Question:
Calculate the following: (22*x**2 - 18*x)*(-11*x**3 + 14*x**2 - 1)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -242*x**5 + 506*x**4 - 252*x**3 - 22*x**2 + 18*x


Question:
Calculate the following: (-2*y - 30)*(27*y**2 - 76)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -54*y**3 - 810*y**2 + 152*y + 2280

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-2*y - 30)*(27*y**2 - 76)
Expanding the part (27*y**2 - 76) using the distributive property, and we got: (27*y**2)*(-2*y - 30) - 76*(-2*y - 30)
<replace-#Step 1>#Step 2:
Current expression: (27*y**2)*(-2*y - 30) - 76*(-2*y - 30)</replace>
Simplifying the partial expression: -76*(-2*y - 30)
Expanding the part (-2*y - 30) using the distributive property, and we got: -2*y*(-76) - 30*(-76)
Replacing -76*(-2*y - 30) with -2*y*(-76) - 30*(-76) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -2*y*(-76) + (27*y**2)*(-2*y - 30) + 2280</replace>
Simplifying the partial expression: (27*y**2)*(-2*y - 30)
Expanding the part (-2*y - 30) using the distributive property, and we got: (-2*y)*(27*y**2) - 810*y**2
Replacing (27*y**2)*(-2*y - 30) with (-2*y)*(27*y**2) - 810*y**2 in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-2*y)*(27*y**2) - 2*y*(-76) - 30*27*y**2 + 2280</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-2*y)*-76 = 152*y
  (-2*y)*(27*y**2) = -54*y**3
  -30*27*y**2 = -810*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -54*y**3 - 810*y**2 + 152*y + 2280</replace>
No more calculations needed.
<answer>-54*y**3 - 810*y**2 + 152*y + 2280</answer>


Question:
Simplify this expression: (24*y + 31)*(-48*y**3 + 33*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: -1152*y**4 - 1488*y**3 + 792*y**2 + 1023*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: (24*y + 31)*(-48*y**3 + 33*y)
Expanding the part (24*y + 31) using the distributive property, and we got: (24*y)*(-48*y**3 + 33*y) + 31*(-48*y**3 + 33*y)
<replace-#Step 1>#Step 2:
Current expression: (24*y)*(-48*y**3 + 33*y) + 31*(-48*y**3 + 33*y)</replace>
Simplifying the partial expression: 31*(-48*y**3 + 33*y)
Expanding the part (-48*y**3 + 33*y) using the distributive property, and we got: (33*y)*31 - 48*y**3*31
Replacing 31*(-48*y**3 + 33*y) with (33*y)*31 - 48*y**3*31 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (24*y)*(-48*y**3 + 33*y) + (33*y)*31 - 48*y**3*31</replace>
Simplifying the partial expression: (24*y)*(-48*y**3 + 33*y)
Expanding the part (-48*y**3 + 33*y) using the distributive property, and we got: (24*y)*(33*y) + (24*y)*(-48*y**3)
Replacing (24*y)*(-48*y**3 + 33*y) with (24*y)*(33*y) + (24*y)*(-48*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (24*y)*(33*y) + (24*y)*(-48*y**3) + (33*y)*31 - 48*y**3*31</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-48*y**3)*31 = -1488*y**3
  (-48*y**3)*(24*y) = -1152*y**4
  (33*y)*31 = 1023*y
  (33*y)*(24*y) = 792*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1152*y**4 - 1488*y**3 + 792*y**2 + 1023*y</replace>
No more calculations needed.
<answer>-1152*y**4 - 1488*y**3 + 792*y**2 + 1023*y</answer>


Question:
Calculate the following: (26*z**3 + 14*z**2)*(-38*z**3 - 37*z - 37)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -988*z**6 - 532*z**5 - 962*z**4 - 1480*z**3 - 518*z**2


Question:
Calculate the following: (-33*x**2 - 20*x + 9)*(18*x**3 - 16*x**2 + 21)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -594*x**5 + 168*x**4 + 482*x**3 - 837*x**2 - 420*x + 189


Question:
Simplify this expression: -62*x**3*(24*x - 50)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1488*x**4 + 3100*x**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -62*x**3*(24*x - 50)
Expanding the part (24*x - 50) using the distributive property, and we got: -(-1)*3100*x**3 + (24*x)*(-62*x**3)
<replace-#Step 1>#Step 2:
Current expression: -(-1)*3100*x**3 + (24*x)*(-62*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -50*(-62*x**3) = 3100*x**3
  (24*x)*(-62*x**3) = -1488*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1488*x**4 + 3100*x**3</replace>
No more calculations needed.
<answer>-1488*x**4 + 3100*x**3</answer>


Question:
Simplify this expression: (24 - 4*y)*(33*y**3 - 35)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -132*y**4 + 792*y**3 + 140*y - 840

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 - 4*y)*(33*y**3 - 35)
Expanding the part (33*y**3 - 35) using the distributive property, and we got: (33*y**3)*(24 - 4*y) - 35*(24 - 4*y)
<replace-#Step 1>#Step 2:
Current expression: (33*y**3)*(24 - 4*y) - 35*(24 - 4*y)</replace>
Simplifying the partial expression: -35*(24 - 4*y)
Expanding the part (24 - 4*y) using the distributive property, and we got: -4*y*(-35) + 24*(-35)
Replacing -35*(24 - 4*y) with -4*y*(-35) + 24*(-35) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -4*y*(-35) + (33*y**3)*(24 - 4*y) - 840</replace>
Simplifying the partial expression: (33*y**3)*(24 - 4*y)
Expanding the part (24 - 4*y) using the distributive property, and we got: (-4*y)*(33*y**3) + 24*(33*y**3)
Replacing (33*y**3)*(24 - 4*y) with (-4*y)*(33*y**3) + 24*(33*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-4*y)*(33*y**3) - 4*y*(-35) + 24*33*y**3 - 840</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-4*y)*-35 = 140*y
  (-4*y)*(33*y**3) = -132*y**4
  24*33*y**3 = 792*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -132*y**4 + 792*y**3 + 140*y - 840</replace>
No more calculations needed.
<answer>-132*y**4 + 792*y**3 + 140*y - 840</answer>


Question:
Simplify this expression: (-30*z**2 - 69*z - 12)*(-40*z**3 + 32*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: 1200*z**5 + 2760*z**4 - 480*z**3 - 2268*z**2 - 522*z - 24


Question:
Simplify this expression: 496*x**3 + 1581*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: 496*x**3 + 1581*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: 496*x**3 + 1581*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: 496*x**3 + 1581*x</replace>
No more calculations needed.
<answer>496*x**3 + 1581*x</answer>


Question:
Calculate the following: 420*z**3 - 270*z**2 - 300*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: 420*z**3 - 270*z**2 - 300*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: 420*z**3 - 270*z**2 - 300*z
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: 420*z**3 - 270*z**2 - 300*z</replace>
No more calculations needed.
<answer>420*z**3 - 270*z**2 - 300*z</answer>


Question:
Simplify this expression: (2 - 14*z**2)*(-82*z**3 + 3*z + 17)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1148*z**5 - 206*z**3 - 238*z**2 + 6*z + 34

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 - 14*z**2)*(-82*z**3 + 3*z + 17)
Expanding the part (2 - 14*z**2) using the distributive property, and we got: (-14*z**2)*(-82*z**3 + 3*z + 17) + 2*(-82*z**3 + 3*z + 17)
<replace-#Step 1>#Step 2:
Current expression: (-14*z**2)*(-82*z**3 + 3*z + 17) + 2*(-82*z**3 + 3*z + 17)</replace>
Simplifying the partial expression: 2*(-82*z**3 + 3*z + 17)
Expanding the part (-82*z**3 + 3*z + 17) using the distributive property, and we got: (3*z)*2 - 82*z**3*2 + 17*2
Replacing 2*(-82*z**3 + 3*z + 17) with (3*z)*2 - 82*z**3*2 + 17*2 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (3*z)*2 + (-14*z**2)*(-82*z**3 + 3*z + 17) - 82*z**3*2 + 34</replace>
Simplifying the partial expression: (-14*z**2)*(-82*z**3 + 3*z + 17)
Expanding the part (-82*z**3 + 3*z + 17) using the distributive property, and we got: 17*(-14*z**2) + (3*z)*(-14*z**2) + (-14*z**2)*(-82*z**3)
Replacing (-14*z**2)*(-82*z**3 + 3*z + 17) with 17*(-14*z**2) + (3*z)*(-14*z**2) + (-14*z**2)*(-82*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 17*(-14)*z**2 + (3*z)*(-14*z**2) + (3*z)*2 + (-14*z**2)*(-82*z**3) - 82*z**3*2 + 34</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-82*z**3)*2 = -164*z**3
  (-82*z**3)*(-14*z**2) = 1148*z**5
  (3*z)*2 = 6*z
  (3*z)*(-14*z**2) = -42*z**3
  17*-14*z**2 = -238*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1148*z**5 - 164*z**3 - 42*z**3 - 238*z**2 + 6*z + 34</replace>
Combining like terms, got 1148*z**5 - 206*z**3 - 238*z**2 + 6*z + 34
<replace-#Step 5>#Step 6:
Current expression: 1148*z**5 - 206*z**3 - 238*z**2 + 6*z + 34</replace>
No more calculations needed.
<answer>1148*z**5 - 206*z**3 - 238*z**2 + 6*z + 34</answer>


