Select The Correct Answer From Each Drop-down Menu.Consider This Expression: $7m^2 + (2m - 1)(m + 9$\]What Expression Is Equivalent To The Given Expression?$\square M^2 + \square M + \square$

Understanding the Given Expression

The given expression is $7m^2 + (2m - 1)(m + 9)$. To find an equivalent expression, we need to simplify the given expression by multiplying the terms inside the parentheses and then combining like terms.

Step 1: Multiply the Terms Inside the Parentheses

To simplify the given expression, we need to multiply the terms inside the parentheses. We can do this by multiplying each term in the first parentheses by each term in the second parentheses.

$$(2m - 1)(m + 9) = 2m(m) + 2m(9) - 1(m) - 1(9)$$

Step 2: Simplify the Expression

Now, we can simplify the expression by combining like terms.

$$2m(m) + 2m(9) - 1(m) - 1(9) = 2m^2 + 18m - m - 9$$

Step 3: Combine Like Terms

We can combine like terms by adding or subtracting the coefficients of the same variables.

$$2m^2 + 18m - m - 9 = 2m^2 + 17m - 9$$

Step 4: Rewrite the Expression

Now, we can rewrite the expression by combining the simplified expression with the remaining term.

$$7m^2 + (2m^2 + 17m - 9)$$

Step 5: Combine Like Terms Again

We can combine like terms again by adding or subtracting the coefficients of the same variables.

$$7m^2 + 2m^2 + 17m - 9 = 9m^2 + 17m - 9$$

Step 6: Write the Equivalent Expression

The equivalent expression is $9m^2 + 17m - 9$.

Select the Correct Answer

Based on the simplified expression, we can select the correct answer from each drop-down menu.

• m^2 term: 9
• m term: 17
• constant term: -9

The final answer is: $\boxed{9m^2 + 17m - 9}$

Discussion

The given expression is $7m^2 + (2m - 1)(m + 9)$. To find an equivalent expression, we need to simplify the given expression by multiplying the terms inside the parentheses and then combining like terms. The equivalent expression is $9m^2 + 17m - 9$.

Key Takeaways

• To simplify an expression, we need to multiply the terms inside the parentheses and then combine like terms.
• We can combine like terms by adding or subtracting the coefficients of the same variables.
• The equivalent expression is $9m^2 + 17m - 9$.

Conclusion

In this discussion, we learned how to simplify an expression by multiplying the terms inside the parentheses and then combining like terms. We also learned how to select the correct answer from each drop-down menu based on the simplified expression. The equivalent expression is $9m^2 + 17m - 9$.

Understanding the Concept of Equivalent Expression

An equivalent expression is an expression that has the same value as another expression, but may be written in a different form. In the previous discussion, we learned how to simplify an expression by multiplying the terms inside the parentheses and then combining like terms. In this Q&A article, we will answer some common questions related to equivalent expressions.

Q: What is an equivalent expression?

A: An equivalent expression is an expression that has the same value as another expression, but may be written in a different form.

Q: How do I simplify an expression to find an equivalent expression?

A: To simplify an expression, you need to multiply the terms inside the parentheses and then combine like terms. You can also use the distributive property to simplify an expression.

Q: What is the distributive property?

A: The distributive property is a property of algebra that states that a single term can be distributed to multiple terms inside parentheses. For example, $a(b + c) = ab + ac$.

Q: How do I use the distributive property to simplify an expression?

A: To use the distributive property, you need to multiply each term inside the parentheses by the term outside the parentheses. For example, $a(b + c) = ab + ac$.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the same variables. For example, $2x + 5x = 7x$.

Q: What is the difference between an equivalent expression and a similar expression?

A: An equivalent expression is an expression that has the same value as another expression, but may be written in a different form. A similar expression is an expression that has a similar structure or pattern, but may not have the same value.

Q: How do I determine if two expressions are equivalent?

A: To determine if two expressions are equivalent, you need to simplify each expression and compare the results. If the two expressions have the same value, then they are equivalent.

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

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

• Not distributing the terms correctly
• Not combining like terms correctly
• Not checking for equivalent expressions

Q: How do I check for equivalent expressions?

A: To check for equivalent expressions, you need to simplify each expression and compare the results. You can also use algebraic properties such as the distributive property and the commutative property to check for equivalent expressions.

Q: What are some real-world applications of equivalent expressions?

A: Equivalent expressions have many real-world applications, including:

• Simplifying complex mathematical expressions
• Solving algebraic equations
• Modeling real-world phenomena

Conclusion

In this Q&A article, we answered some common questions related to equivalent expressions. We learned how to simplify expressions, use the distributive property, combine like terms, and check for equivalent expressions. We also discussed some common mistakes to avoid and some real-world applications of equivalent expressions.