A square with sides \(m+n\) and \(m+n\) is split into four parts. Which part is not formed?

Correct answer: \(m^2-n^2\)

The direct answer is D: \(m^2-n^2\) is not one of the four individual parts. Split each side of the square into lengths \(m\) and \(n\). The partition creates one \(m imes m\) square with area \(m^2\), two rectangles measuring \(m imes n\), each with area \(mn\), and one \(n imes n\) square with area \(n^2\). Thus the complete area is \(m^2+mn+mn+n^2=m^2+2mn+n^2=(m+n)^2\). A, B, and C all describe actual regions in the partition; B occurs twice. D is a difference of two areas, not the area of one of these four regions. It belongs to the separate identity \(m^2-n^2=(m-n)(m+n)\). A common confusion is to treat any expression obtained from algebra as a physical part of the diagram. Memory cue: the four pieces of a sum-square model are two pure squares and two positive mixed rectangles.