Question

Perform the operation(s) and simplify completely.

(4−2x)(−6x2+10x+214−2x)


(1 point)

Answer 1

To perform the operation and simplify the expression \((4-2x)(-6x^2 + 10x + 214 - 2x)\), we first simplify the expression inside the parentheses.

1. Combine like terms in the second part:
\[
10x - 2x = 8x
\]
So, we have:
\[
-6x^2 + 8x + 214
\]

2. Now, we will distribute \((4 - 2x)\) with \((-6x^2 + 8x + 214)\):
\[
(4 - 2x)(-6x^2 + 8x + 214) = 4(-6x^2) + 4(8x) + 4(214) - 2x(-6x^2) - 2x(8x) - 2x(214)
\]

3. Now calculate each term:
- \(4 \cdot -6x^2 = -24x^2\)
- \(4 \cdot 8x = 32x\)
- \(4 \cdot 214 = 856\)
- \(-2x \cdot -6x^2 = 12x^3\)
- \(-2x \cdot 8x = -16x^2\)
- \(-2x \cdot 214 = -428x\)

4. Now combine all of these results:
\[
12x^3 + (-24x^2 - 16x^2) + (32x - 428x) + 856
\]

5. Combine like terms:
- For \(x^3\) terms: \(12x^3\)
- For \(x^2\) terms: \(-24x^2 - 16x^2 = -40x^2\)
- For \(x\) terms: \(32x - 428x = -396x\)
- The constant term is \(856\).

6. Putting it all together:
\[
12x^3 - 40x^2 - 396x + 856
\]

Thus, the completely simplified expression is:
\[
\boxed{12x^3 - 40x^2 - 396x + 856}
\]