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Question 701522: Can you please explain foil for me? I've tried many times but I can't get the hang of it.
Answer by Simnepi(216)   (Show Source):
You can put this solution on YOUR website! FOIL stands for
First, Outer,Inner, Last and is a great way of remembering how to expand two brackets with two terms in. for instance (a+b) and (c+d) where a,b,c and d represent algebraic terms.
(When using FOIL you also have to remember the rules for multiplying positive and negative numbers.)
So lets get back to the brackets
(a+b)(c+d)
Foil says multiply the First terms in the brackets
so multiplying a and c gives +ac
Then, multiply the Outer terms, those that are furthest from the middle of the bracket
so multiplying a and d gives +ad
Then multiply the Inner terms in each bracket, those that are closest together
so multiplying b and c gives +bc
Then,multiply the Last term in each bracket
so multiplying b and d gives +bd
putting all those terms together gives us
(a+b)(c+d)=ac+ad+bc+bd
Lets see if I can show you a couple useful things to help
If you have a bracket which is squared i.e.
this is the same as (x+y)(x+y)
Using FOIL gives us terms
 , +xy, +xy and  i.e.
 simplifying this gives 
so
Let-s look at another but with negative signs i.e.
this is the same as (x-y)(x-y)This time remembering that
positive X negative = negative and
negative X negative = positive
using FOIL this time gives us terms
, -xy, -xy and + i.e.
 simplifying this gives 
so (x-y)^2=x^2-2xy+y^2}}
Hope that helped.
The best thing is to practice a few for yourself!
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