The distributive law with two or more binomials

Maths

In the prior unit, pupils explored the concept of square root, including calculating this on their calculators. In this unit, pupils work with surds and the notion that a surd is both an operation and the result of that operation.

Surds

Expand $$(2\sqrt {3} + \sqrt {3})(\sqrt {3} - 1)$$

Expand $$(\sqrt {2} + 1)(\sqrt {2} - 1)$$

Expand $$(\sqrt {5} + \sqrt {2})(\sqrt {5} - \sqrt {2})$$

Expand $$(3\sqrt {7} - 2\sqrt {3})(\sqrt {7} + \sqrt {3})$$

Expand $$(\sqrt {10} + 2\sqrt {6})(\sqrt {10} - 2\sqrt {6})$$

Expand $$(4\sqrt {2} - \sqrt {5})(4\sqrt {2} + \sqrt {5})$$. What is the result?

Write $$7(2\sqrt {5} + 3\sqrt {3})$$ in the form $$x\sqrt {5} + y\sqrt {3}$$. What is the value of $$x$$?

Write $$7(2\sqrt {5} + 3\sqrt {3})$$ in the form $$x\sqrt {5} + y\sqrt {3}$$. What is the value of $$y$$?

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 $$b$$?

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 $$a$$?

Write $$\sqrt {5}(3\sqrt {5} + 2)-(3\sqrt {5} + 2)$$ in the form $$a-\sqrt {b}$$. What is the value of $$b$$?

Write $$\sqrt {5}(3\sqrt {5} + 2)-(3\sqrt {5} + 2)$$ in the form $$a-\sqrt {b}$$. What is the value of $$a$$?

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