Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3 • ((2x - 1)2)) -  5 • (4x - 1)2

Step  2  :

Equation at the end of step  2  :

  3 • (2x - 1)2 -  5 • (4x - 1)2

Step  3  :

 3.1     Evaluate :  (2x-1)2   =    4x2-4x+1 
 3.2     Evaluate :  (4x-1)2   =    16x2-8x+1 

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   -68x² + 28x - 2  =   -2 • (34x² - 14x + 1) 

Trying to factor by splitting the middle term

 4.2     Factoring  34x² - 14x + 1 

The first term is,  34x²  its coefficient is  34 .
The middle term is,  -14x  its coefficient is  -14 .
The last term, "the constant", is  +1 

Step-1 : Multiply the coefficient of the first term by the constant   34 • 1 = 34 

Step-2 : Find two factors of  34  whose sum equals the coefficient of the middle term, which is   -14 .

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Final result :

  -2 • (34x2 - 14x + 1)