Question

Find the fifth term of$(a+b{)}^8$

Short answer

Fifth term is$70a^4{b}^4$

Step-by-step solution

Given Information

Fifth term of$(a+b{)}^8$

Solution

We have

The $(r+1{)}^{st}$term in the expansion of $(a+b{)}^n$is

$\left(\begin{array}{l}n\\ r\end{array}\right)a^{n-r}{b}^r$

Here

$$\begin{gathered} r+1=5 \\ r=4 \\ n=8 \\ \left(\begin{array}{l}n\\ r\end{array}\right)a^{n-r}{b}^r=\left(\begin{array}{l}8\\ 4\end{array}\right)a^{8-4}{b}^4 \\ =70a^4{b}^4 \end{gathered}$$