# Numbers | Maths with Lemon

Source: https://mathswithlemon.io/aa-numbers-binomialhl.html


## Binomial extention

"I believe that the Binomial Theorem and a Bach Fugue are, in the long run, more important than all the battles of history" James Hilton


#### Binomial expansion with fraction indices


##### What you have to know:

- You must be able to manipulate simple algebraic expressions (If not, check this lesson)
- You must be able to solve simultaneous equations (If not, check this lesson)

##### Key Points

- 1. Watch the video:
- 2. Read this Notes
- 3. Watch this video on a solved problem.

#### Extra


##### Material and references:

- Hodder Book HL(ISBN: 9781510462366) : 2A

##### Key Points

- You should be able to extend the binomial theorem to fractional and negative indices. If \( |x| < 1 \), then for any \( n \in \mathbb{Q} \), \[ (1 + x)^n = 1 + nx + \frac{n(n - 1)}{2!}x^2 + \frac{n(n - 1)(n - 2)}{3!}x^3 +... \]

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