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+3x+24 negative x squared plus 3 x plus 24 −x2−19x−24 negative x squared minus 19 x minus 24 −x2−33x−24

Answer 1

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

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

Let's go step by step.

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

First, we will calculate \( (2x + 6)(3x + 4) \):

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

Now applying the negative sign:

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

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

Now, we combine this result with \( 5x^2 - 7x \):

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

Combining like terms (for \(x^2\) terms and \(x\) terms):

For \(x^2\) terms: \[ -6x^2 + 5x^2 = -x^2 \]

For \(x\) terms: \[ -26x - 7x = -33x \]

Now putting it all together:

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

Conclusion

The simplified expression is:

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

So the final answer is:

−x²−33x−24