GCSE · Algebraic manipulation

Expanding bracketsExam-style questions

Why a multiplier reaches every term inside a bracket, why double brackets need every-with-every (and where the middle term of a square comes from), and how three brackets fall to the same rule two at a time.

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

DifficultyAllLevel 1Level 2Level 3Level 4Level 5
  1. 1
    Expand 3(x+4)3(x + 4)
    Level 1 · 1 markTry it
  2. 2
    Expand 5(2y−3)5(2y - 3)
    Level 1 · 1 markTry it
  3. 3
    Expand and simplify 3(2x−1)−2(x+4)3(2x - 1) - 2(x + 4) (2 marks)
    Level 2 · 2 marksTry it
  4. 4
    (a) Expand and simplify (x+4)(x−7)(x + 4)(x - 7) (2 marks)
    (b) Factorise fully 6x2−9x6x^2 - 9x (1 mark)
    Level 2 · 3 marksTry it
  5. 5
    (a) Expand and simplify (2x+3)(x−4)(2x + 3)(x - 4) [2]

    (b) Factorise 4x2−254x^2 - 25 [1]
    Level 2 · 3 marksTry it

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