Question

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

Answer 1

Let's simplify the expression step by step:

We start with the expression:

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

First, we need to expand \(-(2x + 6)(3x + 4)\):

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

Calculating each term:

- \(2x \cdot 3x = 6x^2\)
- \(2x \cdot 4 = 8x\)
- \(6 \cdot 3x = 18x\)
- \(6 \cdot 4 = 24\)

Now, combine these results:

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

Now, apply the negative sign:

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

Next, we combine this with the rest of the expression:

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

Combine like terms:

1. For \(x^2\) terms:
\(-6x^2 + 5x^2 = -x^2\)

2. For \(x\) terms:
\(-26x - 7x = -33x\)

3. The constant term is:
\(-24\)

Putting it all together gives:

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

So, the fully simplified expression is:

\[
\boxed{-x^2 - 33x - 24}
\]