How to determine time complexity with a simple way?
Asymptotic notation satisfies the following two useful properties:
$$
\Theta(f(n)) + \Theta(g(n)) = \Theta(\max(f(n),g(n)) \\
\Theta(f(n)) \Theta(g(n)) = \Theta(f(n)g(n))
$$
Using these, you can determine that $f(n) = \Theta(4n^2\log^2 n)$.

Now you can check each of 1.-5. individually, using the fact that $n^a\log^bn = O(n^c\log^dn)$ iff $a &lt; c$ or $a=c$ and $b \leq d$.