\[(x - y - z)(x - y - z) =\]
\[= (x - y - z)^{2} = \left( (x - y) - z \right)^{2} =\]
\[= (x - y)^{2} - 2z(x - y) + z^{2} =\]
\[= x^{2} - 2xy + y^{2} - 2xz + 2yz + z^{2} =\]
\[= x^{2} + y^{2} + z^{2} - 2xy - 2xz + 2yz.\]