a) x3 - 2x2 + x - xy2
= x (x2 - 2x + 1 - y2)
= x [(x - 1)2 - y2 ]
= x (x - 1 + y)(x - 1 - y)
b) x3 - 4x2 - 12x + 27
= ( x3 + 33) - (4x2 + 12x)
= (x + 3)(x2 - 3x + 9) - 4x(x + 3)
= (x + 3)(x2 - 3x + 9 - 4x)
= (x + 3)(x2 - 7x + 9)
c) 5x3 - 20x
= 5x(x2 - 4)
= 5x(x - 2)(x + 2)
d) x2 + 2xy - 4 + y2
= ( x + y)2 - 22
= ( x + y + 2)(x + y - 2)