In a square of side (u+v), the areas (u^2+v^2) are shown in a different color. What term is obtained by adding the areas of the remaining two equal rectangles?

Correct answer: (2uv)

The direct answer is option C: 2uv. Imagine the square of side u + v divided into parts of widths u and v in both directions. The u-by-u part has area u², and the v-by-v part has area v²; these are the differently colored squares mentioned in the question. The remaining two parts are rectangles. Each has length u and width v, so each area is uv. Adding the two equal rectangles gives uv + uv = 2uv. This is the middle term in the identity (u + v)² = u² + 2uv + v². Option A gives the area of only one rectangle, not both. Option B is a length expression, not the sum of the two rectangle areas. Option D is a difference of squares and does not represent these two positive rectangular regions. Memory cue: two identical u-by-v rectangles produce the cross-term 2uv.