2000 SMT/Algebra Problems/Problem 2

Problem 2

Evaluate 2000^3 - 1999(2000^2) - 1999^2(2000) + 1999^3

Solution 1 - SUBMITTED BY HOWDOI_YT I can write the first 1999 as 2000-1, and the 3rd 2000 as 1999+1; 2000^3 - 2000^2(2000-1) - 1999^2(1999+1) + 1999^3 = 2000^3 - 2000^3 + 2000^2 - 1999^3 - 1999^2 + 1999^3 = 2000^2 - 1999^2 = (2000 - 1999)(2000 + 1999) = **3999** \qed