Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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

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

share|cite|improve this question
It's already pretty simplified. I think you want its expansion, and for that you should look up the binomial theorem. – Qiaochu Yuan Nov 1 '10 at 23:50
That's as simple as it can get. What exactly do you need, because it seems you don't need the "simple" expression... – J. M. Nov 1 '10 at 23:50
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. – Ross Millikan Nov 1 '10 at 23:52
It will be 1^n + x^n, that is, assuming n is prime and we are in a field with characteristic n ! – crasic Nov 2 '10 at 2:19
up vote 2 down vote accepted

$$1 + n$$

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

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

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

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

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

See if you can spot a pattern!

share|cite|improve this answer
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. – Ben Nov 2 '10 at 0:19
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 $ – crasic Nov 2 '10 at 2:24

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.