13. The coefficient of xin the expansion of (x - 2)° is........
Answers
Answer:
2(1+2x+3x
2
)
6
−x
2
(1+2x+3x
2
)
6
+2(1−4x
2
)
6
−x
2
(1−4x
2
)
6
↓ ↓ ↓ ↓
Coeff of x
2
Coeff of x
0
Coeff of x
2
Coeff of x
0
(1+2x+3x
2
)
6
⇒
∝
1
!∝
2
!∝
3
!
6!
(2n)
∝2
(3x
2
)
∝3
⇒
∝
1
!∝
2
!∝
3
!
6!
2
∝2
3
∝3
x
∝2+2∝3
∝
2
+2∝
3
=2 ∝
2
+2∝
3
=0
∝
3
=1,∝
2
=2,∝
1
=4
∝
2
=0,∝
3
=0,∝
1
=6
∝
3
=1,∝
2
=0,∝
1
=5
2(
2!4!
6!
2
2
+
1!5!
6!
2
0
3
1
)−1(
6!
6!
2
0
3
0
)
(1−4x
2
)
6
=
6
C
r
(−4x
2
)
r
=
6
C
r
(−4)
r
x
2r
for coeff. of x
2
r=1
⇒
6
C
1
(−4)
1
for ecoeff of x
0
,r=0
⇒
6
C
0
(−4)
0
coeff of x
2
⇒
2!4!
6!
×8+
1!5!
6!
×6−
6!
6!
+2×
5!
6!
(−4)−
6!
6!
⇒
2
6×5×8
+6×6−1−2×4×6−1
⇒12−36−1−48−1⇒34