What Is The Product Of The Following Expression? 2 X ( X 2 + X − 5 2x(x^2 + X - 5 2 X ( X 2 + X − 5 ]A. 2 X 3 + X − 5 2x^3 + X - 5 2 X 3 + X − 5 B. 2 X 3 + 2 X − 10 2x^3 + 2x - 10 2 X 3 + 2 X − 10 C. 2 X 3 + 2 X 2 − 5 X 2x^3 + 2x^2 - 5x 2 X 3 + 2 X 2 − 5 X D. 2 X 2 + 2 X 2 − 10 X 2x^2 + 2x^2 - 10x 2 X 2 + 2 X 2 − 10 X

In this article, we will explore the concept of multiplying expressions and apply it to a given problem. We will learn how to multiply expressions with variables and constants, and how to simplify the resulting expression.

Understanding the Problem

The problem asks us to find the product of the expression $2x(x^2 + x - 5)$. To solve this problem, we need to apply the distributive property of multiplication over addition, which states that for any numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.

Step 1: Apply the Distributive Property

To find the product of the given expression, we need to apply the distributive property. We will multiply the term $2x$ with each term inside the parentheses.

2x(x^2 + x - 5) = 2x(x^2) + 2x(x) - 2x(5)

Step 2: Simplify the Expression

Now, we will simplify the expression by combining like terms.

2x(x^2) = 2x^3
2x(x) = 2x^2
-2x(5) = -10x

Step 3: Combine Like Terms

Finally, we will combine the like terms to get the final product.

2x^3 + 2x^2 - 10x

Conclusion

In this article, we learned how to multiply expressions with variables and constants, and how to simplify the resulting expression. We applied the distributive property to find the product of the given expression and simplified the resulting expression by combining like terms. The final product is $2x^3 + 2x^2 - 10x$.

Answer

The correct answer is C. $2x^3 + 2x^2 - 10x$.

Why is this the Correct Answer?

This is the correct answer because we applied the distributive property and simplified the resulting expression by combining like terms. The final product is $2x^3 + 2x^2 - 10x$, which matches option C.

What is the Distributive Property?

The distributive property is a mathematical concept that states that for any numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. This property allows us to multiply a single term with each term inside the parentheses.

How to Apply the Distributive Property

To apply the distributive property, we need to multiply the term with each term inside the parentheses. We will then combine like terms to simplify the resulting expression.

Why is the Distributive Property Important?

The distributive property is an important concept in mathematics because it allows us to multiply expressions with variables and constants. It is used extensively in algebra and is a fundamental concept in mathematics.

Real-World Applications of the Distributive Property

The distributive property has many real-world applications. It is used in physics to describe the motion of objects, in engineering to design buildings and bridges, and in economics to model the behavior of markets.

Conclusion

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In this article, we will answer some of the most frequently asked questions related to the product of the given expression.

Q: What is the distributive property?

A: The distributive property is a mathematical concept that states that for any numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. This property allows us to multiply a single term with each term inside the parentheses.

Q: How do I apply the distributive property?

A: To apply the distributive property, you need to multiply the term with each term inside the parentheses. You will then combine like terms to simplify the resulting expression.

Q: What is the product of the given expression?

A: The product of the given expression $2x(x^2 + x - 5)$ is $2x^3 + 2x^2 - 10x$.

Q: Why is the distributive property important?

A: The distributive property is an important concept in mathematics because it allows us to multiply expressions with variables and constants. It is used extensively in algebra and is a fundamental concept in mathematics.

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

A: The distributive property has many real-world applications. It is used in physics to describe the motion of objects, in engineering to design buildings and bridges, and in economics to model the behavior of markets.

Q: How do I simplify an expression using the distributive property?

A: To simplify an expression using the distributive property, you need to multiply the term with each term inside the parentheses and then combine like terms.

Q: What is the difference between the distributive property and the commutative property?

A: The distributive property states that for any numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. The commutative property states that for any numbers $a$ and $b$, $a + b = b + a$. The distributive property is used to multiply expressions with variables and constants, while the commutative property is used to add expressions with variables and constants.

Q: Can I use the distributive property to multiply expressions with fractions?

A: Yes, you can use the distributive property to multiply expressions with fractions. However, you need to be careful when multiplying fractions and make sure to multiply the numerators and denominators correctly.

Q: How do I multiply expressions with exponents using the distributive property?

A: To multiply expressions with exponents using the distributive property, you need to multiply the exponents and then multiply the coefficients. For example, if you have the expression $2x^2(x^3)$, you would multiply the exponents to get $2x^5$.

Conclusion

In this article, we answered some of the most frequently asked questions related to the product of the given expression. We covered topics such as the distributive property, how to apply it, and its importance in mathematics. We also discussed some real-world applications of the distributive property and provided examples of how to simplify expressions using the distributive property.

Additional Resources

If you want to learn more about the distributive property and how to apply it, we recommend checking out the following resources:

• Khan Academy: Distributive Property
• Mathway: Distributive Property
• Wolfram Alpha: Distributive Property

Final Thoughts

The distributive property is a fundamental concept in mathematics that allows us to multiply expressions with variables and constants. It is used extensively in algebra and is a crucial tool for solving equations and inequalities. By understanding the distributive property and how to apply it, you will be able to simplify complex expressions and solve problems with ease.