*x**3 + 276*x**2 - 828*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: (46*x**2 - 23*x)*(6*x**3 + 60*x + 36)
Expanding the part (46*x**2 - 23*x) using the distributive property, and we got: (-23*x)*(6*x**3 + 60*x + 36) + (46*x**2)*(6*x**3 + 60*x + 36)
<replace-#Step 1>#Step 2:
Current expression: (-23*x)*(6*x**3 + 60*x + 36) + (46*x**2)*(6*x**3 + 60*x + 36)</replace>
Simplifying the partial expression: (-23*x)*(6*x**3 + 60*x + 36)
Expanding the part (6*x**3 + 60*x + 36) using the distributive property, and we got: (-23*x)*(60*x) + (-23*x)*(6*x**3) + 36*(-23*x)
Replacing (-23*x)*(6*x**3 + 60*x + 36) with (-23*x)*(60*x) + (-23*x)*(6*x**3) + 36*(-23*x) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-23*x)*(60*x) + (-23*x)*(6*x**3) + 36*(-23)*x + (46*x**2)*(6*x**3 + 60*x + 36)</replace>
Simplifying the partial expression: (46*x**2)*(6*x**3 + 60*x + 36)
Expanding the part (6*x**3 + 60*x + 36) using the distributive property, and we got: 36*(46*x**2) + (60*x)*(46*x**2) + (46*x**2)*(6*x**3)
Replacing (46*x**2)*(6*x**3 + 60*x + 36) with 36*(46*x**2) + (60*x)*(46*x**2) + (46*x**2)*(6*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-23*x)*(60*x) + (-23*x)*(6*x**3) + 36*46*x**2 + 36*(-23)*x + (60*x)*(46*x**2) + (46*x**2)*(6*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (6*x**3)*(-23*x) = -138*x**4
  (6*x**3)*(46*x**2) = 276*x**5
  (60*x)*(-23*x) = -1380*x**2
  (60*x)*(46*x**2) = 2760*x**3
  36*-23*x = -828*x
  36*46*x**2 = 1656*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 276*x**5 - 138*x**4 + 2760*x**3 - 1380*x**2 + 1656*x**2 - 828*x</replace>
Combining like terms, got 276*x**5 - 138*x**4 + 2760*x**3 + 276*x**2 - 828*x
<replace-#Step 5>#Step 6:
Current expression: 276*x**5 - 138*x**4 + 2760*x**3 + 276*x**2 - 828*x</replace>
No more calculations needed.
<answer>276*x**5 - 138*x**4 + 2760*x**3 + 276*x**2 - 828*x</answer>


Question:
Calculate the following: (-31*y**2 - y)*(-18*y**3 - 30*y - 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: 558*y**5 + 18*y**4 + 930*y**3 + 154*y**2 + 4*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 - y)*(-18*y**3 - 30*y - 4)
Expanding the part (-31*y**2 - y) using the distributive property, and we got: (-y)*(-18*y**3 - 30*y - 4) + (-31*y**2)*(-18*y**3 - 30*y - 4)
<replace-#Step 1>#Step 2:
Current expression: (-y)*(-18*y**3 - 30*y - 4) + (-31*y**2)*(-18*y**3 - 30*y - 4)</replace>
Simplifying the partial expression: (-y)*(-18*y**3 - 30*y - 4)
Expanding the part (-18*y**3 - 30*y - 4) using the distributive property, and we got: (-30*y)*(-y) + (-y)*(-18*y**3) - (-1)*4*y
Replacing (-y)*(-18*y**3 - 30*y - 4) with (-30*y)*(-y) + (-y)*(-18*y**3) - (-1)*4*y in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-30*y)*(-y) + (-y)*(-18*y**3) - 4*(-1)*y + (-31*y**2)*(-18*y**3 - 30*y - 4)</replace>
Simplifying the partial expression: (-31*y**2)*(-18*y**3 - 30*y - 4)
Expanding the part (-18*y**3 - 30*y - 4) using the distributive property, and we got: (-30*y)*(-31*y**2) - (-1)*124*y**2 + (-31*y**2)*(-18*y**3)
Replacing (-31*y**2)*(-18*y**3 - 30*y - 4) with (-30*y)*(-31*y**2) - (-1)*124*y**2 + (-31*y**2)*(-18*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-30*y)*(-y) + (-30*y)*(-31*y**2) + (-y)*(-18*y**3) - 4*(-31)*y**2 - 4*(-1)*y + (-31*y**2)*(-18*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-30*y)*(-y) = 30*y**2
  (-30*y)*(-31*y**2) = 930*y**3
  (-18*y**3)*(-y) = 18*y**4
  (-18*y**3)*(-31*y**2) = 558*y**5
  -4*-1*y = 4*y
  -4*-31*y**2 = 124*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 558*y**5 + 18*y**4 + 930*y**3 + 30*y**2 + 124*y**2 + 4*y</replace>
Combining like terms, got 558*y**5 + 18*y**4 + 930*y**3 + 154*y**2 + 4*y
<replace-#Step 5>#Step 6:
Current expression: 558*y**5 + 18*y**4 + 930*y**3 + 154*y**2 + 4*y</replace>
No more calculations needed.
<answer>558*y**5 + 18*y**4 + 930*y**3 + 154*y**2 + 4*y</answer>


Question:
Calculate the following: (45*y**3 + 5*y)*(-50*y**2 + 34*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: -2250*y**5 + 1530*y**4 + 695*y**3 + 170*y**2 + 105*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (45*y**3 + 5*y)*(-50*y**2 + 34*y + 21)
Expanding the part (45*y**3 + 5*y) using the distributive property, and we got: (5*y)*(-50*y**2 + 34*y + 21) + (45*y**3)*(-50*y**2 + 34*y + 21)
<replace-#Step 1>#Step 2:
Current expression: (5*y)*(-50*y**2 + 34*y + 21) + (45*y**3)*(-50*y**2 + 34*y + 21)</replace>
Simplifying the partial expression: (5*y)*(-50*y**2 + 34*y + 21)
Expanding the part (-50*y**2 + 34*y + 21) using the distributive property, and we got: 21*(5*y) + (5*y)*(34*y) + (5*y)*(-50*y**2)
Replacing (5*y)*(-50*y**2 + 34*y + 21) with 21*(5*y) + (5*y)*(34*y) + (5*y)*(-50*y**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 21*5*y + (5*y)*(34*y) + (5*y)*(-50*y**2) + (45*y**3)*(-50*y**2 + 34*y + 21)</replace>
Simplifying the partial expression: (45*y**3)*(-50*y**2 + 34*y + 21)
Expanding the part (-50*y**2 + 34*y + 21) using the distributive property, and we got: 21*(45*y**3) + (34*y)*(45*y**3) + (-50*y**2)*(45*y**3)
Replacing (45*y**3)*(-50*y**2 + 34*y + 21) with 21*(45*y**3) + (34*y)*(45*y**3) + (-50*y**2)*(45*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 21*45*y**3 + 21*5*y + (5*y)*(34*y) + (5*y)*(-50*y**2) + (34*y)*(45*y**3) + (-50*y**2)*(45*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-50*y**2)*(5*y) = -250*y**3
  (-50*y**2)*(45*y**3) = -2250*y**5
  (34*y)*(5*y) = 170*y**2
  (34*y)*(45*y**3) = 1530*y**4
  21*5*y = 105*y
  21*45*y**3 = 945*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2250*y**5 + 1530*y**4 - 250*y**3 + 945*y**3 + 170*y**2 + 105*y</replace>
Combining like terms, got -2250*y**5 + 1530*y**4 + 695*y**3 + 170*y**2 + 105*y
<replace-#Step 5>#Step 6:
Current expression: -2250*y**5 + 1530*y**4 + 695*y**3 + 170*y**2 + 105*y</replace>
No more calculations needed.
<answer>-2250*y**5 + 1530*y**4 + 695*y**3 + 170*y**2 + 105*y</answer>


