Question:
Calculate the following: -42*y*(20*y**2 - 45*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -840*y**3 + 1890*y**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -42*y*(20*y**2 - 45*y)
Expanding the part (20*y**2 - 45*y) using the distributive property, and we got: (-45*y)*(-42*y) + (-42*y)*(20*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-45*y)*(-42*y) + (-42*y)*(20*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-45*y)*(-42*y) = 1890*y**2
  (20*y**2)*(-42*y) = -840*y**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -840*y**3 + 1890*y**2</replace>
No more calculations needed.
<answer>-840*y**3 + 1890*y**2</answer>


Question:
Simplify this expression: (83*x + 47)*(29*x**3 + 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: 2407*x**4 + 1363*x**3 + 332*x + 188

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: (83*x + 47)*(29*x**3 + 4)
Expanding the part (29*x**3 + 4) using the distributive property, and we got: (29*x**3)*(83*x + 47) + 4*(83*x + 47)
<replace-#Step 1>#Step 2:
Current expression: (29*x**3)*(83*x + 47) + 4*(83*x + 47)</replace>
Simplifying the partial expression: 4*(83*x + 47)
Expanding the part (83*x + 47) using the distributive property, and we got: (83*x)*4 + 47*4
Replacing 4*(83*x + 47) with (83*x)*4 + 47*4 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (83*x)*4 + (29*x**3)*(83*x + 47) + 188</replace>
Simplifying the partial expression: (29*x**3)*(83*x + 47)
Expanding the part (83*x + 47) using the distributive property, and we got: 47*(29*x**3) + (83*x)*(29*x**3)
Replacing (29*x**3)*(83*x + 47) with 47*(29*x**3) + (83*x)*(29*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 47*29*x**3 + (83*x)*(29*x**3) + (83*x)*4 + 188</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (83*x)*4 = 332*x
  (83*x)*(29*x**3) = 2407*x**4
  47*29*x**3 = 1363*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2407*x**4 + 1363*x**3 + 332*x + 188</replace>
No more calculations needed.
<answer>2407*x**4 + 1363*x**3 + 332*x + 188</answer>


Question:
Calculate the following: (9*z**2 - 13)*(40*z**3 - 32*z**2 - 5*z + 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: 360*z**5 - 288*z**4 - 565*z**3 + 578*z**2 + 65*z - 234


Question:
Calculate the following: (-45*z**3 - 3*z**2 + 37)*(-z**3 - 21*z + 5)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 45*z**6 + 3*z**5 + 945*z**4 - 199*z**3 - 15*z**2 - 777*z + 185


Question:
Calculate the following: (42 - 7*z**3)*(44*z**2 - 8)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -308*z**5 + 56*z**3 + 1848*z**2 - 336

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (42 - 7*z**3)*(44*z**2 - 8)
Expanding the part (44*z**2 - 8) using the distributive property, and we got: (44*z**2)*(42 - 7*z**3) - 8*(42 - 7*z**3)
<replace-#Step 1>#Step 2:
Current expression: (44*z**2)*(42 - 7*z**3) - 8*(42 - 7*z**3)</replace>
Simplifying the partial expression: -8*(42 - 7*z**3)
Expanding the part (42 - 7*z**3) using the distributive property, and we got: -7*z**3*(-8) + 42*(-8)
Replacing -8*(42 - 7*z**3) with -7*z**3*(-8) + 42*(-8) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (44*z**2)*(42 - 7*z**3) - 7*z**3*(-8) - 336</replace>
Simplifying the partial expression: (44*z**2)*(42 - 7*z**3)
Expanding the part (42 - 7*z**3) using the distributive property, and we got: 42*(44*z**2) + (44*z**2)*(-7*z**3)
Replacing (44*z**2)*(42 - 7*z**3) with 42*(44*z**2) + (44*z**2)*(-7*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 42*44*z**2 + (44*z**2)*(-7*z**3) - 7*z**3*(-8) - 336</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-7*z**3)*-8 = 56*z**3
  (-7*z**3)*(44*z**2) = -308*z**5
  42*44*z**2 = 1848*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -308*z**5 + 56*z**3 + 1848*z**2 - 336</replace>
No more calculations needed.
<answer>-308*z**5 + 56*z**3 + 1848*z**2 - 336</answer>


Question:
Calculate the following: (-75*x**3 - 40*x**2 - 43)*(23*x**3 - 32*x**2 - 29)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1725*x**6 + 1480*x**5 + 1280*x**4 + 1186*x**3 + 2536*x**2 + 1247


Question:
Simplify this expression: (46 - 34*z**2)*(-87*z - 25)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2958*z**3 + 850*z**2 - 4002*z - 1150

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (46 - 34*z**2)*(-87*z - 25)
Expanding the part (-87*z - 25) using the distributive property, and we got: (-87*z)*(46 - 34*z**2) - 25*(46 - 34*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-87*z)*(46 - 34*z**2) - 25*(46 - 34*z**2)</replace>
Simplifying the partial expression: -25*(46 - 34*z**2)
Expanding the part (46 - 34*z**2) using the distributive property, and we got: -34*z**2*(-25) + 46*(-25)
Replacing -25*(46 - 34*z**2) with -34*z**2*(-25) + 46*(-25) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-87*z)*(46 - 34*z**2) - 34*z**2*(-25) - 1150</replace>
Simplifying the partial expression: (-87*z)*(46 - 34*z**2)
Expanding the part (46 - 34*z**2) using the distributive property, and we got: (-87*z)*(-34*z**2) + 46*(-87*z)
Replacing (-87*z)*(46 - 34*z**2) with (-87*z)*(-34*z**2) + 46*(-87*z) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-87*z)*(-34*z**2) + 46*(-87)*z - 34*z**2*(-25) - 1150</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-34*z**2)*-25 = 850*z**2
  (-34*z**2)*(-87*z) = 2958*z**3
  46*-87*z = -4002*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2958*z**3 + 850*z**2 - 4002*z - 1150</replace>
No more calculations needed.
<answer>2958*z**3 + 850*z**2 - 4002*z - 1150</answer>


Question:
Simplify this expression: (-15*x**2 - 5)*(-40*x**2 - 48*x - 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: 600*x**4 + 720*x**3 + 500*x**2 + 240*x + 100

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*x**2 - 5)*(-40*x**2 - 48*x - 20)
Expanding the part (-15*x**2 - 5) using the distributive property, and we got: (-15*x**2)*(-40*x**2 - 48*x - 20) - 5*(-40*x**2 - 48*x - 20)
<replace-#Step 1>#Step 2:
Current expression: (-15*x**2)*(-40*x**2 - 48*x - 20) - 5*(-40*x**2 - 48*x - 20)</replace>
Simplifying the partial expression: -5*(-40*x**2 - 48*x - 20)
Expanding the part (-40*x**2 - 48*x - 20) using the distributive property, and we got: -48*x*(-5) - 40*x**2*(-5) - 20*(-5)
Replacing -5*(-40*x**2 - 48*x - 20) with -48*x*(-5) - 40*x**2*(-5) - 20*(-5) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -48*x*(-5) - 40*x**2*(-5) + (-15*x**2)*(-40*x**2 - 48*x - 20) + 100</replace>
Simplifying the partial expression: (-15*x**2)*(-40*x**2 - 48*x - 20)
Expanding the part (-40*x**2 - 48*x - 20) using the distributive property, and we got: (-48*x)*(-15*x**2) - (-1)*300*x**2 + (-40*x**2)*(-15*x**2)
Replacing (-15*x**2)*(-40*x**2 - 48*x - 20) with (-48*x)*(-15*x**2) - (-1)*300*x**2 + (-40*x**2)*(-15*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-48*x)*(-15*x**2) - 48*x*(-5) - 20*(-15)*x**2 + (-40*x**2)*(-15*x**2) - 40*x**2*(-5) + 100</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-48*x)*-5 = 240*x
  (-48*x)*(-15*x**2) = 720*x**3
  (-40*x**2)*-5 = 200*x**2
  (-40*x**2)*(-15*x**2) = 600*x**4
  -20*-15*x**2 = 300*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 600*x**4 + 720*x**3 + 200*x**2 + 300*x**2 + 240*x + 100</replace>
Combining like terms, got 600*x**4 + 720*x**3 + 500*x**2 + 240*x + 100
<replace-#Step 5>#Step 6:
Current expression: 600*x**4 + 720*x**3 + 500*x**2 + 240*x + 100</replace>
No more calculations needed.
<answer>600*x**4 + 720*x**3 + 500*x**2 + 240*x + 100</answer>


Question:
Simplify this expression: (-30*x**2 + 47*x + 48)*(x**2 + 49*x - 39)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -30*x**4 - 1423*x**3 + 3521*x**2 + 519*x - 1872


