A square of side m+n is divided into four parts. Two parts have areas m² and n². What is the combined area of the remaining two equal rectangles?

Correct answer: 2mn — 2mn

The direct answer is B: 2mn. A square with side m+n has total area (m+n)². In the four-part model, one m by m square has area m² and one n by n square has area n². The other two regions are rectangles with dimensions m and n, so each rectangle has area mn. Since there are two such rectangles, their combined area is mn+mn=2mn. This gives the identity (m+n)²=m²+2mn+n². A is only the area of one rectangle, not both. C is a length, not an area, and it also lacks the required product of dimensions. D is the sum of the two square regions and does not represent the remaining parts. Memory cue: in a binomial square, the cross term appears twice because the two mixed rectangles are equal.