Factorise : $a^{6} - 26 a^{3} - 27$

(a - 3) (a + 1) (a^{2} + a + 1) (a^{2} + 3 a + 9)

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(a - 3) (a - 1) (a^{2} + a + 1) (a^{2} + 3 a + 9)

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(a - 3) (a + 1) (a^{2} + 3 a + 9) (a^{2} - a + 1)

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(a + 3) (a - 1) (a^{2} + 3 a + 9) (a^{2} + a + 1)

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Solution

The correct option is C $(a - 3) (a + 1) (a^{2} + 3 a + 9) (a^{2} - a + 1)$
$a^{6} - 26 a^{3} - 27$
$= a^{6} - 27 a^{3} + a^{3} - 27$
$= a^{3} (a^{3} - 27) + 1 (a^{3} - 27)$
$= (a^{3} - 27) (a^{3} + 1)$
$= (a - 3) (a^{2} + 3 a + 9) (a + 1) (a^{2} - a + 1)$

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