
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: USA Posts: 2,530 Thanks: 1390 
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: USA Posts: 2,530 Thanks: 1390  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 

Tags 
binomial, expansion, needed 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
(Binomial Expansion) Could someone please help me?  nautudent  Algebra  4  January 9th, 2016 12:07 PM 
Binomial expansion  xXxn0N00b5xXx  Probability and Statistics  2  December 22nd, 2013 11:56 AM 
More Binomial Expansion Help Please :(  n3rdwannab3  Elementary Math  4  February 5th, 2012 08:01 PM 
binomial expansion  hoyy1kolko  Probability and Statistics  2  March 13th, 2011 08:07 AM 
Binomial Expansion  jsmith613  Probability and Statistics  1  November 28th, 2010 03:44 AM 