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

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Uniteasy Admin · Accepted Answer

$$ a^4+b^4+c^4-2a^2b^2-2b^2c^2-2a^2c^2 $$
$$ =a^4+b^4+c^4-2a^2b^2+2b^2c^2-2a^2c^2-4b^2c^2 $$
$$ =(a^2-b^2-c^2)^2-4b^2c^2 $$
$$ =(a^2-b^2-c^2+2bc)(a^2-b^2-c^2-2bc) $$
$$ =\big[ a^2-(b-c)^2\big] \big[ a^2-(b+c)^2\big] $$
$$ =(a-b+c)(a+b-c)(a+b+c)(a-b-c) $$

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