Type The Correct Answer In Each Box.Consider The Expressions Shown Below.${ \begin{array}{|c|c|c|} \hline A & B & C \ \hline -9x^2-2x+7 & 9x^2-2x+2 & 9x^2+2x-7 \ \hline \end{array} }$Complete The Following Statements With The Letter That

Understanding the Problem

The given table consists of three algebraic expressions in the form of quadratic equations. The task is to identify the correct relationship between these expressions by filling in the missing letters in the table.

Analyzing the Expressions

To begin, let's examine each expression individually:

• Expression A: $-9x^2-2x+7$
• Expression B: $9x^2-2x+2$
• Expression C: $9x^2+2x-7$

Identifying Patterns

Upon closer inspection, we can observe that the first two expressions, A and B, have a common term of $-2x$. This suggests that the difference between these two expressions lies in the coefficients of the $x^2$ term.

Comparing Coefficients

Let's compare the coefficients of the $x^2$ term in expressions A and B:

• Expression A: $-9x^2$
• Expression B: $9x^2$

The coefficient of the $x^2$ term in expression A is $-9$, while the coefficient in expression B is $9$. This indicates that the difference between the two expressions is a factor of $-9$.

Determining the Relationship

Based on the analysis, we can conclude that the relationship between expressions A and B is a factor of $-9$. This means that expression A is the result of multiplying expression B by $-9$.

Finding the Correct Answer

With this understanding, we can now fill in the missing letters in the table:

The correct answer is that expression A is the result of multiplying expression B by $-9$.

Conclusion

In this problem, we analyzed the given algebraic expressions and identified the correct relationship between them. By comparing coefficients and understanding the pattern of the expressions, we were able to determine the correct answer. This type of problem requires attention to detail and a solid understanding of algebraic concepts.

Key Takeaways

• The difference between expressions A and B lies in the coefficients of the $x^2$ term.
• The coefficient of the $x^2$ term in expression A is $-9$, while the coefficient in expression B is $9$.
• Expression A is the result of multiplying expression B by $-9$.

Further Practice

To reinforce your understanding of algebraic expressions, try the following exercises:

• Identify the relationship between the expressions $2x^2+3x-1$ and $x^2+2x+4$.
• Determine the result of multiplying the expression $x^2+2x-3$ by $-2$.

By practicing these exercises, you will become more comfortable with identifying patterns in algebraic expressions and determining the correct relationships between them.

Understanding the Problem

The given table consists of three algebraic expressions in the form of quadratic equations. The task is to identify the correct relationship between these expressions by filling in the missing letters in the table.

Q&A Session

Q: What is the main difference between expressions A and B?

A: The main difference between expressions A and B lies in the coefficients of the $x^2$ term. The coefficient of the $x^2$ term in expression A is $-9$, while the coefficient in expression B is $9$.

Q: How do we determine the relationship between expressions A and B?

A: We determine the relationship between expressions A and B by comparing the coefficients of the $x^2$ term. Since the coefficient of the $x^2$ term in expression A is $-9$, we can conclude that expression A is the result of multiplying expression B by $-9$.

Q: What is the correct answer for the relationship between expressions A and B?

A: The correct answer is that expression A is the result of multiplying expression B by $-9$.

Q: How can we apply this understanding to other algebraic expressions?

A: We can apply this understanding to other algebraic expressions by comparing coefficients and identifying patterns. By recognizing the relationships between expressions, we can simplify complex algebraic equations and solve problems more efficiently.

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

A: Some common mistakes to avoid when working with algebraic expressions include:

• Not comparing coefficients carefully
• Not identifying patterns in the expressions
• Not using the correct operations to simplify the expressions

Q: How can we practice and improve our skills in identifying patterns in algebraic expressions?

A: We can practice and improve our skills in identifying patterns in algebraic expressions by:

• Working on exercises and problems that involve algebraic expressions
• Comparing coefficients and identifying patterns in different expressions
• Using online resources and tools to help with algebraic manipulations

Conclusion

In this Q&A session, we discussed the main differences between expressions A and B, how to determine the relationship between them, and how to apply this understanding to other algebraic expressions. We also highlighted common mistakes to avoid and provided tips for practicing and improving our skills in identifying patterns in algebraic expressions.

Key Takeaways

• The main difference between expressions A and B lies in the coefficients of the $x^2$ term.
• We determine the relationship between expressions A and B by comparing the coefficients of the $x^2$ term.
• The correct answer is that expression A is the result of multiplying expression B by $-9$.
• We can apply this understanding to other algebraic expressions by comparing coefficients and identifying patterns.
• Common mistakes to avoid include not comparing coefficients carefully, not identifying patterns in the expressions, and not using the correct operations to simplify the expressions.

Further Practice

To reinforce your understanding of algebraic expressions, try the following exercises:

• Identify the relationship between the expressions $2x^2+3x-1$ and $x^2+2x+4$.
• Determine the result of multiplying the expression $x^2+2x-3$ by $-2$.
• Compare the coefficients of the $x^2$ term in the expressions $3x^2-2x+1$ and $-x^2+2x-3$.

By practicing these exercises, you will become more comfortable with identifying patterns in algebraic expressions and determining the correct relationships between them.