Question

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

Explanation:

Step1: Set up box dimensions

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

Step2: Fill box with products

Multiply row/column terms:

1. $-x^2 \times -5x = 5x^3$
2. $-x^2 \times 2 = -2x^2$
3. $2x \times -5x = -10x^2$
4. $2x \times 2 = 4x$
5. $-5 \times -5x = 25x$
6. $-5 \times 2 = -10$

Box layout:

	$-5x$	$2$
$2x$	$-10x^2$	$4x$
$-5$	$25x$	$-10$

Step3: Combine like terms

Group and simplify:
$5x^3 + (-2x^2 -10x^2) + (4x + 25x) -10$
$=5x^3 -12x^2 +29x -10$

Answer:

Box Setup:

Rows: 3, Columns: 2

Completed Box:

	$-5x$	$2$
$2x$	$-10x^2$	$4x$
$-5$	$25x$	$-10$

Simplified Polynomial:

$5x^3 - 12x^2 + 29x - 10$