Question:
Simplify this expression: (-41*z**2 + 30*z)*(38*z**2 + 22*z + 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: -1558*z**4 + 238*z**3 - 37*z**2 + 510*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: (-41*z**2 + 30*z)*(38*z**2 + 22*z + 17)
Expanding the part (-41*z**2 + 30*z) using the distributive property, and we got: (30*z)*(38*z**2 + 22*z + 17) + (-41*z**2)*(38*z**2 + 22*z + 17)
<replace-#Step 1>#Step 2:
Current expression: (30*z)*(38*z**2 + 22*z + 17) + (-41*z**2)*(38*z**2 + 22*z + 17)</replace>
Simplifying the partial expression: (-41*z**2)*(38*z**2 + 22*z + 17)
Expanding the part (38*z**2 + 22*z + 17) using the distributive property, and we got: 17*(-41*z**2) + (22*z)*(-41*z**2) + (-41*z**2)*(38*z**2)
Replacing (-41*z**2)*(38*z**2 + 22*z + 17) with 17*(-41*z**2) + (22*z)*(-41*z**2) + (-41*z**2)*(38*z**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 17*(-41)*z**2 + (22*z)*(-41*z**2) + (30*z)*(38*z**2 + 22*z + 17) + (-41*z**2)*(38*z**2)</replace>
Simplifying the partial expression: (30*z)*(38*z**2 + 22*z + 17)
Expanding the part (38*z**2 + 22*z + 17) using the distributive property, and we got: 17*(30*z) + (22*z)*(30*z) + (30*z)*(38*z**2)
Replacing (30*z)*(38*z**2 + 22*z + 17) with 17*(30*z) + (22*z)*(30*z) + (30*z)*(38*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 17*(-41)*z**2 + 17*30*z + (22*z)*(30*z) + (22*z)*(-41*z**2) + (30*z)*(38*z**2) + (-41*z**2)*(38*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (22*z)*(-41*z**2) = -902*z**3
  (22*z)*(30*z) = 660*z**2
  (38*z**2)*(-41*z**2) = -1558*z**4
  (38*z**2)*(30*z) = 1140*z**3
  17*-41*z**2 = -697*z**2
  17*30*z = 510*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1558*z**4 - 902*z**3 + 1140*z**3 - 697*z**2 + 660*z**2 + 510*z</replace>
Combining like terms, got -1558*z**4 + 238*z**3 - 37*z**2 + 510*z
<replace-#Step 5>#Step 6:
Current expression: -1558*z**4 + 238*z**3 - 37*z**2 + 510*z</replace>
No more calculations needed.
<answer>-1558*z**4 + 238*z**3 - 37*z**2 + 510*z</answer>


Question:
Simplify this expression: (-3*x**2 + 10*x + 19)*(34*x**2 - 23*x + 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: -102*x**4 + 409*x**3 + 317*x**2 - 107*x + 627


Question:
Calculate the following: (14*x**3 + 64*x + 33)*(17*x**3 - 37*x**2 - 78)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 238*x**6 - 518*x**5 + 1088*x**4 - 2899*x**3 - 1221*x**2 - 4992*x - 2574


Question:
Calculate the following: (22*y**3 + 8)*(35*y**3 + 3*y**2 - 48*y + 17)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 770*y**6 + 66*y**5 - 1056*y**4 + 654*y**3 + 24*y**2 - 384*y + 136


Question:
Calculate the following: (20 - 30*y**2)*(40*y**3 + 31*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: -1200*y**5 - 130*y**3 + 620*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 - 30*y**2)*(40*y**3 + 31*y)
Expanding the part (20 - 30*y**2) using the distributive property, and we got: (-30*y**2)*(40*y**3 + 31*y) + 20*(40*y**3 + 31*y)
<replace-#Step 1>#Step 2:
Current expression: (-30*y**2)*(40*y**3 + 31*y) + 20*(40*y**3 + 31*y)</replace>
Simplifying the partial expression: 20*(40*y**3 + 31*y)
Expanding the part (40*y**3 + 31*y) using the distributive property, and we got: (31*y)*20 + (40*y**3)*20
Replacing 20*(40*y**3 + 31*y) with (31*y)*20 + (40*y**3)*20 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (31*y)*20 + (-30*y**2)*(40*y**3 + 31*y) + (40*y**3)*20</replace>
Simplifying the partial expression: (-30*y**2)*(40*y**3 + 31*y)
Expanding the part (40*y**3 + 31*y) using the distributive property, and we got: (31*y)*(-30*y**2) + (-30*y**2)*(40*y**3)
Replacing (-30*y**2)*(40*y**3 + 31*y) with (31*y)*(-30*y**2) + (-30*y**2)*(40*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (31*y)*(-30*y**2) + (31*y)*20 + (-30*y**2)*(40*y**3) + (40*y**3)*20</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (31*y)*20 = 620*y
  (31*y)*(-30*y**2) = -930*y**3
  (40*y**3)*20 = 800*y**3
  (40*y**3)*(-30*y**2) = -1200*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1200*y**5 - 930*y**3 + 800*y**3 + 620*y</replace>
Combining like terms, got -1200*y**5 - 130*y**3 + 620*y
<replace-#Step 5>#Step 6:
Current expression: -1200*y**5 - 130*y**3 + 620*y</replace>
No more calculations needed.
<answer>-1200*y**5 - 130*y**3 + 620*y</answer>


Question:
Calculate the following: (25*x**2 + 44*x - 4)*(-7*x**3 - 29*x**2 + 61)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -175*x**5 - 1033*x**4 - 1248*x**3 + 1641*x**2 + 2684*x - 244


Question:
Calculate the following: (8*x**3 + 35*x + 49)*(54*x**3 + 24*x**2 + 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: 432*x**6 + 192*x**5 + 2210*x**4 + 3486*x**3 + 2576*x**2 + 1960*x


Question:
Simplify this expression: (37*y**2 - 46)*(63*y**2 + 7)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2331*y**4 - 2639*y**2 - 322

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (37*y**2 - 46)*(63*y**2 + 7)
Expanding the part (37*y**2 - 46) using the distributive property, and we got: (37*y**2)*(63*y**2 + 7) - 46*(63*y**2 + 7)
<replace-#Step 1>#Step 2:
Current expression: (37*y**2)*(63*y**2 + 7) - 46*(63*y**2 + 7)</replace>
Simplifying the partial expression: -46*(63*y**2 + 7)
Expanding the part (63*y**2 + 7) using the distributive property, and we got: (63*y**2)*(-46) + 7*(-46)
Replacing -46*(63*y**2 + 7) with (63*y**2)*(-46) + 7*(-46) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (37*y**2)*(63*y**2 + 7) + (63*y**2)*(-46) - 322</replace>
Simplifying the partial expression: (37*y**2)*(63*y**2 + 7)
Expanding the part (63*y**2 + 7) using the distributive property, and we got: 7*(37*y**2) + (37*y**2)*(63*y**2)
Replacing (37*y**2)*(63*y**2 + 7) with 7*(37*y**2) + (37*y**2)*(63*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 7*37*y**2 + (37*y**2)*(63*y**2) + (63*y**2)*(-46) - 322</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (63*y**2)*-46 = -2898*y**2
  (63*y**2)*(37*y**2) = 2331*y**4
  7*37*y**2 = 259*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2331*y**4 - 2898*y**2 + 259*y**2 - 322</replace>
Combining like terms, got 2331*y**4 - 2639*y**2 - 322
<replace-#Step 5>#Step 6:
Current expression: 2331*y**4 - 2639*y**2 - 322</replace>
No more calculations needed.
<answer>2331*y**4 - 2639*y**2 - 322</answer>


Question:
Calculate the following: (-27*y**3 + 41*y**2)*(-28*y**3 - 19*y**2 - 11*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 756*y**6 - 635*y**5 - 482*y**4 - 451*y**3


Question:
Simplify this expression: (31*y**3 + 30*y**2)*(-4*y**3 + 11*y + 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: -124*y**6 - 120*y**5 + 341*y**4 + 1136*y**3 + 780*y**2


Question:
Calculate the following: 15*x*(43*x**3 + 24*x**2 + 35*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 645*x**4 + 360*x**3 + 525*x**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 15*x*(43*x**3 + 24*x**2 + 35*x)
Expanding the part (43*x**3 + 24*x**2 + 35*x) using the distributive property, and we got: (15*x)*(35*x) + (15*x)*(24*x**2) + (15*x)*(43*x**3)
<replace-#Step 1>#Step 2:
Current expression: (15*x)*(35*x) + (15*x)*(24*x**2) + (15*x)*(43*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (24*x**2)*(15*x) = 360*x**3
  (35*x)*(15*x) = 525*x**2
  (43*x**3)*(15*x) = 645*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 645*x**4 + 360*x**3 + 525*x**2</replace>
No more calculations needed.
<answer>645*x**4 + 360*x**3 + 525*x**2</answer>


