Question

use the box method to distribute and simplify (-6 + 2x)(6x - 6x^2 + 5 - 6x^3). drag and drop the terms to the correct locations of the table. (-6 + 2x)(6x - 6x^2 + 5 - 6x^3) 6x - 6x^2 5 - 6x -6 2x answer attempt 1 out of 2 you must answer all questions above in order to submit.

Explanation:

Step1: Multiply -6 by each term

$-6\times6x=- 36x$, $-6\times(-6x^{2}) = 36x^{2}$, $-6\times5=-30$, $-6\times(-6x^{3}) = 36x^{3}$

Step2: Multiply 2x by each term

$2x\times6x = 12x^{2}$, $2x\times(-6x^{2})=-12x^{3}$, $2x\times5 = 10x$, $2x\times(-6x^{3})=-12x^{4}$

The filled - in table:

	$6x$	$-6x^{2}$	$5$	$-6x^{3}$
$2x$	$12x^{2}$	$-12x^{3}$	$10x$	$-12x^{4}$

To simplify the product $(-6 + 2x)(6x-6x^{2}+5 - 6x^{3})$, we combine like - terms:
\[

$$\begin{align*} &-12x^{4}+(36x^{3}-12x^{3})+(36x^{2}+12x^{2})+(-36x + 10x)-30\\ =&-12x^{4}+24x^{3}+48x^{2}-26x - 30 \end{align*}$$

\]

Answer:

The filled - in table:

	$6x$	$-6x^{2}$	$5$	$-6x^{3}$
$2x$	$12x^{2}$	$-12x^{3}$	$10x$	$-12x^{4}$

The simplified product is $-12x^{4}+24x^{3}+48x^{2}-26x - 30$