My Math Forum  

Go Back   My Math Forum > High School Math Forum > Probability and Statistics

Probability and Statistics Basic Probability and Statistics Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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 (?2-1)^5,and show that ( ?2-1)^5 is the reciprocal of ( ?2+1)^5.

Please help me to solve these question.I need help.i am weak at math.
hoyy1kolko is offline  
 
March 14th, 2011, 09:22 AM   #2
Senior Member
 
skaa's Avatar
 
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^2-ab+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:
(?2-1)^5 is 29?2-41
skaa is offline  
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.
johnny is offline  
March 14th, 2011, 09:32 AM   #4
Global Moderator
 
greg1313's Avatar
 
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:
Originally Posted by hoyy1kolko
. . . show that ( ?2-1)^5 is the reciprocal of ( ?2+1)^5.
greg1313 is offline  
March 14th, 2011, 09:41 AM   #5
Global Moderator
 
The Chaz's Avatar
 
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
The Chaz is offline  
March 16th, 2011, 09:30 PM   #6
Senior Member
 
MarkFL's Avatar
 
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:



MarkFL is offline  
Reply

  My Math Forum > High School Math Forum > Probability and Statistics

Tags
binomial, expansion



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Binomial expansion of (1+x) rnck Probability and Statistics 7 August 24th, 2012 11:44 AM
More Binomial Expansion Help Please :( n3rdwannab3 Elementary Math 4 February 5th, 2012 08:01 PM
binomial expansion hoyy1kolko Probability and Statistics 3 March 14th, 2011 08:04 PM
binomial expansion hoyy1kolko Probability and Statistics 2 March 14th, 2011 07:54 PM
binomial expansion hoyy1kolko Probability and Statistics 2 March 13th, 2011 08:07 AM





Copyright © 2019 My Math Forum. All rights reserved.