How do you factor quadratic equations with two variables?

Question

7131 views around the world

You can reuse this answer
Creative Commons License

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)#