Perform the operation(s) and simplify completely.

Question

−
(
2
x
+
6
)
(
3
x
+
4
)
+
5
x
2
−
7
x


(1 point)
Responses

−
x
2
−
33
x
−
24
negative x squared minus 33 x minus 24

11
x
2
+
19
x
+
24
11 x squared plus 19 x plus 24

−
x
2
−
19
x
−
24
negative x squared minus 19 x minus 24

−
x
2
+
3
x
+
24
negative x squared plus 3 x plus 24

Answer 1

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

1. Distribute:

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

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

2. Negate it:

   \[

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

3. Combine with the rest of the expression:

   Now add \( 5x^2 - 7x \):

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

   Combine like terms:

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

   \[ = -1x^2 - 33x - 24 \]

4. Final result:

   Thus, the simplified expression is:

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

So the correct response is:

\(-x^2 - 33x - 24\) (negative x squared minus 33 x minus 24).