Question:
Simplify this expression: (24*x**2 + 15)*(-4*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: -96*x**5 + 240*x**4 - 60*x**3 + 150*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: (24*x**2 + 15)*(-4*x**3 + 10*x**2)
Expanding the part (24*x**2 + 15) using the distributive property, and we got: (24*x**2)*(-4*x**3 + 10*x**2) + 15*(-4*x**3 + 10*x**2)
<replace-#Step 1>#Step 2:
Current expression: (24*x**2)*(-4*x**3 + 10*x**2) + 15*(-4*x**3 + 10*x**2)</replace>
Simplifying the partial expression: 15*(-4*x**3 + 10*x**2)
Expanding the part (-4*x**3 + 10*x**2) using the distributive property, and we got: (10*x**2)*15 - 4*x**3*15
Replacing 15*(-4*x**3 + 10*x**2) with (10*x**2)*15 - 4*x**3*15 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (10*x**2)*15 + (24*x**2)*(-4*x**3 + 10*x**2) - 4*x**3*15</replace>
Simplifying the partial expression: (24*x**2)*(-4*x**3 + 10*x**2)
Expanding the part (-4*x**3 + 10*x**2) using the distributive property, and we got: (10*x**2)*(24*x**2) + (24*x**2)*(-4*x**3)
Replacing (24*x**2)*(-4*x**3 + 10*x**2) with (10*x**2)*(24*x**2) + (24*x**2)*(-4*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (10*x**2)*(24*x**2) + (10*x**2)*15 + (24*x**2)*(-4*x**3) - 4*x**3*15</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-4*x**3)*15 = -60*x**3
  (-4*x**3)*(24*x**2) = -96*x**5
  (10*x**2)*15 = 150*x**2
  (10*x**2)*(24*x**2) = 240*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -96*x**5 + 240*x**4 - 60*x**3 + 150*x**2</replace>
No more calculations needed.
<answer>-96*x**5 + 240*x**4 - 60*x**3 + 150*x**2</answer>


Question:
Simplify this expression: (-32*y**3 + 39*y**2 + 5)*(-18*y**3 - 4*y + 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: 576*y**6 - 702*y**5 + 128*y**4 - 694*y**3 + 546*y**2 - 20*y + 70


Question:
Simplify this expression: (-15*x**3 - 66)*(6*x**3 + 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: -90*x**6 - 636*x**3 - 1056

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-15*x**3 - 66)*(6*x**3 + 16)
Expanding the part (-15*x**3 - 66) using the distributive property, and we got: (-15*x**3)*(6*x**3 + 16) - 66*(6*x**3 + 16)
<replace-#Step 1>#Step 2:
Current expression: (-15*x**3)*(6*x**3 + 16) - 66*(6*x**3 + 16)</replace>
Simplifying the partial expression: -66*(6*x**3 + 16)
Expanding the part (6*x**3 + 16) using the distributive property, and we got: (6*x**3)*(-66) + 16*(-66)
Replacing -66*(6*x**3 + 16) with (6*x**3)*(-66) + 16*(-66) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-15*x**3)*(6*x**3 + 16) + (6*x**3)*(-66) - 1056</replace>
Simplifying the partial expression: (-15*x**3)*(6*x**3 + 16)
Expanding the part (6*x**3 + 16) using the distributive property, and we got: 16*(-15*x**3) + (-15*x**3)*(6*x**3)
Replacing (-15*x**3)*(6*x**3 + 16) with 16*(-15*x**3) + (-15*x**3)*(6*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 16*(-15)*x**3 + (-15*x**3)*(6*x**3) + (6*x**3)*(-66) - 1056</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (6*x**3)*-66 = -396*x**3
  (6*x**3)*(-15*x**3) = -90*x**6
  16*-15*x**3 = -240*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -90*x**6 - 396*x**3 - 240*x**3 - 1056</replace>
Combining like terms, got -90*x**6 - 636*x**3 - 1056
<replace-#Step 5>#Step 6:
Current expression: -90*x**6 - 636*x**3 - 1056</replace>
No more calculations needed.
<answer>-90*x**6 - 636*x**3 - 1056</answer>


Question:
Simplify this expression: (14 - 31*z)*(33*z**2 - 12*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: -1023*z**3 + 834*z**2 - 168*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: (14 - 31*z)*(33*z**2 - 12*z)
Expanding the part (14 - 31*z) using the distributive property, and we got: (-31*z)*(33*z**2 - 12*z) + 14*(33*z**2 - 12*z)
<replace-#Step 1>#Step 2:
Current expression: (-31*z)*(33*z**2 - 12*z) + 14*(33*z**2 - 12*z)</replace>
Simplifying the partial expression: 14*(33*z**2 - 12*z)
Expanding the part (33*z**2 - 12*z) using the distributive property, and we got: -12*z*14 + (33*z**2)*14
Replacing 14*(33*z**2 - 12*z) with -12*z*14 + (33*z**2)*14 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-31*z)*(33*z**2 - 12*z) - 12*z*14 + (33*z**2)*14</replace>
Simplifying the partial expression: (-31*z)*(33*z**2 - 12*z)
Expanding the part (33*z**2 - 12*z) using the distributive property, and we got: (-31*z)*(-12*z) + (-31*z)*(33*z**2)
Replacing (-31*z)*(33*z**2 - 12*z) with (-31*z)*(-12*z) + (-31*z)*(33*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-31*z)*(-12*z) + (-31*z)*(33*z**2) - 12*z*14 + (33*z**2)*14</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-12*z)*14 = -168*z
  (-12*z)*(-31*z) = 372*z**2
  (33*z**2)*14 = 462*z**2
  (33*z**2)*(-31*z) = -1023*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1023*z**3 + 372*z**2 + 462*z**2 - 168*z</replace>
Combining like terms, got -1023*z**3 + 834*z**2 - 168*z
<replace-#Step 5>#Step 6:
Current expression: -1023*z**3 + 834*z**2 - 168*z</replace>
No more calculations needed.
<answer>-1023*z**3 + 834*z**2 - 168*z</answer>


Question:
Calculate the following: -767*x**4
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -767*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: -767*x**4
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: -767*x**4</replace>
No more calculations needed.
<answer>-767*x**4</answer>


Question:
Simplify this expression: (50 - 7*y**2)*(51*y**2 + 48*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: -357*y**4 - 336*y**3 + 2550*y**2 + 2400*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: (50 - 7*y**2)*(51*y**2 + 48*y)
Expanding the part (50 - 7*y**2) using the distributive property, and we got: (-7*y**2)*(51*y**2 + 48*y) + 50*(51*y**2 + 48*y)
<replace-#Step 1>#Step 2:
Current expression: (-7*y**2)*(51*y**2 + 48*y) + 50*(51*y**2 + 48*y)</replace>
Simplifying the partial expression: 50*(51*y**2 + 48*y)
Expanding the part (51*y**2 + 48*y) using the distributive property, and we got: (48*y)*50 + (51*y**2)*50
Replacing 50*(51*y**2 + 48*y) with (48*y)*50 + (51*y**2)*50 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (48*y)*50 + (-7*y**2)*(51*y**2 + 48*y) + (51*y**2)*50</replace>
Simplifying the partial expression: (-7*y**2)*(51*y**2 + 48*y)
Expanding the part (51*y**2 + 48*y) using the distributive property, and we got: (48*y)*(-7*y**2) + (-7*y**2)*(51*y**2)
Replacing (-7*y**2)*(51*y**2 + 48*y) with (48*y)*(-7*y**2) + (-7*y**2)*(51*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (48*y)*(-7*y**2) + (48*y)*50 + (-7*y**2)*(51*y**2) + (51*y**2)*50</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (48*y)*50 = 2400*y
  (48*y)*(-7*y**2) = -336*y**3
  (51*y**2)*50 = 2550*y**2
  (51*y**2)*(-7*y**2) = -357*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -357*y**4 - 336*y**3 + 2550*y**2 + 2400*y</replace>
No more calculations needed.
<answer>-357*y**4 - 336*y**3 + 2550*y**2 + 2400*y</answer>


Question:
Simplify this expression: (-45*y**2 - 22)*(-42*y**2 - 14*y + 23)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1890*y**4 + 630*y**3 - 111*y**2 + 308*y - 506

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*y**2 - 22)*(-42*y**2 - 14*y + 23)
Expanding the part (-45*y**2 - 22) using the distributive property, and we got: (-45*y**2)*(-42*y**2 - 14*y + 23) - 22*(-42*y**2 - 14*y + 23)
<replace-#Step 1>#Step 2:
Current expression: (-45*y**2)*(-42*y**2 - 14*y + 23) - 22*(-42*y**2 - 14*y + 23)</replace>
Simplifying the partial expression: -22*(-42*y**2 - 14*y + 23)
Expanding the part (-42*y**2 - 14*y + 23) using the distributive property, and we got: -14*y*(-22) - 42*y**2*(-22) + 23*(-22)
Replacing -22*(-42*y**2 - 14*y + 23) with -14*y*(-22) - 42*y**2*(-22) + 23*(-22) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -14*y*(-22) + (-45*y**2)*(-42*y**2 - 14*y + 23) - 42*y**2*(-22) - 506</replace>
Simplifying the partial expression: (-45*y**2)*(-42*y**2 - 14*y + 23)
Expanding the part (-42*y**2 - 14*y + 23) using the distributive property, and we got: (-14*y)*(-45*y**2) + 23*(-45*y**2) + (-45*y**2)*(-42*y**2)
Replacing (-45*y**2)*(-42*y**2 - 14*y + 23) with (-14*y)*(-45*y**2) + 23*(-45*y**2) + (-45*y**2)*(-42*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-14*y)*(-45*y**2) - 14*y*(-22) + 23*(-45)*y**2 + (-45*y**2)*(-42*y**2) - 42*y**2*(-22) - 506</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-42*y**2)*-22 = 924*y**2
  (-42*y**2)*(-45*y**2) = 1890*y**4
  (-14*y)*-22 = 308*y
  (-14*y)*(-45*y**2) = 630*y**3
  23*-45*y**2 = -1035*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1890*y**4 + 630*y**3 - 1035*y**2 + 924*y**2 + 308*y - 506</replace>
Combining like terms, got 1890*y**4 + 630*y**3 - 111*y**2 + 308*y - 506
<replace-#Step 5>#Step 6:
Current expression: 1890*y**4 + 630*y**3 - 111*y**2 + 308*y - 506</replace>
No more calculations needed.
<answer>1890*y**4 + 630*y**3 - 111*y**2 + 308*y - 506</answer>


