binomial theorem
noun Mathematics.
the theorem giving the expansion of a binomial raised to any power.
Origin of binomial theorem
First recorded in 1865–70
Words nearby binomial theorem
binomial coefficient,
binomial distribution,
binomial experiment,
binomial nomenclature,
binomial series,
binomial theorem,
binominal,
binormal,
binotic,
binovular,
binoxalate
British Dictionary definitions for binomial theorem
binomial theorem
noun
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 = x n + nx n – 1 a + [ n (n –1)/2] x n – ² a ² +…+ (n k) x n – k a k + … + a n, where (n k) = n !/(n–k)! k !, the number of combinations of k items selected from n
Scientific definitions for binomial theorem
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.