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

Options

A. `4756`
B. `5476`
C. `5376`
D. `4786`

Answer

C

Explanation

`T_(r+1)=^(9)C_(r)(2x)^(9-r).y^(r)`
`=^(9)C_(r).2^(9-r)x^(9-r).y^(r)`
`"Let " 9-r =6 " and " r=3`
`rArr" "r=3`
`:. " coefficient of "x^(6).y^(3)=^(9)C_(3).2^(9-3)`
`=(|ul9)/(|ul3|ul6).2^(6)`
`=(7xx8xx9)/(1xx2xx3)xx64`
`=84xx64`
`=5376.`