Question:
Simplify this expression: (-z**3 + 42*z**2)*(37*z**3 + 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: -37*z**6 + 1553*z**5 + 42*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: (-z**3 + 42*z**2)*(37*z**3 + z**2)
Expanding the part (37*z**3 + z**2) using the distributive property, and we got: z**2*(-z**3 + 42*z**2) + (37*z**3)*(-z**3 + 42*z**2)
<replace-#Step 1>#Step 2:
Current expression: z**2*(-z**3 + 42*z**2) + (37*z**3)*(-z**3 + 42*z**2)</replace>
Simplifying the partial expression: z**2*(-z**3 + 42*z**2)
Expanding the part (-z**3 + 42*z**2) using the distributive property, and we got: z**2*(42*z**2) + z**2*(-z**3)
Replacing z**2*(-z**3 + 42*z**2) with z**2*(42*z**2) + z**2*(-z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: z**2*(42*z**2) + z**2*(-z**3) + (37*z**3)*(-z**3 + 42*z**2)</replace>
Simplifying the partial expression: (37*z**3)*(-z**3 + 42*z**2)
Expanding the part (-z**3 + 42*z**2) using the distributive property, and we got: (42*z**2)*(37*z**3) + (-z**3)*(37*z**3)
Replacing (37*z**3)*(-z**3 + 42*z**2) with (42*z**2)*(37*z**3) + (-z**3)*(37*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: z**2*(42*z**2) + z**2*(-z**3) + (42*z**2)*(37*z**3) + (-z**3)*(37*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-z**3)*z**2 = -z**5
  (-z**3)*(37*z**3) = -37*z**6
  (42*z**2)*z**2 = 42*z**4
  (42*z**2)*(37*z**3) = 1554*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -37*z**6 - z**5 + 1554*z**5 + 42*z**4</replace>
Combining like terms, got -37*z**6 + 1553*z**5 + 42*z**4
<replace-#Step 5>#Step 6:
Current expression: -37*z**6 + 1553*z**5 + 42*z**4</replace>
No more calculations needed.
<answer>-37*z**6 + 1553*z**5 + 42*z**4</answer>


Question:
Simplify this expression: (-46*z - 16)*(-5*z**3 - 10*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: 230*z**4 + 80*z**3 + 460*z**2 + 160*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-46*z - 16)*(-5*z**3 - 10*z)
Expanding the part (-46*z - 16) using the distributive property, and we got: (-46*z)*(-5*z**3 - 10*z) - 16*(-5*z**3 - 10*z)
<replace-#Step 1>#Step 2:
Current expression: (-46*z)*(-5*z**3 - 10*z) - 16*(-5*z**3 - 10*z)</replace>
Simplifying the partial expression: -16*(-5*z**3 - 10*z)
Expanding the part (-5*z**3 - 10*z) using the distributive property, and we got: -10*z*(-16) - 5*z**3*(-16)
Replacing -16*(-5*z**3 - 10*z) with -10*z*(-16) - 5*z**3*(-16) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-46*z)*(-5*z**3 - 10*z) - 10*z*(-16) - 5*z**3*(-16)</replace>
Simplifying the partial expression: (-46*z)*(-5*z**3 - 10*z)
Expanding the part (-5*z**3 - 10*z) using the distributive property, and we got: (-46*z)*(-10*z) + (-46*z)*(-5*z**3)
Replacing (-46*z)*(-5*z**3 - 10*z) with (-46*z)*(-10*z) + (-46*z)*(-5*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-46*z)*(-10*z) + (-46*z)*(-5*z**3) - 10*z*(-16) - 5*z**3*(-16)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-10*z)*-16 = 160*z
  (-10*z)*(-46*z) = 460*z**2
  (-5*z**3)*-16 = 80*z**3
  (-5*z**3)*(-46*z) = 230*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 230*z**4 + 80*z**3 + 460*z**2 + 160*z</replace>
No more calculations needed.
<answer>230*z**4 + 80*z**3 + 460*z**2 + 160*z</answer>


Question:
Simplify this expression: (2 - 6*x**2)*(33*x**3 + 29)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -198*x**5 + 66*x**3 - 174*x**2 + 58

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 - 6*x**2)*(33*x**3 + 29)
Expanding the part (2 - 6*x**2) using the distributive property, and we got: (-6*x**2)*(33*x**3 + 29) + 2*(33*x**3 + 29)
<replace-#Step 1>#Step 2:
Current expression: (-6*x**2)*(33*x**3 + 29) + 2*(33*x**3 + 29)</replace>
Simplifying the partial expression: 2*(33*x**3 + 29)
Expanding the part (33*x**3 + 29) using the distributive property, and we got: (33*x**3)*2 + 29*2
Replacing 2*(33*x**3 + 29) with (33*x**3)*2 + 29*2 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-6*x**2)*(33*x**3 + 29) + (33*x**3)*2 + 58</replace>
Simplifying the partial expression: (-6*x**2)*(33*x**3 + 29)
Expanding the part (33*x**3 + 29) using the distributive property, and we got: 29*(-6*x**2) + (-6*x**2)*(33*x**3)
Replacing (-6*x**2)*(33*x**3 + 29) with 29*(-6*x**2) + (-6*x**2)*(33*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 29*(-6)*x**2 + (-6*x**2)*(33*x**3) + (33*x**3)*2 + 58</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (33*x**3)*2 = 66*x**3
  (33*x**3)*(-6*x**2) = -198*x**5
  29*-6*x**2 = -174*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -198*x**5 + 66*x**3 - 174*x**2 + 58</replace>
No more calculations needed.
<answer>-198*x**5 + 66*x**3 - 174*x**2 + 58</answer>


Question:
Simplify this expression: 8*z**2*(-26*z - 35)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -208*z**3 - 280*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: 8*z**2*(-26*z - 35)
Expanding the part (-26*z - 35) using the distributive property, and we got: (-26*z)*(8*z**2) - 280*z**2
<replace-#Step 1>#Step 2:
Current expression: (-26*z)*(8*z**2) - 280*z**2</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -35*(8*z**2) = -280*z**2
  (-26*z)*(8*z**2) = -208*z**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -208*z**3 - 280*z**2</replace>
No more calculations needed.
<answer>-208*z**3 - 280*z**2</answer>


Question:
Calculate the following: (x**2 + 11)*(-48*x**3 + 43*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: -48*x**5 + 43*x**4 - 528*x**3 + 473*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: (x**2 + 11)*(-48*x**3 + 43*x**2)
Expanding the part (x**2 + 11) using the distributive property, and we got: x**2*(-48*x**3 + 43*x**2) + 11*(-48*x**3 + 43*x**2)
<replace-#Step 1>#Step 2:
Current expression: x**2*(-48*x**3 + 43*x**2) + 11*(-48*x**3 + 43*x**2)</replace>
Simplifying the partial expression: 11*(-48*x**3 + 43*x**2)
Expanding the part (-48*x**3 + 43*x**2) using the distributive property, and we got: (43*x**2)*11 - 48*x**3*11
Replacing 11*(-48*x**3 + 43*x**2) with (43*x**2)*11 - 48*x**3*11 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: x**2*(-48*x**3 + 43*x**2) + (43*x**2)*11 - 48*x**3*11</replace>
Simplifying the partial expression: x**2*(-48*x**3 + 43*x**2)
Expanding the part (-48*x**3 + 43*x**2) using the distributive property, and we got: x**2*(43*x**2) + x**2*(-48*x**3)
Replacing x**2*(-48*x**3 + 43*x**2) with x**2*(43*x**2) + x**2*(-48*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: x**2*(43*x**2) + x**2*(-48*x**3) + (43*x**2)*11 - 48*x**3*11</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-48*x**3)*11 = -528*x**3
  (-48*x**3)*x**2 = -48*x**5
  (43*x**2)*11 = 473*x**2
  (43*x**2)*x**2 = 43*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -48*x**5 + 43*x**4 - 528*x**3 + 473*x**2</replace>
No more calculations needed.
<answer>-48*x**5 + 43*x**4 - 528*x**3 + 473*x**2</answer>


Question:
Calculate the following: -31*z**2*(50*z**2 + 31*z + 65)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1550*z**4 - 961*z**3 - 2015*z**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -31*z**2*(50*z**2 + 31*z + 65)
Expanding the part (50*z**2 + 31*z + 65) using the distributive property, and we got: 65*(-31*z**2) + (31*z)*(-31*z**2) + (-31*z**2)*(50*z**2)
<replace-#Step 1>#Step 2:
Current expression: 65*(-31*z**2) + (31*z)*(-31*z**2) + (-31*z**2)*(50*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  65*(-31*z**2) = -2015*z**2
  (31*z)*(-31*z**2) = -961*z**3
  (50*z**2)*(-31*z**2) = -1550*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1550*z**4 - 961*z**3 - 2015*z**2</replace>
No more calculations needed.
<answer>-1550*z**4 - 961*z**3 - 2015*z**2</answer>