Question:
Simplify this expression: (2*x + 43)*(14*x**3 + 49*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: 28*x**4 + 700*x**3 + 2107*x**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (2*x + 43)*(14*x**3 + 49*x**2)
Expanding the part (2*x + 43) using the distributive property, and we got: (2*x)*(14*x**3 + 49*x**2) + 43*(14*x**3 + 49*x**2)
<replace-#Step 1>#Step 2:
Current expression: (2*x)*(14*x**3 + 49*x**2) + 43*(14*x**3 + 49*x**2)</replace>
Simplifying the partial expression: 43*(14*x**3 + 49*x**2)
Expanding the part (14*x**3 + 49*x**2) using the distributive property, and we got: (49*x**2)*43 + (14*x**3)*43
Replacing 43*(14*x**3 + 49*x**2) with (49*x**2)*43 + (14*x**3)*43 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (2*x)*(14*x**3 + 49*x**2) + (49*x**2)*43 + (14*x**3)*43</replace>
Simplifying the partial expression: (2*x)*(14*x**3 + 49*x**2)
Expanding the part (14*x**3 + 49*x**2) using the distributive property, and we got: (2*x)*(49*x**2) + (2*x)*(14*x**3)
Replacing (2*x)*(14*x**3 + 49*x**2) with (2*x)*(49*x**2) + (2*x)*(14*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (2*x)*(49*x**2) + (2*x)*(14*x**3) + (49*x**2)*43 + (14*x**3)*43</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (14*x**3)*43 = 602*x**3
  (14*x**3)*(2*x) = 28*x**4
  (49*x**2)*43 = 2107*x**2
  (49*x**2)*(2*x) = 98*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 28*x**4 + 98*x**3 + 602*x**3 + 2107*x**2</replace>
Combining like terms, got 28*x**4 + 700*x**3 + 2107*x**2
<replace-#Step 5>#Step 6:
Current expression: 28*x**4 + 700*x**3 + 2107*x**2</replace>
No more calculations needed.
<answer>28*x**4 + 700*x**3 + 2107*x**2</answer>


Question:
Simplify this expression: -946*z**2 + 220*z + 902
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -946*z**2 + 220*z + 902

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: -946*z**2 + 220*z + 902
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: -946*z**2 + 220*z + 902</replace>
No more calculations needed.
<answer>-946*z**2 + 220*z + 902</answer>


Question:
Simplify this expression: (-5*x**2 - 35)*(-14*x**3 - 75*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: 70*x**5 + 865*x**3 + 225*x**2 + 2625*x + 1575

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-5*x**2 - 35)*(-14*x**3 - 75*x - 45)
Expanding the part (-5*x**2 - 35) using the distributive property, and we got: (-5*x**2)*(-14*x**3 - 75*x - 45) - 35*(-14*x**3 - 75*x - 45)
<replace-#Step 1>#Step 2:
Current expression: (-5*x**2)*(-14*x**3 - 75*x - 45) - 35*(-14*x**3 - 75*x - 45)</replace>
Simplifying the partial expression: -35*(-14*x**3 - 75*x - 45)
Expanding the part (-14*x**3 - 75*x - 45) using the distributive property, and we got: -75*x*(-35) - 14*x**3*(-35) - 45*(-35)
Replacing -35*(-14*x**3 - 75*x - 45) with -75*x*(-35) - 14*x**3*(-35) - 45*(-35) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -75*x*(-35) + (-5*x**2)*(-14*x**3 - 75*x - 45) - 14*x**3*(-35) + 1575</replace>
Simplifying the partial expression: (-5*x**2)*(-14*x**3 - 75*x - 45)
Expanding the part (-14*x**3 - 75*x - 45) using the distributive property, and we got: (-75*x)*(-5*x**2) - (-1)*225*x**2 + (-5*x**2)*(-14*x**3)
Replacing (-5*x**2)*(-14*x**3 - 75*x - 45) with (-75*x)*(-5*x**2) - (-1)*225*x**2 + (-5*x**2)*(-14*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-75*x)*(-5*x**2) - 75*x*(-35) - 45*(-5)*x**2 + (-5*x**2)*(-14*x**3) - 14*x**3*(-35) + 1575</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-75*x)*-35 = 2625*x
  (-75*x)*(-5*x**2) = 375*x**3
  (-14*x**3)*-35 = 490*x**3
  (-14*x**3)*(-5*x**2) = 70*x**5
  -45*-5*x**2 = 225*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 70*x**5 + 375*x**3 + 490*x**3 + 225*x**2 + 2625*x + 1575</replace>
Combining like terms, got 70*x**5 + 865*x**3 + 225*x**2 + 2625*x + 1575
<replace-#Step 5>#Step 6:
Current expression: 70*x**5 + 865*x**3 + 225*x**2 + 2625*x + 1575</replace>
No more calculations needed.
<answer>70*x**5 + 865*x**3 + 225*x**2 + 2625*x + 1575</answer>


Question:
Simplify this expression: (-29*x**2 + 20*x - 39)*(47*x**3 - 10*x**2 + 18*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**5 + 1230*x**4 - 2555*x**3 + 750*x**2 - 702*x


Question:
Simplify this expression: (50 - 42*z**2)*(-38*z - 30)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1596*z**3 + 1260*z**2 - 1900*z - 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: (50 - 42*z**2)*(-38*z - 30)
Expanding the part (-38*z - 30) using the distributive property, and we got: (-38*z)*(50 - 42*z**2) - 30*(50 - 42*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-38*z)*(50 - 42*z**2) - 30*(50 - 42*z**2)</replace>
Simplifying the partial expression: -30*(50 - 42*z**2)
Expanding the part (50 - 42*z**2) using the distributive property, and we got: -42*z**2*(-30) + 50*(-30)
Replacing -30*(50 - 42*z**2) with -42*z**2*(-30) + 50*(-30) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-38*z)*(50 - 42*z**2) - 42*z**2*(-30) - 1500</replace>
Simplifying the partial expression: (-38*z)*(50 - 42*z**2)
Expanding the part (50 - 42*z**2) using the distributive property, and we got: (-38*z)*(-42*z**2) + 50*(-38*z)
Replacing (-38*z)*(50 - 42*z**2) with (-38*z)*(-42*z**2) + 50*(-38*z) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-38*z)*(-42*z**2) + 50*(-38)*z - 42*z**2*(-30) - 1500</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-42*z**2)*-30 = 1260*z**2
  (-42*z**2)*(-38*z) = 1596*z**3
  50*-38*z = -1900*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1596*z**3 + 1260*z**2 - 1900*z - 1500</replace>
No more calculations needed.
<answer>1596*z**3 + 1260*z**2 - 1900*z - 1500</answer>


Question:
Simplify this expression: (13*z**3 - 30*z**2)*(46*z**3 - 17*z**2 + 31*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: 598*z**6 - 1601*z**5 + 913*z**4 - 865*z**3 - 150*z**2


Question:
Calculate the following: (-24*y**2 - 3*y)*(16*y**3 + 22*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: -384*y**5 - 576*y**4 - 66*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: (-24*y**2 - 3*y)*(16*y**3 + 22*y**2)
Expanding the part (-24*y**2 - 3*y) using the distributive property, and we got: (-3*y)*(16*y**3 + 22*y**2) + (-24*y**2)*(16*y**3 + 22*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-3*y)*(16*y**3 + 22*y**2) + (-24*y**2)*(16*y**3 + 22*y**2)</replace>
Simplifying the partial expression: (-24*y**2)*(16*y**3 + 22*y**2)
Expanding the part (16*y**3 + 22*y**2) using the distributive property, and we got: (-24*y**2)*(22*y**2) + (-24*y**2)*(16*y**3)
Replacing (-24*y**2)*(16*y**3 + 22*y**2) with (-24*y**2)*(22*y**2) + (-24*y**2)*(16*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-3*y)*(16*y**3 + 22*y**2) + (-24*y**2)*(22*y**2) + (-24*y**2)*(16*y**3)</replace>
Simplifying the partial expression: (-3*y)*(16*y**3 + 22*y**2)
Expanding the part (16*y**3 + 22*y**2) using the distributive property, and we got: (-3*y)*(22*y**2) + (-3*y)*(16*y**3)
Replacing (-3*y)*(16*y**3 + 22*y**2) with (-3*y)*(22*y**2) + (-3*y)*(16*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-3*y)*(22*y**2) + (-3*y)*(16*y**3) + (-24*y**2)*(22*y**2) + (-24*y**2)*(16*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (16*y**3)*(-24*y**2) = -384*y**5
  (16*y**3)*(-3*y) = -48*y**4
  (22*y**2)*(-24*y**2) = -528*y**4
  (22*y**2)*(-3*y) = -66*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -384*y**5 - 528*y**4 - 48*y**4 - 66*y**3</replace>
Combining like terms, got -384*y**5 - 576*y**4 - 66*y**3
<replace-#Step 5>#Step 6:
Current expression: -384*y**5 - 576*y**4 - 66*y**3</replace>
No more calculations needed.
<answer>-384*y**5 - 576*y**4 - 66*y**3</answer>


Question:
Calculate the following: (-26*z**3 - 46*z**2)*(-4*z**3 - 19*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: 104*z**6 + 184*z**5 + 494*z**4 + 874*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: (-26*z**3 - 46*z**2)*(-4*z**3 - 19*z)
Expanding the part (-26*z**3 - 46*z**2) using the distributive property, and we got: (-46*z**2)*(-4*z**3 - 19*z) + (-26*z**3)*(-4*z**3 - 19*z)
<replace-#Step 1>#Step 2:
Current expression: (-46*z**2)*(-4*z**3 - 19*z) + (-26*z**3)*(-4*z**3 - 19*z)</replace>
Simplifying the partial expression: (-46*z**2)*(-4*z**3 - 19*z)
Expanding the part (-4*z**3 - 19*z) using the distributive property, and we got: (-19*z)*(-46*z**2) + (-46*z**2)*(-4*z**3)
Replacing (-46*z**2)*(-4*z**3 - 19*z) with (-19*z)*(-46*z**2) + (-46*z**2)*(-4*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-19*z)*(-46*z**2) + (-46*z**2)*(-4*z**3) + (-26*z**3)*(-4*z**3 - 19*z)</replace>
Simplifying the partial expression: (-26*z**3)*(-4*z**3 - 19*z)
Expanding the part (-4*z**3 - 19*z) using the distributive property, and we got: (-19*z)*(-26*z**3) + (-26*z**3)*(-4*z**3)
Replacing (-26*z**3)*(-4*z**3 - 19*z) with (-19*z)*(-26*z**3) + (-26*z**3)*(-4*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-19*z)*(-46*z**2) + (-19*z)*(-26*z**3) + (-46*z**2)*(-4*z**3) + (-26*z**3)*(-4*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-19*z)*(-46*z**2) = 874*z**3
  (-19*z)*(-26*z**3) = 494*z**4
  (-4*z**3)*(-46*z**2) = 184*z**5
  (-4*z**3)*(-26*z**3) = 104*z**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 104*z**6 + 184*z**5 + 494*z**4 + 874*z**3</replace>
No more calculations needed.
<answer>104*z**6 + 184*z**5 + 494*z**4 + 874*z**3</answer>


