Find the indicated term in the expansion of the given binomial.

Question

The term containing b⁶

 in the expansion of (a + b²)¹⁴

Answer 1

Let (n + 1)th term is T_{n + 1} = C(14, n)a^14-n(b²)ⁿ = C(14, n)a^14-nb²ⁿ. So, 2n = 6, n = 3 and we have to find 4th term of expansion: T₄ = C(14, 3)a¹¹b⁶ = (14·13·12)/(3·2·1) a¹¹b⁶ = 364a¹¹b⁶

Answer 2

the 4th term is (a^12)^11(b^2)^3 which would give you a^11b^6

the coefficient of this term is 14 choose11(14C11)= 364

so the term is 364a^11b^6