`x) 27x^3 - 8y^3` 

`= (3x)^3 - (2y)^3`

`= (3x - 2y)[(3x)^2 + 2 . 3x . 2y + (2y)^2]`

`= (3x - 2y)(9x^2 + 12xy + 4y^2)`

`i) 10x - 25 - x^2`

`= -(x^2 - 10x + 25)`

`= - (x^2 - 2x . 5 + 5^2)`

`= - (x - 5)^2`

`= - (x-5)(x-5)`

`u) 1/36 x^2 - 100y^2`

`= (1/6x)^2 - (10y)^2`

`= (1/6 x - 10y)(1/6 x + 10y)`

`t) -x^3 + 9x^2 - 27x + 27`

`= -x^3 + 3x^2 . 3 - 3x . 3^2 + 3^3`

`= - (x + 3)^3`

`=-(x - 3)(x - 3)(x - 3)`

`v) x^3 - 3x^2 + 3x - 1`

`= (x - 1)^3`

`= (x - 1)(x - 1)(x - 1)`