help me to factorise 4(x-y)^3-(x-y)

Answer 1

(x-y) is a common factor, so

= (x-y)( 4(x-y)^2 - 1)
now in the second bracket I see a difference of squares
= (x-y)(2(x-y) + 1)(2(x-y) - 1)
= (x-y)(2x - 2y +1)(2x - 2y -1)