Answer 1

It is known that,

\[a^3  -  b^3    =   \left( a - b \right)\left( a^2 + b^2 + ab \right)\]

\[\ 27 m^3  - 216 n^3 \] 

\[ = 27\left[ m^3 - 8 n^3 \right]\] 

\[ = 27\left[ \left( m \right)^3 - \left( 2n \right)^3 \right]\] 

\[ = 27\left[ \left( m - 2n \right)\left\{ \left( m \right)^2 + \left( 2n \right)^2 + \left( m \right) \times \left( 2n \right) \right\} \right]\] 

\[ = 27\left( m - 2n \right)\left( m^2 + 4 n^2 + 2mn \right)\]