SOLUTION: Which term in the expansion of ((1/2x^3) - x^5))^8 is a constant? I know you put it into the equation t (k+1) = (nCk) a^(n-k) b^k to get: = 8Ck (1/(2x^3))^(8-k) (-x^5)^k B

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Question 927305: Which term in the expansion of ((1/2x^3) - x^5))^8 is a constant?
I know you put it into the equation t (k+1) = (nCk) a^(n-k) b^k to get:
= 8Ck (1/(2x^3))^(8-k) (-x^5)^k
But I don't know what to do after.
Thank you for the help!

Answer by Edwin McCravy(20064)   (Show Source): You can put this solution on YOUR website!




Write  with a negative exponent, 



Multiply exponents and write  as  



Multiply exponents again and write  as 



Write  as  and then as 



Next add the exponents of x:  and get 



Now remember what I said in the beginning.
To becom a constant the variable x must be raised to the 0 power:

So we set the exponent of x equal to 0





So we substitute 3 for x:









For your information so as to see what the entire expansion
looks like when simplified:

 

So the constant term is really the 4th term, when k=3.

Edwin


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