a3 - 9 + (a + 1)3 রাশিটির একটি উৎপাদক হবে?
সমাধান
সঠিক উত্তর: Option C
a3 - 9 + (a + 1)3
= a3 - 9 + a3 + 3a2 + 3a + 1
= 2a3 + 3a2 + 3a - 8
= 2a3 - 2a2 + 5a2 - 5a + 8a - 8
= 2a2(a - 1) + 5a(a - 1) + 8(a - 1)
= (a - 1) (2a2 + 5a + 8)
= a3 - 9 + a3 + 3a2 + 3a + 1
= 2a3 + 3a2 + 3a - 8
= 2a3 - 2a2 + 5a2 - 5a + 8a - 8
= 2a2(a - 1) + 5a(a - 1) + 8(a - 1)
= (a - 1) (2a2 + 5a + 8)
