# Substitution

Replacing each letter in an expression with a number, then working out the answer.

Maths (school) · Part 02: Algebra basics · Card 2 of 8 · Last updated 2026-10-19

## Analogy

Like filling a blank in a form: the letters are the blanks and the numbers are what you write in.

## Example

**Find 2x^2 - 5 when x = 3**

2 x 3^2 - 5
= 2 x 9 - 5
= 18 - 5
= 13

## In practice

A taxi fare formula such as 3 + 2m gives a price once you put in the miles.

## Practice

### Flashcards

- **What is 2x^2 - 5 when x = 3?** 13. Square first (9), then 2 x 9 = 18, then take away 5.

## Questions people ask

### Why do you square before multiplying in 2x^2?

Powers only apply to the thing directly next to them. In 2x^2 only the x is squared, not the 2. With x = 3, you work out 3^2 = 9 first, then multiply by 2 to get 18. This follows BIDMAS.

### What happens when you substitute a negative number?

Put the negative number in brackets so the sign is not lost. For x = -2 in x^2, write (-2)^2 = 4, which is positive. Without brackets you might wrongly get -4. Brackets keep the whole number squared. Calculators need the brackets typed in too. Forgetting them is one of the most common ways to lose marks in substitution questions.

## Related concepts

- [Simplifying expressions](https://studyvisually.com/learn/science/maths-school/maths-school-part-2/maths-school-part-2-concept-1)
- [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)
- [Factorising](https://studyvisually.com/learn/science/maths-school/maths-school-part-2/maths-school-part-2-concept-5)

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