Question 77547
As you probably know, FOIL is a crutch that is used to remember how to multiply expressions of the form (a+-b)(c+-d). 
Lets use (a-b)(c-d) as an example:
Foil is an acronymn that stands for:
First(a*c)
Outer (-a*d)
Inner (-b*c)
Last (b*d)

So we have a*c-a*d-b*c+b*d----ans

Lets look at another example and and you can determine the answer quickly by inspection:

(4-2)(6+4)

First (4*6)
Outer (4*4)
Inner (-2*6)
Last (-2*4)

And we have:  24+16-12-8=40-20=20-----------------ans

Now lets look at your problem:


First {{{(3sqrt(2))(6sqrt(2))}}} and this equals(18)(2)=36

Outer{{{(3sqrt(2))(-7sqrt(3))}}} and this equals{{{(-21)(sqrt(6))}}}

Inner{{{(-5sqrt(3))(6sqrt(2))}}} and this equals {{{(-30)(sqrt(6))}}}


Last {{{(-5sqrt(3))(-7sqrt(3))}}} and this equals(35)(3)=105

So we have:

{{{36-21sqrt(6)-30sqrt(6)+105}}} collecting like terms:

{{{141-51sqrt(6)}}}  -------------ans



Hope this helps---ptaylor