Question:
Simplify this expression: (93*y**3 - 27*y)*(14*y**2 - 3*y + 31)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1302*y**5 - 279*y**4 + 2505*y**3 + 81*y**2 - 837*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: (93*y**3 - 27*y)*(14*y**2 - 3*y + 31)
Expanding the part (93*y**3 - 27*y) using the distributive property, and we got: (-27*y)*(14*y**2 - 3*y + 31) + (93*y**3)*(14*y**2 - 3*y + 31)
<replace-#Step 1>#Step 2:
Current expression: (-27*y)*(14*y**2 - 3*y + 31) + (93*y**3)*(14*y**2 - 3*y + 31)</replace>
Simplifying the partial expression: (-27*y)*(14*y**2 - 3*y + 31)
Expanding the part (14*y**2 - 3*y + 31) using the distributive property, and we got: (-27*y)*(-3*y) + (-27*y)*(14*y**2) + 31*(-27*y)
Replacing (-27*y)*(14*y**2 - 3*y + 31) with (-27*y)*(-3*y) + (-27*y)*(14*y**2) + 31*(-27*y) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-27*y)*(-3*y) + (-27*y)*(14*y**2) + 31*(-27)*y + (93*y**3)*(14*y**2 - 3*y + 31)</replace>
Simplifying the partial expression: (93*y**3)*(14*y**2 - 3*y + 31)
Expanding the part (14*y**2 - 3*y + 31) using the distributive property, and we got: (-3*y)*(93*y**3) + 31*(93*y**3) + (14*y**2)*(93*y**3)
Replacing (93*y**3)*(14*y**2 - 3*y + 31) with (-3*y)*(93*y**3) + 31*(93*y**3) + (14*y**2)*(93*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-27*y)*(-3*y) + (-27*y)*(14*y**2) + (-3*y)*(93*y**3) + 31*93*y**3 + 31*(-27)*y + (14*y**2)*(93*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-3*y)*(-27*y) = 81*y**2
  (-3*y)*(93*y**3) = -279*y**4
  (14*y**2)*(-27*y) = -378*y**3
  (14*y**2)*(93*y**3) = 1302*y**5
  31*-27*y = -837*y
  31*93*y**3 = 2883*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1302*y**5 - 279*y**4 - 378*y**3 + 2883*y**3 + 81*y**2 - 837*y</replace>
Combining like terms, got 1302*y**5 - 279*y**4 + 2505*y**3 + 81*y**2 - 837*y
<replace-#Step 5>#Step 6:
Current expression: 1302*y**5 - 279*y**4 + 2505*y**3 + 81*y**2 - 837*y</replace>
No more calculations needed.
<answer>1302*y**5 - 279*y**4 + 2505*y**3 + 81*y**2 - 837*y</answer>


Question:
Simplify this expression: (-27*z**2 - 28)*(-7*z**3 + 29*z**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 189*z**5 - 783*z**4 + 196*z**3 - 812*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: (-27*z**2 - 28)*(-7*z**3 + 29*z**2)
Expanding the part (-27*z**2 - 28) using the distributive property, and we got: (-27*z**2)*(-7*z**3 + 29*z**2) - 28*(-7*z**3 + 29*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-27*z**2)*(-7*z**3 + 29*z**2) - 28*(-7*z**3 + 29*z**2)</replace>
Simplifying the partial expression: -28*(-7*z**3 + 29*z**2)
Expanding the part (-7*z**3 + 29*z**2) using the distributive property, and we got: (29*z**2)*(-28) - 7*z**3*(-28)
Replacing -28*(-7*z**3 + 29*z**2) with (29*z**2)*(-28) - 7*z**3*(-28) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-27*z**2)*(-7*z**3 + 29*z**2) + (29*z**2)*(-28) - 7*z**3*(-28)</replace>
Simplifying the partial expression: (-27*z**2)*(-7*z**3 + 29*z**2)
Expanding the part (-7*z**3 + 29*z**2) using the distributive property, and we got: (-27*z**2)*(29*z**2) + (-27*z**2)*(-7*z**3)
Replacing (-27*z**2)*(-7*z**3 + 29*z**2) with (-27*z**2)*(29*z**2) + (-27*z**2)*(-7*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-27*z**2)*(29*z**2) + (-27*z**2)*(-7*z**3) + (29*z**2)*(-28) - 7*z**3*(-28)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-7*z**3)*-28 = 196*z**3
  (-7*z**3)*(-27*z**2) = 189*z**5
  (29*z**2)*-28 = -812*z**2
  (29*z**2)*(-27*z**2) = -783*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 189*z**5 - 783*z**4 + 196*z**3 - 812*z**2</replace>
No more calculations needed.
<answer>189*z**5 - 783*z**4 + 196*z**3 - 812*z**2</answer>


Question:
Calculate the following: (2*y**2 - 9*y)*(-6*y**2 - 42*y + 18)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -12*y**4 - 30*y**3 + 414*y**2 - 162*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: (2*y**2 - 9*y)*(-6*y**2 - 42*y + 18)
Expanding the part (2*y**2 - 9*y) using the distributive property, and we got: (-9*y)*(-6*y**2 - 42*y + 18) + (2*y**2)*(-6*y**2 - 42*y + 18)
<replace-#Step 1>#Step 2:
Current expression: (-9*y)*(-6*y**2 - 42*y + 18) + (2*y**2)*(-6*y**2 - 42*y + 18)</replace>
Simplifying the partial expression: (-9*y)*(-6*y**2 - 42*y + 18)
Expanding the part (-6*y**2 - 42*y + 18) using the distributive property, and we got: (-42*y)*(-9*y) + (-9*y)*(-6*y**2) + 18*(-9*y)
Replacing (-9*y)*(-6*y**2 - 42*y + 18) with (-42*y)*(-9*y) + (-9*y)*(-6*y**2) + 18*(-9*y) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-42*y)*(-9*y) + (-9*y)*(-6*y**2) + 18*(-9)*y + (2*y**2)*(-6*y**2 - 42*y + 18)</replace>
Simplifying the partial expression: (2*y**2)*(-6*y**2 - 42*y + 18)
Expanding the part (-6*y**2 - 42*y + 18) using the distributive property, and we got: (-42*y)*(2*y**2) + 18*(2*y**2) + (-6*y**2)*(2*y**2)
Replacing (2*y**2)*(-6*y**2 - 42*y + 18) with (-42*y)*(2*y**2) + 18*(2*y**2) + (-6*y**2)*(2*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-42*y)*(-9*y) + (-42*y)*(2*y**2) + (-9*y)*(-6*y**2) + 18*2*y**2 + 18*(-9)*y + (-6*y**2)*(2*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-42*y)*(-9*y) = 378*y**2
  (-42*y)*(2*y**2) = -84*y**3
  (-6*y**2)*(-9*y) = 54*y**3
  (-6*y**2)*(2*y**2) = -12*y**4
  18*-9*y = -162*y
  18*2*y**2 = 36*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -12*y**4 - 84*y**3 + 54*y**3 + 36*y**2 + 378*y**2 - 162*y</replace>
Combining like terms, got -12*y**4 - 30*y**3 + 414*y**2 - 162*y
<replace-#Step 5>#Step 6:
Current expression: -12*y**4 - 30*y**3 + 414*y**2 - 162*y</replace>
No more calculations needed.
<answer>-12*y**4 - 30*y**3 + 414*y**2 - 162*y</answer>


Question:
Calculate the following: (-15*y**3 - 8*y**2)*(44*y**3 + 48*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -660*y**6 - 1072*y**5 - 384*y**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-15*y**3 - 8*y**2)*(44*y**3 + 48*y**2)
Expanding the part (-15*y**3 - 8*y**2) using the distributive property, and we got: (-8*y**2)*(44*y**3 + 48*y**2) + (-15*y**3)*(44*y**3 + 48*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-8*y**2)*(44*y**3 + 48*y**2) + (-15*y**3)*(44*y**3 + 48*y**2)</replace>
Simplifying the partial expression: (-15*y**3)*(44*y**3 + 48*y**2)
Expanding the part (44*y**3 + 48*y**2) using the distributive property, and we got: (48*y**2)*(-15*y**3) + (-15*y**3)*(44*y**3)
Replacing (-15*y**3)*(44*y**3 + 48*y**2) with (48*y**2)*(-15*y**3) + (-15*y**3)*(44*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-8*y**2)*(44*y**3 + 48*y**2) + (48*y**2)*(-15*y**3) + (-15*y**3)*(44*y**3)</replace>
Simplifying the partial expression: (-8*y**2)*(44*y**3 + 48*y**2)
Expanding the part (44*y**3 + 48*y**2) using the distributive property, and we got: (-8*y**2)*(48*y**2) + (-8*y**2)*(44*y**3)
Replacing (-8*y**2)*(44*y**3 + 48*y**2) with (-8*y**2)*(48*y**2) + (-8*y**2)*(44*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-8*y**2)*(48*y**2) + (-8*y**2)*(44*y**3) + (48*y**2)*(-15*y**3) + (-15*y**3)*(44*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (44*y**3)*(-15*y**3) = -660*y**6
  (44*y**3)*(-8*y**2) = -352*y**5
  (48*y**2)*(-15*y**3) = -720*y**5
  (48*y**2)*(-8*y**2) = -384*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -660*y**6 - 720*y**5 - 352*y**5 - 384*y**4</replace>
Combining like terms, got -660*y**6 - 1072*y**5 - 384*y**4
<replace-#Step 5>#Step 6:
Current expression: -660*y**6 - 1072*y**5 - 384*y**4</replace>
No more calculations needed.
<answer>-660*y**6 - 1072*y**5 - 384*y**4</answer>


