Use A Form Of The Distributive Property To Rewrite The Algebraic Expression Without Parentheses.$\[ 8(x+5+3y) \\]$\[ 8(x+5+3y) = \square \\](Simplify Your Answer.)

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Understanding the Distributive Property

The distributive property is a fundamental concept in algebra that allows us to simplify complex expressions by distributing a single value across multiple terms. In this article, we will explore how to use the distributive property to rewrite an algebraic expression without parentheses.

The Distributive Property Formula

The distributive property formula is:

a(b + c) = ab + ac

where a, b, and c are algebraic expressions.

Applying the Distributive Property to the Given Expression

The given expression is:

8(x + 5 + 3y)

To rewrite this expression without parentheses, we will apply the distributive property by distributing the 8 across each term inside the parentheses.

Step 1: Distribute the 8 across the first term

The first term inside the parentheses is x. We will multiply the 8 by x to get:

8x

Step 2: Distribute the 8 across the second term

The second term inside the parentheses is 5. We will multiply the 8 by 5 to get:

40

Step 3: Distribute the 8 across the third term

The third term inside the parentheses is 3y. We will multiply the 8 by 3y to get:

24y

Rewriting the Expression without Parentheses

Now that we have distributed the 8 across each term inside the parentheses, we can rewrite the expression without parentheses as:

8x + 40 + 24y

Simplifying the Expression

The expression 8x + 40 + 24y is already simplified, but we can further simplify it by combining like terms. However, in this case, there are no like terms to combine, so the expression remains the same.

Conclusion

In this article, we used the distributive property to rewrite an algebraic expression without parentheses. We applied the distributive property formula to each term inside the parentheses and simplified the resulting expression. The distributive property is a powerful tool in algebra that allows us to simplify complex expressions and solve equations.

Example Problems

  1. Use the distributive property to rewrite the expression: 4(x + 2 + 3y)
  2. Use the distributive property to rewrite the expression: 6(x + 4 + 2y)
  3. Use the distributive property to rewrite the expression: 9(x + 3 + 2y)

Answer Key

  1. 4x + 8 + 12y
  2. 6x + 24 + 12y
  3. 9x + 27 + 18y

Practice Problems

  1. Use the distributive property to rewrite the expression: 2(x + 5 + 3y)
  2. Use the distributive property to rewrite the expression: 5(x + 2 + 3y)
  3. Use the distributive property to rewrite the expression: 8(x + 4 + 2y)

Answer Key

  1. 2x + 10 + 6y
  2. 5x + 10 + 15y
  3. 8x + 32 + 16y
    Distributive Property in Algebra: Q&A =====================================

Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions about the distributive property in algebra.

Q: What is the distributive property in algebra?

A: The distributive property in algebra is a rule that allows us to simplify complex expressions by distributing a single value across multiple terms. It states that a(b + c) = ab + ac, where a, b, and c are algebraic expressions.

Q: How do I apply the distributive property to an expression?

A: To apply the distributive property to an expression, you need to follow these steps:

  1. Identify the terms inside the parentheses.
  2. Multiply the value outside the parentheses by each term inside the parentheses.
  3. Simplify the resulting expression.

Q: What are some examples of the distributive property in algebra?

A: Here are some examples of the distributive property in algebra:

  • 2(x + 3) = 2x + 6
  • 3(x + 2) = 3x + 6
  • 4(x + 5) = 4x + 20

Q: Can I use the distributive property to simplify expressions with more than two terms?

A: Yes, you can use the distributive property to simplify expressions with more than two terms. For example:

  • 2(x + 3 + 4y) = 2x + 6 + 8y
  • 3(x + 2 + 5y) = 3x + 6 + 15y

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:

  • Forgetting to distribute the value outside the parentheses to each term inside the parentheses.
  • Not simplifying the resulting expression.
  • Using the distributive property incorrectly, such as multiplying the value outside the parentheses by only one term inside the parentheses.

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

A: You should use the distributive property in algebra when you have an expression with parentheses and you want to simplify it. The distributive property is a powerful tool that can help you simplify complex expressions and solve equations.

Q: Can I use the distributive property to solve equations?

A: Yes, you can use the distributive property to solve equations. For example:

  • 2(x + 3) = 10
  • 3(x + 2) = 12

To solve these equations, you can use the distributive property to simplify the expressions and then isolate the variable.

Q: What are some real-world applications of the distributive property in algebra?

A: The distributive property in algebra has many real-world applications, such as:

  • Simplifying complex expressions in physics and engineering.
  • Solving equations in finance and economics.
  • Modeling real-world situations in computer science and data analysis.

Conclusion

In this article, we answered some of the most frequently asked questions about the distributive property in algebra. We covered topics such as how to apply the distributive property, examples of the distributive property, common mistakes to avoid, and real-world applications of the distributive property. We hope this article has helped you understand the distributive property in algebra and how to use it to simplify complex expressions and solve equations.