SOLUTION: Please show the step by step in the FOIL 3√2 - 5√3)(6√2 - 7√3) =

Algebra ->  Radicals -> SOLUTION: Please show the step by step in the FOIL 3√2 - 5√3)(6√2 - 7√3) =      Log On


   

Question 77547: Please show the step by step in the FOIL
3√2 - 5√3)(6√2 - 7√3) =
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
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 %283sqrt%282%29%29%286sqrt%282%29%29 and this equals(18)(2)=36
Outer%283sqrt%282%29%29%28-7sqrt%283%29%29 and this equals%28-21%29%28sqrt%286%29%29
Inner%28-5sqrt%283%29%29%286sqrt%282%29%29 and this equals %28-30%29%28sqrt%286%29%29

Last %28-5sqrt%283%29%29%28-7sqrt%283%29%29 and this equals(35)(3)=105
So we have:
36-21sqrt%286%29-30sqrt%286%29%2B105 collecting like terms:
141-51sqrt%286%29 -------------ans


Hope this helps---ptaylor