Kerala State Board New Syllabus Plus One Maths Notes Chapter 8 Binomial Theorem.

## Kerala Plus One Maths Notes Chapter 8 Binomial Theorem

Binomial theorem gives the expansion of (a + b)n for a rational number ‘n’. In this Unit, we study the binomial theorem for positive integral indices only.

Expanding Binomial Calculator is a free online tool.

I. Binomial Theorem

The expansion of a binomial for any positive integral ‘n’ is given by the binomial theorem.

There are (n + 1) terms in the expansion of (a + b)n.

The sum of the indices of ‘a’ and ‘b’ in every term of the expansion is ‘n’.

The general term in the expansion is tr+1 = nCr an-r br

Middle term in the expansion:

1. If ‘n’ is even, \(\left(\frac{n}{2}+1\right)^{t h}\) term.

2. If ‘n’ is odd, \(\left(\frac{n+1}{2}\right)^{t h}\) and \(\left(\frac{n+1}{2}+1\right)^{b_{t}}\) term.