I lost my notes which included the answer to this question, so I was just wondering if I had done it correctly:

I get:

$\displaystyle k(k-1)^2(k-2)^2 - k(k-1)(k-2)^2 - k(k-1)(k-2)^2$

$\displaystyle = k(k-1)^2(k-2)^2 - 2k(k-1)(k-2)^2$

$\displaystyle =k(k-1)(k-2)^2(k-3)$

Thanks.