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Factorisation Using Algebraic Identities

Factorise: a6...

Question

Factorise:

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

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Solution

$a^{6} - 7 a^{3} - 8 = a^{6} + a^{3} - 8 a^{3} - 8 = a^{3} (a^{3} + 1) - 8 (a^{3} + 1) = (a^{3} - 8) (a^{3} + 1) = [(a)^{3} - (2)^{3}] [(a)^{3} + (1)^{3}] = (a - 2) (a^{2} + 2 a + 4) (a + 1) (a^{2} - a + 1)$

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a^{6} - 7 a^{3} - 8

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