Question

How do you evaluate `(\sqrt 3 +3) ( \sqrt 3 -1)`?

Answer 1

`2sqrt3`

Explanation:

Apply the F.O.I.L method:

F: Multiply the first terms in each parenthesis
O Multiply the two most outer terms
I: Multiply the two most inner terms
L: Multiply the last terms in each parenthesis

F: `(color(red)sqrt3+3)(color(red)sqrt3-1)=sqrt9=3`

O: `(color(red)sqrt3+3)(sqrt3color(red)(-1))=-sqrt3`

I: `(sqrt3+color(red)(3))(color(red)sqrt3-1)=3sqrt3`

L: `(sqrt3+color(red)3)(sqrt3color(red)(-1))=-3`

Combining everything from above we get the expression:

`3-sqrt3+3sqrt3-3`

We can simplify this and arrive to our final solution:

`cancel3+2sqrt3cancel(-3`

`2sqrt3larr` Final Answer