Hey :). Linear Combinations of Random Variables !

Heeey everyone :).

Well I like Math , love it actually , which is quite weird as I don't do Science subjects but am more of a Business person myself lol.

There is no denying that Math can be a pain in the butt at times but hey we can't really live without it :D.

I have my final A level Statistics exam tomorrow , and I'm stuck on Linear Combinations of Random Variables. Particularly calculating the variance ! I do not understand why we can use both these approaches and when: 1.) a^2 x Var(X) and 2.) a x Var(X)

When do we square and when do we not?

This text comes in my book : **"It is important to distinguish clearly between situations in which a single observation is multiplied by a constant and those in which several different observations of the same random variable are added." **

A clearer explanation ANYONE? I would really appreciate the help. Need at least a B on my paper tomorrow.