complex factoring: x^(-1/2) - 2x^(1/2) + x^(3/2)

[kpx001]

To factor : x^(-1/2) - 2x^(1/2) + x^(3/2)

I forgot what to do. I'm guessing I can change some of these to root and square?

For example:

-sqroot[x] - sqroot[2] + 3times sqroot[x]

...but I'm clueless.

 

[pka]

\(\displaystyle \L \begin{array}{rcl}
x^{^{-\frac{{ 1}}{2}} } - 2x^{^{\frac{1}{2}} } + x^{^{\frac{3}{2}} } & = &x^{^{-\frac{{ 1}}{2}} } \left( {1 - 2x + x^2 } \right) \\
& = & x^{^{-\frac{{ 1}}{2}} } \left( {1 - x} \right)^2 \\
& = & \frac{{\left( {1 - x} \right)^2 }}{{\sqrt x }} \\
\end{array}\)

 

[kpx001]

thx but can you please explain to me how x^-1/2 times -2x = -2x^1/2 ?
the way im thinking right now is that it would become +2x^1/2 because of the negatives, but im unsure of the rule. thanks though for the help

 

[pka]

thx but can you please explain to me how x^-1/2 times -2x = -2x^1/2 ?

When one multiplies, one adds exponents. YES?
\(\displaystyle \L x^{ - \frac{1}{2}} \left( { - 2x} \right) = x^{ - \frac{1}{2}} \left( { - 2x^1 } \right) = - 2x^{ - \frac{1}{2} + 1} = - 2x^{\frac{1}{2}}\).