Question:
Simplify this expression: (68*y**3 + 18)*(y**2 + 53*y - 24)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 68*y**5 + 3604*y**4 - 1632*y**3 + 18*y**2 + 954*y - 432

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (68*y**3 + 18)*(y**2 + 53*y - 24)
Expanding the part (68*y**3 + 18) using the distributive property, and we got: (68*y**3)*(y**2 + 53*y - 24) + 18*(y**2 + 53*y - 24)
<replace-#Step 1>#Step 2:
Current expression: (68*y**3)*(y**2 + 53*y - 24) + 18*(y**2 + 53*y - 24)</replace>
Simplifying the partial expression: 18*(y**2 + 53*y - 24)
Expanding the part (y**2 + 53*y - 24) using the distributive property, and we got: y**2*18 + (53*y)*18 - 24*18
Replacing 18*(y**2 + 53*y - 24) with y**2*18 + (53*y)*18 - 24*18 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: y**2*18 + (53*y)*18 + (68*y**3)*(y**2 + 53*y - 24) - 432</replace>
Simplifying the partial expression: (68*y**3)*(y**2 + 53*y - 24)
Expanding the part (y**2 + 53*y - 24) using the distributive property, and we got: -1632*y**3 + y**2*(68*y**3) + (53*y)*(68*y**3)
Replacing (68*y**3)*(y**2 + 53*y - 24) with -1632*y**3 + y**2*(68*y**3) + (53*y)*(68*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -24*68*y**3 + y**2*(68*y**3) + y**2*18 + (53*y)*(68*y**3) + (53*y)*18 - 432</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  y**2*18 = 18*y**2
  y**2*(68*y**3) = 68*y**5
  (53*y)*18 = 954*y
  (53*y)*(68*y**3) = 3604*y**4
  -24*68*y**3 = -1632*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 68*y**5 + 3604*y**4 - 1632*y**3 + 18*y**2 + 954*y - 432</replace>
No more calculations needed.
<answer>68*y**5 + 3604*y**4 - 1632*y**3 + 18*y**2 + 954*y - 432</answer>


Question:
Calculate the following: (26*y**3 + 47*y**2)*(-25*y**2 + 6*y - 32)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -650*y**5 - 1019*y**4 - 550*y**3 - 1504*y**2


Question:
Simplify this expression: 2516*z**3 + 1020*z**2 + 748*z - 2788
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2516*z**3 + 1020*z**2 + 748*z - 2788

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: 2516*z**3 + 1020*z**2 + 748*z - 2788
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: 2516*z**3 + 1020*z**2 + 748*z - 2788</replace>
No more calculations needed.
<answer>2516*z**3 + 1020*z**2 + 748*z - 2788</answer>


Question:
Simplify this expression: (9*y**2 + 48*y)*(-15*y**2 + 20*y - 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: -135*y**4 - 540*y**3 + 582*y**2 - 2016*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (9*y**2 + 48*y)*(-15*y**2 + 20*y - 42)
Expanding the part (9*y**2 + 48*y) using the distributive property, and we got: (48*y)*(-15*y**2 + 20*y - 42) + (9*y**2)*(-15*y**2 + 20*y - 42)
<replace-#Step 1>#Step 2:
Current expression: (48*y)*(-15*y**2 + 20*y - 42) + (9*y**2)*(-15*y**2 + 20*y - 42)</replace>
Simplifying the partial expression: (9*y**2)*(-15*y**2 + 20*y - 42)
Expanding the part (-15*y**2 + 20*y - 42) using the distributive property, and we got: -378*y**2 + (20*y)*(9*y**2) + (-15*y**2)*(9*y**2)
Replacing (9*y**2)*(-15*y**2 + 20*y - 42) with -378*y**2 + (20*y)*(9*y**2) + (-15*y**2)*(9*y**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -42*9*y**2 + (20*y)*(9*y**2) + (48*y)*(-15*y**2 + 20*y - 42) + (-15*y**2)*(9*y**2)</replace>
Simplifying the partial expression: (48*y)*(-15*y**2 + 20*y - 42)
Expanding the part (-15*y**2 + 20*y - 42) using the distributive property, and we got: -2016*y + (20*y)*(48*y) + (48*y)*(-15*y**2)
Replacing (48*y)*(-15*y**2 + 20*y - 42) with -2016*y + (20*y)*(48*y) + (48*y)*(-15*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -42*9*y**2 - 42*48*y + (20*y)*(48*y) + (20*y)*(9*y**2) + (48*y)*(-15*y**2) + (-15*y**2)*(9*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-15*y**2)*(9*y**2) = -135*y**4
  (-15*y**2)*(48*y) = -720*y**3
  (20*y)*(9*y**2) = 180*y**3
  (20*y)*(48*y) = 960*y**2
  -42*9*y**2 = -378*y**2
  -42*48*y = -2016*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -135*y**4 - 720*y**3 + 180*y**3 - 378*y**2 + 960*y**2 - 2016*y</replace>
Combining like terms, got -135*y**4 - 540*y**3 + 582*y**2 - 2016*y
<replace-#Step 5>#Step 6:
Current expression: -135*y**4 - 540*y**3 + 582*y**2 - 2016*y</replace>
No more calculations needed.
<answer>-135*y**4 - 540*y**3 + 582*y**2 - 2016*y</answer>


Question:
Simplify this expression: (30*z**3 - 18*z)*(-48*z**3 - 3*z - 38)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1440*z**6 + 774*z**4 - 1140*z**3 + 54*z**2 + 684*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: (30*z**3 - 18*z)*(-48*z**3 - 3*z - 38)
Expanding the part (30*z**3 - 18*z) using the distributive property, and we got: (-18*z)*(-48*z**3 - 3*z - 38) + (30*z**3)*(-48*z**3 - 3*z - 38)
<replace-#Step 1>#Step 2:
Current expression: (-18*z)*(-48*z**3 - 3*z - 38) + (30*z**3)*(-48*z**3 - 3*z - 38)</replace>
Simplifying the partial expression: (-18*z)*(-48*z**3 - 3*z - 38)
Expanding the part (-48*z**3 - 3*z - 38) using the distributive property, and we got: (-18*z)*(-3*z) + (-18*z)*(-48*z**3) - (-1)*684*z
Replacing (-18*z)*(-48*z**3 - 3*z - 38) with (-18*z)*(-3*z) + (-18*z)*(-48*z**3) - (-1)*684*z in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-18*z)*(-3*z) + (-18*z)*(-48*z**3) - 38*(-18)*z + (30*z**3)*(-48*z**3 - 3*z - 38)</replace>
Simplifying the partial expression: (30*z**3)*(-48*z**3 - 3*z - 38)
Expanding the part (-48*z**3 - 3*z - 38) using the distributive property, and we got: (-3*z)*(30*z**3) - 1140*z**3 + (-48*z**3)*(30*z**3)
Replacing (30*z**3)*(-48*z**3 - 3*z - 38) with (-3*z)*(30*z**3) - 1140*z**3 + (-48*z**3)*(30*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-18*z)*(-3*z) + (-18*z)*(-48*z**3) + (-3*z)*(30*z**3) - 38*30*z**3 - 38*(-18)*z + (-48*z**3)*(30*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-48*z**3)*(-18*z) = 864*z**4
  (-48*z**3)*(30*z**3) = -1440*z**6
  (-3*z)*(-18*z) = 54*z**2
  (-3*z)*(30*z**3) = -90*z**4
  -38*-18*z = 684*z
  -38*30*z**3 = -1140*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1440*z**6 - 90*z**4 + 864*z**4 - 1140*z**3 + 54*z**2 + 684*z</replace>
Combining like terms, got -1440*z**6 + 774*z**4 - 1140*z**3 + 54*z**2 + 684*z
<replace-#Step 5>#Step 6:
Current expression: -1440*z**6 + 774*z**4 - 1140*z**3 + 54*z**2 + 684*z</replace>
No more calculations needed.
<answer>-1440*z**6 + 774*z**4 - 1140*z**3 + 54*z**2 + 684*z</answer>


