x^3 - a^3
The above expression represent differnt of 2 cubes
This can be re- written as
(x - a)^3
(x - a) ( x ^2 + ax + a^2)
expand the bracket
x * x^2 + ax*x + x *a^2 - a * x^2 - a * ax - a * a^2
= x^3 + ax^2 + a^2x - ax^2 - a^2x - a^3
collecting the like terms
= x^3 + ax^2 - ax^2 + a^2x -a^2x - a^3
ax^2 - ax^2 = 0
a^2x - a^2x = 0
Therefore
= x^3 + 0 + 0 - a^3
= x^3 - a^3