Question:
Simplify this expression: (28*y**2 + y)*(-39*y**3 + 42*y**2 - 27*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: -1092*y**5 + 1137*y**4 - 714*y**3 - 27*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: (28*y**2 + y)*(-39*y**3 + 42*y**2 - 27*y)
Expanding the part (28*y**2 + y) using the distributive property, and we got: y*(-39*y**3 + 42*y**2 - 27*y) + (28*y**2)*(-39*y**3 + 42*y**2 - 27*y)
<replace-#Step 1>#Step 2:
Current expression: y*(-39*y**3 + 42*y**2 - 27*y) + (28*y**2)*(-39*y**3 + 42*y**2 - 27*y)</replace>
Simplifying the partial expression: y*(-39*y**3 + 42*y**2 - 27*y)
Expanding the part (-39*y**3 + 42*y**2 - 27*y) using the distributive property, and we got: (-27*y)*y + y*(42*y**2) + y*(-39*y**3)
Replacing y*(-39*y**3 + 42*y**2 - 27*y) with (-27*y)*y + y*(42*y**2) + y*(-39*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-27*y)*y + y*(42*y**2) + y*(-39*y**3) + (28*y**2)*(-39*y**3 + 42*y**2 - 27*y)</replace>
Simplifying the partial expression: (28*y**2)*(-39*y**3 + 42*y**2 - 27*y)
Expanding the part (-39*y**3 + 42*y**2 - 27*y) using the distributive property, and we got: (-27*y)*(28*y**2) + (28*y**2)*(42*y**2) + (28*y**2)*(-39*y**3)
Replacing (28*y**2)*(-39*y**3 + 42*y**2 - 27*y) with (-27*y)*(28*y**2) + (28*y**2)*(42*y**2) + (28*y**2)*(-39*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-27*y)*y + (-27*y)*(28*y**2) + y*(42*y**2) + y*(-39*y**3) + (28*y**2)*(42*y**2) + (28*y**2)*(-39*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-39*y**3)*y = -39*y**4
  (-39*y**3)*(28*y**2) = -1092*y**5
  (-27*y)*y = -27*y**2
  (-27*y)*(28*y**2) = -756*y**3
  (42*y**2)*y = 42*y**3
  (42*y**2)*(28*y**2) = 1176*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1092*y**5 - 39*y**4 + 1176*y**4 - 756*y**3 + 42*y**3 - 27*y**2</replace>
Combining like terms, got -1092*y**5 + 1137*y**4 - 714*y**3 - 27*y**2
<replace-#Step 5>#Step 6:
Current expression: -1092*y**5 + 1137*y**4 - 714*y**3 - 27*y**2</replace>
No more calculations needed.
<answer>-1092*y**5 + 1137*y**4 - 714*y**3 - 27*y**2</answer>


Question:
Calculate the following: (-17*z**3 + 14*z**2)*(38*z**3 + 13*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: -646*z**6 + 532*z**5 - 221*z**4 + 182*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: (-17*z**3 + 14*z**2)*(38*z**3 + 13*z)
Expanding the part (-17*z**3 + 14*z**2) using the distributive property, and we got: (14*z**2)*(38*z**3 + 13*z) + (-17*z**3)*(38*z**3 + 13*z)
<replace-#Step 1>#Step 2:
Current expression: (14*z**2)*(38*z**3 + 13*z) + (-17*z**3)*(38*z**3 + 13*z)</replace>
Simplifying the partial expression: (-17*z**3)*(38*z**3 + 13*z)
Expanding the part (38*z**3 + 13*z) using the distributive property, and we got: (13*z)*(-17*z**3) + (-17*z**3)*(38*z**3)
Replacing (-17*z**3)*(38*z**3 + 13*z) with (13*z)*(-17*z**3) + (-17*z**3)*(38*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (13*z)*(-17*z**3) + (14*z**2)*(38*z**3 + 13*z) + (-17*z**3)*(38*z**3)</replace>
Simplifying the partial expression: (14*z**2)*(38*z**3 + 13*z)
Expanding the part (38*z**3 + 13*z) using the distributive property, and we got: (13*z)*(14*z**2) + (14*z**2)*(38*z**3)
Replacing (14*z**2)*(38*z**3 + 13*z) with (13*z)*(14*z**2) + (14*z**2)*(38*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (13*z)*(14*z**2) + (13*z)*(-17*z**3) + (14*z**2)*(38*z**3) + (-17*z**3)*(38*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (13*z)*(-17*z**3) = -221*z**4
  (13*z)*(14*z**2) = 182*z**3
  (38*z**3)*(-17*z**3) = -646*z**6
  (38*z**3)*(14*z**2) = 532*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -646*z**6 + 532*z**5 - 221*z**4 + 182*z**3</replace>
No more calculations needed.
<answer>-646*z**6 + 532*z**5 - 221*z**4 + 182*z**3</answer>


Question:
Calculate the following: 1566 - 1188*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: 1566 - 1188*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: 1566 - 1188*z
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: 1566 - 1188*z</replace>
No more calculations needed.
<answer>1566 - 1188*z</answer>


Question:
Simplify this expression: (-8*y**3 - 7*y)*(-3*y**3 + 16*y**2 - 8)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 24*y**6 - 128*y**5 + 21*y**4 - 48*y**3 + 56*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: (-8*y**3 - 7*y)*(-3*y**3 + 16*y**2 - 8)
Expanding the part (-8*y**3 - 7*y) using the distributive property, and we got: (-7*y)*(-3*y**3 + 16*y**2 - 8) + (-8*y**3)*(-3*y**3 + 16*y**2 - 8)
<replace-#Step 1>#Step 2:
Current expression: (-7*y)*(-3*y**3 + 16*y**2 - 8) + (-8*y**3)*(-3*y**3 + 16*y**2 - 8)</replace>
Simplifying the partial expression: (-8*y**3)*(-3*y**3 + 16*y**2 - 8)
Expanding the part (-3*y**3 + 16*y**2 - 8) using the distributive property, and we got: -(-1)*64*y**3 + (16*y**2)*(-8*y**3) + (-8*y**3)*(-3*y**3)
Replacing (-8*y**3)*(-3*y**3 + 16*y**2 - 8) with -(-1)*64*y**3 + (16*y**2)*(-8*y**3) + (-8*y**3)*(-3*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-7*y)*(-3*y**3 + 16*y**2 - 8) - 8*(-8)*y**3 + (16*y**2)*(-8*y**3) + (-8*y**3)*(-3*y**3)</replace>
Simplifying the partial expression: (-7*y)*(-3*y**3 + 16*y**2 - 8)
Expanding the part (-3*y**3 + 16*y**2 - 8) using the distributive property, and we got: (-7*y)*(16*y**2) + (-7*y)*(-3*y**3) - (-1)*56*y
Replacing (-7*y)*(-3*y**3 + 16*y**2 - 8) with (-7*y)*(16*y**2) + (-7*y)*(-3*y**3) - (-1)*56*y in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-7*y)*(16*y**2) + (-7*y)*(-3*y**3) - 8*(-8)*y**3 - 8*(-7)*y + (16*y**2)*(-8*y**3) + (-8*y**3)*(-3*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-3*y**3)*(-8*y**3) = 24*y**6
  (-3*y**3)*(-7*y) = 21*y**4
  (16*y**2)*(-8*y**3) = -128*y**5
  (16*y**2)*(-7*y) = -112*y**3
  -8*-8*y**3 = 64*y**3
  -8*-7*y = 56*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 24*y**6 - 128*y**5 + 21*y**4 - 112*y**3 + 64*y**3 + 56*y</replace>
Combining like terms, got 24*y**6 - 128*y**5 + 21*y**4 - 48*y**3 + 56*y
<replace-#Step 5>#Step 6:
Current expression: 24*y**6 - 128*y**5 + 21*y**4 - 48*y**3 + 56*y</replace>
No more calculations needed.
<answer>24*y**6 - 128*y**5 + 21*y**4 - 48*y**3 + 56*y</answer>


