Factorize each of the following algebraic expressions:
(i) `x^2-4x+4y-y^2`
(ii) `3-12(a-b)^2`

Explanation

(i) `x^2-4x+4y-y^2`
`=x^2-4x+4y-y^2`
`=(x^2-y^2)-4(x-y)`
Using identity:
`(a^2-b^2)=(a+b)(a-b)`
`=(x-y)(x+y-4)`
`=(x+y)(x-y)-4(x-y)`

(ii) `3-12(a-b)^2`
`=3{1- 4(a-b)^2}`
`=3[1^2- {2(a-b)}^2]`
Using identity:
`(a^2-b^2)=(a+b)(a-b)`
`=3[{1+2(a-b)}{1-2(a-b)}]`
`=3(1+2ab- 2b)(1 - 2a + 2b)`