Master Combining Like Terms With Distributive Property Worksheet
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Understanding how to combine like terms is an essential skill in algebra that helps students simplify expressions and solve equations efficiently. The distributive property plays a crucial role in this process, making it easier to handle expressions that contain parentheses. In this article, we'll delve into the concept of combining like terms and using the distributive property, providing a clear understanding, examples, and a worksheet to practice these skills.
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 + 5x + 2y), the terms (3x) and (5x) are like terms because they both contain the variable (x). However, (2y) is not a like term with (3x) or (5x) because it contains a different variable.
Identifying Like Terms
When identifying like terms, it is important to look at both the coefficients (the numerical part) and the variable part:
- Example: In the expression (7a + 2b - 3a + 4b):
- Like terms: (7a) and (-3a) (both are (a) terms)
- Like terms: (2b) and (4b) (both are (b) terms)
You can combine like terms by adding or subtracting their coefficients.
The Distributive Property Explained 📚
The distributive property states that multiplying a sum by a number gives the same result as multiplying each addend separately and then adding the products. It can be expressed as:
[ a(b + c) = ab + ac ]
This property is particularly useful for simplifying expressions before combining like terms.
Example of the Distributive Property
Consider the expression (3(x + 4)):
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Apply the distributive property: [ 3(x + 4) = 3x + 12 ]
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Combine like terms: If there are additional terms to combine, you would do so afterward. For instance, if you have (3x + 12 + 2x): [ 3x + 2x + 12 = 5x + 12 ]
How to Combine Like Terms with the Distributive Property
When you combine like terms using the distributive property, follow these steps:
- Distribute any coefficients to terms inside parentheses.
- Combine like terms.
Example Problem
Let's break down the expression (2(3x + 4) + 5x - 6):
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Distribute: [ 2(3x) + 2(4) + 5x - 6 = 6x + 8 + 5x - 6 ]
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Combine like terms: [ (6x + 5x) + (8 - 6) = 11x + 2 ]
Practice Worksheet 📝
To solidify your understanding, practice with the following worksheet. Try to combine like terms using the distributive property where necessary.
Worksheet
| Problem | Solution |
|---|---|
| 1. (4(2x + 3) + 5x) | |
| 2. (3(2y - 5) + 4y + 6) | |
| 3. (5(3a + 2) - 4(a + 1)) | |
| 4. (6(b + 4) - 2(b - 3)) | |
| 5. (7(3c + 2) + c) |
Important Note: Remember to distribute properly and check for errors when combining your like terms!
Answers to Worksheet
- (4(2x + 3) + 5x = 8x + 12 + 5x = 13x + 12)
- (3(2y - 5) + 4y + 6 = 6y - 15 + 4y + 6 = 10y - 9)
- (5(3a + 2) - 4(a + 1) = 15a + 10 - 4a - 4 = 11a + 6)
- (6(b + 4) - 2(b - 3) = 6b + 24 - 2b + 6 = 4b + 30)
- (7(3c + 2) + c = 21c + 14 + c = 22c + 14)
Conclusion
Combining like terms and using the distributive property are fundamental skills in algebra that pave the way for solving more complex mathematical problems. By practicing with the worksheet and examples provided, students can develop confidence in their ability to simplify expressions effectively. Understanding these concepts will not only aid in academics but also in real-world applications that require logical reasoning and problem-solving skills. Happy practicing! 🧠✨