A 10 by 10 square is reduced by removing strips of width 2 to show an 8 by 8 square. Which numerical identity does this explain?

Correct answer: 8² = 10² − 2·10·2 + 2²

The correct answer is A. Since 8 = 10 − 2, substitute a = 10 and b = 2 into (a − b)² = a² − 2ab + b². This gives 8² = 10² − 2(10)(2) + 2². In the area picture, the original 10 by 10 square has area 10². Removing one strip of area 10·2 and another strip of area 10·2 subtracts 40 in total. Their corner overlap, a 2 by 2 square, has been subtracted twice, so 2² = 4 must be added back. The result is 100 − 40 + 4 = 64 = 8². Option B uses plus signs and represents (10 + 2)², not a reduced square. Option C forgets the two rectangular strips and the overlap correction. Option D adds a corner square without representing the removed strips. Common confusion: when two strips are removed, the overlap is counted twice and must be restored once.