# How do you simplify (3sqrt5 + 2sqrt10) (4sqrt5 - 6sqrt10)?

Jun 15, 2016

$\left(3 \sqrt{5} + 2 \sqrt{10}\right) \left(4 \sqrt{5} - 6 \sqrt{10}\right) = 130 \sqrt{2} - 60$

#### Explanation:

$\left(3 \sqrt{5} + 2 \sqrt{10}\right) \left(4 \sqrt{5} - 6 \sqrt{10}\right)$

= $3 \sqrt{5} \left(4 \sqrt{5} + 6 \sqrt{10}\right) + 2 \sqrt{10} \left(4 \sqrt{5} - 6 \sqrt{10}\right)$

= $12 \sqrt{25} + 18 \sqrt{50} + 8 \sqrt{50} - 12 \sqrt{100}$

= $12 \sqrt{5 \times 5} + 18 \sqrt{2 \times 5 \times 5} + 8 \sqrt{2 \times 5 \times 5} - 12 \sqrt{10 \times 10}$

= $12 \times 5 + 18 \times 5 \times \sqrt{2} + 8 \times 5 \times \sqrt{2} - 12 \times 10$

= $60 + 90 \times \sqrt{2} + 40 \sqrt{2} - 120$

= $130 \sqrt{2} - 60$