Factorise and simplify: $64 x^{12} - 512$ .

(4 x^{4} - 8) (16 x^{8} + 32 x^{4} + 64)

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(4 x^{4} - 8) (16 x^{8} - 32 x^{4} + 64)

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(4 x^{4} + 64) (16 x^{8} + 32 x^{4} + 64)

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(4 x^{4} - 8) (16 x^{8} + 64 x^{4} + 64)

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Solution

The correct option is A $(4 x^{4} - 8) (16 x^{8} + 32 x^{4} + 64)$
$64 x^{12} - 512 = (4 x^{4})^{3} - 8^{3}$
We know that the difference of two cubes, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$
So, $(4 x^{4})^{3} - 8^{3} = (4 x^{4} - 8) ((4 x^{4})^{2} + 32 x^{4} + 8^{2})$
$(4 x^{4})^{3} - 8^{3} = (4 x^{4} - 8) (16 x^{8} + 32 x^{4} + 64)$

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