Factorize each of the following expressions:
(i) `x^2-2x y+y^2-x+y`
(ii) `4a^2+12 a b+9b^2-8a-12 b`
(iii) `a^2+b^2-2(a b-a c+b c)`

Explanation

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

(ii)`4a^2+12 a b+9b^2-8a-12 b`
`=2a ( 2a +3b) + 3b (2a + 3b) - 8a -12b`
`=(2a + 3b) (2a +3b) 4 (2a +3b)`
`=(2a + 3b) (2a + 3b -4)`

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