Question

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

Explanation:

Step1: Set up box dimensions

The first binomial $(5x^2 - 2x)$ has 2 terms (rows), the second $(-2x + 3)$ has 2 terms (columns). So use a 2×2 table.

Step2: Fill box with products

Multiply row/column terms:

• Top-left: $5x^2 \times (-2x) = -10x^3$
• Top-right: $5x^2 \times 3 = 15x^2$
• Bottom-left: $-2x \times (-2x) = 4x^2$
• Bottom-right: $-2x \times 3 = -6x$

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

Step3: Combine like terms

Add $15x^2 + 4x^2 = 19x^2$

Step4: Write simplified polynomial

Combine all terms in descending degree.

Answer:

The filled 2×2 table is:

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

The simplified expression is: $-10x^3 + 19x^2 - 6x$