How to find middle term of binomial expansion

Hello everyone, welcome to Pooja Academy blogs today you are going to learn how to find middle term of any binomial expansion 

So there are two methods to find middle term of binomial expansion: 

1. Traditional method or Bookish method : which is long method and will take much of your time but as this method is in you NCERT book so this long method is good for achieving good marks but this method is not recommended for competitive exams. 

2. Pooja Academy method : this method is short method and will be useful for your competitive exams and MCQ based question in which you have very less amount of time to solve it 

In this blog Pooja Academy will teach you both methods. Traditional method will help you in achieving higher marks and Pooja Academy method will help you solve the questions in just few seconds

Solving questions with Traditional method :

Ques ; What is the middle of the binomial expansion (1+2x)²

Ans. Step 1. First check whether the power of binomial is even or odd 

so in this binomial power is 2 which is even 

Step 2. If the power is even then use the formula (n/2 + 1) th term (i.e (2/2 + 1) th term = 2nd term)

Step 3. Now to find 2nd term use general term formula given below:

Step 4.So now middle term of the expansion (1+2x)² is 

If power is odd then there will be two middle terms, Lets take an example of odd power of binomial (1+2x)³

Step 1. If the power is even then use the formula [(n+1)/2]th and [(n+1)/2 +1]th term (i.e [(3+1)/2]th and [(3+1)/2 +1]th term = 2nd and 3rd term)

Step 2. Now to find 2nd and 3rd term use general term formula given below:

Step 3.So now middle terms of the expansion (1+2x)³ are 

Now Pooja Academy Method :

1. If power is even then simply divide the power by 2, Then write the term .

like in above example (1+2x)². Power is even (i.e 2) so divide it by 2 we get 1 as the answer so 

middle term will 

Lets take an another example for better understanding :

Find middle term of binomial expansion of (4x+6)²

as power is even so simply divide the power by 2 we get 1 as answer so middle term of this expansion is 

2. if power is odd then there will be two middle terms so subtract 1 from the power and then divide it by 2. like if the power is 3 which is odd so subtract 1 from the power we get 2 and then divide it by 2 we get 1 as answer so one of the two middle term is  

for next middle term simply write the next term which will be 

And now if you want to practice CBSE question based on middle term click on the link given below

Binomial Exercise