Simplify
6x^2/y^3 X y^-2/9x^2

9x

2

y−3x

2

−y

2

3xy⋅(2x−y

2

)

             6x2y - 3xy3  

Simplify   ———————————————

           9x2y - 3x2 - y2

6.1     Pull out like factors :

  6x2y - 3xy3  =   3xy • (2x - y2)

Trying to factor as a Difference of Squares:

6.2      Factoring:  2x - y2

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  2  is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Trying to factor a multi variable polynomial :

6.3    Factoring    9x2y - 3x2 - y2

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Final result :

 3xy • (2x - y2)

 ———————————————

 9x2y - 3x2 - y2

Terms and topics

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Factoring multivariable polynomials

Multiplying exponents

Factoring binomials as sum or difference of cubes

Related links

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Variables with Exponents - How to Multiply and Divide them

Math Forum - Ask Dr. Math

How to factor five term polynomial - Yahoo Answers

abstract algebra - Factoring multivariate polynomial - Mathematics Stack Exchange

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