Answer
$(x+y+z)(x-y-z)=x^{2}-y^{2}-2yz-z^{2}$
Work Step by Step
$(x+y+z)(x-y-z)$
Multiply each term of the first factor with every term of the second factor:
$x(x-y-z)+y(x-y-z)+z(x-y-z)=...$
$...=x^{2}-xy-xz+xy-y^{2}-yz+xz-yz-z^{2}=...$
Combine like terms and simplify:
$...=x^{2}+(-xy+xy)+(-xz+xz)-y^{2}+(-yz-yz)-z^{2}=$
$...=x^{2}-y^{2}-2yz-z^{2}$