Question:
Simplify this expression: (-10*x**3 - 86*x)*(-8*x**2 + 47*x - 4)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 80*x**5 - 470*x**4 + 728*x**3 - 4042*x**2 + 344*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: (-10*x**3 - 86*x)*(-8*x**2 + 47*x - 4)
Expanding the part (-10*x**3 - 86*x) using the distributive property, and we got: (-86*x)*(-8*x**2 + 47*x - 4) + (-10*x**3)*(-8*x**2 + 47*x - 4)
<replace-#Step 1>#Step 2:
Current expression: (-86*x)*(-8*x**2 + 47*x - 4) + (-10*x**3)*(-8*x**2 + 47*x - 4)</replace>
Simplifying the partial expression: (-86*x)*(-8*x**2 + 47*x - 4)
Expanding the part (-8*x**2 + 47*x - 4) using the distributive property, and we got: (-86*x)*(47*x) + (-86*x)*(-8*x**2) - (-1)*344*x
Replacing (-86*x)*(-8*x**2 + 47*x - 4) with (-86*x)*(47*x) + (-86*x)*(-8*x**2) - (-1)*344*x in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-86*x)*(47*x) + (-86*x)*(-8*x**2) - 4*(-86)*x + (-10*x**3)*(-8*x**2 + 47*x - 4)</replace>
Simplifying the partial expression: (-10*x**3)*(-8*x**2 + 47*x - 4)
Expanding the part (-8*x**2 + 47*x - 4) using the distributive property, and we got: -(-1)*40*x**3 + (47*x)*(-10*x**3) + (-8*x**2)*(-10*x**3)
Replacing (-10*x**3)*(-8*x**2 + 47*x - 4) with -(-1)*40*x**3 + (47*x)*(-10*x**3) + (-8*x**2)*(-10*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-86*x)*(47*x) + (-86*x)*(-8*x**2) - 4*(-10)*x**3 - 4*(-86)*x + (47*x)*(-10*x**3) + (-8*x**2)*(-10*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-8*x**2)*(-86*x) = 688*x**3
  (-8*x**2)*(-10*x**3) = 80*x**5
  (47*x)*(-86*x) = -4042*x**2
  (47*x)*(-10*x**3) = -470*x**4
  -4*-86*x = 344*x
  -4*-10*x**3 = 40*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 80*x**5 - 470*x**4 + 40*x**3 + 688*x**3 - 4042*x**2 + 344*x</replace>
Combining like terms, got 80*x**5 - 470*x**4 + 728*x**3 - 4042*x**2 + 344*x
<replace-#Step 5>#Step 6:
Current expression: 80*x**5 - 470*x**4 + 728*x**3 - 4042*x**2 + 344*x</replace>
No more calculations needed.
<answer>80*x**5 - 470*x**4 + 728*x**3 - 4042*x**2 + 344*x</answer>


Question:
Calculate the following: (-16*z**3 + 9*z)*(7*z**3 - 46*z**2 + 36*z + 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: -112*z**6 + 736*z**5 - 513*z**4 - 1022*z**3 + 324*z**2 + 342*z


Question:
Simplify this expression: (16 - 71*x**3)*(78 - 10*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: 710*x**6 - 5698*x**3 + 1248

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 - 71*x**3)*(78 - 10*x**3)
Expanding the part (16 - 71*x**3) using the distributive property, and we got: (-71*x**3)*(78 - 10*x**3) + 16*(78 - 10*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-71*x**3)*(78 - 10*x**3) + 16*(78 - 10*x**3)</replace>
Simplifying the partial expression: 16*(78 - 10*x**3)
Expanding the part (78 - 10*x**3) using the distributive property, and we got: -10*x**3*16 + 78*16
Replacing 16*(78 - 10*x**3) with -10*x**3*16 + 78*16 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-71*x**3)*(78 - 10*x**3) - 10*x**3*16 + 1248</replace>
Simplifying the partial expression: (-71*x**3)*(78 - 10*x**3)
Expanding the part (78 - 10*x**3) using the distributive property, and we got: 78*(-71*x**3) + (-71*x**3)*(-10*x**3)
Replacing (-71*x**3)*(78 - 10*x**3) with 78*(-71*x**3) + (-71*x**3)*(-10*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 78*(-71)*x**3 + (-71*x**3)*(-10*x**3) - 10*x**3*16 + 1248</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-10*x**3)*16 = -160*x**3
  (-10*x**3)*(-71*x**3) = 710*x**6
  78*-71*x**3 = -5538*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 710*x**6 - 5538*x**3 - 160*x**3 + 1248</replace>
Combining like terms, got 710*x**6 - 5698*x**3 + 1248
<replace-#Step 5>#Step 6:
Current expression: 710*x**6 - 5698*x**3 + 1248</replace>
No more calculations needed.
<answer>710*x**6 - 5698*x**3 + 1248</answer>


Question:
Calculate the following: 17*x**3*(57*x**3 + 28*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: 969*x**6 + 476*x**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 17*x**3*(57*x**3 + 28*x)
Expanding the part (57*x**3 + 28*x) using the distributive property, and we got: (28*x)*(17*x**3) + (17*x**3)*(57*x**3)
<replace-#Step 1>#Step 2:
Current expression: (28*x)*(17*x**3) + (17*x**3)*(57*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (28*x)*(17*x**3) = 476*x**4
  (57*x**3)*(17*x**3) = 969*x**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 969*x**6 + 476*x**4</replace>
No more calculations needed.
<answer>969*x**6 + 476*x**4</answer>


Question:
Calculate the following: (-9*y**2 + 37*y)*(64*y**2 + 28)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -576*y**4 + 2368*y**3 - 252*y**2 + 1036*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: (-9*y**2 + 37*y)*(64*y**2 + 28)
Expanding the part (64*y**2 + 28) using the distributive property, and we got: (64*y**2)*(-9*y**2 + 37*y) + 28*(-9*y**2 + 37*y)
<replace-#Step 1>#Step 2:
Current expression: (64*y**2)*(-9*y**2 + 37*y) + 28*(-9*y**2 + 37*y)</replace>
Simplifying the partial expression: 28*(-9*y**2 + 37*y)
Expanding the part (-9*y**2 + 37*y) using the distributive property, and we got: (37*y)*28 - 9*y**2*28
Replacing 28*(-9*y**2 + 37*y) with (37*y)*28 - 9*y**2*28 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (37*y)*28 - 9*y**2*28 + (64*y**2)*(-9*y**2 + 37*y)</replace>
Simplifying the partial expression: (64*y**2)*(-9*y**2 + 37*y)
Expanding the part (-9*y**2 + 37*y) using the distributive property, and we got: (37*y)*(64*y**2) + (-9*y**2)*(64*y**2)
Replacing (64*y**2)*(-9*y**2 + 37*y) with (37*y)*(64*y**2) + (-9*y**2)*(64*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (37*y)*(64*y**2) + (37*y)*28 + (-9*y**2)*(64*y**2) - 9*y**2*28</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-9*y**2)*28 = -252*y**2
  (-9*y**2)*(64*y**2) = -576*y**4
  (37*y)*28 = 1036*y
  (37*y)*(64*y**2) = 2368*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -576*y**4 + 2368*y**3 - 252*y**2 + 1036*y</replace>
No more calculations needed.
<answer>-576*y**4 + 2368*y**3 - 252*y**2 + 1036*y</answer>


Question:
Simplify this expression: (-2*y - 10)*(82*y**2 + 54*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: -164*y**3 - 928*y**2 - 540*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: (-2*y - 10)*(82*y**2 + 54*y)
Expanding the part (-2*y - 10) using the distributive property, and we got: (-2*y)*(82*y**2 + 54*y) - 10*(82*y**2 + 54*y)
<replace-#Step 1>#Step 2:
Current expression: (-2*y)*(82*y**2 + 54*y) - 10*(82*y**2 + 54*y)</replace>
Simplifying the partial expression: -10*(82*y**2 + 54*y)
Expanding the part (82*y**2 + 54*y) using the distributive property, and we got: (54*y)*(-10) + (82*y**2)*(-10)
Replacing -10*(82*y**2 + 54*y) with (54*y)*(-10) + (82*y**2)*(-10) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-2*y)*(82*y**2 + 54*y) + (54*y)*(-10) + (82*y**2)*(-10)</replace>
Simplifying the partial expression: (-2*y)*(82*y**2 + 54*y)
Expanding the part (82*y**2 + 54*y) using the distributive property, and we got: (-2*y)*(54*y) + (-2*y)*(82*y**2)
Replacing (-2*y)*(82*y**2 + 54*y) with (-2*y)*(54*y) + (-2*y)*(82*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-2*y)*(54*y) + (-2*y)*(82*y**2) + (54*y)*(-10) + (82*y**2)*(-10)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (54*y)*-10 = -540*y
  (54*y)*(-2*y) = -108*y**2
  (82*y**2)*-10 = -820*y**2
  (82*y**2)*(-2*y) = -164*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -164*y**3 - 820*y**2 - 108*y**2 - 540*y</replace>
Combining like terms, got -164*y**3 - 928*y**2 - 540*y
<replace-#Step 5>#Step 6:
Current expression: -164*y**3 - 928*y**2 - 540*y</replace>
No more calculations needed.
<answer>-164*y**3 - 928*y**2 - 540*y</answer>


Question:
Calculate the following: (48 - 29*z**2)*(39*z**2 - 28*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: -1131*z**4 + 812*z**3 + 1872*z**2 - 1344*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: (48 - 29*z**2)*(39*z**2 - 28*z)
Expanding the part (48 - 29*z**2) using the distributive property, and we got: (-29*z**2)*(39*z**2 - 28*z) + 48*(39*z**2 - 28*z)
<replace-#Step 1>#Step 2:
Current expression: (-29*z**2)*(39*z**2 - 28*z) + 48*(39*z**2 - 28*z)</replace>
Simplifying the partial expression: 48*(39*z**2 - 28*z)
Expanding the part (39*z**2 - 28*z) using the distributive property, and we got: -28*z*48 + (39*z**2)*48
Replacing 48*(39*z**2 - 28*z) with -28*z*48 + (39*z**2)*48 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -28*z*48 + (-29*z**2)*(39*z**2 - 28*z) + (39*z**2)*48</replace>
Simplifying the partial expression: (-29*z**2)*(39*z**2 - 28*z)
Expanding the part (39*z**2 - 28*z) using the distributive property, and we got: (-28*z)*(-29*z**2) + (-29*z**2)*(39*z**2)
Replacing (-29*z**2)*(39*z**2 - 28*z) with (-28*z)*(-29*z**2) + (-29*z**2)*(39*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-28*z)*(-29*z**2) - 28*z*48 + (-29*z**2)*(39*z**2) + (39*z**2)*48</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-28*z)*48 = -1344*z
  (-28*z)*(-29*z**2) = 812*z**3
  (39*z**2)*48 = 1872*z**2
  (39*z**2)*(-29*z**2) = -1131*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1131*z**4 + 812*z**3 + 1872*z**2 - 1344*z</replace>
No more calculations needed.
<answer>-1131*z**4 + 812*z**3 + 1872*z**2 - 1344*z</answer>


