GCSE · Algebraic manipulation

Factorising with common factorsExam-style questions

Why factorising is expansion run backwards, what "factorise fully" demands, and why a difference of two squares splits instantly — plus what the factorised form is actually FOR.

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13 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 1Level 2Level 3Level 4Level 5
  1. 1
    Factorise fully 12x2y−18xy212x^2y - 18xy^2
    Level 4 · 2 marksTry it
  2. 2
    Factorise

    (a) y2−49y^2 - 49

    (b) 4a2−25b24a^2 - 25b^2
    Level 4 · 3 marksTry it
  3. 3
    Mia says that x2−9x^2 - 9 factorises as (x−3)2(x - 3)^2.

    Explain why Mia is wrong, and factorise x2−9x^2 - 9 correctly.
    Level 4 · 2 marksTry it
  4. 4
    Factorise fully 20a3b2−15a2b420a^3b^2 - 15a^2b^4
    Level 4 · 2 marksTry it
  5. 5
    Factorise 81−16m281 - 16m^2
    Level 4 · 2 marksTry it