Question:
Calculate the following: 10*y**3*(79*y**3 + 11)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 790*y**6 + 110*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: 10*y**3*(79*y**3 + 11)
Expanding the part (79*y**3 + 11) using the distributive property, and we got: 11*(10*y**3) + (10*y**3)*(79*y**3)
<replace-#Step 1>#Step 2:
Current expression: 11*(10*y**3) + (10*y**3)*(79*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  11*(10*y**3) = 110*y**3
  (79*y**3)*(10*y**3) = 790*y**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 790*y**6 + 110*y**3</replace>
No more calculations needed.
<answer>790*y**6 + 110*y**3</answer>


Question:
Calculate the following: (51*z**3 + 20*z**2)*(21*z**3 + 34*z**2 + 35*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: 1071*z**6 + 2154*z**5 + 2465*z**4 + 700*z**3


Question:
Simplify this expression: -6*y*(5 - 41*y**3)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 246*y**4 - 30*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: -6*y*(5 - 41*y**3)
Expanding the part (5 - 41*y**3) using the distributive property, and we got: (-6*y)*(-41*y**3) + 5*(-6*y)
<replace-#Step 1>#Step 2:
Current expression: (-6*y)*(-41*y**3) + 5*(-6*y)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  5*(-6*y) = -30*y
  (-41*y**3)*(-6*y) = 246*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 246*y**4 - 30*y</replace>
No more calculations needed.
<answer>246*y**4 - 30*y</answer>


Question:
Simplify this expression: (6*y**2 + 11*y)*(47*y**2 + 46*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: 282*y**4 + 793*y**3 + 506*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: (6*y**2 + 11*y)*(47*y**2 + 46*y)
Expanding the part (6*y**2 + 11*y) using the distributive property, and we got: (11*y)*(47*y**2 + 46*y) + (6*y**2)*(47*y**2 + 46*y)
<replace-#Step 1>#Step 2:
Current expression: (11*y)*(47*y**2 + 46*y) + (6*y**2)*(47*y**2 + 46*y)</replace>
Simplifying the partial expression: (6*y**2)*(47*y**2 + 46*y)
Expanding the part (47*y**2 + 46*y) using the distributive property, and we got: (46*y)*(6*y**2) + (6*y**2)*(47*y**2)
Replacing (6*y**2)*(47*y**2 + 46*y) with (46*y)*(6*y**2) + (6*y**2)*(47*y**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (11*y)*(47*y**2 + 46*y) + (46*y)*(6*y**2) + (6*y**2)*(47*y**2)</replace>
Simplifying the partial expression: (11*y)*(47*y**2 + 46*y)
Expanding the part (47*y**2 + 46*y) using the distributive property, and we got: (11*y)*(46*y) + (11*y)*(47*y**2)
Replacing (11*y)*(47*y**2 + 46*y) with (11*y)*(46*y) + (11*y)*(47*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (11*y)*(46*y) + (11*y)*(47*y**2) + (46*y)*(6*y**2) + (6*y**2)*(47*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (46*y)*(6*y**2) = 276*y**3
  (46*y)*(11*y) = 506*y**2
  (47*y**2)*(6*y**2) = 282*y**4
  (47*y**2)*(11*y) = 517*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 282*y**4 + 276*y**3 + 517*y**3 + 506*y**2</replace>
Combining like terms, got 282*y**4 + 793*y**3 + 506*y**2
<replace-#Step 5>#Step 6:
Current expression: 282*y**4 + 793*y**3 + 506*y**2</replace>
No more calculations needed.
<answer>282*y**4 + 793*y**3 + 506*y**2</answer>


Question:
Simplify this expression: (2*z**3 - 7*z**2 - 13)*(3*z**3 + 19*z**2 + 31)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 6*z**6 + 17*z**5 - 133*z**4 + 23*z**3 - 464*z**2 - 403


Question:
Calculate the following: (23*x**3 - 6*x)*(37*x**3 + 33*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 851*x**6 + 537*x**4 - 198*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: (23*x**3 - 6*x)*(37*x**3 + 33*x)
Expanding the part (23*x**3 - 6*x) using the distributive property, and we got: (-6*x)*(37*x**3 + 33*x) + (23*x**3)*(37*x**3 + 33*x)
<replace-#Step 1>#Step 2:
Current expression: (-6*x)*(37*x**3 + 33*x) + (23*x**3)*(37*x**3 + 33*x)</replace>
Simplifying the partial expression: (-6*x)*(37*x**3 + 33*x)
Expanding the part (37*x**3 + 33*x) using the distributive property, and we got: (-6*x)*(33*x) + (-6*x)*(37*x**3)
Replacing (-6*x)*(37*x**3 + 33*x) with (-6*x)*(33*x) + (-6*x)*(37*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-6*x)*(33*x) + (-6*x)*(37*x**3) + (23*x**3)*(37*x**3 + 33*x)</replace>
Simplifying the partial expression: (23*x**3)*(37*x**3 + 33*x)
Expanding the part (37*x**3 + 33*x) using the distributive property, and we got: (33*x)*(23*x**3) + (23*x**3)*(37*x**3)
Replacing (23*x**3)*(37*x**3 + 33*x) with (33*x)*(23*x**3) + (23*x**3)*(37*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-6*x)*(33*x) + (-6*x)*(37*x**3) + (33*x)*(23*x**3) + (23*x**3)*(37*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (33*x)*(-6*x) = -198*x**2
  (33*x)*(23*x**3) = 759*x**4
  (37*x**3)*(-6*x) = -222*x**4
  (37*x**3)*(23*x**3) = 851*x**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 851*x**6 - 222*x**4 + 759*x**4 - 198*x**2</replace>
Combining like terms, got 851*x**6 + 537*x**4 - 198*x**2
<replace-#Step 5>#Step 6:
Current expression: 851*x**6 + 537*x**4 - 198*x**2</replace>
No more calculations needed.
<answer>851*x**6 + 537*x**4 - 198*x**2</answer>


Question:
Calculate the following: (x**2 - 41)*(-22*x**2 + 44*x - 39)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -22*x**4 + 44*x**3 + 863*x**2 - 1804*x + 1599

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (x**2 - 41)*(-22*x**2 + 44*x - 39)
Expanding the part (x**2 - 41) using the distributive property, and we got: x**2*(-22*x**2 + 44*x - 39) - 41*(-22*x**2 + 44*x - 39)
<replace-#Step 1>#Step 2:
Current expression: x**2*(-22*x**2 + 44*x - 39) - 41*(-22*x**2 + 44*x - 39)</replace>
Simplifying the partial expression: -41*(-22*x**2 + 44*x - 39)
Expanding the part (-22*x**2 + 44*x - 39) using the distributive property, and we got: (44*x)*(-41) - 22*x**2*(-41) - 39*(-41)
Replacing -41*(-22*x**2 + 44*x - 39) with (44*x)*(-41) - 22*x**2*(-41) - 39*(-41) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: x**2*(-22*x**2 + 44*x - 39) + (44*x)*(-41) - 22*x**2*(-41) + 1599</replace>
Simplifying the partial expression: x**2*(-22*x**2 + 44*x - 39)
Expanding the part (-22*x**2 + 44*x - 39) using the distributive property, and we got: (44*x)*x**2 + (-22*x**2)*x**2 - 39*x**2
Replacing x**2*(-22*x**2 + 44*x - 39) with (44*x)*x**2 + (-22*x**2)*x**2 - 39*x**2 in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (44*x)*x**2 + (-22*x**2)*x**2 - 39*x**2 + (44*x)*(-41) - 22*x**2*(-41) + 1599</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-22*x**2)*-41 = 902*x**2
  (-22*x**2)*x**2 = -22*x**4
  (44*x)*-41 = -1804*x
  (44*x)*x**2 = 44*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -22*x**4 + 44*x**3 - 39*x**2 + 902*x**2 - 1804*x + 1599</replace>
Combining like terms, got -22*x**4 + 44*x**3 + 863*x**2 - 1804*x + 1599
<replace-#Step 5>#Step 6:
Current expression: -22*x**4 + 44*x**3 + 863*x**2 - 1804*x + 1599</replace>
No more calculations needed.
<answer>-22*x**4 + 44*x**3 + 863*x**2 - 1804*x + 1599</answer>


Question:
Simplify this expression: (-y**3 - 38)*(26*y**3 + 38*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -26*y**6 - 38*y**4 - 988*y**3 - 1444*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: (-y**3 - 38)*(26*y**3 + 38*y)
Expanding the part (-y**3 - 38) using the distributive property, and we got: (-y**3)*(26*y**3 + 38*y) - 38*(26*y**3 + 38*y)
<replace-#Step 1>#Step 2:
Current expression: (-y**3)*(26*y**3 + 38*y) - 38*(26*y**3 + 38*y)</replace>
Simplifying the partial expression: -38*(26*y**3 + 38*y)
Expanding the part (26*y**3 + 38*y) using the distributive property, and we got: (38*y)*(-38) + (26*y**3)*(-38)
Replacing -38*(26*y**3 + 38*y) with (38*y)*(-38) + (26*y**3)*(-38) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (38*y)*(-38) + (-y**3)*(26*y**3 + 38*y) + (26*y**3)*(-38)</replace>
Simplifying the partial expression: (-y**3)*(26*y**3 + 38*y)
Expanding the part (26*y**3 + 38*y) using the distributive property, and we got: (38*y)*(-y**3) + (-y**3)*(26*y**3)
Replacing (-y**3)*(26*y**3 + 38*y) with (38*y)*(-y**3) + (-y**3)*(26*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (38*y)*(-y**3) + (38*y)*(-38) + (-y**3)*(26*y**3) + (26*y**3)*(-38)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (26*y**3)*-38 = -988*y**3
  (26*y**3)*(-y**3) = -26*y**6
  (38*y)*-38 = -1444*y
  (38*y)*(-y**3) = -38*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -26*y**6 - 38*y**4 - 988*y**3 - 1444*y</replace>
No more calculations needed.
<answer>-26*y**6 - 38*y**4 - 988*y**3 - 1444*y</answer>


