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

Aug 7, 2015

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

#### Explanation:

Using the binomial expansion:
${\left(x - 10 z\right)}^{7} = {\text{^7C_0x^7(-10z)^0 + ""^7C_1 x^6 (-10z)^1 + ""^7C_2x^5(-10z)^2 + }}^{7} {C}_{3} {x}^{4} {\left(- 10 z\right)}^{3} + \ldots$
where ""^nC_r = (n!)/((n-r)!r!)

The fourth term is  ""^7C_3 x^4 (-10z)^3
=$\frac{7 \times 6 \times 5}{1 \times 2 \times 3} {x}^{4} \left(- 1000 {z}^{3}\right)$

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