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Factoring polynomials with two variables

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

Common factor

Simple example.

Factor:

20xy2 - 10y2

There is a common factor to the two terms. It is the 10y2. Factor it out:

20xy2 - 10y2 = 10y2(2x - 1)

Factor polynomials with 2 different variables

Example.

Factor the polynomial with 2 different variables:

20x2 + 17xy - 10y2

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

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

20x2 + 25xy - 8xy - 10y2

4. Group the positive and negative terms so:

(20x2 + 25xy) + (-8xy - 10y2)

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

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

6. And the final answer:

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