If the region (a²−b²) in a tile model is rearranged into a rectangle and its length becomes (a+b), what is its width?

Correct answer: (a−b)

The direct answer is option C: a − b. The area of the rearranged rectangle does not change, so area = length × width. We are given area a² − b² and length a + b. Therefore width = (a² − b²)/(a + b). Use the difference-of-squares identity a² − b² = (a + b)(a − b). Cancelling the nonzero factor a + b leaves width a − b. Equivalently, the tile pieces can be rearranged to show the factorisation directly. Option A would make the area (a+b)², not a²−b². Option B has the opposite order and would usually give a negative width when a>b. Option D is a product rather than the required remaining factor. Memory cue: difference of squares splits into sum times difference: a²−b²=(a+b)(a−b).