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