Question

Perform the operation(s) and simplify completely. −(2x+6)(3x+4)+5x2−7x (1 point) Responses −x2−19x−24 negative x squared minus 19 x minus 24 11x2+19x+24 11 x squared plus 19 x plus 24 −x2−33x−24 negative x squared minus 33 x minus 24 −x2+3x+24

Answer 1

Let's start with the expression:

\[
-(2x + 6)(3x + 4) + 5x^2 - 7x
\]

First, we need to expand the expression \(-(2x + 6)(3x + 4)\). Let's perform the multiplication:

\[
(2x + 6)(3x + 4) = 2x \cdot 3x + 2x \cdot 4 + 6 \cdot 3x + 6 \cdot 4
\]

Calculating each term:

- \(2x \cdot 3x = 6x^2\)
- \(2x \cdot 4 = 8x\)
- \(6 \cdot 3x = 18x\)
- \(6 \cdot 4 = 24\)

Adding these together gives:

\[
6x^2 + 8x + 18x + 24 = 6x^2 + 26x + 24
\]

Now, since we need \(-(2x + 6)(3x + 4)\), we have:

\[
-(6x^2 + 26x + 24) = -6x^2 - 26x - 24
\]

Next, we substitute back into the expression we are simplifying:

\[
-6x^2 - 26x - 24 + 5x^2 - 7x
\]

Now, we combine like terms:

1. For \(x^2\) terms:
\(-6x^2 + 5x^2 = -x^2\)

2. For \(x\) terms:
\(-26x - 7x = -33x\)

3. The constant term remains \(-24\).

Combining everything gives:

\[
-x^2 - 33x - 24
\]

Thus, the final simplified expression is:

\[
\boxed{-x^2 - 33x - 24}
\]