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Factoring multivariable polynomials

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We think you wrote:

4x^2+36xy+81y^2

This solution deals with factoring multivariable polynomials.

Solution found

(2x+9y)^2
(2x+9y)^2

Step by Step Solution

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Step  1  :

Equation at the end of step  1  :

  ((4 • (x2)) +  36xy) +  34y2

Step  2  :

Equation at the end of step  2  :

  (22x2 +  36xy) +  34y2

Step  3  :

Trying to factor a multi variable polynomial :

 3.1    Factoring    4x2 + 36xy + 81y2 

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

 
Found a factorization  :  (2x + 9y)•(2x + 9y)

Detecting a perfect square :

 3.2    4x2  +36xy  +81y2  is a perfect square 

 
It factors into  (2x+9y)•(2x+9y)
which is another way of writing  (2x+9y)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 :

  (2x + 9y)2

Why learn this

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