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Algebra 6 Point 10
 

Algebra 6 Point 10

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    Algebra 6 Point 10 Algebra 6 Point 10 Presentation Transcript

    • 6.10 Special Products
      Objectives:
      • To square a binomial
      • To find products of the form (a + b)(a – b)
      Frameworks: 10.P.3
    • How do we square a binomial?
      (x + 3)2 = (x + 3)(x + 3)
      FOIL: = x2 + 3x + 3x + 9
      = x2 + 6x + 9
      Square of a sum:
      (first term)2 + 2(first x last) + (last term)2
    • Squaring a difference:
      (3x - 5)2 = (3x - 5)(3x - 5)
      FOIL: = 9x2 - 15x - 15x + 25
      = 9x2 - 30x + 25
      Square of a difference:
      (first term)2- 2(first x last) + (last term)2
    • Notice
      (x + 3)2 ≠ x2 + 9
      (3x – 5)2≠ 9x2+ 25
      When you square a binomial the product always contains three terms.
    • Square of a Binomial
      (a + b)2 = a2+ 2ab + b2
      (a - b)2 = a2- 2ab + b2
    • Try some:
      (x – 8)(x - 8)
      (2y + 1)2
      (3x - 2)2
      (5a + 1)2
    • What about multiplying the sum and difference of the same 2 terms?
      (x + 6)(x - 6)
      FOIL: = x2 - 6x + 6x - 36
      = x2 - 36
      (first term)2 - (last term)2
      Product of (a + b)(a – b):
      a2- b2
    • Try some:
      (c – 1)(c + 1)
      (4x – 3)(4x + 3)
      (3x + 2)(3x – 2)
    • And now for something really fun:
      (x – 5)2 = (x -8)(x + 8)
      x2– 10x + 25 = x2 – 64
      - x2 = -x2
      – 10x + 25 = – 64
      - 25 - 25
      - 10 x = - 89
      x = 8.9
    • Try another fun one:
      (x – 4)2 = (x -8)(x + 2)
    • Turn to page 234
      Do 1-4