Find the product of (x-1/x) (x+1/x) (x^2+1/x^2) (x^4+1/x^4)
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Answer :-
Using the identity (a+b)(a-b) =a²- b² in all cases
[x+1/x][x-1/x][x²+1/x²][x⁴+1/x⁴]
= [x²- 1/x²][x²+1/x²][x⁴+1/x⁴]
=[(x²)²- (1/x²)²][x⁴+1/x⁴]
=[x⁴- 1/x⁴][x+1/x⁴]
=(x⁴)² - (1/x⁴)²
=x⁸-1/x⁸
Hope it Heplfull Answer
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