Definitions for binomial theorem
bi·no·mi·al the·o·rem

Princeton's WordNetRate this definition:0.0 / 0 votes

1. binomial theoremnoun

   a theorem giving the expansion of a binomial raised to a given power

WiktionaryRate this definition:0.0 / 0 votes

1. binomial theoremnoun

   A formula giving the expansion of a binomial such as raised to any positive integer power, i.e. . It's possible to expand the power into a sum of terms of the form where the coefficient of each term is a positive integer. For example:

WikipediaRate this definition:0.0 / 0 votes

1. Binomial theorem

   In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the polynomial (x + y)n into a sum involving terms of the form axbyc, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending on n and b. For example, for n = 4, The coefficient a in the term of axbyc is known as the binomial coefficient ( n b ) {\displaystyle {\tbinom {n}{b}}} or ( n c ) {\displaystyle {\tbinom {n}{c}}} (the two have the same value). These coefficients for varying n and b can be arranged to form Pascal's triangle. These numbers also occur in combinatorics, where ( n b ) {\displaystyle {\tbinom {n}{b}}} gives the number of different combinations of b elements that can be chosen from an n-element set. Therefore ( n b ) {\displaystyle {\tbinom {n}{b}}} is often pronounced as "n choose b".

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1. binomial theorem

   The binomial theorem is a mathematical principle used to expand expressions that are raised to a power. It defines the algebraic expansion of powers of a binomial, which is an equation or formula frequently used in algebra and calculus. According to the theorem, any power of (x + y) can be expressed as a sum of terms like ax^by^c, where the coefficients (a) of each term are specifically identified numbers known as binomial coefficients.

WikidataRate this definition:0.0 / 0 votes

1. Binomial theorem

   In elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the power into a sum involving terms of the form axy, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending on n and b. When an exponent is zero, the corresponding power is usually omitted from the term. For example, The coefficient a in the term of axy is known as the binomial coefficient or . These coefficients for varying n and b can be arranged to form Pascal's triangle. These numbers also arise in combinatorics, where gives the number of different combinations of b elements that can be chosen from an n-element set.

Matched Categories

1. • Statistics
   • Theorem

How to pronounce binomial theorem?

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How to say binomial theorem in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of binomial theorem in Chaldean Numerology is: 2

2. Pythagorean Numerology

   The numerical value of binomial theorem in Pythagorean Numerology is: 6

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=binomial theorem
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Binomial_Theorem
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Binomial_Theorem
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=binomial theorem