Question

question
use the box method to distribute and simplify $(5x^{2}+2+4x)(x^{2}-5x+4)$. drag and drop the terms to the correct locations of the table
$(5x^{2}+2+4x)(x^{2}-5x+4)$
rows: 3 columns: 3
answer attempt 1 out of 3
you must answer all questions above in order to submit.

Explanation:

Step1: Rearrange polynomials by degree

First polynomial: $5x^2 + 4x + 2$
Second polynomial: $x^2 - 5x + 4$

Step2: Fill box with term products

	$5x^2$	$4x$	$2$
$-5x$	$5x^2 \cdot (-5x) = -25x^3$	$4x \cdot (-5x) = -20x^2$	$2 \cdot (-5x) = -10x$
$4$	$5x^2 \cdot 4 = 20x^2$	$4x \cdot 4 = 16x$	$2 \cdot 4 = 8$

Step3: Combine like terms

• $x^4$ term: $5x^4$
• $x^3$ terms: $4x^3 -25x^3 = -21x^3$
• $x^2$ terms: $2x^2 -20x^2 +20x^2 = 2x^2$
• $x$ terms: $-10x +16x = 6x$
• constant term: $8$

Step4: Combine all simplified terms

$5x^4 -21x^3 +2x^2 +6x +8$

Answer:

Filled box:

	$5x^2$	$4x$	$2$
$-5x$	$-25x^3$	$-20x^2$	$-10x$
$4$	$20x^2$	$16x$	$8$

Simplified polynomial: $5x^4 -21x^3 +2x^2 +6x +8$