Question:
Simplify this expression: (-20*y - 38)*(34*y**3 - 25*y**2 + 21*y + 41)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -680*y**4 - 792*y**3 + 530*y**2 - 1618*y - 1558


Question:
Calculate the following: (-48*x**3 - 19*x**2)*(18*x**3 - 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: -864*x**6 - 342*x**5 + 480*x**3 + 190*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: (-48*x**3 - 19*x**2)*(18*x**3 - 10)
Expanding the part (18*x**3 - 10) using the distributive property, and we got: (18*x**3)*(-48*x**3 - 19*x**2) - 10*(-48*x**3 - 19*x**2)
<replace-#Step 1>#Step 2:
Current expression: (18*x**3)*(-48*x**3 - 19*x**2) - 10*(-48*x**3 - 19*x**2)</replace>
Simplifying the partial expression: -10*(-48*x**3 - 19*x**2)
Expanding the part (-48*x**3 - 19*x**2) using the distributive property, and we got: -19*x**2*(-10) - 48*x**3*(-10)
Replacing -10*(-48*x**3 - 19*x**2) with -19*x**2*(-10) - 48*x**3*(-10) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -19*x**2*(-10) - 48*x**3*(-10) + (18*x**3)*(-48*x**3 - 19*x**2)</replace>
Simplifying the partial expression: (18*x**3)*(-48*x**3 - 19*x**2)
Expanding the part (-48*x**3 - 19*x**2) using the distributive property, and we got: (-19*x**2)*(18*x**3) + (-48*x**3)*(18*x**3)
Replacing (18*x**3)*(-48*x**3 - 19*x**2) with (-19*x**2)*(18*x**3) + (-48*x**3)*(18*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-19*x**2)*(18*x**3) - 19*x**2*(-10) + (-48*x**3)*(18*x**3) - 48*x**3*(-10)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-48*x**3)*-10 = 480*x**3
  (-48*x**3)*(18*x**3) = -864*x**6
  (-19*x**2)*-10 = 190*x**2
  (-19*x**2)*(18*x**3) = -342*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -864*x**6 - 342*x**5 + 480*x**3 + 190*x**2</replace>
No more calculations needed.
<answer>-864*x**6 - 342*x**5 + 480*x**3 + 190*x**2</answer>


Question:
Simplify this expression: -56*y**3*(-18*y**3 - 28*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: 1008*y**6 + 1568*y**4 - 168*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: -56*y**3*(-18*y**3 - 28*y + 3)
Expanding the part (-18*y**3 - 28*y + 3) using the distributive property, and we got: (-28*y)*(-56*y**3) + 3*(-56*y**3) + (-56*y**3)*(-18*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-28*y)*(-56*y**3) + 3*(-56*y**3) + (-56*y**3)*(-18*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  3*(-56*y**3) = -168*y**3
  (-28*y)*(-56*y**3) = 1568*y**4
  (-18*y**3)*(-56*y**3) = 1008*y**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1008*y**6 + 1568*y**4 - 168*y**3</replace>
No more calculations needed.
<answer>1008*y**6 + 1568*y**4 - 168*y**3</answer>


Question:
Calculate the following: (48*x**3 - 73*x)*(7*x**3 + 26*x**2 + 30*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: 336*x**6 + 1248*x**5 + 929*x**4 - 1898*x**3 - 2190*x**2


Question:
Calculate the following: -2205*x - 2772
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2205*x - 2772

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: -2205*x - 2772
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: -2205*x - 2772</replace>
No more calculations needed.
<answer>-2205*x - 2772</answer>


Question:
Simplify this expression: (8*y - 22)*(15*y**3 + 2*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: 120*y**4 - 330*y**3 + 16*y**2 - 44*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: (8*y - 22)*(15*y**3 + 2*y)
Expanding the part (8*y - 22) using the distributive property, and we got: (8*y)*(15*y**3 + 2*y) - 22*(15*y**3 + 2*y)
<replace-#Step 1>#Step 2:
Current expression: (8*y)*(15*y**3 + 2*y) - 22*(15*y**3 + 2*y)</replace>
Simplifying the partial expression: -22*(15*y**3 + 2*y)
Expanding the part (15*y**3 + 2*y) using the distributive property, and we got: (2*y)*(-22) + (15*y**3)*(-22)
Replacing -22*(15*y**3 + 2*y) with (2*y)*(-22) + (15*y**3)*(-22) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (2*y)*(-22) + (8*y)*(15*y**3 + 2*y) + (15*y**3)*(-22)</replace>
Simplifying the partial expression: (8*y)*(15*y**3 + 2*y)
Expanding the part (15*y**3 + 2*y) using the distributive property, and we got: (2*y)*(8*y) + (8*y)*(15*y**3)
Replacing (8*y)*(15*y**3 + 2*y) with (2*y)*(8*y) + (8*y)*(15*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (2*y)*(8*y) + (2*y)*(-22) + (8*y)*(15*y**3) + (15*y**3)*(-22)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (2*y)*-22 = -44*y
  (2*y)*(8*y) = 16*y**2
  (15*y**3)*-22 = -330*y**3
  (15*y**3)*(8*y) = 120*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 120*y**4 - 330*y**3 + 16*y**2 - 44*y</replace>
No more calculations needed.
<answer>120*y**4 - 330*y**3 + 16*y**2 - 44*y</answer>


Question:
Calculate the following: 52*x**3*(47*x**3 - 23*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: 2444*x**6 - 1196*x**5

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 52*x**3*(47*x**3 - 23*x**2)
Expanding the part (47*x**3 - 23*x**2) using the distributive property, and we got: (-23*x**2)*(52*x**3) + (47*x**3)*(52*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-23*x**2)*(52*x**3) + (47*x**3)*(52*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-23*x**2)*(52*x**3) = -1196*x**5
  (47*x**3)*(52*x**3) = 2444*x**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 2444*x**6 - 1196*x**5</replace>
No more calculations needed.
<answer>2444*x**6 - 1196*x**5</answer>


Question:
Calculate the following: (41*y**2 + 13*y + 50)*(-7*y**3 + 9*y**2 + 40*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: -287*y**5 + 278*y**4 + 1407*y**3 + 970*y**2 + 2000*y


Question:
Simplify this expression: 22*x*(45*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: 990*x**2 - 88*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: 22*x*(45*x - 4)
Expanding the part (45*x - 4) using the distributive property, and we got: -88*x + (22*x)*(45*x)
<replace-#Step 1>#Step 2:
Current expression: -88*x + (22*x)*(45*x)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -4*(22*x) = -88*x
  (45*x)*(22*x) = 990*x**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 990*x**2 - 88*x</replace>
No more calculations needed.
<answer>990*x**2 - 88*x</answer>


Question:
Simplify this expression: (8*y + 13)*(-38*y**2 + 39*y - 44)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -304*y**3 - 182*y**2 + 155*y - 572

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*y + 13)*(-38*y**2 + 39*y - 44)
Expanding the part (8*y + 13) using the distributive property, and we got: (8*y)*(-38*y**2 + 39*y - 44) + 13*(-38*y**2 + 39*y - 44)
<replace-#Step 1>#Step 2:
Current expression: (8*y)*(-38*y**2 + 39*y - 44) + 13*(-38*y**2 + 39*y - 44)</replace>
Simplifying the partial expression: 13*(-38*y**2 + 39*y - 44)
Expanding the part (-38*y**2 + 39*y - 44) using the distributive property, and we got: (39*y)*13 - 38*y**2*13 - 44*13
Replacing 13*(-38*y**2 + 39*y - 44) with (39*y)*13 - 38*y**2*13 - 44*13 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (8*y)*(-38*y**2 + 39*y - 44) + (39*y)*13 - 38*y**2*13 - 572</replace>
Simplifying the partial expression: (8*y)*(-38*y**2 + 39*y - 44)
Expanding the part (-38*y**2 + 39*y - 44) using the distributive property, and we got: -352*y + (8*y)*(39*y) + (8*y)*(-38*y**2)
Replacing (8*y)*(-38*y**2 + 39*y - 44) with -352*y + (8*y)*(39*y) + (8*y)*(-38*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -44*8*y + (8*y)*(39*y) + (8*y)*(-38*y**2) + (39*y)*13 - 38*y**2*13 - 572</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-38*y**2)*13 = -494*y**2
  (-38*y**2)*(8*y) = -304*y**3
  (39*y)*13 = 507*y
  (39*y)*(8*y) = 312*y**2
  -44*8*y = -352*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -304*y**3 - 494*y**2 + 312*y**2 - 352*y + 507*y - 572</replace>
Combining like terms, got -304*y**3 - 182*y**2 + 155*y - 572
<replace-#Step 5>#Step 6:
Current expression: -304*y**3 - 182*y**2 + 155*y - 572</replace>
No more calculations needed.
<answer>-304*y**3 - 182*y**2 + 155*y - 572</answer>


