FOIL

FOIL is an acronym for the expansion of a pair of brackets in the form of (a + b)(c + d). It stands for ‘First Outer Inner Last’.

Use FOIL to make sure that you multiply each term in the second pair of brackets with each term in the first pair of brackets.

First – multiply the first term in the first pair of brackets with the first term in the second pair of brackets in order to obtain the value ac.

Outer – multiply the term on the outer side of the first pair of brackets with the term on the outer side of the second pair of brackets in order to obtain the value ad.

Inner – multiply the term on the inner side of the first pair of brackets with the term on the inner side of the second pair of brackets in order to obtain the value bc.

Last – multiply the last term in the first pair of brackets with the last term in the second pair of brackets in order to obtain the value bd.

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