Question:
Calculate the following: (17*z**2 - 5*z)*(11*z**2 - 41*z + 1)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 187*z**4 - 752*z**3 + 222*z**2 - 5*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (17*z**2 - 5*z)*(11*z**2 - 41*z + 1)
Expanding the part (17*z**2 - 5*z) using the distributive property, and we got: (-5*z)*(11*z**2 - 41*z + 1) + (17*z**2)*(11*z**2 - 41*z + 1)
<replace-#Step 1>#Step 2:
Current expression: (-5*z)*(11*z**2 - 41*z + 1) + (17*z**2)*(11*z**2 - 41*z + 1)</replace>
Simplifying the partial expression: (-5*z)*(11*z**2 - 41*z + 1)
Expanding the part (11*z**2 - 41*z + 1) using the distributive property, and we got: (-41*z)*(-5*z) + (-5*z)*(11*z**2) + 1*(-5*z)
Replacing (-5*z)*(11*z**2 - 41*z + 1) with (-41*z)*(-5*z) + (-5*z)*(11*z**2) + 1*(-5*z) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-41*z)*(-5*z) + (-5*z)*(11*z**2) - 5*z + (17*z**2)*(11*z**2 - 41*z + 1)</replace>
Simplifying the partial expression: (17*z**2)*(11*z**2 - 41*z + 1)
Expanding the part (11*z**2 - 41*z + 1) using the distributive property, and we got: (-41*z)*(17*z**2) + 1*(17*z**2) + (11*z**2)*(17*z**2)
Replacing (17*z**2)*(11*z**2 - 41*z + 1) with (-41*z)*(17*z**2) + 1*(17*z**2) + (11*z**2)*(17*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-41*z)*(-5*z) + (-41*z)*(17*z**2) + (-5*z)*(11*z**2) + 17*z**2 - 5*z + (11*z**2)*(17*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-41*z)*(-5*z) = 205*z**2
  (-41*z)*(17*z**2) = -697*z**3
  (11*z**2)*(-5*z) = -55*z**3
  (11*z**2)*(17*z**2) = 187*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 187*z**4 - 697*z**3 - 55*z**3 + 17*z**2 + 205*z**2 - 5*z</replace>
Combining like terms, got 187*z**4 - 752*z**3 + 222*z**2 - 5*z
<replace-#Step 5>#Step 6:
Current expression: 187*z**4 - 752*z**3 + 222*z**2 - 5*z</replace>
No more calculations needed.
<answer>187*z**4 - 752*z**3 + 222*z**2 - 5*z</answer>


Question:
Calculate the following: (-33*z**3 - 30*z - 4)*(46*z**3 - 37*z - 35)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1518*z**6 - 159*z**4 + 971*z**3 + 1110*z**2 + 1198*z + 140


Question:
Calculate the following: (35*z**3 + 17*z**2)*(66*z**3 + 36*z - 13)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2310*z**6 + 1122*z**5 + 1260*z**4 + 157*z**3 - 221*z**2


Question:
Calculate the following: (5*y + 39)*(46*y**3 - 27*y**2 + 6*y + 1)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 230*y**4 + 1659*y**3 - 1023*y**2 + 239*y + 39

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (5*y + 39)*(46*y**3 - 27*y**2 + 6*y + 1)
Expanding the part (5*y + 39) using the distributive property, and we got: (5*y)*(46*y**3 - 27*y**2 + 6*y + 1) + 39*(46*y**3 - 27*y**2 + 6*y + 1)
<replace-#Step 1>#Step 2:
Current expression: (5*y)*(46*y**3 - 27*y**2 + 6*y + 1) + 39*(46*y**3 - 27*y**2 + 6*y + 1)</replace>
Simplifying the partial expression: 39*(46*y**3 - 27*y**2 + 6*y + 1)
Expanding the part (46*y**3 - 27*y**2 + 6*y + 1) using the distributive property, and we got: (6*y)*39 - 27*y**2*39 + (46*y**3)*39 + 1*39
Replacing 39*(46*y**3 - 27*y**2 + 6*y + 1) with (6*y)*39 - 27*y**2*39 + (46*y**3)*39 + 1*39 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (5*y)*(46*y**3 - 27*y**2 + 6*y + 1) + (6*y)*39 - 27*y**2*39 + (46*y**3)*39 + 39</replace>
Simplifying the partial expression: (5*y)*(46*y**3 - 27*y**2 + 6*y + 1)
Expanding the part (46*y**3 - 27*y**2 + 6*y + 1) using the distributive property, and we got: 1*(5*y) + (5*y)*(6*y) + (5*y)*(-27*y**2) + (5*y)*(46*y**3)
Replacing (5*y)*(46*y**3 - 27*y**2 + 6*y + 1) with 1*(5*y) + (5*y)*(6*y) + (5*y)*(-27*y**2) + (5*y)*(46*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 5*y + (5*y)*(6*y) + (5*y)*(-27*y**2) + (5*y)*(46*y**3) + (6*y)*39 - 27*y**2*39 + (46*y**3)*39 + 39</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-27*y**2)*39 = -1053*y**2
  (-27*y**2)*(5*y) = -135*y**3
  (6*y)*39 = 234*y
  (6*y)*(5*y) = 30*y**2
  (46*y**3)*39 = 1794*y**3
  (46*y**3)*(5*y) = 230*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 230*y**4 - 135*y**3 + 1794*y**3 - 1053*y**2 + 30*y**2 + 5*y + 234*y + 39</replace>
Combining like terms, got 230*y**4 + 1659*y**3 - 1023*y**2 + 239*y + 39
<replace-#Step 5>#Step 6:
Current expression: 230*y**4 + 1659*y**3 - 1023*y**2 + 239*y + 39</replace>
No more calculations needed.
<answer>230*y**4 + 1659*y**3 - 1023*y**2 + 239*y + 39</answer>


Question:
Calculate the following: 61*y**3*(-39*y**3 - 24*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: -2379*y**6 - 1464*y**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 61*y**3*(-39*y**3 - 24*y)
Expanding the part (-39*y**3 - 24*y) using the distributive property, and we got: (-24*y)*(61*y**3) + (-39*y**3)*(61*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-24*y)*(61*y**3) + (-39*y**3)*(61*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-39*y**3)*(61*y**3) = -2379*y**6
  (-24*y)*(61*y**3) = -1464*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -2379*y**6 - 1464*y**4</replace>
No more calculations needed.
<answer>-2379*y**6 - 1464*y**4</answer>


Question:
Calculate the following: (2*z**3 - 7*z**2)*(8*z**3 + 49*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: 16*z**6 - 56*z**5 + 98*z**4 - 343*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: (2*z**3 - 7*z**2)*(8*z**3 + 49*z)
Expanding the part (2*z**3 - 7*z**2) using the distributive property, and we got: (-7*z**2)*(8*z**3 + 49*z) + (2*z**3)*(8*z**3 + 49*z)
<replace-#Step 1>#Step 2:
Current expression: (-7*z**2)*(8*z**3 + 49*z) + (2*z**3)*(8*z**3 + 49*z)</replace>
Simplifying the partial expression: (-7*z**2)*(8*z**3 + 49*z)
Expanding the part (8*z**3 + 49*z) using the distributive property, and we got: (49*z)*(-7*z**2) + (-7*z**2)*(8*z**3)
Replacing (-7*z**2)*(8*z**3 + 49*z) with (49*z)*(-7*z**2) + (-7*z**2)*(8*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (49*z)*(-7*z**2) + (-7*z**2)*(8*z**3) + (2*z**3)*(8*z**3 + 49*z)</replace>
Simplifying the partial expression: (2*z**3)*(8*z**3 + 49*z)
Expanding the part (8*z**3 + 49*z) using the distributive property, and we got: (49*z)*(2*z**3) + (2*z**3)*(8*z**3)
Replacing (2*z**3)*(8*z**3 + 49*z) with (49*z)*(2*z**3) + (2*z**3)*(8*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (49*z)*(-7*z**2) + (49*z)*(2*z**3) + (-7*z**2)*(8*z**3) + (2*z**3)*(8*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (8*z**3)*(-7*z**2) = -56*z**5
  (8*z**3)*(2*z**3) = 16*z**6
  (49*z)*(-7*z**2) = -343*z**3
  (49*z)*(2*z**3) = 98*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 16*z**6 - 56*z**5 + 98*z**4 - 343*z**3</replace>
No more calculations needed.
<answer>16*z**6 - 56*z**5 + 98*z**4 - 343*z**3</answer>


Question:
Simplify this expression: (33*z**3 + 6*z**2)*(33*z**3 + 23*z**2 + 8*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: 1089*z**6 + 957*z**5 + 402*z**4 + 48*z**3


Question:
Simplify this expression: -56*y**2*(50*y**3 - 40*y + 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: -2800*y**5 + 2240*y**3 - 672*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: -56*y**2*(50*y**3 - 40*y + 12)
Expanding the part (50*y**3 - 40*y + 12) using the distributive property, and we got: (-40*y)*(-56*y**2) + 12*(-56*y**2) + (-56*y**2)*(50*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-40*y)*(-56*y**2) + 12*(-56*y**2) + (-56*y**2)*(50*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  12*(-56*y**2) = -672*y**2
  (-40*y)*(-56*y**2) = 2240*y**3
  (50*y**3)*(-56*y**2) = -2800*y**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -2800*y**5 + 2240*y**3 - 672*y**2</replace>
No more calculations needed.
<answer>-2800*y**5 + 2240*y**3 - 672*y**2</answer>


Question:
Calculate the following: (14*x**3 + x)*(-4*x**2 + 12*x - 1)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -56*x**5 + 168*x**4 - 18*x**3 + 12*x**2 - x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (14*x**3 + x)*(-4*x**2 + 12*x - 1)
Expanding the part (14*x**3 + x) using the distributive property, and we got: x*(-4*x**2 + 12*x - 1) + (14*x**3)*(-4*x**2 + 12*x - 1)
<replace-#Step 1>#Step 2:
Current expression: x*(-4*x**2 + 12*x - 1) + (14*x**3)*(-4*x**2 + 12*x - 1)</replace>
Simplifying the partial expression: x*(-4*x**2 + 12*x - 1)
Expanding the part (-4*x**2 + 12*x - 1) using the distributive property, and we got: x*(12*x) + x*(-4*x**2) - x
Replacing x*(-4*x**2 + 12*x - 1) with x*(12*x) + x*(-4*x**2) - x in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: x*(12*x) + x*(-4*x**2) - x + (14*x**3)*(-4*x**2 + 12*x - 1)</replace>
Simplifying the partial expression: (14*x**3)*(-4*x**2 + 12*x - 1)
Expanding the part (-4*x**2 + 12*x - 1) using the distributive property, and we got: -14*x**3 + (12*x)*(14*x**3) + (-4*x**2)*(14*x**3)
Replacing (14*x**3)*(-4*x**2 + 12*x - 1) with -14*x**3 + (12*x)*(14*x**3) + (-4*x**2)*(14*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -1*14*x**3 + x*(12*x) + x*(-4*x**2) - x + (12*x)*(14*x**3) + (-4*x**2)*(14*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-4*x**2)*x = -4*x**3
  (-4*x**2)*(14*x**3) = -56*x**5
  (12*x)*x = 12*x**2
  (12*x)*(14*x**3) = 168*x**4
  -1*14*x**3 = -14*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -56*x**5 + 168*x**4 - 14*x**3 - 4*x**3 + 12*x**2 - x</replace>
Combining like terms, got -56*x**5 + 168*x**4 - 18*x**3 + 12*x**2 - x
<replace-#Step 5>#Step 6:
Current expression: -56*x**5 + 168*x**4 - 18*x**3 + 12*x**2 - x</replace>
No more calculations needed.
<answer>-56*x**5 + 168*x**4 - 18*x**3 + 12*x**2 - x</answer>


