Question

`( sqrt 3 + 2 sqrt 10) (4 sqrt 3 - sqrt 10)` How to multiply?

Answer 1

See the entire solution process below:

Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`(color(red)(sqrt(3)) + color(red)(2sqrt(10)))(color(blue)(4sqrt(3)) - color(blue)(sqrt(10)))` becomes:

`(color(red)(sqrt(3)) xx color(blue)(4sqrt(3))) - (color(red)(sqrt(3)) xx color(blue)(sqrt(10))) + (color(red)(2sqrt(10)) xx color(blue)(4sqrt(3))) - (color(red)(2sqrt(10)) xx color(blue)(sqrt(10)))`

`4(sqrt(3))^2 - sqrt(30) + 8sqrt(30) - 2(sqrt(10))^2`

`(4 * 3) - sqrt(30) + 8sqrt(30) - (2 * 10)`

`12 - sqrt(30) + 8sqrt(30) - 20`

We can now group and combine like terms:

`12 - 20 - 1sqrt(30) + 8sqrt(30)`

`(12 - 20) + (-1 + 8)sqrt(30)`

`-8 + 7sqrt(30)`

Or

`7sqrt(30) - 8`