Factorize :
$a^{4} - 343 a$ .

a (a - 7) (a^{3} + a + 36)

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a (a - 7) (a^{2} + 7 a + 49)

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a (4 a - 7) (a^{2} - a + 49)

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a (4 a - 7) (a^{3} + 7 a - 36)

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Solution

The correct option is B $a (a - 7) (a^{2} + 7 a + 49)$
$a^{4} - 343 a$
$= a (a^{3} - 343)$
Using,
$a^{3} - b^{3} = (a - b) (a^{2} + b^{2} + a b)$
$= a (a^{3} - 7^{3})$
$= a (a - 7) (a^{2} + 7^{2} + 7 a)$
$= a (a - 7) (a^{2} + 49 + 7 a)$

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