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

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) (Show Source): You can put this solution on YOUR website!
Let

If we cube both sides of the equation above, we get

This means the original expression is equivalent to

we can factor out a 'z' to get

Then use the difference of squares law

-------------------------------------------------------

So,

Now replace each 'z' with

-------------------------------------------------------

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

The fully factored form is
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