Question:
Calculate the following: (-43*z**3 - 47*z + 1)*(-22*z**3 + 39*z**2 - 14*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**6 - 1677*z**5 + 1636*z**4 - 1855*z**3 + 697*z**2 - 14*z


Question:
Simplify this expression: 6*x**3*(-49*x**2 + 59*x - 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: -294*x**5 + 354*x**4 - 138*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: 6*x**3*(-49*x**2 + 59*x - 23)
Expanding the part (-49*x**2 + 59*x - 23) using the distributive property, and we got: -138*x**3 + (59*x)*(6*x**3) + (-49*x**2)*(6*x**3)
<replace-#Step 1>#Step 2:
Current expression: -138*x**3 + (59*x)*(6*x**3) + (-49*x**2)*(6*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -23*(6*x**3) = -138*x**3
  (-49*x**2)*(6*x**3) = -294*x**5
  (59*x)*(6*x**3) = 354*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -294*x**5 + 354*x**4 - 138*x**3</replace>
No more calculations needed.
<answer>-294*x**5 + 354*x**4 - 138*x**3</answer>


Question:
Calculate the following: (-5*y - 51)*(-51*y**2 - 24*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 255*y**3 + 2721*y**2 + 1224*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: (-5*y - 51)*(-51*y**2 - 24*y)
Expanding the part (-5*y - 51) using the distributive property, and we got: (-5*y)*(-51*y**2 - 24*y) - 51*(-51*y**2 - 24*y)
<replace-#Step 1>#Step 2:
Current expression: (-5*y)*(-51*y**2 - 24*y) - 51*(-51*y**2 - 24*y)</replace>
Simplifying the partial expression: -51*(-51*y**2 - 24*y)
Expanding the part (-51*y**2 - 24*y) using the distributive property, and we got: -24*y*(-51) - 51*y**2*(-51)
Replacing -51*(-51*y**2 - 24*y) with -24*y*(-51) - 51*y**2*(-51) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -24*y*(-51) + (-5*y)*(-51*y**2 - 24*y) - 51*y**2*(-51)</replace>
Simplifying the partial expression: (-5*y)*(-51*y**2 - 24*y)
Expanding the part (-51*y**2 - 24*y) using the distributive property, and we got: (-24*y)*(-5*y) + (-5*y)*(-51*y**2)
Replacing (-5*y)*(-51*y**2 - 24*y) with (-24*y)*(-5*y) + (-5*y)*(-51*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-24*y)*(-5*y) - 24*y*(-51) + (-5*y)*(-51*y**2) - 51*y**2*(-51)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-51*y**2)*-51 = 2601*y**2
  (-51*y**2)*(-5*y) = 255*y**3
  (-24*y)*-51 = 1224*y
  (-24*y)*(-5*y) = 120*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 255*y**3 + 120*y**2 + 2601*y**2 + 1224*y</replace>
Combining like terms, got 255*y**3 + 2721*y**2 + 1224*y
<replace-#Step 5>#Step 6:
Current expression: 255*y**3 + 2721*y**2 + 1224*y</replace>
No more calculations needed.
<answer>255*y**3 + 2721*y**2 + 1224*y</answer>


Question:
Simplify this expression: (29*x**2 - 27)*(-24*x**2 - 21*x + 7)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -696*x**4 - 609*x**3 + 851*x**2 + 567*x - 189

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (29*x**2 - 27)*(-24*x**2 - 21*x + 7)
Expanding the part (29*x**2 - 27) using the distributive property, and we got: (29*x**2)*(-24*x**2 - 21*x + 7) - 27*(-24*x**2 - 21*x + 7)
<replace-#Step 1>#Step 2:
Current expression: (29*x**2)*(-24*x**2 - 21*x + 7) - 27*(-24*x**2 - 21*x + 7)</replace>
Simplifying the partial expression: -27*(-24*x**2 - 21*x + 7)
Expanding the part (-24*x**2 - 21*x + 7) using the distributive property, and we got: -21*x*(-27) - 24*x**2*(-27) + 7*(-27)
Replacing -27*(-24*x**2 - 21*x + 7) with -21*x*(-27) - 24*x**2*(-27) + 7*(-27) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -21*x*(-27) - 24*x**2*(-27) + (29*x**2)*(-24*x**2 - 21*x + 7) - 189</replace>
Simplifying the partial expression: (29*x**2)*(-24*x**2 - 21*x + 7)
Expanding the part (-24*x**2 - 21*x + 7) using the distributive property, and we got: (-21*x)*(29*x**2) + 7*(29*x**2) + (-24*x**2)*(29*x**2)
Replacing (29*x**2)*(-24*x**2 - 21*x + 7) with (-21*x)*(29*x**2) + 7*(29*x**2) + (-24*x**2)*(29*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-21*x)*(29*x**2) - 21*x*(-27) + 7*29*x**2 + (-24*x**2)*(29*x**2) - 24*x**2*(-27) - 189</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-24*x**2)*-27 = 648*x**2
  (-24*x**2)*(29*x**2) = -696*x**4
  (-21*x)*-27 = 567*x
  (-21*x)*(29*x**2) = -609*x**3
  7*29*x**2 = 203*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -696*x**4 - 609*x**3 + 203*x**2 + 648*x**2 + 567*x - 189</replace>
Combining like terms, got -696*x**4 - 609*x**3 + 851*x**2 + 567*x - 189
<replace-#Step 5>#Step 6:
Current expression: -696*x**4 - 609*x**3 + 851*x**2 + 567*x - 189</replace>
No more calculations needed.
<answer>-696*x**4 - 609*x**3 + 851*x**2 + 567*x - 189</answer>


Question:
Calculate the following: (14*x**2 - 41)*(-31*x**2 + 19*x + 22)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -434*x**4 + 266*x**3 + 1579*x**2 - 779*x - 902

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (14*x**2 - 41)*(-31*x**2 + 19*x + 22)
Expanding the part (14*x**2 - 41) using the distributive property, and we got: (14*x**2)*(-31*x**2 + 19*x + 22) - 41*(-31*x**2 + 19*x + 22)
<replace-#Step 1>#Step 2:
Current expression: (14*x**2)*(-31*x**2 + 19*x + 22) - 41*(-31*x**2 + 19*x + 22)</replace>
Simplifying the partial expression: -41*(-31*x**2 + 19*x + 22)
Expanding the part (-31*x**2 + 19*x + 22) using the distributive property, and we got: (19*x)*(-41) - 31*x**2*(-41) + 22*(-41)
Replacing -41*(-31*x**2 + 19*x + 22) with (19*x)*(-41) - 31*x**2*(-41) + 22*(-41) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (19*x)*(-41) - 31*x**2*(-41) + (14*x**2)*(-31*x**2 + 19*x + 22) - 902</replace>
Simplifying the partial expression: (14*x**2)*(-31*x**2 + 19*x + 22)
Expanding the part (-31*x**2 + 19*x + 22) using the distributive property, and we got: 22*(14*x**2) + (19*x)*(14*x**2) + (-31*x**2)*(14*x**2)
Replacing (14*x**2)*(-31*x**2 + 19*x + 22) with 22*(14*x**2) + (19*x)*(14*x**2) + (-31*x**2)*(14*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 22*14*x**2 + (19*x)*(14*x**2) + (19*x)*(-41) + (-31*x**2)*(14*x**2) - 31*x**2*(-41) - 902</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-31*x**2)*-41 = 1271*x**2
  (-31*x**2)*(14*x**2) = -434*x**4
  (19*x)*-41 = -779*x
  (19*x)*(14*x**2) = 266*x**3
  22*14*x**2 = 308*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -434*x**4 + 266*x**3 + 308*x**2 + 1271*x**2 - 779*x - 902</replace>
Combining like terms, got -434*x**4 + 266*x**3 + 1579*x**2 - 779*x - 902
<replace-#Step 5>#Step 6:
Current expression: -434*x**4 + 266*x**3 + 1579*x**2 - 779*x - 902</replace>
No more calculations needed.
<answer>-434*x**4 + 266*x**3 + 1579*x**2 - 779*x - 902</answer>


Question:
Simplify this expression: (-43*x**3 + 39*x**2 + 19*x)*(27*x**3 - 25*x**2 - 21*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: -1161*x**6 + 2128*x**5 + 441*x**4 - 1294*x**3 - 399*x**2


Question:
Calculate the following: 4*x**3*(18*x**3 - 38*x**2 + 83*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: 72*x**6 - 152*x**5 + 332*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: 4*x**3*(18*x**3 - 38*x**2 + 83*x)
Expanding the part (18*x**3 - 38*x**2 + 83*x) using the distributive property, and we got: (83*x)*(4*x**3) + (-38*x**2)*(4*x**3) + (4*x**3)*(18*x**3)
<replace-#Step 1>#Step 2:
Current expression: (83*x)*(4*x**3) + (-38*x**2)*(4*x**3) + (4*x**3)*(18*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-38*x**2)*(4*x**3) = -152*x**5
  (18*x**3)*(4*x**3) = 72*x**6
  (83*x)*(4*x**3) = 332*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 72*x**6 - 152*x**5 + 332*x**4</replace>
No more calculations needed.
<answer>72*x**6 - 152*x**5 + 332*x**4</answer>


Question:
Simplify this expression: (-37*y**3 + 7*y)*(48*y**3 + 35*y**2 - 17)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1776*y**6 - 1295*y**5 + 336*y**4 + 874*y**3 - 119*y