Question:
Calculate the following: (-42*y**2 - 10*y)*(57*y**3 + 55*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: -2394*y**5 - 570*y**4 - 2310*y**3 - 550*y**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-42*y**2 - 10*y)*(57*y**3 + 55*y)
Expanding the part (-42*y**2 - 10*y) using the distributive property, and we got: (-10*y)*(57*y**3 + 55*y) + (-42*y**2)*(57*y**3 + 55*y)
<replace-#Step 1>#Step 2:
Current expression: (-10*y)*(57*y**3 + 55*y) + (-42*y**2)*(57*y**3 + 55*y)</replace>
Simplifying the partial expression: (-42*y**2)*(57*y**3 + 55*y)
Expanding the part (57*y**3 + 55*y) using the distributive property, and we got: (55*y)*(-42*y**2) + (-42*y**2)*(57*y**3)
Replacing (-42*y**2)*(57*y**3 + 55*y) with (55*y)*(-42*y**2) + (-42*y**2)*(57*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-10*y)*(57*y**3 + 55*y) + (55*y)*(-42*y**2) + (-42*y**2)*(57*y**3)</replace>
Simplifying the partial expression: (-10*y)*(57*y**3 + 55*y)
Expanding the part (57*y**3 + 55*y) using the distributive property, and we got: (-10*y)*(55*y) + (-10*y)*(57*y**3)
Replacing (-10*y)*(57*y**3 + 55*y) with (-10*y)*(55*y) + (-10*y)*(57*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-10*y)*(55*y) + (-10*y)*(57*y**3) + (55*y)*(-42*y**2) + (-42*y**2)*(57*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (55*y)*(-42*y**2) = -2310*y**3
  (55*y)*(-10*y) = -550*y**2
  (57*y**3)*(-42*y**2) = -2394*y**5
  (57*y**3)*(-10*y) = -570*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2394*y**5 - 570*y**4 - 2310*y**3 - 550*y**2</replace>
No more calculations needed.
<answer>-2394*y**5 - 570*y**4 - 2310*y**3 - 550*y**2</answer>


Question:
Calculate the following: (15*x**3 + 31*x)*(-23*x**3 - 44*x**2 + 24*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: -345*x**6 - 660*x**5 - 353*x**4 - 1364*x**3 + 744*x**2


Question:
Simplify this expression: 3567 - 2001*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: 3567 - 2001*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: 3567 - 2001*z
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: 3567 - 2001*z</replace>
No more calculations needed.
<answer>3567 - 2001*z</answer>


Question:
Simplify this expression: (-39*x**3 + 39*x)*(4*x**3 + 41*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: -156*x**6 - 1443*x**4 + 1599*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: (-39*x**3 + 39*x)*(4*x**3 + 41*x)
Expanding the part (-39*x**3 + 39*x) using the distributive property, and we got: (39*x)*(4*x**3 + 41*x) + (-39*x**3)*(4*x**3 + 41*x)
<replace-#Step 1>#Step 2:
Current expression: (39*x)*(4*x**3 + 41*x) + (-39*x**3)*(4*x**3 + 41*x)</replace>
Simplifying the partial expression: (-39*x**3)*(4*x**3 + 41*x)
Expanding the part (4*x**3 + 41*x) using the distributive property, and we got: (41*x)*(-39*x**3) + (-39*x**3)*(4*x**3)
Replacing (-39*x**3)*(4*x**3 + 41*x) with (41*x)*(-39*x**3) + (-39*x**3)*(4*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (39*x)*(4*x**3 + 41*x) + (41*x)*(-39*x**3) + (-39*x**3)*(4*x**3)</replace>
Simplifying the partial expression: (39*x)*(4*x**3 + 41*x)
Expanding the part (4*x**3 + 41*x) using the distributive property, and we got: (39*x)*(41*x) + (39*x)*(4*x**3)
Replacing (39*x)*(4*x**3 + 41*x) with (39*x)*(41*x) + (39*x)*(4*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (39*x)*(41*x) + (39*x)*(4*x**3) + (41*x)*(-39*x**3) + (-39*x**3)*(4*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (4*x**3)*(-39*x**3) = -156*x**6
  (4*x**3)*(39*x) = 156*x**4
  (41*x)*(-39*x**3) = -1599*x**4
  (41*x)*(39*x) = 1599*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -156*x**6 - 1599*x**4 + 156*x**4 + 1599*x**2</replace>
Combining like terms, got -156*x**6 - 1443*x**4 + 1599*x**2
<replace-#Step 5>#Step 6:
Current expression: -156*x**6 - 1443*x**4 + 1599*x**2</replace>
No more calculations needed.
<answer>-156*x**6 - 1443*x**4 + 1599*x**2</answer>


Question:
Calculate the following: (28*y**2 - 47*y + 47)*(4*y**3 - 2*y**2 + 75*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: 112*y**5 - 244*y**4 + 2382*y**3 - 3619*y**2 + 3525*y


Question:
Simplify this expression: (34*x**2 + 47)*(95*x**3 - 23*x**2 - 27*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: 3230*x**5 - 782*x**4 + 3547*x**3 - 1081*x**2 - 1269*x


Question:
Simplify this expression: (-31*z**3 - 11)*(-45*z**2 - 18*z + 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: 1395*z**5 + 558*z**4 - 310*z**3 + 495*z**2 + 198*z - 110

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**3 - 11)*(-45*z**2 - 18*z + 10)
Expanding the part (-31*z**3 - 11) using the distributive property, and we got: (-31*z**3)*(-45*z**2 - 18*z + 10) - 11*(-45*z**2 - 18*z + 10)
<replace-#Step 1>#Step 2:
Current expression: (-31*z**3)*(-45*z**2 - 18*z + 10) - 11*(-45*z**2 - 18*z + 10)</replace>
Simplifying the partial expression: -11*(-45*z**2 - 18*z + 10)
Expanding the part (-45*z**2 - 18*z + 10) using the distributive property, and we got: -18*z*(-11) - 45*z**2*(-11) + 10*(-11)
Replacing -11*(-45*z**2 - 18*z + 10) with -18*z*(-11) - 45*z**2*(-11) + 10*(-11) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -18*z*(-11) - 45*z**2*(-11) + (-31*z**3)*(-45*z**2 - 18*z + 10) - 110</replace>
Simplifying the partial expression: (-31*z**3)*(-45*z**2 - 18*z + 10)
Expanding the part (-45*z**2 - 18*z + 10) using the distributive property, and we got: (-18*z)*(-31*z**3) + 10*(-31*z**3) + (-45*z**2)*(-31*z**3)
Replacing (-31*z**3)*(-45*z**2 - 18*z + 10) with (-18*z)*(-31*z**3) + 10*(-31*z**3) + (-45*z**2)*(-31*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-18*z)*(-31*z**3) - 18*z*(-11) + 10*(-31)*z**3 + (-45*z**2)*(-31*z**3) - 45*z**2*(-11) - 110</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-45*z**2)*-11 = 495*z**2
  (-45*z**2)*(-31*z**3) = 1395*z**5
  (-18*z)*-11 = 198*z
  (-18*z)*(-31*z**3) = 558*z**4
  10*-31*z**3 = -310*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1395*z**5 + 558*z**4 - 310*z**3 + 495*z**2 + 198*z - 110</replace>
No more calculations needed.
<answer>1395*z**5 + 558*z**4 - 310*z**3 + 495*z**2 + 198*z - 110</answer>


Question:
Simplify this expression: (37*z**2 - 10*z - 32)*(-2*z**3 - 9*z**2 + 19)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -74*z**5 - 313*z**4 + 154*z**3 + 991*z**2 - 190*z - 608


Question:
Calculate the following: (26*x - 22)*(39*x**2 - 18)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1014*x**3 - 858*x**2 - 468*x + 396

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (26*x - 22)*(39*x**2 - 18)
Expanding the part (26*x - 22) using the distributive property, and we got: (26*x)*(39*x**2 - 18) - 22*(39*x**2 - 18)
<replace-#Step 1>#Step 2:
Current expression: (26*x)*(39*x**2 - 18) - 22*(39*x**2 - 18)</replace>
Simplifying the partial expression: -22*(39*x**2 - 18)
Expanding the part (39*x**2 - 18) using the distributive property, and we got: (39*x**2)*(-22) - 18*(-22)
Replacing -22*(39*x**2 - 18) with (39*x**2)*(-22) - 18*(-22) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (26*x)*(39*x**2 - 18) + (39*x**2)*(-22) + 396</replace>
Simplifying the partial expression: (26*x)*(39*x**2 - 18)
Expanding the part (39*x**2 - 18) using the distributive property, and we got: -468*x + (26*x)*(39*x**2)
Replacing (26*x)*(39*x**2 - 18) with -468*x + (26*x)*(39*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -18*26*x + (26*x)*(39*x**2) + (39*x**2)*(-22) + 396</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (39*x**2)*-22 = -858*x**2
  (39*x**2)*(26*x) = 1014*x**3
  -18*26*x = -468*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1014*x**3 - 858*x**2 - 468*x + 396</replace>
No more calculations needed.
<answer>1014*x**3 - 858*x**2 - 468*x + 396</answer>


