Question

Find the middle term in the expansion of `(2ax - b/x^2)^12`.

Answer 1

Since the power of binomial is even, it has one middle term which is the `(12 + 2)^"th"/2` term and it is given by

T₇ = `""^12"C"_6  (2ax)^6  ((-b)/x^2)^6`

= `""^12"C"_6  (2^6 a^6 x^6 * (-b)^6)/x^12`

= `""^12"C"_6  (2^6 a^6 b^6)/x^6`

= `(59136a^6b^6)/x^6`