In the visual model of a square with side a+b, which partition represents a²+2ab+b²?

Correct answer: One a² square, one b² square, and two ab rectangles

Direct answer: A. Divide each side of the large square into lengths a and b. The resulting four regions are an a by a square with area a², an a by b rectangle with area ab, a second b by a rectangle with area ab, and a b by b square with area b². Adding them gives a²+ab+ab+b²=a²+2ab+b², which is exactly (a+b)². B has two a² squares instead of the two different cross-rectangles. C includes only one ab rectangle and therefore gives a²+ab+b², missing ab. D has the wrong number and type of square regions and omits both cross-rectangles. Memory cue: the 2 in 2ab comes from two identical rectangles, not from one rectangle being doubled by guesswork.