Factor each expression by factoring put the GCF.
(3n + 1)(4n + 1) + (n + 2)(4n + 1)

16n^2+16n+3

Steps:

I used the foil method:

(3n+1)(4n+1) = 12n^2+3n+4n+1
(n+2)(4n+1) = 4n^2+n+8n+2

Now combine like terms:

12n^2 + 4n^2 = 16n^2
3n + 4n + n + 8n = 16n
1 + 2 = 3

Put them together:

16n^2 + 16n + 3

Since there's nothing each variable has in common, that's the simplest answer you can get.