Question:
Calculate the following: (21 - 36*x**3)*(9*x**2 + 20*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -324*x**5 - 720*x**4 + 189*x**2 + 420*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (21 - 36*x**3)*(9*x**2 + 20*x)
Expanding the part (21 - 36*x**3) using the distributive property, and we got: (-36*x**3)*(9*x**2 + 20*x) + 21*(9*x**2 + 20*x)
<replace-#Step 1>#Step 2:
Current expression: (-36*x**3)*(9*x**2 + 20*x) + 21*(9*x**2 + 20*x)</replace>
Simplifying the partial expression: 21*(9*x**2 + 20*x)
Expanding the part (9*x**2 + 20*x) using the distributive property, and we got: (20*x)*21 + (9*x**2)*21
Replacing 21*(9*x**2 + 20*x) with (20*x)*21 + (9*x**2)*21 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (20*x)*21 + (9*x**2)*21 + (-36*x**3)*(9*x**2 + 20*x)</replace>
Simplifying the partial expression: (-36*x**3)*(9*x**2 + 20*x)
Expanding the part (9*x**2 + 20*x) using the distributive property, and we got: (20*x)*(-36*x**3) + (9*x**2)*(-36*x**3)
Replacing (-36*x**3)*(9*x**2 + 20*x) with (20*x)*(-36*x**3) + (9*x**2)*(-36*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (20*x)*(-36*x**3) + (20*x)*21 + (9*x**2)*(-36*x**3) + (9*x**2)*21</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (9*x**2)*21 = 189*x**2
  (9*x**2)*(-36*x**3) = -324*x**5
  (20*x)*21 = 420*x
  (20*x)*(-36*x**3) = -720*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -324*x**5 - 720*x**4 + 189*x**2 + 420*x</replace>
No more calculations needed.
<answer>-324*x**5 - 720*x**4 + 189*x**2 + 420*x</answer>


Question:
Simplify this expression: (35 - 24*y**2)*(-12*y**3 + 39*y**2 - 47*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: 288*y**5 - 936*y**4 + 708*y**3 + 1365*y**2 - 1645*y


Question:
Calculate the following: (-32*x**3 + 35*x**2)*(18*x**3 + 23*x**2 - 31*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -576*x**6 - 106*x**5 + 1797*x**4 - 1085*x**3


Question:
Simplify this expression: (-40*y**2 - 12*y - 30)*(-12*y**3 - 43*y**2 + 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: 480*y**5 + 1864*y**4 + 876*y**3 + 1210*y**2 - 24*y - 60


Question:
Calculate the following: 17*x**2*(-60*x**3 - 18*x**2 - 4*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: -1020*x**5 - 306*x**4 - 68*x**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 17*x**2*(-60*x**3 - 18*x**2 - 4*x)
Expanding the part (-60*x**3 - 18*x**2 - 4*x) using the distributive property, and we got: (-4*x)*(17*x**2) + (-18*x**2)*(17*x**2) + (17*x**2)*(-60*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-4*x)*(17*x**2) + (-18*x**2)*(17*x**2) + (17*x**2)*(-60*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-60*x**3)*(17*x**2) = -1020*x**5
  (-18*x**2)*(17*x**2) = -306*x**4
  (-4*x)*(17*x**2) = -68*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1020*x**5 - 306*x**4 - 68*x**3</replace>
No more calculations needed.
<answer>-1020*x**5 - 306*x**4 - 68*x**3</answer>


Question:
Simplify this expression: (-50*x**3 - 18*x)*(44*x**3 + 5*x**2 + 9)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2200*x**6 - 250*x**5 - 792*x**4 - 540*x**3 - 162*x


Question:
Simplify this expression: 24*z**2*(49*z**2 - 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: 1176*z**4 - 1128*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: 24*z**2*(49*z**2 - 47)
Expanding the part (49*z**2 - 47) using the distributive property, and we got: -1128*z**2 + (24*z**2)*(49*z**2)
<replace-#Step 1>#Step 2:
Current expression: -1128*z**2 + (24*z**2)*(49*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -47*(24*z**2) = -1128*z**2
  (49*z**2)*(24*z**2) = 1176*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1176*z**4 - 1128*z**2</replace>
No more calculations needed.
<answer>1176*z**4 - 1128*z**2</answer>


Question:
Calculate the following: (2*x**3 + 20*x**2)*(26*x**3 + 7*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: 52*x**6 + 534*x**5 + 140*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: (2*x**3 + 20*x**2)*(26*x**3 + 7*x**2)
Expanding the part (2*x**3 + 20*x**2) using the distributive property, and we got: (20*x**2)*(26*x**3 + 7*x**2) + (2*x**3)*(26*x**3 + 7*x**2)
<replace-#Step 1>#Step 2:
Current expression: (20*x**2)*(26*x**3 + 7*x**2) + (2*x**3)*(26*x**3 + 7*x**2)</replace>
Simplifying the partial expression: (2*x**3)*(26*x**3 + 7*x**2)
Expanding the part (26*x**3 + 7*x**2) using the distributive property, and we got: (7*x**2)*(2*x**3) + (2*x**3)*(26*x**3)
Replacing (2*x**3)*(26*x**3 + 7*x**2) with (7*x**2)*(2*x**3) + (2*x**3)*(26*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (7*x**2)*(2*x**3) + (20*x**2)*(26*x**3 + 7*x**2) + (2*x**3)*(26*x**3)</replace>
Simplifying the partial expression: (20*x**2)*(26*x**3 + 7*x**2)
Expanding the part (26*x**3 + 7*x**2) using the distributive property, and we got: (7*x**2)*(20*x**2) + (20*x**2)*(26*x**3)
Replacing (20*x**2)*(26*x**3 + 7*x**2) with (7*x**2)*(20*x**2) + (20*x**2)*(26*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (7*x**2)*(20*x**2) + (7*x**2)*(2*x**3) + (20*x**2)*(26*x**3) + (2*x**3)*(26*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (7*x**2)*(2*x**3) = 14*x**5
  (7*x**2)*(20*x**2) = 140*x**4
  (26*x**3)*(2*x**3) = 52*x**6
  (26*x**3)*(20*x**2) = 520*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 52*x**6 + 14*x**5 + 520*x**5 + 140*x**4</replace>
Combining like terms, got 52*x**6 + 534*x**5 + 140*x**4
<replace-#Step 5>#Step 6:
Current expression: 52*x**6 + 534*x**5 + 140*x**4</replace>
No more calculations needed.
<answer>52*x**6 + 534*x**5 + 140*x**4</answer>


Question:
Calculate the following: -58*y**2*(33*y**2 - 11*y + 1)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1914*y**4 + 638*y**3 - 58*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: -58*y**2*(33*y**2 - 11*y + 1)
Expanding the part (33*y**2 - 11*y + 1) using the distributive property, and we got: (-11*y)*(-58*y**2) + 1*(-58*y**2) + (-58*y**2)*(33*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-11*y)*(-58*y**2) + 1*(-58*y**2) + (-58*y**2)*(33*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  1*(-58*y**2) = -58*y**2
  (-11*y)*(-58*y**2) = 638*y**3
  (33*y**2)*(-58*y**2) = -1914*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1914*y**4 + 638*y**3 - 58*y**2</replace>
No more calculations needed.
<answer>-1914*y**4 + 638*y**3 - 58*y**2</answer>


Question:
Calculate the following: -96*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: -96*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: -96*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: -96*z**2</replace>
No more calculations needed.
<answer>-96*z**2</answer>


Question:
Simplify this expression: 16*y**3*(3*y**2 - 10*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: 48*y**5 - 160*y**4 + 160*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: 16*y**3*(3*y**2 - 10*y + 10)
Expanding the part (3*y**2 - 10*y + 10) using the distributive property, and we got: (-10*y)*(16*y**3) + 10*(16*y**3) + (3*y**2)*(16*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-10*y)*(16*y**3) + 10*(16*y**3) + (3*y**2)*(16*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  10*(16*y**3) = 160*y**3
  (-10*y)*(16*y**3) = -160*y**4
  (3*y**2)*(16*y**3) = 48*y**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 48*y**5 - 160*y**4 + 160*y**3</replace>
No more calculations needed.
<answer>48*y**5 - 160*y**4 + 160*y**3</answer>


Question:
Simplify this expression: (-45*z**3 + 9*z**2)*(-50*z**3 - 39*z**2 - 1)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2250*z**6 + 1305*z**5 - 351*z**4 + 45*z**3 - 9*z**2


