Question:
Calculate the following: (36*z - 22)*(-15*z**3 + 27*z**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -540*z**4 + 1302*z**3 - 594*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: (36*z - 22)*(-15*z**3 + 27*z**2)
Expanding the part (36*z - 22) using the distributive property, and we got: (36*z)*(-15*z**3 + 27*z**2) - 22*(-15*z**3 + 27*z**2)
<replace-#Step 1>#Step 2:
Current expression: (36*z)*(-15*z**3 + 27*z**2) - 22*(-15*z**3 + 27*z**2)</replace>
Simplifying the partial expression: -22*(-15*z**3 + 27*z**2)
Expanding the part (-15*z**3 + 27*z**2) using the distributive property, and we got: (27*z**2)*(-22) - 15*z**3*(-22)
Replacing -22*(-15*z**3 + 27*z**2) with (27*z**2)*(-22) - 15*z**3*(-22) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (36*z)*(-15*z**3 + 27*z**2) + (27*z**2)*(-22) - 15*z**3*(-22)</replace>
Simplifying the partial expression: (36*z)*(-15*z**3 + 27*z**2)
Expanding the part (-15*z**3 + 27*z**2) using the distributive property, and we got: (36*z)*(27*z**2) + (36*z)*(-15*z**3)
Replacing (36*z)*(-15*z**3 + 27*z**2) with (36*z)*(27*z**2) + (36*z)*(-15*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (36*z)*(27*z**2) + (36*z)*(-15*z**3) + (27*z**2)*(-22) - 15*z**3*(-22)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-15*z**3)*-22 = 330*z**3
  (-15*z**3)*(36*z) = -540*z**4
  (27*z**2)*-22 = -594*z**2
  (27*z**2)*(36*z) = 972*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -540*z**4 + 330*z**3 + 972*z**3 - 594*z**2</replace>
Combining like terms, got -540*z**4 + 1302*z**3 - 594*z**2
<replace-#Step 5>#Step 6:
Current expression: -540*z**4 + 1302*z**3 - 594*z**2</replace>
No more calculations needed.
<answer>-540*z**4 + 1302*z**3 - 594*z**2</answer>


Question:
Calculate the following: (-13*x**2 + 21*x)*(15*x**3 - 72*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: -195*x**5 + 1251*x**4 - 1512*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: (-13*x**2 + 21*x)*(15*x**3 - 72*x**2)
Expanding the part (15*x**3 - 72*x**2) using the distributive property, and we got: (-72*x**2)*(-13*x**2 + 21*x) + (15*x**3)*(-13*x**2 + 21*x)
<replace-#Step 1>#Step 2:
Current expression: (-72*x**2)*(-13*x**2 + 21*x) + (15*x**3)*(-13*x**2 + 21*x)</replace>
Simplifying the partial expression: (-72*x**2)*(-13*x**2 + 21*x)
Expanding the part (-13*x**2 + 21*x) using the distributive property, and we got: (21*x)*(-72*x**2) + (-72*x**2)*(-13*x**2)
Replacing (-72*x**2)*(-13*x**2 + 21*x) with (21*x)*(-72*x**2) + (-72*x**2)*(-13*x**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (21*x)*(-72*x**2) + (-72*x**2)*(-13*x**2) + (15*x**3)*(-13*x**2 + 21*x)</replace>
Simplifying the partial expression: (15*x**3)*(-13*x**2 + 21*x)
Expanding the part (-13*x**2 + 21*x) using the distributive property, and we got: (21*x)*(15*x**3) + (-13*x**2)*(15*x**3)
Replacing (15*x**3)*(-13*x**2 + 21*x) with (21*x)*(15*x**3) + (-13*x**2)*(15*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (21*x)*(-72*x**2) + (21*x)*(15*x**3) + (-72*x**2)*(-13*x**2) + (-13*x**2)*(15*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-13*x**2)*(-72*x**2) = 936*x**4
  (-13*x**2)*(15*x**3) = -195*x**5
  (21*x)*(-72*x**2) = -1512*x**3
  (21*x)*(15*x**3) = 315*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -195*x**5 + 315*x**4 + 936*x**4 - 1512*x**3</replace>
Combining like terms, got -195*x**5 + 1251*x**4 - 1512*x**3
<replace-#Step 5>#Step 6:
Current expression: -195*x**5 + 1251*x**4 - 1512*x**3</replace>
No more calculations needed.
<answer>-195*x**5 + 1251*x**4 - 1512*x**3</answer>


Question:
Calculate the following: (28*y**2 + 29*y)*(58*y**3 + 71)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1624*y**5 + 1682*y**4 + 1988*y**2 + 2059*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (28*y**2 + 29*y)*(58*y**3 + 71)
Expanding the part (58*y**3 + 71) using the distributive property, and we got: (58*y**3)*(28*y**2 + 29*y) + 71*(28*y**2 + 29*y)
<replace-#Step 1>#Step 2:
Current expression: (58*y**3)*(28*y**2 + 29*y) + 71*(28*y**2 + 29*y)</replace>
Simplifying the partial expression: 71*(28*y**2 + 29*y)
Expanding the part (28*y**2 + 29*y) using the distributive property, and we got: (29*y)*71 + (28*y**2)*71
Replacing 71*(28*y**2 + 29*y) with (29*y)*71 + (28*y**2)*71 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (29*y)*71 + (28*y**2)*71 + (58*y**3)*(28*y**2 + 29*y)</replace>
Simplifying the partial expression: (58*y**3)*(28*y**2 + 29*y)
Expanding the part (28*y**2 + 29*y) using the distributive property, and we got: (29*y)*(58*y**3) + (28*y**2)*(58*y**3)
Replacing (58*y**3)*(28*y**2 + 29*y) with (29*y)*(58*y**3) + (28*y**2)*(58*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (29*y)*(58*y**3) + (29*y)*71 + (28*y**2)*(58*y**3) + (28*y**2)*71</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (28*y**2)*71 = 1988*y**2
  (28*y**2)*(58*y**3) = 1624*y**5
  (29*y)*71 = 2059*y
  (29*y)*(58*y**3) = 1682*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1624*y**5 + 1682*y**4 + 1988*y**2 + 2059*y</replace>
No more calculations needed.
<answer>1624*y**5 + 1682*y**4 + 1988*y**2 + 2059*y</answer>


Question:
Simplify this expression: -35*z**2*(-40*z**3 + 47*z + 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: 1400*z**5 - 1645*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: -35*z**2*(-40*z**3 + 47*z + 21)
Expanding the part (-40*z**3 + 47*z + 21) using the distributive property, and we got: 21*(-35*z**2) + (47*z)*(-35*z**2) + (-35*z**2)*(-40*z**3)
<replace-#Step 1>#Step 2:
Current expression: 21*(-35*z**2) + (47*z)*(-35*z**2) + (-35*z**2)*(-40*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  21*(-35*z**2) = -735*z**2
  (-40*z**3)*(-35*z**2) = 1400*z**5
  (47*z)*(-35*z**2) = -1645*z**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1400*z**5 - 1645*z**3 - 735*z**2</replace>
No more calculations needed.
<answer>1400*z**5 - 1645*z**3 - 735*z**2</answer>


Question:
Calculate the following: (-13*y**3 + 33*y**2)*(5*y**3 + 23)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -65*y**6 + 165*y**5 - 299*y**3 + 759*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: (-13*y**3 + 33*y**2)*(5*y**3 + 23)
Expanding the part (5*y**3 + 23) using the distributive property, and we got: (5*y**3)*(-13*y**3 + 33*y**2) + 23*(-13*y**3 + 33*y**2)
<replace-#Step 1>#Step 2:
Current expression: (5*y**3)*(-13*y**3 + 33*y**2) + 23*(-13*y**3 + 33*y**2)</replace>
Simplifying the partial expression: 23*(-13*y**3 + 33*y**2)
Expanding the part (-13*y**3 + 33*y**2) using the distributive property, and we got: (33*y**2)*23 - 13*y**3*23
Replacing 23*(-13*y**3 + 33*y**2) with (33*y**2)*23 - 13*y**3*23 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (33*y**2)*23 - 13*y**3*23 + (5*y**3)*(-13*y**3 + 33*y**2)</replace>
Simplifying the partial expression: (5*y**3)*(-13*y**3 + 33*y**2)
Expanding the part (-13*y**3 + 33*y**2) using the distributive property, and we got: (33*y**2)*(5*y**3) + (-13*y**3)*(5*y**3)
Replacing (5*y**3)*(-13*y**3 + 33*y**2) with (33*y**2)*(5*y**3) + (-13*y**3)*(5*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (33*y**2)*(5*y**3) + (33*y**2)*23 + (-13*y**3)*(5*y**3) - 13*y**3*23</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-13*y**3)*23 = -299*y**3
  (-13*y**3)*(5*y**3) = -65*y**6
  (33*y**2)*23 = 759*y**2
  (33*y**2)*(5*y**3) = 165*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -65*y**6 + 165*y**5 - 299*y**3 + 759*y**2</replace>
No more calculations needed.
<answer>-65*y**6 + 165*y**5 - 299*y**3 + 759*y**2</answer>


Question:
Calculate the following: (29*z - 25)*(-z**2 - 10)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -29*z**3 + 25*z**2 - 290*z + 250

