New to sage, trying to calculate a trinomial in sage

[newbie43]

I just installed sage on my linux server and i was wondering if anyone
could tell me what im doing wrong here with this equation.

The Equation says to factor this

1/9x^2 -1/6xy^2 + 1/16y^4

the answer they give in the textbook for the above equation is this

(1/3x -1/4y^2)


I put the equation into the sage command line like this

x, y = var ('x, y')

factor(1/9*x^2 -1/6*x*y^2 + 1/16*y^4)

the answer i end up with using sage from this command is
1/144*(3*y^2 - 4*x)^2

am i calculating this properly from within sage?
any help would be appreciated thanks.

[David Joyner]

On Tue, Nov 17, 2009 at 3:31 PM, newbie43 <bert...@gmail.com> wrote:
>
> I just installed sage on my linux server and i was wondering if anyone
> could tell me what im doing wrong here with this equation.
>
> The Equation says to factor this
>
> 1/9x^2 -1/6xy^2 + 1/16y^4
>
> the answer they give in the textbook for the above equation is this
>
> (1/3x -1/4y^2)
>
>
> I put the equation into the sage command line like this
>
> x, y = var ('x, y')
>
> factor(1/9*x^2 -1/6*x*y^2 + 1/16*y^4)
>
> the answer i end up with using sage from this command is
> 1/144*(3*y^2 - 4*x)^2

Pull the 1/144=1/12^2 inside the other facttor and you get
the textbook form above.