Question:
Simplify this expression: (64*z**2 - 15)*(-42*z**3 - 35*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2688*z**5 - 1610*z**3 + 525*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: (64*z**2 - 15)*(-42*z**3 - 35*z)
Expanding the part (64*z**2 - 15) using the distributive property, and we got: (64*z**2)*(-42*z**3 - 35*z) - 15*(-42*z**3 - 35*z)
<replace-#Step 1>#Step 2:
Current expression: (64*z**2)*(-42*z**3 - 35*z) - 15*(-42*z**3 - 35*z)</replace>
Simplifying the partial expression: -15*(-42*z**3 - 35*z)
Expanding the part (-42*z**3 - 35*z) using the distributive property, and we got: -35*z*(-15) - 42*z**3*(-15)
Replacing -15*(-42*z**3 - 35*z) with -35*z*(-15) - 42*z**3*(-15) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -35*z*(-15) + (64*z**2)*(-42*z**3 - 35*z) - 42*z**3*(-15)</replace>
Simplifying the partial expression: (64*z**2)*(-42*z**3 - 35*z)
Expanding the part (-42*z**3 - 35*z) using the distributive property, and we got: (-35*z)*(64*z**2) + (64*z**2)*(-42*z**3)
Replacing (64*z**2)*(-42*z**3 - 35*z) with (-35*z)*(64*z**2) + (64*z**2)*(-42*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-35*z)*(64*z**2) - 35*z*(-15) + (64*z**2)*(-42*z**3) - 42*z**3*(-15)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-42*z**3)*-15 = 630*z**3
  (-42*z**3)*(64*z**2) = -2688*z**5
  (-35*z)*-15 = 525*z
  (-35*z)*(64*z**2) = -2240*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2688*z**5 - 2240*z**3 + 630*z**3 + 525*z</replace>
Combining like terms, got -2688*z**5 - 1610*z**3 + 525*z
<replace-#Step 5>#Step 6:
Current expression: -2688*z**5 - 1610*z**3 + 525*z</replace>
No more calculations needed.
<answer>-2688*z**5 - 1610*z**3 + 525*z</answer>


Question:
Calculate the following: (-21*x**3 - 18*x**2)*(-12*x**2 - 9*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: 252*x**5 + 405*x**4 + 141*x**3 - 18*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: (-21*x**3 - 18*x**2)*(-12*x**2 - 9*x + 1)
Expanding the part (-21*x**3 - 18*x**2) using the distributive property, and we got: (-18*x**2)*(-12*x**2 - 9*x + 1) + (-21*x**3)*(-12*x**2 - 9*x + 1)
<replace-#Step 1>#Step 2:
Current expression: (-18*x**2)*(-12*x**2 - 9*x + 1) + (-21*x**3)*(-12*x**2 - 9*x + 1)</replace>
Simplifying the partial expression: (-21*x**3)*(-12*x**2 - 9*x + 1)
Expanding the part (-12*x**2 - 9*x + 1) using the distributive property, and we got: (-9*x)*(-21*x**3) + 1*(-21*x**3) + (-12*x**2)*(-21*x**3)
Replacing (-21*x**3)*(-12*x**2 - 9*x + 1) with (-9*x)*(-21*x**3) + 1*(-21*x**3) + (-12*x**2)*(-21*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-9*x)*(-21*x**3) - 21*x**3 + (-18*x**2)*(-12*x**2 - 9*x + 1) + (-12*x**2)*(-21*x**3)</replace>
Simplifying the partial expression: (-18*x**2)*(-12*x**2 - 9*x + 1)
Expanding the part (-12*x**2 - 9*x + 1) using the distributive property, and we got: (-9*x)*(-18*x**2) + 1*(-18*x**2) + (-18*x**2)*(-12*x**2)
Replacing (-18*x**2)*(-12*x**2 - 9*x + 1) with (-9*x)*(-18*x**2) + 1*(-18*x**2) + (-18*x**2)*(-12*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-9*x)*(-18*x**2) + (-9*x)*(-21*x**3) - 21*x**3 - 18*x**2 + (-18*x**2)*(-12*x**2) + (-12*x**2)*(-21*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-12*x**2)*(-21*x**3) = 252*x**5
  (-12*x**2)*(-18*x**2) = 216*x**4
  (-9*x)*(-21*x**3) = 189*x**4
  (-9*x)*(-18*x**2) = 162*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 252*x**5 + 189*x**4 + 216*x**4 - 21*x**3 + 162*x**3 - 18*x**2</replace>
Combining like terms, got 252*x**5 + 405*x**4 + 141*x**3 - 18*x**2
<replace-#Step 5>#Step 6:
Current expression: 252*x**5 + 405*x**4 + 141*x**3 - 18*x**2</replace>
No more calculations needed.
<answer>252*x**5 + 405*x**4 + 141*x**3 - 18*x**2</answer>


Question:
Simplify this expression: -25*x**3*(68*x**2 - 25*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1700*x**5 + 625*x**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -25*x**3*(68*x**2 - 25*x)
Expanding the part (68*x**2 - 25*x) using the distributive property, and we got: (-25*x)*(-25*x**3) + (68*x**2)*(-25*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-25*x)*(-25*x**3) + (68*x**2)*(-25*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-25*x)*(-25*x**3) = 625*x**4
  (68*x**2)*(-25*x**3) = -1700*x**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1700*x**5 + 625*x**4</replace>
No more calculations needed.
<answer>-1700*x**5 + 625*x**4</answer>


Question:
Calculate the following: 6*y**3*(70*y**3 + 36*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: 420*y**6 + 216*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: 6*y**3*(70*y**3 + 36*y)
Expanding the part (70*y**3 + 36*y) using the distributive property, and we got: (36*y)*(6*y**3) + (6*y**3)*(70*y**3)
<replace-#Step 1>#Step 2:
Current expression: (36*y)*(6*y**3) + (6*y**3)*(70*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (36*y)*(6*y**3) = 216*y**4
  (70*y**3)*(6*y**3) = 420*y**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 420*y**6 + 216*y**4</replace>
No more calculations needed.
<answer>420*y**6 + 216*y**4</answer>


Question:
Simplify this expression: (1 - 36*x**2)*(31*x**2 - 57*x - 10)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1116*x**4 + 2052*x**3 + 391*x**2 - 57*x - 10

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: (1 - 36*x**2)*(31*x**2 - 57*x - 10)
Expanding the part (1 - 36*x**2) using the distributive property, and we got: (-36*x**2)*(31*x**2 - 57*x - 10) + 1*(31*x**2 - 57*x - 10)
<replace-#Step 1>#Step 2:
Current expression: (-36*x**2)*(31*x**2 - 57*x - 10) + 1*(31*x**2 - 57*x - 10)</replace>
Simplifying the partial expression: 1*(31*x**2 - 57*x - 10)
Expanding the part (31*x**2 - 57*x - 10) using the distributive property, and we got: -57*x*1 + (31*x**2)*1 - 10*1
Replacing 1*(31*x**2 - 57*x - 10) with -57*x*1 + (31*x**2)*1 - 10*1 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -57*x*1 + (-36*x**2)*(31*x**2 - 57*x - 10) + (31*x**2)*1 - 10</replace>
Simplifying the partial expression: (-36*x**2)*(31*x**2 - 57*x - 10)
Expanding the part (31*x**2 - 57*x - 10) using the distributive property, and we got: (-57*x)*(-36*x**2) - (-1)*360*x**2 + (-36*x**2)*(31*x**2)
Replacing (-36*x**2)*(31*x**2 - 57*x - 10) with (-57*x)*(-36*x**2) - (-1)*360*x**2 + (-36*x**2)*(31*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-57*x)*(-36*x**2) - 57*x*1 - 10*(-36)*x**2 + (-36*x**2)*(31*x**2) + (31*x**2)*1 - 10</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-57*x)*1 = -57*x
  (-57*x)*(-36*x**2) = 2052*x**3
  (31*x**2)*1 = 31*x**2
  (31*x**2)*(-36*x**2) = -1116*x**4
  -10*-36*x**2 = 360*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1116*x**4 + 2052*x**3 + 31*x**2 + 360*x**2 - 57*x - 10</replace>
Combining like terms, got -1116*x**4 + 2052*x**3 + 391*x**2 - 57*x - 10
<replace-#Step 5>#Step 6:
Current expression: -1116*x**4 + 2052*x**3 + 391*x**2 - 57*x - 10</replace>
No more calculations needed.
<answer>-1116*x**4 + 2052*x**3 + 391*x**2 - 57*x - 10</answer>


Question:
Calculate the following: (58*z + 42)*(49*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: 2842*z**4 + 2058*z**3 + 2378*z + 1722

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (58*z + 42)*(49*z**3 + 41)
Expanding the part (49*z**3 + 41) using the distributive property, and we got: (49*z**3)*(58*z + 42) + 41*(58*z + 42)
<replace-#Step 1>#Step 2:
Current expression: (49*z**3)*(58*z + 42) + 41*(58*z + 42)</replace>
Simplifying the partial expression: 41*(58*z + 42)
Expanding the part (58*z + 42) using the distributive property, and we got: (58*z)*41 + 42*41
Replacing 41*(58*z + 42) with (58*z)*41 + 42*41 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (58*z)*41 + (49*z**3)*(58*z + 42) + 1722</replace>
Simplifying the partial expression: (49*z**3)*(58*z + 42)
Expanding the part (58*z + 42) using the distributive property, and we got: 42*(49*z**3) + (58*z)*(49*z**3)
Replacing (49*z**3)*(58*z + 42) with 42*(49*z**3) + (58*z)*(49*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 42*49*z**3 + (58*z)*(49*z**3) + (58*z)*41 + 1722</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (58*z)*41 = 2378*z
  (58*z)*(49*z**3) = 2842*z**4
  42*49*z**3 = 2058*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2842*z**4 + 2058*z**3 + 2378*z + 1722</replace>
No more calculations needed.
<answer>2842*z**4 + 2058*z**3 + 2378*z + 1722</answer>


Question:
Simplify this expression: (-49*y**2 - 38)*(30*y**3 + 32*y**2 + 36*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: -1470*y**5 - 1568*y**4 - 2904*y**3 - 1216*y**2 - 1368*y


