When the square of side x − y is subtracted from the square of side x + 2y, what area does the visual model give?

Correct answer: 6xy + 3y²

The direct answer is C: 6xy + 3y². The required area is (x+2y)² − (x−y)². Instead of expanding both squares separately, use a²−b²=(a−b)(a+b). The first factor is (x+2y)−(x−y)=3y, and the second is (x+2y)+(x−y)=2x+y. Multiplying gives 3y(2x+y)=6xy+3y². Thus C is exact. A has only half the required xy coefficient. B has the wrong sign for the y² term, which should be positive because both factors contribute positive y terms. D has an incorrect xy coefficient. A useful check is direct expansion: (x+2y)²=x²+4xy+4y² and (x−y)²=x²−2xy+y²; subtracting gives 6xy+3y². The cancellation of x² is expected in a difference of squares.