Question

w.5 add polynomials to find perimeter bas find the perimeter. simplify your answer. x+1 x-1 rectangle diagram x-1 x+1

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \). From the diagram, the length is \( x + 1 \) and the width is \( x - 1 \). Alternatively, we can sum all four sides: \( (x + 1)+(x - 1)+(x + 1)+(x - 1) \).

Step2: Combine like terms

First, expand the sum: \( x + 1 + x - 1 + x + 1 + x - 1 \). Now, combine the \( x \)-terms: \( x + x + x + x = 4x \). Then, combine the constant terms: \( 1 - 1 + 1 - 1 = 0 \). So the perimeter is \( 4x \).

Answer:

\( 4x \)