Combining Like Terms Worksheet Answers Explained
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When it comes to mastering algebra, understanding how to combine like terms is a fundamental skill that students must develop. This technique simplifies expressions and makes solving equations much more manageable. In this article, we will explore combining like terms, provide examples, and present a worksheet along with explanations for the answers.
What Are Like Terms? 🤔
Like terms are terms in an expression that have the same variable raised to the same power. For example, in the expression (3x + 4x + 2y - 5y), the terms (3x) and (4x) are like terms, as are (2y) and (-5y). On the other hand, (3x) and (2y) are not like terms because they have different variables.
Identifying Like Terms
To identify like terms:
- Look at the coefficients (the numbers in front of the variables).
- Check if the variables are the same, including their exponents.
Why Is Combining Like Terms Important? 💡
Combining like terms simplifies expressions, making them easier to work with. It also helps in solving equations more efficiently, which is crucial for students as they progress in their math education.
How to Combine Like Terms
- Identify like terms.
- Add or subtract the coefficients.
- Keep the variable part the same.
Example 1:
Combine the like terms in the expression (5a + 3a - 2b + 4b).
- Step 1: Identify like terms: (5a) and (3a) are like terms, and (-2b) and (4b) are like terms.
- Step 2: Combine them:
- (5a + 3a = 8a)
- (-2b + 4b = 2b)
- Final Answer: (8a + 2b)
Example 2:
Combine the like terms in the expression (7x^2 - 2x + 4x^2 + 3x - 1).
- Step 1: Identify like terms: (7x^2) and (4x^2); (-2x) and (3x) are like terms.
- Step 2: Combine them:
- (7x^2 + 4x^2 = 11x^2)
- (-2x + 3x = 1x)
- Final Answer: (11x^2 + x - 1)
Example 3:
Combine the terms in (2y^3 - 4y^3 + 3y^2 + y^2 + y - 5).
- Step 1: Identify like terms: (2y^3) and (-4y^3); (3y^2) and (y^2); and (y) is by itself.
- Step 2: Combine them:
- (2y^3 - 4y^3 = -2y^3)
- (3y^2 + 1y^2 = 4y^2)
- Final Answer: (-2y^3 + 4y^2 + y - 5)
Combining Like Terms Worksheet 📋
To help reinforce this concept, let's present a worksheet that contains various expressions for students to practice. Below, you will find different expressions along with their answers.
Worksheet
| Expression | Combined Result |
|---|---|
| 3x + 5x + 2y - 4y | 8x - 2y |
| 6a - 3b + 4a + 8b - 2 | 10a + 5b - 2 |
| 2x^2 + 4x - 6 + 5x^2 - 2x | 7x^2 + 2x - 6 |
| 9y - 3y + 8 - y | 5y + 8 |
| -2m + 3m + 4 - 5m + m | -3m + 4 |
Answer Explanations
-
3x + 5x + 2y - 4y: Combine (3x) and (5x) to get (8x) and (2y - 4y) to get (-2y).
Combined Result: (8x - 2y)
-
6a - 3b + 4a + 8b - 2: Combine (6a + 4a) to get (10a) and (-3b + 8b) to get (5b). The (-2) remains as it is.
Combined Result: (10a + 5b - 2)
-
2x^2 + 4x - 6 + 5x^2 - 2: Combine (2x^2 + 5x^2) to get (7x^2) and (4x) stays as (4x). The constants combine as (-6 - 2 = -6).
Combined Result: (7x^2 + 2x - 6)
-
9y - 3y + 8 - y: Combine (9y - 3y - y) to get (5y) and (8) remains unchanged.
Combined Result: (5y + 8)
-
-2m + 3m + 4 - 5m + m: Combine (-2m + 3m + m - 5m) to get (-3m) and (4) remains unchanged.
Combined Result: (-3m + 4)
Conclusion
Combining like terms is a crucial aspect of algebra that simplifies mathematical expressions, making them easier to understand and solve. Practicing with worksheets helps students solidify their understanding and improves their problem-solving skills. With the concepts and examples covered in this article, you should now feel more comfortable with identifying and combining like terms in algebraic expressions. Keep practicing, and soon, this skill will become second nature! 💪📚