Solution - Factoring multivariable polynomials

Step  1  :

Equation at the end of step  1  :

   ((((10•(x3))•y)+((5•(x2))•(y3)))-(2•5y2)) 
  (—————————————————————————————————————————•x)•y
                       5                    
 Step  2  :

Equation at the end of step  2  :

   ((((10•(x3))•y)+(5x2•y3))-(2•5y2)) 
  (——————————————————————————————————•x)•y
                   5                 
 Step  3  :

Equation at the end of step  3  :

   ((((2•5x3)•y)+5x2y3)-(2•5y2)) 
  (—————————————————————————————•x)•y
                 5              

Step  4  :

            10x3y + 5x2y3 - 10y2 
 Simplify   ————————————————————
                     5          

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   10x³y + 5x²y³ - 10y²  =   5y • (2x³ + x²y² - 2y) 

Trying to factor a multi variable polynomial :

 5.2    Factoring    2x³ + x²y² - 2y 

Try to factor this multi-variable trinomial using trial and error 

 Factorization fails

Equation at the end of step  5  :

  (y • (2x3 + x2y2 - 2y) • x) • y

Step  6  :

Equation at the end of step  6  :

  xy • (2x3 + x2y2 - 2y) • y

Step  7  :

Multiplying exponential expressions :

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

Final result :

  xy2 • (2x3 + x2y2 - 2y)