Question:
Simplify this expression: (10*y + 40)*(-45*y**2 - 33)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -450*y**3 - 1800*y**2 - 330*y - 1320

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (10*y + 40)*(-45*y**2 - 33)
Expanding the part (-45*y**2 - 33) using the distributive property, and we got: (-45*y**2)*(10*y + 40) - 33*(10*y + 40)
<replace-#Step 1>#Step 2:
Current expression: (-45*y**2)*(10*y + 40) - 33*(10*y + 40)</replace>
Simplifying the partial expression: -33*(10*y + 40)
Expanding the part (10*y + 40) using the distributive property, and we got: (10*y)*(-33) + 40*(-33)
Replacing -33*(10*y + 40) with (10*y)*(-33) + 40*(-33) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (10*y)*(-33) + (-45*y**2)*(10*y + 40) - 1320</replace>
Simplifying the partial expression: (-45*y**2)*(10*y + 40)
Expanding the part (10*y + 40) using the distributive property, and we got: 40*(-45*y**2) + (10*y)*(-45*y**2)
Replacing (-45*y**2)*(10*y + 40) with 40*(-45*y**2) + (10*y)*(-45*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 40*(-45)*y**2 + (10*y)*(-45*y**2) + (10*y)*(-33) - 1320</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (10*y)*-33 = -330*y
  (10*y)*(-45*y**2) = -450*y**3
  40*-45*y**2 = -1800*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -450*y**3 - 1800*y**2 - 330*y - 1320</replace>
No more calculations needed.
<answer>-450*y**3 - 1800*y**2 - 330*y - 1320</answer>


Question:
Calculate the following: (67 - 13*x**3)*(-24*x**3 - 42*x**2 + 49*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 312*x**6 + 546*x**5 - 637*x**4 - 1608*x**3 - 2814*x**2 + 3283*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: (67 - 13*x**3)*(-24*x**3 - 42*x**2 + 49*x)
Expanding the part (67 - 13*x**3) using the distributive property, and we got: (-13*x**3)*(-24*x**3 - 42*x**2 + 49*x) + 67*(-24*x**3 - 42*x**2 + 49*x)
<replace-#Step 1>#Step 2:
Current expression: (-13*x**3)*(-24*x**3 - 42*x**2 + 49*x) + 67*(-24*x**3 - 42*x**2 + 49*x)</replace>
Simplifying the partial expression: 67*(-24*x**3 - 42*x**2 + 49*x)
Expanding the part (-24*x**3 - 42*x**2 + 49*x) using the distributive property, and we got: (49*x)*67 - 42*x**2*67 - 24*x**3*67
Replacing 67*(-24*x**3 - 42*x**2 + 49*x) with (49*x)*67 - 42*x**2*67 - 24*x**3*67 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (49*x)*67 - 42*x**2*67 - 24*x**3*67 + (-13*x**3)*(-24*x**3 - 42*x**2 + 49*x)</replace>
Simplifying the partial expression: (-13*x**3)*(-24*x**3 - 42*x**2 + 49*x)
Expanding the part (-24*x**3 - 42*x**2 + 49*x) using the distributive property, and we got: (49*x)*(-13*x**3) + (-42*x**2)*(-13*x**3) + (-24*x**3)*(-13*x**3)
Replacing (-13*x**3)*(-24*x**3 - 42*x**2 + 49*x) with (49*x)*(-13*x**3) + (-42*x**2)*(-13*x**3) + (-24*x**3)*(-13*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (49*x)*(-13*x**3) + (49*x)*67 + (-42*x**2)*(-13*x**3) - 42*x**2*67 + (-24*x**3)*(-13*x**3) - 24*x**3*67</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-42*x**2)*67 = -2814*x**2
  (-42*x**2)*(-13*x**3) = 546*x**5
  (-24*x**3)*67 = -1608*x**3
  (-24*x**3)*(-13*x**3) = 312*x**6
  (49*x)*67 = 3283*x
  (49*x)*(-13*x**3) = -637*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 312*x**6 + 546*x**5 - 637*x**4 - 1608*x**3 - 2814*x**2 + 3283*x</replace>
No more calculations needed.
<answer>312*x**6 + 546*x**5 - 637*x**4 - 1608*x**3 - 2814*x**2 + 3283*x</answer>


Question:
Simplify this expression: (8 - 17*z**3)*(-101*z**3 + 21*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: 1717*z**6 - 357*z**5 - 808*z**3 + 168*z**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (8 - 17*z**3)*(-101*z**3 + 21*z**2)
Expanding the part (8 - 17*z**3) using the distributive property, and we got: (-17*z**3)*(-101*z**3 + 21*z**2) + 8*(-101*z**3 + 21*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-17*z**3)*(-101*z**3 + 21*z**2) + 8*(-101*z**3 + 21*z**2)</replace>
Simplifying the partial expression: 8*(-101*z**3 + 21*z**2)
Expanding the part (-101*z**3 + 21*z**2) using the distributive property, and we got: (21*z**2)*8 - 101*z**3*8
Replacing 8*(-101*z**3 + 21*z**2) with (21*z**2)*8 - 101*z**3*8 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (21*z**2)*8 - 101*z**3*8 + (-17*z**3)*(-101*z**3 + 21*z**2)</replace>
Simplifying the partial expression: (-17*z**3)*(-101*z**3 + 21*z**2)
Expanding the part (-101*z**3 + 21*z**2) using the distributive property, and we got: (21*z**2)*(-17*z**3) + (-101*z**3)*(-17*z**3)
Replacing (-17*z**3)*(-101*z**3 + 21*z**2) with (21*z**2)*(-17*z**3) + (-101*z**3)*(-17*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (21*z**2)*(-17*z**3) + (21*z**2)*8 + (-101*z**3)*(-17*z**3) - 101*z**3*8</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-101*z**3)*8 = -808*z**3
  (-101*z**3)*(-17*z**3) = 1717*z**6
  (21*z**2)*8 = 168*z**2
  (21*z**2)*(-17*z**3) = -357*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1717*z**6 - 357*z**5 - 808*z**3 + 168*z**2</replace>
No more calculations needed.
<answer>1717*z**6 - 357*z**5 - 808*z**3 + 168*z**2</answer>


Question:
Simplify this expression: (37*z**3 + 57*z**2)*(38*z**3 + 26*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: 1406*z**6 + 3128*z**5 + 1482*z**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (37*z**3 + 57*z**2)*(38*z**3 + 26*z**2)
Expanding the part (38*z**3 + 26*z**2) using the distributive property, and we got: (26*z**2)*(37*z**3 + 57*z**2) + (38*z**3)*(37*z**3 + 57*z**2)
<replace-#Step 1>#Step 2:
Current expression: (26*z**2)*(37*z**3 + 57*z**2) + (38*z**3)*(37*z**3 + 57*z**2)</replace>
Simplifying the partial expression: (26*z**2)*(37*z**3 + 57*z**2)
Expanding the part (37*z**3 + 57*z**2) using the distributive property, and we got: (26*z**2)*(57*z**2) + (26*z**2)*(37*z**3)
Replacing (26*z**2)*(37*z**3 + 57*z**2) with (26*z**2)*(57*z**2) + (26*z**2)*(37*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (26*z**2)*(57*z**2) + (26*z**2)*(37*z**3) + (38*z**3)*(37*z**3 + 57*z**2)</replace>
Simplifying the partial expression: (38*z**3)*(37*z**3 + 57*z**2)
Expanding the part (37*z**3 + 57*z**2) using the distributive property, and we got: (57*z**2)*(38*z**3) + (37*z**3)*(38*z**3)
Replacing (38*z**3)*(37*z**3 + 57*z**2) with (57*z**2)*(38*z**3) + (37*z**3)*(38*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (26*z**2)*(57*z**2) + (26*z**2)*(37*z**3) + (57*z**2)*(38*z**3) + (37*z**3)*(38*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (37*z**3)*(26*z**2) = 962*z**5
  (37*z**3)*(38*z**3) = 1406*z**6
  (57*z**2)*(26*z**2) = 1482*z**4
  (57*z**2)*(38*z**3) = 2166*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1406*z**6 + 962*z**5 + 2166*z**5 + 1482*z**4</replace>
Combining like terms, got 1406*z**6 + 3128*z**5 + 1482*z**4
<replace-#Step 5>#Step 6:
Current expression: 1406*z**6 + 3128*z**5 + 1482*z**4</replace>
No more calculations needed.
<answer>1406*z**6 + 3128*z**5 + 1482*z**4</answer>


Question:
Calculate the following: (13*x**2 + 24*x - 27)*(-29*x**3 + 45*x**2 - 27*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -377*x**5 - 111*x**4 + 1512*x**3 - 1863*x**2 + 729*x


Question:
Calculate the following: (31 - 10*z)*(-13*z**2 - 46)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 130*z**3 - 403*z**2 + 460*z - 1426

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (31 - 10*z)*(-13*z**2 - 46)
Expanding the part (-13*z**2 - 46) using the distributive property, and we got: (-13*z**2)*(31 - 10*z) - 46*(31 - 10*z)
<replace-#Step 1>#Step 2:
Current expression: (-13*z**2)*(31 - 10*z) - 46*(31 - 10*z)</replace>
Simplifying the partial expression: -46*(31 - 10*z)
Expanding the part (31 - 10*z) using the distributive property, and we got: -10*z*(-46) + 31*(-46)
Replacing -46*(31 - 10*z) with -10*z*(-46) + 31*(-46) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -10*z*(-46) + (-13*z**2)*(31 - 10*z) - 1426</replace>
Simplifying the partial expression: (-13*z**2)*(31 - 10*z)
Expanding the part (31 - 10*z) using the distributive property, and we got: (-10*z)*(-13*z**2) + 31*(-13*z**2)
Replacing (-13*z**2)*(31 - 10*z) with (-10*z)*(-13*z**2) + 31*(-13*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-10*z)*(-13*z**2) - 10*z*(-46) + 31*(-13)*z**2 - 1426</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-10*z)*-46 = 460*z
  (-10*z)*(-13*z**2) = 130*z**3
  31*-13*z**2 = -403*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 130*z**3 - 403*z**2 + 460*z - 1426</replace>
No more calculations needed.
<answer>130*z**3 - 403*z**2 + 460*z - 1426</answer>


