Question

the perimeter formula for a rectangle is 2l + 2w, where l is the length and w is the width. (8x − 1) in
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(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.

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1. distribute 2 to each term in the parentheses.

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1. combine like terms.

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Explanation:

Step1: Substitute length and width

Given length \( l = 8x - 1 \) and width \( w = 2x + 4 \), substitute into \( 2l + 2w \):
\( 2(8x - 1) + 2(2x + 4) \)

Step2: Distribute the 2s

Distribute 2 to each term in parentheses:
\( 2\times8x - 2\times1 + 2\times2x + 2\times4 = 16x - 2 + 4x + 8 \)

Step3: Combine like terms

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

Answer:

1. \( 2(8x - 1) + 2(2x + 4) \)
2. \( 16x - 2 + 4x + 8 \)
3. \( 20x + 6 \)