Question:
Simplify this expression: (-23*z**2 - 4*z)*(22*z**2 - 10)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -506*z**4 - 88*z**3 + 230*z**2 + 40*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: (-23*z**2 - 4*z)*(22*z**2 - 10)
Expanding the part (22*z**2 - 10) using the distributive property, and we got: (22*z**2)*(-23*z**2 - 4*z) - 10*(-23*z**2 - 4*z)
<replace-#Step 1>#Step 2:
Current expression: (22*z**2)*(-23*z**2 - 4*z) - 10*(-23*z**2 - 4*z)</replace>
Simplifying the partial expression: -10*(-23*z**2 - 4*z)
Expanding the part (-23*z**2 - 4*z) using the distributive property, and we got: -4*z*(-10) - 23*z**2*(-10)
Replacing -10*(-23*z**2 - 4*z) with -4*z*(-10) - 23*z**2*(-10) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -4*z*(-10) - 23*z**2*(-10) + (22*z**2)*(-23*z**2 - 4*z)</replace>
Simplifying the partial expression: (22*z**2)*(-23*z**2 - 4*z)
Expanding the part (-23*z**2 - 4*z) using the distributive property, and we got: (-4*z)*(22*z**2) + (-23*z**2)*(22*z**2)
Replacing (22*z**2)*(-23*z**2 - 4*z) with (-4*z)*(22*z**2) + (-23*z**2)*(22*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-4*z)*(22*z**2) - 4*z*(-10) + (-23*z**2)*(22*z**2) - 23*z**2*(-10)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-23*z**2)*-10 = 230*z**2
  (-23*z**2)*(22*z**2) = -506*z**4
  (-4*z)*-10 = 40*z
  (-4*z)*(22*z**2) = -88*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -506*z**4 - 88*z**3 + 230*z**2 + 40*z</replace>
No more calculations needed.
<answer>-506*z**4 - 88*z**3 + 230*z**2 + 40*z</answer>


Question:
Simplify this expression: (-53*z**2 - 46*z)*(-51*z**3 - 46*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: 2703*z**5 + 2346*z**4 + 2438*z**3 + 2116*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: (-53*z**2 - 46*z)*(-51*z**3 - 46*z)
Expanding the part (-53*z**2 - 46*z) using the distributive property, and we got: (-46*z)*(-51*z**3 - 46*z) + (-53*z**2)*(-51*z**3 - 46*z)
<replace-#Step 1>#Step 2:
Current expression: (-46*z)*(-51*z**3 - 46*z) + (-53*z**2)*(-51*z**3 - 46*z)</replace>
Simplifying the partial expression: (-53*z**2)*(-51*z**3 - 46*z)
Expanding the part (-51*z**3 - 46*z) using the distributive property, and we got: (-46*z)*(-53*z**2) + (-53*z**2)*(-51*z**3)
Replacing (-53*z**2)*(-51*z**3 - 46*z) with (-46*z)*(-53*z**2) + (-53*z**2)*(-51*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-46*z)*(-53*z**2) + (-46*z)*(-51*z**3 - 46*z) + (-53*z**2)*(-51*z**3)</replace>
Simplifying the partial expression: (-46*z)*(-51*z**3 - 46*z)
Expanding the part (-51*z**3 - 46*z) using the distributive property, and we got: (-46*z)*(-51*z**3) + (-46*z)*(-46*z)
Replacing (-46*z)*(-51*z**3 - 46*z) with (-46*z)*(-51*z**3) + (-46*z)*(-46*z) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-46*z)*(-53*z**2) + (-46*z)*(-51*z**3) + (-46*z)*(-46*z) + (-53*z**2)*(-51*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-51*z**3)*(-53*z**2) = 2703*z**5
  (-51*z**3)*(-46*z) = 2346*z**4
  (-46*z)*(-53*z**2) = 2438*z**3
  (-46*z)*(-46*z) = 2116*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2703*z**5 + 2346*z**4 + 2438*z**3 + 2116*z**2</replace>
No more calculations needed.
<answer>2703*z**5 + 2346*z**4 + 2438*z**3 + 2116*z**2</answer>


Question:
Simplify this expression: (32*x**2 + 50)*(36*x**3 - 57*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: 1152*x**5 - 24*x**3 - 2850*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: (32*x**2 + 50)*(36*x**3 - 57*x)
Expanding the part (32*x**2 + 50) using the distributive property, and we got: (32*x**2)*(36*x**3 - 57*x) + 50*(36*x**3 - 57*x)
<replace-#Step 1>#Step 2:
Current expression: (32*x**2)*(36*x**3 - 57*x) + 50*(36*x**3 - 57*x)</replace>
Simplifying the partial expression: 50*(36*x**3 - 57*x)
Expanding the part (36*x**3 - 57*x) using the distributive property, and we got: -57*x*50 + (36*x**3)*50
Replacing 50*(36*x**3 - 57*x) with -57*x*50 + (36*x**3)*50 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -57*x*50 + (32*x**2)*(36*x**3 - 57*x) + (36*x**3)*50</replace>
Simplifying the partial expression: (32*x**2)*(36*x**3 - 57*x)
Expanding the part (36*x**3 - 57*x) using the distributive property, and we got: (-57*x)*(32*x**2) + (32*x**2)*(36*x**3)
Replacing (32*x**2)*(36*x**3 - 57*x) with (-57*x)*(32*x**2) + (32*x**2)*(36*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-57*x)*(32*x**2) - 57*x*50 + (32*x**2)*(36*x**3) + (36*x**3)*50</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-57*x)*50 = -2850*x
  (-57*x)*(32*x**2) = -1824*x**3
  (36*x**3)*50 = 1800*x**3
  (36*x**3)*(32*x**2) = 1152*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1152*x**5 - 1824*x**3 + 1800*x**3 - 2850*x</replace>
Combining like terms, got 1152*x**5 - 24*x**3 - 2850*x
<replace-#Step 5>#Step 6:
Current expression: 1152*x**5 - 24*x**3 - 2850*x</replace>
No more calculations needed.
<answer>1152*x**5 - 24*x**3 - 2850*x</answer>


Question:
Simplify this expression: (-14*x**3 - 20*x)*(-7*x**3 - 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: 98*x**6 + 140*x**4 + 448*x**3 + 640*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: (-14*x**3 - 20*x)*(-7*x**3 - 32)
Expanding the part (-7*x**3 - 32) using the distributive property, and we got: (-7*x**3)*(-14*x**3 - 20*x) - 32*(-14*x**3 - 20*x)
<replace-#Step 1>#Step 2:
Current expression: (-7*x**3)*(-14*x**3 - 20*x) - 32*(-14*x**3 - 20*x)</replace>
Simplifying the partial expression: -32*(-14*x**3 - 20*x)
Expanding the part (-14*x**3 - 20*x) using the distributive property, and we got: -20*x*(-32) - 14*x**3*(-32)
Replacing -32*(-14*x**3 - 20*x) with -20*x*(-32) - 14*x**3*(-32) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -20*x*(-32) - 14*x**3*(-32) + (-7*x**3)*(-14*x**3 - 20*x)</replace>
Simplifying the partial expression: (-7*x**3)*(-14*x**3 - 20*x)
Expanding the part (-14*x**3 - 20*x) using the distributive property, and we got: (-20*x)*(-7*x**3) + (-14*x**3)*(-7*x**3)
Replacing (-7*x**3)*(-14*x**3 - 20*x) with (-20*x)*(-7*x**3) + (-14*x**3)*(-7*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-20*x)*(-7*x**3) - 20*x*(-32) + (-14*x**3)*(-7*x**3) - 14*x**3*(-32)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-20*x)*-32 = 640*x
  (-20*x)*(-7*x**3) = 140*x**4
  (-14*x**3)*-32 = 448*x**3
  (-14*x**3)*(-7*x**3) = 98*x**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 98*x**6 + 140*x**4 + 448*x**3 + 640*x</replace>
No more calculations needed.
<answer>98*x**6 + 140*x**4 + 448*x**3 + 640*x</answer>


Question:
Calculate the following: (76*y**3 + 13*y**2)*(14*y**3 - 23*y + 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: 1064*y**6 + 182*y**5 - 1748*y**4 + 81*y**3 + 65*y**2


Question:
Calculate the following: 22*x**3*(21*x**2 - 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: 462*x**5 - 1056*x**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 22*x**3*(21*x**2 - 48)
Expanding the part (21*x**2 - 48) using the distributive property, and we got: -1056*x**3 + (21*x**2)*(22*x**3)
<replace-#Step 1>#Step 2:
Current expression: -1056*x**3 + (21*x**2)*(22*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -48*(22*x**3) = -1056*x**3
  (21*x**2)*(22*x**3) = 462*x**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 462*x**5 - 1056*x**3</replace>
No more calculations needed.
<answer>462*x**5 - 1056*x**3</answer>


Question:
Simplify this expression: 24*z**3 + 56*z**2 - 28*z + 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: 24*z**3 + 56*z**2 - 28*z + 36

Let's solve 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*z**3 + 56*z**2 - 28*z + 36
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: 24*z**3 + 56*z**2 - 28*z + 36</replace>
No more calculations needed.
<answer>24*z**3 + 56*z**2 - 28*z + 36</answer>


Question:
Simplify this expression: (-36*y**3 - 12*y)*(-36*y**3 + 22*y**2 + 70*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: 1296*y**6 - 792*y**5 - 2088*y**4 - 264*y**3 - 840*y**2


Question:
Calculate the following: (27*y**3 + 29)*(-46*y**3 + 16*y**2 - 12)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1242*y**6 + 432*y**5 - 1658*y**3 + 464*y**2 - 348

