Find the coefficient of the x^9in the expansion of (3x* - 1/x)^6

Calculate the binomial coefficient and appropriate powers of
2
and
3
to find that the required coefficient is:
1088640

Explanation:
(
2
x
+
3
)
10
=
10
∑
k
=
0

(
10
k
)
2
10
−
k
3
k
x
10
−
k

The term in
x
6
is the one for
k
=
4
, so has coefficient:
(
10
4
)
2
6
⋅
3
4

=
10
!
4
!
6
!
⋅
64
⋅
81

=
10
×
9
×
8
×
7
4
×
3
×
2
×
1
⋅
64
⋅
81

=
210
⋅
64
⋅
81
=
1088640

Instead of calculating
(
10
4
)
, you can pick it out from the appropriate row of Pascal's triangle...
enter image source here

4x 20 is 80 but if ther machine is broken then there is none you have to redo the test

Is there more information?