You would have already learnt how to expand single brackets such as 3a(2b + 7), and double brackets such as (x + 5)(x - 7).
Expanding three (or more!) brackets if very similar, although it might look a little tricky at the start. Let's have a look at an example first.
(x + 3)(x - 5)(x + 4)
We are not going to do it all at once. Instead, we are just going to expand and simplify the first two brackets.
Use whatever method you are most comfortable with. You might want to highlight the like terms to help you with simplifying.
(x + 3)(x - 5) = x2 + 3x - 5x - 15 = x2 - 2x - 15
We are now going to use this answer and multiply it out with the third bracket.
(x2 - 2x - 15)(x + 4) = x3 + 4x2 - 2x2 - 8x -15x - 60 = x3 + 2x2 - 23x - 60
Here we are then, (x + 3)(x - 5)(x + 4) = x3 + 2x2 - 23x - 60
The key to success here is to take time to expand each set of brackets.
Don't rush it: it's easy to make a mistake with so many terms, different powers and signs to think about.