Show that $3^{2n+1}-4^{n+1}+6^n$ is never prime for natural n except 1. Show that $3^{2n+1}-4^{n+1}+6^n$ is never prime for natural n except 1. I tried factoring this expression but couldn't get very far. It is simple to show for even n but odd n was more difficult, at least for me.

$$3 \cdot 3^{2n}-4\cdot 2^{2n}+2^n\cdot  3^n$$ has the form
$$3x^2-4y^2+xy=(x-y)(3x+4y)$$
