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Year 10
Higher

The distributive law with two or more binomials

You can use the distributive law to two or more binomials.

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New
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Year 10
Higher

The distributive law with two or more binomials

You can use the distributive law to two or more binomials.

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Share activities with pupils
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Lesson details

Key learning points

  1. The distributive law can be used with expressions containing surds.
  2. This can be extended to finding the product of two or more binomials.
  3. Any binomial could contain surd terms.

Keywords

  • The distributive law - a(b + c) = ab + ac

Common misconception

Pupils may suggest using FOIL (or similar) to expand both brackets and make errors whilst doing so.

The grid method is derived from the area model and therefore the area model supports expanding both one binomial and two binomials.

Pupils may benefit from using one representation throughout their learning on multiplication. This will help them to see that this is all connected and it is not disjointed topics.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Write $$7(2\sqrt {5} + 3\sqrt {3})$$ in the form $$x\sqrt {5} + y\sqrt {3}$$. What is the value of $$x$$?
Correct Answer: 14
Q2.
Write $$7(2\sqrt {5} + 3\sqrt {3})$$ in the form $$x\sqrt {5} + y\sqrt {3}$$. What is the value of $$y$$?
Correct Answer: 21
Q3.
Write $$5\sqrt {3}(2\sqrt {8} + 3\sqrt {2})-\sqrt {3}(\sqrt {8} + 2\sqrt {2})$$ in the form $$a\sqrt {b}$$. What is the value of $$b$$?
Correct Answer: 6
Q4.
Write $$5\sqrt {3}(2\sqrt {8} + 3\sqrt {2})-\sqrt {3}(\sqrt {8} + 2\sqrt {2})$$ in the form $$a\sqrt {b}$$. What is the value of $$a$$?
Correct Answer: 31
Q5.
Write $$\sqrt {5}(3\sqrt {5} + 2)-(3\sqrt {5} + 2)$$ in the form $$a-\sqrt {b}$$. What is the value of $$b$$?
Correct Answer: 5
Q6.
Write $$\sqrt {5}(3\sqrt {5} + 2)-(3\sqrt {5} + 2)$$ in the form $$a-\sqrt {b}$$. What is the value of $$a$$?
Correct Answer: 13

Exit quiz

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6 Questions

Q1.
Expand $$(2\sqrt {3} + \sqrt {3})(\sqrt {3} - 1)$$
$$3 + 3\sqrt {3}$$
$$9 + 3\sqrt {3}$$
$$3 - 3\sqrt {3}$$
Correct answer: $$9 - 3\sqrt {3}$$
Q2.
Expand $$(\sqrt {2} + 1)(\sqrt {2} - 1)$$
Correct answer: $$1$$
$$1 + 2\sqrt {2}$$
$$3$$
$$3 + 2\sqrt {2}$$
Q3.
Expand $$(\sqrt {5} + \sqrt {2})(\sqrt {5} - \sqrt {2})$$
$$3 + 2\sqrt {10}$$
Correct answer: $$3$$
$$7 + 2\sqrt {10}$$
$$7$$
Q4.
Expand $$(3\sqrt {7} - 2\sqrt {3})(\sqrt {7} + \sqrt {3})$$
$$15 + 5\sqrt {21}$$
Correct answer: $$15 + \sqrt {21}$$
$$27 + \sqrt {21}$$
$$27 + 5\sqrt {21}$$
Q5.
Expand $$(\sqrt {10} + 2\sqrt {6})(\sqrt {10} - 2\sqrt {6})$$
Correct answer: $$-14$$
$$-14 - 4\sqrt{60}$$
$$-14 - 4\sqrt{15}$$
$$-14 + 4\sqrt{15}$$
Q6.
Expand $$(4\sqrt {2} - \sqrt {5})(4\sqrt {2} + \sqrt {5})$$. What is the result?
Correct Answer: 27