Question

use the box method to distribute and simplify $(-6x - 4)(-x^3 + 4x^2 - x + 6)$. drag and drop the terms to the correct locations of the table.
$(-6x - 4)(-x^3 + 4x^2 - x + 6)$
rows: o columns: o

Explanation:

Step1: Identify table dimensions

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

Step2: Fill table with products

Calculate each row-column product:

• Row $-6x$:

$(-6x)(-x^3) = 6x^4$, $(-6x)(4x^2) = -24x^3$, $(-6x)(-x) = 6x^2$, $(-6x)(6) = -36x$

• Row $-4$:

$(-4)(-x^3) = 4x^3$, $(-4)(4x^2) = -16x^2$, $(-4)(-x) = 4x$, $(-4)(6) = -24$

The completed table is:

	$-x^3$	$4x^2$	$-x$	$6$
$-4$	$4x^3$	$-16x^2$	$4x$	$-24$

Step3: Combine like terms

Group and add terms with the same exponent:

• $x^4$ term: $6x^4$
• $x^3$ terms: $-24x^3 + 4x^3 = -20x^3$
• $x^2$ terms: $6x^2 - 16x^2 = -10x^2$
• $x$ terms: $-36x + 4x = -32x$
• Constant term: $-24$

Step4: Write simplified polynomial

Combine all combined terms in descending order of exponents.

Answer:

Completed table:

	$-x^3$	$4x^2$	$-x$	$6$
$-4$	$4x^3$	$-16x^2$	$4x$	$-24$

Simplified expression: $6x^4 - 20x^3 - 10x^2 - 32x - 24$