Question

Perform the operation(s) and simplify completely.
−(2x+6)(3x+4)+5x
2
−7x
A) 11x
2
+19x+24 B) −x
2
+3x+24 C) −x
2
−33x−24 D) −x
2
−19x−24

Answer 1

Let's simplify the expression step by step:

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

First, we'll expand the product \(-(2x + 6)(3x + 4)\):

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

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

3. **Combine with \( 5x^2 - 7x \)**:
\[
-6x^2 - 26x - 24 + 5x^2 - 7x
\]

4. **Combine like terms**:
- **For \( x^2 \) terms**: \(-6x^2 + 5x^2 = -x^2\)
- **For \( x \) terms**: \(-26x - 7x = -33x\)
- **The constant term**: \(-24\)

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

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

Now we can compare with the options given:

A) \( 11x^2 + 19x + 24 \)
B) \( -x^2 + 3x + 24 \)
C) \( -x^2 - 33x - 24 \)
D) \( -x^2 - 19x - 24 \)

The correct answer is **C) \(-x^2 - 33x - 24\)**.