Question:
Calculate the following: -2829*x**3 + 3381*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: -2829*x**3 + 3381*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: -2829*x**3 + 3381*x**2
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: -2829*x**3 + 3381*x**2</replace>
No more calculations needed.
<answer>-2829*x**3 + 3381*x**2</answer>


Question:
Calculate the following: (18 - 20*z**2)*(-90*z**3 - 31*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: 1800*z**5 - 1000*z**3 - 558*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: (18 - 20*z**2)*(-90*z**3 - 31*z)
Expanding the part (18 - 20*z**2) using the distributive property, and we got: (-20*z**2)*(-90*z**3 - 31*z) + 18*(-90*z**3 - 31*z)
<replace-#Step 1>#Step 2:
Current expression: (-20*z**2)*(-90*z**3 - 31*z) + 18*(-90*z**3 - 31*z)</replace>
Simplifying the partial expression: 18*(-90*z**3 - 31*z)
Expanding the part (-90*z**3 - 31*z) using the distributive property, and we got: -31*z*18 - 90*z**3*18
Replacing 18*(-90*z**3 - 31*z) with -31*z*18 - 90*z**3*18 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -31*z*18 + (-20*z**2)*(-90*z**3 - 31*z) - 90*z**3*18</replace>
Simplifying the partial expression: (-20*z**2)*(-90*z**3 - 31*z)
Expanding the part (-90*z**3 - 31*z) using the distributive property, and we got: (-31*z)*(-20*z**2) + (-20*z**2)*(-90*z**3)
Replacing (-20*z**2)*(-90*z**3 - 31*z) with (-31*z)*(-20*z**2) + (-20*z**2)*(-90*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-31*z)*(-20*z**2) - 31*z*18 + (-20*z**2)*(-90*z**3) - 90*z**3*18</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-90*z**3)*18 = -1620*z**3
  (-90*z**3)*(-20*z**2) = 1800*z**5
  (-31*z)*18 = -558*z
  (-31*z)*(-20*z**2) = 620*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1800*z**5 - 1620*z**3 + 620*z**3 - 558*z</replace>
Combining like terms, got 1800*z**5 - 1000*z**3 - 558*z
<replace-#Step 5>#Step 6:
Current expression: 1800*z**5 - 1000*z**3 - 558*z</replace>
No more calculations needed.
<answer>1800*z**5 - 1000*z**3 - 558*z</answer>


Question:
Calculate the following: -37*z**2*(46*z**3 + 13*z**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1702*z**5 - 481*z**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -37*z**2*(46*z**3 + 13*z**2)
Expanding the part (46*z**3 + 13*z**2) using the distributive property, and we got: (-37*z**2)*(13*z**2) + (-37*z**2)*(46*z**3)
<replace-#Step 1>#Step 2:
Current expression: (-37*z**2)*(13*z**2) + (-37*z**2)*(46*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (13*z**2)*(-37*z**2) = -481*z**4
  (46*z**3)*(-37*z**2) = -1702*z**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1702*z**5 - 481*z**4</replace>
No more calculations needed.
<answer>-1702*z**5 - 481*z**4</answer>


Question:
Simplify this expression: (21 - 29*x)*(x**2 - 44)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -29*x**3 + 21*x**2 + 1276*x - 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: (21 - 29*x)*(x**2 - 44)
Expanding the part (x**2 - 44) using the distributive property, and we got: x**2*(21 - 29*x) - 44*(21 - 29*x)
<replace-#Step 1>#Step 2:
Current expression: x**2*(21 - 29*x) - 44*(21 - 29*x)</replace>
Simplifying the partial expression: -44*(21 - 29*x)
Expanding the part (21 - 29*x) using the distributive property, and we got: -29*x*(-44) + 21*(-44)
Replacing -44*(21 - 29*x) with -29*x*(-44) + 21*(-44) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -29*x*(-44) + x**2*(21 - 29*x) - 924</replace>
Simplifying the partial expression: x**2*(21 - 29*x)
Expanding the part (21 - 29*x) using the distributive property, and we got: (-29*x)*x**2 + 21*x**2
Replacing x**2*(21 - 29*x) with (-29*x)*x**2 + 21*x**2 in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-29*x)*x**2 - 29*x*(-44) + 21*x**2 - 924</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-29*x)*-44 = 1276*x
  (-29*x)*x**2 = -29*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -29*x**3 + 21*x**2 + 1276*x - 924</replace>
No more calculations needed.
<answer>-29*x**3 + 21*x**2 + 1276*x - 924</answer>


Question:
Simplify this expression: (53*y**2 + 35)*(31*y**3 + 5*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1643*y**5 + 265*y**4 + 1085*y**3 + 175*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: (53*y**2 + 35)*(31*y**3 + 5*y**2)
Expanding the part (53*y**2 + 35) using the distributive property, and we got: (53*y**2)*(31*y**3 + 5*y**2) + 35*(31*y**3 + 5*y**2)
<replace-#Step 1>#Step 2:
Current expression: (53*y**2)*(31*y**3 + 5*y**2) + 35*(31*y**3 + 5*y**2)</replace>
Simplifying the partial expression: 35*(31*y**3 + 5*y**2)
Expanding the part (31*y**3 + 5*y**2) using the distributive property, and we got: (5*y**2)*35 + (31*y**3)*35
Replacing 35*(31*y**3 + 5*y**2) with (5*y**2)*35 + (31*y**3)*35 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (5*y**2)*35 + (53*y**2)*(31*y**3 + 5*y**2) + (31*y**3)*35</replace>
Simplifying the partial expression: (53*y**2)*(31*y**3 + 5*y**2)
Expanding the part (31*y**3 + 5*y**2) using the distributive property, and we got: (5*y**2)*(53*y**2) + (53*y**2)*(31*y**3)
Replacing (53*y**2)*(31*y**3 + 5*y**2) with (5*y**2)*(53*y**2) + (53*y**2)*(31*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (5*y**2)*(53*y**2) + (5*y**2)*35 + (53*y**2)*(31*y**3) + (31*y**3)*35</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (5*y**2)*35 = 175*y**2
  (5*y**2)*(53*y**2) = 265*y**4
  (31*y**3)*35 = 1085*y**3
  (31*y**3)*(53*y**2) = 1643*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1643*y**5 + 265*y**4 + 1085*y**3 + 175*y**2</replace>
No more calculations needed.
<answer>1643*y**5 + 265*y**4 + 1085*y**3 + 175*y**2</answer>


Question:
Simplify this expression: -1209*z**3 - 124*z**2 + 2232
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1209*z**3 - 124*z**2 + 2232

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: -1209*z**3 - 124*z**2 + 2232
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: -1209*z**3 - 124*z**2 + 2232</replace>
No more calculations needed.
<answer>-1209*z**3 - 124*z**2 + 2232</answer>


Question:
Simplify this expression: (-17*x**2 + 69*x)*(-15*x**3 - 3*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: 255*x**5 - 984*x**4 - 207*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: (-17*x**2 + 69*x)*(-15*x**3 - 3*x**2)
Expanding the part (-17*x**2 + 69*x) using the distributive property, and we got: (69*x)*(-15*x**3 - 3*x**2) + (-17*x**2)*(-15*x**3 - 3*x**2)
<replace-#Step 1>#Step 2:
Current expression: (69*x)*(-15*x**3 - 3*x**2) + (-17*x**2)*(-15*x**3 - 3*x**2)</replace>
Simplifying the partial expression: (-17*x**2)*(-15*x**3 - 3*x**2)
Expanding the part (-15*x**3 - 3*x**2) using the distributive property, and we got: (-17*x**2)*(-3*x**2) + (-17*x**2)*(-15*x**3)
Replacing (-17*x**2)*(-15*x**3 - 3*x**2) with (-17*x**2)*(-3*x**2) + (-17*x**2)*(-15*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (69*x)*(-15*x**3 - 3*x**2) + (-17*x**2)*(-3*x**2) + (-17*x**2)*(-15*x**3)</replace>
Simplifying the partial expression: (69*x)*(-15*x**3 - 3*x**2)
Expanding the part (-15*x**3 - 3*x**2) using the distributive property, and we got: (69*x)*(-3*x**2) + (69*x)*(-15*x**3)
Replacing (69*x)*(-15*x**3 - 3*x**2) with (69*x)*(-3*x**2) + (69*x)*(-15*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (69*x)*(-3*x**2) + (69*x)*(-15*x**3) + (-17*x**2)*(-3*x**2) + (-17*x**2)*(-15*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-15*x**3)*(-17*x**2) = 255*x**5
  (-15*x**3)*(69*x) = -1035*x**4
  (-3*x**2)*(-17*x**2) = 51*x**4
  (-3*x**2)*(69*x) = -207*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 255*x**5 - 1035*x**4 + 51*x**4 - 207*x**3</replace>
Combining like terms, got 255*x**5 - 984*x**4 - 207*x**3
<replace-#Step 5>#Step 6:
Current expression: 255*x**5 - 984*x**4 - 207*x**3</replace>
No more calculations needed.
<answer>255*x**5 - 984*x**4 - 207*x**3</answer>


Question:
Simplify this expression: (19*z**3 + 43)*(37*z**3 + 6*z**2 - 38)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 703*z**6 + 114*z**5 + 869*z**3 + 258*z**2 - 1634

