# Expanding brackets

Multiplying everything inside the brackets by the number or letter outside.

Maths (school) · Part 02: Algebra basics · Card 3 of 8 · Last updated 2026-10-19

## Analogy

Like handing out a gift to every guest at a table, not just the first one.

## Example

**3(x + 4)**

3 x x = 3x
3 x 4 = 12
So 3(x + 4) = 3x + 12

## In practice

A gym charges 3 pounds per class plus 4 pounds booking: 3(x + 4) means each class costs 3 times (x + 4).

## Practice

### Flashcards

- **Expand 3(x + 4).** 3x + 12. Multiply both terms by 3.

## Questions people ask

### Do you multiply the number by everything inside the bracket?

Yes. Every term inside gets multiplied, not just the first one. In 5(2x - 3), the 5 multiplies 2x to give 10x and also multiplies -3 to give -15. The answer is 10x - 15. Check with x = 1: 5(2 - 3) = -5 and 10 - 15 = -5.

### What if there is a minus sign in front of the bracket?

A minus outside flips the sign of every term inside. So -(x + 4) becomes -x - 4, and -2(x - 3) becomes -2x + 6. Forgetting to flip the second term is the most common mistake. Think of the minus as multiplying by -1.

## 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)
- [Double brackets](https://studyvisually.com/learn/science/maths-school/maths-school-part-2/maths-school-part-2-concept-4)
- [Factorising](https://studyvisually.com/learn/science/maths-school/maths-school-part-2/maths-school-part-2-concept-5)

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