Question:
Calculate the following: (31*x**3 + 45*x)*(-16*x**3 + 47*x - 45)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -496*x**6 + 737*x**4 - 1395*x**3 + 2115*x**2 - 2025*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (31*x**3 + 45*x)*(-16*x**3 + 47*x - 45)
Expanding the part (31*x**3 + 45*x) using the distributive property, and we got: (45*x)*(-16*x**3 + 47*x - 45) + (31*x**3)*(-16*x**3 + 47*x - 45)
<replace-#Step 1>#Step 2:
Current expression: (45*x)*(-16*x**3 + 47*x - 45) + (31*x**3)*(-16*x**3 + 47*x - 45)</replace>
Simplifying the partial expression: (31*x**3)*(-16*x**3 + 47*x - 45)
Expanding the part (-16*x**3 + 47*x - 45) using the distributive property, and we got: -1395*x**3 + (47*x)*(31*x**3) + (-16*x**3)*(31*x**3)
Replacing (31*x**3)*(-16*x**3 + 47*x - 45) with -1395*x**3 + (47*x)*(31*x**3) + (-16*x**3)*(31*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -45*31*x**3 + (45*x)*(-16*x**3 + 47*x - 45) + (47*x)*(31*x**3) + (-16*x**3)*(31*x**3)</replace>
Simplifying the partial expression: (45*x)*(-16*x**3 + 47*x - 45)
Expanding the part (-16*x**3 + 47*x - 45) using the distributive property, and we got: -2025*x + (45*x)*(47*x) + (45*x)*(-16*x**3)
Replacing (45*x)*(-16*x**3 + 47*x - 45) with -2025*x + (45*x)*(47*x) + (45*x)*(-16*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -45*31*x**3 - 45*45*x + (45*x)*(47*x) + (45*x)*(-16*x**3) + (47*x)*(31*x**3) + (-16*x**3)*(31*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-16*x**3)*(31*x**3) = -496*x**6
  (-16*x**3)*(45*x) = -720*x**4
  (47*x)*(31*x**3) = 1457*x**4
  (47*x)*(45*x) = 2115*x**2
  -45*31*x**3 = -1395*x**3
  -45*45*x = -2025*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -496*x**6 - 720*x**4 + 1457*x**4 - 1395*x**3 + 2115*x**2 - 2025*x</replace>
Combining like terms, got -496*x**6 + 737*x**4 - 1395*x**3 + 2115*x**2 - 2025*x
<replace-#Step 5>#Step 6:
Current expression: -496*x**6 + 737*x**4 - 1395*x**3 + 2115*x**2 - 2025*x</replace>
No more calculations needed.
<answer>-496*x**6 + 737*x**4 - 1395*x**3 + 2115*x**2 - 2025*x</answer>


Question:
Simplify this expression: (20*x - 6)*(16*x**3 + 28*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: 320*x**4 + 464*x**3 - 168*x**2 + 260*x - 78

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (20*x - 6)*(16*x**3 + 28*x**2 + 13)
Expanding the part (20*x - 6) using the distributive property, and we got: (20*x)*(16*x**3 + 28*x**2 + 13) - 6*(16*x**3 + 28*x**2 + 13)
<replace-#Step 1>#Step 2:
Current expression: (20*x)*(16*x**3 + 28*x**2 + 13) - 6*(16*x**3 + 28*x**2 + 13)</replace>
Simplifying the partial expression: -6*(16*x**3 + 28*x**2 + 13)
Expanding the part (16*x**3 + 28*x**2 + 13) using the distributive property, and we got: (28*x**2)*(-6) + (16*x**3)*(-6) + 13*(-6)
Replacing -6*(16*x**3 + 28*x**2 + 13) with (28*x**2)*(-6) + (16*x**3)*(-6) + 13*(-6) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (20*x)*(16*x**3 + 28*x**2 + 13) + (28*x**2)*(-6) + (16*x**3)*(-6) - 78</replace>
Simplifying the partial expression: (20*x)*(16*x**3 + 28*x**2 + 13)
Expanding the part (16*x**3 + 28*x**2 + 13) using the distributive property, and we got: 13*(20*x) + (20*x)*(28*x**2) + (20*x)*(16*x**3)
Replacing (20*x)*(16*x**3 + 28*x**2 + 13) with 13*(20*x) + (20*x)*(28*x**2) + (20*x)*(16*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 13*20*x + (20*x)*(28*x**2) + (20*x)*(16*x**3) + (28*x**2)*(-6) + (16*x**3)*(-6) - 78</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (16*x**3)*-6 = -96*x**3
  (16*x**3)*(20*x) = 320*x**4
  (28*x**2)*-6 = -168*x**2
  (28*x**2)*(20*x) = 560*x**3
  13*20*x = 260*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 320*x**4 - 96*x**3 + 560*x**3 - 168*x**2 + 260*x - 78</replace>
Combining like terms, got 320*x**4 + 464*x**3 - 168*x**2 + 260*x - 78
<replace-#Step 5>#Step 6:
Current expression: 320*x**4 + 464*x**3 - 168*x**2 + 260*x - 78</replace>
No more calculations needed.
<answer>320*x**4 + 464*x**3 - 168*x**2 + 260*x - 78</answer>


Question:
Simplify this expression: (41*x**2 - 55)*(35*x**3 + 22*x**2 - 33)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1435*x**5 + 902*x**4 - 1925*x**3 - 2563*x**2 + 1815


Question:
Calculate the following: (23 - 42*z**2)*(-20*z**2 - 21)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 840*z**4 + 422*z**2 - 483

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 - 42*z**2)*(-20*z**2 - 21)
Expanding the part (-20*z**2 - 21) using the distributive property, and we got: (-20*z**2)*(23 - 42*z**2) - 21*(23 - 42*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-20*z**2)*(23 - 42*z**2) - 21*(23 - 42*z**2)</replace>
Simplifying the partial expression: -21*(23 - 42*z**2)
Expanding the part (23 - 42*z**2) using the distributive property, and we got: -42*z**2*(-21) + 23*(-21)
Replacing -21*(23 - 42*z**2) with -42*z**2*(-21) + 23*(-21) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -42*z**2*(-21) + (-20*z**2)*(23 - 42*z**2) - 483</replace>
Simplifying the partial expression: (-20*z**2)*(23 - 42*z**2)
Expanding the part (23 - 42*z**2) using the distributive property, and we got: 23*(-20*z**2) + (-42*z**2)*(-20*z**2)
Replacing (-20*z**2)*(23 - 42*z**2) with 23*(-20*z**2) + (-42*z**2)*(-20*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 23*(-20)*z**2 + (-42*z**2)*(-20*z**2) - 42*z**2*(-21) - 483</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-42*z**2)*-21 = 882*z**2
  (-42*z**2)*(-20*z**2) = 840*z**4
  23*-20*z**2 = -460*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 840*z**4 - 460*z**2 + 882*z**2 - 483</replace>
Combining like terms, got 840*z**4 + 422*z**2 - 483
<replace-#Step 5>#Step 6:
Current expression: 840*z**4 + 422*z**2 - 483</replace>
No more calculations needed.
<answer>840*z**4 + 422*z**2 - 483</answer>


Question:
Calculate the following: (-6*z**3 + 9*z + 12)*(-2*z**3 + 30*z - 64)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*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*z**6 - 198*z**4 + 360*z**3 + 270*z**2 - 216*z - 768


Question:
Simplify this expression: (34*z**2 + 41*z)*(-44*z**3 + 47*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: -1496*z**5 - 206*z**4 + 1927*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: (34*z**2 + 41*z)*(-44*z**3 + 47*z**2)
Expanding the part (-44*z**3 + 47*z**2) using the distributive property, and we got: (47*z**2)*(34*z**2 + 41*z) + (-44*z**3)*(34*z**2 + 41*z)
<replace-#Step 1>#Step 2:
Current expression: (47*z**2)*(34*z**2 + 41*z) + (-44*z**3)*(34*z**2 + 41*z)</replace>
Simplifying the partial expression: (-44*z**3)*(34*z**2 + 41*z)
Expanding the part (34*z**2 + 41*z) using the distributive property, and we got: (41*z)*(-44*z**3) + (34*z**2)*(-44*z**3)
Replacing (-44*z**3)*(34*z**2 + 41*z) with (41*z)*(-44*z**3) + (34*z**2)*(-44*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (41*z)*(-44*z**3) + (34*z**2)*(-44*z**3) + (47*z**2)*(34*z**2 + 41*z)</replace>
Simplifying the partial expression: (47*z**2)*(34*z**2 + 41*z)
Expanding the part (34*z**2 + 41*z) using the distributive property, and we got: (41*z)*(47*z**2) + (34*z**2)*(47*z**2)
Replacing (47*z**2)*(34*z**2 + 41*z) with (41*z)*(47*z**2) + (34*z**2)*(47*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (41*z)*(47*z**2) + (41*z)*(-44*z**3) + (34*z**2)*(47*z**2) + (34*z**2)*(-44*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (34*z**2)*(-44*z**3) = -1496*z**5
  (34*z**2)*(47*z**2) = 1598*z**4
  (41*z)*(-44*z**3) = -1804*z**4
  (41*z)*(47*z**2) = 1927*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1496*z**5 - 1804*z**4 + 1598*z**4 + 1927*z**3</replace>
Combining like terms, got -1496*z**5 - 206*z**4 + 1927*z**3
<replace-#Step 5>#Step 6:
Current expression: -1496*z**5 - 206*z**4 + 1927*z**3</replace>
No more calculations needed.
<answer>-1496*z**5 - 206*z**4 + 1927*z**3</answer>


Question:
Calculate the following: (25*x**2 - 10)*(-74*x**3 + 17*x - 12)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1850*x**5 + 1165*x**3 - 300*x**2 - 170*x + 120

