This is a nifty system with an even niftier acronym that makes it easy to multiply polynomials with 2 terms.

$(a+b)(c+d)$

The FOIL method helps us remember to multiply:

Putting it all together:

$(a+b)(c+d) = ac + ad + bc + bd$

Let's look at another example:

$(2x + 3)(x + 4)$

Using FOIL:

Putting it all together:

$(2x + 3)(x + 4) = 2x^2 + 8x + 3x + 12$

Often, after doing FOIL, you can combine like terms to clean up a bit more:

$2x^2 + 11x + 12$

The FOIL method is a handy way to keep track of all the terms when multiplying binomials!