Question

Find the coefficient of x¹⁹ in (x⁵-x-²)⁸
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Answer 1

Answer:

Consider the first 2 factors (x−1) and (x−2)

(x−1)(x−2)=x

2

−(1+2)x

1

+(1×2)

Similarly, for the rest of the terms, we can write ,

(x−1)(x−2)(x−3)....(x−19)(x−20)

=x

20

−(1+2+3+.......+19+20)x

19

+(1×2+2×3+......19×20)x

18

∴ Coefficient of x

19

=−(1+2+3+..........+19+20)=−[

2

20

(1+20)]=−10×21=−210

Step-by-step explanation:

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