What is the coefficient of x^101 y^99 in the expansion of (2x - 3y)^200? A. C(200, 99) 2^101 (3)^99 B. C(200, 99) 2^101(-3)^99 C. P(200, 99) 2^101(3)^99 D. P(200, 99) 2^101(-3)^99 E. C(200, 2) 2^101(-3)^99

fabler107 2022-11-20 Answered
What is the coefficient of x 101 y 99 in the expansion of ( 2 x 3 y ) 200 ?
A. C ( 200 , 99 ) 2 101 ( 3 ) 99
B. C ( 200 , 99 ) 2 101 ( 3 ) 99
C. P ( 200 , 99 ) 2 101 ( 3 ) 99
D. P ( 200 , 99 ) 2 101 ( 3 ) 99
E. C ( 200 , 2 ) 2 101 ( 3 ) 99
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Answers (1)

siriceboynu1
Answered 2022-11-21 Author has 12 answers
Solution:
Given expansion ( 2 x 9 y ) 200 the coefficient of x 101 y 99
( x + a ) n Generate term T γ + 1 = n r γ x n γ a γ
= 200 c γ 2 200 γ x 200 γ ( 3 ) γ y γ
here r=99, 200-99=101
= 200 c 9 9 2 200 99 x 200 99 ( 3 ) 99 y 99
= 200 c 9 9 2 101 x 101 ( 3 ) 99 y 99
The coefficient of x 101 y 99 is
200 c 9 9 2 101 ( 3 ) 99
option B
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