Questions: Subtract. (5 x^3-5 x^2+4 x-4)-(9 x^3-8 x^2+4) (5 x^3-5 x^2+4 x-4)-(9 x^3-8 x^2+4)= (Simplify your answer.)

Subtract. (5 x^3-5 x^2+4 x-4)-(9 x^3-8 x^2+4) (5 x^3-5 x^2+4 x-4)-(9 x^3-8 x^2+4)= (Simplify your answer.)
Transcript text: Subtract. \[ \left(5 x^{3}-5 x^{2}+4 x-4\right)-\left(9 x^{3}-8 x^{2}+4\right) \] \[ \left(5 x^{3}-5 x^{2}+4 x-4\right)-\left(9 x^{3}-8 x^{2}+4\right)= \] (Simplify your answer.)
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Solution

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Solution Steps

Step 1: Distribute the negative sign

First, distribute the negative sign to each term inside the second parentheses: (5x3−5x2+4x−4)−(9x3−8x2+4)=5x3−5x2+4x−4−9x3+8x2−4. \left(5x^{3} - 5x^{2} + 4x - 4\right) - \left(9x^{3} - 8x^{2} + 4\right) = 5x^{3} - 5x^{2} + 4x - 4 - 9x^{3} + 8x^{2} - 4.

Step 2: Combine like terms

Next, combine like terms:

  • 5x3−9x3=−4x35x^{3} - 9x^{3} = -4x^{3},
  • −5x2+8x2=3x2-5x^{2} + 8x^{2} = 3x^{2},
  • 4x4x remains as is,
  • −4−4=−8-4 - 4 = -8.

So, the expression simplifies to: −4x3+3x2+4x−8. -4x^{3} + 3x^{2} + 4x - 8.

Final Answer

The simplified expression is: −4x3+3x2+4x−8. \boxed{-4x^{3} + 3x^{2} + 4x - 8}.

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