(x - 1/x)^2 (x+1/x)^2

$$(x -\frac{1}{x})^2 (x+\frac{1}{x})^2\\\\
=(x -\frac{1}{x}) (x+\frac{1}{x})\times(x -\frac{1}{x})(x+\frac{1}{x})\\\\
=\left(x^2 -\frac{1}{x^2}\right)^2\\\\
=x^4-2+\frac{1}{x^4}\\\\$$

(x - 1/x)^2 (x+1/x)^2 = 

[(x - 1/x) (x+1/x)]^2

[x^2 -1 + 1 - 1/x^2]^2  =

[x^2 - 1/x^2]^2  =

(x^2 - 1/x^2) (x^2 - 1/x^2) =

x^4 -1 -1 + 1/x^4 =

x^4 - 2 + 1/x^4

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(x/3-1/2)(x/2+1/3) =

(1/6)x^2 - (1/4)x + (1/9)x - 1/6 =

(1/6)x^2 - (5/36)x - 1/6