A function fff satisfies f(x+y)=f(x)+f(y)+3xyf(x+y) = f(x) + f(y) + 3xyf(x+y)=f(x)+f(y)+3xy. Given f(1)=4f(1) = 4f(1)=4, determine f(n)f(n)f(n) for a positive integer nnn.
f(n)=32n2+52nf(n) = \frac{3}{2}n^2 + \frac{5}{2}nf(n)=23n2+25n
f(n)=3n2+1f(n) = 3n^2 + 1f(n)=3n2+1
f(n)=n2+3nf(n) = n^2 + 3nf(n)=n2+3n
f(n)=2n2+2nf(n) = 2n^2 + 2nf(n)=2n2+2n