# How do you find the 4th term in the expansion of the binomial (x-10z)^7?

##### 1 Answer
Jul 7, 2017

$- 35000 {x}^{4} {z}^{3}$

#### Explanation:

$\text{using the "color(blue)"binomial theorem}$

•color(white)(x)(x+y)^n=sum_(r=0)^n((n),(r))x^(n-r)y^r

"where " ((n),(r))=(n!)/(r!(n-r)!

$\text{the general term is } \left(\begin{matrix}n \\ r\end{matrix}\right) {x}^{n - r} {y}^{r}$

$\text{and " T_(r+1)=((n),(r))x^(n-r)y^rlarrcolor(red)" the nth term}$

$\text{here " x=x" and } y = - 10 z$

$\textcolor{b l u e}{\text{for fourth term use r = 3}}$

$\Rightarrow {T}_{4} = \left(\begin{matrix}7 \\ 3\end{matrix}\right) {x}^{4} {\left(- 10 z\right)}^{3}$

$\textcolor{w h i t e}{\Rightarrow {T}_{4}} = 35 {x}^{4} \left(- 1000 {z}^{3}\right)$

$\textcolor{w h i t e}{\Rightarrow {T}_{4}} = - 35000 {x}^{4} {z}^{3}$