FOIL

When two binomials are multiplied, their product can be expanded by FOIL.

The letters stand for First, Outer, Inner, Last.

The following examples illustrate the use of FOIL:

Example 1:  Expand (2x + 5)(3x + 4)

Solution:

We multiply 2x by each of the terms in 3x + 4 and then multiply 5 by each term in 3x + 4, and combine the like terms in the middle.  2x and 3x are the First terms of each binomial, 2x and 4 are the Outer terms, 5 and 3x are the Inner terms, and 5 and 4 are the Last terms.

The pattern for FOIL is:

 

We get:  (2x + 5)(3x + 4) = 6x² + 23x + 20

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