Answer:
The correct option is 6
Step-by-step explanation:
Given expression,
[tex](2m-3n)^9[/tex]
By the binomial expansion,
[tex](a+b)^x = \sum _{r=0}^{x} ^xC_r a^{x-r} b^{r}[/tex]
Where,
[tex]^xC_r=\frac{x!}{r!(x-r)!}[/tex]
Thus,
[tex](2m-3n)^9 = \sum _{r=0}^{9} ^9C_r (2m)^{9-r} (-3n)^{r}[/tex]
For finding the term containing [tex]m^3[/tex]
9 - r = 3
⇒ 9 - 3 = r
⇒ r = 6
i.e. the required term is,
[tex]^9C_6 (2m)^{3} (-3n)^{6}[/tex]
Hence, the power of n in that term = 6.
