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The coefficient of x^3 in the expansion of (1+3x)^2 / 1-2x will be? Ans: 50

The coefficient of x^3 in the expansion of (1+3x)^2 / 1-2x will be?
Ans: 50

Grade:12th pass

2 Answers

Aditya Gupta
2081 Points
4 years ago
we know thw identity: (1 – y)^(-1)= 1+y+y^2+y^3+..................
so,  (1+3x)^2 / (1-2x )=  (1+3x)^2*(1 – 2x)^(-1)= (1+6x+9x^2)*(1+2x+4x^2+8x^3+.........)
so, coeff of x^3 is 1*8 + 6*4 + 9*2= 26+24
= 50
kindly approve :)
Arun
25750 Points
4 years ago
Dear student
 
it can be written as 
( 1 + 9x^2 + 6x) (1 – 2x)^-1
 
 = ( 1 + 9x^2 + 6x) ( 1 + 2x + 4x^2 + 8x^3+ …..)
 
hence coefficient of x3 = 8 + 18 + 24 = 50

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