Knowledge Organiser: Expanding Brackets
This topic summary covers Knowledge Organiser: Expanding Brackets within Expanding Brackets for GCSE Mathematics. Revise Expanding Brackets in Algebra for GCSE Mathematics with 14 exam-style questions and 3 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 13 of 13 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 13 of 13
Practice
14 questions
Recall
3 flashcards
Knowledge Organiser: Expanding Brackets
Key Terms
- Expand: Remove brackets by multiplying out every term inside
- Distribute: Multiply the outside term by each term inside the bracket
- FOIL: First, Outside, Inside, Last — method for two brackets
- Collect like terms: Simplify by adding terms with the same variable/power
- Perfect square: (a + b)² = a² + 2ab + b²
- Difference of two squares: (a + b)(a − b) = a² − b²
Must-Know Facts
- Single bracket: multiply the outside term by EVERY term inside
- Negative outside: −3(x + 2) = −3x − 6 (both terms change sign)
- Double brackets: gives 4 products, then collect the x terms
- (x + a)(x + b) = x² + (a+b)x + ab
- (x + 3)² = x² + 6x + 9 (NOT x² + 9)
- (x + 3)(x − 3) = x² − 9 (the middle terms cancel)
Key Formulas
- a(b + c) = ab + ac
- (a + b)(c + d) = ac + ad + bc + bd
- (a + b)² = a² + 2ab + b²
- (a − b)² = a² − 2ab + b²
- (a + b)(a − b) = a² − b²
Common Mistakes
- FOIL errors: Forgetting the outer or inner terms — write out all four products: First, Outer, Inner, Last
- (a + b)² = a² + b²: Wrong — the middle term 2ab is always missing when students rush
- Sign errors: (x − 3)(x − 2) — the constant term is +6 (negative × negative = positive)
- Single bracket: 3(x + 4) — must multiply 3 by BOTH terms: 3x + 12, not 3x + 4
- Difference of two squares: Don't expand (a + b)(a − b) the long way — use a² − b² directly
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Practice Questions for Expanding Brackets
Which expression is equivalent to 3(x + 2)?
Expand -2(3x - 5)
Quick Recall Flashcards
14 questions on Expanding Brackets — practise free
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