Question
Factorise: $\text{x}^4+\frac{4}{\text{x}^4}$
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Answer
$\text{x}^4+\frac{4}{\text{x}^4}$ $=\text{x}^4+\frac{4}{\text{x}^4}+4-4$ $=\big(\text{x}^2\big)^2+\Big(\frac{2}{\text{x}^2}\Big)^2+2\big(\text{x}^2\big)\Big(\frac{2}{\text{x}^2}\Big)-2^2$ $=\bigg[\big(\text{x}^2\big)^2+\Big(\frac{2}{\text{x}^2}\Big)^2+2\big(\text{x}^2\big)\Big(\frac{2}{\text{x}^2}\Big)\bigg]-2^2$ $=\Big[\text{x}^2+\frac{2}{\text{x}^2}\Big]^2-2^2$ $=\Big(\text{x}^2+\frac{2}{\text{x}^2}+2\Big)\Big(\text{x}^2+\frac{2}{\text{x}^2}-2\Big)$
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