Question

question
use the box method to distribute and simplify \\((4 + 2x - 4x^2)(-2 - 3x)\\). drag and drop the terms to the correct locations of the table.
\\((4 + 2x - 4x^2)(-2 - 3x)\\)

Explanation:

Step1: Set up the box table

Create a 3-row (for terms of $4+2x-4x^2$) and 2-column (for terms of $-2-3x$) table:

	$-2$	$-3x$
$2x$
$-4x^2$

Step2: Calculate each box entry

Multiply row and column terms:

• $4 \times (-2) = -8$
• $4 \times (-3x) = -12x$
• $2x \times (-2) = -4x$
• $2x \times (-3x) = -6x^2$
• $-4x^2 \times (-2) = 8x^2$
• $-4x^2 \times (-3x) = 12x^3$

Fill the table:

	$-2$	$-3x$
$2x$	$-4x$	$-6x^2$
$-4x^2$	$8x^2$	$12x^3$

Step3: Combine like terms

Group and add terms by degree:

• Cubic term: $12x^3$
• Quadratic terms: $-6x^2 + 8x^2 = 2x^2$
• Linear terms: $-12x - 4x = -16x$
• Constant term: $-8$

Combine all terms: $12x^3 + 2x^2 - 16x - 8$

Answer:

Filled box table:

	$-2$	$-3x$
$2x$	$-4x$	$-6x^2$
$-4x^2$	$8x^2$	$12x^3$

Simplified expression: $12x^3 + 2x^2 - 16x - 8$