Apply The Distributive Property To The Following Expression:$\[ 4(x+10) \\]A. \[$ 4x + 14 \$\]B. \[$ 4x + 10 \$\]C. \[$ 4x + 40 \$\]D. \[$ X + 40 \$\]

by ADMIN 151 views

Understanding the Distributive Property

The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses. This property is denoted by the formula:

a(b + c) = ab + ac

where a, b, and c are algebraic expressions.

Applying the Distributive Property to the Given Expression

In this problem, we are given the expression 4(x + 10) and asked to apply the distributive property to simplify it. To do this, we need to multiply the term outside the parentheses, which is 4, with each term inside the parentheses, which are x and 10.

Step 1: Multiply 4 with x

Using the distributive property, we multiply 4 with x to get:

4x

Step 2: Multiply 4 with 10

Next, we multiply 4 with 10 to get:

40

Step 3: Combine the Results

Now that we have multiplied 4 with each term inside the parentheses, we can combine the results to get the final simplified expression:

4x + 40

Evaluating the Answer Choices

Now that we have simplified the expression using the distributive property, let's evaluate the answer choices to see which one matches our result.

  • A. 4x + 14: This is incorrect because we multiplied 4 with 10 to get 40, not 14.
  • B. 4x + 10: This is incorrect because we multiplied 4 with 10 to get 40, not 10.
  • C. 4x + 40: This is correct because it matches our simplified expression.
  • D. x + 40: This is incorrect because we multiplied 4 with x to get 4x, not x.

Conclusion

In conclusion, applying the distributive property to the expression 4(x + 10) results in the simplified expression 4x + 40. This is the correct answer choice.

Real-World Applications of the Distributive Property

The distributive property has many real-world applications in fields such as physics, engineering, and economics. For example, in physics, the distributive property is used to calculate the force exerted on an object by multiple forces. In engineering, it is used to design and analyze complex systems. In economics, it is used to model and analyze economic systems.

Tips and Tricks for Applying the Distributive Property

Here are some tips and tricks for applying the distributive property:

  • Make sure to multiply each term inside the parentheses with the term outside the parentheses.
  • Use the distributive property to simplify complex expressions.
  • Practice, practice, practice! The more you practice applying the distributive property, the more comfortable you will become with it.

Common Mistakes to Avoid

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

  • Failing to multiply each term inside the parentheses with the term outside the parentheses.
  • Not using the distributive property to simplify complex expressions.
  • Not practicing enough to become comfortable with the distributive property.

Conclusion

Frequently Asked Questions

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses.

Q: How do I apply the distributive property?

A: To apply the distributive property, you need to multiply each term inside the parentheses with the term outside the parentheses. For example, if you have the expression 4(x + 10), you would multiply 4 with x to get 4x, and multiply 4 with 10 to get 40.

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

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

  • Failing to multiply each term inside the parentheses with the term outside the parentheses.
  • Not using the distributive property to simplify complex expressions.
  • Not practicing enough to become comfortable with the distributive property.

Q: How do I simplify complex expressions using the distributive property?

A: To simplify complex expressions using the distributive property, you need to multiply each term inside the parentheses with the term outside the parentheses, and then combine the results. For example, if you have the expression 3(2x + 5), you would multiply 3 with 2x to get 6x, and multiply 3 with 5 to get 15. Then, you would combine the results to get 6x + 15.

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

A: The distributive property has many real-world applications in fields such as physics, engineering, and economics. For example, in physics, the distributive property is used to calculate the force exerted on an object by multiple forces. In engineering, it is used to design and analyze complex systems. In economics, it is used to model and analyze economic systems.

Q: How can I practice applying the distributive property?

A: You can practice applying the distributive property by working through algebraic expressions and simplifying them using the distributive property. You can also try solving problems that involve the distributive property, such as those found in algebra textbooks or online resources.

Q: What are some tips for mastering the distributive property?

A: Some tips for mastering the distributive property include:

  • Practicing regularly to become comfortable with the distributive property.
  • Using the distributive property to simplify complex expressions.
  • Paying attention to the terms inside the parentheses and multiplying each term with the term outside the parentheses.
  • Checking your work to ensure that you have applied the distributive property correctly.

Q: Can I apply the distributive property to expressions with variables and constants?

A: Yes, you can apply the distributive property to expressions with variables and constants. For example, if you have the expression 2(x + 3), you would multiply 2 with x to get 2x, and multiply 2 with 3 to get 6.

Q: Can I apply the distributive property to expressions with exponents?

A: Yes, you can apply the distributive property to expressions with exponents. For example, if you have the expression 3(2x^2 + 5), you would multiply 3 with 2x^2 to get 6x^2, and multiply 3 with 5 to get 15.

Conclusion

In conclusion, the distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses. By applying the distributive property to a wide range of algebraic expressions, you can simplify complex expressions and become more comfortable with algebraic manipulations. With practice and patience, you can master the distributive property and apply it to a wide range of real-world problems.