Question:
Calculate the following: (-41*y**2 - 30)*(8*y**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: -328*y**4 - 281*y**2 - 30

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**2 - 30)*(8*y**2 + 1)
Expanding the part (8*y**2 + 1) using the distributive property, and we got: (8*y**2)*(-41*y**2 - 30) + 1*(-41*y**2 - 30)
<replace-#Step 1>#Step 2:
Current expression: (8*y**2)*(-41*y**2 - 30) + 1*(-41*y**2 - 30)</replace>
Simplifying the partial expression: 1*(-41*y**2 - 30)
Expanding the part (-41*y**2 - 30) using the distributive property, and we got: -41*y**2*1 - 30*1
Replacing 1*(-41*y**2 - 30) with -41*y**2*1 - 30*1 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -41*y**2*1 + (8*y**2)*(-41*y**2 - 30) - 30</replace>
Simplifying the partial expression: (8*y**2)*(-41*y**2 - 30)
Expanding the part (-41*y**2 - 30) using the distributive property, and we got: -240*y**2 + (-41*y**2)*(8*y**2)
Replacing (8*y**2)*(-41*y**2 - 30) with -240*y**2 + (-41*y**2)*(8*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -30*8*y**2 + (-41*y**2)*(8*y**2) - 41*y**2*1 - 30</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-41*y**2)*1 = -41*y**2
  (-41*y**2)*(8*y**2) = -328*y**4
  -30*8*y**2 = -240*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -328*y**4 - 240*y**2 - 41*y**2 - 30</replace>
Combining like terms, got -328*y**4 - 281*y**2 - 30
<replace-#Step 5>#Step 6:
Current expression: -328*y**4 - 281*y**2 - 30</replace>
No more calculations needed.
<answer>-328*y**4 - 281*y**2 - 30</answer>


Question:
Simplify this expression: (32 - 22*y**3)*(14*y**2 - 7)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -308*y**5 + 154*y**3 + 448*y**2 - 224

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (32 - 22*y**3)*(14*y**2 - 7)
Expanding the part (14*y**2 - 7) using the distributive property, and we got: (14*y**2)*(32 - 22*y**3) - 7*(32 - 22*y**3)
<replace-#Step 1>#Step 2:
Current expression: (14*y**2)*(32 - 22*y**3) - 7*(32 - 22*y**3)</replace>
Simplifying the partial expression: -7*(32 - 22*y**3)
Expanding the part (32 - 22*y**3) using the distributive property, and we got: -22*y**3*(-7) + 32*(-7)
Replacing -7*(32 - 22*y**3) with -22*y**3*(-7) + 32*(-7) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (14*y**2)*(32 - 22*y**3) - 22*y**3*(-7) - 224</replace>
Simplifying the partial expression: (14*y**2)*(32 - 22*y**3)
Expanding the part (32 - 22*y**3) using the distributive property, and we got: 32*(14*y**2) + (14*y**2)*(-22*y**3)
Replacing (14*y**2)*(32 - 22*y**3) with 32*(14*y**2) + (14*y**2)*(-22*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 32*14*y**2 + (14*y**2)*(-22*y**3) - 22*y**3*(-7) - 224</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-22*y**3)*-7 = 154*y**3
  (-22*y**3)*(14*y**2) = -308*y**5
  32*14*y**2 = 448*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -308*y**5 + 154*y**3 + 448*y**2 - 224</replace>
No more calculations needed.
<answer>-308*y**5 + 154*y**3 + 448*y**2 - 224</answer>


Question:
Calculate the following: (69*y**2 + 24*y)*(54*y**3 + 17*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: 3726*y**5 + 2469*y**4 + 408*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: (69*y**2 + 24*y)*(54*y**3 + 17*y**2)
Expanding the part (54*y**3 + 17*y**2) using the distributive property, and we got: (17*y**2)*(69*y**2 + 24*y) + (54*y**3)*(69*y**2 + 24*y)
<replace-#Step 1>#Step 2:
Current expression: (17*y**2)*(69*y**2 + 24*y) + (54*y**3)*(69*y**2 + 24*y)</replace>
Simplifying the partial expression: (17*y**2)*(69*y**2 + 24*y)
Expanding the part (69*y**2 + 24*y) using the distributive property, and we got: (24*y)*(17*y**2) + (17*y**2)*(69*y**2)
Replacing (17*y**2)*(69*y**2 + 24*y) with (24*y)*(17*y**2) + (17*y**2)*(69*y**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (24*y)*(17*y**2) + (17*y**2)*(69*y**2) + (54*y**3)*(69*y**2 + 24*y)</replace>
Simplifying the partial expression: (54*y**3)*(69*y**2 + 24*y)
Expanding the part (69*y**2 + 24*y) using the distributive property, and we got: (24*y)*(54*y**3) + (69*y**2)*(54*y**3)
Replacing (54*y**3)*(69*y**2 + 24*y) with (24*y)*(54*y**3) + (69*y**2)*(54*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (24*y)*(17*y**2) + (24*y)*(54*y**3) + (17*y**2)*(69*y**2) + (69*y**2)*(54*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (24*y)*(17*y**2) = 408*y**3
  (24*y)*(54*y**3) = 1296*y**4
  (69*y**2)*(17*y**2) = 1173*y**4
  (69*y**2)*(54*y**3) = 3726*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 3726*y**5 + 1173*y**4 + 1296*y**4 + 408*y**3</replace>
Combining like terms, got 3726*y**5 + 2469*y**4 + 408*y**3
<replace-#Step 5>#Step 6:
Current expression: 3726*y**5 + 2469*y**4 + 408*y**3</replace>
No more calculations needed.
<answer>3726*y**5 + 2469*y**4 + 408*y**3</answer>


Question:
Simplify this expression: (27*x + 10)*(-8*x**3 + 3*x**2 + 33)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -216*x**4 + x**3 + 30*x**2 + 891*x + 330

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (27*x + 10)*(-8*x**3 + 3*x**2 + 33)
Expanding the part (27*x + 10) using the distributive property, and we got: (27*x)*(-8*x**3 + 3*x**2 + 33) + 10*(-8*x**3 + 3*x**2 + 33)
<replace-#Step 1>#Step 2:
Current expression: (27*x)*(-8*x**3 + 3*x**2 + 33) + 10*(-8*x**3 + 3*x**2 + 33)</replace>
Simplifying the partial expression: 10*(-8*x**3 + 3*x**2 + 33)
Expanding the part (-8*x**3 + 3*x**2 + 33) using the distributive property, and we got: (3*x**2)*10 - 8*x**3*10 + 33*10
Replacing 10*(-8*x**3 + 3*x**2 + 33) with (3*x**2)*10 - 8*x**3*10 + 33*10 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (27*x)*(-8*x**3 + 3*x**2 + 33) + (3*x**2)*10 - 8*x**3*10 + 330</replace>
Simplifying the partial expression: (27*x)*(-8*x**3 + 3*x**2 + 33)
Expanding the part (-8*x**3 + 3*x**2 + 33) using the distributive property, and we got: 33*(27*x) + (27*x)*(3*x**2) + (27*x)*(-8*x**3)
Replacing (27*x)*(-8*x**3 + 3*x**2 + 33) with 33*(27*x) + (27*x)*(3*x**2) + (27*x)*(-8*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 33*27*x + (27*x)*(3*x**2) + (27*x)*(-8*x**3) + (3*x**2)*10 - 8*x**3*10 + 330</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-8*x**3)*10 = -80*x**3
  (-8*x**3)*(27*x) = -216*x**4
  (3*x**2)*10 = 30*x**2
  (3*x**2)*(27*x) = 81*x**3
  33*27*x = 891*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -216*x**4 - 80*x**3 + 81*x**3 + 30*x**2 + 891*x + 330</replace>
Combining like terms, got -216*x**4 + x**3 + 30*x**2 + 891*x + 330
<replace-#Step 5>#Step 6:
Current expression: -216*x**4 + x**3 + 30*x**2 + 891*x + 330</replace>
No more calculations needed.
<answer>-216*x**4 + x**3 + 30*x**2 + 891*x + 330</answer>


Question:
Calculate the following: (-61*z**2 - 50*z - 25)*(-10*z**3 + 73*z**2 + 21*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 610*z**5 - 3953*z**4 - 4681*z**3 - 2875*z**2 - 525*z


Question:
Simplify this expression: (-30*z**2 + 34*z)*(27*z**2 + 73)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -810*z**4 + 918*z**3 - 2190*z**2 + 2482*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-30*z**2 + 34*z)*(27*z**2 + 73)
Expanding the part (27*z**2 + 73) using the distributive property, and we got: (27*z**2)*(-30*z**2 + 34*z) + 73*(-30*z**2 + 34*z)
<replace-#Step 1>#Step 2:
Current expression: (27*z**2)*(-30*z**2 + 34*z) + 73*(-30*z**2 + 34*z)</replace>
Simplifying the partial expression: 73*(-30*z**2 + 34*z)
Expanding the part (-30*z**2 + 34*z) using the distributive property, and we got: (34*z)*73 - 30*z**2*73
Replacing 73*(-30*z**2 + 34*z) with (34*z)*73 - 30*z**2*73 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (34*z)*73 - 30*z**2*73 + (27*z**2)*(-30*z**2 + 34*z)</replace>
Simplifying the partial expression: (27*z**2)*(-30*z**2 + 34*z)
Expanding the part (-30*z**2 + 34*z) using the distributive property, and we got: (34*z)*(27*z**2) + (-30*z**2)*(27*z**2)
Replacing (27*z**2)*(-30*z**2 + 34*z) with (34*z)*(27*z**2) + (-30*z**2)*(27*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (34*z)*(27*z**2) + (34*z)*73 + (-30*z**2)*(27*z**2) - 30*z**2*73</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-30*z**2)*73 = -2190*z**2
  (-30*z**2)*(27*z**2) = -810*z**4
  (34*z)*73 = 2482*z
  (34*z)*(27*z**2) = 918*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -810*z**4 + 918*z**3 - 2190*z**2 + 2482*z</replace>
No more calculations needed.
<answer>-810*z**4 + 918*z**3 - 2190*z**2 + 2482*z</answer>


