Expanding, Factorising and Algebraic Fractions
Manipulate expressions through collection, expansion, factorisation and algebraic fractions.
How to study for GCSE Mathematics
Use 601 original multiple-choice questions to learn connected methods, explain why they work, practise exact non-calculator execution and use a calculator strategically on designated papers.
Core concepts
Concept 1
Collecting like terms
Exam cue: Preserve every sign, expand systematically, then factor by identifying the greatest common structure.
Concept 2
Single and double brackets
Exam cue: Re-expand a factorised answer or substitute a permitted value into the original and simplified forms.
Concept 3
Factorisation and algebraic fractions
Exam cue: Represent the information clearly, choose a justified method and communicate each step with correct notation and units.
Targeted study blocks
Tier coverage
Foundation core with Higher-tier extensions
Foundation expands and factorises simpler expressions and quadratics. Higher includes more complex quadratics, identities, proof and algebraic-fraction manipulation.
Calculator structure
Prepare for calculator and non-calculator papers
Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Risk pitfalls and guardrails
Cancelling terms across addition instead of cancelling common factors.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Giving an unsupported answer when the command requires working, proof, reasoning or interpretation.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Assuming a topic belongs only to calculator or non-calculator papers; any specification content can be assessed on any paper.
Guardrail: Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Memory anchors
Like terms
Terms with the same variable part and powers.
Difference of two squares
a² − b² = (a − b)(a + b).
Cancel algebraic fractions
Factor first, state restrictions, then cancel common factors.
Expanding, Factorising and Algebraic Fractions: method
Preserve every sign, expand systematically, then factor by identifying the greatest common structure.
Expanding, Factorising and Algebraic Fractions: check
Re-expand a factorised answer or substitute a permitted value into the original and simplified forms.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Foundation · AO1 technique · Non-calculator — Simplify 3(x−4)+2(x+5).
Shared F/H · AO1 technique · Non-calculator — Which quadratic is equivalent to the product (x+3)(x−5)?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
What is Pass Harbor?
Completely free exam prep for 247 UK exams.
- Practice questions
- Flashcards
- Study guides
- Mock exams
- No registration
- No paywall
- Start instantly
“No more expensive exam prep. Quality study tools should be accessible to everyone.”