# Factorising

The reverse of expanding: pulling out the biggest common factor and putting the rest in brackets.

Maths (school) · Part 02: Algebra basics · Card 5 of 8 · Last updated 2026-10-19

## Analogy

Like packing: you find what every item shares and take it out the front.

## Example

**6x + 9**

Biggest number in both: 3
6x + 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.

## Related concepts

- [Simplifying expressions](https://studyvisually.com/learn/science/maths-school/maths-school-part-2/maths-school-part-2-concept-1)
- [Substitution](https://studyvisually.com/learn/science/maths-school/maths-school-part-2/maths-school-part-2-concept-2)
- [Expanding brackets](https://studyvisually.com/learn/science/maths-school/maths-school-part-2/maths-school-part-2-concept-3)
- [Double brackets](https://studyvisually.com/learn/science/maths-school/maths-school-part-2/maths-school-part-2-concept-4)

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