中4 a.maths

(1 - 2x)^2 = 1 - 4x + 4x^2
( 1 + 1/x)^7 = 1 + 7/x + 21/x^2 + ..........
1 x 1 = 1
( - 4x)(7/x) = - 28
(4x^2)(21/x^2) = 84
so constant term = 1 - 28 + 84 = 57.
(- 4x)(1) = - 4x
(4x^2)(7/x) = 28x
so coefficient of x = - 4 + 28 = 24.

Find,in the explansion of (1－2x)^2(1+1/x)^7
(a) the constant term
(1－2x)^2=1－4x+4x^2
(1)with 1
1^7=1===>1*1=1
(2)with －4x
c(7,1)=7==>－4*7=－28
(3)with 4x^2
c(7,2)=21==>4*21=84
Ans=1－28+84=57

(b) the coefficient of x
(1－2x)^2=1－4x+4x^2
(1)with 1
0===>0
(2)with －4x
1==>－4*1=－4
(3)with 4x^2
c(7,1)=7==>4*7=28
Ans=0－4+28=24