Question

find the area of the rectangle. the area of the rectangle is (simplify your answer.) (2x - 7) yards (2x + 7) yards

Explanation:

Step1: Recall the formula for the area of a rectangle

The area \( A \) of a rectangle is given by the product of its length and width, i.e., \( A = \text{length} \times \text{width} \). Here, the length is \( (2x + 7) \) yards and the width is \( (2x - 7) \) yards. So we need to calculate \( (2x + 7)(2x - 7) \).

Step2: Apply the difference of squares formula

The difference of squares formula states that \( (a + b)(a - b) = a^2 - b^2 \). In this case, \( a = 2x \) and \( b = 7 \). Substituting these values into the formula, we get:

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Answer:

The area of the rectangle is \( 4x^2 - 49 \) square yards.