Question:
Simplify this expression: (42*z**3 - 43*z**2)*(19*z**2 - 7*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: 798*z**5 - 1111*z**4 + 1981*z**3 - 1720*z**2


Question:
Simplify this expression: (5*x**3 - 49*x**2)*(29*x**3 + 39)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 145*x**6 - 1421*x**5 + 195*x**3 - 1911*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: (5*x**3 - 49*x**2)*(29*x**3 + 39)
Expanding the part (29*x**3 + 39) using the distributive property, and we got: (29*x**3)*(5*x**3 - 49*x**2) + 39*(5*x**3 - 49*x**2)
<replace-#Step 1>#Step 2:
Current expression: (29*x**3)*(5*x**3 - 49*x**2) + 39*(5*x**3 - 49*x**2)</replace>
Simplifying the partial expression: 39*(5*x**3 - 49*x**2)
Expanding the part (5*x**3 - 49*x**2) using the distributive property, and we got: -49*x**2*39 + (5*x**3)*39
Replacing 39*(5*x**3 - 49*x**2) with -49*x**2*39 + (5*x**3)*39 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -49*x**2*39 + (5*x**3)*39 + (29*x**3)*(5*x**3 - 49*x**2)</replace>
Simplifying the partial expression: (29*x**3)*(5*x**3 - 49*x**2)
Expanding the part (5*x**3 - 49*x**2) using the distributive property, and we got: (-49*x**2)*(29*x**3) + (5*x**3)*(29*x**3)
Replacing (29*x**3)*(5*x**3 - 49*x**2) with (-49*x**2)*(29*x**3) + (5*x**3)*(29*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-49*x**2)*(29*x**3) - 49*x**2*39 + (5*x**3)*(29*x**3) + (5*x**3)*39</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-49*x**2)*39 = -1911*x**2
  (-49*x**2)*(29*x**3) = -1421*x**5
  (5*x**3)*39 = 195*x**3
  (5*x**3)*(29*x**3) = 145*x**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 145*x**6 - 1421*x**5 + 195*x**3 - 1911*x**2</replace>
No more calculations needed.
<answer>145*x**6 - 1421*x**5 + 195*x**3 - 1911*x**2</answer>


Question:
Simplify this expression: -45*z*(12*z**3 + 4*z**2 + 30*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -540*z**4 - 180*z**3 - 1350*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: -45*z*(12*z**3 + 4*z**2 + 30*z)
Expanding the part (12*z**3 + 4*z**2 + 30*z) using the distributive property, and we got: (-45*z)*(30*z) + (-45*z)*(4*z**2) + (-45*z)*(12*z**3)
<replace-#Step 1>#Step 2:
Current expression: (-45*z)*(30*z) + (-45*z)*(4*z**2) + (-45*z)*(12*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (4*z**2)*(-45*z) = -180*z**3
  (12*z**3)*(-45*z) = -540*z**4
  (30*z)*(-45*z) = -1350*z**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -540*z**4 - 180*z**3 - 1350*z**2</replace>
No more calculations needed.
<answer>-540*z**4 - 180*z**3 - 1350*z**2</answer>


Question:
Simplify this expression: -1156*y**3 - 1700
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1156*y**3 - 1700

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: -1156*y**3 - 1700
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: -1156*y**3 - 1700</replace>
No more calculations needed.
<answer>-1156*y**3 - 1700</answer>


Question:
Simplify this expression: 15*z**3 + 54*z**2 - 54
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 15*z**3 + 54*z**2 - 54

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*z**3 + 54*z**2 - 54
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: 15*z**3 + 54*z**2 - 54</replace>
No more calculations needed.
<answer>15*z**3 + 54*z**2 - 54</answer>


Question:
Calculate the following: 42*x**3*(-12*x**2 - 11*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -504*x**5 - 462*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: 42*x**3*(-12*x**2 - 11*x)
Expanding the part (-12*x**2 - 11*x) using the distributive property, and we got: (-11*x)*(42*x**3) + (-12*x**2)*(42*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-11*x)*(42*x**3) + (-12*x**2)*(42*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-12*x**2)*(42*x**3) = -504*x**5
  (-11*x)*(42*x**3) = -462*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -504*x**5 - 462*x**4</replace>
No more calculations needed.
<answer>-504*x**5 - 462*x**4</answer>


Question:
Calculate the following: (26*z - 17)*(25*z**3 - 17)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 650*z**4 - 425*z**3 - 442*z + 289

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 - 17)*(25*z**3 - 17)
Expanding the part (25*z**3 - 17) using the distributive property, and we got: (25*z**3)*(26*z - 17) - 17*(26*z - 17)
<replace-#Step 1>#Step 2:
Current expression: (25*z**3)*(26*z - 17) - 17*(26*z - 17)</replace>
Simplifying the partial expression: -17*(26*z - 17)
Expanding the part (26*z - 17) using the distributive property, and we got: (26*z)*(-17) - 17*(-17)
Replacing -17*(26*z - 17) with (26*z)*(-17) - 17*(-17) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (26*z)*(-17) + (25*z**3)*(26*z - 17) + 289</replace>
Simplifying the partial expression: (25*z**3)*(26*z - 17)
Expanding the part (26*z - 17) using the distributive property, and we got: -425*z**3 + (26*z)*(25*z**3)
Replacing (25*z**3)*(26*z - 17) with -425*z**3 + (26*z)*(25*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -17*25*z**3 + (26*z)*(25*z**3) + (26*z)*(-17) + 289</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (26*z)*-17 = -442*z
  (26*z)*(25*z**3) = 650*z**4
  -17*25*z**3 = -425*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 650*z**4 - 425*z**3 - 442*z + 289</replace>
No more calculations needed.
<answer>650*z**4 - 425*z**3 - 442*z + 289</answer>


Question:
Calculate the following: 663*y**3 - 663*y**2 - 1170
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 663*y**3 - 663*y**2 - 1170

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: 663*y**3 - 663*y**2 - 1170
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: 663*y**3 - 663*y**2 - 1170</replace>
No more calculations needed.
<answer>663*y**3 - 663*y**2 - 1170</answer>


Question:
Calculate the following: -10*x*(23*x**2 - 32*x + 42)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -230*x**3 + 320*x**2 - 420*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -10*x*(23*x**2 - 32*x + 42)
Expanding the part (23*x**2 - 32*x + 42) using the distributive property, and we got: (-32*x)*(-10*x) + (-10*x)*(23*x**2) + 42*(-10*x)
<replace-#Step 1>#Step 2:
Current expression: (-32*x)*(-10*x) + (-10*x)*(23*x**2) + 42*(-10*x)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  42*(-10*x) = -420*x
  (-32*x)*(-10*x) = 320*x**2
  (23*x**2)*(-10*x) = -230*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -230*x**3 + 320*x**2 - 420*x</replace>
No more calculations needed.
<answer>-230*x**3 + 320*x**2 - 420*x</answer>


Question:
Simplify this expression: (4*x**3 - 10*x - 49)*(68*x**3 + 19*x**2 - 36*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: 272*x**6 + 76*x**5 - 824*x**4 - 3522*x**3 - 571*x**2 + 1764*x


Question:
Calculate the following: -70*z**3*(24*z**3 - 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: -1680*z**6 + 140*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: -70*z**3*(24*z**3 - 2)
Expanding the part (24*z**3 - 2) using the distributive property, and we got: -(-1)*140*z**3 + (-70*z**3)*(24*z**3)
<replace-#Step 1>#Step 2:
Current expression: -(-1)*140*z**3 + (-70*z**3)*(24*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -2*(-70*z**3) = 140*z**3
  (24*z**3)*(-70*z**3) = -1680*z**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1680*z**6 + 140*z**3</replace>
No more calculations needed.
<answer>-1680*z**6 + 140*z**3</answer>


Question:
Simplify this expression: (24*y**3 + 19*y)*(18*y**3 + 12*y**2 - 39*y + 46)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 432*y**6 + 288*y**5 - 594*y**4 + 1332*y**3 - 741*y**2 + 874*y


Question:
Simplify this expression: (19 - 59*y**3)*(-25*y**3 + 48*y**2 + 6)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1475*y**6 - 2832*y**5 - 829*y**3 + 912*y**2 + 114

