This topic summary covers Knowledge Organiser: Simplifying Expressions within Simplifying Expressions for GCSE Mathematics. Revise Simplifying Expressions in Algebra for GCSE Mathematics with 11 exam-style questions and 5 flashcards. Use this page as part of a wider topic revision path rather than treating it as an isolated fact. It is section 19 of 19 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Knowledge Organiser: Simplifying Expressions
Key Terms
- Like terms: Terms with the same variable(s) and power(s) (e.g. 3x and 5x)
- Collecting like terms: Adding/subtracting terms that are the same type
- Simplify: Rewrite an expression in its shortest, most compact form
- Index / power: The small number showing how many times to multiply (e.g. x³)
- Substitution: Replacing a letter with a given number value
Must-Know Facts
- 3x and 5x are like terms (both x); 3x and 5x² are NOT like terms (different powers)
- 3x and 3y are NOT like terms (different variables)
- When multiplying: x × x = x², and 3x × 2x = 6x²
- When dividing: 6x² ÷ 2x = 3x (divide coefficients, subtract powers)
- Always substitute negative numbers in brackets: (−3)² = 9, not −9
- The "invisible" coefficient: x means 1x, so 3x + x = 4x
Key Methods
- Collecting like terms: group same variables, add/subtract coefficients
- Multiplying terms: multiply coefficients × multiply variables (add powers)
- Dividing terms: divide coefficients ÷ divide variables (subtract powers)
- Substitution: replace each letter, use brackets for negatives, use BIDMAS
Common Mistakes
- Adding unlike terms: 3x + 2y cannot be simplified — only like terms (same letter and power) can be collected
- Confusing x and x²: 3x + 2x² cannot be simplified — they are different types of term even though they share x
- Sign errors when collecting: In 5x − 3x, the result is 2x not 8x — subtract the coefficients, especially with negatives
- Multiplying powers incorrectly: x² × x³ = x⁵ (add powers), not x⁶ — and x × x = x², not 2x
Practice questions for Simplifying Expressions
Which two terms are like terms?
Explain why 3x + 2x² cannot be simplified to 5x³.
Quick recall flashcards
Like Terms
Terms with same letter and power: 2x and 5x are like terms
Substitution
Replace each letter with its given value, then calculate