Question

find the product (a-1/a) (a+1/a) (a²+1/a²) (a⁴+1/a⁴) using a suitable identity.​

Answer 1

$(a - \frac{1}{a} )(a + \frac{1}{a} )( {a}^{2} + \frac{1}{ {a}^{2} } )( {a}^{4} + \frac{1}{ {a}^{4} } ) \\ = ( {a}^{2} - \frac{1}{ {a}^{2} } )( {a}^{2} + \frac{1}{ {a}^{2} } )( {a}^{4} + \frac{1}{ {a}^{4} } ) \\ = ( {a}^{4} - \frac{1}{ {a}^{4} } )( {a}^{4} + \frac{1}{ {a}^{4} } ) \\ = ( { {a}^{4} })^{2} - ( { \frac{1}{ {a}^{4} } })^{2} \\ = {a}^{8} - \frac{1}{ {a}^{8} }$