Question

4x^2 - y^2 - 3xy + 2x - 2y

Answer 1

4x² - 3xy - y² + 2x - 2y 
(4x + y)(x - y) + 2(x - y) 
(x - y)(4x + y + 2)

Answer 2

factorization.   do it in steps.

First take      4x^2 - y^2 - 3xy   or    [4 (x/y)^2 - 3 (x/y)  - 1] * y^2
                     [ 4 x/y  + 1 ] [ x/y  - 1 * y^2
                     ( 4x + y)  (x - y)

So LET   4 x^2 - y^2 - 3 x y + 2 x - 2 y
                              =  (4x + y + b) (x - y + c)
  Multiply and  compare coefficients, we get   b = 2,  c = 0

So answer   (4x + y +2 ) (x - y)