Combining Like Terms Worksheet Answers Explained
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Understanding how to combine like terms is a foundational skill in algebra. This skill is essential for simplifying expressions and solving equations, making it critical for students to master. In this article, we will explore combining like terms, provide clarity on solving such problems, and present a sample worksheet along with detailed answers and explanations. Let's dive in! 📘
What are Like Terms? 🤔
Like terms are terms that have the same variable raised to the same power. For example, in the expression (3x^2 + 5x^2 - 2x + 4), the terms (3x^2) and (5x^2) are like terms because they both contain the variable (x^2). However, (-2x) and (4) are not like terms because one is a variable term and the other is a constant.
Examples of Like Terms
- (2a) and (5a) are like terms.
- (4b^2) and (-2b^2) are like terms.
- (7c) and (3c) are like terms.
- (x) and (7) are NOT like terms.
How to Combine Like Terms 🛠️
Combining like terms involves adding or subtracting the coefficients of the like terms. The variable part remains unchanged.
Step-by-Step Process:
- Identify Like Terms: Look for terms that have the same variable and exponent.
- Group Like Terms: Once identified, group these terms together.
- Add/Subtract Coefficients: Perform the addition or subtraction on the coefficients while keeping the variable part the same.
- Write the Simplified Expression: Combine the results to write a simplified expression.
Sample Worksheet 📊
Let’s create a small worksheet to practice combining like terms. Below are some expressions for students to simplify:
- (4x + 5x - 3 + 7)
- (2y^2 - 3y + 4y^2 + 5)
- (3a + 4b - 2a + 7b - 5)
- (6m - 2n + 3n + 8 - 4m)
- (5p^2 + 2p - 4p^2 + 3 + 6p)
Answers and Explanations 📝
Now, let's provide the answers to the worksheet along with explanations.
<table> <tr> <th>Expression</th> <th>Simplified Expression</th> <th>Explanation</th> </tr> <tr> <td>1. (4x + 5x - 3 + 7)</td> <td>(9x + 4)</td> <td>Combine (4x) and (5x) to get (9x) and combine (-3) and (7) to get (4).</td> </tr> <tr> <td>2. (2y^2 - 3y + 4y^2 + 5)</td> <td>(6y^2 - 3y + 5)</td> <td>Combine (2y^2) and (4y^2) to get (6y^2); the linear term remains as (-3y) and the constant is (5).</td> </tr> <tr> <td>3. (3a + 4b - 2a + 7b - 5)</td> <td>(a + 11b - 5)</td> <td>Combine (3a - 2a) to get (a) and (4b + 7b) to get (11b); the constant remains (-5).</td> </tr> <tr> <td>4. (6m - 2n + 3n + 8 - 4m)</td> <td>(2m + n + 8)</td> <td>Combine (6m - 4m) to get (2m); combine (-2n + 3n) to get (n), and the constant (8) stays the same.</td> </tr> <tr> <td>5. (5p^2 + 2p - 4p^2 + 3 + 6p)</td> <td>(p^2 + 8p + 3)</td> <td>Combine (5p^2 - 4p^2) to get (p^2); combine (2p + 6p) to get (8p) and the constant (3) remains unchanged.</td> </tr> </table>
Important Notes 📌
- Ensure to align similar types of terms when combining them.
- Remember that constants (numerical values without variables) can also be combined, just like variable terms.
- Practicing with various expressions can help solidify your understanding of this key algebraic concept.
Conclusion
Combining like terms is a vital skill in algebra that simplifies expressions and lays the groundwork for more complex mathematical concepts. With practice through worksheets and guided exercises, students can gain confidence in identifying and simplifying like terms effectively. By mastering this skill, they pave their path to success in future math challenges. Keep practicing, and you'll become proficient in no time! ✨