s Find the coefficient of x? in the product (x2 – 3x + 1)(5x + 2)
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Answered by
0
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
Answered by
0
Step-by-step explanation:
(x-5)(x+3)(x+7)=(x2-5x+3 +15)(x+7)
=. (x2-2x-15)(x+7)
x3-2x-15x+7x2-14x105
= x3 + 5x2 -29x -105
therefore the coefficient x2 is 5 and the coefficient of x is -29
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