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Forgive the total beginner question, it's been a few years since I needed to do this stuff.

What is the expansion of $(1 + x)^n$?

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    It will be 1^n + x^n, that is, assuming n is prime and we are in a field with characteristic n !2010-11-02

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$1 + n$

$1 + 2n + n^2$

$1 + 3n + 3n^2 + n^3$

$1 + 4n + 6n^2 + 4n^3 + n^4$

$1 + 5n + 10n^2 + 10n^3 + 5n^4 + n^5$

$1 + 6n + 15n^2 + 20n^3 + 15n^4 + 6n^5 + n^6$

See if you can spot a pattern!

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    In binomial expansion its written as the sum over all the terms, that is $(x+y)^n = \sum_{k=0}^n \binom{n}{k} x^{n-k}y^k $2010-11-02