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Factoring multivariable polynomials

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We think you wrote:

2x^2+12xy+18y^2

This solution deals with factoring multivariable polynomials.

Solution found

2*(x+3y)^2
2*(x+3y)^2

Step by Step Solution

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Step  1  :

Equation at the end of step  1  :

  ((2 • (x2)) +  12xy) +  (2•32y2)

Step  2  :

Equation at the end of step  2  :

  (2x2 +  12xy) +  (2•32y2)

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   2x2 + 12xy + 18y2  =   2 • (x2 + 6xy + 9y2) 

Trying to factor a multi variable polynomial :

 4.2    Factoring    x2 + 6xy + 9y2 

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

 
Found a factorization  :  (x + 3y)•(x + 3y)

Detecting a perfect square :

 4.3    x2  +6xy  +9y2  is a perfect square 

 
It factors into  (x+3y)•(x+3y)
which is another way of writing  (x+3y)2

How to recognize a perfect square trinomial:  

 
• It has three terms  

 
• Two of its terms are perfect squares themselves  

 
• The remaining term is twice the product of the square roots of the other two terms

Final result :

  2 • (x + 3y)2

Why learn this

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