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When simplifying algebraic expressions, an important skill is combining like terms. Like terms are terms that have the exact same variables raised to the same powers. For instance,

• "5y", "7y", and "-6y" are like terms because they all contain the variable "y" to the first power.
• They can be combined by performing arithmetic operations on their coefficients.

Combining these like terms involves adding or subtracting their coefficients while keeping the variables and exponents unchanged. In our example, this means calculating the sum or difference of the coefficients of "y": \[5 + 7 - 6\]. This gives us a new coefficient for "y", simplifying the expression to \(6y\).

By understanding how to correctly identify and combine like terms, you can simplify complex algebraic expressions more easily, making further calculations much quicker and less error-prone.

Coefficients are the numbers in front of the variables in algebraic expressions. They indicate how many times the variable is multiplied. For example, in the expression "5y", "5" is the coefficient of "y".

When combining like terms, it is crucial to focus on these coefficients:

• Add them together if the operation is addition.
• Subtract them if the operation is subtraction.

In the expression we just simplified, the coefficients are "5", "7", and "6", corresponding to the variable "y". When combined as \[5 + 7 - 6\], the result is "6", showing that the term simplifies to "6y".

Knowing how coefficients affect the overall expression is key to mastering algebraic simplification. They dictate the magnitude of the terms in the expression, and changing them affects the outcome, even if the variables remain constant.

Variables are symbols used to represent numbers in algebraic expressions. They can stand for unknowns or variables that may change. In our example, "y" is the variable. Variables are essential because they allow us to form general models and equations that can solve real-world problems.

When simplifying expressions, it's important to keep variables consistent. This means:

• Recognize that "5y", "7y", and "-6y" all share the same variable "y".
• This shared variable allows terms to be combined effectively.

While the coefficients change through addition or subtraction, the variable stays constant. Remember that different variables like "x", "z", or different powers of "y" (like "y^2", "y^3") cannot be combined in this manner unless they are like terms with similar variables and exponents. Understanding the role of variables helps to ensure accuracy when simplifying expressions.