Question:
Simplify this expression: 13*y*(8*y**3 + 31)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 104*y**4 + 403*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: 13*y*(8*y**3 + 31)
Expanding the part (8*y**3 + 31) using the distributive property, and we got: 31*(13*y) + (13*y)*(8*y**3)
<replace-#Step 1>#Step 2:
Current expression: 31*(13*y) + (13*y)*(8*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  31*(13*y) = 403*y
  (8*y**3)*(13*y) = 104*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 104*y**4 + 403*y</replace>
No more calculations needed.
<answer>104*y**4 + 403*y</answer>


Question:
Simplify this expression: 16*x**2*(-39*x**2 - 20*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: -624*x**4 - 320*x**3 - 240*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: 16*x**2*(-39*x**2 - 20*x - 15)
Expanding the part (-39*x**2 - 20*x - 15) using the distributive property, and we got: (-20*x)*(16*x**2) - 240*x**2 + (-39*x**2)*(16*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-20*x)*(16*x**2) - 240*x**2 + (-39*x**2)*(16*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -15*(16*x**2) = -240*x**2
  (-39*x**2)*(16*x**2) = -624*x**4
  (-20*x)*(16*x**2) = -320*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -624*x**4 - 320*x**3 - 240*x**2</replace>
No more calculations needed.
<answer>-624*x**4 - 320*x**3 - 240*x**2</answer>


Question:
Calculate the following: (6*z**2 - 35*z)*(-44*z**3 - 13*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: -264*z**5 + 1462*z**4 + 455*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: (6*z**2 - 35*z)*(-44*z**3 - 13*z**2)
Expanding the part (-44*z**3 - 13*z**2) using the distributive property, and we got: (-13*z**2)*(6*z**2 - 35*z) + (-44*z**3)*(6*z**2 - 35*z)
<replace-#Step 1>#Step 2:
Current expression: (-13*z**2)*(6*z**2 - 35*z) + (-44*z**3)*(6*z**2 - 35*z)</replace>
Simplifying the partial expression: (-44*z**3)*(6*z**2 - 35*z)
Expanding the part (6*z**2 - 35*z) using the distributive property, and we got: (-35*z)*(-44*z**3) + (6*z**2)*(-44*z**3)
Replacing (-44*z**3)*(6*z**2 - 35*z) with (-35*z)*(-44*z**3) + (6*z**2)*(-44*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-35*z)*(-44*z**3) + (-13*z**2)*(6*z**2 - 35*z) + (6*z**2)*(-44*z**3)</replace>
Simplifying the partial expression: (-13*z**2)*(6*z**2 - 35*z)
Expanding the part (6*z**2 - 35*z) using the distributive property, and we got: (-35*z)*(-13*z**2) + (-13*z**2)*(6*z**2)
Replacing (-13*z**2)*(6*z**2 - 35*z) with (-35*z)*(-13*z**2) + (-13*z**2)*(6*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-35*z)*(-13*z**2) + (-35*z)*(-44*z**3) + (-13*z**2)*(6*z**2) + (6*z**2)*(-44*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-35*z)*(-44*z**3) = 1540*z**4
  (-35*z)*(-13*z**2) = 455*z**3
  (6*z**2)*(-44*z**3) = -264*z**5
  (6*z**2)*(-13*z**2) = -78*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -264*z**5 - 78*z**4 + 1540*z**4 + 455*z**3</replace>
Combining like terms, got -264*z**5 + 1462*z**4 + 455*z**3
<replace-#Step 5>#Step 6:
Current expression: -264*z**5 + 1462*z**4 + 455*z**3</replace>
No more calculations needed.
<answer>-264*z**5 + 1462*z**4 + 455*z**3</answer>


Question:
Calculate the following: -675*z**3 - 570*z**2 - 390
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: -675*z**3 - 570*z**2 - 390

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -675*z**3 - 570*z**2 - 390
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: -675*z**3 - 570*z**2 - 390</replace>
No more calculations needed.
<answer>-675*z**3 - 570*z**2 - 390</answer>


Question:
Simplify this expression: (-49*z - 39)*(9*z**3 + 11*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -441*z**4 - 351*z**3 - 539*z**2 - 429*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: (-49*z - 39)*(9*z**3 + 11*z)
Expanding the part (-49*z - 39) using the distributive property, and we got: (-49*z)*(9*z**3 + 11*z) - 39*(9*z**3 + 11*z)
<replace-#Step 1>#Step 2:
Current expression: (-49*z)*(9*z**3 + 11*z) - 39*(9*z**3 + 11*z)</replace>
Simplifying the partial expression: -39*(9*z**3 + 11*z)
Expanding the part (9*z**3 + 11*z) using the distributive property, and we got: (11*z)*(-39) + (9*z**3)*(-39)
Replacing -39*(9*z**3 + 11*z) with (11*z)*(-39) + (9*z**3)*(-39) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-49*z)*(9*z**3 + 11*z) + (11*z)*(-39) + (9*z**3)*(-39)</replace>
Simplifying the partial expression: (-49*z)*(9*z**3 + 11*z)
Expanding the part (9*z**3 + 11*z) using the distributive property, and we got: (-49*z)*(11*z) + (-49*z)*(9*z**3)
Replacing (-49*z)*(9*z**3 + 11*z) with (-49*z)*(11*z) + (-49*z)*(9*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-49*z)*(11*z) + (-49*z)*(9*z**3) + (11*z)*(-39) + (9*z**3)*(-39)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (9*z**3)*-39 = -351*z**3
  (9*z**3)*(-49*z) = -441*z**4
  (11*z)*-39 = -429*z
  (11*z)*(-49*z) = -539*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -441*z**4 - 351*z**3 - 539*z**2 - 429*z</replace>
No more calculations needed.
<answer>-441*z**4 - 351*z**3 - 539*z**2 - 429*z</answer>


Question:
Calculate the following: (31*y - 35)*(-2*y**2 - 29*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: -62*y**3 - 829*y**2 + 1015*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 - 35)*(-2*y**2 - 29*y)
Expanding the part (31*y - 35) using the distributive property, and we got: (31*y)*(-2*y**2 - 29*y) - 35*(-2*y**2 - 29*y)
<replace-#Step 1>#Step 2:
Current expression: (31*y)*(-2*y**2 - 29*y) - 35*(-2*y**2 - 29*y)</replace>
Simplifying the partial expression: -35*(-2*y**2 - 29*y)
Expanding the part (-2*y**2 - 29*y) using the distributive property, and we got: -29*y*(-35) - 2*y**2*(-35)
Replacing -35*(-2*y**2 - 29*y) with -29*y*(-35) - 2*y**2*(-35) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -29*y*(-35) + (31*y)*(-2*y**2 - 29*y) - 2*y**2*(-35)</replace>
Simplifying the partial expression: (31*y)*(-2*y**2 - 29*y)
Expanding the part (-2*y**2 - 29*y) using the distributive property, and we got: (-29*y)*(31*y) + (31*y)*(-2*y**2)
Replacing (31*y)*(-2*y**2 - 29*y) with (-29*y)*(31*y) + (31*y)*(-2*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-29*y)*(31*y) - 29*y*(-35) + (31*y)*(-2*y**2) - 2*y**2*(-35)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-29*y)*-35 = 1015*y
  (-29*y)*(31*y) = -899*y**2
  (-2*y**2)*-35 = 70*y**2
  (-2*y**2)*(31*y) = -62*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -62*y**3 - 899*y**2 + 70*y**2 + 1015*y</replace>
Combining like terms, got -62*y**3 - 829*y**2 + 1015*y
<replace-#Step 5>#Step 6:
Current expression: -62*y**3 - 829*y**2 + 1015*y</replace>
No more calculations needed.
<answer>-62*y**3 - 829*y**2 + 1015*y</answer>


