Each side of a square model is divided into parts x and y. The model contains one square of area x², one square of area y², and two rectangles of area xy. Which algebraic identity does this model represent?

Correct answer: (x+y)²=x²+2xy+y²

Direct answer: C, (x+y)²=x²+2xy+y². The full figure is a square because both its total length and total breadth are x+y. Its area is therefore (x+y)². Dividing it into four regions gives one x-by-x square with area x², two x-by-y rectangles with areas xy and xy, and one y-by-y square with area y². Adding these areas gives x²+xy+xy+y²=x²+2xy+y². A is the identity for subtracting lengths, so its middle term is negative. B describes a difference of squares and has no two positive xy rectangles. D has incorrect signs and does not describe these four positive regions. Memory cue: two added rectangular parts produce +2xy.