EvoN1020v Posted January 23, 2006 Share Posted January 23, 2006 I am wondering if anyone could factor this for me? [math]a^{4} + 2b^{4} + c^{4} - 2a^{2}c^{2} - 2a^{2}b^{2} + 2b^{2}c^{2}[/math] Link to comment Share on other sites More sharing options...
the tree Posted January 23, 2006 Share Posted January 23, 2006 Well I can't do it, I can simplify it a bit but that'll be of little use. [math]a^{4} + 2b^{4} + c^{4} - 2a^{2}c^{2} - 2a^{2}b^{2} + 2b^{2}c^{2}[/math] [math]a^{4}+c^{4}+2(b^{4}-ac^{4}-a^{2}b^{2}+b^{2}c^{2})[/math] [math]a^{4}+c^{4}+2[b(b^{3}+bc^{2})-a(c^{4}+ab^{2})][/math] Link to comment Share on other sites More sharing options...
Quantasm Posted January 23, 2006 Share Posted January 23, 2006 I think it's (a2+b2-c2)2 Link to comment Share on other sites More sharing options...
EvoN1020v Posted January 24, 2006 Author Share Posted January 24, 2006 How did you do that Quantasm? And if possible use Latex please, because I want to avoid confusion. Link to comment Share on other sites More sharing options...
m4rc Posted January 24, 2006 Share Posted January 24, 2006 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? Link to comment Share on other sites More sharing options...
JustStuit Posted January 24, 2006 Share Posted January 24, 2006 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. Link to comment Share on other sites More sharing options...
Tartaglia Posted January 24, 2006 Share Posted January 24, 2006 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 Link to comment Share on other sites More sharing options...
EvoN1020v Posted January 24, 2006 Author Share Posted January 24, 2006 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. Link to comment Share on other sites More sharing options...
EvoN1020v Posted January 24, 2006 Author Share Posted January 24, 2006 Also Tartaglia , how did you factor it? Can we figure it our by our own hands, not gadgets please? Link to comment Share on other sites More sharing options...
Tartaglia Posted January 24, 2006 Share Posted January 24, 2006 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 Link to comment Share on other sites More sharing options...
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