Sure, let's simplify the given expression step-by-step.
You are given the expression:
[tex]\[
-(5x - 2)(4x + 8) + 3x^2 - 9x
\][/tex]
Step 1: Let's expand the first part of the expression [tex]\(-(5x - 2)(4x + 8)\)[/tex].
Using the distributive property (FOIL method), we get:
[tex]\[
(5x - 2)(4x + 8) = 5x \cdot 4x + 5x \cdot 8 - 2 \cdot 4x - 2 \cdot 8
\][/tex]
[tex]\[
= 20x^2 + 40x - 8x - 16
\][/tex]
[tex]\[
= 20x^2 + 32x - 16
\][/tex]
Because we have a negative sign in front of [tex]\((5x - 2)(4x + 8)\)[/tex], we distribute the negative sign:
[tex]\[
-(20x^2 + 32x - 16) = -20x^2 - 32x + 16
\][/tex]
Step 2: Now, add this result to the remaining terms of the expression, [tex]\(3x^2 - 9x\)[/tex]:
[tex]\[
-20x^2 - 32x + 16 + 3x^2 - 9x
\][/tex]
Step 3: Combine like terms:
[tex]\[
(-20x^2 + 3x^2) + (-32x - 9x) + 16
\][/tex]
[tex]\[
= -17x^2 - 41x + 16
\][/tex]
So, the simplified form of the given expression is:
[tex]\[
-17x^2 - 41x + 16
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{-17x^2 - 41x + 16}
\][/tex]