Question:
Calculate the following: (36*z + 9)*(-12*z**3 + 70*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: -432*z**4 - 108*z**3 + 2520*z**2 + 630*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: (36*z + 9)*(-12*z**3 + 70*z)
Expanding the part (36*z + 9) using the distributive property, and we got: (36*z)*(-12*z**3 + 70*z) + 9*(-12*z**3 + 70*z)
<replace-#Step 1>#Step 2:
Current expression: (36*z)*(-12*z**3 + 70*z) + 9*(-12*z**3 + 70*z)</replace>
Simplifying the partial expression: 9*(-12*z**3 + 70*z)
Expanding the part (-12*z**3 + 70*z) using the distributive property, and we got: (70*z)*9 - 12*z**3*9
Replacing 9*(-12*z**3 + 70*z) with (70*z)*9 - 12*z**3*9 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (36*z)*(-12*z**3 + 70*z) + (70*z)*9 - 12*z**3*9</replace>
Simplifying the partial expression: (36*z)*(-12*z**3 + 70*z)
Expanding the part (-12*z**3 + 70*z) using the distributive property, and we got: (36*z)*(70*z) + (36*z)*(-12*z**3)
Replacing (36*z)*(-12*z**3 + 70*z) with (36*z)*(70*z) + (36*z)*(-12*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (36*z)*(70*z) + (36*z)*(-12*z**3) + (70*z)*9 - 12*z**3*9</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-12*z**3)*9 = -108*z**3
  (-12*z**3)*(36*z) = -432*z**4
  (70*z)*9 = 630*z
  (70*z)*(36*z) = 2520*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -432*z**4 - 108*z**3 + 2520*z**2 + 630*z</replace>
No more calculations needed.
<answer>-432*z**4 - 108*z**3 + 2520*z**2 + 630*z</answer>


Question:
Calculate the following: (48*x**3 + 39*x + 9)*(60*x**3 + 40*x**2 - 14)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2880*x**6 + 1920*x**5 + 2340*x**4 + 1428*x**3 + 360*x**2 - 546*x - 126


Question:
Calculate the following: (-20*z**3 - 8*z**2 - 28)*(43*z**3 - 44*z**2 - 6*z - 12)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -860*z**6 + 536*z**5 + 472*z**4 - 916*z**3 + 1328*z**2 + 168*z + 336


Question:
Calculate the following: (46 - 4*y)*(36*y**2 + 92)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -144*y**3 + 1656*y**2 - 368*y + 4232

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (46 - 4*y)*(36*y**2 + 92)
Expanding the part (46 - 4*y) using the distributive property, and we got: (-4*y)*(36*y**2 + 92) + 46*(36*y**2 + 92)
<replace-#Step 1>#Step 2:
Current expression: (-4*y)*(36*y**2 + 92) + 46*(36*y**2 + 92)</replace>
Simplifying the partial expression: 46*(36*y**2 + 92)
Expanding the part (36*y**2 + 92) using the distributive property, and we got: (36*y**2)*46 + 92*46
Replacing 46*(36*y**2 + 92) with (36*y**2)*46 + 92*46 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-4*y)*(36*y**2 + 92) + (36*y**2)*46 + 4232</replace>
Simplifying the partial expression: (-4*y)*(36*y**2 + 92)
Expanding the part (36*y**2 + 92) using the distributive property, and we got: (-4*y)*(36*y**2) + 92*(-4*y)
Replacing (-4*y)*(36*y**2 + 92) with (-4*y)*(36*y**2) + 92*(-4*y) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-4*y)*(36*y**2) + 92*(-4)*y + (36*y**2)*46 + 4232</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (36*y**2)*46 = 1656*y**2
  (36*y**2)*(-4*y) = -144*y**3
  92*-4*y = -368*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -144*y**3 + 1656*y**2 - 368*y + 4232</replace>
No more calculations needed.
<answer>-144*y**3 + 1656*y**2 - 368*y + 4232</answer>


Question:
Simplify this expression: (41 - 35*z**2)*(36*z**2 - 35*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1260*z**4 + 1225*z**3 + 1476*z**2 - 1435*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: (41 - 35*z**2)*(36*z**2 - 35*z)
Expanding the part (41 - 35*z**2) using the distributive property, and we got: (-35*z**2)*(36*z**2 - 35*z) + 41*(36*z**2 - 35*z)
<replace-#Step 1>#Step 2:
Current expression: (-35*z**2)*(36*z**2 - 35*z) + 41*(36*z**2 - 35*z)</replace>
Simplifying the partial expression: 41*(36*z**2 - 35*z)
Expanding the part (36*z**2 - 35*z) using the distributive property, and we got: -35*z*41 + (36*z**2)*41
Replacing 41*(36*z**2 - 35*z) with -35*z*41 + (36*z**2)*41 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -35*z*41 + (-35*z**2)*(36*z**2 - 35*z) + (36*z**2)*41</replace>
Simplifying the partial expression: (-35*z**2)*(36*z**2 - 35*z)
Expanding the part (36*z**2 - 35*z) using the distributive property, and we got: (-35*z)*(-35*z**2) + (-35*z**2)*(36*z**2)
Replacing (-35*z**2)*(36*z**2 - 35*z) with (-35*z)*(-35*z**2) + (-35*z**2)*(36*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-35*z)*(-35*z**2) - 35*z*41 + (-35*z**2)*(36*z**2) + (36*z**2)*41</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-35*z)*41 = -1435*z
  (-35*z)*(-35*z**2) = 1225*z**3
  (36*z**2)*41 = 1476*z**2
  (36*z**2)*(-35*z**2) = -1260*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1260*z**4 + 1225*z**3 + 1476*z**2 - 1435*z</replace>
No more calculations needed.
<answer>-1260*z**4 + 1225*z**3 + 1476*z**2 - 1435*z</answer>


Question:
Simplify this expression: (-32*x**3 - 33*x)*(-25*x**3 - 96*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: 800*x**6 + 3072*x**5 + 825*x**4 + 3168*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: (-32*x**3 - 33*x)*(-25*x**3 - 96*x**2)
Expanding the part (-25*x**3 - 96*x**2) using the distributive property, and we got: (-96*x**2)*(-32*x**3 - 33*x) + (-25*x**3)*(-32*x**3 - 33*x)
<replace-#Step 1>#Step 2:
Current expression: (-96*x**2)*(-32*x**3 - 33*x) + (-25*x**3)*(-32*x**3 - 33*x)</replace>
Simplifying the partial expression: (-96*x**2)*(-32*x**3 - 33*x)
Expanding the part (-32*x**3 - 33*x) using the distributive property, and we got: (-33*x)*(-96*x**2) + (-96*x**2)*(-32*x**3)
Replacing (-96*x**2)*(-32*x**3 - 33*x) with (-33*x)*(-96*x**2) + (-96*x**2)*(-32*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-33*x)*(-96*x**2) + (-96*x**2)*(-32*x**3) + (-25*x**3)*(-32*x**3 - 33*x)</replace>
Simplifying the partial expression: (-25*x**3)*(-32*x**3 - 33*x)
Expanding the part (-32*x**3 - 33*x) using the distributive property, and we got: (-33*x)*(-25*x**3) + (-32*x**3)*(-25*x**3)
Replacing (-25*x**3)*(-32*x**3 - 33*x) with (-33*x)*(-25*x**3) + (-32*x**3)*(-25*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-33*x)*(-96*x**2) + (-33*x)*(-25*x**3) + (-96*x**2)*(-32*x**3) + (-32*x**3)*(-25*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-33*x)*(-96*x**2) = 3168*x**3
  (-33*x)*(-25*x**3) = 825*x**4
  (-32*x**3)*(-96*x**2) = 3072*x**5
  (-32*x**3)*(-25*x**3) = 800*x**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 800*x**6 + 3072*x**5 + 825*x**4 + 3168*x**3</replace>
No more calculations needed.
<answer>800*x**6 + 3072*x**5 + 825*x**4 + 3168*x**3</answer>


Question:
Calculate the following: (76*x**2 + 10*x + 5)*(-40*x**3 + 7*x**2 - 6*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: -3040*x**5 + 132*x**4 - 586*x**3 - 25*x**2 - 30*x


Question:
Simplify this expression: (1 - 20*x)*(28*x**3 + 20*x**2 + 31*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -560*x**4 - 372*x**3 - 600*x**2 + 31*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: (1 - 20*x)*(28*x**3 + 20*x**2 + 31*x)
Expanding the part (1 - 20*x) using the distributive property, and we got: (-20*x)*(28*x**3 + 20*x**2 + 31*x) + 1*(28*x**3 + 20*x**2 + 31*x)
<replace-#Step 1>#Step 2:
Current expression: (-20*x)*(28*x**3 + 20*x**2 + 31*x) + 1*(28*x**3 + 20*x**2 + 31*x)</replace>
Simplifying the partial expression: 1*(28*x**3 + 20*x**2 + 31*x)
Expanding the part (28*x**3 + 20*x**2 + 31*x) using the distributive property, and we got: (31*x)*1 + (20*x**2)*1 + (28*x**3)*1
Replacing 1*(28*x**3 + 20*x**2 + 31*x) with (31*x)*1 + (20*x**2)*1 + (28*x**3)*1 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-20*x)*(28*x**3 + 20*x**2 + 31*x) + (31*x)*1 + (20*x**2)*1 + (28*x**3)*1</replace>
Simplifying the partial expression: (-20*x)*(28*x**3 + 20*x**2 + 31*x)
Expanding the part (28*x**3 + 20*x**2 + 31*x) using the distributive property, and we got: (-20*x)*(31*x) + (-20*x)*(20*x**2) + (-20*x)*(28*x**3)
Replacing (-20*x)*(28*x**3 + 20*x**2 + 31*x) with (-20*x)*(31*x) + (-20*x)*(20*x**2) + (-20*x)*(28*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-20*x)*(31*x) + (-20*x)*(20*x**2) + (-20*x)*(28*x**3) + (31*x)*1 + (20*x**2)*1 + (28*x**3)*1</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (20*x**2)*1 = 20*x**2
  (20*x**2)*(-20*x) = -400*x**3
  (28*x**3)*1 = 28*x**3
  (28*x**3)*(-20*x) = -560*x**4
  (31*x)*1 = 31*x
  (31*x)*(-20*x) = -620*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -560*x**4 - 400*x**3 + 28*x**3 - 620*x**2 + 20*x**2 + 31*x</replace>
Combining like terms, got -560*x**4 - 372*x**3 - 600*x**2 + 31*x
<replace-#Step 5>#Step 6:
Current expression: -560*x**4 - 372*x**3 - 600*x**2 + 31*x</replace>
No more calculations needed.
<answer>-560*x**4 - 372*x**3 - 600*x**2 + 31*x</answer>


