Question

subtract.
$(-6r^{3}+9r^{2}-r + 2)-(-r^{3}+r^{2}+7r + 8)$

Explanation:

Step1: Distribute the negative sign

We need to distribute the negative sign to each term in the second polynomial. So, \((-6r^{3}+9r^{2}-r + 2)-(-r^{3}+r^{2}+7r + 8)=-6r^{3}+9r^{2}-r + 2 + r^{3}-r^{2}-7r - 8\)

Step2: Combine like terms for \(r^{3}\) terms

The \(r^{3}\) terms are \(-6r^{3}\) and \(r^{3}\). Combining them: \(-6r^{3}+r^{3}=-5r^{3}\)

Step3: Combine like terms for \(r^{2}\) terms

The \(r^{2}\) terms are \(9r^{2}\) and \(-r^{2}\). Combining them: \(9r^{2}-r^{2}=8r^{2}\)

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

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

Step5: Combine constant terms

The constant terms are \(2\) and \(-8\). Combining them: \(2 - 8=-6\)

Step6: Combine all the results

Putting all the combined terms together: \(-5r^{3}+8r^{2}-8r - 6\)

Answer:

\(-5r^{3}+8r^{2}-8r - 6\)