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When you encounter algebraic expressions like the one given in the exercise, it's essential to recognize similar or like terms. These terms are those that have the same variables raised to the same powers. For example, the terms in the expression \(6n + 13n - 15n\) are all like terms because they have the variable \(n\) in common. By identifying these terms, you can simplify an expression by combining them.To combine like terms:

• Ensure the terms have the same variable: If terms differ by more than their coefficients, they cannot be combined (e.g., \(5x\) and \(3x^2\) can't be combined).
• Add or subtract their coefficients: Focus only on the numerical part attached to the variable. In our example, you deal only with the numbers \(6, 13,\) and \(-15\).

Combining like terms helps to simplify expressions, making them easier to understand and solve in equations.

Simplifying expressions involves several steps aimed at reducing an expression to its easiest form without changing its value. For the expression \(6n + 13n - 15n\), simplifying means combining all like terms to get the cleanest possible expression.The main goal here is to combine those similar terms by performing arithmetic operations on their coefficients. This process eliminates any unnecessary complexity, enabling a solver to focus on key parts of an expression or equation.After combining similar terms, you derive a simpler form, like turning \(6n + 13n - 15n\) into \(4n\). Simplified expressions are straightforward and make further calculations like solving equations or evaluating values much more manageable.

Arithmetic operations are fundamental in algebra, especially while simplifying expressions. These operations involve basic mathematical tasks: addition, subtraction, multiplication, and division. In the context of simplifying expressions, you primarily deal with adding and subtracting the coefficients of like terms.For the expression \(6n + 13n - 15n\), arithmetic operations help combine the coefficients:

• Add: First, add the coefficients \(6\) and \(13\) to get \(19\).
• Subtract: Then, subtract \(15\) from \(19\), resulting in \(4\).

Arithmetic operations allow you to express the expression in its simplest form, \(4n\), by showing the result of the remaining coefficient. Understanding these operations, especially in the context of variables and algebraic expressions, is crucial for solving more complex problems.