Question:
Simplify this expression: (21*x**2 - 4)*(-7*x**3 - 12*x - 33)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -147*x**5 - 224*x**3 - 693*x**2 + 48*x + 132

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (21*x**2 - 4)*(-7*x**3 - 12*x - 33)
Expanding the part (21*x**2 - 4) using the distributive property, and we got: (21*x**2)*(-7*x**3 - 12*x - 33) - 4*(-7*x**3 - 12*x - 33)
<replace-#Step 1>#Step 2:
Current expression: (21*x**2)*(-7*x**3 - 12*x - 33) - 4*(-7*x**3 - 12*x - 33)</replace>
Simplifying the partial expression: -4*(-7*x**3 - 12*x - 33)
Expanding the part (-7*x**3 - 12*x - 33) using the distributive property, and we got: -12*x*(-4) - 7*x**3*(-4) - 33*(-4)
Replacing -4*(-7*x**3 - 12*x - 33) with -12*x*(-4) - 7*x**3*(-4) - 33*(-4) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -12*x*(-4) + (21*x**2)*(-7*x**3 - 12*x - 33) - 7*x**3*(-4) + 132</replace>
Simplifying the partial expression: (21*x**2)*(-7*x**3 - 12*x - 33)
Expanding the part (-7*x**3 - 12*x - 33) using the distributive property, and we got: (-12*x)*(21*x**2) - 693*x**2 + (21*x**2)*(-7*x**3)
Replacing (21*x**2)*(-7*x**3 - 12*x - 33) with (-12*x)*(21*x**2) - 693*x**2 + (21*x**2)*(-7*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-12*x)*(21*x**2) - 12*x*(-4) - 33*21*x**2 + (21*x**2)*(-7*x**3) - 7*x**3*(-4) + 132</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-12*x)*-4 = 48*x
  (-12*x)*(21*x**2) = -252*x**3
  (-7*x**3)*-4 = 28*x**3
  (-7*x**3)*(21*x**2) = -147*x**5
  -33*21*x**2 = -693*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -147*x**5 - 252*x**3 + 28*x**3 - 693*x**2 + 48*x + 132</replace>
Combining like terms, got -147*x**5 - 224*x**3 - 693*x**2 + 48*x + 132
<replace-#Step 5>#Step 6:
Current expression: -147*x**5 - 224*x**3 - 693*x**2 + 48*x + 132</replace>
No more calculations needed.
<answer>-147*x**5 - 224*x**3 - 693*x**2 + 48*x + 132</answer>


Question:
Calculate the following: (-14*z**2 - 4*z)*(-z**3 - 41)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 14*z**5 + 4*z**4 + 574*z**2 + 164*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**2 - 4*z)*(-z**3 - 41)
Expanding the part (-z**3 - 41) using the distributive property, and we got: (-z**3)*(-14*z**2 - 4*z) - 41*(-14*z**2 - 4*z)
<replace-#Step 1>#Step 2:
Current expression: (-z**3)*(-14*z**2 - 4*z) - 41*(-14*z**2 - 4*z)</replace>
Simplifying the partial expression: -41*(-14*z**2 - 4*z)
Expanding the part (-14*z**2 - 4*z) using the distributive property, and we got: -4*z*(-41) - 14*z**2*(-41)
Replacing -41*(-14*z**2 - 4*z) with -4*z*(-41) - 14*z**2*(-41) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -4*z*(-41) - 14*z**2*(-41) + (-z**3)*(-14*z**2 - 4*z)</replace>
Simplifying the partial expression: (-z**3)*(-14*z**2 - 4*z)
Expanding the part (-14*z**2 - 4*z) using the distributive property, and we got: (-4*z)*(-z**3) + (-14*z**2)*(-z**3)
Replacing (-z**3)*(-14*z**2 - 4*z) with (-4*z)*(-z**3) + (-14*z**2)*(-z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-4*z)*(-z**3) - 4*z*(-41) + (-14*z**2)*(-z**3) - 14*z**2*(-41)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-14*z**2)*-41 = 574*z**2
  (-14*z**2)*(-z**3) = 14*z**5
  (-4*z)*-41 = 164*z
  (-4*z)*(-z**3) = 4*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 14*z**5 + 4*z**4 + 574*z**2 + 164*z</replace>
No more calculations needed.
<answer>14*z**5 + 4*z**4 + 574*z**2 + 164*z</answer>


Question:
Simplify this expression: (-45*y**3 - 27*y**2 + 10*y)*(-20*y**3 + 16*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: 900*y**6 - 180*y**5 - 632*y**4 + 2365*y**3 + 1323*y**2 - 490*y


Question:
Calculate the following: (-47*z**3 + 35*z + 32)*(17*z**3 - 22*z - 27)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -799*z**6 + 1629*z**4 + 1813*z**3 - 770*z**2 - 1649*z - 864


Question:
Calculate the following: (38*y**3 + 15*y)*(-28*y**3 - 80*y**2 - 31)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1064*y**6 - 3040*y**5 - 420*y**4 - 2378*y**3 - 465*y


Question:
Simplify this expression: (16*y**3 + 39*y**2)*(29*y**3 + 25*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: 464*y**6 + 1531*y**5 + 975*y**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (16*y**3 + 39*y**2)*(29*y**3 + 25*y**2)
Expanding the part (16*y**3 + 39*y**2) using the distributive property, and we got: (39*y**2)*(29*y**3 + 25*y**2) + (16*y**3)*(29*y**3 + 25*y**2)
<replace-#Step 1>#Step 2:
Current expression: (39*y**2)*(29*y**3 + 25*y**2) + (16*y**3)*(29*y**3 + 25*y**2)</replace>
Simplifying the partial expression: (16*y**3)*(29*y**3 + 25*y**2)
Expanding the part (29*y**3 + 25*y**2) using the distributive property, and we got: (25*y**2)*(16*y**3) + (16*y**3)*(29*y**3)
Replacing (16*y**3)*(29*y**3 + 25*y**2) with (25*y**2)*(16*y**3) + (16*y**3)*(29*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (25*y**2)*(16*y**3) + (39*y**2)*(29*y**3 + 25*y**2) + (16*y**3)*(29*y**3)</replace>
Simplifying the partial expression: (39*y**2)*(29*y**3 + 25*y**2)
Expanding the part (29*y**3 + 25*y**2) using the distributive property, and we got: (25*y**2)*(39*y**2) + (39*y**2)*(29*y**3)
Replacing (39*y**2)*(29*y**3 + 25*y**2) with (25*y**2)*(39*y**2) + (39*y**2)*(29*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (25*y**2)*(39*y**2) + (25*y**2)*(16*y**3) + (39*y**2)*(29*y**3) + (16*y**3)*(29*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (25*y**2)*(16*y**3) = 400*y**5
  (25*y**2)*(39*y**2) = 975*y**4
  (29*y**3)*(16*y**3) = 464*y**6
  (29*y**3)*(39*y**2) = 1131*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 464*y**6 + 400*y**5 + 1131*y**5 + 975*y**4</replace>
Combining like terms, got 464*y**6 + 1531*y**5 + 975*y**4
<replace-#Step 5>#Step 6:
Current expression: 464*y**6 + 1531*y**5 + 975*y**4</replace>
No more calculations needed.
<answer>464*y**6 + 1531*y**5 + 975*y**4</answer>


Question:
Calculate the following: -1520*z**3 - 440*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: -1520*z**3 - 440*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: -1520*z**3 - 440*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: -1520*z**3 - 440*z**2</replace>
No more calculations needed.
<answer>-1520*z**3 - 440*z**2</answer>


Question:
Calculate the following: (-91*z - 41)*(-41*z**3 - 43*z**2 + 51*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: 3731*z**4 + 5594*z**3 - 2878*z**2 - 2091*z


Question:
Calculate the following: -79*x**2*(41*x**3 - 2*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -3239*x**5 + 158*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: -79*x**2*(41*x**3 - 2*x)
Expanding the part (41*x**3 - 2*x) using the distributive property, and we got: (-2*x)*(-79*x**2) + (-79*x**2)*(41*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-2*x)*(-79*x**2) + (-79*x**2)*(41*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-2*x)*(-79*x**2) = 158*x**3
  (41*x**3)*(-79*x**2) = -3239*x**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -3239*x**5 + 158*x**3</replace>
No more calculations needed.
<answer>-3239*x**5 + 158*x**3</answer>


