To determine how many terms are in the binomial expansion of [tex]\((3x + 5)^9\)[/tex], we can use the properties of binomial expansions.
For any binomial expression of the form [tex]\((a + b)^n\)[/tex], the number of terms in its expansion is given by [tex]\(n + 1\)[/tex], where [tex]\(n\)[/tex] is the exponent.
In this case, the exponent [tex]\(n\)[/tex] is 9.
So, the number of terms in the expansion of [tex]\((3x + 5)^9\)[/tex] is calculated as:
[tex]\[ n + 1 = 9 + 1 = 10 \][/tex]
Therefore, the number of terms in the binomial expansion of [tex]\((3x + 5)^9\)[/tex] is [tex]\(10\)[/tex].
The correct answer is:
10
