Question

Perform the operation(s) and simplify completely.
(1 point)
-\left(5x-2\right)\left(4x+8\right)+3x^2-9x

Answer 1

To simplify the expression \(-\left(5x-2\right)\left(4x+8\right)+3x^2-9x\), we will first expand the product and then combine like terms.

1. **Expand \(-\left(5x-2\right)\left(4x+8\right)\)**:

\[
(5x - 2)(4x + 8) = 5x \cdot 4x + 5x \cdot 8 - 2 \cdot 4x - 2 \cdot 8
\]
\[
= 20x^2 + 40x - 8x - 16
\]
\[
= 20x^2 + 32x - 16
\]

Now, applying the negative sign:

\[
-\left(20x^2 + 32x - 16\right) = -20x^2 - 32x + 16
\]

2. **Combine this with \(3x^2 - 9x\)**:

\[
-20x^2 - 32x + 16 + 3x^2 - 9x
\]

Now, combine like terms:

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

3. **Final expression**:
\[
-17x^2 - 41x + 16
\]

Thus, the simplified expression is:

\[
\boxed{-17x^2 - 41x + 16}
\]