Factorize each of the following expressions:
(1) `a x y+b c x y-a z-b c z`
(2) `l m^2-m n^2-l m+n^2`
(3) `x^3-y^2+x-x^2y^2`
(4) `6x y+6-9y-4x`

Explanation

(i)`a x y+b c x y-a z-b c z`
`=a(xy-z)+bc(xy-z)`
`=(xy-z)(a+bc)`

(ii) `l m^2-m n^2-l m+n^2`
`=lm(m-1)-n^2(m-1)`
`=(lm-n^2)(m-1)`

(iii)`x^3-y^2+x-x^2y^2`
`=x^2(x-y^2)+1(x-y^2)`
`=(x^2+1)(x-y^2)`

(iv) `6x y+6-9y-4x`
`=3y(2x-3)-2(2x-3)`
`=(3y-2)(2x-3)`