How would I expand 3 brackets, e.g. (x + 3)(x + 4)(x + 2)?

Expanding 3 brackets is very much the same method as expanding 2. In the example you gave, to start you would expand the first two brackets out using the FOIL method (firsts, outsides, insides and leftovers), giving (x²+ 4x +3x +12). You would show this in your line of working as (x²+ 4x + 3x +12)(x + 2). Next you simplify the expansion you have just completed so it makes it easier for you to multiply with the 3rd bracket: (x²+ 7x +12)(x + 2). Then expand the brackets, again using the FOIL method to give: (x³+ 2x² + 7x²+ 12x +14x + 24), simplifying to give the answer of: (x³+ 9x² + 26x +24)