Solution - Simplification or other simple results

Step  1  :

Multiplying exponential expressions :

 1.1    a¹ multiplied by a² = a^{(1 + 2)} = a³

Equation at the end of step  1  :

  5a3 -  3a

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   5a³ - 3a  =   a • (5a² - 3) 

Trying to factor as a Difference of Squares :

 3.2      Factoring:  5a² - 3 

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 :  5  is not a square !!

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

Final result :

  a • (5a2 - 3)