Question

perform the operation(s) and simplify completely. −(5x−2)(4x+8)+3x2−9x (1 point) Responses −17x2−41x+16 negative 17 x squared minus 41 x plus 16 −17x2+23x−16 negative 17 x squared plus 23 x minus 16 23x2+23x−16 23 x squared plus 23 x minus 16 3x2+10

Answer 1

To simplify the expression \(- (5x - 2)(4x + 8) + 3x^2 - 9x\), we will follow these steps:

1. **Expand the product:**
\[
- (5x - 2)(4x + 8)
\]
First, we need to expand \((5x - 2)(4x + 8)\):
\[
= 5x \cdot 4x + 5x \cdot 8 - 2 \cdot 4x - 2 \cdot 8
\]
\[
= 20x^2 + 40x - 8x - 16
\]
\[
= 20x^2 + 32x - 16
\]

Now apply the negative:
\[
- (20x^2 + 32x - 16) = -20x^2 - 32x + 16
\]

2. **Combine with the other terms:**
Now add \(3x^2 - 9x\):
\[
-20x^2 - 32x + 16 + 3x^2 - 9x
\]

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

4. **Final expression:**
Combining all these results gives:
\[
-17x^2 - 41x + 16
\]

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