Question

factorise
$a {}^{3} - \frac{1}{a {}^{3} } - 2a + \frac{2}{a}$

Answer 1

${a}^{3} - \frac{1}{ {a}^{3} } - 2a + \frac{2}{a} \\ = > (a - \frac{1}{a} )( {a}^{2} + \frac{1}{ {a}^{2} } + a \times \frac{1}{a} ) - \\ 2(a - \frac{1}{a} ) \\ = > (a - \frac{1}{a} )( {a}^{2} + \frac{1}{ {a}^{2} } + 1 - 2) \\ \\ = > (a - \frac{1}{a} )( {a}^{2} + \frac{1}{ {a}^{2} } - 1)$