Question:
Simplify this expression: (-4*z**2 + 33*z + 36)*(11*z**2 - 21*z - 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: -44*z**4 + 447*z**3 - 185*z**2 - 1680*z - 1008


Question:
Calculate the following: (21*x**2 + 19*x)*(-8*x**3 - 40*x + 22)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -168*x**5 - 152*x**4 - 840*x**3 - 298*x**2 + 418*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: (21*x**2 + 19*x)*(-8*x**3 - 40*x + 22)
Expanding the part (21*x**2 + 19*x) using the distributive property, and we got: (19*x)*(-8*x**3 - 40*x + 22) + (21*x**2)*(-8*x**3 - 40*x + 22)
<replace-#Step 1>#Step 2:
Current expression: (19*x)*(-8*x**3 - 40*x + 22) + (21*x**2)*(-8*x**3 - 40*x + 22)</replace>
Simplifying the partial expression: (19*x)*(-8*x**3 - 40*x + 22)
Expanding the part (-8*x**3 - 40*x + 22) using the distributive property, and we got: (-40*x)*(19*x) + 22*(19*x) + (19*x)*(-8*x**3)
Replacing (19*x)*(-8*x**3 - 40*x + 22) with (-40*x)*(19*x) + 22*(19*x) + (19*x)*(-8*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-40*x)*(19*x) + 22*19*x + (19*x)*(-8*x**3) + (21*x**2)*(-8*x**3 - 40*x + 22)</replace>
Simplifying the partial expression: (21*x**2)*(-8*x**3 - 40*x + 22)
Expanding the part (-8*x**3 - 40*x + 22) using the distributive property, and we got: (-40*x)*(21*x**2) + 22*(21*x**2) + (21*x**2)*(-8*x**3)
Replacing (21*x**2)*(-8*x**3 - 40*x + 22) with (-40*x)*(21*x**2) + 22*(21*x**2) + (21*x**2)*(-8*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-40*x)*(19*x) + (-40*x)*(21*x**2) + 22*21*x**2 + 22*19*x + (19*x)*(-8*x**3) + (21*x**2)*(-8*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-40*x)*(19*x) = -760*x**2
  (-40*x)*(21*x**2) = -840*x**3
  (-8*x**3)*(19*x) = -152*x**4
  (-8*x**3)*(21*x**2) = -168*x**5
  22*19*x = 418*x
  22*21*x**2 = 462*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -168*x**5 - 152*x**4 - 840*x**3 - 760*x**2 + 462*x**2 + 418*x</replace>
Combining like terms, got -168*x**5 - 152*x**4 - 840*x**3 - 298*x**2 + 418*x
<replace-#Step 5>#Step 6:
Current expression: -168*x**5 - 152*x**4 - 840*x**3 - 298*x**2 + 418*x</replace>
No more calculations needed.
<answer>-168*x**5 - 152*x**4 - 840*x**3 - 298*x**2 + 418*x</answer>


Question:
Simplify this expression: (67*z**2 + 35*z)*(33*z**3 + 21*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: 2211*z**5 + 1155*z**4 + 1407*z**3 + 735*z**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (67*z**2 + 35*z)*(33*z**3 + 21*z)
Expanding the part (33*z**3 + 21*z) using the distributive property, and we got: (21*z)*(67*z**2 + 35*z) + (33*z**3)*(67*z**2 + 35*z)
<replace-#Step 1>#Step 2:
Current expression: (21*z)*(67*z**2 + 35*z) + (33*z**3)*(67*z**2 + 35*z)</replace>
Simplifying the partial expression: (21*z)*(67*z**2 + 35*z)
Expanding the part (67*z**2 + 35*z) using the distributive property, and we got: (21*z)*(35*z) + (21*z)*(67*z**2)
Replacing (21*z)*(67*z**2 + 35*z) with (21*z)*(35*z) + (21*z)*(67*z**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (21*z)*(35*z) + (21*z)*(67*z**2) + (33*z**3)*(67*z**2 + 35*z)</replace>
Simplifying the partial expression: (33*z**3)*(67*z**2 + 35*z)
Expanding the part (67*z**2 + 35*z) using the distributive property, and we got: (35*z)*(33*z**3) + (67*z**2)*(33*z**3)
Replacing (33*z**3)*(67*z**2 + 35*z) with (35*z)*(33*z**3) + (67*z**2)*(33*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (21*z)*(35*z) + (21*z)*(67*z**2) + (35*z)*(33*z**3) + (67*z**2)*(33*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (35*z)*(21*z) = 735*z**2
  (35*z)*(33*z**3) = 1155*z**4
  (67*z**2)*(21*z) = 1407*z**3
  (67*z**2)*(33*z**3) = 2211*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2211*z**5 + 1155*z**4 + 1407*z**3 + 735*z**2</replace>
No more calculations needed.
<answer>2211*z**5 + 1155*z**4 + 1407*z**3 + 735*z**2</answer>


Question:
Calculate the following: (-34*x**3 - 9)*(50*x**2 - 23*x - 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: -1700*x**5 + 782*x**4 + 714*x**3 - 450*x**2 + 207*x + 189

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*x**3 - 9)*(50*x**2 - 23*x - 21)
Expanding the part (-34*x**3 - 9) using the distributive property, and we got: (-34*x**3)*(50*x**2 - 23*x - 21) - 9*(50*x**2 - 23*x - 21)
<replace-#Step 1>#Step 2:
Current expression: (-34*x**3)*(50*x**2 - 23*x - 21) - 9*(50*x**2 - 23*x - 21)</replace>
Simplifying the partial expression: -9*(50*x**2 - 23*x - 21)
Expanding the part (50*x**2 - 23*x - 21) using the distributive property, and we got: -23*x*(-9) + (50*x**2)*(-9) - 21*(-9)
Replacing -9*(50*x**2 - 23*x - 21) with -23*x*(-9) + (50*x**2)*(-9) - 21*(-9) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -23*x*(-9) + (50*x**2)*(-9) + (-34*x**3)*(50*x**2 - 23*x - 21) + 189</replace>
Simplifying the partial expression: (-34*x**3)*(50*x**2 - 23*x - 21)
Expanding the part (50*x**2 - 23*x - 21) using the distributive property, and we got: (-23*x)*(-34*x**3) - (-1)*714*x**3 + (50*x**2)*(-34*x**3)
Replacing (-34*x**3)*(50*x**2 - 23*x - 21) with (-23*x)*(-34*x**3) - (-1)*714*x**3 + (50*x**2)*(-34*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-23*x)*(-34*x**3) - 23*x*(-9) - 21*(-34)*x**3 + (50*x**2)*(-34*x**3) + (50*x**2)*(-9) + 189</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-23*x)*-9 = 207*x
  (-23*x)*(-34*x**3) = 782*x**4
  (50*x**2)*-9 = -450*x**2
  (50*x**2)*(-34*x**3) = -1700*x**5
  -21*-34*x**3 = 714*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1700*x**5 + 782*x**4 + 714*x**3 - 450*x**2 + 207*x + 189</replace>
No more calculations needed.
<answer>-1700*x**5 + 782*x**4 + 714*x**3 - 450*x**2 + 207*x + 189</answer>


Question:
Calculate the following: (44 - 39*y)*(-22*y**3 - 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: 858*y**4 - 968*y**3 + 1950*y - 2200

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: (44 - 39*y)*(-22*y**3 - 50)
Expanding the part (-22*y**3 - 50) using the distributive property, and we got: (-22*y**3)*(44 - 39*y) - 50*(44 - 39*y)
<replace-#Step 1>#Step 2:
Current expression: (-22*y**3)*(44 - 39*y) - 50*(44 - 39*y)</replace>
Simplifying the partial expression: -50*(44 - 39*y)
Expanding the part (44 - 39*y) using the distributive property, and we got: -39*y*(-50) + 44*(-50)
Replacing -50*(44 - 39*y) with -39*y*(-50) + 44*(-50) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -39*y*(-50) + (-22*y**3)*(44 - 39*y) - 2200</replace>
Simplifying the partial expression: (-22*y**3)*(44 - 39*y)
Expanding the part (44 - 39*y) using the distributive property, and we got: (-39*y)*(-22*y**3) + 44*(-22*y**3)
Replacing (-22*y**3)*(44 - 39*y) with (-39*y)*(-22*y**3) + 44*(-22*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-39*y)*(-22*y**3) - 39*y*(-50) + 44*(-22)*y**3 - 2200</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-39*y)*-50 = 1950*y
  (-39*y)*(-22*y**3) = 858*y**4
  44*-22*y**3 = -968*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 858*y**4 - 968*y**3 + 1950*y - 2200</replace>
No more calculations needed.
<answer>858*y**4 - 968*y**3 + 1950*y - 2200</answer>


