Question:উৎপাদকে বিশ্লেষণ কর: `a^2 + 6a + 8 - y^2 + 2y`
Answer `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 ------------ 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)
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