Question:
Simplify this expression: (36*x**3 + 11*x)*(-12*x**3 - 17*x - 26)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -432*x**6 - 744*x**4 - 936*x**3 - 187*x**2 - 286*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: (36*x**3 + 11*x)*(-12*x**3 - 17*x - 26)
Expanding the part (36*x**3 + 11*x) using the distributive property, and we got: (11*x)*(-12*x**3 - 17*x - 26) + (36*x**3)*(-12*x**3 - 17*x - 26)
<replace-#Step 1>#Step 2:
Current expression: (11*x)*(-12*x**3 - 17*x - 26) + (36*x**3)*(-12*x**3 - 17*x - 26)</replace>
Simplifying the partial expression: (11*x)*(-12*x**3 - 17*x - 26)
Expanding the part (-12*x**3 - 17*x - 26) using the distributive property, and we got: (-17*x)*(11*x) - 286*x + (11*x)*(-12*x**3)
Replacing (11*x)*(-12*x**3 - 17*x - 26) with (-17*x)*(11*x) - 286*x + (11*x)*(-12*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-17*x)*(11*x) - 26*11*x + (11*x)*(-12*x**3) + (36*x**3)*(-12*x**3 - 17*x - 26)</replace>
Simplifying the partial expression: (36*x**3)*(-12*x**3 - 17*x - 26)
Expanding the part (-12*x**3 - 17*x - 26) using the distributive property, and we got: (-17*x)*(36*x**3) - 936*x**3 + (-12*x**3)*(36*x**3)
Replacing (36*x**3)*(-12*x**3 - 17*x - 26) with (-17*x)*(36*x**3) - 936*x**3 + (-12*x**3)*(36*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-17*x)*(11*x) + (-17*x)*(36*x**3) - 26*36*x**3 - 26*11*x + (11*x)*(-12*x**3) + (-12*x**3)*(36*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-17*x)*(11*x) = -187*x**2
  (-17*x)*(36*x**3) = -612*x**4
  (-12*x**3)*(11*x) = -132*x**4
  (-12*x**3)*(36*x**3) = -432*x**6
  -26*11*x = -286*x
  -26*36*x**3 = -936*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -432*x**6 - 612*x**4 - 132*x**4 - 936*x**3 - 187*x**2 - 286*x</replace>
Combining like terms, got -432*x**6 - 744*x**4 - 936*x**3 - 187*x**2 - 286*x
<replace-#Step 5>#Step 6:
Current expression: -432*x**6 - 744*x**4 - 936*x**3 - 187*x**2 - 286*x</replace>
No more calculations needed.
<answer>-432*x**6 - 744*x**4 - 936*x**3 - 187*x**2 - 286*x</answer>


Question:
Calculate the following: -924*y**3 - 1302*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**3 - 1302*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: -924*y**3 - 1302*y
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: -924*y**3 - 1302*y</replace>
No more calculations needed.
<answer>-924*y**3 - 1302*y</answer>


Question:
Simplify this expression: (-16*y**2 - 38)*(48*y**3 + 7*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -768*y**5 - 112*y**4 - 1824*y**3 - 266*y**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-16*y**2 - 38)*(48*y**3 + 7*y**2)
Expanding the part (-16*y**2 - 38) using the distributive property, and we got: (-16*y**2)*(48*y**3 + 7*y**2) - 38*(48*y**3 + 7*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-16*y**2)*(48*y**3 + 7*y**2) - 38*(48*y**3 + 7*y**2)</replace>
Simplifying the partial expression: -38*(48*y**3 + 7*y**2)
Expanding the part (48*y**3 + 7*y**2) using the distributive property, and we got: (7*y**2)*(-38) + (48*y**3)*(-38)
Replacing -38*(48*y**3 + 7*y**2) with (7*y**2)*(-38) + (48*y**3)*(-38) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-16*y**2)*(48*y**3 + 7*y**2) + (7*y**2)*(-38) + (48*y**3)*(-38)</replace>
Simplifying the partial expression: (-16*y**2)*(48*y**3 + 7*y**2)
Expanding the part (48*y**3 + 7*y**2) using the distributive property, and we got: (-16*y**2)*(7*y**2) + (-16*y**2)*(48*y**3)
Replacing (-16*y**2)*(48*y**3 + 7*y**2) with (-16*y**2)*(7*y**2) + (-16*y**2)*(48*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-16*y**2)*(7*y**2) + (-16*y**2)*(48*y**3) + (7*y**2)*(-38) + (48*y**3)*(-38)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (7*y**2)*-38 = -266*y**2
  (7*y**2)*(-16*y**2) = -112*y**4
  (48*y**3)*-38 = -1824*y**3
  (48*y**3)*(-16*y**2) = -768*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -768*y**5 - 112*y**4 - 1824*y**3 - 266*y**2</replace>
No more calculations needed.
<answer>-768*y**5 - 112*y**4 - 1824*y**3 - 266*y**2</answer>


Question:
Calculate the following: (47*x + 11)*(35*x**3 - 23*x**2 - 32*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1645*x**4 - 696*x**3 - 1757*x**2 - 352*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: (47*x + 11)*(35*x**3 - 23*x**2 - 32*x)
Expanding the part (47*x + 11) using the distributive property, and we got: (47*x)*(35*x**3 - 23*x**2 - 32*x) + 11*(35*x**3 - 23*x**2 - 32*x)
<replace-#Step 1>#Step 2:
Current expression: (47*x)*(35*x**3 - 23*x**2 - 32*x) + 11*(35*x**3 - 23*x**2 - 32*x)</replace>
Simplifying the partial expression: 11*(35*x**3 - 23*x**2 - 32*x)
Expanding the part (35*x**3 - 23*x**2 - 32*x) using the distributive property, and we got: -32*x*11 - 23*x**2*11 + (35*x**3)*11
Replacing 11*(35*x**3 - 23*x**2 - 32*x) with -32*x*11 - 23*x**2*11 + (35*x**3)*11 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -32*x*11 + (47*x)*(35*x**3 - 23*x**2 - 32*x) - 23*x**2*11 + (35*x**3)*11</replace>
Simplifying the partial expression: (47*x)*(35*x**3 - 23*x**2 - 32*x)
Expanding the part (35*x**3 - 23*x**2 - 32*x) using the distributive property, and we got: (-32*x)*(47*x) + (47*x)*(-23*x**2) + (47*x)*(35*x**3)
Replacing (47*x)*(35*x**3 - 23*x**2 - 32*x) with (-32*x)*(47*x) + (47*x)*(-23*x**2) + (47*x)*(35*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-32*x)*(47*x) - 32*x*11 + (47*x)*(-23*x**2) + (47*x)*(35*x**3) - 23*x**2*11 + (35*x**3)*11</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-32*x)*11 = -352*x
  (-32*x)*(47*x) = -1504*x**2
  (-23*x**2)*11 = -253*x**2
  (-23*x**2)*(47*x) = -1081*x**3
  (35*x**3)*11 = 385*x**3
  (35*x**3)*(47*x) = 1645*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1645*x**4 - 1081*x**3 + 385*x**3 - 1504*x**2 - 253*x**2 - 352*x</replace>
Combining like terms, got 1645*x**4 - 696*x**3 - 1757*x**2 - 352*x
<replace-#Step 5>#Step 6:
Current expression: 1645*x**4 - 696*x**3 - 1757*x**2 - 352*x</replace>
No more calculations needed.
<answer>1645*x**4 - 696*x**3 - 1757*x**2 - 352*x</answer>


Question:
Calculate the following: (38*y**2 + 1)*(-10*y**3 + 34*y**2 + 49)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -380*y**5 + 1292*y**4 - 10*y**3 + 1896*y**2 + 49

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (38*y**2 + 1)*(-10*y**3 + 34*y**2 + 49)
Expanding the part (38*y**2 + 1) using the distributive property, and we got: (38*y**2)*(-10*y**3 + 34*y**2 + 49) + 1*(-10*y**3 + 34*y**2 + 49)
<replace-#Step 1>#Step 2:
Current expression: (38*y**2)*(-10*y**3 + 34*y**2 + 49) + 1*(-10*y**3 + 34*y**2 + 49)</replace>
Simplifying the partial expression: 1*(-10*y**3 + 34*y**2 + 49)
Expanding the part (-10*y**3 + 34*y**2 + 49) using the distributive property, and we got: (34*y**2)*1 - 10*y**3*1 + 49*1
Replacing 1*(-10*y**3 + 34*y**2 + 49) with (34*y**2)*1 - 10*y**3*1 + 49*1 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (34*y**2)*1 + (38*y**2)*(-10*y**3 + 34*y**2 + 49) - 10*y**3*1 + 49</replace>
Simplifying the partial expression: (38*y**2)*(-10*y**3 + 34*y**2 + 49)
Expanding the part (-10*y**3 + 34*y**2 + 49) using the distributive property, and we got: 49*(38*y**2) + (34*y**2)*(38*y**2) + (38*y**2)*(-10*y**3)
Replacing (38*y**2)*(-10*y**3 + 34*y**2 + 49) with 49*(38*y**2) + (34*y**2)*(38*y**2) + (38*y**2)*(-10*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 49*38*y**2 + (34*y**2)*(38*y**2) + (34*y**2)*1 + (38*y**2)*(-10*y**3) - 10*y**3*1 + 49</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-10*y**3)*1 = -10*y**3
  (-10*y**3)*(38*y**2) = -380*y**5
  (34*y**2)*1 = 34*y**2
  (34*y**2)*(38*y**2) = 1292*y**4
  49*38*y**2 = 1862*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -380*y**5 + 1292*y**4 - 10*y**3 + 34*y**2 + 1862*y**2 + 49</replace>
Combining like terms, got -380*y**5 + 1292*y**4 - 10*y**3 + 1896*y**2 + 49
<replace-#Step 5>#Step 6:
Current expression: -380*y**5 + 1292*y**4 - 10*y**3 + 1896*y**2 + 49</replace>
No more calculations needed.
<answer>-380*y**5 + 1292*y**4 - 10*y**3 + 1896*y**2 + 49</answer>


