Question

(x+1/x)(x_1/x)(x^2+1/x^2)(x^4+1/x^4)

Answer 1

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

(x^4-1/x^4)(x^4+1/x^4)
(x^8+1/x^8)

Answer 2

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