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

  `= {(3a + 1) - (2a - 3)} {(3a + 1)^2 + (3a + 1) (2a - 3) + (2a - 3)^2}`

  `= (3a + 1 - 2a + 3) {(3a)^2 + 2.3a. 1 + (1)^2 + 3a. 2a + 1. 2a`

                            `- 3.3a - 3 + (2a)^2 - 2.2a .3 + (3)^2}`

   `= (a + 4) (9a^2 + 6a + 1 + 6a^2 + 2a - 9a - 3 + 4a^2 - 12a + 9`

   `= (a + 4) (19a^2 - 13a + 7)`   (Ans)

`(x + 5) (x - 9) - 15`

  `= x^2 + 5x - 9x - 45 - 15`

  `= x^2 - 4x - 60`

  `= x^2 - 10x + 6x - 60`

  `= x(x - 10) + 6(x - 10)`

  `= (x + 6) (x - 10)`  (Ans)

`(x + 2) (x + 3) (x + 4) (x + 5) - 48`

  `= (x + 2) (x + 5) (x + 3) (x + 4) - 48`

  `= (x^2 + 2x + 5x + 10) (x^2 + 3x + 4x + 12) - 48`

  `= (x^2 + 7x + 10) (x^2 + 7x + 12) - 48`

   ধরি, `x^2 + 7x + 10 = a`

  :.প্রদত্ত রাশি,

    `= x^2 + 7x + 12 = x^2 + 7x + 10 + 2 = a + 2`

    `= a(a + 2) - 48`

    `= a^2 + 2a - 48`

    `= a^2 + 8a - 6a - 48`

    `= a(a + 8) - 6(a + 8)`

    `= (a + 8) (a - 6)`

    `= (x^2 + 7x + 10 + 8) (x^2 + 7x + 10 - 6)`

                                        [a এর মান বসিয়ে]

    `= (x^2 + 7x + 18) (x^2 + 7x + 4)`

    `= (x^2 + 7x + 4) (x^2 + 7x + 18)`  (Ans)

বামপক্ষ  
  `= x^3 + 9x^2 + 26x + 24`

  `= x^3 + 9x^2 + 27x + 27 - x - 3`

  `= x^3 + 3.x^2.3 + 3.x.3^2 + 3^3 - (x + 3)`

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

  `= (x + 3) {(x + 3)^2 - 1}`

  `= (x + 3) {(x + 3)^2 - (1)^2}`

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

  `= (x + 3) (x + 4) (x + 2)`

  `= (x + 2) (x + 3) (x + 4)`

   = ডানপক্ষ

    `:. x^2 + 9x^2 + 26x + 24 = (x + 2) (x + 3) (x + 4)` (দেখানো হলো)

বামপক্ষ,  
 `= (x + 1) (x + 2) (3x - 1) (3x - 4)`

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

 `= (3x^2 + 3x - x - 1) (3x^2 + 6x - 4x - 8)`

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

    = ডানপক্ষ

   `:. (x + 1) (x + 2) (3x - 1) (3x - 4) = (3x^2 + 2x - 1) (3x^2 + 2x - 8)` (দেখানো হলো)