In a visual proof, ((a+b)^2-(a-b)^2) is rearranged into four equal rectangles. What is the area of each rectangle?

Correct answer: ab

The direct answer is D: each rectangle has area ab. Apply the difference-of-squares identity with A=a+b and B=a-b: A^2-B^2=(A-B)(A+B). The first factor is (a+b)-(a-b)=2b, and the second is (a+b)+(a-b)=2a. Hence the total difference is (2b)(2a)=4ab. The visual proof says this total area is rearranged into four equal rectangles, so each one has area 4ab divided by 4, namely ab. A is the total area, not the area of one rectangle. B would be half the total and does not fit four equal parts. C is the difference of the separate squares a^2 and b^2, not this expression. D is correct. Memory cue: when a total area is split into four equal pieces, divide by four after simplifying the total.