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (19 - 59*y**3)*(-25*y**3 + 48*y**2 + 6)
Expanding the part (19 - 59*y**3) using the distributive property, and we got: (-59*y**3)*(-25*y**3 + 48*y**2 + 6) + 19*(-25*y**3 + 48*y**2 + 6)
<replace-#Step 1>#Step 2:
Current expression: (-59*y**3)*(-25*y**3 + 48*y**2 + 6) + 19*(-25*y**3 + 48*y**2 + 6)</replace>
Simplifying the partial expression: 19*(-25*y**3 + 48*y**2 + 6)
Expanding the part (-25*y**3 + 48*y**2 + 6) using the distributive property, and we got: (48*y**2)*19 - 25*y**3*19 + 6*19
Replacing 19*(-25*y**3 + 48*y**2 + 6) with (48*y**2)*19 - 25*y**3*19 + 6*19 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (48*y**2)*19 + (-59*y**3)*(-25*y**3 + 48*y**2 + 6) - 25*y**3*19 + 114</replace>
Simplifying the partial expression: (-59*y**3)*(-25*y**3 + 48*y**2 + 6)
Expanding the part (-25*y**3 + 48*y**2 + 6) using the distributive property, and we got: 6*(-59*y**3) + (48*y**2)*(-59*y**3) + (-59*y**3)*(-25*y**3)
Replacing (-59*y**3)*(-25*y**3 + 48*y**2 + 6) with 6*(-59*y**3) + (48*y**2)*(-59*y**3) + (-59*y**3)*(-25*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 6*(-59)*y**3 + (48*y**2)*(-59*y**3) + (48*y**2)*19 + (-59*y**3)*(-25*y**3) - 25*y**3*19 + 114</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-25*y**3)*19 = -475*y**3
  (-25*y**3)*(-59*y**3) = 1475*y**6
  (48*y**2)*19 = 912*y**2
  (48*y**2)*(-59*y**3) = -2832*y**5
  6*-59*y**3 = -354*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1475*y**6 - 2832*y**5 - 475*y**3 - 354*y**3 + 912*y**2 + 114</replace>
Combining like terms, got 1475*y**6 - 2832*y**5 - 829*y**3 + 912*y**2 + 114
<replace-#Step 5>#Step 6:
Current expression: 1475*y**6 - 2832*y**5 - 829*y**3 + 912*y**2 + 114</replace>
No more calculations needed.
<answer>1475*y**6 - 2832*y**5 - 829*y**3 + 912*y**2 + 114</answer>


Question:
Simplify this expression: (21 - 32*x**2)*(32*x**3 + 4*x**2 - 49)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1024*x**5 - 128*x**4 + 672*x**3 + 1652*x**2 - 1029

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 - 32*x**2)*(32*x**3 + 4*x**2 - 49)
Expanding the part (21 - 32*x**2) using the distributive property, and we got: (-32*x**2)*(32*x**3 + 4*x**2 - 49) + 21*(32*x**3 + 4*x**2 - 49)
<replace-#Step 1>#Step 2:
Current expression: (-32*x**2)*(32*x**3 + 4*x**2 - 49) + 21*(32*x**3 + 4*x**2 - 49)</replace>
Simplifying the partial expression: 21*(32*x**3 + 4*x**2 - 49)
Expanding the part (32*x**3 + 4*x**2 - 49) using the distributive property, and we got: (4*x**2)*21 + (32*x**3)*21 - 49*21
Replacing 21*(32*x**3 + 4*x**2 - 49) with (4*x**2)*21 + (32*x**3)*21 - 49*21 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-32*x**2)*(32*x**3 + 4*x**2 - 49) + (4*x**2)*21 + (32*x**3)*21 - 1029</replace>
Simplifying the partial expression: (-32*x**2)*(32*x**3 + 4*x**2 - 49)
Expanding the part (32*x**3 + 4*x**2 - 49) using the distributive property, and we got: -(-1)*1568*x**2 + (-32*x**2)*(4*x**2) + (-32*x**2)*(32*x**3)
Replacing (-32*x**2)*(32*x**3 + 4*x**2 - 49) with -(-1)*1568*x**2 + (-32*x**2)*(4*x**2) + (-32*x**2)*(32*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -49*(-32)*x**2 + (-32*x**2)*(4*x**2) + (-32*x**2)*(32*x**3) + (4*x**2)*21 + (32*x**3)*21 - 1029</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (4*x**2)*21 = 84*x**2
  (4*x**2)*(-32*x**2) = -128*x**4
  (32*x**3)*21 = 672*x**3
  (32*x**3)*(-32*x**2) = -1024*x**5
  -49*-32*x**2 = 1568*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1024*x**5 - 128*x**4 + 672*x**3 + 84*x**2 + 1568*x**2 - 1029</replace>
Combining like terms, got -1024*x**5 - 128*x**4 + 672*x**3 + 1652*x**2 - 1029
<replace-#Step 5>#Step 6:
Current expression: -1024*x**5 - 128*x**4 + 672*x**3 + 1652*x**2 - 1029</replace>
No more calculations needed.
<answer>-1024*x**5 - 128*x**4 + 672*x**3 + 1652*x**2 - 1029</answer>


Question:
Calculate the following: (3*z + 48)*(-6*z**2 - 30*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -18*z**3 - 378*z**2 - 1440*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: (3*z + 48)*(-6*z**2 - 30*z)
Expanding the part (3*z + 48) using the distributive property, and we got: (3*z)*(-6*z**2 - 30*z) + 48*(-6*z**2 - 30*z)
<replace-#Step 1>#Step 2:
Current expression: (3*z)*(-6*z**2 - 30*z) + 48*(-6*z**2 - 30*z)</replace>
Simplifying the partial expression: 48*(-6*z**2 - 30*z)
Expanding the part (-6*z**2 - 30*z) using the distributive property, and we got: -30*z*48 - 6*z**2*48
Replacing 48*(-6*z**2 - 30*z) with -30*z*48 - 6*z**2*48 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -30*z*48 + (3*z)*(-6*z**2 - 30*z) - 6*z**2*48</replace>
Simplifying the partial expression: (3*z)*(-6*z**2 - 30*z)
Expanding the part (-6*z**2 - 30*z) using the distributive property, and we got: (-30*z)*(3*z) + (3*z)*(-6*z**2)
Replacing (3*z)*(-6*z**2 - 30*z) with (-30*z)*(3*z) + (3*z)*(-6*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-30*z)*(3*z) - 30*z*48 + (3*z)*(-6*z**2) - 6*z**2*48</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-30*z)*48 = -1440*z
  (-30*z)*(3*z) = -90*z**2
  (-6*z**2)*48 = -288*z**2
  (-6*z**2)*(3*z) = -18*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -18*z**3 - 288*z**2 - 90*z**2 - 1440*z</replace>
Combining like terms, got -18*z**3 - 378*z**2 - 1440*z
<replace-#Step 5>#Step 6:
Current expression: -18*z**3 - 378*z**2 - 1440*z</replace>
No more calculations needed.
<answer>-18*z**3 - 378*z**2 - 1440*z</answer>


Question:
Calculate the following: (14*x**3 - 41*x**2 - 34)*(49*x**3 + 39*x + 45)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 686*x**6 - 2009*x**5 + 546*x**4 - 2635*x**3 - 1845*x**2 - 1326*x - 1530


Question:
Calculate the following: (-49*z**3 - 22*z**2 + 44)*(-26*z**3 + 37*z + 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: 1274*z**6 + 572*z**5 - 1813*z**4 - 3085*z**3 - 506*z**2 + 1628*z + 1012


Question:
Simplify this expression: (10*y**3 + 24*y)*(-27*y**2 + 11*y + 50)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -270*y**5 + 110*y**4 - 148*y**3 + 264*y**2 + 1200*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: (10*y**3 + 24*y)*(-27*y**2 + 11*y + 50)
Expanding the part (10*y**3 + 24*y) using the distributive property, and we got: (24*y)*(-27*y**2 + 11*y + 50) + (10*y**3)*(-27*y**2 + 11*y + 50)
<replace-#Step 1>#Step 2:
Current expression: (24*y)*(-27*y**2 + 11*y + 50) + (10*y**3)*(-27*y**2 + 11*y + 50)</replace>
Simplifying the partial expression: (10*y**3)*(-27*y**2 + 11*y + 50)
Expanding the part (-27*y**2 + 11*y + 50) using the distributive property, and we got: 50*(10*y**3) + (11*y)*(10*y**3) + (-27*y**2)*(10*y**3)
Replacing (10*y**3)*(-27*y**2 + 11*y + 50) with 50*(10*y**3) + (11*y)*(10*y**3) + (-27*y**2)*(10*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 50*10*y**3 + (11*y)*(10*y**3) + (24*y)*(-27*y**2 + 11*y + 50) + (-27*y**2)*(10*y**3)</replace>
Simplifying the partial expression: (24*y)*(-27*y**2 + 11*y + 50)
Expanding the part (-27*y**2 + 11*y + 50) using the distributive property, and we got: 50*(24*y) + (11*y)*(24*y) + (24*y)*(-27*y**2)
Replacing (24*y)*(-27*y**2 + 11*y + 50) with 50*(24*y) + (11*y)*(24*y) + (24*y)*(-27*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 50*10*y**3 + 50*24*y + (11*y)*(24*y) + (11*y)*(10*y**3) + (24*y)*(-27*y**2) + (-27*y**2)*(10*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-27*y**2)*(10*y**3) = -270*y**5
  (-27*y**2)*(24*y) = -648*y**3
  (11*y)*(10*y**3) = 110*y**4
  (11*y)*(24*y) = 264*y**2
  50*10*y**3 = 500*y**3
  50*24*y = 1200*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -270*y**5 + 110*y**4 - 648*y**3 + 500*y**3 + 264*y**2 + 1200*y</replace>
Combining like terms, got -270*y**5 + 110*y**4 - 148*y**3 + 264*y**2 + 1200*y
<replace-#Step 5>#Step 6:
Current expression: -270*y**5 + 110*y**4 - 148*y**3 + 264*y**2 + 1200*y</replace>
No more calculations needed.
<answer>-270*y**5 + 110*y**4 - 148*y**3 + 264*y**2 + 1200*y</answer>


Question:
Calculate the following: (-82*x**2 - 47*x)*(-17*x**3 + 12*x**2 - 10*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1394*x**5 - 185*x**4 + 256*x**3 + 470*x**2