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (29*z - 25)*(-z**2 - 10)
Expanding the part (29*z - 25) using the distributive property, and we got: (29*z)*(-z**2 - 10) - 25*(-z**2 - 10)
<replace-#Step 1>#Step 2:
Current expression: (29*z)*(-z**2 - 10) - 25*(-z**2 - 10)</replace>
Simplifying the partial expression: -25*(-z**2 - 10)
Expanding the part (-z**2 - 10) using the distributive property, and we got: -z**2*(-25) - 10*(-25)
Replacing -25*(-z**2 - 10) with -z**2*(-25) - 10*(-25) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (29*z)*(-z**2 - 10) - z**2*(-25) + 250</replace>
Simplifying the partial expression: (29*z)*(-z**2 - 10)
Expanding the part (-z**2 - 10) using the distributive property, and we got: -290*z + (29*z)*(-z**2)
Replacing (29*z)*(-z**2 - 10) with -290*z + (29*z)*(-z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -10*29*z + (29*z)*(-z**2) - z**2*(-25) + 250</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-z**2)*-25 = 25*z**2
  (-z**2)*(29*z) = -29*z**3
  -10*29*z = -290*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -29*z**3 + 25*z**2 - 290*z + 250</replace>
No more calculations needed.
<answer>-29*z**3 + 25*z**2 - 290*z + 250</answer>


Question:
Simplify this expression: (45 - 11*x)*(30*x**3 - 15)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -330*x**4 + 1350*x**3 + 165*x - 675

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (45 - 11*x)*(30*x**3 - 15)
Expanding the part (30*x**3 - 15) using the distributive property, and we got: (30*x**3)*(45 - 11*x) - 15*(45 - 11*x)
<replace-#Step 1>#Step 2:
Current expression: (30*x**3)*(45 - 11*x) - 15*(45 - 11*x)</replace>
Simplifying the partial expression: -15*(45 - 11*x)
Expanding the part (45 - 11*x) using the distributive property, and we got: -11*x*(-15) + 45*(-15)
Replacing -15*(45 - 11*x) with -11*x*(-15) + 45*(-15) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -11*x*(-15) + (30*x**3)*(45 - 11*x) - 675</replace>
Simplifying the partial expression: (30*x**3)*(45 - 11*x)
Expanding the part (45 - 11*x) using the distributive property, and we got: (-11*x)*(30*x**3) + 45*(30*x**3)
Replacing (30*x**3)*(45 - 11*x) with (-11*x)*(30*x**3) + 45*(30*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-11*x)*(30*x**3) - 11*x*(-15) + 45*30*x**3 - 675</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-11*x)*-15 = 165*x
  (-11*x)*(30*x**3) = -330*x**4
  45*30*x**3 = 1350*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -330*x**4 + 1350*x**3 + 165*x - 675</replace>
No more calculations needed.
<answer>-330*x**4 + 1350*x**3 + 165*x - 675</answer>


Question:
Simplify this expression: 67*z**2
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 67*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
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: 67*z**2</replace>
No more calculations needed.
<answer>67*z**2</answer>


Question:
Simplify this expression: (49 - 16*z**2)*(12*z**3 + 4)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -192*z**5 + 588*z**3 - 64*z**2 + 196

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (49 - 16*z**2)*(12*z**3 + 4)
Expanding the part (12*z**3 + 4) using the distributive property, and we got: (12*z**3)*(49 - 16*z**2) + 4*(49 - 16*z**2)
<replace-#Step 1>#Step 2:
Current expression: (12*z**3)*(49 - 16*z**2) + 4*(49 - 16*z**2)</replace>
Simplifying the partial expression: 4*(49 - 16*z**2)
Expanding the part (49 - 16*z**2) using the distributive property, and we got: -16*z**2*4 + 49*4
Replacing 4*(49 - 16*z**2) with -16*z**2*4 + 49*4 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -16*z**2*4 + (12*z**3)*(49 - 16*z**2) + 196</replace>
Simplifying the partial expression: (12*z**3)*(49 - 16*z**2)
Expanding the part (49 - 16*z**2) using the distributive property, and we got: 49*(12*z**3) + (-16*z**2)*(12*z**3)
Replacing (12*z**3)*(49 - 16*z**2) with 49*(12*z**3) + (-16*z**2)*(12*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 49*12*z**3 + (-16*z**2)*(12*z**3) - 16*z**2*4 + 196</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-16*z**2)*4 = -64*z**2
  (-16*z**2)*(12*z**3) = -192*z**5
  49*12*z**3 = 588*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -192*z**5 + 588*z**3 - 64*z**2 + 196</replace>
No more calculations needed.
<answer>-192*z**5 + 588*z**3 - 64*z**2 + 196</answer>


Question:
Calculate the following: (-13*z - 45)*(-10*z**3 - 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: 130*z**4 + 450*z**3 + 455*z + 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: (-13*z - 45)*(-10*z**3 - 35)
Expanding the part (-13*z - 45) using the distributive property, and we got: (-13*z)*(-10*z**3 - 35) - 45*(-10*z**3 - 35)
<replace-#Step 1>#Step 2:
Current expression: (-13*z)*(-10*z**3 - 35) - 45*(-10*z**3 - 35)</replace>
Simplifying the partial expression: -45*(-10*z**3 - 35)
Expanding the part (-10*z**3 - 35) using the distributive property, and we got: -10*z**3*(-45) - 35*(-45)
Replacing -45*(-10*z**3 - 35) with -10*z**3*(-45) - 35*(-45) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-13*z)*(-10*z**3 - 35) - 10*z**3*(-45) + 1575</replace>
Simplifying the partial expression: (-13*z)*(-10*z**3 - 35)
Expanding the part (-10*z**3 - 35) using the distributive property, and we got: (-13*z)*(-10*z**3) - (-1)*455*z
Replacing (-13*z)*(-10*z**3 - 35) with (-13*z)*(-10*z**3) - (-1)*455*z in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-13*z)*(-10*z**3) - 35*(-13)*z - 10*z**3*(-45) + 1575</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-10*z**3)*-45 = 450*z**3
  (-10*z**3)*(-13*z) = 130*z**4
  -35*-13*z = 455*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 130*z**4 + 450*z**3 + 455*z + 1575</replace>
No more calculations needed.
<answer>130*z**4 + 450*z**3 + 455*z + 1575</answer>


Question:
Simplify this expression: 32*y*(-15*y**3 + 35*y**2 + 8*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -480*y**4 + 1120*y**3 + 256*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: 32*y*(-15*y**3 + 35*y**2 + 8*y)
Expanding the part (-15*y**3 + 35*y**2 + 8*y) using the distributive property, and we got: (8*y)*(32*y) + (32*y)*(35*y**2) + (32*y)*(-15*y**3)
<replace-#Step 1>#Step 2:
Current expression: (8*y)*(32*y) + (32*y)*(35*y**2) + (32*y)*(-15*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-15*y**3)*(32*y) = -480*y**4
  (8*y)*(32*y) = 256*y**2
  (35*y**2)*(32*y) = 1120*y**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -480*y**4 + 1120*y**3 + 256*y**2</replace>
No more calculations needed.
<answer>-480*y**4 + 1120*y**3 + 256*y**2</answer>


Question:
Calculate the following: (-13*x**3 - 13*x + 13)*(46*x**3 + 32*x**2 - 28*x + 10)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -598*x**6 - 416*x**5 - 234*x**4 + 52*x**3 + 780*x**2 - 494*x + 130


Question:
Calculate the following: (3*x**2 - 32*x - 44)*(-18*x**3 + 34*x**2 + 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: -54*x**5 + 678*x**4 - 296*x**3 - 1385*x**2 - 1184*x - 1628


Question:
Calculate the following: (-14*z**3 + 41*z**2)*(26*z**3 - 33*z + 36)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -364*z**6 + 1066*z**5 + 462*z**4 - 1857*z**3 + 1476*z**2


Question:
Calculate the following: (4 - 41*x**2)*(11*x**2 - 18*x - 39)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -451*x**4 + 738*x**3 + 1643*x**2 - 72*x - 156

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (4 - 41*x**2)*(11*x**2 - 18*x - 39)
Expanding the part (4 - 41*x**2) using the distributive property, and we got: (-41*x**2)*(11*x**2 - 18*x - 39) + 4*(11*x**2 - 18*x - 39)
<replace-#Step 1>#Step 2:
Current expression: (-41*x**2)*(11*x**2 - 18*x - 39) + 4*(11*x**2 - 18*x - 39)</replace>
Simplifying the partial expression: 4*(11*x**2 - 18*x - 39)
Expanding the part (11*x**2 - 18*x - 39) using the distributive property, and we got: -18*x*4 + (11*x**2)*4 - 39*4
Replacing 4*(11*x**2 - 18*x - 39) with -18*x*4 + (11*x**2)*4 - 39*4 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -18*x*4 + (-41*x**2)*(11*x**2 - 18*x - 39) + (11*x**2)*4 - 156</replace>
Simplifying the partial expression: (-41*x**2)*(11*x**2 - 18*x - 39)
Expanding the part (11*x**2 - 18*x - 39) using the distributive property, and we got: (-18*x)*(-41*x**2) - (-1)*1599*x**2 + (-41*x**2)*(11*x**2)
Replacing (-41*x**2)*(11*x**2 - 18*x - 39) with (-18*x)*(-41*x**2) - (-1)*1599*x**2 + (-41*x**2)*(11*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-18*x)*(-41*x**2) - 18*x*4 - 39*(-41)*x**2 + (-41*x**2)*(11*x**2) + (11*x**2)*4 - 156</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-18*x)*4 = -72*x
  (-18*x)*(-41*x**2) = 738*x**3
  (11*x**2)*4 = 44*x**2
  (11*x**2)*(-41*x**2) = -451*x**4
  -39*-41*x**2 = 1599*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -451*x**4 + 738*x**3 + 44*x**2 + 1599*x**2 - 72*x - 156</replace>
Combining like terms, got -451*x**4 + 738*x**3 + 1643*x**2 - 72*x - 156
<replace-#Step 5>#Step 6:
Current expression: -451*x**4 + 738*x**3 + 1643*x**2 - 72*x - 156</replace>
No more calculations needed.
<answer>-451*x**4 + 738*x**3 + 1643*x**2 - 72*x - 156</answer>


