\(x^3+7y=y^3+7x\)
\(pt\Leftrightarrow x^3-y^3+7y-7x=0\)
\(\Leftrightarrow\left(x^3-y^3\right)-7\left(x-y\right)=0\)
\(\Leftrightarrow\left(x-y\right)\left(x^2+xy+y^2\right)-7\left(x-y\right)=0\)
\(\Leftrightarrow\left(x-y\right)\left(x^2+xy+y^2-7\right)=0\)