Which algebraic expression is best represented by an area model that divides a large square into four parts—two squares of different sizes and two congruent rectangles?

Correct answer: a^2+2ab+b^2

The direct answer is A. Take a large square with side a+b and divide each side into lengths a and b. This creates four regions: an a by a square with area a^2, a b by b square with area b^2, and two congruent rectangles, each measuring a by b and therefore having area ab. Adding all four non-overlapping parts gives a^2+ab+ab+b^2=a^2+2ab+b^2. This is the identity (a+b)^2. B describes a difference of squares, which involves removing regions rather than adding all four parts. C counts only one of the two ab rectangles, so it misses part of the model. D has a negative middle term and corresponds to (a-b)^2, not a large square split using a+b. Memory cue: two matching cross-rectangles always contribute 2ab in a complete square area model.