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September 9th, 2011, 08:01 PM   #1
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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 .......
(a-b)^ n = ? where n= 1,2,3,4 .......

Examples :

can we compute/deduce the formula for

(a+b) ^ 10 = ?

(a-b) ^ 20 = ?

Thanks & Regards,
Prashant S Akerkar
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September 9th, 2011, 08:04 PM   #2
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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
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September 10th, 2011, 12:50 AM   #3
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I corrected the title for you. The binomial theorem provides such a formula for an arbitrarily large integer value of n.
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September 10th, 2011, 02:56 AM   #4
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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
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File Type: png Pascal\'s Triangle.png (5.5 KB, 459 views)
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September 10th, 2011, 03:47 AM   #5
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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
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November 15th, 2011, 12:10 AM   #6
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Re: Algebraic Square, Cube Formulas / Equations.

Thank you.

Attaching Image ....

Thanks & Regards,
Prashant S Akerkar
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File Type: jpg Binomial Theorem.jpg (7.9 KB, 401 views)
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