With Descartes the use of exponents as now employed for denoting the powers of a quantity becomes systematic; and without some such step by which the homogeneity of successive powers is at once recognized, the binomial theorem could scarcely have been detected.

The binomial theorem gives a formula for writing down the coefficient of any stated term in the expansion of any stated power of a given binomial.

This is the binomial theorem for a positive integral index.

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Application of Binomial Theorem to Rational Integral Functions.

The binomial theorem is a celebrated theorem, originally due to Sir Isaac Newton, by which any power of a binomial can be expressed as a series.