Solution - Factoring multivariable polynomials

Step  1  :

Equation at the end of step  1  :

  ((0 -  (a2)) -  4ax) -  22x2

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -a² - 4ax - 4x²  =   -1 • (a² + 4ax + 4x²) 

Trying to factor a multi variable polynomial :

 3.2    Factoring    a² + 4ax + 4x² 

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

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

Detecting a perfect square :

 3.3    a²  +4ax  +4x²  is a perfect square 

 It factors into  (a+2x)•(a+2x)
which is another way of writing  (a+2x)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 + 2x)2