A square of side \(a+b\) is divided into four parts with dimensions \(a\times a\), \(a\times b\), \(b\times a\), and \(b\times b\). Which identity does this model represent?

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

Correct answer: A, \((a+b)^2=a^2+2ab+b^2\). The entire figure is a square whose side is \(a+b\), so its area is \((a+b)^2\). The four partitioned areas are \(a^2\), \(ab\), \(ab\), and \(b^2\). Their total is \(a^2+ab+ab+b^2=a^2+2ab+b^2\). Option A includes both equal rectangular regions. Option B has a negative middle term and belongs to a side of \(a-b\). Option C incorrectly says the two corner squares alone equal the whole square; the two \(ab\) rectangles are missing. Option D includes only one of the two rectangles. A useful check is to count every region before simplifying: two \(ab\) regions must produce \(2ab\).