What Is The Product?A. { -9x(5-2x)$}$B. ${ 18x^2-45x\$} C. { -18x^2-45x$}$D. { -18x-45x$}$E. ${ 18x-45x\$}

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In mathematics, the product of two algebraic expressions is a fundamental concept that is used to simplify complex expressions and solve equations. In this article, we will explore the concept of the product of two algebraic expressions and how to identify the correct product from a given set of options.

Understanding Algebraic Expressions

Before we dive into the concept of the product of two algebraic expressions, it is essential to understand what an algebraic expression is. An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Algebraic expressions can be simple or complex, and they can be used to represent a wide range of mathematical concepts.

The Product of Two Algebraic Expressions

The product of two algebraic expressions is a new algebraic expression that is obtained by multiplying the two original expressions together. When multiplying two algebraic expressions, we need to follow the rules of multiplication, which include multiplying each term in the first expression by each term in the second expression.

Example 1: Multiplying Two Simple Algebraic Expressions

Let's consider two simple algebraic expressions: 2x and 3x. To find the product of these two expressions, we need to multiply each term in the first expression by each term in the second expression.

2x Γ— 3x = (2 Γ— 3)x^2 = 6x^2

In this example, we multiplied each term in the first expression (2x) by each term in the second expression (3x) to obtain the product 6x^2.

Example 2: Multiplying Two Complex Algebraic Expressions

Let's consider two complex algebraic expressions: 2x^2 - 3x and x + 2. To find the product of these two expressions, we need to multiply each term in the first expression by each term in the second expression.

(2x^2 - 3x) Γ— (x + 2) = 2x^3 + 4x^2 - 3x^2 - 6x = 2x^3 + x^2 - 6x

In this example, we multiplied each term in the first expression (2x^2 - 3x) by each term in the second expression (x + 2) to obtain the product 2x^3 + x^2 - 6x.

Identifying the Correct Product

Now that we have explored the concept of the product of two algebraic expressions, let's consider the options provided in the problem statement.

A. {-9x(5-2x)$}$ B. ${18x^2-45x\$} C. {-18x^2-45x$}$ D. {-18x-45x$}$ E. ${18x-45x\$}

To identify the correct product, we need to multiply the two given expressions together.

The first expression is -9x, and the second expression is (5-2x). To find the product, we need to multiply each term in the first expression by each term in the second expression.

-9x Γ— (5-2x) = -9x Γ— 5 + (-9x) Γ— (-2x) = -45x + 18x^2

Comparing the result with the options provided, we can see that the correct product is:

B. ${18x^2-45x\$}

Conclusion

In this article, we will address some of the most frequently asked questions about the product of algebraic expressions. Whether you are a student, a teacher, or simply someone who wants to learn more about algebra, this article will provide you with the answers you need.

Q: What is the product of two algebraic expressions?

A: The product of two algebraic expressions is a new algebraic expression that is obtained by multiplying the two original expressions together. When multiplying two algebraic expressions, we need to follow the rules of multiplication, which include multiplying each term in the first expression by each term in the second expression.

Q: How do I multiply two algebraic expressions?

A: To multiply two algebraic expressions, you need to follow the rules of multiplication. This includes multiplying each term in the first expression by each term in the second expression. For example, if you have the expressions 2x and 3x, you would multiply each term in the first expression by each term in the second expression to obtain the product 6x^2.

Q: What is the difference between the product and the sum of two algebraic expressions?

A: The product of two algebraic expressions is a new algebraic expression that is obtained by multiplying the two original expressions together. The sum of two algebraic expressions, on the other hand, is a new algebraic expression that is obtained by adding the two original expressions together. For example, if you have the expressions 2x and 3x, the product would be 6x^2, while the sum would be 5x.

Q: Can I simplify the product of two algebraic expressions?

A: Yes, you can simplify the product of two algebraic expressions. To simplify the product, you need to combine like terms and eliminate any unnecessary terms. For example, if you have the product 2x^2 + 3x^2, you can simplify it by combining the like terms to obtain 5x^2.

Q: How do I identify the correct product of two algebraic expressions?

A: To identify the correct product of two algebraic expressions, you need to multiply each term in the first expression by each term in the second expression. You can then compare the result with the options provided to determine the correct product.

Q: What are some common mistakes to avoid when multiplying algebraic expressions?

A: Some common mistakes to avoid when multiplying algebraic expressions include:

  • Failing to multiply each term in the first expression by each term in the second expression
  • Failing to combine like terms
  • Failing to eliminate unnecessary terms
  • Making errors when multiplying or dividing terms

Q: How can I practice multiplying algebraic expressions?

A: There are many ways to practice multiplying algebraic expressions, including:

  • Using online resources and practice problems
  • Working with a tutor or teacher
  • Practicing with real-world examples and applications
  • Creating your own practice problems and exercises

Conclusion

In this article, we addressed some of the most frequently asked questions about the product of algebraic expressions. Whether you are a student, a teacher, or simply someone who wants to learn more about algebra, this article provided you with the answers you need. By following the rules of multiplication and simplifying complex expressions, you can identify the correct product and solve equations.