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 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.

Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.