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Factoring Two Variables

Introduction to factoring two variables:

An expression can be factored by the decomposition of the given expression into the product of some other expressions. If the product ofthe resultant factors gives the given expression, then the factored expression is correct or the solved expression is not correct. Now we are going to see about the factoring of two variables.


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Procedure for factoring two variables:

The following points are the factoring of the two variables are as follows,

  • First the given expression should be taken

  • Then the middle variable can be spliced to give the resultant of that variable be same

  • The common factors can be taken out from the expression

  • Then combine the terms of the factors.

  • If you multiply the two factor terms then the resultant will be given the expression


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Problems for factoring two variables:


Example 1:

              18x2 – 9xy – 2y2

Solution:

First take the given expression

                       18x2 – 9xy – 2y2

 The above expression value can be written as,

                    18x2 – 12xy + 3xy – 2y2

Take the common factors out from the above expression we get,

                     6x (3x – 2y) + y (3x – 2y)

The next step is combining the factors of the terms we get,

                      (6x + y) (3x – 2y)

Example 2:

Factor the two variables equation: 2a2 + 7ab – 15b2

Solution:

First take the given expression

                      2a2 + 7ab – 15b2

The above expression value can be written as,

                      2a2 + 10ab 3ab – 15b2

Take the common factors out from the above expression we get,

                        2a (a + 5b) -3b (a + 5b)

The next step is combining the factors of the terms we get,

                          (2a – 3b) (a + 5b)

 Example 3:

                     Factorize the expression: x2 – 8xy + 12y2

Solution:

First take the given expression

                            x2 – 8xy + 12y2

The above expression value can be written as,

                         x2 – 4xy- 4xy + 12y2

Take the common factors out from the above expression we get,

                        x (x – 4y) -3y (x – 4y)

The next step is combining the factors of the terms we get,

                           (x – 3y) (x – 4y)