# Numbers | Maths with Lemon

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


## Binomial expansion

"In mathematics the art of proposing a question must be held of higher value than solving it." Georg Cantor


#### Binomial expansion


##### 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)
- You must know the properties of exponents (If not, check this lesson)

##### Key Points

- 1. Watch the video:
- 2. Read these Notes

#### Extra


##### Material and references:

- Hodder Book SL(ISBN: 9781510462359) : 13B

##### Key Points

- 1. You should be able to use the binomial theorem to expand expressions of the form \( (a + b)^n \), where \( n \in \mathbb{Z}^+ \): The important part of the formula is \[ {^nC_r}a^{n-r}b^r \] which gives all the terms. 2. You should be able to use Pascal’s triangle to find the coefficients in a binomial expansion, and the formula \[ {^nC_r} = \frac{n!}{r!(n - r)!} \] to find the coefficients in a binomial expansion.

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