[discia] GCSE Maths › Algebra › Expanding and Factorising Quadratics

Expanding and Factorising Quadratics

discia.org 10 questions · 24 marks
Name Date
  1. Non-calculator 1 mark
    Which one of these expressions is equivalent to \(x^2 + 7x + 12\)?
    A \((x + 12)(x + 1)\) B \((x + 3)(x + 4)\) C \((x - 3)(x - 4)\) D \((x + 2)(x + 5)\)
    Write down the letter of your answer.
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    Option B
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  2. Non-calculator 2 marks

    Expand and simplify \((3x - 2)(4x - 5)\)

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    \(12x^2 - 23x + 10\)
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  3. Non-calculator 2 marks

    Multiply out the brackets and simplify \((3t - 4)^2\)

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    \(9t^2 - 24t + 16\)
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  4. Non-calculator 2 marks

    Factorise \(w^2 - 4w - 32\)

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    \((w + 4)(w - 8)\)
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  5. Non-calculator Higher3 marks
    (a)

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

    (b)

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

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    (a) \(k^2 - 81\)
    (b) \((5k + 2)(5k - 2)\)
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  6. Non-calculator 2 marks

    \((k - 5)(k + a) = k^2 - 13k + 40\)

    Calculate the value of \(a\).

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    \(-8\)
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  7. Non-calculator Higher2 marks

    Write \(2x^2 - 13x + 20\) as a product of two brackets.

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    \((2x - 5)(x - 4)\)
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  8. Non-calculator 4 marks

    You must show your working.

    Show that \((3x + 2)(x + 6) + 2x(x + 5) - 5(x^2 + 6x + 4)\) simplifies to an integer.

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    The \(x^2\) terms and the \(x\) terms both cancel, leaving the integer \(-8\).
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  9. Non-calculator Higher3 marks

    The diagram shows a sketch of a quadratic curve. It is not drawn accurately.

    xy(1, 0)(5, 0)(0, -10)

    The curve crosses the \(x\)-axis at two of the labelled points and the \(y\)-axis at the third.

    Work out an equation of the curve. Give your answer in the form \(y = ax^2 + bx + c\).

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    \(y = -2x^2 + 12x - 10\)
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  10. Non-calculator 3 marks

    \((x + a)(x + 4a) \equiv x^2 + bx + 256\)

    Work out the two possible values of \(b\).

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    \(b = -40\) or \(b = 40\)
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discia.org Expanding and Factorising Quadratics · sheet 1
Answers Expanding and Factorising Quadratics · sheet 1
  1. Option B
  2. \(12x^2 - 23x + 10\)
  3. \(9t^2 - 24t + 16\)
  4. \((w + 4)(w - 8)\)
  5. (a) \(k^2 - 81\)
    (b) \((5k + 2)(5k - 2)\)
  6. \(-8\)
  7. \((2x - 5)(x - 4)\)
  8. The \(x^2\) terms and the \(x\) terms both cancel, leaving the integer \(-8\).
  9. \(y = -2x^2 + 12x - 10\)
  10. \(b = -40\) or \(b = 40\)
discia.org Expanding and Factorising Quadratics · sheet 1