$\begin{array}{l}
C1:\,\,{x^2} - 6x{y^2} + 8{y^4}\\
= {x^2} - 4x{y^2} - 2x{y^2} + 8{y^4}\\
= \left( {{x^2} - 4x{y^2}} \right) - \left( {2x{y^2} - 8{y^4}} \right)\\
= x\left( {x - 4{y^2}} \right) - 2{y^2}\left( {x - 4{y^2}} \right)\\
= \left( {x - 4{y^2}} \right)\left( {x - 2{y^2}} \right)\\
C2:\,\,\,{x^2} - 6x{y^2} + 8{y^4}\\
= {x^2} - 2.x.\left( {3{y^2}} \right) + 9{y^4} - {y^4}\\
= {x^2} - 2.x.\left( {3{y^2}} \right) + {\left( {3{y^2}} \right)^2} - {y^4}\\
= {\left( {x - 3{y^2}} \right)^2} - {\left( {{y^2}} \right)^2}\\
= \left( {x - 3{y^2} + {y^2}} \right)\left( {x - 3{y^2} - {y^2}} \right)\\
= \left( {x - 2{y^2}} \right)\left( {x - 4{y^2}} \right)
\end{array}$
