In an algebra-tile model, if both sides of a square are x+y, which set of tiles is needed to represent its area?

Correct answer: One x² tile, two xy tiles and one y² tile

The correct answer is C. A square with side x+y can be divided by the x and y boundaries in both directions. The x-by-x part is one x² tile. The x-by-y and y-by-x parts are two separate rectangles, each represented by an xy tile. The y-by-y part is one y² tile. Adding these regions gives x²+xy+xy+y²=x²+2xy+y², which is (x+y)². Option A has only one xy tile and misses one of the two cross-regions. Option B gives the y² tile a negative sign, although all lengths and areas in this square are positive. Option D has an extra x² tile. Memory cue: a binomial square has one first square, two cross-rectangles, and one second square.