nested parentheses

Nested parentheses are grouping symbols tucked inside other grouping symbols, like a small box placed inside a larger box. To keep the layers readable, writers often alternate shapes: round ( ), then square [ ], then curly { } as you go outward.

An expression like 2[3 + (x - 1)] has the parentheses (x - 1) nested inside the brackets. The rule for handling them is simple: work from the inside out. Simplify the innermost group first, then the next layer, and so on until the outermost. The order-of-operations convention guarantees this gives a single well-defined value.

Nesting only changes the order in which you do the work, not the meaning of the operations. If you instead worked outward-in, or distributed across the wrong layer, you would likely break a sign or skip a term — so resist the urge and always finish the inner bracket before touching the outer one.