Question

Perform the operation(s) and simplify completely. −(5x−2)(4x+8)+3x2−9x (1 point) Responses 3x2+10 3 x squared plus 10 −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

Answer 1

Let's simplify the expression step by step:

Given:
\[
-(5x - 2)(4x + 8) + 3x^2 - 9x
\]

First, we will expand the term \(-(5x - 2)(4x + 8)\).

Using the distributive property (FOIL method):
\[
(5x - 2)(4x + 8) = 5x \cdot 4x + 5x \cdot 8 - 2 \cdot 4x - 2 \cdot 8
\]
\[
= 20x^2 + 40x - 8x - 16
\]
\[
= 20x^2 + 32x - 16
\]

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

Next, we combine this result with \(3x^2 - 9x\):
\[
-20x^2 - 32x + 16 + 3x^2 - 9x
\]
Now, we combine like terms:
- The \(x^2\) terms:
\[
-20x^2 + 3x^2 = -17x^2
\]

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

- The constant term:
\[
16
\]

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

The final simplified expression is:
\[
\boxed{-17x^2 - 41x + 16}
\]