Question:
Simplify this expression: (30*y**2 - 46*y)*(47*y**3 + 41*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: 1410*y**5 - 932*y**4 - 1886*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: (30*y**2 - 46*y)*(47*y**3 + 41*y**2)
Expanding the part (30*y**2 - 46*y) using the distributive property, and we got: (-46*y)*(47*y**3 + 41*y**2) + (30*y**2)*(47*y**3 + 41*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-46*y)*(47*y**3 + 41*y**2) + (30*y**2)*(47*y**3 + 41*y**2)</replace>
Simplifying the partial expression: (-46*y)*(47*y**3 + 41*y**2)
Expanding the part (47*y**3 + 41*y**2) using the distributive property, and we got: (-46*y)*(41*y**2) + (-46*y)*(47*y**3)
Replacing (-46*y)*(47*y**3 + 41*y**2) with (-46*y)*(41*y**2) + (-46*y)*(47*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-46*y)*(41*y**2) + (-46*y)*(47*y**3) + (30*y**2)*(47*y**3 + 41*y**2)</replace>
Simplifying the partial expression: (30*y**2)*(47*y**3 + 41*y**2)
Expanding the part (47*y**3 + 41*y**2) using the distributive property, and we got: (30*y**2)*(41*y**2) + (30*y**2)*(47*y**3)
Replacing (30*y**2)*(47*y**3 + 41*y**2) with (30*y**2)*(41*y**2) + (30*y**2)*(47*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-46*y)*(41*y**2) + (-46*y)*(47*y**3) + (30*y**2)*(41*y**2) + (30*y**2)*(47*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (41*y**2)*(-46*y) = -1886*y**3
  (41*y**2)*(30*y**2) = 1230*y**4
  (47*y**3)*(-46*y) = -2162*y**4
  (47*y**3)*(30*y**2) = 1410*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1410*y**5 - 2162*y**4 + 1230*y**4 - 1886*y**3</replace>
Combining like terms, got 1410*y**5 - 932*y**4 - 1886*y**3
<replace-#Step 5>#Step 6:
Current expression: 1410*y**5 - 932*y**4 - 1886*y**3</replace>
No more calculations needed.
<answer>1410*y**5 - 932*y**4 - 1886*y**3</answer>


Question:
Simplify this expression: 6*y**3*(6*y**2 - 11*y - 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: 36*y**5 - 66*y**4 - 120*y**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 6*y**3*(6*y**2 - 11*y - 20)
Expanding the part (6*y**2 - 11*y - 20) using the distributive property, and we got: (-11*y)*(6*y**3) - 120*y**3 + (6*y**2)*(6*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-11*y)*(6*y**3) - 120*y**3 + (6*y**2)*(6*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -20*(6*y**3) = -120*y**3
  (-11*y)*(6*y**3) = -66*y**4
  (6*y**2)*(6*y**3) = 36*y**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 36*y**5 - 66*y**4 - 120*y**3</replace>
No more calculations needed.
<answer>36*y**5 - 66*y**4 - 120*y**3</answer>


Question:
Simplify this expression: (16 - 35*y)*(-10*y**3 - 15*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 350*y**4 - 160*y**3 + 525*y**2 - 240*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: (16 - 35*y)*(-10*y**3 - 15*y)
Expanding the part (16 - 35*y) using the distributive property, and we got: (-35*y)*(-10*y**3 - 15*y) + 16*(-10*y**3 - 15*y)
<replace-#Step 1>#Step 2:
Current expression: (-35*y)*(-10*y**3 - 15*y) + 16*(-10*y**3 - 15*y)</replace>
Simplifying the partial expression: 16*(-10*y**3 - 15*y)
Expanding the part (-10*y**3 - 15*y) using the distributive property, and we got: -15*y*16 - 10*y**3*16
Replacing 16*(-10*y**3 - 15*y) with -15*y*16 - 10*y**3*16 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-35*y)*(-10*y**3 - 15*y) - 15*y*16 - 10*y**3*16</replace>
Simplifying the partial expression: (-35*y)*(-10*y**3 - 15*y)
Expanding the part (-10*y**3 - 15*y) using the distributive property, and we got: (-35*y)*(-15*y) + (-35*y)*(-10*y**3)
Replacing (-35*y)*(-10*y**3 - 15*y) with (-35*y)*(-15*y) + (-35*y)*(-10*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-35*y)*(-15*y) + (-35*y)*(-10*y**3) - 15*y*16 - 10*y**3*16</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-15*y)*16 = -240*y
  (-15*y)*(-35*y) = 525*y**2
  (-10*y**3)*16 = -160*y**3
  (-10*y**3)*(-35*y) = 350*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 350*y**4 - 160*y**3 + 525*y**2 - 240*y</replace>
No more calculations needed.
<answer>350*y**4 - 160*y**3 + 525*y**2 - 240*y</answer>


Question:
Simplify this expression: (7 - 45*y)*(25*y**2 - 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: -1125*y**3 + 175*y**2 + 225*y - 35

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 - 45*y)*(25*y**2 - 5)
Expanding the part (25*y**2 - 5) using the distributive property, and we got: (25*y**2)*(7 - 45*y) - 5*(7 - 45*y)
<replace-#Step 1>#Step 2:
Current expression: (25*y**2)*(7 - 45*y) - 5*(7 - 45*y)</replace>
Simplifying the partial expression: -5*(7 - 45*y)
Expanding the part (7 - 45*y) using the distributive property, and we got: -45*y*(-5) + 7*(-5)
Replacing -5*(7 - 45*y) with -45*y*(-5) + 7*(-5) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -45*y*(-5) + (25*y**2)*(7 - 45*y) - 35</replace>
Simplifying the partial expression: (25*y**2)*(7 - 45*y)
Expanding the part (7 - 45*y) using the distributive property, and we got: (-45*y)*(25*y**2) + 7*(25*y**2)
Replacing (25*y**2)*(7 - 45*y) with (-45*y)*(25*y**2) + 7*(25*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-45*y)*(25*y**2) - 45*y*(-5) + 7*25*y**2 - 35</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-45*y)*-5 = 225*y
  (-45*y)*(25*y**2) = -1125*y**3
  7*25*y**2 = 175*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1125*y**3 + 175*y**2 + 225*y - 35</replace>
No more calculations needed.
<answer>-1125*y**3 + 175*y**2 + 225*y - 35</answer>


Question:
Calculate the following: (39*x**2 - 30)*(-15*x**3 - 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: -585*x**5 + 450*x**3 - 702*x**2 + 540

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (39*x**2 - 30)*(-15*x**3 - 18)
Expanding the part (39*x**2 - 30) using the distributive property, and we got: (39*x**2)*(-15*x**3 - 18) - 30*(-15*x**3 - 18)
<replace-#Step 1>#Step 2:
Current expression: (39*x**2)*(-15*x**3 - 18) - 30*(-15*x**3 - 18)</replace>
Simplifying the partial expression: -30*(-15*x**3 - 18)
Expanding the part (-15*x**3 - 18) using the distributive property, and we got: -15*x**3*(-30) - 18*(-30)
Replacing -30*(-15*x**3 - 18) with -15*x**3*(-30) - 18*(-30) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (39*x**2)*(-15*x**3 - 18) - 15*x**3*(-30) + 540</replace>
Simplifying the partial expression: (39*x**2)*(-15*x**3 - 18)
Expanding the part (-15*x**3 - 18) using the distributive property, and we got: -702*x**2 + (39*x**2)*(-15*x**3)
Replacing (39*x**2)*(-15*x**3 - 18) with -702*x**2 + (39*x**2)*(-15*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -18*39*x**2 + (39*x**2)*(-15*x**3) - 15*x**3*(-30) + 540</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-15*x**3)*-30 = 450*x**3
  (-15*x**3)*(39*x**2) = -585*x**5
  -18*39*x**2 = -702*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -585*x**5 + 450*x**3 - 702*x**2 + 540</replace>
No more calculations needed.
<answer>-585*x**5 + 450*x**3 - 702*x**2 + 540</answer>


Question:
Calculate the following: (31*z**2 + 29*z)*(42*z**2 - 11*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1302*z**4 + 877*z**3 - 319*z**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (31*z**2 + 29*z)*(42*z**2 - 11*z)
Expanding the part (42*z**2 - 11*z) using the distributive property, and we got: (-11*z)*(31*z**2 + 29*z) + (42*z**2)*(31*z**2 + 29*z)
<replace-#Step 1>#Step 2:
Current expression: (-11*z)*(31*z**2 + 29*z) + (42*z**2)*(31*z**2 + 29*z)</replace>
Simplifying the partial expression: (-11*z)*(31*z**2 + 29*z)
Expanding the part (31*z**2 + 29*z) using the distributive property, and we got: (-11*z)*(29*z) + (-11*z)*(31*z**2)
Replacing (-11*z)*(31*z**2 + 29*z) with (-11*z)*(29*z) + (-11*z)*(31*z**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-11*z)*(29*z) + (-11*z)*(31*z**2) + (42*z**2)*(31*z**2 + 29*z)</replace>
Simplifying the partial expression: (42*z**2)*(31*z**2 + 29*z)
Expanding the part (31*z**2 + 29*z) using the distributive property, and we got: (29*z)*(42*z**2) + (31*z**2)*(42*z**2)
Replacing (42*z**2)*(31*z**2 + 29*z) with (29*z)*(42*z**2) + (31*z**2)*(42*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-11*z)*(29*z) + (-11*z)*(31*z**2) + (29*z)*(42*z**2) + (31*z**2)*(42*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (29*z)*(-11*z) = -319*z**2
  (29*z)*(42*z**2) = 1218*z**3
  (31*z**2)*(-11*z) = -341*z**3
  (31*z**2)*(42*z**2) = 1302*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1302*z**4 - 341*z**3 + 1218*z**3 - 319*z**2</replace>
Combining like terms, got 1302*z**4 + 877*z**3 - 319*z**2
<replace-#Step 5>#Step 6:
Current expression: 1302*z**4 + 877*z**3 - 319*z**2</replace>
No more calculations needed.
<answer>1302*z**4 + 877*z**3 - 319*z**2</answer>


