Changes made to your input should not affect the solution:

 (1): "a3"   was replaced by   "a^3". 

 2.1     Pull out like factors :

   a³ - 9a  =   a • (a² - 9) 

 2.2      Factoring:  a² - 9 

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 : 9 is the square of 3
Check :  a²  is the square of  a¹ 

Factorization is :       (a + 3)  •  (a - 3) 

  a • (a + 3) • (a - 3)