Understanding and proving Big O notation in discrete math

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I am new to discrete math and there is something that I don't get about this big oh solution. The question is asking to show that $f(n)=n^2+2n+1$ is $O(n^2)$ and to prove that we set the equation $n^2+2n^2+n^2=4n^2$.

I am just confused as to why we raised the single $n$ power to $n$ squared? And the $1$ to $n$ squared?