Answer: The number of terms in the binomial expansion of [tex](3x-5)^9[/tex] is 10.
Step-by-step explanation: We are given to find the number of terms in the following binomial expansion:
[tex]B=(3x-5)^9~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
the number of terms in the binomial expansion of [tex](x+y)^p[/tex]is given by
[tex]N_t=p+1.[/tex]
In the given binomial expansion (i), we have
[tex]p=9.[/tex]
Therefore, the number of terms in the given binomial expansion will be
[tex]N_t=p+1=9+1=10.[/tex]
Thus, there are 10 terms in the binomial expansion of [tex](3x-5)^9.[/tex]
