Factoring a polynomial with two variables is simple. The following examples will help you to factor polynomials with two variables.

Simple example.

Factor:

20xy^{2} - 10y^{2}

There is a common factor to the two terms. It is the 10y^{2}. Factor it out:

20xy^{2} - 10y^{2} = 10y^{2}(2x - 1)

Example.

Factor the polynomial with 2 different variables:

20x^{2} + 17xy - 10y^{2}

How to resolve the problem?

1. The first term coefficient is 20 and the third term coefficient is -10.

Find the product:

20 * (-10) = -200

2. Find two factors of the -200 that add to 17, it is the second term coefficient.

These factors are 25 and -8:

25 * (-8) = -200

25 - 8 = 17

17xy = 25xy - 8xy

25 - 8 = 17

17xy = 25xy - 8xy

3. Replace 17xy with 25xy - 8xy:

20x^{2} + 25xy - 8xy - 10y^{2}

4. Group the positive and negative terms so:

(20x^{2} + 25xy) + (-8xy - 10y^{2})

5. Factor out the common factors: 5x and -2y:

5x(4x + 5y) - 2y(4x + 5y)

6. And the final answer:

(4x + 5y)(5x - 2y)