2.05  Factoring Difference of Squares

Perfect Square Trinomials

Basic Algebra: One Step at a Time.  Pages 157-163:  67, 72, 74, 75

Dr. Robert J. Rapalje

Seminole Community College

Sanford, FL  32773

                                                                            

To see Section 2.05, with detailed explanations, examples, exercises, and answers, click here!

 

p. 162:   67.           Notice that   and   are both perfect squares.

                                                  The First times First must be :      times

 

                     

 

                                                   The Last times Last must be 16:      4 times 4.

                    

 

                                                   Because the 16 is negative, use opposite signs.

                    

 

The factor is itself a difference of squares, and so it must be re-factored.  However, the factor is the SUM of squares.  It does not re-factor, and it must be left as it is in the final answer.

 

                   

                      Final Answer!!

 

 

p. 162:   72.      Notice that   and   are both perfect squares.

                                                  The First times First must be :     times

 

                          

 

                                                   The Last times Last must be  81:  9 times 9.

                        

 

                                                   Because the 16 is negative, use opposite signs.

                        

 

The factor is itself a difference of squares, and so it must be re-factored.  However, the factor is the SUM of squares.  It does not re-factor, and it must be left as it is in the final answer.

 

                     

                        Final Answer!!

 

p. 163:  74.         

                            Notice that First times First must be :   times                                          

                     

                                                The Last times Last must be  and the

                                                OI  term must add up to 13x2      (Try 9 • 4, both positive)                                           

                     

                      O term is 4x2, and the I term is  9x2, for a total of 13x2 ,   

 

The factors and are both sums of squares!  They cannot be NOT  re-factored so this is the final answer.

 

 p. 162:  75.         

                           Notice that First times First must be :   times                                          

                 

                                                The Last times Last must be  and the

                                                OI  term must add up to 13x2      (Try 9 • 4, both negative)                                                                                        

                 

                  O term is −4x2, and the I term is −9x2, for a total of −13x2   

 

The factors and are both difference of squares.  Each must be re-factored so this is NOT the final answer.

 

               

          Final Answer!!

 

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Dr. Robert J. Rapalje Altamonte Springs Campus
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