Question:
Calculate the following: (56*z + 54)*(-2*z**3 - 22*z**2 - 21)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -112*z**4 - 1340*z**3 - 1188*z**2 - 1176*z - 1134

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*z + 54)*(-2*z**3 - 22*z**2 - 21)
Expanding the part (56*z + 54) using the distributive property, and we got: (56*z)*(-2*z**3 - 22*z**2 - 21) + 54*(-2*z**3 - 22*z**2 - 21)
<replace-#Step 1>#Step 2:
Current expression: (56*z)*(-2*z**3 - 22*z**2 - 21) + 54*(-2*z**3 - 22*z**2 - 21)</replace>
Simplifying the partial expression: 54*(-2*z**3 - 22*z**2 - 21)
Expanding the part (-2*z**3 - 22*z**2 - 21) using the distributive property, and we got: -22*z**2*54 - 2*z**3*54 - 21*54
Replacing 54*(-2*z**3 - 22*z**2 - 21) with -22*z**2*54 - 2*z**3*54 - 21*54 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (56*z)*(-2*z**3 - 22*z**2 - 21) - 22*z**2*54 - 2*z**3*54 - 1134</replace>
Simplifying the partial expression: (56*z)*(-2*z**3 - 22*z**2 - 21)
Expanding the part (-2*z**3 - 22*z**2 - 21) using the distributive property, and we got: -1176*z + (56*z)*(-22*z**2) + (56*z)*(-2*z**3)
Replacing (56*z)*(-2*z**3 - 22*z**2 - 21) with -1176*z + (56*z)*(-22*z**2) + (56*z)*(-2*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -21*56*z + (56*z)*(-22*z**2) + (56*z)*(-2*z**3) - 22*z**2*54 - 2*z**3*54 - 1134</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-22*z**2)*54 = -1188*z**2
  (-22*z**2)*(56*z) = -1232*z**3
  (-2*z**3)*54 = -108*z**3
  (-2*z**3)*(56*z) = -112*z**4
  -21*56*z = -1176*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -112*z**4 - 1232*z**3 - 108*z**3 - 1188*z**2 - 1176*z - 1134</replace>
Combining like terms, got -112*z**4 - 1340*z**3 - 1188*z**2 - 1176*z - 1134
<replace-#Step 5>#Step 6:
Current expression: -112*z**4 - 1340*z**3 - 1188*z**2 - 1176*z - 1134</replace>
No more calculations needed.
<answer>-112*z**4 - 1340*z**3 - 1188*z**2 - 1176*z - 1134</answer>


Question:
Calculate the following: (37 - 18*y**3)*(25*y**2 - 39*y + 16)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -450*y**5 + 702*y**4 - 288*y**3 + 925*y**2 - 1443*y + 592

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 - 18*y**3)*(25*y**2 - 39*y + 16)
Expanding the part (37 - 18*y**3) using the distributive property, and we got: (-18*y**3)*(25*y**2 - 39*y + 16) + 37*(25*y**2 - 39*y + 16)
<replace-#Step 1>#Step 2:
Current expression: (-18*y**3)*(25*y**2 - 39*y + 16) + 37*(25*y**2 - 39*y + 16)</replace>
Simplifying the partial expression: 37*(25*y**2 - 39*y + 16)
Expanding the part (25*y**2 - 39*y + 16) using the distributive property, and we got: -39*y*37 + (25*y**2)*37 + 16*37
Replacing 37*(25*y**2 - 39*y + 16) with -39*y*37 + (25*y**2)*37 + 16*37 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -39*y*37 + (25*y**2)*37 + (-18*y**3)*(25*y**2 - 39*y + 16) + 592</replace>
Simplifying the partial expression: (-18*y**3)*(25*y**2 - 39*y + 16)
Expanding the part (25*y**2 - 39*y + 16) using the distributive property, and we got: (-39*y)*(-18*y**3) + 16*(-18*y**3) + (25*y**2)*(-18*y**3)
Replacing (-18*y**3)*(25*y**2 - 39*y + 16) with (-39*y)*(-18*y**3) + 16*(-18*y**3) + (25*y**2)*(-18*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-39*y)*(-18*y**3) - 39*y*37 + 16*(-18)*y**3 + (25*y**2)*(-18*y**3) + (25*y**2)*37 + 592</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-39*y)*37 = -1443*y
  (-39*y)*(-18*y**3) = 702*y**4
  (25*y**2)*37 = 925*y**2
  (25*y**2)*(-18*y**3) = -450*y**5
  16*-18*y**3 = -288*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -450*y**5 + 702*y**4 - 288*y**3 + 925*y**2 - 1443*y + 592</replace>
No more calculations needed.
<answer>-450*y**5 + 702*y**4 - 288*y**3 + 925*y**2 - 1443*y + 592</answer>


Question:
Simplify this expression: (34 - 38*z**3)*(27*z**3 + 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: -1026*z**6 - 412*z**3 + 1190

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 - 38*z**3)*(27*z**3 + 35)
Expanding the part (34 - 38*z**3) using the distributive property, and we got: (-38*z**3)*(27*z**3 + 35) + 34*(27*z**3 + 35)
<replace-#Step 1>#Step 2:
Current expression: (-38*z**3)*(27*z**3 + 35) + 34*(27*z**3 + 35)</replace>
Simplifying the partial expression: 34*(27*z**3 + 35)
Expanding the part (27*z**3 + 35) using the distributive property, and we got: (27*z**3)*34 + 35*34
Replacing 34*(27*z**3 + 35) with (27*z**3)*34 + 35*34 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-38*z**3)*(27*z**3 + 35) + (27*z**3)*34 + 1190</replace>
Simplifying the partial expression: (-38*z**3)*(27*z**3 + 35)
Expanding the part (27*z**3 + 35) using the distributive property, and we got: 35*(-38*z**3) + (-38*z**3)*(27*z**3)
Replacing (-38*z**3)*(27*z**3 + 35) with 35*(-38*z**3) + (-38*z**3)*(27*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 35*(-38)*z**3 + (-38*z**3)*(27*z**3) + (27*z**3)*34 + 1190</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (27*z**3)*34 = 918*z**3
  (27*z**3)*(-38*z**3) = -1026*z**6
  35*-38*z**3 = -1330*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1026*z**6 - 1330*z**3 + 918*z**3 + 1190</replace>
Combining like terms, got -1026*z**6 - 412*z**3 + 1190
<replace-#Step 5>#Step 6:
Current expression: -1026*z**6 - 412*z**3 + 1190</replace>
No more calculations needed.
<answer>-1026*z**6 - 412*z**3 + 1190</answer>


Question:
Calculate the following: (-2*x**3 - 46*x)*(14*x**3 + 4)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -28*x**6 - 644*x**4 - 8*x**3 - 184*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: (-2*x**3 - 46*x)*(14*x**3 + 4)
Expanding the part (14*x**3 + 4) using the distributive property, and we got: (14*x**3)*(-2*x**3 - 46*x) + 4*(-2*x**3 - 46*x)
<replace-#Step 1>#Step 2:
Current expression: (14*x**3)*(-2*x**3 - 46*x) + 4*(-2*x**3 - 46*x)</replace>
Simplifying the partial expression: 4*(-2*x**3 - 46*x)
Expanding the part (-2*x**3 - 46*x) using the distributive property, and we got: -46*x*4 - 2*x**3*4
Replacing 4*(-2*x**3 - 46*x) with -46*x*4 - 2*x**3*4 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -46*x*4 - 2*x**3*4 + (14*x**3)*(-2*x**3 - 46*x)</replace>
Simplifying the partial expression: (14*x**3)*(-2*x**3 - 46*x)
Expanding the part (-2*x**3 - 46*x) using the distributive property, and we got: (-46*x)*(14*x**3) + (-2*x**3)*(14*x**3)
Replacing (14*x**3)*(-2*x**3 - 46*x) with (-46*x)*(14*x**3) + (-2*x**3)*(14*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-46*x)*(14*x**3) - 46*x*4 + (-2*x**3)*(14*x**3) - 2*x**3*4</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-46*x)*4 = -184*x
  (-46*x)*(14*x**3) = -644*x**4
  (-2*x**3)*4 = -8*x**3
  (-2*x**3)*(14*x**3) = -28*x**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -28*x**6 - 644*x**4 - 8*x**3 - 184*x</replace>
No more calculations needed.
<answer>-28*x**6 - 644*x**4 - 8*x**3 - 184*x</answer>


Question:
Calculate the following: (7 - 15*x**2)*(22 - 12*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: 180*x**5 - 84*x**3 - 330*x**2 + 154

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 - 15*x**2)*(22 - 12*x**3)
Expanding the part (7 - 15*x**2) using the distributive property, and we got: (-15*x**2)*(22 - 12*x**3) + 7*(22 - 12*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-15*x**2)*(22 - 12*x**3) + 7*(22 - 12*x**3)</replace>
Simplifying the partial expression: 7*(22 - 12*x**3)
Expanding the part (22 - 12*x**3) using the distributive property, and we got: -12*x**3*7 + 22*7
Replacing 7*(22 - 12*x**3) with -12*x**3*7 + 22*7 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-15*x**2)*(22 - 12*x**3) - 12*x**3*7 + 154</replace>
Simplifying the partial expression: (-15*x**2)*(22 - 12*x**3)
Expanding the part (22 - 12*x**3) using the distributive property, and we got: 22*(-15*x**2) + (-15*x**2)*(-12*x**3)
Replacing (-15*x**2)*(22 - 12*x**3) with 22*(-15*x**2) + (-15*x**2)*(-12*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 22*(-15)*x**2 + (-15*x**2)*(-12*x**3) - 12*x**3*7 + 154</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-12*x**3)*7 = -84*x**3
  (-12*x**3)*(-15*x**2) = 180*x**5
  22*-15*x**2 = -330*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 180*x**5 - 84*x**3 - 330*x**2 + 154</replace>
No more calculations needed.
<answer>180*x**5 - 84*x**3 - 330*x**2 + 154</answer>


