Wednesday, 22 February 2012

Solving Binomial Expansion

In college algebra is the part of arithmetic, which perform the calculation on the variables. In the algebra, expressions are written in the form polynomial which is a part of secondary board of education andhra pradesh. The binomial polynomial (polynomials worksheet) contains two terms. These two terms can be considered as a collection of or arranging the two monomial with operators and brackets option. Through this session we are discussing about Solving Binomial Expansion. Dividing Polynomials can be defined as two variables which perform some expression or some operation. Like a2 – b2 = (a + b) (a – b)
The algebra provides the lots of way to solve the binomial expression. In the mathematics to solve the binomial expression we use the concept of expansion of binomial theorem. Binomial theorem can generally be represented by the formula given by Blaise Pascal in the 17th century. The most generic example of binomial expression is given below:
(a + b)2 = a2 + 2ab + b2
 In the more general term binomial formula can be expressed as a:
     (a + b)n = ∑∞i=0  (n/i) ai bn-i
Here (n/i)  is a binomial coefficient and ‘n’ is a real number.
In the simple term binomial expression can be written as:
(a + b)2 = a2 + 2ab + b2
(a + b)3 = a3 + 3a2b + 3ab2  + b3
As same like binomial theorem formula can be written as:
(a + b)n = an + n(an-1 b1) + n(n-1)/2! (an-2 b2) + n(n-1) (n-2)/3! (an-3 b3)+……….+ bn

Here we will show you binomial expansion examples and how to solve the binomial expression. (Know more about Binomial Expansion in broad manner, here,)
Example1: Solve the binomial given expression (a + 5)3.
Solution:  Given that (a + 5)3, as we can see that it’s a binomial expression. So this can be solved by following the binomial expansion formula:
So, solution become in simplified formula:
      (a + 5)3 = a5 + 3x2 (5) + 3x (5)2 + 53  
      (a + 5)3 = a5 + 15 x2 + 75x + 125
As clear from the above solution, we can easily solve the binomial related problems.
In the next session we are going to discuss Binomial Experiment and Read more maths topics of different grades such as  How to do Estimate Quotients in the upcoming sessions here.

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