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					          Algebra

10.7 Factoring Special Products
                    Use the Patterns!
                                         First and last terms are perfect squares!



     (2x + 3)2                          4x² + 12x + 9                                 Perfect Square Trinomial!


                                      The middle term is twice the product of the square roots
                                                 of the first and third terms.




    (2p - 4) (2p + 4)                4p² - 16                      Difference of two squares (DTS)!

                                            The difference of… two squares!



                                       First and last terms are perfect squares!


     (2x - y)2                       4x² - 4xy + y²                                  Perfect Square Trinomial!

                                     The middle term is twice the product of the square roots
                                                of the first and third terms.

The key is to recognize when you see a perfect square trinomial or a DTS!
                          Factoring Patterns!
        First and last terms are perfect squares!



       a² + 2ab + b2                                 Perfect Square Trinomial!
                                                                                 (a + b)2
     The middle term is twice the product of the square roots
                of the first and third terms.




     a² - b2                      Difference of two squares (DTS)!
                                                                                 (a - b)(a + b)
 The difference of… two squares!



      First and last terms are perfect squares!


    a² - 2ab + b²                                   Perfect Square Trinomial!    (a - b)2
    The middle term is twice the product of the square roots
               of the first and third terms.

The key is to recognize when you see a perfect square trinomial or a DTS!
                    Factor!

2x²- 18                 2(x + 3)(x – 3)
   2(x²- 9)  DTS!



49t²- ¼r2              (7t + ½r)(7t – ½r)
   DTS!




81x²- 25y²              (9x – 5y)(9x + 5y)
   DTS!




27x²- 12                3(3x + 2)(3x – 2)
  3(9x²- 4)
          DTS!
                                   Factor!

-3x²- 18x - 27                               -3(x + 3)2
   -3(x²+ 6x + 9)
                 Perfect Square Trinomial!


9y²- 60y + 100                               (3y – 10)2
  Perfect Square Trinomial!




2x²- 12x + 18                                2(x – 3)2
 2(x²- 6x + 9)
       Perfect Square Trinomial!




49x²+ 84x + 36                               (7x + 6)2
    Perfect Square Trinomial!
                                                   Solve!
              3x²- 30x = -75                                  (x – 5)2 = 0
               3x²- 30x + 75 = 0                                 x= 5
                 x²- 10x + 25 = 0
Divide each side by 3!


                            Perfect Square Trinomial!




             36y²- 121 = 0                              (6y + 11)(6y – 11) = 0
                                                         y = 11/6, -11/6
                   DTS!




             -6x²+ 8x + 14 = 0
  Divide each side by -2!
                                                            (x + 1 )(3x - 7) = 0
              3x²- 4x – 7 = 0                                  x = -1, 7/3
                                                      Solve!
            4x²- 1 = 0                                    (2x + 1)(2x – 1) = 0
                   DTS!
                                                                   x = ½, -½


           7x²- 10x = -3                                       (7x – 3 )(x – 1) = 0
            7x²- 10x + 3 = 0                                       x = 1, 3/7

           32x²- 80x + 50 = 0
Divide each side by 2!
                                                                (4x – 5)2 = 0
            16x²- 40x + 25 = 0                                    x = 5/4
                          Perfect Square Trinomial!
                                HW
• P. 622-624 (#19-61, 83-93) Odds




 Maybe factor out instead of divide each side by GCF as it applies to Ch 11

				
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