Question

How do you use the Binomial Theorem to expand `(1/3x – 9) ^20`?

Answer 1

It will be almost impossible to provide the entire answer, but I will tell you how to do so.

Explanation:

The binomial theorem states that:

`(x+a)^n=sum_(k=0)^n((n),(k))x^(n-k)a^k`, where `((n),(k))=(n!)/(k!(n-k)!)`.

Here, `x=1/3x,a=-9,n=20`.

So the above equation becomes:

`(1/3x-9)^20=sum_(k=0)^20((20),(k))(1/3x)^(20-k)(-9)^k`

If you were to solve the above, you would get your answer.