How do you factor quadratic equations with two variables?

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Answer 1 · 2015-03-28T01:16:56

It depends on the quadratic:

$4x^2-9y^2=(2x+3y)(2x-3y)$ is a special product.
As is
$25x^2-30xy+9y^2=(5x-3y)^2$

$12x^2-9xy+6y$ has a common factor of $3$ , but that's all.

$x^2-4xy-5y^2$ is factored by trial and error.

If it is easily factorable, it must look like $(x+ay)(x+by)$

where $ab=5$ and $a+b=-4$

It's really a lot like factoring: $x^2-4x-5$

$x^2-4x-5=(x-5)(x+1)$

$x^2-4xy-5y^2 = (x-5y)(x+y)$