Simplify The Expression Using The Distributive Property.$\[ 6(3x + 2) = \square \\]

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Introduction

The distributive property is a fundamental concept in algebra that allows us to simplify complex expressions by distributing a single value to multiple terms. In this article, we will explore how to simplify the expression 6(3x + 2) using the distributive property.

Understanding the Distributive Property

The distributive property states that for any real numbers a, b, and c, the following equation holds:

a(b + c) = ab + ac

This means that we can distribute the value of a to both b and c, resulting in the sum of the products ab and ac.

Applying the Distributive Property

Now, let's apply the distributive property to the given expression 6(3x + 2). We can rewrite the expression as:

6(3x + 2) = 6(3x) + 6(2)

Using the distributive property, we can simplify the expression further:

6(3x) = 18x 6(2) = 12

Therefore, the simplified expression is:

18x + 12

Step-by-Step Solution

Here's a step-by-step solution to simplify the expression using the distributive property:

  1. Distribute the value 6 to both terms inside the parentheses: 6(3x + 2) = 6(3x) + 6(2)
  2. Simplify each term: 6(3x) = 18x and 6(2) = 12
  3. Combine the simplified terms: 18x + 12

Example Problems

Here are a few example problems that demonstrate how to simplify expressions using the distributive property:

Example 1

Simplify the expression 4(2x + 5)

Using the distributive property, we can rewrite the expression as:

4(2x + 5) = 4(2x) + 4(5) = 8x + 20

Example 2

Simplify the expression 3(2x - 4)

Using the distributive property, we can rewrite the expression as:

3(2x - 4) = 3(2x) - 3(4) = 6x - 12

Example 3

Simplify the expression 2(3x + 2)

Using the distributive property, we can rewrite the expression as:

2(3x + 2) = 2(3x) + 2(2) = 6x + 4

Conclusion

In this article, we have learned how to simplify the expression 6(3x + 2) using the distributive property. We have also explored example problems that demonstrate how to apply the distributive property to simplify complex expressions. By mastering the distributive property, you will be able to simplify a wide range of algebraic expressions and solve problems with ease.

Key Takeaways

  • The distributive property states that a(b + c) = ab + ac
  • We can distribute a single value to multiple terms using the distributive property
  • The distributive property can be used to simplify complex expressions
  • Example problems demonstrate how to apply the distributive property to simplify expressions

Further Reading

If you want to learn more about the distributive property and how to apply it to simplify expressions, here are some additional resources:

  • Khan Academy: Distributive Property
  • Mathway: Distributive Property
  • Algebra.com: Distributive Property

Introduction

The distributive property is a fundamental concept in algebra that allows us to simplify complex expressions by distributing a single value to multiple terms. In this article, we will answer some frequently asked questions (FAQs) about the distributive property.

Q: What is the distributive property?

A: The distributive property is a mathematical concept that states that for any real numbers a, b, and c, the following equation holds:

a(b + c) = ab + ac

This means that we can distribute the value of a to both b and c, resulting in the sum of the products ab and ac.

Q: How do I apply the distributive property?

A: To apply the distributive property, simply multiply the value outside the parentheses to each term inside the parentheses. For example, if we have the expression 6(3x + 2), we can rewrite it as:

6(3x + 2) = 6(3x) + 6(2) = 18x + 12

Q: What are some common mistakes to avoid when using the distributive property?

A: Here are some common mistakes to avoid when using the distributive property:

  • Not distributing the value to each term inside the parentheses: Make sure to multiply the value outside the parentheses to each term inside the parentheses.
  • Not simplifying the expression: After distributing the value, simplify the expression by combining like terms.
  • Not checking for errors: Double-check your work to ensure that you have applied the distributive property correctly.

Q: Can I use the distributive property with negative numbers?

A: Yes, you can use the distributive property with negative numbers. For example, if we have the expression -3(2x - 4), we can rewrite it as:

-3(2x - 4) = -3(2x) + (-3)(-4) = -6x + 12

Q: Can I use the distributive property with fractions?

A: Yes, you can use the distributive property with fractions. For example, if we have the expression 1/2(3x + 2), we can rewrite it as:

1/2(3x + 2) = 1/2(3x) + 1/2(2) = 3/2x + 1

Q: How do I know when to use the distributive property?

A: You should use the distributive property when you have an expression with parentheses and you want to simplify it. The distributive property is particularly useful when you have expressions with multiple terms inside the parentheses.

Q: Can I use the distributive property with exponents?

A: Yes, you can use the distributive property with exponents. For example, if we have the expression 2^3(2x + 3), we can rewrite it as:

2^3(2x + 3) = 2^3(2x) + 2^3(3) = 8(2x) + 8(3) = 16x + 24

Conclusion

In this article, we have answered some frequently asked questions (FAQs) about the distributive property. We have covered topics such as how to apply the distributive property, common mistakes to avoid, and how to use the distributive property with negative numbers, fractions, and exponents. By mastering the distributive property, you will be able to simplify complex expressions and solve problems with ease.

Key Takeaways

  • The distributive property states that a(b + c) = ab + ac
  • We can distribute a single value to multiple terms using the distributive property
  • The distributive property can be used to simplify complex expressions
  • Example problems demonstrate how to apply the distributive property to simplify expressions

Further Reading

If you want to learn more about the distributive property and how to apply it to simplify expressions, here are some additional resources:

  • Khan Academy: Distributive Property
  • Mathway: Distributive Property
  • Algebra.com: Distributive Property

By following these resources, you will be able to deepen your understanding of the distributive property and become proficient in simplifying complex expressions.