Find the coefficent of`x^(6)y^(3)` in the expansion of `(x+2y)^(9)`.

Explanation

The general term in the expansion of `(x+2y)^(9)` is given by
`T_(r+1)=.^(9)C_(r) xx x^((9-r)) xx(2y)^(r)`
`rArr T_(r+1)=.^(9)C_(r) xx2^(r) xxx^((9-r)) xxy^(r)." "`...(i)
We have to find the coeffcient of `x^(6)y^(3)`.
Putting r=3 in (i), we get
`T_(3+1)=.^(9)C_(3) xx 2^(3) xx (x^(6)y^(3))`.
`:." coefficient of "x^(6) y^(3)` in the given expansion
`=(.^(9)C_(3) xx 2^(3))=((9 xx8xx7)/(3xx2xx1) xx8) =672`.
Hence, the coefficient of `x^(6)y^(3)` in the given expansion is 672.