<s>[INST] Binomial coefficient question? I'm unsure how to do these types of questions, so any help would be great:

Find the coefficient of $x^2$ in the expansion of $(x+1/x)^3(x-1/x)^5$

Thanks
 [/INST] Here is how you advance. Try to simplify the expression as
$$(x+1/x)^3(x-1/x)^5= -\frac{1}{x^8}(1+x^2)^3(1-x^2)^5= -\frac{1}{x^8}(1-x^4)^3(1-x^2)^2$$
$$ = -\frac{1}{x^8}(1-x^2)^2(1-x^4)^3$$
$$ = -\frac{1}{x^8}(1-2x^2+x^4)(1-3x^{4}+3x^8-x^{12})=\dots\,.  $$
Can you finish it now?
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