Question

How do you multiply (√2x - √6)²?

Answer 1

Use FOIL to find `(sqrt(2)x-sqrt(6))^2 = 2x^2-4sqrt(3)x+6`

Explanation:

`(sqrt(2)x-sqrt(6))^2`

`= (sqrt(2)x-sqrt(6))(sqrt(2)x-sqrt(6))`

`=underbrace(sqrt(2)x*sqrt(2)x)_color(blue)("First") + underbrace(sqrt(2)x*-sqrt(6))_color(blue)("Outside") + underbrace(-sqrt(6)*sqrt(2)x)_color(blue)("Inside") + underbrace(-sqrt(6)*-sqrt(6))_color(blue)("Last")`

`=2x^2-2sqrt(2)sqrt(6)x+6`

`=2x^2-2sqrt(2*6)x + 6`

`=2x^2-2sqrt(2^2*3)x+6`

`=2x^2-4sqrt(3)x+6`

...using `sqrt(ab) = sqrt(a)sqrt(b)` for `a, b >= 0`