`x^3 + 3x^2 + 3x + 2`

  `= x^3 + 3x^2 + 3x + 1 + 1`

  `= (x)^3 + 3.x^2.1 + 3.x.1^2 + (1)^3 + 1`

  `= (x + 1)^3 + (1)^3`

  `= {(x + 1) + 1} {(x + 1)^2 - (x + 1) 1 + (1)^2}`

  `= (x + 1 + 1) (x^2 + 2x + 1 - x - 1 + 1)`

  `= (x + 2) (x^2 + x + 1)`  (Ans)

`a^3 - 6a^2 + 12a - 9`

  `= a^3 - 6a^2 + 12a - 8 - 1`

  `= a^3 - 3.a^2.2 + 3.a.2^2 - 2^3 - 1`

  `= (a - 2)^3 - 1`

  `= (a - 2)^3 - (1)^3`

  `= (a - 2 - 1) {(a - 2)^2 + (a - 2).1 + 1^2}`

  `= (a - 3) (a^2 - 4a + 4 + a - 2 + 1)`

  `= (a - 3) (a^2 - 3a + 3)`   (Ans)

`a^3 - 9b^3 + (a + b)^3`

  `= a^3 - b^3 + (a + b)^3 - 8b^3`

  `= (a - b) (a^2 + ab + b^2) + (a + b)^3 - (2b)^3`

  `= (a - b) (a^2 + ab + b^2) + (a + b - 2b) {(a + b)^2 + (a + b).2b + (2b)^2}`

  `= (a - b) (a^2 + ab + b^2) + (a - b) (a^2 + 2ab + b^2 + 2ab + 2b^2 + 4b^2)`

  `= (a - b) (a^2 + ab + b^2) + (a - b) (a^2 + 4ab + 7b^2)`

  `= (a - b) (a^2 + ab + b^2 + a^2 + 4ab + 7b^2)`

  `= (a - b) (2a^2 + 5ab + 8b^2)`  (Ans)

`8x^2 + 12x^2 + 6x - 63`

  `= 8x^2 + 12x^2 + 6x + 1 - 64`

  `= (2x)^3 + 3.(2x)^2.1 + 3.2x. (1)^2 + (1)^3 - 64`

  `= (2x + 1)^3 - (4)^3`

  `= (2x + 1 - 4) {((2x + 1)^2 + (2x + 1) .4 + 4^2}`

  `= (2x - 3) {(2x)^2 + 2.2x.1 + (1)^2 + 8x + 4 + 16}`

  `= (2x - 3) (4x^2 + 4x + 1 + 8x + 20)`

  `= (2x - 3) (4x^2 + 12x + 21)`  (Ans)

`8a^3 + b^3/(27) = (2a)^3 + (b/3)^3`

  `= (2a + b/3) {(2a)^2 - 2a.b/3 + (b/3)^2}`

  `= (2a + b/3) (4a^2 - (2ab)/3 + b^2/9)`

  `= ((6a + b)/3) ((36a^2 - 6ab + b^2)/9)`

  `= 1/(27) (6a + b) (36a^2 - 6ab + b^2)`  (Ans)