(a) 6 The coefficient of x2 in the expansion of the product 9. (2-x2). ((1 + 2x + 3x2)6+ (1 - 4x2)) is
Answers
Answer:
Correct option is
A
106
Let a=((1+2x+3x
2
)
6
+(1−4x
2
)
6
)
∴ Coefficient of x
2
in the expansion of the product (2−x)
2
((1+2x+3x
2
)
6
+(1−4x
2
)
6
)
=2( Coefficient of x
2
in a)−1(Constant of expansion)
In the expansion of ((1+2x+3x
2
)
6
+(1−4x
2
)
6
),
Constant =1+1=2
Coefficient of x
2
= Coefficient of x
2
in (
6
C
0
(1+2x)
6
(3x
2
)
0
)+ Coefficient of x
2
in (
6
C
1
(1+2x)
5
3)−
6
C
1
(4)
=
6
C
2
4+6×3−24
=6=+18−24=54
Then, coefficient of x
2
in (2−x)
2
((1+2x+3x
2
)
6
+(1−4x
2
)
6
)
=2×54−1(2)=108−2=106
Answer:
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x⁻¹, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the number.