In a square of side \(m+n\), which can be the largest square part among its four parts?

Correct answer: \(m^2\)

Direct answer: option C, \(m^2\). In the area model for \((m+n)^2\), the four parts are a square of area \(m^2\), two rectangles of area \(mn\) each, and a square of area \(n^2\). Among these, the square-shaped parts are \(m^2\) and \(n^2\). If \(m>n\), then squaring preserves the order for positive lengths, so \(m^2>n^2\); consequently, the \(m^2\) square is the larger square part. The wording “can be” is important because no relation between \(m\) and \(n\) is stated: if \(n>m\), then \(n^2\) would be larger, and if they are equal, the two square parts would be equal. Option A is the area of one rectangle, not a square. Option B is the combined area of two rectangles, not one square part. Option D is a length, while the question asks for a square part described by its area. Memory cue: in \((m+n)^2\), the square pieces are \(m^2\) and \(n^2\); \(mn\) pieces are rectangles.