Assume x > y. Which rectangle can directly represent x² − y² as an area?

Correct answer: A rectangle with length x + y and breadth x − y

Direct answer: Option A is correct. The difference-of-squares identity is x² − y² = (x + y)(x − y). Therefore, a rectangle with length x + y and breadth x − y has area (x + y)(x − y), exactly equal to x² − y². The condition x > y ensures that x − y is positive, so it can represent a physical breadth. Option B has area (x − y)², which is a square of the difference, not the difference of the squares. Option C has area x(x − y) = x² − xy. Option D has area (x + y)². None of these equals x² − y² in general. Memory cue: difference of squares factors into conjugate factors with the same middle term and opposite signs.