My Math Forum find the constant term when (1+x^2)(x-(3/x))^4

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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^4-12x^2+54-108/(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, '54-108=-54' where does the 54 bit come from please? Id really appreciate a step-by-step 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
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Quote:
 Originally Posted by rhubarb123 (x-(3/x))^4 = x^4-12x^2+54-108/(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, '54-108=-54' where does the 54 bit come from please? Id really appreciate a step-by-step explanation!
You have stated the problem in a VERY confusing manner.

x^4-12x^2+54-108/(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

 Tags constant, find, term, x2x3 or x4

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