Find the product:

$(x+y-z)\left(x^{2}+y^{2}+z^{2}-x y+y z+z x\right)$

$=[x+y+(-z)]\left[x^{2}+y^{2}+(-z)^{2}-x y-y \times(-z)-[-z] \times x\right]$

$=x^{3}+y^{3}+(-z)^{3}-3 x \times y \times(-z)$

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