Which arrangement of shapes represents \(a^2+2ab+b^2\) in a square model?

Correct answer: One square of side \(a+b\), containing two squares of areas \(a^2\) and \(b^2\), and two equal rectangles of area \(ab\).

The correct answer is A. The expression \(a^2+2ab+b^2\) is the expansion of \((a+b)^2\), so the complete shape must be a square with side \(a+b\). Divide each side into parts of lengths \(a\) and \(b\). This creates one \(a\)-by-\(a\) square of area \(a^2\), one \(b\)-by-\(b\) square of area \(b^2\), and two \(a\)-by-\(b\) rectangles, each of area \(ab\). Their sum is exactly \(a^2+ab+ab+b^2=a^2+2ab+b^2\). Option B has only one \(ab\) rectangle and does not form the stated complete square. Option C does not ensure the required areas or the terms \(a^2\), \(b^2\), and \(2ab\). Option D describes disconnected rectangles and omits both square terms. The key clue is the coefficient 2: it requires two equal cross-rectangles.