In an area diagram, a strip of width b is removed from a big square. Which identity does this show?

Correct answer: (a−b)²=a²−2ab+b²

The correct answer is C. Removing a strip of width b from a square whose side is a leaves a smaller square with side a−b. The area of that remaining square is therefore (a−b)². Expanding it gives (a−b)(a−b)=a²−ab−ab+b²=a²−2ab+b². The two negative ab terms represent the two rectangular portions removed in the area model, while the b-by-b corner is counted back, producing +b². Option A describes adding a strip, not removing one. Option B is not a valid equality in general; the difference of squares is a²−b²=(a+b)(a−b). Option D is not the square identity. The key is to connect removal with subtraction in the side length. Memory cue: a minus inside a square creates a negative double-product term, but the last square remains positive.