Solution - Factoring multivariable polynomials

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "v2"   was replaced by   "v^2".  1 more similar replacement(s).

Step  1  :

Equation at the end of step  1  :

  ((9 • (u2)) +  48uv) +  26v2
 Step  2  :

Equation at the end of step  2  :

  (32u2 +  48uv) +  26v2

Step  3  :

Trying to factor a multi variable polynomial :

 3.1    Factoring    9u² + 48uv + 64v² 

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

 Found a factorization  :  (3u + 8v)•(3u + 8v)

Detecting a perfect square :

 3.2    9u²  +48uv  +64v²  is a perfect square 

 It factors into  (3u+8v)•(3u+8v)
which is another way of writing  (3u+8v)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 :

  (3u + 8v)2