Curriculum fit: GCSE Maths Algebra (Foundation and Higher). US: Grade 6-7 expressions, Algebra I (Common Core Algebra: Seeing Structure in Expressions).
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What Is It?
An algebraic expression uses letters to stand for numbers, for example 3x + 2y − 5. Simplifying means writing it in a shorter, tidier form without changing its value.
Terms are 'like terms' when they have exactly the same letters raised to the same powers. Like terms can be added or subtracted, but unlike terms cannot.
Key Formulas and Ideas
- Like terms: 4x and 7x are like terms; 4x and 7x² are not.
- Multiplying terms: multiply the numbers, then multiply the letters. 3a × 2b = 6ab.
- Dividing terms: divide the numbers and cancel the letters. 6x² ÷ 2x = 3x.
Worked Examples
Collecting Like Terms
Simplify 3x + 2y + 5x − y.
- Group the x terms: 3x + 5x = 8x.
- Group the y terms: 2y − y = y.
- Combine: 8x + y.
✓ Answer 8x + y
Multiplying Terms
Simplify 2a × 3a².
- Multiply the numbers: 2 × 3 = 6.
- Multiply the letters: a × a² = a³.
✓ Answer 6a³
Brackets
Expand and simplify 4(x + 2) − 3(x − 1).
- Expand the first bracket: 4x + 8.
- Expand the second: −3x + 3 (the minus changes both signs).
- Collect like terms: 4x − 3x + 8 + 3 = x + 11.
✓ Answer x + 11
Common Mistakes to Avoid
- Adding unlike terms, such as writing 3x + 2y as 5xy.
- Forgetting that the sign belongs to the term after it: in 5 − 2x, the term is −2x.
- Not changing both signs when a minus sits outside a bracket.
- Writing x × x as 2x instead of x².
- Adding the coefficients of x and x² as if they were like terms.
Practice Questions
Frequently Asked Questions
What is a coefficient?
The number in front of a letter. In 7x the coefficient is 7.
Is 3xy the same as 3yx?
Yes, because multiplication can be done in any order. It is usual to write letters alphabetically.
Keep Going With These Guides
Expanding and Factorising Brackets (Factoring) Explained
Multiply out single and double brackets, take out common factors and use the difference of two squares. GCSE factorising and US factoring.
GCSEHigh SchoolSolving Linear Equations Step by Step (With Examples)
Learn the balance method for solving linear equations, including brackets and x on both sides, with worked examples for GCSE and Algebra 1.
KS3GCSEMiddle SchoolHigh SchoolIndices and Exponent Rules: The Laws of Indices Explained
Learn the index laws for multiplying, dividing and raising powers, plus zero and negative indices. UK indices and US exponent rules, with examples.
GCSEHigh SchoolSources and Review
- DfE: GCSE mathematics subject content and assessment objectives
- Common Core State Standards: Mathematics (high school)
Reviewed by StudyMorrow editorial review on 5 Nov 2026.