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

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

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

−x2+3x+24

Answer 1

Let's break down the expression step by step:

The expression is:
\[
-(2x + 6)(3x + 4) + 5x^2 - 7x
\]

### Step 1: Distributing the first part

First, we will simplify \(-(2x + 6)(3x + 4)\).

Using the distributive property (FOIL):
\[
(2x + 6)(3x + 4) = 2x \cdot 3x + 2x \cdot 4 + 6 \cdot 3x + 6 \cdot 4
\]
\[
= 6x^2 + 8x + 18x + 24
\]
\[
= 6x^2 + 26x + 24
\]

Now we apply the negative sign:
\[
-(6x^2 + 26x + 24) = -6x^2 - 26x - 24
\]

### Step 2: Combine it with the other terms

Now let's add \(5x^2 - 7x\):
\[
-6x^2 - 26x - 24 + 5x^2 - 7x
\]

### Step 3: Combine like terms

- For the \(x^2\) terms: \(-6x^2 + 5x^2 = -1x^2\)
- For the \(x\) terms: \(-26x - 7x = -33x\)
- The constant term remains: \(-24\)

Putting it all together:
\[
-x^2 - 33x - 24
\]

### Final Result:
The simplified expression is:
\[
\boxed{-x^2 - 33x - 24}
\]

Therefore, the correct response is:
**−x²−33x−24 (negative x squared minus 33 x minus 24)**.