**Binomial Theorem:**

**\boxed{(a+b)^n=\begin{pmatrix}n\\0\end{pmatrix}a^nb^0+\begin{pmatrix}n\\1\end{pmatrix}a^{n-1}b^1+\begin{pmatrix}n\\2\end{pmatrix}a^{n-2}b^2+\begin{pmatrix}n\\3\end{pmatrix}a^{n-4}b^4+……..\begin{pmatrix}n\\n-1\end{pmatrix}a^1b^{n-1}+\begin{pmatrix}n\\n\end{pmatrix}a^0b^n}**

**where a and b are real numbers and n\geq1**

- \begin{pmatrix}n\\0\end{pmatrix},\begin{pmatrix}n\\1\end{pmatrix},\begin{pmatrix}n\\2\end{pmatrix},……….,\begin{pmatrix}n\\n\end{pmatrix} are binomial cofficient.

- a and b are exponents and n is called index.

- The exponent of a decreases from index to zero.

- The exponent of b increases from zero to index.

- The degree of each terms is equal to its index.

- The numbers of terms in the expansion is one greater than its index.

Example

**Using** **Binomial Theorem:**

**\boxed{(a+b)^n=\begin{pmatrix}n\\0\end{pmatrix}a^nb^0+\begin{pmatrix}n\\1\end{pmatrix}a^{n-1}b^1+\begin{pmatrix}n\\2\end{pmatrix}a^{n-2}b^2+\begin{pmatrix}n\\3\end{pmatrix}a^{n-4}b^4+……..\begin{pmatrix}n\\n-1\end{pmatrix}a^1b^{n-1}+\begin{pmatrix}n\\n\end{pmatrix}a^0b^n}**

**HERE**

**put in above expansion.**

you can also see roles theorem