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (27*y**3 + 29)*(-46*y**3 + 16*y**2 - 12)
Expanding the part (27*y**3 + 29) using the distributive property, and we got: (27*y**3)*(-46*y**3 + 16*y**2 - 12) + 29*(-46*y**3 + 16*y**2 - 12)
<replace-#Step 1>#Step 2:
Current expression: (27*y**3)*(-46*y**3 + 16*y**2 - 12) + 29*(-46*y**3 + 16*y**2 - 12)</replace>
Simplifying the partial expression: 29*(-46*y**3 + 16*y**2 - 12)
Expanding the part (-46*y**3 + 16*y**2 - 12) using the distributive property, and we got: (16*y**2)*29 - 46*y**3*29 - 12*29
Replacing 29*(-46*y**3 + 16*y**2 - 12) with (16*y**2)*29 - 46*y**3*29 - 12*29 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (16*y**2)*29 - 46*y**3*29 + (27*y**3)*(-46*y**3 + 16*y**2 - 12) - 348</replace>
Simplifying the partial expression: (27*y**3)*(-46*y**3 + 16*y**2 - 12)
Expanding the part (-46*y**3 + 16*y**2 - 12) using the distributive property, and we got: -324*y**3 + (16*y**2)*(27*y**3) + (-46*y**3)*(27*y**3)
Replacing (27*y**3)*(-46*y**3 + 16*y**2 - 12) with -324*y**3 + (16*y**2)*(27*y**3) + (-46*y**3)*(27*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -12*27*y**3 + (16*y**2)*(27*y**3) + (16*y**2)*29 + (-46*y**3)*(27*y**3) - 46*y**3*29 - 348</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-46*y**3)*29 = -1334*y**3
  (-46*y**3)*(27*y**3) = -1242*y**6
  (16*y**2)*29 = 464*y**2
  (16*y**2)*(27*y**3) = 432*y**5
  -12*27*y**3 = -324*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1242*y**6 + 432*y**5 - 1334*y**3 - 324*y**3 + 464*y**2 - 348</replace>
Combining like terms, got -1242*y**6 + 432*y**5 - 1658*y**3 + 464*y**2 - 348
<replace-#Step 5>#Step 6:
Current expression: -1242*y**6 + 432*y**5 - 1658*y**3 + 464*y**2 - 348</replace>
No more calculations needed.
<answer>-1242*y**6 + 432*y**5 - 1658*y**3 + 464*y**2 - 348</answer>


Question:
Simplify this expression: (37*z**3 - 10*z**2 + 27*z)*(10*z**3 + 39*z**2 + 9*z - 15)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 370*z**6 + 1343*z**5 + 213*z**4 + 408*z**3 + 393*z**2 - 405*z


Question:
Calculate the following: (35*z**2 + 41)*(-4*z**3 - 37*z - 1)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -140*z**5 - 1459*z**3 - 35*z**2 - 1517*z - 41

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (35*z**2 + 41)*(-4*z**3 - 37*z - 1)
Expanding the part (35*z**2 + 41) using the distributive property, and we got: (35*z**2)*(-4*z**3 - 37*z - 1) + 41*(-4*z**3 - 37*z - 1)
<replace-#Step 1>#Step 2:
Current expression: (35*z**2)*(-4*z**3 - 37*z - 1) + 41*(-4*z**3 - 37*z - 1)</replace>
Simplifying the partial expression: 41*(-4*z**3 - 37*z - 1)
Expanding the part (-4*z**3 - 37*z - 1) using the distributive property, and we got: -37*z*41 - 4*z**3*41 - 1*41
Replacing 41*(-4*z**3 - 37*z - 1) with -37*z*41 - 4*z**3*41 - 1*41 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -37*z*41 + (35*z**2)*(-4*z**3 - 37*z - 1) - 4*z**3*41 - 41</replace>
Simplifying the partial expression: (35*z**2)*(-4*z**3 - 37*z - 1)
Expanding the part (-4*z**3 - 37*z - 1) using the distributive property, and we got: (-37*z)*(35*z**2) - 35*z**2 + (35*z**2)*(-4*z**3)
Replacing (35*z**2)*(-4*z**3 - 37*z - 1) with (-37*z)*(35*z**2) - 35*z**2 + (35*z**2)*(-4*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-37*z)*(35*z**2) - 37*z*41 - 1*35*z**2 + (35*z**2)*(-4*z**3) - 4*z**3*41 - 41</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-37*z)*41 = -1517*z
  (-37*z)*(35*z**2) = -1295*z**3
  (-4*z**3)*41 = -164*z**3
  (-4*z**3)*(35*z**2) = -140*z**5
  -1*35*z**2 = -35*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -140*z**5 - 1295*z**3 - 164*z**3 - 35*z**2 - 1517*z - 41</replace>
Combining like terms, got -140*z**5 - 1459*z**3 - 35*z**2 - 1517*z - 41
<replace-#Step 5>#Step 6:
Current expression: -140*z**5 - 1459*z**3 - 35*z**2 - 1517*z - 41</replace>
No more calculations needed.
<answer>-140*z**5 - 1459*z**3 - 35*z**2 - 1517*z - 41</answer>


Question:
Simplify this expression: (-3*z**3 + 31*z**2)*(-40*z**3 + 50*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: 120*z**6 - 1240*z**5 - 150*z**4 + 1688*z**3 - 1426*z**2


Question:
Calculate the following: (13*x**2 - 37)*(46*x**2 + 27*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: 598*x**4 + 351*x**3 - 1676*x**2 - 999*x - 74

Let's solve 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*x**2 - 37)*(46*x**2 + 27*x + 2)
Expanding the part (13*x**2 - 37) using the distributive property, and we got: (13*x**2)*(46*x**2 + 27*x + 2) - 37*(46*x**2 + 27*x + 2)
<replace-#Step 1>#Step 2:
Current expression: (13*x**2)*(46*x**2 + 27*x + 2) - 37*(46*x**2 + 27*x + 2)</replace>
Simplifying the partial expression: -37*(46*x**2 + 27*x + 2)
Expanding the part (46*x**2 + 27*x + 2) using the distributive property, and we got: (27*x)*(-37) + (46*x**2)*(-37) + 2*(-37)
Replacing -37*(46*x**2 + 27*x + 2) with (27*x)*(-37) + (46*x**2)*(-37) + 2*(-37) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (27*x)*(-37) + (13*x**2)*(46*x**2 + 27*x + 2) + (46*x**2)*(-37) - 74</replace>
Simplifying the partial expression: (13*x**2)*(46*x**2 + 27*x + 2)
Expanding the part (46*x**2 + 27*x + 2) using the distributive property, and we got: 2*(13*x**2) + (27*x)*(13*x**2) + (13*x**2)*(46*x**2)
Replacing (13*x**2)*(46*x**2 + 27*x + 2) with 2*(13*x**2) + (27*x)*(13*x**2) + (13*x**2)*(46*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 2*13*x**2 + (27*x)*(13*x**2) + (27*x)*(-37) + (13*x**2)*(46*x**2) + (46*x**2)*(-37) - 74</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (27*x)*-37 = -999*x
  (27*x)*(13*x**2) = 351*x**3
  (46*x**2)*-37 = -1702*x**2
  (46*x**2)*(13*x**2) = 598*x**4
  2*13*x**2 = 26*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 598*x**4 + 351*x**3 - 1702*x**2 + 26*x**2 - 999*x - 74</replace>
Combining like terms, got 598*x**4 + 351*x**3 - 1676*x**2 - 999*x - 74
<replace-#Step 5>#Step 6:
Current expression: 598*x**4 + 351*x**3 - 1676*x**2 - 999*x - 74</replace>
No more calculations needed.
<answer>598*x**4 + 351*x**3 - 1676*x**2 - 999*x - 74</answer>


Question:
Calculate the following: (27 - 8*y)*(6*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: -48*y**4 + 162*y**3 - 144*y**2 + 486*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (27 - 8*y)*(6*y**3 + 18*y)
Expanding the part (27 - 8*y) using the distributive property, and we got: (-8*y)*(6*y**3 + 18*y) + 27*(6*y**3 + 18*y)
<replace-#Step 1>#Step 2:
Current expression: (-8*y)*(6*y**3 + 18*y) + 27*(6*y**3 + 18*y)</replace>
Simplifying the partial expression: 27*(6*y**3 + 18*y)
Expanding the part (6*y**3 + 18*y) using the distributive property, and we got: (18*y)*27 + (6*y**3)*27
Replacing 27*(6*y**3 + 18*y) with (18*y)*27 + (6*y**3)*27 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-8*y)*(6*y**3 + 18*y) + (18*y)*27 + (6*y**3)*27</replace>
Simplifying the partial expression: (-8*y)*(6*y**3 + 18*y)
Expanding the part (6*y**3 + 18*y) using the distributive property, and we got: (-8*y)*(18*y) + (-8*y)*(6*y**3)
Replacing (-8*y)*(6*y**3 + 18*y) with (-8*y)*(18*y) + (-8*y)*(6*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-8*y)*(18*y) + (-8*y)*(6*y**3) + (18*y)*27 + (6*y**3)*27</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (6*y**3)*27 = 162*y**3
  (6*y**3)*(-8*y) = -48*y**4
  (18*y)*27 = 486*y
  (18*y)*(-8*y) = -144*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -48*y**4 + 162*y**3 - 144*y**2 + 486*y</replace>
No more calculations needed.
<answer>-48*y**4 + 162*y**3 - 144*y**2 + 486*y</answer>


Question:
Calculate the following: (-8*z**2 - 6*z + 87)*(-51*z**3 + 15*z**2 + 44)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 408*z**5 + 186*z**4 - 4527*z**3 + 953*z**2 - 264*z + 3828


Question:
Calculate the following: (38*y**2 + 31)*(-39*y**3 + 24*y**2 - 5*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: -1482*y**5 + 912*y**4 - 1399*y**3 + 744*y**2 - 155*y