Question:
Simplify this expression: (-17*x**3 + 12*x)*(-6*x**3 + 37*x**2 - 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: 102*x**6 - 629*x**5 - 72*x**4 + 461*x**3 - 12*x


Question:
Simplify this expression: (-38*z**3 - 21)*(15*z**3 - 2*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: -570*z**6 + 76*z**4 - 315*z**3 + 42*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: (-38*z**3 - 21)*(15*z**3 - 2*z)
Expanding the part (-38*z**3 - 21) using the distributive property, and we got: (-38*z**3)*(15*z**3 - 2*z) - 21*(15*z**3 - 2*z)
<replace-#Step 1>#Step 2:
Current expression: (-38*z**3)*(15*z**3 - 2*z) - 21*(15*z**3 - 2*z)</replace>
Simplifying the partial expression: -21*(15*z**3 - 2*z)
Expanding the part (15*z**3 - 2*z) using the distributive property, and we got: -2*z*(-21) + (15*z**3)*(-21)
Replacing -21*(15*z**3 - 2*z) with -2*z*(-21) + (15*z**3)*(-21) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -2*z*(-21) + (-38*z**3)*(15*z**3 - 2*z) + (15*z**3)*(-21)</replace>
Simplifying the partial expression: (-38*z**3)*(15*z**3 - 2*z)
Expanding the part (15*z**3 - 2*z) using the distributive property, and we got: (-2*z)*(-38*z**3) + (-38*z**3)*(15*z**3)
Replacing (-38*z**3)*(15*z**3 - 2*z) with (-2*z)*(-38*z**3) + (-38*z**3)*(15*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-2*z)*(-38*z**3) - 2*z*(-21) + (-38*z**3)*(15*z**3) + (15*z**3)*(-21)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-2*z)*-21 = 42*z
  (-2*z)*(-38*z**3) = 76*z**4
  (15*z**3)*-21 = -315*z**3
  (15*z**3)*(-38*z**3) = -570*z**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -570*z**6 + 76*z**4 - 315*z**3 + 42*z</replace>
No more calculations needed.
<answer>-570*z**6 + 76*z**4 - 315*z**3 + 42*z</answer>


Question:
Simplify this expression: (-11*y**3 - 30*y**2 + 74)*(-19*y**3 + 26*y**2 - 28*y - 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: 209*y**6 + 284*y**5 - 472*y**4 - 489*y**3 + 2134*y**2 - 2072*y - 518


Question:
Simplify this expression: (-45*x**2 + 43*x - 11)*(-27*x**3 - 21*x**2 + 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: 1215*x**5 - 216*x**4 - 606*x**3 - 1794*x**2 + 1935*x - 495


Question:
Simplify this expression: (18*z**3 + 31*z**2 + 7*z)*(29*z**3 + 7*z**2 + 19)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 522*z**6 + 1025*z**5 + 420*z**4 + 391*z**3 + 589*z**2 + 133*z


Question:
Calculate the following: (-37*x**3 - 57*x**2)*(14*x**3 - 12*x**2 - 18)
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: -518*x**6 - 354*x**5 + 684*x**4 + 666*x**3 + 1026*x**2


Question:
Calculate the following: -152*x**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: -152*x**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: -152*x**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: -152*x**5</replace>
No more calculations needed.
<answer>-152*x**5</answer>


Question:
Simplify this expression: 50*x**2*(17*x**2 - 3*x - 27)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 850*x**4 - 150*x**3 - 1350*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: 50*x**2*(17*x**2 - 3*x - 27)
Expanding the part (17*x**2 - 3*x - 27) using the distributive property, and we got: (-3*x)*(50*x**2) - 1350*x**2 + (17*x**2)*(50*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-3*x)*(50*x**2) - 1350*x**2 + (17*x**2)*(50*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -27*(50*x**2) = -1350*x**2
  (-3*x)*(50*x**2) = -150*x**3
  (17*x**2)*(50*x**2) = 850*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 850*x**4 - 150*x**3 - 1350*x**2</replace>
No more calculations needed.
<answer>850*x**4 - 150*x**3 - 1350*x**2</answer>


Question:
Calculate the following: (-17*x - 29)*(-x**3 + 7*x**2 + 5*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: 17*x**4 - 90*x**3 - 288*x**2 - 145*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: (-17*x - 29)*(-x**3 + 7*x**2 + 5*x)
Expanding the part (-17*x - 29) using the distributive property, and we got: (-17*x)*(-x**3 + 7*x**2 + 5*x) - 29*(-x**3 + 7*x**2 + 5*x)
<replace-#Step 1>#Step 2:
Current expression: (-17*x)*(-x**3 + 7*x**2 + 5*x) - 29*(-x**3 + 7*x**2 + 5*x)</replace>
Simplifying the partial expression: -29*(-x**3 + 7*x**2 + 5*x)
Expanding the part (-x**3 + 7*x**2 + 5*x) using the distributive property, and we got: (5*x)*(-29) + (7*x**2)*(-29) - x**3*(-29)
Replacing -29*(-x**3 + 7*x**2 + 5*x) with (5*x)*(-29) + (7*x**2)*(-29) - x**3*(-29) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-17*x)*(-x**3 + 7*x**2 + 5*x) + (5*x)*(-29) + (7*x**2)*(-29) - x**3*(-29)</replace>
Simplifying the partial expression: (-17*x)*(-x**3 + 7*x**2 + 5*x)
Expanding the part (-x**3 + 7*x**2 + 5*x) using the distributive property, and we got: (-17*x)*(5*x) + (-17*x)*(7*x**2) + (-17*x)*(-x**3)
Replacing (-17*x)*(-x**3 + 7*x**2 + 5*x) with (-17*x)*(5*x) + (-17*x)*(7*x**2) + (-17*x)*(-x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-17*x)*(5*x) + (-17*x)*(7*x**2) + (-17*x)*(-x**3) + (5*x)*(-29) + (7*x**2)*(-29) - x**3*(-29)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-x**3)*-29 = 29*x**3
  (-x**3)*(-17*x) = 17*x**4
  (5*x)*-29 = -145*x
  (5*x)*(-17*x) = -85*x**2
  (7*x**2)*-29 = -203*x**2
  (7*x**2)*(-17*x) = -119*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 17*x**4 - 119*x**3 + 29*x**3 - 203*x**2 - 85*x**2 - 145*x</replace>
Combining like terms, got 17*x**4 - 90*x**3 - 288*x**2 - 145*x
<replace-#Step 5>#Step 6:
Current expression: 17*x**4 - 90*x**3 - 288*x**2 - 145*x</replace>
No more calculations needed.
<answer>17*x**4 - 90*x**3 - 288*x**2 - 145*x</answer>


Question:
Simplify this expression: (-3*x**3 + 14*x - 11)*(-x**3 - 42*x**2 + 43*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: 3*x**6 + 126*x**5 - 143*x**4 - 577*x**3 + 1064*x**2 - 473*x


