# proving long asymptotic bounds

I'm trying to find ways this simplify this formula and assuming numbers but that doesn't seem to help, the question is asking to prove or disprove:

$$3n(\log_{}n)^2 + 4n = \Omega (2n^2 \log_{}n +1)$$

I tried to assume $$n_0$$ as $$1$$ and $$10$$ to simplify it but that didn't help to find a positive constant $$c$$.

• The claim is false. – Yuval Filmus Oct 12 at 6:34
• How to simplify it so I don’t need to assume numbers – Xi N Oct 12 at 16:38
• You can drop the low-order terms on both sides. – Yuval Filmus Oct 12 at 16:51
• Does that work for proving things? – Xi N Oct 12 at 17:03
• It works perfectly. Try to understand why, though. – Yuval Filmus Oct 12 at 17:31