Question:
Simplify this expression: (-25*x**3 - 7*x)*(-34*x**3 - 28*x**2 + 16*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 850*x**6 + 700*x**5 - 162*x**4 + 196*x**3 - 112*x**2


Question:
Simplify this expression: (-88*x**2 - 14)*(33*x**2 - 58*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: -2904*x**4 + 5104*x**3 - 462*x**2 + 812*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: (-88*x**2 - 14)*(33*x**2 - 58*x)
Expanding the part (-88*x**2 - 14) using the distributive property, and we got: (-88*x**2)*(33*x**2 - 58*x) - 14*(33*x**2 - 58*x)
<replace-#Step 1>#Step 2:
Current expression: (-88*x**2)*(33*x**2 - 58*x) - 14*(33*x**2 - 58*x)</replace>
Simplifying the partial expression: -14*(33*x**2 - 58*x)
Expanding the part (33*x**2 - 58*x) using the distributive property, and we got: -58*x*(-14) + (33*x**2)*(-14)
Replacing -14*(33*x**2 - 58*x) with -58*x*(-14) + (33*x**2)*(-14) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -58*x*(-14) + (-88*x**2)*(33*x**2 - 58*x) + (33*x**2)*(-14)</replace>
Simplifying the partial expression: (-88*x**2)*(33*x**2 - 58*x)
Expanding the part (33*x**2 - 58*x) using the distributive property, and we got: (-58*x)*(-88*x**2) + (-88*x**2)*(33*x**2)
Replacing (-88*x**2)*(33*x**2 - 58*x) with (-58*x)*(-88*x**2) + (-88*x**2)*(33*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-58*x)*(-88*x**2) - 58*x*(-14) + (-88*x**2)*(33*x**2) + (33*x**2)*(-14)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-58*x)*-14 = 812*x
  (-58*x)*(-88*x**2) = 5104*x**3
  (33*x**2)*-14 = -462*x**2
  (33*x**2)*(-88*x**2) = -2904*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2904*x**4 + 5104*x**3 - 462*x**2 + 812*x</replace>
No more calculations needed.
<answer>-2904*x**4 + 5104*x**3 - 462*x**2 + 812*x</answer>


Question:
Simplify this expression: (-x**2 + 18*x + 41)*(-48*x**3 + 46*x**2 - 11*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**5 - 910*x**4 - 1129*x**3 + 1688*x**2 - 451*x


Question:
Calculate the following: (-16*z**3 - 11*z**2)*(-13*z**3 + 6*z**2 + 28*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 208*z**6 + 47*z**5 - 514*z**4 - 308*z**3


Question:
Simplify this expression: (-40*x**2 + 8*x)*(-13*x**2 - 12*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: 520*x**4 + 376*x**3 - 96*x**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-40*x**2 + 8*x)*(-13*x**2 - 12*x)
Expanding the part (-40*x**2 + 8*x) using the distributive property, and we got: (8*x)*(-13*x**2 - 12*x) + (-40*x**2)*(-13*x**2 - 12*x)
<replace-#Step 1>#Step 2:
Current expression: (8*x)*(-13*x**2 - 12*x) + (-40*x**2)*(-13*x**2 - 12*x)</replace>
Simplifying the partial expression: (-40*x**2)*(-13*x**2 - 12*x)
Expanding the part (-13*x**2 - 12*x) using the distributive property, and we got: (-12*x)*(-40*x**2) + (-40*x**2)*(-13*x**2)
Replacing (-40*x**2)*(-13*x**2 - 12*x) with (-12*x)*(-40*x**2) + (-40*x**2)*(-13*x**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-12*x)*(-40*x**2) + (8*x)*(-13*x**2 - 12*x) + (-40*x**2)*(-13*x**2)</replace>
Simplifying the partial expression: (8*x)*(-13*x**2 - 12*x)
Expanding the part (-13*x**2 - 12*x) using the distributive property, and we got: (-12*x)*(8*x) + (8*x)*(-13*x**2)
Replacing (8*x)*(-13*x**2 - 12*x) with (-12*x)*(8*x) + (8*x)*(-13*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-12*x)*(8*x) + (-12*x)*(-40*x**2) + (8*x)*(-13*x**2) + (-40*x**2)*(-13*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-13*x**2)*(-40*x**2) = 520*x**4
  (-13*x**2)*(8*x) = -104*x**3
  (-12*x)*(-40*x**2) = 480*x**3
  (-12*x)*(8*x) = -96*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 520*x**4 - 104*x**3 + 480*x**3 - 96*x**2</replace>
Combining like terms, got 520*x**4 + 376*x**3 - 96*x**2
<replace-#Step 5>#Step 6:
Current expression: 520*x**4 + 376*x**3 - 96*x**2</replace>
No more calculations needed.
<answer>520*x**4 + 376*x**3 - 96*x**2</answer>


Question:
Simplify this expression: (-48*x**3 - 3*x**2 - 38*x)*(-18*x**3 - 20*x**2 - 31*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: 864*x**6 + 1014*x**5 + 2232*x**4 + 853*x**3 + 1178*x**2


Question:
Calculate the following: (-33*x**2 - 9)*(-25*x**2 - 30)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 825*x**4 + 1215*x**2 + 270

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**2 - 9)*(-25*x**2 - 30)
Expanding the part (-25*x**2 - 30) using the distributive property, and we got: (-25*x**2)*(-33*x**2 - 9) - 30*(-33*x**2 - 9)
<replace-#Step 1>#Step 2:
Current expression: (-25*x**2)*(-33*x**2 - 9) - 30*(-33*x**2 - 9)</replace>
Simplifying the partial expression: -30*(-33*x**2 - 9)
Expanding the part (-33*x**2 - 9) using the distributive property, and we got: -33*x**2*(-30) - 9*(-30)
Replacing -30*(-33*x**2 - 9) with -33*x**2*(-30) - 9*(-30) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -33*x**2*(-30) + (-25*x**2)*(-33*x**2 - 9) + 270</replace>
Simplifying the partial expression: (-25*x**2)*(-33*x**2 - 9)
Expanding the part (-33*x**2 - 9) using the distributive property, and we got: -(-1)*225*x**2 + (-33*x**2)*(-25*x**2)
Replacing (-25*x**2)*(-33*x**2 - 9) with -(-1)*225*x**2 + (-33*x**2)*(-25*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -9*(-25)*x**2 + (-33*x**2)*(-25*x**2) - 33*x**2*(-30) + 270</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-33*x**2)*-30 = 990*x**2
  (-33*x**2)*(-25*x**2) = 825*x**4
  -9*-25*x**2 = 225*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 825*x**4 + 225*x**2 + 990*x**2 + 270</replace>
Combining like terms, got 825*x**4 + 1215*x**2 + 270
<replace-#Step 5>#Step 6:
Current expression: 825*x**4 + 1215*x**2 + 270</replace>
No more calculations needed.
<answer>825*x**4 + 1215*x**2 + 270</answer>


Question:
Simplify this expression: (-25*y**3 + 8*y + 43)*(62*y**3 - 17*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: -1550*y**6 + 921*y**4 + 1966*y**3 - 136*y**2 - 507*y + 1204


Question:
Calculate the following: (-14*x**2 + 69*x + 13)*(-36*x**3 - 20*x**2 + 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: 504*x**5 - 2204*x**4 - 1862*x**3 - 191*x**2 + 13*x


Question:
Calculate the following: (-7*z**3 + 3*z)*(18*z**3 + 42*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: -126*z**6 - 240*z**4 + 126*z**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-7*z**3 + 3*z)*(18*z**3 + 42*z)
Expanding the part (-7*z**3 + 3*z) using the distributive property, and we got: (3*z)*(18*z**3 + 42*z) + (-7*z**3)*(18*z**3 + 42*z)
<replace-#Step 1>#Step 2:
Current expression: (3*z)*(18*z**3 + 42*z) + (-7*z**3)*(18*z**3 + 42*z)</replace>
Simplifying the partial expression: (-7*z**3)*(18*z**3 + 42*z)
Expanding the part (18*z**3 + 42*z) using the distributive property, and we got: (42*z)*(-7*z**3) + (-7*z**3)*(18*z**3)
Replacing (-7*z**3)*(18*z**3 + 42*z) with (42*z)*(-7*z**3) + (-7*z**3)*(18*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (3*z)*(18*z**3 + 42*z) + (42*z)*(-7*z**3) + (-7*z**3)*(18*z**3)</replace>
Simplifying the partial expression: (3*z)*(18*z**3 + 42*z)
Expanding the part (18*z**3 + 42*z) using the distributive property, and we got: (3*z)*(42*z) + (3*z)*(18*z**3)
Replacing (3*z)*(18*z**3 + 42*z) with (3*z)*(42*z) + (3*z)*(18*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (3*z)*(42*z) + (3*z)*(18*z**3) + (42*z)*(-7*z**3) + (-7*z**3)*(18*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (18*z**3)*(-7*z**3) = -126*z**6
  (18*z**3)*(3*z) = 54*z**4
  (42*z)*(-7*z**3) = -294*z**4
  (42*z)*(3*z) = 126*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -126*z**6 - 294*z**4 + 54*z**4 + 126*z**2</replace>
Combining like terms, got -126*z**6 - 240*z**4 + 126*z**2
<replace-#Step 5>#Step 6:
Current expression: -126*z**6 - 240*z**4 + 126*z**2</replace>
No more calculations needed.
<answer>-126*z**6 - 240*z**4 + 126*z**2</answer>


