In an area model of a square with side a, strips of width b are removed along two adjacent sides. The common b×b corner is added once to correct for being removed twice. Which identity does this model represent?

Correct answer: (a−b)²=a²−2ab+b²

Direct answer: Option A is correct. Start with the a by a square, whose area is a². Removing a strip of width b along one side removes area ab, and removing an equal strip along the adjacent side removes another ab. The corner where the strips meet is b by b, so it was counted as removed twice. Adding it back once gives a²−ab−ab+b²=a²−2ab+b². The remaining figure has side length a−b, so its area is (a−b)². Option B describes adding strips rather than removing them. Option C is the difference of two complete squares and uses a different model. Option D forgets the overlap correction and is therefore missing the +b² term. Memory cue: for a square of a difference, subtract two cross-products and add back the corner square.