Why does the xy term not remain when a rectangle with sides (x+y) and (x−y) is expanded in an area model?

Correct answer: Because the xy and −xy terms cancel each other

The direct answer is option A. Divide the rectangle into four parts by using x and y along one direction and x and −y along the other. The four signed areas are x·x = x², x·(−y) = −xy, y·x = xy, and y·(−y) = −y². The two middle contributions are equal in magnitude but opposite in sign: xy + (−xy) = 0. Therefore the xy term disappears, leaving x² − y². Option B is wrong because two xy-shaped regions are formed; their values cancel rather than fail to exist. Option C is wrong because x² does not become zero. Option D is wrong because the y² contribution is negative here, not the reason for cancellation. The identity is (x+y)(x−y)=x²−y². A useful warning is that unlike terms cannot cancel; only like terms with opposite signs, such as xy and −xy, can do so.