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 Dependent Variable

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# Multiplying Binomials

In this section you will learn a rule that makes multiplication of binomials simpler.

## The FOIL Method

We can use the distributive property to find the product of two binomials. For example,

 = (x + 2)x + (x + 2)3 Distributive property = x2 + 2x + 3x + 6 Distributive property = x2 + 5x + 6 Combine like terms

There are four terms in x2 + 2x + 3x + 6. The term x2 is the product of the first terms of each binomial, x and x. The term 3x is the product of the two outer terms, 3 and x. The term 2x is the product of the two inner terms, 2 and x. The term 6 is the product of the last term of each binomial, 2 and 3. We can connect the terms multiplied by lines as follows:

 F = First terms O = Outer terms I = Inner terms L = Last terms

If you remember the word FOIL, you can get the product of the two binomials much faster than writing out all of the steps above. This method is called the FOIL method. The name should make it easier to remember.

Example 1:

Using the FOIL method

Find each product.

a) (x + 2)(x - 4)

b) (2x + 5)(3x - 4)

c) (a - b)(2a - b)

d) (x + 3)(y + 5)

Solution

 a) Combine the like terms
 b) (2x + 5)(3x - 4) = 6x2 - 8x + 15x - 20 = 6x2 + 7x - 20 Combine the like terms
 c) (a - b)(2a - b) = 2a2 - ab -2ab + b2 = 2a2 - 3ab + b2 Combine the like terms
 d) (x + 3)(y + 5) = xy + 5x + 3y + 15 There are no like terms to combine.