If m - 5n = 2, then the value of (m³ - 125n³ - 30mn) is?

A. 6

B. 7

C. 8

D. 9

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & {\text{Given, }}m - 5n = 2 \cr & {\text{Find, }}{m^3} - 125{n^3} - 30mn \cr & \Rightarrow m - 5n = 2 \cr & \left( {{\text{Cubing both sides}}} \right) \cr & \Rightarrow {\left( {m - 5n} \right)^3} = {2^3} \cr & \Rightarrow {m^3} - 125{n^3} - 3m \times 5n\left( {m - 5n} \right) = 8 \cr & \Rightarrow {m^3} - 125{n^3} - 15mn \times 2 = 8 \cr & \Rightarrow {m^3} - 125{n^3} - 30mn = 8 \cr} $$