Question

How do you find the coefficient of `a` of the term `ax^5` in the expansion of the binomial `(x+3)^12`?

Answer 1

The coefficient of `x^5` is `1732104`

Explanation:

the term of `x^r` in the expansion of `(x+a)^n` is

`C_r^nx^ra^(n-r)`

Hence, the term containing `x^5` in the expansion of `(x+3)^12` is

`C_5^12x^5 3^7=(12*11*10*9*8)/(1*2*3*4*5)x^5xx2187`

= `792xx2187`

= `1732104`