Question:
Simplify this expression: 1470 - 1078*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: 1470 - 1078*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: 1470 - 1078*z
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: 1470 - 1078*z</replace>
No more calculations needed.
<answer>1470 - 1078*z</answer>


Question:
Simplify this expression: (-9*z**2 - 30*z + 56)*(-8*z**3 - z**2 + 1)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 72*z**5 + 249*z**4 - 418*z**3 - 65*z**2 - 30*z + 56


Question:
Calculate the following: (5*z**2 + 28*z)*(62*z**3 - 6*z**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 310*z**5 + 1706*z**4 - 168*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: (5*z**2 + 28*z)*(62*z**3 - 6*z**2)
Expanding the part (62*z**3 - 6*z**2) using the distributive property, and we got: (-6*z**2)*(5*z**2 + 28*z) + (62*z**3)*(5*z**2 + 28*z)
<replace-#Step 1>#Step 2:
Current expression: (-6*z**2)*(5*z**2 + 28*z) + (62*z**3)*(5*z**2 + 28*z)</replace>
Simplifying the partial expression: (-6*z**2)*(5*z**2 + 28*z)
Expanding the part (5*z**2 + 28*z) using the distributive property, and we got: (28*z)*(-6*z**2) + (-6*z**2)*(5*z**2)
Replacing (-6*z**2)*(5*z**2 + 28*z) with (28*z)*(-6*z**2) + (-6*z**2)*(5*z**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (28*z)*(-6*z**2) + (-6*z**2)*(5*z**2) + (62*z**3)*(5*z**2 + 28*z)</replace>
Simplifying the partial expression: (62*z**3)*(5*z**2 + 28*z)
Expanding the part (5*z**2 + 28*z) using the distributive property, and we got: (28*z)*(62*z**3) + (5*z**2)*(62*z**3)
Replacing (62*z**3)*(5*z**2 + 28*z) with (28*z)*(62*z**3) + (5*z**2)*(62*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (28*z)*(-6*z**2) + (28*z)*(62*z**3) + (-6*z**2)*(5*z**2) + (5*z**2)*(62*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (5*z**2)*(-6*z**2) = -30*z**4
  (5*z**2)*(62*z**3) = 310*z**5
  (28*z)*(-6*z**2) = -168*z**3
  (28*z)*(62*z**3) = 1736*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 310*z**5 - 30*z**4 + 1736*z**4 - 168*z**3</replace>
Combining like terms, got 310*z**5 + 1706*z**4 - 168*z**3
<replace-#Step 5>#Step 6:
Current expression: 310*z**5 + 1706*z**4 - 168*z**3</replace>
No more calculations needed.
<answer>310*z**5 + 1706*z**4 - 168*z**3</answer>


Question:
Calculate the following: 37*y**2*(-30*y**3 - 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: -1110*y**5 - 777*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: 37*y**2*(-30*y**3 - 21)
Expanding the part (-30*y**3 - 21) using the distributive property, and we got: -777*y**2 + (37*y**2)*(-30*y**3)
<replace-#Step 1>#Step 2:
Current expression: -777*y**2 + (37*y**2)*(-30*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -21*(37*y**2) = -777*y**2
  (-30*y**3)*(37*y**2) = -1110*y**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1110*y**5 - 777*y**2</replace>
No more calculations needed.
<answer>-1110*y**5 - 777*y**2</answer>


Question:
Calculate the following: (16*y**2 - 29)*(74*y**3 + 61*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: 1184*y**5 - 1170*y**3 - 1769*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*y**2 - 29)*(74*y**3 + 61*y)
Expanding the part (16*y**2 - 29) using the distributive property, and we got: (16*y**2)*(74*y**3 + 61*y) - 29*(74*y**3 + 61*y)
<replace-#Step 1>#Step 2:
Current expression: (16*y**2)*(74*y**3 + 61*y) - 29*(74*y**3 + 61*y)</replace>
Simplifying the partial expression: -29*(74*y**3 + 61*y)
Expanding the part (74*y**3 + 61*y) using the distributive property, and we got: (61*y)*(-29) + (74*y**3)*(-29)
Replacing -29*(74*y**3 + 61*y) with (61*y)*(-29) + (74*y**3)*(-29) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (61*y)*(-29) + (16*y**2)*(74*y**3 + 61*y) + (74*y**3)*(-29)</replace>
Simplifying the partial expression: (16*y**2)*(74*y**3 + 61*y)
Expanding the part (74*y**3 + 61*y) using the distributive property, and we got: (61*y)*(16*y**2) + (16*y**2)*(74*y**3)
Replacing (16*y**2)*(74*y**3 + 61*y) with (61*y)*(16*y**2) + (16*y**2)*(74*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (61*y)*(16*y**2) + (61*y)*(-29) + (16*y**2)*(74*y**3) + (74*y**3)*(-29)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (61*y)*-29 = -1769*y
  (61*y)*(16*y**2) = 976*y**3
  (74*y**3)*-29 = -2146*y**3
  (74*y**3)*(16*y**2) = 1184*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1184*y**5 - 2146*y**3 + 976*y**3 - 1769*y</replace>
Combining like terms, got 1184*y**5 - 1170*y**3 - 1769*y
<replace-#Step 5>#Step 6:
Current expression: 1184*y**5 - 1170*y**3 - 1769*y</replace>
No more calculations needed.
<answer>1184*y**5 - 1170*y**3 - 1769*y</answer>


Question:
Calculate the following: (-28*x**3 - 19*x**2)*(27*x**3 + 8*x + 51)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*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*x**6 - 513*x**5 - 224*x**4 - 1580*x**3 - 969*x**2


Question:
Simplify this expression: (9*z**2 + 54*z)*(36*z**2 + 27)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 324*z**4 + 1944*z**3 + 243*z**2 + 1458*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: (9*z**2 + 54*z)*(36*z**2 + 27)
Expanding the part (36*z**2 + 27) using the distributive property, and we got: (36*z**2)*(9*z**2 + 54*z) + 27*(9*z**2 + 54*z)
<replace-#Step 1>#Step 2:
Current expression: (36*z**2)*(9*z**2 + 54*z) + 27*(9*z**2 + 54*z)</replace>
Simplifying the partial expression: 27*(9*z**2 + 54*z)
Expanding the part (9*z**2 + 54*z) using the distributive property, and we got: (54*z)*27 + (9*z**2)*27
Replacing 27*(9*z**2 + 54*z) with (54*z)*27 + (9*z**2)*27 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (54*z)*27 + (9*z**2)*27 + (36*z**2)*(9*z**2 + 54*z)</replace>
Simplifying the partial expression: (36*z**2)*(9*z**2 + 54*z)
Expanding the part (9*z**2 + 54*z) using the distributive property, and we got: (54*z)*(36*z**2) + (9*z**2)*(36*z**2)
Replacing (36*z**2)*(9*z**2 + 54*z) with (54*z)*(36*z**2) + (9*z**2)*(36*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (54*z)*(36*z**2) + (54*z)*27 + (9*z**2)*(36*z**2) + (9*z**2)*27</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (9*z**2)*27 = 243*z**2
  (9*z**2)*(36*z**2) = 324*z**4
  (54*z)*27 = 1458*z
  (54*z)*(36*z**2) = 1944*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 324*z**4 + 1944*z**3 + 243*z**2 + 1458*z</replace>
No more calculations needed.
<answer>324*z**4 + 1944*z**3 + 243*z**2 + 1458*z</answer>


Question:
Calculate the following: (49 - 9*x**2)*(22*x**2 + 13*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: -198*x**4 - 117*x**3 + 1078*x**2 + 637*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: (49 - 9*x**2)*(22*x**2 + 13*x)
Expanding the part (49 - 9*x**2) using the distributive property, and we got: (-9*x**2)*(22*x**2 + 13*x) + 49*(22*x**2 + 13*x)
<replace-#Step 1>#Step 2:
Current expression: (-9*x**2)*(22*x**2 + 13*x) + 49*(22*x**2 + 13*x)</replace>
Simplifying the partial expression: 49*(22*x**2 + 13*x)
Expanding the part (22*x**2 + 13*x) using the distributive property, and we got: (13*x)*49 + (22*x**2)*49
Replacing 49*(22*x**2 + 13*x) with (13*x)*49 + (22*x**2)*49 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (13*x)*49 + (-9*x**2)*(22*x**2 + 13*x) + (22*x**2)*49</replace>
Simplifying the partial expression: (-9*x**2)*(22*x**2 + 13*x)
Expanding the part (22*x**2 + 13*x) using the distributive property, and we got: (13*x)*(-9*x**2) + (-9*x**2)*(22*x**2)
Replacing (-9*x**2)*(22*x**2 + 13*x) with (13*x)*(-9*x**2) + (-9*x**2)*(22*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (13*x)*(-9*x**2) + (13*x)*49 + (-9*x**2)*(22*x**2) + (22*x**2)*49</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (13*x)*49 = 637*x
  (13*x)*(-9*x**2) = -117*x**3
  (22*x**2)*49 = 1078*x**2
  (22*x**2)*(-9*x**2) = -198*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -198*x**4 - 117*x**3 + 1078*x**2 + 637*x</replace>
No more calculations needed.
<answer>-198*x**4 - 117*x**3 + 1078*x**2 + 637*x</answer>


