SOLUTION: I have never come across determining which term in the expansion of an equation is a constant, can you help me for the term: (1/(2x^3) - x^5)^8 for which is a constant? thank

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Question 647856: I have never come across determining which term in the expansion of an equation is a constant, can you help me for the term:
(1/(2x^3) - x^5)^8 for which is a constant?
thank you much

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


There are 9 terms in the expansion, each one is of this form:

, where k goes from 0 through 8

 Simplifying











Subtract exponents of x



Simplifying:





The only time x raised to a power is NOT a variable, but a
constant, is when the exponent of the power is 0, since x0 = 1,
and 1 is a constant, not a variable.


Therefore we take the exponent of x, which is 8k-24, and set it
 equal to 0:

8k-24 = 0
   8k = 24
    k = 3

So we substitute k = 3 in

















Edwin

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


There are 9 terms in the expansion, each one is of this form:

, where k goes from 0 through 8

 Simplifying











Subtract exponents of x



Simplifying:





The only time x raised to a power is NOT a variable, but a
constant, is when the exponent of the power is 0, since x0 = 1,
and 1 is a constant, not a variable.


Therefore we take the exponent of x, which is 8k-24, and set it
 equal to 0:

8k-24 = 0
   8k = 24
    k = 3

So we substitute k = 3 in



















Edwin

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