Inside a square of side \(x+4\), a square of side \(x-4\) is drawn. What is the difference of the two areas?

Correct answer: \(16x\)

Answer: B, \(16x\). The larger square has area \((x+4)^2\), and the smaller square has area \((x-4)^2\). The required difference is therefore \((x+4)^2-(x-4)^2\). Use the identity \((p+q)^2-(p-q)^2=4pq\), with \(p=x\) and \(q=4\): the difference is \(4\cdot x\cdot4=16x\). Direct expansion confirms it: \(x^2+8x+16-(x^2-8x+16)=16x\). A is only half the result. C is the area of a square with side expression involving 4, not the requested difference. D is a constant and ignores \(x\). Memory cue: the difference between the squares of \(x+r\) and \(x-r\) is \(4xr\).