From teh answer in my textbook and the result given in wolframAlpha/Maple etc i know that this:

$\displaystyle \frac{16}{27}u^3 + \frac{4}{45}u^5$

Simplifies to this:

$\displaystyle \frac{4}{135}u^3(20 + 3u^2)$

But i don't see how they work out that $\displaystyle \frac{4}{135}$ is the factor to take out.

If there computer can work it out consistently im assuming theres a technique/method used to find it? Could anyone point me in the right direction?

Thank you