Question:` a^4 - 27a^2 + 1`
`a^4 - 27a^2 + 1 = (a^2)^2 - 2.a^2.1 + (1)^2 - 25a^2`
` = (a^2 - 1)^2 - (5a)^2`
`= {(a^2 - 1) + 5a} {(a^2 - 1) - 5a}`
`= (a^2 + 5a - 1) (a^2 - 5a - 1)` (Ans)Question:উৎপাদকে বিশ্লেষণ কর: `x^4 - 6x^2y^2 + y^4`
`x^4 - 6x^2y^2 + y^4 = (x^2)^2 - 2x^2y^2 + (y^2)^2 - 4x^2y^2`
`= (x^2 - y^2)^2 - (2xy)^2`
`= (x^2 - y^2 + 2xy) (x^2 - y^2 - 2xy)`
`= (x^2 + 2xy - y^2) (x^2 - 2xy - y^2)`Question:উৎপাদকে বিশ্লেষণ কর: `(a^2 - b^2) (x^2 - y^2) + 4abxy`
`a^2 - b^2) (x^2 - y^2) + 4abxy`
`= a^2x^2 - a^2y^2 - b^2x^2 + b^2y^2 + 4abxy`
`= a^2x^2 + 2axby + b^2y^2 - a^2y^2 + 2axby - b^2x^2`
`= (a^2x^2 + 2abxy + b^2y^2) - (a^2y^2 - 2abxy + b^2x^2)`
`= {(ax)^2 + 2ax.by + (by)^2} - {(ay)^2 - 2.ay.bx + (bx)^2}`
`= (ax + by)^2 - (ay - bx)^2`
`= {(ax + by) + (ay - bx)} {(ax + by) - (ay - bx)}`
`= (ax + by + ay - bx)^2`
`= {(ax + by) + (ay - bx)}{(ax + by) - (ay - bx)}`
`= (ax + by + ay - bc) (ax + by - ay + bx)` (Ans)Question:উৎপাদকে বিশ্লেষণ কর: `4a^2 - 12ab + 9b^2 - 4c^2`
`4a^2 - 12ab + 9b^2 -4c^2` `= (2a)^2 - 2.2a.3b + (3b)^2 - 4c^2` `= (2a - 3b)^2 - (2c)^2` `= (2a - 3b + 2c) (2a - 3b - 2c)` (Ans)
Question:উৎপাদকে বিশ্লেষণ কর: `9x^4 - 45a^2x^2 + 36a^4`
`9x^4 - 45a^2x^2 + 36a^4`
`= 9(x^4 - 5a^2x^2 + 4a^2)`
`= 9(x^4 - 4a^2x^2 - a^2x^2 + 4a^4)`
`= 9{x^2(x^2 - 4a^2) - a^2(x^2 - 4a^2)}`
`= 9(x^2 - a^2) (x^2 - 4a^2)`
`= 9(x^2 - a^2){x^2 - (2a)^2}`
`= 9(x + a) (x - a) (x + 2a) (x - 2a)` (Ans)