Question

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

Answer 1

Let's simplify the expression \(- (5x - 2)(4x + 8) + 3x^2 - 9x\) step by step.

1. **Distribute:** Start by expanding \(-(5x - 2)(4x + 8)\).

\[
(5x - 2)(4x + 8) = 5x(4x) + 5x(8) - 2(4x) - 2(8)
\]

Calculating each term:

- \(5x \cdot 4x = 20x^2\)
- \(5x \cdot 8 = 40x\)
- \(-2 \cdot 4x = -8x\)
- \(-2 \cdot 8 = -16\)

Now combine all those terms:

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

Now apply the negative sign:

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

2. **Combine with the other terms:** Now substitute this back into the original expression:

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

Next, combine like terms:

- Combine \( -20x^2 + 3x^2 \):

\[
-20x^2 + 3x^2 = -17x^2
\]

- Combine \( -32x - 9x \):

\[
-32x - 9x = -41x
\]

So now, we have:

\[
-17x^2 - 41x + 16
\]

3. **Final answer:** The simplified expression is:

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