The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Teaching Notes 5.8: Multiplying Two Binomials

To multiply two binomials, students may use thedistributive property two times. Because this

can be confusing, the acronym FOIL is helpful for remembering the process.

1. Explain the steps for multiplying two binomials by applying the distributive property twice.
   
   
   • Start with the first term of the first binomial. Multiply each term of the second binomial
     by the first term of the first binomial.
   
   
   • Multiply each term of the second binomial by the second term of the first binomial.
   
   
   • Simplify the answer.
   
   
   
   


2. Provide this example to demonstrate the application of the distributive property:

(x+2)(x+7)=x(x+7)+2(x+7)=x^2 + 7 x+ 2 x+ 14 =x^2 + 9 x+ 14

3. Explain that FOIL is an acronym that refers to thefirst, outer, inner,andlastterms of bino-
   mials. This will help your students remember how to multiply binomials.


4. Review the information and examples on the worksheet with your students. Be sure that
   your students can apply FOIL. Also remind them that if any terms in the binomials are sub-
   tracted, they must rewrite the subtraction as addition. Review the steps for rewriting in
   detail if necessary.

EXTRA HELP:

The FOIL method applies to only the multiplication of two binomials.

ANSWER KEY:

(1)x^2 + 2 x− 15 (2)x^2 +x− 56 (3)x^2 − 7 x+ 6 (4) 8 x^2 − 2 x− 3

(5)− 2 x^2 + 19 x− 24 (6)x^3 + 3 x^2 +x+ 3 (7)x^3 + 2 x^2 − 5 x− 10 (8) 2 x^2 − 5 xy− 3 y^2

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(Challenge)Subtraction was not rewritten as addition. (x−3)(x+4)=(x+(−3))(x+4)=

------------------------------------------------------------------------------------------x^2 +^4 x+(−^3 x)+(−12)=x^2 +x−^12

190 THE ALGEBRA TEACHER’S GUIDE