Which expansion is correctly shown by the area model of a square with side \(x-2\)?

Correct answer: \(x^2-4x+4\)

The correct answer is A, \(x^2-4x+4\). Apply the identity \((a-b)^2=a^2-2ab+b^2\) with \(a=x\) and \(b=2\). This gives \((x-2)^2=x^2-2(x)(2)+2^2=x^2-4x+4\). In the area model, the original \(x^2\) square loses two rectangular strips, each of area \(2x\), and the small corner square of area 4 is accounted for positively, producing the same result. Option B uses the plus identity and therefore has the wrong sign for the middle term. Option C forgets the factor 2 in the two equal strips, so it has \(-2x\) instead of \(-4x\). Option D has both an incorrect sign pattern and an incorrect constant term. Memory cue: for \((x-2)^2\), the middle term is negative and equals twice \(x\) times 2.