In which situation does the area model show (a^2-b^2) instead of (a^2+2ab+b^2)?

Correct answer: A square of side (b) is removed from a square of side (a)

Direct answer: B is correct. Start with a large square whose side is a, so its area is a^2. If a smaller square whose side is b is removed from it, the removed area is b^2. The part left over therefore has area a^2-b^2. This is different from the complete square of side a+b, whose parts are a^2, two rectangles of area ab, and b^2, giving a^2+2ab+b^2. Option A describes addition, so it produces the plus identity, not a difference. Option B correctly describes subtraction of one square from another. Option C adds two ab rectangles and therefore belongs to the middle-term construction of (a+b)^2. Option D describes the expansion of (a-b)^2, which equals a^2-2ab+b^2; it is not the direct large-square-minus-small-square model asked here. Memory cue: “large square minus small square” means a^2-b^2; “two strips” usually signals the middle term.