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Question
In the following expansion, find the indicated term.
`(2x^2 + 3/(2x))^8`, 3rd term
Solution
We know that the (r + 1)th term in the expansion of (a + b)n is
tr+1 = nCr an–r br
Here a = 2x2, b = `3/(2x)`, n = 8 and for t3, r = 2
∴ 3rd term in the expansion of `(2x^2 + 3/(2x))^8`
= t3 = `""^8"C"_2(2x^2)^6 (3/(2x))^2`
= `(8 xx 7)/(1 xx 2) xx 2^6.x^12 xx 3^2/(2^2.x^2)`
= 28 × 24 × 32.x10
= 4032 x10
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