Factoring a difference of 2 cubes I am trying to factorize the expression $(a - 2)^3 - (a + 1)^3$ and obviously I would want to put it in the form of $(a - b)(a^2 + ab + b^2)$
So I start off with the first $(a - b)$ and I get $(a - 2) - (a + 1)$ which I simplify from $(a^2 + a -2a -2)$ to $(a^2 -3a -2)$
Now I'm up to $(a^2 + ab + b^2)$ and I $a^2$ would equal to $(a^2 - 4)$, $ab$ would be $(a - 2) * (a + 1)$ which is $(a^2 + a -2a -2)$  and $b^2$ would be $(a^2 + 1)$..
Then we get $(a^2 - 3a - 2)((a^2 - 4) (a^2 + a - 4a)(a^2 + 1)) $
At this point I get confused because I'm not sure if I did anything correct, and I don't know how to continue this. Any help is much appreciated
Regards,

you have $$(a - 2)^3 - (a + 1)^3=[(a - 2) - (a + 1)][(a - 2)^2+(a - 2)(a + 1) + (a + 1)^2]
\\=[-3][a^2-4a +4+a^2 - a -2 + a^2 +2a+ 1]
\\=-3(3a^2-3a+3)
\\=-9(a^2-a+1)$$
