Math CentralQuandaries & Queries


Question from Rosa, a student:

How do you factor 9x^2 - 12y^2?

Hi Rosa,

If the coefficients have to be integers then the most you can do is

\[9x^2 - 12y^2 = 3\left(3 x^2 - 4 y^2\right).\]

If this problem comes from a high school text book then this is probably what is expected.

If it is not required that the coefficients be integers then you can write

\[9x^2 - 12y^2 = \large \left( 3x\right)^2 - \normalsize \left(\sqrt{12} y\right)^2\]

and factor it as a difference of squares.


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