Question

find the independent of x in the expansion ​

Answer 1

Explanation:

Given term to expand is (

x

3x

2

−

3x

1

)

6

We know that T

r+1

=

n

C

r

a

n−r

b

r

T

r+1

=

6

C

r

(

2

3x

2

)

6−r

(

3x

−1

)

r

=

6

C

r

(

2

3

)

6−r

(

3

−1

)

r

(x

12−2r−r)

We need to find the term independent of x Power of x is 0

x

12−3r

=x

0

⇒12−3r=0⇒12=3r⇒r=4

T

4+1

=

6

C

4

(

2

3

)

6−4

(

3

−1

)

4

⇒

2!4!

6!

(

2

2

3

2

)

2

(

3

2

1

)

=

2!×4!

6×5×4!

×

2

2

×3

2

1

⇒

12

5