find the independent of x in the expansion
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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
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