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 - 10)*(-74*x**3 + 17*x - 12)
Expanding the part (25*x**2 - 10) using the distributive property, and we got: (25*x**2)*(-74*x**3 + 17*x - 12) - 10*(-74*x**3 + 17*x - 12)
<replace-#Step 1>#Step 2:
Current expression: (25*x**2)*(-74*x**3 + 17*x - 12) - 10*(-74*x**3 + 17*x - 12)</replace>
Simplifying the partial expression: -10*(-74*x**3 + 17*x - 12)
Expanding the part (-74*x**3 + 17*x - 12) using the distributive property, and we got: (17*x)*(-10) - 74*x**3*(-10) - 12*(-10)
Replacing -10*(-74*x**3 + 17*x - 12) with (17*x)*(-10) - 74*x**3*(-10) - 12*(-10) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (17*x)*(-10) + (25*x**2)*(-74*x**3 + 17*x - 12) - 74*x**3*(-10) + 120</replace>
Simplifying the partial expression: (25*x**2)*(-74*x**3 + 17*x - 12)
Expanding the part (-74*x**3 + 17*x - 12) using the distributive property, and we got: -300*x**2 + (17*x)*(25*x**2) + (25*x**2)*(-74*x**3)
Replacing (25*x**2)*(-74*x**3 + 17*x - 12) with -300*x**2 + (17*x)*(25*x**2) + (25*x**2)*(-74*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -12*25*x**2 + (17*x)*(25*x**2) + (17*x)*(-10) + (25*x**2)*(-74*x**3) - 74*x**3*(-10) + 120</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-74*x**3)*-10 = 740*x**3
  (-74*x**3)*(25*x**2) = -1850*x**5
  (17*x)*-10 = -170*x
  (17*x)*(25*x**2) = 425*x**3
  -12*25*x**2 = -300*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1850*x**5 + 425*x**3 + 740*x**3 - 300*x**2 - 170*x + 120</replace>
Combining like terms, got -1850*x**5 + 1165*x**3 - 300*x**2 - 170*x + 120
<replace-#Step 5>#Step 6:
Current expression: -1850*x**5 + 1165*x**3 - 300*x**2 - 170*x + 120</replace>
No more calculations needed.
<answer>-1850*x**5 + 1165*x**3 - 300*x**2 - 170*x + 120</answer>


Question:
Simplify this expression: (50*z**3 - 30)*(-43*z**3 - 33*z**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: -2150*z**6 - 1650*z**5 + 290*z**3 + 990*z**2 + 600


Question:
Simplify this expression: -27*x*(-17*x**3 - 33*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: 459*x**4 + 891*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: -27*x*(-17*x**3 - 33*x**2)
Expanding the part (-17*x**3 - 33*x**2) using the distributive property, and we got: (-27*x)*(-33*x**2) + (-27*x)*(-17*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-27*x)*(-33*x**2) + (-27*x)*(-17*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-33*x**2)*(-27*x) = 891*x**3
  (-17*x**3)*(-27*x) = 459*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 459*x**4 + 891*x**3</replace>
No more calculations needed.
<answer>459*x**4 + 891*x**3</answer>


Question:
Simplify this expression: (46*x**3 - 12)*(-5*x**3 - 14*x**2 + 22*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: -230*x**6 - 644*x**5 + 1012*x**4 + 60*x**3 + 168*x**2 - 264*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (46*x**3 - 12)*(-5*x**3 - 14*x**2 + 22*x)
Expanding the part (46*x**3 - 12) using the distributive property, and we got: (46*x**3)*(-5*x**3 - 14*x**2 + 22*x) - 12*(-5*x**3 - 14*x**2 + 22*x)
<replace-#Step 1>#Step 2:
Current expression: (46*x**3)*(-5*x**3 - 14*x**2 + 22*x) - 12*(-5*x**3 - 14*x**2 + 22*x)</replace>
Simplifying the partial expression: -12*(-5*x**3 - 14*x**2 + 22*x)
Expanding the part (-5*x**3 - 14*x**2 + 22*x) using the distributive property, and we got: (22*x)*(-12) - 14*x**2*(-12) - 5*x**3*(-12)
Replacing -12*(-5*x**3 - 14*x**2 + 22*x) with (22*x)*(-12) - 14*x**2*(-12) - 5*x**3*(-12) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (22*x)*(-12) - 14*x**2*(-12) - 5*x**3*(-12) + (46*x**3)*(-5*x**3 - 14*x**2 + 22*x)</replace>
Simplifying the partial expression: (46*x**3)*(-5*x**3 - 14*x**2 + 22*x)
Expanding the part (-5*x**3 - 14*x**2 + 22*x) using the distributive property, and we got: (22*x)*(46*x**3) + (-14*x**2)*(46*x**3) + (-5*x**3)*(46*x**3)
Replacing (46*x**3)*(-5*x**3 - 14*x**2 + 22*x) with (22*x)*(46*x**3) + (-14*x**2)*(46*x**3) + (-5*x**3)*(46*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (22*x)*(46*x**3) + (22*x)*(-12) + (-14*x**2)*(46*x**3) - 14*x**2*(-12) + (-5*x**3)*(46*x**3) - 5*x**3*(-12)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-14*x**2)*-12 = 168*x**2
  (-14*x**2)*(46*x**3) = -644*x**5
  (-5*x**3)*-12 = 60*x**3
  (-5*x**3)*(46*x**3) = -230*x**6
  (22*x)*-12 = -264*x
  (22*x)*(46*x**3) = 1012*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -230*x**6 - 644*x**5 + 1012*x**4 + 60*x**3 + 168*x**2 - 264*x</replace>
No more calculations needed.
<answer>-230*x**6 - 644*x**5 + 1012*x**4 + 60*x**3 + 168*x**2 - 264*x</answer>


Question:
Calculate the following: (50*z**3 + 52*z**2 + 49)*(60*z**3 + 6*z**2 - 41*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: 3000*z**6 + 3420*z**5 - 1738*z**4 + 808*z**3 + 294*z**2 - 2009*z


Question:
Calculate the following: (33 - 36*x**3)*(23*x - 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: -828*x**4 + 468*x**3 + 759*x - 429

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (33 - 36*x**3)*(23*x - 13)
Expanding the part (23*x - 13) using the distributive property, and we got: (23*x)*(33 - 36*x**3) - 13*(33 - 36*x**3)
<replace-#Step 1>#Step 2:
Current expression: (23*x)*(33 - 36*x**3) - 13*(33 - 36*x**3)</replace>
Simplifying the partial expression: -13*(33 - 36*x**3)
Expanding the part (33 - 36*x**3) using the distributive property, and we got: -36*x**3*(-13) + 33*(-13)
Replacing -13*(33 - 36*x**3) with -36*x**3*(-13) + 33*(-13) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (23*x)*(33 - 36*x**3) - 36*x**3*(-13) - 429</replace>
Simplifying the partial expression: (23*x)*(33 - 36*x**3)
Expanding the part (33 - 36*x**3) using the distributive property, and we got: 33*(23*x) + (23*x)*(-36*x**3)
Replacing (23*x)*(33 - 36*x**3) with 33*(23*x) + (23*x)*(-36*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 33*23*x + (23*x)*(-36*x**3) - 36*x**3*(-13) - 429</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-36*x**3)*-13 = 468*x**3
  (-36*x**3)*(23*x) = -828*x**4
  33*23*x = 759*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -828*x**4 + 468*x**3 + 759*x - 429</replace>
No more calculations needed.
<answer>-828*x**4 + 468*x**3 + 759*x - 429</answer>


Question:
Calculate the following: -94*y*(26*y**3 + 30*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: -2444*y**4 - 2820*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: -94*y*(26*y**3 + 30*y)
Expanding the part (26*y**3 + 30*y) using the distributive property, and we got: (-94*y)*(30*y) + (-94*y)*(26*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-94*y)*(30*y) + (-94*y)*(26*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (26*y**3)*(-94*y) = -2444*y**4
  (30*y)*(-94*y) = -2820*y**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -2444*y**4 - 2820*y**2</replace>
No more calculations needed.
<answer>-2444*y**4 - 2820*y**2</answer>


Question:
Calculate the following: (-48*y**3 - 40*y**2 - 21)*(23*y**3 + 43*y**2 - 12*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: -1104*y**6 - 2984*y**5 - 1144*y**4 - 3*y**3 - 903*y**2 + 252*y


Question:
Calculate the following: (30 - 14*x)*(44*x**2 - 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: -616*x**3 + 1320*x**2 + 700*x - 1500

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: (30 - 14*x)*(44*x**2 - 50)
Expanding the part (44*x**2 - 50) using the distributive property, and we got: (44*x**2)*(30 - 14*x) - 50*(30 - 14*x)
<replace-#Step 1>#Step 2:
Current expression: (44*x**2)*(30 - 14*x) - 50*(30 - 14*x)</replace>
Simplifying the partial expression: -50*(30 - 14*x)
Expanding the part (30 - 14*x) using the distributive property, and we got: -14*x*(-50) + 30*(-50)
Replacing -50*(30 - 14*x) with -14*x*(-50) + 30*(-50) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -14*x*(-50) + (44*x**2)*(30 - 14*x) - 1500</replace>
Simplifying the partial expression: (44*x**2)*(30 - 14*x)
Expanding the part (30 - 14*x) using the distributive property, and we got: (-14*x)*(44*x**2) + 30*(44*x**2)
Replacing (44*x**2)*(30 - 14*x) with (-14*x)*(44*x**2) + 30*(44*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-14*x)*(44*x**2) - 14*x*(-50) + 30*44*x**2 - 1500</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-14*x)*-50 = 700*x
  (-14*x)*(44*x**2) = -616*x**3
  30*44*x**2 = 1320*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -616*x**3 + 1320*x**2 + 700*x - 1500</replace>
No more calculations needed.
<answer>-616*x**3 + 1320*x**2 + 700*x - 1500</answer>


