Question

(x-1/x) (x+1/x) (x^2+1/x^2)​

Answer 1

Answer:

$answer$

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

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

$\tt{x(x+\dfrac{1}{x})-\dfrac{1}{x}(x+\dfrac{1}{x})\times(x^2+\dfrac{1}{x^2}}$

$\tt{(x^2+1-1-\dfrac{1}{x^2})\times(x^2+\dfrac{1}{x^2})}$

$\tt{[(x^2-\dfrac{1}{x^2})(x^2+\dfrac{1}{x^2}]}$

$\tt{(x^2(x^2+\dfrac{1}{x^2})-(\dfrac{1}{x^2}(x^2+\dfrac{1}{x^2})}$

$\tt{(x^4+1-1-\dfrac{1}{x^4}})$

$\tt{(x^4-\dfrac{1}{x^4})}$

$\mapsto\boxed{\sf\red{x^4-\dfrac{1}{x^4}}}$