Question:
Simplify this expression: -16*y**3*(36 - 28*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: 448*y**4 - 576*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: -16*y**3*(36 - 28*y)
Expanding the part (36 - 28*y) using the distributive property, and we got: (-28*y)*(-16*y**3) + 36*(-16*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-28*y)*(-16*y**3) + 36*(-16*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  36*(-16*y**3) = -576*y**3
  (-28*y)*(-16*y**3) = 448*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 448*y**4 - 576*y**3</replace>
No more calculations needed.
<answer>448*y**4 - 576*y**3</answer>


Question:
Simplify this expression: (66 - 47*z)*(-33*z**3 - 24*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: 1551*z**4 - 2178*z**3 + 1128*z**2 - 2242*z + 924

Let's solve 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: (66 - 47*z)*(-33*z**3 - 24*z + 14)
Expanding the part (66 - 47*z) using the distributive property, and we got: (-47*z)*(-33*z**3 - 24*z + 14) + 66*(-33*z**3 - 24*z + 14)
<replace-#Step 1>#Step 2:
Current expression: (-47*z)*(-33*z**3 - 24*z + 14) + 66*(-33*z**3 - 24*z + 14)</replace>
Simplifying the partial expression: 66*(-33*z**3 - 24*z + 14)
Expanding the part (-33*z**3 - 24*z + 14) using the distributive property, and we got: -24*z*66 - 33*z**3*66 + 14*66
Replacing 66*(-33*z**3 - 24*z + 14) with -24*z*66 - 33*z**3*66 + 14*66 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-47*z)*(-33*z**3 - 24*z + 14) - 24*z*66 - 33*z**3*66 + 924</replace>
Simplifying the partial expression: (-47*z)*(-33*z**3 - 24*z + 14)
Expanding the part (-33*z**3 - 24*z + 14) using the distributive property, and we got: (-47*z)*(-24*z) + (-47*z)*(-33*z**3) + 14*(-47*z)
Replacing (-47*z)*(-33*z**3 - 24*z + 14) with (-47*z)*(-24*z) + (-47*z)*(-33*z**3) + 14*(-47*z) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-47*z)*(-24*z) + (-47*z)*(-33*z**3) - 24*z*66 + 14*(-47)*z - 33*z**3*66 + 924</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-33*z**3)*66 = -2178*z**3
  (-33*z**3)*(-47*z) = 1551*z**4
  (-24*z)*66 = -1584*z
  (-24*z)*(-47*z) = 1128*z**2
  14*-47*z = -658*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1551*z**4 - 2178*z**3 + 1128*z**2 - 1584*z - 658*z + 924</replace>
Combining like terms, got 1551*z**4 - 2178*z**3 + 1128*z**2 - 2242*z + 924
<replace-#Step 5>#Step 6:
Current expression: 1551*z**4 - 2178*z**3 + 1128*z**2 - 2242*z + 924</replace>
No more calculations needed.
<answer>1551*z**4 - 2178*z**3 + 1128*z**2 - 2242*z + 924</answer>


Question:
Calculate the following: -4*z**2*(17*z**3 - 31*z**2 - 45*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: -68*z**5 + 124*z**4 + 180*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: -4*z**2*(17*z**3 - 31*z**2 - 45*z)
Expanding the part (17*z**3 - 31*z**2 - 45*z) using the distributive property, and we got: (-45*z)*(-4*z**2) + (-31*z**2)*(-4*z**2) + (-4*z**2)*(17*z**3)
<replace-#Step 1>#Step 2:
Current expression: (-45*z)*(-4*z**2) + (-31*z**2)*(-4*z**2) + (-4*z**2)*(17*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-45*z)*(-4*z**2) = 180*z**3
  (-31*z**2)*(-4*z**2) = 124*z**4
  (17*z**3)*(-4*z**2) = -68*z**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -68*z**5 + 124*z**4 + 180*z**3</replace>
No more calculations needed.
<answer>-68*z**5 + 124*z**4 + 180*z**3</answer>


Question:
Simplify this expression: -73*y**3*(-19*y**2 + 27*y + 17)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1387*y**5 - 1971*y**4 - 1241*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: -73*y**3*(-19*y**2 + 27*y + 17)
Expanding the part (-19*y**2 + 27*y + 17) using the distributive property, and we got: 17*(-73*y**3) + (27*y)*(-73*y**3) + (-19*y**2)*(-73*y**3)
<replace-#Step 1>#Step 2:
Current expression: 17*(-73*y**3) + (27*y)*(-73*y**3) + (-19*y**2)*(-73*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  17*(-73*y**3) = -1241*y**3
  (-19*y**2)*(-73*y**3) = 1387*y**5
  (27*y)*(-73*y**3) = -1971*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1387*y**5 - 1971*y**4 - 1241*y**3</replace>
No more calculations needed.
<answer>1387*y**5 - 1971*y**4 - 1241*y**3</answer>


Question:
Calculate the following: (16*x**2 - 36*x)*(-10*x**3 - 52*x**2 + 49)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -160*x**5 - 472*x**4 + 1872*x**3 + 784*x**2 - 1764*x


Question:
Simplify this expression: (21 - 34*z)*(16*z**3 + 30*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: -544*z**4 + 336*z**3 - 1020*z**2 + 630*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: (21 - 34*z)*(16*z**3 + 30*z)
Expanding the part (21 - 34*z) using the distributive property, and we got: (-34*z)*(16*z**3 + 30*z) + 21*(16*z**3 + 30*z)
<replace-#Step 1>#Step 2:
Current expression: (-34*z)*(16*z**3 + 30*z) + 21*(16*z**3 + 30*z)</replace>
Simplifying the partial expression: 21*(16*z**3 + 30*z)
Expanding the part (16*z**3 + 30*z) using the distributive property, and we got: (30*z)*21 + (16*z**3)*21
Replacing 21*(16*z**3 + 30*z) with (30*z)*21 + (16*z**3)*21 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-34*z)*(16*z**3 + 30*z) + (30*z)*21 + (16*z**3)*21</replace>
Simplifying the partial expression: (-34*z)*(16*z**3 + 30*z)
Expanding the part (16*z**3 + 30*z) using the distributive property, and we got: (-34*z)*(30*z) + (-34*z)*(16*z**3)
Replacing (-34*z)*(16*z**3 + 30*z) with (-34*z)*(30*z) + (-34*z)*(16*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-34*z)*(30*z) + (-34*z)*(16*z**3) + (30*z)*21 + (16*z**3)*21</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (16*z**3)*21 = 336*z**3
  (16*z**3)*(-34*z) = -544*z**4
  (30*z)*21 = 630*z
  (30*z)*(-34*z) = -1020*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -544*z**4 + 336*z**3 - 1020*z**2 + 630*z</replace>
No more calculations needed.
<answer>-544*z**4 + 336*z**3 - 1020*z**2 + 630*z</answer>


Question:
Simplify this expression: (11*z**3 + 74)*(-45*z**3 + 18*z + 42)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -495*z**6 + 198*z**4 - 2868*z**3 + 1332*z + 3108

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (11*z**3 + 74)*(-45*z**3 + 18*z + 42)
Expanding the part (11*z**3 + 74) using the distributive property, and we got: (11*z**3)*(-45*z**3 + 18*z + 42) + 74*(-45*z**3 + 18*z + 42)
<replace-#Step 1>#Step 2:
Current expression: (11*z**3)*(-45*z**3 + 18*z + 42) + 74*(-45*z**3 + 18*z + 42)</replace>
Simplifying the partial expression: 74*(-45*z**3 + 18*z + 42)
Expanding the part (-45*z**3 + 18*z + 42) using the distributive property, and we got: (18*z)*74 - 45*z**3*74 + 42*74
Replacing 74*(-45*z**3 + 18*z + 42) with (18*z)*74 - 45*z**3*74 + 42*74 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (18*z)*74 - 45*z**3*74 + (11*z**3)*(-45*z**3 + 18*z + 42) + 3108</replace>
Simplifying the partial expression: (11*z**3)*(-45*z**3 + 18*z + 42)
Expanding the part (-45*z**3 + 18*z + 42) using the distributive property, and we got: 42*(11*z**3) + (18*z)*(11*z**3) + (-45*z**3)*(11*z**3)
Replacing (11*z**3)*(-45*z**3 + 18*z + 42) with 42*(11*z**3) + (18*z)*(11*z**3) + (-45*z**3)*(11*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 42*11*z**3 + (18*z)*(11*z**3) + (18*z)*74 + (-45*z**3)*(11*z**3) - 45*z**3*74 + 3108</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-45*z**3)*74 = -3330*z**3
  (-45*z**3)*(11*z**3) = -495*z**6
  (18*z)*74 = 1332*z
  (18*z)*(11*z**3) = 198*z**4
  42*11*z**3 = 462*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -495*z**6 + 198*z**4 - 3330*z**3 + 462*z**3 + 1332*z + 3108</replace>
Combining like terms, got -495*z**6 + 198*z**4 - 2868*z**3 + 1332*z + 3108
<replace-#Step 5>#Step 6:
Current expression: -495*z**6 + 198*z**4 - 2868*z**3 + 1332*z + 3108</replace>
No more calculations needed.
<answer>-495*z**6 + 198*z**4 - 2868*z**3 + 1332*z + 3108</answer>


