Factoring multivariable polynomials

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