3^(n+2)-2^(n+2)+3^n-2^n
=3^(n+2)+3^n-2^(n+2)-2^n
=3^n*(3^2+1)-2^n*(2^2+1)
=10*3^n-5*2^n
=10*3^n-10*2^(n-1)是10的倍数.