Question:
Calculate the following: (34*y**2 - 67)*(28*y**3 + 9*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: 952*y**5 + 306*y**4 - 1876*y**3 - 603*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: (34*y**2 - 67)*(28*y**3 + 9*y**2)
Expanding the part (34*y**2 - 67) using the distributive property, and we got: (34*y**2)*(28*y**3 + 9*y**2) - 67*(28*y**3 + 9*y**2)
<replace-#Step 1>#Step 2:
Current expression: (34*y**2)*(28*y**3 + 9*y**2) - 67*(28*y**3 + 9*y**2)</replace>
Simplifying the partial expression: -67*(28*y**3 + 9*y**2)
Expanding the part (28*y**3 + 9*y**2) using the distributive property, and we got: (9*y**2)*(-67) + (28*y**3)*(-67)
Replacing -67*(28*y**3 + 9*y**2) with (9*y**2)*(-67) + (28*y**3)*(-67) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (9*y**2)*(-67) + (34*y**2)*(28*y**3 + 9*y**2) + (28*y**3)*(-67)</replace>
Simplifying the partial expression: (34*y**2)*(28*y**3 + 9*y**2)
Expanding the part (28*y**3 + 9*y**2) using the distributive property, and we got: (9*y**2)*(34*y**2) + (34*y**2)*(28*y**3)
Replacing (34*y**2)*(28*y**3 + 9*y**2) with (9*y**2)*(34*y**2) + (34*y**2)*(28*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (9*y**2)*(34*y**2) + (9*y**2)*(-67) + (34*y**2)*(28*y**3) + (28*y**3)*(-67)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (9*y**2)*-67 = -603*y**2
  (9*y**2)*(34*y**2) = 306*y**4
  (28*y**3)*-67 = -1876*y**3
  (28*y**3)*(34*y**2) = 952*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 952*y**5 + 306*y**4 - 1876*y**3 - 603*y**2</replace>
No more calculations needed.
<answer>952*y**5 + 306*y**4 - 1876*y**3 - 603*y**2</answer>


Question:
Simplify this expression: (4*z**2 - 4*z)*(-37*z**3 + 11*z - 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: -148*z**5 + 148*z**4 + 44*z**3 - 204*z**2 + 160*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: (4*z**2 - 4*z)*(-37*z**3 + 11*z - 40)
Expanding the part (4*z**2 - 4*z) using the distributive property, and we got: (-4*z)*(-37*z**3 + 11*z - 40) + (4*z**2)*(-37*z**3 + 11*z - 40)
<replace-#Step 1>#Step 2:
Current expression: (-4*z)*(-37*z**3 + 11*z - 40) + (4*z**2)*(-37*z**3 + 11*z - 40)</replace>
Simplifying the partial expression: (-4*z)*(-37*z**3 + 11*z - 40)
Expanding the part (-37*z**3 + 11*z - 40) using the distributive property, and we got: (-4*z)*(11*z) + (-4*z)*(-37*z**3) - (-1)*160*z
Replacing (-4*z)*(-37*z**3 + 11*z - 40) with (-4*z)*(11*z) + (-4*z)*(-37*z**3) - (-1)*160*z in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-4*z)*(11*z) + (-4*z)*(-37*z**3) - 40*(-4)*z + (4*z**2)*(-37*z**3 + 11*z - 40)</replace>
Simplifying the partial expression: (4*z**2)*(-37*z**3 + 11*z - 40)
Expanding the part (-37*z**3 + 11*z - 40) using the distributive property, and we got: -160*z**2 + (11*z)*(4*z**2) + (4*z**2)*(-37*z**3)
Replacing (4*z**2)*(-37*z**3 + 11*z - 40) with -160*z**2 + (11*z)*(4*z**2) + (4*z**2)*(-37*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-4*z)*(11*z) + (-4*z)*(-37*z**3) - 40*4*z**2 - 40*(-4)*z + (11*z)*(4*z**2) + (4*z**2)*(-37*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-37*z**3)*(-4*z) = 148*z**4
  (-37*z**3)*(4*z**2) = -148*z**5
  (11*z)*(-4*z) = -44*z**2
  (11*z)*(4*z**2) = 44*z**3
  -40*-4*z = 160*z
  -40*4*z**2 = -160*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -148*z**5 + 148*z**4 + 44*z**3 - 160*z**2 - 44*z**2 + 160*z</replace>
Combining like terms, got -148*z**5 + 148*z**4 + 44*z**3 - 204*z**2 + 160*z
<replace-#Step 5>#Step 6:
Current expression: -148*z**5 + 148*z**4 + 44*z**3 - 204*z**2 + 160*z</replace>
No more calculations needed.
<answer>-148*z**5 + 148*z**4 + 44*z**3 - 204*z**2 + 160*z</answer>


Question:
Calculate the following: (14 - 15*z**3)*(-38*z**2 + 18*z + 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: 570*z**5 - 270*z**4 - 105*z**3 - 532*z**2 + 252*z + 98

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (14 - 15*z**3)*(-38*z**2 + 18*z + 7)
Expanding the part (14 - 15*z**3) using the distributive property, and we got: (-15*z**3)*(-38*z**2 + 18*z + 7) + 14*(-38*z**2 + 18*z + 7)
<replace-#Step 1>#Step 2:
Current expression: (-15*z**3)*(-38*z**2 + 18*z + 7) + 14*(-38*z**2 + 18*z + 7)</replace>
Simplifying the partial expression: 14*(-38*z**2 + 18*z + 7)
Expanding the part (-38*z**2 + 18*z + 7) using the distributive property, and we got: (18*z)*14 - 38*z**2*14 + 7*14
Replacing 14*(-38*z**2 + 18*z + 7) with (18*z)*14 - 38*z**2*14 + 7*14 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (18*z)*14 - 38*z**2*14 + (-15*z**3)*(-38*z**2 + 18*z + 7) + 98</replace>
Simplifying the partial expression: (-15*z**3)*(-38*z**2 + 18*z + 7)
Expanding the part (-38*z**2 + 18*z + 7) using the distributive property, and we got: 7*(-15*z**3) + (18*z)*(-15*z**3) + (-38*z**2)*(-15*z**3)
Replacing (-15*z**3)*(-38*z**2 + 18*z + 7) with 7*(-15*z**3) + (18*z)*(-15*z**3) + (-38*z**2)*(-15*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 7*(-15)*z**3 + (18*z)*(-15*z**3) + (18*z)*14 + (-38*z**2)*(-15*z**3) - 38*z**2*14 + 98</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-38*z**2)*14 = -532*z**2
  (-38*z**2)*(-15*z**3) = 570*z**5
  (18*z)*14 = 252*z
  (18*z)*(-15*z**3) = -270*z**4
  7*-15*z**3 = -105*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 570*z**5 - 270*z**4 - 105*z**3 - 532*z**2 + 252*z + 98</replace>
No more calculations needed.
<answer>570*z**5 - 270*z**4 - 105*z**3 - 532*z**2 + 252*z + 98</answer>


Question:
Simplify this expression: (-31*x**2 + 13*x)*(43*x**3 + 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: -1333*x**5 + 559*x**4 - 1457*x**2 + 611*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: (-31*x**2 + 13*x)*(43*x**3 + 47)
Expanding the part (43*x**3 + 47) using the distributive property, and we got: (43*x**3)*(-31*x**2 + 13*x) + 47*(-31*x**2 + 13*x)
<replace-#Step 1>#Step 2:
Current expression: (43*x**3)*(-31*x**2 + 13*x) + 47*(-31*x**2 + 13*x)</replace>
Simplifying the partial expression: 47*(-31*x**2 + 13*x)
Expanding the part (-31*x**2 + 13*x) using the distributive property, and we got: (13*x)*47 - 31*x**2*47
Replacing 47*(-31*x**2 + 13*x) with (13*x)*47 - 31*x**2*47 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (13*x)*47 - 31*x**2*47 + (43*x**3)*(-31*x**2 + 13*x)</replace>
Simplifying the partial expression: (43*x**3)*(-31*x**2 + 13*x)
Expanding the part (-31*x**2 + 13*x) using the distributive property, and we got: (13*x)*(43*x**3) + (-31*x**2)*(43*x**3)
Replacing (43*x**3)*(-31*x**2 + 13*x) with (13*x)*(43*x**3) + (-31*x**2)*(43*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (13*x)*(43*x**3) + (13*x)*47 + (-31*x**2)*(43*x**3) - 31*x**2*47</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-31*x**2)*47 = -1457*x**2
  (-31*x**2)*(43*x**3) = -1333*x**5
  (13*x)*47 = 611*x
  (13*x)*(43*x**3) = 559*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1333*x**5 + 559*x**4 - 1457*x**2 + 611*x</replace>
No more calculations needed.
<answer>-1333*x**5 + 559*x**4 - 1457*x**2 + 611*x</answer>


Question:
Calculate the following: (59*x + 11)*(-19*x**3 - 49*x + 29)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1121*x**4 - 209*x**3 - 2891*x**2 + 1172*x + 319

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (59*x + 11)*(-19*x**3 - 49*x + 29)
Expanding the part (59*x + 11) using the distributive property, and we got: (59*x)*(-19*x**3 - 49*x + 29) + 11*(-19*x**3 - 49*x + 29)
<replace-#Step 1>#Step 2:
Current expression: (59*x)*(-19*x**3 - 49*x + 29) + 11*(-19*x**3 - 49*x + 29)</replace>
Simplifying the partial expression: 11*(-19*x**3 - 49*x + 29)
Expanding the part (-19*x**3 - 49*x + 29) using the distributive property, and we got: -49*x*11 - 19*x**3*11 + 29*11
Replacing 11*(-19*x**3 - 49*x + 29) with -49*x*11 - 19*x**3*11 + 29*11 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -49*x*11 + (59*x)*(-19*x**3 - 49*x + 29) - 19*x**3*11 + 319</replace>
Simplifying the partial expression: (59*x)*(-19*x**3 - 49*x + 29)
Expanding the part (-19*x**3 - 49*x + 29) using the distributive property, and we got: (-49*x)*(59*x) + 29*(59*x) + (59*x)*(-19*x**3)
Replacing (59*x)*(-19*x**3 - 49*x + 29) with (-49*x)*(59*x) + 29*(59*x) + (59*x)*(-19*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-49*x)*(59*x) - 49*x*11 + 29*59*x + (59*x)*(-19*x**3) - 19*x**3*11 + 319</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-49*x)*11 = -539*x
  (-49*x)*(59*x) = -2891*x**2
  (-19*x**3)*11 = -209*x**3
  (-19*x**3)*(59*x) = -1121*x**4
  29*59*x = 1711*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1121*x**4 - 209*x**3 - 2891*x**2 - 539*x + 1711*x + 319</replace>
Combining like terms, got -1121*x**4 - 209*x**3 - 2891*x**2 + 1172*x + 319
<replace-#Step 5>#Step 6:
Current expression: -1121*x**4 - 209*x**3 - 2891*x**2 + 1172*x + 319</replace>
No more calculations needed.
<answer>-1121*x**4 - 209*x**3 - 2891*x**2 + 1172*x + 319</answer>


