Question

find a completely simplified expression for the area of the (blue) shaded rectangle: 2x + 9 2x - 9 area =

Explanation:

Step1: Recall the area formula for a rectangle

The area formula for a rectangle is \(A = \text{length}\times\text{width}\). Here, the length is \(2x + 9\) and the width is \(2x-9\). So, \(A=(2x + 9)(2x - 9)\).

Step2: Apply the difference - of - squares formula \((a + b)(a - b)=a^{2}-b^{2}\)

Let \(a = 2x\) and \(b = 9\). Then \((2x + 9)(2x - 9)=(2x)^{2}-9^{2}\).

Step3: Simplify the exponents

\((2x)^{2}=4x^{2}\) and \(9^{2}=81\). So, \(A = 4x^{2}-81\).

Answer:

\(4x^{2}-81\)