Final answer:
To find the ninth term of the binomial expansion of (3x + 2y)^15, use the binomial theorem, calculating 15C8 * (3x)^7 * (2y)^8. This is a high school level algebra problem involving series expansions and the binomial theorem.
Step-by-step explanation:
The student is asking about the ninth term of the binomial expansion of (3x + 2y)15. To find any specific term in a binomial expansion, we use the binomial theorem, which is represented as:
(a + b)n = an + nan-1b + n(n-1)/2!an-2b2 + ...
The general term (r+1)th term in the expansion (a + b)n is given by nCr * an-r * br, where nCr is the combination of n items taken r at a time.
In this case, to find the ninth term of the expansion of (3x + 2y)15, we'll have to find T9 = 15C8 * (3x)15-8 * (2y)8, since the term index (r) starts from 0. By calculating the values and simplifying, we can find the ninth term of the expansion.
This is a high school level algebra problem, typically covered in courses focused on polynomial expressions and series expansions.