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Math Help - Factoring

  1. #1
    Junior Member DIOGYK's Avatar
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    Factoring

    Hello.
    This is another problem from my book that I've been unable to solve.


    Problem 122. Factor:
    (b) x(y^2-z^2)+y(z^2-x^2)+z(x^2-y^2);


    Thanks in advance.
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  2. #2
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    Re: Factoring

    Well isn't it obvious? x = 4^2 because y^2 told x^2 to lend him a power from z^2;
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  3. #3
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    Re: Factoring

    Hello, DIOGYK!

    122.\text{ Factor: }\;x(y^2-z^2)+y(z^2-x^2)+z(x^2-y^2)

    \begin{array}{cc} \text{Expand:} & xy^2 - xz^2 + yz^2 - x^2y + x^2z - y^2z \\ \text{Rearrange:} & x^2z - x^2y -xz^2 + xy^2 + yz^2 - y^2z \\ \text{Factor:} & x^2(z-y) -x(z^2-y^2) + yz(z-y) \\ \text{Factor:} & x^2(z-y) - x(z-y)(z+y) - yz(z-y) \\ \text{Factor:} & (z-y)\big[x^2 - x(z+y) + yz \big] \\ \text{Expand:} & (z-y)(x^2-xz - xy + yz) \\ \text{Factor:} & (z-y)\big[x(x-z) - y(x-z)\big] \\ \text{Factor:} & (z-y)(x-z)(x-y) \\ \text{Rearrange:} & (x-y)(y-z)(z-x) \end{array}
    Thanks from DIOGYK
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  4. #4
    Junior Member DIOGYK's Avatar
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    Re: Factoring

    Thank you Soroban for very clear explanation. I should have tried more myself, this wasn't hard.

    That's the problem uperkurk, y^2 didn't tell me what it told x^2.
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