BINOMIAL THEOREM Definition & Meaning

binomial theorem

Mathematics.

binomial theorem

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 + nx ⁿ^–¹a + [ n ( n –1)/2�� xn ^–² a ² +…+ ( nk ) xn ^–kak + … + an , where ( nk ) = n !/( ��–k )! k !, the number of combinations of k items selected from n

binomial theorem

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-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 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 + 3 a ²b + 3 ab ² + b ³.

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First recorded in 1865–70

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Examples have not been reviewed.

Given his obsession with the binomial theorem, we based the code we created for him on Pascal’s triangle.

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Expand by the binomial theorem and simplify: 8.

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The binomial theorem operates irrespective of the values substituted for its symbols.

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Later still he made what seemed to be approaches toward Newton’s binomial theorem.

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Expand each term by the binomial theorem, and let us fix our attention on the coefficient of yn−1.

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