Question

Find the coefficient of the $x^4$ term of $(x+2{)}^7$.

Short answer

Coefficient of the$x^4$term is$280$

Step-by-step solution

Given Information

Coefficient of the $x^4$ term of $(x+2{)}^7$.

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$a=x,b=2,n=7$

$$\begin{gathered} n-r=4 \\ 7-r=4 \\ r=3 \\ \left(\begin{array}{l}n\\ r\end{array}\right)a^{n-r}{b}^r=\left(\begin{array}{l}7\\ 3\end{array}\right)x^{7-3}{2}^3 \\ =35\times 8x^4 \\ =280x^4 \end{gathered}$$

Coefficient is $280$