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Answer:
(i) (x+1/x)(x-1/x)(1/x²+x²)(x⁴+1/x⁴).
(x+1/x)(x-1/x).
By using formula (a+b)(a-b)=a²-b² where a=x & b=1/x.
(x+1/x)(x-1/x)=(x)²-(1/x)².
=(x²-1/x²).
(1/x²+x²)(x²-1/x²).
By using formula (a+b)(a-b)=a²-b² where a=x² & b=1/x².
(1/x²+x²)(x²-1/x²)=(x²)²-(1/x²)².
=(x⁴-1/x⁴).
(x⁴+1/x⁴)(x⁴-1/x⁴).
By using formula (a+b)(a-b)=a²-b² where a=x⁴ & b=1/x⁴.
(x⁴+1/x⁴)(x⁴-1/x⁴)=(x⁴)²-(1/x⁴)².
=(x^8-1/x^8).
I think this is your answer.