Results 1 to 3 of 3

Thread: a binomial thm problem

  1. #1
    Member
    Joined
    Sep 2007
    Posts
    176

    a binomial thm problem

    a binomial thm problem
    Attached Thumbnails Attached Thumbnails a binomial thm problem-p90-q4-re.ex4-bk1.gif  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by afeasfaerw23231233 View Post
    a binomial thm problem
    i'm sorry. i don't see a much nicer way to do this problem. i would have done it with brute force like you did
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    11,122
    Thanks
    719
    Awards
    1
    $\displaystyle (1 + 2x)^4(1- x)^3$

    The most clever thing I can come up with is to define two new variables:
    $\displaystyle y = 1 + \frac{x}{2}$
    and
    $\displaystyle z = \frac{3x}{2}$

    Then
    $\displaystyle y + z = 1 + 2x$
    and
    $\displaystyle y - z = 1 - x$

    Thus
    $\displaystyle (1 + 2x)^4(1- x)^3 = (y + z)^4(y - z)^3$

    $\displaystyle = [(y + z)^3(y - z)^3](y + z)$

    $\displaystyle = (y^2 - z^2)^3(y + z)$

    $\displaystyle = ([1 + 2x]^2 - [1 - x]^2)^3(1 + 2x)$
    etc.

    But I doubt this actually cuts down on the work load.

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. binomial problem!
    Posted in the Statistics Forum
    Replies: 2
    Last Post: Jan 13th 2012, 07:07 AM
  2. Binomial Problem!!
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: May 31st 2010, 07:14 PM
  3. Binomial Theorem problem!
    Posted in the Statistics Forum
    Replies: 1
    Last Post: Jan 19th 2010, 10:40 AM
  4. problem on binomial
    Posted in the Algebra Forum
    Replies: 7
    Last Post: Jun 18th 2008, 03:01 AM
  5. another binomial problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Jan 11th 2008, 01:44 AM

Search Tags


/mathhelpforum @mathhelpforum