Question

use the box method to distribute and simplify (1 + 6x³ + 4x² - 6x)(-4x - 3). drag and drop the terms to the correct locations of the table.
(1 + 6x³ + 4x² - 6x)(-4x - 3)
rows:
columns:
answer
attempt 1 out of 2

Explanation:

Step1: Order polynomial terms

First polynomial: $6x^3, 4x^2, -6x, 1$; Second: $-4x, -3$

Step2: Create box table

Multiply each row × column term (as above)

Step3: Combine like terms

Sum terms by degree: $-24x^4 -34x^3 +12x^2 +14x -3$

Answer:

First, list the terms of the first polynomial: $6x^3$, $4x^2$, $-6x$, $1$ (ordered by degree). List the terms of the second polynomial: $-4x$, $-3$. Create a 4-row (for first polynomial terms) × 2-column (for second polynomial terms) table and multiply each row term by each column term:

	$-4x$	$-3$
$4x^2$	$-16x^3$	$-12x^2$
$-6x$	$24x^2$	$18x$
$1$	$-4x$	$-3$

Combine like terms:
$-24x^4 + (-18x^3 -16x^3) + (-12x^2 +24x^2) + (18x -4x) + (-3)$
$=-24x^4 -34x^3 +12x^2 +14x -3$

Final simplified form: $-24x^4 - 34x^3 + 12x^2 + 14x - 3$