In an area model of a square of side a, two ab rectangles are removed and their common b² part is added back once. Which identity does this visual model represent?

Correct answer: (a−b)² = a² − 2ab + b²

The direct answer is option A. Begin with the large square of area a². Removing one ab rectangle subtracts ab, and removing two subtracts 2ab, giving a² − 2ab. The two removed regions overlap in a b-by-b square, whose area is b². That common part has been subtracted twice, so it must be added back once. The final area is a² − 2ab + b², which is exactly (a−b)². Option B has positive cross-terms and represents adding strips rather than removing them. Option C is the difference-of-squares identity; it contains no 2ab term and describes a product of two different factors. Option D has an incorrect expansion: (a+b)(a−b) equals a²−b², not the expression shown. The inclusion–exclusion idea is important in the visual model: subtract both removed rectangles, then restore their overlap once. Memory cue: a square of a difference has two negative cross-terms and one positive small square.