Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

   (((15•(x3))•y)-52xy3) 
  (—————————————————————•x)•y
             5          
 Step  2  :

Equation at the end of step  2  :

   (((3•5x3) • y) - 52xy3) 
  (——————————————————————— • x) • y
              5           

Step  3  :

            15x3y - 25xy3
 Simplify   —————————————
                  5      

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   15x³y - 25xy³  =   5xy • (3x² - 5y²) 

Trying to factor as a Difference of Squares :

 4.2      Factoring:  3x² - 5y² 

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

Equation at the end of step  4  :

  (xy • (3x2 - 5y2) • x) • y

Step  5  :

Multiplying exponential expressions :

 5.1    x¹ multiplied by x¹ = x^{(1 + 1)} = x²

Equation at the end of step  5  :

  x2y • (3x2 - 5y2) • y

Step  6  :

Multiplying exponential expressions :

 6.1    y¹ multiplied by y¹ = y^{(1 + 1)} = y²

Final result :

  x2y2 • (3x2 - 5y2)