\(3^{n+2}+2^{n+3}+3^n+2^{n+1}=\left(3^{n+2}+3^n\right)+\left(2^{n+3}+2^{n+1}\right)\)
\(=3^n\left(3^2+1\right)+2^{n+1}\left(2^2+1\right)\)
\(=3^n\cdot10+2^{n+1}\cdot5\)
\(=3^n\cdot10+2^n\cdot2\cdot5\)
\(=3^n\cdot10+2^n\cdot10\)
\(=10\left(3^n+2^n\right)⋮10\)