Expanding removes brackets by multiplying every term inside by the term outside. Factorising is the reverse — writing an expression as a product of factors. At Higher tier you need to expand double brackets and factorise quadratics.
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Revising expanding & factorising the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Expanding & factorising GCSE” on the site for the complete guide.
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Key facts to remember
1Expanding double brackets: (a + b)(c + d) = ac + ad + bc + bd (FOIL method).
2(a + b)² = a² + 2ab + b² — a perfect square.
3(a + b)(a − b) = a² − b² — difference of two squares.
4To factorise x² + bx + c, find two numbers that multiply to c and add to b.
5Always check your factorisation by expanding back out.
6Take out common factors first before attempting to factorise quadratics.