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Combining Like Terms Worksheet Answer Key Explained

6 min read 11-16-2024
Combining Like Terms Worksheet Answer Key Explained

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In this article, we will explore the concept of combining like terms, a fundamental skill in algebra that is essential for simplifying expressions. Mastering this skill not only aids in solving equations but also lays the foundation for more complex mathematical concepts. We will discuss what like terms are, how to combine them, and provide a detailed explanation of an answer key for a combining like terms worksheet. 📚

What are Like Terms? 🤔

Like terms are terms that have the same variable raised to the same power. For instance, in the expression (3x + 5x - 2y + 7y), (3x) and (5x) are like terms, as are (-2y) and (7y). When combining like terms, you can add or subtract the coefficients (the numerical parts) while keeping the variable part the same.

Identifying Like Terms

To identify like terms, follow these simple steps:

  1. Look at the Variables: Check the variables in each term. They must be identical.
  2. Check the Exponents: Ensure the exponents on the variables are also the same.

For example, in (2a^2 + 3a^2 + 4a):

  • (2a^2) and (3a^2) are like terms.
  • (4a) is not a like term with (2a^2) or (3a^2).

How to Combine Like Terms 🧮

To combine like terms, you simply perform addition or subtraction on the coefficients while keeping the variable part unchanged. Here’s how to do it:

  1. Group Like Terms: Organize the expression by grouping similar terms together.
  2. Add/Subtract Coefficients: Calculate the sum or difference of the coefficients.
  3. Rewrite the Expression: Substitute the result back into the expression.

Example of Combining Like Terms

Let’s take the expression (4x + 3x - 2 + 6):

  1. Group Like Terms: (4x + 3x) are like terms, and (-2 + 6) are constants.
  2. Add Coefficients:
    • For (4x + 3x): (4 + 3 = 7) ➜ Result: (7x)
    • For (-2 + 6): (-2 + 6 = 4) ➜ Result: (4)
  3. Rewrite the Expression: Combine results ➜ (7x + 4)

Combining Like Terms Worksheet Answer Key Explained

Now, let's look at a sample worksheet on combining like terms and provide an answer key along with explanations for clarity.

Sample Worksheet Problems

  1. (2x + 3x - 4 + 5)
  2. (5a + 6b - 3a + 4b)
  3. (7y - 2y + 8 + 1)
  4. (10m - 4n + 3m + n)

Answer Key

Here’s the answer key with detailed explanations:

<table> <tr> <th>Problem</th> <th>Answer</th> <th>Explanation</th> </tr> <tr> <td>1. (2x + 3x - 4 + 5)</td> <td>5x + 1</td> <td>Combine (2x) and (3x) to get (5x), and (-4 + 5) gives (1).</td> </tr> <tr> <td>2. (5a + 6b - 3a + 4b)</td> <td>2a + 10b</td> <td>Combine (5a) and (-3a) to get (2a), and (6b + 4b) gives (10b).</td> </tr> <tr> <td>3. (7y - 2y + 8 + 1)</td> <td>5y + 9</td> <td>Combine (7y - 2y) to get (5y), and (8 + 1) gives (9).</td> </tr> <tr> <td>4. (10m - 4n + 3m + n)</td> <td>13m - 3n</td> <td>Combine (10m + 3m) to get (13m), and (-4n + n) gives (-3n).</td> </tr> </table>

Important Notes 📝

  • Order of Operations: Always follow the correct order of operations when combining terms.
  • Keep Variables Consistent: Ensure you keep the variables consistent to avoid confusion.

Practice Makes Perfect 💪

Combining like terms is a skill that improves with practice. Here are some tips to master this important algebraic concept:

  1. Work on Worksheets: Regularly practice with worksheets that focus on combining like terms.
  2. Use Visual Aids: Visualizing the terms can help identify like terms more easily.
  3. Check Your Work: After simplifying an expression, go back and check your steps to ensure accuracy.

By practicing combining like terms, students can enhance their understanding of algebra, which is crucial for tackling more complex equations and concepts. With continued practice, anyone can become proficient at combining like terms and applying this skill in various mathematical scenarios. ✨

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