<s>[INST] What is the fastest way to calculate $(x+1)^3-(x-1)^3$? 
What is the fastest way to calculate $(x+1)^3-(x-1)^3$?

My teacher gives me this question, and I use 5 minutes to calculate it, and there is an error. I want to know if there is a faster method to do it.
 [/INST] $\mathbf{Method\ 1}:$ $$S=(x+1)^3 - (x-1)^3 = 2((x+1)^2 + (x-1)^2 + (x+1)(x-1))$$$$=2(2(x^2+1) + x^2 -1)$$ $$=2(3x^2 + 1)$$ $$=6x^2+2$$ $\mathbf{Method\ 2:}$ $$(x+1)^3 = \displaystyle\sum_{r=0}^3\binom 3rx^r$$ $$(x-1)^3=\displaystyle\sum_{r=0}^3(-1)^r\binom 3rx^r$$ Clearly in their addition only terms with even $r$ remain. Here, they are $r = 0,2$. So the sum is$$2\left(\binom 30 + \binom 32x^2\right)$$ $$=6x^2 + 2$$ In any case we have the solution $$\boxed{S = 6x^2+2}$$
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