SOLUTION: Im not sure how to factor and simplify this (x+3)^(1/2)-(x+3)^(3/2) Thank you for your help.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Im not sure how to factor and simplify this (x+3)^(1/2)-(x+3)^(3/2) Thank you for your help.      Log On


   

Question 986866: Im not sure how to factor and simplify this (x+3)^(1/2)-(x+3)^(3/2)
Thank you for your help.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let z+=+%28x%2B3%29%5E%281%2F2%29%5E%22%22

If we cube both sides of the equation above, we get z%5E3+=+%28%28x%2B3%29%5E%281%2F2%29%5E%22%22%29%5E3+=+%28x%2B3%29%5E%283%2F2%29

This means the original expression %28x%2B3%29%5E%281%2F2%29%5E%22%22-%28x%2B3%29%5E%283%2F2%29 is equivalent to z-z%5E3

we can factor out a 'z' to get z-z%5E3=z%281-z%5E2%29

Then use the difference of squares law z%281-z%5E2%29=z%281-z%29%281%2Bz%29

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So, z-z%5E3=z%281-z%29%281%2Bz%29

Now replace each 'z' with %28x%2B3%29%5E%281%2F2%29%5E%22%22


z-z%5E3=z%281-z%29%281%2Bz%29





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Yes it's very ugly, but it's a factored form of the original expression

The fully factored form is