Question

1/8x^3-216y^3


pls answer the question​

Answer 1

8 • (x - 3y) • (x2 + 3xy + 9y2)

Step-by-step explanation:

1

(8 • (x3)) - (23•33y3)

8x3 - 216y3  =   8 • (x3 - 27y3) 

23x3 - (23•33y3)

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 :  27  is the cube of   3 

Check :  x3 is the cube of   x1

Check :  y3 is the cube of   y1

Factorization is :

             (x - 3y)  •  (x2 + 3xy + 9y2) 

Factoring    x2 + 3xy + 9y2 

Try to factor this multi-variable trinomial using

Answer = 8 • (x - 3y) • (x2 + 3xy + 9y2)