Question

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

Answer 1

To simplify the expression \( -(2x+6)(3x+4)+5x^2−7x \), we will follow these steps:

1. **Expand the product**: \( -(2x + 6)(3x + 4) \).
2. **Combine like terms**.

Let's go step by step.

### Step 1: Expand \( -(2x + 6)(3x + 4) \)

First, we will calculate \( (2x + 6)(3x + 4) \):

\[
(2x + 6)(3x + 4) = 2x \cdot 3x + 2x \cdot 4 + 6 \cdot 3x + 6 \cdot 4
\]
\[
= 6x^2 + 8x + 18x + 24
\]
\[
= 6x^2 + 26x + 24
\]

Now applying the negative sign:

\[
-(2x + 6)(3x + 4) = - (6x^2 + 26x + 24) = -6x^2 - 26x - 24
\]

### Step 2: Combine with \( 5x^2 - 7x \)

Now, we combine this result with \( 5x^2 - 7x \):

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

Combining like terms (for \(x^2\) terms and \(x\) terms):

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

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

Now putting it all together:

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

### Conclusion

The simplified expression is:

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

So the final answer is:

**−x²−33x−24**