Tricky Equation With Factorisation

Some factorisations are not obvious. Consider the equation
\[x-y^2= xy^2-x^2\]

The right hand side factorises to give  
\[x-y^2=x(y^2-x)\]

Subtract  
\[x(y^2-x)\]
  from both sides to give
\[x-y^2+x(x-y^2)=0\]

Now we can factorise both sides completely.
\[(1+x)(x-y^2)=0\]

Hence  
\[1+x=0 \rightarrow x=-1\]
  and  
\[y\]
  is arbitrary or  
\[x-y^2=0 \rightarrow y = \pm \sqrt{x}\]
  which is the graph of  
\[y= \sqrt{x}\]
  together with it's reflection in the x - axis.

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