# Binomial-theorem Sentence Examples

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.The

**binomial theorem**for positive integral index may then be written (x + y) n = -iyi +.If we represent this expression by f (x), the expression obtained by changing x into x-+-h is f(x+h); and each term of this may be expanded by the

**binomial theorem**.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.More generally, if we have obtained a as an approximate value for the pth root of N, the

**binomial theorem**gives as an approximate formula p,IN =a+6, where N = a P + pap - 19.If we make large enough to expand the numerator using the

**binomial theorem**(so that behaves as ), then as.Example 1.. 15 Use the

**binomial theorem**to expand (x + y) 5.