Factoring Multiple Variable Polynomials This is in relation to a problem dealing with the three-dimensional analogue of Pell's Equation.  I would like to factor
$ x^3+Dy^3+D^2z^3-3Dxyz $ into $\frac{1}{2}(x+Dy+D^2y)$ and another factor.
I would like just a hint on how to go about doing this as I'm pretty much stumped.
EDIT: I think the factor I was looking for is $\frac{1}{2}(x+Ny+N^2z)$ where $N=D^3$.

You've got the factor wrong.  There is a well-known identity
$$a^3 + b^3 + c^3 - 3abc = \frac{1}{2} \left( a + b + c \right) \left( (a - b)^2 + (b - c)^2 + (c - a)^2 \right)$$
which you were probably thinking of, but to get the correct factorization you should take $a = x, b = \sqrt[3]{D} y, c = \sqrt[3]{D^2} z$. 
