Question 701522
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. 
{{{(x+y)^2}}}
this is the same as (x+y)(x+y)
Using FOIL gives us terms 
{{{x^2}}}, +xy, +xy and {{{y^2}}} i.e.
{{{x^2+xy+xy+y^2}}} simplifying this gives {{{x^2+2xy+y^2}}}
so{{{(x+y)^2=x^2+2xy+y^2}}}
Let-s look at another but with negative signs i.e.
{{{x-y)^2}}}
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 
{{{x^2}}}, -xy, -xy and +{{{y^2}}} i.e.

{{{x^2-xy=xy+y^2}}} simplifying this gives {{{x^2-2xy+y^2}}}
so{{{(x-y)^2=x^2-2xy+y^2}}
Hope that helped.
The best thing is to practice a few for yourself!