<s>[INST] Reference (database) for polynomials 
Suppose I want to know what is known about the following polynomial 
  $$x^4 - 2x^2y^2 - 2x^2z^2 + y^4 - 2y^2z^2 + z^4.$$

Where can one find such information?
 [/INST] It's just
$$(x+y+z)(x-y-z)(x+y-z)(x-y+z).$$
We can get it by the following way.
$$x^4+y^4+z^4-2x^2y^2-2x^2z^2-2y^2z^2=$$
$$=x^4+y^4+z^4-2x^2y^2-2x^2z^2+2y^2z^2-4y^2z^2=$$
$$=(x^2-y^2-z^2)^2-(2yz)^2=$$
$$=(x^2-y^2-z^2-2yz)(x^2-y^2-z^2+2yz)=$$
$$=(x^2-(y+z)^2)(x^2-(y-z)^2),$$
which gives the final factorization. 
Also, the area of a triangle with sides-lengths $x$, $y$ and $z$ it's
$$\frac{1}{4}\sqrt{2x^2y^2+2x^2z^2+2y^2z^2-x^4-y^4-z^4}$$ 
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