Factorise: $2 x - 32 x^{5}$

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Solution

We need to factorise $2 x - 32 x^{5}$
Here we can take $2 x$ common.
Thus we have $2 x - 32 x^{5} = 2 x (1 - 16 x^{4})$
Further it can be written as $2 x (1 - 16 x^{4}) = 2 x [1^{2} - (4 x^{2})^{2}]$
$= 2 x (1 - 4 x^{2}) (1 + 4 x^{2})$
$= 2 x (1 + 4 x^{2}) (1 - 2 x) (1 + 2 x)$
Here we used $(a^{2} - b^{2}) = (a + b) (a - b)$
Thus factors are $2, x, (1 + 4 x^{2}), (1 - 2 x), (1 + 2 x)$ .

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