Question

Factorise:
$x^4+\frac{4}{x^4}$

Answer 1

$$\begin{gathered} x^4+\frac{4}{x^4} \\ =x^4+\frac{4}{x^4}+4-4 \\ =\left[{\left(x^2\right)}^2+{\left(\frac{2}{x^2}\right)}^2+2\times \left(x^2\right)\times \left(\frac{2}{x^2}\right)\right]-2^2 \\ ={\left(x^2+\frac{2}{x^2}\right)}^2-2^2\left[a^2+2ab+b^2={\left(a+b\right)}^2\right] \\ =\left(x^2+\frac{2}{x^2}+2\right)\left(x^2+\frac{2}{x^2}-2\right)\left[a^2-b^2=\left(a+b\right)\left(a-b\right)\right] \end{gathered}$$