Factorise : $y^{16} - 63 y^{8} - 64$

(y^{8} - 1) (y^{4} + 8) (y^{4} - 8)

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{(y^{4} + 8)}^{2} (y^{8} + 1)

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{(y^{4} - 8)}^{2} (y^{8} - 1)

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(y^{4} + 8) (y^{4} - 8) (y^{8} + 1)

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Solution

The correct option is D $(y^{4} + 8) (y^{4} - 8) (y^{8} + 1)$
$y^{16} - 63 y^{8} - 64$
$= y^{16} - 64 y^{8} + y^{8} - 64$
$= y^{8} (y^{8} - 64) + 1 (y^{8} - 64)$
$= (y^{8} - 64) (y^{8} + 1)$
$= (y^{4} - 8) (y^{4} + 8) (y^{8} + 1)$

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