Question

How do you multiply `(6-[3sqrt2])(6+[3sqrt2])`?

Answer 1

`(6-[3sqrt(2])(6+[3sqrt(2)])`
`color(white)("XXXX")` `color(white)("XXXX")` `color(white)("XXXX")` `color(white)("XXXX")` `= 18`

Explanation:

In general
`color(white)("XXXX")` `(a+b)(a-b) = a^2-b^2`
(this is commonly referred to as the difference of quares)

So
`color(white)("XXXX")` `(6-[3sqrt(2])(6+[3sqrt(2)])`

`color(white)("XXXX")` `color(white)("XXXX")` `= 6^2 - [3sqrt(2)]^2`

`color(white)("XXXX")` `color(white)("XXXX")` `= 36 - 18`

`color(white)("XXXX")` `color(white)("XXXX")` `= 18`