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Math Help - factorising - difference of squares

  1. #1
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    factorising - difference of squares

    hi,

    i have been asked to factorise the following

    l^8-256

    using the difference of squares a^2-b^2=(a+b)(a-b) and by working from the lowest term (l^2-2^2), i managed to get a solution but its was more down to guesswork than a systematic attempt to solve this.

    (l^4+16)(l^2+4)(l+2)(l-2)

    is there a way of dealing with these type of questions?

    thanks
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by sammy28 View Post
    hi,

    i have been asked to factorise the following

    l^8-265

    using the difference of squares a^2-b^2=(a+b)(a-b) and by working from the lowest term (l^2-2^2), i managed to get a solution but its was more down to guesswork than a systematic attempt to solve this.

    (l^4+16)(l^2+4)(l+2)(l-2)

    is there a way of dealing with these type of questions?


    thanks
    Hi sammy28,

    Isn't that supposed to be l^8-256?
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  3. #3
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    oops,
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  4. #4
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    Quote Originally Posted by masters View Post
    Hi sammy28,

    Isn't that supposed to be l^8-256?
    l^8-256 is the difference of two squares. Look at it this way:

    ((l^4)^2-16^2)

    (l^4-16)(l^4+16)

    ((l^2)^2-4^2)(l^4+16)

    (l^2-4)(l^2+4)(l^4+16)

    (l-2)(l+2)(l^2+4)(l^4+16)
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  5. #5
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    thanks masters
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