Question

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

Answer 1

`-35000x^4 z^3`

Explanation:

Using the binomial expansion:
`(x-10z)^7 = ""^7C_0x^7(-10z)^0 + ""^7C_1 x^6 (-10z)^1 + ""^7C_2x^5(-10z)^2 + ""^7C_3 x^4(-10z)^3 + ...`
where `""^nC_r = (n!)/((n-r)!r!)`

The fourth term is `""^7C_3 x^4 (-10z)^3`
=`(7xx6xx5) /(1xx2xx3) x^4 (-1000z^3)`

= `-35000x^4 z^3`