2000 SMT/Algebra Problems/Problem 2

Problem 2

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

I can rewrite the first $1999$ as $(2000-1)$ , and the third $2000$ as $(1999+1)$ ;

$2000^3 - 2000^2(2000-1) - 1999^2(1999+1) + 1999^3$

$= 2000^3 - 2000^3 + 2000^2 - 1999^3 - 1999^2 + 1999^3$

$= 2000^2 - 1999^2$

$= (2000 - 1999)(2000 + 1999)$

$= 3999 \qquad \blacksquare$