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Factors of Algebraic Expressions and Factorisation

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Question

Simplify : $x^{8} - (x^{2} - \frac{1}{x^{2}}) (x^{4} + \frac{1}{x^{4}}) (x^{2} + \frac{1}{x^{2}})$

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Solution

$\begin{matrix} x^{8} - (x^{2} - \frac{1}{x}) (x^{4} + \frac{1}{x^{4}}) (x^{2} + \frac{1}{x^{2}}) x^{8} - (x^{4} - \frac{1}{x^{4}}) (x^{4} + \frac{1}{x^{4}}) x^{8} - (x^{8} - \frac{1}{x^{8}}) x^{8} - x^{8} + \frac{1}{x^{8}} \frac{1}{x^{8}} \end{matrix}$

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