Which visual arrangement can most directly show \((a+b)^2-(a-b)^2=4ab\)?

Correct answer: Taking the difference of two square areas and leaving four \(ab\) rectangles

The direct answer is A. Begin with a square of side \(a+b\), whose area is \((a+b)^2\), and compare it with a square of side \(a-b\), whose area is \((a-b)^2\). When the smaller square is subtracted from the larger square, the two \(a^2\) parts cancel and the two \(b^2\) parts also cancel. What remains consists of four rectangular regions, each having side lengths \(a\) and \(b\), so each has area \(ab\). Their total area is therefore \(ab+ab+ab+ab=4ab\). Option B repeats an \(a^2\) region but does not represent the subtraction. Option C removes only one \(b^2\) square, so it cannot produce four \(ab\) rectangles. Option D concerns halving a length, not comparing areas. Memory cue: in a difference-of-squares picture, cancel matching square pieces and count the remaining cross-rectangles.