[discia] GCSE Maths › Algebra › Expanding and Factorising

Expanding and Factorising

discia.org 10 questions · 25 marks
Name Date
  1. Either paper 3 marks
    (a)

    Expand \(7(4t + 3)\)

    (b)

    Expand \(-7(t - 2)\)

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    (a) \(28t + 21\)
    (b) \(-7t + 14\)
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  2. Either paper 2 marks
    (a)

    Factorise fully \(10x - 2\)

    (b)

    Factorise fully \(36x + 42y\)

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    (a) \(2(5x - 1)\)
    (b) \(6(6x + 7y)\)
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  3. Either paper 3 marks

    Expand and simplify fully \(6(5y + 5) + 4(4y - 2)\)

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    \(46y + 22\)
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  4. Either paper 2 marks

    Write \((x + 2)(x - 3)\) in the form \(x^2 + bx + c\), where \(b\) and \(c\) are integers.

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    \(x^2 -x - 6\)
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  5. Either paper 2 marks

    \(3(5k + c) = 15k + 12\)

    Work out the value of \(c\).

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    \(4\)
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  6. Either paper 2 marks

    \(12t + 16 = k(3t + 4)\)

    Work out the value of \(k\).

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    \(4\)
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  7. Either paper 3 marks

    Expand and simplify \(8(2m - 2) - 4(3m + 7)\)

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    \(4m - 44\)
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  8. Either paper 4 marks
    (a)

    Factorise completely \(30m^2 - 42m\)

    (b)

    Factorise completely \(48mn + 40m\)

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    (a) \(6m(5m - 7)\)
    (b) \(8m(6n + 5)\)
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  9. Either paper 1 mark

    Here is a student's attempt to expand and simplify:

    \((x^2 + 3x - 12) - (x^2 -x - 10) = x^2 + 3x - 12 - x^2 -x - 10 = 2x - 22\)

    Explain what has gone wrong in this working.

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    When the bracket was subtracted, the sign of \(-x\) was not changed and the sign of \(- 10\) was not changed.
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  10. Either paper 3 marks
    (a)

    Multiply out \(8(4t - 8)\)

    (b)

    Multiply out \(-5(3t - 6)\)

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    (a) \(32t - 64\)
    (b) \(-15t + 30\)
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discia.org Expanding and Factorising · sheet 1
Answers Expanding and Factorising · sheet 1
  1. (a) \(28t + 21\)
    (b) \(-7t + 14\)
  2. (a) \(2(5x - 1)\)
    (b) \(6(6x + 7y)\)
  3. \(46y + 22\)
  4. \(x^2 -x - 6\)
  5. \(4\)
  6. \(4\)
  7. \(4m - 44\)
  8. (a) \(6m(5m - 7)\)
    (b) \(8m(6n + 5)\)
  9. When the bracket was subtracted, the sign of \(-x\) was not changed and the sign of \(- 10\) was not changed.
  10. (a) \(32t - 64\)
    (b) \(-15t + 30\)
discia.org Expanding and Factorising · sheet 1