a3 − 9 + (a + 1)3 রাশিটির একটি উৎপাদক (a − 1) এবং অপর একটি উৎপাদক?
Solution
Correct Answer: Option A
a3 − 9 + (a + 1)3
= a3 − 9 + a3 + 3a2 +3a + 1
=2a3 + 3a2 +3a − 8
= 2a3 − 2a2 5a2 − 5a + 8a − 1
= 2a2 (a − 1) + 5a (1 − 1) + 8(a − 1)
= (a − 1)(2a2 + 5a + 8)
= a3 − 9 + a3 + 3a2 +3a + 1
=2a3 + 3a2 +3a − 8
= 2a3 − 2a2 5a2 − 5a + 8a − 1
= 2a2 (a − 1) + 5a (1 − 1) + 8(a − 1)
= (a − 1)(2a2 + 5a + 8)
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