# Binomial Theorem

The following formula allows one to find the powers of a binomial. It is known as the **binomial theorem**.

Observe that:

The** number of terms** is** n + 1**.

The coefficients are combinatorial numbers corresponding to the nth row of Pascal's triangle.

In the development of the binomial, the exponents of * a* are decreasing, one by one, from

**n**to

**zero**; and the exponents of

**are increasing, one by one, from**

*b***zero**to

**n**, therefore, the sum of the exponents of

**and**

*a***in each term is equal to**

*b***n**.

In the case that one of the terms of the binomial is negative, alternate the positive and negative signs.

#### Examples

1.

2.

3.

4.

5.

6.

**Calculation of the Term which Occupies the Place k **

#### Examples

1. Find the fifth term of the development .

2.Find the fourth term of the development is:

3.Find the eighth term of the development

4.Find the fifth term of the development .

5.Find the independent term of the development .

The exponent of * a* with the independent term is 0, therefore, take only the literal part and equal it to a

^{0}.