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factrorize $-a^3+a^2b+a^2c+ab^2-2abc+ac^2-b^3+b^2c+bc^2-c^3$

or $$ -(a^3 + b^3 + c^3) + (a^2 b + a b^2 + b^2 c + b c^2 + c^2 a + c a^2) - 2(abc) $$

It is a so long polynomial I don't have any ideas for starting factoring what should I do?

Will Jagy
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Taha Akbari
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    Assuming it can be factored, it looks to me very much like the product of three factors of the form $(\pm a \pm b \pm c)$, perhaps one of $a, b, c$ is lacking from one of the factors as well. Try playing around with that, and see what you get. – Arthur Nov 13 '16 at 12:54
  • is there a typo in you term? twice $a^2b$? – Dr. Sonnhard Graubner Nov 13 '16 at 13:45

1 Answers1

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$$ ( a +b - c) ( b + c - a ) ( c + a - b) $$ This is one factor short of Heron's formula, $$ (a + b + c) ( a +b - c) ( b + c - a ) ( c + a - b) = 2 (b^2 c^2 + c^2 a^2 + a^2 b^2) - (a^4 + b^4 + c^4) $$

Will Jagy
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