Solution - Simplification or other simple results

Step  1  :

Trying to factor as a Difference of Squares :

 1.1      Factoring:  m³²⁰¹²⁰-100 

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 : 100 is the square of 10
Check :  m³²⁰¹²⁰  is the square of  m¹⁶⁰⁰⁶⁰ 

Factorization is :       (m¹⁶⁰⁰⁶⁰ + 10)  •  (m¹⁶⁰⁰⁶⁰ - 10) 

Trying to factor as a Difference of Squares :

 1.2      Factoring:  m¹⁶⁰⁰⁶⁰ - 10 

Check : 10 is not a square !!

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

Final result :

  (10 + m160060) • (m160060 - 10)