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)Question:উৎপাদকে বিশ্লেষণ কর: `a^2 + 6a + 8 - y^2 + 2y`
`a^2 + 6a + 8 - y^2 + 2y`
`= a^2 + 4a + 2a + 8 - y^2 + 2y`
`= a(a + 4) + 2(a + 4) - y^2 + 2y`
`= (a + 4) (a + 2) + 2y - y^2`
ধরি, a + b = p
a + 2 = q
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2 = p - q [বিয়োগ করে]
:. p - q = 2
এখন, `(a + 4) (a + 2) + 2y - y^2`
`= pq + (p - q) y - y^2`
[:. a + 4 = p, a + 2 = q এবং 2 = p - q]
`= pq + py - qy - y^2`
`= p(q + y) - y(q + y)`
`= (q + y) (p - y)`
`= (a + 2 + y) (a + 4 - y)` [p, q]
`= (a + y + 2) (a - y + 4)` (Ans)
বিকল্প সমাধান:
`a^2 + 6a + 8 - y^2 + 2y`
`= a^2 + 6a + 9 - y^2 + 2y - 1`
`= a^2 + 6a + 9 - (y^2 - 2y + 1)`
`= {(a)^2 + 2.a.3 + (3)^2} - {(y)^2 - 2.y.1 + (1)^2}`
`= (a + 3)^2 - (y - 1)^2`
`= (a + 3 + y - 1) (a + 3 - y + 1)`
`= (a + y + 2) (a - y + 4)` (Ans)Question:উৎপাদকে বিশ্লেষণ কর: `16x^2 - 25y^2 - 8xz + 10yz`
`16x^2 - 25y^2 - 8xz + 10yz`
`= (4x)^2 - (5y)^2 - 2z(4x - 5y)`
`= (4x + 5y) (4x - 5y) - 2z(4x - 5y)`
`= (4x - 5y) (4x + 5y - 2z)` (Ans)Question:উৎপাদকে বিশ্লেষণ কর: `2b^2c^2 + 2c^2a^2 + 2a^2b^2 - a^4 - b^4 - c^4`
`2b^2c^2 + 2c^2a^2 + 2a^2b^2 - a^4 - b^4 - c^4`
`= 4a^2b^2 - a^4 - b^4 - c^4 - 2a^2b^2 + 2b^2c^2 + 2c^2a^2`
`= 4a^2b^2 - (a^4 + b^4 + c^4 + 2a^2b^2 - 2b^2c^2 - 2c^2a^2)`
`= 4a^2b^2 - {(a^2)^2 + (b^2)^2 + (-c^2)^2 + 2a^2b^2 + 2b^2`
`(-c^2) + (-c^2)a^2}`
`= (2ab)^2 - (a^2 + b^2 - c^2)^2`
`= (2ab + a^2 + b^2 - c^2) (2ab - a^2 - b^2 + c^2)`
`= {(a^2 + 2ab + b^2) - c^2} {c^2 - (a^2 - 2ab + b^2)}`
`= {(a + b)^2 - c^2} {c^2 - (a - b)^2}`
`= (a + b + c) (a + b - c) (c + a - b) (c - a + b)`
`= (a + b + c) (a + b - c) (b + c - a) (c + a - b)`
`= (a + b + c) (b + c - a) (c + a - b) (a + b - c)` (Ans)