what is x3 + y3 -z3+3xyz

the given expression is : $x^{3} + y^{3} - z^{3} + 3 x y z$

using the identity: $a^{3} + b^{3} + c^{3} - 3 a b c = (a + b + c) (a^{2} + b^{2} + c^{2} - a b - b c - c a)$

therefore

$x^{3} + y^{3} - z^{3} + 3 x y z$

$= x^{3} + y^{3} + (- z)^{3} - 3 * x * y * (- z) = (x + y - z) [x^{2} + y^{2} + z^{2} - x y + y z + z x]$

hope this helps you.

cheers!!