Factorize :

64 - $a^{3} b^{3}$

(3 + 4 a b) (16 + 4 a b + a^{2} b^{2})

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(3 + 4 a b) (16 + 4 a b - a^{2} b^{2})

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(3 - 4 a b) (16 + 4 a b - a^{2} b^{2})

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none of the above

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Solution

The correct option is D none of the above
$64 - a^{3} b^{3}$
$= 4^{3} - (a b)^{3}$
Using,

$(a^{3} - b^{3}) = (a - b) (a^{2} + a b + b^{2})$
$= (4 - a b) (16 + 4 a b + a^{2} b^{2})$

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