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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 Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post WWRtelescoping Advanced Statistics 2 April 13th, 2014 09:51 AM bongantedd Algebra 2 February 26th, 2014 04:38 PM OrangeLightning Elementary Math 6 April 23rd, 2013 02:14 PM kingkos Algebra 4 December 20th, 2012 11:51 AM rowdy3 Algebra 2 November 11th, 2010 10:01 PM

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