Question

How do you factor `192u^3 - 81`?

Answer 1

`3(16u^2+12u+9)`

Explanation:

`3(64u^3-27)`
`3[(4u)^3-(3)^3)]`
We know that `a^3-b^3=(a-b)(a^2+ab+b^2)`
In this case, `a=4u` and `b=3`
Therefore:
`(4u)^3-(3)^3=(4u-3)(16u^2+12u+9)`
`3(16u^2+12u+9)` (we still have the 3 leftover from before)