Question

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

Explanation:

Step1: Set up box dimensions

The first binomial $(x+2)$ has 2 terms (rows), the polynomial $(-6x^3 -2x^2 +6x +2)$ has 4 terms (columns). So the box is 2 rows × 4 columns.

Step2: Fill box with products

Multiply each row term by each column term:

• Row 1 ($x$):

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

• Row 2 ($2$):

$2 \times (-6x^3) = -12x^3$, $2 \times (-2x^2) = -4x^2$, $2 \times 6x = 12x$, $2 \times 2 = 4$

The filled box (rows × columns) is:

	$-6x^3$	$-2x^2$	$6x$	$2$
$2$	$-12x^3$	$-4x^2$	$12x$	$4$

Step3: Combine like terms

Group and add terms with the same exponent:

• $x^4$ term: $-6x^4$
• $x^3$ terms: $-2x^3 -12x^3 = -14x^3$
• $x^2$ terms: $6x^2 -4x^2 = 2x^2$
• $x$ terms: $2x +12x = 14x$
• Constant term: $4$

Step4: Write simplified polynomial

Combine all terms in descending order of exponents.

Answer:

Filled box:

	$-6x^3$	$-2x^2$	$6x$	$2$
$2$	$-12x^3$	$-4x^2$	$12x$	$4$

Simplified expression: $-6x^4 -14x^3 +2x^2 +14x +4$