Factorise: x^2-2+1 x^2 -y^2 - Vidyadip

Question

Factorise:
$\text{x}^2-2+\frac{1}{\text{x}^2}-\text{y}^2$

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Answer

$\text{x}^2-2+\frac{1}{\text{x}^2}-\text{y}^2$
$=\Big(\text{x}^2-2(\text{x}^2)\Big(\frac{1}{\text{x}^2}\Big)+\frac{1}{\text{x}^2}\Big)-\text{y}^2$
$=\Big(\text{x}-\frac{1}{\text{x}}\Big)^2-\text{y}^2$
$=\Big(\text{x}-\frac{1}{\text{x}}+\text{y}\Big)\Big(\text{x}-\frac{1}{\text{x}}-\text{y}\Big)$

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