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In algebra, terms are considered 'like terms' when they contain exactly the same variables raised to the same power. Identifying like terms is a crucial first step when simplifying expressions. When expressions are simplified, like terms can be combined to make the expression shorter and more manageable.

Let's look at an easy example: in the expression \(2a + 3 + 5a\), \(2a\) and \(5a\) are like terms. They both contain the variable \(a\), and it is important that \(a\) is raised to the same power in both terms. It's like collecting apples; you wouldn't mix apples and oranges. The same principle applies here!

Remember, constants, or numbers without variables, like \(3\) in our example, are also considered like terms by themselves and should not be mixed with terms that have variables.

Coefficients are the numerical parts attached to the variables in an algebraic term. Understanding coefficients is key when combining like terms because they dictate how many times you count each variable.

In our expression \(2a + 3 + 5a\), we have the coefficients \(2\) and \(5\) for the terms \(2a\) and \(5a\), respectively. When we combine like terms, we focus on these coefficients. Adding them together, as in \(2 + 5 = 7\), gives us the new coefficient for \(a\) in the simplified expression \(7a\).

Notice that the constant \(3\) doesn't have a variable, so it is treated separately in the simplification process. A constant can be thought of as still having a coefficient, which would simply be itself.

Variables are symbols used to represent unknown values or values that can change. They are the backbone of algebraic expressions and equations. Understanding how variables work is key to mastering algebra.

In the expression provided, the variable \(a\) represents a value we may not know or that varies. We use variables to simplify expressions and write equations that can solve real-world problems.

A variable can take on different values, but when simplifying like terms, it’s important they remain the same between the terms you are combining. This consistency is what allows us to add the coefficients of like terms together to create a more streamlined expression.