In an area model, what expansion is obtained by adding the parts of \((x+3)(x+3)\)?

Correct answer: \(x^2+6x+9\)

The correct answer is C, \(x^2+6x+9\). Treat \((x+3)(x+3)\) as a square with both side lengths split into \(x\) and 3. The area model then has four parts: an \(x\) by \(x\) square with area \(x^2\), two rectangles each measuring \(x\) by 3 with areas \(3x\) and \(3x\), and a 3 by 3 square with area 9. Adding them gives \(x^2+3x+3x+9=x^2+6x+9\). Option A includes only one \(3x\) rectangle. Option B incorrectly changes the two middle parts into \(9x\). Option D has the wrong constant term because the small square has area 9, not 3. The identity check is \((a+b)^2=a^2+2ab+b^2\), with \(a=x\) and \(b=3\).