Question:
Calculate the following: (27*x**3 - 10)*(-42*x**3 + 36*x**2 + 50*x + 9)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1134*x**6 + 972*x**5 + 1350*x**4 + 663*x**3 - 360*x**2 - 500*x - 90


Question:
Calculate the following: (-46*z**3 - 11*z)*(-45*z**3 + 42*z**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2070*z**6 - 1932*z**5 + 495*z**4 - 462*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: (-46*z**3 - 11*z)*(-45*z**3 + 42*z**2)
Expanding the part (-46*z**3 - 11*z) using the distributive property, and we got: (-11*z)*(-45*z**3 + 42*z**2) + (-46*z**3)*(-45*z**3 + 42*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-11*z)*(-45*z**3 + 42*z**2) + (-46*z**3)*(-45*z**3 + 42*z**2)</replace>
Simplifying the partial expression: (-46*z**3)*(-45*z**3 + 42*z**2)
Expanding the part (-45*z**3 + 42*z**2) using the distributive property, and we got: (42*z**2)*(-46*z**3) + (-46*z**3)*(-45*z**3)
Replacing (-46*z**3)*(-45*z**3 + 42*z**2) with (42*z**2)*(-46*z**3) + (-46*z**3)*(-45*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-11*z)*(-45*z**3 + 42*z**2) + (42*z**2)*(-46*z**3) + (-46*z**3)*(-45*z**3)</replace>
Simplifying the partial expression: (-11*z)*(-45*z**3 + 42*z**2)
Expanding the part (-45*z**3 + 42*z**2) using the distributive property, and we got: (-11*z)*(42*z**2) + (-11*z)*(-45*z**3)
Replacing (-11*z)*(-45*z**3 + 42*z**2) with (-11*z)*(42*z**2) + (-11*z)*(-45*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-11*z)*(42*z**2) + (-11*z)*(-45*z**3) + (42*z**2)*(-46*z**3) + (-46*z**3)*(-45*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-45*z**3)*(-46*z**3) = 2070*z**6
  (-45*z**3)*(-11*z) = 495*z**4
  (42*z**2)*(-46*z**3) = -1932*z**5
  (42*z**2)*(-11*z) = -462*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2070*z**6 - 1932*z**5 + 495*z**4 - 462*z**3</replace>
No more calculations needed.
<answer>2070*z**6 - 1932*z**5 + 495*z**4 - 462*z**3</answer>


Question:
Calculate the following: -43*z**2*(22*z**3 - 34*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -946*z**5 + 1462*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: -43*z**2*(22*z**3 - 34*z)
Expanding the part (22*z**3 - 34*z) using the distributive property, and we got: (-34*z)*(-43*z**2) + (-43*z**2)*(22*z**3)
<replace-#Step 1>#Step 2:
Current expression: (-34*z)*(-43*z**2) + (-43*z**2)*(22*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-34*z)*(-43*z**2) = 1462*z**3
  (22*z**3)*(-43*z**2) = -946*z**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -946*z**5 + 1462*z**3</replace>
No more calculations needed.
<answer>-946*z**5 + 1462*z**3</answer>


Question:
Simplify this expression: (-31*z - 34)*(50*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: -1550*z**3 - 1452*z**2 + 272*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: (-31*z - 34)*(50*z**2 - 8*z)
Expanding the part (-31*z - 34) using the distributive property, and we got: (-31*z)*(50*z**2 - 8*z) - 34*(50*z**2 - 8*z)
<replace-#Step 1>#Step 2:
Current expression: (-31*z)*(50*z**2 - 8*z) - 34*(50*z**2 - 8*z)</replace>
Simplifying the partial expression: -34*(50*z**2 - 8*z)
Expanding the part (50*z**2 - 8*z) using the distributive property, and we got: -8*z*(-34) + (50*z**2)*(-34)
Replacing -34*(50*z**2 - 8*z) with -8*z*(-34) + (50*z**2)*(-34) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-31*z)*(50*z**2 - 8*z) - 8*z*(-34) + (50*z**2)*(-34)</replace>
Simplifying the partial expression: (-31*z)*(50*z**2 - 8*z)
Expanding the part (50*z**2 - 8*z) using the distributive property, and we got: (-31*z)*(-8*z) + (-31*z)*(50*z**2)
Replacing (-31*z)*(50*z**2 - 8*z) with (-31*z)*(-8*z) + (-31*z)*(50*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-31*z)*(-8*z) + (-31*z)*(50*z**2) - 8*z*(-34) + (50*z**2)*(-34)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-8*z)*-34 = 272*z
  (-8*z)*(-31*z) = 248*z**2
  (50*z**2)*-34 = -1700*z**2
  (50*z**2)*(-31*z) = -1550*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1550*z**3 - 1700*z**2 + 248*z**2 + 272*z</replace>
Combining like terms, got -1550*z**3 - 1452*z**2 + 272*z
<replace-#Step 5>#Step 6:
Current expression: -1550*z**3 - 1452*z**2 + 272*z</replace>
No more calculations needed.
<answer>-1550*z**3 - 1452*z**2 + 272*z</answer>


Question:
Simplify this expression: (-9*x**2 - 6*x)*(-17*x**3 - 18*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: 153*x**5 + 102*x**4 + 162*x**3 + 81*x**2 - 18*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: (-9*x**2 - 6*x)*(-17*x**3 - 18*x + 3)
Expanding the part (-9*x**2 - 6*x) using the distributive property, and we got: (-6*x)*(-17*x**3 - 18*x + 3) + (-9*x**2)*(-17*x**3 - 18*x + 3)
<replace-#Step 1>#Step 2:
Current expression: (-6*x)*(-17*x**3 - 18*x + 3) + (-9*x**2)*(-17*x**3 - 18*x + 3)</replace>
Simplifying the partial expression: (-9*x**2)*(-17*x**3 - 18*x + 3)
Expanding the part (-17*x**3 - 18*x + 3) using the distributive property, and we got: (-18*x)*(-9*x**2) + 3*(-9*x**2) + (-9*x**2)*(-17*x**3)
Replacing (-9*x**2)*(-17*x**3 - 18*x + 3) with (-18*x)*(-9*x**2) + 3*(-9*x**2) + (-9*x**2)*(-17*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-18*x)*(-9*x**2) + (-6*x)*(-17*x**3 - 18*x + 3) + 3*(-9)*x**2 + (-9*x**2)*(-17*x**3)</replace>
Simplifying the partial expression: (-6*x)*(-17*x**3 - 18*x + 3)
Expanding the part (-17*x**3 - 18*x + 3) using the distributive property, and we got: (-18*x)*(-6*x) + (-6*x)*(-17*x**3) + 3*(-6*x)
Replacing (-6*x)*(-17*x**3 - 18*x + 3) with (-18*x)*(-6*x) + (-6*x)*(-17*x**3) + 3*(-6*x) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-18*x)*(-6*x) + (-18*x)*(-9*x**2) + (-6*x)*(-17*x**3) + 3*(-9)*x**2 + 3*(-6)*x + (-9*x**2)*(-17*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-18*x)*(-9*x**2) = 162*x**3
  (-18*x)*(-6*x) = 108*x**2
  (-17*x**3)*(-9*x**2) = 153*x**5
  (-17*x**3)*(-6*x) = 102*x**4
  3*-9*x**2 = -27*x**2
  3*-6*x = -18*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 153*x**5 + 102*x**4 + 162*x**3 - 27*x**2 + 108*x**2 - 18*x</replace>
Combining like terms, got 153*x**5 + 102*x**4 + 162*x**3 + 81*x**2 - 18*x
<replace-#Step 5>#Step 6:
Current expression: 153*x**5 + 102*x**4 + 162*x**3 + 81*x**2 - 18*x</replace>
No more calculations needed.
<answer>153*x**5 + 102*x**4 + 162*x**3 + 81*x**2 - 18*x</answer>


Question:
Calculate the following: (-74*z**2 + 17*z)*(44*z**2 - 31)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -3256*z**4 + 748*z**3 + 2294*z**2 - 527*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: (-74*z**2 + 17*z)*(44*z**2 - 31)
Expanding the part (44*z**2 - 31) using the distributive property, and we got: (44*z**2)*(-74*z**2 + 17*z) - 31*(-74*z**2 + 17*z)
<replace-#Step 1>#Step 2:
Current expression: (44*z**2)*(-74*z**2 + 17*z) - 31*(-74*z**2 + 17*z)</replace>
Simplifying the partial expression: -31*(-74*z**2 + 17*z)
Expanding the part (-74*z**2 + 17*z) using the distributive property, and we got: (17*z)*(-31) - 74*z**2*(-31)
Replacing -31*(-74*z**2 + 17*z) with (17*z)*(-31) - 74*z**2*(-31) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (17*z)*(-31) - 74*z**2*(-31) + (44*z**2)*(-74*z**2 + 17*z)</replace>
Simplifying the partial expression: (44*z**2)*(-74*z**2 + 17*z)
Expanding the part (-74*z**2 + 17*z) using the distributive property, and we got: (17*z)*(44*z**2) + (-74*z**2)*(44*z**2)
Replacing (44*z**2)*(-74*z**2 + 17*z) with (17*z)*(44*z**2) + (-74*z**2)*(44*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (17*z)*(44*z**2) + (17*z)*(-31) + (-74*z**2)*(44*z**2) - 74*z**2*(-31)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-74*z**2)*-31 = 2294*z**2
  (-74*z**2)*(44*z**2) = -3256*z**4
  (17*z)*-31 = -527*z
  (17*z)*(44*z**2) = 748*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -3256*z**4 + 748*z**3 + 2294*z**2 - 527*z</replace>
No more calculations needed.
<answer>-3256*z**4 + 748*z**3 + 2294*z**2 - 527*z</answer>


