A square area model contains regions of areas \(a^2\), \(b^2\), and two congruent rectangles each of area \(ab\). Which identity does it represent?

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

The direct answer is A. The whole figure is a square whose side is made by joining lengths \(a\) and \(b\), so its side is \(a+b\) and its area is \((a+b)^2\). The model is divided into one region of area \(a^2\), one of area \(b^2\), and two congruent rectangles, each of area \(ab\). Adding these areas gives \(a^2+ab+ab+b^2=a^2+2ab+b^2\). Therefore \((a+b)^2=a^2+2ab+b^2\). Option B would require negative mixed regions, which are not shown. Option C describes a difference of squares and would involve subtracting one square. Option D is false because the product of a sum and a difference gives \(a^2-b^2\), not \(a^2+b^2\). Memory cue: two positive \(ab\) rectangles mean \(+2ab\).