Question:
Simplify this expression: (-18*y**2 - 37*y)*(14*y**2 - 49*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: -252*y**4 + 364*y**3 + 1813*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: (-18*y**2 - 37*y)*(14*y**2 - 49*y)
Expanding the part (14*y**2 - 49*y) using the distributive property, and we got: (-49*y)*(-18*y**2 - 37*y) + (14*y**2)*(-18*y**2 - 37*y)
<replace-#Step 1>#Step 2:
Current expression: (-49*y)*(-18*y**2 - 37*y) + (14*y**2)*(-18*y**2 - 37*y)</replace>
Simplifying the partial expression: (-49*y)*(-18*y**2 - 37*y)
Expanding the part (-18*y**2 - 37*y) using the distributive property, and we got: (-49*y)*(-37*y) + (-49*y)*(-18*y**2)
Replacing (-49*y)*(-18*y**2 - 37*y) with (-49*y)*(-37*y) + (-49*y)*(-18*y**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-49*y)*(-37*y) + (-49*y)*(-18*y**2) + (14*y**2)*(-18*y**2 - 37*y)</replace>
Simplifying the partial expression: (14*y**2)*(-18*y**2 - 37*y)
Expanding the part (-18*y**2 - 37*y) using the distributive property, and we got: (-37*y)*(14*y**2) + (-18*y**2)*(14*y**2)
Replacing (14*y**2)*(-18*y**2 - 37*y) with (-37*y)*(14*y**2) + (-18*y**2)*(14*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-49*y)*(-37*y) + (-49*y)*(-18*y**2) + (-37*y)*(14*y**2) + (-18*y**2)*(14*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-37*y)*(-49*y) = 1813*y**2
  (-37*y)*(14*y**2) = -518*y**3
  (-18*y**2)*(-49*y) = 882*y**3
  (-18*y**2)*(14*y**2) = -252*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -252*y**4 - 518*y**3 + 882*y**3 + 1813*y**2</replace>
Combining like terms, got -252*y**4 + 364*y**3 + 1813*y**2
<replace-#Step 5>#Step 6:
Current expression: -252*y**4 + 364*y**3 + 1813*y**2</replace>
No more calculations needed.
<answer>-252*y**4 + 364*y**3 + 1813*y**2</answer>


Question:
Simplify this expression: (20 - 8*y**3)*(-22*y**3 + 8*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 176*y**6 - 64*y**4 - 440*y**3 + 160*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 - 8*y**3)*(-22*y**3 + 8*y)
Expanding the part (20 - 8*y**3) using the distributive property, and we got: (-8*y**3)*(-22*y**3 + 8*y) + 20*(-22*y**3 + 8*y)
<replace-#Step 1>#Step 2:
Current expression: (-8*y**3)*(-22*y**3 + 8*y) + 20*(-22*y**3 + 8*y)</replace>
Simplifying the partial expression: 20*(-22*y**3 + 8*y)
Expanding the part (-22*y**3 + 8*y) using the distributive property, and we got: (8*y)*20 - 22*y**3*20
Replacing 20*(-22*y**3 + 8*y) with (8*y)*20 - 22*y**3*20 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (8*y)*20 - 22*y**3*20 + (-8*y**3)*(-22*y**3 + 8*y)</replace>
Simplifying the partial expression: (-8*y**3)*(-22*y**3 + 8*y)
Expanding the part (-22*y**3 + 8*y) using the distributive property, and we got: (8*y)*(-8*y**3) + (-22*y**3)*(-8*y**3)
Replacing (-8*y**3)*(-22*y**3 + 8*y) with (8*y)*(-8*y**3) + (-22*y**3)*(-8*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (8*y)*(-8*y**3) + (8*y)*20 + (-22*y**3)*(-8*y**3) - 22*y**3*20</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-22*y**3)*20 = -440*y**3
  (-22*y**3)*(-8*y**3) = 176*y**6
  (8*y)*20 = 160*y
  (8*y)*(-8*y**3) = -64*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 176*y**6 - 64*y**4 - 440*y**3 + 160*y</replace>
No more calculations needed.
<answer>176*y**6 - 64*y**4 - 440*y**3 + 160*y</answer>


Question:
Calculate the following: 36*z**3*(-43*z**3 + 23*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: -1548*z**6 + 828*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: 36*z**3*(-43*z**3 + 23*z)
Expanding the part (-43*z**3 + 23*z) using the distributive property, and we got: (23*z)*(36*z**3) + (-43*z**3)*(36*z**3)
<replace-#Step 1>#Step 2:
Current expression: (23*z)*(36*z**3) + (-43*z**3)*(36*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-43*z**3)*(36*z**3) = -1548*z**6
  (23*z)*(36*z**3) = 828*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1548*z**6 + 828*z**4</replace>
No more calculations needed.
<answer>-1548*z**6 + 828*z**4</answer>


Question:
Calculate the following: (-28*x**2 + 12*x)*(58*x**3 - 20*x**2 - 45*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: -1624*x**5 + 1256*x**4 + 1020*x**3 - 540*x**2


Question:
Calculate the following: (16*z + 58)*(14*z**2 + 36*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: 224*z**3 + 1388*z**2 + 2088*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: (16*z + 58)*(14*z**2 + 36*z)
Expanding the part (16*z + 58) using the distributive property, and we got: (16*z)*(14*z**2 + 36*z) + 58*(14*z**2 + 36*z)
<replace-#Step 1>#Step 2:
Current expression: (16*z)*(14*z**2 + 36*z) + 58*(14*z**2 + 36*z)</replace>
Simplifying the partial expression: 58*(14*z**2 + 36*z)
Expanding the part (14*z**2 + 36*z) using the distributive property, and we got: (36*z)*58 + (14*z**2)*58
Replacing 58*(14*z**2 + 36*z) with (36*z)*58 + (14*z**2)*58 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (16*z)*(14*z**2 + 36*z) + (36*z)*58 + (14*z**2)*58</replace>
Simplifying the partial expression: (16*z)*(14*z**2 + 36*z)
Expanding the part (14*z**2 + 36*z) using the distributive property, and we got: (16*z)*(36*z) + (16*z)*(14*z**2)
Replacing (16*z)*(14*z**2 + 36*z) with (16*z)*(36*z) + (16*z)*(14*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (16*z)*(36*z) + (16*z)*(14*z**2) + (36*z)*58 + (14*z**2)*58</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (14*z**2)*58 = 812*z**2
  (14*z**2)*(16*z) = 224*z**3
  (36*z)*58 = 2088*z
  (36*z)*(16*z) = 576*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 224*z**3 + 576*z**2 + 812*z**2 + 2088*z</replace>
Combining like terms, got 224*z**3 + 1388*z**2 + 2088*z
<replace-#Step 5>#Step 6:
Current expression: 224*z**3 + 1388*z**2 + 2088*z</replace>
No more calculations needed.
<answer>224*z**3 + 1388*z**2 + 2088*z</answer>


Question:
Calculate the following: (x**3 - 4*x**2 - 45)*(32*x**3 - 12*x - 26)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 32*x**6 - 128*x**5 - 12*x**4 - 1418*x**3 + 104*x**2 + 540*x + 1170


Question:
Calculate the following: (44*x**2 + 52*x + 38)*(22*x**3 - 3*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: 968*x**5 + 1012*x**4 + 680*x**3 + 458*x**2 + 676*x + 494


Question:
Calculate the following: (-32*y**2 - 4)*(-40*y**3 + 19*y**2 - 3)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1280*y**5 - 608*y**4 + 160*y**3 + 20*y**2 + 12

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 - 4)*(-40*y**3 + 19*y**2 - 3)
Expanding the part (-32*y**2 - 4) using the distributive property, and we got: (-32*y**2)*(-40*y**3 + 19*y**2 - 3) - 4*(-40*y**3 + 19*y**2 - 3)
<replace-#Step 1>#Step 2:
Current expression: (-32*y**2)*(-40*y**3 + 19*y**2 - 3) - 4*(-40*y**3 + 19*y**2 - 3)</replace>
Simplifying the partial expression: -4*(-40*y**3 + 19*y**2 - 3)
Expanding the part (-40*y**3 + 19*y**2 - 3) using the distributive property, and we got: (19*y**2)*(-4) - 40*y**3*(-4) - 3*(-4)
Replacing -4*(-40*y**3 + 19*y**2 - 3) with (19*y**2)*(-4) - 40*y**3*(-4) - 3*(-4) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-32*y**2)*(-40*y**3 + 19*y**2 - 3) + (19*y**2)*(-4) - 40*y**3*(-4) + 12</replace>
Simplifying the partial expression: (-32*y**2)*(-40*y**3 + 19*y**2 - 3)
Expanding the part (-40*y**3 + 19*y**2 - 3) using the distributive property, and we got: -(-1)*96*y**2 + (-32*y**2)*(19*y**2) + (-32*y**2)*(-40*y**3)
Replacing (-32*y**2)*(-40*y**3 + 19*y**2 - 3) with -(-1)*96*y**2 + (-32*y**2)*(19*y**2) + (-32*y**2)*(-40*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -3*(-32)*y**2 + (-32*y**2)*(19*y**2) + (-32*y**2)*(-40*y**3) + (19*y**2)*(-4) - 40*y**3*(-4) + 12</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-40*y**3)*-4 = 160*y**3
  (-40*y**3)*(-32*y**2) = 1280*y**5
  (19*y**2)*-4 = -76*y**2
  (19*y**2)*(-32*y**2) = -608*y**4
  -3*-32*y**2 = 96*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1280*y**5 - 608*y**4 + 160*y**3 - 76*y**2 + 96*y**2 + 12</replace>
Combining like terms, got 1280*y**5 - 608*y**4 + 160*y**3 + 20*y**2 + 12
<replace-#Step 5>#Step 6:
Current expression: 1280*y**5 - 608*y**4 + 160*y**3 + 20*y**2 + 12</replace>
No more calculations needed.
<answer>1280*y**5 - 608*y**4 + 160*y**3 + 20*y**2 + 12</answer>