Question:
Simplify this expression: -330*z**2 + 880*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: -330*z**2 + 880*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: -330*z**2 + 880*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: -330*z**2 + 880*z</replace>
No more calculations needed.
<answer>-330*z**2 + 880*z</answer>


Question:
Calculate the following: (-25*z**2 + 26*z)*(-6*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: 150*z**4 + 819*z**3 - 1014*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: (-25*z**2 + 26*z)*(-6*z**2 - 39*z)
Expanding the part (-6*z**2 - 39*z) using the distributive property, and we got: (-39*z)*(-25*z**2 + 26*z) + (-6*z**2)*(-25*z**2 + 26*z)
<replace-#Step 1>#Step 2:
Current expression: (-39*z)*(-25*z**2 + 26*z) + (-6*z**2)*(-25*z**2 + 26*z)</replace>
Simplifying the partial expression: (-39*z)*(-25*z**2 + 26*z)
Expanding the part (-25*z**2 + 26*z) using the distributive property, and we got: (-39*z)*(26*z) + (-39*z)*(-25*z**2)
Replacing (-39*z)*(-25*z**2 + 26*z) with (-39*z)*(26*z) + (-39*z)*(-25*z**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-39*z)*(26*z) + (-39*z)*(-25*z**2) + (-6*z**2)*(-25*z**2 + 26*z)</replace>
Simplifying the partial expression: (-6*z**2)*(-25*z**2 + 26*z)
Expanding the part (-25*z**2 + 26*z) using the distributive property, and we got: (26*z)*(-6*z**2) + (-25*z**2)*(-6*z**2)
Replacing (-6*z**2)*(-25*z**2 + 26*z) with (26*z)*(-6*z**2) + (-25*z**2)*(-6*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-39*z)*(26*z) + (-39*z)*(-25*z**2) + (26*z)*(-6*z**2) + (-25*z**2)*(-6*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-25*z**2)*(-39*z) = 975*z**3
  (-25*z**2)*(-6*z**2) = 150*z**4
  (26*z)*(-39*z) = -1014*z**2
  (26*z)*(-6*z**2) = -156*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 150*z**4 - 156*z**3 + 975*z**3 - 1014*z**2</replace>
Combining like terms, got 150*z**4 + 819*z**3 - 1014*z**2
<replace-#Step 5>#Step 6:
Current expression: 150*z**4 + 819*z**3 - 1014*z**2</replace>
No more calculations needed.
<answer>150*z**4 + 819*z**3 - 1014*z**2</answer>


Question:
Simplify this expression: (-20*z**2 - 6)*(-42*z**2 - 2*z - 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: 840*z**4 + 40*z**3 + 1072*z**2 + 12*z + 246

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-20*z**2 - 6)*(-42*z**2 - 2*z - 41)
Expanding the part (-20*z**2 - 6) using the distributive property, and we got: (-20*z**2)*(-42*z**2 - 2*z - 41) - 6*(-42*z**2 - 2*z - 41)
<replace-#Step 1>#Step 2:
Current expression: (-20*z**2)*(-42*z**2 - 2*z - 41) - 6*(-42*z**2 - 2*z - 41)</replace>
Simplifying the partial expression: -6*(-42*z**2 - 2*z - 41)
Expanding the part (-42*z**2 - 2*z - 41) using the distributive property, and we got: -2*z*(-6) - 42*z**2*(-6) - 41*(-6)
Replacing -6*(-42*z**2 - 2*z - 41) with -2*z*(-6) - 42*z**2*(-6) - 41*(-6) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -2*z*(-6) - 42*z**2*(-6) + (-20*z**2)*(-42*z**2 - 2*z - 41) + 246</replace>
Simplifying the partial expression: (-20*z**2)*(-42*z**2 - 2*z - 41)
Expanding the part (-42*z**2 - 2*z - 41) using the distributive property, and we got: (-2*z)*(-20*z**2) - (-1)*820*z**2 + (-42*z**2)*(-20*z**2)
Replacing (-20*z**2)*(-42*z**2 - 2*z - 41) with (-2*z)*(-20*z**2) - (-1)*820*z**2 + (-42*z**2)*(-20*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-2*z)*(-20*z**2) - 2*z*(-6) - 41*(-20)*z**2 + (-42*z**2)*(-20*z**2) - 42*z**2*(-6) + 246</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-42*z**2)*-6 = 252*z**2
  (-42*z**2)*(-20*z**2) = 840*z**4
  (-2*z)*-6 = 12*z
  (-2*z)*(-20*z**2) = 40*z**3
  -41*-20*z**2 = 820*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 840*z**4 + 40*z**3 + 252*z**2 + 820*z**2 + 12*z + 246</replace>
Combining like terms, got 840*z**4 + 40*z**3 + 1072*z**2 + 12*z + 246
<replace-#Step 5>#Step 6:
Current expression: 840*z**4 + 40*z**3 + 1072*z**2 + 12*z + 246</replace>
No more calculations needed.
<answer>840*z**4 + 40*z**3 + 1072*z**2 + 12*z + 246</answer>


Question:
Simplify this expression: (4*z + 105)*(-8*z**2 - 51)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -32*z**3 - 840*z**2 - 204*z - 5355

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*z + 105)*(-8*z**2 - 51)
Expanding the part (-8*z**2 - 51) using the distributive property, and we got: (-8*z**2)*(4*z + 105) - 51*(4*z + 105)
<replace-#Step 1>#Step 2:
Current expression: (-8*z**2)*(4*z + 105) - 51*(4*z + 105)</replace>
Simplifying the partial expression: -51*(4*z + 105)
Expanding the part (4*z + 105) using the distributive property, and we got: (4*z)*(-51) + 105*(-51)
Replacing -51*(4*z + 105) with (4*z)*(-51) + 105*(-51) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (4*z)*(-51) + (-8*z**2)*(4*z + 105) - 5355</replace>
Simplifying the partial expression: (-8*z**2)*(4*z + 105)
Expanding the part (4*z + 105) using the distributive property, and we got: 105*(-8*z**2) + (4*z)*(-8*z**2)
Replacing (-8*z**2)*(4*z + 105) with 105*(-8*z**2) + (4*z)*(-8*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 105*(-8)*z**2 + (4*z)*(-8*z**2) + (4*z)*(-51) - 5355</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (4*z)*-51 = -204*z
  (4*z)*(-8*z**2) = -32*z**3
  105*-8*z**2 = -840*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -32*z**3 - 840*z**2 - 204*z - 5355</replace>
No more calculations needed.
<answer>-32*z**3 - 840*z**2 - 204*z - 5355</answer>


Question:
Calculate the following: (31*z**3 - 44)*(-14*z**3 - 2*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: -434*z**6 - 62*z**5 - 651*z**4 + 616*z**3 + 88*z**2 + 924*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (31*z**3 - 44)*(-14*z**3 - 2*z**2 - 21*z)
Expanding the part (31*z**3 - 44) using the distributive property, and we got: (31*z**3)*(-14*z**3 - 2*z**2 - 21*z) - 44*(-14*z**3 - 2*z**2 - 21*z)
<replace-#Step 1>#Step 2:
Current expression: (31*z**3)*(-14*z**3 - 2*z**2 - 21*z) - 44*(-14*z**3 - 2*z**2 - 21*z)</replace>
Simplifying the partial expression: -44*(-14*z**3 - 2*z**2 - 21*z)
Expanding the part (-14*z**3 - 2*z**2 - 21*z) using the distributive property, and we got: -21*z*(-44) - 2*z**2*(-44) - 14*z**3*(-44)
Replacing -44*(-14*z**3 - 2*z**2 - 21*z) with -21*z*(-44) - 2*z**2*(-44) - 14*z**3*(-44) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -21*z*(-44) - 2*z**2*(-44) - 14*z**3*(-44) + (31*z**3)*(-14*z**3 - 2*z**2 - 21*z)</replace>
Simplifying the partial expression: (31*z**3)*(-14*z**3 - 2*z**2 - 21*z)
Expanding the part (-14*z**3 - 2*z**2 - 21*z) using the distributive property, and we got: (-21*z)*(31*z**3) + (-2*z**2)*(31*z**3) + (-14*z**3)*(31*z**3)
Replacing (31*z**3)*(-14*z**3 - 2*z**2 - 21*z) with (-21*z)*(31*z**3) + (-2*z**2)*(31*z**3) + (-14*z**3)*(31*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-21*z)*(31*z**3) - 21*z*(-44) + (-2*z**2)*(31*z**3) - 2*z**2*(-44) + (-14*z**3)*(31*z**3) - 14*z**3*(-44)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-21*z)*-44 = 924*z
  (-21*z)*(31*z**3) = -651*z**4
  (-14*z**3)*-44 = 616*z**3
  (-14*z**3)*(31*z**3) = -434*z**6
  (-2*z**2)*-44 = 88*z**2
  (-2*z**2)*(31*z**3) = -62*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -434*z**6 - 62*z**5 - 651*z**4 + 616*z**3 + 88*z**2 + 924*z</replace>
No more calculations needed.
<answer>-434*z**6 - 62*z**5 - 651*z**4 + 616*z**3 + 88*z**2 + 924*z</answer>


Question:
Calculate the following: (37 - 3*y**2)*(-40*y**3 + 49*y**2 + 48*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 120*y**5 - 147*y**4 - 1624*y**3 + 1813*y**2 + 1776*y


