A) \[\left( {{x}^{8}}-\frac{1}{{{x}^{8}}} \right)\]
B) \[\left( {{x}^{4}}-\frac{1}{{{x}^{4}}} \right)\]
C) \[\left( {{x}^{2}}-\frac{1}{{{x}^{2}}} \right)\]
D) \[\left( {{x}^{8}}+\frac{1}{{{x}^{8}}} \right)\]
Correct Answer: A
Solution :
(a): \[\left( x-\frac{1}{x} \right)\left( x+\frac{1}{x} \right)={{x}^{2}}-{{\left( \frac{1}{x} \right)}^{2}}={{x}^{2}}-\frac{1}{{{x}^{2}}}\] Then, \[\left( {{x}^{2}}-\frac{1}{{{x}^{2}}} \right)\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)={{x}^{4}}-\frac{1}{{{x}^{4}}}\]. Then, \[\left( {{x}^{4}}-\frac{1}{{{x}^{4}}} \right)\times \left( {{x}^{4}}+\frac{1}{{{x}^{4}}} \right)={{x}^{8}}-\frac{1}{{{x}^{8}}}\]
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