Question:
Calculate the following: -17*y**3*(24*y + 101)
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*y**4 - 1717*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: -17*y**3*(24*y + 101)
Expanding the part (24*y + 101) using the distributive property, and we got: 101*(-17*y**3) + (24*y)*(-17*y**3)
<replace-#Step 1>#Step 2:
Current expression: 101*(-17*y**3) + (24*y)*(-17*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  101*(-17*y**3) = -1717*y**3
  (24*y)*(-17*y**3) = -408*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -408*y**4 - 1717*y**3</replace>
No more calculations needed.
<answer>-408*y**4 - 1717*y**3</answer>


Question:
Simplify this expression: (34*y**3 - 31*y**2)*(46*y**3 - 13*y + 18)
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: 1564*y**6 - 1426*y**5 - 442*y**4 + 1015*y**3 - 558*y**2


Question:
Calculate the following: (-22*x**3 + 23*x**2 + 12*x)*(33*x**3 - x + 41)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -726*x**6 + 759*x**5 + 418*x**4 - 925*x**3 + 931*x**2 + 492*x


Question:
Calculate the following: (-15*z**2 - 4*z - 31)*(42*z**3 - 37*z**2 + 42*z - 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: -630*z**5 + 387*z**4 - 1784*z**3 + 1174*z**2 - 1250*z + 403


Question:
Calculate the following: (-48*y**2 - 13*y - 30)*(-23*y**3 - 35*y**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: 1104*y**5 + 1979*y**4 + 1145*y**3 + 3114*y**2 + 559*y + 1290


Question:
Simplify this expression: (36*x**3 + 27*x**2)*(46*x**3 + 4*x + 50)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1656*x**6 + 1242*x**5 + 144*x**4 + 1908*x**3 + 1350*x**2


Question:
Simplify this expression: (9*z**3 - 10)*(-33*z**3 - 3*z**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: -297*z**6 - 27*z**5 + 654*z**3 + 30*z**2 - 360

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (9*z**3 - 10)*(-33*z**3 - 3*z**2 + 36)
Expanding the part (9*z**3 - 10) using the distributive property, and we got: (9*z**3)*(-33*z**3 - 3*z**2 + 36) - 10*(-33*z**3 - 3*z**2 + 36)
<replace-#Step 1>#Step 2:
Current expression: (9*z**3)*(-33*z**3 - 3*z**2 + 36) - 10*(-33*z**3 - 3*z**2 + 36)</replace>
Simplifying the partial expression: -10*(-33*z**3 - 3*z**2 + 36)
Expanding the part (-33*z**3 - 3*z**2 + 36) using the distributive property, and we got: -3*z**2*(-10) - 33*z**3*(-10) + 36*(-10)
Replacing -10*(-33*z**3 - 3*z**2 + 36) with -3*z**2*(-10) - 33*z**3*(-10) + 36*(-10) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -3*z**2*(-10) - 33*z**3*(-10) + (9*z**3)*(-33*z**3 - 3*z**2 + 36) - 360</replace>
Simplifying the partial expression: (9*z**3)*(-33*z**3 - 3*z**2 + 36)
Expanding the part (-33*z**3 - 3*z**2 + 36) using the distributive property, and we got: 36*(9*z**3) + (-3*z**2)*(9*z**3) + (-33*z**3)*(9*z**3)
Replacing (9*z**3)*(-33*z**3 - 3*z**2 + 36) with 36*(9*z**3) + (-3*z**2)*(9*z**3) + (-33*z**3)*(9*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 36*9*z**3 + (-3*z**2)*(9*z**3) - 3*z**2*(-10) + (-33*z**3)*(9*z**3) - 33*z**3*(-10) - 360</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-33*z**3)*-10 = 330*z**3
  (-33*z**3)*(9*z**3) = -297*z**6
  (-3*z**2)*-10 = 30*z**2
  (-3*z**2)*(9*z**3) = -27*z**5
  36*9*z**3 = 324*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -297*z**6 - 27*z**5 + 324*z**3 + 330*z**3 + 30*z**2 - 360</replace>
Combining like terms, got -297*z**6 - 27*z**5 + 654*z**3 + 30*z**2 - 360
<replace-#Step 5>#Step 6:
Current expression: -297*z**6 - 27*z**5 + 654*z**3 + 30*z**2 - 360</replace>
No more calculations needed.
<answer>-297*z**6 - 27*z**5 + 654*z**3 + 30*z**2 - 360</answer>


Question:
Simplify this expression: -77*y**2*(55*y**3 + 5*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: -4235*y**5 - 385*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: -77*y**2*(55*y**3 + 5*y**2)
Expanding the part (55*y**3 + 5*y**2) using the distributive property, and we got: (-77*y**2)*(5*y**2) + (-77*y**2)*(55*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-77*y**2)*(5*y**2) + (-77*y**2)*(55*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (5*y**2)*(-77*y**2) = -385*y**4
  (55*y**3)*(-77*y**2) = -4235*y**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -4235*y**5 - 385*y**4</replace>
No more calculations needed.
<answer>-4235*y**5 - 385*y**4</answer>


Question:
Calculate the following: (24*y**3 - 6)*(-2*y**3 - 33*y - 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: -48*y**6 - 792*y**4 - 180*y**3 + 198*y + 48

Let's solve 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: (24*y**3 - 6)*(-2*y**3 - 33*y - 8)
Expanding the part (24*y**3 - 6) using the distributive property, and we got: (24*y**3)*(-2*y**3 - 33*y - 8) - 6*(-2*y**3 - 33*y - 8)
<replace-#Step 1>#Step 2:
Current expression: (24*y**3)*(-2*y**3 - 33*y - 8) - 6*(-2*y**3 - 33*y - 8)</replace>
Simplifying the partial expression: -6*(-2*y**3 - 33*y - 8)
Expanding the part (-2*y**3 - 33*y - 8) using the distributive property, and we got: -33*y*(-6) - 2*y**3*(-6) - 8*(-6)
Replacing -6*(-2*y**3 - 33*y - 8) with -33*y*(-6) - 2*y**3*(-6) - 8*(-6) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -33*y*(-6) - 2*y**3*(-6) + (24*y**3)*(-2*y**3 - 33*y - 8) + 48</replace>
Simplifying the partial expression: (24*y**3)*(-2*y**3 - 33*y - 8)
Expanding the part (-2*y**3 - 33*y - 8) using the distributive property, and we got: (-33*y)*(24*y**3) - 192*y**3 + (-2*y**3)*(24*y**3)
Replacing (24*y**3)*(-2*y**3 - 33*y - 8) with (-33*y)*(24*y**3) - 192*y**3 + (-2*y**3)*(24*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-33*y)*(24*y**3) - 33*y*(-6) - 8*24*y**3 + (-2*y**3)*(24*y**3) - 2*y**3*(-6) + 48</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-33*y)*-6 = 198*y
  (-33*y)*(24*y**3) = -792*y**4
  (-2*y**3)*-6 = 12*y**3
  (-2*y**3)*(24*y**3) = -48*y**6
  -8*24*y**3 = -192*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -48*y**6 - 792*y**4 - 192*y**3 + 12*y**3 + 198*y + 48</replace>
Combining like terms, got -48*y**6 - 792*y**4 - 180*y**3 + 198*y + 48
<replace-#Step 5>#Step 6:
Current expression: -48*y**6 - 792*y**4 - 180*y**3 + 198*y + 48</replace>
No more calculations needed.
<answer>-48*y**6 - 792*y**4 - 180*y**3 + 198*y + 48</answer>


