x^4+y^4+z^4-2x²y²-2x²z²-2y²z²
=(x^4+2x²y²+y^4)-2x²z²-2y²z²+z^4-4x²y²
=(x²+y²)²-2z²(x²+y²)+z^4-4x²y²
=(x²+y²-z²)²-4x²y²
=(x²+y²-z²+2xy)(x²+y²-z²-2xy)
=[(x+y)²-z²][(x-y)²-z²]
=(x+y+z)(x+y-z)(x-y+z)(x-y-z)