Why is the small \(b^2\) square added in the visual model of \((a-b)^2\)?

Correct answer: Because the corner is subtracted twice

Direct answer: A is correct. Start with a large square of side \(a\), so its area is \(a^2\). To make a square of side \(a-b\), remove a strip of width \(b\) from one side; its area is \(ab\). Remove another strip of width \(b\) from the adjacent side; its area is another \(ab\). The small corner where the strips overlap has dimensions \(b\) by \(b\), so its area is \(b^2\). That corner has been included in both removed strips and therefore subtracted twice. We add it back once, giving \(a^2-ab-ab+b^2=a^2-2ab+b^2\). B is wrong because the corner is removed as part of both strips. C is wrong because the original \(a^2\) is not increased. D is wrong because \(2ab\) is subtracted, not added. Memory cue: in a square of a difference, subtract two \(ab\) parts and restore the doubly counted \(b^2\) corner.