Factorise:
Question:

Factorise:

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

 

Solution:

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

$=x^{4}+\frac{4}{x^{4}}+4-4$

$=\left[\left(x^{2}\right)^{2}+\left(\frac{2}{x^{2}}\right)^{2}+2 \times\left(x^{2}\right) \times\left(\frac{2}{x^{2}}\right)\right]-2^{2}$

$=\left(x^{2}+\frac{2}{x^{2}}\right)^{2}-2^{2} \quad\left[a^{2}+2 a b+b^{2}=(a+b)^{2}\right]$

$=\left(x^{2}+\frac{2}{x^{2}}+2\right)\left(x^{2}+\frac{2}{x^{2}}-2\right) \quad\left[a^{2}-b^{2}=(a+b)(a-b)\right]$

 

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