Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (25 • (a2)) -  72b4
 Step  2  :

Equation at the end of step  2  :

  52a2 -  72b4

Step  3  :

Trying to factor as a Difference of Squares :

 3.1      Factoring:  25a²-49b⁴ 

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 :  25  is the square of  5 
Check : 49 is the square of 7
Check :  a²  is the square of  a¹ 

Check :  b⁴  is the square of  b² 

Factorization is :       (5a + 7b²)  •  (5a - 7b²) 

Trying to factor as a Difference of Squares :

 3.2      Factoring:  5a - 7b² 

Check :  5  is not a square !!

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

Final result :

  (5a + 7b2) • (5a - 7b2)