Question:
Simplify this expression: (-27*y**3 - 30*y**2)*(14*y**3 - 20)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -378*y**6 - 420*y**5 + 540*y**3 + 600*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: (-27*y**3 - 30*y**2)*(14*y**3 - 20)
Expanding the part (14*y**3 - 20) using the distributive property, and we got: (14*y**3)*(-27*y**3 - 30*y**2) - 20*(-27*y**3 - 30*y**2)
<replace-#Step 1>#Step 2:
Current expression: (14*y**3)*(-27*y**3 - 30*y**2) - 20*(-27*y**3 - 30*y**2)</replace>
Simplifying the partial expression: -20*(-27*y**3 - 30*y**2)
Expanding the part (-27*y**3 - 30*y**2) using the distributive property, and we got: -30*y**2*(-20) - 27*y**3*(-20)
Replacing -20*(-27*y**3 - 30*y**2) with -30*y**2*(-20) - 27*y**3*(-20) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -30*y**2*(-20) - 27*y**3*(-20) + (14*y**3)*(-27*y**3 - 30*y**2)</replace>
Simplifying the partial expression: (14*y**3)*(-27*y**3 - 30*y**2)
Expanding the part (-27*y**3 - 30*y**2) using the distributive property, and we got: (-30*y**2)*(14*y**3) + (-27*y**3)*(14*y**3)
Replacing (14*y**3)*(-27*y**3 - 30*y**2) with (-30*y**2)*(14*y**3) + (-27*y**3)*(14*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-30*y**2)*(14*y**3) - 30*y**2*(-20) + (-27*y**3)*(14*y**3) - 27*y**3*(-20)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-30*y**2)*-20 = 600*y**2
  (-30*y**2)*(14*y**3) = -420*y**5
  (-27*y**3)*-20 = 540*y**3
  (-27*y**3)*(14*y**3) = -378*y**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -378*y**6 - 420*y**5 + 540*y**3 + 600*y**2</replace>
No more calculations needed.
<answer>-378*y**6 - 420*y**5 + 540*y**3 + 600*y**2</answer>


Question:
Simplify this expression: -21*z**3*(-16*z**2 + 36*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 336*z**5 - 756*z**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -21*z**3*(-16*z**2 + 36*z)
Expanding the part (-16*z**2 + 36*z) using the distributive property, and we got: (36*z)*(-21*z**3) + (-16*z**2)*(-21*z**3)
<replace-#Step 1>#Step 2:
Current expression: (36*z)*(-21*z**3) + (-16*z**2)*(-21*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-16*z**2)*(-21*z**3) = 336*z**5
  (36*z)*(-21*z**3) = -756*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 336*z**5 - 756*z**4</replace>
No more calculations needed.
<answer>336*z**5 - 756*z**4</answer>


Question:
Calculate the following: (-46*y**2 + 27*y)*(23*y**3 + 39*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: -1058*y**5 - 1173*y**4 + 1053*y**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-46*y**2 + 27*y)*(23*y**3 + 39*y**2)
Expanding the part (-46*y**2 + 27*y) using the distributive property, and we got: (27*y)*(23*y**3 + 39*y**2) + (-46*y**2)*(23*y**3 + 39*y**2)
<replace-#Step 1>#Step 2:
Current expression: (27*y)*(23*y**3 + 39*y**2) + (-46*y**2)*(23*y**3 + 39*y**2)</replace>
Simplifying the partial expression: (-46*y**2)*(23*y**3 + 39*y**2)
Expanding the part (23*y**3 + 39*y**2) using the distributive property, and we got: (-46*y**2)*(39*y**2) + (-46*y**2)*(23*y**3)
Replacing (-46*y**2)*(23*y**3 + 39*y**2) with (-46*y**2)*(39*y**2) + (-46*y**2)*(23*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (27*y)*(23*y**3 + 39*y**2) + (-46*y**2)*(39*y**2) + (-46*y**2)*(23*y**3)</replace>
Simplifying the partial expression: (27*y)*(23*y**3 + 39*y**2)
Expanding the part (23*y**3 + 39*y**2) using the distributive property, and we got: (27*y)*(39*y**2) + (27*y)*(23*y**3)
Replacing (27*y)*(23*y**3 + 39*y**2) with (27*y)*(39*y**2) + (27*y)*(23*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (27*y)*(39*y**2) + (27*y)*(23*y**3) + (-46*y**2)*(39*y**2) + (-46*y**2)*(23*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (23*y**3)*(-46*y**2) = -1058*y**5
  (23*y**3)*(27*y) = 621*y**4
  (39*y**2)*(-46*y**2) = -1794*y**4
  (39*y**2)*(27*y) = 1053*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1058*y**5 - 1794*y**4 + 621*y**4 + 1053*y**3</replace>
Combining like terms, got -1058*y**5 - 1173*y**4 + 1053*y**3
<replace-#Step 5>#Step 6:
Current expression: -1058*y**5 - 1173*y**4 + 1053*y**3</replace>
No more calculations needed.
<answer>-1058*y**5 - 1173*y**4 + 1053*y**3</answer>


Question:
Calculate the following: (-49*x**3 - 40)*(-49*x**3 - 29*x - 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: 2401*x**6 + 1421*x**4 + 3479*x**3 + 1160*x + 1240

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*x**3 - 40)*(-49*x**3 - 29*x - 31)
Expanding the part (-49*x**3 - 40) using the distributive property, and we got: (-49*x**3)*(-49*x**3 - 29*x - 31) - 40*(-49*x**3 - 29*x - 31)
<replace-#Step 1>#Step 2:
Current expression: (-49*x**3)*(-49*x**3 - 29*x - 31) - 40*(-49*x**3 - 29*x - 31)</replace>
Simplifying the partial expression: -40*(-49*x**3 - 29*x - 31)
Expanding the part (-49*x**3 - 29*x - 31) using the distributive property, and we got: -29*x*(-40) - 49*x**3*(-40) - 31*(-40)
Replacing -40*(-49*x**3 - 29*x - 31) with -29*x*(-40) - 49*x**3*(-40) - 31*(-40) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -29*x*(-40) + (-49*x**3)*(-49*x**3 - 29*x - 31) - 49*x**3*(-40) + 1240</replace>
Simplifying the partial expression: (-49*x**3)*(-49*x**3 - 29*x - 31)
Expanding the part (-49*x**3 - 29*x - 31) using the distributive property, and we got: (-29*x)*(-49*x**3) - (-1)*1519*x**3 + (-49*x**3)*(-49*x**3)
Replacing (-49*x**3)*(-49*x**3 - 29*x - 31) with (-29*x)*(-49*x**3) - (-1)*1519*x**3 + (-49*x**3)*(-49*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-29*x)*(-49*x**3) - 29*x*(-40) - 31*(-49)*x**3 - 49*x**3*(-40) + (-49*x**3)*(-49*x**3) + 1240</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-49*x**3)*-40 = 1960*x**3
  (-49*x**3)*(-49*x**3) = 2401*x**6
  (-29*x)*-40 = 1160*x
  (-29*x)*(-49*x**3) = 1421*x**4
  -31*-49*x**3 = 1519*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2401*x**6 + 1421*x**4 + 1519*x**3 + 1960*x**3 + 1160*x + 1240</replace>
Combining like terms, got 2401*x**6 + 1421*x**4 + 3479*x**3 + 1160*x + 1240
<replace-#Step 5>#Step 6:
Current expression: 2401*x**6 + 1421*x**4 + 3479*x**3 + 1160*x + 1240</replace>
No more calculations needed.
<answer>2401*x**6 + 1421*x**4 + 3479*x**3 + 1160*x + 1240</answer>


Question:
Simplify this expression: (50 - 49*x**2)*(-9*x**3 + 30*x**2 - 17*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: 441*x**5 - 1470*x**4 + 383*x**3 + 1500*x**2 - 850*x


Question:
Simplify this expression: (97*y + 33)*(-42*y**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: -4074*y**3 - 1386*y**2 - 1261*y - 429

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (97*y + 33)*(-42*y**2 - 13)
Expanding the part (-42*y**2 - 13) using the distributive property, and we got: (-42*y**2)*(97*y + 33) - 13*(97*y + 33)
<replace-#Step 1>#Step 2:
Current expression: (-42*y**2)*(97*y + 33) - 13*(97*y + 33)</replace>
Simplifying the partial expression: -13*(97*y + 33)
Expanding the part (97*y + 33) using the distributive property, and we got: (97*y)*(-13) + 33*(-13)
Replacing -13*(97*y + 33) with (97*y)*(-13) + 33*(-13) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (97*y)*(-13) + (-42*y**2)*(97*y + 33) - 429</replace>
Simplifying the partial expression: (-42*y**2)*(97*y + 33)
Expanding the part (97*y + 33) using the distributive property, and we got: 33*(-42*y**2) + (97*y)*(-42*y**2)
Replacing (-42*y**2)*(97*y + 33) with 33*(-42*y**2) + (97*y)*(-42*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 33*(-42)*y**2 + (97*y)*(-42*y**2) + (97*y)*(-13) - 429</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (97*y)*-13 = -1261*y
  (97*y)*(-42*y**2) = -4074*y**3
  33*-42*y**2 = -1386*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -4074*y**3 - 1386*y**2 - 1261*y - 429</replace>
No more calculations needed.
<answer>-4074*y**3 - 1386*y**2 - 1261*y - 429</answer>


