My Math Forum Binomial Expansion Help Needed!

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 April 16th, 2017, 11:28 AM #1 Newbie   Joined: Sep 2016 From: Markham Posts: 3 Thanks: 0 Binomial Expansion Help Needed! I came across a question, which was: Find the coefficient of c^4d^11 in the expansion of (2c+5d)(c+d)^14. I can do it easily with the (c+d) bracket, but the (2c+5d) complicates it for me. Could someone help me out? Thanks a lot!
 April 16th, 2017, 11:33 AM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,197 Thanks: 1152 is this supposed to be $[(2c+5d)(c+c)]^{14}$ or $(2c+5d)(c+d)^{14}$ ?
 April 16th, 2017, 11:34 AM #3 Newbie   Joined: Sep 2016 From: Markham Posts: 3 Thanks: 0 The latter.
April 16th, 2017, 11:52 AM   #4
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Quote:
 Originally Posted by romsek $(2c+5d)(c+d)^{14}$
well first expand out the right term

$(2c+5d) \displaystyle \sum_{k=0}^{14} \binom{14}{k} c^k d^{14-k}$

now do the multiplication

$\displaystyle 2\sum_{k=0}^{14}\binom{14}{k} c^{k+1} d^{14-k} + 5\displaystyle \sum_{k=0}^{14}\binom{14}{k} c^k d^{14-k+1}$

grab the $c^4 d^{11}$ coefficents from each sum

$\displaystyle 2 \binom{14}{3} + 5 \binom{14}{4}$

and I leave you to evaluate that last expression

 Tags binomial, expansion, needed

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