Question:
Simplify this expression: (47*z**2 - 15)*(11*z**3 - 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: 517*z**5 - 165*z**3 - 1504*z**2 + 480

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (47*z**2 - 15)*(11*z**3 - 32)
Expanding the part (11*z**3 - 32) using the distributive property, and we got: (11*z**3)*(47*z**2 - 15) - 32*(47*z**2 - 15)
<replace-#Step 1>#Step 2:
Current expression: (11*z**3)*(47*z**2 - 15) - 32*(47*z**2 - 15)</replace>
Simplifying the partial expression: -32*(47*z**2 - 15)
Expanding the part (47*z**2 - 15) using the distributive property, and we got: (47*z**2)*(-32) - 15*(-32)
Replacing -32*(47*z**2 - 15) with (47*z**2)*(-32) - 15*(-32) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (47*z**2)*(-32) + (11*z**3)*(47*z**2 - 15) + 480</replace>
Simplifying the partial expression: (11*z**3)*(47*z**2 - 15)
Expanding the part (47*z**2 - 15) using the distributive property, and we got: -165*z**3 + (47*z**2)*(11*z**3)
Replacing (11*z**3)*(47*z**2 - 15) with -165*z**3 + (47*z**2)*(11*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -15*11*z**3 + (47*z**2)*(11*z**3) + (47*z**2)*(-32) + 480</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (47*z**2)*-32 = -1504*z**2
  (47*z**2)*(11*z**3) = 517*z**5
  -15*11*z**3 = -165*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 517*z**5 - 165*z**3 - 1504*z**2 + 480</replace>
No more calculations needed.
<answer>517*z**5 - 165*z**3 - 1504*z**2 + 480</answer>


Question:
Simplify this expression: (-33*y**3 - 30*y**2 + 9*y)*(28*y**3 - 20*y**2 - 25*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: -924*y**6 - 180*y**5 + 1677*y**4 + 570*y**3 - 225*y**2


Question:
Calculate the following: (-13*z**2 - 13*z)*(-19*z**2 + 24*z - 29)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 247*z**4 - 65*z**3 + 65*z**2 + 377*z


Question:
Calculate the following: -546*x**2 - 234
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -546*x**2 - 234

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: -546*x**2 - 234
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: -546*x**2 - 234</replace>
No more calculations needed.
<answer>-546*x**2 - 234</answer>


Question:
Simplify this expression: (48*y + 26)*(56*y**3 + 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: 2688*y**4 + 1456*y**3 + 288*y + 156

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (48*y + 26)*(56*y**3 + 6)
Expanding the part (56*y**3 + 6) using the distributive property, and we got: (56*y**3)*(48*y + 26) + 6*(48*y + 26)
<replace-#Step 1>#Step 2:
Current expression: (56*y**3)*(48*y + 26) + 6*(48*y + 26)</replace>
Simplifying the partial expression: 6*(48*y + 26)
Expanding the part (48*y + 26) using the distributive property, and we got: (48*y)*6 + 26*6
Replacing 6*(48*y + 26) with (48*y)*6 + 26*6 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (48*y)*6 + (56*y**3)*(48*y + 26) + 156</replace>
Simplifying the partial expression: (56*y**3)*(48*y + 26)
Expanding the part (48*y + 26) using the distributive property, and we got: 26*(56*y**3) + (48*y)*(56*y**3)
Replacing (56*y**3)*(48*y + 26) with 26*(56*y**3) + (48*y)*(56*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 26*56*y**3 + (48*y)*(56*y**3) + (48*y)*6 + 156</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (48*y)*6 = 288*y
  (48*y)*(56*y**3) = 2688*y**4
  26*56*y**3 = 1456*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2688*y**4 + 1456*y**3 + 288*y + 156</replace>
No more calculations needed.
<answer>2688*y**4 + 1456*y**3 + 288*y + 156</answer>


Question:
Calculate the following: (x**2 + 14*x)*(x**3 - 59*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: x**5 + 14*x**4 - 59*x**3 - 826*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: (x**2 + 14*x)*(x**3 - 59*x)
Expanding the part (x**2 + 14*x) using the distributive property, and we got: x**2*(x**3 - 59*x) + (14*x)*(x**3 - 59*x)
<replace-#Step 1>#Step 2:
Current expression: x**2*(x**3 - 59*x) + (14*x)*(x**3 - 59*x)</replace>
Simplifying the partial expression: x**2*(x**3 - 59*x)
Expanding the part (x**3 - 59*x) using the distributive property, and we got: (-59*x)*x**2 + x**2*x**3
Replacing x**2*(x**3 - 59*x) with (-59*x)*x**2 + x**2*x**3 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-59*x)*x**2 + x**2*x**3 + (14*x)*(x**3 - 59*x)</replace>
Simplifying the partial expression: (14*x)*(x**3 - 59*x)
Expanding the part (x**3 - 59*x) using the distributive property, and we got: (-59*x)*(14*x) + (14*x)*x**3
Replacing (14*x)*(x**3 - 59*x) with (-59*x)*(14*x) + (14*x)*x**3 in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-59*x)*x**2 + (-59*x)*(14*x) + (14*x)*x**3 + x**2*x**3</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  x**3*x**2 = x**5
  x**3*(14*x) = 14*x**4
  (-59*x)*x**2 = -59*x**3
  (-59*x)*(14*x) = -826*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: x**5 + 14*x**4 - 59*x**3 - 826*x**2</replace>
No more calculations needed.
<answer>x**5 + 14*x**4 - 59*x**3 - 826*x**2</answer>


Question:
Calculate the following: (-47*y**3 + 3*y**2)*(32*y**3 + 5*y - 31)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1504*y**6 + 96*y**5 - 235*y**4 + 1472*y**3 - 93*y**2


Question:
Simplify this expression: -4*x*(-6*x**3 - 44*x - 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: 24*x**4 + 176*x**2 + 56*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: -4*x*(-6*x**3 - 44*x - 14)
Expanding the part (-6*x**3 - 44*x - 14) using the distributive property, and we got: (-44*x)*(-4*x) + (-4*x)*(-6*x**3) - (-1)*56*x
<replace-#Step 1>#Step 2:
Current expression: (-44*x)*(-4*x) + (-4*x)*(-6*x**3) - (-1)*56*x</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -14*(-4*x) = 56*x
  (-44*x)*(-4*x) = 176*x**2
  (-6*x**3)*(-4*x) = 24*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 24*x**4 + 176*x**2 + 56*x</replace>
No more calculations needed.
<answer>24*x**4 + 176*x**2 + 56*x</answer>


Question:
Calculate the following: (25*y**3 + 18*y**2 - 30)*(30*y**3 + 12*y - 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: 750*y**6 + 540*y**5 + 300*y**4 - 1859*y**3 - 846*y**2 - 360*y + 1410


Question:
Calculate the following: 19*x**3*(-11*x**2 + 7*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: -209*x**5 + 133*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: 19*x**3*(-11*x**2 + 7*x)
Expanding the part (-11*x**2 + 7*x) using the distributive property, and we got: (7*x)*(19*x**3) + (-11*x**2)*(19*x**3)
<replace-#Step 1>#Step 2:
Current expression: (7*x)*(19*x**3) + (-11*x**2)*(19*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-11*x**2)*(19*x**3) = -209*x**5
  (7*x)*(19*x**3) = 133*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -209*x**5 + 133*x**4</replace>
No more calculations needed.
<answer>-209*x**5 + 133*x**4</answer>


Question:
Calculate the following: (-46*z**2 + 47*z)*(21*z**3 - z - 82)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -966*z**5 + 987*z**4 + 46*z**3 + 3725*z**2 - 3854*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-46*z**2 + 47*z)*(21*z**3 - z - 82)
Expanding the part (-46*z**2 + 47*z) using the distributive property, and we got: (47*z)*(21*z**3 - z - 82) + (-46*z**2)*(21*z**3 - z - 82)
<replace-#Step 1>#Step 2:
Current expression: (47*z)*(21*z**3 - z - 82) + (-46*z**2)*(21*z**3 - z - 82)</replace>
Simplifying the partial expression: (-46*z**2)*(21*z**3 - z - 82)
Expanding the part (21*z**3 - z - 82) using the distributive property, and we got: (-z)*(-46*z**2) - (-1)*3772*z**2 + (-46*z**2)*(21*z**3)
Replacing (-46*z**2)*(21*z**3 - z - 82) with (-z)*(-46*z**2) - (-1)*3772*z**2 + (-46*z**2)*(21*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-z)*(-46*z**2) - 82*(-46)*z**2 + (47*z)*(21*z**3 - z - 82) + (-46*z**2)*(21*z**3)</replace>
Simplifying the partial expression: (47*z)*(21*z**3 - z - 82)
Expanding the part (21*z**3 - z - 82) using the distributive property, and we got: (-z)*(47*z) - 3854*z + (47*z)*(21*z**3)
Replacing (47*z)*(21*z**3 - z - 82) with (-z)*(47*z) - 3854*z + (47*z)*(21*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-z)*(47*z) + (-z)*(-46*z**2) - 82*(-46)*z**2 - 82*47*z + (47*z)*(21*z**3) + (-46*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:
  (-z)*(-46*z**2) = 46*z**3
  (-z)*(47*z) = -47*z**2
  (21*z**3)*(-46*z**2) = -966*z**5
  (21*z**3)*(47*z) = 987*z**4
  -82*-46*z**2 = 3772*z**2
  -82*47*z = -3854*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -966*z**5 + 987*z**4 + 46*z**3 - 47*z**2 + 3772*z**2 - 3854*z</replace>
Combining like terms, got -966*z**5 + 987*z**4 + 46*z**3 + 3725*z**2 - 3854*z
<replace-#Step 5>#Step 6:
Current expression: -966*z**5 + 987*z**4 + 46*z**3 + 3725*z**2 - 3854*z</replace>
No more calculations needed.
<answer>-966*z**5 + 987*z**4 + 46*z**3 + 3725*z**2 - 3854*z</answer>


