Factoring multivariable polynomials

Step  1  :

Equation at the end of step  1  :

  ((x2) +  16xy) +  26y2

Step  2  :

Trying to factor a multi variable polynomial :

 2.1    Factoring    x² + 16xy + 64y² 

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

 Found a factorization  :  (x + 8y)•(x + 8y)

Detecting a perfect square :

 2.2    x²  +16xy  +64y²  is a perfect square 

 It factors into  (x+8y)•(x+8y)
which is another way of writing  (x+8y)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 :

  (x + 8y)2