Prove assertion that $(n+2lnn{)}^3$inO$(n^3)$ is true by definition. Clearly provide and demarcate the following elements in your proof:

Give a formal definition of the asymptotic notation that includes the relevant inequality. $[4$ points$]$

State what the function $f(n)$ and $g(n)$ in the definition are with respect to the claim. $[4$ points$]$ points$]$

Provide detailed algebraic manipulation and mathematical arguments to derive the constants. $[10$ points$]$

Give concluding remarks that include how the constants that you derive make the inequality in the definition hold and the proposition true. $[3$ points$]$