Question:
Calculate the following: (29*x**2 + 5)*(43*x**3 - 10*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: 1247*x**5 - 290*x**4 + 215*x**3 - 50*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: (29*x**2 + 5)*(43*x**3 - 10*x**2)
Expanding the part (29*x**2 + 5) using the distributive property, and we got: (29*x**2)*(43*x**3 - 10*x**2) + 5*(43*x**3 - 10*x**2)
<replace-#Step 1>#Step 2:
Current expression: (29*x**2)*(43*x**3 - 10*x**2) + 5*(43*x**3 - 10*x**2)</replace>
Simplifying the partial expression: 5*(43*x**3 - 10*x**2)
Expanding the part (43*x**3 - 10*x**2) using the distributive property, and we got: -10*x**2*5 + (43*x**3)*5
Replacing 5*(43*x**3 - 10*x**2) with -10*x**2*5 + (43*x**3)*5 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -10*x**2*5 + (29*x**2)*(43*x**3 - 10*x**2) + (43*x**3)*5</replace>
Simplifying the partial expression: (29*x**2)*(43*x**3 - 10*x**2)
Expanding the part (43*x**3 - 10*x**2) using the distributive property, and we got: (-10*x**2)*(29*x**2) + (29*x**2)*(43*x**3)
Replacing (29*x**2)*(43*x**3 - 10*x**2) with (-10*x**2)*(29*x**2) + (29*x**2)*(43*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-10*x**2)*(29*x**2) - 10*x**2*5 + (29*x**2)*(43*x**3) + (43*x**3)*5</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-10*x**2)*5 = -50*x**2
  (-10*x**2)*(29*x**2) = -290*x**4
  (43*x**3)*5 = 215*x**3
  (43*x**3)*(29*x**2) = 1247*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1247*x**5 - 290*x**4 + 215*x**3 - 50*x**2</replace>
No more calculations needed.
<answer>1247*x**5 - 290*x**4 + 215*x**3 - 50*x**2</answer>


Question:
Calculate the following: (48*x**3 + 28*x - 37)*(59*x**3 + 9*x**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: 2832*x**6 + 432*x**5 + 1652*x**4 - 1067*x**3 - 333*x**2 + 504*x - 666


Question:
Calculate the following: (-33*x**3 - 13*x**2 + 40)*(60*x**3 + 3*x**2 + 31*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1980*x**6 - 879*x**5 - 1062*x**4 + 1997*x**3 + 120*x**2 + 1240*x


Question:
Simplify this expression: (88*z**3 - 29*z)*(31*z**3 - 28*z - 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: 2728*z**6 - 3363*z**4 - 2024*z**3 + 812*z**2 + 667*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: (88*z**3 - 29*z)*(31*z**3 - 28*z - 23)
Expanding the part (88*z**3 - 29*z) using the distributive property, and we got: (-29*z)*(31*z**3 - 28*z - 23) + (88*z**3)*(31*z**3 - 28*z - 23)
<replace-#Step 1>#Step 2:
Current expression: (-29*z)*(31*z**3 - 28*z - 23) + (88*z**3)*(31*z**3 - 28*z - 23)</replace>
Simplifying the partial expression: (-29*z)*(31*z**3 - 28*z - 23)
Expanding the part (31*z**3 - 28*z - 23) using the distributive property, and we got: (-29*z)*(-28*z) + (-29*z)*(31*z**3) - (-1)*667*z
Replacing (-29*z)*(31*z**3 - 28*z - 23) with (-29*z)*(-28*z) + (-29*z)*(31*z**3) - (-1)*667*z in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-29*z)*(-28*z) + (-29*z)*(31*z**3) - 23*(-29)*z + (88*z**3)*(31*z**3 - 28*z - 23)</replace>
Simplifying the partial expression: (88*z**3)*(31*z**3 - 28*z - 23)
Expanding the part (31*z**3 - 28*z - 23) using the distributive property, and we got: (-28*z)*(88*z**3) - 2024*z**3 + (31*z**3)*(88*z**3)
Replacing (88*z**3)*(31*z**3 - 28*z - 23) with (-28*z)*(88*z**3) - 2024*z**3 + (31*z**3)*(88*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-29*z)*(-28*z) + (-29*z)*(31*z**3) + (-28*z)*(88*z**3) - 23*88*z**3 - 23*(-29)*z + (31*z**3)*(88*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-28*z)*(-29*z) = 812*z**2
  (-28*z)*(88*z**3) = -2464*z**4
  (31*z**3)*(-29*z) = -899*z**4
  (31*z**3)*(88*z**3) = 2728*z**6
  -23*-29*z = 667*z
  -23*88*z**3 = -2024*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2728*z**6 - 2464*z**4 - 899*z**4 - 2024*z**3 + 812*z**2 + 667*z</replace>
Combining like terms, got 2728*z**6 - 3363*z**4 - 2024*z**3 + 812*z**2 + 667*z
<replace-#Step 5>#Step 6:
Current expression: 2728*z**6 - 3363*z**4 - 2024*z**3 + 812*z**2 + 667*z</replace>
No more calculations needed.
<answer>2728*z**6 - 3363*z**4 - 2024*z**3 + 812*z**2 + 667*z</answer>


Question:
Calculate the following: -40*y**3*(-3*y**3 - 7*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: 120*y**6 + 280*y**5

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -40*y**3*(-3*y**3 - 7*y**2)
Expanding the part (-3*y**3 - 7*y**2) using the distributive property, and we got: (-7*y**2)*(-40*y**3) + (-40*y**3)*(-3*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-7*y**2)*(-40*y**3) + (-40*y**3)*(-3*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-7*y**2)*(-40*y**3) = 280*y**5
  (-3*y**3)*(-40*y**3) = 120*y**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 120*y**6 + 280*y**5</replace>
No more calculations needed.
<answer>120*y**6 + 280*y**5</answer>


Question:
Simplify this expression: (-26*x**2 - 37)*(x**3 - 42*x**2 + 44*x + 7)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -26*x**5 + 1092*x**4 - 1181*x**3 + 1372*x**2 - 1628*x - 259


Question:
Simplify this expression: 138 - 69*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: 138 - 69*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: 138 - 69*x
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: 138 - 69*x</replace>
No more calculations needed.
<answer>138 - 69*x</answer>


Question:
Simplify this expression: 99*z*(-7*z**3 - 9*z**2 - 9*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: -693*z**4 - 891*z**3 - 891*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: 99*z*(-7*z**3 - 9*z**2 - 9*z)
Expanding the part (-7*z**3 - 9*z**2 - 9*z) using the distributive property, and we got: (-9*z)*(99*z) + (99*z)*(-9*z**2) + (99*z)*(-7*z**3)
<replace-#Step 1>#Step 2:
Current expression: (-9*z)*(99*z) + (99*z)*(-9*z**2) + (99*z)*(-7*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-9*z)*(99*z) = -891*z**2
  (-9*z**2)*(99*z) = -891*z**3
  (-7*z**3)*(99*z) = -693*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -693*z**4 - 891*z**3 - 891*z**2</replace>
No more calculations needed.
<answer>-693*z**4 - 891*z**3 - 891*z**2</answer>


Question:
Calculate the following: (-59*x**2 + 44*x)*(3*x**3 + 37*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: -177*x**5 + 132*x**4 - 2183*x**3 + 1628*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: (-59*x**2 + 44*x)*(3*x**3 + 37*x)
Expanding the part (-59*x**2 + 44*x) using the distributive property, and we got: (44*x)*(3*x**3 + 37*x) + (-59*x**2)*(3*x**3 + 37*x)
<replace-#Step 1>#Step 2:
Current expression: (44*x)*(3*x**3 + 37*x) + (-59*x**2)*(3*x**3 + 37*x)</replace>
Simplifying the partial expression: (-59*x**2)*(3*x**3 + 37*x)
Expanding the part (3*x**3 + 37*x) using the distributive property, and we got: (37*x)*(-59*x**2) + (-59*x**2)*(3*x**3)
Replacing (-59*x**2)*(3*x**3 + 37*x) with (37*x)*(-59*x**2) + (-59*x**2)*(3*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (37*x)*(-59*x**2) + (44*x)*(3*x**3 + 37*x) + (-59*x**2)*(3*x**3)</replace>
Simplifying the partial expression: (44*x)*(3*x**3 + 37*x)
Expanding the part (3*x**3 + 37*x) using the distributive property, and we got: (37*x)*(44*x) + (44*x)*(3*x**3)
Replacing (44*x)*(3*x**3 + 37*x) with (37*x)*(44*x) + (44*x)*(3*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (37*x)*(44*x) + (37*x)*(-59*x**2) + (44*x)*(3*x**3) + (-59*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)*(-59*x**2) = -177*x**5
  (3*x**3)*(44*x) = 132*x**4
  (37*x)*(-59*x**2) = -2183*x**3
  (37*x)*(44*x) = 1628*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -177*x**5 + 132*x**4 - 2183*x**3 + 1628*x**2</replace>
No more calculations needed.
<answer>-177*x**5 + 132*x**4 - 2183*x**3 + 1628*x**2</answer>


Question:
Simplify this expression: (-3*x**3 + 26*x**2 + 40)*(13*x**3 + 20*x**2 + 34*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: -39*x**6 + 278*x**5 + 418*x**4 + 1404*x**3 + 800*x**2 + 1360*x