Question:
Calculate the following: -14*y**3*(-15*y**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: 210*y**5 + 294*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: -14*y**3*(-15*y**2 - 21)
Expanding the part (-15*y**2 - 21) using the distributive property, and we got: -(-1)*294*y**3 + (-15*y**2)*(-14*y**3)
<replace-#Step 1>#Step 2:
Current expression: -(-1)*294*y**3 + (-15*y**2)*(-14*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -21*(-14*y**3) = 294*y**3
  (-15*y**2)*(-14*y**3) = 210*y**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 210*y**5 + 294*y**3</replace>
No more calculations needed.
<answer>210*y**5 + 294*y**3</answer>


Question:
Simplify this expression: (-81*x**3 - 13*x)*(-24*x**3 - 38*x**2 - 11)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1944*x**6 + 3078*x**5 + 312*x**4 + 1385*x**3 + 143*x


Question:
Calculate the following: (21 - 38*y**2)*(-12*y**2 - 20*y - 39)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 456*y**4 + 760*y**3 + 1230*y**2 - 420*y - 819

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 - 38*y**2)*(-12*y**2 - 20*y - 39)
Expanding the part (21 - 38*y**2) using the distributive property, and we got: (-38*y**2)*(-12*y**2 - 20*y - 39) + 21*(-12*y**2 - 20*y - 39)
<replace-#Step 1>#Step 2:
Current expression: (-38*y**2)*(-12*y**2 - 20*y - 39) + 21*(-12*y**2 - 20*y - 39)</replace>
Simplifying the partial expression: 21*(-12*y**2 - 20*y - 39)
Expanding the part (-12*y**2 - 20*y - 39) using the distributive property, and we got: -20*y*21 - 12*y**2*21 - 39*21
Replacing 21*(-12*y**2 - 20*y - 39) with -20*y*21 - 12*y**2*21 - 39*21 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -20*y*21 + (-38*y**2)*(-12*y**2 - 20*y - 39) - 12*y**2*21 - 819</replace>
Simplifying the partial expression: (-38*y**2)*(-12*y**2 - 20*y - 39)
Expanding the part (-12*y**2 - 20*y - 39) using the distributive property, and we got: (-20*y)*(-38*y**2) - (-1)*1482*y**2 + (-38*y**2)*(-12*y**2)
Replacing (-38*y**2)*(-12*y**2 - 20*y - 39) with (-20*y)*(-38*y**2) - (-1)*1482*y**2 + (-38*y**2)*(-12*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-20*y)*(-38*y**2) - 20*y*21 - 39*(-38)*y**2 + (-38*y**2)*(-12*y**2) - 12*y**2*21 - 819</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-20*y)*21 = -420*y
  (-20*y)*(-38*y**2) = 760*y**3
  (-12*y**2)*21 = -252*y**2
  (-12*y**2)*(-38*y**2) = 456*y**4
  -39*-38*y**2 = 1482*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 456*y**4 + 760*y**3 - 252*y**2 + 1482*y**2 - 420*y - 819</replace>
Combining like terms, got 456*y**4 + 760*y**3 + 1230*y**2 - 420*y - 819
<replace-#Step 5>#Step 6:
Current expression: 456*y**4 + 760*y**3 + 1230*y**2 - 420*y - 819</replace>
No more calculations needed.
<answer>456*y**4 + 760*y**3 + 1230*y**2 - 420*y - 819</answer>


Question:
Calculate the following: (x**3 + 48)*(37*x**3 + 25*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 37*x**6 + 25*x**4 + 1776*x**3 + 1200*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: (x**3 + 48)*(37*x**3 + 25*x)
Expanding the part (x**3 + 48) using the distributive property, and we got: x**3*(37*x**3 + 25*x) + 48*(37*x**3 + 25*x)
<replace-#Step 1>#Step 2:
Current expression: x**3*(37*x**3 + 25*x) + 48*(37*x**3 + 25*x)</replace>
Simplifying the partial expression: 48*(37*x**3 + 25*x)
Expanding the part (37*x**3 + 25*x) using the distributive property, and we got: (25*x)*48 + (37*x**3)*48
Replacing 48*(37*x**3 + 25*x) with (25*x)*48 + (37*x**3)*48 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: x**3*(37*x**3 + 25*x) + (25*x)*48 + (37*x**3)*48</replace>
Simplifying the partial expression: x**3*(37*x**3 + 25*x)
Expanding the part (37*x**3 + 25*x) using the distributive property, and we got: (25*x)*x**3 + x**3*(37*x**3)
Replacing x**3*(37*x**3 + 25*x) with (25*x)*x**3 + x**3*(37*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (25*x)*x**3 + x**3*(37*x**3) + (25*x)*48 + (37*x**3)*48</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (25*x)*48 = 1200*x
  (25*x)*x**3 = 25*x**4
  (37*x**3)*48 = 1776*x**3
  (37*x**3)*x**3 = 37*x**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 37*x**6 + 25*x**4 + 1776*x**3 + 1200*x</replace>
No more calculations needed.
<answer>37*x**6 + 25*x**4 + 1776*x**3 + 1200*x</answer>


Question:
Simplify this expression: (36*z**2 - 62*z)*(18*z**3 - 41*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: 648*z**5 - 2592*z**4 + 2542*z**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (36*z**2 - 62*z)*(18*z**3 - 41*z**2)
Expanding the part (36*z**2 - 62*z) using the distributive property, and we got: (-62*z)*(18*z**3 - 41*z**2) + (36*z**2)*(18*z**3 - 41*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-62*z)*(18*z**3 - 41*z**2) + (36*z**2)*(18*z**3 - 41*z**2)</replace>
Simplifying the partial expression: (-62*z)*(18*z**3 - 41*z**2)
Expanding the part (18*z**3 - 41*z**2) using the distributive property, and we got: (-62*z)*(-41*z**2) + (-62*z)*(18*z**3)
Replacing (-62*z)*(18*z**3 - 41*z**2) with (-62*z)*(-41*z**2) + (-62*z)*(18*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-62*z)*(-41*z**2) + (-62*z)*(18*z**3) + (36*z**2)*(18*z**3 - 41*z**2)</replace>
Simplifying the partial expression: (36*z**2)*(18*z**3 - 41*z**2)
Expanding the part (18*z**3 - 41*z**2) using the distributive property, and we got: (-41*z**2)*(36*z**2) + (36*z**2)*(18*z**3)
Replacing (36*z**2)*(18*z**3 - 41*z**2) with (-41*z**2)*(36*z**2) + (36*z**2)*(18*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-62*z)*(-41*z**2) + (-62*z)*(18*z**3) + (-41*z**2)*(36*z**2) + (36*z**2)*(18*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-41*z**2)*(-62*z) = 2542*z**3
  (-41*z**2)*(36*z**2) = -1476*z**4
  (18*z**3)*(-62*z) = -1116*z**4
  (18*z**3)*(36*z**2) = 648*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 648*z**5 - 1476*z**4 - 1116*z**4 + 2542*z**3</replace>
Combining like terms, got 648*z**5 - 2592*z**4 + 2542*z**3
<replace-#Step 5>#Step 6:
Current expression: 648*z**5 - 2592*z**4 + 2542*z**3</replace>
No more calculations needed.
<answer>648*z**5 - 2592*z**4 + 2542*z**3</answer>


Question:
Simplify this expression: (-36*x**3 - 43*x**2 - 42*x)*(-9*x**3 + 12*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: 324*x**6 - 45*x**5 + 942*x**4 + 786*x**3 + 1260*x**2


Question:
Calculate the following: (39*y**3 + 30*y)*(26*y**2 + 31*y + 47)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1014*y**5 + 1209*y**4 + 2613*y**3 + 930*y**2 + 1410*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: (39*y**3 + 30*y)*(26*y**2 + 31*y + 47)
Expanding the part (39*y**3 + 30*y) using the distributive property, and we got: (30*y)*(26*y**2 + 31*y + 47) + (39*y**3)*(26*y**2 + 31*y + 47)
<replace-#Step 1>#Step 2:
Current expression: (30*y)*(26*y**2 + 31*y + 47) + (39*y**3)*(26*y**2 + 31*y + 47)</replace>
Simplifying the partial expression: (30*y)*(26*y**2 + 31*y + 47)
Expanding the part (26*y**2 + 31*y + 47) using the distributive property, and we got: 47*(30*y) + (30*y)*(31*y) + (30*y)*(26*y**2)
Replacing (30*y)*(26*y**2 + 31*y + 47) with 47*(30*y) + (30*y)*(31*y) + (30*y)*(26*y**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 47*30*y + (30*y)*(31*y) + (30*y)*(26*y**2) + (39*y**3)*(26*y**2 + 31*y + 47)</replace>
Simplifying the partial expression: (39*y**3)*(26*y**2 + 31*y + 47)
Expanding the part (26*y**2 + 31*y + 47) using the distributive property, and we got: 47*(39*y**3) + (31*y)*(39*y**3) + (26*y**2)*(39*y**3)
Replacing (39*y**3)*(26*y**2 + 31*y + 47) with 47*(39*y**3) + (31*y)*(39*y**3) + (26*y**2)*(39*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 47*39*y**3 + 47*30*y + (30*y)*(31*y) + (30*y)*(26*y**2) + (31*y)*(39*y**3) + (26*y**2)*(39*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (26*y**2)*(30*y) = 780*y**3
  (26*y**2)*(39*y**3) = 1014*y**5
  (31*y)*(30*y) = 930*y**2
  (31*y)*(39*y**3) = 1209*y**4
  47*30*y = 1410*y
  47*39*y**3 = 1833*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1014*y**5 + 1209*y**4 + 780*y**3 + 1833*y**3 + 930*y**2 + 1410*y</replace>
Combining like terms, got 1014*y**5 + 1209*y**4 + 2613*y**3 + 930*y**2 + 1410*y
<replace-#Step 5>#Step 6:
Current expression: 1014*y**5 + 1209*y**4 + 2613*y**3 + 930*y**2 + 1410*y</replace>
No more calculations needed.
<answer>1014*y**5 + 1209*y**4 + 2613*y**3 + 930*y**2 + 1410*y</answer>


