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# Binomial Expansion Calculator

The binomial formula is used when we have to multiply a binomial by itself for ‘n’ number of times.

## What is a Binomial Expansion Calculator?

'Binomial Expansion Calculator' is an online tool that helps to calculate the expansion of the given binomial term. Online Binomial Expansion Calculator helps you to calculate the expansion of the given binomial term in a few seconds.

## How to Use Binomial Expansion Calculator?

Please follow the steps below on how to use the calculator:

**Step 1:**Enter the binomial term and the power value in the given input boxes.**Step 2:**Click on the**"Expand"**button to find the expansion of the given binomial term.**Step 3:**Click on the**"Reset"**button to clear the fields and enter the new values.

## How to Find Binomial Expansion Calculator?

The binomial formula is used to solve the binomial expression. Binomial is a type of polynomial with exactly two terms. The formula to calculate the binomial expansion is given by

**(a + b) ^{n} = ^{n}C_{0 }a^{n} + ^{n}C_{1 }a^{n - 1 }b + ^{n}C_{2 }a^{n-2} b^{2 }+ ^{n}C_{3 }a^{n - 3 }b^{3} ................ + ^{n}C_{n - 1 }a b^{n - 1 }+ ^{n}C_{n }b^{n}**

Let us see an example to understand briefly.

**Solved Example:**

Expand (x + 5)^{3}

**Solution:**

Given: Expression = (x + 5)^{3}

⇒ (x + 5)^{3} = ^{3}C_{0 x}^{3} + ^{3}C_{1 x}^{3 - 1}(5) + ^{3}C_{2 x}^{3 - 2} (5^{2}) + ^{3}C_{3 x}^{3 - 3 }(5^{3}).

⇒ x^{3} + 15x^{2} + 75x + 125

Similarly, you can try the calculator to expand the given binomial expressions:

- (3x - 5)
^{4} - (2x + 7)
^{7}

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