write the coffiecient of x² in the expansion of (x-2)²
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11th
Maths
Binomial Theorem
Special Cases of Binomial Theorem
The coefficient of x^2 in t...
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Asked on October 15, 2019 by
Varaganti Rohilla
The coefficient of x
2
in the expansion of the product (2−x
2
)⋅((1+2x+3x
2
)
6
+(1−4x
2
)
6
) is
MEDIUM
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VIDEO EXPLANATION
ANSWER
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
Step-by-step explanation:
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Answer:
(x-2)²= x²-4
the coefficient of x² in (x-2)² is -4.
Step-by-step explanation:
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