Question:
Calculate the following: (39*z**3 + 41)*(-z**2 - 28*z - 28)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -39*z**5 - 1092*z**4 - 1092*z**3 - 41*z**2 - 1148*z - 1148

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*z**3 + 41)*(-z**2 - 28*z - 28)
Expanding the part (39*z**3 + 41) using the distributive property, and we got: (39*z**3)*(-z**2 - 28*z - 28) + 41*(-z**2 - 28*z - 28)
<replace-#Step 1>#Step 2:
Current expression: (39*z**3)*(-z**2 - 28*z - 28) + 41*(-z**2 - 28*z - 28)</replace>
Simplifying the partial expression: 41*(-z**2 - 28*z - 28)
Expanding the part (-z**2 - 28*z - 28) using the distributive property, and we got: -28*z*41 - z**2*41 - 28*41
Replacing 41*(-z**2 - 28*z - 28) with -28*z*41 - z**2*41 - 28*41 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -28*z*41 - z**2*41 + (39*z**3)*(-z**2 - 28*z - 28) - 1148</replace>
Simplifying the partial expression: (39*z**3)*(-z**2 - 28*z - 28)
Expanding the part (-z**2 - 28*z - 28) using the distributive property, and we got: (-28*z)*(39*z**3) - 1092*z**3 + (-z**2)*(39*z**3)
Replacing (39*z**3)*(-z**2 - 28*z - 28) with (-28*z)*(39*z**3) - 1092*z**3 + (-z**2)*(39*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-28*z)*(39*z**3) - 28*z*41 - 28*39*z**3 + (-z**2)*(39*z**3) - z**2*41 - 1148</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-z**2)*41 = -41*z**2
  (-z**2)*(39*z**3) = -39*z**5
  (-28*z)*41 = -1148*z
  (-28*z)*(39*z**3) = -1092*z**4
  -28*39*z**3 = -1092*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -39*z**5 - 1092*z**4 - 1092*z**3 - 41*z**2 - 1148*z - 1148</replace>
No more calculations needed.
<answer>-39*z**5 - 1092*z**4 - 1092*z**3 - 41*z**2 - 1148*z - 1148</answer>


Question:
Simplify this expression: (14 - 69*y)*(2*y**3 + 15*y**2 + 36*y - 48)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*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**4 - 1007*y**3 - 2274*y**2 + 3816*y - 672


Question:
Calculate the following: (29*z**3 - 13*z**2)*(69*z**3 + 49*z**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: 2001*z**6 + 524*z**5 - 637*z**4 + 58*z**3 - 26*z**2


Question:
Simplify this expression: (-52*x**3 + 69*x)*(40*x**2 - 25*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: -2080*x**5 + 1300*x**4 + 4112*x**3 - 1725*x**2 - 1794*x


Question:
Simplify this expression: (-4*x**2 - 44*x)*(-33*x**3 - 43*x**2 + 48)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*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*x**5 + 1624*x**4 + 1892*x**3 - 192*x**2 - 2112*x


Question:
Calculate the following: (80*x**2 - 1)*(44*x**3 - 16*x**2 - 9*x - 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: 3520*x**5 - 1280*x**4 - 764*x**3 - 2544*x**2 + 9*x + 32


Question:
Simplify this expression: (9*y + 27)*(64*y**3 - 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: 576*y**4 + 1728*y**3 - 441*y - 1323

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (9*y + 27)*(64*y**3 - 49)
Expanding the part (64*y**3 - 49) using the distributive property, and we got: (64*y**3)*(9*y + 27) - 49*(9*y + 27)
<replace-#Step 1>#Step 2:
Current expression: (64*y**3)*(9*y + 27) - 49*(9*y + 27)</replace>
Simplifying the partial expression: -49*(9*y + 27)
Expanding the part (9*y + 27) using the distributive property, and we got: (9*y)*(-49) + 27*(-49)
Replacing -49*(9*y + 27) with (9*y)*(-49) + 27*(-49) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (9*y)*(-49) + (64*y**3)*(9*y + 27) - 1323</replace>
Simplifying the partial expression: (64*y**3)*(9*y + 27)
Expanding the part (9*y + 27) using the distributive property, and we got: 27*(64*y**3) + (9*y)*(64*y**3)
Replacing (64*y**3)*(9*y + 27) with 27*(64*y**3) + (9*y)*(64*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 27*64*y**3 + (9*y)*(64*y**3) + (9*y)*(-49) - 1323</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (9*y)*-49 = -441*y
  (9*y)*(64*y**3) = 576*y**4
  27*64*y**3 = 1728*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 576*y**4 + 1728*y**3 - 441*y - 1323</replace>
No more calculations needed.
<answer>576*y**4 + 1728*y**3 - 441*y - 1323</answer>


Question:
Simplify this expression: (27*z**2 - 14*z)*(-46*z**3 - 12*z**2 + 43)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1242*z**5 + 320*z**4 + 168*z**3 + 1161*z**2 - 602*z


Question:
Calculate the following: (8 - 6*x)*(48*x**3 + 23*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: -288*x**4 + 246*x**3 + 184*x**2 + 108*x - 144

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (8 - 6*x)*(48*x**3 + 23*x**2 - 18)
Expanding the part (8 - 6*x) using the distributive property, and we got: (-6*x)*(48*x**3 + 23*x**2 - 18) + 8*(48*x**3 + 23*x**2 - 18)
<replace-#Step 1>#Step 2:
Current expression: (-6*x)*(48*x**3 + 23*x**2 - 18) + 8*(48*x**3 + 23*x**2 - 18)</replace>
Simplifying the partial expression: 8*(48*x**3 + 23*x**2 - 18)
Expanding the part (48*x**3 + 23*x**2 - 18) using the distributive property, and we got: (23*x**2)*8 + (48*x**3)*8 - 18*8
Replacing 8*(48*x**3 + 23*x**2 - 18) with (23*x**2)*8 + (48*x**3)*8 - 18*8 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-6*x)*(48*x**3 + 23*x**2 - 18) + (23*x**2)*8 + (48*x**3)*8 - 144</replace>
Simplifying the partial expression: (-6*x)*(48*x**3 + 23*x**2 - 18)
Expanding the part (48*x**3 + 23*x**2 - 18) using the distributive property, and we got: (-6*x)*(23*x**2) + (-6*x)*(48*x**3) - (-1)*108*x
Replacing (-6*x)*(48*x**3 + 23*x**2 - 18) with (-6*x)*(23*x**2) + (-6*x)*(48*x**3) - (-1)*108*x in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-6*x)*(23*x**2) + (-6*x)*(48*x**3) - 18*(-6)*x + (23*x**2)*8 + (48*x**3)*8 - 144</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (23*x**2)*8 = 184*x**2
  (23*x**2)*(-6*x) = -138*x**3
  (48*x**3)*8 = 384*x**3
  (48*x**3)*(-6*x) = -288*x**4
  -18*-6*x = 108*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -288*x**4 - 138*x**3 + 384*x**3 + 184*x**2 + 108*x - 144</replace>
Combining like terms, got -288*x**4 + 246*x**3 + 184*x**2 + 108*x - 144
<replace-#Step 5>#Step 6:
Current expression: -288*x**4 + 246*x**3 + 184*x**2 + 108*x - 144</replace>
No more calculations needed.
<answer>-288*x**4 + 246*x**3 + 184*x**2 + 108*x - 144</answer>


Question:
Simplify this expression: 343*x**3 + 294*x**2 - 308*x + 245
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 343*x**3 + 294*x**2 - 308*x + 245

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: 343*x**3 + 294*x**2 - 308*x + 245
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: 343*x**3 + 294*x**2 - 308*x + 245</replace>
No more calculations needed.
<answer>343*x**3 + 294*x**2 - 308*x + 245</answer>


Question:
Calculate the following: 6480*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: 6480*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: 6480*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: 6480*z</replace>
No more calculations needed.
<answer>6480*z</answer>


Question:
Simplify this expression: 85*y*(-40*y**2 - 11*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -3400*y**3 - 935*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: 85*y*(-40*y**2 - 11*y)
Expanding the part (-40*y**2 - 11*y) using the distributive property, and we got: (-11*y)*(85*y) + (85*y)*(-40*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-11*y)*(85*y) + (85*y)*(-40*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-40*y**2)*(85*y) = -3400*y**3
  (-11*y)*(85*y) = -935*y**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -3400*y**3 - 935*y**2</replace>
No more calculations needed.
<answer>-3400*y**3 - 935*y**2</answer>


