Binomial Theorem
Pronunciation: /baɪˈnoʊ.mi.əl ˈθiər.əm/ Explain
The binomial theorem states that when raising a
binomial
to an integer power, the binomial coefficients can
be calculated using the combination
where
n is the integer power, and
k
is the order of the coefficient.
^{[2]} This is expressed mathematically with the expression
Start with the simple binomial
In this expression
So the first term is
The next two terms are
and
This gives a result of
You can use long multiplication to verify this result.
References
- McAdams, David E.. All Math Words Dictionary, binomial theorem. 2nd Classroom edition 20150108-4799968. pg 27. Life is a Story Problem LLC. January 8, 2015. Buy the book
- binomial theorem. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 6/19/2018. http://www.merriam-webster.com/dictionary/binomial theorem. Buy the book
- Fine, Henry B., Ph. D.. Number-System of Algebra Treated Theoretically and Historically. 2nd edition. pp 44-53. www.archive.org. D. C. Heath & Co., Boston, U.S.A.. 1907. Last Accessed 6/19/2018. http://www.archive.org/stream/thenumbersystemo17920gut/17920-pdf#page/n53/mode/1up/search/binomial. Buy the book
More Information
- McAdams, David E.. Binomial. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/22/2018. http://www.allmathwords.org/en/b/binomial.html.
Cite this article as:
McAdams, David E. Binomial Theorem. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/b/binomialtheorem.html.
Image Credits
Revision History
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
6/22/2018: Removed broken links, updated license, implemented new markup. (
McAdams, David E.)
12/19/2009: Added "References". (
McAdams, David E.)
12/3/2008: Changed equations to images. (
McAdams, David E.)
6/28/2008: Replaced equations with dHot_Eqn.class (
McAdams, David E.)
6/7/2008: Corrected link errors. Corrected spelling (
McAdams, David E.)
4/18/2008: Initial version. (
McAdams, David E.)