If a square of side a+b is divided into four parts, which partition correctly gives a visual representation of a²+2ab+b²?

Correct answer: One a×a square, one b×b square, and two a×b rectangles

Direct answer: Option A is correct. Divide both sides of the large square, each of length a+b, into parts of lengths a and b. This creates four regions: an a by a square with area a², a b by b square with area b², and two rectangles, each measuring a by b and having area ab. Adding the four regions gives a² + ab + ab + b² = a² + 2ab + b², which is the expansion of (a+b)². Option B has two copies of each square and does not match the four-part division. Option C contains only one ab rectangle, so it misses one ab term. Option D has no a² or b² square. The key warning is that the middle term 2ab comes from two separate equal rectangles.