Question:
Calculate the following: (-7*z**3 + 44*z)*(5*z**3 + 34*z**2 + 48*z + 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: -35*z**6 - 238*z**5 - 116*z**4 + 1195*z**3 + 2112*z**2 + 1892*z


Question:
Calculate the following: (35 - 3*x**2)*(-18*x**3 - 30*x**2 - 49*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: 54*x**5 + 90*x**4 - 483*x**3 - 1050*x**2 - 1715*x


Question:
Simplify this expression: (-33*z**2 - 20*z - 7)*(7*z**3 + 7*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: -231*z**5 - 140*z**4 - 280*z**3 + 2005*z**2 + 1251*z + 455


Question:
Calculate the following: (-37*z**3 + 20*z + 13)*(38*z**3 + 15*z**2 - 42*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1406*z**6 - 555*z**5 + 2314*z**4 + 794*z**3 - 645*z**2 - 546*z


Question:
Calculate the following: (3*x - 5)*(46*x**3 - 16*x**2 - 46*x + 50)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 138*x**4 - 278*x**3 - 58*x**2 + 380*x - 250


Question:
Simplify this expression: (-64*z**2 + 24*z)*(89*z**2 + 47*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: -5696*z**4 - 872*z**3 + 1128*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: (-64*z**2 + 24*z)*(89*z**2 + 47*z)
Expanding the part (-64*z**2 + 24*z) using the distributive property, and we got: (24*z)*(89*z**2 + 47*z) + (-64*z**2)*(89*z**2 + 47*z)
<replace-#Step 1>#Step 2:
Current expression: (24*z)*(89*z**2 + 47*z) + (-64*z**2)*(89*z**2 + 47*z)</replace>
Simplifying the partial expression: (-64*z**2)*(89*z**2 + 47*z)
Expanding the part (89*z**2 + 47*z) using the distributive property, and we got: (47*z)*(-64*z**2) + (-64*z**2)*(89*z**2)
Replacing (-64*z**2)*(89*z**2 + 47*z) with (47*z)*(-64*z**2) + (-64*z**2)*(89*z**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (24*z)*(89*z**2 + 47*z) + (47*z)*(-64*z**2) + (-64*z**2)*(89*z**2)</replace>
Simplifying the partial expression: (24*z)*(89*z**2 + 47*z)
Expanding the part (89*z**2 + 47*z) using the distributive property, and we got: (24*z)*(47*z) + (24*z)*(89*z**2)
Replacing (24*z)*(89*z**2 + 47*z) with (24*z)*(47*z) + (24*z)*(89*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (24*z)*(47*z) + (24*z)*(89*z**2) + (47*z)*(-64*z**2) + (-64*z**2)*(89*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (47*z)*(-64*z**2) = -3008*z**3
  (47*z)*(24*z) = 1128*z**2
  (89*z**2)*(-64*z**2) = -5696*z**4
  (89*z**2)*(24*z) = 2136*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -5696*z**4 - 3008*z**3 + 2136*z**3 + 1128*z**2</replace>
Combining like terms, got -5696*z**4 - 872*z**3 + 1128*z**2
<replace-#Step 5>#Step 6:
Current expression: -5696*z**4 - 872*z**3 + 1128*z**2</replace>
No more calculations needed.
<answer>-5696*z**4 - 872*z**3 + 1128*z**2</answer>


Question:
Simplify this expression: (-45*x**3 + 2*x**2 - 45*x)*(35*x**3 + 50*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: -1575*x**6 - 2180*x**5 - 1160*x**4 - 2264*x**3 + 315*x**2


Question:
Simplify this expression: -3*y*(-46*y - 72)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 138*y**2 + 216*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: -3*y*(-46*y - 72)
Expanding the part (-46*y - 72) using the distributive property, and we got: (-46*y)*(-3*y) - (-1)*216*y
<replace-#Step 1>#Step 2:
Current expression: (-46*y)*(-3*y) - (-1)*216*y</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -72*(-3*y) = 216*y
  (-46*y)*(-3*y) = 138*y**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 138*y**2 + 216*y</replace>
No more calculations needed.
<answer>138*y**2 + 216*y</answer>


Question:
Simplify this expression: -22*x**2*(-70*x**3 + 5*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: 1540*x**5 - 110*x**3 - 88*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: -22*x**2*(-70*x**3 + 5*x + 4)
Expanding the part (-70*x**3 + 5*x + 4) using the distributive property, and we got: 4*(-22*x**2) + (5*x)*(-22*x**2) + (-22*x**2)*(-70*x**3)
<replace-#Step 1>#Step 2:
Current expression: 4*(-22*x**2) + (5*x)*(-22*x**2) + (-22*x**2)*(-70*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  4*(-22*x**2) = -88*x**2
  (-70*x**3)*(-22*x**2) = 1540*x**5
  (5*x)*(-22*x**2) = -110*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1540*x**5 - 110*x**3 - 88*x**2</replace>
No more calculations needed.
<answer>1540*x**5 - 110*x**3 - 88*x**2</answer>


Question:
Calculate the following: (3 - 23*y**2)*(25*y**3 - 50*y**2 + 3*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: -575*y**5 + 1150*y**4 + 6*y**3 - 472*y**2 + 9*y + 42


Question:
Calculate the following: 8*x**2*(43*x**3 + 38*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: 344*x**5 + 304*x**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 8*x**2*(43*x**3 + 38*x)
Expanding the part (43*x**3 + 38*x) using the distributive property, and we got: (38*x)*(8*x**2) + (8*x**2)*(43*x**3)
<replace-#Step 1>#Step 2:
Current expression: (38*x)*(8*x**2) + (8*x**2)*(43*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (38*x)*(8*x**2) = 304*x**3
  (43*x**3)*(8*x**2) = 344*x**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 344*x**5 + 304*x**3</replace>
No more calculations needed.
<answer>344*x**5 + 304*x**3</answer>


Question:
Simplify this expression: (-15*z**2 + 30*z)*(-38*z**2 - 35*z + 30)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 570*z**4 - 615*z**3 - 1500*z**2 + 900*z


Question:
Calculate the following: (28 - 50*y)*(17*y**3 - 43*y**2 - 64*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: -850*y**4 + 2626*y**3 + 1996*y**2 - 1792*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (28 - 50*y)*(17*y**3 - 43*y**2 - 64*y)
Expanding the part (28 - 50*y) using the distributive property, and we got: (-50*y)*(17*y**3 - 43*y**2 - 64*y) + 28*(17*y**3 - 43*y**2 - 64*y)
<replace-#Step 1>#Step 2:
Current expression: (-50*y)*(17*y**3 - 43*y**2 - 64*y) + 28*(17*y**3 - 43*y**2 - 64*y)</replace>
Simplifying the partial expression: 28*(17*y**3 - 43*y**2 - 64*y)
Expanding the part (17*y**3 - 43*y**2 - 64*y) using the distributive property, and we got: -64*y*28 - 43*y**2*28 + (17*y**3)*28
Replacing 28*(17*y**3 - 43*y**2 - 64*y) with -64*y*28 - 43*y**2*28 + (17*y**3)*28 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -64*y*28 + (-50*y)*(17*y**3 - 43*y**2 - 64*y) - 43*y**2*28 + (17*y**3)*28</replace>
Simplifying the partial expression: (-50*y)*(17*y**3 - 43*y**2 - 64*y)
Expanding the part (17*y**3 - 43*y**2 - 64*y) using the distributive property, and we got: (-64*y)*(-50*y) + (-50*y)*(-43*y**2) + (-50*y)*(17*y**3)
Replacing (-50*y)*(17*y**3 - 43*y**2 - 64*y) with (-64*y)*(-50*y) + (-50*y)*(-43*y**2) + (-50*y)*(17*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-64*y)*(-50*y) - 64*y*28 + (-50*y)*(-43*y**2) + (-50*y)*(17*y**3) - 43*y**2*28 + (17*y**3)*28</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-64*y)*28 = -1792*y
  (-64*y)*(-50*y) = 3200*y**2
  (-43*y**2)*28 = -1204*y**2
  (-43*y**2)*(-50*y) = 2150*y**3
  (17*y**3)*28 = 476*y**3
  (17*y**3)*(-50*y) = -850*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -850*y**4 + 476*y**3 + 2150*y**3 - 1204*y**2 + 3200*y**2 - 1792*y</replace>
Combining like terms, got -850*y**4 + 2626*y**3 + 1996*y**2 - 1792*y
<replace-#Step 5>#Step 6:
Current expression: -850*y**4 + 2626*y**3 + 1996*y**2 - 1792*y</replace>
No more calculations needed.
<answer>-850*y**4 + 2626*y**3 + 1996*y**2 - 1792*y</answer>


