In which situation will a visual model definitely have two equal rectangular strips?

Correct answer: The square model of (a + b)²

Direct answer: A. A square with side a + b can be divided into four parts: one square of area a², one square of area b², and two rectangular regions. Each rectangular region has dimensions a and b, so each has area ab. Thus (a + b)² = a² + ab + ab + b² = a² + 2ab + b². The two middle rectangles are equal because the large figure is a square and the same two lengths occur in both directions. Option A guarantees the pair of equal ab strips. In option B, the two cross-rectangles have areas ab and ac, which are not generally equal. In option C, the corresponding areas are −ab and −ac in a signed model; they are not necessarily equal either. Option D represents a difference of squares, usually by cutting and rearranging pieces, and it does not necessarily contain two equal rectangular strips. Memory cue: the middle term 2ab in (a + b)² comes from two equal ab rectangles.