Question

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

Answer 1

`16yx^3`.

Explanation:

The `(r+1)^(th)` term `T_(r+1)`, in the expansion of `(a+b)^n` is,

`T_(r+1)=""^nC_r*a^(n-r)*b^r`

So, in our case, for the read. `4^(th)` term, `T_4` we have,

`r=3, n=4, a=4y, and, b=x`

`:. T_4=""^4C_3*(4y)^(4-3)*x^3`

`T_4=4*4y*x^3=16yx^3`