Resources I've found on time complexity are unclear about when it is okay to ignore terms in a time complexity equation, specifically with non-polynomial examples.

It's clear to me that given something of the form n2 + n + 1, the last two terms are insignificant.

Specifically, given two categorizations, 2n, and n*(2n), is the second in the same order as the first? Does the additional n multiplication there matter? Usually resources just say xn is in an exponential and grows much faster... then move on.

I can understand why it wouldn't since 2n will greatly outpace n, but because they're not being added together, it would matter greatly when comparing the two equations, in fact the difference between them will always be a factor of n, which seems important to say the least.