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

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

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

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

First, we can expand \((2x + 6)(3x + 4)\):

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

Now, adding the negative sign in front:

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

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

Now, we substitute this back into our original expression:

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

Now combine the terms:

• Combine the \(x^2\) terms: \(-6x^2 + 5x^2 = -1x^2\)
• Combine the \(x\) terms: \(-26x - 7x = -33x\)
• The constant term is \(-24\).

Putting it all together, we get:

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

So, the fully simplified expression is:

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

The correct response is: \(-x^2 - 33x - 24\) (negative x squared minus 33 x minus 24).