How to perform this manipulation? (1)        $ z^2y+xy^2+x^2z-(x^2y+xz^2+y^2z) $
(2)        $ (x-y)(y-z)(z-x) $
How to go from STEP (1) to STEP (2). Nothing I do seems to work. I tried combining terms but that doesn't help. 
I do not want to go from step 2 to step 1. I arrived at step 1 in some question and I need to go from 1 to 2 to match my answer given in the textbook.
I see a lot of comments asking me to just expand 2 and arrive at 1. I could see that too but I am really curious to know how it is done the other way around. Added to that, if you get (1) while solving some question, you obviously have to go from 1 to 2 and not from 2 to 1.

Pair the positive and negative terms to get one of the factors
\begin{eqnarray*}
z^2y+xy^2+x^2z-(x^2y+xz^2+y^2z) = z^2y -xz^2+xy^2-x^2y +x^2z-y^2z
\end{eqnarray*}
Pull off this factor
\begin{eqnarray*}
(x-y)(-z^2-xy+(x+y)z)   
\end{eqnarray*}
The content of the second bracket is easily shown to be what is required. 
