Question

use the box method to distribute and simplify $(-2x - 2)(5 - 4x + 2x^2 + x^3)$. drag and drop the terms to the correct locations of the table. $(-2x - 2)(5 - 4x + 2x^2 + x^3)$ rows: $\boldsymbol{circ}$ columns: $\boldsymbol{circ}$

Explanation:

Step1: Set up box dimensions

The first binomial $(-2x - 2)$ has 2 terms (rows), the polynomial $(5 - 4x + 2x^2 + x^3)$ has 4 terms (columns). So rows=2, columns=4.

Step2: Fill box with products

	$x^3$	$2x^2$	$-4x$	$5$
$-2$	$-2 \cdot x^3 = -2x^3$	$-2 \cdot 2x^2 = -4x^2$	$-2 \cdot (-4x) = 8x$	$-2 \cdot 5 = -10$

Step3: Combine like terms

Combine $x^4$: $-2x^4$
Combine $x^3$: $-4x^3 -2x^3 = -6x^3$
Combine $x^2$: $8x^2 -4x^2 = 4x^2$
Combine $x$: $-10x +8x = -2x$
Constant term: $-10$

Step4: Write simplified polynomial

Arrange terms in descending degree: $-2x^4 -6x^3 +4x^2 -2x -10$

Answer:

Box Setup:

Rows: 2, Columns: 4

Filled Box:

	$x^3$	$2x^2$	$-4x$	$5$
$-2$	$-2x^3$	$-4x^2$	$8x$	$-10$

Simplified Expression:

$-2x^4 -6x^3 +4x^2 -2x -10$