How to Combine Like Terms in Algebraic Expressions
Quick Answer
To combine like terms, identify terms with the same variable parts. In the expression 9 + q²r², you cannot combine the constant 9 with the variable term q²r², so it remains as is.
Combining like terms is a fundamental skill in algebra that helps simplify expressions and solve equations more efficiently. Like terms are terms that have identical variable parts raised to the same powers. For instance, in the expression 9 + q²r², we see two different types of terms: the constant term 9 and the variable term q²r².
In this case, 9 is a numerical value, while q²r² involves variables q and r, each raised to the second power. Since these terms are not alike, they cannot be combined. The expression remains as 9 + q²r².
### Understanding Like Terms
To understand why you cannot combine these terms, consider what like terms are. Like terms must have the same variables raised to the same powers. For example, 3x and 5x are like terms because they both contain the variable x to the first power. You can combine them to get 8x.
On the other hand, 3x and 5y are not like terms because they involve different variables. You cannot combine them, so the expression would stay as 3x + 5y.
### Real-World Applications
Understanding how to combine like terms is crucial not just for solving math problems in school, but for real-world applications as well. For instance, if you are budgeting your expenses, you might have different categories such as groceries and entertainment. You can combine expenses within the same category to get a clearer idea of your total spending.
### More Examples
Let’s look at some more examples:
1. **Example 1:** 4a + 5a = 9a (like terms)
2. **Example 2:** 7b² + 3b + 2b² = 9b² + 3b (combine like terms b² and leave 3b as is)
3. **Example 3:** 10 + 4x - 3 + 2x = 7 + 6x (combine 10 and -3, and 4x and 2x)
### Practice Makes Perfect
To get better at combining like terms, practice with various expressions. Write down different algebraic expressions and identify the like terms within them. Remember, if the variables and their powers match, you can combine them!
In summary, combining like terms is a key step in simplifying algebraic expressions. By breaking down expressions into their constituent like terms, you can make complex problems more manageable and improve your overall math skills.
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