A visual model consists of one large square, two equal rectangles, and one small square with areas \(a^2\), \(ab\), \(ab\), and \(b^2\), respectively. Which identity does it represent?

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

Answer: A, \((a+b)^2=a^2+2ab+b^2\). Add the four displayed areas: \(a^2+ab+ab+b^2=a^2+2ab+b^2\). The two rectangles produce the positive middle term because both have area \(ab\). The complete outer square has side length \(a+b\), since its side is made from consecutive lengths \(a\) and \(b\); therefore its total area is \((a+b)^2\). This proves option A. B would require the two rectangles to be negative or removed, which is not the model shown. C represents a product of conjugate expressions and has only the two square areas with opposite signs, not two positive rectangles. D incorrectly omits the cross-term \(2ab\). Memory cue: two positive \(ab\) rectangles mean “plus twice ab”; two negative cross-parts would indicate the square-of-a-difference identity.