Question

Simplify (x+1/x)(x-1/x)(x^2+1/x^2)(x^4+1/x^4)

Answer 1

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Answer 2

SOLUTION:

$(x - \frac{1}{x} )(x + \frac{1}{x} )( {x}^{2} + \frac{1}{ {x}^{2} } )( {x}^{4} + \frac{1}{ {x}^{4} } )$

$= > ( {x}^{2} - \frac{1}{ {x}^{2} } )( {x}^{2} + \frac{1}{ {x}^{2} } )( {x}^{4} + \frac{1}{ {x}^{4} } )$

$= > (( {x}^{2} )^{2} - ( \frac{1}{ {x}^{2} } )^{2} )( {x}^{4} + \frac{1}{ {x}^{4} } )$

$= > ( {x}^{4} - \frac{1}{ {x}^{4} })( {x}^{4} + \frac{1}{ {x}^{4} } )$

$= > ( {x}^{4})^{2} - ( \frac{1}{ {x}^{4} } )^{2}$

$= > {x}^{8} - \frac{1}{ {x}^{8} }$