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.

You were going in the correct direction, as you said:
$a^3 + b^3 = (a+b)(a^2 - ab + b^2)$
If we apply the same here:
$^3+12^2+48+64 = ^3+ 4^3 + 12^2+48 = (n+4)(n^2 - 4n + 16) + 12n(n+4)$
If we take (n+4) common, we get:
$(n+4)(n^2 - 4n + 16 + 12n) = (n+4)(n^2 + 8n + 16) = (n+4)(n+4)^2 = (n+4)^3$Cheers
