📚 Topic Summary
In Algebra, identifying and combining like terms is a fundamental skill. Like terms are terms that have the same variable(s) raised to the same power. For example, $3x$ and $-5x$ are like terms because they both have the variable $x$ raised to the power of 1. We can combine like terms by adding or subtracting their coefficients. On the other hand, $3x$ and $3x^2$ are not like terms because the variable $x$ is raised to different powers.
Combining like terms simplifies expressions and makes them easier to work with. This process involves adding or subtracting the coefficients of the like terms while keeping the variable and exponent the same. For instance, $2y + 5y - 3y = 4y$. Mastering this skill is crucial for solving equations and simplifying more complex algebraic expressions.
🧠 Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Coefficient |
A. Terms that have the same variable(s) raised to the same power. |
| 2. Variable |
B. A symbol (usually a letter) representing an unknown value. |
| 3. Constant |
C. A term without a variable; its value does not change. |
| 4. Like Terms |
D. The numerical factor of a term containing a variable. |
| 5. Term |
E. A single number or variable, or numbers and variables multiplied together. |
Answer Key: 1-D, 2-B, 3-C, 4-A, 5-E
✏️ Part B: Fill in the Blanks
Complete the following paragraph with the correct terms.
In algebra, a ___________ is a symbol, usually a letter, that represents an unknown value. The ___________ is the number that multiplies the variable. ___________ are terms that have the same variable raised to the same power, and we can ___________ them by adding or subtracting their coefficients. A ___________ is a number that stands alone.
Word Bank: combine, variable, like terms, constant, coefficient
Answer Key: variable, coefficient, like terms, combine, constant
🤔 Part C: Critical Thinking
Explain, in your own words, why it is important to be able to identify and combine like terms in algebraic expressions. Give an example of a real-world situation where this skill might be useful.