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Math Help - Factoring problem.

  1. #1
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    Factoring problem.

    Hello, I am reviewing some algebra concepts for a class I will be taking in the spring. I a trying to factor the polynomial: x4-11x2y2+y4. I know the answer is (x2-3xy-y2)(x2+3xy-y2). A hint was given to add a term to make a complete square, and then immediately subtract the term which yields a difference of two squares which can then be factored. I cannot figure out what term to add to this equation to put it in the form of a difference of two squares. If someone could explain to me the steps to take in order to factor this, or provide some intuition on how this works I would greatly appreciate it. Thank you for your time and consideration.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Factoring problem.

    You could write:

    x^4-11x^2y^2+y^4=(x^4-2x^2y^2+y^4)-9x^2y^2=(x^2-y^2)^2-(3xy)^2=

    (x^2-y^2+3xy)(x^2-y^2-3xy)=(x^2+3xy-y^2)(x^2-3xy-y^2)
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  3. #3
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    Re: Factoring problem.

    Thank you for your help, I don't know why I didn't see that before.
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