Question

find a completely simplified expression for the area of the (blue) shaded rectangle: 4x + 4 4x - 4 area = add work check answer

Explanation:

Step1: Recall the formula for the area of a rectangle

The area \(A\) of a rectangle is given by \(A=\text{length}\times\text{width}\). Here, the length is \(4x + 4\) and the width is \(4x-4\). So, \(A=(4x + 4)(4x-4)\).

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

Let \(a = 4x\) and \(b = 4\). Then \((4x + 4)(4x-4)=(4x)^{2}-4^{2}\).

Step3: Simplify the expression

\((4x)^{2}-4^{2}=16x^{2}-16\)

Answer:

\(16x^{2}-16\)