Basic Mathematics for College Students

Multiply binomials.

The distributive property can also be used to multiply binomials. For example, to

multiply and , we think of as a single quantity and distribute it

over each term of.

Distribute the multiplication

by 3aand by 5.

Multiply the monomials.

Combine like terms.

In the third line of the solution, notice that each term of has been multiplied

by each term of. This example suggests the following rule.

Multiplying Binomials

To multiply two binomials, multiply each term of one binomial by each term of

the other binomial, and then combine like terms.

We can use a shortcut method, called the FOIL method,to multiply binomials. FOIL

is an acronym for First terms,Outer terms,Inner terms,Last terms. To use the FOIL

method to multiply by , we

1. multiply the First terms and to obtain ,


2. multiply the Outer terms and 5 to obtain ,


3. multiply the Inner terms 4 and to obtain , and


4. multiply the Last terms 4 and 5 to obtain 20.
   Then we simplify the resulting polynomial, if possible.
   Outer

First F O I L

Inner

Last

Multiply the monomials.

Combine like terms.

The Language of Algebra An acronymis an abbreviation of several words

in such a way that the abbreviation itself forms a word. The acronymFOIL

helps us remember the order to follow when multiplying two binomials:

First,Outer,Inner,Last.

 6 a^2  22 a 20

 6 a^2  10 a 12 a 20

(2a4)(3a5) 2 a(3a) 2 a(5)4(3a)4(5)

3 a 12 a

2 a 10 a

2 a 3 a 6 a^2

2 a 4 3 a 5

2 a 4

3 a 5

 6 a^2  22 a 20

 6 a^2  12 a 10 a 20

(2a) 3 a(4) 3 a(2a) 5 (4) 5

(2a4) 3 a(2a4) 5

(2a4)(3a5)(2a4) 3 a(2a4) 5

3 a 5

2 a 4 3 a 5 2 a 4

3

A-16 Appendix II Polynomials

EXAMPLE (^3) Multiply: a. b.
StrategyWe will use the FOIL method.
WHYIn each case we are to find the product of two binomials, and the FOIL
method is a shortcut for multiplying two binomials.
(x5)(x7) (3x4)(2x3)