Question:
Simplify this expression: (-15*y**2 + y)*(6*y**3 + 39*y - 26)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -90*y**5 + 6*y**4 - 585*y**3 + 429*y**2 - 26*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: (-15*y**2 + y)*(6*y**3 + 39*y - 26)
Expanding the part (-15*y**2 + y) using the distributive property, and we got: y*(6*y**3 + 39*y - 26) + (-15*y**2)*(6*y**3 + 39*y - 26)
<replace-#Step 1>#Step 2:
Current expression: y*(6*y**3 + 39*y - 26) + (-15*y**2)*(6*y**3 + 39*y - 26)</replace>
Simplifying the partial expression: y*(6*y**3 + 39*y - 26)
Expanding the part (6*y**3 + 39*y - 26) using the distributive property, and we got: y*(39*y) + y*(6*y**3) - 26*y
Replacing y*(6*y**3 + 39*y - 26) with y*(39*y) + y*(6*y**3) - 26*y in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: y*(39*y) + y*(6*y**3) - 26*y + (-15*y**2)*(6*y**3 + 39*y - 26)</replace>
Simplifying the partial expression: (-15*y**2)*(6*y**3 + 39*y - 26)
Expanding the part (6*y**3 + 39*y - 26) using the distributive property, and we got: -(-1)*390*y**2 + (39*y)*(-15*y**2) + (-15*y**2)*(6*y**3)
Replacing (-15*y**2)*(6*y**3 + 39*y - 26) with -(-1)*390*y**2 + (39*y)*(-15*y**2) + (-15*y**2)*(6*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -26*(-15)*y**2 + y*(39*y) + y*(6*y**3) - 26*y + (39*y)*(-15*y**2) + (-15*y**2)*(6*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (6*y**3)*y = 6*y**4
  (6*y**3)*(-15*y**2) = -90*y**5
  (39*y)*y = 39*y**2
  (39*y)*(-15*y**2) = -585*y**3
  -26*-15*y**2 = 390*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -90*y**5 + 6*y**4 - 585*y**3 + 39*y**2 + 390*y**2 - 26*y</replace>
Combining like terms, got -90*y**5 + 6*y**4 - 585*y**3 + 429*y**2 - 26*y
<replace-#Step 5>#Step 6:
Current expression: -90*y**5 + 6*y**4 - 585*y**3 + 429*y**2 - 26*y</replace>
No more calculations needed.
<answer>-90*y**5 + 6*y**4 - 585*y**3 + 429*y**2 - 26*y</answer>


Question:
Simplify this expression: (25*y**2 + 27)*(-19*y**3 - 13*y - 22)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -475*y**5 - 838*y**3 - 550*y**2 - 351*y - 594

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (25*y**2 + 27)*(-19*y**3 - 13*y - 22)
Expanding the part (25*y**2 + 27) using the distributive property, and we got: (25*y**2)*(-19*y**3 - 13*y - 22) + 27*(-19*y**3 - 13*y - 22)
<replace-#Step 1>#Step 2:
Current expression: (25*y**2)*(-19*y**3 - 13*y - 22) + 27*(-19*y**3 - 13*y - 22)</replace>
Simplifying the partial expression: 27*(-19*y**3 - 13*y - 22)
Expanding the part (-19*y**3 - 13*y - 22) using the distributive property, and we got: -13*y*27 - 19*y**3*27 - 22*27
Replacing 27*(-19*y**3 - 13*y - 22) with -13*y*27 - 19*y**3*27 - 22*27 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -13*y*27 + (25*y**2)*(-19*y**3 - 13*y - 22) - 19*y**3*27 - 594</replace>
Simplifying the partial expression: (25*y**2)*(-19*y**3 - 13*y - 22)
Expanding the part (-19*y**3 - 13*y - 22) using the distributive property, and we got: (-13*y)*(25*y**2) - 550*y**2 + (25*y**2)*(-19*y**3)
Replacing (25*y**2)*(-19*y**3 - 13*y - 22) with (-13*y)*(25*y**2) - 550*y**2 + (25*y**2)*(-19*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-13*y)*(25*y**2) - 13*y*27 - 22*25*y**2 + (25*y**2)*(-19*y**3) - 19*y**3*27 - 594</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-19*y**3)*27 = -513*y**3
  (-19*y**3)*(25*y**2) = -475*y**5
  (-13*y)*27 = -351*y
  (-13*y)*(25*y**2) = -325*y**3
  -22*25*y**2 = -550*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -475*y**5 - 513*y**3 - 325*y**3 - 550*y**2 - 351*y - 594</replace>
Combining like terms, got -475*y**5 - 838*y**3 - 550*y**2 - 351*y - 594
<replace-#Step 5>#Step 6:
Current expression: -475*y**5 - 838*y**3 - 550*y**2 - 351*y - 594</replace>
No more calculations needed.
<answer>-475*y**5 - 838*y**3 - 550*y**2 - 351*y - 594</answer>


Question:
Calculate the following: (-53*z**2 + 3*z + 37)*(-18*z**2 - 63*z - 32)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 954*z**4 + 3285*z**3 + 841*z**2 - 2427*z - 1184


Question:
Calculate the following: (22 - 48*z**3)*(47*z**3 + 18*z**2 - 20)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2256*z**6 - 864*z**5 + 1994*z**3 + 396*z**2 - 440

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (22 - 48*z**3)*(47*z**3 + 18*z**2 - 20)
Expanding the part (22 - 48*z**3) using the distributive property, and we got: (-48*z**3)*(47*z**3 + 18*z**2 - 20) + 22*(47*z**3 + 18*z**2 - 20)
<replace-#Step 1>#Step 2:
Current expression: (-48*z**3)*(47*z**3 + 18*z**2 - 20) + 22*(47*z**3 + 18*z**2 - 20)</replace>
Simplifying the partial expression: 22*(47*z**3 + 18*z**2 - 20)
Expanding the part (47*z**3 + 18*z**2 - 20) using the distributive property, and we got: (18*z**2)*22 + (47*z**3)*22 - 20*22
Replacing 22*(47*z**3 + 18*z**2 - 20) with (18*z**2)*22 + (47*z**3)*22 - 20*22 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (18*z**2)*22 + (-48*z**3)*(47*z**3 + 18*z**2 - 20) + (47*z**3)*22 - 440</replace>
Simplifying the partial expression: (-48*z**3)*(47*z**3 + 18*z**2 - 20)
Expanding the part (47*z**3 + 18*z**2 - 20) using the distributive property, and we got: -(-1)*960*z**3 + (18*z**2)*(-48*z**3) + (-48*z**3)*(47*z**3)
Replacing (-48*z**3)*(47*z**3 + 18*z**2 - 20) with -(-1)*960*z**3 + (18*z**2)*(-48*z**3) + (-48*z**3)*(47*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -20*(-48)*z**3 + (18*z**2)*(-48*z**3) + (18*z**2)*22 + (-48*z**3)*(47*z**3) + (47*z**3)*22 - 440</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (18*z**2)*22 = 396*z**2
  (18*z**2)*(-48*z**3) = -864*z**5
  (47*z**3)*22 = 1034*z**3
  (47*z**3)*(-48*z**3) = -2256*z**6
  -20*-48*z**3 = 960*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2256*z**6 - 864*z**5 + 960*z**3 + 1034*z**3 + 396*z**2 - 440</replace>
Combining like terms, got -2256*z**6 - 864*z**5 + 1994*z**3 + 396*z**2 - 440
<replace-#Step 5>#Step 6:
Current expression: -2256*z**6 - 864*z**5 + 1994*z**3 + 396*z**2 - 440</replace>
No more calculations needed.
<answer>-2256*z**6 - 864*z**5 + 1994*z**3 + 396*z**2 - 440</answer>


Question:
Calculate the following: (41*y**3 - 14)*(-y**2 + 50*y + 17)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -41*y**5 + 2050*y**4 + 697*y**3 + 14*y**2 - 700*y - 238

