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Using the “FOIL” Method to Multiply Two Binomials

To multiply a binomial by a binomial, we use the Distributive Property twice.

For example, let’s multiply (a + b)(c + d).

Distribute (c + d) to both a and b. (a + b)(c + d) = a(c + d) + b(c + d)
Distribute both a and b to  each term in (c + d). = ac + ad + bc + bd

Notice that each term in (a + b) has been multiplied by each term in (c + d).

To remember how to multiply two binomials, we use the word FOIL.

FOIL stands for First, Outer, Inner, Last.

• The product of the First terms is ac.

• The product of the Outer terms is ad.

• The product of the Inner terms is bc.

• The product of the Last terms is bd.

Note:

This picture may help you remember how to use the FOIL method. The arcs form a “face.”

 

Example 1

Find: (x - 2)(x + 5)

Solution   F   O   I   L
Use FOIL.

Simplify each product.

Combine like terms.

(x - 2)(x + 5) =

=

=

(x)(x)

x2

x2

+

+

+

(x)(5)

5x

 

+

-

3x

(-2)(x)

2x

 

+

-

-

(-2)(5)

10

10

So, (x - 2)(x + 5) = x2 + 3x - 10.

 

Example 2

Find: (3w - 7)(9w - 5)

Solution   F   O   I L
Use FOIL.

Simplify each product.

Combine like terms.

(3w - 7)(9w - 5) =

=

=

(3w)(9w)

27w2

27w2

+

-

-

(3w)(-5)

15w

 

+

-

78w

(-7)(9w)

63w

 

+

+

+

(-7)(-5)

35

35

So, (3w - 7)(9w - 5) = 27w2 - 78w + 35.

 
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