When a square of side (m+n) is divided into four parts, which term appears twice?

Correct answer: mn

The correct answer is C: mn. Divide both sides of the square into segments m and n. The four parts are an m-by-m square with area m², an m-by-n rectangle with area mn, another n-by-m rectangle with area mn, and an n-by-n square with area n². Thus the term mn occurs in two separate regions. When the two rectangular areas are combined, they become mn+mn=2mn, which is the middle term in (m+n)²=m²+2mn+n². Option A appears once, in the m² corner square. Option B appears once, in the n² corner square. Option D is the combined total of the two rectangles, not the area of one repeated part. Therefore C is correct. The phrase “appears twice” asks for the individual region label, not their sum.