Question:
Calculate the following: (-15*y**3 - 30*y**2 + 3*y)*(14*y**3 - 64*y - 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: -210*y**6 - 420*y**5 + 1002*y**4 + 2565*y**3 + 1098*y**2 - 129*y


Question:
Simplify this expression: (-38*y**3 + 34*y)*(-29*y**3 + 37*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1102*y**6 - 2392*y**4 + 1258*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**3 + 34*y)*(-29*y**3 + 37*y)
Expanding the part (-38*y**3 + 34*y) using the distributive property, and we got: (34*y)*(-29*y**3 + 37*y) + (-38*y**3)*(-29*y**3 + 37*y)
<replace-#Step 1>#Step 2:
Current expression: (34*y)*(-29*y**3 + 37*y) + (-38*y**3)*(-29*y**3 + 37*y)</replace>
Simplifying the partial expression: (-38*y**3)*(-29*y**3 + 37*y)
Expanding the part (-29*y**3 + 37*y) using the distributive property, and we got: (37*y)*(-38*y**3) + (-38*y**3)*(-29*y**3)
Replacing (-38*y**3)*(-29*y**3 + 37*y) with (37*y)*(-38*y**3) + (-38*y**3)*(-29*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (34*y)*(-29*y**3 + 37*y) + (37*y)*(-38*y**3) + (-38*y**3)*(-29*y**3)</replace>
Simplifying the partial expression: (34*y)*(-29*y**3 + 37*y)
Expanding the part (-29*y**3 + 37*y) using the distributive property, and we got: (34*y)*(37*y) + (34*y)*(-29*y**3)
Replacing (34*y)*(-29*y**3 + 37*y) with (34*y)*(37*y) + (34*y)*(-29*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (34*y)*(37*y) + (34*y)*(-29*y**3) + (37*y)*(-38*y**3) + (-38*y**3)*(-29*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-29*y**3)*(-38*y**3) = 1102*y**6
  (-29*y**3)*(34*y) = -986*y**4
  (37*y)*(-38*y**3) = -1406*y**4
  (37*y)*(34*y) = 1258*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1102*y**6 - 1406*y**4 - 986*y**4 + 1258*y**2</replace>
Combining like terms, got 1102*y**6 - 2392*y**4 + 1258*y**2
<replace-#Step 5>#Step 6:
Current expression: 1102*y**6 - 2392*y**4 + 1258*y**2</replace>
No more calculations needed.
<answer>1102*y**6 - 2392*y**4 + 1258*y**2</answer>


Question:
Calculate the following: (43*x + 13)*(29*x**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: 1247*x**3 + 377*x**2 - 1892*x - 572

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (43*x + 13)*(29*x**2 - 44)
Expanding the part (29*x**2 - 44) using the distributive property, and we got: (29*x**2)*(43*x + 13) - 44*(43*x + 13)
<replace-#Step 1>#Step 2:
Current expression: (29*x**2)*(43*x + 13) - 44*(43*x + 13)</replace>
Simplifying the partial expression: -44*(43*x + 13)
Expanding the part (43*x + 13) using the distributive property, and we got: (43*x)*(-44) + 13*(-44)
Replacing -44*(43*x + 13) with (43*x)*(-44) + 13*(-44) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (43*x)*(-44) + (29*x**2)*(43*x + 13) - 572</replace>
Simplifying the partial expression: (29*x**2)*(43*x + 13)
Expanding the part (43*x + 13) using the distributive property, and we got: 13*(29*x**2) + (43*x)*(29*x**2)
Replacing (29*x**2)*(43*x + 13) with 13*(29*x**2) + (43*x)*(29*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 13*29*x**2 + (43*x)*(29*x**2) + (43*x)*(-44) - 572</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (43*x)*-44 = -1892*x
  (43*x)*(29*x**2) = 1247*x**3
  13*29*x**2 = 377*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1247*x**3 + 377*x**2 - 1892*x - 572</replace>
No more calculations needed.
<answer>1247*x**3 + 377*x**2 - 1892*x - 572</answer>


Question:
Simplify this expression: (32*z**3 + 43)*(-15*z**2 - z + 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: -480*z**5 - 32*z**4 + 1472*z**3 - 645*z**2 - 43*z + 1978

Let's solve 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*z**3 + 43)*(-15*z**2 - z + 46)
Expanding the part (32*z**3 + 43) using the distributive property, and we got: (32*z**3)*(-15*z**2 - z + 46) + 43*(-15*z**2 - z + 46)
<replace-#Step 1>#Step 2:
Current expression: (32*z**3)*(-15*z**2 - z + 46) + 43*(-15*z**2 - z + 46)</replace>
Simplifying the partial expression: 43*(-15*z**2 - z + 46)
Expanding the part (-15*z**2 - z + 46) using the distributive property, and we got: -z*43 - 15*z**2*43 + 46*43
Replacing 43*(-15*z**2 - z + 46) with -z*43 - 15*z**2*43 + 46*43 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -z*43 - 15*z**2*43 + (32*z**3)*(-15*z**2 - z + 46) + 1978</replace>
Simplifying the partial expression: (32*z**3)*(-15*z**2 - z + 46)
Expanding the part (-15*z**2 - z + 46) using the distributive property, and we got: (-z)*(32*z**3) + 46*(32*z**3) + (-15*z**2)*(32*z**3)
Replacing (32*z**3)*(-15*z**2 - z + 46) with (-z)*(32*z**3) + 46*(32*z**3) + (-15*z**2)*(32*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-z)*(32*z**3) - z*43 + 46*32*z**3 + (-15*z**2)*(32*z**3) - 15*z**2*43 + 1978</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-z)*43 = -43*z
  (-z)*(32*z**3) = -32*z**4
  (-15*z**2)*43 = -645*z**2
  (-15*z**2)*(32*z**3) = -480*z**5
  46*32*z**3 = 1472*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -480*z**5 - 32*z**4 + 1472*z**3 - 645*z**2 - 43*z + 1978</replace>
No more calculations needed.
<answer>-480*z**5 - 32*z**4 + 1472*z**3 - 645*z**2 - 43*z + 1978</answer>


Question:
Simplify this expression: (-5*x**3 + 9*x**2 + 78*x)*(5*x**3 - 6*x - 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: -25*x**6 + 45*x**5 + 420*x**4 + x**3 - 567*x**2 - 858*x


Question:
Simplify this expression: (40*z - 35)*(-6*z**2 + 47*z - 58)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -240*z**3 + 2090*z**2 - 3965*z + 2030

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (40*z - 35)*(-6*z**2 + 47*z - 58)
Expanding the part (40*z - 35) using the distributive property, and we got: (40*z)*(-6*z**2 + 47*z - 58) - 35*(-6*z**2 + 47*z - 58)
<replace-#Step 1>#Step 2:
Current expression: (40*z)*(-6*z**2 + 47*z - 58) - 35*(-6*z**2 + 47*z - 58)</replace>
Simplifying the partial expression: -35*(-6*z**2 + 47*z - 58)
Expanding the part (-6*z**2 + 47*z - 58) using the distributive property, and we got: (47*z)*(-35) - 6*z**2*(-35) - 58*(-35)
Replacing -35*(-6*z**2 + 47*z - 58) with (47*z)*(-35) - 6*z**2*(-35) - 58*(-35) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (40*z)*(-6*z**2 + 47*z - 58) + (47*z)*(-35) - 6*z**2*(-35) + 2030</replace>
Simplifying the partial expression: (40*z)*(-6*z**2 + 47*z - 58)
Expanding the part (-6*z**2 + 47*z - 58) using the distributive property, and we got: -2320*z + (40*z)*(47*z) + (40*z)*(-6*z**2)
Replacing (40*z)*(-6*z**2 + 47*z - 58) with -2320*z + (40*z)*(47*z) + (40*z)*(-6*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -58*40*z + (40*z)*(47*z) + (40*z)*(-6*z**2) + (47*z)*(-35) - 6*z**2*(-35) + 2030</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-6*z**2)*-35 = 210*z**2
  (-6*z**2)*(40*z) = -240*z**3
  (47*z)*-35 = -1645*z
  (47*z)*(40*z) = 1880*z**2
  -58*40*z = -2320*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -240*z**3 + 210*z**2 + 1880*z**2 - 2320*z - 1645*z + 2030</replace>
Combining like terms, got -240*z**3 + 2090*z**2 - 3965*z + 2030
<replace-#Step 5>#Step 6:
Current expression: -240*z**3 + 2090*z**2 - 3965*z + 2030</replace>
No more calculations needed.
<answer>-240*z**3 + 2090*z**2 - 3965*z + 2030</answer>


