Question

multiplying polynomials and simplifying expressions
representing perimeter using a polynomial expression
the perimeter formula for a rectangle is 2l + 2w, where l is the length and w is the width.
(8x - 1) in
(2x + 4) in
complete the steps to find an expression that represents the perimeter of the rectangle.

1. substitute the expressions for length and width into the formula 2l + 2w.
2. distribute 2 to each term in the parentheses.
3. combine like terms.

inches
algebra | part 2a 2025-2026

Explanation:

Step1: Substitute length and width

The perimeter formula is \( P = 2l + 2w \), where \( l = 8x - 1 \) and \( w = 2x + 4 \). Substitute these into the formula:
\( P = 2(8x - 1) + 2(2x + 4) \)

Step2: Distribute the 2

Distribute 2 to each term inside the parentheses:
\( 2(8x - 1) = 16x - 2 \) and \( 2(2x + 4) = 4x + 8 \). So now \( P = 16x - 2 + 4x + 8 \)

Step3: Combine like terms

Combine the \( x \)-terms and constant terms:
\( 16x + 4x = 20x \) and \( -2 + 8 = 6 \). Thus, \( P = 20x + 6 \)

Answer:

The perimeter expression is \( 20x + 6 \) inches.