$a)$

$\left(x-2y\right)\left(y-2z\right)\left(z-2x\right)=$

$=\left(xy-2xz-2y^2+4yz\right)\left(z-2x\right)=$

$=xyz-2x^{2}y-2x{z}^2+4x^{2}z-2y^{2}z+4x{y}^2+4y{z}^2-8xyz=$

$=-2x^{2}y+4x{y}^2-2x{z}^2-2y^{2}z+4y{z}^2+4x^{2}z-7xyz$