A visual model compares \(a^2+2ab+b^2\) with \((a+b)^2\) and \(a^2+b^2\). Which area belongs only to the cross rectangles?

Correct answer: \((2ab)\)

The correct answer is C: the combined area of the cross rectangles is \(2ab\). In the square model for \((a+b)^2\), the regions are an \(a^2\) square, a \(b^2\) square, and two cross rectangles. Each cross rectangle has side lengths \(a\) and \(b\), so each area is \(ab\). Since there are two of them, their combined area is \(ab+ab=2ab\). Adding the corner squares gives \(a^2+2ab+b^2\). A is the combined area of the two square regions, not the cross rectangles. B gives the area of only one cross rectangle and misses the second one. D gives a length expression, not an area, because it has only one dimension. The comparison \((a+b)^2-(a^2+b^2)=2ab\) also confirms the answer. Memory cue: the coefficient 2 counts the two identical rectangles.