What is the Binomial Theorem? (and How to Use It) | Algebra, Binomial Expansion, Summation Notation

What is the binomial theorem and how do we use it? We go over that, including a pretty gnarly binomial theorem example, in today’s math lesson! The binomial theorem is used to expand binomials raised to the power of positive integers.

Expanding binomials that are raised to powers much greater than 2 is a massive pain, and takes a long time. Thankfully, with the binomial theorem, while the process is still a bit difficult, we are able to find the expansions of these expressions much easier. The binomial theorem is also great because it keeps us fresh on binomial coefficients (which are denoted and calculated the same way as combinations), and gives us good practice using summation notation, as well as a host of other fundamental skills.

Happy New Year! Here is to a fruitful and mathful 2019!

I hope you find this video helpful, and be sure to ask any questions down in the comments!

+WRATH OF MATH+

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[WrathofMath]

Happy new year everyone! This is my first lesson in 4K, so if you have a 4K device, bump that resolution up! Most, if not all, future lessons will be in 4K. As I say, these are the swankiest math videos on the internet.

[jingyiwang]

You explain these mathematical concepts really well. And I really enjoy your explanation with some examples. These really help! I will have my discrete mathematics exam tomorrow, in which this will be covered. Thank you so much for your help!

[dintresmith]

You explain concepts very well. Are you able to make videos covering discrete and continuous distributions for Probability Theory? Thank you

[shadowvai]

I didn't understand anything from my doc but thanks to you I can solve any problem 🤍🤍🤍

[garoemarichal]

you are a legend, very good explanation

[isobar]

Hi and thanks for nice and clear explanation. But what about fractional powers...does it still apply?

[mustansirhussain]

Nice explanation and also good method of teaching.
But i think you should write in a good manner in order to attract the viewers.
Love for Pakistan...

[challengedays]

thank you so for the clear explanation.🤩🤩

[Sammy]

Hello. Is there summation notation exactly the same as the binomial formlua

[TheJayaldae]

You didn’t explain how you’re calculating (4 choose 0) (4 choose 1) etc