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