Factorize :
$a^{6} - 7 a^{3} - 8$

(a + 2) (a - 1) (a^{2} + 2 a + 4) (a^{2} - a + 1)

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(a - 2) (a + 1) (a^{2} + 2 a + 4) (a^{2} - a + 1)

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(a + 2) (a - 1) (a^{2} - 2 a + 4) (a^{2} + a + 1)

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(a - 2) (a - 1) (a^{2} + 2 a + 4) (a^{2} + a + 1)

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Solution

The correct option is B $(a - 2) (a + 1) (a^{2} + 2 a + 4) (a^{2} - a + 1)$
$a^{6} - 7 a^{3} - 8$
$= a^{6} - 8 a^{3} + a^{3} - 8$
$= a^{3} (a^{3} - 8) + (a^{3} - 8)$
$= (a^{3} - 8) (a^{3} + 1)$
$= (a^{3} - 2^{3}) (a^{3} + 1)$
$= (a - 2) (a^{2} + a (2) + 2^{2}) (a + 1) (a^{2} - a (1) + 1^{2})$
$= (a - 2) (a^{2} + 2 a + 4) (a + 1) (a^{2} - a + 1)$
$= (a - 2) (a + 1) (a^{2} + 2 a + 4) (a^{2} - a + 1)$

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