The distributive law with two or more binomials | Maths

Starter quiz

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

'14' ✓
Write $7(2\sqrt {5} + 3\sqrt {3})$ in the form $x\sqrt {5} + y\sqrt {3}$ . What is the value of $y$ ?

'21' ✓
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 $b$ ?

'6' ✓
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 $a$ ?

'31' ✓
Write $\sqrt {5}(3\sqrt {5} + 2)-(3\sqrt {5} + 2)$ in the form $a-\sqrt {b}$ . What is the value of $b$ ?

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

'13' ✓

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

$3 + 3\sqrt {3}$

$9 + 3\sqrt {3}$

$3 - 3\sqrt {3}$

$9 - 3\sqrt {3}$ ✓
Expand $(\sqrt {2} + 1)(\sqrt {2} - 1)$

$1$ ✓

$1 + 2\sqrt {2}$

$3$

$3 + 2\sqrt {2}$
Expand $(\sqrt {5} + \sqrt {2})(\sqrt {5} - \sqrt {2})$

$3 + 2\sqrt {10}$

$3$ ✓

$7 + 2\sqrt {10}$

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

$15 + 5\sqrt {21}$

$15 + \sqrt {21}$ ✓

$27 + \sqrt {21}$

$27 + 5\sqrt {21}$
Expand $(\sqrt {10} + 2\sqrt {6})(\sqrt {10} - 2\sqrt {6})$

$-14$ ✓

$-14 - 4\sqrt{60}$

$-14 - 4\sqrt{15}$

$-14 + 4\sqrt{15}$
Expand $(4\sqrt {2} - \sqrt {5})(4\sqrt {2} + \sqrt {5})$ . What is the result?

'27' ✓

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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.

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