Factorise the following: $2 a^{3} - 54 b^{3}$

2 (a b + 3 b) (a^{2} + 3 b + 9 a b^{2})

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2 (a + 2 b) (a^{3} + 3 a b - 9 b^{3})

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(a - 3 b) (a^{2} + 3 b + 9 a b^{2})

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2 (a - 3 b) (a^{2} + 3 a b + 9 b^{2})

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Solution

The correct option is D $2 (a - 3 b) (a^{2} + 3 a b + 9 b^{2})$
$2 a^{3} - 54 b^{3}$
Using, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$
$= 2 (a^{3} - 27 b^{3})$
$= 2 [(a)^{3} - (3 b)^{3}]$
$= 2 (a - 3 b) [(a)^{2} + (a) (3 b) + (3 b)^{2}]$
$= 2 (a - 3 b) (a^{2} + 3 a b + 9 b^{2})$

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