<s>[INST] Expansion $(x+{\frac{1}{x}})^4 (x-{\frac{1}{x}})^2$ 
Expand $(x+{\frac{1}{x}})^4 (x-{\frac{1}{x}})^2$

Right now, I am able to expand this expression by simplifying it to:
$\frac{(x^2+1)^4 (x^2-1)^2}{x^6}$
I used the formula $(a+b)^2$ and $(a-b)^2$ a bunch of times to arrive at the answer. But, is there any simpler/smarter way to do this?
 [/INST] $$(x+{\frac{1}{x}})^4 (x-{\frac{1}{x}})^2= \frac {(x^2+1)^4(x^2-1)^2}{x^6}=$$
$$\frac {(x^4-1)^2(x^2+1)^2}{x^6} =\frac {(x^8-2x^4+1)(x^4+2x^2+1)}{x^6}=$$
$$\frac{x^{12} +2x^{10} -x^8-4x^6-x^4+2x^2+1}{x^6}=$$
$$x^{6} +2x^{4} -x^2-4-\frac {1}{x^2}+\frac {2}{x^4}+\frac {1}{x^6}$$
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