The distributive law says that multiplying a sum is the same as multiplying each addend and summing the result.

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.

In this unit pupils will learn how to recognise surds, handle them in calculations and rationalise fractions with surds as denominators.

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 $$a$$?

This lesson will be removed by end of Summer Term 2025.

The distributive law with two or more binomials

Lesson outcome

This lesson will be removed by end of Summer Term 2025.