Question

Solve by an identity (2x^3+2y^3)

Answer 1

Equation at the end of step 1

 (2 • (x3)) +  2y3

STEP  

2

:

Equation at the end of step

2

:

 2x3 +  2y3

STEP

3

:

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  2x3 + 2y3  =   2 • (x3 + y3)  

Trying to factor as a Sum of Cubes:

4.2      Factoring:  x3 + y3  

Theory : A sum of two perfect cubes,  a3 + b3 can be factored into  :

            (a+b) • (a2-ab+b2)

Proof  : (a+b) • (a2-ab+b2) =

   a3-a2b+ab2+ba2-b2a+b3 =

   a3+(a2b-ba2)+(ab2-b2a)+b3=

   a3+0+0+b3=

   a3+b3

Check :  x3 is the cube of   x1

Check :  y3 is the cube of   y1

Factorization is :

            (x + y)  •  (x2 - xy + y2)  

Trying to factor a multi variable polynomial :

4.3    Factoring    x2 - xy + y2  

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

Factorization fails

Final result :

 2 • (x + y) • (x2 - xy + y2)