Question:
Simplify this expression: -67*x**2*(-19*x**2 + 14*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: 1273*x**4 - 938*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: -67*x**2*(-19*x**2 + 14*x)
Expanding the part (-19*x**2 + 14*x) using the distributive property, and we got: (14*x)*(-67*x**2) + (-67*x**2)*(-19*x**2)
<replace-#Step 1>#Step 2:
Current expression: (14*x)*(-67*x**2) + (-67*x**2)*(-19*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-19*x**2)*(-67*x**2) = 1273*x**4
  (14*x)*(-67*x**2) = -938*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1273*x**4 - 938*x**3</replace>
No more calculations needed.
<answer>1273*x**4 - 938*x**3</answer>


Question:
Simplify this expression: (-12*y**3 - 25*y**2)*(30*y**3 + 30*y**2 + 29)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -360*y**6 - 1110*y**5 - 750*y**4 - 348*y**3 - 725*y**2


Question:
Simplify this expression: (-41*z**3 + 5*z**2 + 13*z)*(-18*z**3 - 36*z**2 - 36)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 738*z**6 + 1386*z**5 - 414*z**4 + 1008*z**3 - 180*z**2 - 468*z


Question:
Simplify this expression: (-18*x**3 - 50*x**2 - 19*x)*(-7*x**3 - 43*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: 126*x**6 + 1124*x**5 + 2283*x**4 + 799*x**3 - 50*x**2 - 19*x


Question:
Calculate the following: (-39*z**2 - 11)*(12*z**3 + 40*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: -468*z**5 - 1692*z**3 - 440*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: (-39*z**2 - 11)*(12*z**3 + 40*z)
Expanding the part (-39*z**2 - 11) using the distributive property, and we got: (-39*z**2)*(12*z**3 + 40*z) - 11*(12*z**3 + 40*z)
<replace-#Step 1>#Step 2:
Current expression: (-39*z**2)*(12*z**3 + 40*z) - 11*(12*z**3 + 40*z)</replace>
Simplifying the partial expression: -11*(12*z**3 + 40*z)
Expanding the part (12*z**3 + 40*z) using the distributive property, and we got: (40*z)*(-11) + (12*z**3)*(-11)
Replacing -11*(12*z**3 + 40*z) with (40*z)*(-11) + (12*z**3)*(-11) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (40*z)*(-11) + (-39*z**2)*(12*z**3 + 40*z) + (12*z**3)*(-11)</replace>
Simplifying the partial expression: (-39*z**2)*(12*z**3 + 40*z)
Expanding the part (12*z**3 + 40*z) using the distributive property, and we got: (40*z)*(-39*z**2) + (-39*z**2)*(12*z**3)
Replacing (-39*z**2)*(12*z**3 + 40*z) with (40*z)*(-39*z**2) + (-39*z**2)*(12*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (40*z)*(-39*z**2) + (40*z)*(-11) + (-39*z**2)*(12*z**3) + (12*z**3)*(-11)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (12*z**3)*-11 = -132*z**3
  (12*z**3)*(-39*z**2) = -468*z**5
  (40*z)*-11 = -440*z
  (40*z)*(-39*z**2) = -1560*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -468*z**5 - 1560*z**3 - 132*z**3 - 440*z</replace>
Combining like terms, got -468*z**5 - 1692*z**3 - 440*z
<replace-#Step 5>#Step 6:
Current expression: -468*z**5 - 1692*z**3 - 440*z</replace>
No more calculations needed.
<answer>-468*z**5 - 1692*z**3 - 440*z</answer>


Question:
Simplify this expression: (7 - 25*z**2)*(-15*z**2 - 43*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: 375*z**4 + 1075*z**3 - 105*z**2 - 301*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: (7 - 25*z**2)*(-15*z**2 - 43*z)
Expanding the part (7 - 25*z**2) using the distributive property, and we got: (-25*z**2)*(-15*z**2 - 43*z) + 7*(-15*z**2 - 43*z)
<replace-#Step 1>#Step 2:
Current expression: (-25*z**2)*(-15*z**2 - 43*z) + 7*(-15*z**2 - 43*z)</replace>
Simplifying the partial expression: 7*(-15*z**2 - 43*z)
Expanding the part (-15*z**2 - 43*z) using the distributive property, and we got: -43*z*7 - 15*z**2*7
Replacing 7*(-15*z**2 - 43*z) with -43*z*7 - 15*z**2*7 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -43*z*7 + (-25*z**2)*(-15*z**2 - 43*z) - 15*z**2*7</replace>
Simplifying the partial expression: (-25*z**2)*(-15*z**2 - 43*z)
Expanding the part (-15*z**2 - 43*z) using the distributive property, and we got: (-43*z)*(-25*z**2) + (-25*z**2)*(-15*z**2)
Replacing (-25*z**2)*(-15*z**2 - 43*z) with (-43*z)*(-25*z**2) + (-25*z**2)*(-15*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-43*z)*(-25*z**2) - 43*z*7 + (-25*z**2)*(-15*z**2) - 15*z**2*7</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-43*z)*7 = -301*z
  (-43*z)*(-25*z**2) = 1075*z**3
  (-15*z**2)*7 = -105*z**2
  (-15*z**2)*(-25*z**2) = 375*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 375*z**4 + 1075*z**3 - 105*z**2 - 301*z</replace>
No more calculations needed.
<answer>375*z**4 + 1075*z**3 - 105*z**2 - 301*z</answer>


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

Answer: -846*y**4 + 796*y**3 - 78*y**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (2 - 18*y)*(47*y**3 - 39*y**2)
Expanding the part (2 - 18*y) using the distributive property, and we got: (-18*y)*(47*y**3 - 39*y**2) + 2*(47*y**3 - 39*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-18*y)*(47*y**3 - 39*y**2) + 2*(47*y**3 - 39*y**2)</replace>
Simplifying the partial expression: 2*(47*y**3 - 39*y**2)
Expanding the part (47*y**3 - 39*y**2) using the distributive property, and we got: -39*y**2*2 + (47*y**3)*2
Replacing 2*(47*y**3 - 39*y**2) with -39*y**2*2 + (47*y**3)*2 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-18*y)*(47*y**3 - 39*y**2) - 39*y**2*2 + (47*y**3)*2</replace>
Simplifying the partial expression: (-18*y)*(47*y**3 - 39*y**2)
Expanding the part (47*y**3 - 39*y**2) using the distributive property, and we got: (-18*y)*(-39*y**2) + (-18*y)*(47*y**3)
Replacing (-18*y)*(47*y**3 - 39*y**2) with (-18*y)*(-39*y**2) + (-18*y)*(47*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-18*y)*(-39*y**2) + (-18*y)*(47*y**3) - 39*y**2*2 + (47*y**3)*2</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-39*y**2)*2 = -78*y**2
  (-39*y**2)*(-18*y) = 702*y**3
  (47*y**3)*2 = 94*y**3
  (47*y**3)*(-18*y) = -846*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -846*y**4 + 94*y**3 + 702*y**3 - 78*y**2</replace>
Combining like terms, got -846*y**4 + 796*y**3 - 78*y**2
<replace-#Step 5>#Step 6:
Current expression: -846*y**4 + 796*y**3 - 78*y**2</replace>
No more calculations needed.
<answer>-846*y**4 + 796*y**3 - 78*y**2</answer>


Question:
Simplify this expression: (26*x**2 - 33)*(5*x**3 - 44*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: 130*x**5 - 1144*x**4 - 165*x**3 + 1452*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: (26*x**2 - 33)*(5*x**3 - 44*x**2)
Expanding the part (26*x**2 - 33) using the distributive property, and we got: (26*x**2)*(5*x**3 - 44*x**2) - 33*(5*x**3 - 44*x**2)
<replace-#Step 1>#Step 2:
Current expression: (26*x**2)*(5*x**3 - 44*x**2) - 33*(5*x**3 - 44*x**2)</replace>
Simplifying the partial expression: -33*(5*x**3 - 44*x**2)
Expanding the part (5*x**3 - 44*x**2) using the distributive property, and we got: -44*x**2*(-33) + (5*x**3)*(-33)
Replacing -33*(5*x**3 - 44*x**2) with -44*x**2*(-33) + (5*x**3)*(-33) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -44*x**2*(-33) + (26*x**2)*(5*x**3 - 44*x**2) + (5*x**3)*(-33)</replace>
Simplifying the partial expression: (26*x**2)*(5*x**3 - 44*x**2)
Expanding the part (5*x**3 - 44*x**2) using the distributive property, and we got: (-44*x**2)*(26*x**2) + (26*x**2)*(5*x**3)
Replacing (26*x**2)*(5*x**3 - 44*x**2) with (-44*x**2)*(26*x**2) + (26*x**2)*(5*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-44*x**2)*(26*x**2) - 44*x**2*(-33) + (26*x**2)*(5*x**3) + (5*x**3)*(-33)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-44*x**2)*-33 = 1452*x**2
  (-44*x**2)*(26*x**2) = -1144*x**4
  (5*x**3)*-33 = -165*x**3
  (5*x**3)*(26*x**2) = 130*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 130*x**5 - 1144*x**4 - 165*x**3 + 1452*x**2</replace>
No more calculations needed.
<answer>130*x**5 - 1144*x**4 - 165*x**3 + 1452*x**2</answer>


