Solution - Simplification or other simple results

Step  1  :

Trying to factor as a Difference of Squares :

 1.1      Factoring:  a⁴-r⁴⁴ 

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 :  a⁴  is the square of  a² 

Check :  r⁴⁴  is the square of  r²² 

Factorization is :       (a² + r²²)  •  (a² - r²²) 

Trying to factor as a Difference of Squares :

 1.2      Factoring:  a² - r²² 

Check :  a²  is the square of  a¹ 

Check :  r²²  is the square of  r¹¹ 

Factorization is :       (a + r¹¹)  •  (a - r¹¹) 

Final result :

  (r22 + a2) • (r11 + a) • (a - r11)