\(a,17x^3y^2-34x^2y^2+51x^2y^3\)
\(=17x^2y^2\left(x-2+3y\right)\)
\(b,16x^2\left(x^2-y\right)-10y\left(y-x^2\right)\)
\(=16x^2\left(x^2-y\right)+10y\left(x^2-y\right)\)
\(=\left(x^2-y\right)\left(16x^2+10y\right)\)
\(=2\left(x^2-y\right)\left(8x^2+5y\right)\)
\(c,x^2+2xy+y^2-xz-yz\)
\(=\left(x^2+2xy+y^2\right)-\left(xz+yz\right)\)
\(=\left(x+y\right)^2-z\left(x+y\right)\)
\(=\left(x+y\right)\left(x+y-z\right)\)
\(d,64xy-96x^2y+48x^3y-8x^4y\)
\(=8xy\left(8-12x+6x^2-x^3\right)\)
\(=-8xy\left(x^3-6x^2+12x-8\right)\)
\(=-8xy\left(x-2\right)^3\)