In a visual model of an algebraic identity, a large square is divided into one small square, two congruent rectangles, and another small square. Which identity does it represent?

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

The correct answer is A: \((a+b)^2=a^2+2ab+b^2\). Imagine a square whose side is made from lengths \(a\) and \(b\), so its full side is \(a+b\). Its total area is therefore \((a+b)^2\). The partition creates one square of area \(a^2\), one square of area \(b^2\), and two congruent rectangles. Each rectangle has length \(a\) and width \(b\), so each has area \(ab\); together they have area \(2ab\). Adding all four regions gives \(a^2+2ab+b^2\). B would require subtraction strips and a negative middle term. C describes two squares whose difference is rearranged into a rectangle, not this four-part large square. D incorrectly omits the two rectangle areas; in general, \(a^2+b^2\) is not equal to \((a+b)^2\). Memory cue: two equal cross-rectangles mean \(2ab\), while two subtraction strips usually signal \(-2ab\).