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

Explanation

(i)`x(x+z)-y(y+z)`
`=x^2+xz−y^2−yz`
`=x^2−y^2+xz−yz`
`=(x−y)(x+y)+z(x−y)`
`=(x−y)(x+y+z)`

(ii) `a^2-b^2-a-b`
`=(a^2-b^2)-(a+b)`
`=(a+b)(a-b)-(a+b)`
`=(a+b)[(a-b)-1]`
​`=(a+b)(a-b-1)`