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May 16th, 2014, 11:47 AM   #1
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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
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May 16th, 2014, 01:05 PM   #2
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"constant term"???
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May 16th, 2014, 09:38 PM   #3
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Quote:
Originally Posted by rhubarb123 View Post
(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
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