Expanding & Factorising — Year 8 Revision Notes
These notes cover expanding single brackets, collecting like terms, and factorising by taking out a common factor — all at Year 8 (Stage 8) level.
Expanding a single bracket
To expand a bracket, multiply every term inside it by the term outside. So 4(x + 3) = 4 × x + 4 × 3 = 4x + 12. Take care with signs: a negative outside the bracket changes the sign of every term inside, so −2(x − 5) = −2x + 10.
Key Facts & Formulas
- a(b + c) = ab + ac
- 4(x + 3) = 4x + 12
Tips
- Multiply every term inside the bracket, not just the first.
- Decide the sign of each term before writing it down.
Expanding and collecting like terms
Often you expand a bracket and then simplify by collecting like terms. For example, 3(x + 2) + 2x = 3x + 6 + 2x = 5x + 6. Expand first, then gather the x terms and the number terms separately.
Key Facts & Formulas
- 3(x + 2) + 2x = 5x + 6
Tips
- Expand fully before collecting like terms.
- Keep x terms and constant terms in separate groups.
Factorising with a common factor
Factorising is the reverse of expanding. Find the highest common factor of all the terms, write it outside a bracket, and put what is left inside. For 6x + 9, the highest common factor is 3, so it becomes 3(2x + 3). Always check by expanding your answer.
Key Facts & Formulas
- ab + ac = a(b + c)
- 6x + 9 = 3(2x + 3)
Tips
- Take out the highest common factor, not just any factor.
- Check by expanding the bracket again.
Revision Checklist
- I can expand a single bracket, including with negative terms
- I can expand and then collect like terms
- I can factorise by taking out the highest common factor
- I can check my answer by expanding or factorising the other way
Frequently Asked Questions
Is 2(3x + 6) fully factorised?
No. Both terms inside still share a factor of 3, and outside is 2, so the highest common factor of 6x + 12 is 6. Fully factorised it is 6(x + 2).
Build strong foundations in Expanding & Factorising
A free trial class with Teacher Rig helps your Year 8 child master Expanding & Factorising now — so IGCSE Maths feels familiar, not frightening, later.
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