Question:
Simplify this expression: (21*z + 49)*(25*z**3 - 44*z**2 + 20*z - 21)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 525*z**4 + 301*z**3 - 1736*z**2 + 539*z - 1029


Question:
Calculate the following: (-22*z**3 + 54*z**2 - 13)*(33*z**3 - 13*z**2 - 9*z - 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: -726*z**6 + 2068*z**5 - 504*z**4 - 431*z**3 - 1019*z**2 + 117*z + 286


Question:
Calculate the following: (12*x - 19)*(-35*x**3 + 16*x - 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: -420*x**4 + 665*x**3 + 192*x**2 - 796*x + 779

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: (12*x - 19)*(-35*x**3 + 16*x - 41)
Expanding the part (12*x - 19) using the distributive property, and we got: (12*x)*(-35*x**3 + 16*x - 41) - 19*(-35*x**3 + 16*x - 41)
<replace-#Step 1>#Step 2:
Current expression: (12*x)*(-35*x**3 + 16*x - 41) - 19*(-35*x**3 + 16*x - 41)</replace>
Simplifying the partial expression: -19*(-35*x**3 + 16*x - 41)
Expanding the part (-35*x**3 + 16*x - 41) using the distributive property, and we got: (16*x)*(-19) - 35*x**3*(-19) - 41*(-19)
Replacing -19*(-35*x**3 + 16*x - 41) with (16*x)*(-19) - 35*x**3*(-19) - 41*(-19) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (12*x)*(-35*x**3 + 16*x - 41) + (16*x)*(-19) - 35*x**3*(-19) + 779</replace>
Simplifying the partial expression: (12*x)*(-35*x**3 + 16*x - 41)
Expanding the part (-35*x**3 + 16*x - 41) using the distributive property, and we got: -492*x + (12*x)*(16*x) + (12*x)*(-35*x**3)
Replacing (12*x)*(-35*x**3 + 16*x - 41) with -492*x + (12*x)*(16*x) + (12*x)*(-35*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -41*12*x + (12*x)*(16*x) + (12*x)*(-35*x**3) + (16*x)*(-19) - 35*x**3*(-19) + 779</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-35*x**3)*-19 = 665*x**3
  (-35*x**3)*(12*x) = -420*x**4
  (16*x)*-19 = -304*x
  (16*x)*(12*x) = 192*x**2
  -41*12*x = -492*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -420*x**4 + 665*x**3 + 192*x**2 - 492*x - 304*x + 779</replace>
Combining like terms, got -420*x**4 + 665*x**3 + 192*x**2 - 796*x + 779
<replace-#Step 5>#Step 6:
Current expression: -420*x**4 + 665*x**3 + 192*x**2 - 796*x + 779</replace>
No more calculations needed.
<answer>-420*x**4 + 665*x**3 + 192*x**2 - 796*x + 779</answer>


Question:
Simplify this expression: (33*y**3 - 33)*(-4*y**3 + 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: -132*y**6 + 33*y**4 + 693*y**3 - 33*y - 561

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (33*y**3 - 33)*(-4*y**3 + y + 17)
Expanding the part (33*y**3 - 33) using the distributive property, and we got: (33*y**3)*(-4*y**3 + y + 17) - 33*(-4*y**3 + y + 17)
<replace-#Step 1>#Step 2:
Current expression: (33*y**3)*(-4*y**3 + y + 17) - 33*(-4*y**3 + y + 17)</replace>
Simplifying the partial expression: -33*(-4*y**3 + y + 17)
Expanding the part (-4*y**3 + y + 17) using the distributive property, and we got: y*(-33) - 4*y**3*(-33) + 17*(-33)
Replacing -33*(-4*y**3 + y + 17) with y*(-33) - 4*y**3*(-33) + 17*(-33) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: y*(-33) - 4*y**3*(-33) + (33*y**3)*(-4*y**3 + y + 17) - 561</replace>
Simplifying the partial expression: (33*y**3)*(-4*y**3 + y + 17)
Expanding the part (-4*y**3 + y + 17) using the distributive property, and we got: 17*(33*y**3) + y*(33*y**3) + (-4*y**3)*(33*y**3)
Replacing (33*y**3)*(-4*y**3 + y + 17) with 17*(33*y**3) + y*(33*y**3) + (-4*y**3)*(33*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 17*33*y**3 + y*(33*y**3) + y*(-33) + (-4*y**3)*(33*y**3) - 4*y**3*(-33) - 561</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  y*-33 = -33*y
  y*(33*y**3) = 33*y**4
  (-4*y**3)*-33 = 132*y**3
  (-4*y**3)*(33*y**3) = -132*y**6
  17*33*y**3 = 561*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -132*y**6 + 33*y**4 + 132*y**3 + 561*y**3 - 33*y - 561</replace>
Combining like terms, got -132*y**6 + 33*y**4 + 693*y**3 - 33*y - 561
<replace-#Step 5>#Step 6:
Current expression: -132*y**6 + 33*y**4 + 693*y**3 - 33*y - 561</replace>
No more calculations needed.
<answer>-132*y**6 + 33*y**4 + 693*y**3 - 33*y - 561</answer>


Question:
Simplify this expression: (-30*x**3 + 10*x**2 - 41)*(5*x**3 - 49*x - 1)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -150*x**6 + 50*x**5 + 1470*x**4 - 665*x**3 - 10*x**2 + 2009*x + 41


Question:
Simplify this expression: (-33*y**2 + 12*y)*(-65*y**3 + 33*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2145*y**5 - 1869*y**4 + 396*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: (-33*y**2 + 12*y)*(-65*y**3 + 33*y**2)
Expanding the part (-65*y**3 + 33*y**2) using the distributive property, and we got: (33*y**2)*(-33*y**2 + 12*y) + (-65*y**3)*(-33*y**2 + 12*y)
<replace-#Step 1>#Step 2:
Current expression: (33*y**2)*(-33*y**2 + 12*y) + (-65*y**3)*(-33*y**2 + 12*y)</replace>
Simplifying the partial expression: (-65*y**3)*(-33*y**2 + 12*y)
Expanding the part (-33*y**2 + 12*y) using the distributive property, and we got: (12*y)*(-65*y**3) + (-33*y**2)*(-65*y**3)
Replacing (-65*y**3)*(-33*y**2 + 12*y) with (12*y)*(-65*y**3) + (-33*y**2)*(-65*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (12*y)*(-65*y**3) + (-33*y**2)*(-65*y**3) + (33*y**2)*(-33*y**2 + 12*y)</replace>
Simplifying the partial expression: (33*y**2)*(-33*y**2 + 12*y)
Expanding the part (-33*y**2 + 12*y) using the distributive property, and we got: (12*y)*(33*y**2) + (-33*y**2)*(33*y**2)
Replacing (33*y**2)*(-33*y**2 + 12*y) with (12*y)*(33*y**2) + (-33*y**2)*(33*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (12*y)*(33*y**2) + (12*y)*(-65*y**3) + (-33*y**2)*(33*y**2) + (-33*y**2)*(-65*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-33*y**2)*(-65*y**3) = 2145*y**5
  (-33*y**2)*(33*y**2) = -1089*y**4
  (12*y)*(-65*y**3) = -780*y**4
  (12*y)*(33*y**2) = 396*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2145*y**5 - 1089*y**4 - 780*y**4 + 396*y**3</replace>
Combining like terms, got 2145*y**5 - 1869*y**4 + 396*y**3
<replace-#Step 5>#Step 6:
Current expression: 2145*y**5 - 1869*y**4 + 396*y**3</replace>
No more calculations needed.
<answer>2145*y**5 - 1869*y**4 + 396*y**3</answer>


Question:
Simplify this expression: (-72*z**2 - 43*z)*(-31*z**3 + 13*z**2 + 27*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: 2232*z**5 + 397*z**4 - 2503*z**3 - 1161*z**2


Question:
Calculate the following: (-25*x**2 + 32*x - 32)*(35*x**3 - 52*x**2 + 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: -875*x**5 + 2420*x**4 - 2784*x**3 + 564*x**2 + 1408*x - 1408


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

Answer: 72*y**5 + 44*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: 4*y**2*(18*y**3 + 11*y)
Expanding the part (18*y**3 + 11*y) using the distributive property, and we got: (11*y)*(4*y**2) + (4*y**2)*(18*y**3)
<replace-#Step 1>#Step 2:
Current expression: (11*y)*(4*y**2) + (4*y**2)*(18*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (11*y)*(4*y**2) = 44*y**3
  (18*y**3)*(4*y**2) = 72*y**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 72*y**5 + 44*y**3</replace>
No more calculations needed.
<answer>72*y**5 + 44*y**3</answer>


