A square has side p+q. It is divided into one square of area p², one square of area q², and two equal rectangles of area pq each. Which identity does this visual model represent?

Correct answer: (p+q)²=p²+2pq+q²

The direct answer is A. The whole figure is a square whose side is p+q, so its total area is (p+q)². The parts have areas p², pq, pq and q². Adding them gives p²+pq+pq+q²=p²+2pq+q². Therefore (p+q)²=p²+2pq+q². B describes the square of a difference; its two cross-regions would contribute a negative middle term in an algebraic representation. C describes a difference of squares and would involve a product of two different side lengths, not one complete square divided into four positive regions. D misses one of the two pq rectangles. The visual count is the key: two equal pq regions always combine to 2pq. Memory cue: square of a sum means first square, twice the product, last square.