Question

perform the indicated operation.
(-3x^{3}-3x^{2}-7x + 6)-(5x^{3}+8x^{2}-6x - 7)
(-3x^{3}-3x^{2}-7x + 6)-(5x^{3}+8x^{2}-6x - 7)=
simplify your answer. do not factor.)

Explanation:

Step1: Distribute the negative sign

We need to distribute the negative sign to each term inside the second parentheses. So, \((-3x^3 - 3x^2 - 7x + 6) - (5x^3 + 8x^2 - 6x - 7)\) becomes \(-3x^3 - 3x^2 - 7x + 6 - 5x^3 - 8x^2 + 6x + 7\).

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

Combine the \(x^3\) terms: \(-3x^3 - 5x^3 = -8x^3\).

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

Combine the \(x^2\) terms: \(-3x^2 - 8x^2 = -11x^2\).

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

Combine the \(x\) terms: \(-7x + 6x = -x\).

Step5: Combine constant terms

Combine the constant terms: \(6 + 7 = 13\).

Step6: Write the simplified expression

Putting it all together, we get \(-8x^3 - 11x^2 - x + 13\).

Answer:

\(-8x^3 - 11x^2 - x + 13\)