Factorise : $z^{2} - 4 z^{6} + z^{8} - 4$

(z^{2} - 1) (z^{6} - 1)

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(z^{2} + 4) (z^{6} - 1)

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(z^{2} - 4) (z^{6} + 1)

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(z^{2} + 4) (z^{6} + 1)

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Solution

The correct option is C $(z^{2} - 4) (z^{6} + 1)$
$z^{2} - 4 z^{6} + z^{8} - 4$
$= z^{8} - 4 z^{6} + z^{2} - 4$
$= z^{6} (z^{2} - 1) + 1 (z^{2} - 4)$
$= (z^{2} - 4) (z^{6} + 1)$

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