<s>[INST] Simplify $ z^4+z^2+1$ 
$$ z^4+z^2+1$$ 

I'm trying to get this form: $(z^2+z+1)(z^2-z+1)$ but don't know how.
I tried: $z^2(z^2+1)+1$
 [/INST] Using just the $\;a^n \pm b^n$ identities:
$$
\require{cancel}
z^4+z^2+1=\frac{z^6-1}{z^2-1}=\frac{(z^3-1)(z^3+1)}{z^2-1}=\frac{\cancel{(z-1)}(z^2+z+1)\,\cancel{(z+1)}(z^2-z+1)}{\cancel{z^2-1}}
$$
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