Answer:
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
