A square model is divided using lengths \(a\) and \(b\). It contains one square of area \(a^2\), one square of area \(b^2\), and two equal rectangles each of area \(ab\). Which identity does it represent?

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

The correct answer is A: \((a+b)^2=a^2+2ab+b^2\). The outside shape is a square whose side is made from two lengths, \(a+b\), so its total area is \((a+b)^2\). The internal pieces have areas \(a^2\), \(ab\), \(ab\), and \(b^2\). Adding them gives \(a^2+ab+ab+b^2=a^2+2ab+b^2\). The two equal rectangles are important because they create two copies of \(ab\), not one. Option B would require the two cross-regions to have negative area or to be subtracted, which does not match the stated model. Option C describes a product of conjugate binomials and would have one positive and one negative contribution, giving no two positive \(ab\) rectangles. Option D incorrectly omits the two cross-products. A reliable memory cue is: a plus-shaped division of a square contains two positive cross-rectangles, so the middle term must be \(+2ab\).