Expanding and factorising are opposites. Expanding removes brackets: 5(x − 7) = 5x − 35. Factorising puts them back by taking out a common factor: 5x − 35 = 5(x − 7).
To factorise, find the highest common factor of all the terms. For 12x + 18, the HCF of 12 and 18 is 6, so 12x + 18 = 6(2x + 3). Check by expanding your answer: it should give you back what you started with.
Worked example
Factorise fully 10x + 15
- The HCF of 10 and 15 is 5.
- 10x ÷ 5 = 2x and 15 ÷ 5 = 3.
Answer:5(2x + 3)
Key words
- factorise
- write as a product using brackets
- common factor
- a factor shared by all the terms
- fully
- using the highest common factor
Practise this
New questions every time.
Common Core-referenced: 7.EE.A.1