In a visual model, two strips of width \(b\) are removed from a square of side \(a\). When the common \(b\times b\) corner is added back once, which identity is represented, where \(a>b\)?

Correct answer: \((a-b)^2=a^2-2ab+b^2\)

The direct answer is A: \((a-b)^2=a^2-2ab+b^2\). Begin with the original square, whose area is \(a^2\). Each removed strip has dimensions \(a\times b\), so each has area \(ab\). Removing both strips gives \(a^2-2ab\). However, the two strips overlap in the corner square of area \(b^2\); that corner was subtracted twice, so it must be added once. The remaining figure is a square whose side is \(a-b\), and its area is therefore \((a-b)^2\). Option B is the difference-of-squares identity and involves two complete squares, not this two-strip removal. Option C is the square-of-a-sum identity, so it has a positive middle term. Option D has no valid general area interpretation and fails by expansion. Memory cue: remove two rectangles, then add their overlap once.