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (19*z**3 + 43)*(37*z**3 + 6*z**2 - 38)
Expanding the part (19*z**3 + 43) using the distributive property, and we got: (19*z**3)*(37*z**3 + 6*z**2 - 38) + 43*(37*z**3 + 6*z**2 - 38)
<replace-#Step 1>#Step 2:
Current expression: (19*z**3)*(37*z**3 + 6*z**2 - 38) + 43*(37*z**3 + 6*z**2 - 38)</replace>
Simplifying the partial expression: 43*(37*z**3 + 6*z**2 - 38)
Expanding the part (37*z**3 + 6*z**2 - 38) using the distributive property, and we got: (6*z**2)*43 + (37*z**3)*43 - 38*43
Replacing 43*(37*z**3 + 6*z**2 - 38) with (6*z**2)*43 + (37*z**3)*43 - 38*43 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (6*z**2)*43 + (19*z**3)*(37*z**3 + 6*z**2 - 38) + (37*z**3)*43 - 1634</replace>
Simplifying the partial expression: (19*z**3)*(37*z**3 + 6*z**2 - 38)
Expanding the part (37*z**3 + 6*z**2 - 38) using the distributive property, and we got: -722*z**3 + (6*z**2)*(19*z**3) + (19*z**3)*(37*z**3)
Replacing (19*z**3)*(37*z**3 + 6*z**2 - 38) with -722*z**3 + (6*z**2)*(19*z**3) + (19*z**3)*(37*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -38*19*z**3 + (6*z**2)*(19*z**3) + (6*z**2)*43 + (19*z**3)*(37*z**3) + (37*z**3)*43 - 1634</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (6*z**2)*43 = 258*z**2
  (6*z**2)*(19*z**3) = 114*z**5
  (37*z**3)*43 = 1591*z**3
  (37*z**3)*(19*z**3) = 703*z**6
  -38*19*z**3 = -722*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 703*z**6 + 114*z**5 - 722*z**3 + 1591*z**3 + 258*z**2 - 1634</replace>
Combining like terms, got 703*z**6 + 114*z**5 + 869*z**3 + 258*z**2 - 1634
<replace-#Step 5>#Step 6:
Current expression: 703*z**6 + 114*z**5 + 869*z**3 + 258*z**2 - 1634</replace>
No more calculations needed.
<answer>703*z**6 + 114*z**5 + 869*z**3 + 258*z**2 - 1634</answer>


Question:
Simplify this expression: (27*y**2 - 8*y + 18)*(-44*y**3 + 27*y**2 + 19*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: -1188*y**5 + 1081*y**4 - 495*y**3 + 334*y**2 + 342*y


Question:
Calculate the following: (-41*z**2 - 30)*(35*z**3 + 43*z**2 - 34*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: -1435*z**5 - 1763*z**4 + 344*z**3 - 1290*z**2 + 1020*z


Question:
Calculate the following: (-20*z**3 - 43)*(37*z**3 - 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: -740*z**6 - 751*z**3 + 1806

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*z**3 - 43)*(37*z**3 - 42)
Expanding the part (-20*z**3 - 43) using the distributive property, and we got: (-20*z**3)*(37*z**3 - 42) - 43*(37*z**3 - 42)
<replace-#Step 1>#Step 2:
Current expression: (-20*z**3)*(37*z**3 - 42) - 43*(37*z**3 - 42)</replace>
Simplifying the partial expression: -43*(37*z**3 - 42)
Expanding the part (37*z**3 - 42) using the distributive property, and we got: (37*z**3)*(-43) - 42*(-43)
Replacing -43*(37*z**3 - 42) with (37*z**3)*(-43) - 42*(-43) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-20*z**3)*(37*z**3 - 42) + (37*z**3)*(-43) + 1806</replace>
Simplifying the partial expression: (-20*z**3)*(37*z**3 - 42)
Expanding the part (37*z**3 - 42) using the distributive property, and we got: -(-1)*840*z**3 + (-20*z**3)*(37*z**3)
Replacing (-20*z**3)*(37*z**3 - 42) with -(-1)*840*z**3 + (-20*z**3)*(37*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -42*(-20)*z**3 + (-20*z**3)*(37*z**3) + (37*z**3)*(-43) + 1806</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (37*z**3)*-43 = -1591*z**3
  (37*z**3)*(-20*z**3) = -740*z**6
  -42*-20*z**3 = 840*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -740*z**6 - 1591*z**3 + 840*z**3 + 1806</replace>
Combining like terms, got -740*z**6 - 751*z**3 + 1806
<replace-#Step 5>#Step 6:
Current expression: -740*z**6 - 751*z**3 + 1806</replace>
No more calculations needed.
<answer>-740*z**6 - 751*z**3 + 1806</answer>


Question:
Calculate the following: (50 - 48*y**2)*(14*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: -672*y**4 - 260*y**2 + 1000

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (50 - 48*y**2)*(14*y**2 + 20)
Expanding the part (14*y**2 + 20) using the distributive property, and we got: (14*y**2)*(50 - 48*y**2) + 20*(50 - 48*y**2)
<replace-#Step 1>#Step 2:
Current expression: (14*y**2)*(50 - 48*y**2) + 20*(50 - 48*y**2)</replace>
Simplifying the partial expression: 20*(50 - 48*y**2)
Expanding the part (50 - 48*y**2) using the distributive property, and we got: -48*y**2*20 + 50*20
Replacing 20*(50 - 48*y**2) with -48*y**2*20 + 50*20 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -48*y**2*20 + (14*y**2)*(50 - 48*y**2) + 1000</replace>
Simplifying the partial expression: (14*y**2)*(50 - 48*y**2)
Expanding the part (50 - 48*y**2) using the distributive property, and we got: 50*(14*y**2) + (-48*y**2)*(14*y**2)
Replacing (14*y**2)*(50 - 48*y**2) with 50*(14*y**2) + (-48*y**2)*(14*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 50*14*y**2 + (-48*y**2)*(14*y**2) - 48*y**2*20 + 1000</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-48*y**2)*20 = -960*y**2
  (-48*y**2)*(14*y**2) = -672*y**4
  50*14*y**2 = 700*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -672*y**4 - 960*y**2 + 700*y**2 + 1000</replace>
Combining like terms, got -672*y**4 - 260*y**2 + 1000
<replace-#Step 5>#Step 6:
Current expression: -672*y**4 - 260*y**2 + 1000</replace>
No more calculations needed.
<answer>-672*y**4 - 260*y**2 + 1000</answer>


Question:
Simplify this expression: (7*z**2 - 31*z)*(59*z**3 + 44*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 413*z**5 - 1829*z**4 + 308*z**3 - 1364*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: (7*z**2 - 31*z)*(59*z**3 + 44*z)
Expanding the part (7*z**2 - 31*z) using the distributive property, and we got: (-31*z)*(59*z**3 + 44*z) + (7*z**2)*(59*z**3 + 44*z)
<replace-#Step 1>#Step 2:
Current expression: (-31*z)*(59*z**3 + 44*z) + (7*z**2)*(59*z**3 + 44*z)</replace>
Simplifying the partial expression: (-31*z)*(59*z**3 + 44*z)
Expanding the part (59*z**3 + 44*z) using the distributive property, and we got: (-31*z)*(44*z) + (-31*z)*(59*z**3)
Replacing (-31*z)*(59*z**3 + 44*z) with (-31*z)*(44*z) + (-31*z)*(59*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-31*z)*(44*z) + (-31*z)*(59*z**3) + (7*z**2)*(59*z**3 + 44*z)</replace>
Simplifying the partial expression: (7*z**2)*(59*z**3 + 44*z)
Expanding the part (59*z**3 + 44*z) using the distributive property, and we got: (44*z)*(7*z**2) + (7*z**2)*(59*z**3)
Replacing (7*z**2)*(59*z**3 + 44*z) with (44*z)*(7*z**2) + (7*z**2)*(59*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-31*z)*(44*z) + (-31*z)*(59*z**3) + (44*z)*(7*z**2) + (7*z**2)*(59*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (44*z)*(-31*z) = -1364*z**2
  (44*z)*(7*z**2) = 308*z**3
  (59*z**3)*(-31*z) = -1829*z**4
  (59*z**3)*(7*z**2) = 413*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 413*z**5 - 1829*z**4 + 308*z**3 - 1364*z**2</replace>
No more calculations needed.
<answer>413*z**5 - 1829*z**4 + 308*z**3 - 1364*z**2</answer>


Question:
Simplify this expression: (-13*y**3 + 35*y**2)*(6*y**3 - 25*y**2 + 27)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -78*y**6 + 535*y**5 - 875*y**4 - 351*y**3 + 945*y**2


Question:
Simplify this expression: (34*y**3 - 3*y**2)*(76*y**3 + 10*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: 2584*y**6 - 228*y**5 + 340*y**4 - 30*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: (34*y**3 - 3*y**2)*(76*y**3 + 10*y)
Expanding the part (34*y**3 - 3*y**2) using the distributive property, and we got: (-3*y**2)*(76*y**3 + 10*y) + (34*y**3)*(76*y**3 + 10*y)
<replace-#Step 1>#Step 2:
Current expression: (-3*y**2)*(76*y**3 + 10*y) + (34*y**3)*(76*y**3 + 10*y)</replace>
Simplifying the partial expression: (-3*y**2)*(76*y**3 + 10*y)
Expanding the part (76*y**3 + 10*y) using the distributive property, and we got: (10*y)*(-3*y**2) + (-3*y**2)*(76*y**3)
Replacing (-3*y**2)*(76*y**3 + 10*y) with (10*y)*(-3*y**2) + (-3*y**2)*(76*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (10*y)*(-3*y**2) + (-3*y**2)*(76*y**3) + (34*y**3)*(76*y**3 + 10*y)</replace>
Simplifying the partial expression: (34*y**3)*(76*y**3 + 10*y)
Expanding the part (76*y**3 + 10*y) using the distributive property, and we got: (10*y)*(34*y**3) + (34*y**3)*(76*y**3)
Replacing (34*y**3)*(76*y**3 + 10*y) with (10*y)*(34*y**3) + (34*y**3)*(76*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (10*y)*(-3*y**2) + (10*y)*(34*y**3) + (-3*y**2)*(76*y**3) + (34*y**3)*(76*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (10*y)*(-3*y**2) = -30*y**3
  (10*y)*(34*y**3) = 340*y**4
  (76*y**3)*(-3*y**2) = -228*y**5
  (76*y**3)*(34*y**3) = 2584*y**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2584*y**6 - 228*y**5 + 340*y**4 - 30*y**3</replace>
No more calculations needed.
<answer>2584*y**6 - 228*y**5 + 340*y**4 - 30*y**3</answer>


