Which of the following partitions is correct in a visual model of the identity \((a+b)^2\)?

Correct answer: A square of side \(a+b\): one \(a^2\) square, one \(b^2\) square, and two \(ab\) rectangles

Answer: A. Split each side of the large square of side \(a+b\) into lengths \(a\) and \(b\). The four resulting regions are an \(a\)-by-\(a\) square with area \(a^2\), a \(b\)-by-\(b\) square with area \(b^2\), and two rectangles measuring \(a\)-by-\(b\), each with area \(ab\). Thus the total is \(a^2+ab+ab+b^2=(a+b)^2\). B leaves out one rectangle, so its total is too small. C describes a different rectangle and is related to the difference of squares. D counts two \(a^2\) squares that do not arise from this partition. Memory cue: splitting both directions creates four pieces: square, rectangle, rectangle, square.