Factorising
The reverse of expanding: pulling out the biggest common factor and putting the rest in brackets.
Last updated
Analogy
Like packing: you find what every item shares and take it out the front.
Example
Biggest number in both: 36x + 9 = 3(2x + 3)Check: 3 x 2x = 6x, 3 x 3 = 9
In practice
Splitting 6 packs and 9 snacks into identical party bags: 3 bags with 2 packs and 3 snacks each.
Practice
Flashcards
- Factorise 6x + 9.3(2x + 3). The biggest common factor is 3.
Questions people ask
How do you check a factorised answer?
Expand it again. If you get back the original expression, you are right. For 3(2x + 3), multiply: 3 x 2x = 6x and 3 x 3 = 9, giving 6x + 9. A quick check like this catches most slips.
How do you factorise with letters, like 4x^2 + 6x?
Take out the biggest number and the most letters shared by both terms. Both have a factor of 2 and an x, so 2x goes outside. Inside you put what is left: 2x(2x + 3). Expanding checks it. Check by expanding: 2x times 2x is 4x^2 and 2x times 3 is 6x, which matches the start.