Suppose you’re working on an algebraic expression that involves variables, addition, multiplication, and parentheses. You try repeatedly to expand it using the distributive law.
How do you know that the expression won’t continue to expand forever?
For example, expanding
(x + y)(s(u + v) + t)
x(s(u + v) + t) + y(s(u + v) + t),
which has more parentheses than the original expression.