If a square of side (a-b) has final area (a^2-2ab+b^2), why does the (+b^2) part appear?

Correct answer: Because the corner (b^2) part is subtracted twice and added once

The direct answer is B. Start with a large square of area a^2. To represent a square whose side is a-b, remove a strip of area ab from one side and another strip of area ab from the adjacent side. This gives a^2-ab-ab=a^2-2ab. However, the small corner where the two strips meet has area b^2. That corner lies in both removed strips, so it has been subtracted twice even though it should be removed only once. We therefore add it back once, obtaining a^2-2ab+b^2. A is wrong because the corner is not simply left untouched; it is counted twice during subtraction. B correctly describes the correction. C is false because b^2 is zero only when b=0, not always. D is wrong because the expression uses addition and subtraction of areas, not multiplication of a^2 by b^2. Memory cue: in a difference-square model, the corner correction produces the final positive b^2 term.