Find the term independent of `x`in the expansion of `(1+x+2x^3)[(3x^2/

1.	Find the term independent of `x`in the expansion of `(1+x+2x^3)[(3x^2//2)-(1//3)]^9`
Answer» Correct Answer - `17/54` In the expansion of `E = ( 3/2x^(2) - 1/ (3x))^(9)` , we have `T_(r+1) = (-1)^(r)^(9)C_(r)(3/2x^(2))(9-r) (1/(3x))^(r)` `rArr T_(r+1) = (-1)^(r)^(9)C_(r)(3(9-2r))/(2^((9-r)))* x^((18-3r)).` `(1+ x + 2x^(3)) [(a_(0) xx 1/x^(3)+a_(1) xx 1/x + a^(2))" from E"]` `=(1+x+2x^(3)) [ {(-1)^(7)^(9)C_(7)3^(-5)/2^(2) xx1/(x^(3))}+ {(-1)^(6)^(9)C_(6) 3^(-3)/2^(3)xxx^(0)}]` `[(x=-1 rArr18-3r = -1 rArr " r is faction"),(18-3r=0 rArr r=6 and 18-3r = -3 rArr r=7)]` `=(1+ x+ 2x^(3))[(-1)/(27x^(3))+7/18]` `:. " required term " ((-2)/27+7/18) = 17/54.`

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Find the term independent of `x`in the expansion of `(1+x+2x^3)[(3x^2//2)-(1//3)]^9`

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