Find the 6th term of the binomial expansion of 2cd10 please

Find the 6th term of the binomial expansion of (2c-d)¹⁰

^{please show me how to work this out completely}

Solution

(2c - d)^10

(a + b)^n

General rth term will be = a^(n -r) b^(r) nCr

and nCr = n! / ( r! (n-r)! )

for given terms, r = 6

6th term = (2c)^(10-6) (-d)^(6) [ 10! / (6! 4! ) ]

        = 16 c^4 d^6 ( 210)

         = 3360 c^4 d^6