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

1 Answer
Alan P.
May 27, 2015

#((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.

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