If a large square is divided into four regions with areas x², xy, xy, and y², which algebraic identity does the model represent?

Correct answer: (x + y)² = x² + 2xy + y²

The correct answer is A. The large square has side length x + y, because its side is made from an x segment and a y segment. Its four regions have areas x², xy, xy, and y². Adding them gives x² + xy + xy + y² = x² + 2xy + y². Since the whole figure is a square of side x + y, its area is also (x + y)². Hence (x + y)² = x² + 2xy + y². Option B has negative middle terms, which would correspond to a subtraction model. Option C is a valid difference-of-squares identity, but it does not match the four positive regions shown. Option D is false because the product of conjugates gives x² − y², not x² + y². Check the signs of the regions before choosing an identity.