In a square area model, each side is divided into two parts, a and b. The areas of the resulting regions are a², ab, ab, and b². Which algebraic identity does this model represent?

Correct answer: (a+b)^2=a^2+2ab+b^2

The direct answer is A: (a+b)^2=a^2+2ab+b^2. Each side of the outside square is split into lengths a and b, so the full side is a+b and the total area is (a+b)^2. The four smaller regions have areas a×a=a^2, a×b=ab, b×a=ab, and b×b=b^2. Adding them gives a^2+ab+ab+b^2=a^2+2ab+b^2. Therefore the model represents option A. B would require the two cross-regions to be negative, which is not the case when the lengths are added. C and D describe the difference-of-squares identity: they involve one plus factor and one minus factor, not a square divided into four positive regions with side a+b. The main memory cue is to count both ab rectangles; forgetting one changes 2ab into ab and leads to an incomplete expansion.