Question:
Calculate the following: (7 - 12*x**2)*(-12*x**2 - 33*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: 144*x**4 + 396*x**3 - 84*x**2 - 231*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (7 - 12*x**2)*(-12*x**2 - 33*x)
Expanding the part (7 - 12*x**2) using the distributive property, and we got: (-12*x**2)*(-12*x**2 - 33*x) + 7*(-12*x**2 - 33*x)
<replace-#Step 1>#Step 2:
Current expression: (-12*x**2)*(-12*x**2 - 33*x) + 7*(-12*x**2 - 33*x)</replace>
Simplifying the partial expression: 7*(-12*x**2 - 33*x)
Expanding the part (-12*x**2 - 33*x) using the distributive property, and we got: -33*x*7 - 12*x**2*7
Replacing 7*(-12*x**2 - 33*x) with -33*x*7 - 12*x**2*7 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -33*x*7 + (-12*x**2)*(-12*x**2 - 33*x) - 12*x**2*7</replace>
Simplifying the partial expression: (-12*x**2)*(-12*x**2 - 33*x)
Expanding the part (-12*x**2 - 33*x) using the distributive property, and we got: (-33*x)*(-12*x**2) + (-12*x**2)*(-12*x**2)
Replacing (-12*x**2)*(-12*x**2 - 33*x) with (-33*x)*(-12*x**2) + (-12*x**2)*(-12*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-33*x)*(-12*x**2) - 33*x*7 + (-12*x**2)*(-12*x**2) - 12*x**2*7</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-33*x)*7 = -231*x
  (-33*x)*(-12*x**2) = 396*x**3
  (-12*x**2)*7 = -84*x**2
  (-12*x**2)*(-12*x**2) = 144*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 144*x**4 + 396*x**3 - 84*x**2 - 231*x</replace>
No more calculations needed.
<answer>144*x**4 + 396*x**3 - 84*x**2 - 231*x</answer>


Question:
Calculate the following: (33*x**3 - 38*x**2 - 9)*(41*x**3 + 79*x**2 - 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: 1353*x**6 + 1049*x**5 - 3002*x**4 - 1128*x**3 + 163*x**2 + 207


Question:
Simplify this expression: (29*x**3 - 43*x**2)*(-47*x**3 + 23*x**2 + 10*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: -1363*x**6 + 2688*x**5 - 699*x**4 - 430*x**3


Question:
Simplify this expression: (45*y**3 + 24*y)*(46*y**3 - 66*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: 2070*y**6 - 2970*y**5 + 2814*y**4 - 1584*y**3 + 912*y**2


Question:
Calculate the following: (2*y**3 - 24)*(-22*y**3 + 50*y + 44)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -44*y**6 + 100*y**4 + 616*y**3 - 1200*y - 1056

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**3 - 24)*(-22*y**3 + 50*y + 44)
Expanding the part (2*y**3 - 24) using the distributive property, and we got: (2*y**3)*(-22*y**3 + 50*y + 44) - 24*(-22*y**3 + 50*y + 44)
<replace-#Step 1>#Step 2:
Current expression: (2*y**3)*(-22*y**3 + 50*y + 44) - 24*(-22*y**3 + 50*y + 44)</replace>
Simplifying the partial expression: -24*(-22*y**3 + 50*y + 44)
Expanding the part (-22*y**3 + 50*y + 44) using the distributive property, and we got: (50*y)*(-24) - 22*y**3*(-24) + 44*(-24)
Replacing -24*(-22*y**3 + 50*y + 44) with (50*y)*(-24) - 22*y**3*(-24) + 44*(-24) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (50*y)*(-24) - 22*y**3*(-24) + (2*y**3)*(-22*y**3 + 50*y + 44) - 1056</replace>
Simplifying the partial expression: (2*y**3)*(-22*y**3 + 50*y + 44)
Expanding the part (-22*y**3 + 50*y + 44) using the distributive property, and we got: 44*(2*y**3) + (50*y)*(2*y**3) + (-22*y**3)*(2*y**3)
Replacing (2*y**3)*(-22*y**3 + 50*y + 44) with 44*(2*y**3) + (50*y)*(2*y**3) + (-22*y**3)*(2*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 44*2*y**3 + (50*y)*(2*y**3) + (50*y)*(-24) + (-22*y**3)*(2*y**3) - 22*y**3*(-24) - 1056</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-22*y**3)*-24 = 528*y**3
  (-22*y**3)*(2*y**3) = -44*y**6
  (50*y)*-24 = -1200*y
  (50*y)*(2*y**3) = 100*y**4
  44*2*y**3 = 88*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -44*y**6 + 100*y**4 + 88*y**3 + 528*y**3 - 1200*y - 1056</replace>
Combining like terms, got -44*y**6 + 100*y**4 + 616*y**3 - 1200*y - 1056
<replace-#Step 5>#Step 6:
Current expression: -44*y**6 + 100*y**4 + 616*y**3 - 1200*y - 1056</replace>
No more calculations needed.
<answer>-44*y**6 + 100*y**4 + 616*y**3 - 1200*y - 1056</answer>


Question:
Calculate the following: (-24*z - 18)*(11*z**3 + 69*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: -264*z**4 - 198*z**3 - 1656*z**2 - 1242*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: (-24*z - 18)*(11*z**3 + 69*z)
Expanding the part (-24*z - 18) using the distributive property, and we got: (-24*z)*(11*z**3 + 69*z) - 18*(11*z**3 + 69*z)
<replace-#Step 1>#Step 2:
Current expression: (-24*z)*(11*z**3 + 69*z) - 18*(11*z**3 + 69*z)</replace>
Simplifying the partial expression: -18*(11*z**3 + 69*z)
Expanding the part (11*z**3 + 69*z) using the distributive property, and we got: (69*z)*(-18) + (11*z**3)*(-18)
Replacing -18*(11*z**3 + 69*z) with (69*z)*(-18) + (11*z**3)*(-18) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-24*z)*(11*z**3 + 69*z) + (69*z)*(-18) + (11*z**3)*(-18)</replace>
Simplifying the partial expression: (-24*z)*(11*z**3 + 69*z)
Expanding the part (11*z**3 + 69*z) using the distributive property, and we got: (-24*z)*(69*z) + (-24*z)*(11*z**3)
Replacing (-24*z)*(11*z**3 + 69*z) with (-24*z)*(69*z) + (-24*z)*(11*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-24*z)*(69*z) + (-24*z)*(11*z**3) + (69*z)*(-18) + (11*z**3)*(-18)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (11*z**3)*-18 = -198*z**3
  (11*z**3)*(-24*z) = -264*z**4
  (69*z)*-18 = -1242*z
  (69*z)*(-24*z) = -1656*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -264*z**4 - 198*z**3 - 1656*z**2 - 1242*z</replace>
No more calculations needed.
<answer>-264*z**4 - 198*z**3 - 1656*z**2 - 1242*z</answer>


Question:
Calculate the following: (-83*x**3 + 28*x**2)*(26*x**3 - 28*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: -2158*x**6 + 3052*x**5 - 784*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: (-83*x**3 + 28*x**2)*(26*x**3 - 28*x**2)
Expanding the part (-83*x**3 + 28*x**2) using the distributive property, and we got: (28*x**2)*(26*x**3 - 28*x**2) + (-83*x**3)*(26*x**3 - 28*x**2)
<replace-#Step 1>#Step 2:
Current expression: (28*x**2)*(26*x**3 - 28*x**2) + (-83*x**3)*(26*x**3 - 28*x**2)</replace>
Simplifying the partial expression: (-83*x**3)*(26*x**3 - 28*x**2)
Expanding the part (26*x**3 - 28*x**2) using the distributive property, and we got: (-28*x**2)*(-83*x**3) + (-83*x**3)*(26*x**3)
Replacing (-83*x**3)*(26*x**3 - 28*x**2) with (-28*x**2)*(-83*x**3) + (-83*x**3)*(26*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-28*x**2)*(-83*x**3) + (28*x**2)*(26*x**3 - 28*x**2) + (-83*x**3)*(26*x**3)</replace>
Simplifying the partial expression: (28*x**2)*(26*x**3 - 28*x**2)
Expanding the part (26*x**3 - 28*x**2) using the distributive property, and we got: (-28*x**2)*(28*x**2) + (28*x**2)*(26*x**3)
Replacing (28*x**2)*(26*x**3 - 28*x**2) with (-28*x**2)*(28*x**2) + (28*x**2)*(26*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-28*x**2)*(28*x**2) + (-28*x**2)*(-83*x**3) + (28*x**2)*(26*x**3) + (-83*x**3)*(26*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**2)*(-83*x**3) = 2324*x**5
  (-28*x**2)*(28*x**2) = -784*x**4
  (26*x**3)*(-83*x**3) = -2158*x**6
  (26*x**3)*(28*x**2) = 728*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2158*x**6 + 728*x**5 + 2324*x**5 - 784*x**4</replace>
Combining like terms, got -2158*x**6 + 3052*x**5 - 784*x**4
<replace-#Step 5>#Step 6:
Current expression: -2158*x**6 + 3052*x**5 - 784*x**4</replace>
No more calculations needed.
<answer>-2158*x**6 + 3052*x**5 - 784*x**4</answer>


Question:
Calculate the following: (23 - 38*y**3)*(5*y**3 + 19*y - 7)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -190*y**6 - 722*y**4 + 381*y**3 + 437*y - 161

