a)x^3-x+3x^2y+3xy^2+y^3-y
=(x^3+3x^2y+3xy^2+y^3)-(x+y)
=(x+y)^3-(x+y)
=(x+y)[(x+y)^2-1]
=(x+y)(x+y-1)(x+y+1)
b)81x^2-6yz-9y^2-z^2
=81x^2-(9y^2-6yz+z^2)
=81x^2-(3y-z)^2
=(9x)^2-(3y-z)^2
=(9x-3y+z)(9x+3y-z)
c)12x^2-72x+60
=12(x^2-6x+5)
=12(x^2-x-5x+5)
=12[x(x-1)-5(x-1)]
=12(x-1)(x-5)