Question

What is the fourth term of the expansion of the binomial (2x + 5)^5?

Answer 1

ok, 1 bionimial theorem coming right up

for a binomial expansion of (a+b)^n
the kth term is

`\left(\begin{array}{ccc}n\\k-1\end{array}\right)a^(n-(r-1))b^(k-1)`

`\left(\begin{array}{ccc}n\\k-1\end{array}\right)` means
`(n!)/((k-1)!(n-(k-1))!)`

n is 5
4th term
4-1=3
and a=2x
b=5
so

`\left(\begin{array}{ccc}5\\4-1\end{array}\right)(2x)^(5-(4-1))5^(4-1)`

`\left(\begin{array}{ccc}5\\3\end{array}\right)(2x)^(2)5^(3)`

`\left(\begin{array}{ccc}5\\3\end{array}\right)(2x)^(2)5^(3)`
(10)(4x^2)(125)
5000x^2 is the 4th term