Question

on solving x9+y9=? what is the answer

Answer 1

Trying to factor as a Difference of Cubes:

 1.1      Factoring:  x9-y9 

Theory : A difference 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 :  x9 is the cube of   x3

Check :  y9 is the cube of   y3

Factorization is :
             (x3 - y3)  •  (x6 + x3y3 + y6) 

Trying to factor as a Difference of Cubes:

 1.2      Factoring:  x3 - y3 

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 :

 1.3    Factoring    x2 + xy + y2 

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

 Factorization fails

Trying to factor a multi variable polynomial :

 1.4    Factoring    x6 + x3y3 + y6 

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

 Factorization fails

Final result :

(x - y) • (x2 + xy + y2) • (x6 + x3y3 + y6)