91Ó°ÊÓ

When simplifying algebraic expressions, one crucial step is **combining like terms**. Like terms are terms that have the exact same variables raised to the same powers. For example, in the expression \(9.6m + 7.22n + (-2.19m) + (-0.65n)\), we see the variables *m* and *n*. Terms like \(9.6m\) and \(-2.19m\) are like terms because they both include the variable *m*. Similarly, \(7.22n\) and \(-0.65n\) are like terms as they both include the variable *n*.

Combining like terms makes an expression easier to work with and paves the way for further simplification. To combine the terms, you simply add or subtract their coefficients (the numerical factor in front of the variable). For instance, with the *m* terms in our example, you combine \(9.6m - 2.19m\).
This results in \(7.41m\), much simpler to understand and work with. Similarly, for the *n* terms, \(7.22n - 0.65n\) results in \(6.57n\).

The first step in solving any algebraic expression is **grouping variables**. This means identifying terms that contain the same variable and rearranging the expression to place them together. Grouping helps you see which terms can be combined.

In the given example, we started with: \(9.6m + 7.22n + (-2.19m) + (-0.65n)\).

The next thing to do is identify and group each term by its variable:

• The *m* terms: \(9.6m\) and \(-2.19m\)
• The *n* terms: \(7.22n\) and \(-0.65n\)

This reorganization gives us: \( (9.6m - 2.19m) + (7.22n - 0.65n) \). Now, it's clear which terms need to be combined.

In algebraic expressions, a **coefficient** is the numerical factor that multiplies a variable. For example, in the term \(9.6m\), the coefficient is 9.6. Similarly, in \(-2.19m\), the coefficient is -2.19.

To simplify expressions, we need to focus on the coefficients when combining like terms. Using our example, to combine the `m` terms, we perform the operation: \(9.6 - 2.19 = 7.41 \). This gives us the simplified term \(7.41m\).

Similarly, for the `n` terms, the operation \(7.22 - 0.65 = 6.57 \) results in \(6.57n\).

Coefficients play a critical role in simplifying algebraic expressions, making the process mathematical yet straightforward. By paying attention to coefficients, you ensure that terms are combined accurately.