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

A. 27

B. 8

C. 64

D. 0

Answer: Option C

Solution(By Examveda Team)

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