Factorize $27 m^{3} - 216 n^{3}$

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Solution

$27 m^{3} - 216 n^{3}$

$= 3^{3} m^{3} - 6^{3} n^{3}$

$= {(3 m)}^{3} - {(6 n)}^{3}$

$= (3 m - 6 n) [{(3 m)}^{2} + {(6 n)}^{2} + 3 m .6 n]$

$= (3 m - 6 n) (9 m^{2} + 36 n^{2} + 18 m n)$

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