In the subtraction model of a square with side a−5, what is the final corner that must be added back?

Correct answer: 25, overlap square

The direct answer is option C: 25. Begin with a square of side a, whose area is a². To make the remaining figure have side a−5, remove a strip of width 5 along one side and another strip of width 5 along the adjacent side. Each strip has area 5a, so subtracting both gives a²−5a−5a=a²−10a. However, the two strips overlap at one corner. That 5 by 5 corner has area 25 and has been subtracted twice, although it should be removed only once. We therefore add 25 back, giving a²−10a+25=(a−5)². Option A is only the area of one strip, not the final correction. Option B is the combined area of the two strips before correcting the overlap. Option D is the area of the original square, not the small corner. Memory cue: in a subtraction model, subtract the two strips and add back the overlap once.