# How do you factor 2x^3 - 4x?

Apr 21, 2016

$2 {x}^{3} - 4 x = 2 x \left(x - \sqrt{2}\right) \left(x + \sqrt{2}\right)$

#### Explanation:

The difference of squares identity can be written:

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

We use this with $a = x$ and $b = \sqrt{2}$ later.

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First note that both terms are divisible by $2$ and by $x$, so they are both divisible by $2 x$, so separate that out as a factor first...

$2 {x}^{3} - 4 x = 2 x \left({x}^{2} - 2\right) = 2 x \left({x}^{2} - {\left(\sqrt{2}\right)}^{2}\right) = 2 x \left(x - \sqrt{2}\right) \left(x + \sqrt{2}\right)$