Question

what is the FOIL method

Answer 1

http://www.mathsisfun.com/definitions/foil-method.html

Answer 2

method to expand 2 term brackets ^

Answer 3

Another (hardly different) way to deal with multiplying binomials is by breaking up like so:
\[(a+b)(c+d)~~\iff~~a(c+d)+b(c+d)=\underbrace{ac}_{\text{F}}+\underbrace{ad}_{\text{O}}+\underbrace{bc}_{\text{I}}+\underbrace{bd}_{\text{L}}\]