Question

question
use the box method to distribute and simplify \\((6 - 6x)(4 - 4x^2 + x)\\). drag and drop the terms to the correct locations of the table.
\\((6 - 6x)(4 - 4x^2 + x)\\)
rows:
columns:

Explanation:

Step1: Set up box dimensions

The first binomial $(6-6x)$ has 2 terms, so rows = 2. The trinomial $(4-4x^2+x)$ has 3 terms, so columns = 3.

Step2: Fill box with products

	$4$	$-4x^2$	$x$
$-6x$	$-6x\times4=-24x$	$-6x\times(-4x^2)=24x^3$	$-6x\times x=-6x^2$

Step3: Combine like terms

Group and add terms:
$24 + (6x-24x) + (-24x^2-6x^2) + 24x^3$
$=24 -18x -30x^2 +24x^3$

Step4: Rearrange in standard form

Sort terms by descending degree:
$24x^3 -30x^2 -18x +24$

Answer:

Completed Box:

	$4$	$-4x^2$	$x$
$-6x$	$-24x$	$24x^3$	$-6x^2$

Simplified Polynomial:

$24x^3 - 30x^2 - 18x + 24$