Find the coefficient of x9 in the expansion of [x2-(1/3x)]9 Plz help - Maths - Binomial Theorem

Question

Find the coefficient of x9 in the expansion of
[x2-(1/3x)] 9
Plz help

Ashwini Kumar · Accepted Answer

We have,x2-13x9=x2-3x-19rth term of the expansion=9Cr-1x29-r-13x-1r-1=9Cr-1x29-r-13x1-r=9Cr-1×31-rx20-2rx1-r=9Cr-1×31-rx20-2r+1-r=9Cr-1×31-rx21-3rHere, 21-3r=9⇒12=3r∴r=4For r=4,coefficient=9Cr-1×31-r=9C3×31-4=9!3!×6!×127=7×8×91×2×3×127=289

Find the coefficient of x9 in the expansion of [x2-(1/3x)] 9 Plz help

Find the coefficient of x⁹ in the expansion of [x²-(1/3x)] ^{9

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