### Identity NO. 1 : Algebra

18Sep07

Today used all my fuel resources for the next week. But lucky in Katowice I’ve learned something extremely beautiful.

Truth is the following identity:

$x^4 + y^4 + z^4 - 2x^2y^2 - 2y^2z^2 - 2x^2z^2 = \\ (x+y+z)(x+y-z)(x-y+z)(-x+y+z)$

Pretty cool, huh?

It’s easy to get from the right side to the left side, but the inverse way doesn’t look that easy.

But it is J. All you got to do is to solve the square equation looking for x and treat y, z as parameters.