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Sum

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

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#### Solution

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

T_{7} = `""^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`

Concept: General and Middle Terms

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