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

1 Answer
Oct 18, 2017

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