Solution - Factoring multivariable polynomials

Step  1  :

Equation at the end of step  1  :

  ((a3)-((4•(a2))•b))+22ab2
 Step  2  :

Equation at the end of step  2  :

  ((a3) -  (22a2 • b)) +  22ab2

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   a³ - 4a²b + 4ab²  =   a • (a² - 4ab + 4b²) 

Trying to factor a multi variable polynomial :

 4.2    Factoring    a² - 4ab + 4b² 

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

 Found a factorization  :  (a - 2b)•(a - 2b)

Detecting a perfect square :

 4.3    a²  -4ab  +4b²  is a perfect square 

 It factors into  (a-2b)•(a-2b)
which is another way of writing  (a-2b)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 :

  a • (a - 2b)2