a3 - 9b3+ (a + b)3 এর একটি উৎপাদক (a - b) হলে অপরটি কত?
Solution
Correct Answer: Option C
a3 - 9b3+ (a + b)3
= a3 - b3+ (a + b)3 - 8b3
= (a - b) (a2 + ab + b2) + (a + b)3 - (2b)3
= (a - b) (a2 + ab + b2) + (a + b - 2b) (a2 + 2ab + b2 + 2ab + 2b2 + 4b2)
= (a - b) (a2 + ab + b2) + (a - b) (a2 + 4ab + 7b2)
= (a - b) (2a2 + 5ab + 8b2)
= a3 - b3+ (a + b)3 - 8b3
= (a - b) (a2 + ab + b2) + (a + b)3 - (2b)3
= (a - b) (a2 + ab + b2) + (a + b - 2b) (a2 + 2ab + b2 + 2ab + 2b2 + 4b2)
= (a - b) (a2 + ab + b2) + (a - b) (a2 + 4ab + 7b2)
= (a - b) (2a2 + 5ab + 8b2)
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