Question

How do you find the fourth term of `((2x-z)^2 )^6`?

Answer 1

`((2x-z)^2)^6 = (2x-z)^12`

The fourth term of this expansion is
`color(red)(12C4) * (2x)^4 * (-z)^(12-4)`

`= (12!)/((4!)(8!)) * 16x^4 * z^8`

`= (495) *16x^4z^8`

`=7920x^4z^8`

`color(red)("Note")`
I'm not certain of the current notation standard for this expression: "12 Choose 4" and have used the form I learned more than 50 years ago.