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.
Hint: remember the binomial theorem $(a+b)^3 = a^3 + 3 a^2 b + 3 b^2 a + b^3.$
Now guess what $a$ and $b$ might be here.
I'm not sure what the question is; Is it to find what $a$ and $b$ are? If so, we multiply out the right side and receive a . Now, set $n=a$. Then the $b^3$ term must correspond to 64 (otherwise there would be an n). Therefore, $64 = b^3$, so $b = 4$.