Question

* How many term are in the expansion of [(3x^2+7x)^3]^5​

Answer 1

There are 16 terms in the expansion.

Explanation:

Number of terms in a binomial expansion:

The number of terms in a binomial expansion

`(a + b)^n`

Is n + 1.

Power property:

For a power elevated to another power, we have that:

`(a^b)^c = a^(b*c)`

In this question:

`[(3x^2 + 7x)^3]^5 = (3x^2 + 7x)^(3*5) = (3x^2 + 7x)^(15)`

So
`n = 15`, then the number of terms is
`n + 1 = 15 + 1 = 16`

There are 16 terms in the expansion.