Question

How do you factor `27(K^3)-8`?

Answer 1

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

Explanation:

This is an example of the difference of two cubes.
Look for the pattern here:

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

`x^3 + 8 = (x + 2)(x^2 - 2x + 4)`

Hint: There are 2 brackets in the answer. The first is easy to find.
The second bracket is formed from the first bracket.

Using the same pattern...

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