Question

perform the operation.
$(10x^2 - 7x + 7) - (4x^2 + 5x - 9)$

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:
$$(10x^3 - 7x + 7) - 4x^2 - 5x + 9$$

Step2: Combine like terms

Now, we combine the like terms. The \(x^3\) term: \(10x^3\) (no other \(x^3\) terms). The \(x^2\) term: \(-4x^2\) (no other \(x^2\) terms). The \(x\) terms: \(-7x - 5x = -12x\). The constant terms: \(7 + 9 = 16\).
Putting it all together, we get:
$$10x^3 - 4x^2 - 12x + 16$$

Answer:

\(10x^3 - 4x^2 - 12x + 16\)