Hello Codeforces!
Please help me on this mathematical problem:
Given x and k, (x, k are Natural numbers) Find formula of xk - (x - 1)k, corectly open the brackets.
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What do you mean by formula? Isn't xk - (x - 1)k already a formula?
open the brackets.
Use the binomial theorem:
The first term xk will cancle.
I don't see how is it related to competitive programming at all. You could use Newton's formula to open the brackets and get binomial coefficients, but that won't be easier to calculate (in fact, it would be even harder), so I don't see much use for it. Will you please give a problem where this is needed (or you think this is needed)? It's likely it has more elegant solution than one you propose.