Question:
Calculate the following: (-11*y**3 + 17*y**2 - 33*y)*(y**3 - 23*y + 21)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -11*y**6 + 17*y**5 + 220*y**4 - 622*y**3 + 1116*y**2 - 693*y


Question:
Calculate the following: (17*x**2 - 66)*(25*x**3 + 18*x**2 + 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: 425*x**5 + 306*x**4 - 1650*x**3 - 610*x**2 - 2244

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (17*x**2 - 66)*(25*x**3 + 18*x**2 + 34)
Expanding the part (17*x**2 - 66) using the distributive property, and we got: (17*x**2)*(25*x**3 + 18*x**2 + 34) - 66*(25*x**3 + 18*x**2 + 34)
<replace-#Step 1>#Step 2:
Current expression: (17*x**2)*(25*x**3 + 18*x**2 + 34) - 66*(25*x**3 + 18*x**2 + 34)</replace>
Simplifying the partial expression: -66*(25*x**3 + 18*x**2 + 34)
Expanding the part (25*x**3 + 18*x**2 + 34) using the distributive property, and we got: (18*x**2)*(-66) + (25*x**3)*(-66) + 34*(-66)
Replacing -66*(25*x**3 + 18*x**2 + 34) with (18*x**2)*(-66) + (25*x**3)*(-66) + 34*(-66) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (17*x**2)*(25*x**3 + 18*x**2 + 34) + (18*x**2)*(-66) + (25*x**3)*(-66) - 2244</replace>
Simplifying the partial expression: (17*x**2)*(25*x**3 + 18*x**2 + 34)
Expanding the part (25*x**3 + 18*x**2 + 34) using the distributive property, and we got: 34*(17*x**2) + (17*x**2)*(18*x**2) + (17*x**2)*(25*x**3)
Replacing (17*x**2)*(25*x**3 + 18*x**2 + 34) with 34*(17*x**2) + (17*x**2)*(18*x**2) + (17*x**2)*(25*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 34*17*x**2 + (17*x**2)*(18*x**2) + (17*x**2)*(25*x**3) + (18*x**2)*(-66) + (25*x**3)*(-66) - 2244</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (18*x**2)*-66 = -1188*x**2
  (18*x**2)*(17*x**2) = 306*x**4
  (25*x**3)*-66 = -1650*x**3
  (25*x**3)*(17*x**2) = 425*x**5
  34*17*x**2 = 578*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 425*x**5 + 306*x**4 - 1650*x**3 - 1188*x**2 + 578*x**2 - 2244</replace>
Combining like terms, got 425*x**5 + 306*x**4 - 1650*x**3 - 610*x**2 - 2244
<replace-#Step 5>#Step 6:
Current expression: 425*x**5 + 306*x**4 - 1650*x**3 - 610*x**2 - 2244</replace>
No more calculations needed.
<answer>425*x**5 + 306*x**4 - 1650*x**3 - 610*x**2 - 2244</answer>


Question:
Calculate the following: (22*y**2 + 45*y + 20)*(-45*y**3 - 13*y**2 - 10*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -990*y**5 - 2311*y**4 - 1705*y**3 - 710*y**2 - 200*y


Question:
Simplify this expression: (-20*y**2 + 30*y + 33)*(43*y**3 - 28*y**2 - 43)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -860*y**5 + 1850*y**4 + 579*y**3 - 64*y**2 - 1290*y - 1419


Question:
Calculate the following: (-34*x**2 + 4*x)*(39*x**3 - 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: -1326*x**5 + 156*x**4 + 442*x**2 - 52*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: (-34*x**2 + 4*x)*(39*x**3 - 13)
Expanding the part (39*x**3 - 13) using the distributive property, and we got: (39*x**3)*(-34*x**2 + 4*x) - 13*(-34*x**2 + 4*x)
<replace-#Step 1>#Step 2:
Current expression: (39*x**3)*(-34*x**2 + 4*x) - 13*(-34*x**2 + 4*x)</replace>
Simplifying the partial expression: -13*(-34*x**2 + 4*x)
Expanding the part (-34*x**2 + 4*x) using the distributive property, and we got: (4*x)*(-13) - 34*x**2*(-13)
Replacing -13*(-34*x**2 + 4*x) with (4*x)*(-13) - 34*x**2*(-13) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (4*x)*(-13) - 34*x**2*(-13) + (39*x**3)*(-34*x**2 + 4*x)</replace>
Simplifying the partial expression: (39*x**3)*(-34*x**2 + 4*x)
Expanding the part (-34*x**2 + 4*x) using the distributive property, and we got: (4*x)*(39*x**3) + (-34*x**2)*(39*x**3)
Replacing (39*x**3)*(-34*x**2 + 4*x) with (4*x)*(39*x**3) + (-34*x**2)*(39*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (4*x)*(39*x**3) + (4*x)*(-13) + (-34*x**2)*(39*x**3) - 34*x**2*(-13)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-34*x**2)*-13 = 442*x**2
  (-34*x**2)*(39*x**3) = -1326*x**5
  (4*x)*-13 = -52*x
  (4*x)*(39*x**3) = 156*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1326*x**5 + 156*x**4 + 442*x**2 - 52*x</replace>
No more calculations needed.
<answer>-1326*x**5 + 156*x**4 + 442*x**2 - 52*x</answer>


Question:
Simplify this expression: -495*x**3 + 88*x**2 - 385*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: -495*x**3 + 88*x**2 - 385*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: -495*x**3 + 88*x**2 - 385*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: -495*x**3 + 88*x**2 - 385*x</replace>
No more calculations needed.
<answer>-495*x**3 + 88*x**2 - 385*x</answer>


Question:
Simplify this expression: (2*z**2 - 35*z)*(-50*z**3 - 40*z**2 + 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: -100*z**5 + 1670*z**4 + 1402*z**3 - 35*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: (2*z**2 - 35*z)*(-50*z**3 - 40*z**2 + z)
Expanding the part (2*z**2 - 35*z) using the distributive property, and we got: (-35*z)*(-50*z**3 - 40*z**2 + z) + (2*z**2)*(-50*z**3 - 40*z**2 + z)
<replace-#Step 1>#Step 2:
Current expression: (-35*z)*(-50*z**3 - 40*z**2 + z) + (2*z**2)*(-50*z**3 - 40*z**2 + z)</replace>
Simplifying the partial expression: (-35*z)*(-50*z**3 - 40*z**2 + z)
Expanding the part (-50*z**3 - 40*z**2 + z) using the distributive property, and we got: (-35*z)*z + (-35*z)*(-40*z**2) + (-35*z)*(-50*z**3)
Replacing (-35*z)*(-50*z**3 - 40*z**2 + z) with (-35*z)*z + (-35*z)*(-40*z**2) + (-35*z)*(-50*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-35*z)*z + (-35*z)*(-40*z**2) + (-35*z)*(-50*z**3) + (2*z**2)*(-50*z**3 - 40*z**2 + z)</replace>
Simplifying the partial expression: (2*z**2)*(-50*z**3 - 40*z**2 + z)
Expanding the part (-50*z**3 - 40*z**2 + z) using the distributive property, and we got: z*(2*z**2) + (-40*z**2)*(2*z**2) + (2*z**2)*(-50*z**3)
Replacing (2*z**2)*(-50*z**3 - 40*z**2 + z) with z*(2*z**2) + (-40*z**2)*(2*z**2) + (2*z**2)*(-50*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-35*z)*z + (-35*z)*(-40*z**2) + (-35*z)*(-50*z**3) + z*(2*z**2) + (-40*z**2)*(2*z**2) + (2*z**2)*(-50*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  z*(-35*z) = -35*z**2
  z*(2*z**2) = 2*z**3
  (-50*z**3)*(-35*z) = 1750*z**4
  (-50*z**3)*(2*z**2) = -100*z**5
  (-40*z**2)*(-35*z) = 1400*z**3
  (-40*z**2)*(2*z**2) = -80*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -100*z**5 - 80*z**4 + 1750*z**4 + 2*z**3 + 1400*z**3 - 35*z**2</replace>
Combining like terms, got -100*z**5 + 1670*z**4 + 1402*z**3 - 35*z**2
<replace-#Step 5>#Step 6:
Current expression: -100*z**5 + 1670*z**4 + 1402*z**3 - 35*z**2</replace>
No more calculations needed.
<answer>-100*z**5 + 1670*z**4 + 1402*z**3 - 35*z**2</answer>


