binomial theorem | |
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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 + <[i>n(n--1)/2] x^{n}^{--}²a² +…+ (^{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 |
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 x^{m}, the second term is mx^{m-1}y, and for each additional term the power of x decreases by 1 while the power of y increases by 1, until the last term y^{m} is reached. The coefficient of x^{m-r} is m![r!(m-r)!]. Thus the expansion of (a + b)^{3} is a^{3} + 3a^{2}b + 3ab^{2} + b^{3}. |