Question:
Simplify this expression: (-7*x - 1)*(47*x**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: -329*x**3 - 47*x**2 - 91*x - 13

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 - 1)*(47*x**2 + 13)
Expanding the part (-7*x - 1) using the distributive property, and we got: (-7*x)*(47*x**2 + 13) - (47*x**2 + 13)
<replace-#Step 1>#Step 2:
Current expression: (-7*x)*(47*x**2 + 13) - (47*x**2 + 13)</replace>
Simplifying the partial expression: -(47*x**2 + 13)
Expanding the part (47*x**2 + 13) using the distributive property, and we got: (47*x**2)*(-1) + 13*(-1)
Replacing -(47*x**2 + 13) with (47*x**2)*(-1) + 13*(-1) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-7*x)*(47*x**2 + 13) + (47*x**2)*(-1) - 13</replace>
Simplifying the partial expression: (-7*x)*(47*x**2 + 13)
Expanding the part (47*x**2 + 13) using the distributive property, and we got: (-7*x)*(47*x**2) + 13*(-7*x)
Replacing (-7*x)*(47*x**2 + 13) with (-7*x)*(47*x**2) + 13*(-7*x) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-7*x)*(47*x**2) + 13*(-7)*x + (47*x**2)*(-1) - 13</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (47*x**2)*-1 = -47*x**2
  (47*x**2)*(-7*x) = -329*x**3
  13*-7*x = -91*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -329*x**3 - 47*x**2 - 91*x - 13</replace>
No more calculations needed.
<answer>-329*x**3 - 47*x**2 - 91*x - 13</answer>


Question:
Simplify this expression: (-7*x**2 - 10*x + 36)*(41*x**2 - 37*x - 48)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -287*x**4 - 151*x**3 + 2182*x**2 - 852*x - 1728


Question:
Calculate the following: (60 - 3*x)*(-49*x**2 - 6*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 147*x**3 - 2922*x**2 - 360*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: (60 - 3*x)*(-49*x**2 - 6*x)
Expanding the part (60 - 3*x) using the distributive property, and we got: (-3*x)*(-49*x**2 - 6*x) + 60*(-49*x**2 - 6*x)
<replace-#Step 1>#Step 2:
Current expression: (-3*x)*(-49*x**2 - 6*x) + 60*(-49*x**2 - 6*x)</replace>
Simplifying the partial expression: 60*(-49*x**2 - 6*x)
Expanding the part (-49*x**2 - 6*x) using the distributive property, and we got: -6*x*60 - 49*x**2*60
Replacing 60*(-49*x**2 - 6*x) with -6*x*60 - 49*x**2*60 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -6*x*60 + (-3*x)*(-49*x**2 - 6*x) - 49*x**2*60</replace>
Simplifying the partial expression: (-3*x)*(-49*x**2 - 6*x)
Expanding the part (-49*x**2 - 6*x) using the distributive property, and we got: (-6*x)*(-3*x) + (-3*x)*(-49*x**2)
Replacing (-3*x)*(-49*x**2 - 6*x) with (-6*x)*(-3*x) + (-3*x)*(-49*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-6*x)*(-3*x) - 6*x*60 + (-3*x)*(-49*x**2) - 49*x**2*60</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-49*x**2)*60 = -2940*x**2
  (-49*x**2)*(-3*x) = 147*x**3
  (-6*x)*60 = -360*x
  (-6*x)*(-3*x) = 18*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 147*x**3 - 2940*x**2 + 18*x**2 - 360*x</replace>
Combining like terms, got 147*x**3 - 2922*x**2 - 360*x
<replace-#Step 5>#Step 6:
Current expression: 147*x**3 - 2922*x**2 - 360*x</replace>
No more calculations needed.
<answer>147*x**3 - 2922*x**2 - 360*x</answer>


Question:
Simplify this expression: (11*z - 23)*(45*z + 34)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 495*z**2 - 661*z - 782

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (11*z - 23)*(45*z + 34)
Expanding the part (11*z - 23) using the distributive property, and we got: (11*z)*(45*z + 34) - 23*(45*z + 34)
<replace-#Step 1>#Step 2:
Current expression: (11*z)*(45*z + 34) - 23*(45*z + 34)</replace>
Simplifying the partial expression: -23*(45*z + 34)
Expanding the part (45*z + 34) using the distributive property, and we got: (45*z)*(-23) + 34*(-23)
Replacing -23*(45*z + 34) with (45*z)*(-23) + 34*(-23) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (11*z)*(45*z + 34) + (45*z)*(-23) - 782</replace>
Simplifying the partial expression: (11*z)*(45*z + 34)
Expanding the part (45*z + 34) using the distributive property, and we got: 34*(11*z) + (11*z)*(45*z)
Replacing (11*z)*(45*z + 34) with 34*(11*z) + (11*z)*(45*z) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 34*11*z + (11*z)*(45*z) + (45*z)*(-23) - 782</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (45*z)*-23 = -1035*z
  (45*z)*(11*z) = 495*z**2
  34*11*z = 374*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 495*z**2 - 1035*z + 374*z - 782</replace>
Combining like terms, got 495*z**2 - 661*z - 782
<replace-#Step 5>#Step 6:
Current expression: 495*z**2 - 661*z - 782</replace>
No more calculations needed.
<answer>495*z**2 - 661*z - 782</answer>


Question:
Calculate the following: (13 - 8*x**3)*(49*x**2 - 6*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -392*x**5 + 48*x**4 + 637*x**2 - 78*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: (13 - 8*x**3)*(49*x**2 - 6*x)
Expanding the part (13 - 8*x**3) using the distributive property, and we got: (-8*x**3)*(49*x**2 - 6*x) + 13*(49*x**2 - 6*x)
<replace-#Step 1>#Step 2:
Current expression: (-8*x**3)*(49*x**2 - 6*x) + 13*(49*x**2 - 6*x)</replace>
Simplifying the partial expression: 13*(49*x**2 - 6*x)
Expanding the part (49*x**2 - 6*x) using the distributive property, and we got: -6*x*13 + (49*x**2)*13
Replacing 13*(49*x**2 - 6*x) with -6*x*13 + (49*x**2)*13 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -6*x*13 + (49*x**2)*13 + (-8*x**3)*(49*x**2 - 6*x)</replace>
Simplifying the partial expression: (-8*x**3)*(49*x**2 - 6*x)
Expanding the part (49*x**2 - 6*x) using the distributive property, and we got: (-6*x)*(-8*x**3) + (49*x**2)*(-8*x**3)
Replacing (-8*x**3)*(49*x**2 - 6*x) with (-6*x)*(-8*x**3) + (49*x**2)*(-8*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-6*x)*(-8*x**3) - 6*x*13 + (49*x**2)*(-8*x**3) + (49*x**2)*13</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-6*x)*13 = -78*x
  (-6*x)*(-8*x**3) = 48*x**4
  (49*x**2)*13 = 637*x**2
  (49*x**2)*(-8*x**3) = -392*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -392*x**5 + 48*x**4 + 637*x**2 - 78*x</replace>
No more calculations needed.
<answer>-392*x**5 + 48*x**4 + 637*x**2 - 78*x</answer>


Question:
Calculate the following: -y**3*(28*y**3 - 10*y + 23)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -28*y**6 + 10*y**4 - 23*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: -y**3*(28*y**3 - 10*y + 23)
Expanding the part (28*y**3 - 10*y + 23) using the distributive property, and we got: (-10*y)*(-y**3) + 23*(-y**3) + (-y**3)*(28*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-10*y)*(-y**3) + 23*(-y**3) + (-y**3)*(28*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  23*(-y**3) = -23*y**3
  (-10*y)*(-y**3) = 10*y**4
  (28*y**3)*(-y**3) = -28*y**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -28*y**6 + 10*y**4 - 23*y**3</replace>
No more calculations needed.
<answer>-28*y**6 + 10*y**4 - 23*y**3</answer>


Question:
Simplify this expression: (47*z**2 - 19)*(36*z**3 - 27*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: 1692*z**5 - 1953*z**3 + 513*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: (47*z**2 - 19)*(36*z**3 - 27*z)
Expanding the part (47*z**2 - 19) using the distributive property, and we got: (47*z**2)*(36*z**3 - 27*z) - 19*(36*z**3 - 27*z)
<replace-#Step 1>#Step 2:
Current expression: (47*z**2)*(36*z**3 - 27*z) - 19*(36*z**3 - 27*z)</replace>
Simplifying the partial expression: -19*(36*z**3 - 27*z)
Expanding the part (36*z**3 - 27*z) using the distributive property, and we got: -27*z*(-19) + (36*z**3)*(-19)
Replacing -19*(36*z**3 - 27*z) with -27*z*(-19) + (36*z**3)*(-19) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -27*z*(-19) + (47*z**2)*(36*z**3 - 27*z) + (36*z**3)*(-19)</replace>
Simplifying the partial expression: (47*z**2)*(36*z**3 - 27*z)
Expanding the part (36*z**3 - 27*z) using the distributive property, and we got: (-27*z)*(47*z**2) + (47*z**2)*(36*z**3)
Replacing (47*z**2)*(36*z**3 - 27*z) with (-27*z)*(47*z**2) + (47*z**2)*(36*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-27*z)*(47*z**2) - 27*z*(-19) + (47*z**2)*(36*z**3) + (36*z**3)*(-19)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-27*z)*-19 = 513*z
  (-27*z)*(47*z**2) = -1269*z**3
  (36*z**3)*-19 = -684*z**3
  (36*z**3)*(47*z**2) = 1692*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1692*z**5 - 1269*z**3 - 684*z**3 + 513*z</replace>
Combining like terms, got 1692*z**5 - 1953*z**3 + 513*z
<replace-#Step 5>#Step 6:
Current expression: 1692*z**5 - 1953*z**3 + 513*z</replace>
No more calculations needed.
<answer>1692*z**5 - 1953*z**3 + 513*z</answer>