Question:
Calculate the following: (26*y**2 + 27)*(-12*y**3 + 19*y**2 - 8*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: -312*y**5 + 494*y**4 - 532*y**3 + 513*y**2 - 216*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 + 27)*(-12*y**3 + 19*y**2 - 8*y)
Expanding the part (26*y**2 + 27) using the distributive property, and we got: (26*y**2)*(-12*y**3 + 19*y**2 - 8*y) + 27*(-12*y**3 + 19*y**2 - 8*y)
<replace-#Step 1>#Step 2:
Current expression: (26*y**2)*(-12*y**3 + 19*y**2 - 8*y) + 27*(-12*y**3 + 19*y**2 - 8*y)</replace>
Simplifying the partial expression: 27*(-12*y**3 + 19*y**2 - 8*y)
Expanding the part (-12*y**3 + 19*y**2 - 8*y) using the distributive property, and we got: -8*y*27 + (19*y**2)*27 - 12*y**3*27
Replacing 27*(-12*y**3 + 19*y**2 - 8*y) with -8*y*27 + (19*y**2)*27 - 12*y**3*27 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -8*y*27 + (19*y**2)*27 + (26*y**2)*(-12*y**3 + 19*y**2 - 8*y) - 12*y**3*27</replace>
Simplifying the partial expression: (26*y**2)*(-12*y**3 + 19*y**2 - 8*y)
Expanding the part (-12*y**3 + 19*y**2 - 8*y) using the distributive property, and we got: (-8*y)*(26*y**2) + (19*y**2)*(26*y**2) + (26*y**2)*(-12*y**3)
Replacing (26*y**2)*(-12*y**3 + 19*y**2 - 8*y) with (-8*y)*(26*y**2) + (19*y**2)*(26*y**2) + (26*y**2)*(-12*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-8*y)*(26*y**2) - 8*y*27 + (19*y**2)*(26*y**2) + (19*y**2)*27 + (26*y**2)*(-12*y**3) - 12*y**3*27</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-12*y**3)*27 = -324*y**3
  (-12*y**3)*(26*y**2) = -312*y**5
  (-8*y)*27 = -216*y
  (-8*y)*(26*y**2) = -208*y**3
  (19*y**2)*27 = 513*y**2
  (19*y**2)*(26*y**2) = 494*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -312*y**5 + 494*y**4 - 324*y**3 - 208*y**3 + 513*y**2 - 216*y</replace>
Combining like terms, got -312*y**5 + 494*y**4 - 532*y**3 + 513*y**2 - 216*y
<replace-#Step 5>#Step 6:
Current expression: -312*y**5 + 494*y**4 - 532*y**3 + 513*y**2 - 216*y</replace>
No more calculations needed.
<answer>-312*y**5 + 494*y**4 - 532*y**3 + 513*y**2 - 216*y</answer>


Question:
Simplify this expression: (23*y + 26)*(-30*y**3 - 29*y**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: -690*y**4 - 1447*y**3 - 754*y**2 + 805*y + 910

Let's solve 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*y + 26)*(-30*y**3 - 29*y**2 + 35)
Expanding the part (23*y + 26) using the distributive property, and we got: (23*y)*(-30*y**3 - 29*y**2 + 35) + 26*(-30*y**3 - 29*y**2 + 35)
<replace-#Step 1>#Step 2:
Current expression: (23*y)*(-30*y**3 - 29*y**2 + 35) + 26*(-30*y**3 - 29*y**2 + 35)</replace>
Simplifying the partial expression: 26*(-30*y**3 - 29*y**2 + 35)
Expanding the part (-30*y**3 - 29*y**2 + 35) using the distributive property, and we got: -29*y**2*26 - 30*y**3*26 + 35*26
Replacing 26*(-30*y**3 - 29*y**2 + 35) with -29*y**2*26 - 30*y**3*26 + 35*26 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (23*y)*(-30*y**3 - 29*y**2 + 35) - 29*y**2*26 - 30*y**3*26 + 910</replace>
Simplifying the partial expression: (23*y)*(-30*y**3 - 29*y**2 + 35)
Expanding the part (-30*y**3 - 29*y**2 + 35) using the distributive property, and we got: 35*(23*y) + (23*y)*(-29*y**2) + (23*y)*(-30*y**3)
Replacing (23*y)*(-30*y**3 - 29*y**2 + 35) with 35*(23*y) + (23*y)*(-29*y**2) + (23*y)*(-30*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 35*23*y + (23*y)*(-29*y**2) + (23*y)*(-30*y**3) - 29*y**2*26 - 30*y**3*26 + 910</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-30*y**3)*26 = -780*y**3
  (-30*y**3)*(23*y) = -690*y**4
  (-29*y**2)*26 = -754*y**2
  (-29*y**2)*(23*y) = -667*y**3
  35*23*y = 805*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -690*y**4 - 780*y**3 - 667*y**3 - 754*y**2 + 805*y + 910</replace>
Combining like terms, got -690*y**4 - 1447*y**3 - 754*y**2 + 805*y + 910
<replace-#Step 5>#Step 6:
Current expression: -690*y**4 - 1447*y**3 - 754*y**2 + 805*y + 910</replace>
No more calculations needed.
<answer>-690*y**4 - 1447*y**3 - 754*y**2 + 805*y + 910</answer>


Question:
Simplify this expression: (39*y**2 - 5)*(17*y**3 - 2*y**2 + 47)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 663*y**5 - 78*y**4 - 85*y**3 + 1843*y**2 - 235

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (39*y**2 - 5)*(17*y**3 - 2*y**2 + 47)
Expanding the part (39*y**2 - 5) using the distributive property, and we got: (39*y**2)*(17*y**3 - 2*y**2 + 47) - 5*(17*y**3 - 2*y**2 + 47)
<replace-#Step 1>#Step 2:
Current expression: (39*y**2)*(17*y**3 - 2*y**2 + 47) - 5*(17*y**3 - 2*y**2 + 47)</replace>
Simplifying the partial expression: -5*(17*y**3 - 2*y**2 + 47)
Expanding the part (17*y**3 - 2*y**2 + 47) using the distributive property, and we got: -2*y**2*(-5) + (17*y**3)*(-5) + 47*(-5)
Replacing -5*(17*y**3 - 2*y**2 + 47) with -2*y**2*(-5) + (17*y**3)*(-5) + 47*(-5) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -2*y**2*(-5) + (39*y**2)*(17*y**3 - 2*y**2 + 47) + (17*y**3)*(-5) - 235</replace>
Simplifying the partial expression: (39*y**2)*(17*y**3 - 2*y**2 + 47)
Expanding the part (17*y**3 - 2*y**2 + 47) using the distributive property, and we got: 47*(39*y**2) + (-2*y**2)*(39*y**2) + (39*y**2)*(17*y**3)
Replacing (39*y**2)*(17*y**3 - 2*y**2 + 47) with 47*(39*y**2) + (-2*y**2)*(39*y**2) + (39*y**2)*(17*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 47*39*y**2 + (-2*y**2)*(39*y**2) - 2*y**2*(-5) + (39*y**2)*(17*y**3) + (17*y**3)*(-5) - 235</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-2*y**2)*-5 = 10*y**2
  (-2*y**2)*(39*y**2) = -78*y**4
  (17*y**3)*-5 = -85*y**3
  (17*y**3)*(39*y**2) = 663*y**5
  47*39*y**2 = 1833*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 663*y**5 - 78*y**4 - 85*y**3 + 10*y**2 + 1833*y**2 - 235</replace>
Combining like terms, got 663*y**5 - 78*y**4 - 85*y**3 + 1843*y**2 - 235
<replace-#Step 5>#Step 6:
Current expression: 663*y**5 - 78*y**4 - 85*y**3 + 1843*y**2 - 235</replace>
No more calculations needed.
<answer>663*y**5 - 78*y**4 - 85*y**3 + 1843*y**2 - 235</answer>