Question:
Calculate the following: (-11*x**3 + 20*x)*(28*x**3 + 41)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -308*x**6 + 560*x**4 - 451*x**3 + 820*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: (-11*x**3 + 20*x)*(28*x**3 + 41)
Expanding the part (28*x**3 + 41) using the distributive property, and we got: (28*x**3)*(-11*x**3 + 20*x) + 41*(-11*x**3 + 20*x)
<replace-#Step 1>#Step 2:
Current expression: (28*x**3)*(-11*x**3 + 20*x) + 41*(-11*x**3 + 20*x)</replace>
Simplifying the partial expression: 41*(-11*x**3 + 20*x)
Expanding the part (-11*x**3 + 20*x) using the distributive property, and we got: (20*x)*41 - 11*x**3*41
Replacing 41*(-11*x**3 + 20*x) with (20*x)*41 - 11*x**3*41 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (20*x)*41 - 11*x**3*41 + (28*x**3)*(-11*x**3 + 20*x)</replace>
Simplifying the partial expression: (28*x**3)*(-11*x**3 + 20*x)
Expanding the part (-11*x**3 + 20*x) using the distributive property, and we got: (20*x)*(28*x**3) + (-11*x**3)*(28*x**3)
Replacing (28*x**3)*(-11*x**3 + 20*x) with (20*x)*(28*x**3) + (-11*x**3)*(28*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (20*x)*(28*x**3) + (20*x)*41 + (-11*x**3)*(28*x**3) - 11*x**3*41</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-11*x**3)*41 = -451*x**3
  (-11*x**3)*(28*x**3) = -308*x**6
  (20*x)*41 = 820*x
  (20*x)*(28*x**3) = 560*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -308*x**6 + 560*x**4 - 451*x**3 + 820*x</replace>
No more calculations needed.
<answer>-308*x**6 + 560*x**4 - 451*x**3 + 820*x</answer>


Question:
Simplify this expression: (24 - 6*y)*(-71*y**3 + 50*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: 426*y**4 - 2004*y**3 + 1200*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: (24 - 6*y)*(-71*y**3 + 50*y**2)
Expanding the part (24 - 6*y) using the distributive property, and we got: (-6*y)*(-71*y**3 + 50*y**2) + 24*(-71*y**3 + 50*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-6*y)*(-71*y**3 + 50*y**2) + 24*(-71*y**3 + 50*y**2)</replace>
Simplifying the partial expression: 24*(-71*y**3 + 50*y**2)
Expanding the part (-71*y**3 + 50*y**2) using the distributive property, and we got: (50*y**2)*24 - 71*y**3*24
Replacing 24*(-71*y**3 + 50*y**2) with (50*y**2)*24 - 71*y**3*24 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-6*y)*(-71*y**3 + 50*y**2) + (50*y**2)*24 - 71*y**3*24</replace>
Simplifying the partial expression: (-6*y)*(-71*y**3 + 50*y**2)
Expanding the part (-71*y**3 + 50*y**2) using the distributive property, and we got: (-6*y)*(50*y**2) + (-6*y)*(-71*y**3)
Replacing (-6*y)*(-71*y**3 + 50*y**2) with (-6*y)*(50*y**2) + (-6*y)*(-71*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-6*y)*(50*y**2) + (-6*y)*(-71*y**3) + (50*y**2)*24 - 71*y**3*24</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-71*y**3)*24 = -1704*y**3
  (-71*y**3)*(-6*y) = 426*y**4
  (50*y**2)*24 = 1200*y**2
  (50*y**2)*(-6*y) = -300*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 426*y**4 - 1704*y**3 - 300*y**3 + 1200*y**2</replace>
Combining like terms, got 426*y**4 - 2004*y**3 + 1200*y**2
<replace-#Step 5>#Step 6:
Current expression: 426*y**4 - 2004*y**3 + 1200*y**2</replace>
No more calculations needed.
<answer>426*y**4 - 2004*y**3 + 1200*y**2</answer>


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

Answer: -351*z**4 + 78*z**2 + 455*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: 13*z*(-27*z**3 + 6*z + 35)
Expanding the part (-27*z**3 + 6*z + 35) using the distributive property, and we got: 35*(13*z) + (6*z)*(13*z) + (13*z)*(-27*z**3)
<replace-#Step 1>#Step 2:
Current expression: 35*(13*z) + (6*z)*(13*z) + (13*z)*(-27*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  35*(13*z) = 455*z
  (-27*z**3)*(13*z) = -351*z**4
  (6*z)*(13*z) = 78*z**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -351*z**4 + 78*z**2 + 455*z</replace>
No more calculations needed.
<answer>-351*z**4 + 78*z**2 + 455*z</answer>


Question:
Simplify this expression: (-34*y**3 - 5*y - 1)*(-13*y**3 - 22*y + 8)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 442*y**6 + 813*y**4 - 259*y**3 + 110*y**2 - 18*y - 8


Question:
Simplify this expression: 126*z + 99
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 126*z + 99

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: 126*z + 99
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: 126*z + 99</replace>
No more calculations needed.
<answer>126*z + 99</answer>


Question:
Simplify this expression: 36*y**3*(48*y**3 - 43*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1728*y**6 - 1548*y**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 36*y**3*(48*y**3 - 43*y)
Expanding the part (48*y**3 - 43*y) using the distributive property, and we got: (-43*y)*(36*y**3) + (36*y**3)*(48*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-43*y)*(36*y**3) + (36*y**3)*(48*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-43*y)*(36*y**3) = -1548*y**4
  (48*y**3)*(36*y**3) = 1728*y**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1728*y**6 - 1548*y**4</replace>
No more calculations needed.
<answer>1728*y**6 - 1548*y**4</answer>


Question:
Simplify this expression: (-16*x**3 + 8*x)*(-24*x**3 + 9*x**2 - 30*x + 6)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 384*x**6 - 144*x**5 + 288*x**4 - 24*x**3 - 240*x**2 + 48*x


Question:
Simplify this expression: (50*x**3 + 20*x)*(-14*x**3 + 50*x**2 - 26*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: -700*x**6 + 2500*x**5 - 1580*x**4 + 1000*x**3 - 520*x**2


Question:
Calculate the following: (2*x**3 + 47*x)*(18*x**3 + 5*x**2 - 47*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: 36*x**6 + 10*x**5 + 752*x**4 + 235*x**3 - 2209*x**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (2*x**3 + 47*x)*(18*x**3 + 5*x**2 - 47*x)
Expanding the part (2*x**3 + 47*x) using the distributive property, and we got: (47*x)*(18*x**3 + 5*x**2 - 47*x) + (2*x**3)*(18*x**3 + 5*x**2 - 47*x)
<replace-#Step 1>#Step 2:
Current expression: (47*x)*(18*x**3 + 5*x**2 - 47*x) + (2*x**3)*(18*x**3 + 5*x**2 - 47*x)</replace>
Simplifying the partial expression: (2*x**3)*(18*x**3 + 5*x**2 - 47*x)
Expanding the part (18*x**3 + 5*x**2 - 47*x) using the distributive property, and we got: (-47*x)*(2*x**3) + (5*x**2)*(2*x**3) + (2*x**3)*(18*x**3)
Replacing (2*x**3)*(18*x**3 + 5*x**2 - 47*x) with (-47*x)*(2*x**3) + (5*x**2)*(2*x**3) + (2*x**3)*(18*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-47*x)*(2*x**3) + (47*x)*(18*x**3 + 5*x**2 - 47*x) + (5*x**2)*(2*x**3) + (2*x**3)*(18*x**3)</replace>
Simplifying the partial expression: (47*x)*(18*x**3 + 5*x**2 - 47*x)
Expanding the part (18*x**3 + 5*x**2 - 47*x) using the distributive property, and we got: (-47*x)*(47*x) + (47*x)*(5*x**2) + (47*x)*(18*x**3)
Replacing (47*x)*(18*x**3 + 5*x**2 - 47*x) with (-47*x)*(47*x) + (47*x)*(5*x**2) + (47*x)*(18*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-47*x)*(47*x) + (-47*x)*(2*x**3) + (47*x)*(5*x**2) + (47*x)*(18*x**3) + (5*x**2)*(2*x**3) + (2*x**3)*(18*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-47*x)*(2*x**3) = -94*x**4
  (-47*x)*(47*x) = -2209*x**2
  (5*x**2)*(2*x**3) = 10*x**5
  (5*x**2)*(47*x) = 235*x**3
  (18*x**3)*(2*x**3) = 36*x**6
  (18*x**3)*(47*x) = 846*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 36*x**6 + 10*x**5 - 94*x**4 + 846*x**4 + 235*x**3 - 2209*x**2</replace>
Combining like terms, got 36*x**6 + 10*x**5 + 752*x**4 + 235*x**3 - 2209*x**2
<replace-#Step 5>#Step 6:
Current expression: 36*x**6 + 10*x**5 + 752*x**4 + 235*x**3 - 2209*x**2</replace>
No more calculations needed.
<answer>36*x**6 + 10*x**5 + 752*x**4 + 235*x**3 - 2209*x**2</answer>


Question:
Simplify this expression: -420*x**3
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -420*x**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -420*x**3
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: -420*x**3</replace>
No more calculations needed.
<answer>-420*x**3</answer>


Question:
Simplify this expression: (21 - 21*z**3)*(-25*z**3 + 33*z**2 - 39*z - 37)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 525*z**6 - 693*z**5 + 819*z**4 + 252*z**3 + 693*z**2 - 819*z - 777