A way of remembering how to multiply two binomials. Stands for First, Outer, Inner, Last. This means you multiply the first terms of the binomials, then the outer terms of the binomials (the first term of the first binomial multiplied by the last term of the second), then the inner terms (the reverse of "Outer"), then the last terms in both polynomials. What it gives you, if done correctly, is a trinomial in quadratic standard form.
Example:
(x+3)(x+6)
(x*x)+(x*6)+(3*x)+(6*3)
x2+9x+18
Here's a harder example:
{4x-2)(3x+4)
(4x*3x)+(4x*4)+(-2*3x)+(-2*4)
12x2+16x-6x-8
12x2+10x-8
Simple, eh?