Question:
Calculate the following: (34*z**2 + 1)*(48*z**2 + 1)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1632*z**4 + 82*z**2 + 1

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (34*z**2 + 1)*(48*z**2 + 1)
Expanding the part (34*z**2 + 1) using the distributive property, and we got: (34*z**2)*(48*z**2 + 1) + 1*(48*z**2 + 1)
<replace-#Step 1>#Step 2:
Current expression: (34*z**2)*(48*z**2 + 1) + 1*(48*z**2 + 1)</replace>
Simplifying the partial expression: 1*(48*z**2 + 1)
Expanding the part (48*z**2 + 1) using the distributive property, and we got: (48*z**2)*1 + 1*1
Replacing 1*(48*z**2 + 1) with (48*z**2)*1 + 1*1 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (34*z**2)*(48*z**2 + 1) + (48*z**2)*1 + 1</replace>
Simplifying the partial expression: (34*z**2)*(48*z**2 + 1)
Expanding the part (48*z**2 + 1) using the distributive property, and we got: 1*(34*z**2) + (34*z**2)*(48*z**2)
Replacing (34*z**2)*(48*z**2 + 1) with 1*(34*z**2) + (34*z**2)*(48*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 34*z**2 + (34*z**2)*(48*z**2) + (48*z**2)*1 + 1</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (48*z**2)*1 = 48*z**2
  (48*z**2)*(34*z**2) = 1632*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1632*z**4 + 34*z**2 + 48*z**2 + 1</replace>
Combining like terms, got 1632*z**4 + 82*z**2 + 1
<replace-#Step 5>#Step 6:
Current expression: 1632*z**4 + 82*z**2 + 1</replace>
No more calculations needed.
<answer>1632*z**4 + 82*z**2 + 1</answer>


Question:
Calculate the following: (-18*x**3 + 22*x)*(-47*x**3 + 29*x**2 + 25*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: 846*x**6 - 522*x**5 - 1484*x**4 + 638*x**3 + 550*x**2


Question:
Simplify this expression: (2*x**2 - 15)*(-48*x**3 - 48*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: -96*x**5 - 96*x**4 + 720*x**3 + 720*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**2 - 15)*(-48*x**3 - 48*x**2)
Expanding the part (2*x**2 - 15) using the distributive property, and we got: (2*x**2)*(-48*x**3 - 48*x**2) - 15*(-48*x**3 - 48*x**2)
<replace-#Step 1>#Step 2:
Current expression: (2*x**2)*(-48*x**3 - 48*x**2) - 15*(-48*x**3 - 48*x**2)</replace>
Simplifying the partial expression: -15*(-48*x**3 - 48*x**2)
Expanding the part (-48*x**3 - 48*x**2) using the distributive property, and we got: -48*x**2*(-15) - 48*x**3*(-15)
Replacing -15*(-48*x**3 - 48*x**2) with -48*x**2*(-15) - 48*x**3*(-15) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -48*x**2*(-15) + (2*x**2)*(-48*x**3 - 48*x**2) - 48*x**3*(-15)</replace>
Simplifying the partial expression: (2*x**2)*(-48*x**3 - 48*x**2)
Expanding the part (-48*x**3 - 48*x**2) using the distributive property, and we got: (-48*x**2)*(2*x**2) + (2*x**2)*(-48*x**3)
Replacing (2*x**2)*(-48*x**3 - 48*x**2) with (-48*x**2)*(2*x**2) + (2*x**2)*(-48*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-48*x**2)*(2*x**2) - 48*x**2*(-15) + (2*x**2)*(-48*x**3) - 48*x**3*(-15)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-48*x**2)*-15 = 720*x**2
  (-48*x**2)*(2*x**2) = -96*x**4
  (-48*x**3)*-15 = 720*x**3
  (-48*x**3)*(2*x**2) = -96*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -96*x**5 - 96*x**4 + 720*x**3 + 720*x**2</replace>
No more calculations needed.
<answer>-96*x**5 - 96*x**4 + 720*x**3 + 720*x**2</answer>


Question:
Simplify this expression: 1127*z**3 + 392*z - 2352
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1127*z**3 + 392*z - 2352

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: 1127*z**3 + 392*z - 2352
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: 1127*z**3 + 392*z - 2352</replace>
No more calculations needed.
<answer>1127*z**3 + 392*z - 2352</answer>


Question:
Simplify this expression: (32 - 47*y**3)*(32*y**3 - 2*y**2 - 33)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1504*y**6 + 94*y**5 + 2575*y**3 - 64*y**2 - 1056

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (32 - 47*y**3)*(32*y**3 - 2*y**2 - 33)
Expanding the part (32 - 47*y**3) using the distributive property, and we got: (-47*y**3)*(32*y**3 - 2*y**2 - 33) + 32*(32*y**3 - 2*y**2 - 33)
<replace-#Step 1>#Step 2:
Current expression: (-47*y**3)*(32*y**3 - 2*y**2 - 33) + 32*(32*y**3 - 2*y**2 - 33)</replace>
Simplifying the partial expression: 32*(32*y**3 - 2*y**2 - 33)
Expanding the part (32*y**3 - 2*y**2 - 33) using the distributive property, and we got: -2*y**2*32 + (32*y**3)*32 - 33*32
Replacing 32*(32*y**3 - 2*y**2 - 33) with -2*y**2*32 + (32*y**3)*32 - 33*32 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -2*y**2*32 + (-47*y**3)*(32*y**3 - 2*y**2 - 33) + (32*y**3)*32 - 1056</replace>
Simplifying the partial expression: (-47*y**3)*(32*y**3 - 2*y**2 - 33)
Expanding the part (32*y**3 - 2*y**2 - 33) using the distributive property, and we got: -(-1)*1551*y**3 + (-2*y**2)*(-47*y**3) + (-47*y**3)*(32*y**3)
Replacing (-47*y**3)*(32*y**3 - 2*y**2 - 33) with -(-1)*1551*y**3 + (-2*y**2)*(-47*y**3) + (-47*y**3)*(32*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -33*(-47)*y**3 + (-2*y**2)*(-47*y**3) - 2*y**2*32 + (-47*y**3)*(32*y**3) + (32*y**3)*32 - 1056</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-2*y**2)*32 = -64*y**2
  (-2*y**2)*(-47*y**3) = 94*y**5
  (32*y**3)*32 = 1024*y**3
  (32*y**3)*(-47*y**3) = -1504*y**6
  -33*-47*y**3 = 1551*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1504*y**6 + 94*y**5 + 1024*y**3 + 1551*y**3 - 64*y**2 - 1056</replace>
Combining like terms, got -1504*y**6 + 94*y**5 + 2575*y**3 - 64*y**2 - 1056
<replace-#Step 5>#Step 6:
Current expression: -1504*y**6 + 94*y**5 + 2575*y**3 - 64*y**2 - 1056</replace>
No more calculations needed.
<answer>-1504*y**6 + 94*y**5 + 2575*y**3 - 64*y**2 - 1056</answer>


Question:
Calculate the following: (-23*y**3 - 19)*(21*y**3 - 42*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: -483*y**6 + 966*y**5 - 399*y**3 + 798*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: (-23*y**3 - 19)*(21*y**3 - 42*y**2)
Expanding the part (-23*y**3 - 19) using the distributive property, and we got: (-23*y**3)*(21*y**3 - 42*y**2) - 19*(21*y**3 - 42*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-23*y**3)*(21*y**3 - 42*y**2) - 19*(21*y**3 - 42*y**2)</replace>
Simplifying the partial expression: -19*(21*y**3 - 42*y**2)
Expanding the part (21*y**3 - 42*y**2) using the distributive property, and we got: -42*y**2*(-19) + (21*y**3)*(-19)
Replacing -19*(21*y**3 - 42*y**2) with -42*y**2*(-19) + (21*y**3)*(-19) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -42*y**2*(-19) + (-23*y**3)*(21*y**3 - 42*y**2) + (21*y**3)*(-19)</replace>
Simplifying the partial expression: (-23*y**3)*(21*y**3 - 42*y**2)
Expanding the part (21*y**3 - 42*y**2) using the distributive property, and we got: (-42*y**2)*(-23*y**3) + (-23*y**3)*(21*y**3)
Replacing (-23*y**3)*(21*y**3 - 42*y**2) with (-42*y**2)*(-23*y**3) + (-23*y**3)*(21*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-42*y**2)*(-23*y**3) - 42*y**2*(-19) + (-23*y**3)*(21*y**3) + (21*y**3)*(-19)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-42*y**2)*-19 = 798*y**2
  (-42*y**2)*(-23*y**3) = 966*y**5
  (21*y**3)*-19 = -399*y**3
  (21*y**3)*(-23*y**3) = -483*y**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -483*y**6 + 966*y**5 - 399*y**3 + 798*y**2</replace>
No more calculations needed.
<answer>-483*y**6 + 966*y**5 - 399*y**3 + 798*y**2</answer>