Question:
Simplify this expression: (-36*z**3 + 24*z**2)*(-29*z**3 - 9*z**2 - 11)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1044*z**6 - 372*z**5 - 216*z**4 + 396*z**3 - 264*z**2


Question:
Calculate the following: (14*y**2 - 47*y)*(14*y**3 + 25*y + 42)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 196*y**5 - 658*y**4 + 350*y**3 - 587*y**2 - 1974*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: (14*y**2 - 47*y)*(14*y**3 + 25*y + 42)
Expanding the part (14*y**2 - 47*y) using the distributive property, and we got: (-47*y)*(14*y**3 + 25*y + 42) + (14*y**2)*(14*y**3 + 25*y + 42)
<replace-#Step 1>#Step 2:
Current expression: (-47*y)*(14*y**3 + 25*y + 42) + (14*y**2)*(14*y**3 + 25*y + 42)</replace>
Simplifying the partial expression: (-47*y)*(14*y**3 + 25*y + 42)
Expanding the part (14*y**3 + 25*y + 42) using the distributive property, and we got: (-47*y)*(25*y) + (-47*y)*(14*y**3) + 42*(-47*y)
Replacing (-47*y)*(14*y**3 + 25*y + 42) with (-47*y)*(25*y) + (-47*y)*(14*y**3) + 42*(-47*y) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-47*y)*(25*y) + (-47*y)*(14*y**3) + 42*(-47)*y + (14*y**2)*(14*y**3 + 25*y + 42)</replace>
Simplifying the partial expression: (14*y**2)*(14*y**3 + 25*y + 42)
Expanding the part (14*y**3 + 25*y + 42) using the distributive property, and we got: 42*(14*y**2) + (25*y)*(14*y**2) + (14*y**2)*(14*y**3)
Replacing (14*y**2)*(14*y**3 + 25*y + 42) with 42*(14*y**2) + (25*y)*(14*y**2) + (14*y**2)*(14*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-47*y)*(25*y) + (-47*y)*(14*y**3) + 42*14*y**2 + 42*(-47)*y + (25*y)*(14*y**2) + (14*y**2)*(14*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (14*y**3)*(-47*y) = -658*y**4
  (14*y**3)*(14*y**2) = 196*y**5
  (25*y)*(-47*y) = -1175*y**2
  (25*y)*(14*y**2) = 350*y**3
  42*-47*y = -1974*y
  42*14*y**2 = 588*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 196*y**5 - 658*y**4 + 350*y**3 - 1175*y**2 + 588*y**2 - 1974*y</replace>
Combining like terms, got 196*y**5 - 658*y**4 + 350*y**3 - 587*y**2 - 1974*y
<replace-#Step 5>#Step 6:
Current expression: 196*y**5 - 658*y**4 + 350*y**3 - 587*y**2 - 1974*y</replace>
No more calculations needed.
<answer>196*y**5 - 658*y**4 + 350*y**3 - 587*y**2 - 1974*y</answer>


Question:
Simplify this expression: (-39*z**3 + 44*z**2)*(-20*z**3 - 35*z**2 - 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: 780*z**6 + 485*z**5 - 1540*z**4 + 1560*z**3 - 1760*z**2


Question:
Calculate the following: 52*z*(-28*z**2 + 43*z - 38)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1456*z**3 + 2236*z**2 - 1976*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: 52*z*(-28*z**2 + 43*z - 38)
Expanding the part (-28*z**2 + 43*z - 38) using the distributive property, and we got: -1976*z + (43*z)*(52*z) + (52*z)*(-28*z**2)
<replace-#Step 1>#Step 2:
Current expression: -1976*z + (43*z)*(52*z) + (52*z)*(-28*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -38*(52*z) = -1976*z
  (-28*z**2)*(52*z) = -1456*z**3
  (43*z)*(52*z) = 2236*z**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1456*z**3 + 2236*z**2 - 1976*z</replace>
No more calculations needed.
<answer>-1456*z**3 + 2236*z**2 - 1976*z</answer>


Question:
Simplify this expression: (-6*x**3 + 31*x)*(-12*x**3 - 40*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: 72*x**6 + 240*x**5 - 576*x**4 - 1240*x**3 + 1054*x**2


Question:
Simplify this expression: -215*z**3 - 45*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: -215*z**3 - 45*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: -215*z**3 - 45*z**2
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: -215*z**3 - 45*z**2</replace>
No more calculations needed.
<answer>-215*z**3 - 45*z**2</answer>


Question:
Calculate the following: -1200*y**2 - 225
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1200*y**2 - 225

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: -1200*y**2 - 225
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: -1200*y**2 - 225</replace>
No more calculations needed.
<answer>-1200*y**2 - 225</answer>


Question:
Simplify this expression: (46*x**2 - 26)*(-42*x**3 + 40*x - 44)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1932*x**5 + 2932*x**3 - 2024*x**2 - 1040*x + 1144

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (46*x**2 - 26)*(-42*x**3 + 40*x - 44)
Expanding the part (46*x**2 - 26) using the distributive property, and we got: (46*x**2)*(-42*x**3 + 40*x - 44) - 26*(-42*x**3 + 40*x - 44)
<replace-#Step 1>#Step 2:
Current expression: (46*x**2)*(-42*x**3 + 40*x - 44) - 26*(-42*x**3 + 40*x - 44)</replace>
Simplifying the partial expression: -26*(-42*x**3 + 40*x - 44)
Expanding the part (-42*x**3 + 40*x - 44) using the distributive property, and we got: (40*x)*(-26) - 42*x**3*(-26) - 44*(-26)
Replacing -26*(-42*x**3 + 40*x - 44) with (40*x)*(-26) - 42*x**3*(-26) - 44*(-26) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (40*x)*(-26) + (46*x**2)*(-42*x**3 + 40*x - 44) - 42*x**3*(-26) + 1144</replace>
Simplifying the partial expression: (46*x**2)*(-42*x**3 + 40*x - 44)
Expanding the part (-42*x**3 + 40*x - 44) using the distributive property, and we got: -2024*x**2 + (40*x)*(46*x**2) + (46*x**2)*(-42*x**3)
Replacing (46*x**2)*(-42*x**3 + 40*x - 44) with -2024*x**2 + (40*x)*(46*x**2) + (46*x**2)*(-42*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -44*46*x**2 + (40*x)*(46*x**2) + (40*x)*(-26) + (46*x**2)*(-42*x**3) - 42*x**3*(-26) + 1144</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-42*x**3)*-26 = 1092*x**3
  (-42*x**3)*(46*x**2) = -1932*x**5
  (40*x)*-26 = -1040*x
  (40*x)*(46*x**2) = 1840*x**3
  -44*46*x**2 = -2024*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1932*x**5 + 1092*x**3 + 1840*x**3 - 2024*x**2 - 1040*x + 1144</replace>
Combining like terms, got -1932*x**5 + 2932*x**3 - 2024*x**2 - 1040*x + 1144
<replace-#Step 5>#Step 6:
Current expression: -1932*x**5 + 2932*x**3 - 2024*x**2 - 1040*x + 1144</replace>
No more calculations needed.
<answer>-1932*x**5 + 2932*x**3 - 2024*x**2 - 1040*x + 1144</answer>


Question:
Calculate the following: (11 - 29*x)*(-53*x**3 + 13*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1537*x**4 - 583*x**3 - 377*x**2 + 143*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (11 - 29*x)*(-53*x**3 + 13*x)
Expanding the part (11 - 29*x) using the distributive property, and we got: (-29*x)*(-53*x**3 + 13*x) + 11*(-53*x**3 + 13*x)
<replace-#Step 1>#Step 2:
Current expression: (-29*x)*(-53*x**3 + 13*x) + 11*(-53*x**3 + 13*x)</replace>
Simplifying the partial expression: 11*(-53*x**3 + 13*x)
Expanding the part (-53*x**3 + 13*x) using the distributive property, and we got: (13*x)*11 - 53*x**3*11
Replacing 11*(-53*x**3 + 13*x) with (13*x)*11 - 53*x**3*11 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-29*x)*(-53*x**3 + 13*x) + (13*x)*11 - 53*x**3*11</replace>
Simplifying the partial expression: (-29*x)*(-53*x**3 + 13*x)
Expanding the part (-53*x**3 + 13*x) using the distributive property, and we got: (-29*x)*(13*x) + (-29*x)*(-53*x**3)
Replacing (-29*x)*(-53*x**3 + 13*x) with (-29*x)*(13*x) + (-29*x)*(-53*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-29*x)*(13*x) + (-29*x)*(-53*x**3) + (13*x)*11 - 53*x**3*11</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-53*x**3)*11 = -583*x**3
  (-53*x**3)*(-29*x) = 1537*x**4
  (13*x)*11 = 143*x
  (13*x)*(-29*x) = -377*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1537*x**4 - 583*x**3 - 377*x**2 + 143*x</replace>
No more calculations needed.
<answer>1537*x**4 - 583*x**3 - 377*x**2 + 143*x</answer>


