Q* Find the middle term in the expansion of [x/3+9y]10
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Answer:
It is known that in the expansion (a+b)
n
if n is even, then the middle terms is (
2
n
+1)
th
term.
Therefore, the middle term in the expansion of (
3
x
+9y)
10
is (
2
10
+1)
th
term
which is, T
6
=T
5+1
=
10
C
5
(
3
x
)
10−5
(9y)
5
=
5!5!
10!
.
3
5
x
5
.9
5
.y
5
=
5.4.3.2.5!
10.9.8.7.6.5!
3
5
1
.3
10
.x
5
y
5
=252×3
5
.x
5
.y
5
=61236x
5
y
5
Thus the middle term in the expansion of (
3
x
+9y)
10
is 61236x
5
y
5
Step-by-step explanation:
hope it I will help u
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