Question

How do you find the 8th term in the expansion of the binomial `(4x+3y)^9`?

Answer 1

`1259712x^2y^7`

Explanation:

The binomial theorem states that `(a+b)^n=sum_(r=0)^n""(""_r^n)a^(n-r)b^r`. In this question, `a=4x`, `b=3y`, and `n=9`.

The eight term occurs when `r=8-1=7` (since we sum starting with `r=0`).

We just need to substitute these values in `(""_r^n)a^(n-r)b^(r)` to get `(""_7^9)(4x)^(9-7)(3y)^7=36*16x^2*2187*y^7=1259712x^2y^7`.