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Byju's Answer
Standard XII
Mathematics
Sum of Coefficients of All Terms
Find the coef...
Question
Find the coefficient of
a
4
in the product
(
1
+
2
a
)
4
(
2
−
a
)
5
using binomial theorem.
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Solution
⇒
(1+2a)^4$
⇒
4
C
1
+
4
C
1
(
2
a
)
+
4
C
2
(
2
a
)
2
+
4
C
3
(
2
a
)
3
+
4
C
4
(
2
a
)
4
⇒
1
+
8
a
+
24
a
2
+
32
a
3
+
16
a
4
(
2
−
a
)
5
⇒
5
C
0
2
5
−
5
C
1
2
4
(
a
)
+
5
C
2
2
3
(
a
)
2
−
5
C
3
2
2
a
3
+
5
C
4
2
a
4
−
5
C
5
a
5
⇒
32
−
80
a
+
80
a
3
+
10
a
4
−
a
5
∴
Coefficient of
a
4
is
⇒
1
×
10
a
4
+
(
8
a
)
(
80
a
3
)
+
32
a
3
(
−
80
a
)
+
16
a
4
(
32
)
⇒
10
a
4
+
640
a
4
−
2560
a
4
+
512
a
4
⇒
−
1.398
x
4
.
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is:
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