Question

use the box method to distribute and simplify $(5x + 1)(-5x^2 + 2x)$. drag and drop the terms to the correct locations of the table.
$(5x + 1)\left(-5x^2 + 2x\
ight)$
rows: o columns: o

Explanation:

Step1: Set up box dimensions

The first binomial $(5x + 1)$ has 2 terms (rows), the second $(-5x^2 + 2x)$ has 2 terms (columns). So we use a 2×2 box.

Step2: Fill box with products

Multiply row terms by column terms:

• Top-left: $5x \times (-5x^2) = -25x^3$
• Top-right: $5x \times 2x = 10x^2$
• Bottom-left: $1 \times (-5x^2) = -5x^2$
• Bottom-right: $1 \times 2x = 2x$

	$-5x^2$	$2x$
$1$	$-5x^2$	$2x$

Step3: Combine like terms

Add the $x^2$ terms: $10x^2 + (-5x^2) = 5x^2$

Step4: Write simplified polynomial

Combine all non-like terms in descending order of exponents.

Answer:

The filled 2×2 box is as shown above, and the simplified expression is $-25x^3 + 5x^2 + 2x$