Question

Perform the operation(s) and simplify completely.
-(2x+6) (3x+4)+5x^2-7x




A
11x2+19x+2411x^2+19x+2411x
2
+19x+24

B
−x2.+3x+24-x^{2.}+3x+24−x
2.
+3x+24

C
−x2−33x−24-x^2-33x-24−x
2
−33x−24

D
−x2−19x−24-x^2-19x-24−x
2
−19x−24

Answer 1

Let's perform the operations step-by-step:

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

2. **Add \(5x^2 - 7x\) to \(-6x^2 - 26x - 24\)**:
\[
-6x^2 - 26x - 24 + 5x^2 - 7x
\]
Combine like terms:
\[
(-6x^2 + 5x^2) + (-26x - 7x) - 24 = -x^2 - 33x - 24
\]

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

Now, checking the provided options:
- Option A: \(11x^2 + 19x + 24\)
- Option B: \(-x^2 + 3x + 24\)
- Option C: \(-x^2 - 33x - 24\)
- Option D: \(-x^2 - 19x - 24\)

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