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When dealing with algebraic expressions, removing parentheses correctly is crucial. Parentheses often group terms to indicate operations that should be performed first. To remove parentheses, especially when a negative sign is involved, you need to distribute the negative sign to each term inside the parentheses. For example, in the expression \(- (4 - 5)\), the negative sign outside the parentheses will change the signs of the terms inside:
\(- (4 - 5)\) becomes \(-4 + 5\).
This simplifies further to \(- (-1) = 1\). This same logic applies to the second part of the expression: \(- (7 - 8)\) becomes \(- 7 + 8\), which simplifies to \(- (-1) = 1\).
The key step here is to remember that a negative sign in front of the parentheses impacts every term inside it.

After removing the parentheses and appropriately changing the signs, the next step is to combine like terms. Like terms are terms that have the same variables raised to the same power. In this case, we only have constants to combine. From the previous step, we simplified the expression to:
\(1 + 1\).
This part is straightforward, with no need to match variable parts. You simply add the constants together:
\(1 + 1 = 2\).
Combining like terms reduces the expression to its simplest form.

Handling negative numbers correctly is vital in algebra. A common point of confusion is how to deal with negative signs, especially when they appear outside parentheses. Recall from the earlier step that a negative sign outside the parentheses \'flips\' the signs of the terms inside. For example, with \(- (4 - 5)\), the negative sign changes both terms to their opposites, resulting in \(-4 + 5\). This simplifies to \(1\). The same process applies to \(- (7 - 8)\), which also simplifies to \(1\).
Always ensure to distribute the negative signs accurately. Neglecting to change the signs within the parentheses is a common mistake. Correctly managing negatives helps avoid errors in simplification. Remember, \(-(-a) = a\), effectively turning a double negative into a positive. This concept underpins much of the simplification process in algebra.