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Math Help - Express x⁴ + y⁴ + z⁴ - 2yz - 2zx - 2xy as the product of four factors.

  1. #1
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    Express x⁴ + y⁴ + z⁴ - 2yz - 2zx - 2xy as the product of four factors.

    Hi,

    How do I start this?

    Express x^4 + y^4 + z^4 - 2y^2z^2 - 2z^2x^2 - 2x^2y^2 as the product of four factors.
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  2. #2
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    Does this work?

    If you put the numbers (x,y,z) = (2,1,1) your expression is zero. This means (x-y-z) could be a factor. By symmetry, (-x+y-z) and (-x-y+z) could also be factors. Last, (-2,1,1) also makes your expression zero. So (x+y+z) should be a factor. Try multiplying:
    <br />
(x-y-z)(-x+y-z)(-x-y+z)(x+y+z)<br />
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  3. #3
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    Quote Originally Posted by qmech View Post
    If you put the numbers (x,y,z) = (2,1,1) your expression is zero. This means (x-y-z) could be a factor. By symmetry, (-x+y-z) and (-x-y+z) could also be factors. Last, (-2,1,1) also makes your expression zero. So (x+y+z) should be a factor. Try multiplying:
    <br />
(x-y-z)(-x+y-z)(-x-y+z)(x+y+z)<br />
    (x-y-z)(-x+y-z)(-x-y+z)(x+y+z)
    = x^4 + x^3z - y^2x^2 - x^2yz
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  4. #4
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    Am I corect?
    Is the question finished?
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  5. #5
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    \left ( x-y-z \right )\left ( x+y-z \right )\left ( x-y+z \right )\left ( x+y+z \right )
    hope it's right !
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