What does binomial theorem mean?
Definitions for binomial theorem
bi·no·mi·al the·o·rem
This dictionary definitions page includes all the possible meanings, example usage and translations of the word binomial theorem.
Princeton's WordNet
binomial theoremnoun
a theorem giving the expansion of a binomial raised to a given power
Wiktionary
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:
Wikipedia
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".
ChatGPT
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.
Wikidata
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
Numerology
Chaldean Numerology
The numerical value of binomial theorem in Chaldean Numerology is: 2
Pythagorean Numerology
The numerical value of binomial theorem in Pythagorean Numerology is: 6
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"binomial theorem." Definitions.net. STANDS4 LLC, 2024. Web. 13 May 2024. <https://www.definitions.net/definition/binomial+theorem>.
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