Thursday, 5 July 2018

BINOMIAL THEOREM NOTE BY PLANCESS

In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the polynomial (x + y)n into a sum involving terms of the form a xb yc, where the exponents b and c are non negative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending on n and b.


The coefficient a in the term of a xb yc is known as the binomial coefficient nb  or nc (the two have the same value). These coefficients for varying n and b can be arranged to form Pascal's triangle. These numbers also arise in combinatorics, where nb  gives the number of different combinations of b elements that can be chosen from an n-element set.

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