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Math Help - Factorisation

  1. #1
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    Factorisation

    Factorize:   a^{2}-\left ( b+c \right )^{2}

    Iíve expanded it to see if I can find any solution:

      \left ( b+c \right )^{2}=b^{2}+2bc+c^{2}

      a^{2}-\left ( b^{2}+2bc+c^{2} \right )


      a^{2}-  b^{2}-2bc-c^{2} \right )


    But I canít get any further.
    What should I do now to simplify it? Please explain and show me a couple of clues or something?
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: Factorisation

    Quote Originally Posted by Benjy View Post
    Factorize:   a^{2}-\left ( b+c \right )^{2}

    Iíve expanded it to see if I can find any solution:

      \left ( b+c \right )^{2}=b^{2}+2bc+c^{2}

      a^{2}-\left ( b^{2}+2bc+c^{2} \right )


      a^{2}-  b^{2}-2bc-c^{2} \right )


    But I canít get any further.
    What should I do now to simplify it? Please explain and show me a couple of clues or something?
    Answer:  (a-(b+c))(a+(b+c))
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  3. #3
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    Re: Factorisation

    Quote Originally Posted by Benjy View Post
    Factorize:   a^{2}-\left ( b+c \right )^{2}
      a^{2}-\left ( b+c \right )^{2}=[a-(b+c)][a+(b+c)]
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  4. #4
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    Re: Factorisation

    Quote Originally Posted by Also sprach Zarathustra View Post
    Answer:  (a-(b+c))(a+(b+c))

    Quote Originally Posted by Plato View Post
      a^{2}-\left ( b+c \right )^{2}=[a-(b+c)][a+(b+c)]
    Thanks! Could you please explain methodically how you should do to find this solution.
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  5. #5
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: Factorisation

    Quote Originally Posted by Benjy View Post
    Thanks! Could you please explain methodically how you should do to find this solution.
    Plato, he's yours.
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  6. #6
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    Re: Factorisation

    Quote Originally Posted by Also sprach Zarathustra View Post
    Plato, he's yours.
    No I will let you have this one.
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  7. #7
    MHF Contributor Siron's Avatar
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    Re: Factorisation

    @ Benjy:
    Notice:
    a^2-b^2=(a-b)\cdot (a+b)
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  8. #8
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: Factorisation

    Quote Originally Posted by Siron View Post
    @ Benjy:
    Notice:
    a^2-b^2=(a-b)\cdot (a+b)
    "methodically" a and b are already taken, so you, Siron should say: x^2-y^2=(x-y)(x+y)
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  9. #9
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    Cool Re: Factorisation

    Quote Originally Posted by Siron View Post
    @ Benjy:
    Notice:
    a^2-b^2=(a-b)\cdot (a+b)
    Quote Originally Posted by Also sprach Zarathustra View Post
    "methodically" a and b are already taken, so you, Siron should say: x^2-y^2=(x-y)(x+y)



    thanks. I'm actually familiar with this one. But the one that I posted was much more complicated I think.
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  10. #10
    MHF Contributor Siron's Avatar
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    Re: Factorisation

    In case of factorisation it's very important to know the (most important) special products and even more important if you can recognize them.
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