Each side of a square is \(a+b\). It is divided into four regions with areas \(a^2\), \(ab\), \(ab\), and \(b^2\). Which algebraic identity does this visual model represent?

Correct answer: \((a+b)^2=a^2+2ab+b^2\)

Answer: A. The entire figure is a square with side \(a+b\), so its total area is \((a+b)^2\). The four stated regions have areas \(a^2\), \(ab\), \(ab\), and \(b^2\). Adding them gives \(a^2+ab+ab+b^2=a^2+2ab+b^2\). Equating the total area with the sum of the parts produces \((a+b)^2=a^2+2ab+b^2\). B describes a square with subtraction and therefore has a negative middle term. C and D are equivalent forms of the difference-of-squares identity; they involve factors \(a+b\) and \(a-b\), not four regions with two positive \(ab\) parts. Memory cue: two positive \(ab\) regions mean the middle term is \(+2ab\).