Question:
Calculate the following: (23*x**3 - 33*x**2)*(73*x**3 - 35*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: 1679*x**6 - 3214*x**5 + 1155*x**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (23*x**3 - 33*x**2)*(73*x**3 - 35*x**2)
Expanding the part (73*x**3 - 35*x**2) using the distributive property, and we got: (-35*x**2)*(23*x**3 - 33*x**2) + (73*x**3)*(23*x**3 - 33*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-35*x**2)*(23*x**3 - 33*x**2) + (73*x**3)*(23*x**3 - 33*x**2)</replace>
Simplifying the partial expression: (-35*x**2)*(23*x**3 - 33*x**2)
Expanding the part (23*x**3 - 33*x**2) using the distributive property, and we got: (-35*x**2)*(-33*x**2) + (-35*x**2)*(23*x**3)
Replacing (-35*x**2)*(23*x**3 - 33*x**2) with (-35*x**2)*(-33*x**2) + (-35*x**2)*(23*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-35*x**2)*(-33*x**2) + (-35*x**2)*(23*x**3) + (73*x**3)*(23*x**3 - 33*x**2)</replace>
Simplifying the partial expression: (73*x**3)*(23*x**3 - 33*x**2)
Expanding the part (23*x**3 - 33*x**2) using the distributive property, and we got: (-33*x**2)*(73*x**3) + (23*x**3)*(73*x**3)
Replacing (73*x**3)*(23*x**3 - 33*x**2) with (-33*x**2)*(73*x**3) + (23*x**3)*(73*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-35*x**2)*(-33*x**2) + (-35*x**2)*(23*x**3) + (-33*x**2)*(73*x**3) + (23*x**3)*(73*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-33*x**2)*(-35*x**2) = 1155*x**4
  (-33*x**2)*(73*x**3) = -2409*x**5
  (23*x**3)*(-35*x**2) = -805*x**5
  (23*x**3)*(73*x**3) = 1679*x**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1679*x**6 - 2409*x**5 - 805*x**5 + 1155*x**4</replace>
Combining like terms, got 1679*x**6 - 3214*x**5 + 1155*x**4
<replace-#Step 5>#Step 6:
Current expression: 1679*x**6 - 3214*x**5 + 1155*x**4</replace>
No more calculations needed.
<answer>1679*x**6 - 3214*x**5 + 1155*x**4</answer>


Question:
Simplify this expression: (-46*x**3 + 28*x)*(-21*x**3 + 15*x**2 + 52)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 966*x**6 - 690*x**5 - 588*x**4 - 1972*x**3 + 1456*x


Question:
Calculate the following: (-8*z**2 + 34*z)*(38*z**3 - 48*z - 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: -304*z**5 + 1292*z**4 + 384*z**3 - 1424*z**2 - 884*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: (-8*z**2 + 34*z)*(38*z**3 - 48*z - 26)
Expanding the part (-8*z**2 + 34*z) using the distributive property, and we got: (34*z)*(38*z**3 - 48*z - 26) + (-8*z**2)*(38*z**3 - 48*z - 26)
<replace-#Step 1>#Step 2:
Current expression: (34*z)*(38*z**3 - 48*z - 26) + (-8*z**2)*(38*z**3 - 48*z - 26)</replace>
Simplifying the partial expression: (-8*z**2)*(38*z**3 - 48*z - 26)
Expanding the part (38*z**3 - 48*z - 26) using the distributive property, and we got: (-48*z)*(-8*z**2) - (-1)*208*z**2 + (-8*z**2)*(38*z**3)
Replacing (-8*z**2)*(38*z**3 - 48*z - 26) with (-48*z)*(-8*z**2) - (-1)*208*z**2 + (-8*z**2)*(38*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-48*z)*(-8*z**2) - 26*(-8)*z**2 + (34*z)*(38*z**3 - 48*z - 26) + (-8*z**2)*(38*z**3)</replace>
Simplifying the partial expression: (34*z)*(38*z**3 - 48*z - 26)
Expanding the part (38*z**3 - 48*z - 26) using the distributive property, and we got: (-48*z)*(34*z) - 884*z + (34*z)*(38*z**3)
Replacing (34*z)*(38*z**3 - 48*z - 26) with (-48*z)*(34*z) - 884*z + (34*z)*(38*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-48*z)*(34*z) + (-48*z)*(-8*z**2) - 26*(-8)*z**2 - 26*34*z + (34*z)*(38*z**3) + (-8*z**2)*(38*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)*(-8*z**2) = 384*z**3
  (-48*z)*(34*z) = -1632*z**2
  (38*z**3)*(-8*z**2) = -304*z**5
  (38*z**3)*(34*z) = 1292*z**4
  -26*-8*z**2 = 208*z**2
  -26*34*z = -884*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -304*z**5 + 1292*z**4 + 384*z**3 - 1632*z**2 + 208*z**2 - 884*z</replace>
Combining like terms, got -304*z**5 + 1292*z**4 + 384*z**3 - 1424*z**2 - 884*z
<replace-#Step 5>#Step 6:
Current expression: -304*z**5 + 1292*z**4 + 384*z**3 - 1424*z**2 - 884*z</replace>
No more calculations needed.
<answer>-304*z**5 + 1292*z**4 + 384*z**3 - 1424*z**2 - 884*z</answer>


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

Answer: 93*z**3 - 27*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: -3*z**2*(9 - 31*z)
Expanding the part (9 - 31*z) using the distributive property, and we got: (-31*z)*(-3*z**2) + 9*(-3*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-31*z)*(-3*z**2) + 9*(-3*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  9*(-3*z**2) = -27*z**2
  (-31*z)*(-3*z**2) = 93*z**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 93*z**3 - 27*z**2</replace>
No more calculations needed.
<answer>93*z**3 - 27*z**2</answer>


Question:
Simplify this expression: (-26*z**3 - 34)*(-z**3 + 46*z + 47)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 26*z**6 - 1196*z**4 - 1188*z**3 - 1564*z - 1598

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 - 34)*(-z**3 + 46*z + 47)
Expanding the part (-26*z**3 - 34) using the distributive property, and we got: (-26*z**3)*(-z**3 + 46*z + 47) - 34*(-z**3 + 46*z + 47)
<replace-#Step 1>#Step 2:
Current expression: (-26*z**3)*(-z**3 + 46*z + 47) - 34*(-z**3 + 46*z + 47)</replace>
Simplifying the partial expression: -34*(-z**3 + 46*z + 47)
Expanding the part (-z**3 + 46*z + 47) using the distributive property, and we got: (46*z)*(-34) - z**3*(-34) + 47*(-34)
Replacing -34*(-z**3 + 46*z + 47) with (46*z)*(-34) - z**3*(-34) + 47*(-34) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (46*z)*(-34) + (-26*z**3)*(-z**3 + 46*z + 47) - z**3*(-34) - 1598</replace>
Simplifying the partial expression: (-26*z**3)*(-z**3 + 46*z + 47)
Expanding the part (-z**3 + 46*z + 47) using the distributive property, and we got: 47*(-26*z**3) + (46*z)*(-26*z**3) + (-26*z**3)*(-z**3)
Replacing (-26*z**3)*(-z**3 + 46*z + 47) with 47*(-26*z**3) + (46*z)*(-26*z**3) + (-26*z**3)*(-z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 47*(-26)*z**3 + (46*z)*(-26*z**3) + (46*z)*(-34) + (-26*z**3)*(-z**3) - z**3*(-34) - 1598</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-z**3)*-34 = 34*z**3
  (-z**3)*(-26*z**3) = 26*z**6
  (46*z)*-34 = -1564*z
  (46*z)*(-26*z**3) = -1196*z**4
  47*-26*z**3 = -1222*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 26*z**6 - 1196*z**4 - 1222*z**3 + 34*z**3 - 1564*z - 1598</replace>
Combining like terms, got 26*z**6 - 1196*z**4 - 1188*z**3 - 1564*z - 1598
<replace-#Step 5>#Step 6:
Current expression: 26*z**6 - 1196*z**4 - 1188*z**3 - 1564*z - 1598</replace>
No more calculations needed.
<answer>26*z**6 - 1196*z**4 - 1188*z**3 - 1564*z - 1598</answer>


Question:
Simplify this expression: (-21*y**3 - 52)*(-21*y**3 - 8*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: 441*y**6 + 168*y**5 + 1092*y**3 + 416*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: (-21*y**3 - 52)*(-21*y**3 - 8*y**2)
Expanding the part (-21*y**3 - 52) using the distributive property, and we got: (-21*y**3)*(-21*y**3 - 8*y**2) - 52*(-21*y**3 - 8*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-21*y**3)*(-21*y**3 - 8*y**2) - 52*(-21*y**3 - 8*y**2)</replace>
Simplifying the partial expression: -52*(-21*y**3 - 8*y**2)
Expanding the part (-21*y**3 - 8*y**2) using the distributive property, and we got: -8*y**2*(-52) - 21*y**3*(-52)
Replacing -52*(-21*y**3 - 8*y**2) with -8*y**2*(-52) - 21*y**3*(-52) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -8*y**2*(-52) + (-21*y**3)*(-21*y**3 - 8*y**2) - 21*y**3*(-52)</replace>
Simplifying the partial expression: (-21*y**3)*(-21*y**3 - 8*y**2)
Expanding the part (-21*y**3 - 8*y**2) using the distributive property, and we got: (-8*y**2)*(-21*y**3) + (-21*y**3)*(-21*y**3)
Replacing (-21*y**3)*(-21*y**3 - 8*y**2) with (-8*y**2)*(-21*y**3) + (-21*y**3)*(-21*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-8*y**2)*(-21*y**3) - 8*y**2*(-52) - 21*y**3*(-52) + (-21*y**3)*(-21*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-21*y**3)*-52 = 1092*y**3
  (-21*y**3)*(-21*y**3) = 441*y**6
  (-8*y**2)*-52 = 416*y**2
  (-8*y**2)*(-21*y**3) = 168*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 441*y**6 + 168*y**5 + 1092*y**3 + 416*y**2</replace>
No more calculations needed.
<answer>441*y**6 + 168*y**5 + 1092*y**3 + 416*y**2</answer>


Question:
Simplify this expression: (13*z**3 - 7*z**2 - 19*z)*(-16*z**3 - 6*z**2 + 11*z - 47)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -208*z**6 + 34*z**5 + 489*z**4 - 574*z**3 + 120*z**2 + 893*z


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

Answer: -1680*x**6 + 1336*x**5 - 176*x**4 + 1225*x**3 - 770*x**2


Question:
Simplify this expression: -3*z**3 - 171*z - 123
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -3*z**3 - 171*z - 123

