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Simplifying an algebraic expression means making it easier to understand and work with. In the example provided, the process involves taking the expression \(2(6x)\) and rewriting it in the simplest form. Here, simplification involves performing basic operations and, sometimes, combining like terms.

For this specific exercise, the simplification does not involve combining like terms since there is only one term \((6x)\) affected by multiplication. Instead, the focus is on correctly carrying out arithmetic operations to reduce the expression. The goal is to transform the expression into its simplest appearance while retaining the same value. Simplifying expressions not only makes them smaller but also makes it easier to substitute values into the variables if necessary.

Basic algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols. It is foundational for understanding how mathematical expressions are constructed and manipulated. Algebra uses variables, such as \(x\), which can represent numbers in equations and expressions.

In this exercise, the expression \(2(6x)\) involves a variable \(x\) and requires you to apply the basic principles of algebra. Understanding how to handle expressions with variables is crucial in algebra. It allows you to manipulate equations, solve for unknowns, and understand relationships between different mathematical entities. Basic algebra sets the groundwork for more complex topics, making it an essential skill in both mathematics and real-life problem-solving.

Multiplying terms in an expression involves applying the arithmetic operation of multiplication to numbers and variables within the expression. In expressions like \(2(6x)\), multiplication is implied when a number is adjacent to parentheses.

Here’s how it works:

• Identify each component of the multiplication. In our example, these are the number 2 and the term \(6x\).
• Multiply the coefficient of the variable (6) by the number outside the parentheses (2).
• Combine these results with the variable \(x\). This results in a new expression: \(12x\).

Remember, when multiplying terms, you are distributing the outside number through the terms inside the parentheses, multiplying each component separately and combining the results. Doing so ensures that every component of the expression is correctly accounted for in the simplification process.