Solution - Factoring multivariable polynomials

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "y4"   was replaced by   "y^4".  3 more similar replacement(s).

Step  1  :

Equation at the end of step  1  :

  ((x4)-((x2)•(y2)))-2y4

Step  2  :

Trying to factor a multi variable polynomial :

 2.1    Factoring    x⁴ - x²y² - 2y⁴ 

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

 Found a factorization  :  (x² + y²)•(x² - 2y²)

Trying to factor as a Difference of Squares :

 2.2      Factoring:  x²-2y² 

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 : 2 is not a square !!

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

Final result :

  (x2 + y2) • (x2 - 2y2)