Factorising Differences of Powers

The "Difference of squares"
\[x^2-y^2=(x-y)(x+y)\]

is only one of a sequence of important factorisation.
In fact  
\[x^n-y^n\]
  factorises for all positive  
\[n\]
  with  
\[(x-y)\]
  as a factor, since when 
\[x=y\]
,  
\[x^n-y^n=0\]
.
In fact
\[x^3-y^3=(x-y)(x^2+xy+y^2)\]

\[x^4-y^4=(x-y)(x^3+x^2y+xy^2+y^3)\]

\[x^5-y^5=(x-y)(x^4+x^3y+x^2y^2+xy^3+y^4)\]

And so on.

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