### Instruction: What is the absolute value of the difference between the squares of 101 and 99?### Response: 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.