A hard expansion Watch

rbnphlp
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#1
Report Thread starter 9 years ago
#1
((x^4-X^-2)^5) . ((x-x^-1)^6)

show that x^-12= -15

I tried the following :
((x^4-X^-2)^5) =

=(X^4)^5 (1-x^-6)^5( i dont even kno if thats rite)

And expanded the brackets and did the same for the ((x-x^-1)^6) , and added the two expansions to get the coefficient x^-12 whichi i got to be 30.


could anyone point out to me what i doing wrong??
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darkness9999
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#2
Report 9 years ago
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what do you mean show that x^-12 = -15? the coefficient of x^{-12} ?
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rbnphlp
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#3
Report Thread starter 9 years ago
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(Original post by darkness9999)
what do you mean show that x^-12 = -15? the coefficient of x^{-12} ?
yes
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darkness9999
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#4
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I would expand each of them normaly using the  (a+b)^n expansion ... after that

consider the multiplication of the exponents of x that will add to -12 ... that should work -.-'
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rbnphlp
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#5
Report Thread starter 9 years ago
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(Original post by darkness9999)
I would expand each of them normaly using the  (a+b)^n expansion ... after that

consider the multiplication of the exponents of x that will add to -12 ... that should work -.-'
hmm k , cheers
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DFranklin
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#6
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((x^4-X^-2)^5) . ((x-x^-1)^6) = x^-16(x^6-1)^5 (x^2-1)^6.

So what you are looking for is the coefficient of x^4 in (x^6-1)^5 (x^2-1)^6. Now the only term in the expansion of (x^6-1)^5 that can matter is the constant term (the next term is 5x^6, which is too big a power of x), which is -1.

Can you finish from there?
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