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April 16th, 2017, 10:28 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, 10:33 AM  #2 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,410 Thanks: 715 
is this supposed to be $[(2c+5d)(c+c)]^{14}$ or $(2c+5d)(c+d)^{14}$ ? 
April 16th, 2017, 10:34 AM  #3 
Newbie Joined: Sep 2016 From: Markham Posts: 3 Thanks: 0 
The latter.

April 16th, 2017, 10:52 AM  #4 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,410 Thanks: 715  well first expand out the right term $(2c+5d) \displaystyle \sum_{k=0}^{14} \binom{14}{k} c^k d^{14k}$ now do the multiplication $\displaystyle 2\sum_{k=0}^{14}\binom{14}{k} c^{k+1} d^{14k} + 5\displaystyle \sum_{k=0}^{14}\binom{14}{k} c^k d^{14k+1}$ 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 

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binomial, expansion, needed 
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