Question

How do you use FOIL to multiply `(sqrt2-sqrt3)(sqrt2-sqrt3)`?

Answer 1

`(color(red)(sqrt(2))color(blue)(-sqrt3))(color(green)(sqrt(2))-color(orange)(sqrt(3)))`

F irst terms: `color(red)(sqrt(2))xxcolor(green)(sqrt(2)) = 2`
O utside terms: `color(red)(sqrt(2))xxcolor(orange)((-sqrt(3))) = -sqrt(6)`
I nside terms: `color(blue)((-sqrt(3)))xxcolor(green)(sqrt(2)) = -sqrt(6)`
L ast terms: `color(blue)((-sqrt(3)))xxcolor(orange)((-sqrt(-3))) = 3`

Sum of FOIL
`color(white)("XXXX")` `=5 - 2sqrt(6)`