Factorize the following:

The greatest common factor of the terms $2 x^{3} y^{2},-4 x^{2} y^{3}$ and $8 x y^{4}$ of the expression $2 x^{3} y^{2}-4 x^{2} y^{3}+8 x y^{4} y^{64}$ is $2 x y^{2}$.

Now,

$2 x^{3} y^{2}=2 x y^{2} \times x^{2}$

$-4 x^{2} y^{3}=2 x y^{2} \times-2 x y$

$8 x y^{4}=2 x y^{2} \times 4 y^{2}$

Hence, the expression 2x3y2 - 4x2y3 + 8xy4 ​can be factorised as 2xy2(x2 - 2xy + 4y2)​.