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  and  from .

 

Step 2: Determine the Binomial Coefficient

In the expansion of , the coefficients can be found using Pascal's Triangle. The coefficients in the 7th 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

Row 6: 1, 6, 15, 20, 15, 6, 1

Row 7: 1, 7, 21, 35, 35, 21, 7, 1.

 

The coefficients from the 7th row of Pascal's Triangle are: 1, 7, 21, 35, 35, 21, 7, 1.

For the term that includes , the corresponding coefficient is 35.

 

Step 3: Calculate the Full Term

Now, we can calculate the specific term:

Term = 35 ·

Click "Show Answer" to reveal the answer and analysis