Which area model represents the identity (a+b)^2=a^2+2ab+b^2?

Correct answer: A square of side (a+b) divided into a^2, b^2, and two ab rectangles

The direct answer is option A. Start with one large square whose side is a+b. Divide each side into pieces of lengths a and b. The four resulting regions are an a-by-a square with area a^2, an a-by-b rectangle with area ab, a b-by-a rectangle with area ab, and a b-by-b square with area b^2. Adding their areas gives a^2+ab+ab+b^2 = a^2+2ab+b^2, which equals (a+b)^2. Option B describes a rectangle with area (a+b)(a−b) = a^2−b^2, so it represents a difference of squares, not a square of a sum. Option C lists separate shapes and misses the two cross-rectangles required by the identity. Option D involves subtraction and does not create the four positive parts in the stated expansion. Memory cue: the middle term 2ab means there must be two congruent ab rectangles.