# 8. Binomial Theorem

If you feel like giving up, just look back on how far you are already.

## BINOMIAL THEOREM CLASS 11 MATHS

The expansion of a binomial for any positive integer n is given by Binomial Theorem, which is (a + b)n
= nC0an + nC1an – 1 b + nC2an – 2 b2 + … + nCn – 1 abn – 1 + nCnbn

The coefficients of the expansions are arranged in an array. This array is called Pascal’s triangle.

The general term of an expansion (a + b)n is Tr + 1 = nCran – r. br

In the expansion (a + b)n , if n is even, then the middle term is the $\left ( \frac{n}{2} + 1 \right )^\text{th}$ term. If n is odd, then the middle terms are $\frac{n + 1}{2}$ and $\left ( \frac{n + 1}{2} +1 \right )$ terms.