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In algebra, an expression is a combination of numbers, variables (like \( a \), \( b \), and \( c \)) and arithmetic operations (such as addition, subtraction, multiplication, and division). These expressions do not have an equals sign. For example, the expression \((a + 2b - c)\) is an algebraic expression, which means it can be simplified or manipulated using various algebraic properties. One of these properties is the distributive property, which allows us to multiply a term by an entire expression inside parentheses. By understanding how to work with algebraic expressions, you begin to unlock many other important algebraic techniques that are crucial for solving equations.

When multiplying terms in an algebraic expression, especially one in parentheses, you apply the distributive property. This property is a way that allows you to remove the parentheses by distributing the outside term to each term inside. For instance, in \( 2(a + 2b - c) \), you multiply \( 2 \) by each term inside:

• Multiply 2 by \( a \) to get \( 2a \).
• Multiply 2 by \( 2b \) to get \( 4b \).
• Multiply 2 by \( -c \) to get \( -2c \).

Each operation involves not just handling the numbers (coefficients), but also preserving the variables and their signs. This consistent approach helps in maintaining the structure of algebraic expressions accurately.

After distributing and rewriting an expression, it's important to simplify it by combining like terms. Like terms are terms that have the exact same variable part. For example, \( 2a \) and \( a \) are like terms, while \( 2a \) and \( 2b \) are not, because they have different variables. In the expression \( 2a + 4b - 2c \), there are no like terms to combine further, as each term is distinct with different variables. This step of combining like terms is crucial for simplification and plays a significant role in solving algebraic equations efficiently. It reduces the expression to its simplest form, making it easier to work with in further mathematical operations or problem-solving scenarios.