Question

In the following exercises, expand each binomial.

$(a+b{)}^6$

Short answer

Expansion is$a^6+6a^{5}b+15a^4{b}^2+20a^3{b}^3+15a^2{b}^4+6a{b}^5+b^6$

Step-by-step solution

Step 1. Given Information

Expand$(a+b{)}^6$

Step 2. Solution 

We have

$$\begin{gathered} (a+b{)}^6=\left(\begin{array}{c}6\\ 0\end{array}\right)a^{6-0}{b}^{6-6}+\left(\begin{array}{c}6\\ 1\end{array}\right)a^{6-1}{b}^{6-5}+\left(\begin{array}{c}6\\ 2\end{array}\right)a^{6-2}{b}^{6-4}+\left(\begin{array}{c}6\\ 3\end{array}\right)a^{6-3}{b}^{6-3}+\left(\begin{array}{c}6\\ 4\end{array}\right)a^{6-4}{b}^{6-2}+\left(\begin{array}{c}6\\ 5\end{array}\right)a^{6-5}{b}^{6-1}+\left(\begin{array}{c}6\\ 6\end{array}\right)a^{6-6}{b}^{6-0} \\ =a^6+6a^{5}b+15a^4{b}^2+20a^3{b}^3+15a^2{b}^4+6a{b}^5+b^6 \end{gathered}$$