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. $(4 + 2x - 4x^2)(-2 - 3x)$ rows: columns:

Explanation:

Step1: Set up box dimensions

First polynomial has 3 terms, second has 2 terms. So we use a 3-row, 2-column box (or 2-row, 3-column; rows = number of terms in first polynomial, columns = number of terms in second polynomial).
Rows: 3, Columns: 2

Step2: Label box with terms

Label rows with $4$, $2x$, $-4x^2$; label columns with $-2$, $-3x$.

Step3: Calculate each box product

• Row1, Column1: $4 \times (-2) = -8$
• Row1, Column2: $4 \times (-3x) = -12x$
• Row2, Column1: $2x \times (-2) = -4x$
• Row2, Column2: $2x \times (-3x) = -6x^2$
• Row3, Column1: $-4x^2 \times (-2) = 8x^2$
• Row3, Column2: $-4x^2 \times (-3x) = 12x^3$

Step4: Combine like terms

Group and simplify:
$$12x^3 + (-6x^2 + 8x^2) + (-12x - 4x) + (-8)$$
$$=12x^3 + 2x^2 - 16x - 8$$

Answer:

Box Fill (row by row, left to right):

1. $-8$, $-12x$
2. $-4x$, $-6x^2$
3. $8x^2$, $12x^3$

Simplified final expression:

$12x^3 + 2x^2 - 16x - 8$

Box Dimensions:

Rows: 3, Columns: 2