Factorize each of the following expressions:
(1)`a(a+b-c)-b c`
(2) `x^2-11 x y-x+11 y`
(3)`a b-a-b+1`
(4) `x^2+y-x y-x`

Explanation

(i)`a(a+b-c)-b c`
`=a^2+ab−ac−bc`
`=a(a+b)−c(a+b)`
`=(a+b)(a−c)`

(ii) `x^2-11 x y-x+11 y`
`=x (x – 1) – 11y (x – 1)`
`= (x – 11y) (x – 1)`

(iii)`a b-a-b+1`
`= a(b-1)-1(b-1)`
`= (a-1)(b-1)`

(iv) `x^2+y-x y-x`
`= x²-xy+y-x`
`= x(x-y) -1(x-y)`
`= (x-y)(x-1)`