[nooonuii]

$x^4+y^4+z^4=(x+y+z)(x^3+y^3+z^3)-(xy+yz+zx)(x^2+y^2+z^2)+xyz(x+y+z)$

$x^3+y^3+z^2 = (x+y+z)(x^2+y^2+z^2) - (xy+yz+zx)(x+y+z) + xyz(1+1+1)$

$x^2+y^2+z^2 = (x+y+z)(x+y+z) - 2(xy+yz+zx)$