Question:
Calculate the following: (47 - 24*y**2)*(-25*y**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: 600*y**4 - 24*y**3 - 1175*y**2 + 47*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (47 - 24*y**2)*(-25*y**2 + y)
Expanding the part (47 - 24*y**2) using the distributive property, and we got: (-24*y**2)*(-25*y**2 + y) + 47*(-25*y**2 + y)
<replace-#Step 1>#Step 2:
Current expression: (-24*y**2)*(-25*y**2 + y) + 47*(-25*y**2 + y)</replace>
Simplifying the partial expression: 47*(-25*y**2 + y)
Expanding the part (-25*y**2 + y) using the distributive property, and we got: y*47 - 25*y**2*47
Replacing 47*(-25*y**2 + y) with y*47 - 25*y**2*47 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: y*47 - 25*y**2*47 + (-24*y**2)*(-25*y**2 + y)</replace>
Simplifying the partial expression: (-24*y**2)*(-25*y**2 + y)
Expanding the part (-25*y**2 + y) using the distributive property, and we got: y*(-24*y**2) + (-25*y**2)*(-24*y**2)
Replacing (-24*y**2)*(-25*y**2 + y) with y*(-24*y**2) + (-25*y**2)*(-24*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: y*(-24*y**2) + y*47 + (-25*y**2)*(-24*y**2) - 25*y**2*47</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  y*47 = 47*y
  y*(-24*y**2) = -24*y**3
  (-25*y**2)*47 = -1175*y**2
  (-25*y**2)*(-24*y**2) = 600*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 600*y**4 - 24*y**3 - 1175*y**2 + 47*y</replace>
No more calculations needed.
<answer>600*y**4 - 24*y**3 - 1175*y**2 + 47*y</answer>


Question:
Calculate the following: -1974*z**2 + 1512*z - 3192
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1974*z**2 + 1512*z - 3192

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: -1974*z**2 + 1512*z - 3192
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: -1974*z**2 + 1512*z - 3192</replace>
No more calculations needed.
<answer>-1974*z**2 + 1512*z - 3192</answer>


Question:
Calculate the following: (43*z**2 - 40*z)*(32*z**3 - 30*z**2 - 39*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: 1376*z**5 - 2570*z**4 - 477*z**3 + 1560*z**2


Question:
Calculate the following: (-46*z**2 - 28*z + 6)*(-13*z**3 - 9*z**2 + 50*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: 598*z**5 + 778*z**4 - 2126*z**3 - 1454*z**2 + 300*z


Question:
Calculate the following: (-13*z**3 - 36)*(33*z**3 - 16)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -429*z**6 - 980*z**3 + 576

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-13*z**3 - 36)*(33*z**3 - 16)
Expanding the part (-13*z**3 - 36) using the distributive property, and we got: (-13*z**3)*(33*z**3 - 16) - 36*(33*z**3 - 16)
<replace-#Step 1>#Step 2:
Current expression: (-13*z**3)*(33*z**3 - 16) - 36*(33*z**3 - 16)</replace>
Simplifying the partial expression: -36*(33*z**3 - 16)
Expanding the part (33*z**3 - 16) using the distributive property, and we got: (33*z**3)*(-36) - 16*(-36)
Replacing -36*(33*z**3 - 16) with (33*z**3)*(-36) - 16*(-36) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-13*z**3)*(33*z**3 - 16) + (33*z**3)*(-36) + 576</replace>
Simplifying the partial expression: (-13*z**3)*(33*z**3 - 16)
Expanding the part (33*z**3 - 16) using the distributive property, and we got: -(-1)*208*z**3 + (-13*z**3)*(33*z**3)
Replacing (-13*z**3)*(33*z**3 - 16) with -(-1)*208*z**3 + (-13*z**3)*(33*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -16*(-13)*z**3 + (-13*z**3)*(33*z**3) + (33*z**3)*(-36) + 576</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (33*z**3)*-36 = -1188*z**3
  (33*z**3)*(-13*z**3) = -429*z**6
  -16*-13*z**3 = 208*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -429*z**6 - 1188*z**3 + 208*z**3 + 576</replace>
Combining like terms, got -429*z**6 - 980*z**3 + 576
<replace-#Step 5>#Step 6:
Current expression: -429*z**6 - 980*z**3 + 576</replace>
No more calculations needed.
<answer>-429*z**6 - 980*z**3 + 576</answer>


Question:
Calculate the following: -27*x*(-3*x**3 + 42*x - 21)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 81*x**4 - 1134*x**2 + 567*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: -27*x*(-3*x**3 + 42*x - 21)
Expanding the part (-3*x**3 + 42*x - 21) using the distributive property, and we got: (-27*x)*(42*x) + (-27*x)*(-3*x**3) - (-1)*567*x
<replace-#Step 1>#Step 2:
Current expression: (-27*x)*(42*x) + (-27*x)*(-3*x**3) - (-1)*567*x</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -21*(-27*x) = 567*x
  (-3*x**3)*(-27*x) = 81*x**4
  (42*x)*(-27*x) = -1134*x**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 81*x**4 - 1134*x**2 + 567*x</replace>
No more calculations needed.
<answer>81*x**4 - 1134*x**2 + 567*x</answer>


Question:
Calculate the following: (-12*x - 79)*(-30*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: 360*x**3 + 2370*x**2 + 12*x + 79

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: (-12*x - 79)*(-30*x**2 - 1)
Expanding the part (-30*x**2 - 1) using the distributive property, and we got: (-30*x**2)*(-12*x - 79) - (-12*x - 79)
<replace-#Step 1>#Step 2:
Current expression: (-30*x**2)*(-12*x - 79) - (-12*x - 79)</replace>
Simplifying the partial expression: -(-12*x - 79)
Expanding the part (-12*x - 79) using the distributive property, and we got: -12*x*(-1) - 79*(-1)
Replacing -(-12*x - 79) with -12*x*(-1) - 79*(-1) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -12*x*(-1) + (-30*x**2)*(-12*x - 79) + 79</replace>
Simplifying the partial expression: (-30*x**2)*(-12*x - 79)
Expanding the part (-12*x - 79) using the distributive property, and we got: (-12*x)*(-30*x**2) - (-1)*2370*x**2
Replacing (-30*x**2)*(-12*x - 79) with (-12*x)*(-30*x**2) - (-1)*2370*x**2 in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-12*x)*(-30*x**2) - 12*x*(-1) - 79*(-30)*x**2 + 79</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-12*x)*-1 = 12*x
  (-12*x)*(-30*x**2) = 360*x**3
  -79*-30*x**2 = 2370*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 360*x**3 + 2370*x**2 + 12*x + 79</replace>
No more calculations needed.
<answer>360*x**3 + 2370*x**2 + 12*x + 79</answer>


Question:
Simplify this expression: (21*z + 23)*(31*z**3 + 41*z**2 + 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: 651*z**4 + 1574*z**3 + 943*z**2 + 546*z + 598

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (21*z + 23)*(31*z**3 + 41*z**2 + 26)
Expanding the part (21*z + 23) using the distributive property, and we got: (21*z)*(31*z**3 + 41*z**2 + 26) + 23*(31*z**3 + 41*z**2 + 26)
<replace-#Step 1>#Step 2:
Current expression: (21*z)*(31*z**3 + 41*z**2 + 26) + 23*(31*z**3 + 41*z**2 + 26)</replace>
Simplifying the partial expression: 23*(31*z**3 + 41*z**2 + 26)
Expanding the part (31*z**3 + 41*z**2 + 26) using the distributive property, and we got: (41*z**2)*23 + (31*z**3)*23 + 26*23
Replacing 23*(31*z**3 + 41*z**2 + 26) with (41*z**2)*23 + (31*z**3)*23 + 26*23 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (21*z)*(31*z**3 + 41*z**2 + 26) + (41*z**2)*23 + (31*z**3)*23 + 598</replace>
Simplifying the partial expression: (21*z)*(31*z**3 + 41*z**2 + 26)
Expanding the part (31*z**3 + 41*z**2 + 26) using the distributive property, and we got: 26*(21*z) + (21*z)*(41*z**2) + (21*z)*(31*z**3)
Replacing (21*z)*(31*z**3 + 41*z**2 + 26) with 26*(21*z) + (21*z)*(41*z**2) + (21*z)*(31*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 26*21*z + (21*z)*(41*z**2) + (21*z)*(31*z**3) + (41*z**2)*23 + (31*z**3)*23 + 598</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (31*z**3)*23 = 713*z**3
  (31*z**3)*(21*z) = 651*z**4
  (41*z**2)*23 = 943*z**2
  (41*z**2)*(21*z) = 861*z**3
  26*21*z = 546*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 651*z**4 + 713*z**3 + 861*z**3 + 943*z**2 + 546*z + 598</replace>
Combining like terms, got 651*z**4 + 1574*z**3 + 943*z**2 + 546*z + 598
<replace-#Step 5>#Step 6:
Current expression: 651*z**4 + 1574*z**3 + 943*z**2 + 546*z + 598</replace>
No more calculations needed.
<answer>651*z**4 + 1574*z**3 + 943*z**2 + 546*z + 598</answer>


Question:
Simplify this expression: (-16*y**3 - 7*y**2 - 44)*(-14*y**3 - 27*y**2 - 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: 224*y**6 + 530*y**5 + 189*y**4 + 968*y**3 + 1342*y**2 + 968


Question:
Calculate the following: (-26*z**3 + 33*z)*(38*z**3 - 6*z**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: -988*z**6 + 156*z**5 + 1254*z**4 + 868*z**3 - 1353*z


