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I know that

$(a+b)^2=a^2+b^2+2ab$ and $(a+b)^3=a^3+b^3+3ab(a+b)$

So i think it must be a formula that describes $(a+b)^n$, but I don't know what.

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$(a+b)^n = \sum_{i=0}^n \binom{n}{i} a^i b^{n-i}$ – user38268 Mar 17 '12 at 14:39
up vote 3 down vote accepted

Use the Binomial Theorem:

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