<s>[INST] Evaluating $\frac{2013^3-2\cdot 2013^2\cdot 2014+3\cdot 2013\cdot 2014^2-2014^3+1}{2013\cdot 2014}$ What is the value of $$\frac{2013^3-2\cdot 2013^2\cdot 2014+3\cdot 2013\cdot 2014^2-2014^3+1}{2013\cdot 2014}?$$

What I have tried:
$$\implies\frac{2013^2(2013-2\cdot2014)+2014^2(3\cdot 2013-2014)+1}{2013\cdot 2014}$$
$$\implies\frac{2013^2(-2015)+2014^2(4025)+1}{2013\cdot 2014}$$
I'm not sure what to do next...
Help is appreciated!
Furthermore, if you are nice, could you also help me on this problem(Transferring bases of numbers.) too?
Thanks!
Max0815
 [/INST] HINT:
Let $a=2013$ and $b=2014$. You have:
$$\frac{a^3 - 2a^2b + 3ab^2 - b^3 + 1}{ab}$$
Recall that $(a-b)^3=a^3-3a^2b+3ab^2-b^3$ and use that to simplify.
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