<s>[INST] How to factorise this expression $ x^2-y^2-x+y$ This part can be factorised as  $x^2-y^2=(x+y)(x-y)$, How would the rest of the expression be factorised ?
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 [/INST] Another method to factor $${ x }^{ 2 }-x+\frac { 1 }{ 4 } -{ y }^{ 2 }+y-\frac { 1 }{ 4 } ={ \left( x-\frac { 1 }{ 2 }  \right)  }^{ 2 }-{ \left( y-\frac { 1 }{ 2 }  \right)  }^{ 2 }=\left( x-\frac { 1 }{ 2 } +y-\frac { 1 }{ 2 }  \right) \left( x-\frac { 1 }{ 2 } -y+\frac { 1 }{ 2 }  \right) =\left( x-y \right) \left( x+y-1 \right) $$
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