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March 14th, 2011, 06:13 AM  #1 
Senior Member Joined: Dec 2010 Posts: 233 Thanks: 0  help binomial expansion
1.without using tables or calculator,evaluate ( ?7+?3)^6+(?7?3)^6. 2.Obtain the binomial expansion of ( ?2+1)^5 in the form m?2 + n, where m and n are integers.State the corresponding result for the expansion of (?21)^5,and show that ( ?21)^5 is the reciprocal of ( ?2+1)^5. Please help me to solve these question.I need help.i am weak at math. 
March 14th, 2011, 09:22 AM  #2 
Senior Member Joined: Mar 2011 From: Chicago, IL Posts: 214 Thanks: 77  Re: help binomial expansion
1. Use this formula: a^3+b^3=(a+b)(a^2ab+b^2) , for your case: (( ?7+?3)^2)^3+((?7?3)^2)^3 , the result is 7040. 2. Just use: (a+b)^5=a^5+5a^4*b+10a^3*b^2+10a^2*b^3+5a*b^4+b^5 , so: (?2+1)^5 is 29?2+41 and: (?21)^5 is 29?241 
March 14th, 2011, 09:30 AM  #3 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 
Above problems only requires basic algebra, and above average mathematical talent.

March 14th, 2011, 09:32 AM  #4  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond  Re: help binomial expansion Quote:
 
March 14th, 2011, 09:41 AM  #5 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,767 Thanks: 5  Re: help binomial expansion
I hope I have what it takes...! Using the above suggestion, we have I'll try the squaring first... Then "a + b" is just 20. So... (20)(368  16) = 20*352 = 7040 
March 16th, 2011, 09:30 PM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: help binomial expansion
2.) If we define: , , Then it can be shown that: , , , , Thus: 

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