If the side of a square is divided into two parts, x and y, which algebraic identity is represented by the area model of the whole square?

Correct answer: \((x+y)^2=x^2+2xy+y^2\)

The correct answer is A: \((x+y)^2=x^2+2xy+y^2\). The whole square has side length \(x+y\), so its area is \((x+y)^2\). Divide the square using the x-part and the y-part on both directions. This creates four regions: one square of area \(x^2\), two rectangles each of area \(xy\), and one square of area \(y^2\). Adding them gives \(x^2+xy+xy+y^2=x^2+2xy+y^2\). Option A matches all four regions. Option B represents a square with side difference, not a side sum. Options C and D are equivalent forms of the difference-of-squares identity and involve subtraction, so they do not describe this four-part sum model. Memory cue: the two identical middle rectangles produce the term \(2xy\).