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 $1999+1$ ; $2000^3 - 2000^2(2000-1) - 1999^2(1999+1) + 1999^3$ $= 2000^3 - 2000^3 + 2000^2 - 1999^3 - 1999^2 + 1999^3$ $= 2000^2 - 1999^2$ $= (2000 - 1999)(2000 + 1999)$ $= 3999 \blacksquare$

Page

Toolbox

Search

2000 SMT/Algebra Problems/Problem 2

Problem 2

Solution 1 - SUBMITTED BY HOWDOI_YT