0
$\begingroup$

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

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

  • 2
    It's already pretty simplified. I think you want its _expansion_, and for that you should look up the binomial theorem.2010-11-01
  • 0
    That's as simple as it can get. What exactly do you need, because it seems you don't need the "simple" expression...2010-11-01
  • 0
    You could start with n=2 and use the distributive law. Then you will be on the way for n=3 and may see a pattern.2010-11-01
  • 0
    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

1 Answers 1

2

$$1 + n$$

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

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

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

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

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

See if you can spot a pattern!

  • 1
    Thanks muad. Generalizing the expansion would take the notation used on the binomial theorem page, I presume, with coefficients matching entries in pascals triangle. I will have to work out how to insert mathematical notation here.2010-11-02
  • 0
    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