Problem factorising a simple equation

Question

I have to factorise the equation $x^2-y^2-z^2+2yz+x+y-z$. .How do I do it?Please help.

Answer 1

$$x^2-y^2-z^2+2yz+x+y-z$$ $$=x^2-(y-z)^2+x+y-z$$ $$=(x+y-z)(x-y+z)+(x+y-z)$$ $$=(x+y-z)(x-y+z+1)$$