➕ Topic Summary
Combining like terms is a fundamental skill in algebra. It involves simplifying expressions by grouping terms that have the same variable raised to the same power. For example, in the expression $3x + 5y - 2x$, the terms $3x$ and $-2x$ are like terms because they both contain the variable $x$ raised to the power of 1. We can combine them to get $x$. The simplified expression becomes $x + 5y$. This process makes expressions easier to understand and work with.
The goal is to rewrite algebraic expressions in a more compact and manageable form. Remember, only terms with identical variable parts can be combined. Constants (numbers without variables) are also like terms and can be combined.
🔤 Part A: Vocabulary
Match each term with its definition:
- Term
- Coefficient
- Variable
- Constant
- Like Terms
- A symbol (usually a letter) representing an unknown value.
- Terms that have the same variable(s) raised to the same power(s).
- A number on its own, without any variables.
- A single number or variable, or numbers and variables multiplied together.
- The numerical factor of a term that contains a variable.
(Answers: 1-4, 2-5, 3-1, 4-3, 5-2)
✍️ Part B: Fill in the Blanks
Combining _______ _______ involves simplifying an algebraic expression by adding or subtracting terms that have the same _______. The number in front of the variable is called the _______. A _______ is a term that has no variable.
(Answers: like, terms, variable, coefficient, constant)
🤔 Part C: Critical Thinking
Explain, in your own words, why it's important to combine like terms when solving algebraic equations. Give an example of how it simplifies the process.