Binomial Expression: An expression consisting of two terms, connected by or sign is called binomial expression.

Binomial Theorem: If and are real numbers then for all , we have

This expression has the following properties:

i) It has terms

ii) The sum of the indices of and in each terms is n

iii) The coefficients of terms equidistant from the beginning and the end are equal.

iv) The general term

v) can also be expressed as

vi) Replacing by in the expression , we get

The general term in the expansion of is

vii) Putting and replacing by , in the expression we get

viii) Putting in the expression , we get

This is the expansion of in descending powers of . In this case,

ix) Addition and Subtraction

Similarly,

x) If and denote respectively the sum of odd terms and even terms in the expansion of , then

(a) and

(b)

(c)

(d)