Question

Perform the operation(s) and simplify completely.

(4−2x)(−6x2+10x+214−2x)

(1 point)
Responses

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

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

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

−6x2+10x+21

Answer 1

To simplify the expression \((4 - 2x)(-6x^2 + 10x + 21 - 2x)\), let's first simplify what we have inside the parentheses.

Combining like terms inside the second parentheses:
\[
-6x^2 + 10x + 21 - 2x = -6x^2 + (10x - 2x) + 21 = -6x^2 + 8x + 21
\]

Now we rewrite the expression as:
\[
(4 - 2x)(-6x^2 + 8x + 21)
\]

Next, we'll use the distributive property (FOIL method) to multiply the two binomials.

1. Multiply \(4\) by each term in the polynomial \(-6x^2 + 8x + 21\):
\[
4 \cdot -6x^2 = -24x^2
\]
\[
4 \cdot 8x = 32x
\]
\[
4 \cdot 21 = 84
\]

2. Multiply \(-2x\) by each term in the polynomial \(-6x^2 + 8x + 21\):
\[
-2x \cdot -6x^2 = 12x^3
\]
\[
-2x \cdot 8x = -16x^2
\]
\[
-2x \cdot 21 = -42x
\]

Now combine all the results together:
\[
-24x^2 + 32x + 84 + 12x^3 - 16x^2 - 42x
\]

Now we rearrange and group like terms:
\[
12x^3 + (-24x^2 - 16x^2) + (32x - 42x) + 84
\]
\[
12x^3 - 40x^2 - 10x + 84
\]

So the final expression after simplification is:
\[
12x^3 - 40x^2 - 10x + 84
\]

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