Question:
Calculate the following: (-25*x - 48)*(-19*x**2 - 45)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 475*x**3 + 912*x**2 + 1125*x + 2160

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-25*x - 48)*(-19*x**2 - 45)
Expanding the part (-25*x - 48) using the distributive property, and we got: (-25*x)*(-19*x**2 - 45) - 48*(-19*x**2 - 45)
<replace-#Step 1>#Step 2:
Current expression: (-25*x)*(-19*x**2 - 45) - 48*(-19*x**2 - 45)</replace>
Simplifying the partial expression: -48*(-19*x**2 - 45)
Expanding the part (-19*x**2 - 45) using the distributive property, and we got: -19*x**2*(-48) - 45*(-48)
Replacing -48*(-19*x**2 - 45) with -19*x**2*(-48) - 45*(-48) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-25*x)*(-19*x**2 - 45) - 19*x**2*(-48) + 2160</replace>
Simplifying the partial expression: (-25*x)*(-19*x**2 - 45)
Expanding the part (-19*x**2 - 45) using the distributive property, and we got: (-25*x)*(-19*x**2) - (-1)*1125*x
Replacing (-25*x)*(-19*x**2 - 45) with (-25*x)*(-19*x**2) - (-1)*1125*x in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-25*x)*(-19*x**2) - 45*(-25)*x - 19*x**2*(-48) + 2160</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-19*x**2)*-48 = 912*x**2
  (-19*x**2)*(-25*x) = 475*x**3
  -45*-25*x = 1125*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 475*x**3 + 912*x**2 + 1125*x + 2160</replace>
No more calculations needed.
<answer>475*x**3 + 912*x**2 + 1125*x + 2160</answer>


Question:
Simplify this expression: (10*z - 29)*(-13*z**3 + 12*z - 32)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -130*z**4 + 377*z**3 + 120*z**2 - 668*z + 928

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (10*z - 29)*(-13*z**3 + 12*z - 32)
Expanding the part (10*z - 29) using the distributive property, and we got: (10*z)*(-13*z**3 + 12*z - 32) - 29*(-13*z**3 + 12*z - 32)
<replace-#Step 1>#Step 2:
Current expression: (10*z)*(-13*z**3 + 12*z - 32) - 29*(-13*z**3 + 12*z - 32)</replace>
Simplifying the partial expression: -29*(-13*z**3 + 12*z - 32)
Expanding the part (-13*z**3 + 12*z - 32) using the distributive property, and we got: (12*z)*(-29) - 13*z**3*(-29) - 32*(-29)
Replacing -29*(-13*z**3 + 12*z - 32) with (12*z)*(-29) - 13*z**3*(-29) - 32*(-29) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (10*z)*(-13*z**3 + 12*z - 32) + (12*z)*(-29) - 13*z**3*(-29) + 928</replace>
Simplifying the partial expression: (10*z)*(-13*z**3 + 12*z - 32)
Expanding the part (-13*z**3 + 12*z - 32) using the distributive property, and we got: -320*z + (10*z)*(12*z) + (10*z)*(-13*z**3)
Replacing (10*z)*(-13*z**3 + 12*z - 32) with -320*z + (10*z)*(12*z) + (10*z)*(-13*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -32*10*z + (10*z)*(12*z) + (10*z)*(-13*z**3) + (12*z)*(-29) - 13*z**3*(-29) + 928</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-13*z**3)*-29 = 377*z**3
  (-13*z**3)*(10*z) = -130*z**4
  (12*z)*-29 = -348*z
  (12*z)*(10*z) = 120*z**2
  -32*10*z = -320*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -130*z**4 + 377*z**3 + 120*z**2 - 348*z - 320*z + 928</replace>
Combining like terms, got -130*z**4 + 377*z**3 + 120*z**2 - 668*z + 928
<replace-#Step 5>#Step 6:
Current expression: -130*z**4 + 377*z**3 + 120*z**2 - 668*z + 928</replace>
No more calculations needed.
<answer>-130*z**4 + 377*z**3 + 120*z**2 - 668*z + 928</answer>


Question:
Simplify this expression: (47*y**3 + 4)*(-20*y**2 + 26*y - 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: -940*y**5 + 1222*y**4 - 1692*y**3 - 80*y**2 + 104*y - 144

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (47*y**3 + 4)*(-20*y**2 + 26*y - 36)
Expanding the part (47*y**3 + 4) using the distributive property, and we got: (47*y**3)*(-20*y**2 + 26*y - 36) + 4*(-20*y**2 + 26*y - 36)
<replace-#Step 1>#Step 2:
Current expression: (47*y**3)*(-20*y**2 + 26*y - 36) + 4*(-20*y**2 + 26*y - 36)</replace>
Simplifying the partial expression: 4*(-20*y**2 + 26*y - 36)
Expanding the part (-20*y**2 + 26*y - 36) using the distributive property, and we got: (26*y)*4 - 20*y**2*4 - 36*4
Replacing 4*(-20*y**2 + 26*y - 36) with (26*y)*4 - 20*y**2*4 - 36*4 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (26*y)*4 - 20*y**2*4 + (47*y**3)*(-20*y**2 + 26*y - 36) - 144</replace>
Simplifying the partial expression: (47*y**3)*(-20*y**2 + 26*y - 36)
Expanding the part (-20*y**2 + 26*y - 36) using the distributive property, and we got: -1692*y**3 + (26*y)*(47*y**3) + (-20*y**2)*(47*y**3)
Replacing (47*y**3)*(-20*y**2 + 26*y - 36) with -1692*y**3 + (26*y)*(47*y**3) + (-20*y**2)*(47*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -36*47*y**3 + (26*y)*(47*y**3) + (26*y)*4 + (-20*y**2)*(47*y**3) - 20*y**2*4 - 144</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-20*y**2)*4 = -80*y**2
  (-20*y**2)*(47*y**3) = -940*y**5
  (26*y)*4 = 104*y
  (26*y)*(47*y**3) = 1222*y**4
  -36*47*y**3 = -1692*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -940*y**5 + 1222*y**4 - 1692*y**3 - 80*y**2 + 104*y - 144</replace>
No more calculations needed.
<answer>-940*y**5 + 1222*y**4 - 1692*y**3 - 80*y**2 + 104*y - 144</answer>


Question:
Simplify this expression: (29*x**2 + 6*x)*(-21*x**3 + 3*x**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -609*x**5 - 39*x**4 + 18*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: (29*x**2 + 6*x)*(-21*x**3 + 3*x**2)
Expanding the part (-21*x**3 + 3*x**2) using the distributive property, and we got: (3*x**2)*(29*x**2 + 6*x) + (-21*x**3)*(29*x**2 + 6*x)
<replace-#Step 1>#Step 2:
Current expression: (3*x**2)*(29*x**2 + 6*x) + (-21*x**3)*(29*x**2 + 6*x)</replace>
Simplifying the partial expression: (-21*x**3)*(29*x**2 + 6*x)
Expanding the part (29*x**2 + 6*x) using the distributive property, and we got: (6*x)*(-21*x**3) + (29*x**2)*(-21*x**3)
Replacing (-21*x**3)*(29*x**2 + 6*x) with (6*x)*(-21*x**3) + (29*x**2)*(-21*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (6*x)*(-21*x**3) + (3*x**2)*(29*x**2 + 6*x) + (29*x**2)*(-21*x**3)</replace>
Simplifying the partial expression: (3*x**2)*(29*x**2 + 6*x)
Expanding the part (29*x**2 + 6*x) using the distributive property, and we got: (6*x)*(3*x**2) + (3*x**2)*(29*x**2)
Replacing (3*x**2)*(29*x**2 + 6*x) with (6*x)*(3*x**2) + (3*x**2)*(29*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (6*x)*(3*x**2) + (6*x)*(-21*x**3) + (3*x**2)*(29*x**2) + (29*x**2)*(-21*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (6*x)*(-21*x**3) = -126*x**4
  (6*x)*(3*x**2) = 18*x**3
  (29*x**2)*(-21*x**3) = -609*x**5
  (29*x**2)*(3*x**2) = 87*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -609*x**5 - 126*x**4 + 87*x**4 + 18*x**3</replace>
Combining like terms, got -609*x**5 - 39*x**4 + 18*x**3
<replace-#Step 5>#Step 6:
Current expression: -609*x**5 - 39*x**4 + 18*x**3</replace>
No more calculations needed.
<answer>-609*x**5 - 39*x**4 + 18*x**3</answer>


Question:
Calculate the following: (-36*y**3 - 28*y)*(41*y**3 - 28*y + 24)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1476*y**6 - 140*y**4 - 864*y**3 + 784*y**2 - 672*y


