F	irst	- multiply the first terms from each binomial
O	uter	- multiply the outer terms from each binomial
I	nner	- multiply the inner terms from each binomial
L	ast	- multiply the last terms from each binomials

Example:

Solve (2x + y)(x + 5y).

1. Use the FOIL method to multiply the terms.

First + Outer + Inner + Last 2x2 + (2x)(5y) + xy + 5y2

2. Combine like terms.

(2x + y)(x + 5y)	=	2x2 + (2x)(5y) + xy + 5y2
	=	2x2 + 10xy + xy + 5y2
	=	2x2 + 11xy + 5y2