Question:
Calculate the following: (z**3 + 33*z)*(47*z**3 - 32*z**2 - 25)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 47*z**6 - 32*z**5 + 1551*z**4 - 1081*z**3 - 825*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: (z**3 + 33*z)*(47*z**3 - 32*z**2 - 25)
Expanding the part (z**3 + 33*z) using the distributive property, and we got: z**3*(47*z**3 - 32*z**2 - 25) + (33*z)*(47*z**3 - 32*z**2 - 25)
<replace-#Step 1>#Step 2:
Current expression: z**3*(47*z**3 - 32*z**2 - 25) + (33*z)*(47*z**3 - 32*z**2 - 25)</replace>
Simplifying the partial expression: z**3*(47*z**3 - 32*z**2 - 25)
Expanding the part (47*z**3 - 32*z**2 - 25) using the distributive property, and we got: (-32*z**2)*z**3 + z**3*(47*z**3) - 25*z**3
Replacing z**3*(47*z**3 - 32*z**2 - 25) with (-32*z**2)*z**3 + z**3*(47*z**3) - 25*z**3 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-32*z**2)*z**3 + z**3*(47*z**3) - 25*z**3 + (33*z)*(47*z**3 - 32*z**2 - 25)</replace>
Simplifying the partial expression: (33*z)*(47*z**3 - 32*z**2 - 25)
Expanding the part (47*z**3 - 32*z**2 - 25) using the distributive property, and we got: -825*z + (33*z)*(-32*z**2) + (33*z)*(47*z**3)
Replacing (33*z)*(47*z**3 - 32*z**2 - 25) with -825*z + (33*z)*(-32*z**2) + (33*z)*(47*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-32*z**2)*z**3 + z**3*(47*z**3) - 25*z**3 - 25*33*z + (33*z)*(-32*z**2) + (33*z)*(47*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-32*z**2)*z**3 = -32*z**5
  (-32*z**2)*(33*z) = -1056*z**3
  (47*z**3)*z**3 = 47*z**6
  (47*z**3)*(33*z) = 1551*z**4
  -25*33*z = -825*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 47*z**6 - 32*z**5 + 1551*z**4 - 1056*z**3 - 25*z**3 - 825*z</replace>
Combining like terms, got 47*z**6 - 32*z**5 + 1551*z**4 - 1081*z**3 - 825*z
<replace-#Step 5>#Step 6:
Current expression: 47*z**6 - 32*z**5 + 1551*z**4 - 1081*z**3 - 825*z</replace>
No more calculations needed.
<answer>47*z**6 - 32*z**5 + 1551*z**4 - 1081*z**3 - 825*z</answer>


Question:
Simplify this expression: (45*z**3 - 37*z)*(84*z**3 + 44)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 3780*z**6 - 3108*z**4 + 1980*z**3 - 1628*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: (45*z**3 - 37*z)*(84*z**3 + 44)
Expanding the part (84*z**3 + 44) using the distributive property, and we got: (84*z**3)*(45*z**3 - 37*z) + 44*(45*z**3 - 37*z)
<replace-#Step 1>#Step 2:
Current expression: (84*z**3)*(45*z**3 - 37*z) + 44*(45*z**3 - 37*z)</replace>
Simplifying the partial expression: 44*(45*z**3 - 37*z)
Expanding the part (45*z**3 - 37*z) using the distributive property, and we got: -37*z*44 + (45*z**3)*44
Replacing 44*(45*z**3 - 37*z) with -37*z*44 + (45*z**3)*44 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -37*z*44 + (45*z**3)*44 + (84*z**3)*(45*z**3 - 37*z)</replace>
Simplifying the partial expression: (84*z**3)*(45*z**3 - 37*z)
Expanding the part (45*z**3 - 37*z) using the distributive property, and we got: (-37*z)*(84*z**3) + (45*z**3)*(84*z**3)
Replacing (84*z**3)*(45*z**3 - 37*z) with (-37*z)*(84*z**3) + (45*z**3)*(84*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-37*z)*(84*z**3) - 37*z*44 + (45*z**3)*(84*z**3) + (45*z**3)*44</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-37*z)*44 = -1628*z
  (-37*z)*(84*z**3) = -3108*z**4
  (45*z**3)*44 = 1980*z**3
  (45*z**3)*(84*z**3) = 3780*z**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 3780*z**6 - 3108*z**4 + 1980*z**3 - 1628*z</replace>
No more calculations needed.
<answer>3780*z**6 - 3108*z**4 + 1980*z**3 - 1628*z</answer>


Question:
Calculate the following: (-18*x**3 - 16*x)*(45*x**3 - 21)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -810*x**6 - 720*x**4 + 378*x**3 + 336*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: (-18*x**3 - 16*x)*(45*x**3 - 21)
Expanding the part (45*x**3 - 21) using the distributive property, and we got: (45*x**3)*(-18*x**3 - 16*x) - 21*(-18*x**3 - 16*x)
<replace-#Step 1>#Step 2:
Current expression: (45*x**3)*(-18*x**3 - 16*x) - 21*(-18*x**3 - 16*x)</replace>
Simplifying the partial expression: -21*(-18*x**3 - 16*x)
Expanding the part (-18*x**3 - 16*x) using the distributive property, and we got: -16*x*(-21) - 18*x**3*(-21)
Replacing -21*(-18*x**3 - 16*x) with -16*x*(-21) - 18*x**3*(-21) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -16*x*(-21) - 18*x**3*(-21) + (45*x**3)*(-18*x**3 - 16*x)</replace>
Simplifying the partial expression: (45*x**3)*(-18*x**3 - 16*x)
Expanding the part (-18*x**3 - 16*x) using the distributive property, and we got: (-16*x)*(45*x**3) + (-18*x**3)*(45*x**3)
Replacing (45*x**3)*(-18*x**3 - 16*x) with (-16*x)*(45*x**3) + (-18*x**3)*(45*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-16*x)*(45*x**3) - 16*x*(-21) + (-18*x**3)*(45*x**3) - 18*x**3*(-21)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-18*x**3)*-21 = 378*x**3
  (-18*x**3)*(45*x**3) = -810*x**6
  (-16*x)*-21 = 336*x
  (-16*x)*(45*x**3) = -720*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -810*x**6 - 720*x**4 + 378*x**3 + 336*x</replace>
No more calculations needed.
<answer>-810*x**6 - 720*x**4 + 378*x**3 + 336*x</answer>


Question:
Simplify this expression: (-31*y**3 + 27*y - 13)*(-11*y**3 + 5*y**2 + 20*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: 341*y**6 - 155*y**5 - 917*y**4 + 588*y**3 + 475*y**2 - 530*y + 130


Question:
Simplify this expression: (40*z**2 + 15*z)*(-36*z**3 + 31*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: -1440*z**5 + 700*z**4 + 465*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: (40*z**2 + 15*z)*(-36*z**3 + 31*z**2)
Expanding the part (-36*z**3 + 31*z**2) using the distributive property, and we got: (31*z**2)*(40*z**2 + 15*z) + (-36*z**3)*(40*z**2 + 15*z)
<replace-#Step 1>#Step 2:
Current expression: (31*z**2)*(40*z**2 + 15*z) + (-36*z**3)*(40*z**2 + 15*z)</replace>
Simplifying the partial expression: (-36*z**3)*(40*z**2 + 15*z)
Expanding the part (40*z**2 + 15*z) using the distributive property, and we got: (15*z)*(-36*z**3) + (40*z**2)*(-36*z**3)
Replacing (-36*z**3)*(40*z**2 + 15*z) with (15*z)*(-36*z**3) + (40*z**2)*(-36*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (15*z)*(-36*z**3) + (31*z**2)*(40*z**2 + 15*z) + (40*z**2)*(-36*z**3)</replace>
Simplifying the partial expression: (31*z**2)*(40*z**2 + 15*z)
Expanding the part (40*z**2 + 15*z) using the distributive property, and we got: (15*z)*(31*z**2) + (31*z**2)*(40*z**2)
Replacing (31*z**2)*(40*z**2 + 15*z) with (15*z)*(31*z**2) + (31*z**2)*(40*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (15*z)*(31*z**2) + (15*z)*(-36*z**3) + (31*z**2)*(40*z**2) + (40*z**2)*(-36*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (15*z)*(-36*z**3) = -540*z**4
  (15*z)*(31*z**2) = 465*z**3
  (40*z**2)*(-36*z**3) = -1440*z**5
  (40*z**2)*(31*z**2) = 1240*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1440*z**5 - 540*z**4 + 1240*z**4 + 465*z**3</replace>
Combining like terms, got -1440*z**5 + 700*z**4 + 465*z**3
<replace-#Step 5>#Step 6:
Current expression: -1440*z**5 + 700*z**4 + 465*z**3</replace>
No more calculations needed.
<answer>-1440*z**5 + 700*z**4 + 465*z**3</answer>


Question:
Calculate the following: (10 - 50*y**3)*(32*y**2 - 8*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1600*y**5 + 400*y**4 + 320*y**2 - 80*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 - 50*y**3)*(32*y**2 - 8*y)
Expanding the part (10 - 50*y**3) using the distributive property, and we got: (-50*y**3)*(32*y**2 - 8*y) + 10*(32*y**2 - 8*y)
<replace-#Step 1>#Step 2:
Current expression: (-50*y**3)*(32*y**2 - 8*y) + 10*(32*y**2 - 8*y)</replace>
Simplifying the partial expression: 10*(32*y**2 - 8*y)
Expanding the part (32*y**2 - 8*y) using the distributive property, and we got: -8*y*10 + (32*y**2)*10
Replacing 10*(32*y**2 - 8*y) with -8*y*10 + (32*y**2)*10 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -8*y*10 + (32*y**2)*10 + (-50*y**3)*(32*y**2 - 8*y)</replace>
Simplifying the partial expression: (-50*y**3)*(32*y**2 - 8*y)
Expanding the part (32*y**2 - 8*y) using the distributive property, and we got: (-8*y)*(-50*y**3) + (32*y**2)*(-50*y**3)
Replacing (-50*y**3)*(32*y**2 - 8*y) with (-8*y)*(-50*y**3) + (32*y**2)*(-50*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-8*y)*(-50*y**3) - 8*y*10 + (32*y**2)*(-50*y**3) + (32*y**2)*10</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-8*y)*10 = -80*y
  (-8*y)*(-50*y**3) = 400*y**4
  (32*y**2)*10 = 320*y**2
  (32*y**2)*(-50*y**3) = -1600*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1600*y**5 + 400*y**4 + 320*y**2 - 80*y</replace>
No more calculations needed.
<answer>-1600*y**5 + 400*y**4 + 320*y**2 - 80*y</answer>


