Expanding Triple Brackets 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.

1. 3 marks

   Expand and simplify \((x {a:+})(x {b:+})(x {c:+})\)

2. 3 marks

   Expand and simplify fully \((x - 1)(x - 5)^2\)

3. 5 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 \(x = 2\).

4. 2 marks

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

   Work out the value of \(k\).

5. 2 marks

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

6. 3 marks

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

7. 3 marks

   Multiply out the brackets and simplify

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

8. 4 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 \(r\).

9. 3 marks

   Expand and simplify \(({kk}x {a:+})(x {b:+})(x {c:+})\)

10. 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 \(ax^3 + bx^2 + cx\).

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