Which model explains the formation of \(2ab\), \(2bc\), and \(2ca\) in \((a+b+c)^2\)?

Correct answer: A square divided into three parts

The correct answer is A: a square divided into three parts. Divide each side of a large square into lengths \(a\), \(b\), and \(c\). The area model contains three diagonal squares with areas \(a^2\), \(b^2\), and \(c^2\). For each pair of different lengths, there are two matching rectangles: two \(a\)-by-\(b\) rectangles give \(2ab\), two \(b\)-by-\(c\) rectangles give \(2bc\), and two \(c\)-by-\(a\) rectangles give \(2ca\). Adding all regions gives \((a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca\). Option B has no two-dimensional areas, option C does not divide the square into these paired rectangles, and option D does not represent the required square expansion. Memory cue: every pair appears twice as two opposite rectangular regions.