Factoring 4 terms polynomial I am trying to factor the following polynomial: $$ 8x^3 -4x^2y -18xy^2 + 9y^3 $$
$$ (a-b)^3 = a^3 -3a^2b + 3ab^2 - b^3 $$
Thanks
 A: Look at the following factorisation, I thought of:
$$\begin{align*}8x^3-4x^2y-18xy^2+9y^3&=4x^2(2x-y)-9y^2(2x-y)\\&=(4x^2-9y^2)(2x-y)\\&=(2x+3y)(2x-3y)(2x-y)\end{align*}$$
I also want to add that, it is natural to think of the cubic identity you gave us, but $9y^3$ doesn't look good when trying to write as a perfect cube. Also, in particular, in using any identity of this kind, intuitively, since $x^2y$ term has a negative sign, it shoud have come from coefficient of $y$, which means the $y^3$ term must have had a negative coefficient, which is not the case!
Also the negative sign in $xy^2$ suggests on the similar line of thinking that, $x^3$ should have had a negative sign which is also not the case. So, this identity is not worth pursuing here!
Hope this helps!
A: Hint: Maybe look at the pretty much equivalent problem of factoring
$8x^3-4x^2-18x+9$.
We can use the Rational Roots Theorem to find the rational roots of this, if any (and there are).  We can also make life simpler by writing $2x=w$, which yields
$w^3-w^2-9w+9$. 
Or else we can note that
$8x^2-4x^2-18x+9=4x^2(2x^2-1)-9(2x-1)$.
Or else we can start from the original expression, and write it as $4x^2(2x-y)-9(2x-y)$. 
And there are other ways. 
