### Binomial Expansion Basics For A Level Maths

Hello A Level Pure Maths students! **Binomial expansion **is a topic you’ll encounter time and again on your practice exam papers, so it’s certainly worth investing the **time **and **energy** in developing a solid understanding of the underlying principles.

We know that the long and complex-looking formulae can seem a little daunting, but don’t let this put you off! In this blog post, our **in-house Maths expert** Simon breaks down every aspect of this topic specifically to help out **confused A Level students**.

Once you’ve read through the explanation a couple of times and tried the example question, make sure to keep **building on your knowledge** by exploring the more advanced aspects of the topic. You’ll find the links to the relevant revision notes (complete with** diagrams** and **more worked examples**) at the bottom of this post.

#### **Getting started: the Binomial Theorem**

We use this theorem to calculate each of the terms in the expansion.

Now, we could expand in a step-by-step method, however this would be time consuming and prone to error.

Instead, we can use this theorem:

**Using the Theorem in practice**

When applying this theorem, it’s important to work slowly and carefully, using new lines for each step and always double-checking your answers.

*Remember that ! means **factorial *

*5! = 5x4x3x2x1 *

The below example shows each of the terms of the expansion of

**Calculating nCr on a calculator**

Although you may be able to work out the first lines of answers in your head, **you’ll need a calculator** for the majority.

Use the nCr button on your scientific calculator as below.

**Important points to remember**

If asked to calculate a specific term in the expansion, Always go for the r value **one lower than the required term** (because starts at r = 0). For example, to find the 4th term, you are looking for not

- Look at the pattern
- Start at , then etc
- Powers of
**a**start at**n**and decrease by 1 - Powers of
**b**start at 0 and increase by 1

- These are the shortcuts (but they hide the pattern):
**=****= 1****= n**

**Using Binomial Expansion to solve exam-style questions **

You could be asked to calculate the **coefficient** of a particular term in an expansion:

Or to find the** first few terms** of the expansion:

Or to solve problems involving **unknowns:**

**Worked example **

Ready for a worked example? Try this on your own **before** scrolling down to the answer.

**Find the first four terms, in ascending powers of x, in the expansion of**

**Did you get the correct answer? Ready to keep going? Find the full set of revision notes and many more worked examples here: **