SECTION 9-8
 Perfect Squares and
Differences of Squares
Essential Questions

How do you factor perfect square trinomials?
How do you factor the difference of perfect squares?


Wh...
Vocabulary
1. Perfect Square Trinomial:



2. Difference of Two Squares:
Vocabulary
1. Perfect Square Trinomial: A trinomial that can be factored
   into a binomial squared


2. Difference of Two ...
Vocabulary
1. Perfect Square Trinomial: A trinomial that can be factored
   into a binomial squared


2. Difference of Two ...
Perfect Square Trinomial
                     2
          ( a − b)
Perfect Square Trinomial
                      2
           ( a − b)
        ( a − b)( a − b)
Perfect Square Trinomial
                        2
             ( a − b)
         ( a − b)( a − b)
         2             ...
Perfect Square Trinomial
                            2
                 ( a − b)
         ( a − b)( a − b)
         2     ...
Perfect Square Trinomial
                            2
                 ( a − b)
         ( a − b)( a − b)
         2     ...
Perfect Square Trinomial
                            2
                 ( a − b)
         ( a − b)( a − b)
         2     ...
Perfect Square Trinomial
                            2
                 ( a − b)
         ( a − b)( a − b)
         2     ...
Perfect Square Trinomial
                                      2
                           ( a − b)
                   ( ...
Example 1
                  Factor.
       2                       2
a. 9x + 12x + 4             b. y − 20 y + 100



   2...
Example 1
                  Factor.
       2                       2
a. 9x + 12x + 4             b. y − 20 y + 100

   (3x...
Example 1
                    Factor.
       2                         2
a. 9x + 12x + 4               b. y − 20 y + 100
 ...
Example 1
                    Factor.
       2                         2
a. 9x + 12x + 4               b. y − 20 y + 100
 ...
Example 1
                    Factor.
       2                         2
a. 9x + 12x + 4               b. y − 20 y + 100
 ...
Example 1
                     Factor.
       2                          2
a. 9x + 12x + 4                b. y − 20 y + 10...
Example 1
                     Factor.
       2                           2
a. 9x + 12x + 4                b. y − 20 y + 1...
Difference of Squares
       ( a − b)( a + b)
Difference of Squares
       ( a − b)( a + b)
       2                  2
      a + ab − ab − b
Difference of Squares
       ( a − b)( a + b)
       2                  2
      a + ab − ab − b
            2     2
      ...
Difference of Squares
       ( a − b)( a + b)
       2                  2
      a + ab − ab − b
            2     2
      ...
Difference of Squares
       ( a − b)( a + b)
       2                  2
      a + ab − ab − b
            2     2
      ...
Difference of Squares
                      ( a − b)( a + b)
                      2                  2
                  ...
Example 2
                     Factor.
         2                         2
 a. 64x − 81                    b. r − 121


 ...
Example 2
                     Factor.
          2                        2
 a. 64x − 81                    b. r − 121
(8x...
Example 2
                     Factor.
          2                        2
 a. 64x − 81                    b. r − 121
(8x...
Example 2
                     Factor.
         2                         2
 a. 64x − 81                    b. r − 121
(8x...
Example 2
                     Factor.
         2                           2
 a. 64x − 81                     b. r − 121
...
Example 2
                     Factor.
         2                            2
 a. 64x − 81                     b. r − 121...
Example 2
                     Factor.
           2                          2
 a. 64x − 81                     b. r − 121...
Example 2
                     Factor.
          2                           2
 a. 64x − 81                     b. r − 121...
Example 2
                     Factor.
          2                                2
 a. 64x − 81                          ...
Example 2
                             Factor.
                  2                                2
           a. 64x − 81...
Example 2
                                      Factor.
                  2                                         2
    ...
Example 2
                                      Factor.
                  2                                         2
    ...
Example 2
                                      Factor.
                  2                                         2
    ...
Homework
Homework


              p. 410 #1-42 multiples of 3




“There are two kinds of men who never amount to much:
 those who ...
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Integrated Math 2 Section 9-8

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Perfect Squares and Differences of Squares

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  • Integrated Math 2 Section 9-8

