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In algebra, simplifying expressions is all about making expressions simpler without changing their value. This involves combining like terms and simplifying any parts of the expression, such as numbers inside parentheses or fractions. The goal is to rewrite the expression in the simplest form possible for easier calculation and understanding.

For example, consider the expression \((-5 + 3) a - (2 + 5) b - (3 + 8) b\). To simplify it, you first deal with any operations, such as subtraction or addition, inside the parentheses. Reducing these internal calculations makes it much easier to approach the overall expression.

By employing this technique, you convert the expression into a more transparent form, step by step, ensuring clarity and ease of further manipulation anytime you encounter a similar algebraic expression.

Combining like terms is an essential process in algebra. Like terms are terms that have identical variable parts raised to the same power. For example, \(-7b\) and \(-11b\) have the same variable, \(b\), and can thus be combined.

Let's take the example given: after simplifying the parentheses, the expression becomes \(-2a - 7b - 11b\). Here, \(-7b\) and \(-11b\) are like terms. We can combine them to form \(-18b\). This simplifies the expression further to \(-2a - 18b\).

It's important to note that only like terms can be combined. Terms like \(-2a\) and \(-18b\) cannot be combined since their variable parts are different.

Parentheses simplification involves calculating and reducing any expression within parentheses first. Parentheses in an algebraic expression often indicate which operations should be completed first, guiding the order of operations in the expression.

Consider the expression \((-5 + 3) a - (2 + 5) b - (3 + 8) b\). By simplifying the terms in the parentheses, we get \(-2\), \(7\), and \(11\) respectively. This changes the original expression into \(-2a - 7b - 11b\).

Simplifying the parts within parentheses makes the rest of the expression easier to handle. It's crucial to perform these steps first to give a clear path for further simplification and combination of like terms.