Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (x2) -  13x40
 Step  2  :
 Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   x² - 13x⁴⁰  =   -x² • (13x³⁸ - 1) 

Trying to factor as a Difference of Squares :

 3.2      Factoring:  13x³⁸ - 1 

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 :  13  is not a square !!

Ruling : Binomial can not be factored as the
difference of two perfect squares

Final result :

  -x2 • (13x38 - 1)