    1. 1. SECTION 9-8 Perfect Squares and Differences of Squares
    2. 2. Essential Questions How do you factor perfect square trinomials? How do you factor the difference of perfect squares? Where you’ll see this: Travel, number sense, modeling, geography
    3. 3. Vocabulary 1. Perfect Square Trinomial: 2. Difference of Two Squares:
    4. 4. Vocabulary 1. Perfect Square Trinomial: A trinomial that can be factored into a binomial squared 2. Difference of Two Squares:
    5. 5. Vocabulary 1. Perfect Square Trinomial: A trinomial that can be factored into a binomial squared 2. Difference of Two Squares: A polynomial that can be factored into two binomials with the same terms but different signs in between
    6. 6. Perfect Square Trinomial 2 ( a − b)
    7. 7. Perfect Square Trinomial 2 ( a − b) ( a − b)( a − b)
    8. 8. Perfect Square Trinomial 2 ( a − b) ( a − b)( a − b) 2 2 a − ab − ab + b
    9. 9. Perfect Square Trinomial 2 ( a − b) ( a − b)( a − b) 2 2 a − ab − ab + b 2 2 a − 2ab + b
    10. 10. Perfect Square Trinomial 2 ( a − b) ( a − b)( a − b) 2 2 a − ab − ab + b 2 2 a − 2ab + b
    11. 11. Perfect Square Trinomial 2 ( a − b) ( a − b)( a − b) 2 2 a − ab − ab + b 2 2 a − 2ab + b
    12. 12. Perfect Square Trinomial 2 ( a − b) ( a − b)( a − b) 2 2 a − ab − ab + b 2 2 a − 2ab + b
    13. 13. Perfect Square Trinomial 2 ( a − b) ( a − b)( a − b) 2 2 a − ab − ab + b 2 2 a − 2ab + b First term squared, last term squared, middle term is 2 times first term times last term
    14. 14. Example 1 Factor. 2 2 a. 9x + 12x + 4 b. y − 20 y + 100 2 2 c. x − 14x + 49 d. x + 7x + 14
    15. 15. Example 1 Factor. 2 2 a. 9x + 12x + 4 b. y − 20 y + 100 (3x 2 2 c. x − 14x + 49 d. x + 7x + 14
    16. 16. Example 1 Factor. 2 2 a. 9x + 12x + 4 b. y − 20 y + 100 2 (3x +2) 2 2 c. x − 14x + 49 d. x + 7x + 14
    17. 17. Example 1 Factor. 2 2 a. 9x + 12x + 4 b. y − 20 y + 100 2 (3x +2) (y 2 2 c. x − 14x + 49 d. x + 7x + 14
    18. 18. Example 1 Factor. 2 2 a. 9x + 12x + 4 b. y − 20 y + 100 2 2 (3x +2) ( y −10) 2 2 c. x − 14x + 49 d. x + 7x + 14
    19. 19. Example 1 Factor. 2 2 a. 9x + 12x + 4 b. y − 20 y + 100 2 2 (3x +2) ( y −10) 2 2 c. x − 14x + 49 d. x + 7x + 14 2 ( x − 7)
    20. 20. Example 1 Factor. 2 2 a. 9x + 12x + 4 b. y − 20 y + 100 2 2 (3x +2) ( y −10) 2 2 c. x − 14x + 49 d. x + 7x + 14 2 ( x − 7) Not a perfect square trinomial
    21. 21. Difference of Squares ( a − b)( a + b)
    22. 22. Difference of Squares ( a − b)( a + b) 2 2 a + ab − ab − b
    23. 23. Difference of Squares ( a − b)( a + b) 2 2 a + ab − ab − b 2 2 a −b
    24. 24. Difference of Squares ( a − b)( a + b) 2 2 a + ab − ab − b 2 2 a −b
    25. 25. Difference of Squares ( a − b)( a + b) 2 2 a + ab − ab − b 2 2 a −b
    26. 26. Difference of Squares ( a − b)( a + b) 2 2 a + ab − ab − b 2 2 a −b First term squared, last term squared, subtraction between the two terms
    27. 27. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 2 2 c. t − 900 d. y + 100 4 4 8 2 e. 25x y − 36z f. 16h − 144
    28. 28. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x 2 2 c. t − 900 d. y + 100 4 4 8 2 e. 25x y − 36z f. 16h − 144
    29. 29. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x −9) 2 2 c. t − 900 d. y + 100 4 4 8 2 e. 25x y − 36z f. 16h − 144
    30. 30. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x −9) (8x + 9) 2 2 c. t − 900 d. y + 100 4 4 8 2 e. 25x y − 36z f. 16h − 144
    31. 31. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x −9) (8x + 9) (r + 11) 2 2 c. t − 900 d. y + 100 4 4 8 2 e. 25x y − 36z f. 16h − 144
    32. 32. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x −9) (8x + 9) (r + 11) (r − 11) 2 2 c. t − 900 d. y + 100 4 4 8 2 e. 25x y − 36z f. 16h − 144
    33. 33. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x −9) (8x + 9) (r + 11) (r − 11) 2 2 c. t − 900 d. y + 100 (t + 30) 4 4 8 2 e. 25x y − 36z f. 16h − 144
    34. 34. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x −9) (8x + 9) (r + 11) (r − 11) 2 2 c. t − 900 d. y + 100 (t + 30) (t − 30) 4 4 8 2 e. 25x y − 36z f. 16h − 144
    35. 35. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x −9) (8x + 9) (r + 11) (r − 11) 2 2 c. t − 900 d. y + 100 (t + 30) (t − 30) Not a difference of squares 4 4 8 2 e. 25x y − 36z f. 16h − 144
    36. 36. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x −9) (8x + 9) (r + 11) (r − 11) 2 2 c. t − 900 d. y + 100 (t + 30) (t − 30) Not a difference of squares 4 4 8 2 e. 25x y − 36z f. 16h − 144 2 2 4 (5x y + 6z )
    37. 37. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x −9) (8x + 9) (r + 11) (r − 11) 2 2 c. t − 900 d. y + 100 (t + 30) (t − 30) Not a difference of squares 4 4 8 2 e. 25x y − 36z f. 16h − 144 2 2 4 2 2 4 (5x y + 6z ) (5x y − 6z )
    38. 38. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x −9) (8x + 9) (r + 11) (r − 11) 2 2 c. t − 900 d. y + 100 (t + 30) (t − 30) Not a difference of squares 4 4 8 2 e. 25x y − 36z f. 16h − 144 2 2 4 2 2 4 (5x y + 6z ) (5x y − 6z ) (4h + 12)
    39. 39. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x −9) (8x + 9) (r + 11) (r − 11) 2 2 c. t − 900 d. y + 100 (t + 30) (t − 30) Not a difference of squares 4 4 8 2 e. 25x y − 36z f. 16h − 144 2 2 4 2 2 4 (5x y + 6z ) (5x y − 6z ) (4h + 12) (4h − 12)
    40. 40. Homework
    41. 41. Homework p. 410 #1-42 multiples of 3 “There are two kinds of men who never amount to much: those who cannot do what they are told and those who can do nothing else.” - Cyrus H. Curtis
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