3x^4y-9x^3y^2-54x^2y^3
＝3x²y(x²-3xy-18y²)
＝3x²y[(x²-6xy)+(3xy-18y²)]
＝3x²y[x(x-6y)+3y(x-6y)]
＝3x²y(x-6y)(x+3y).