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Question

Find the coefficient of x8 in (1+x)8(1x)2.


A

= + + + .............+

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B

= + 2 + 3 + .............+ 9

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C

= + 2 + 2 + .............+ 2

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D

= + 3 + 3 + .............+ 3

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Solution

The correct option is B

= + 2 + 3 + .............+ 9


Coefficient of x8 in (1+x)8(1x)2

Write the binomial expansion of (1+x)8(1x)2.

= coefficient of x8 in (8C0+8C1x+8C2x2+.............+8C8x8)

× (1+2x+3x2+4x3+..............+9x8+..............)

= 9. 8C0 + 8. 8C1 + 7.8C2 + .................+ 1.8C8

= 8C0 + 28C1 + 3 8C2 +.............+ 98C8


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