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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: 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
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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 Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post nautudent Algebra 4 January 9th, 2016 12:07 PM xXxn0N00b5xXx Probability and Statistics 2 December 22nd, 2013 11:56 AM n3rdwannab3 Elementary Math 4 February 5th, 2012 08:01 PM hoyy1kolko Probability and Statistics 2 March 13th, 2011 08:07 AM jsmith613 Probability and Statistics 1 November 28th, 2010 03:44 AM

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