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Thread: Hard factoring problem

  1. #1
    Aug 2011

    Question Hard factoring problem

    Hi. I had this practice problem for learning factoring:

    $\displaystyle 4a^2c^2-(a^2-b^2+c^2)^2$

    I eventually gave up, but the answer was:

    $\displaystyle (a+b+c)(a+b-c)(a-b+c)(b-a+c)$

    I'm wondering if anyone understands what steps were taken. (Which unfortunately were not described on the answer page.) I tried distributing, grouping, and factoring formulas, but the closest I got (if you want to call it progress) was:

    $\displaystyle (a^2+b^2)^2+c(3a^2c-a^2+b^2+b^2c-c^3)$

    Anyway, I'm about at the point now where I can hardly see the numbers clearly...
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  2. #2
    Member anonimnystefy's Avatar
    Jul 2011

    Re: Hard factoring problem

    hi infraRed

    you can write that like this:
    $\displaystyle (2ac)^2-(a^2-b^2+c^2)^2$

    try to factor this expression with difference of the squares method.
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