In a diagram, two \(a\times b\) rectangles are subtracted from a large \(a\times a\) square and a \(b\times b\) square is added back. Which identity is formed?

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

The direct answer is C: \((a-b)^2=a^2-2ab+b^2\). Begin with the large square of side \(a\), whose area is \(a^2\). Removing two rectangles, each measuring \(a\times b\), removes \(ab+ab=2ab\). The small square has side \(b\), so adding it contributes \(b^2\). Therefore the remaining area is \(a^2-2ab+b^2\). This remaining shape is a square with side \(a-b\), so its area is \((a-b)^2\). A has plus signs and describes \((a+b)^2\), where the rectangles are added rather than subtracted. B describes a product of a sum and a difference; its expanded form has no \(b^2\) term. D is an unrelated three-term expression and does not describe this area arrangement. Memory cue: two removed equal rectangles create the middle term \(-2ab\); the added small square supplies \(+b^2\).