# Factoring

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I am wondering if anyone could factor this for me?

$a^{4} + 2b^{4} + c^{4} - 2a^{2}c^{2} - 2a^{2}b^{2} + 2b^{2}c^{2}$

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Well I can't do it, I can simplify it a bit but that'll be of little use.

$a^{4} + 2b^{4} + c^{4} - 2a^{2}c^{2} - 2a^{2}b^{2} + 2b^{2}c^{2}$

$a^{4}+c^{4}+2(b^{4}-ac^{4}-a^{2}b^{2}+b^{2}c^{2})$

$a^{4}+c^{4}+2[b(b^{3}+bc^{2})-a(c^{4}+ab^{2})]$

I think it's

(a2+b2-c2)2

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How did you do that Quantasm? And if possible use Latex please, because I want to avoid confusion.

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Quantasm's answer is wrong. You can tell by expanding his expression. I could not factor your expression (either on paper or using mathcad) therefore I think that it can't be done.

By the way is this homework? Why else would you need to factor that expression?

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I tried factoring on my trusty 89 and got a nonsense answer so I'm pretty sure it can't be. It's been pretty good about factoring.

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I suspect there may be a mistake in the question. If the coefficient of B^4 is 1 instead of 2 it factorises

a^{4} + b^{4} + c^{4} - 2a^{2}c^{2} - 2a^{2}b^{2} + 2b^{2}c^{2}

= (-a^2+b^2+c^2)^2

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Quantasm's answer is wrong. You can tell by expanding his expression. I could not factor your expression (either on paper or using mathcad) therefore I think that it can't be done.

By the way is this homework? Why else would you need to factor that expression?

Nope, it's not homework at all. I was just challenging myself. Relative to this thread: http://www.scienceforums.net/forums/showthread.php?t=17549. See the big crazy formula and the simple formula? I was just trying to factor the big formula and see if it would arrive to the small formula.

That's all.

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Also Tartaglia , how did you factor it? Can we figure it our by our own hands, not gadgets please?

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Evo - The one I put up is an obvious square (x+y-z)^2 = X^2+y^2+z^2+2xy-2xz-2yz. That's why I think there may be a mistake in your original

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