Question:
Calculate the following: 713*y**2 - 124*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: 713*y**2 - 124*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: 713*y**2 - 124*y
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: 713*y**2 - 124*y</replace>
No more calculations needed.
<answer>713*y**2 - 124*y</answer>


Question:
Calculate the following: (-26*y**2 + 21*y)*(18*y**2 - 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: -468*y**4 + 378*y**3 + 832*y**2 - 672*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 + 21*y)*(18*y**2 - 32)
Expanding the part (18*y**2 - 32) using the distributive property, and we got: (18*y**2)*(-26*y**2 + 21*y) - 32*(-26*y**2 + 21*y)
<replace-#Step 1>#Step 2:
Current expression: (18*y**2)*(-26*y**2 + 21*y) - 32*(-26*y**2 + 21*y)</replace>
Simplifying the partial expression: -32*(-26*y**2 + 21*y)
Expanding the part (-26*y**2 + 21*y) using the distributive property, and we got: (21*y)*(-32) - 26*y**2*(-32)
Replacing -32*(-26*y**2 + 21*y) with (21*y)*(-32) - 26*y**2*(-32) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (21*y)*(-32) - 26*y**2*(-32) + (18*y**2)*(-26*y**2 + 21*y)</replace>
Simplifying the partial expression: (18*y**2)*(-26*y**2 + 21*y)
Expanding the part (-26*y**2 + 21*y) using the distributive property, and we got: (21*y)*(18*y**2) + (-26*y**2)*(18*y**2)
Replacing (18*y**2)*(-26*y**2 + 21*y) with (21*y)*(18*y**2) + (-26*y**2)*(18*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (21*y)*(18*y**2) + (21*y)*(-32) + (-26*y**2)*(18*y**2) - 26*y**2*(-32)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-26*y**2)*-32 = 832*y**2
  (-26*y**2)*(18*y**2) = -468*y**4
  (21*y)*-32 = -672*y
  (21*y)*(18*y**2) = 378*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -468*y**4 + 378*y**3 + 832*y**2 - 672*y</replace>
No more calculations needed.
<answer>-468*y**4 + 378*y**3 + 832*y**2 - 672*y</answer>


Question:
Calculate the following: (23*y - 29)*(23*y**3 + 69*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: 529*y**4 + 920*y**3 - 2001*y**2 - 805*y + 1015

Let's solve 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 - 29)*(23*y**3 + 69*y**2 - 35)
Expanding the part (23*y - 29) using the distributive property, and we got: (23*y)*(23*y**3 + 69*y**2 - 35) - 29*(23*y**3 + 69*y**2 - 35)
<replace-#Step 1>#Step 2:
Current expression: (23*y)*(23*y**3 + 69*y**2 - 35) - 29*(23*y**3 + 69*y**2 - 35)</replace>
Simplifying the partial expression: -29*(23*y**3 + 69*y**2 - 35)
Expanding the part (23*y**3 + 69*y**2 - 35) using the distributive property, and we got: (69*y**2)*(-29) + (23*y**3)*(-29) - 35*(-29)
Replacing -29*(23*y**3 + 69*y**2 - 35) with (69*y**2)*(-29) + (23*y**3)*(-29) - 35*(-29) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (23*y)*(23*y**3 + 69*y**2 - 35) + (69*y**2)*(-29) + (23*y**3)*(-29) + 1015</replace>
Simplifying the partial expression: (23*y)*(23*y**3 + 69*y**2 - 35)
Expanding the part (23*y**3 + 69*y**2 - 35) using the distributive property, and we got: -805*y + (23*y)*(69*y**2) + (23*y)*(23*y**3)
Replacing (23*y)*(23*y**3 + 69*y**2 - 35) with -805*y + (23*y)*(69*y**2) + (23*y)*(23*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -35*23*y + (23*y)*(69*y**2) + (23*y)*(23*y**3) + (69*y**2)*(-29) + (23*y**3)*(-29) + 1015</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (23*y**3)*-29 = -667*y**3
  (23*y**3)*(23*y) = 529*y**4
  (69*y**2)*-29 = -2001*y**2
  (69*y**2)*(23*y) = 1587*y**3
  -35*23*y = -805*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 529*y**4 - 667*y**3 + 1587*y**3 - 2001*y**2 - 805*y + 1015</replace>
Combining like terms, got 529*y**4 + 920*y**3 - 2001*y**2 - 805*y + 1015
<replace-#Step 5>#Step 6:
Current expression: 529*y**4 + 920*y**3 - 2001*y**2 - 805*y + 1015</replace>
No more calculations needed.
<answer>529*y**4 + 920*y**3 - 2001*y**2 - 805*y + 1015</answer>


Question:
Simplify this expression: (57*y + 37)*(36*y**3 + 36)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2052*y**4 + 1332*y**3 + 2052*y + 1332

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (57*y + 37)*(36*y**3 + 36)
Expanding the part (36*y**3 + 36) using the distributive property, and we got: (36*y**3)*(57*y + 37) + 36*(57*y + 37)
<replace-#Step 1>#Step 2:
Current expression: (36*y**3)*(57*y + 37) + 36*(57*y + 37)</replace>
Simplifying the partial expression: 36*(57*y + 37)
Expanding the part (57*y + 37) using the distributive property, and we got: (57*y)*36 + 37*36
Replacing 36*(57*y + 37) with (57*y)*36 + 37*36 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (57*y)*36 + (36*y**3)*(57*y + 37) + 1332</replace>
Simplifying the partial expression: (36*y**3)*(57*y + 37)
Expanding the part (57*y + 37) using the distributive property, and we got: 37*(36*y**3) + (57*y)*(36*y**3)
Replacing (36*y**3)*(57*y + 37) with 37*(36*y**3) + (57*y)*(36*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 37*36*y**3 + (57*y)*(36*y**3) + (57*y)*36 + 1332</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (57*y)*36 = 2052*y
  (57*y)*(36*y**3) = 2052*y**4
  37*36*y**3 = 1332*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2052*y**4 + 1332*y**3 + 2052*y + 1332</replace>
No more calculations needed.
<answer>2052*y**4 + 1332*y**3 + 2052*y + 1332</answer>


Question:
Simplify this expression: (33 - 96*y**2)*(-57*y**3 + 13*y**2 - 49)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 5472*y**5 - 1248*y**4 - 1881*y**3 + 5133*y**2 - 1617


Question:
Calculate the following: (-38*z**3 + 17*z**2 + 10*z)*(64*z**3 - 22*z + 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: -2432*z**6 + 1088*z**5 + 1476*z**4 - 1096*z**3 + 103*z**2 + 190*z


Question:
Simplify this expression: (-14*z**2 + 40*z)*(-29*z**3 + 32*z - 10)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 406*z**5 - 1160*z**4 - 448*z**3 + 1420*z**2 - 400*z


Question:
Calculate the following: (14 - 41*y)*(3*y - 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: -123*y**2 + 1846*y - 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: (14 - 41*y)*(3*y - 44)
Expanding the part (3*y - 44) using the distributive property, and we got: (3*y)*(14 - 41*y) - 44*(14 - 41*y)
<replace-#Step 1>#Step 2:
Current expression: (3*y)*(14 - 41*y) - 44*(14 - 41*y)</replace>
Simplifying the partial expression: -44*(14 - 41*y)
Expanding the part (14 - 41*y) using the distributive property, and we got: -41*y*(-44) + 14*(-44)
Replacing -44*(14 - 41*y) with -41*y*(-44) + 14*(-44) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -41*y*(-44) + (3*y)*(14 - 41*y) - 616</replace>
Simplifying the partial expression: (3*y)*(14 - 41*y)
Expanding the part (14 - 41*y) using the distributive property, and we got: (-41*y)*(3*y) + 14*(3*y)
Replacing (3*y)*(14 - 41*y) with (-41*y)*(3*y) + 14*(3*y) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-41*y)*(3*y) - 41*y*(-44) + 14*3*y - 616</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-41*y)*-44 = 1804*y
  (-41*y)*(3*y) = -123*y**2
  14*3*y = 42*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -123*y**2 + 42*y + 1804*y - 616</replace>
Combining like terms, got -123*y**2 + 1846*y - 616
<replace-#Step 5>#Step 6:
Current expression: -123*y**2 + 1846*y - 616</replace>
No more calculations needed.
<answer>-123*y**2 + 1846*y - 616</answer>


Question:
Simplify this expression: (22*x**3 - 30*x**2 - 24)*(19*x**3 - 35*x**2 + 41*x + 24)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 418*x**6 - 1340*x**5 + 1952*x**4 - 1158*x**3 + 120*x**2 - 984*x - 576


Question:
Simplify this expression: (-6*y**2 - 33)*(39*y**3 + 36*y + 19)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -234*y**5 - 1503*y**3 - 114*y**2 - 1188*y - 627

