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Perform the operation(s) and simplify completely.

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



A
11x2+19x+2411x^2+19x+2411x
2
+19x+24

B
−x2.+3x+24-x^{2.}+3x+24−x
2.
+3x+24

C
−x2−33x−24-x^2-33x-24−x
2
−33x−24

D
−x2−19x−24-x^2-19x-24−x
2
−19x−24

1 answer

Let's perform the operations step-by-step:

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

  2. Add \(5x^2 - 7x\) to \(-6x^2 - 26x - 24\): \[ -6x^2 - 26x - 24 + 5x^2 - 7x \] Combine like terms: \[ (-6x^2 + 5x^2) + (-26x - 7x) - 24 = -x^2 - 33x - 24 \]

So, the simplified expression is: \[ -x^2 - 33x - 24 \]

Now, checking the provided options:

  • Option A: \(11x^2 + 19x + 24\)
  • Option B: \(-x^2 + 3x + 24\)
  • Option C: \(-x^2 - 33x - 24\)
  • Option D: \(-x^2 - 19x - 24\)

The correct answer is C: \(-x^2 - 33x - 24\).