# Binomial Theorem

**Statement:**

where

*n*is a positive integer.

**Proof of this theorem is done by mathematical induction**

**Proof:**

[

**Note**:

a) The alternate terms are negative

b) The sign of the last term depends on the value of

*n*.]

**Remark:**Even though binomial theorem can be applied for negative integral indices and rational indices [with same conditions attached] we are not dealing with those situations in this chapter.

**Example 1:**Find the expansion of

**Solution:**

**Example 2:**

Simplify using binomial theorem

**Solution:**

**Example 3:**

Find the value of power of 11, using binomial theorem.

**Solution:**