Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  1 -  52n2

Step  2  :

Trying to factor as a Difference of Squares :

 2.1      Factoring:  1-25n² 

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 :  1  is the square of  1 
Check : 25 is the square of 5
Check :  n²  is the square of  n¹ 

Factorization is :       (1 + 5n)  •  (1 - 5n) 

Final result :

  (5n + 1) • (1 - 5n)