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 - 38*y**3)*(5*y**3 + 19*y - 7)
Expanding the part (23 - 38*y**3) using the distributive property, and we got: (-38*y**3)*(5*y**3 + 19*y - 7) + 23*(5*y**3 + 19*y - 7)
<replace-#Step 1>#Step 2:
Current expression: (-38*y**3)*(5*y**3 + 19*y - 7) + 23*(5*y**3 + 19*y - 7)</replace>
Simplifying the partial expression: 23*(5*y**3 + 19*y - 7)
Expanding the part (5*y**3 + 19*y - 7) using the distributive property, and we got: (19*y)*23 + (5*y**3)*23 - 7*23
Replacing 23*(5*y**3 + 19*y - 7) with (19*y)*23 + (5*y**3)*23 - 7*23 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (19*y)*23 + (-38*y**3)*(5*y**3 + 19*y - 7) + (5*y**3)*23 - 161</replace>
Simplifying the partial expression: (-38*y**3)*(5*y**3 + 19*y - 7)
Expanding the part (5*y**3 + 19*y - 7) using the distributive property, and we got: -(-1)*266*y**3 + (19*y)*(-38*y**3) + (-38*y**3)*(5*y**3)
Replacing (-38*y**3)*(5*y**3 + 19*y - 7) with -(-1)*266*y**3 + (19*y)*(-38*y**3) + (-38*y**3)*(5*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -7*(-38)*y**3 + (19*y)*(-38*y**3) + (19*y)*23 + (-38*y**3)*(5*y**3) + (5*y**3)*23 - 161</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (5*y**3)*23 = 115*y**3
  (5*y**3)*(-38*y**3) = -190*y**6
  (19*y)*23 = 437*y
  (19*y)*(-38*y**3) = -722*y**4
  -7*-38*y**3 = 266*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -190*y**6 - 722*y**4 + 115*y**3 + 266*y**3 + 437*y - 161</replace>
Combining like terms, got -190*y**6 - 722*y**4 + 381*y**3 + 437*y - 161
<replace-#Step 5>#Step 6:
Current expression: -190*y**6 - 722*y**4 + 381*y**3 + 437*y - 161</replace>
No more calculations needed.
<answer>-190*y**6 - 722*y**4 + 381*y**3 + 437*y - 161</answer>


Question:
Simplify this expression: -8455*y**2 - 3382*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: -8455*y**2 - 3382*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: -8455*y**2 - 3382*y
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: -8455*y**2 - 3382*y</replace>
No more calculations needed.
<answer>-8455*y**2 - 3382*y</answer>


Question:
Calculate the following: -63*x**3*(-86*x**3 - 9*x - 46)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 5418*x**6 + 567*x**4 + 2898*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: -63*x**3*(-86*x**3 - 9*x - 46)
Expanding the part (-86*x**3 - 9*x - 46) using the distributive property, and we got: (-9*x)*(-63*x**3) - (-1)*2898*x**3 + (-86*x**3)*(-63*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-9*x)*(-63*x**3) - (-1)*2898*x**3 + (-86*x**3)*(-63*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -46*(-63*x**3) = 2898*x**3
  (-86*x**3)*(-63*x**3) = 5418*x**6
  (-9*x)*(-63*x**3) = 567*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 5418*x**6 + 567*x**4 + 2898*x**3</replace>
No more calculations needed.
<answer>5418*x**6 + 567*x**4 + 2898*x**3</answer>


Question:
Calculate the following: (40*x**2 + 22*x)*(50*x**3 + 22*x**2 + 20*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2000*x**5 + 1980*x**4 + 1284*x**3 + 440*x**2


Question:
Simplify this expression: (28*x - 78)*(41*x**3 - 56*x - 17)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1148*x**4 - 3198*x**3 - 1568*x**2 + 3892*x + 1326

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 - 78)*(41*x**3 - 56*x - 17)
Expanding the part (28*x - 78) using the distributive property, and we got: (28*x)*(41*x**3 - 56*x - 17) - 78*(41*x**3 - 56*x - 17)
<replace-#Step 1>#Step 2:
Current expression: (28*x)*(41*x**3 - 56*x - 17) - 78*(41*x**3 - 56*x - 17)</replace>
Simplifying the partial expression: -78*(41*x**3 - 56*x - 17)
Expanding the part (41*x**3 - 56*x - 17) using the distributive property, and we got: -56*x*(-78) + (41*x**3)*(-78) - 17*(-78)
Replacing -78*(41*x**3 - 56*x - 17) with -56*x*(-78) + (41*x**3)*(-78) - 17*(-78) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -56*x*(-78) + (28*x)*(41*x**3 - 56*x - 17) + (41*x**3)*(-78) + 1326</replace>
Simplifying the partial expression: (28*x)*(41*x**3 - 56*x - 17)
Expanding the part (41*x**3 - 56*x - 17) using the distributive property, and we got: (-56*x)*(28*x) - 476*x + (28*x)*(41*x**3)
Replacing (28*x)*(41*x**3 - 56*x - 17) with (-56*x)*(28*x) - 476*x + (28*x)*(41*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-56*x)*(28*x) - 56*x*(-78) - 17*28*x + (28*x)*(41*x**3) + (41*x**3)*(-78) + 1326</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-56*x)*-78 = 4368*x
  (-56*x)*(28*x) = -1568*x**2
  (41*x**3)*-78 = -3198*x**3
  (41*x**3)*(28*x) = 1148*x**4
  -17*28*x = -476*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1148*x**4 - 3198*x**3 - 1568*x**2 - 476*x + 4368*x + 1326</replace>
Combining like terms, got 1148*x**4 - 3198*x**3 - 1568*x**2 + 3892*x + 1326
<replace-#Step 5>#Step 6:
Current expression: 1148*x**4 - 3198*x**3 - 1568*x**2 + 3892*x + 1326</replace>
No more calculations needed.
<answer>1148*x**4 - 3198*x**3 - 1568*x**2 + 3892*x + 1326</answer>


Question:
Simplify this expression: (9 - 45*y)*(24*y**3 + 3*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: -1080*y**4 + 216*y**3 - 135*y**2 - 1233*y + 252

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 - 45*y)*(24*y**3 + 3*y + 28)
Expanding the part (9 - 45*y) using the distributive property, and we got: (-45*y)*(24*y**3 + 3*y + 28) + 9*(24*y**3 + 3*y + 28)
<replace-#Step 1>#Step 2:
Current expression: (-45*y)*(24*y**3 + 3*y + 28) + 9*(24*y**3 + 3*y + 28)</replace>
Simplifying the partial expression: 9*(24*y**3 + 3*y + 28)
Expanding the part (24*y**3 + 3*y + 28) using the distributive property, and we got: (3*y)*9 + (24*y**3)*9 + 28*9
Replacing 9*(24*y**3 + 3*y + 28) with (3*y)*9 + (24*y**3)*9 + 28*9 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-45*y)*(24*y**3 + 3*y + 28) + (3*y)*9 + (24*y**3)*9 + 252</replace>
Simplifying the partial expression: (-45*y)*(24*y**3 + 3*y + 28)
Expanding the part (24*y**3 + 3*y + 28) using the distributive property, and we got: (-45*y)*(3*y) + (-45*y)*(24*y**3) + 28*(-45*y)
Replacing (-45*y)*(24*y**3 + 3*y + 28) with (-45*y)*(3*y) + (-45*y)*(24*y**3) + 28*(-45*y) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-45*y)*(3*y) + (-45*y)*(24*y**3) + 28*(-45)*y + (3*y)*9 + (24*y**3)*9 + 252</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (3*y)*9 = 27*y
  (3*y)*(-45*y) = -135*y**2
  (24*y**3)*9 = 216*y**3
  (24*y**3)*(-45*y) = -1080*y**4
  28*-45*y = -1260*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1080*y**4 + 216*y**3 - 135*y**2 - 1260*y + 27*y + 252</replace>
Combining like terms, got -1080*y**4 + 216*y**3 - 135*y**2 - 1233*y + 252
<replace-#Step 5>#Step 6:
Current expression: -1080*y**4 + 216*y**3 - 135*y**2 - 1233*y + 252</replace>
No more calculations needed.
<answer>-1080*y**4 + 216*y**3 - 135*y**2 - 1233*y + 252</answer>


Question:
Calculate the following: (-2*y**3 - 29*y + 37)*(40*y**3 - 2*y + 5)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -80*y**6 - 1156*y**4 + 1470*y**3 + 58*y**2 - 219*y + 185


Question:
Simplify this expression: -74*y**2*(29*y**3 + 34*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: -2146*y**5 - 2516*y**4 + 2812*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: -74*y**2*(29*y**3 + 34*y**2 - 38*y)
Expanding the part (29*y**3 + 34*y**2 - 38*y) using the distributive property, and we got: (-38*y)*(-74*y**2) + (-74*y**2)*(34*y**2) + (-74*y**2)*(29*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-38*y)*(-74*y**2) + (-74*y**2)*(34*y**2) + (-74*y**2)*(29*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)*(-74*y**2) = 2812*y**3
  (29*y**3)*(-74*y**2) = -2146*y**5
  (34*y**2)*(-74*y**2) = -2516*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -2146*y**5 - 2516*y**4 + 2812*y**3</replace>
No more calculations needed.
<answer>-2146*y**5 - 2516*y**4 + 2812*y**3</answer>


