Question

PLEASE HELP!!!!
Factor this expression completely.
x^3 1/8 - y^3 1/27

Answer 1

This expression is the difference of two cubes:

x^3 y^3
----- - -------
2^3 3^3

The rule here is a^3 - b^3 = (a - b)(a^2 + ab + b^2), so


x^3 y^3 x^2 x^3y^3 y^2
----- - ------- = (x/2 - y/3)*(-------- + ----------- + --------- )
2^3 3^3 2^2 6^3 3^2