find the product of (x-1/x)(x+1/x)(x^2+1/x).
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using the formula (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
[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
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