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Express as the product of four factors

  1. Nov 23, 2009 #1
    1. The problem statement, all variables and given/known data
    Express as the product of four factors
    Is this correct?
    [tex]a^6 - b^6 = (a - b)(a^5 + a^4b + a^3b^2 + a^2b^3 + ab^4 + b^3)[/tex]
     
  2. jcsd
  3. Nov 23, 2009 #2

    HallsofIvy

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    What you have written is true. It is not a "correct" response to the problem because, obviously, it does not have four factors. Start again. Think of [itex]a^6- b^6[/itex] as [itex](a^3)^2- (a^3)^2[/itex].
     
  4. Nov 23, 2009 #3
    I don't get it?!
     
  5. Nov 23, 2009 #4
    Hi MorallyObtuse,
    By the law of indices (a m)n=amxn
    and so you can also represent it like this(like HallsofIvy said)
    =(a^3)^2-(b^3)^2
    And then you can simplyfy it like this
    =(a^3-b^3)(a^3+b^3)
    and finaly u have your 4 terms
    (a-b) (a^2+ab+b^2) (a+b)(a^2-ab+b^2)
    I think you get it.
     
  6. Nov 23, 2009 #5
    No I don't get it:biggrin::biggrin::biggrin:
     
  7. Nov 23, 2009 #6

    Mark44

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    a6 - b6 = (a3 + b3)(a3 - b3)
    Each factor on the right can be further factored using known formulas for the sum of cubes and difference of cubes.
     
  8. Nov 24, 2009 #7

    HallsofIvy

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    Then you should talk to your teacher about it.
     
  9. Nov 24, 2009 #8
    I did get it, just joking with 1/2" :biggrin:
     
  10. Nov 24, 2009 #9
    And thanks very much :)

    [itex](a-b) (a^2+ab+b^2) (a+b)(a^2-ab+b^2)[/itex]
     
  11. Nov 24, 2009 #10

    Borek

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    [tex]1 \times 1 \times 1 \times (a^6 - b^6)[/tex]
     
  12. Nov 24, 2009 #11

    Mark44

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    Heck, I can find 7 factors!
    [tex]1 \times 1 \times 1 \times 1 \times 1 \times 1 \times (a^6 - b^6)[/tex]:biggrin:
     
  13. Nov 24, 2009 #12

    HallsofIvy

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    Yes, but that would be marked wrong because the problem asked for four factors. Borek's brilliant answer gets the gold star!
     
  14. Nov 25, 2009 #13

    Mark44

    Staff: Mentor

    I was hoping for extra credit because I went above and beyond the requirements.
     
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