If a square is divided into parts \(p^2\), \(pq\), \(pq\), and \(q^2\), what is its total area?

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

Direct answer: option B, \(p^2+2pq+q^2\). The total area of a figure made from non-overlapping pieces is found by adding the area of every piece exactly once. Here the four pieces have areas \(p^2\), \(pq\), \(pq\), and \(q^2\). Therefore, total area \(=p^2+pq+pq+q^2=p^2+2pq+q^2\). This is the area form of the identity \((p+q)^2=p^2+2pq+q^2\): one square has area \(p^2\), two middle rectangles have total area \(2pq\), and the other square has area \(q^2\). Option A is incomplete because it omits both \(pq\) parts. Option C belongs to the difference identity \((p-q)^2\), where the middle term is negative, but here both given rectangular areas are positive. Option D is a perimeter-like expression, not an area sum, and it also does not include the products \(p^2\) and \(q^2\). Memory cue: two equal middle rectangles mean \(pq+pq=2pq\).