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When working with algebraic expressions, combining like terms is an essential technique for simplifying expressions. It helps to make calculations easier by grouping similar types of terms together.
"Like terms" are those that have the same variable part. This means they have the same letters and each variable raised to the same powers. For example, in the expression \((2x - 1) + (10x - 7)\), both \(2x\) and \(10x\) are like terms because they both contain the variable \(x\) raised to the first power. They are distinct from the constants, which are numbers without variables.
To combine these like terms, simply add or subtract their coefficients (the numerical parts in front of the variables). In our example: \(2x + 10x = 12x\). Doing this step simplifies the expression by reducing the total number of terms.

Constants are the numbers in an algebraic expression that do not change. They are not attached to variables, and they hold a fixed value. In any operation, you treat constants as ordinary numbers—we can add, subtract, multiply, or divide them.
Taking our exercise \((2x - 1) + (10x - 7)\), both \(-1\) and \(-7\) are constants. These numbers remain constant and independent because no variable accompanies them. Therefore, while simplifying the expression, constants are combined separately from coefficients of like terms.
By adding our constants together: \(-1 + (-7) = -8\), which results in a single constant term. Combining constants is as simple as basic arithmetic. This process helps streamline the equation, paving the way for easier manipulation and further calculations.

Linear expressions are foundational elements in algebra holding variables with only the first power. Notably, they do not have any exponents greater than one or include products of variables, making them straightforward and easier to work with.
Consider our simplified expression \(12x - 8\). This expression is a classic linear expression because the highest power of the variable \(x\) is one. Such expressions represent straight lines when plotted on a graph, with \(12x\) modeling the slope and \(-8\) acting as the y-intercept.
When simplifying, understanding linear expressions becomes prominent in allowing us to further explore other complex types of expressions. By mastering linear expressions, students can move ahead to quadratic or even polynomial expressions with greater confidence. This foundational knowledge paves the way for future topics like graphing linear equations and calculating slopes.