a) \(4x^2-81=\left(2x\right)^2-9^2=\left(2x-9\right)\left(2x+9\right)\)
b) \(3\left(x-y\right)+5x\left(y-x\right)=3\left(x-y\right)-5x\left(x-y\right)=\left(x-y\right)\left(3-5x\right)\)
c) \(x\left(x+y\right)+6x+6y=x\left(x+y\right)+6\left(x+y\right)=\left(x+y\right)\left(x+6\right)\)
d) \(20x-5y=5\left(4x-y\right)\)
e) \(=2xy\left(5xy-4y+2y\right)\)
g) \(4xy+8xyz=4xy\left(1+2z\right)\)