<s>[INST] What are the steps to factor $x^2 - 1$ into $(x+1)(x-1)$? Does $(x+1)(x-1) = x^2+1x-1x-1$? If so where are the $+1x$ and the $-1x$ when it is being factored from $x^2-1$ into $(x+1)(x-1)$?
What exactly are we dividing $x^2-1$ by to get $(x+1)(x-1)$ and how did you know what to divide it by?
 [/INST] Let $y:=x-1$. Then
$$x^2-1=(y+1)^2-1=y^2+2y$$ which obviously factors as $$(y+2)y=(x+1)(x-1).$$
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