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Thread: factoring a large polynomial

  1. #1
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    factoring a large polynomial

    In completely factored form

    $\displaystyle a^2x^2-b^2y^2+b^2x^2-a^2y^2$

    is.......


    a) $\displaystyle (a-b)(a+b)(x^2+y^2)$
    b) $\displaystyle (a^2+b^2)(x^2-y^2)$
    c) $\displaystyle (a^2-b^2)(x^2+y^2)$
    d) $\displaystyle (a+b)(x-y)$
    e) $\displaystyle (a^2+b^2)(x+y)(x-y)$

    what would be the answer?

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  2. #2
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    Quote Originally Posted by alaricepent View Post
    In completely factored form

    $\displaystyle a^2x^2-b^2y^2+b^2x^2-a^2y^2$

    is.......


    a) $\displaystyle (a-b)(a+b)(x^2+y^2)$
    b) $\displaystyle (a^2+b^2)(x^2-y^2)$
    c) $\displaystyle (a^2-b^2)(x^2+y^2)$
    d) $\displaystyle (a+b)(x-y)$
    e) $\displaystyle (a^2+b^2)(x+y)(x-y)$

    what would be the answer?

    HELP!!
    $\displaystyle a^2x^2-b^2y^2+b^2x^2-a^2y^2$

    $\displaystyle =a^2x^2+b^2x^2-a^2y^2-b^2y^2$

    $\displaystyle =x^2(a^2+b^2)-y^2(a^2+b^2)$

    $\displaystyle =(a^2+b^2)(x^2-y^2)$

    $\displaystyle =(a^2+b^2)(x+y)(x-y)$

    Did you get it now???
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