If the area of a square is 9x^2 - 12xy + 4y^2, what is the perimeter of the square?
Hi magentarita,
$\displaystyle 9x^2-12xy+4y^2$ can be factored into $\displaystyle (3x-2y)^2$
Now we know that the area of a square is $\displaystyle s^2$, where $\displaystyle s$ is one side.
That means that $\displaystyle s=3x-2y$
We have 4 of them, so $\displaystyle P=4(3x-2y)=12x-8y$
$\displaystyle 9x^2 - 12xy + 4y^2 $
$\displaystyle = (3x)^2 - 6xy-6xy +(2y)^2$
$\displaystyle =3x(3x-2y) - 2y(3x-2y)
$
$\displaystyle =(3x-2y)(3x-2y) = (3x-2y)^2 $
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You should remember the formula that
$\displaystyle a^2 - 2ab +b^2 = (a-b)^2 $
Here a = 3x & b= 2y
To learn how to factor quadratics, try some online lessons. :wink: