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

Name Date

WORKSHEET 5.14: FACTORING THE DIFFERENCE OF SQUARES

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Follow the steps below to factor the difference of squares:

1. Determine if the binomial can be written as the difference of two numbers or expres-
   sions raised to the second power. Write each as a base squared.


2. Substitute each base in the formulaa^2 −b^2 =(a+b)(a−b).


3. UseFOILtocheckyourwork.

EXAMPLE

Factor 25 − 9 x^8.

25 = 52 ; 9 x^8 =(3x^4 )^2

a= 5 ;b=(3x^4 ); 52 −(3x^4 )^2 =(5+ 3 x^4 )(5− 3 x^4 )

(5+ 3 x^4 )(5− 3 x^4 )= 25 − 15 x^4 + 15 x^4 − 9 x^8 = 25 − 9 x^8

DIRECTIONS: Factor each binomial.

1. x^2 − 100 2. 1 − 16 x^10 3. 49 −y^12


2. 9 − 100 x^2 5. 64 −y^2 6. x^2 y^2 − 25


3. 144 −x^8 8. x^6 − 121 9. a^4 b^2 − 81


4. x^6 y^6 − 144 11. 4 x^2 − 1 12. 36 x^10 − 25 y^2

CHALLENGE:Crystal factored 4+x^16 as (2−x^8 )(2+x^8 ). Was she correct?

Explain your reasoning.

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.