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Simplifying expressions involves reducing a mathematical statement to its most basic form. When you are simplifying, you are making the expression more compact and easier to understand. The goal is to have as few terms as possible.
To do this, you need to:

• Identify like terms, which are terms that have the exact same variable components.
• Combine these like terms by performing the required mathematical operations.
• Simplify any remaining mathematical expressions if possible.

Simplifying expressions often makes solving and understanding problems easier, especially in higher-level math. It's a fundamental skill that is applied in various areas of mathematics.

Combining like terms is one of the key steps in simplifying expressions. Like terms are terms whose variables and their exponents are exactly the same.
For example, in the expression \(-12x + 8x\), both terms are like terms because they both contain the variable \(x\).
When combining like terms, follow these steps:

• Identify which terms can be combined – look for common variables and exponents.
• Add or subtract the coefficients of these terms. The variable part remains unchanged.

In our example, combine the coefficients:

• Take the first coefficient, \(-12\), and add the second coefficient, \(8\).
• The result is \(-4\), leading to the simplified term \(-4x\).

This process makes expressions easier to work with and understand.

Mathematical operations are the foundation of working with expressions. In simplifying and combining like terms, the basic operations of addition and subtraction take center stage.
When performing these operations:

• Addition involves combining numbers or expressions to get a total. It's represented by the plus sign \(+\).
• Subtraction is taking one quantity away from another, represented by the minus sign \(-\).

These operations are used to manipulate coefficients of like terms. For instance, in the expression \(-12x + 8x\), the coefficients \(-12\) and \(8\) are combined using subtraction, leading to \(-4\).
Mathematical operations also extend to multiplication and division, but when simplifying expressions by combining like terms, addition and subtraction are most commonly employed. Ensuring a strong grasp on these basic operations is crucial for effective problem solving in mathematics.