Hannah Factored The Expression $24xy + 15y$. Her Work Is Shown Below:1. GCF $(24xy, 15y) = 3y$2. $24xy / 3 = 8xy$, $15y / 3 = 5y$3. $3(24xy + 15y$\]What Are The Errors In Hannah's Work? Check All That Apply.-

Introduction

Factoring expressions is a crucial skill in algebra, and it requires attention to detail and a solid understanding of the underlying concepts. In this article, we will examine Hannah's work on factoring the expression $24xy + 15y$ and identify the errors in her approach.

Hannah's Work

Hannah's work on factoring the expression $24xy + 15y$ is shown below:

1. GCF $(24xy, 15y) = 3y$
2. $24xy / 3 = 8xy$, $15y / 3 = 5y$
3. $3(24xy + 15y$

Error 1: Incorrect Greatest Common Factor (GCF)

The first error in Hannah's work is the incorrect GCF. The GCF of $24xy$ and $15y$ is not $3y$. To find the GCF, we need to identify the common factors of both expressions. The common factors of $24xy$ are $1, 2, 3, 4, 6, 8, 12, 24$, and the common factors of $15y$ are $1, 3, 5, 15$. The greatest common factor of both expressions is $3$, not $3y$.

Error 2: Incorrect Division

The second error in Hannah's work is the incorrect division. When Hannah divides $24xy$ by $3$, she gets $8xy$, which is correct. However, when she divides $15y$ by $3$, she gets $5y$, which is also correct. However, the error lies in the fact that she did not simplify the expression correctly. The correct simplification of the expression $24xy + 15y$ is $3(8xy + 5y)$, not $3(24xy + 15y)$.

Error 3: Incorrect Factoring

The third error in Hannah's work is the incorrect factoring. Hannah's final answer is $3(24xy + 15y)$, which is incorrect. The correct factored form of the expression $24xy + 15y$ is $3(8xy + 5y)$.

Conclusion

In conclusion, Hannah's work on factoring the expression $24xy + 15y$ contains three errors: incorrect GCF, incorrect division, and incorrect factoring. To factor the expression correctly, we need to identify the GCF, simplify the expression, and factor it correctly.

Step-by-Step Solution

To factor the expression $24xy + 15y$, we need to follow these steps:

1. Identify the GCF: The GCF of $24xy$ and $15y$ is $3$.
2. Simplify the expression: Divide both expressions by the GCF: $24xy / 3 = 8xy$ and $15y / 3 = 5y$.
3. Factor the expression: The factored form of the expression is $3(8xy + 5y)$.

Final Answer

Introduction

In our previous article, we examined Hannah's work on factoring the expression $24xy + 15y$ and identified the errors in her approach. In this article, we will provide a Q&A section to help clarify any doubts and provide additional information on factoring expressions.

Q&A Section

Q: What is the greatest common factor (GCF) of $24xy$ and $15y$? A: The GCF of $24xy$ and $15y$ is $3$.

Q: Why is the GCF of $24xy$ and $15y$ not $3y$? A: The GCF is the greatest common factor of both expressions, not the product of the common factors. In this case, the common factors of $24xy$ are $1, 2, 3, 4, 6, 8, 12, 24$, and the common factors of $15y$ are $1, 3, 5, 15$. The greatest common factor of both expressions is $3$, not $3y$.

Q: How do I simplify the expression $24xy + 15y$? A: To simplify the expression, divide both terms by the GCF, which is $3$. This gives us $24xy / 3 = 8xy$ and $15y / 3 = 5y$. The simplified expression is $8xy + 5y$.

Q: How do I factor the expression $8xy + 5y$? A: To factor the expression, we need to identify the common factor of both terms. In this case, the common factor is $5y$. We can factor out $5y$ from both terms, leaving us with $5y(8x + 1)$.

Q: What is the final factored form of the expression $24xy + 15y$? A: The final factored form of the expression $24xy + 15y$ is $3(8xy + 5y)$.

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

• Incorrect GCF: Make sure to identify the greatest common factor of both expressions.
• Incorrect division: Make sure to divide both terms by the GCF correctly.
• Incorrect factoring: Make sure to factor the expression correctly, taking into account any common factors.

Conclusion

In conclusion, factoring expressions requires attention to detail and a solid understanding of the underlying concepts. By following the steps outlined in this article and avoiding common mistakes, you can ensure that your factoring is accurate and effective.

Additional Resources

For additional resources on factoring expressions, including video tutorials and practice problems, please visit our website.

Final Answer

The final answer is $3(8xy + 5y)$.