Question

How many terms are in the expansion of the binomial below? (x^3 + 2/x)^8A: 9B: 8C: 11D: 10

Answer 1

Given expression is

`(x^3+(2)/(x))^8`

This is of the form

`(a+b)^n`
`\text{where}a=x^3,\text{ b=}(2)/(x)\text{ and n=8}`

Recall that

`In\text{ the binomial expansion of }(a+b)^n,\text{ there are total n+1 terms.}`

Here n=8.

`In\text{ the binomial expansion of }(x^3+(2)/(x))^8,\text{ there are total 8+1=9 terms.}`

Hence option A is correct.