Question

In the following exercises, expand each binomial.

$(m+n{)}^5$

Short answer

Expansion is$m^5+5m^{4}n+10m^3{n}^2+10m^2{n}^3+5m{n}^4+n^5$

Step-by-step solution

Step 1. Given Information

Expand$(m+n{)}^5$

Step 2. Solution 

We have

$$\begin{gathered} (m+n{)}^5=\left(\begin{array}{l}5\\ 0\end{array}\right)m^{5-0}{n}^{5-5}+\left(\begin{array}{l}5\\ 1\end{array}\right)m^{5-1}{n}^{5-4}+\left(\begin{array}{l}5\\ 2\end{array}\right)m^{5-2}{n}^{5-3}+\left(\begin{array}{l}5\\ 3\end{array}\right)m^{5-3}{n}^{5-2}+\left(\begin{array}{l}5\\ 4\end{array}\right)m^{5-4}{n}^{5-1}+\left(\begin{array}{l}5\\ 5\end{array}\right)m^{5-5}{n}^{5-0} \\ =m^5+5m^{4}n+10m^3{n}^2+10m^2{n}^3+5m{n}^4+n^5 \end{gathered}$$