A difference of $n$th powers always carries the factor $x-y$.Suggest a slogan
For \(n\ge1\), in \(\ZZ[x,y]\), \[ x^n-y^n=(x-y)\qty{x^{n-1}+x^{n-2}y+\cdots+xy^{n-2}+y^{n-1}}=(x-y)\sum_{k=0}^{n-1}x^{n-1-k}y^k. \]
This is FF-ED3CD over the commutative ring \(R=\ZZ[y]\) with \(a=y\).
How does $x^n - y^n$ factor?
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FF-2AKVHFactorization of $x^n + y^n$ for odd $n$variant-of