Fiducia TogetherAlgebraic expression
Letters standing for numbers, and the difference between an expression, an equation, a formula and an identity.
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.
What it is
An expression is a collection of terms with no equals sign: 3x + 2. An equation has an equals sign and can be solved: 3x + 2 = 11. A formula relates quantities: A = πr². An identity is true for every value, written with ≡.
Where it applies
All of algebra, at both tiers.
How it works
The distinction decides what you can DO. You simplify or expand an expression; you solve an equation; you substitute into a formula.
Asking a student to "solve" an expression is a question that cannot be answered, and questions never do.
How to use it in your work
Read whether the question says simplify, expand, factorise or solve. Each wants a different final line.
Never write an equals sign where there is nothing to equal — it costs marks and confuses your own working.
Where to get help
Your teacher, your board's specification for what is on your paper, and Bitesize for worked examples. The maths song runs the topics in order.
Revise this with a song
These are ours. We write revision songs because a lot of people remember a tune when they cannot remember a page, and because revising out loud in the kitchen beats staring at a highlighter.
- The Maths Song The GCSE maths topics, in order.
Where to read more
Last reviewed 2026-08-28 by Fiducia Together · Next review due 2027-08-28
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.