Question

How do you factor completely `27+8t^3`?

Answer 1

`27 + 8t^3 = (3+2t)(9-6t+4t^2)`

Explanation:

`27, 8 and t^3` are all cubes. Once you recognise that fact, you can factorise this expression by the general rule for "Sum of cubes".

`x^3 +y^3 = (x+y)(x^2-xy+y^2)`

`27 + 8t^3 = (3+2t)(9-6t+4t^2)`