What is the coefficient of x^3 in the expansion of (x+2)^5?
10
1
40
315
Answers
Answered by
0
Step-by-step explanation:
Co-efficient of x
5
in (1+x
2
)
5
(1+x)
4
Binomial expansion of
(a+b)
n
=
n
C
a
a
n
+
n
C
1
a
n−1
b
1
+...
n
C
2
a
n−r
b
r
+...
∴(1+x
2
)
5
(1+x)
4
(
5
C
0
(1)+
5
C
1
(1)x
2
+
5
C
2
(1)(x
2
)
2
+
5
C
3
(x
2
)
3
+
5
C
4
(x
2
)
4
+
5
C
c
(x
2
)
5
)
×(
4
C
0
(1)+
4
C
1
(x)+
4
C
2
(x)
2
+
4
C
3
(x)
3
+
4
C
4
(x)
4
)
∴{
5
C
2
x
4
×
4
C
1
x+
5
C
1
x+
5
C
1
(x
2
)×
4
C
3
(x)
3
}
∴ coefficient of x
5
⇒(
2×1
5×4
×4)x
5
+(5×4)x
5
⇒(10×4+20)x
5
⇒60x
5
∴ coefficient of x
5
⇒
60
(option D)
Similar questions