Perform the operation(s) and simplify completely.

−(2x+6)(3x+4)+5x2−7x


(1 point)
Responses

−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
negative x squared minus 33 x minus 24

11x2+19x+24
11 x squared plus 19 x plus 24
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1 answer

Let's simplify the expression step by step:

Given: \[ -(2x + 6)(3x + 4) + 5x^2 - 7x \] First, we'll start by expanding the product \(-(2x + 6)(3x + 4)\).

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

  2. Now, applying the negative sign: \[ -(6x^2 + 26x + 24) = -6x^2 - 26x - 24 \]

  3. Now, we substitute this back into the original expression: \[ -6x^2 - 26x - 24 + 5x^2 - 7x \]

  4. Combine like terms:

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

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

  • For constant terms: \[-24\] (there are no other constants to combine with).

Thus, we get: \[ -x^2 - 33x - 24 \]

The simplified expression is: \[ -x^2 - 33x - 24 \]

So the answer is: −x²−33x−24 (negative x squared minus 33 x minus 24).