Question:
Simplify this expression: (-19*z**2 + 82*z)*(16*z**3 + 30*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -304*z**5 + 1312*z**4 - 570*z**3 + 2460*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: (-19*z**2 + 82*z)*(16*z**3 + 30*z)
Expanding the part (-19*z**2 + 82*z) using the distributive property, and we got: (82*z)*(16*z**3 + 30*z) + (-19*z**2)*(16*z**3 + 30*z)
<replace-#Step 1>#Step 2:
Current expression: (82*z)*(16*z**3 + 30*z) + (-19*z**2)*(16*z**3 + 30*z)</replace>
Simplifying the partial expression: (-19*z**2)*(16*z**3 + 30*z)
Expanding the part (16*z**3 + 30*z) using the distributive property, and we got: (30*z)*(-19*z**2) + (-19*z**2)*(16*z**3)
Replacing (-19*z**2)*(16*z**3 + 30*z) with (30*z)*(-19*z**2) + (-19*z**2)*(16*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (30*z)*(-19*z**2) + (82*z)*(16*z**3 + 30*z) + (-19*z**2)*(16*z**3)</replace>
Simplifying the partial expression: (82*z)*(16*z**3 + 30*z)
Expanding the part (16*z**3 + 30*z) using the distributive property, and we got: (30*z)*(82*z) + (82*z)*(16*z**3)
Replacing (82*z)*(16*z**3 + 30*z) with (30*z)*(82*z) + (82*z)*(16*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (30*z)*(82*z) + (30*z)*(-19*z**2) + (82*z)*(16*z**3) + (-19*z**2)*(16*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (16*z**3)*(-19*z**2) = -304*z**5
  (16*z**3)*(82*z) = 1312*z**4
  (30*z)*(-19*z**2) = -570*z**3
  (30*z)*(82*z) = 2460*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -304*z**5 + 1312*z**4 - 570*z**3 + 2460*z**2</replace>
No more calculations needed.
<answer>-304*z**5 + 1312*z**4 - 570*z**3 + 2460*z**2</answer>


Question:
Simplify this expression: (23 - 38*x**3)*(3*x**3 + 42*x - 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: -114*x**6 - 1596*x**4 + 1399*x**3 + 966*x - 805

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (23 - 38*x**3)*(3*x**3 + 42*x - 35)
Expanding the part (23 - 38*x**3) using the distributive property, and we got: (-38*x**3)*(3*x**3 + 42*x - 35) + 23*(3*x**3 + 42*x - 35)
<replace-#Step 1>#Step 2:
Current expression: (-38*x**3)*(3*x**3 + 42*x - 35) + 23*(3*x**3 + 42*x - 35)</replace>
Simplifying the partial expression: 23*(3*x**3 + 42*x - 35)
Expanding the part (3*x**3 + 42*x - 35) using the distributive property, and we got: (42*x)*23 + (3*x**3)*23 - 35*23
Replacing 23*(3*x**3 + 42*x - 35) with (42*x)*23 + (3*x**3)*23 - 35*23 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (42*x)*23 + (-38*x**3)*(3*x**3 + 42*x - 35) + (3*x**3)*23 - 805</replace>
Simplifying the partial expression: (-38*x**3)*(3*x**3 + 42*x - 35)
Expanding the part (3*x**3 + 42*x - 35) using the distributive property, and we got: -(-1)*1330*x**3 + (42*x)*(-38*x**3) + (-38*x**3)*(3*x**3)
Replacing (-38*x**3)*(3*x**3 + 42*x - 35) with -(-1)*1330*x**3 + (42*x)*(-38*x**3) + (-38*x**3)*(3*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -35*(-38)*x**3 + (42*x)*(-38*x**3) + (42*x)*23 + (-38*x**3)*(3*x**3) + (3*x**3)*23 - 805</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (3*x**3)*23 = 69*x**3
  (3*x**3)*(-38*x**3) = -114*x**6
  (42*x)*23 = 966*x
  (42*x)*(-38*x**3) = -1596*x**4
  -35*-38*x**3 = 1330*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -114*x**6 - 1596*x**4 + 69*x**3 + 1330*x**3 + 966*x - 805</replace>
Combining like terms, got -114*x**6 - 1596*x**4 + 1399*x**3 + 966*x - 805
<replace-#Step 5>#Step 6:
Current expression: -114*x**6 - 1596*x**4 + 1399*x**3 + 966*x - 805</replace>
No more calculations needed.
<answer>-114*x**6 - 1596*x**4 + 1399*x**3 + 966*x - 805</answer>


Question:
Calculate the following: (-14*z**2 - 19*z)*(-28*z**3 + 17*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: 392*z**5 + 294*z**4 - 323*z**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-14*z**2 - 19*z)*(-28*z**3 + 17*z**2)
Expanding the part (-28*z**3 + 17*z**2) using the distributive property, and we got: (17*z**2)*(-14*z**2 - 19*z) + (-28*z**3)*(-14*z**2 - 19*z)
<replace-#Step 1>#Step 2:
Current expression: (17*z**2)*(-14*z**2 - 19*z) + (-28*z**3)*(-14*z**2 - 19*z)</replace>
Simplifying the partial expression: (-28*z**3)*(-14*z**2 - 19*z)
Expanding the part (-14*z**2 - 19*z) using the distributive property, and we got: (-19*z)*(-28*z**3) + (-14*z**2)*(-28*z**3)
Replacing (-28*z**3)*(-14*z**2 - 19*z) with (-19*z)*(-28*z**3) + (-14*z**2)*(-28*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-19*z)*(-28*z**3) + (-14*z**2)*(-28*z**3) + (17*z**2)*(-14*z**2 - 19*z)</replace>
Simplifying the partial expression: (17*z**2)*(-14*z**2 - 19*z)
Expanding the part (-14*z**2 - 19*z) using the distributive property, and we got: (-19*z)*(17*z**2) + (-14*z**2)*(17*z**2)
Replacing (17*z**2)*(-14*z**2 - 19*z) with (-19*z)*(17*z**2) + (-14*z**2)*(17*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-19*z)*(17*z**2) + (-19*z)*(-28*z**3) + (-14*z**2)*(17*z**2) + (-14*z**2)*(-28*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-19*z)*(-28*z**3) = 532*z**4
  (-19*z)*(17*z**2) = -323*z**3
  (-14*z**2)*(-28*z**3) = 392*z**5
  (-14*z**2)*(17*z**2) = -238*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 392*z**5 - 238*z**4 + 532*z**4 - 323*z**3</replace>
Combining like terms, got 392*z**5 + 294*z**4 - 323*z**3
<replace-#Step 5>#Step 6:
Current expression: 392*z**5 + 294*z**4 - 323*z**3</replace>
No more calculations needed.
<answer>392*z**5 + 294*z**4 - 323*z**3</answer>


Question:
Calculate the following: (-6*x - 35)*(17*x**3 + 9*x**2 - 24)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -102*x**4 - 649*x**3 - 315*x**2 + 144*x + 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: (-6*x - 35)*(17*x**3 + 9*x**2 - 24)
Expanding the part (-6*x - 35) using the distributive property, and we got: (-6*x)*(17*x**3 + 9*x**2 - 24) - 35*(17*x**3 + 9*x**2 - 24)
<replace-#Step 1>#Step 2:
Current expression: (-6*x)*(17*x**3 + 9*x**2 - 24) - 35*(17*x**3 + 9*x**2 - 24)</replace>
Simplifying the partial expression: -35*(17*x**3 + 9*x**2 - 24)
Expanding the part (17*x**3 + 9*x**2 - 24) using the distributive property, and we got: (9*x**2)*(-35) + (17*x**3)*(-35) - 24*(-35)
Replacing -35*(17*x**3 + 9*x**2 - 24) with (9*x**2)*(-35) + (17*x**3)*(-35) - 24*(-35) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-6*x)*(17*x**3 + 9*x**2 - 24) + (9*x**2)*(-35) + (17*x**3)*(-35) + 840</replace>
Simplifying the partial expression: (-6*x)*(17*x**3 + 9*x**2 - 24)
Expanding the part (17*x**3 + 9*x**2 - 24) using the distributive property, and we got: (-6*x)*(9*x**2) + (-6*x)*(17*x**3) - (-1)*144*x
Replacing (-6*x)*(17*x**3 + 9*x**2 - 24) with (-6*x)*(9*x**2) + (-6*x)*(17*x**3) - (-1)*144*x in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-6*x)*(9*x**2) + (-6*x)*(17*x**3) - 24*(-6)*x + (9*x**2)*(-35) + (17*x**3)*(-35) + 840</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (9*x**2)*-35 = -315*x**2
  (9*x**2)*(-6*x) = -54*x**3
  (17*x**3)*-35 = -595*x**3
  (17*x**3)*(-6*x) = -102*x**4
  -24*-6*x = 144*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -102*x**4 - 595*x**3 - 54*x**3 - 315*x**2 + 144*x + 840</replace>
Combining like terms, got -102*x**4 - 649*x**3 - 315*x**2 + 144*x + 840
<replace-#Step 5>#Step 6:
Current expression: -102*x**4 - 649*x**3 - 315*x**2 + 144*x + 840</replace>
No more calculations needed.
<answer>-102*x**4 - 649*x**3 - 315*x**2 + 144*x + 840</answer>


Question:
Calculate the following: (63*x**3 - 49*x)*(-30*x**3 - 15*x**2 + 22*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: -1890*x**6 - 945*x**5 + 2856*x**4 + 735*x**3 - 1078*x**2


