Algebra-2

To find the middle term in the expansion of  using the binomial expansion and Pascal's Triangle, we can follow these clear steps:

 

Step 1: Identify the Expression

We are expanding:

 

Step 2: Total Number of Terms

The total number of terms in the expansion is :

.

Since there are 7 terms, the middle term corresponds to the 4th term.

 

Step 3: Determine the Fourth Term

The binomial expansion can be expressed as:

.

Where:

,

,

.

The 4th term (which corresponds to  in the binomial expansion) can be expressed as:

Fourth Term = .

This can be rewritten as:

Fourth Term = .

 

Step 4: Constructing Pascal's Triangle

To find the coefficient (