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Binomial Expansion question C4

Find the first three terms of the binomial expansion of:

4(2x−1)−1−2(x2+1)−14(2x-1)^{-1} -2(x^{2}+1)^{-1}

Here is what I did:

4(−1)−1(−2x+1)−1[br]=−4(1+2x+4x2)=−4−8x−16x2[br][br]−2(x2+1)−1[br]=−2(1−x2+x4)=−2+2x2−2x4[br][br]−2+2x2−2x4−4−8x−16x2=−6−8x−14x2−2x4[br][br] 4(-1)^{-1} (-2x+1)^{-1} [br]= -4(1 + 2x + 4x^2) = -4 -8x -16x^2[br][br]-2(x^2 +1)^{-1}[br]= -2(1 - x^2 + x^4) = -2 +2x^2 -2x^4[br][br]-2 + 2x^2 - 2x^4 -4 -8x -16x^2 = -6 - 8x - 14x^2 -2x^4[br][br]

So the first three terms are -6, -8x and -14x^2 but this doesn't seem to be correct. Where have i gone wrong in the method?
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Zacken
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Original post by IDontKnowReally
Find the first three terms of the binomial expansion of:

4(2x−1)−1−2(x2+1)−14(2x-1)^{-1} -2(x^{2}+1)^{-1}

Here is what I did:

4(−1)−1(−2x+1)−1[br]=−4(1+2x+4x2)=−4−8x−16x2[br][br]−2(x2+1)−1[br]=−2(1−x2+x4)=−2+2x2−2x4[br][br]−2+2x2−2x4−4−8x−16x2=−6−8x−14x2−2x4[br][br] 4(-1)^{-1} (-2x+1)^{-1} [br]= -4(1 + 2x + 4x^2) = -4 -8x -16x^2 [br] [br]-2(x^2 +1)^{-1} [br]= -2(1 - x^2 + x^4) = -2 +2x^2 -2x^4 [br] [br]-2 + 2x^2 - 2x^4 -4 -8x -16x^2 = -6 - 8x - 14x^2 -2x^4 [br] [br]

So the first three terms are -6, -8x and -14x^2 but this doesn't seem to be correct. Where have i gone wrong in the method?


It is correct.

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