Answer:
There are 16 terms in the expansion.
Step-by-step explanation:
Number of terms in a binomial expansion:
The number of terms in a binomial expansion
[tex](a + b)^n[/tex]
Is n + 1.
Power property:
For a power elevated to another power, we have that:
[tex](a^b)^c = a^{b*c}[/tex]
In this question:
[tex][(3x^2 + 7x)^3]^5 = (3x^2 + 7x)^{3*5} = (3x^2 + 7x)^{15}[/tex]
So [tex]n = 15[/tex], then the number of terms is [tex]n + 1 = 15 + 1 = 16[/tex]
There are 16 terms in the expansion.
