Factorise:

$a^{4} - 343 a$

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Solution

$W e k n o w a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2}) a^{4} - 343 a = a (a^{3} - 343) = a (a^{3} - 7^{3}) = a [(a - 7) (a^{2} + 7 a + 7^{2})] = a [(a - 7) (a^{2} + 7 a + 49)] = a (a - 7) (a^{2} + 7 a + 49)$

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