Solution - Factoring multivariable polynomials

Step  1  :

Equation at the end of step  1  :

  (((5•(x4))•(y2))-((20•(x3))•(y3)))-(52x2•y4)
 Step  2  :

Equation at the end of step  2  :

  (((5•(x4))•(y2))-((22•5x3)•y3))-52x2y4
 Step  3  :

Equation at the end of step  3  :

  ((5x4 • y2) -  (22•5x3y3)) -  52x2y4

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   5x⁴y² - 20x³y³ - 25x²y⁴  =   5x²y² • (x² - 4xy - 5y²) 

Trying to factor a multi variable polynomial :

 5.2    Factoring    x² - 4xy - 5y² 

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

 Found a factorization  :  (x + y)•(x - 5y)

Final result :

  5x2y2 • (x + y) • (x - 5y)