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Byju's Answer
Standard XI
Mathematics
Binomial Coefficients
Expand using ...
Question
Expand using Binomial Theorem
(
1
+
x
2
−
2
x
)
4
,
x
≠
0
and let the sum of coefficients of the terms in the expansion be
t
. Find
10000
t
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Solution
⇒
(
1
+
x
2
−
2
x
)
4
Let
a
=
1
+
x
2
,
b
=
2
x
⇒
(
4
0
)
(
1
+
x
2
)
4
−
(
4
1
)
(
1
+
x
2
)
3
(
2
x
)
+
(
4
2
)
(
1
+
x
2
)
2
(
2
x
)
2
−
(
4
3
)
(
1
+
x
2
)
1
(
2
x
)
3
+
(
4
4
)
(
2
x
)
4
⇒
(
1
+
x
2
)
4
−
8
x
(
1
+
x
2
)
3
+
24
x
2
(
1
+
x
2
)
2
−
32
x
3
(
1
+
x
2
)
1
+
(
2
x
)
4
We will use binomial expansion for
(
1
+
x
2
)
4
,
(
1
+
x
2
)
3
⇒
[
1
+
4.
x
2
+
6.
x
2
4
+
4.
x
3
8
+
x
4
16
]
−
8
x
[
1
+
3.
x
2
+
3
x
2
4
+
x
3
8
]
+
24
x
2
[
1
+
x
2
4
+
x
]
−
32
x
3
[
1
+
x
2
]
+
16
x
4
=
x
4
16
+
x
3
2
+
x
2
2
−
4
x
−
5
+
16
x
+
8
x
2
−
32
x
3
+
16
x
4
This is the final binomial expansion of above expression
∴
sum of coefficients=
1
16
+
1
2
+
1
2
−
4
−
5
+
16
+
8
−
32
+
16
=
1
16
=
t
⇒
10000
t
=
625
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