Which identity is most suitably shown by adding two differently shaded strips to a single (a) by (a) square?

Correct answer: (a+b)^2=a^2+2ab+b^2 / two strips and corner

The correct answer is A: (a+b)^2=a^2+2ab+b^2. Start with one square of side a, whose area is a^2. Add a rectangular strip of dimensions a by b along one side; its area is ab. Add a second strip of the same dimensions along the adjacent side; its area is another ab. The remaining corner is a b by b square with area b^2. The completed figure has side a+b, so its area is (a+b)^2, equal to a^2+ab+ab+b^2=a^2+2ab+b^2. Option A describes addition of both strips and the corner. Option B represents a difference-of-squares arrangement, where a region is removed rather than added. Option C also involves removing strips to make a smaller square of side a-b. Option D is an equivalent difference-of-squares identity but uses a rectangle with sides a+b and a-b, not two added strips to an a-square. Memory cue: added strips give plus signs; removed strips give minus signs.