If (x - 4)(x2 + 4x + 16) = x3 - p, then p is equal to?

Answer: Option C

$$\begin{array}{rl}& \text{We know that }\\ & a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)\\ & x^3-p=\left(x-4\right)\left(x^2+4x+16\right)\\ & \Rightarrow x^3-p=\left(x^3-4^3\right)\\ & \Rightarrow p=4^3\left(\text{By comparison}\right)\\ & \text{So, }p=64\end{array}$$