From a large square of side p, two strips of width q are removed from the top and the right. The corner square of area q² is added back because it was removed twice. What is the remaining area?

Correct answer: p² − 2pq + q² — p² − 2pq + q²

The direct answer is A: p² − 2pq + q². The original square has area p². Each removed strip has one dimension p and the other q, so each has area pq. Removing both strips gives p² − pq − pq, or p² − 2pq. However, the top-right corner belongs to both strips. It was therefore subtracted twice even though it should be removed only once. Add that overlapping q by q square back once: p² − 2pq + q². This expression is also (p−q)², which makes sense because the remaining central square has side p−q. B has positive strip terms and represents addition rather than removal. C subtracts the overlap correction incorrectly and loses the two strip areas. D has no correct area decomposition. Memory cue: in overlapping subtraction, subtract both parts and add their common overlap once.