Combine Like Terms with Distributive Property Made Easy

Combining Like Terms with the Distributive Property: A Step-by-Step Guide

When working with algebraic expressions, it’s essential to understand how to combine like terms using the distributive property. In this article, we’ll break down the concept of like terms, explain the distributive property, and provide a step-by-step guide on how to combine like terms.

What are Like Terms?

Like terms are terms that have the same variable(s) raised to the same power. For example:

• 2x and 3x are like terms because they both have the variable x raised to the power of 1.
• 4y^2 and 2y^2 are like terms because they both have the variable y raised to the power of 2.

What is the Distributive Property?

The distributive property is a mathematical concept that allows us to expand a single term across multiple terms inside parentheses. The distributive property states that:

a(b + c) = ab + ac

In other words, when we multiply a single term (a) by a group of terms inside parentheses (b + c), we can distribute the single term to each term inside the parentheses.

How to Combine Like Terms using the Distributive Property

Now that we understand like terms and the distributive property, let’s dive into the step-by-step process of combining like terms:

1. Identify the like terms: Look for terms that have the same variable(s) raised to the same power.
2. Apply the distributive property: Use the distributive property to expand any single terms across multiple terms inside parentheses.
3. Combine the like terms: Add or subtract the like terms by combining their coefficients (the numbers in front of the variables).

Let’s use an example to illustrate this process:

Example 1:

2(x + 3) + 4x

Step 1: Identify the like terms

In this example, the like terms are 2x and 4x.

Step 2: Apply the distributive property

Using the distributive property, we can expand the first term as follows:

2(x + 3) = 2x + 6

Step 3: Combine the like terms

Now we can combine the like terms:

2x + 6 + 4x = 6x + 6

Answer: 6x + 6

More Examples

Let’s try a few more examples to solidify our understanding:

Example 2:

x^2 + 3x^2 - 2x

Step 1: Identify the like terms

In this example, the like terms are x^2 and 3x^2.

Step 2: Apply the distributive property

No distributive property is needed in this example.

Step 3: Combine the like terms

Now we can combine the like terms:

x^2 + 3x^2 = 4x^2

Then, we can combine the remaining term:

4x^2 - 2x

Answer: 4x^2 - 2x

Example 3:

2(y - 4) + 5y

Step 1: Identify the like terms

In this example, the like terms are 2y and 5y.

Step 2: Apply the distributive property

Using the distributive property, we can expand the first term as follows:

2(y - 4) = 2y - 8

Step 3: Combine the like terms

Now we can combine the like terms:

2y - 8 + 5y = 7y - 8

Answer: 7y - 8

Common Mistakes to Avoid

When combining like terms, it’s essential to avoid common mistakes such as:

• Forgetting to apply the distributive property
• Combining unlike terms
• Missing coefficients

Conclusion

Combining like terms using the distributive property is a fundamental concept in algebra. By following the step-by-step process outlined in this article, you’ll be able to simplify complex expressions and solve equations with ease. Remember to identify like terms, apply the distributive property, and combine like terms to arrive at the correct solution.

📝 Note: Always double-check your work to ensure you haven't missed any like terms or applied the distributive property incorrectly.

Related Terms:

• Easy Distributive Property Worksheet PDF