A square has each side divided into two parts, \(a\) and \(b\). Which identity represents the total area of the resulting visual model?

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

Correct answer: A, \(a^2+2ab+b^2\). Each side of the large square has length \(a+b\), so its area is \((a+b)^2\). Dividing both directions creates four regions: an \(a\times a\) square of area \(a^2\), two rectangles of area \(ab\) each, and a \(b\times b\) square of area \(b^2\). Adding all regions gives \(a^2+ab+ab+b^2=a^2+2ab+b^2\). Option A is exactly this result. Option B is a difference of squares, so it has no two positive middle rectangles. Option C is the identity for \((a-b)^2\), with negative middle terms. Option D incorrectly counts two copies of each square and omits the correct two \(ab\) contributions. Memory cue: for a plus square, the middle term is always \(+2ab\).