Question

Perform the operation(s) and simplify completely.

−(5x−2)(4x+8)+3x2−9x

(1 point)
Responses

−17x2+23x−16
negative 17 x squared plus 23 x minus 16

3x2+10
3 x squared plus 10

23x2+23x−16
23 x squared plus 23 x minus 16

−17x2−41x+16

Answers

GPT-4o mini
To simplify the expression \(- (5x - 2)(4x + 8) + 3x^2 - 9x\), let's break it down step by step.

1. **First, expand the product**:
\[
- (5x - 2)(4x + 8)
\]
Using the distributive property (FOIL method):
\[
= - (20x^2 + 40x - 8)
\]
Simplifying gives:
\[
= -20x^2 - 40x + 8
\]

2. **Next, combine this with the other terms in the expression**:
\[
-20x^2 - 40x + 8 + 3x^2 - 9x
\]

3. **Combine like terms**:
- For \(x^2\) terms: \(-20x^2 + 3x^2 = -17x^2\)
- For \(x\) terms: \(-40x - 9x = -49x\)
- The constant term remains \(8\).

Putting it all together:
\[
-17x^2 - 49x + 8
\]

None of the given multiple choice answers match this result. Please double-check the relationships or provide any modifications to the initial expression that might affect the outcome.