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.

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