What is the absolute value of the difference between the squares of 101 and 99?
I need to find the absolute value of (101^2 - 99^2). I could use a calculator or do the arithmetic by hand, but I notice that this is a difference of squares, which has a special factorization. I can rewrite (101^2 - 99^2) as (101 + 99)(101 - 99). This simplifies to (200)(2) = 400. The absolute value of 400 is just 400, so that's my answer.

