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In algebra, negative signs can sometimes be tricky, but understanding their rules is essential. If we see a negative sign in front of a variable, it simply means we are changing the sign of the variable. For example, a negative in front of the variable x, written as (-x), means we have the opposite of x.

Things get more interesting when we have more than one negative sign. For instance, having --x means we have two negatives. According to algebra rules, two negatives cancel each other out, making a positive. So, --x simplifies to x.

Here are some important points to remember about dealing with negatives:

• A single negative sign changes the sign of the variable it is in front of.
• Two negative signs together cancel each other out, thus making a positive.
• Negative signs within parentheses need special attention as they affect all terms inside the parentheses.

Removing parentheses in algebraic expressions is a straightforward process, but there are important rules to follow. Parentheses in algebra indicate that the terms inside should be treated as a single unit. To remove them, especially when there is a negative sign outside, follow these steps:

1. Look at the sign directly outside the parentheses. If it is a negative sign, it will change the signs of all terms inside.
2. Apply the sign to each term inside the parentheses.

Consider the expression: -(-x - y). Here, you have a negative sign outside and negative signs with variables inside the parentheses.

The negative sign outside will distribute to both −x and −y, changing their signs:

-(-x) = x

-(-y) = y

Combining these, we get the simplified expression: (x + y)

Essential points to keep in mind:

• Distribute the outside sign to every term inside parentheses.


• Negatives outside parentheses change the signs of all terms inside.


• Always recheck by combining like terms if necessary.

Algebraic simplification often involves combining like terms and reducing expressions to their simplest form. Simplification makes equations more manageable and easier to solve. Here are the steps for simplification:

1. Remove any parentheses using the rules discussed.
2. Combine like terms by adding or subtracting their coefficients.
3. Simplify constants, if any, and write the final expression.

Let's revisit the given expression: -(-x - y).

After removing the parentheses by distributing the negative sign, we got: (x + y).

In this scenario, there are no like terms to combine, so this expression is fully simplified. This process is essential for solving more complex equations and performing operations efficiently.

Remember these key tips:

• Always perform operations within parentheses first.


• Distribute any outside signs properly.


• Combine like terms for a more straightforward expression.