Question:
Simplify this expression: (30*y**2 + y)*(-24*y**2 - 47*y + 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: -720*y**4 - 1434*y**3 + 1363*y**2 + 47*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: (30*y**2 + y)*(-24*y**2 - 47*y + 47)
Expanding the part (30*y**2 + y) using the distributive property, and we got: y*(-24*y**2 - 47*y + 47) + (30*y**2)*(-24*y**2 - 47*y + 47)
<replace-#Step 1>#Step 2:
Current expression: y*(-24*y**2 - 47*y + 47) + (30*y**2)*(-24*y**2 - 47*y + 47)</replace>
Simplifying the partial expression: y*(-24*y**2 - 47*y + 47)
Expanding the part (-24*y**2 - 47*y + 47) using the distributive property, and we got: (-47*y)*y + y*(-24*y**2) + 47*y
Replacing y*(-24*y**2 - 47*y + 47) with (-47*y)*y + y*(-24*y**2) + 47*y in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-47*y)*y + y*(-24*y**2) + 47*y + (30*y**2)*(-24*y**2 - 47*y + 47)</replace>
Simplifying the partial expression: (30*y**2)*(-24*y**2 - 47*y + 47)
Expanding the part (-24*y**2 - 47*y + 47) using the distributive property, and we got: (-47*y)*(30*y**2) + 47*(30*y**2) + (-24*y**2)*(30*y**2)
Replacing (30*y**2)*(-24*y**2 - 47*y + 47) with (-47*y)*(30*y**2) + 47*(30*y**2) + (-24*y**2)*(30*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-47*y)*y + (-47*y)*(30*y**2) + 47*30*y**2 + y*(-24*y**2) + 47*y + (-24*y**2)*(30*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-47*y)*y = -47*y**2
  (-47*y)*(30*y**2) = -1410*y**3
  (-24*y**2)*y = -24*y**3
  (-24*y**2)*(30*y**2) = -720*y**4
  47*30*y**2 = 1410*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -720*y**4 - 1410*y**3 - 24*y**3 - 47*y**2 + 1410*y**2 + 47*y</replace>
Combining like terms, got -720*y**4 - 1434*y**3 + 1363*y**2 + 47*y
<replace-#Step 5>#Step 6:
Current expression: -720*y**4 - 1434*y**3 + 1363*y**2 + 47*y</replace>
No more calculations needed.
<answer>-720*y**4 - 1434*y**3 + 1363*y**2 + 47*y</answer>


Question:
Calculate the following: (-31*x**3 - 31*x**2)*(-29*x**2 + 24*x - 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: 899*x**5 + 155*x**4 + 775*x**3 + 1519*x**2


Question:
Calculate the following: (-18*z**3 + 30*z)*(28*z**3 + 49*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: -504*z**6 - 882*z**5 + 1092*z**4 + 1470*z**3 - 420*z**2


Question:
Simplify this expression: (-3*z**2 - 14)*(15*z**2 + 39*z - 3)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -45*z**4 - 117*z**3 - 201*z**2 - 546*z + 42

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-3*z**2 - 14)*(15*z**2 + 39*z - 3)
Expanding the part (-3*z**2 - 14) using the distributive property, and we got: (-3*z**2)*(15*z**2 + 39*z - 3) - 14*(15*z**2 + 39*z - 3)
<replace-#Step 1>#Step 2:
Current expression: (-3*z**2)*(15*z**2 + 39*z - 3) - 14*(15*z**2 + 39*z - 3)</replace>
Simplifying the partial expression: -14*(15*z**2 + 39*z - 3)
Expanding the part (15*z**2 + 39*z - 3) using the distributive property, and we got: (39*z)*(-14) + (15*z**2)*(-14) - 3*(-14)
Replacing -14*(15*z**2 + 39*z - 3) with (39*z)*(-14) + (15*z**2)*(-14) - 3*(-14) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (39*z)*(-14) + (-3*z**2)*(15*z**2 + 39*z - 3) + (15*z**2)*(-14) + 42</replace>
Simplifying the partial expression: (-3*z**2)*(15*z**2 + 39*z - 3)
Expanding the part (15*z**2 + 39*z - 3) using the distributive property, and we got: -(-1)*9*z**2 + (39*z)*(-3*z**2) + (-3*z**2)*(15*z**2)
Replacing (-3*z**2)*(15*z**2 + 39*z - 3) with -(-1)*9*z**2 + (39*z)*(-3*z**2) + (-3*z**2)*(15*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -3*(-3)*z**2 + (39*z)*(-3*z**2) + (39*z)*(-14) + (-3*z**2)*(15*z**2) + (15*z**2)*(-14) + 42</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (15*z**2)*-14 = -210*z**2
  (15*z**2)*(-3*z**2) = -45*z**4
  (39*z)*-14 = -546*z
  (39*z)*(-3*z**2) = -117*z**3
  -3*-3*z**2 = 9*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -45*z**4 - 117*z**3 - 210*z**2 + 9*z**2 - 546*z + 42</replace>
Combining like terms, got -45*z**4 - 117*z**3 - 201*z**2 - 546*z + 42
<replace-#Step 5>#Step 6:
Current expression: -45*z**4 - 117*z**3 - 201*z**2 - 546*z + 42</replace>
No more calculations needed.
<answer>-45*z**4 - 117*z**3 - 201*z**2 - 546*z + 42</answer>


Question:
Calculate the following: (34*z - 33)*(-15*z**2 + 29*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: -510*z**3 + 1481*z**2 - 957*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: (34*z - 33)*(-15*z**2 + 29*z)
Expanding the part (34*z - 33) using the distributive property, and we got: (34*z)*(-15*z**2 + 29*z) - 33*(-15*z**2 + 29*z)
<replace-#Step 1>#Step 2:
Current expression: (34*z)*(-15*z**2 + 29*z) - 33*(-15*z**2 + 29*z)</replace>
Simplifying the partial expression: -33*(-15*z**2 + 29*z)
Expanding the part (-15*z**2 + 29*z) using the distributive property, and we got: (29*z)*(-33) - 15*z**2*(-33)
Replacing -33*(-15*z**2 + 29*z) with (29*z)*(-33) - 15*z**2*(-33) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (29*z)*(-33) + (34*z)*(-15*z**2 + 29*z) - 15*z**2*(-33)</replace>
Simplifying the partial expression: (34*z)*(-15*z**2 + 29*z)
Expanding the part (-15*z**2 + 29*z) using the distributive property, and we got: (29*z)*(34*z) + (34*z)*(-15*z**2)
Replacing (34*z)*(-15*z**2 + 29*z) with (29*z)*(34*z) + (34*z)*(-15*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (29*z)*(34*z) + (29*z)*(-33) + (34*z)*(-15*z**2) - 15*z**2*(-33)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-15*z**2)*-33 = 495*z**2
  (-15*z**2)*(34*z) = -510*z**3
  (29*z)*-33 = -957*z
  (29*z)*(34*z) = 986*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -510*z**3 + 495*z**2 + 986*z**2 - 957*z</replace>
Combining like terms, got -510*z**3 + 1481*z**2 - 957*z
<replace-#Step 5>#Step 6:
Current expression: -510*z**3 + 1481*z**2 - 957*z</replace>
No more calculations needed.
<answer>-510*z**3 + 1481*z**2 - 957*z</answer>


Question:
Calculate the following: (-50*x**3 - 44)*(-39*x**3 - 23*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: 1950*x**6 + 1150*x**4 + 1716*x**3 + 1012*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: (-50*x**3 - 44)*(-39*x**3 - 23*x)
Expanding the part (-50*x**3 - 44) using the distributive property, and we got: (-50*x**3)*(-39*x**3 - 23*x) - 44*(-39*x**3 - 23*x)
<replace-#Step 1>#Step 2:
Current expression: (-50*x**3)*(-39*x**3 - 23*x) - 44*(-39*x**3 - 23*x)</replace>
Simplifying the partial expression: -44*(-39*x**3 - 23*x)
Expanding the part (-39*x**3 - 23*x) using the distributive property, and we got: -23*x*(-44) - 39*x**3*(-44)
Replacing -44*(-39*x**3 - 23*x) with -23*x*(-44) - 39*x**3*(-44) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -23*x*(-44) + (-50*x**3)*(-39*x**3 - 23*x) - 39*x**3*(-44)</replace>
Simplifying the partial expression: (-50*x**3)*(-39*x**3 - 23*x)
Expanding the part (-39*x**3 - 23*x) using the distributive property, and we got: (-23*x)*(-50*x**3) + (-50*x**3)*(-39*x**3)
Replacing (-50*x**3)*(-39*x**3 - 23*x) with (-23*x)*(-50*x**3) + (-50*x**3)*(-39*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-23*x)*(-50*x**3) - 23*x*(-44) + (-50*x**3)*(-39*x**3) - 39*x**3*(-44)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-39*x**3)*-44 = 1716*x**3
  (-39*x**3)*(-50*x**3) = 1950*x**6
  (-23*x)*-44 = 1012*x
  (-23*x)*(-50*x**3) = 1150*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1950*x**6 + 1150*x**4 + 1716*x**3 + 1012*x</replace>
No more calculations needed.
<answer>1950*x**6 + 1150*x**4 + 1716*x**3 + 1012*x</answer>