<s>[INST] Solving a Polynomial Equation by Factoring. $n^3+12n^2+48n+64$
I know the sum of two cubes formula, $(a+b)(a^2-ab+b^2)$. I'm not sure how to apply it here? Any help would be appreciated.
 [/INST] Here it is an approach based on the Binomial Theorem:
\begin{align*}
n^{3} + 12n^{2} + 48n + 64 = {3\choose 0}n^{3}4^{0} + {3\choose 1}n^{2}4^{1} + {3\choose 2}n4^{2} + {3\choose 3}n^{0}4^{3} = (n+4)^{3}
\end{align*}
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