Which Answer Choice Results From Using The Distributive Property To Rewrite The Expression Below?$\[5(x+8)\\]A. $\[5x + 40\\] B. $\[5x + 8\\] C. $\[5(8x)\\] D. $\[5 + 8x\\]

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Introduction

The distributive property is a fundamental concept in algebra that allows us to expand and simplify expressions by multiplying each term inside the parentheses with the term outside. In this article, we will explore how to use the distributive property to rewrite an expression and identify the correct answer choice.

Understanding the Distributive Property

The distributive property states that for any real numbers a, b, and c:

a(b + c) = ab + ac

This means that we can distribute the term outside the parentheses (a) to each term inside the parentheses (b and c) and multiply them separately.

Applying the Distributive Property

Let's apply the distributive property to the given expression:

5(x + 8)

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

5x + 5(8)

Now, we can simplify the expression by multiplying 5 with 8:

5x + 40

Answer Choice Analysis

Now that we have rewritten the expression using the distributive property, let's analyze the answer choices:

A. 5x + 40

This answer choice matches our rewritten expression, which is the correct result of using the distributive property.

B. 5x + 8

This answer choice is incorrect because it does not take into account the multiplication of 5 with 8.

C. 5(8x)

This answer choice is incorrect because it does not apply the distributive property correctly. The correct result would be 40x, not 5(8x).

D. 5 + 8x

This answer choice is incorrect because it does not apply the distributive property correctly. The correct result would be 5x + 40, not 5 + 8x.

Conclusion

In conclusion, the correct answer choice is A. 5x + 40, which is the result of using the distributive property to rewrite the expression 5(x + 8).

Tips and Tricks

  • When applying the distributive property, make sure to multiply each term inside the parentheses with the term outside.
  • Use the distributive property to simplify expressions and make them easier to work with.
  • Practice, practice, practice! The more you practice using the distributive property, the more comfortable you will become with it.

Common Mistakes

  • Failing to apply the distributive property correctly can lead to incorrect results.
  • Not simplifying expressions using the distributive property can make them more difficult to work with.
  • Not practicing the distributive property regularly can lead to a lack of understanding and confidence in using it.

Real-World Applications

The distributive property has many real-world applications, including:

  • Simplifying complex expressions in physics and engineering
  • Solving systems of linear equations in economics and finance
  • Modeling population growth and decay in biology and ecology

Final Thoughts

Introduction

The distributive property is a fundamental concept in algebra that can be challenging to understand and apply. In this article, we will address some of the most frequently asked questions about the distributive property, providing clear and concise answers to help you better understand this important concept.

Q: What is the distributive property?

A: The distributive property is a mathematical concept that allows us to expand and simplify expressions by multiplying each term inside the parentheses with the term outside. It states that for any real numbers a, b, and c:

a(b + c) = ab + ac

Q: How do I apply the distributive property?

A: To apply the distributive property, simply multiply each term inside the parentheses with the term outside. For example, if we have the expression 5(x + 8), we can rewrite it as:

5x + 5(8)

Then, we can simplify the expression by multiplying 5 with 8:

5x + 40

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

A: Some common mistakes to avoid when using the distributive property include:

  • Failing to apply the distributive property correctly, resulting in incorrect results.
  • Not simplifying expressions using the distributive property, making them more difficult to work with.
  • Not practicing the distributive property regularly, leading to a lack of understanding and confidence in using it.

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. For example, if you have the expression 3(x + 2), you can use the distributive property to rewrite it as:

3x + 6

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

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

-2x + 6

Q: Can I use the distributive property with fractions?

A: Yes, you can use the distributive property with fractions. For example, if you have the expression 1/2(x + 4), you can use the distributive property to rewrite it as:

1/2x + 2

Q: How do I apply the distributive property to expressions with multiple parentheses?

A: To apply the distributive property to expressions with multiple parentheses, simply work from the innermost parentheses outwards. For example, if you have the expression 2(3x + 4), you can use the distributive property to rewrite it as:

6x + 8

Conclusion

In conclusion, the distributive property is a powerful tool in algebra that allows us to simplify and expand expressions. By understanding and applying the distributive property, we can make complex expressions easier to work with and solve. Remember to practice regularly and avoid common mistakes to become proficient in using the distributive property.

Tips and Tricks

  • Practice, practice, practice! The more you practice using the distributive property, the more comfortable you will become with it.
  • Use the distributive property to simplify expressions and make them easier to work with.
  • Be careful when applying the distributive property to expressions with negative numbers or fractions.

Common Misconceptions

  • Some people believe that the distributive property only applies to expressions with two terms inside the parentheses. However, the distributive property can be applied to expressions with any number of terms inside the parentheses.
  • Some people believe that the distributive property only applies to expressions with positive numbers. However, the distributive property can be applied to expressions with negative numbers and fractions as well.

Real-World Applications

The distributive property has many real-world applications, including:

  • Simplifying complex expressions in physics and engineering
  • Solving systems of linear equations in economics and finance
  • Modeling population growth and decay in biology and ecology

Final Thoughts

The distributive property is a fundamental concept in algebra that can be challenging to understand and apply. However, with practice and patience, you can become proficient in using the distributive property to simplify and expand expressions. Remember to practice regularly and avoid common mistakes to become a master of the distributive property.