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In algebra, distribution is a fundamental technique used to simplify expressions by eliminating parentheses. It involves multiplying a single term by each term inside the parentheses. For example, in the expression \(6(2x - 1)\), distribution allows us to clear the parentheses by multiplying 6 with each of the terms inside: the \(2x\) and the \(-1\). We first calculate \(6 \, \times \, 2x = 12x\) and then \(6 \, \times \, (-1) = -6\). This gives us a new expression: \(12x - 6\).
Distribution not only simplifies expressions but also helps in setting up equations for solving. By distributing, we maintain the equality by applying the same operation—multiplication in this case—to each part of the expression within the parentheses. This ensures we do not inadvertently change the value of the expression.

Combining like terms is another key skill in simplifying algebraic expressions. Like terms are terms that have the same variable raised to the same power. In the context of our example \(12x - 6 - 12x\), we identify \(12x\) and \(-12x\) as like terms because they both comprise the variable \(x\) raised to the first power.
To combine them, we simply add their coefficients. In this case, we have \(12 - 12 = 0\). Subtracting these yields zero, effectively eliminating the \(x\) terms from our expression, simplifying our equation to just the constant \(-6\).

• Combining like terms streamlines expressions and reduces them to their simplest form.
• This step is crucial for solving equations efficiently, getting us closer to the solution.

An algebraic expression is a mathematical phrase that can include numbers, variables, and operational symbols like plus (+) or minus (-). Unlike equations, algebraic expressions do not contain an equals sign. They are used to represent real-world scenarios or mathematical concepts in a concise form.
Our expression \(6(2x - 1) - 12x\) is a classic algebraic expression containing both numerical coefficients and the variable \(x\). The challenge is to simplify it as we did by using distribution and combining like terms.

• Algebraic expressions can be manipulated to reveal different properties and relationships.
• Simplifying them involves steps such as distribution and combining like terms, making complex problems more manageable.

Simplifying such expressions allows us to understand the relationships between variables and constants, laying a foundation for more advanced algebraic problem-solving.