Question:
Simplify this expression: (18*z - 2)*(-20*z**3 + 40*z**2 + 20*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: -360*z**4 + 760*z**3 + 280*z**2 - 40*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: (18*z - 2)*(-20*z**3 + 40*z**2 + 20*z)
Expanding the part (18*z - 2) using the distributive property, and we got: (18*z)*(-20*z**3 + 40*z**2 + 20*z) - 2*(-20*z**3 + 40*z**2 + 20*z)
<replace-#Step 1>#Step 2:
Current expression: (18*z)*(-20*z**3 + 40*z**2 + 20*z) - 2*(-20*z**3 + 40*z**2 + 20*z)</replace>
Simplifying the partial expression: -2*(-20*z**3 + 40*z**2 + 20*z)
Expanding the part (-20*z**3 + 40*z**2 + 20*z) using the distributive property, and we got: (20*z)*(-2) + (40*z**2)*(-2) - 20*z**3*(-2)
Replacing -2*(-20*z**3 + 40*z**2 + 20*z) with (20*z)*(-2) + (40*z**2)*(-2) - 20*z**3*(-2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (18*z)*(-20*z**3 + 40*z**2 + 20*z) + (20*z)*(-2) + (40*z**2)*(-2) - 20*z**3*(-2)</replace>
Simplifying the partial expression: (18*z)*(-20*z**3 + 40*z**2 + 20*z)
Expanding the part (-20*z**3 + 40*z**2 + 20*z) using the distributive property, and we got: (18*z)*(20*z) + (18*z)*(40*z**2) + (18*z)*(-20*z**3)
Replacing (18*z)*(-20*z**3 + 40*z**2 + 20*z) with (18*z)*(20*z) + (18*z)*(40*z**2) + (18*z)*(-20*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (18*z)*(20*z) + (18*z)*(40*z**2) + (18*z)*(-20*z**3) + (20*z)*(-2) + (40*z**2)*(-2) - 20*z**3*(-2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-20*z**3)*-2 = 40*z**3
  (-20*z**3)*(18*z) = -360*z**4
  (20*z)*-2 = -40*z
  (20*z)*(18*z) = 360*z**2
  (40*z**2)*-2 = -80*z**2
  (40*z**2)*(18*z) = 720*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -360*z**4 + 40*z**3 + 720*z**3 - 80*z**2 + 360*z**2 - 40*z</replace>
Combining like terms, got -360*z**4 + 760*z**3 + 280*z**2 - 40*z
<replace-#Step 5>#Step 6:
Current expression: -360*z**4 + 760*z**3 + 280*z**2 - 40*z</replace>
No more calculations needed.
<answer>-360*z**4 + 760*z**3 + 280*z**2 - 40*z</answer>


Question:
Calculate the following: (59*y**2 - 48*y)*(67*y**3 + 41*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: 3953*y**5 - 797*y**4 - 1968*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: (59*y**2 - 48*y)*(67*y**3 + 41*y**2)
Expanding the part (59*y**2 - 48*y) using the distributive property, and we got: (-48*y)*(67*y**3 + 41*y**2) + (59*y**2)*(67*y**3 + 41*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-48*y)*(67*y**3 + 41*y**2) + (59*y**2)*(67*y**3 + 41*y**2)</replace>
Simplifying the partial expression: (-48*y)*(67*y**3 + 41*y**2)
Expanding the part (67*y**3 + 41*y**2) using the distributive property, and we got: (-48*y)*(41*y**2) + (-48*y)*(67*y**3)
Replacing (-48*y)*(67*y**3 + 41*y**2) with (-48*y)*(41*y**2) + (-48*y)*(67*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-48*y)*(41*y**2) + (-48*y)*(67*y**3) + (59*y**2)*(67*y**3 + 41*y**2)</replace>
Simplifying the partial expression: (59*y**2)*(67*y**3 + 41*y**2)
Expanding the part (67*y**3 + 41*y**2) using the distributive property, and we got: (41*y**2)*(59*y**2) + (59*y**2)*(67*y**3)
Replacing (59*y**2)*(67*y**3 + 41*y**2) with (41*y**2)*(59*y**2) + (59*y**2)*(67*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-48*y)*(41*y**2) + (-48*y)*(67*y**3) + (41*y**2)*(59*y**2) + (59*y**2)*(67*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (41*y**2)*(-48*y) = -1968*y**3
  (41*y**2)*(59*y**2) = 2419*y**4
  (67*y**3)*(-48*y) = -3216*y**4
  (67*y**3)*(59*y**2) = 3953*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 3953*y**5 - 3216*y**4 + 2419*y**4 - 1968*y**3</replace>
Combining like terms, got 3953*y**5 - 797*y**4 - 1968*y**3
<replace-#Step 5>#Step 6:
Current expression: 3953*y**5 - 797*y**4 - 1968*y**3</replace>
No more calculations needed.
<answer>3953*y**5 - 797*y**4 - 1968*y**3</answer>


Question:
Calculate the following: (-30*z**3 + 30*z**2)*(9*z**3 - 33*z**2 + 49*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: -270*z**6 + 1260*z**5 - 2460*z**4 + 1530*z**3 - 60*z**2


Question:
Simplify this expression: (33*z**2 + 7)*(56*z**3 - 3*z**2 - 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: 1848*z**5 - 99*z**4 + 392*z**3 - 1308*z**2 - 273

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*z**2 + 7)*(56*z**3 - 3*z**2 - 39)
Expanding the part (33*z**2 + 7) using the distributive property, and we got: (33*z**2)*(56*z**3 - 3*z**2 - 39) + 7*(56*z**3 - 3*z**2 - 39)
<replace-#Step 1>#Step 2:
Current expression: (33*z**2)*(56*z**3 - 3*z**2 - 39) + 7*(56*z**3 - 3*z**2 - 39)</replace>
Simplifying the partial expression: 7*(56*z**3 - 3*z**2 - 39)
Expanding the part (56*z**3 - 3*z**2 - 39) using the distributive property, and we got: -3*z**2*7 + (56*z**3)*7 - 39*7
Replacing 7*(56*z**3 - 3*z**2 - 39) with -3*z**2*7 + (56*z**3)*7 - 39*7 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -3*z**2*7 + (33*z**2)*(56*z**3 - 3*z**2 - 39) + (56*z**3)*7 - 273</replace>
Simplifying the partial expression: (33*z**2)*(56*z**3 - 3*z**2 - 39)
Expanding the part (56*z**3 - 3*z**2 - 39) using the distributive property, and we got: -1287*z**2 + (-3*z**2)*(33*z**2) + (33*z**2)*(56*z**3)
Replacing (33*z**2)*(56*z**3 - 3*z**2 - 39) with -1287*z**2 + (-3*z**2)*(33*z**2) + (33*z**2)*(56*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -39*33*z**2 + (-3*z**2)*(33*z**2) - 3*z**2*7 + (33*z**2)*(56*z**3) + (56*z**3)*7 - 273</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-3*z**2)*7 = -21*z**2
  (-3*z**2)*(33*z**2) = -99*z**4
  (56*z**3)*7 = 392*z**3
  (56*z**3)*(33*z**2) = 1848*z**5
  -39*33*z**2 = -1287*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1848*z**5 - 99*z**4 + 392*z**3 - 1287*z**2 - 21*z**2 - 273</replace>
Combining like terms, got 1848*z**5 - 99*z**4 + 392*z**3 - 1308*z**2 - 273
<replace-#Step 5>#Step 6:
Current expression: 1848*z**5 - 99*z**4 + 392*z**3 - 1308*z**2 - 273</replace>
No more calculations needed.
<answer>1848*z**5 - 99*z**4 + 392*z**3 - 1308*z**2 - 273</answer>


Question:
Calculate the following: (2*y**3 + 10*y)*(25*y**2 + 86*y + 23)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 50*y**5 + 172*y**4 + 296*y**3 + 860*y**2 + 230*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: (2*y**3 + 10*y)*(25*y**2 + 86*y + 23)
Expanding the part (2*y**3 + 10*y) using the distributive property, and we got: (10*y)*(25*y**2 + 86*y + 23) + (2*y**3)*(25*y**2 + 86*y + 23)
<replace-#Step 1>#Step 2:
Current expression: (10*y)*(25*y**2 + 86*y + 23) + (2*y**3)*(25*y**2 + 86*y + 23)</replace>
Simplifying the partial expression: (2*y**3)*(25*y**2 + 86*y + 23)
Expanding the part (25*y**2 + 86*y + 23) using the distributive property, and we got: 23*(2*y**3) + (86*y)*(2*y**3) + (25*y**2)*(2*y**3)
Replacing (2*y**3)*(25*y**2 + 86*y + 23) with 23*(2*y**3) + (86*y)*(2*y**3) + (25*y**2)*(2*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 23*2*y**3 + (10*y)*(25*y**2 + 86*y + 23) + (86*y)*(2*y**3) + (25*y**2)*(2*y**3)</replace>
Simplifying the partial expression: (10*y)*(25*y**2 + 86*y + 23)
Expanding the part (25*y**2 + 86*y + 23) using the distributive property, and we got: 23*(10*y) + (10*y)*(86*y) + (10*y)*(25*y**2)
Replacing (10*y)*(25*y**2 + 86*y + 23) with 23*(10*y) + (10*y)*(86*y) + (10*y)*(25*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 23*2*y**3 + 23*10*y + (10*y)*(86*y) + (10*y)*(25*y**2) + (86*y)*(2*y**3) + (25*y**2)*(2*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)*(2*y**3) = 50*y**5
  (25*y**2)*(10*y) = 250*y**3
  (86*y)*(2*y**3) = 172*y**4
  (86*y)*(10*y) = 860*y**2
  23*2*y**3 = 46*y**3
  23*10*y = 230*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 50*y**5 + 172*y**4 + 46*y**3 + 250*y**3 + 860*y**2 + 230*y</replace>
Combining like terms, got 50*y**5 + 172*y**4 + 296*y**3 + 860*y**2 + 230*y
<replace-#Step 5>#Step 6:
Current expression: 50*y**5 + 172*y**4 + 296*y**3 + 860*y**2 + 230*y</replace>
No more calculations needed.
<answer>50*y**5 + 172*y**4 + 296*y**3 + 860*y**2 + 230*y</answer>