Question:
Simplify this expression: (35*x**2 + 48)*(-3*x**3 - 69*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: -105*x**5 - 2415*x**4 - 144*x**3 - 3312*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: (35*x**2 + 48)*(-3*x**3 - 69*x**2)
Expanding the part (35*x**2 + 48) using the distributive property, and we got: (35*x**2)*(-3*x**3 - 69*x**2) + 48*(-3*x**3 - 69*x**2)
<replace-#Step 1>#Step 2:
Current expression: (35*x**2)*(-3*x**3 - 69*x**2) + 48*(-3*x**3 - 69*x**2)</replace>
Simplifying the partial expression: 48*(-3*x**3 - 69*x**2)
Expanding the part (-3*x**3 - 69*x**2) using the distributive property, and we got: -69*x**2*48 - 3*x**3*48
Replacing 48*(-3*x**3 - 69*x**2) with -69*x**2*48 - 3*x**3*48 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -69*x**2*48 + (35*x**2)*(-3*x**3 - 69*x**2) - 3*x**3*48</replace>
Simplifying the partial expression: (35*x**2)*(-3*x**3 - 69*x**2)
Expanding the part (-3*x**3 - 69*x**2) using the distributive property, and we got: (-69*x**2)*(35*x**2) + (35*x**2)*(-3*x**3)
Replacing (35*x**2)*(-3*x**3 - 69*x**2) with (-69*x**2)*(35*x**2) + (35*x**2)*(-3*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-69*x**2)*(35*x**2) - 69*x**2*48 + (35*x**2)*(-3*x**3) - 3*x**3*48</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-69*x**2)*48 = -3312*x**2
  (-69*x**2)*(35*x**2) = -2415*x**4
  (-3*x**3)*48 = -144*x**3
  (-3*x**3)*(35*x**2) = -105*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -105*x**5 - 2415*x**4 - 144*x**3 - 3312*x**2</replace>
No more calculations needed.
<answer>-105*x**5 - 2415*x**4 - 144*x**3 - 3312*x**2</answer>


Question:
Calculate the following: 182*x**2 - 56*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: 182*x**2 - 56*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 182*x**2 - 56*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: 182*x**2 - 56*x</replace>
No more calculations needed.
<answer>182*x**2 - 56*x</answer>


Question:
Simplify this expression: (-34*x - 21)*(16*x**3 + 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: -544*x**4 - 336*x**3 - 1530*x**2 - 945*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-34*x - 21)*(16*x**3 + 45*x)
Expanding the part (-34*x - 21) using the distributive property, and we got: (-34*x)*(16*x**3 + 45*x) - 21*(16*x**3 + 45*x)
<replace-#Step 1>#Step 2:
Current expression: (-34*x)*(16*x**3 + 45*x) - 21*(16*x**3 + 45*x)</replace>
Simplifying the partial expression: -21*(16*x**3 + 45*x)
Expanding the part (16*x**3 + 45*x) using the distributive property, and we got: (45*x)*(-21) + (16*x**3)*(-21)
Replacing -21*(16*x**3 + 45*x) with (45*x)*(-21) + (16*x**3)*(-21) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-34*x)*(16*x**3 + 45*x) + (45*x)*(-21) + (16*x**3)*(-21)</replace>
Simplifying the partial expression: (-34*x)*(16*x**3 + 45*x)
Expanding the part (16*x**3 + 45*x) using the distributive property, and we got: (-34*x)*(45*x) + (-34*x)*(16*x**3)
Replacing (-34*x)*(16*x**3 + 45*x) with (-34*x)*(45*x) + (-34*x)*(16*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-34*x)*(45*x) + (-34*x)*(16*x**3) + (45*x)*(-21) + (16*x**3)*(-21)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (16*x**3)*-21 = -336*x**3
  (16*x**3)*(-34*x) = -544*x**4
  (45*x)*-21 = -945*x
  (45*x)*(-34*x) = -1530*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -544*x**4 - 336*x**3 - 1530*x**2 - 945*x</replace>
No more calculations needed.
<answer>-544*x**4 - 336*x**3 - 1530*x**2 - 945*x</answer>


Question:
Calculate the following: (-40*x**3 - 5*x**2)*(57*x**3 + 3*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: -2280*x**6 - 285*x**5 - 120*x**4 - 15*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: (-40*x**3 - 5*x**2)*(57*x**3 + 3*x)
Expanding the part (-40*x**3 - 5*x**2) using the distributive property, and we got: (-5*x**2)*(57*x**3 + 3*x) + (-40*x**3)*(57*x**3 + 3*x)
<replace-#Step 1>#Step 2:
Current expression: (-5*x**2)*(57*x**3 + 3*x) + (-40*x**3)*(57*x**3 + 3*x)</replace>
Simplifying the partial expression: (-40*x**3)*(57*x**3 + 3*x)
Expanding the part (57*x**3 + 3*x) using the distributive property, and we got: (3*x)*(-40*x**3) + (-40*x**3)*(57*x**3)
Replacing (-40*x**3)*(57*x**3 + 3*x) with (3*x)*(-40*x**3) + (-40*x**3)*(57*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (3*x)*(-40*x**3) + (-5*x**2)*(57*x**3 + 3*x) + (-40*x**3)*(57*x**3)</replace>
Simplifying the partial expression: (-5*x**2)*(57*x**3 + 3*x)
Expanding the part (57*x**3 + 3*x) using the distributive property, and we got: (3*x)*(-5*x**2) + (-5*x**2)*(57*x**3)
Replacing (-5*x**2)*(57*x**3 + 3*x) with (3*x)*(-5*x**2) + (-5*x**2)*(57*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (3*x)*(-5*x**2) + (3*x)*(-40*x**3) + (-5*x**2)*(57*x**3) + (-40*x**3)*(57*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (3*x)*(-40*x**3) = -120*x**4
  (3*x)*(-5*x**2) = -15*x**3
  (57*x**3)*(-40*x**3) = -2280*x**6
  (57*x**3)*(-5*x**2) = -285*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2280*x**6 - 285*x**5 - 120*x**4 - 15*x**3</replace>
No more calculations needed.
<answer>-2280*x**6 - 285*x**5 - 120*x**4 - 15*x**3</answer>


Question:
Calculate the following: (-18*y**3 - 12)*(35*y**3 + 36*y**2 - 46*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -630*y**6 - 648*y**5 + 828*y**4 - 420*y**3 - 432*y**2 + 552*y


Question:
Simplify this expression: (-7*z**3 + 5*z)*(5*z**3 - 17*z**2 + 36*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -35*z**6 + 119*z**5 - 227*z**4 - 85*z**3 + 180*z**2


Question:
Calculate the following: 1924*x**2 + 2288*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: 1924*x**2 + 2288*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: 1924*x**2 + 2288*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: 1924*x**2 + 2288*x</replace>
No more calculations needed.
<answer>1924*x**2 + 2288*x</answer>


Question:
Calculate the following: (18*x**2 + 2)*(-21*x**3 + 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: -378*x**5 + 498*x**3 + 60*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (18*x**2 + 2)*(-21*x**3 + 30*x)
Expanding the part (18*x**2 + 2) using the distributive property, and we got: (18*x**2)*(-21*x**3 + 30*x) + 2*(-21*x**3 + 30*x)
<replace-#Step 1>#Step 2:
Current expression: (18*x**2)*(-21*x**3 + 30*x) + 2*(-21*x**3 + 30*x)</replace>
Simplifying the partial expression: 2*(-21*x**3 + 30*x)
Expanding the part (-21*x**3 + 30*x) using the distributive property, and we got: (30*x)*2 - 21*x**3*2
Replacing 2*(-21*x**3 + 30*x) with (30*x)*2 - 21*x**3*2 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (30*x)*2 + (18*x**2)*(-21*x**3 + 30*x) - 21*x**3*2</replace>
Simplifying the partial expression: (18*x**2)*(-21*x**3 + 30*x)
Expanding the part (-21*x**3 + 30*x) using the distributive property, and we got: (30*x)*(18*x**2) + (18*x**2)*(-21*x**3)
Replacing (18*x**2)*(-21*x**3 + 30*x) with (30*x)*(18*x**2) + (18*x**2)*(-21*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (30*x)*(18*x**2) + (30*x)*2 + (18*x**2)*(-21*x**3) - 21*x**3*2</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-21*x**3)*2 = -42*x**3
  (-21*x**3)*(18*x**2) = -378*x**5
  (30*x)*2 = 60*x
  (30*x)*(18*x**2) = 540*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -378*x**5 - 42*x**3 + 540*x**3 + 60*x</replace>
Combining like terms, got -378*x**5 + 498*x**3 + 60*x
<replace-#Step 5>#Step 6:
Current expression: -378*x**5 + 498*x**3 + 60*x</replace>
No more calculations needed.
<answer>-378*x**5 + 498*x**3 + 60*x</answer>


Question:
Simplify this expression: -47*y*(21 - 42*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1974*y**3 - 987*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: -47*y*(21 - 42*y**2)
Expanding the part (21 - 42*y**2) using the distributive property, and we got: (-47*y)*(-42*y**2) + 21*(-47*y)
<replace-#Step 1>#Step 2:
Current expression: (-47*y)*(-42*y**2) + 21*(-47*y)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  21*(-47*y) = -987*y
  (-42*y**2)*(-47*y) = 1974*y**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1974*y**3 - 987*y</replace>
No more calculations needed.
<answer>1974*y**3 - 987*y</answer>