A square model has one region of area \(x^2\), two rectangular regions of area \(2x\) each, and four unit squares. Which identity does the complete square represent?

Correct answer: \((x+2)^2=x^2+4x+4\)

The correct answer is A: \((x+2)^2=x^2+4x+4\). Begin with the areas in the model. The large \(x\)-by-\(x\) square has area \(x^2\). The two strips have areas \(2x\) and \(2x\), so together they contribute \(4x\). The four unit squares contribute \(4\). The pieces form one larger square whose side is \(x+2\), so its area is \((x+2)^2\). Expanding confirms that \((x+2)^2=x^2+4x+4\). Option B has a negative middle term and would describe subtraction strips. Option C is a difference-of-squares identity with no middle strips. Option D has only \(2x\), not the required \(4x\), and is not the area of the complete square. Memory cue: for \((x+c)^2\), use \(x^2+2cx+c^2\).