$(4x^3y - 6x^2y^2 + 4xy^3 - y^4)$ can be expressed as:
Answer & explanation
Correct answer: option 3
(4x3y - 6x2y2 + 4xy3 - y4)
= 2xy3 - 2x2y2 - y4 + 4x3y + 2xy3 - 4x2y2
= -y2 (-2xy + 2x2 + y2) + 2xy (2x2 + y2 - 2xy)
= (2xy - y2) (2x2 + y2 - 2xy)
= (x2 - x2 - y2 + 2xy) (x2 + x2 + y2 - 2xy)
= [x2 - (x - y)2] [x2 + (x - y)2]
= x4 - (x - y)4