\(a,2x^2y^2\left(x^8y^2-x^2y^8-\dfrac{1}{2}y^5\right)=2x^2y^2.x^8y^2-2x^2y^2.x^2y^8-2x^2y^2.\dfrac{1}{2}y^5\\ =2x^{10}y^4-2x^4y^{10}-x^2y^7\\ ---\\ b,-\dfrac{1}{3}xy\left(3x^8y^2-6x^2+y^2\right)=-\dfrac{1}{3}.3.x.x^8.y.y^2-\dfrac{1}{3}.\left(-6\right).x.x^2.y-\dfrac{1}{3}.x.y.y^2\\ =-x^9y^3+2x^3y-\dfrac{1}{3}xy^3\\ ---\\ c,\left(-2xy^2+\dfrac{2}{3}y^2+4xy^2\right).\dfrac{3}{2}xy=-2.\dfrac{3}{2}x.x.y.y^3+\dfrac{2}{3}.\dfrac{3}{2}.xy.y^2+4.\dfrac{3}{2}.xy.xy^2\\ =-3x^2y^4+xy^3+6x^2y^3\)
\(d,\left(x^2+2xy-3\right)\left(-xy\right)=-xy.x^2-xy.2xy+3xy\\ =-x^3y-2x^2y^2+3xy\\ e,\dfrac{1}{2}x^2y\left(2x^8-\dfrac{2}{5}xy^2-1\right)=\dfrac{1}{2}.2.x^2x^8.y-\dfrac{1}{2}.\dfrac{2}{5}x^2y.xy^2-\dfrac{1}{2}.1.x^2y\\ =x^{10}y-\dfrac{1}{5}x^3y^3-\dfrac{1}{2}x^2y\\ f,\left(-xy^2\right)^2.\left(x^2-2x+1\right)=\left[\left(-xy\right).\left(x-1\right)\right]^2\\=\left[-x^2y+xy\right]^2=\left(-x^2y\right)^2+2.\left(-x^2y\right).xy+\left(xy\right)^2\\ =x^4y^2-2x^3y^2+x^2y^2\)
