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Byju's Answer
Standard XII
Mathematics
Binomial Expression
Expand the fo...
Question
Expand the following expression in ascending powers of
x
as far as
x
3
.
3
+
x
2
−
x
−
x
2
.
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Solution
Let
3
+
x
2
−
x
−
x
2
=
a
0
+
a
1
x
+
a
2
x
2
+
a
3
x
3
+
.
.
.
.
.
.
Then,
(
3
+
x
)
=
(
2
−
x
−
x
2
)
[
a
0
+
a
1
x
+
a
2
x
2
+
a
3
x
3
+
.
.
.
.
.
.
]
On equating coefficients, we get
a
0
=
3
2
,
2
a
1
−
a
0
=
1
Whence
a
1
=
5
4
Also, for values of
n
>
1
,
2
a
n
−
a
n
−
1
−
a
n
−
2
=
0
∴
2
a
2
=
11
4
a
2
=
11
8
Also ,
2
a
3
=
11
8
+
5
4
i.e.
a
3
=
21
16
Hence ,
3
+
x
2
−
x
−
x
2
=
3
2
+
5
4
x
+
11
8
x
2
+
21
16
x
3
+
.
.
.
.
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0
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