Question

Middle term in the expansion of (a³ + ba)²⁸ is ______.

Answer 1

Middle term in the expansion of (a³ + ba)²⁸ is `""^28"C"_14  a^56 b^14`.

Explanation:

Number of term in the expansion (a³ + ba)²⁸

= 28 + 1

= 29 (odd)

∴ Middle term = `(29 + 1)/2` = 15^th term

∴ T₁₅ = T₁₄₊₁

= `""^28"C"_14  (a^3)^(28 - 14) *  (ba)^14`

= `""^28"C"_14  (a)^42 * b^14 * a^14`

= `""^28"C"_14  a^56b^14`.