Combining like terms is a fundamental skill in algebra. It involves simplifying expressions by adding or subtracting terms that have the same variable raised to the same power. For example, $3x + 2x$ can be simplified to $5x$ because both terms have the variable $x$ raised to the power of 1. However, $3x + 2y$ cannot be combined because the terms have different variables.
The key to combining like terms is to focus on the variable and its exponent. If they are the same, you can combine the coefficients (the numbers in front of the variables). This process makes complex algebraic expressions easier to work with and solve.
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Coefficient | A. Terms that have the same variable raised to the same power. |
| 2. Variable | B. A symbol (usually a letter) representing an unknown value. |
| 3. Constant | C. A term without any variables. |
| 4. Like Terms | D. The numerical factor of a term containing variables. |
| 5. Expression | E. A mathematical phrase containing numbers, variables, and operators. |
Complete the following paragraph with the correct words:
To combine like _____, you need to identify terms that have the same _____. You can then add or subtract their _____. For example, in the expression $5x + 3y + 2x$, the like terms are $5x$ and _____. Combining them results in _____.
Explain, in your own words, why it is important to combine like terms when solving algebraic equations. Provide an example to support your explanation.
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