Question

$m^3 + 64n^3 =$

Explanation:

Step1: Recognize sum of cubes

Identify $m^3 + 64n^3$ as $a^3 + b^3$, where $a=m$, $b=4n$ (since $4^3=64$).

Step2: Apply sum of cubes formula

Use the identity $a^3 + b^3=(a+b)(a^2-ab+b^2)$.
Substitute $a=m$, $b=4n$:

$$\begin{align*} m^3 + (4n)^3&=(m+4n)(m^2 - m(4n) + (4n)^2)\\ &=(m+4n)(m^2 -4mn +16n^2) \end{align*}$$

Answer:

$(m + 4n)(m^2 - 4mn + 16n^2)$