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In mathematics, simplifying expressions involves transforming them into a simpler or more compact form without changing their value. This process often includes combining like terms and ensuring all operations are completed properly. To simplify the expression \(-8 + 4(3)\), first perform any multiplication within the expression.

* Begin by identifying the operation that needs to be performed: multiplication (\(4 \times 3\)).* This results in \(12\), so substitute this back into the expression: \(-8 + 12\).* Finally, perform the addition to arrive at the simplest form: \(4\).
The key to simplifying is to carefully follow mathematical operations while combining any like terms or constants whenever possible.

The order of operations is fundamental in ensuring expressions are simplified correctly. A useful mnemonic is PEMDAS:

• **P**: Parentheses
• **E**: Exponents (powers and roots)
• **M**: Multiplication
• **D**: Division
• **A**: Addition
• **S**: Subtraction

In the expression \(-8 + 4(3)\), the multiplication \(4(3)\) is performed before the addition due to PEMDAS. This is given precedence because multiplication comes before addition in the order of operations. By consistently applying these rules, mathematical expressions are handled systematically, preventing mistakes. Remember, operations embedded in parentheses always take priority. However, in this example, since there are no parentheses other than the multiplication itself, it immediately proceeds.

Basic arithmetic encompasses the foundational operations: addition, subtraction, multiplication, and division. These operations are used to compute and simplify expressions. For the expression \(-8 + 4(3)\):

* **Multiplication**: Calculate \(4 \times 3 = 12\).* **Addition**: Combine numbers by adding (or subtracting) the products and other constants, such as \(-8 + 12\), leading to \(4\).
Understanding the purpose and process of each operation is key. Basic arithmetic operations allow the manipulation and transformation of numbers, which is essential in simplification and solving mathematical problems. Once you're comfortable with these operations, you can confidently approach more complex expressions by breaking them down into simpler components.