Simplify Nested Parentheses

Simplifying nested parentheses

Nested parentheses mean one group is inside another. To simplify, work from the outside inward and pay close attention to signs in front of each group.

1) Distribute through the outer parentheses

If a number or a minus sign is in front of parentheses, multiply it by every term inside the group. This is what removes the outer grouping symbols.

• A plus sign in front of parentheses leaves the signs inside unchanged.
• A minus sign in front of parentheses changes every sign inside.

2) Simplify the inner group carefully

If there is another set of parentheses inside, simplify that group too. Apply distribution one layer at a time until no parentheses remain.

3) Combine like terms

After all grouping symbols are removed, collect terms with the same variable part and combine constants.

4) Check your signs

A good check is to look back at each minus sign in front of parentheses. A common mistake is forgetting to change every sign in the group.

Quick example idea

Start by simplifying the innermost parentheses, then rewrite the expression without grouping symbols, and finally combine like terms.

Final check

Your final answer should have no parentheses left and should be fully simplified.