Question:
Simplify this expression: (-2*y**2 - 24)*(26*y**3 + 33*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: -52*y**5 - 66*y**4 - 624*y**3 - 792*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: (-2*y**2 - 24)*(26*y**3 + 33*y**2)
Expanding the part (-2*y**2 - 24) using the distributive property, and we got: (-2*y**2)*(26*y**3 + 33*y**2) - 24*(26*y**3 + 33*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-2*y**2)*(26*y**3 + 33*y**2) - 24*(26*y**3 + 33*y**2)</replace>
Simplifying the partial expression: -24*(26*y**3 + 33*y**2)
Expanding the part (26*y**3 + 33*y**2) using the distributive property, and we got: (33*y**2)*(-24) + (26*y**3)*(-24)
Replacing -24*(26*y**3 + 33*y**2) with (33*y**2)*(-24) + (26*y**3)*(-24) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-2*y**2)*(26*y**3 + 33*y**2) + (33*y**2)*(-24) + (26*y**3)*(-24)</replace>
Simplifying the partial expression: (-2*y**2)*(26*y**3 + 33*y**2)
Expanding the part (26*y**3 + 33*y**2) using the distributive property, and we got: (-2*y**2)*(33*y**2) + (-2*y**2)*(26*y**3)
Replacing (-2*y**2)*(26*y**3 + 33*y**2) with (-2*y**2)*(33*y**2) + (-2*y**2)*(26*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-2*y**2)*(33*y**2) + (-2*y**2)*(26*y**3) + (33*y**2)*(-24) + (26*y**3)*(-24)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (26*y**3)*-24 = -624*y**3
  (26*y**3)*(-2*y**2) = -52*y**5
  (33*y**2)*-24 = -792*y**2
  (33*y**2)*(-2*y**2) = -66*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -52*y**5 - 66*y**4 - 624*y**3 - 792*y**2</replace>
No more calculations needed.
<answer>-52*y**5 - 66*y**4 - 624*y**3 - 792*y**2</answer>


Question:
Simplify this expression: (38 - 10*y**3)*(-15*y**2 + y - 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: 150*y**5 - 10*y**4 + 100*y**3 - 570*y**2 + 38*y - 380

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: (38 - 10*y**3)*(-15*y**2 + y - 10)
Expanding the part (38 - 10*y**3) using the distributive property, and we got: (-10*y**3)*(-15*y**2 + y - 10) + 38*(-15*y**2 + y - 10)
<replace-#Step 1>#Step 2:
Current expression: (-10*y**3)*(-15*y**2 + y - 10) + 38*(-15*y**2 + y - 10)</replace>
Simplifying the partial expression: 38*(-15*y**2 + y - 10)
Expanding the part (-15*y**2 + y - 10) using the distributive property, and we got: y*38 - 15*y**2*38 - 10*38
Replacing 38*(-15*y**2 + y - 10) with y*38 - 15*y**2*38 - 10*38 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: y*38 - 15*y**2*38 + (-10*y**3)*(-15*y**2 + y - 10) - 380</replace>
Simplifying the partial expression: (-10*y**3)*(-15*y**2 + y - 10)
Expanding the part (-15*y**2 + y - 10) using the distributive property, and we got: -(-1)*100*y**3 + y*(-10*y**3) + (-15*y**2)*(-10*y**3)
Replacing (-10*y**3)*(-15*y**2 + y - 10) with -(-1)*100*y**3 + y*(-10*y**3) + (-15*y**2)*(-10*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -10*(-10)*y**3 + y*(-10*y**3) + y*38 + (-15*y**2)*(-10*y**3) - 15*y**2*38 - 380</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  y*38 = 38*y
  y*(-10*y**3) = -10*y**4
  (-15*y**2)*38 = -570*y**2
  (-15*y**2)*(-10*y**3) = 150*y**5
  -10*-10*y**3 = 100*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 150*y**5 - 10*y**4 + 100*y**3 - 570*y**2 + 38*y - 380</replace>
No more calculations needed.
<answer>150*y**5 - 10*y**4 + 100*y**3 - 570*y**2 + 38*y - 380</answer>


Question:
Simplify this expression: (-47*x**2 - 35*x)*(-4*x**3 - 23*x**2 + 34*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: 188*x**5 + 1221*x**4 - 793*x**3 - 1190*x**2


Question:
Calculate the following: (28*y**2 - 48)*(-49*y**3 - 39*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: -1372*y**5 - 1092*y**4 + 2352*y**3 + 1872*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: (28*y**2 - 48)*(-49*y**3 - 39*y**2)
Expanding the part (28*y**2 - 48) using the distributive property, and we got: (28*y**2)*(-49*y**3 - 39*y**2) - 48*(-49*y**3 - 39*y**2)
<replace-#Step 1>#Step 2:
Current expression: (28*y**2)*(-49*y**3 - 39*y**2) - 48*(-49*y**3 - 39*y**2)</replace>
Simplifying the partial expression: -48*(-49*y**3 - 39*y**2)
Expanding the part (-49*y**3 - 39*y**2) using the distributive property, and we got: -39*y**2*(-48) - 49*y**3*(-48)
Replacing -48*(-49*y**3 - 39*y**2) with -39*y**2*(-48) - 49*y**3*(-48) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -39*y**2*(-48) + (28*y**2)*(-49*y**3 - 39*y**2) - 49*y**3*(-48)</replace>
Simplifying the partial expression: (28*y**2)*(-49*y**3 - 39*y**2)
Expanding the part (-49*y**3 - 39*y**2) using the distributive property, and we got: (-39*y**2)*(28*y**2) + (28*y**2)*(-49*y**3)
Replacing (28*y**2)*(-49*y**3 - 39*y**2) with (-39*y**2)*(28*y**2) + (28*y**2)*(-49*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-39*y**2)*(28*y**2) - 39*y**2*(-48) + (28*y**2)*(-49*y**3) - 49*y**3*(-48)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-49*y**3)*-48 = 2352*y**3
  (-49*y**3)*(28*y**2) = -1372*y**5
  (-39*y**2)*-48 = 1872*y**2
  (-39*y**2)*(28*y**2) = -1092*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1372*y**5 - 1092*y**4 + 2352*y**3 + 1872*y**2</replace>
No more calculations needed.
<answer>-1372*y**5 - 1092*y**4 + 2352*y**3 + 1872*y**2</answer>


Question:
Simplify this expression: -6*y**3*(38*y**3 - 3*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: -228*y**6 + 18*y**5 - 84*y**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -6*y**3*(38*y**3 - 3*y**2 + 14)
Expanding the part (38*y**3 - 3*y**2 + 14) using the distributive property, and we got: 14*(-6*y**3) + (-3*y**2)*(-6*y**3) + (-6*y**3)*(38*y**3)
<replace-#Step 1>#Step 2:
Current expression: 14*(-6*y**3) + (-3*y**2)*(-6*y**3) + (-6*y**3)*(38*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  14*(-6*y**3) = -84*y**3
  (-3*y**2)*(-6*y**3) = 18*y**5
  (38*y**3)*(-6*y**3) = -228*y**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -228*y**6 + 18*y**5 - 84*y**3</replace>
No more calculations needed.
<answer>-228*y**6 + 18*y**5 - 84*y**3</answer>


Question:
Calculate the following: 56*z**2*(-29*z**3 - 47)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1624*z**5 - 2632*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: 56*z**2*(-29*z**3 - 47)
Expanding the part (-29*z**3 - 47) using the distributive property, and we got: -2632*z**2 + (56*z**2)*(-29*z**3)
<replace-#Step 1>#Step 2:
Current expression: -2632*z**2 + (56*z**2)*(-29*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -47*(56*z**2) = -2632*z**2
  (-29*z**3)*(56*z**2) = -1624*z**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1624*z**5 - 2632*z**2</replace>
No more calculations needed.
<answer>-1624*z**5 - 2632*z**2</answer>


Question:
Simplify this expression: -16*y**2*(3*y - 38)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -48*y**3 + 608*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: -16*y**2*(3*y - 38)
Expanding the part (3*y - 38) using the distributive property, and we got: -(-1)*608*y**2 + (3*y)*(-16*y**2)
<replace-#Step 1>#Step 2:
Current expression: -(-1)*608*y**2 + (3*y)*(-16*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -38*(-16*y**2) = 608*y**2
  (3*y)*(-16*y**2) = -48*y**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -48*y**3 + 608*y**2</replace>
No more calculations needed.
<answer>-48*y**3 + 608*y**2</answer>


Question:
Simplify this expression: (29 - 32*y)*(-23*y**3 - 11*y - 38)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 736*y**4 - 667*y**3 + 352*y**2 + 897*y - 1102

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 - 32*y)*(-23*y**3 - 11*y - 38)
Expanding the part (29 - 32*y) using the distributive property, and we got: (-32*y)*(-23*y**3 - 11*y - 38) + 29*(-23*y**3 - 11*y - 38)
<replace-#Step 1>#Step 2:
Current expression: (-32*y)*(-23*y**3 - 11*y - 38) + 29*(-23*y**3 - 11*y - 38)</replace>
Simplifying the partial expression: 29*(-23*y**3 - 11*y - 38)
Expanding the part (-23*y**3 - 11*y - 38) using the distributive property, and we got: -11*y*29 - 23*y**3*29 - 38*29
Replacing 29*(-23*y**3 - 11*y - 38) with -11*y*29 - 23*y**3*29 - 38*29 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-32*y)*(-23*y**3 - 11*y - 38) - 11*y*29 - 23*y**3*29 - 1102</replace>
Simplifying the partial expression: (-32*y)*(-23*y**3 - 11*y - 38)
Expanding the part (-23*y**3 - 11*y - 38) using the distributive property, and we got: (-32*y)*(-11*y) + (-32*y)*(-23*y**3) - (-1)*1216*y
Replacing (-32*y)*(-23*y**3 - 11*y - 38) with (-32*y)*(-11*y) + (-32*y)*(-23*y**3) - (-1)*1216*y in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-32*y)*(-11*y) + (-32*y)*(-23*y**3) - 11*y*29 - 38*(-32)*y - 23*y**3*29 - 1102</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-23*y**3)*29 = -667*y**3
  (-23*y**3)*(-32*y) = 736*y**4
  (-11*y)*29 = -319*y
  (-11*y)*(-32*y) = 352*y**2
  -38*-32*y = 1216*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 736*y**4 - 667*y**3 + 352*y**2 - 319*y + 1216*y - 1102</replace>
Combining like terms, got 736*y**4 - 667*y**3 + 352*y**2 + 897*y - 1102
<replace-#Step 5>#Step 6:
Current expression: 736*y**4 - 667*y**3 + 352*y**2 + 897*y - 1102</replace>
No more calculations needed.
<answer>736*y**4 - 667*y**3 + 352*y**2 + 897*y - 1102</answer>