Question:
Calculate the following: (49*z**2 - 4*z)*(16*z**3 + 72)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 784*z**5 - 64*z**4 + 3528*z**2 - 288*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: (49*z**2 - 4*z)*(16*z**3 + 72)
Expanding the part (16*z**3 + 72) using the distributive property, and we got: (16*z**3)*(49*z**2 - 4*z) + 72*(49*z**2 - 4*z)
<replace-#Step 1>#Step 2:
Current expression: (16*z**3)*(49*z**2 - 4*z) + 72*(49*z**2 - 4*z)</replace>
Simplifying the partial expression: 72*(49*z**2 - 4*z)
Expanding the part (49*z**2 - 4*z) using the distributive property, and we got: -4*z*72 + (49*z**2)*72
Replacing 72*(49*z**2 - 4*z) with -4*z*72 + (49*z**2)*72 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -4*z*72 + (49*z**2)*72 + (16*z**3)*(49*z**2 - 4*z)</replace>
Simplifying the partial expression: (16*z**3)*(49*z**2 - 4*z)
Expanding the part (49*z**2 - 4*z) using the distributive property, and we got: (-4*z)*(16*z**3) + (49*z**2)*(16*z**3)
Replacing (16*z**3)*(49*z**2 - 4*z) with (-4*z)*(16*z**3) + (49*z**2)*(16*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-4*z)*(16*z**3) - 4*z*72 + (49*z**2)*(16*z**3) + (49*z**2)*72</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-4*z)*72 = -288*z
  (-4*z)*(16*z**3) = -64*z**4
  (49*z**2)*72 = 3528*z**2
  (49*z**2)*(16*z**3) = 784*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 784*z**5 - 64*z**4 + 3528*z**2 - 288*z</replace>
No more calculations needed.
<answer>784*z**5 - 64*z**4 + 3528*z**2 - 288*z</answer>


Question:
Simplify this expression: (32*z**3 + 12*z + 15)*(44*z**3 + 41*z**2 - 10*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1408*z**6 + 1312*z**5 + 208*z**4 + 1152*z**3 + 495*z**2 - 150*z


Question:
Simplify this expression: (-29*y**3 + 22*y + 44)*(21*y**3 - 30*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: -609*y**6 + 1332*y**4 + 2055*y**3 - 660*y**2 - 2178*y - 1716


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

Answer: 504*x**4 - 840*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: 28*x**2*(18*x**2 - 30)
Expanding the part (18*x**2 - 30) using the distributive property, and we got: -840*x**2 + (18*x**2)*(28*x**2)
<replace-#Step 1>#Step 2:
Current expression: -840*x**2 + (18*x**2)*(28*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -30*(28*x**2) = -840*x**2
  (18*x**2)*(28*x**2) = 504*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 504*x**4 - 840*x**2</replace>
No more calculations needed.
<answer>504*x**4 - 840*x**2</answer>


Question:
Simplify this expression: (40*y**3 + 8*y)*(44*y**3 - 7*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1760*y**6 - 280*y**5 + 352*y**4 - 56*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: (40*y**3 + 8*y)*(44*y**3 - 7*y**2)
Expanding the part (44*y**3 - 7*y**2) using the distributive property, and we got: (-7*y**2)*(40*y**3 + 8*y) + (44*y**3)*(40*y**3 + 8*y)
<replace-#Step 1>#Step 2:
Current expression: (-7*y**2)*(40*y**3 + 8*y) + (44*y**3)*(40*y**3 + 8*y)</replace>
Simplifying the partial expression: (-7*y**2)*(40*y**3 + 8*y)
Expanding the part (40*y**3 + 8*y) using the distributive property, and we got: (8*y)*(-7*y**2) + (-7*y**2)*(40*y**3)
Replacing (-7*y**2)*(40*y**3 + 8*y) with (8*y)*(-7*y**2) + (-7*y**2)*(40*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (8*y)*(-7*y**2) + (-7*y**2)*(40*y**3) + (44*y**3)*(40*y**3 + 8*y)</replace>
Simplifying the partial expression: (44*y**3)*(40*y**3 + 8*y)
Expanding the part (40*y**3 + 8*y) using the distributive property, and we got: (8*y)*(44*y**3) + (40*y**3)*(44*y**3)
Replacing (44*y**3)*(40*y**3 + 8*y) with (8*y)*(44*y**3) + (40*y**3)*(44*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (8*y)*(-7*y**2) + (8*y)*(44*y**3) + (-7*y**2)*(40*y**3) + (40*y**3)*(44*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (8*y)*(-7*y**2) = -56*y**3
  (8*y)*(44*y**3) = 352*y**4
  (40*y**3)*(-7*y**2) = -280*y**5
  (40*y**3)*(44*y**3) = 1760*y**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1760*y**6 - 280*y**5 + 352*y**4 - 56*y**3</replace>
No more calculations needed.
<answer>1760*y**6 - 280*y**5 + 352*y**4 - 56*y**3</answer>


Question:
Simplify this expression: (-13*y**3 + 39*y - 21)*(21*y**3 + 83*y**2 - 48*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -273*y**6 - 1079*y**5 + 1443*y**4 + 2796*y**3 - 3615*y**2 + 1008*y


Question:
Calculate the following: (58*y**2 + 31*y + 46)*(41*y**3 + 11*y**2 - 10*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2378*y**5 + 1909*y**4 + 1647*y**3 + 196*y**2 - 460*y


Question:
Calculate the following: (-12*z**2 - 24*z + 45)*(-41*z**3 + 49*z**2 + 25*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: 492*z**5 + 396*z**4 - 3321*z**3 + 1605*z**2 + 1125*z


Question:
Simplify this expression: (28*x - 1)*(44*x**3 - 35*x**2 + 38*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1232*x**4 - 1024*x**3 + 1099*x**2 - 38*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: (28*x - 1)*(44*x**3 - 35*x**2 + 38*x)
Expanding the part (28*x - 1) using the distributive property, and we got: (28*x)*(44*x**3 - 35*x**2 + 38*x) - (44*x**3 - 35*x**2 + 38*x)
<replace-#Step 1>#Step 2:
Current expression: (28*x)*(44*x**3 - 35*x**2 + 38*x) - (44*x**3 - 35*x**2 + 38*x)</replace>
Simplifying the partial expression: -(44*x**3 - 35*x**2 + 38*x)
Expanding the part (44*x**3 - 35*x**2 + 38*x) using the distributive property, and we got: (38*x)*(-1) - 35*x**2*(-1) + (44*x**3)*(-1)
Replacing -(44*x**3 - 35*x**2 + 38*x) with (38*x)*(-1) - 35*x**2*(-1) + (44*x**3)*(-1) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (28*x)*(44*x**3 - 35*x**2 + 38*x) + (38*x)*(-1) - 35*x**2*(-1) + (44*x**3)*(-1)</replace>
Simplifying the partial expression: (28*x)*(44*x**3 - 35*x**2 + 38*x)
Expanding the part (44*x**3 - 35*x**2 + 38*x) using the distributive property, and we got: (28*x)*(38*x) + (28*x)*(-35*x**2) + (28*x)*(44*x**3)
Replacing (28*x)*(44*x**3 - 35*x**2 + 38*x) with (28*x)*(38*x) + (28*x)*(-35*x**2) + (28*x)*(44*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (28*x)*(38*x) + (28*x)*(-35*x**2) + (28*x)*(44*x**3) + (38*x)*(-1) - 35*x**2*(-1) + (44*x**3)*(-1)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-35*x**2)*-1 = 35*x**2
  (-35*x**2)*(28*x) = -980*x**3
  (38*x)*-1 = -38*x
  (38*x)*(28*x) = 1064*x**2
  (44*x**3)*-1 = -44*x**3
  (44*x**3)*(28*x) = 1232*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1232*x**4 - 980*x**3 - 44*x**3 + 35*x**2 + 1064*x**2 - 38*x</replace>
Combining like terms, got 1232*x**4 - 1024*x**3 + 1099*x**2 - 38*x
<replace-#Step 5>#Step 6:
Current expression: 1232*x**4 - 1024*x**3 + 1099*x**2 - 38*x</replace>
No more calculations needed.
<answer>1232*x**4 - 1024*x**3 + 1099*x**2 - 38*x</answer>


Question:
Calculate the following: (-35*y**2 - 43*y + 30)*(-19*y**3 + 31*y**2 + 57)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 665*y**5 - 268*y**4 - 1903*y**3 - 1065*y**2 - 2451*y + 1710


Question:
Simplify this expression: (19 - x)*(44 - 19*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: 19*x**3 - 361*x**2 - 44*x + 836

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (19 - x)*(44 - 19*x**2)
Expanding the part (19 - x) using the distributive property, and we got: (-x)*(44 - 19*x**2) + 19*(44 - 19*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-x)*(44 - 19*x**2) + 19*(44 - 19*x**2)</replace>
Simplifying the partial expression: 19*(44 - 19*x**2)
Expanding the part (44 - 19*x**2) using the distributive property, and we got: -19*x**2*19 + 44*19
Replacing 19*(44 - 19*x**2) with -19*x**2*19 + 44*19 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-x)*(44 - 19*x**2) - 19*x**2*19 + 836</replace>
Simplifying the partial expression: (-x)*(44 - 19*x**2)
Expanding the part (44 - 19*x**2) using the distributive property, and we got: (-x)*(-19*x**2) + 44*(-x)
Replacing (-x)*(44 - 19*x**2) with (-x)*(-19*x**2) + 44*(-x) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-x)*(-19*x**2) + 44*(-1)*x - 19*x**2*19 + 836</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-19*x**2)*19 = -361*x**2
  (-19*x**2)*(-x) = 19*x**3
  44*-1*x = -44*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 19*x**3 - 361*x**2 - 44*x + 836</replace>
No more calculations needed.
<answer>19*x**3 - 361*x**2 - 44*x + 836</answer>


Question:
Simplify this expression: (-49*x**2 - 24)*(49*x**2 - 33*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2401*x**4 + 1617*x**3 - 1176*x**2 + 792*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-49*x**2 - 24)*(49*x**2 - 33*x)
Expanding the part (-49*x**2 - 24) using the distributive property, and we got: (-49*x**2)*(49*x**2 - 33*x) - 24*(49*x**2 - 33*x)
<replace-#Step 1>#Step 2:
Current expression: (-49*x**2)*(49*x**2 - 33*x) - 24*(49*x**2 - 33*x)</replace>
Simplifying the partial expression: -24*(49*x**2 - 33*x)
Expanding the part (49*x**2 - 33*x) using the distributive property, and we got: -33*x*(-24) + (49*x**2)*(-24)
Replacing -24*(49*x**2 - 33*x) with -33*x*(-24) + (49*x**2)*(-24) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -33*x*(-24) + (-49*x**2)*(49*x**2 - 33*x) + (49*x**2)*(-24)</replace>
Simplifying the partial expression: (-49*x**2)*(49*x**2 - 33*x)
Expanding the part (49*x**2 - 33*x) using the distributive property, and we got: (-33*x)*(-49*x**2) + (-49*x**2)*(49*x**2)
Replacing (-49*x**2)*(49*x**2 - 33*x) with (-33*x)*(-49*x**2) + (-49*x**2)*(49*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-33*x)*(-49*x**2) - 33*x*(-24) + (-49*x**2)*(49*x**2) + (49*x**2)*(-24)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-33*x)*-24 = 792*x
  (-33*x)*(-49*x**2) = 1617*x**3
  (49*x**2)*-24 = -1176*x**2
  (49*x**2)*(-49*x**2) = -2401*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2401*x**4 + 1617*x**3 - 1176*x**2 + 792*x</replace>
No more calculations needed.
<answer>-2401*x**4 + 1617*x**3 - 1176*x**2 + 792*x</answer>


