Question

How do you factor completely `a^3-10`?

Answer 1

`a^3 -10 = (a-root3 10)(a^2+aroot3 10 +root3 10^2)`

Explanation:

`10` is not a perfect cube, but we can show its cube root as `root3 10` which is an irrational number.

The difference of cubes factorises as:
`x^3 -y^3 = (x-y)(x^2 +xy+y^2)`

`a^3 -10 = (a-root3 10)(a^2+aroot3 10 +root3 10^2)`