Question

Perform the operation(s) and simplify completely.

−(2x+6)(3x+4)+5x2−7x


(1 point)
Responses

−x2+3x+24
negative x squared plus 3 x plus 24

−x2−19x−24
negative x squared minus 19 x minus 24

−x2−33x−24
negative x squared minus 33 x minus 24

11x2+19x+24
11 x squared plus 19 x plus 24
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Answer 1

Let's simplify the expression step by step:

Given:
\[
-(2x + 6)(3x + 4) + 5x^2 - 7x
\]
First, we'll start by expanding the product \(-(2x + 6)(3x + 4)\).

1. Expand \((2x + 6)(3x + 4)\):
\[
(2x)(3x) + (2x)(4) + (6)(3x) + (6)(4) = 6x^2 + 8x + 18x + 24 = 6x^2 + 26x + 24
\]

2. Now, applying the negative sign:
\[
-(6x^2 + 26x + 24) = -6x^2 - 26x - 24
\]

3. Now, we substitute this back into the original expression:
\[
-6x^2 - 26x - 24 + 5x^2 - 7x
\]

4. Combine like terms:
- For \(x^2\) terms:
\[-6x^2 + 5x^2 = -x^2\]

- For \(x\) terms:
\[-26x - 7x = -33x\]

- For constant terms:
\[-24\] (there are no other constants to combine with).

Thus, we get:
\[
-x^2 - 33x - 24
\]

The simplified expression is:
\[
-x^2 - 33x - 24
\]

So the answer is:
**−x²−33x−24** (negative x squared minus 33 x minus 24).