Question

Find the coefficient of the $x^5$ term of$(x+4{)}^8$

Short answer

Coefficient of$x^5$is$3584$

Step-by-step solution

Given Information

Coefficient of the $x^5$ term of$(x+4{)}^8$

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 role="math" localid="1645254400169" $a=x,b=4,n=8$

$$\begin{gathered} 8-r=5 \\ r=3 \end{gathered}$$

$$\begin{gathered} \left(\begin{array}{l}n\\ r\end{array}\right)a^{n-r}{b}^r=\left(\begin{array}{l}8\\ 3\end{array}\right)x^{8-3}{4}^3 \\ =56\times 64x^5 \\ =3584x^5 \end{gathered}$$

Coefficient is$3584$