In the model of a square with side (a-b), why is (b^2) added after removing two (ab) strips from (a^2)?

Correct answer: Because (b^2) has been removed twice

Direct answer: A. Begin with the large a-by-a square, whose area is a^2. To create the smaller square of side a-b, one strip of width b is removed from the top and another strip of width b from the side. Each strip has area ab. However, the two strips overlap at one corner in a b-by-b square. That corner has area b^2 and is included in both removed strips, so it has been subtracted twice. The desired removal should count it only once. Adding b^2 back once corrects the double subtraction: a^2-ab-ab+b^2=a^2-2ab+b^2=(a-b)^2. Option A states this exact overlap reason. Option B is false because b^2 is generally positive. Option C is false because ab and b^2 are not generally equal. Option D reverses the construction; the original a^2 is the starting area, not an extra amount to subtract. Common warning: “add back” does not mean adding a new region; it corrects an overlap error.