Combine Like Terms & Distributive Property Worksheet Guide
Table of Contents :
Combining like terms and applying the distributive property are fundamental concepts in algebra that serve as building blocks for solving equations. Understanding these concepts not only makes algebra more manageable but also helps students develop critical thinking skills. In this guide, we'll explore these two essential topics and provide examples, tips, and a worksheet to solidify your understanding.
Understanding Like Terms
Like terms are terms that have the same variables raised to the same powers. They can be combined through addition or subtraction to simplify expressions. For instance, in the expression (3x + 5x), both terms are "like terms" because they both contain the variable (x).
Examples of Like Terms
- (2a) and (5a) are like terms (combine to (7a))
- (4y^2) and (3y^2) are like terms (combine to (7y^2))
- (7) and (10) are like terms (combine to (17))
Non-Like Terms
Terms that cannot be combined are known as non-like terms. For example, in the expression (2x + 3y), (2x) and (3y) cannot be combined because they contain different variables.
The Distributive Property
The distributive property states that (a(b + c) = ab + ac). This means that when you multiply a number by a sum, you can distribute the multiplication to each term inside the parentheses.
Using the Distributive Property
Example 1
If you have the expression (3(x + 4)), you can use the distributive property as follows:
[ 3(x + 4) = 3 \cdot x + 3 \cdot 4 = 3x + 12 ]
Example 2
For the expression (2(a + b + 5)):
[ 2(a + b + 5) = 2a + 2b + 10 ]
Combining Both Concepts
Often, you’ll use both combining like terms and the distributive property in the same problem. Let’s work through an example.
Example Problem
Simplify the expression (4(2x + 3) + 5x - 6).
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Apply the Distributive Property: [ 4(2x) + 4(3) + 5x - 6 = 8x + 12 + 5x - 6 ]
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Combine Like Terms: [ 8x + 5x + 12 - 6 = 13x + 6 ]
So, the simplified expression is (13x + 6).
Important Notes:
"When combining like terms, always ensure that the variables and their powers match. When applying the distributive property, make sure to distribute the number to every term inside the parentheses."
Practice Worksheet
Here’s a simple worksheet to help you practice combining like terms and using the distributive property.
Problems
- Simplify: (5(x + 2) + 3x - 4)
- Simplify: (2(a + 3b) - 7 + 4b)
- Simplify: (3(2x + 5) + 4x - 6)
- Simplify: (6y + 4(y - 2) - 3)
- Simplify: (5(a + 4) - 2(a + 2))
Solutions
| Problem | Answer |
|---|---|
| 1 | (8x + 6) |
| 2 | (2a + 11b - 7) |
| 3 | (10x + 9) |
| 4 | (10y - 8) |
| 5 | (3a + 14) |
Conclusion
Combining like terms and using the distributive property are crucial skills in algebra that can simplify expressions and make solving equations easier. Practice using these concepts with various examples, and refer back to this guide as needed to strengthen your understanding. Mastery of these skills will provide a solid foundation for future math challenges and enhance your problem-solving abilities. Happy studying! 🎓✨