Monique Is Factoring The Expression $4x + 16xy$. Her Work Is Shown Below:Factors Of $4x: 1, 2, 4, X$ Factors Of $16xy: 1, 2, 4, 8, 16, X, Y$ GCF: $4x$ Factored Expression: $4x(0 + 4y$\]Which Best Describes

Introduction

Factoring expressions is a fundamental concept in algebra, and it requires a thorough understanding of the properties of numbers and variables. In this article, we will analyze Monique's work on factoring the expression $4x + 16xy$ and identify the correct step-by-step process.

Understanding the Expression

The given expression is $4x + 16xy$. To factor this expression, we need to identify the greatest common factor (GCF) of the two terms. The GCF is the largest expression that divides both terms without leaving a remainder.

Factors of $4x$

The factors of $4x$ are:

• 1: The multiplicative identity, which does not change the value of the expression.
• 2: A factor of 4, which is a multiple of 2.
• 4: A factor of 4, which is a multiple of 2.
• x: The variable x, which is a factor of the expression.

Factors of $16xy$

The factors of $16xy$ are:

• 1: The multiplicative identity, which does not change the value of the expression.
• 2: A factor of 16, which is a multiple of 2.
• 4: A factor of 16, which is a multiple of 2.
• 8: A factor of 16, which is a multiple of 2.
• 16: A factor of 16, which is a multiple of 2.
• x: The variable x, which is a factor of the expression.
• y: The variable y, which is a factor of the expression.

Identifying the GCF

The GCF of $4x$ and $16xy$ is $4x$. This is because $4x$ is the largest expression that divides both terms without leaving a remainder.

Factoring the Expression

To factor the expression $4x + 16xy$, we need to multiply the GCF by the remaining factors. The remaining factors are $0 + 4y$, which can be simplified to $4y$.

Correct Factored Expression

The correct factored expression is $4x(4y)$. This can be simplified to $16xy$.

Conclusion

In conclusion, Monique's work on factoring the expression $4x + 16xy$ is incorrect. The correct factored expression is $4x(4y)$, which can be simplified to $16xy$. This article has provided a step-by-step analysis of the expression and identified the correct GCF and factored expression.

Common Mistakes in Factoring

There are several common mistakes that students make when factoring expressions. These include:

• Incorrectly identifying the GCF: Students may incorrectly identify the GCF of the two terms, which can lead to an incorrect factored expression.
• Not simplifying the remaining factors: Students may not simplify the remaining factors, which can lead to an incorrect factored expression.
• Not checking the work: Students may not check their work, which can lead to an incorrect factored expression.

Tips for Factoring Expressions

To factor expressions correctly, students should follow these tips:

• Identify the GCF: The GCF is the largest expression that divides both terms without leaving a remainder.
• Simplify the remaining factors: The remaining factors should be simplified to their simplest form.
• Check the work: The work should be checked to ensure that it is correct.

Conclusion

Introduction

In our previous article, we analyzed Monique's work on factoring the expression $4x + 16xy$ and identified the correct step-by-step process. In this article, we will provide a Q&A section to help students understand the concept of factoring expressions and address any common questions or concerns.

Q&A: Factoring Expressions

Q: What is the greatest common factor (GCF) of two terms?

A: The GCF is the largest expression that divides both terms without leaving a remainder.

Q: How do I identify the GCF of two terms?

A: To identify the GCF, you need to list the factors of each term and find the largest expression that is common to both terms.

Q: What are the factors of $4x$?

A: The factors of $4x$ are:

• 1: The multiplicative identity, which does not change the value of the expression.
• 2: A factor of 4, which is a multiple of 2.
• 4: A factor of 4, which is a multiple of 2.
• x: The variable x, which is a factor of the expression.

Q: What are the factors of $16xy$?

A: The factors of $16xy$ are:

• 1: The multiplicative identity, which does not change the value of the expression.
• 2: A factor of 16, which is a multiple of 2.
• 4: A factor of 16, which is a multiple of 2.
• 8: A factor of 16, which is a multiple of 2.
• 16: A factor of 16, which is a multiple of 2.
• x: The variable x, which is a factor of the expression.
• y: The variable y, which is a factor of the expression.

Q: What is the GCF of $4x$ and $16xy$?

A: The GCF of $4x$ and $16xy$ is $4x$. This is because $4x$ is the largest expression that divides both terms without leaving a remainder.

Q: How do I factor the expression $4x + 16xy$?

A: To factor the expression $4x + 16xy$, you need to multiply the GCF by the remaining factors. The remaining factors are $0 + 4y$, which can be simplified to $4y$.

Q: What is the correct factored expression?

A: The correct factored expression is $4x(4y)$, which can be simplified to $16xy$.

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

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

• Incorrectly identifying the GCF: Students may incorrectly identify the GCF of the two terms, which can lead to an incorrect factored expression.
• Not simplifying the remaining factors: Students may not simplify the remaining factors, which can lead to an incorrect factored expression.
• Not checking the work: Students may not check their work, which can lead to an incorrect factored expression.

Q: How can I practice factoring expressions?

A: You can practice factoring expressions by working through examples and exercises in your textbook or online resources. You can also try factoring expressions on your own and checking your work to ensure that it is correct.

Conclusion

In conclusion, factoring expressions is a fundamental concept in algebra that requires a thorough understanding of the properties of numbers and variables. By following the tips and avoiding common mistakes, students can factor expressions correctly and simplify complex expressions. We hope that this Q&A section has helped to address any common questions or concerns and provide a better understanding of the concept of factoring expressions.