Question:
Calculate the following: (-20*y**2 - 31)*(-7*y**3 - 11*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 140*y**5 + 437*y**3 + 341*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: (-20*y**2 - 31)*(-7*y**3 - 11*y)
Expanding the part (-20*y**2 - 31) using the distributive property, and we got: (-20*y**2)*(-7*y**3 - 11*y) - 31*(-7*y**3 - 11*y)
<replace-#Step 1>#Step 2:
Current expression: (-20*y**2)*(-7*y**3 - 11*y) - 31*(-7*y**3 - 11*y)</replace>
Simplifying the partial expression: -31*(-7*y**3 - 11*y)
Expanding the part (-7*y**3 - 11*y) using the distributive property, and we got: -11*y*(-31) - 7*y**3*(-31)
Replacing -31*(-7*y**3 - 11*y) with -11*y*(-31) - 7*y**3*(-31) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -11*y*(-31) + (-20*y**2)*(-7*y**3 - 11*y) - 7*y**3*(-31)</replace>
Simplifying the partial expression: (-20*y**2)*(-7*y**3 - 11*y)
Expanding the part (-7*y**3 - 11*y) using the distributive property, and we got: (-11*y)*(-20*y**2) + (-20*y**2)*(-7*y**3)
Replacing (-20*y**2)*(-7*y**3 - 11*y) with (-11*y)*(-20*y**2) + (-20*y**2)*(-7*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-11*y)*(-20*y**2) - 11*y*(-31) + (-20*y**2)*(-7*y**3) - 7*y**3*(-31)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-11*y)*-31 = 341*y
  (-11*y)*(-20*y**2) = 220*y**3
  (-7*y**3)*-31 = 217*y**3
  (-7*y**3)*(-20*y**2) = 140*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 140*y**5 + 217*y**3 + 220*y**3 + 341*y</replace>
Combining like terms, got 140*y**5 + 437*y**3 + 341*y
<replace-#Step 5>#Step 6:
Current expression: 140*y**5 + 437*y**3 + 341*y</replace>
No more calculations needed.
<answer>140*y**5 + 437*y**3 + 341*y</answer>


Question:
Calculate the following: 28*x**3*(37*x**3 - 38*x + 15)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1036*x**6 - 1064*x**4 + 420*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: 28*x**3*(37*x**3 - 38*x + 15)
Expanding the part (37*x**3 - 38*x + 15) using the distributive property, and we got: (-38*x)*(28*x**3) + 15*(28*x**3) + (28*x**3)*(37*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-38*x)*(28*x**3) + 15*(28*x**3) + (28*x**3)*(37*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  15*(28*x**3) = 420*x**3
  (-38*x)*(28*x**3) = -1064*x**4
  (37*x**3)*(28*x**3) = 1036*x**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1036*x**6 - 1064*x**4 + 420*x**3</replace>
No more calculations needed.
<answer>1036*x**6 - 1064*x**4 + 420*x**3</answer>


Question:
Calculate the following: (75 - 49*y)*(-33*y**3 + 30*y**2 + 34*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1617*y**4 - 3945*y**3 + 584*y**2 + 2550*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: (75 - 49*y)*(-33*y**3 + 30*y**2 + 34*y)
Expanding the part (75 - 49*y) using the distributive property, and we got: (-49*y)*(-33*y**3 + 30*y**2 + 34*y) + 75*(-33*y**3 + 30*y**2 + 34*y)
<replace-#Step 1>#Step 2:
Current expression: (-49*y)*(-33*y**3 + 30*y**2 + 34*y) + 75*(-33*y**3 + 30*y**2 + 34*y)</replace>
Simplifying the partial expression: 75*(-33*y**3 + 30*y**2 + 34*y)
Expanding the part (-33*y**3 + 30*y**2 + 34*y) using the distributive property, and we got: (34*y)*75 + (30*y**2)*75 - 33*y**3*75
Replacing 75*(-33*y**3 + 30*y**2 + 34*y) with (34*y)*75 + (30*y**2)*75 - 33*y**3*75 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-49*y)*(-33*y**3 + 30*y**2 + 34*y) + (34*y)*75 + (30*y**2)*75 - 33*y**3*75</replace>
Simplifying the partial expression: (-49*y)*(-33*y**3 + 30*y**2 + 34*y)
Expanding the part (-33*y**3 + 30*y**2 + 34*y) using the distributive property, and we got: (-49*y)*(34*y) + (-49*y)*(30*y**2) + (-49*y)*(-33*y**3)
Replacing (-49*y)*(-33*y**3 + 30*y**2 + 34*y) with (-49*y)*(34*y) + (-49*y)*(30*y**2) + (-49*y)*(-33*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-49*y)*(34*y) + (-49*y)*(30*y**2) + (-49*y)*(-33*y**3) + (34*y)*75 + (30*y**2)*75 - 33*y**3*75</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-33*y**3)*75 = -2475*y**3
  (-33*y**3)*(-49*y) = 1617*y**4
  (30*y**2)*75 = 2250*y**2
  (30*y**2)*(-49*y) = -1470*y**3
  (34*y)*75 = 2550*y
  (34*y)*(-49*y) = -1666*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1617*y**4 - 2475*y**3 - 1470*y**3 - 1666*y**2 + 2250*y**2 + 2550*y</replace>
Combining like terms, got 1617*y**4 - 3945*y**3 + 584*y**2 + 2550*y
<replace-#Step 5>#Step 6:
Current expression: 1617*y**4 - 3945*y**3 + 584*y**2 + 2550*y</replace>
No more calculations needed.
<answer>1617*y**4 - 3945*y**3 + 584*y**2 + 2550*y</answer>


Question:
Simplify this expression: (31 - 40*y)*(12*y + 28)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -480*y**2 - 748*y + 868

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 - 40*y)*(12*y + 28)
Expanding the part (12*y + 28) using the distributive property, and we got: (12*y)*(31 - 40*y) + 28*(31 - 40*y)
<replace-#Step 1>#Step 2:
Current expression: (12*y)*(31 - 40*y) + 28*(31 - 40*y)</replace>
Simplifying the partial expression: 28*(31 - 40*y)
Expanding the part (31 - 40*y) using the distributive property, and we got: -40*y*28 + 31*28
Replacing 28*(31 - 40*y) with -40*y*28 + 31*28 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -40*y*28 + (12*y)*(31 - 40*y) + 868</replace>
Simplifying the partial expression: (12*y)*(31 - 40*y)
Expanding the part (31 - 40*y) using the distributive property, and we got: (-40*y)*(12*y) + 31*(12*y)
Replacing (12*y)*(31 - 40*y) with (-40*y)*(12*y) + 31*(12*y) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-40*y)*(12*y) - 40*y*28 + 31*12*y + 868</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-40*y)*28 = -1120*y
  (-40*y)*(12*y) = -480*y**2
  31*12*y = 372*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -480*y**2 - 1120*y + 372*y + 868</replace>
Combining like terms, got -480*y**2 - 748*y + 868
<replace-#Step 5>#Step 6:
Current expression: -480*y**2 - 748*y + 868</replace>
No more calculations needed.
<answer>-480*y**2 - 748*y + 868</answer>


Question:
Calculate the following: (-21*x**2 - 46*x)*(-20*x**3 + 29*x**2 + 43*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 420*x**5 + 311*x**4 - 2237*x**3 - 1978*x**2


Question:
Calculate the following: (-39*y**2 + 21*y)*(61*y**3 + 38*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2379*y**5 - 201*y**4 + 798*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: (-39*y**2 + 21*y)*(61*y**3 + 38*y**2)
Expanding the part (-39*y**2 + 21*y) using the distributive property, and we got: (21*y)*(61*y**3 + 38*y**2) + (-39*y**2)*(61*y**3 + 38*y**2)
<replace-#Step 1>#Step 2:
Current expression: (21*y)*(61*y**3 + 38*y**2) + (-39*y**2)*(61*y**3 + 38*y**2)</replace>
Simplifying the partial expression: (-39*y**2)*(61*y**3 + 38*y**2)
Expanding the part (61*y**3 + 38*y**2) using the distributive property, and we got: (-39*y**2)*(38*y**2) + (-39*y**2)*(61*y**3)
Replacing (-39*y**2)*(61*y**3 + 38*y**2) with (-39*y**2)*(38*y**2) + (-39*y**2)*(61*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (21*y)*(61*y**3 + 38*y**2) + (-39*y**2)*(38*y**2) + (-39*y**2)*(61*y**3)</replace>
Simplifying the partial expression: (21*y)*(61*y**3 + 38*y**2)
Expanding the part (61*y**3 + 38*y**2) using the distributive property, and we got: (21*y)*(38*y**2) + (21*y)*(61*y**3)
Replacing (21*y)*(61*y**3 + 38*y**2) with (21*y)*(38*y**2) + (21*y)*(61*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (21*y)*(38*y**2) + (21*y)*(61*y**3) + (-39*y**2)*(38*y**2) + (-39*y**2)*(61*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (38*y**2)*(-39*y**2) = -1482*y**4
  (38*y**2)*(21*y) = 798*y**3
  (61*y**3)*(-39*y**2) = -2379*y**5
  (61*y**3)*(21*y) = 1281*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2379*y**5 - 1482*y**4 + 1281*y**4 + 798*y**3</replace>
Combining like terms, got -2379*y**5 - 201*y**4 + 798*y**3
<replace-#Step 5>#Step 6:
Current expression: -2379*y**5 - 201*y**4 + 798*y**3</replace>
No more calculations needed.
<answer>-2379*y**5 - 201*y**4 + 798*y**3</answer>