Question:
Simplify this expression: (3 - 48*x)*(x**3 + 16*x**2 - 20*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -48*x**4 - 765*x**3 + 1008*x**2 - 60*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: (3 - 48*x)*(x**3 + 16*x**2 - 20*x)
Expanding the part (3 - 48*x) using the distributive property, and we got: (-48*x)*(x**3 + 16*x**2 - 20*x) + 3*(x**3 + 16*x**2 - 20*x)
<replace-#Step 1>#Step 2:
Current expression: (-48*x)*(x**3 + 16*x**2 - 20*x) + 3*(x**3 + 16*x**2 - 20*x)</replace>
Simplifying the partial expression: 3*(x**3 + 16*x**2 - 20*x)
Expanding the part (x**3 + 16*x**2 - 20*x) using the distributive property, and we got: -20*x*3 + x**3*3 + (16*x**2)*3
Replacing 3*(x**3 + 16*x**2 - 20*x) with -20*x*3 + x**3*3 + (16*x**2)*3 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-48*x)*(x**3 + 16*x**2 - 20*x) - 20*x*3 + x**3*3 + (16*x**2)*3</replace>
Simplifying the partial expression: (-48*x)*(x**3 + 16*x**2 - 20*x)
Expanding the part (x**3 + 16*x**2 - 20*x) using the distributive property, and we got: (-48*x)*(-20*x) + (-48*x)*x**3 + (-48*x)*(16*x**2)
Replacing (-48*x)*(x**3 + 16*x**2 - 20*x) with (-48*x)*(-20*x) + (-48*x)*x**3 + (-48*x)*(16*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-48*x)*(-20*x) + (-48*x)*x**3 + (-48*x)*(16*x**2) - 20*x*3 + x**3*3 + (16*x**2)*3</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  x**3*3 = 3*x**3
  x**3*(-48*x) = -48*x**4
  (-20*x)*3 = -60*x
  (-20*x)*(-48*x) = 960*x**2
  (16*x**2)*3 = 48*x**2
  (16*x**2)*(-48*x) = -768*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -48*x**4 - 768*x**3 + 3*x**3 + 48*x**2 + 960*x**2 - 60*x</replace>
Combining like terms, got -48*x**4 - 765*x**3 + 1008*x**2 - 60*x
<replace-#Step 5>#Step 6:
Current expression: -48*x**4 - 765*x**3 + 1008*x**2 - 60*x</replace>
No more calculations needed.
<answer>-48*x**4 - 765*x**3 + 1008*x**2 - 60*x</answer>


Question:
Calculate the following: (22*y**3 - 40*y**2)*(-27*y**2 + 14*y - 56)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -594*y**5 + 1388*y**4 - 1792*y**3 + 2240*y**2


Question:
Calculate the following: (39*z**2 - 13*z)*(-87*z**3 + 17*z**2 - 18)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -3393*z**5 + 1794*z**4 - 221*z**3 - 702*z**2 + 234*z


Question:
Simplify this expression: (-6*x**3 - 27*x**2)*(55*x**3 - 27*x**2 + 49)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -330*x**6 - 1323*x**5 + 729*x**4 - 294*x**3 - 1323*x**2


Question:
Calculate the following: 57*z**2*(-4*z**2 - 15*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -228*z**4 - 855*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: 57*z**2*(-4*z**2 - 15*z)
Expanding the part (-4*z**2 - 15*z) using the distributive property, and we got: (-15*z)*(57*z**2) + (-4*z**2)*(57*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-15*z)*(57*z**2) + (-4*z**2)*(57*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-15*z)*(57*z**2) = -855*z**3
  (-4*z**2)*(57*z**2) = -228*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -228*z**4 - 855*z**3</replace>
No more calculations needed.
<answer>-228*z**4 - 855*z**3</answer>


Question:
Calculate the following: 21*x**2*(-22*x**3 + 40*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: -462*x**5 + 840*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: 21*x**2*(-22*x**3 + 40*x)
Expanding the part (-22*x**3 + 40*x) using the distributive property, and we got: (40*x)*(21*x**2) + (21*x**2)*(-22*x**3)
<replace-#Step 1>#Step 2:
Current expression: (40*x)*(21*x**2) + (21*x**2)*(-22*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-22*x**3)*(21*x**2) = -462*x**5
  (40*x)*(21*x**2) = 840*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -462*x**5 + 840*x**3</replace>
No more calculations needed.
<answer>-462*x**5 + 840*x**3</answer>


Question:
Simplify this expression: (20 - 9*y)*(44*y**3 - 15*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: -396*y**4 + 1015*y**3 - 300*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: (20 - 9*y)*(44*y**3 - 15*y**2)
Expanding the part (20 - 9*y) using the distributive property, and we got: (-9*y)*(44*y**3 - 15*y**2) + 20*(44*y**3 - 15*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-9*y)*(44*y**3 - 15*y**2) + 20*(44*y**3 - 15*y**2)</replace>
Simplifying the partial expression: 20*(44*y**3 - 15*y**2)
Expanding the part (44*y**3 - 15*y**2) using the distributive property, and we got: -15*y**2*20 + (44*y**3)*20
Replacing 20*(44*y**3 - 15*y**2) with -15*y**2*20 + (44*y**3)*20 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-9*y)*(44*y**3 - 15*y**2) - 15*y**2*20 + (44*y**3)*20</replace>
Simplifying the partial expression: (-9*y)*(44*y**3 - 15*y**2)
Expanding the part (44*y**3 - 15*y**2) using the distributive property, and we got: (-9*y)*(-15*y**2) + (-9*y)*(44*y**3)
Replacing (-9*y)*(44*y**3 - 15*y**2) with (-9*y)*(-15*y**2) + (-9*y)*(44*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-9*y)*(-15*y**2) + (-9*y)*(44*y**3) - 15*y**2*20 + (44*y**3)*20</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-15*y**2)*20 = -300*y**2
  (-15*y**2)*(-9*y) = 135*y**3
  (44*y**3)*20 = 880*y**3
  (44*y**3)*(-9*y) = -396*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -396*y**4 + 135*y**3 + 880*y**3 - 300*y**2</replace>
Combining like terms, got -396*y**4 + 1015*y**3 - 300*y**2
<replace-#Step 5>#Step 6:
Current expression: -396*y**4 + 1015*y**3 - 300*y**2</replace>
No more calculations needed.
<answer>-396*y**4 + 1015*y**3 - 300*y**2</answer>


Question:
Simplify this expression: (-49*x**3 - 23*x)*(-13*x**3 - 28*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: 637*x**6 + 1372*x**5 + 299*x**4 + 1281*x**3 + 299*x


Question:
Calculate the following: (22*x**2 - 78)*(42*x**3 + 12*x**2 + 3*x - 36)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 924*x**5 + 264*x**4 - 3210*x**3 - 1728*x**2 - 234*x + 2808


Question:
Simplify this expression: (-42*y**3 + 2*y)*(46*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: -1932*y**6 - 2016*y**5 + 92*y**4 + 96*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: (-42*y**3 + 2*y)*(46*y**3 + 48*y**2)
Expanding the part (-42*y**3 + 2*y) using the distributive property, and we got: (2*y)*(46*y**3 + 48*y**2) + (-42*y**3)*(46*y**3 + 48*y**2)
<replace-#Step 1>#Step 2:
Current expression: (2*y)*(46*y**3 + 48*y**2) + (-42*y**3)*(46*y**3 + 48*y**2)</replace>
Simplifying the partial expression: (-42*y**3)*(46*y**3 + 48*y**2)
Expanding the part (46*y**3 + 48*y**2) using the distributive property, and we got: (48*y**2)*(-42*y**3) + (-42*y**3)*(46*y**3)
Replacing (-42*y**3)*(46*y**3 + 48*y**2) with (48*y**2)*(-42*y**3) + (-42*y**3)*(46*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (2*y)*(46*y**3 + 48*y**2) + (48*y**2)*(-42*y**3) + (-42*y**3)*(46*y**3)</replace>
Simplifying the partial expression: (2*y)*(46*y**3 + 48*y**2)
Expanding the part (46*y**3 + 48*y**2) using the distributive property, and we got: (2*y)*(48*y**2) + (2*y)*(46*y**3)
Replacing (2*y)*(46*y**3 + 48*y**2) with (2*y)*(48*y**2) + (2*y)*(46*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (2*y)*(48*y**2) + (2*y)*(46*y**3) + (48*y**2)*(-42*y**3) + (-42*y**3)*(46*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (46*y**3)*(-42*y**3) = -1932*y**6
  (46*y**3)*(2*y) = 92*y**4
  (48*y**2)*(-42*y**3) = -2016*y**5
  (48*y**2)*(2*y) = 96*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1932*y**6 - 2016*y**5 + 92*y**4 + 96*y**3</replace>
No more calculations needed.
<answer>-1932*y**6 - 2016*y**5 + 92*y**4 + 96*y**3</answer>


Question:
Calculate the following: (-33*x**3 + 4*x)*(-7*x**3 - 12*x - 40)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 231*x**6 + 368*x**4 + 1320*x**3 - 48*x**2 - 160*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: (-33*x**3 + 4*x)*(-7*x**3 - 12*x - 40)
Expanding the part (-33*x**3 + 4*x) using the distributive property, and we got: (4*x)*(-7*x**3 - 12*x - 40) + (-33*x**3)*(-7*x**3 - 12*x - 40)
<replace-#Step 1>#Step 2:
Current expression: (4*x)*(-7*x**3 - 12*x - 40) + (-33*x**3)*(-7*x**3 - 12*x - 40)</replace>
Simplifying the partial expression: (-33*x**3)*(-7*x**3 - 12*x - 40)
Expanding the part (-7*x**3 - 12*x - 40) using the distributive property, and we got: (-12*x)*(-33*x**3) - (-1)*1320*x**3 + (-33*x**3)*(-7*x**3)
Replacing (-33*x**3)*(-7*x**3 - 12*x - 40) with (-12*x)*(-33*x**3) - (-1)*1320*x**3 + (-33*x**3)*(-7*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-12*x)*(-33*x**3) - 40*(-33)*x**3 + (4*x)*(-7*x**3 - 12*x - 40) + (-33*x**3)*(-7*x**3)</replace>
Simplifying the partial expression: (4*x)*(-7*x**3 - 12*x - 40)
Expanding the part (-7*x**3 - 12*x - 40) using the distributive property, and we got: (-12*x)*(4*x) - 160*x + (4*x)*(-7*x**3)
Replacing (4*x)*(-7*x**3 - 12*x - 40) with (-12*x)*(4*x) - 160*x + (4*x)*(-7*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-12*x)*(4*x) + (-12*x)*(-33*x**3) - 40*(-33)*x**3 - 40*4*x + (4*x)*(-7*x**3) + (-33*x**3)*(-7*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-12*x)*(-33*x**3) = 396*x**4
  (-12*x)*(4*x) = -48*x**2
  (-7*x**3)*(-33*x**3) = 231*x**6
  (-7*x**3)*(4*x) = -28*x**4
  -40*-33*x**3 = 1320*x**3
  -40*4*x = -160*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 231*x**6 - 28*x**4 + 396*x**4 + 1320*x**3 - 48*x**2 - 160*x</replace>
Combining like terms, got 231*x**6 + 368*x**4 + 1320*x**3 - 48*x**2 - 160*x
<replace-#Step 5>#Step 6:
Current expression: 231*x**6 + 368*x**4 + 1320*x**3 - 48*x**2 - 160*x</replace>
No more calculations needed.
<answer>231*x**6 + 368*x**4 + 1320*x**3 - 48*x**2 - 160*x</answer>


