Find the coefficient of `x^5""in(x+3)^8`

Answer

N/a

Explanation

Let the (r+1)th term in the expansion of `(x+3)^(8)` contains `x^(5)`.
`:. T_((r+1))=^(8)C_(r)(x)^{8-r).(3)^(r)`
`"Let " x^(8-r) =x^(5) rArr 8-r=5`
`rArr " "r=8-5=3`
`"Now " T_(3+1)=^(8)C_(3)x^(5)(3)^(3)`
Clearly the coefficient of `x^(5) =^(8) C_(3).(3)^(3)`
`=(8xx7xx6)/(3xx2xx1).27`
`=56xx27 =1512`
`:.` coefficient of `x^(5)` in the expansion of `(x+3)^(8)=1512`