Use FOIL to multiply


The letters of the word "FOIL" is an acronym for 

"F=FIRSTS", "O=OUTERS", "I=INNERS", "L=LASTS"

The FIRSTS:
The terms  and  are the FIRSTS, because
 comes FIRST in  and  comes 
FIRST in 

So we multiply the two FIRSTS,  and get
, so we write that down under the original
problem:




The OUTERS:
The terms  and  are the OUTERS, because
 and  are on the outside of ,
the ones located the farthest apart. 

So we multiply the two OUTERS,  and get
, so we write that down under the original
problem next to the . like this::




The INNERS:
The terms  and  are the INNERS, because
 and  are on the inside of ,
the ones located in the middle. 

So we multiply the two INNERS,  and get
, so we write that down under the original
problem:




The LASTS:
The terms  and  are the LASSTS, because
 comes LAST in  and  comes 
FIRST in 

So we multiply the two LASTS,  and get
, so we tack that on down under 
the original problem:




Now that we have finished the "FOIL" process, we look
to see if there are any like terms that will combine:

We see that the middle two terms  will
combine to give , so underneath we replace
the  by  and get





Edwin