<s>[INST] Tricky Decomposition Decompose the following polynomial:
$A=x^4(y^2+z^2) + y^4(z^2+x^2) + z^4(x^2+y^2) +2x^2 y^2 z^2 $
(by the way I'm not quite sure about the tags and the title feel free to edit them if you wish)
 [/INST] $$
A = x^4(y^2+z^2) + x^2(y^4+2y^2 z^2 +z^4) +y^2z^2(y^2+z^2) \\
= (y^2+z^2)\left(x^4+(y^2+z^2)x^2 +y^2z^2\right) \\
=(y^2+z^2)(x^2+y^2)(z^2+x^2)
$$ 
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