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -3*z**3 - 171*z - 123
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: -3*z**3 - 171*z - 123</replace>
No more calculations needed.
<answer>-3*z**3 - 171*z - 123</answer>


Question:
Calculate the following: (27*y**2 + 3*y)*(-57*y**3 + 23*y**2 - 14)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1539*y**5 + 450*y**4 + 69*y**3 - 378*y**2 - 42*y


Question:
Simplify this expression: (16*y**3 + 38*y - 52)*(27*y**3 - 24*y**2 - 49*y - 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: 432*y**6 - 384*y**5 + 242*y**4 - 2412*y**3 - 614*y**2 + 2320*y + 312


Question:
Calculate the following: (-41*z**2 - 2*z + 42)*(-18*z**3 - 57*z**2 - 13)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 738*z**5 + 2373*z**4 - 642*z**3 - 1861*z**2 + 26*z - 546


Question:
Calculate the following: (4*z**3 - 6*z**2)*(44*z**3 - 42*z**2 - 18)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 176*z**6 - 432*z**5 + 252*z**4 - 72*z**3 + 108*z**2


Question:
Simplify this expression: (-20*y**3 + 13*y**2)*(49*y**3 + 77)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -980*y**6 + 637*y**5 - 1540*y**3 + 1001*y**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-20*y**3 + 13*y**2)*(49*y**3 + 77)
Expanding the part (49*y**3 + 77) using the distributive property, and we got: (49*y**3)*(-20*y**3 + 13*y**2) + 77*(-20*y**3 + 13*y**2)
<replace-#Step 1>#Step 2:
Current expression: (49*y**3)*(-20*y**3 + 13*y**2) + 77*(-20*y**3 + 13*y**2)</replace>
Simplifying the partial expression: 77*(-20*y**3 + 13*y**2)
Expanding the part (-20*y**3 + 13*y**2) using the distributive property, and we got: (13*y**2)*77 - 20*y**3*77
Replacing 77*(-20*y**3 + 13*y**2) with (13*y**2)*77 - 20*y**3*77 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (13*y**2)*77 - 20*y**3*77 + (49*y**3)*(-20*y**3 + 13*y**2)</replace>
Simplifying the partial expression: (49*y**3)*(-20*y**3 + 13*y**2)
Expanding the part (-20*y**3 + 13*y**2) using the distributive property, and we got: (13*y**2)*(49*y**3) + (-20*y**3)*(49*y**3)
Replacing (49*y**3)*(-20*y**3 + 13*y**2) with (13*y**2)*(49*y**3) + (-20*y**3)*(49*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (13*y**2)*(49*y**3) + (13*y**2)*77 + (-20*y**3)*(49*y**3) - 20*y**3*77</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-20*y**3)*77 = -1540*y**3
  (-20*y**3)*(49*y**3) = -980*y**6
  (13*y**2)*77 = 1001*y**2
  (13*y**2)*(49*y**3) = 637*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -980*y**6 + 637*y**5 - 1540*y**3 + 1001*y**2</replace>
No more calculations needed.
<answer>-980*y**6 + 637*y**5 - 1540*y**3 + 1001*y**2</answer>


Question:
Calculate the following: (17*z**3 + 45*z**2)*(41*z**3 + 44*z - 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: 697*z**6 + 1845*z**5 + 748*z**4 + 1878*z**3 - 270*z**2


Question:
Simplify this expression: (15*x**2 - 45*x)*(-3*x**3 + 10*x - 58)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -45*x**5 + 135*x**4 + 150*x**3 - 1320*x**2 + 2610*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: (15*x**2 - 45*x)*(-3*x**3 + 10*x - 58)
Expanding the part (15*x**2 - 45*x) using the distributive property, and we got: (-45*x)*(-3*x**3 + 10*x - 58) + (15*x**2)*(-3*x**3 + 10*x - 58)
<replace-#Step 1>#Step 2:
Current expression: (-45*x)*(-3*x**3 + 10*x - 58) + (15*x**2)*(-3*x**3 + 10*x - 58)</replace>
Simplifying the partial expression: (-45*x)*(-3*x**3 + 10*x - 58)
Expanding the part (-3*x**3 + 10*x - 58) using the distributive property, and we got: (-45*x)*(10*x) + (-45*x)*(-3*x**3) - (-1)*2610*x
Replacing (-45*x)*(-3*x**3 + 10*x - 58) with (-45*x)*(10*x) + (-45*x)*(-3*x**3) - (-1)*2610*x in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-45*x)*(10*x) + (-45*x)*(-3*x**3) - 58*(-45)*x + (15*x**2)*(-3*x**3 + 10*x - 58)</replace>
Simplifying the partial expression: (15*x**2)*(-3*x**3 + 10*x - 58)
Expanding the part (-3*x**3 + 10*x - 58) using the distributive property, and we got: -870*x**2 + (10*x)*(15*x**2) + (15*x**2)*(-3*x**3)
Replacing (15*x**2)*(-3*x**3 + 10*x - 58) with -870*x**2 + (10*x)*(15*x**2) + (15*x**2)*(-3*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-45*x)*(10*x) + (-45*x)*(-3*x**3) - 58*15*x**2 - 58*(-45)*x + (10*x)*(15*x**2) + (15*x**2)*(-3*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-3*x**3)*(-45*x) = 135*x**4
  (-3*x**3)*(15*x**2) = -45*x**5
  (10*x)*(-45*x) = -450*x**2
  (10*x)*(15*x**2) = 150*x**3
  -58*-45*x = 2610*x
  -58*15*x**2 = -870*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -45*x**5 + 135*x**4 + 150*x**3 - 870*x**2 - 450*x**2 + 2610*x</replace>
Combining like terms, got -45*x**5 + 135*x**4 + 150*x**3 - 1320*x**2 + 2610*x
<replace-#Step 5>#Step 6:
Current expression: -45*x**5 + 135*x**4 + 150*x**3 - 1320*x**2 + 2610*x</replace>
No more calculations needed.
<answer>-45*x**5 + 135*x**4 + 150*x**3 - 1320*x**2 + 2610*x</answer>


Question:
Calculate the following: (-46*z**3 + 6*z)*(-17*z**2 - 13*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: 782*z**5 + 598*z**4 - 1482*z**3 - 78*z**2 + 180*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: (-46*z**3 + 6*z)*(-17*z**2 - 13*z + 30)
Expanding the part (-46*z**3 + 6*z) using the distributive property, and we got: (6*z)*(-17*z**2 - 13*z + 30) + (-46*z**3)*(-17*z**2 - 13*z + 30)
<replace-#Step 1>#Step 2:
Current expression: (6*z)*(-17*z**2 - 13*z + 30) + (-46*z**3)*(-17*z**2 - 13*z + 30)</replace>
Simplifying the partial expression: (-46*z**3)*(-17*z**2 - 13*z + 30)
Expanding the part (-17*z**2 - 13*z + 30) using the distributive property, and we got: (-13*z)*(-46*z**3) + 30*(-46*z**3) + (-17*z**2)*(-46*z**3)
Replacing (-46*z**3)*(-17*z**2 - 13*z + 30) with (-13*z)*(-46*z**3) + 30*(-46*z**3) + (-17*z**2)*(-46*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-13*z)*(-46*z**3) + 30*(-46)*z**3 + (6*z)*(-17*z**2 - 13*z + 30) + (-17*z**2)*(-46*z**3)</replace>
Simplifying the partial expression: (6*z)*(-17*z**2 - 13*z + 30)
Expanding the part (-17*z**2 - 13*z + 30) using the distributive property, and we got: (-13*z)*(6*z) + 30*(6*z) + (6*z)*(-17*z**2)
Replacing (6*z)*(-17*z**2 - 13*z + 30) with (-13*z)*(6*z) + 30*(6*z) + (6*z)*(-17*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-13*z)*(6*z) + (-13*z)*(-46*z**3) + 30*(-46)*z**3 + 30*6*z + (6*z)*(-17*z**2) + (-17*z**2)*(-46*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-17*z**2)*(-46*z**3) = 782*z**5
  (-17*z**2)*(6*z) = -102*z**3
  (-13*z)*(-46*z**3) = 598*z**4
  (-13*z)*(6*z) = -78*z**2
  30*-46*z**3 = -1380*z**3
  30*6*z = 180*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 782*z**5 + 598*z**4 - 1380*z**3 - 102*z**3 - 78*z**2 + 180*z</replace>
Combining like terms, got 782*z**5 + 598*z**4 - 1482*z**3 - 78*z**2 + 180*z
<replace-#Step 5>#Step 6:
Current expression: 782*z**5 + 598*z**4 - 1482*z**3 - 78*z**2 + 180*z</replace>
No more calculations needed.
<answer>782*z**5 + 598*z**4 - 1482*z**3 - 78*z**2 + 180*z</answer>


Question:
Calculate the following: 47*z**3*(-2*z**2 - 11*z - 40)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -94*z**5 - 517*z**4 - 1880*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: 47*z**3*(-2*z**2 - 11*z - 40)
Expanding the part (-2*z**2 - 11*z - 40) using the distributive property, and we got: (-11*z)*(47*z**3) - 1880*z**3 + (-2*z**2)*(47*z**3)
<replace-#Step 1>#Step 2:
Current expression: (-11*z)*(47*z**3) - 1880*z**3 + (-2*z**2)*(47*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -40*(47*z**3) = -1880*z**3
  (-11*z)*(47*z**3) = -517*z**4
  (-2*z**2)*(47*z**3) = -94*z**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -94*z**5 - 517*z**4 - 1880*z**3</replace>
No more calculations needed.
<answer>-94*z**5 - 517*z**4 - 1880*z**3</answer>