In a visual model of \(x^2-y^2\), a smaller square of area \(y^2\) is removed from a larger square of area \(x^2\), and the remaining parts are rearranged. What are the sides of the rectangle formed?

Correct answer: \((x+y),(x-y)\)

The direct answer is A: the rectangle has sides \(x+y\) and \(x-y\). The original large square has area \(x^2\), and removing the smaller square of area \(y^2\) leaves \(x^2-y^2\). The difference-of-squares identity says \(x^2-y^2=(x+y)(x-y)\), so the rearranged pieces must form a rectangle with those two side lengths. Option B has area \(y(x+y)\), which is not generally \(x^2-y^2\). Option C has area \(x(x-y)=x^2-xy\), missing the required \(-y^2\) term. Option D has area \((x-y)^2=x^2-2xy+y^2\), a different expression. The rearrangement changes the shape but not the total area. Memory cue: removing one square from another turns the difference of their side lengths into the two factors \(x+y\) and \(x-y\).