A side of a square is divided into two parts, a and b. Its area model contains a², b², and two rectangles of area ab. Which identity does this diagram represent?

Correct answer: (a+b)²=a²+2ab+b²

The correct answer is A. Dividing each side into lengths a and b makes the full side a+b, so the large square has area (a+b)². Its four parts have areas a², ab, ab, and b². Adding them gives a²+ab+ab+b²=a²+2ab+b². Option A states exactly this relationship. Option B is wrong because it has a negative middle term; that would correspond to subtracting two ab regions in a difference model. Option C is wrong because it is the difference-of-squares identity and describes a different arrangement involving factors a+b and a−b. Option D is wrong because it leaves out the two ab rectangles and falsely says the sum of two square areas equals the area of the larger square. The diagram supplies two equal positive cross-regions, so their combined contribution must be +2ab. Memory cue: count regions first, then add their areas.