a.
\(5x^2-5xy-10x+10y=5x\left(x-y\right)-10\left(x-y\right)=\left(x-y\right)\left(5x-10\right)=5\left(x-y\right)\left(x-2\right)\)
b.
\(4x^2+8xy-3x-6y=4x\left(x+2y\right)-3\left(x+2y\right)=\left(x+2y\right)\left(4x-3\right)\)
c.
\(2x^2+2y^2-x^2z+z-y^2z-2=2\left(x^2+y^2\right)-z\left(x^2+y^2\right)+\left(z-2\right)=\left(x^2+y^2\right)\left(2-z\right)-\left(2-z\right)=\left(2-z\right)\left(x^2+y^2-1\right)\)