Which partition is correct in the area model of the algebraic identity (a+b)²?

Correct answer: A square of side a+b is divided into one a² square, one b² square, and two rectangles each of area ab.

The direct answer is A. Begin with a square whose side is a+b. Divide each side into segments a and b. This creates four regions: an a by a square with area a², a b by b square with area b², and two rectangles, each with dimensions a by b and area ab. Adding them gives a²+ab+ab+b²=a²+2ab+b², which equals (a+b)². B describes only one rectangle and gives ab, so it misses most of the large square. C concerns a difference, a−b, and does not produce the sum-square identity; its parts would not all be equal in general. D uses a triangle, whose area would be one-half base times height, not the area of the square. Therefore A is correct. Memory cue: the square of a two-term sum always has two equal cross-rectangles.