Find the 9th term in the expansion of (3x-y÷3)^12?

1 Answer
Mar 13, 2018

T_{9}\ =\ \frac{55x^4y^8}{9}

Explanation:


The \ \ (r+1)\ th\ \ term of an expression \ \ (a+x)^n\ \ by using binomial theorem can be found by the general term formula:

T_{r+1}\ =\ ((n),(r))a^{n-r}x^r

Here, we are required to find the \ \ 9th\ \ term, so put \ \ r=8\ \ in the above stated formula to get:

T_{8+1}\ =\ ((12),(8))(3x)^{12-8}(y/3)^8

T_{9}\ =\ \frac{12!}{8!(12-8)!}\cdot(3x)^4(y/3)^8

Simplify to get:

T_{9}\ =\ \frac{55x^4y^8}{9}

That's it!