Factorize each of the following expressions:
`x^2+2x y+y^2-a^2+2a b-b^2`
`25 x^2-10 x+1-36 y^2`

Explanation

(i)`x^2+2x y+y^2-a^2+2a b-b^2`
`=(x^2+2xy+y^2)−(a^2−2ab+b^2)`
`=(x+y)^2−(a−b)^2`
`=[(x+y)+(a−b)][(x+y)−(a−b)]`
`=x^2+2xy+y^2−a^2+2ab−b^2`
`=(x+y+a−b)(x+y−a+b)`

(ii)`25 x^2-10 x+1-36 y^2`
`=[(5x)^2−2×5x×1+1^2]−(6y)^2`
`=(5x−1)^2 −(6y)^2`
`=(5x−1+6y)(5x−1−6y)`