A square has side (m-2). Which parts must be subtracted and added from the (m^2) model to get the correct area?

Correct answer: Subtract (4m), add (4)

The direct answer is B: subtract 4m and add 4. Begin with a square of side m, whose area is m^2. To change each side from m to m-2, remove a strip of width 2 along one direction and another strip of width 2 along the other direction. Each strip has area 2m, so the total first subtraction is 2m+2m=4m. However, the 2 by 2 corner lies in both removed strips, so it has been subtracted twice. It must be restored once; its area is 2×2=4. Thus the remaining area is m^2-4m+4, which is exactly (m-2)^2. A subtracts only one strip and is incomplete. B correctly handles both strips and the overlap. C reverses the roles of the removed strips and the corner. D uses 2 rather than the corner area 4. Memory cue: (m-c)^2=m^2-2cm+c^2.