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May 16th, 2014, 11:47 AM  #1 
Newbie Joined: May 2014 From: england Posts: 11 Thanks: 0  find the constant term when (1+x^2)(x(3/x))^4
(x(3/x))^4 = x^412x^2+54108/(x^2)+(81/x^4) find the constant term when (1+x^2)(x(3/x))^4 hello. Im afraid im struggling with this. I understand that the constant term of the second bracket when multiplied by the first bracket would be the 108 because x^2 * x^2 is 1 but in the markscheme it says, '54108=54' where does the 54 bit come from please? Id really appreciate a stepbystep explanation! thanks A LOT 
May 16th, 2014, 01:05 PM  #2 
Senior Member Joined: Nov 2013 From: Baku Posts: 502 Thanks: 56 Math Focus: Geometry 
"constant term"???

May 16th, 2014, 09:38 PM  #3  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Quote:
x^412x^2+54108/(x^2)+(81/x^4) is same as: (x^8  12x^6 + 54x^4 [ 108]x^2 + 81) / x^4 Seems that you want to know why the constant [108] becomes 54; easy enough: you state that a multiplication by (x^2 + 1) is made: this results in x^2 * (108x^2) = 108x^4; BUT you will be also multiplying 1 * 54x^4: so the result will be 54x^4; do you follow? The final multiplication by (x^2 + 1) will result in: (x^10  11x^8 + 42x^6  54x^4  27x^2 + 81) / x^4  

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constant, find, term, x2x3 or x4 
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