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

Answer 1

To simplify the expression \(- (5x - 2)(4x + 8) + 3x^2 - 9x\), let's start by expanding the product \(-(5x - 2)(4x + 8)\):

1. **Distribute**:
\[
(5x - 2)(4x + 8) = 5x \cdot 4x + 5x \cdot 8 - 2 \cdot 4x - 2 \cdot 8
\]
\[
= 20x^2 + 40x - 8x - 16
\]
\[
= 20x^2 + 32x - 16
\]

2. **Apply the negative sign**:
\[
- (20x^2 + 32x - 16) = -20x^2 - 32x + 16
\]

Now, we will add the remaining terms \(3x^2 - 9x\):

3. **Combine the terms**:
\[
-20x^2 - 32x + 16 + 3x^2 - 9x
\]
Combine like terms:
- For \(x^2\):
\[
-20x^2 + 3x^2 = -17x^2
\]
- For \(x\):
\[
-32x - 9x = -41x
\]
- Constant term:
\[
16
\]

Putting it all together:
\[
-17x^2 - 41x + 16
\]

Thus, the final simplified expression is:
\[
-17x^2 - 41x + 16
\]

The correct answer is:
**−17x²−41x+16**.