# binomial theorem

## binomial theorem

noun Mathematics.
the theorem giving the expansion of a binomial raised to any power.

Origin:
1865–70

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World English Dictionary
 binomial theorem —n 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 + nxn--1a + <[i>n(n--1)/2] xn--²a² +…+ (nk) xn--kak + … + an, where (nk) = n!/(n--k)!k!, the number of combinations of k items selected from n

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American Heritage
Science Dictionary
 binomial theorem   Mathematics The 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.
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