a, (x + 2y)^2 - (x - y)^2 = (x + 2y - x + y)(x + 2y + x - y) = 3y . (2x + y) 
b, (x+1)^3 + (x -1)^3 = (x + 1 + x - 1)[(x + 1)^2 - (x +1)(x - 1) + (x -1)^2]
= 2x(x^2 + 2x + 1 - x^2 + 1 + x^2 - 2x + 1)
= 2x(x^2 + 3)
c, 9x^2  - 3x + 2y - 4y^2
= 9x^2 - 4y^2 - (3x - 2y)
= (3x - 2y)(3x + 2y) - (3x -2y)
= (3x - 2y)(3x + 2y - 1)
d, 4x^2 - 4xy + 2x - y + y^2
= 4x^2 - 4xy + y^2 + 2x- y 
= (2x - y)^2 + (2x - y)
= (2x - y)(2x - y + 1)
e, x^3 + 3x^2 + 3x + 1 - y^3
= (x + 1)^3 - y^3
= (x + 1 - y)[(x + 1)^2 + (x + 1)y + y^2]
= (x - y + 1)(x^2 + 2x + 1 + xy + y + y^2)
f, x^3 - 2x^2y + xy^2- 4x
= x(x^2 - 2xy + y^2 - 4)
= x[(x + y)^2 - 2^2]
= x(x + y - 2)(x + y + 2)