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-6*y**2 - 33)*(39*y**3 + 36*y + 19)
Expanding the part (-6*y**2 - 33) using the distributive property, and we got: (-6*y**2)*(39*y**3 + 36*y + 19) - 33*(39*y**3 + 36*y + 19)
<replace-#Step 1>#Step 2:
Current expression: (-6*y**2)*(39*y**3 + 36*y + 19) - 33*(39*y**3 + 36*y + 19)</replace>
Simplifying the partial expression: -33*(39*y**3 + 36*y + 19)
Expanding the part (39*y**3 + 36*y + 19) using the distributive property, and we got: (36*y)*(-33) + (39*y**3)*(-33) + 19*(-33)
Replacing -33*(39*y**3 + 36*y + 19) with (36*y)*(-33) + (39*y**3)*(-33) + 19*(-33) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (36*y)*(-33) + (-6*y**2)*(39*y**3 + 36*y + 19) + (39*y**3)*(-33) - 627</replace>
Simplifying the partial expression: (-6*y**2)*(39*y**3 + 36*y + 19)
Expanding the part (39*y**3 + 36*y + 19) using the distributive property, and we got: 19*(-6*y**2) + (36*y)*(-6*y**2) + (-6*y**2)*(39*y**3)
Replacing (-6*y**2)*(39*y**3 + 36*y + 19) with 19*(-6*y**2) + (36*y)*(-6*y**2) + (-6*y**2)*(39*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 19*(-6)*y**2 + (36*y)*(-6*y**2) + (36*y)*(-33) + (-6*y**2)*(39*y**3) + (39*y**3)*(-33) - 627</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (36*y)*-33 = -1188*y
  (36*y)*(-6*y**2) = -216*y**3
  (39*y**3)*-33 = -1287*y**3
  (39*y**3)*(-6*y**2) = -234*y**5
  19*-6*y**2 = -114*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -234*y**5 - 1287*y**3 - 216*y**3 - 114*y**2 - 1188*y - 627</replace>
Combining like terms, got -234*y**5 - 1503*y**3 - 114*y**2 - 1188*y - 627
<replace-#Step 5>#Step 6:
Current expression: -234*y**5 - 1503*y**3 - 114*y**2 - 1188*y - 627</replace>
No more calculations needed.
<answer>-234*y**5 - 1503*y**3 - 114*y**2 - 1188*y - 627</answer>


Question:
Simplify this expression: (16*y + 31)*(y**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: 16*y**3 + 31*y**2 - 288*y - 558

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (16*y + 31)*(y**2 - 18)
Expanding the part (y**2 - 18) using the distributive property, and we got: y**2*(16*y + 31) - 18*(16*y + 31)
<replace-#Step 1>#Step 2:
Current expression: y**2*(16*y + 31) - 18*(16*y + 31)</replace>
Simplifying the partial expression: -18*(16*y + 31)
Expanding the part (16*y + 31) using the distributive property, and we got: (16*y)*(-18) + 31*(-18)
Replacing -18*(16*y + 31) with (16*y)*(-18) + 31*(-18) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: y**2*(16*y + 31) + (16*y)*(-18) - 558</replace>
Simplifying the partial expression: y**2*(16*y + 31)
Expanding the part (16*y + 31) using the distributive property, and we got: (16*y)*y**2 + 31*y**2
Replacing y**2*(16*y + 31) with (16*y)*y**2 + 31*y**2 in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (16*y)*y**2 + 31*y**2 + (16*y)*(-18) - 558</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (16*y)*-18 = -288*y
  (16*y)*y**2 = 16*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 16*y**3 + 31*y**2 - 288*y - 558</replace>
No more calculations needed.
<answer>16*y**3 + 31*y**2 - 288*y - 558</answer>


Question:
Simplify this expression: (43 - 35*z**2)*(-25*z - 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: 875*z**3 + 665*z**2 - 1075*z - 817

Let's solve 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 - 35*z**2)*(-25*z - 19)
Expanding the part (-25*z - 19) using the distributive property, and we got: (-25*z)*(43 - 35*z**2) - 19*(43 - 35*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-25*z)*(43 - 35*z**2) - 19*(43 - 35*z**2)</replace>
Simplifying the partial expression: -19*(43 - 35*z**2)
Expanding the part (43 - 35*z**2) using the distributive property, and we got: -35*z**2*(-19) + 43*(-19)
Replacing -19*(43 - 35*z**2) with -35*z**2*(-19) + 43*(-19) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-25*z)*(43 - 35*z**2) - 35*z**2*(-19) - 817</replace>
Simplifying the partial expression: (-25*z)*(43 - 35*z**2)
Expanding the part (43 - 35*z**2) using the distributive property, and we got: (-25*z)*(-35*z**2) + 43*(-25*z)
Replacing (-25*z)*(43 - 35*z**2) with (-25*z)*(-35*z**2) + 43*(-25*z) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-25*z)*(-35*z**2) + 43*(-25)*z - 35*z**2*(-19) - 817</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-35*z**2)*-19 = 665*z**2
  (-35*z**2)*(-25*z) = 875*z**3
  43*-25*z = -1075*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 875*z**3 + 665*z**2 - 1075*z - 817</replace>
No more calculations needed.
<answer>875*z**3 + 665*z**2 - 1075*z - 817</answer>


Question:
Simplify this expression: (37*x**2 - 9)*(39*x**3 + 4*x**2 + 16*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1443*x**5 + 148*x**4 + 241*x**3 - 36*x**2 - 144*x


Question:
Calculate the following: (7*x**2 - 44)*(-37*x**3 + 9*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: -259*x**5 + 63*x**4 + 1628*x**3 - 396*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: (7*x**2 - 44)*(-37*x**3 + 9*x**2)
Expanding the part (7*x**2 - 44) using the distributive property, and we got: (7*x**2)*(-37*x**3 + 9*x**2) - 44*(-37*x**3 + 9*x**2)
<replace-#Step 1>#Step 2:
Current expression: (7*x**2)*(-37*x**3 + 9*x**2) - 44*(-37*x**3 + 9*x**2)</replace>
Simplifying the partial expression: -44*(-37*x**3 + 9*x**2)
Expanding the part (-37*x**3 + 9*x**2) using the distributive property, and we got: (9*x**2)*(-44) - 37*x**3*(-44)
Replacing -44*(-37*x**3 + 9*x**2) with (9*x**2)*(-44) - 37*x**3*(-44) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (7*x**2)*(-37*x**3 + 9*x**2) + (9*x**2)*(-44) - 37*x**3*(-44)</replace>
Simplifying the partial expression: (7*x**2)*(-37*x**3 + 9*x**2)
Expanding the part (-37*x**3 + 9*x**2) using the distributive property, and we got: (7*x**2)*(9*x**2) + (7*x**2)*(-37*x**3)
Replacing (7*x**2)*(-37*x**3 + 9*x**2) with (7*x**2)*(9*x**2) + (7*x**2)*(-37*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (7*x**2)*(9*x**2) + (7*x**2)*(-37*x**3) + (9*x**2)*(-44) - 37*x**3*(-44)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-37*x**3)*-44 = 1628*x**3
  (-37*x**3)*(7*x**2) = -259*x**5
  (9*x**2)*-44 = -396*x**2
  (9*x**2)*(7*x**2) = 63*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -259*x**5 + 63*x**4 + 1628*x**3 - 396*x**2</replace>
No more calculations needed.
<answer>-259*x**5 + 63*x**4 + 1628*x**3 - 396*x**2</answer>


Question:
Simplify this expression: -47*y*(-17*y**2 - 6*y - 16)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 799*y**3 + 282*y**2 + 752*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: -47*y*(-17*y**2 - 6*y - 16)
Expanding the part (-17*y**2 - 6*y - 16) using the distributive property, and we got: (-47*y)*(-6*y) + (-47*y)*(-17*y**2) - (-1)*752*y
<replace-#Step 1>#Step 2:
Current expression: (-47*y)*(-6*y) + (-47*y)*(-17*y**2) - (-1)*752*y</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -16*(-47*y) = 752*y
  (-17*y**2)*(-47*y) = 799*y**3
  (-6*y)*(-47*y) = 282*y**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 799*y**3 + 282*y**2 + 752*y</replace>
No more calculations needed.
<answer>799*y**3 + 282*y**2 + 752*y</answer>


Question:
Calculate the following: (10*y + 50)*(15*y**3 + 22*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: 150*y**4 + 750*y**3 + 220*y**2 + 1480*y + 1900

Let's solve 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 + 50)*(15*y**3 + 22*y + 38)
Expanding the part (10*y + 50) using the distributive property, and we got: (10*y)*(15*y**3 + 22*y + 38) + 50*(15*y**3 + 22*y + 38)
<replace-#Step 1>#Step 2:
Current expression: (10*y)*(15*y**3 + 22*y + 38) + 50*(15*y**3 + 22*y + 38)</replace>
Simplifying the partial expression: 50*(15*y**3 + 22*y + 38)
Expanding the part (15*y**3 + 22*y + 38) using the distributive property, and we got: (22*y)*50 + (15*y**3)*50 + 38*50
Replacing 50*(15*y**3 + 22*y + 38) with (22*y)*50 + (15*y**3)*50 + 38*50 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (10*y)*(15*y**3 + 22*y + 38) + (22*y)*50 + (15*y**3)*50 + 1900</replace>
Simplifying the partial expression: (10*y)*(15*y**3 + 22*y + 38)
Expanding the part (15*y**3 + 22*y + 38) using the distributive property, and we got: 38*(10*y) + (10*y)*(22*y) + (10*y)*(15*y**3)
Replacing (10*y)*(15*y**3 + 22*y + 38) with 38*(10*y) + (10*y)*(22*y) + (10*y)*(15*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 38*10*y + (10*y)*(22*y) + (10*y)*(15*y**3) + (22*y)*50 + (15*y**3)*50 + 1900</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (15*y**3)*50 = 750*y**3
  (15*y**3)*(10*y) = 150*y**4
  (22*y)*50 = 1100*y
  (22*y)*(10*y) = 220*y**2
  38*10*y = 380*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 150*y**4 + 750*y**3 + 220*y**2 + 380*y + 1100*y + 1900</replace>
Combining like terms, got 150*y**4 + 750*y**3 + 220*y**2 + 1480*y + 1900
<replace-#Step 5>#Step 6:
Current expression: 150*y**4 + 750*y**3 + 220*y**2 + 1480*y + 1900</replace>
No more calculations needed.
<answer>150*y**4 + 750*y**3 + 220*y**2 + 1480*y + 1900</answer>


