SOLUTION: use binomial theorem to expand the following up to 4 terms: {{{1/sqrt((4-3x^2))^3}}}

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Question 276711: use binomial theorem to expand the following up to 4 terms:

Found 2 solutions by Edwin McCravy, AnlytcPhil:
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!


Express the denominator as the  power



Then as a negative exponent:



We want to get a binomial that starts with 1, not 4.

Factor out 4 in the parentheses:






 simplifies to 


So we have



So we now expand 

 and then multiply it by 

We use the infinite binomial series:



Substituting ,   becomes 

Substituting ,  becomes 

Therefore  becomes  or 


Substituting ,  becomes 

Substituting ,  becomes 

Therefore  becomes  or



So the expansion to 4 terms of 

is



So we multiply that by  and that will be the binomial
series to 4 terms.

Edwin
Answer by AnlytcPhil(1807)   (Show Source): You can put this solution on YOUR website!


Express the denominator as the  power



Then as a negative exponent:



We want to get a binomial that starts with 1, not 4.

Factor out 4 in the parentheses:






 simplifies to 


So we have



So we now expand 

 and then multiply it by 

We use the infinite binomial series:



Substituting ,   becomes 

Substituting ,  becomes 

Therefore  becomes  or 


Substituting ,  becomes 

Substituting ,  becomes 

Therefore  becomes  or



So the expansion to 4 terms of 

is



So we multiply that by  and that will be the binomial
series to 4 terms.

Edwin
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