Multiplying Polynomials 99
The FOIL Method
From the last problem, you can see that to fi nd the product of two binomi-
als, you compute four products, called partial products, using the terms of
the two binomials. The FOIL method is a quick way to get those four partial
products. Here is how FOIL works for fi nding the four partial products for
(ab)(cd).
- Multiply the two First terms: ac.
- Multiply the two Outer terms: ad.
- Multiply the two Inner terms: bc.
- Multiply the two Last terms: bd.
Notice that FOIL is an acronym for fi rst, outer, inner, and last. The inner
and outer partial products are the middle terms.
Problem Find the product using the FOIL method.
a. ())))()(((
b. ()))))(((()(
c. ())))))((()(((
d. ()y^2
Solution
a. () 54 x 4 () 232 x
Step 1. Find the partial products using the acronym FOIL.
() 54 x 4 () 232 x
= 52 xx⋅ 2 − 53 xx⋅ 3 ++ 4242 ⋅ − 43 ⋅ = 10 xx^2 − 1515 + 8 x
First Outer Inner Last M
iddle termii s
−^12
Step 2. Simplify.
= 10 xx^2 − 717 − 2
Step 3. State the main result.
() 54 x 4 () 223 x = 1010 xxx^27172
Be aware that the FOIL method works
only for the product of two binomials.
Forgetting to compute the middle terms
is the most common error when fi nding
the product of two binomials.
