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September 9th, 2011, 08:01 PM  #1 
Banned Camp Joined: Aug 2011 Posts: 534 Thanks: 2  Algebraic Square, Cube Formulas / Equations.
We have the following formulas 1. (a + b)^2 = a^2 + 2ab + b^2 2. (a ? b)^2 = a^2 ? 2ab + b^2 3. (a + b)^3 = a^3 + b^3 + 3ab(a + b); 4. (a ? b)^3 = a^3 ? b^3 ? 3ab(a ? b); Question : Up to what maximum value of n we can compute/deduce the formula? i.e (a+b)^ n = ? where n= 1,2,3,4 ....... (ab)^ n = ? where n= 1,2,3,4 ....... Examples : can we compute/deduce the formula for (a+b) ^ 10 = ? (ab) ^ 20 = ? Thanks & Regards, Prashant S Akerkar 
September 9th, 2011, 08:04 PM  #2 
Banned Camp Joined: Aug 2011 Posts: 534 Thanks: 2  Re: Algebraic Square, Cube Formulas / Equations.
The Topic name is : Algebraic Square, Cube Formulas / Equations. and not Algerabic Square, Cube Formulas / Equations. Thanks & Regards, Prashant S Akerkar 
September 10th, 2011, 12:50 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,833 Thanks: 2161 
I corrected the title for you. The binomial theorem provides such a formula for an arbitrarily large integer value of n.

September 10th, 2011, 02:56 AM  #4 
Banned Camp Joined: Aug 2011 Posts: 534 Thanks: 2  Re: Algebraic Square, Cube Formulas / Equations.
Thank you. http://en.wikipedia.org/wiki/Binomial As you mention, "Binomial Theorem" should be the correct title. The Pascal's Triangle Figure is depicted for n = 7 i.e (a + b) ^ n. Questions  1. So can we reach to a conclusion that through Binomial Theorem we can compute any formula for larger values of n ? i.e we can also write the formula for (a + b) ^ 100 where n=100 and draw the Pascal's Triangle. 2. The Binomial Theorem is written with n as integer value, what will be the formula for n exponent as a decimal/float value ? i,e n= 2.1, n=3.2, n=4.6 etc i.e. is the following expression valid for a binomial ? (a + b) ^ 2.1 = ? (a + b) ^ 3.2 = ? if Yes, what will be the formula, if No why ? Thanks & Regards, Prashant S Akerkar 
September 10th, 2011, 03:47 AM  #5 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Algebraic Square, Cube Formulas / Equations.
If you look further down that same Wikipedia link that skipjack gave you, you will find the "generalized binomial theorem": http://en.wikipedia.org/wiki/Binomial_t ... al_theorem 
November 15th, 2011, 12:10 AM  #6 
Banned Camp Joined: Aug 2011 Posts: 534 Thanks: 2  Re: Algebraic Square, Cube Formulas / Equations.
Thank you. Attaching Image .... Thanks & Regards, Prashant S Akerkar 

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