A side of a square is divided into two parts, x and y. The visual model contains one square of area x², one square of area y², and two rectangles each of area xy. Which algebraic identity does this model represent?

Correct answer: (x+y)² = x² + 2xy + y²

The direct answer is option A. The entire square has side length x+y because the original side is split into adjacent parts x and y. Therefore its total area is (x+y)². The partition contains one x-by-x square with area x², one y-by-y square with area y², and two crosswise rectangles, each with area xy. Adding the pieces gives x² + xy + xy + y² = x² + 2xy + y². Option B describes a model with two negative cross-rectangles, which would correspond to (x−y)², not the stated positive pieces. Options C and D concern products of a sum and a difference and do not match two positive xy rectangles. In an area model, count how many xy rectangles appear and inspect their signs. Two positive rectangles mean +2xy. Memory cue: the square of a sum has positive middle term; the square of a difference has negative middle term.