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Question

Find the coefficient of x6y3 in the expansion of (x+2y)9


Solution

The general term in the expansion of (x+2y)9 is given by
Tr+1=9Cr×x(9r)×(2y)rTr+1=9Cr×2r×x(9r)×yr
 we have to find the coefficient of x6y3
Putting r = 3 in (i), we getT(3+1)=9C3×23×(x6y3)coefficient of x6y3 in the given expansion=(9C3×23)=(9×8×73×2×1×8)=672.
 Hence the coefficient of x6y3 in the given expansion is 672.

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