Question

How do you simplify `(6+ sqrt3)(6-sqrt3)`?

Answer 1

You may find it helpful to use the mnemonic FOIL - First, Outside, Inside, Last.

That means multiply both first terms together (`6xx6`),
add the product of the outside terms (`6xx-sqrt(3)`)
add the product of the inside terms (`sqrt(3)xx6`)
add the product of the last terms (`sqrt(3)xx-sqrt(3)`)

So

`(6+sqrt(3))(6-sqrt(3))`

`= 6^2-cancel(6sqrt(3))+cancel(6sqrt(3))-sqrt(3)^2`

`= 36-3 = 33`

Alternatively, you could use the identity of difference of squares:

`a^2-b^2 = (a-b)(a+b)`

to get:

`(6+sqrt(3))(6-sqrt(3)) = 6^2-sqrt(3)^2 = 36 - 3 = 33`