Discia GCSE Maths › Algebra › Expanding and Factorising Quadratics

Expanding and Factorising Quadratics worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

10 questions 22 marks Sheet 1
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  1. 2 marks

    Expand and simplify \((2y - 7)(3y - 7)\)

  2. 2 marks

    Expand and simplify \((2x + 7)^2\)

  3. 2 marks

    Write \(w^2 + 6w + 5\) as a product of two brackets.

  4. 3 marks
    (a)

    Expand and simplify \((w + 11)(w - 11)\)

    (b)

    Factorise \(16w^2 - 49\)

  5. 2 marks

    \((y + 5)(y + a) = y^2 + 10y + 25\)

    Calculate the value of \(a\).

  6. 2 marks

    Factorise fully \(2y^2 - 11y - 6\)

  7. 2 marks

    Write \((4t + 5)(2t - 3)\) in the form \(at^2 + bt + c\), where \(a\), \(b\) and \(c\) are integers.

  8. 2 marks

    Write \((w + 4)^2\) in the form \(aw^2 + bw + c\), where \(a\), \(b\) and \(c\) are integers.

  9. 2 marks

    Factorise \(t^2 - 9t + 18\)

  10. 3 marks
    (a)

    Multiply out the brackets and simplify \((k + 9)(k - 9)\)

    (b)

    Factorise completely \(25k^2 - 4\)

Answers

  1. \(6y^2 - 35y + 49\)
  2. \(4x^2 + 28x + 49\)
  3. \((w + 5)(w + 1)\)
  4. (a) \(w^2 - 121\)
    (b) \((4w + 7)(4w - 7)\)
  5. \(5\)
  6. \((2y + 1)(y - 6)\)
  7. \(8t^2 - 2t - 15\)
  8. \(w^2 + 8w + 16\)
  9. \((t - 6)(t - 3)\)
  10. (a) \(k^2 - 81\)
    (b) \((5k + 2)(5k - 2)\)

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