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: \[ \left(5x^{3} - 5x^{2} + 4x - 4\right) - \left(9x^{3} - 8x^{2} + 4\right) = 5x^{3} - 5x^{2} + 4x - 4 - 9x^{3} + 8x^{2} - 4. \]

Step 2: Combine like terms

Next, combine like terms:

  • \(5x^{3} - 9x^{3} = -4x^{3}\),
  • \(-5x^{2} + 8x^{2} = 3x^{2}\),
  • \(4x\) remains as is,
  • \(-4 - 4 = -8\).

So, the expression simplifies to: \[ -4x^{3} + 3x^{2} + 4x - 8. \]

Final Answer

The simplified expression is: \[ \boxed{-4x^{3} + 3x^{2} + 4x - 8}. \]

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