Which expression is represented by the area of a square with side \(u-v\)?

Correct answer: \(u^2-2uv+v^2\)

The correct answer is B. The area of a square is side times side, so a square with side \(u-v\) has area \((u-v)^2\). Apply the identity \((p-q)^2=p^2-2pq+q^2\), with \(p=u\) and \(q=v\). This gives \((u-v)^2=u^2-2uv+v^2\). The negative middle term appears because the two cross-regions are subtracted in the visual arrangement. Option A, \(u^2-v^2\), is the difference of squares and factors as \((u+v)(u-v)\); it is not the square of \(u-v\). Option C is the identity for \((u+v)^2\). Option D does not follow from squaring a binomial. Memory cue: a minus inside a square produces a negative middle term, but the final square term remains positive.