Question:
Simplify this expression: (-23*y**2 - 40*y)*(3*y**3 + 16*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -69*y**5 - 488*y**4 - 640*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: (-23*y**2 - 40*y)*(3*y**3 + 16*y**2)
Expanding the part (-23*y**2 - 40*y) using the distributive property, and we got: (-40*y)*(3*y**3 + 16*y**2) + (-23*y**2)*(3*y**3 + 16*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-40*y)*(3*y**3 + 16*y**2) + (-23*y**2)*(3*y**3 + 16*y**2)</replace>
Simplifying the partial expression: (-40*y)*(3*y**3 + 16*y**2)
Expanding the part (3*y**3 + 16*y**2) using the distributive property, and we got: (-40*y)*(16*y**2) + (-40*y)*(3*y**3)
Replacing (-40*y)*(3*y**3 + 16*y**2) with (-40*y)*(16*y**2) + (-40*y)*(3*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-40*y)*(16*y**2) + (-40*y)*(3*y**3) + (-23*y**2)*(3*y**3 + 16*y**2)</replace>
Simplifying the partial expression: (-23*y**2)*(3*y**3 + 16*y**2)
Expanding the part (3*y**3 + 16*y**2) using the distributive property, and we got: (-23*y**2)*(16*y**2) + (-23*y**2)*(3*y**3)
Replacing (-23*y**2)*(3*y**3 + 16*y**2) with (-23*y**2)*(16*y**2) + (-23*y**2)*(3*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-40*y)*(16*y**2) + (-40*y)*(3*y**3) + (-23*y**2)*(16*y**2) + (-23*y**2)*(3*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (3*y**3)*(-40*y) = -120*y**4
  (3*y**3)*(-23*y**2) = -69*y**5
  (16*y**2)*(-40*y) = -640*y**3
  (16*y**2)*(-23*y**2) = -368*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -69*y**5 - 368*y**4 - 120*y**4 - 640*y**3</replace>
Combining like terms, got -69*y**5 - 488*y**4 - 640*y**3
<replace-#Step 5>#Step 6:
Current expression: -69*y**5 - 488*y**4 - 640*y**3</replace>
No more calculations needed.
<answer>-69*y**5 - 488*y**4 - 640*y**3</answer>


Question:
Simplify this expression: (27*z**2 - 5*z + 18)*(48*z**3 + 28*z - 8)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1296*z**5 - 240*z**4 + 1620*z**3 - 356*z**2 + 544*z - 144


Question:
Simplify this expression: (-3*z**2 - 20*z + 27)*(26*z**3 - 20*z**2 + 47*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -78*z**5 - 460*z**4 + 961*z**3 - 1480*z**2 + 1269*z


Question:
Simplify this expression: (-43*y**3 - 27*y**2 - 43)*(-2*y**3 + 54*y**2 + 38*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: 86*y**6 - 2268*y**5 - 3092*y**4 - 940*y**3 - 2322*y**2 - 1634*y


Question:
Calculate the following: (-8*x - 41)*(-10*x**2 - 108*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: 80*x**3 + 1274*x**2 + 4428*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: (-8*x - 41)*(-10*x**2 - 108*x)
Expanding the part (-8*x - 41) using the distributive property, and we got: (-8*x)*(-10*x**2 - 108*x) - 41*(-10*x**2 - 108*x)
<replace-#Step 1>#Step 2:
Current expression: (-8*x)*(-10*x**2 - 108*x) - 41*(-10*x**2 - 108*x)</replace>
Simplifying the partial expression: -41*(-10*x**2 - 108*x)
Expanding the part (-10*x**2 - 108*x) using the distributive property, and we got: -108*x*(-41) - 10*x**2*(-41)
Replacing -41*(-10*x**2 - 108*x) with -108*x*(-41) - 10*x**2*(-41) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -108*x*(-41) + (-8*x)*(-10*x**2 - 108*x) - 10*x**2*(-41)</replace>
Simplifying the partial expression: (-8*x)*(-10*x**2 - 108*x)
Expanding the part (-10*x**2 - 108*x) using the distributive property, and we got: (-108*x)*(-8*x) + (-8*x)*(-10*x**2)
Replacing (-8*x)*(-10*x**2 - 108*x) with (-108*x)*(-8*x) + (-8*x)*(-10*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-108*x)*(-8*x) - 108*x*(-41) + (-8*x)*(-10*x**2) - 10*x**2*(-41)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-108*x)*-41 = 4428*x
  (-108*x)*(-8*x) = 864*x**2
  (-10*x**2)*-41 = 410*x**2
  (-10*x**2)*(-8*x) = 80*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 80*x**3 + 410*x**2 + 864*x**2 + 4428*x</replace>
Combining like terms, got 80*x**3 + 1274*x**2 + 4428*x
<replace-#Step 5>#Step 6:
Current expression: 80*x**3 + 1274*x**2 + 4428*x</replace>
No more calculations needed.
<answer>80*x**3 + 1274*x**2 + 4428*x</answer>


Question:
Calculate the following: (-27*z**2 - 77*z + 30)*(-20*z**3 + z - 24)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 540*z**5 + 1540*z**4 - 627*z**3 + 571*z**2 + 1878*z - 720


Question:
Calculate the following: (51*y - 9)*(30*y**2 + 34*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1530*y**3 + 1464*y**2 - 306*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: (51*y - 9)*(30*y**2 + 34*y)
Expanding the part (51*y - 9) using the distributive property, and we got: (51*y)*(30*y**2 + 34*y) - 9*(30*y**2 + 34*y)
<replace-#Step 1>#Step 2:
Current expression: (51*y)*(30*y**2 + 34*y) - 9*(30*y**2 + 34*y)</replace>
Simplifying the partial expression: -9*(30*y**2 + 34*y)
Expanding the part (30*y**2 + 34*y) using the distributive property, and we got: (34*y)*(-9) + (30*y**2)*(-9)
Replacing -9*(30*y**2 + 34*y) with (34*y)*(-9) + (30*y**2)*(-9) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (34*y)*(-9) + (51*y)*(30*y**2 + 34*y) + (30*y**2)*(-9)</replace>
Simplifying the partial expression: (51*y)*(30*y**2 + 34*y)
Expanding the part (30*y**2 + 34*y) using the distributive property, and we got: (34*y)*(51*y) + (51*y)*(30*y**2)
Replacing (51*y)*(30*y**2 + 34*y) with (34*y)*(51*y) + (51*y)*(30*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (34*y)*(51*y) + (34*y)*(-9) + (51*y)*(30*y**2) + (30*y**2)*(-9)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (30*y**2)*-9 = -270*y**2
  (30*y**2)*(51*y) = 1530*y**3
  (34*y)*-9 = -306*y
  (34*y)*(51*y) = 1734*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1530*y**3 - 270*y**2 + 1734*y**2 - 306*y</replace>
Combining like terms, got 1530*y**3 + 1464*y**2 - 306*y
<replace-#Step 5>#Step 6:
Current expression: 1530*y**3 + 1464*y**2 - 306*y</replace>
No more calculations needed.
<answer>1530*y**3 + 1464*y**2 - 306*y</answer>


Question:
Calculate the following: -208*y**2 + 784*y - 432
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -208*y**2 + 784*y - 432

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: -208*y**2 + 784*y - 432
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: -208*y**2 + 784*y - 432</replace>
No more calculations needed.
<answer>-208*y**2 + 784*y - 432</answer>


Question:
Simplify this expression: (44*y**3 + 15)*(-47*y**3 + 32*y**2 + 44*y + 31)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2068*y**6 + 1408*y**5 + 1936*y**4 + 659*y**3 + 480*y**2 + 660*y + 465


Question:
Calculate the following: (-29*x**2 - 22*x)*(8*x**3 + 38*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: -232*x**5 - 176*x**4 - 1102*x**3 + 614*x**2 + 1100*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: (-29*x**2 - 22*x)*(8*x**3 + 38*x - 50)
Expanding the part (-29*x**2 - 22*x) using the distributive property, and we got: (-22*x)*(8*x**3 + 38*x - 50) + (-29*x**2)*(8*x**3 + 38*x - 50)
<replace-#Step 1>#Step 2:
Current expression: (-22*x)*(8*x**3 + 38*x - 50) + (-29*x**2)*(8*x**3 + 38*x - 50)</replace>
Simplifying the partial expression: (-29*x**2)*(8*x**3 + 38*x - 50)
Expanding the part (8*x**3 + 38*x - 50) using the distributive property, and we got: -(-1)*1450*x**2 + (38*x)*(-29*x**2) + (-29*x**2)*(8*x**3)
Replacing (-29*x**2)*(8*x**3 + 38*x - 50) with -(-1)*1450*x**2 + (38*x)*(-29*x**2) + (-29*x**2)*(8*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-22*x)*(8*x**3 + 38*x - 50) - 50*(-29)*x**2 + (38*x)*(-29*x**2) + (-29*x**2)*(8*x**3)</replace>
Simplifying the partial expression: (-22*x)*(8*x**3 + 38*x - 50)
Expanding the part (8*x**3 + 38*x - 50) using the distributive property, and we got: (-22*x)*(38*x) + (-22*x)*(8*x**3) - (-1)*1100*x
Replacing (-22*x)*(8*x**3 + 38*x - 50) with (-22*x)*(38*x) + (-22*x)*(8*x**3) - (-1)*1100*x in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-22*x)*(38*x) + (-22*x)*(8*x**3) - 50*(-29)*x**2 - 50*(-22)*x + (38*x)*(-29*x**2) + (-29*x**2)*(8*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (8*x**3)*(-29*x**2) = -232*x**5
  (8*x**3)*(-22*x) = -176*x**4
  (38*x)*(-29*x**2) = -1102*x**3
  (38*x)*(-22*x) = -836*x**2
  -50*-29*x**2 = 1450*x**2
  -50*-22*x = 1100*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -232*x**5 - 176*x**4 - 1102*x**3 - 836*x**2 + 1450*x**2 + 1100*x</replace>
Combining like terms, got -232*x**5 - 176*x**4 - 1102*x**3 + 614*x**2 + 1100*x
<replace-#Step 5>#Step 6:
Current expression: -232*x**5 - 176*x**4 - 1102*x**3 + 614*x**2 + 1100*x</replace>
No more calculations needed.
<answer>-232*x**5 - 176*x**4 - 1102*x**3 + 614*x**2 + 1100*x</answer>


