Algebra | Binomial Theorem

Binomial Theorem

What you’ll learn
Binomial Theorem

Requirements
Basic Combination Knowledge
Description
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What do you understand by Binomial Theorem?
We know how to find the squares and cubes of binomials like a + b and a – b. E.g. (a+b)2, (a-b)3 etc. However, for higher powers calculation becomes difficult. This difficulty was overcome by a theorem known as binomial theorem. It gives an easier way to expand (a + b)n, where n is an integer or a rational number. Total number of terms in expansion = index count +1. g. expansion of (a + b)2, has 3 terms. Powers of the first quantity ‘a’ go on decreasing by 1 whereas the powers of the second quantity ‘b’ increase by 1, in the successive terms. In each term of the expansion, the sum of the indices of a and b is the same and is equal to the index of a + b.
The topics and sub-topics covered in binomial theorem are:
Introduction
Binomial theorem for positive integral indices
Binomial theorem for any positive integer n
Special Cases
General and Middle Term