Solution - Factoring multivariable polynomials

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "b2"   was replaced by   "b^2".  1 more similar replacement(s).

Step  1  :

Step  2  :

Pulling out like terms :

 2.1     Pull out like factors :

   -a² - 2ab - b²  =   -1 • (a² + 2ab + b²) 

Trying to factor a multi variable polynomial :

 2.2    Factoring    a² + 2ab + b² 

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

 Found a factorization  :  (a + b)•(a + b)

Detecting a perfect square :

 2.3    a²  +2ab  +b²  is a perfect square 

 It factors into  (a+b)•(a+b)
which is another way of writing  (a+b)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 :

  -1 • (a + b)2