[discia] GCSE Maths › Algebra › Expanding Triple Brackets

Expanding Triple Brackets

discia.org 10 questions · 32 marks
Name Date
  1. Either paper Higher3 marks

    Expand and simplify \((x + 3)(x + 2)(x + 1)\)

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    \(x^3 + 6x^2 + 11x + 6\)
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  2. Either paper Higher3 marks

    Expand and simplify fully \((x + 6)(x - 5)^2\)

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    \(x^3 - 4x^2 - 35x + 150\)
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  3. Either paper Higher5 marks

    A cuboid has length \((x + 2)\) cm, width \((x + 5)\) cm and height \((x + 1)\) cm.

    (a)

    Work out an expression for the volume of the cuboid.

    Give your answer in the form \(x^3 + px^2 + qx + r\).

    (b)

    Calculate the volume of the cuboid when \(x = 2\).

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    (a) \(x^3 + 8x^2 + 17x + 10\)
    (b) \(84\ \text{cm³}\)
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  4. Either paper Higher2 marks

    When \((x + 6)(x - 1)(x + k)\) is expanded, the constant term is \(-6\).

    Work out the value of \(k\).

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    \(1\)
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  5. Either paper Higher2 marks

    Expand and simplify \((x + 1)(x^2 +x - 7)\)

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    \(x^3 + 2x^2 - 6x - 7\)
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  6. Either paper Higher3 marks

    Expand and simplify \((w + 1)^3\)

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    \(w^3 + 3w^2 + 3w + 1\)
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  7. Either paper 3 marks

    Multiply out the brackets and simplify

    \(2x(x + 7)(x - 5)\)

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    \(2x^3 + 4x^2 - 70x\)
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  8. Either paper Higher4 marks

    When \((x - 3)(x + 2)(x - 1)\) is expanded and simplified, the result can be written as

    \(x^3 + px^2 + qx + r\)

    (a)

    State the value of \(p\).

    (b)

    Work out the value of \(q\).

    (c)

    State the value of \(r\).

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    (a) \(-2\)
    (b) \(-5\)
    (c) \(6\)
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  9. Either paper Higher3 marks

    Expand and simplify fully \((2x + 3)(x - 3)(x + 2)\)

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    \(2x^3 +x^2 - 15x - 18\)
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  10. Either paper 4 marks

    A piece of card is \(17\) cm long and \(11\) cm wide.

    Squares of side \(x\) cm are cut from its four corners. The sides are then folded up to make an open box with no lid.

    Find an expression, in terms of \(x\), for the volume of the box in cm³.

    Give your answer in the form \(ax^3 + bx^2 + cx\).

    Show answer
    \(4x^3 - 56x^2 + 187x\)
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discia.org Expanding Triple Brackets · sheet 1
Answers Expanding Triple Brackets · sheet 1
  1. \(x^3 + 6x^2 + 11x + 6\)
  2. \(x^3 - 4x^2 - 35x + 150\)
  3. (a) \(x^3 + 8x^2 + 17x + 10\)
    (b) \(84\ \text{cm³}\)
  4. \(1\)
  5. \(x^3 + 2x^2 - 6x - 7\)
  6. \(w^3 + 3w^2 + 3w + 1\)
  7. \(2x^3 + 4x^2 - 70x\)
  8. (a) \(-2\)
    (b) \(-5\)
    (c) \(6\)
  9. \(2x^3 +x^2 - 15x - 18\)
  10. \(4x^3 - 56x^2 + 187x\)
discia.org Expanding Triple Brackets · sheet 1