How do you factor ##x^3 + 1/8##?

This problem involves factoring the sum of cubes.

##(a^3+b^3)=(a+b)(a^2-ab+b^2)##

For the expression ##(x^3+1/8)##:

##a=root3(x^3)=x##

##b=root3(1/8)=1/2##

Solution:

##(x^3+1/8)## =

##(x+1/2)(x^2-(x*1/2)+(1/2)^2)## =

##(x+1/2)(x^2-x/2+1/4)##