Multiply: $24x(x - 21$\]Enter The Correct Answer.

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Introduction

In mathematics, multiplying expressions is a fundamental operation that involves combining two or more algebraic expressions using the multiplication operation. In this article, we will focus on multiplying the expression $24x(x - 21)$, which is a common problem in algebra. We will break down the solution into step-by-step instructions, providing a clear and concise explanation of each step.

Understanding the Expression

Before we start multiplying, let's take a closer look at the expression $24x(x - 21)$. This expression consists of three parts:

• $24x$: This is a numerical coefficient multiplied by a variable $x$.
• $(x - 21)$: This is a binomial expression, which is a polynomial with two terms.

Step 1: Multiply the Numerical Coefficient by the Variable

The first step in multiplying the expression $24x(x - 21)$ is to multiply the numerical coefficient $24$ by the variable $x$. This can be done using the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.

24x(x - 21) = 24x \cdot x - 24x \cdot 21

Step 2: Multiply the Variable by the Binomial Expression

The next step is to multiply the variable $x$ by the binomial expression $(x - 21)$. This can be done using the distributive property again.

24x \cdot x - 24x \cdot 21 = 24x^2 - 24x \cdot 21

Step 3: Multiply the Numerical Coefficient by the Binomial Expression

The final step is to multiply the numerical coefficient $24$ by the binomial expression $(x - 21)$. This can be done using the distributive property once again.

24x^2 - 24x \cdot 21 = 24x^2 - 504x

Simplifying the Expression

The final expression is $24x^2 - 504x$. This is the result of multiplying the expression $24x(x - 21)$.

Conclusion

In this article, we have shown how to multiply the expression $24x(x - 21)$ using the distributive property. We have broken down the solution into step-by-step instructions, providing a clear and concise explanation of each step. By following these steps, you should be able to multiply any expression of the form $ax(x - b)$.

Common Mistakes to Avoid

When multiplying expressions, it's easy to make mistakes. Here are some common mistakes to avoid:

• Not using the distributive property: The distributive property is a fundamental concept in algebra that allows us to multiply expressions. Make sure to use it when multiplying expressions.
• Not following the order of operations: When multiplying expressions, make sure to follow the order of operations (PEMDAS). This means that you should multiply the numerical coefficient by the variable first, then multiply the variable by the binomial expression.
• Not simplifying the expression: After multiplying the expression, make sure to simplify it by combining like terms.

Practice Problems

Here are some practice problems to help you practice multiplying expressions:

• Multiply the expression $36y(y - 18)$.
• Multiply the expression $48z(z - 24)$.
• Multiply the expression $60w(w - 30)$.

Answer Key

Here are the answers to the practice problems:

• $36y^2 - 648y$
• $48z^2 - 1152z$
• $60w^2 - 1800w$

Conclusion

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Introduction

In our previous article, we showed how to multiply the expression $24x(x - 21)$ using the distributive property. In this article, we will answer some common questions that students often have when multiplying expressions.

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that allows us to multiply expressions. It states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. This means that we can multiply a numerical coefficient by a binomial expression by multiplying the numerical coefficient by each term in the binomial expression.

Q: How do I multiply a numerical coefficient by a variable?

A: To multiply a numerical coefficient by a variable, we simply multiply the numerical coefficient by the variable. For example, if we have the expression $3x$, we can multiply it by $4$ to get $12x$.

Q: How do I multiply a variable by a binomial expression?

A: To multiply a variable by a binomial expression, we use the distributive property. We multiply the variable by each term in the binomial expression and then combine the results. For example, if we have the expression $x(y + 2)$, we can multiply it by $3$ to get $3xy + 6x$.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify an expression?

A: To simplify an expression, we combine like terms. Like terms are terms that have the same variable raised to the same power. For example, if we have the expression $2x + 3x$, we can combine the like terms to get $5x$.

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

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

• Not using the distributive property
• Not following the order of operations
• Not simplifying the expression
• Not combining like terms

Q: How can I practice multiplying expressions?

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

• Using online resources, such as Khan Academy or Mathway
• Working with a tutor or teacher
• Practicing with worksheets or exercises
• Solving real-world problems that involve multiplying expressions

Conclusion

In this article, we have answered some common questions that students often have when multiplying expressions. We have also provided some tips and resources for practicing multiplying expressions. Remember to use the distributive property, follow the order of operations, and simplify expressions to get the correct answer. With practice, you should become more confident in multiplying expressions.

Additional Resources

Here are some additional resources that you may find helpful when multiplying expressions:

• Khan Academy: Multiplying Expressions
• Mathway: Multiplying Expressions
• Algebra.com: Multiplying Expressions
• IXL: Multiplying Expressions

Practice Problems

Here are some practice problems to help you practice multiplying expressions:

• Multiply the expression $36y(y - 18)$.
• Multiply the expression $48z(z - 24)$.
• Multiply the expression $60w(w - 30)$.

Answer Key

Here are the answers to the practice problems:

• $36y^2 - 648y$
• $48z^2 - 1152z$
• $60w^2 - 1800w$

Conclusion

In this article, we have provided a Q&A guide to multiplying expressions. We have answered some common questions, provided tips and resources for practicing multiplying expressions, and included some practice problems and answer key. Remember to use the distributive property, follow the order of operations, and simplify expressions to get the correct answer. With practice, you should become more confident in multiplying expressions.