In which visual model do \(a^2+2ab+b^2\) and \((a+b)^2\) represent the same area?

Correct answer: A square with side \(a+b\)

Correct answer: A, a square with side \(a+b\). The area of that square is \((a+b)^2\). Divide each side into parts \(a\) and \(b\): the four regions have areas \(a^2\), \(ab\), \(ab\), and \(b^2\). Their sum is \(a^2+2ab+b^2\), so both expressions describe the same total area. Option B gives \((a-b)^2=a^2-2ab+b^2\), with a negative middle term. Option C gives \((a+b)(a-b)=a^2-b^2\), the difference of squares. Option D has area only \(ab\), so it cannot equal the complete expression in general. Memory cue: the outside shape tells you the squared binomial; a side marked \(a+b\) means the positive-square identity.