Question

use the box method to distribute and simplify $(-4x - 2x^2 + 3)(-6 - 6x)$. drag and drop the terms to the correct locations of the table.
$(-4x - 2x^2 + 3)(-6 - 6x)$
rows:
columns:
answer
you must answer all questions above in order to submit.

Explanation:

Step1: Set up box dimensions

First polynomial has 3 terms, second has 2 terms: Rows = 3, Columns = 2.

Step2: Label rows/columns

Rows: $-2x^2$, $-4x$, $3$; Columns: $-6$, $-6x$

Step3: Calculate box entries

1. $(-2x^2)(-6) = 12x^2$
2. $(-2x^2)(-6x) = 12x^3$
3. $(-4x)(-6) = 24x$
4. $(-4x)(-6x) = 24x^2$
5. $(3)(-6) = -18$
6. $(3)(-6x) = -18x$

Step4: Combine like terms

$$12x^3 + (12x^2+24x^2) + (24x-18x) - 18$$
$$=12x^3 + 36x^2 + 6x - 18$$

Box Table:

	$-6$	$-6x$
$-4x$	$24x$	$24x^2$
$3$	$-18$	$-18x$

Answer:

Simplified form: $12x^3 + 36x^2 + 6x - 18$
Rows = 3, Columns = 2 (with table entries as above)