`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)

`a^3 - 1/8 = a^3 - (1/2)^3`

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

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

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

  `= 1/8 (2a - 1) (4a^2 + 2a + 1)`  (Ans)

`a^6/(27) - b^6 = (a^2/3) - (b^2)^3`

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

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

`4a^2 + 1/4a^2 - 2 + 4a - 1/a`

  `= (2a)^2 + (1/(2a))^2 - 2.2a.1/(2a) + 2(2a - 1/(2a))`

  `= (2a - 1/(2a)^2 + 2(2a - 1/(2a))`

  `= (2a - 1/(2a) (2a - 1/(2a) + 2)`  (Ans)