Question

Perform the operation(s) and simplify completely. (4−2x)(−6x2+10x+214−2x) (1 point) Responses −6x2+10x+21 negative 6 x squared plus 10 x plus 21 −x3+5x2−6x+3 negative x cubed plus 5 x squared minus 6 x plus 3 −x2+2x−8 negative x squared plus 2 x minus 8 −x2−2x+12

Answer 1

Let's simplify the expression \((4 - 2x)(-6x^2 + 10x + 21 - 2x)\).

First, simplify the expression inside the parentheses:

\[
-6x^2 + 10x + 21 - 2x = -6x^2 + (10x - 2x) + 21 = -6x^2 + 8x + 21
\]

Now, we can multiply \((4 - 2x)\) with \((-6x^2 + 8x + 21)\):

Using the distributive property (FOIL), we have:

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

Calculating each term:

1. \(4 \cdot -6x^2 = -24x^2\)
2. \(4 \cdot 8x = 32x\)
3. \(4 \cdot 21 = 84\)
4. \(-2x \cdot -6x^2 = 12x^3\)
5. \(-2x \cdot 8x = -16x^2\)
6. \(-2x \cdot 21 = -42x\)

Now, combine all these terms:

\[
-24x^2 + 32x + 84 + 12x^3 - 16x^2 - 42x
\]

Now, combine like terms:

- For \(x^3\): \(12x^3\)
- For \(x^2\): \(-24x^2 - 16x^2 = -40x^2\)
- For \(x\): \(32x - 42x = -10x\)

Putting it all together, we have:

\[
12x^3 - 40x^2 - 10x + 84
\]

Thus, the final simplified expression is:

\[
12x^3 - 40x^2 - 10x + 84
\]

None of the responses offered match this final result. If an answer needs to be picked from the options provided, consider reviewing the question for any errors in the provided options.