a) 3x^2 - 6xy + 3y^2 = 3(x-y)^2
b) x^2 - xy + 3x - 3y = (x-y)(x+3)
c) x^3 + 2x^2y + xy^2 - 16x = x ( x^2 + 2xy + y^2 - 16 ) = x(x+y+4)(x+y-4)
d) x^3-x+3x^2y+3xy^2+y^3-y = (x+y)^3 - (x+y) = (x+y)(x+y-1)(x+y+1)
e) 9x^2-1 = (3x-1)(3x+1)
f) 9(x-y)^2 - (x+y)^2 = (3x-3y)^2 - (x+y)^2 = (3x-3y-x-y)(3x-3y+x+y) = (2x-4y)(4x-2y) = 4(x-2y)(2x-y)