Question

find the area of the rectangle.
(3x + 2) yards
(3x - 2) yards
the area of the rectangle is
(simplify your answer.)

Explanation:

Step1: Recall the area formula for a rectangle

The area \(A\) of a rectangle is given by \(A = \text{length}\times\text{width}\). Here, the length \(l=(3x + 2)\) yards and the width \(w=(3x - 2)\) yards. So, \(A=(3x + 2)(3x - 2)\).

Step2: Apply the difference - of - squares formula

The difference - of - squares formula is \((a + b)(a - b)=a^{2}-b^{2}\). Let \(a = 3x\) and \(b = 2\). Then \((3x + 2)(3x - 2)=(3x)^{2}-2^{2}\).

Step3: Simplify the expression

\((3x)^{2}-2^{2}=9x^{2}-4\).

Answer:

\(9x^{2}-4\) square yards