Perform the operation(s) and simplify completely.

Question

(4−2x)(−6x2+10x+214−2x)


(1 point)
Responses

−x3+5x2−6x+3
negative x cubed plus 5 x squared minus 6 x plus 3

−6x2+10x+21
negative 6 x squared plus 10 x plus 21

−x2−2x+12
negative x squared minus 2 x plus 12

−x2+2x−8
negative x squared plus 2 x minus 8

Answer 1

To perform the operation and simplify \((4 - 2x)(-6x^2 + 10x + 21 - 2x)\), we start by simplifying the expression inside the parentheses.

1. Combine the like terms in \(-6x^2 + 10x + 21 - 2x\): \[ -6x^2 + (10x - 2x) + 21 = -6x^2 + 8x + 21 \]

Next, substitute this back into the original expression: \[ (4 - 2x)(-6x^2 + 8x + 21) \]

2. Now, we will distribute \((4 - 2x)\) across \((-6x^2 + 8x + 21)\):

   \[ = 4(-6x^2) + 4(8x) + 4(21) - 2x(-6x^2) - 2x(8x) - 2x(21) \]

   This expands to: \[ = -24x^2 + 32x + 84 + 12x^3 - 16x^2 - 42x \]

3. Now, combine the like terms: \[ 12x^3 + (-24x^2 - 16x^2) + (32x - 42x) + 84 \] \[ = 12x^3 - 40x^2 - 10x + 84 \]

The fully simplified expression is: \[ 12x^3 - 40x^2 - 10x + 84 \]

There seems to be no option that matches directly to our final answer, but let's verify:

• None of the responses provided:
  • \(-x^3 + 5x^2 - 6x + 3\)
  • \(-6x^2 + 10x + 21\)
  • \(-x^2 - 2x + 12\)
  • \(-x^2 + 2x - 8\)

...matches the calculated result of \(12x^3 - 40x^2 - 10x + 84\).

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