Question

33. What are the factors of:
a. x3 - y3
​

Answer 1

Step-by-step explanation:

Factoring:  x3-y3 

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 :  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 :

 1.2    Factoring    x2 + xy + y2 

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

 Factorization fails

Final result :

(x - y) • (x2 + xy + y2)