Question:
Simplify this expression: -936*z**3 - 912*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: -936*z**3 - 912*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: -936*z**3 - 912*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: -936*z**3 - 912*z**2</replace>
No more calculations needed.
<answer>-936*z**3 - 912*z**2</answer>


Question:
Calculate the following: (41*y**2 - 25*y)*(-45*y**3 - 29*y - 8)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1845*y**5 + 1125*y**4 - 1189*y**3 + 397*y**2 + 200*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: (41*y**2 - 25*y)*(-45*y**3 - 29*y - 8)
Expanding the part (41*y**2 - 25*y) using the distributive property, and we got: (-25*y)*(-45*y**3 - 29*y - 8) + (41*y**2)*(-45*y**3 - 29*y - 8)
<replace-#Step 1>#Step 2:
Current expression: (-25*y)*(-45*y**3 - 29*y - 8) + (41*y**2)*(-45*y**3 - 29*y - 8)</replace>
Simplifying the partial expression: (-25*y)*(-45*y**3 - 29*y - 8)
Expanding the part (-45*y**3 - 29*y - 8) using the distributive property, and we got: (-29*y)*(-25*y) + (-25*y)*(-45*y**3) - (-1)*200*y
Replacing (-25*y)*(-45*y**3 - 29*y - 8) with (-29*y)*(-25*y) + (-25*y)*(-45*y**3) - (-1)*200*y in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-29*y)*(-25*y) + (-25*y)*(-45*y**3) - 8*(-25)*y + (41*y**2)*(-45*y**3 - 29*y - 8)</replace>
Simplifying the partial expression: (41*y**2)*(-45*y**3 - 29*y - 8)
Expanding the part (-45*y**3 - 29*y - 8) using the distributive property, and we got: (-29*y)*(41*y**2) - 328*y**2 + (41*y**2)*(-45*y**3)
Replacing (41*y**2)*(-45*y**3 - 29*y - 8) with (-29*y)*(41*y**2) - 328*y**2 + (41*y**2)*(-45*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-29*y)*(-25*y) + (-29*y)*(41*y**2) + (-25*y)*(-45*y**3) - 8*41*y**2 - 8*(-25)*y + (41*y**2)*(-45*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-45*y**3)*(-25*y) = 1125*y**4
  (-45*y**3)*(41*y**2) = -1845*y**5
  (-29*y)*(-25*y) = 725*y**2
  (-29*y)*(41*y**2) = -1189*y**3
  -8*-25*y = 200*y
  -8*41*y**2 = -328*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1845*y**5 + 1125*y**4 - 1189*y**3 - 328*y**2 + 725*y**2 + 200*y</replace>
Combining like terms, got -1845*y**5 + 1125*y**4 - 1189*y**3 + 397*y**2 + 200*y
<replace-#Step 5>#Step 6:
Current expression: -1845*y**5 + 1125*y**4 - 1189*y**3 + 397*y**2 + 200*y</replace>
No more calculations needed.
<answer>-1845*y**5 + 1125*y**4 - 1189*y**3 + 397*y**2 + 200*y</answer>


Question:
Calculate the following: (-22*x**3 + 3*x)*(-19*x**3 - 23*x - 8)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 418*x**6 + 449*x**4 + 176*x**3 - 69*x**2 - 24*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-22*x**3 + 3*x)*(-19*x**3 - 23*x - 8)
Expanding the part (-22*x**3 + 3*x) using the distributive property, and we got: (3*x)*(-19*x**3 - 23*x - 8) + (-22*x**3)*(-19*x**3 - 23*x - 8)
<replace-#Step 1>#Step 2:
Current expression: (3*x)*(-19*x**3 - 23*x - 8) + (-22*x**3)*(-19*x**3 - 23*x - 8)</replace>
Simplifying the partial expression: (-22*x**3)*(-19*x**3 - 23*x - 8)
Expanding the part (-19*x**3 - 23*x - 8) using the distributive property, and we got: (-23*x)*(-22*x**3) - (-1)*176*x**3 + (-22*x**3)*(-19*x**3)
Replacing (-22*x**3)*(-19*x**3 - 23*x - 8) with (-23*x)*(-22*x**3) - (-1)*176*x**3 + (-22*x**3)*(-19*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-23*x)*(-22*x**3) - 8*(-22)*x**3 + (3*x)*(-19*x**3 - 23*x - 8) + (-22*x**3)*(-19*x**3)</replace>
Simplifying the partial expression: (3*x)*(-19*x**3 - 23*x - 8)
Expanding the part (-19*x**3 - 23*x - 8) using the distributive property, and we got: (-23*x)*(3*x) - 24*x + (3*x)*(-19*x**3)
Replacing (3*x)*(-19*x**3 - 23*x - 8) with (-23*x)*(3*x) - 24*x + (3*x)*(-19*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-23*x)*(3*x) + (-23*x)*(-22*x**3) - 8*(-22)*x**3 - 8*3*x + (3*x)*(-19*x**3) + (-22*x**3)*(-19*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-23*x)*(-22*x**3) = 506*x**4
  (-23*x)*(3*x) = -69*x**2
  (-19*x**3)*(-22*x**3) = 418*x**6
  (-19*x**3)*(3*x) = -57*x**4
  -8*-22*x**3 = 176*x**3
  -8*3*x = -24*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 418*x**6 - 57*x**4 + 506*x**4 + 176*x**3 - 69*x**2 - 24*x</replace>
Combining like terms, got 418*x**6 + 449*x**4 + 176*x**3 - 69*x**2 - 24*x
<replace-#Step 5>#Step 6:
Current expression: 418*x**6 + 449*x**4 + 176*x**3 - 69*x**2 - 24*x</replace>
No more calculations needed.
<answer>418*x**6 + 449*x**4 + 176*x**3 - 69*x**2 - 24*x</answer>


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

Answer: -18*x**5 + 162*x**4 - 360*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: 18*x**2*(-x**3 + 9*x**2 - 20*x)
Expanding the part (-x**3 + 9*x**2 - 20*x) using the distributive property, and we got: (-20*x)*(18*x**2) + (9*x**2)*(18*x**2) + (18*x**2)*(-x**3)
<replace-#Step 1>#Step 2:
Current expression: (-20*x)*(18*x**2) + (9*x**2)*(18*x**2) + (18*x**2)*(-x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-x**3)*(18*x**2) = -18*x**5
  (-20*x)*(18*x**2) = -360*x**3
  (9*x**2)*(18*x**2) = 162*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -18*x**5 + 162*x**4 - 360*x**3</replace>
No more calculations needed.
<answer>-18*x**5 + 162*x**4 - 360*x**3</answer>


Question:
Calculate the following: (-28*x**3 - 61*x)*(-3*x**3 - 18*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: 84*x**6 + 687*x**4 + 1098*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: (-28*x**3 - 61*x)*(-3*x**3 - 18*x)
Expanding the part (-28*x**3 - 61*x) using the distributive property, and we got: (-61*x)*(-3*x**3 - 18*x) + (-28*x**3)*(-3*x**3 - 18*x)
<replace-#Step 1>#Step 2:
Current expression: (-61*x)*(-3*x**3 - 18*x) + (-28*x**3)*(-3*x**3 - 18*x)</replace>
Simplifying the partial expression: (-61*x)*(-3*x**3 - 18*x)
Expanding the part (-3*x**3 - 18*x) using the distributive property, and we got: (-61*x)*(-18*x) + (-61*x)*(-3*x**3)
Replacing (-61*x)*(-3*x**3 - 18*x) with (-61*x)*(-18*x) + (-61*x)*(-3*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-61*x)*(-18*x) + (-61*x)*(-3*x**3) + (-28*x**3)*(-3*x**3 - 18*x)</replace>
Simplifying the partial expression: (-28*x**3)*(-3*x**3 - 18*x)
Expanding the part (-3*x**3 - 18*x) using the distributive property, and we got: (-18*x)*(-28*x**3) + (-28*x**3)*(-3*x**3)
Replacing (-28*x**3)*(-3*x**3 - 18*x) with (-18*x)*(-28*x**3) + (-28*x**3)*(-3*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-61*x)*(-18*x) + (-61*x)*(-3*x**3) + (-18*x)*(-28*x**3) + (-28*x**3)*(-3*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-18*x)*(-61*x) = 1098*x**2
  (-18*x)*(-28*x**3) = 504*x**4
  (-3*x**3)*(-61*x) = 183*x**4
  (-3*x**3)*(-28*x**3) = 84*x**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 84*x**6 + 183*x**4 + 504*x**4 + 1098*x**2</replace>
Combining like terms, got 84*x**6 + 687*x**4 + 1098*x**2
<replace-#Step 5>#Step 6:
Current expression: 84*x**6 + 687*x**4 + 1098*x**2</replace>
No more calculations needed.
<answer>84*x**6 + 687*x**4 + 1098*x**2</answer>


Question:
Calculate the following: (-15*x**2 - 20)*(40*x**3 + 45*x**2 - 16*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: -600*x**5 - 675*x**4 - 560*x**3 - 900*x**2 + 320*x


Question:
Simplify this expression: (-23*x**2 - 37*x)*(-46*x**2 - 27*x + 44)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1058*x**4 + 2323*x**3 - 13*x**2 - 1628*x