Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3x25 • x) -  12
 Step  2  :
 Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   3x²⁶ - 12  =   3 • (x²⁶ - 4) 

Trying to factor as a Difference of Squares :

 3.2      Factoring:  x²⁶ - 4 

Theory : A difference of two perfect squares,  A² - B²  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A² - AB + BA - B² =
         A² - AB + AB - B² =
         A² - B²

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 4 is the square of 2
Check :  x²⁶  is the square of  x¹³ 

Factorization is :       (x¹³ + 2)  •  (x¹³ - 2) 

Final result :

  3 • (x13 + 2) • (x13 - 2)