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