Question:
Simplify this expression: (51*z - 16)*(-48*z**3 + 30*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: -2448*z**4 + 2298*z**3 - 480*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: (51*z - 16)*(-48*z**3 + 30*z**2)
Expanding the part (51*z - 16) using the distributive property, and we got: (51*z)*(-48*z**3 + 30*z**2) - 16*(-48*z**3 + 30*z**2)
<replace-#Step 1>#Step 2:
Current expression: (51*z)*(-48*z**3 + 30*z**2) - 16*(-48*z**3 + 30*z**2)</replace>
Simplifying the partial expression: -16*(-48*z**3 + 30*z**2)
Expanding the part (-48*z**3 + 30*z**2) using the distributive property, and we got: (30*z**2)*(-16) - 48*z**3*(-16)
Replacing -16*(-48*z**3 + 30*z**2) with (30*z**2)*(-16) - 48*z**3*(-16) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (51*z)*(-48*z**3 + 30*z**2) + (30*z**2)*(-16) - 48*z**3*(-16)</replace>
Simplifying the partial expression: (51*z)*(-48*z**3 + 30*z**2)
Expanding the part (-48*z**3 + 30*z**2) using the distributive property, and we got: (51*z)*(30*z**2) + (51*z)*(-48*z**3)
Replacing (51*z)*(-48*z**3 + 30*z**2) with (51*z)*(30*z**2) + (51*z)*(-48*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (51*z)*(30*z**2) + (51*z)*(-48*z**3) + (30*z**2)*(-16) - 48*z**3*(-16)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-48*z**3)*-16 = 768*z**3
  (-48*z**3)*(51*z) = -2448*z**4
  (30*z**2)*-16 = -480*z**2
  (30*z**2)*(51*z) = 1530*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2448*z**4 + 768*z**3 + 1530*z**3 - 480*z**2</replace>
Combining like terms, got -2448*z**4 + 2298*z**3 - 480*z**2
<replace-#Step 5>#Step 6:
Current expression: -2448*z**4 + 2298*z**3 - 480*z**2</replace>
No more calculations needed.
<answer>-2448*z**4 + 2298*z**3 - 480*z**2</answer>


Question:
Calculate the following: (11 - 2*z**2)*(68*z**3 - 24*z**2 - 13)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -136*z**5 + 48*z**4 + 748*z**3 - 238*z**2 - 143

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (11 - 2*z**2)*(68*z**3 - 24*z**2 - 13)
Expanding the part (11 - 2*z**2) using the distributive property, and we got: (-2*z**2)*(68*z**3 - 24*z**2 - 13) + 11*(68*z**3 - 24*z**2 - 13)
<replace-#Step 1>#Step 2:
Current expression: (-2*z**2)*(68*z**3 - 24*z**2 - 13) + 11*(68*z**3 - 24*z**2 - 13)</replace>
Simplifying the partial expression: 11*(68*z**3 - 24*z**2 - 13)
Expanding the part (68*z**3 - 24*z**2 - 13) using the distributive property, and we got: -24*z**2*11 + (68*z**3)*11 - 13*11
Replacing 11*(68*z**3 - 24*z**2 - 13) with -24*z**2*11 + (68*z**3)*11 - 13*11 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -24*z**2*11 + (-2*z**2)*(68*z**3 - 24*z**2 - 13) + (68*z**3)*11 - 143</replace>
Simplifying the partial expression: (-2*z**2)*(68*z**3 - 24*z**2 - 13)
Expanding the part (68*z**3 - 24*z**2 - 13) using the distributive property, and we got: -(-1)*26*z**2 + (-24*z**2)*(-2*z**2) + (-2*z**2)*(68*z**3)
Replacing (-2*z**2)*(68*z**3 - 24*z**2 - 13) with -(-1)*26*z**2 + (-24*z**2)*(-2*z**2) + (-2*z**2)*(68*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -13*(-2)*z**2 + (-24*z**2)*(-2*z**2) - 24*z**2*11 + (-2*z**2)*(68*z**3) + (68*z**3)*11 - 143</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-24*z**2)*11 = -264*z**2
  (-24*z**2)*(-2*z**2) = 48*z**4
  (68*z**3)*11 = 748*z**3
  (68*z**3)*(-2*z**2) = -136*z**5
  -13*-2*z**2 = 26*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -136*z**5 + 48*z**4 + 748*z**3 - 264*z**2 + 26*z**2 - 143</replace>
Combining like terms, got -136*z**5 + 48*z**4 + 748*z**3 - 238*z**2 - 143
<replace-#Step 5>#Step 6:
Current expression: -136*z**5 + 48*z**4 + 748*z**3 - 238*z**2 - 143</replace>
No more calculations needed.
<answer>-136*z**5 + 48*z**4 + 748*z**3 - 238*z**2 - 143</answer>


Question:
Calculate the following: 217*y - 196
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 217*y - 196

Let's solve 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: 217*y - 196
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: 217*y - 196</replace>
No more calculations needed.
<answer>217*y - 196</answer>


Question:
Calculate the following: (20*x + 48)*(-39*x**3 - x**2 + 9*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: -780*x**4 - 1892*x**3 + 132*x**2 + 432*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (20*x + 48)*(-39*x**3 - x**2 + 9*x)
Expanding the part (20*x + 48) using the distributive property, and we got: (20*x)*(-39*x**3 - x**2 + 9*x) + 48*(-39*x**3 - x**2 + 9*x)
<replace-#Step 1>#Step 2:
Current expression: (20*x)*(-39*x**3 - x**2 + 9*x) + 48*(-39*x**3 - x**2 + 9*x)</replace>
Simplifying the partial expression: 48*(-39*x**3 - x**2 + 9*x)
Expanding the part (-39*x**3 - x**2 + 9*x) using the distributive property, and we got: (9*x)*48 - x**2*48 - 39*x**3*48
Replacing 48*(-39*x**3 - x**2 + 9*x) with (9*x)*48 - x**2*48 - 39*x**3*48 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (9*x)*48 + (20*x)*(-39*x**3 - x**2 + 9*x) - x**2*48 - 39*x**3*48</replace>
Simplifying the partial expression: (20*x)*(-39*x**3 - x**2 + 9*x)
Expanding the part (-39*x**3 - x**2 + 9*x) using the distributive property, and we got: (9*x)*(20*x) + (20*x)*(-x**2) + (20*x)*(-39*x**3)
Replacing (20*x)*(-39*x**3 - x**2 + 9*x) with (9*x)*(20*x) + (20*x)*(-x**2) + (20*x)*(-39*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (9*x)*(20*x) + (9*x)*48 + (20*x)*(-x**2) + (20*x)*(-39*x**3) - x**2*48 - 39*x**3*48</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-x**2)*48 = -48*x**2
  (-x**2)*(20*x) = -20*x**3
  (-39*x**3)*48 = -1872*x**3
  (-39*x**3)*(20*x) = -780*x**4
  (9*x)*48 = 432*x
  (9*x)*(20*x) = 180*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -780*x**4 - 1872*x**3 - 20*x**3 - 48*x**2 + 180*x**2 + 432*x</replace>
Combining like terms, got -780*x**4 - 1892*x**3 + 132*x**2 + 432*x
<replace-#Step 5>#Step 6:
Current expression: -780*x**4 - 1892*x**3 + 132*x**2 + 432*x</replace>
No more calculations needed.
<answer>-780*x**4 - 1892*x**3 + 132*x**2 + 432*x</answer>


Question:
Calculate the following: 24*x*(34 - 36*x**3)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -864*x**4 + 816*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: 24*x*(34 - 36*x**3)
Expanding the part (34 - 36*x**3) using the distributive property, and we got: 34*(24*x) + (24*x)*(-36*x**3)
<replace-#Step 1>#Step 2:
Current expression: 34*(24*x) + (24*x)*(-36*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  34*(24*x) = 816*x
  (-36*x**3)*(24*x) = -864*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -864*x**4 + 816*x</replace>
No more calculations needed.
<answer>-864*x**4 + 816*x</answer>


Question:
Calculate the following: -1620*z**3 + 2220*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: -1620*z**3 + 2220*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: -1620*z**3 + 2220*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: -1620*z**3 + 2220*z</replace>
No more calculations needed.
<answer>-1620*z**3 + 2220*z</answer>


Question:
Simplify this expression: 36*x**2*(-7*x**2 + 21*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: -252*x**4 + 756*x**3 + 180*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: 36*x**2*(-7*x**2 + 21*x + 5)
Expanding the part (-7*x**2 + 21*x + 5) using the distributive property, and we got: 5*(36*x**2) + (21*x)*(36*x**2) + (-7*x**2)*(36*x**2)
<replace-#Step 1>#Step 2:
Current expression: 5*(36*x**2) + (21*x)*(36*x**2) + (-7*x**2)*(36*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  5*(36*x**2) = 180*x**2
  (-7*x**2)*(36*x**2) = -252*x**4
  (21*x)*(36*x**2) = 756*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -252*x**4 + 756*x**3 + 180*x**2</replace>
No more calculations needed.
<answer>-252*x**4 + 756*x**3 + 180*x**2</answer>


Question:
Simplify this expression: 35*x**2*(-47*x**2 - 42)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1645*x**4 - 1470*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: 35*x**2*(-47*x**2 - 42)
Expanding the part (-47*x**2 - 42) using the distributive property, and we got: -1470*x**2 + (-47*x**2)*(35*x**2)
<replace-#Step 1>#Step 2:
Current expression: -1470*x**2 + (-47*x**2)*(35*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -42*(35*x**2) = -1470*x**2
  (-47*x**2)*(35*x**2) = -1645*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1645*x**4 - 1470*x**2</replace>
No more calculations needed.
<answer>-1645*x**4 - 1470*x**2</answer>


