Manipulating / simplifying surds

Hi

anyone can explain me please how to simplify these surds -

Pls check the Jpeg i have uploaded here
http://freeimagehosting.net/image.php?2711d7e5ab.jpg
as i cant type the square root sign (ctrl 252!?) on the keyboard

thanks a lot

(a + sqrt(b)) * (a - sqrt(b)) =>
a^2 - sqrt(b)^2 =>
a^2 - b


(1 + sqrt(2))^2 - (2 * sqrt(2) - sqrt(2))^2 =>
(1 + 2 * sqrt(2) + 2) - (4 * 2 - 2 * 2 * 2 + 2) =>
(3 + 2 * sqrt(2)) - (8 - 8 + 2) =>
3 + 2sqrt(2) - 2 =>
2 * sqrt(2) + 1



(1 + sqrt(2))^2 - (1 - sqrt(2))^2 =>
(1 + 2sqrt(2) + 2) - (1 - 2sqrt(2) + 2) =>
(3 + 2sqrt(2)) - (3 - 2sqrt(2)) =>
3 + 2sqrt(2) - 3 + 2sqrt(2) =
4 * sqrt(2)

Just use FOIL for the first one:
(a + sqrt(b))(a - sqrt(b)) =
a^2 + sqrt(a)sqrt(b) - sqrt(a)sqrt(b) - (sqrt(b)^2) =
a^2 - b

For the last one, multiply out the squares, and most terms subtract out to zero:
(1 + sqrt(2))^2 - (1 - sqrt(2))^2 =
1^2 + 2sqrt(2) + sqrt(2)^2 - (1^2 - 2sqrt(2) + sqrt(2)^2) =
4 sqrt(2)

a^2 -b

is the first one