Factoring polynomials with 2 variables

Question

How do I factor polynomials when they have 2 variables like these:

30x²-+11xy-30y²

and

45x²-59xy+6y²

There are so many possibilities to try. Is there any other easier way of doing this besides trying every possibility?

Answer 1

Given Second polynomial is 45x^2-59xy+6y^2

45x^2-54xy-5xy+6y^2

9x(5x-6y)-y(5x-6y)

Take common out (5x-6y) from above expression.

Facyoring of 45x^2-59xy+6y^2 is (5x-6y)(9x-y).

Answer 2

The first exprssion is 30x² -11xy - 30y²

= 30x²- 36xy + 25xy - 30y²

= 6x(5x - 6y) + 5y(5x - 6y)

= (5x -6y)(6x + 5y)

Factoring of 30x² -11xy - 30y²  is (5x - 6y)(6x + 5y).