Question:
Calculate the following: (31*y**2 - 44)*(41*y**3 - 23*y**2 + 20)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1271*y**5 - 713*y**4 - 1804*y**3 + 1632*y**2 - 880

Let's solve 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 - 44)*(41*y**3 - 23*y**2 + 20)
Expanding the part (31*y**2 - 44) using the distributive property, and we got: (31*y**2)*(41*y**3 - 23*y**2 + 20) - 44*(41*y**3 - 23*y**2 + 20)
<replace-#Step 1>#Step 2:
Current expression: (31*y**2)*(41*y**3 - 23*y**2 + 20) - 44*(41*y**3 - 23*y**2 + 20)</replace>
Simplifying the partial expression: -44*(41*y**3 - 23*y**2 + 20)
Expanding the part (41*y**3 - 23*y**2 + 20) using the distributive property, and we got: -23*y**2*(-44) + (41*y**3)*(-44) + 20*(-44)
Replacing -44*(41*y**3 - 23*y**2 + 20) with -23*y**2*(-44) + (41*y**3)*(-44) + 20*(-44) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -23*y**2*(-44) + (31*y**2)*(41*y**3 - 23*y**2 + 20) + (41*y**3)*(-44) - 880</replace>
Simplifying the partial expression: (31*y**2)*(41*y**3 - 23*y**2 + 20)
Expanding the part (41*y**3 - 23*y**2 + 20) using the distributive property, and we got: 20*(31*y**2) + (-23*y**2)*(31*y**2) + (31*y**2)*(41*y**3)
Replacing (31*y**2)*(41*y**3 - 23*y**2 + 20) with 20*(31*y**2) + (-23*y**2)*(31*y**2) + (31*y**2)*(41*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 20*31*y**2 + (-23*y**2)*(31*y**2) - 23*y**2*(-44) + (31*y**2)*(41*y**3) + (41*y**3)*(-44) - 880</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-23*y**2)*-44 = 1012*y**2
  (-23*y**2)*(31*y**2) = -713*y**4
  (41*y**3)*-44 = -1804*y**3
  (41*y**3)*(31*y**2) = 1271*y**5
  20*31*y**2 = 620*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1271*y**5 - 713*y**4 - 1804*y**3 + 620*y**2 + 1012*y**2 - 880</replace>
Combining like terms, got 1271*y**5 - 713*y**4 - 1804*y**3 + 1632*y**2 - 880
<replace-#Step 5>#Step 6:
Current expression: 1271*y**5 - 713*y**4 - 1804*y**3 + 1632*y**2 - 880</replace>
No more calculations needed.
<answer>1271*y**5 - 713*y**4 - 1804*y**3 + 1632*y**2 - 880</answer>


Question:
Simplify this expression: (-42*y**2 + 45*y)*(11*y**2 + 33*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -462*y**4 - 891*y**3 + 1485*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: (-42*y**2 + 45*y)*(11*y**2 + 33*y)
Expanding the part (-42*y**2 + 45*y) using the distributive property, and we got: (45*y)*(11*y**2 + 33*y) + (-42*y**2)*(11*y**2 + 33*y)
<replace-#Step 1>#Step 2:
Current expression: (45*y)*(11*y**2 + 33*y) + (-42*y**2)*(11*y**2 + 33*y)</replace>
Simplifying the partial expression: (-42*y**2)*(11*y**2 + 33*y)
Expanding the part (11*y**2 + 33*y) using the distributive property, and we got: (33*y)*(-42*y**2) + (-42*y**2)*(11*y**2)
Replacing (-42*y**2)*(11*y**2 + 33*y) with (33*y)*(-42*y**2) + (-42*y**2)*(11*y**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (33*y)*(-42*y**2) + (45*y)*(11*y**2 + 33*y) + (-42*y**2)*(11*y**2)</replace>
Simplifying the partial expression: (45*y)*(11*y**2 + 33*y)
Expanding the part (11*y**2 + 33*y) using the distributive property, and we got: (33*y)*(45*y) + (45*y)*(11*y**2)
Replacing (45*y)*(11*y**2 + 33*y) with (33*y)*(45*y) + (45*y)*(11*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (33*y)*(45*y) + (33*y)*(-42*y**2) + (45*y)*(11*y**2) + (-42*y**2)*(11*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (11*y**2)*(-42*y**2) = -462*y**4
  (11*y**2)*(45*y) = 495*y**3
  (33*y)*(-42*y**2) = -1386*y**3
  (33*y)*(45*y) = 1485*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -462*y**4 - 1386*y**3 + 495*y**3 + 1485*y**2</replace>
Combining like terms, got -462*y**4 - 891*y**3 + 1485*y**2
<replace-#Step 5>#Step 6:
Current expression: -462*y**4 - 891*y**3 + 1485*y**2</replace>
No more calculations needed.
<answer>-462*y**4 - 891*y**3 + 1485*y**2</answer>


Question:
Simplify this expression: (10*x**3 + 34*x**2 - 16)*(31*x**3 - 47*x**2 + 6)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 310*x**6 + 584*x**5 - 1598*x**4 - 436*x**3 + 956*x**2 - 96


Question:
Simplify this expression: 32*x**2*(-2*x**2 + 27*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: -64*x**4 + 864*x**3 - 1600*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: 32*x**2*(-2*x**2 + 27*x - 50)
Expanding the part (-2*x**2 + 27*x - 50) using the distributive property, and we got: -1600*x**2 + (27*x)*(32*x**2) + (-2*x**2)*(32*x**2)
<replace-#Step 1>#Step 2:
Current expression: -1600*x**2 + (27*x)*(32*x**2) + (-2*x**2)*(32*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -50*(32*x**2) = -1600*x**2
  (-2*x**2)*(32*x**2) = -64*x**4
  (27*x)*(32*x**2) = 864*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -64*x**4 + 864*x**3 - 1600*x**2</replace>
No more calculations needed.
<answer>-64*x**4 + 864*x**3 - 1600*x**2</answer>


Question:
Simplify this expression: (-56*x**2 + 42*x - 50)*(13*x**3 - 19*x**2 + 22)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -728*x**5 + 1610*x**4 - 1448*x**3 - 282*x**2 + 924*x - 1100


Question:
Simplify this expression: (-y**2 - 49*y)*(-25*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: 25*y**5 + 1225*y**4 + 39*y**2 + 1911*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-y**2 - 49*y)*(-25*y**3 - 39)
Expanding the part (-25*y**3 - 39) using the distributive property, and we got: (-25*y**3)*(-y**2 - 49*y) - 39*(-y**2 - 49*y)
<replace-#Step 1>#Step 2:
Current expression: (-25*y**3)*(-y**2 - 49*y) - 39*(-y**2 - 49*y)</replace>
Simplifying the partial expression: -39*(-y**2 - 49*y)
Expanding the part (-y**2 - 49*y) using the distributive property, and we got: -49*y*(-39) - y**2*(-39)
Replacing -39*(-y**2 - 49*y) with -49*y*(-39) - y**2*(-39) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -49*y*(-39) - y**2*(-39) + (-25*y**3)*(-y**2 - 49*y)</replace>
Simplifying the partial expression: (-25*y**3)*(-y**2 - 49*y)
Expanding the part (-y**2 - 49*y) using the distributive property, and we got: (-49*y)*(-25*y**3) + (-y**2)*(-25*y**3)
Replacing (-25*y**3)*(-y**2 - 49*y) with (-49*y)*(-25*y**3) + (-y**2)*(-25*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-49*y)*(-25*y**3) - 49*y*(-39) + (-y**2)*(-25*y**3) - y**2*(-39)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-y**2)*-39 = 39*y**2
  (-y**2)*(-25*y**3) = 25*y**5
  (-49*y)*-39 = 1911*y
  (-49*y)*(-25*y**3) = 1225*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 25*y**5 + 1225*y**4 + 39*y**2 + 1911*y</replace>
No more calculations needed.
<answer>25*y**5 + 1225*y**4 + 39*y**2 + 1911*y</answer>


Question:
Simplify this expression: (49 - 43*x)*(46*x**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: -1978*x**3 + 2254*x**2 + 1849*x - 2107

Let's solve 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 - 43*x)*(46*x**2 - 43)
Expanding the part (46*x**2 - 43) using the distributive property, and we got: (46*x**2)*(49 - 43*x) - 43*(49 - 43*x)
<replace-#Step 1>#Step 2:
Current expression: (46*x**2)*(49 - 43*x) - 43*(49 - 43*x)</replace>
Simplifying the partial expression: -43*(49 - 43*x)
Expanding the part (49 - 43*x) using the distributive property, and we got: -43*x*(-43) + 49*(-43)
Replacing -43*(49 - 43*x) with -43*x*(-43) + 49*(-43) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -43*x*(-43) + (46*x**2)*(49 - 43*x) - 2107</replace>
Simplifying the partial expression: (46*x**2)*(49 - 43*x)
Expanding the part (49 - 43*x) using the distributive property, and we got: (-43*x)*(46*x**2) + 49*(46*x**2)
Replacing (46*x**2)*(49 - 43*x) with (-43*x)*(46*x**2) + 49*(46*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-43*x)*(46*x**2) - 43*x*(-43) + 49*46*x**2 - 2107</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-43*x)*-43 = 1849*x
  (-43*x)*(46*x**2) = -1978*x**3
  49*46*x**2 = 2254*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1978*x**3 + 2254*x**2 + 1849*x - 2107</replace>
No more calculations needed.
<answer>-1978*x**3 + 2254*x**2 + 1849*x - 2107</answer>