How do you factorise $x^3z - x^3y - y^3z + yz^3 + xy^3 - xz^3$? I'm trying to factorise
$$ x^3z - x^3y - y^3z + yz^3 + xy^3 - xz^3 $$
into four linear factors.  By plugging it into WolframAlpha I've learned that it's
$$-(x-y)(x-z)(y-z)(x+y+z)$$
My question is: what are the steps involved in factorising the expression? Is there a method I don't know about that I'd have access to with my limited maths?
Really appreciate any help!

Here's the way we did this when I was beginning high school: as it's a symmetric function of 3 variables, at some point we have to break the symmetry. All we meed is remarkable identities:
The expression can be rewritten as
\begin{align*}
(x^3-y^3)z&+(z^3-x^3)y+(y^3-z^3)x  =(x^3-y^3)z+(z^3-y^3+y^3-x^3)y+(y^3-z^3)x\\
& =(x^3-y^3)(z-y)+(y^3-z^3)(x-y)\\
& =(x-y)(z-y)(x^2+xy+y^2)+(x-y)(y-z)(y^2+yz+z^2)\\
&= (x-y)(y-z)(z^2+yz-x^2-xy)\\
&= (x-y)(y-z)\bigl((z-x)(z+x)+y(z-x)\bigr)\\
&=(x-y)(y-z)(z-x)(x+y+z).
\end{align*}
