Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  52x2 -  81

Step  2  :

Trying to factor as a Difference of Squares :

 2.1      Factoring:  25x²-81 

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 : 81 is the square of 9
Check :  x²  is the square of  x¹ 

Factorization is :       (5x + 9)  •  (5x - 9) 

Final result :

  (5x + 9) • (5x - 9)