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (41*y**3 - 14)*(-y**2 + 50*y + 17)
Expanding the part (41*y**3 - 14) using the distributive property, and we got: (41*y**3)*(-y**2 + 50*y + 17) - 14*(-y**2 + 50*y + 17)
<replace-#Step 1>#Step 2:
Current expression: (41*y**3)*(-y**2 + 50*y + 17) - 14*(-y**2 + 50*y + 17)</replace>
Simplifying the partial expression: -14*(-y**2 + 50*y + 17)
Expanding the part (-y**2 + 50*y + 17) using the distributive property, and we got: (50*y)*(-14) - y**2*(-14) + 17*(-14)
Replacing -14*(-y**2 + 50*y + 17) with (50*y)*(-14) - y**2*(-14) + 17*(-14) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (50*y)*(-14) - y**2*(-14) + (41*y**3)*(-y**2 + 50*y + 17) - 238</replace>
Simplifying the partial expression: (41*y**3)*(-y**2 + 50*y + 17)
Expanding the part (-y**2 + 50*y + 17) using the distributive property, and we got: 17*(41*y**3) + (50*y)*(41*y**3) + (-y**2)*(41*y**3)
Replacing (41*y**3)*(-y**2 + 50*y + 17) with 17*(41*y**3) + (50*y)*(41*y**3) + (-y**2)*(41*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 17*41*y**3 + (50*y)*(41*y**3) + (50*y)*(-14) + (-y**2)*(41*y**3) - y**2*(-14) - 238</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-y**2)*-14 = 14*y**2
  (-y**2)*(41*y**3) = -41*y**5
  (50*y)*-14 = -700*y
  (50*y)*(41*y**3) = 2050*y**4
  17*41*y**3 = 697*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -41*y**5 + 2050*y**4 + 697*y**3 + 14*y**2 - 700*y - 238</replace>
No more calculations needed.
<answer>-41*y**5 + 2050*y**4 + 697*y**3 + 14*y**2 - 700*y - 238</answer>


Question:
Calculate the following: -616*y**3 - 1034*y**2 + 2024
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -616*y**3 - 1034*y**2 + 2024

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: -616*y**3 - 1034*y**2 + 2024
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: -616*y**3 - 1034*y**2 + 2024</replace>
No more calculations needed.
<answer>-616*y**3 - 1034*y**2 + 2024</answer>


Question:
Calculate the following: (3*x**3 - 38)*(76*x**3 - 23*x**2 - 45*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 228*x**6 - 69*x**5 - 135*x**4 - 2888*x**3 + 874*x**2 + 1710*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (3*x**3 - 38)*(76*x**3 - 23*x**2 - 45*x)
Expanding the part (3*x**3 - 38) using the distributive property, and we got: (3*x**3)*(76*x**3 - 23*x**2 - 45*x) - 38*(76*x**3 - 23*x**2 - 45*x)
<replace-#Step 1>#Step 2:
Current expression: (3*x**3)*(76*x**3 - 23*x**2 - 45*x) - 38*(76*x**3 - 23*x**2 - 45*x)</replace>
Simplifying the partial expression: -38*(76*x**3 - 23*x**2 - 45*x)
Expanding the part (76*x**3 - 23*x**2 - 45*x) using the distributive property, and we got: -45*x*(-38) - 23*x**2*(-38) + (76*x**3)*(-38)
Replacing -38*(76*x**3 - 23*x**2 - 45*x) with -45*x*(-38) - 23*x**2*(-38) + (76*x**3)*(-38) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -45*x*(-38) - 23*x**2*(-38) + (3*x**3)*(76*x**3 - 23*x**2 - 45*x) + (76*x**3)*(-38)</replace>
Simplifying the partial expression: (3*x**3)*(76*x**3 - 23*x**2 - 45*x)
Expanding the part (76*x**3 - 23*x**2 - 45*x) using the distributive property, and we got: (-45*x)*(3*x**3) + (-23*x**2)*(3*x**3) + (3*x**3)*(76*x**3)
Replacing (3*x**3)*(76*x**3 - 23*x**2 - 45*x) with (-45*x)*(3*x**3) + (-23*x**2)*(3*x**3) + (3*x**3)*(76*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-45*x)*(3*x**3) - 45*x*(-38) + (-23*x**2)*(3*x**3) - 23*x**2*(-38) + (3*x**3)*(76*x**3) + (76*x**3)*(-38)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-45*x)*-38 = 1710*x
  (-45*x)*(3*x**3) = -135*x**4
  (-23*x**2)*-38 = 874*x**2
  (-23*x**2)*(3*x**3) = -69*x**5
  (76*x**3)*-38 = -2888*x**3
  (76*x**3)*(3*x**3) = 228*x**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 228*x**6 - 69*x**5 - 135*x**4 - 2888*x**3 + 874*x**2 + 1710*x</replace>
No more calculations needed.
<answer>228*x**6 - 69*x**5 - 135*x**4 - 2888*x**3 + 874*x**2 + 1710*x</answer>


Question:
Simplify this expression: (-21*y**3 - 27)*(-45*y**3 - 38*y**2 + 46)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 945*y**6 + 798*y**5 + 249*y**3 + 1026*y**2 - 1242


Question:
Simplify this expression: (14*z + 19)*(45*z**3 + 23*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 630*z**4 + 855*z**3 + 322*z**2 + 437*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*z + 19)*(45*z**3 + 23*z)
Expanding the part (14*z + 19) using the distributive property, and we got: (14*z)*(45*z**3 + 23*z) + 19*(45*z**3 + 23*z)
<replace-#Step 1>#Step 2:
Current expression: (14*z)*(45*z**3 + 23*z) + 19*(45*z**3 + 23*z)</replace>
Simplifying the partial expression: 19*(45*z**3 + 23*z)
Expanding the part (45*z**3 + 23*z) using the distributive property, and we got: (23*z)*19 + (45*z**3)*19
Replacing 19*(45*z**3 + 23*z) with (23*z)*19 + (45*z**3)*19 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (14*z)*(45*z**3 + 23*z) + (23*z)*19 + (45*z**3)*19</replace>
Simplifying the partial expression: (14*z)*(45*z**3 + 23*z)
Expanding the part (45*z**3 + 23*z) using the distributive property, and we got: (14*z)*(23*z) + (14*z)*(45*z**3)
Replacing (14*z)*(45*z**3 + 23*z) with (14*z)*(23*z) + (14*z)*(45*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (14*z)*(23*z) + (14*z)*(45*z**3) + (23*z)*19 + (45*z**3)*19</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (23*z)*19 = 437*z
  (23*z)*(14*z) = 322*z**2
  (45*z**3)*19 = 855*z**3
  (45*z**3)*(14*z) = 630*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 630*z**4 + 855*z**3 + 322*z**2 + 437*z</replace>
No more calculations needed.
<answer>630*z**4 + 855*z**3 + 322*z**2 + 437*z</answer>


Question:
Calculate the following: (40*x**2 - 23*x - 27)*(-x**3 + 5*x**2 - 41*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: -40*x**5 + 223*x**4 - 1728*x**3 + 808*x**2 + 1107*x


Question:
Calculate the following: (30 - 26*y**2)*(46*y**2 + 41)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1196*y**4 + 314*y**2 + 1230

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 - 26*y**2)*(46*y**2 + 41)
Expanding the part (30 - 26*y**2) using the distributive property, and we got: (-26*y**2)*(46*y**2 + 41) + 30*(46*y**2 + 41)
<replace-#Step 1>#Step 2:
Current expression: (-26*y**2)*(46*y**2 + 41) + 30*(46*y**2 + 41)</replace>
Simplifying the partial expression: 30*(46*y**2 + 41)
Expanding the part (46*y**2 + 41) using the distributive property, and we got: (46*y**2)*30 + 41*30
Replacing 30*(46*y**2 + 41) with (46*y**2)*30 + 41*30 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-26*y**2)*(46*y**2 + 41) + (46*y**2)*30 + 1230</replace>
Simplifying the partial expression: (-26*y**2)*(46*y**2 + 41)
Expanding the part (46*y**2 + 41) using the distributive property, and we got: 41*(-26*y**2) + (-26*y**2)*(46*y**2)
Replacing (-26*y**2)*(46*y**2 + 41) with 41*(-26*y**2) + (-26*y**2)*(46*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 41*(-26)*y**2 + (-26*y**2)*(46*y**2) + (46*y**2)*30 + 1230</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (46*y**2)*30 = 1380*y**2
  (46*y**2)*(-26*y**2) = -1196*y**4
  41*-26*y**2 = -1066*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1196*y**4 - 1066*y**2 + 1380*y**2 + 1230</replace>
Combining like terms, got -1196*y**4 + 314*y**2 + 1230
<replace-#Step 5>#Step 6:
Current expression: -1196*y**4 + 314*y**2 + 1230</replace>
No more calculations needed.
<answer>-1196*y**4 + 314*y**2 + 1230</answer>


Question:
Simplify this expression: (-11*z**3 - 16*z**2)*(8*z**2 - 14*z - 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: -88*z**5 + 26*z**4 + 697*z**3 + 688*z**2