Question

perform the operation and simplify completely -(5x-2)(4x+8)+3x^2-9x

Answer 1

To simplify the expression \(- (5x - 2)(4x + 8) + 3x^2 - 9x\), we can break it down step by step.

1. **Distribute the first term**:
\[
- (5x - 2)(4x + 8)
\]
To perform this operation, we first need to multiply \( (5x - 2) \) and \( (4x + 8) \):

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

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

2. **Combine the rest of the expression**:
Now we have:
\[
-20x^2 - 32x + 16 + 3x^2 - 9x
\]

3. **Combine like terms**:
Combine the \(x^2\) terms:
\[
-20x^2 + 3x^2 = -17x^2
\]

Combine the \(x\) terms:
\[
-32x - 9x = -41x
\]

The constant term remains:
\[
+ 16
\]

4. **Final expression**:
Putting it all together, we get:
\[
-17x^2 - 41x + 16
\]

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