Factorising & Expanding — GCSE Mathematics Revision
Revise Factorising & Expanding for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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Go to Quadratic EquationsWhat is Factorising & Expanding?
Expanding means multiplying out brackets: a(b + c) = ab + ac. Factorising is the reverse — taking out common factors or writing a quadratic as a product of two brackets. Single-bracket factorising finds the HCF of all terms. Double-bracket factorising splits a quadratic ax² + bx + c into two linear factors. The difference of two squares is a special case: a² - b² = (a+b)(a-b).
Step-by-step explanationWorked example
Expand and simplify (2x + 3)(x - 4). Use FOIL: 2x² - 8x + 3x - 12 = 2x² - 5x - 12.
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Common mistakes
- 1Forgetting to multiply the outer term by EVERY term inside the bracket.
- 2Not collecting like terms after expanding double brackets (missing the middle terms).
- 3Factorising x² + 5x + 6 as (x+2)(x+4) instead of (x+2)(x+3) — the factors must multiply to give 6 AND add to give 5.
- 4Missing the difference of two squares pattern, e.g. not recognising 9x² - 16 = (3x+4)(3x-4).
Factorising & Expanding exam questions
Exam-style questions for Factorising & Expanding with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel and OCR specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Factorising & Expanding
Core concept
Expanding means multiplying out brackets: a(b + c) = ab + ac. Factorising is the reverse — taking out common factors or writing a quadratic as a product of two brackets. Single-bracket factorising fin…
Frequently asked questions
What is the difference of two squares?
It is the identity a² - b² = (a + b)(a - b). Recognise it when you see a subtraction of two perfect squares, like x² - 25 = (x + 5)(x - 5).
How do I factorise when the coefficient of x² is not 1?
For ax² + bx + c where a ≠ 1, find two numbers that multiply to give ac and add to give b. Split the middle term using these numbers, then factorise by grouping.