Question:
Calculate the following: (29*z**2 + 50*z)*(-6*z**3 + 27*z**2 - 16*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: -174*z**5 + 483*z**4 + 886*z**3 - 800*z**2


Question:
Calculate the following: (-56*x**3 + 31*x)*(-10*x**2 + 27*x + 2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 560*x**5 - 1512*x**4 - 422*x**3 + 837*x**2 + 62*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: (-56*x**3 + 31*x)*(-10*x**2 + 27*x + 2)
Expanding the part (-56*x**3 + 31*x) using the distributive property, and we got: (31*x)*(-10*x**2 + 27*x + 2) + (-56*x**3)*(-10*x**2 + 27*x + 2)
<replace-#Step 1>#Step 2:
Current expression: (31*x)*(-10*x**2 + 27*x + 2) + (-56*x**3)*(-10*x**2 + 27*x + 2)</replace>
Simplifying the partial expression: (-56*x**3)*(-10*x**2 + 27*x + 2)
Expanding the part (-10*x**2 + 27*x + 2) using the distributive property, and we got: 2*(-56*x**3) + (27*x)*(-56*x**3) + (-10*x**2)*(-56*x**3)
Replacing (-56*x**3)*(-10*x**2 + 27*x + 2) with 2*(-56*x**3) + (27*x)*(-56*x**3) + (-10*x**2)*(-56*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 2*(-56)*x**3 + (27*x)*(-56*x**3) + (31*x)*(-10*x**2 + 27*x + 2) + (-10*x**2)*(-56*x**3)</replace>
Simplifying the partial expression: (31*x)*(-10*x**2 + 27*x + 2)
Expanding the part (-10*x**2 + 27*x + 2) using the distributive property, and we got: 2*(31*x) + (27*x)*(31*x) + (31*x)*(-10*x**2)
Replacing (31*x)*(-10*x**2 + 27*x + 2) with 2*(31*x) + (27*x)*(31*x) + (31*x)*(-10*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 2*(-56)*x**3 + 2*31*x + (27*x)*(31*x) + (27*x)*(-56*x**3) + (31*x)*(-10*x**2) + (-10*x**2)*(-56*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-10*x**2)*(-56*x**3) = 560*x**5
  (-10*x**2)*(31*x) = -310*x**3
  (27*x)*(-56*x**3) = -1512*x**4
  (27*x)*(31*x) = 837*x**2
  2*-56*x**3 = -112*x**3
  2*31*x = 62*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 560*x**5 - 1512*x**4 - 310*x**3 - 112*x**3 + 837*x**2 + 62*x</replace>
Combining like terms, got 560*x**5 - 1512*x**4 - 422*x**3 + 837*x**2 + 62*x
<replace-#Step 5>#Step 6:
Current expression: 560*x**5 - 1512*x**4 - 422*x**3 + 837*x**2 + 62*x</replace>
No more calculations needed.
<answer>560*x**5 - 1512*x**4 - 422*x**3 + 837*x**2 + 62*x</answer>


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

Answer: -2*x**2 - 39*x

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


Question:
Simplify this expression: (28*y**3 + 5)*(-19*y**3 + 42*y**2 + 45*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -532*y**6 + 1176*y**5 + 1260*y**4 - 95*y**3 + 210*y**2 + 225*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: (28*y**3 + 5)*(-19*y**3 + 42*y**2 + 45*y)
Expanding the part (28*y**3 + 5) using the distributive property, and we got: (28*y**3)*(-19*y**3 + 42*y**2 + 45*y) + 5*(-19*y**3 + 42*y**2 + 45*y)
<replace-#Step 1>#Step 2:
Current expression: (28*y**3)*(-19*y**3 + 42*y**2 + 45*y) + 5*(-19*y**3 + 42*y**2 + 45*y)</replace>
Simplifying the partial expression: 5*(-19*y**3 + 42*y**2 + 45*y)
Expanding the part (-19*y**3 + 42*y**2 + 45*y) using the distributive property, and we got: (45*y)*5 + (42*y**2)*5 - 19*y**3*5
Replacing 5*(-19*y**3 + 42*y**2 + 45*y) with (45*y)*5 + (42*y**2)*5 - 19*y**3*5 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (45*y)*5 + (42*y**2)*5 - 19*y**3*5 + (28*y**3)*(-19*y**3 + 42*y**2 + 45*y)</replace>
Simplifying the partial expression: (28*y**3)*(-19*y**3 + 42*y**2 + 45*y)
Expanding the part (-19*y**3 + 42*y**2 + 45*y) using the distributive property, and we got: (45*y)*(28*y**3) + (42*y**2)*(28*y**3) + (-19*y**3)*(28*y**3)
Replacing (28*y**3)*(-19*y**3 + 42*y**2 + 45*y) with (45*y)*(28*y**3) + (42*y**2)*(28*y**3) + (-19*y**3)*(28*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (45*y)*(28*y**3) + (45*y)*5 + (42*y**2)*(28*y**3) + (42*y**2)*5 + (-19*y**3)*(28*y**3) - 19*y**3*5</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-19*y**3)*5 = -95*y**3
  (-19*y**3)*(28*y**3) = -532*y**6
  (42*y**2)*5 = 210*y**2
  (42*y**2)*(28*y**3) = 1176*y**5
  (45*y)*5 = 225*y
  (45*y)*(28*y**3) = 1260*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -532*y**6 + 1176*y**5 + 1260*y**4 - 95*y**3 + 210*y**2 + 225*y</replace>
No more calculations needed.
<answer>-532*y**6 + 1176*y**5 + 1260*y**4 - 95*y**3 + 210*y**2 + 225*y</answer>


Question:
Calculate the following: (-16*z**2 + 12*z)*(26*z**3 + 29*z - 42)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -416*z**5 + 312*z**4 - 464*z**3 + 1020*z**2 - 504*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: (-16*z**2 + 12*z)*(26*z**3 + 29*z - 42)
Expanding the part (-16*z**2 + 12*z) using the distributive property, and we got: (12*z)*(26*z**3 + 29*z - 42) + (-16*z**2)*(26*z**3 + 29*z - 42)
<replace-#Step 1>#Step 2:
Current expression: (12*z)*(26*z**3 + 29*z - 42) + (-16*z**2)*(26*z**3 + 29*z - 42)</replace>
Simplifying the partial expression: (-16*z**2)*(26*z**3 + 29*z - 42)
Expanding the part (26*z**3 + 29*z - 42) using the distributive property, and we got: -(-1)*672*z**2 + (29*z)*(-16*z**2) + (-16*z**2)*(26*z**3)
Replacing (-16*z**2)*(26*z**3 + 29*z - 42) with -(-1)*672*z**2 + (29*z)*(-16*z**2) + (-16*z**2)*(26*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -42*(-16)*z**2 + (12*z)*(26*z**3 + 29*z - 42) + (29*z)*(-16*z**2) + (-16*z**2)*(26*z**3)</replace>
Simplifying the partial expression: (12*z)*(26*z**3 + 29*z - 42)
Expanding the part (26*z**3 + 29*z - 42) using the distributive property, and we got: -504*z + (12*z)*(29*z) + (12*z)*(26*z**3)
Replacing (12*z)*(26*z**3 + 29*z - 42) with -504*z + (12*z)*(29*z) + (12*z)*(26*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -42*(-16)*z**2 - 42*12*z + (12*z)*(29*z) + (12*z)*(26*z**3) + (29*z)*(-16*z**2) + (-16*z**2)*(26*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (26*z**3)*(-16*z**2) = -416*z**5
  (26*z**3)*(12*z) = 312*z**4
  (29*z)*(-16*z**2) = -464*z**3
  (29*z)*(12*z) = 348*z**2
  -42*-16*z**2 = 672*z**2
  -42*12*z = -504*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -416*z**5 + 312*z**4 - 464*z**3 + 348*z**2 + 672*z**2 - 504*z</replace>
Combining like terms, got -416*z**5 + 312*z**4 - 464*z**3 + 1020*z**2 - 504*z
<replace-#Step 5>#Step 6:
Current expression: -416*z**5 + 312*z**4 - 464*z**3 + 1020*z**2 - 504*z</replace>
No more calculations needed.
<answer>-416*z**5 + 312*z**4 - 464*z**3 + 1020*z**2 - 504*z</answer>