Question

perform the indicated operation.
$(-7x^3 + 3x^2 + 7x - 7) - (9x^3 + 2x^2 + x + 1)$
$(-7x^3 + 3x^2 + 7x - 7) - (9x^3 + 2x^2 + x + 1) = \square$
(simplify your answer. do not factor.)

Explanation:

Step1: Distribute the negative sign

To subtract the second polynomial from the first, we distribute the negative sign to each term in the second polynomial:
\((-7x^3 + 3x^2 + 7x - 7) - 9x^3 - 2x^2 - x - 1\)

Step2: Combine like terms for \(x^3\) terms

The \(x^3\) terms are \(-7x^3\) and \(-9x^3\). Combining them:
\(-7x^3 - 9x^3 = -16x^3\)

Step3: Combine like terms for \(x^2\) terms

The \(x^2\) terms are \(3x^2\) and \(-2x^2\). Combining them:
\(3x^2 - 2x^2 = x^2\)

Step4: Combine like terms for \(x\) terms

The \(x\) terms are \(7x\) and \(-x\). Combining them:
\(7x - x = 6x\)

Step5: Combine constant terms

The constant terms are \(-7\) and \(-1\). Combining them:
\(-7 - 1 = -8\)

Step6: Combine all combined terms

Putting all the combined terms together:
\(-16x^3 + x^2 + 6x - 8\)

Answer:

\(-16x^3 + x^2 + 6x - 8\)