Basic Expanding & Factorising
How do I expand brackets?
- Expanding brackets means multiplying all the terms inside a bracket by the term outside of the bracket
- For GCSE Mathematics you will have learnt how to expand a single bracket
- Multiply each term inside the bracket by the term outside the bracket
- You will also have learnt how to expand double brackets
- You can turn this into two single brackets by multiplying each term inside one bracket by the other bracket
- For Level 2 Further Mathematics you might get more than two terms in a bracket
- Therefore using a grid or turning the expression into single brackets will be more helpful than using FOIL
- A bracket that is raised to the power of 2 can also be written as a double bracket
- Write as a double bracket and then expand
- Do not just square each term inside the bracket
- Be very careful when working with negatives
- Remember to simplify expressions where possible
How do I factorise out a term from an expression?
- Factorising is the opposite of expanding
- Firstly find the highest common factor of each term in the expression and put this outside a bracket
- The highest common factor could be a single number or a variable or both
- If the terms involve the same variable(s) to different powers then the highest common factor will include the variable(s) with the smallest power
- The highest common factor could also contain brackets
- The highest common factor could be a single number or a variable or both
- Then find what you need to multiply the highest common factor by to get each term
- You might need to use the index law:
Worked example
Expand and simplify .
The second bracket has more than two terms so turn the expression into single bracket expansions
Collect like terms
(b)
Factorise fully .
There are two terms in this expression; and
Both contain the common factor
As a bracket is a factor, using "big square brackets" can help keep track of what's left
Simplify the "big square brackets"
The whole expression is now fully simplified (but it's always worth checking!)