Simplify the product (x+1/x)(x^2+1/x^2)(x^4+1/x^4)(x^8+1/x^8)

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(x+1/x)(x^2 + 1/x^2/(x^4 + 1/x^4)(x^8+1/x^8)

==> Let us multiply and divide by x -1/x

==>[ (x-1/x)(x+1/x)(x^2 +1/x^2)(x^4 + 1/x^4)(x^8+ 1/x^8)]/(x1/x)]

=( x^2 -1/x^2)(x^2 + 1/x^2 )(x^4+ 1/x^4)(x^8+1/x^8)]/(x-1/x)

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

=(x^8-1/x^8)(x^8+1/x^8)]/(x-1/x)

=(x^16-1/x^16)/(x-1/x)

 

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