Factorise:
$x - 8 x y^{3}$

x (1 - 2 y) (1 + 2 y + 4 y^{2})

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x (1 + 2 y) (1 + 2 y + 4 y^{2})

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x (1 - 2 y) (1 - 2 y + 4 y^{2})

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x (1 + 2 y) (1 - 2 y + 4 y^{2})

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Solution

The correct option is B $x (1 - 2 y) (1 + 2 y + 4 y^{2})$
Formula used: $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$
Given, $x - 8 x y^{3} = x (1 - 8 y^{3})$
$= x [1^{3} - (2 y)^{3}]$
$= x [(1 - 2 y) (1^{2} + 1 \times 2 y + (2 y)^{2})]$
$= x (1 - 2 y) (1 + 2 y + 4 y^{2})$
Hence, Option A is correct.

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