GCSE Maths • Foundation & Higher
GCSE Algebra Revision Guide
Build confidence with expressions, brackets, factorising, substitution and algebraic proof with our comprehensive guide.
Foundation
Exam practice
Worked examples
What You'll Learn
Simplify Expressions
Combine like terms and simplify algebraic expressions.
Expand Brackets
Multiply terms inside brackets and simplify the result.
Factorise Expressions
Find the greatest common factor and factorise.
Substitute Values
Replace variables with values and evaluate expressions.
Write Algebraic Proofs
Use algebra to prove statements are always true.
Key Algebra Rules
Like terms
3x + 7x = 10x
Expand brackets
3(x + 4) = 3x + 12
Factorise
6x + 12 = 6(x + 2)
Substitution
If x = 4, then 3x = 12
Proof forms
Even = 2n
Odd = 2n + 1
Algebra Lessons
Collecting Like Terms
Identify matching variables and combine coefficients correctly.
Expanding Brackets
Multiply every term inside a bracket and simplify.
Factorising Basics
Find the greatest common factor & place it outside the bracket.
Substitution
Replace variables with values, use brackets and follow BIDMAS.
Algebraic Proof
Use variables to prove a statement is always true.
Worked Examples
Example 1: Collect like terms
4x + 8 + 6x + 3 = 10x + 11
Step 1: Group like terms.
(4x + 6x) + (8 + 3)
Step 2: Add the coefficients.
10x + 11
(4x + 6x) + (8 + 3)
Step 2: Add the coefficients.
10x + 11
Example 2: Expand brackets
2(x + 5) = 2x + 10
Step 1: Multiply 2 by each term.
2 × x = 2x and 2 × 5 = 10
Step 2: Write without brackets.
2x + 10
2 × x = 2x and 2 × 5 = 10
Step 2: Write without brackets.
2x + 10
Example 3: Substitution
If a = 6, then 2a + 4 = 16
Step 1: Replace a with 6.
2 × 6 + 4
Step 2: Calculate.
12 + 4 = 16
2 × 6 + 4
Step 2: Calculate.
12 + 4 = 16
- Common GCSE Mistakes
- Combining unlike terms (e.g., saying 2x + 3 = 5x)
- Missing negative signs when expanding brackets
- Forgetting to multiply every term in the bracket
- Not placing negative values in brackets when substituting
- Exam Tips
- Show every algebraic step to secure method marks
- Check your factorising by expanding the brackets again
- Use correct notation (e.g., write 4x, not 4 × x)
- Write a clear conclusion for algebraic proof questions
Ready to Practice?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Algebra Tutorial
Clear, step-by-step explanation of expanding brackets, simplifying complex expressions, and solving for x. Perfect for visual learners who need a breakdown of the rules in action.
- 12 minute comprehensive guide
- High-definition whiteboard walk-through
Continue Your GCSE Maths Revision
Continue Your GCSE Maths Revision
Frequently Asked Questions
Like terms are terms that contain the exact same variables raised to the exact same powers. For example, 3x and 5x are like terms and can be added to make 8x. However, 3x and 5y are not like terms, and 3x and 3x² are not like terms.
To expand a single bracket, multiply the term outside the bracket by each term inside the bracket. For example, 3(x + 4) becomes 3 × x + 3 × 4, which simplifies to 3x + 12.
The easiest way to check your factorising is to expand the brackets of your answer. If you end up with the original expression, your factorising is correct.
Always use brackets when substituting negative values, especially when squaring them. For example, if x = -3, then x² should be written as (-3)², which is 9.
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