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When working with algebraic expressions, you will often encounter parentheses (also known as grouping symbols) that need to be removed. In order to simplify an expression, it is essential to understand how to eliminate these parentheses correctly.

To remove parentheses, particularly when they are preceded by a negative sign or any other coefficient, you need to distribute that sign or coefficient to each term inside the parentheses. This process is known as distribution.

For example, given the expression \(-(9x + 1)\), the negative sign outside the parentheses must be distributed to each term inside the parentheses— \(9x\) and \(1\). This will help eliminate the parentheses correctly.

Distributing a negative sign, or minus sign, across terms inside parentheses is a crucial step in simplifying algebraic expressions. When you see a negative sign outside the parentheses, it signifies that you need to multiply each term inside by \(-1\).

This means that for each term inside the parentheses:

• \(+\) term becomes \(-\) term
• \(-\) term becomes \(+\) term

In the example -\((9x + 1)\), distributing the negative sign results in:

• \(9x\) becomes \-9x\
• \(1\) becomes \-1\

Therefore, the expression transforms to: \(-9x - 1\).

Once the parentheses have been removed and the negative sign has been distributed, the final step is to simplify the expression. Simplification means combining like terms and ensuring the expression is in its simplest form.

In the example, after distributing the negative sign: \(-(9x) - (1) = -9x - 1\), there are no like terms to combine, so the expression is already simplified.

Key tips for simplification:

• Combine like terms if possible. Like terms have the same variable raised to the same power.
• Check your work by ensuring all parentheses have been correctly removed and all signs have been correctly distributed.

Thus, the simplified form of the given expression \( -(9x + 1) \) is \(-9x - 1.\)