Binomial Theorem Introduction

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A binomial is an algebraic expression of two terms which are connected by the operations '+' or '-'.

For example, x - y, a + 3b, x³ + 4y etc. are binomials.

We know that,

For n = 1,2,3,4, the expansion of (a + b)ⁿ, has been expressed in a very systematical manner in terms of combinatorial coefficients. The above expression suggest the conjecture that (a + b)ⁿ should be expressible in the form

for every natural number n.

In fact, this conjecture is valid and we establish it by using the principle of mathematical induction.