Algebra-2

To find the coefficient of in the expansion of using Pascal's Triangle, we can follow these steps:

Step 1: Identify the Term

To find the term containing , we need:

from

from

 

Step 2: Determine the Binomial Coefficient

In the expansion of , the coefficients can be found using Pascal's Triangle. The coefficients in the 5th row are:

Row 0: 1

Row 1: 1, 1

Row 2: 1, 2, 1

Row 3: 1, 3, 3, 1

Row 4: 1, 4, 6, 4, 1

Row 5: 1, 5, 10, 10, 5, 1

 

The coefficients from the 5th row of Pascal's Triangle are: 1, 5, 10, 10, 5, 1

For the term that includes , the corresponding coefficient is 5.

 

Step 3: Calculate the Full Term

Now, we can calculate the specific term:

Term =

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