Question:
Calculate the following: (-35*x**3 - 56*x - 42)*(-35*x**3 + 42*x**2 - 7)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1225*x**6 - 1470*x**5 + 1960*x**4 - 637*x**3 - 1764*x**2 + 392*x + 294


Question:
Simplify this expression: (25*x**2 + x)*(14*x**3 - 26)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 350*x**5 + 14*x**4 - 650*x**2 - 26*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: (25*x**2 + x)*(14*x**3 - 26)
Expanding the part (14*x**3 - 26) using the distributive property, and we got: (14*x**3)*(25*x**2 + x) - 26*(25*x**2 + x)
<replace-#Step 1>#Step 2:
Current expression: (14*x**3)*(25*x**2 + x) - 26*(25*x**2 + x)</replace>
Simplifying the partial expression: -26*(25*x**2 + x)
Expanding the part (25*x**2 + x) using the distributive property, and we got: x*(-26) + (25*x**2)*(-26)
Replacing -26*(25*x**2 + x) with x*(-26) + (25*x**2)*(-26) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: x*(-26) + (25*x**2)*(-26) + (14*x**3)*(25*x**2 + x)</replace>
Simplifying the partial expression: (14*x**3)*(25*x**2 + x)
Expanding the part (25*x**2 + x) using the distributive property, and we got: x*(14*x**3) + (25*x**2)*(14*x**3)
Replacing (14*x**3)*(25*x**2 + x) with x*(14*x**3) + (25*x**2)*(14*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: x*(14*x**3) + x*(-26) + (25*x**2)*(14*x**3) + (25*x**2)*(-26)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  x*-26 = -26*x
  x*(14*x**3) = 14*x**4
  (25*x**2)*-26 = -650*x**2
  (25*x**2)*(14*x**3) = 350*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 350*x**5 + 14*x**4 - 650*x**2 - 26*x</replace>
No more calculations needed.
<answer>350*x**5 + 14*x**4 - 650*x**2 - 26*x</answer>


Question:
Calculate the following: -2867*z**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: -2867*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: -2867*z**3
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: -2867*z**3</replace>
No more calculations needed.
<answer>-2867*z**3</answer>


Question:
Calculate the following: (13*z**2 + 39*z + 41)*(8*z**3 + 7*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: 104*z**5 + 312*z**4 + 419*z**3 + 871*z**2 + 2081*z + 1886

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*z**2 + 39*z + 41)*(8*z**3 + 7*z + 46)
Expanding the part (13*z**2 + 39*z + 41) using the distributive property, and we got: (39*z)*(8*z**3 + 7*z + 46) + (13*z**2)*(8*z**3 + 7*z + 46) + 41*(8*z**3 + 7*z + 46)
<replace-#Step 1>#Step 2:
Current expression: (39*z)*(8*z**3 + 7*z + 46) + (13*z**2)*(8*z**3 + 7*z + 46) + 41*(8*z**3 + 7*z + 46)</replace>
Simplifying the partial expression: 41*(8*z**3 + 7*z + 46)
Expanding the part (8*z**3 + 7*z + 46) using the distributive property, and we got: (7*z)*41 + (8*z**3)*41 + 46*41
Replacing 41*(8*z**3 + 7*z + 46) with (7*z)*41 + (8*z**3)*41 + 46*41 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (7*z)*41 + (39*z)*(8*z**3 + 7*z + 46) + (13*z**2)*(8*z**3 + 7*z + 46) + (8*z**3)*41 + 1886</replace>
Simplifying the partial expression: (13*z**2)*(8*z**3 + 7*z + 46)
Expanding the part (8*z**3 + 7*z + 46) using the distributive property, and we got: 46*(13*z**2) + (7*z)*(13*z**2) + (13*z**2)*(8*z**3)
Replacing (13*z**2)*(8*z**3 + 7*z + 46) with 46*(13*z**2) + (7*z)*(13*z**2) + (13*z**2)*(8*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 46*13*z**2 + (7*z)*(13*z**2) + (7*z)*41 + (39*z)*(8*z**3 + 7*z + 46) + (13*z**2)*(8*z**3) + (8*z**3)*41 + 1886</replace>
Simplifying the partial expression: (39*z)*(8*z**3 + 7*z + 46)
Expanding the part (8*z**3 + 7*z + 46) using the distributive property, and we got: 46*(39*z) + (7*z)*(39*z) + (39*z)*(8*z**3)
Replacing (39*z)*(8*z**3 + 7*z + 46) with 46*(39*z) + (7*z)*(39*z) + (39*z)*(8*z**3) in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 46*13*z**2 + 46*39*z + (7*z)*(39*z) + (7*z)*(13*z**2) + (7*z)*41 + (39*z)*(8*z**3) + (13*z**2)*(8*z**3) + (8*z**3)*41 + 1886</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (7*z)*41 = 287*z
  (7*z)*(13*z**2) = 91*z**3
  (7*z)*(39*z) = 273*z**2
  (8*z**3)*41 = 328*z**3
  (8*z**3)*(13*z**2) = 104*z**5
  (8*z**3)*(39*z) = 312*z**4
  46*13*z**2 = 598*z**2
  46*39*z = 1794*z
Replacing them in the overall expression.
<replace-#Step 5>#Step 6:
Current expression: 104*z**5 + 312*z**4 + 91*z**3 + 328*z**3 + 273*z**2 + 598*z**2 + 287*z + 1794*z + 1886</replace>
Combining like terms, got 104*z**5 + 312*z**4 + 419*z**3 + 871*z**2 + 2081*z + 1886
<replace-#Step 6>#Step 7:
Current expression: 104*z**5 + 312*z**4 + 419*z**3 + 871*z**2 + 2081*z + 1886</replace>
No more calculations needed.
<answer>104*z**5 + 312*z**4 + 419*z**3 + 871*z**2 + 2081*z + 1886</answer>


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

Answer: 729*z**5 + 1593*z**4 + 450*z**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (27*z**2 + 9*z)*(27*z**3 + 50*z**2)
Expanding the part (27*z**2 + 9*z) using the distributive property, and we got: (9*z)*(27*z**3 + 50*z**2) + (27*z**2)*(27*z**3 + 50*z**2)
<replace-#Step 1>#Step 2:
Current expression: (9*z)*(27*z**3 + 50*z**2) + (27*z**2)*(27*z**3 + 50*z**2)</replace>
Simplifying the partial expression: (9*z)*(27*z**3 + 50*z**2)
Expanding the part (27*z**3 + 50*z**2) using the distributive property, and we got: (9*z)*(50*z**2) + (9*z)*(27*z**3)
Replacing (9*z)*(27*z**3 + 50*z**2) with (9*z)*(50*z**2) + (9*z)*(27*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (9*z)*(50*z**2) + (9*z)*(27*z**3) + (27*z**2)*(27*z**3 + 50*z**2)</replace>
Simplifying the partial expression: (27*z**2)*(27*z**3 + 50*z**2)
Expanding the part (27*z**3 + 50*z**2) using the distributive property, and we got: (27*z**2)*(50*z**2) + (27*z**2)*(27*z**3)
Replacing (27*z**2)*(27*z**3 + 50*z**2) with (27*z**2)*(50*z**2) + (27*z**2)*(27*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (9*z)*(50*z**2) + (9*z)*(27*z**3) + (27*z**2)*(50*z**2) + (27*z**2)*(27*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (27*z**3)*(9*z) = 243*z**4
  (27*z**3)*(27*z**2) = 729*z**5
  (50*z**2)*(9*z) = 450*z**3
  (50*z**2)*(27*z**2) = 1350*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 729*z**5 + 243*z**4 + 1350*z**4 + 450*z**3</replace>
Combining like terms, got 729*z**5 + 1593*z**4 + 450*z**3
<replace-#Step 5>#Step 6:
Current expression: 729*z**5 + 1593*z**4 + 450*z**3</replace>
No more calculations needed.
<answer>729*z**5 + 1593*z**4 + 450*z**3</answer>


Question:
Calculate the following: (-27*x**2 + 12*x)*(26*x**3 + 12*x**2 + 76*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: -702*x**5 - 12*x**4 - 1908*x**3 + 912*x**2


Question:
Simplify this expression: (32*y**2 - 3)*(-33*y**3 + 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: -1056*y**5 + 995*y**3 - 84*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (32*y**2 - 3)*(-33*y**3 + 28*y)
Expanding the part (32*y**2 - 3) using the distributive property, and we got: (32*y**2)*(-33*y**3 + 28*y) - 3*(-33*y**3 + 28*y)
<replace-#Step 1>#Step 2:
Current expression: (32*y**2)*(-33*y**3 + 28*y) - 3*(-33*y**3 + 28*y)</replace>
Simplifying the partial expression: -3*(-33*y**3 + 28*y)
Expanding the part (-33*y**3 + 28*y) using the distributive property, and we got: (28*y)*(-3) - 33*y**3*(-3)
Replacing -3*(-33*y**3 + 28*y) with (28*y)*(-3) - 33*y**3*(-3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (28*y)*(-3) + (32*y**2)*(-33*y**3 + 28*y) - 33*y**3*(-3)</replace>
Simplifying the partial expression: (32*y**2)*(-33*y**3 + 28*y)
Expanding the part (-33*y**3 + 28*y) using the distributive property, and we got: (28*y)*(32*y**2) + (32*y**2)*(-33*y**3)
Replacing (32*y**2)*(-33*y**3 + 28*y) with (28*y)*(32*y**2) + (32*y**2)*(-33*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (28*y)*(32*y**2) + (28*y)*(-3) + (32*y**2)*(-33*y**3) - 33*y**3*(-3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-33*y**3)*-3 = 99*y**3
  (-33*y**3)*(32*y**2) = -1056*y**5
  (28*y)*-3 = -84*y
  (28*y)*(32*y**2) = 896*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1056*y**5 + 99*y**3 + 896*y**3 - 84*y</replace>
Combining like terms, got -1056*y**5 + 995*y**3 - 84*y
<replace-#Step 5>#Step 6:
Current expression: -1056*y**5 + 995*y**3 - 84*y</replace>
No more calculations needed.
<answer>-1056*y**5 + 995*y**3 - 84*y</answer>