How do you expand triple brackets?

Triple brackets are like every other number of brackets:

Every term in each bracket needs to be multiplied with every term in other brackets.

Specifically in case of triple brackets, the simplest way is to choose one of the brackets and write its terms as multipliers of the remaining two brackets.

Example:

(x+1)(x+2)(x+3) = x(x+2)(x+3) + 1(x+2)(x+3) = x(x²+5x+6) + 1(x²+5x+6) =

=x³ + 5x² + 6x + x² + 5x + 6 = x³ + 6x² + 11x + 6

When expanding three brackets, we want to first make the problem appear a bit simpler. We know how to expand 2 brackets (with FOIL), so we treat one pair of brackets as if it is one bracket, making the expansion simpler. Then, we can expand the next set of brackets and we’re done!