Question:
Calculate the following: (22*z - 29)*(25*z**3 - 2*z - 32)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 550*z**4 - 725*z**3 - 44*z**2 - 646*z + 928

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (22*z - 29)*(25*z**3 - 2*z - 32)
Expanding the part (22*z - 29) using the distributive property, and we got: (22*z)*(25*z**3 - 2*z - 32) - 29*(25*z**3 - 2*z - 32)
<replace-#Step 1>#Step 2:
Current expression: (22*z)*(25*z**3 - 2*z - 32) - 29*(25*z**3 - 2*z - 32)</replace>
Simplifying the partial expression: -29*(25*z**3 - 2*z - 32)
Expanding the part (25*z**3 - 2*z - 32) using the distributive property, and we got: -2*z*(-29) + (25*z**3)*(-29) - 32*(-29)
Replacing -29*(25*z**3 - 2*z - 32) with -2*z*(-29) + (25*z**3)*(-29) - 32*(-29) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -2*z*(-29) + (22*z)*(25*z**3 - 2*z - 32) + (25*z**3)*(-29) + 928</replace>
Simplifying the partial expression: (22*z)*(25*z**3 - 2*z - 32)
Expanding the part (25*z**3 - 2*z - 32) using the distributive property, and we got: (-2*z)*(22*z) - 704*z + (22*z)*(25*z**3)
Replacing (22*z)*(25*z**3 - 2*z - 32) with (-2*z)*(22*z) - 704*z + (22*z)*(25*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-2*z)*(22*z) - 2*z*(-29) - 32*22*z + (22*z)*(25*z**3) + (25*z**3)*(-29) + 928</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-2*z)*-29 = 58*z
  (-2*z)*(22*z) = -44*z**2
  (25*z**3)*-29 = -725*z**3
  (25*z**3)*(22*z) = 550*z**4
  -32*22*z = -704*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 550*z**4 - 725*z**3 - 44*z**2 - 704*z + 58*z + 928</replace>
Combining like terms, got 550*z**4 - 725*z**3 - 44*z**2 - 646*z + 928
<replace-#Step 5>#Step 6:
Current expression: 550*z**4 - 725*z**3 - 44*z**2 - 646*z + 928</replace>
No more calculations needed.
<answer>550*z**4 - 725*z**3 - 44*z**2 - 646*z + 928</answer>


Question:
Simplify this expression: -120*x**2*(-68*x**2 - 32*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: 8160*x**4 + 3840*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: -120*x**2*(-68*x**2 - 32*x)
Expanding the part (-68*x**2 - 32*x) using the distributive property, and we got: (-32*x)*(-120*x**2) + (-120*x**2)*(-68*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-32*x)*(-120*x**2) + (-120*x**2)*(-68*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-68*x**2)*(-120*x**2) = 8160*x**4
  (-32*x)*(-120*x**2) = 3840*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 8160*x**4 + 3840*x**3</replace>
No more calculations needed.
<answer>8160*x**4 + 3840*x**3</answer>


Question:
Simplify this expression: 1275*z**3 + 2465*z**2 + 2380*z - 3145
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1275*z**3 + 2465*z**2 + 2380*z - 3145

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: 1275*z**3 + 2465*z**2 + 2380*z - 3145
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: 1275*z**3 + 2465*z**2 + 2380*z - 3145</replace>
No more calculations needed.
<answer>1275*z**3 + 2465*z**2 + 2380*z - 3145</answer>


Question:
Calculate the following: -51*y*(-9*y**2 - 21*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: 459*y**3 + 1071*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: -51*y*(-9*y**2 - 21*y)
Expanding the part (-9*y**2 - 21*y) using the distributive property, and we got: (-51*y)*(-21*y) + (-51*y)*(-9*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-51*y)*(-21*y) + (-51*y)*(-9*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-21*y)*(-51*y) = 1071*y**2
  (-9*y**2)*(-51*y) = 459*y**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 459*y**3 + 1071*y**2</replace>
No more calculations needed.
<answer>459*y**3 + 1071*y**2</answer>


Question:
Calculate the following: (-41*y - 25)*(39*y**3 + 3*y**2 - 32*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: -1599*y**4 - 1098*y**3 + 1237*y**2 + 1456*y + 400


Question:
Calculate the following: (-44*x**3 + 6*x)*(11*x**3 + 30*x**2 + 4*x + 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: -484*x**6 - 1320*x**5 - 110*x**4 - 1140*x**3 + 24*x**2 + 180*x


Question:
Simplify this expression: (14*x**3 - 23*x**2 + 20*x)*(32*x**3 - 6*x**2 - 50)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 448*x**6 - 820*x**5 + 778*x**4 - 820*x**3 + 1150*x**2 - 1000*x


Question:
Simplify this expression: (9*z - 3)*(-56*z**2 - 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: -504*z**3 + 168*z**2 - 144*z + 48

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 - 3)*(-56*z**2 - 16)
Expanding the part (-56*z**2 - 16) using the distributive property, and we got: (-56*z**2)*(9*z - 3) - 16*(9*z - 3)
<replace-#Step 1>#Step 2:
Current expression: (-56*z**2)*(9*z - 3) - 16*(9*z - 3)</replace>
Simplifying the partial expression: -16*(9*z - 3)
Expanding the part (9*z - 3) using the distributive property, and we got: (9*z)*(-16) - 3*(-16)
Replacing -16*(9*z - 3) with (9*z)*(-16) - 3*(-16) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (9*z)*(-16) + (-56*z**2)*(9*z - 3) + 48</replace>
Simplifying the partial expression: (-56*z**2)*(9*z - 3)
Expanding the part (9*z - 3) using the distributive property, and we got: -(-1)*168*z**2 + (9*z)*(-56*z**2)
Replacing (-56*z**2)*(9*z - 3) with -(-1)*168*z**2 + (9*z)*(-56*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -3*(-56)*z**2 + (9*z)*(-56*z**2) + (9*z)*(-16) + 48</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (9*z)*-16 = -144*z
  (9*z)*(-56*z**2) = -504*z**3
  -3*-56*z**2 = 168*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -504*z**3 + 168*z**2 - 144*z + 48</replace>
No more calculations needed.
<answer>-504*z**3 + 168*z**2 - 144*z + 48</answer>


Question:
Simplify this expression: (-13*z**3 - 22*z**2 - 44)*(-11*z**3 + 50*z + 34)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 143*z**6 + 242*z**5 - 650*z**4 - 1058*z**3 - 748*z**2 - 2200*z - 1496


Question:
Calculate the following: (67*z**2 + 23)*(-7*z**3 - 35*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: -469*z**5 - 2345*z**4 - 161*z**3 - 805*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 + 23)*(-7*z**3 - 35*z**2)
Expanding the part (67*z**2 + 23) using the distributive property, and we got: (67*z**2)*(-7*z**3 - 35*z**2) + 23*(-7*z**3 - 35*z**2)
<replace-#Step 1>#Step 2:
Current expression: (67*z**2)*(-7*z**3 - 35*z**2) + 23*(-7*z**3 - 35*z**2)</replace>
Simplifying the partial expression: 23*(-7*z**3 - 35*z**2)
Expanding the part (-7*z**3 - 35*z**2) using the distributive property, and we got: -35*z**2*23 - 7*z**3*23
Replacing 23*(-7*z**3 - 35*z**2) with -35*z**2*23 - 7*z**3*23 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -35*z**2*23 + (67*z**2)*(-7*z**3 - 35*z**2) - 7*z**3*23</replace>
Simplifying the partial expression: (67*z**2)*(-7*z**3 - 35*z**2)
Expanding the part (-7*z**3 - 35*z**2) using the distributive property, and we got: (-35*z**2)*(67*z**2) + (67*z**2)*(-7*z**3)
Replacing (67*z**2)*(-7*z**3 - 35*z**2) with (-35*z**2)*(67*z**2) + (67*z**2)*(-7*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-35*z**2)*(67*z**2) - 35*z**2*23 + (67*z**2)*(-7*z**3) - 7*z**3*23</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-35*z**2)*23 = -805*z**2
  (-35*z**2)*(67*z**2) = -2345*z**4
  (-7*z**3)*23 = -161*z**3
  (-7*z**3)*(67*z**2) = -469*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -469*z**5 - 2345*z**4 - 161*z**3 - 805*z**2</replace>
No more calculations needed.
<answer>-469*z**5 - 2345*z**4 - 161*z**3 - 805*z**2</answer>