Factorise:

$a^{6} + 27 b^{3}$

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Solution

$W e k n o w a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2}) a^{6} + 27 b^{3} = (a^{2})^{3} - (3 b)^{3} = (a^{2} + 3 b) ((a^{2})^{2} - 3 a^{2} b + (3 b)^{2}) = (a^{2} + 3 b) (a^{4} - 3 a^{2} b + 9 b^{2})$

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