In a square visual model, one large square is divided into four parts: one square of area a², another square of area b², and two rectangles each of area ab. Which algebraic identity does this model represent?

Correct answer: (a+b)²=a²+2ab+b²

The correct answer is A. The large square has side length a+b, so its total area is (a+b)². The four smaller regions have areas a², ab, ab, and b². Adding them gives a²+ab+ab+b²=a²+2ab+b². Therefore, the model proves (a+b)²=a²+2ab+b². Option B is wrong because the middle term there is −2ab; that identity represents a square built from a difference, not two positive ab rectangles. Option C is wrong because it represents the difference of two squares and has only two factors, not the four positive regions described. Option D is wrong because it incorrectly omits the two ab regions; in general, (a+b)² is not merely a²+b². The important step is to count both identical rectangles, so ab+ab becomes 2ab. Memory cue: a plus square has a positive doubled middle term.