Question

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

Answer 1

Solution:-


$a {}^{3} - \frac{1}{a {}^{3} } - 2a + \frac{2}{a} \\ ( {a} - \frac{1}{a} )( {a}^{2} + {b}^{2} + ab) - 2(a - \frac{1}{a} ) \\ (a - \frac{1}{a} )( {a}^{2} + {b}^{2} + ab - 2)ans$

Answer 2

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