Question:
Simplify this expression: (-17*z**3 - 44)*(-27*z**2 + 42*z - 14)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 459*z**5 - 714*z**4 + 238*z**3 + 1188*z**2 - 1848*z + 616

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-17*z**3 - 44)*(-27*z**2 + 42*z - 14)
Expanding the part (-17*z**3 - 44) using the distributive property, and we got: (-17*z**3)*(-27*z**2 + 42*z - 14) - 44*(-27*z**2 + 42*z - 14)
<replace-#Step 1>#Step 2:
Current expression: (-17*z**3)*(-27*z**2 + 42*z - 14) - 44*(-27*z**2 + 42*z - 14)</replace>
Simplifying the partial expression: -44*(-27*z**2 + 42*z - 14)
Expanding the part (-27*z**2 + 42*z - 14) using the distributive property, and we got: (42*z)*(-44) - 27*z**2*(-44) - 14*(-44)
Replacing -44*(-27*z**2 + 42*z - 14) with (42*z)*(-44) - 27*z**2*(-44) - 14*(-44) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (42*z)*(-44) - 27*z**2*(-44) + (-17*z**3)*(-27*z**2 + 42*z - 14) + 616</replace>
Simplifying the partial expression: (-17*z**3)*(-27*z**2 + 42*z - 14)
Expanding the part (-27*z**2 + 42*z - 14) using the distributive property, and we got: -(-1)*238*z**3 + (42*z)*(-17*z**3) + (-27*z**2)*(-17*z**3)
Replacing (-17*z**3)*(-27*z**2 + 42*z - 14) with -(-1)*238*z**3 + (42*z)*(-17*z**3) + (-27*z**2)*(-17*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -14*(-17)*z**3 + (42*z)*(-17*z**3) + (42*z)*(-44) + (-27*z**2)*(-17*z**3) - 27*z**2*(-44) + 616</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-27*z**2)*-44 = 1188*z**2
  (-27*z**2)*(-17*z**3) = 459*z**5
  (42*z)*-44 = -1848*z
  (42*z)*(-17*z**3) = -714*z**4
  -14*-17*z**3 = 238*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 459*z**5 - 714*z**4 + 238*z**3 + 1188*z**2 - 1848*z + 616</replace>
No more calculations needed.
<answer>459*z**5 - 714*z**4 + 238*z**3 + 1188*z**2 - 1848*z + 616</answer>


Question:
Calculate the following: (-34*x**3 - 38*x**2 + 40*x)*(8*x**3 + 27*x**2 - 20*x + 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: -272*x**6 - 1222*x**5 - 26*x**4 + 208*x**3 - 2624*x**2 + 1920*x


Question:
Calculate the following: (-74*y**3 + 49*y**2 + 23)*(12*y**3 - 21*y + 40)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -888*y**6 + 588*y**5 + 1554*y**4 - 3713*y**3 + 1960*y**2 - 483*y + 920


Question:
Calculate the following: 12*y*(34*y**2 + 43*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: 408*y**3 + 516*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: 12*y*(34*y**2 + 43*y)
Expanding the part (34*y**2 + 43*y) using the distributive property, and we got: (12*y)*(43*y) + (12*y)*(34*y**2)
<replace-#Step 1>#Step 2:
Current expression: (12*y)*(43*y) + (12*y)*(34*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (34*y**2)*(12*y) = 408*y**3
  (43*y)*(12*y) = 516*y**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 408*y**3 + 516*y**2</replace>
No more calculations needed.
<answer>408*y**3 + 516*y**2</answer>


Question:
Simplify this expression: (25*y**3 + 25*y + 3)*(49*y**3 - 12*y**2 + 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: 1225*y**6 - 300*y**5 + 1225*y**4 + 547*y**3 - 36*y**2 + 700*y + 84


Question:
Simplify this expression: -700*x**3 - 1596*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: -700*x**3 - 1596*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: -700*x**3 - 1596*x**2
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: -700*x**3 - 1596*x**2</replace>
No more calculations needed.
<answer>-700*x**3 - 1596*x**2</answer>


Question:
Simplify this expression: (74*x**3 + 19)*(-20*x**3 + 9*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: -1480*x**6 + 666*x**4 - 2748*x**3 + 171*x - 608

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (74*x**3 + 19)*(-20*x**3 + 9*x - 32)
Expanding the part (74*x**3 + 19) using the distributive property, and we got: (74*x**3)*(-20*x**3 + 9*x - 32) + 19*(-20*x**3 + 9*x - 32)
<replace-#Step 1>#Step 2:
Current expression: (74*x**3)*(-20*x**3 + 9*x - 32) + 19*(-20*x**3 + 9*x - 32)</replace>
Simplifying the partial expression: 19*(-20*x**3 + 9*x - 32)
Expanding the part (-20*x**3 + 9*x - 32) using the distributive property, and we got: (9*x)*19 - 20*x**3*19 - 32*19
Replacing 19*(-20*x**3 + 9*x - 32) with (9*x)*19 - 20*x**3*19 - 32*19 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (9*x)*19 - 20*x**3*19 + (74*x**3)*(-20*x**3 + 9*x - 32) - 608</replace>
Simplifying the partial expression: (74*x**3)*(-20*x**3 + 9*x - 32)
Expanding the part (-20*x**3 + 9*x - 32) using the distributive property, and we got: -2368*x**3 + (9*x)*(74*x**3) + (-20*x**3)*(74*x**3)
Replacing (74*x**3)*(-20*x**3 + 9*x - 32) with -2368*x**3 + (9*x)*(74*x**3) + (-20*x**3)*(74*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -32*74*x**3 + (9*x)*(74*x**3) + (9*x)*19 + (-20*x**3)*(74*x**3) - 20*x**3*19 - 608</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-20*x**3)*19 = -380*x**3
  (-20*x**3)*(74*x**3) = -1480*x**6
  (9*x)*19 = 171*x
  (9*x)*(74*x**3) = 666*x**4
  -32*74*x**3 = -2368*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1480*x**6 + 666*x**4 - 2368*x**3 - 380*x**3 + 171*x - 608</replace>
Combining like terms, got -1480*x**6 + 666*x**4 - 2748*x**3 + 171*x - 608
<replace-#Step 5>#Step 6:
Current expression: -1480*x**6 + 666*x**4 - 2748*x**3 + 171*x - 608</replace>
No more calculations needed.
<answer>-1480*x**6 + 666*x**4 - 2748*x**3 + 171*x - 608</answer>