Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((3 • (x2)) • y) -  (32x3 • y3)
 Step  2  :

Equation at the end of step  2  :

  (3x2 • y) -  32x3y3

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   3x²y - 9x³y³  =   -3x²y • (3xy² - 1) 

Trying to factor as a Difference of Squares :

 4.2      Factoring:  3xy² - 1 

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 :  3  is not a square !!

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

Final result :

  -3x2y • (3xy2 - 1)