Question

求(2x-3y)^9展开式中各项系数绝对值的和。要求方法，谢谢！

Answer 1

原式展开后为 = ax^9+bx^8*y+cx^7*y^2+...+i*y^9
令x=1，y=-1，上式刚好=a+b+c+d+...+i
因此，各项系数绝对值的和 = (2*1-3*(-1))^9 = 5^9

Answer 2

(2x-3y)^9展开式中各项系数绝对值的和
令x=1 y=-1
(2x-3y)^9=(2+3)^9=5^9

Answer 3

(2x-3y)^9

=2^9 .( x- (3/2)y)^9
consider
(1+x)^n = nC0 +nC1x+nC2x^2+....+nCn. x^n
x= 2/3
(1+3/2)^9 = nC0 +nC1.(3/2) +nC2.(3/2)+....+nCn. (3/2)^n
5^9/2^9 = nC0 +nC1.(3/2) +nC2.(3/2)+....+nCn. (3/2)^n
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(2x-3y)^9展开式中各项系数绝对值的和
=2^9 .[ nC0 +nC1.(3/2) +nC2.(3/2)+....+nCn. (3/2)^n ]
=2^9 . (5^9/2^9 )
=5^9

Answer 4

(2x-3y)^9
令x=1 y=-1带入得
(2+3)^9=5^9

系数和为 5^9