# binomial theorem

noun, Mathematics
1.
the theorem giving the expansion of a binomial raised to any power.
Origin of binomial theorem
1865-1870
1865-70
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2015.
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Examples from the Web for binomial theorem
Historical Examples
• The binomial theorem operates irrespective of the values substituted for its symbols.

• You might as well try to rush the Proof of the binomial theorem.

Walter Besant
• At the age of twenty-one he wrote a treatise upon the binomial theorem, which has had a European vogue.

Sir Arthur Conan Doyle
• (a) Write the middle term of the expansion of by the binomial theorem.

Romeyn Henry Rivenburg
• In this letter he gave a much fuller account of his binomial theorem and indicated a method of proof.

• Very like the binomial theorem as one thought over that comparison.

H. G. Wells
• The activity of mind awakened by music over waters is very different from that awakened by the binomial theorem.

Clayton Hamilton
• At nineteen such a woman is still immature; and moreover until she was twenty, Honoria had not mastered the binomial theorem.

Sir Harry Johnston
• Suppose we are concerned in proving the law of expansion of the binomial theorem.

John Dewey
• A chapter catches my attention in the middle of the volume; it is headed, Newton's binomial theorem.

J. Henri Fabre
British Dictionary definitions for binomial theorem

## binomial theorem

noun
1.
a mathematical theorem that gives the expansion of any binomial raised to a positive integral power, n. It contains n + 1 terms: (x + a)n = xn + nxn1a + [n(n–1)/2] xn²a² +…+ (nk) xnkak + … + an, where (nk) = n!/(n–k)!k!, the number of combinations of k items selected from n
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
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binomial theorem in Science
 binomial theorem   MathematicsThe theorem that specifies the expansion of any power of a binomial, that is, (a + b)m. According to the binomial theorem, the first term of the expansion is xm, the second term is mxm-1y, and for each additional term the power of x decreases by 1 while the power of y increases by 1, until the last term ym is reached. The coefficient of xm-r is m![r!(m-r)!]. Thus the expansion of (a + b)3 is a3 + 3a2b + 3ab2 + b3.
The American Heritage® Science Dictionary
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### Word Value for binomial

12
16
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