A square area model has side \(p+q\). It is divided into one square of area \(p^2\), one square of area \(q^2\), and two rectangles each of area \(pq\). Which algebraic identity does this model represent?

Correct answer: \((p+q)^2=p^2+2pq+q^2\)

The direct answer is A. The entire square has side \(p+q\), so its area is \((p+q)^2\). The partition divides that area into four parts: one \(p^2\) square, one \(q^2\) square, and two rectangles each of area \(pq\). Adding them gives \(p^2+pq+pq+q^2=p^2+2pq+q^2\). Therefore \((p+q)^2=p^2+2pq+q^2\). Option B describes a square of side \(p-q\), where the cross terms are negative, not the given all-positive partition. Option C represents a difference of two squares and would require subtraction and factors \(p+q\) and \(p-q\). Option D is false: \((p+q)(p-q)=p^2-q^2\), not \(p^2+q^2\). Memory cue: two equal \(pq\) rectangles create the middle term \(2pq\).