Question:উৎপাদকে বিশ্লেষণ কর: `a^3 - 1/8`
`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)Question:উৎপাদকে বিশ্লেষণ কর: `a^6/(27) - b^6`
`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)Question:উৎপাদকে বিশ্লেষণ কর: `4a^2 + 1/4a^2 - 2 + 4a - 1/a`
`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)
Question:উৎপাদকে বিশ্লেষণ কর: `(3a + 1)^3 - (2a - 3)^3`
`(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)Question:উৎপাদকে বিশ্লেষণ কর: `(x + 5) (x - 9) - 15`
`(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)