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When working with algebraic expressions, 'like terms' are terms that contain the same variables raised to the same power. This means only the coefficients (numbers in front of the variables) are different. For example, in the expression:
9.6m + 7.22n - 2.19m - 0.65n, the like terms are '9.6m' and '-2.19m', and '7.22n' and '-0.65n'.
Identifying like terms is crucial because it allows you to combine them and simplify the expression efficiently.
To easily spot like terms, look for the same variables and make sure they match exactly. Only then you can add or subtract them together.

After identifying like terms, the next step is 'combining coefficients'. The coefficient is the numerical part of a term.
Let's take our example: (9.6m) + (-2.19m) + (7.22n) + (-0.65n), we combine coefficients of like terms:

• For 'm' terms: Combine 9.6 and -2.19. That gives us:

\[ 9.6m - 2.19m = 7.41m \]
• For 'n' terms: Combine 7.22 and -0.65. That gives us:

\[ 7.22n - 0.65n = 6.57n \]

Be careful with negative signs when combining coefficients; they can change the result. With practice, combining coefficients becomes second nature.

The final and satisfying part of working through an algebraic expression is simplifying it. This makes it cleaner and easier to work with or interpret.
Simplification involves combining like terms through addition or subtraction of their coefficients, as shown in our previous steps.
After combining the coefficients, you rewrite the expression with the simplified terms.
In our example:
9.6m + 7.22n - 2.19m - 0.65n becomes:
7.41m + 6.57n
This is the simplified form. Always double-check if all like terms are combined and ensure your resulting expression is as neat as possible.
Simplifying expressions can make solving equations easier and provides clear insight into the relationships between variables.