Question

In the following exercises, expand each binomial.

$(s+t{)}^7$

Short answer

Expansion is$s^7+7s^{6}t+21s^5{t}^2+35s^4{t}^3+35s^3{t}^4+21s^2{t}^5+7s{t}^6+t^7$

Step-by-step solution

Given Information

Expand$(s+t{)}^7$

Solution

We have

$$\begin{gathered} (s+t{)}^7=\left(\begin{array}{c}7\\ 0\end{array}\right)s^{7-0}{t}^{7-7}+\left(\begin{array}{c}7\\ 1\end{array}\right)s^{7-1}{t}^{7-6}+\left(\begin{array}{c}7\\ 2\end{array}\right)s^{7-2}{t}^{7-5}+\left(\begin{array}{c}7\\ 3\end{array}\right)s^{7-3}{t}^{7-4}+\left(\begin{array}{c}7\\ 4\end{array}\right)s^{7-4}{t}^{7-3}+\left(\begin{array}{c}7\\ 5\end{array}\right)s^{7-5}{t}^{7-2}+\left(\begin{array}{c}7\\ 6\end{array}\right)s^{7-6}{t}^{7-1}+\left(\begin{array}{c}7\\ 7\end{array}\right)s^{7-7}{t}^{7-0} \\ =s^7+7s^{6}t+21s^5{t}^2+35s^4{t}^3+35s^3{t}^4+21s^2{t}^5+7s{t}^6+t^7 \end{gathered}$$